Properties

Label 4002.2.a.w.1.1
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 1.1
Root \(1.73205\)
Character \(\chi\) = 4002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(+3.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(+3.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+3.00000 q^{10}\) \(-2.73205 q^{11}\) \(+1.00000 q^{12}\) \(+1.26795 q^{13}\) \(+3.00000 q^{14}\) \(+3.00000 q^{15}\) \(+1.00000 q^{16}\) \(-6.46410 q^{17}\) \(+1.00000 q^{18}\) \(+2.46410 q^{19}\) \(+3.00000 q^{20}\) \(+3.00000 q^{21}\) \(-2.73205 q^{22}\) \(+1.00000 q^{23}\) \(+1.00000 q^{24}\) \(+4.00000 q^{25}\) \(+1.26795 q^{26}\) \(+1.00000 q^{27}\) \(+3.00000 q^{28}\) \(-1.00000 q^{29}\) \(+3.00000 q^{30}\) \(+0.732051 q^{31}\) \(+1.00000 q^{32}\) \(-2.73205 q^{33}\) \(-6.46410 q^{34}\) \(+9.00000 q^{35}\) \(+1.00000 q^{36}\) \(-7.19615 q^{37}\) \(+2.46410 q^{38}\) \(+1.26795 q^{39}\) \(+3.00000 q^{40}\) \(+12.1244 q^{41}\) \(+3.00000 q^{42}\) \(+1.92820 q^{43}\) \(-2.73205 q^{44}\) \(+3.00000 q^{45}\) \(+1.00000 q^{46}\) \(+11.3923 q^{47}\) \(+1.00000 q^{48}\) \(+2.00000 q^{49}\) \(+4.00000 q^{50}\) \(-6.46410 q^{51}\) \(+1.26795 q^{52}\) \(+9.46410 q^{53}\) \(+1.00000 q^{54}\) \(-8.19615 q^{55}\) \(+3.00000 q^{56}\) \(+2.46410 q^{57}\) \(-1.00000 q^{58}\) \(+3.53590 q^{59}\) \(+3.00000 q^{60}\) \(+6.39230 q^{61}\) \(+0.732051 q^{62}\) \(+3.00000 q^{63}\) \(+1.00000 q^{64}\) \(+3.80385 q^{65}\) \(-2.73205 q^{66}\) \(-9.46410 q^{67}\) \(-6.46410 q^{68}\) \(+1.00000 q^{69}\) \(+9.00000 q^{70}\) \(+5.66025 q^{71}\) \(+1.00000 q^{72}\) \(-12.9282 q^{73}\) \(-7.19615 q^{74}\) \(+4.00000 q^{75}\) \(+2.46410 q^{76}\) \(-8.19615 q^{77}\) \(+1.26795 q^{78}\) \(-17.1244 q^{79}\) \(+3.00000 q^{80}\) \(+1.00000 q^{81}\) \(+12.1244 q^{82}\) \(-4.53590 q^{83}\) \(+3.00000 q^{84}\) \(-19.3923 q^{85}\) \(+1.92820 q^{86}\) \(-1.00000 q^{87}\) \(-2.73205 q^{88}\) \(-5.46410 q^{89}\) \(+3.00000 q^{90}\) \(+3.80385 q^{91}\) \(+1.00000 q^{92}\) \(+0.732051 q^{93}\) \(+11.3923 q^{94}\) \(+7.39230 q^{95}\) \(+1.00000 q^{96}\) \(+4.00000 q^{97}\) \(+2.00000 q^{98}\) \(-2.73205 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 8q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 2q^{62} \) \(\mathstrut +\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 18q^{65} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut +\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut -\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 18q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 2q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 2q^{92} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut -\mathstrut 6q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(11\) −2.73205 −0.823744 −0.411872 0.911242i \(-0.635125\pi\)
−0.411872 + 0.911242i \(0.635125\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.26795 0.351666 0.175833 0.984420i \(-0.443738\pi\)
0.175833 + 0.984420i \(0.443738\pi\)
\(14\) 3.00000 0.801784
\(15\) 3.00000 0.774597
\(16\) 1.00000 0.250000
\(17\) −6.46410 −1.56777 −0.783887 0.620903i \(-0.786766\pi\)
−0.783887 + 0.620903i \(0.786766\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.46410 0.565304 0.282652 0.959223i \(-0.408786\pi\)
0.282652 + 0.959223i \(0.408786\pi\)
\(20\) 3.00000 0.670820
\(21\) 3.00000 0.654654
\(22\) −2.73205 −0.582475
\(23\) 1.00000 0.208514
\(24\) 1.00000 0.204124
\(25\) 4.00000 0.800000
\(26\) 1.26795 0.248665
\(27\) 1.00000 0.192450
\(28\) 3.00000 0.566947
\(29\) −1.00000 −0.185695
\(30\) 3.00000 0.547723
\(31\) 0.732051 0.131480 0.0657401 0.997837i \(-0.479059\pi\)
0.0657401 + 0.997837i \(0.479059\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.73205 −0.475589
\(34\) −6.46410 −1.10858
\(35\) 9.00000 1.52128
\(36\) 1.00000 0.166667
\(37\) −7.19615 −1.18304 −0.591520 0.806290i \(-0.701472\pi\)
−0.591520 + 0.806290i \(0.701472\pi\)
\(38\) 2.46410 0.399730
\(39\) 1.26795 0.203034
\(40\) 3.00000 0.474342
\(41\) 12.1244 1.89351 0.946753 0.321960i \(-0.104342\pi\)
0.946753 + 0.321960i \(0.104342\pi\)
\(42\) 3.00000 0.462910
\(43\) 1.92820 0.294048 0.147024 0.989133i \(-0.453031\pi\)
0.147024 + 0.989133i \(0.453031\pi\)
\(44\) −2.73205 −0.411872
\(45\) 3.00000 0.447214
\(46\) 1.00000 0.147442
\(47\) 11.3923 1.66174 0.830869 0.556468i \(-0.187844\pi\)
0.830869 + 0.556468i \(0.187844\pi\)
\(48\) 1.00000 0.144338
\(49\) 2.00000 0.285714
\(50\) 4.00000 0.565685
\(51\) −6.46410 −0.905155
\(52\) 1.26795 0.175833
\(53\) 9.46410 1.29999 0.649997 0.759937i \(-0.274770\pi\)
0.649997 + 0.759937i \(0.274770\pi\)
\(54\) 1.00000 0.136083
\(55\) −8.19615 −1.10517
\(56\) 3.00000 0.400892
\(57\) 2.46410 0.326378
\(58\) −1.00000 −0.131306
\(59\) 3.53590 0.460335 0.230167 0.973151i \(-0.426073\pi\)
0.230167 + 0.973151i \(0.426073\pi\)
\(60\) 3.00000 0.387298
\(61\) 6.39230 0.818451 0.409225 0.912433i \(-0.365799\pi\)
0.409225 + 0.912433i \(0.365799\pi\)
\(62\) 0.732051 0.0929705
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) 3.80385 0.471809
\(66\) −2.73205 −0.336292
\(67\) −9.46410 −1.15622 −0.578112 0.815957i \(-0.696210\pi\)
−0.578112 + 0.815957i \(0.696210\pi\)
\(68\) −6.46410 −0.783887
\(69\) 1.00000 0.120386
\(70\) 9.00000 1.07571
\(71\) 5.66025 0.671749 0.335874 0.941907i \(-0.390968\pi\)
0.335874 + 0.941907i \(0.390968\pi\)
\(72\) 1.00000 0.117851
\(73\) −12.9282 −1.51313 −0.756566 0.653917i \(-0.773124\pi\)
−0.756566 + 0.653917i \(0.773124\pi\)
\(74\) −7.19615 −0.836536
\(75\) 4.00000 0.461880
\(76\) 2.46410 0.282652
\(77\) −8.19615 −0.934038
\(78\) 1.26795 0.143567
\(79\) −17.1244 −1.92664 −0.963320 0.268354i \(-0.913520\pi\)
−0.963320 + 0.268354i \(0.913520\pi\)
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) 12.1244 1.33891
\(83\) −4.53590 −0.497880 −0.248940 0.968519i \(-0.580082\pi\)
−0.248940 + 0.968519i \(0.580082\pi\)
\(84\) 3.00000 0.327327
\(85\) −19.3923 −2.10339
\(86\) 1.92820 0.207924
\(87\) −1.00000 −0.107211
\(88\) −2.73205 −0.291238
\(89\) −5.46410 −0.579194 −0.289597 0.957149i \(-0.593521\pi\)
−0.289597 + 0.957149i \(0.593521\pi\)
\(90\) 3.00000 0.316228
\(91\) 3.80385 0.398752
\(92\) 1.00000 0.104257
\(93\) 0.732051 0.0759101
\(94\) 11.3923 1.17503
\(95\) 7.39230 0.758434
\(96\) 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
\(99\) −2.73205 −0.274581
\(100\) 4.00000 0.400000
\(101\) 3.07180 0.305655 0.152828 0.988253i \(-0.451162\pi\)
0.152828 + 0.988253i \(0.451162\pi\)
\(102\) −6.46410 −0.640041
\(103\) 14.8564 1.46385 0.731923 0.681388i \(-0.238623\pi\)
0.731923 + 0.681388i \(0.238623\pi\)
\(104\) 1.26795 0.124333
\(105\) 9.00000 0.878310
\(106\) 9.46410 0.919235
\(107\) −1.19615 −0.115636 −0.0578182 0.998327i \(-0.518414\pi\)
−0.0578182 + 0.998327i \(0.518414\pi\)
\(108\) 1.00000 0.0962250
\(109\) −8.00000 −0.766261 −0.383131 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) −8.19615 −0.781472
\(111\) −7.19615 −0.683029
\(112\) 3.00000 0.283473
\(113\) −9.39230 −0.883554 −0.441777 0.897125i \(-0.645652\pi\)
−0.441777 + 0.897125i \(0.645652\pi\)
\(114\) 2.46410 0.230784
\(115\) 3.00000 0.279751
\(116\) −1.00000 −0.0928477
\(117\) 1.26795 0.117222
\(118\) 3.53590 0.325506
\(119\) −19.3923 −1.77769
\(120\) 3.00000 0.273861
\(121\) −3.53590 −0.321445
\(122\) 6.39230 0.578732
\(123\) 12.1244 1.09322
\(124\) 0.732051 0.0657401
\(125\) −3.00000 −0.268328
\(126\) 3.00000 0.267261
\(127\) 4.53590 0.402496 0.201248 0.979540i \(-0.435500\pi\)
0.201248 + 0.979540i \(0.435500\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.92820 0.169769
\(130\) 3.80385 0.333620
\(131\) −7.80385 −0.681825 −0.340913 0.940095i \(-0.610736\pi\)
−0.340913 + 0.940095i \(0.610736\pi\)
\(132\) −2.73205 −0.237795
\(133\) 7.39230 0.640994
\(134\) −9.46410 −0.817574
\(135\) 3.00000 0.258199
\(136\) −6.46410 −0.554292
\(137\) 0.928203 0.0793018 0.0396509 0.999214i \(-0.487375\pi\)
0.0396509 + 0.999214i \(0.487375\pi\)
\(138\) 1.00000 0.0851257
\(139\) 7.85641 0.666372 0.333186 0.942861i \(-0.391876\pi\)
0.333186 + 0.942861i \(0.391876\pi\)
\(140\) 9.00000 0.760639
\(141\) 11.3923 0.959405
\(142\) 5.66025 0.474998
\(143\) −3.46410 −0.289683
\(144\) 1.00000 0.0833333
\(145\) −3.00000 −0.249136
\(146\) −12.9282 −1.06995
\(147\) 2.00000 0.164957
\(148\) −7.19615 −0.591520
\(149\) 5.00000 0.409616 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) 4.00000 0.326599
\(151\) −10.1244 −0.823908 −0.411954 0.911205i \(-0.635154\pi\)
−0.411954 + 0.911205i \(0.635154\pi\)
\(152\) 2.46410 0.199865
\(153\) −6.46410 −0.522592
\(154\) −8.19615 −0.660465
\(155\) 2.19615 0.176399
\(156\) 1.26795 0.101517
\(157\) −3.73205 −0.297850 −0.148925 0.988848i \(-0.547581\pi\)
−0.148925 + 0.988848i \(0.547581\pi\)
\(158\) −17.1244 −1.36234
\(159\) 9.46410 0.750552
\(160\) 3.00000 0.237171
\(161\) 3.00000 0.236433
\(162\) 1.00000 0.0785674
\(163\) −23.7321 −1.85884 −0.929419 0.369027i \(-0.879691\pi\)
−0.929419 + 0.369027i \(0.879691\pi\)
\(164\) 12.1244 0.946753
\(165\) −8.19615 −0.638070
\(166\) −4.53590 −0.352054
\(167\) −7.85641 −0.607947 −0.303973 0.952680i \(-0.598313\pi\)
−0.303973 + 0.952680i \(0.598313\pi\)
\(168\) 3.00000 0.231455
\(169\) −11.3923 −0.876331
\(170\) −19.3923 −1.48732
\(171\) 2.46410 0.188435
\(172\) 1.92820 0.147024
\(173\) 11.7321 0.891971 0.445986 0.895040i \(-0.352853\pi\)
0.445986 + 0.895040i \(0.352853\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 12.0000 0.907115
\(176\) −2.73205 −0.205936
\(177\) 3.53590 0.265774
\(178\) −5.46410 −0.409552
\(179\) −10.3923 −0.776757 −0.388379 0.921500i \(-0.626965\pi\)
−0.388379 + 0.921500i \(0.626965\pi\)
\(180\) 3.00000 0.223607
\(181\) −5.12436 −0.380890 −0.190445 0.981698i \(-0.560993\pi\)
−0.190445 + 0.981698i \(0.560993\pi\)
\(182\) 3.80385 0.281960
\(183\) 6.39230 0.472533
\(184\) 1.00000 0.0737210
\(185\) −21.5885 −1.58721
\(186\) 0.732051 0.0536766
\(187\) 17.6603 1.29145
\(188\) 11.3923 0.830869
\(189\) 3.00000 0.218218
\(190\) 7.39230 0.536294
\(191\) −26.1244 −1.89029 −0.945146 0.326648i \(-0.894081\pi\)
−0.945146 + 0.326648i \(0.894081\pi\)
\(192\) 1.00000 0.0721688
\(193\) 2.53590 0.182538 0.0912690 0.995826i \(-0.470908\pi\)
0.0912690 + 0.995826i \(0.470908\pi\)
\(194\) 4.00000 0.287183
\(195\) 3.80385 0.272399
\(196\) 2.00000 0.142857
\(197\) 14.2679 1.01655 0.508275 0.861195i \(-0.330283\pi\)
0.508275 + 0.861195i \(0.330283\pi\)
\(198\) −2.73205 −0.194158
\(199\) −17.3205 −1.22782 −0.613909 0.789377i \(-0.710404\pi\)
−0.613909 + 0.789377i \(0.710404\pi\)
\(200\) 4.00000 0.282843
\(201\) −9.46410 −0.667546
\(202\) 3.07180 0.216131
\(203\) −3.00000 −0.210559
\(204\) −6.46410 −0.452578
\(205\) 36.3731 2.54041
\(206\) 14.8564 1.03509
\(207\) 1.00000 0.0695048
\(208\) 1.26795 0.0879165
\(209\) −6.73205 −0.465666
\(210\) 9.00000 0.621059
\(211\) 0.803848 0.0553391 0.0276696 0.999617i \(-0.491191\pi\)
0.0276696 + 0.999617i \(0.491191\pi\)
\(212\) 9.46410 0.649997
\(213\) 5.66025 0.387834
\(214\) −1.19615 −0.0817673
\(215\) 5.78461 0.394507
\(216\) 1.00000 0.0680414
\(217\) 2.19615 0.149085
\(218\) −8.00000 −0.541828
\(219\) −12.9282 −0.873607
\(220\) −8.19615 −0.552584
\(221\) −8.19615 −0.551333
\(222\) −7.19615 −0.482974
\(223\) 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
\(226\) −9.39230 −0.624767
\(227\) 5.58846 0.370919 0.185459 0.982652i \(-0.440623\pi\)
0.185459 + 0.982652i \(0.440623\pi\)
\(228\) 2.46410 0.163189
\(229\) 2.80385 0.185283 0.0926417 0.995700i \(-0.470469\pi\)
0.0926417 + 0.995700i \(0.470469\pi\)
\(230\) 3.00000 0.197814
\(231\) −8.19615 −0.539267
\(232\) −1.00000 −0.0656532
\(233\) −11.3205 −0.741631 −0.370816 0.928707i \(-0.620922\pi\)
−0.370816 + 0.928707i \(0.620922\pi\)
\(234\) 1.26795 0.0828884
\(235\) 34.1769 2.22946
\(236\) 3.53590 0.230167
\(237\) −17.1244 −1.11235
\(238\) −19.3923 −1.25702
\(239\) 19.8564 1.28440 0.642202 0.766535i \(-0.278021\pi\)
0.642202 + 0.766535i \(0.278021\pi\)
\(240\) 3.00000 0.193649
\(241\) 10.2679 0.661417 0.330708 0.943733i \(-0.392712\pi\)
0.330708 + 0.943733i \(0.392712\pi\)
\(242\) −3.53590 −0.227296
\(243\) 1.00000 0.0641500
\(244\) 6.39230 0.409225
\(245\) 6.00000 0.383326
\(246\) 12.1244 0.773021
\(247\) 3.12436 0.198798
\(248\) 0.732051 0.0464853
\(249\) −4.53590 −0.287451
\(250\) −3.00000 −0.189737
\(251\) −5.46410 −0.344891 −0.172446 0.985019i \(-0.555167\pi\)
−0.172446 + 0.985019i \(0.555167\pi\)
\(252\) 3.00000 0.188982
\(253\) −2.73205 −0.171763
\(254\) 4.53590 0.284608
\(255\) −19.3923 −1.21439
\(256\) 1.00000 0.0625000
\(257\) −19.2679 −1.20190 −0.600951 0.799286i \(-0.705211\pi\)
−0.600951 + 0.799286i \(0.705211\pi\)
\(258\) 1.92820 0.120045
\(259\) −21.5885 −1.34144
\(260\) 3.80385 0.235905
\(261\) −1.00000 −0.0618984
\(262\) −7.80385 −0.482123
\(263\) −9.05256 −0.558205 −0.279102 0.960261i \(-0.590037\pi\)
−0.279102 + 0.960261i \(0.590037\pi\)
\(264\) −2.73205 −0.168146
\(265\) 28.3923 1.74413
\(266\) 7.39230 0.453251
\(267\) −5.46410 −0.334398
\(268\) −9.46410 −0.578112
\(269\) 5.66025 0.345112 0.172556 0.985000i \(-0.444797\pi\)
0.172556 + 0.985000i \(0.444797\pi\)
\(270\) 3.00000 0.182574
\(271\) −16.7846 −1.01959 −0.509796 0.860295i \(-0.670279\pi\)
−0.509796 + 0.860295i \(0.670279\pi\)
\(272\) −6.46410 −0.391944
\(273\) 3.80385 0.230219
\(274\) 0.928203 0.0560748
\(275\) −10.9282 −0.658995
\(276\) 1.00000 0.0601929
\(277\) −5.12436 −0.307893 −0.153946 0.988079i \(-0.549198\pi\)
−0.153946 + 0.988079i \(0.549198\pi\)
\(278\) 7.85641 0.471196
\(279\) 0.732051 0.0438267
\(280\) 9.00000 0.537853
\(281\) 20.5359 1.22507 0.612534 0.790444i \(-0.290150\pi\)
0.612534 + 0.790444i \(0.290150\pi\)
\(282\) 11.3923 0.678402
\(283\) −22.5885 −1.34274 −0.671372 0.741120i \(-0.734295\pi\)
−0.671372 + 0.741120i \(0.734295\pi\)
\(284\) 5.66025 0.335874
\(285\) 7.39230 0.437882
\(286\) −3.46410 −0.204837
\(287\) 36.3731 2.14703
\(288\) 1.00000 0.0589256
\(289\) 24.7846 1.45792
\(290\) −3.00000 −0.176166
\(291\) 4.00000 0.234484
\(292\) −12.9282 −0.756566
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 2.00000 0.116642
\(295\) 10.6077 0.617604
\(296\) −7.19615 −0.418268
\(297\) −2.73205 −0.158530
\(298\) 5.00000 0.289642
\(299\) 1.26795 0.0733274
\(300\) 4.00000 0.230940
\(301\) 5.78461 0.333419
\(302\) −10.1244 −0.582591
\(303\) 3.07180 0.176470
\(304\) 2.46410 0.141326
\(305\) 19.1769 1.09807
\(306\) −6.46410 −0.369528
\(307\) −22.9282 −1.30858 −0.654291 0.756243i \(-0.727033\pi\)
−0.654291 + 0.756243i \(0.727033\pi\)
\(308\) −8.19615 −0.467019
\(309\) 14.8564 0.845151
\(310\) 2.19615 0.124733
\(311\) 28.3205 1.60591 0.802954 0.596041i \(-0.203260\pi\)
0.802954 + 0.596041i \(0.203260\pi\)
\(312\) 1.26795 0.0717835
\(313\) 4.12436 0.233122 0.116561 0.993184i \(-0.462813\pi\)
0.116561 + 0.993184i \(0.462813\pi\)
\(314\) −3.73205 −0.210612
\(315\) 9.00000 0.507093
\(316\) −17.1244 −0.963320
\(317\) 27.6603 1.55355 0.776777 0.629775i \(-0.216853\pi\)
0.776777 + 0.629775i \(0.216853\pi\)
\(318\) 9.46410 0.530720
\(319\) 2.73205 0.152965
\(320\) 3.00000 0.167705
\(321\) −1.19615 −0.0667627
\(322\) 3.00000 0.167183
\(323\) −15.9282 −0.886269
\(324\) 1.00000 0.0555556
\(325\) 5.07180 0.281333
\(326\) −23.7321 −1.31440
\(327\) −8.00000 −0.442401
\(328\) 12.1244 0.669456
\(329\) 34.1769 1.88423
\(330\) −8.19615 −0.451183
\(331\) −29.4449 −1.61844 −0.809218 0.587508i \(-0.800109\pi\)
−0.809218 + 0.587508i \(0.800109\pi\)
\(332\) −4.53590 −0.248940
\(333\) −7.19615 −0.394347
\(334\) −7.85641 −0.429883
\(335\) −28.3923 −1.55124
\(336\) 3.00000 0.163663
\(337\) −7.07180 −0.385225 −0.192613 0.981275i \(-0.561696\pi\)
−0.192613 + 0.981275i \(0.561696\pi\)
\(338\) −11.3923 −0.619660
\(339\) −9.39230 −0.510120
\(340\) −19.3923 −1.05170
\(341\) −2.00000 −0.108306
\(342\) 2.46410 0.133243
\(343\) −15.0000 −0.809924
\(344\) 1.92820 0.103962
\(345\) 3.00000 0.161515
\(346\) 11.7321 0.630719
\(347\) −8.85641 −0.475437 −0.237718 0.971334i \(-0.576400\pi\)
−0.237718 + 0.971334i \(0.576400\pi\)
\(348\) −1.00000 −0.0536056
\(349\) 14.3923 0.770402 0.385201 0.922833i \(-0.374132\pi\)
0.385201 + 0.922833i \(0.374132\pi\)
\(350\) 12.0000 0.641427
\(351\) 1.26795 0.0676781
\(352\) −2.73205 −0.145619
\(353\) −4.53590 −0.241422 −0.120711 0.992688i \(-0.538517\pi\)
−0.120711 + 0.992688i \(0.538517\pi\)
\(354\) 3.53590 0.187931
\(355\) 16.9808 0.901245
\(356\) −5.46410 −0.289597
\(357\) −19.3923 −1.02635
\(358\) −10.3923 −0.549250
\(359\) −7.73205 −0.408082 −0.204041 0.978962i \(-0.565408\pi\)
−0.204041 + 0.978962i \(0.565408\pi\)
\(360\) 3.00000 0.158114
\(361\) −12.9282 −0.680432
\(362\) −5.12436 −0.269330
\(363\) −3.53590 −0.185587
\(364\) 3.80385 0.199376
\(365\) −38.7846 −2.03008
\(366\) 6.39230 0.334131
\(367\) 31.6603 1.65265 0.826326 0.563192i \(-0.190427\pi\)
0.826326 + 0.563192i \(0.190427\pi\)
\(368\) 1.00000 0.0521286
\(369\) 12.1244 0.631169
\(370\) −21.5885 −1.12233
\(371\) 28.3923 1.47406
\(372\) 0.732051 0.0379551
\(373\) 17.0718 0.883944 0.441972 0.897029i \(-0.354279\pi\)
0.441972 + 0.897029i \(0.354279\pi\)
\(374\) 17.6603 0.913190
\(375\) −3.00000 −0.154919
\(376\) 11.3923 0.587513
\(377\) −1.26795 −0.0653027
\(378\) 3.00000 0.154303
\(379\) −23.8564 −1.22542 −0.612711 0.790307i \(-0.709921\pi\)
−0.612711 + 0.790307i \(0.709921\pi\)
\(380\) 7.39230 0.379217
\(381\) 4.53590 0.232381
\(382\) −26.1244 −1.33664
\(383\) 20.1962 1.03198 0.515988 0.856596i \(-0.327425\pi\)
0.515988 + 0.856596i \(0.327425\pi\)
\(384\) 1.00000 0.0510310
\(385\) −24.5885 −1.25314
\(386\) 2.53590 0.129074
\(387\) 1.92820 0.0980161
\(388\) 4.00000 0.203069
\(389\) −13.8564 −0.702548 −0.351274 0.936273i \(-0.614251\pi\)
−0.351274 + 0.936273i \(0.614251\pi\)
\(390\) 3.80385 0.192615
\(391\) −6.46410 −0.326904
\(392\) 2.00000 0.101015
\(393\) −7.80385 −0.393652
\(394\) 14.2679 0.718809
\(395\) −51.3731 −2.58486
\(396\) −2.73205 −0.137291
\(397\) 0.339746 0.0170514 0.00852568 0.999964i \(-0.497286\pi\)
0.00852568 + 0.999964i \(0.497286\pi\)
\(398\) −17.3205 −0.868199
\(399\) 7.39230 0.370078
\(400\) 4.00000 0.200000
\(401\) −25.7128 −1.28404 −0.642018 0.766689i \(-0.721903\pi\)
−0.642018 + 0.766689i \(0.721903\pi\)
\(402\) −9.46410 −0.472026
\(403\) 0.928203 0.0462371
\(404\) 3.07180 0.152828
\(405\) 3.00000 0.149071
\(406\) −3.00000 −0.148888
\(407\) 19.6603 0.974523
\(408\) −6.46410 −0.320021
\(409\) 19.1244 0.945639 0.472819 0.881159i \(-0.343236\pi\)
0.472819 + 0.881159i \(0.343236\pi\)
\(410\) 36.3731 1.79634
\(411\) 0.928203 0.0457849
\(412\) 14.8564 0.731923
\(413\) 10.6077 0.521971
\(414\) 1.00000 0.0491473
\(415\) −13.6077 −0.667975
\(416\) 1.26795 0.0621663
\(417\) 7.85641 0.384730
\(418\) −6.73205 −0.329275
\(419\) −9.58846 −0.468427 −0.234213 0.972185i \(-0.575251\pi\)
−0.234213 + 0.972185i \(0.575251\pi\)
\(420\) 9.00000 0.439155
\(421\) 30.3923 1.48123 0.740615 0.671929i \(-0.234534\pi\)
0.740615 + 0.671929i \(0.234534\pi\)
\(422\) 0.803848 0.0391307
\(423\) 11.3923 0.553913
\(424\) 9.46410 0.459617
\(425\) −25.8564 −1.25422
\(426\) 5.66025 0.274240
\(427\) 19.1769 0.928036
\(428\) −1.19615 −0.0578182
\(429\) −3.46410 −0.167248
\(430\) 5.78461 0.278959
\(431\) 30.1962 1.45450 0.727249 0.686374i \(-0.240799\pi\)
0.727249 + 0.686374i \(0.240799\pi\)
\(432\) 1.00000 0.0481125
\(433\) 11.5167 0.553455 0.276728 0.960948i \(-0.410750\pi\)
0.276728 + 0.960948i \(0.410750\pi\)
\(434\) 2.19615 0.105419
\(435\) −3.00000 −0.143839
\(436\) −8.00000 −0.383131
\(437\) 2.46410 0.117874
\(438\) −12.9282 −0.617733
\(439\) 21.1962 1.01164 0.505819 0.862640i \(-0.331191\pi\)
0.505819 + 0.862640i \(0.331191\pi\)
\(440\) −8.19615 −0.390736
\(441\) 2.00000 0.0952381
\(442\) −8.19615 −0.389851
\(443\) 25.1769 1.19619 0.598096 0.801425i \(-0.295924\pi\)
0.598096 + 0.801425i \(0.295924\pi\)
\(444\) −7.19615 −0.341514
\(445\) −16.3923 −0.777070
\(446\) 8.00000 0.378811
\(447\) 5.00000 0.236492
\(448\) 3.00000 0.141737
\(449\) 8.66025 0.408703 0.204351 0.978898i \(-0.434492\pi\)
0.204351 + 0.978898i \(0.434492\pi\)
\(450\) 4.00000 0.188562
\(451\) −33.1244 −1.55976
\(452\) −9.39230 −0.441777
\(453\) −10.1244 −0.475684
\(454\) 5.58846 0.262279
\(455\) 11.4115 0.534981
\(456\) 2.46410 0.115392
\(457\) 30.9090 1.44586 0.722930 0.690921i \(-0.242795\pi\)
0.722930 + 0.690921i \(0.242795\pi\)
\(458\) 2.80385 0.131015
\(459\) −6.46410 −0.301718
\(460\) 3.00000 0.139876
\(461\) −8.05256 −0.375045 −0.187523 0.982260i \(-0.560046\pi\)
−0.187523 + 0.982260i \(0.560046\pi\)
\(462\) −8.19615 −0.381320
\(463\) −31.1769 −1.44891 −0.724457 0.689320i \(-0.757909\pi\)
−0.724457 + 0.689320i \(0.757909\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 2.19615 0.101844
\(466\) −11.3205 −0.524412
\(467\) 22.1962 1.02712 0.513558 0.858055i \(-0.328327\pi\)
0.513558 + 0.858055i \(0.328327\pi\)
\(468\) 1.26795 0.0586110
\(469\) −28.3923 −1.31103
\(470\) 34.1769 1.57646
\(471\) −3.73205 −0.171964
\(472\) 3.53590 0.162753
\(473\) −5.26795 −0.242221
\(474\) −17.1244 −0.786548
\(475\) 9.85641 0.452243
\(476\) −19.3923 −0.888845
\(477\) 9.46410 0.433331
\(478\) 19.8564 0.908211
\(479\) −1.85641 −0.0848214 −0.0424107 0.999100i \(-0.513504\pi\)
−0.0424107 + 0.999100i \(0.513504\pi\)
\(480\) 3.00000 0.136931
\(481\) −9.12436 −0.416035
\(482\) 10.2679 0.467692
\(483\) 3.00000 0.136505
\(484\) −3.53590 −0.160723
\(485\) 12.0000 0.544892
\(486\) 1.00000 0.0453609
\(487\) 12.5167 0.567184 0.283592 0.958945i \(-0.408474\pi\)
0.283592 + 0.958945i \(0.408474\pi\)
\(488\) 6.39230 0.289366
\(489\) −23.7321 −1.07320
\(490\) 6.00000 0.271052
\(491\) −23.6603 −1.06777 −0.533886 0.845556i \(-0.679269\pi\)
−0.533886 + 0.845556i \(0.679269\pi\)
\(492\) 12.1244 0.546608
\(493\) 6.46410 0.291128
\(494\) 3.12436 0.140571
\(495\) −8.19615 −0.368390
\(496\) 0.732051 0.0328701
\(497\) 16.9808 0.761691
\(498\) −4.53590 −0.203258
\(499\) −18.0526 −0.808144 −0.404072 0.914727i \(-0.632405\pi\)
−0.404072 + 0.914727i \(0.632405\pi\)
\(500\) −3.00000 −0.134164
\(501\) −7.85641 −0.350998
\(502\) −5.46410 −0.243875
\(503\) −8.66025 −0.386142 −0.193071 0.981185i \(-0.561845\pi\)
−0.193071 + 0.981185i \(0.561845\pi\)
\(504\) 3.00000 0.133631
\(505\) 9.21539 0.410079
\(506\) −2.73205 −0.121454
\(507\) −11.3923 −0.505950
\(508\) 4.53590 0.201248
\(509\) 14.1244 0.626051 0.313026 0.949745i \(-0.398657\pi\)
0.313026 + 0.949745i \(0.398657\pi\)
\(510\) −19.3923 −0.858706
\(511\) −38.7846 −1.71573
\(512\) 1.00000 0.0441942
\(513\) 2.46410 0.108793
\(514\) −19.2679 −0.849873
\(515\) 44.5692 1.96395
\(516\) 1.92820 0.0848844
\(517\) −31.1244 −1.36885
\(518\) −21.5885 −0.948542
\(519\) 11.7321 0.514980
\(520\) 3.80385 0.166810
\(521\) −5.51666 −0.241689 −0.120845 0.992671i \(-0.538560\pi\)
−0.120845 + 0.992671i \(0.538560\pi\)
\(522\) −1.00000 −0.0437688
\(523\) 4.24871 0.185783 0.0928916 0.995676i \(-0.470389\pi\)
0.0928916 + 0.995676i \(0.470389\pi\)
\(524\) −7.80385 −0.340913
\(525\) 12.0000 0.523723
\(526\) −9.05256 −0.394710
\(527\) −4.73205 −0.206131
\(528\) −2.73205 −0.118897
\(529\) 1.00000 0.0434783
\(530\) 28.3923 1.23328
\(531\) 3.53590 0.153445
\(532\) 7.39230 0.320497
\(533\) 15.3731 0.665881
\(534\) −5.46410 −0.236455
\(535\) −3.58846 −0.155143
\(536\) −9.46410 −0.408787
\(537\) −10.3923 −0.448461
\(538\) 5.66025 0.244031
\(539\) −5.46410 −0.235356
\(540\) 3.00000 0.129099
\(541\) 28.3205 1.21759 0.608797 0.793326i \(-0.291652\pi\)
0.608797 + 0.793326i \(0.291652\pi\)
\(542\) −16.7846 −0.720961
\(543\) −5.12436 −0.219907
\(544\) −6.46410 −0.277146
\(545\) −24.0000 −1.02805
\(546\) 3.80385 0.162790
\(547\) 1.32051 0.0564608 0.0282304 0.999601i \(-0.491013\pi\)
0.0282304 + 0.999601i \(0.491013\pi\)
\(548\) 0.928203 0.0396509
\(549\) 6.39230 0.272817
\(550\) −10.9282 −0.465980
\(551\) −2.46410 −0.104974
\(552\) 1.00000 0.0425628
\(553\) −51.3731 −2.18461
\(554\) −5.12436 −0.217713
\(555\) −21.5885 −0.916379
\(556\) 7.85641 0.333186
\(557\) 17.9282 0.759642 0.379821 0.925060i \(-0.375986\pi\)
0.379821 + 0.925060i \(0.375986\pi\)
\(558\) 0.732051 0.0309902
\(559\) 2.44486 0.103407
\(560\) 9.00000 0.380319
\(561\) 17.6603 0.745617
\(562\) 20.5359 0.866255
\(563\) 2.67949 0.112927 0.0564636 0.998405i \(-0.482018\pi\)
0.0564636 + 0.998405i \(0.482018\pi\)
\(564\) 11.3923 0.479703
\(565\) −28.1769 −1.18541
\(566\) −22.5885 −0.949464
\(567\) 3.00000 0.125988
\(568\) 5.66025 0.237499
\(569\) −31.3923 −1.31603 −0.658017 0.753003i \(-0.728604\pi\)
−0.658017 + 0.753003i \(0.728604\pi\)
\(570\) 7.39230 0.309630
\(571\) 41.9090 1.75384 0.876918 0.480640i \(-0.159596\pi\)
0.876918 + 0.480640i \(0.159596\pi\)
\(572\) −3.46410 −0.144841
\(573\) −26.1244 −1.09136
\(574\) 36.3731 1.51818
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) −34.4449 −1.43396 −0.716979 0.697095i \(-0.754476\pi\)
−0.716979 + 0.697095i \(0.754476\pi\)
\(578\) 24.7846 1.03090
\(579\) 2.53590 0.105388
\(580\) −3.00000 −0.124568
\(581\) −13.6077 −0.564542
\(582\) 4.00000 0.165805
\(583\) −25.8564 −1.07086
\(584\) −12.9282 −0.534973
\(585\) 3.80385 0.157270
\(586\) 6.00000 0.247858
\(587\) −34.1769 −1.41063 −0.705316 0.708893i \(-0.749195\pi\)
−0.705316 + 0.708893i \(0.749195\pi\)
\(588\) 2.00000 0.0824786
\(589\) 1.80385 0.0743262
\(590\) 10.6077 0.436712
\(591\) 14.2679 0.586905
\(592\) −7.19615 −0.295760
\(593\) 26.5359 1.08970 0.544849 0.838534i \(-0.316587\pi\)
0.544849 + 0.838534i \(0.316587\pi\)
\(594\) −2.73205 −0.112097
\(595\) −58.1769 −2.38502
\(596\) 5.00000 0.204808
\(597\) −17.3205 −0.708881
\(598\) 1.26795 0.0518503
\(599\) −21.6077 −0.882866 −0.441433 0.897294i \(-0.645530\pi\)
−0.441433 + 0.897294i \(0.645530\pi\)
\(600\) 4.00000 0.163299
\(601\) −20.7846 −0.847822 −0.423911 0.905704i \(-0.639343\pi\)
−0.423911 + 0.905704i \(0.639343\pi\)
\(602\) 5.78461 0.235763
\(603\) −9.46410 −0.385408
\(604\) −10.1244 −0.411954
\(605\) −10.6077 −0.431264
\(606\) 3.07180 0.124783
\(607\) −17.1244 −0.695056 −0.347528 0.937670i \(-0.612979\pi\)
−0.347528 + 0.937670i \(0.612979\pi\)
\(608\) 2.46410 0.0999325
\(609\) −3.00000 −0.121566
\(610\) 19.1769 0.776451
\(611\) 14.4449 0.584377
\(612\) −6.46410 −0.261296
\(613\) −39.8564 −1.60979 −0.804893 0.593421i \(-0.797777\pi\)
−0.804893 + 0.593421i \(0.797777\pi\)
\(614\) −22.9282 −0.925307
\(615\) 36.3731 1.46670
\(616\) −8.19615 −0.330232
\(617\) −48.8564 −1.96688 −0.983442 0.181221i \(-0.941995\pi\)
−0.983442 + 0.181221i \(0.941995\pi\)
\(618\) 14.8564 0.597612
\(619\) −31.0000 −1.24600 −0.622998 0.782224i \(-0.714085\pi\)
−0.622998 + 0.782224i \(0.714085\pi\)
\(620\) 2.19615 0.0881996
\(621\) 1.00000 0.0401286
\(622\) 28.3205 1.13555
\(623\) −16.3923 −0.656744
\(624\) 1.26795 0.0507586
\(625\) −29.0000 −1.16000
\(626\) 4.12436 0.164842
\(627\) −6.73205 −0.268852
\(628\) −3.73205 −0.148925
\(629\) 46.5167 1.85474
\(630\) 9.00000 0.358569
\(631\) −17.0000 −0.676759 −0.338380 0.941010i \(-0.609879\pi\)
−0.338380 + 0.941010i \(0.609879\pi\)
\(632\) −17.1244 −0.681170
\(633\) 0.803848 0.0319501
\(634\) 27.6603 1.09853
\(635\) 13.6077 0.540005
\(636\) 9.46410 0.375276
\(637\) 2.53590 0.100476
\(638\) 2.73205 0.108163
\(639\) 5.66025 0.223916
\(640\) 3.00000 0.118585
\(641\) 1.53590 0.0606643 0.0303322 0.999540i \(-0.490343\pi\)
0.0303322 + 0.999540i \(0.490343\pi\)
\(642\) −1.19615 −0.0472084
\(643\) 35.9090 1.41611 0.708056 0.706157i \(-0.249573\pi\)
0.708056 + 0.706157i \(0.249573\pi\)
\(644\) 3.00000 0.118217
\(645\) 5.78461 0.227769
\(646\) −15.9282 −0.626687
\(647\) 14.5885 0.573531 0.286766 0.958001i \(-0.407420\pi\)
0.286766 + 0.958001i \(0.407420\pi\)
\(648\) 1.00000 0.0392837
\(649\) −9.66025 −0.379198
\(650\) 5.07180 0.198932
\(651\) 2.19615 0.0860740
\(652\) −23.7321 −0.929419
\(653\) 38.3923 1.50241 0.751203 0.660071i \(-0.229474\pi\)
0.751203 + 0.660071i \(0.229474\pi\)
\(654\) −8.00000 −0.312825
\(655\) −23.4115 −0.914765
\(656\) 12.1244 0.473377
\(657\) −12.9282 −0.504377
\(658\) 34.1769 1.33235
\(659\) 32.0000 1.24654 0.623272 0.782006i \(-0.285803\pi\)
0.623272 + 0.782006i \(0.285803\pi\)
\(660\) −8.19615 −0.319035
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) −29.4449 −1.14441
\(663\) −8.19615 −0.318312
\(664\) −4.53590 −0.176027
\(665\) 22.1769 0.859984
\(666\) −7.19615 −0.278845
\(667\) −1.00000 −0.0387202
\(668\) −7.85641 −0.303973
\(669\) 8.00000 0.309298
\(670\) −28.3923 −1.09689
\(671\) −17.4641 −0.674194
\(672\) 3.00000 0.115728
\(673\) 19.0000 0.732396 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(674\) −7.07180 −0.272395
\(675\) 4.00000 0.153960
\(676\) −11.3923 −0.438166
\(677\) −34.7846 −1.33688 −0.668441 0.743766i \(-0.733038\pi\)
−0.668441 + 0.743766i \(0.733038\pi\)
\(678\) −9.39230 −0.360709
\(679\) 12.0000 0.460518
\(680\) −19.3923 −0.743661
\(681\) 5.58846 0.214150
\(682\) −2.00000 −0.0765840
\(683\) −28.4641 −1.08915 −0.544574 0.838713i \(-0.683309\pi\)
−0.544574 + 0.838713i \(0.683309\pi\)
\(684\) 2.46410 0.0942173
\(685\) 2.78461 0.106394
\(686\) −15.0000 −0.572703
\(687\) 2.80385 0.106973
\(688\) 1.92820 0.0735121
\(689\) 12.0000 0.457164
\(690\) 3.00000 0.114208
\(691\) 5.51666 0.209864 0.104932 0.994479i \(-0.466538\pi\)
0.104932 + 0.994479i \(0.466538\pi\)
\(692\) 11.7321 0.445986
\(693\) −8.19615 −0.311346
\(694\) −8.85641 −0.336185
\(695\) 23.5692 0.894031
\(696\) −1.00000 −0.0379049
\(697\) −78.3731 −2.96859
\(698\) 14.3923 0.544757
\(699\) −11.3205 −0.428181
\(700\) 12.0000 0.453557
\(701\) 17.7846 0.671715 0.335858 0.941913i \(-0.390974\pi\)
0.335858 + 0.941913i \(0.390974\pi\)
\(702\) 1.26795 0.0478557
\(703\) −17.7321 −0.668777
\(704\) −2.73205 −0.102968
\(705\) 34.1769 1.28718
\(706\) −4.53590 −0.170711
\(707\) 9.21539 0.346580
\(708\) 3.53590 0.132887
\(709\) 21.6603 0.813468 0.406734 0.913547i \(-0.366668\pi\)
0.406734 + 0.913547i \(0.366668\pi\)
\(710\) 16.9808 0.637277
\(711\) −17.1244 −0.642214
\(712\) −5.46410 −0.204776
\(713\) 0.732051 0.0274155
\(714\) −19.3923 −0.725739
\(715\) −10.3923 −0.388650
\(716\) −10.3923 −0.388379
\(717\) 19.8564 0.741551
\(718\) −7.73205 −0.288558
\(719\) 27.8038 1.03691 0.518454 0.855105i \(-0.326508\pi\)
0.518454 + 0.855105i \(0.326508\pi\)
\(720\) 3.00000 0.111803
\(721\) 44.5692 1.65984
\(722\) −12.9282 −0.481138
\(723\) 10.2679 0.381869
\(724\) −5.12436 −0.190445
\(725\) −4.00000 −0.148556
\(726\) −3.53590 −0.131229
\(727\) 28.2487 1.04769 0.523843 0.851815i \(-0.324498\pi\)
0.523843 + 0.851815i \(0.324498\pi\)
\(728\) 3.80385 0.140980
\(729\) 1.00000 0.0370370
\(730\) −38.7846 −1.43548
\(731\) −12.4641 −0.461001
\(732\) 6.39230 0.236266
\(733\) 10.9282 0.403642 0.201821 0.979422i \(-0.435314\pi\)
0.201821 + 0.979422i \(0.435314\pi\)
\(734\) 31.6603 1.16860
\(735\) 6.00000 0.221313
\(736\) 1.00000 0.0368605
\(737\) 25.8564 0.952433
\(738\) 12.1244 0.446304
\(739\) −36.3923 −1.33871 −0.669356 0.742942i \(-0.733430\pi\)
−0.669356 + 0.742942i \(0.733430\pi\)
\(740\) −21.5885 −0.793607
\(741\) 3.12436 0.114776
\(742\) 28.3923 1.04231
\(743\) 11.4449 0.419871 0.209936 0.977715i \(-0.432675\pi\)
0.209936 + 0.977715i \(0.432675\pi\)
\(744\) 0.732051 0.0268383
\(745\) 15.0000 0.549557
\(746\) 17.0718 0.625043
\(747\) −4.53590 −0.165960
\(748\) 17.6603 0.645723
\(749\) −3.58846 −0.131119
\(750\) −3.00000 −0.109545
\(751\) 5.32051 0.194148 0.0970740 0.995277i \(-0.469052\pi\)
0.0970740 + 0.995277i \(0.469052\pi\)
\(752\) 11.3923 0.415435
\(753\) −5.46410 −0.199123
\(754\) −1.26795 −0.0461760
\(755\) −30.3731 −1.10539
\(756\) 3.00000 0.109109
\(757\) 9.19615 0.334240 0.167120 0.985937i \(-0.446553\pi\)
0.167120 + 0.985937i \(0.446553\pi\)
\(758\) −23.8564 −0.866504
\(759\) −2.73205 −0.0991672
\(760\) 7.39230 0.268147
\(761\) 22.1962 0.804610 0.402305 0.915506i \(-0.368209\pi\)
0.402305 + 0.915506i \(0.368209\pi\)
\(762\) 4.53590 0.164318
\(763\) −24.0000 −0.868858
\(764\) −26.1244 −0.945146
\(765\) −19.3923 −0.701130
\(766\) 20.1962 0.729717
\(767\) 4.48334 0.161884
\(768\) 1.00000 0.0360844
\(769\) 46.0526 1.66070 0.830349 0.557244i \(-0.188141\pi\)
0.830349 + 0.557244i \(0.188141\pi\)
\(770\) −24.5885 −0.886106
\(771\) −19.2679 −0.693918
\(772\) 2.53590 0.0912690
\(773\) −26.9808 −0.970431 −0.485215 0.874395i \(-0.661259\pi\)
−0.485215 + 0.874395i \(0.661259\pi\)
\(774\) 1.92820 0.0693078
\(775\) 2.92820 0.105184
\(776\) 4.00000 0.143592
\(777\) −21.5885 −0.774482
\(778\) −13.8564 −0.496776
\(779\) 29.8756 1.07041
\(780\) 3.80385 0.136200
\(781\) −15.4641 −0.553349
\(782\) −6.46410 −0.231156
\(783\) −1.00000 −0.0357371
\(784\) 2.00000 0.0714286
\(785\) −11.1962 −0.399608
\(786\) −7.80385 −0.278354
\(787\) −16.1962 −0.577330 −0.288665 0.957430i \(-0.593211\pi\)
−0.288665 + 0.957430i \(0.593211\pi\)
\(788\) 14.2679 0.508275
\(789\) −9.05256 −0.322280
\(790\) −51.3731 −1.82777
\(791\) −28.1769 −1.00186
\(792\) −2.73205 −0.0970792
\(793\) 8.10512 0.287821
\(794\) 0.339746 0.0120571
\(795\) 28.3923 1.00697
\(796\) −17.3205 −0.613909
\(797\) 47.2295 1.67295 0.836477 0.548002i \(-0.184611\pi\)
0.836477 + 0.548002i \(0.184611\pi\)
\(798\) 7.39230 0.261685
\(799\) −73.6410 −2.60523
\(800\) 4.00000 0.141421
\(801\) −5.46410 −0.193065
\(802\) −25.7128 −0.907951
\(803\) 35.3205 1.24643
\(804\) −9.46410 −0.333773
\(805\) 9.00000 0.317208
\(806\) 0.928203 0.0326946
\(807\) 5.66025 0.199250
\(808\) 3.07180 0.108065
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 3.00000 0.105409
\(811\) 29.5692 1.03832 0.519158 0.854678i \(-0.326246\pi\)
0.519158 + 0.854678i \(0.326246\pi\)
\(812\) −3.00000 −0.105279
\(813\) −16.7846 −0.588662
\(814\) 19.6603 0.689092
\(815\) −71.1962 −2.49389
\(816\) −6.46410 −0.226289
\(817\) 4.75129 0.166227
\(818\) 19.1244 0.668667
\(819\) 3.80385 0.132917
\(820\) 36.3731 1.27020
\(821\) 0.535898 0.0187030 0.00935149 0.999956i \(-0.497023\pi\)
0.00935149 + 0.999956i \(0.497023\pi\)
\(822\) 0.928203 0.0323748
\(823\) −40.3013 −1.40481 −0.702407 0.711776i \(-0.747891\pi\)
−0.702407 + 0.711776i \(0.747891\pi\)
\(824\) 14.8564 0.517547
\(825\) −10.9282 −0.380471
\(826\) 10.6077 0.369089
\(827\) −34.9282 −1.21457 −0.607286 0.794483i \(-0.707742\pi\)
−0.607286 + 0.794483i \(0.707742\pi\)
\(828\) 1.00000 0.0347524
\(829\) −35.3923 −1.22923 −0.614613 0.788829i \(-0.710688\pi\)
−0.614613 + 0.788829i \(0.710688\pi\)
\(830\) −13.6077 −0.472330
\(831\) −5.12436 −0.177762
\(832\) 1.26795 0.0439582
\(833\) −12.9282 −0.447936
\(834\) 7.85641 0.272045
\(835\) −23.5692 −0.815646
\(836\) −6.73205 −0.232833
\(837\) 0.732051 0.0253034
\(838\) −9.58846 −0.331228
\(839\) 23.7321 0.819321 0.409661 0.912238i \(-0.365647\pi\)
0.409661 + 0.912238i \(0.365647\pi\)
\(840\) 9.00000 0.310530
\(841\) 1.00000 0.0344828
\(842\) 30.3923 1.04739
\(843\) 20.5359 0.707294
\(844\) 0.803848 0.0276696
\(845\) −34.1769 −1.17572
\(846\) 11.3923 0.391676
\(847\) −10.6077 −0.364485
\(848\) 9.46410 0.324999
\(849\) −22.5885 −0.775234
\(850\) −25.8564 −0.886867
\(851\) −7.19615 −0.246681
\(852\) 5.66025 0.193917
\(853\) 43.7846 1.49916 0.749578 0.661916i \(-0.230256\pi\)
0.749578 + 0.661916i \(0.230256\pi\)
\(854\) 19.1769 0.656221
\(855\) 7.39230 0.252811
\(856\) −1.19615 −0.0408836
\(857\) −26.4449 −0.903339 −0.451670 0.892185i \(-0.649171\pi\)
−0.451670 + 0.892185i \(0.649171\pi\)
\(858\) −3.46410 −0.118262
\(859\) −25.5885 −0.873067 −0.436533 0.899688i \(-0.643794\pi\)
−0.436533 + 0.899688i \(0.643794\pi\)
\(860\) 5.78461 0.197254
\(861\) 36.3731 1.23959
\(862\) 30.1962 1.02849
\(863\) 5.94744 0.202453 0.101227 0.994863i \(-0.467723\pi\)
0.101227 + 0.994863i \(0.467723\pi\)
\(864\) 1.00000 0.0340207
\(865\) 35.1962 1.19671
\(866\) 11.5167 0.391352
\(867\) 24.7846 0.841729
\(868\) 2.19615 0.0745423
\(869\) 46.7846 1.58706
\(870\) −3.00000 −0.101710
\(871\) −12.0000 −0.406604
\(872\) −8.00000 −0.270914
\(873\) 4.00000 0.135379
\(874\) 2.46410 0.0833495
\(875\) −9.00000 −0.304256
\(876\) −12.9282 −0.436804
\(877\) 11.1244 0.375643 0.187821 0.982203i \(-0.439857\pi\)
0.187821 + 0.982203i \(0.439857\pi\)
\(878\) 21.1962 0.715335
\(879\) 6.00000 0.202375
\(880\) −8.19615 −0.276292
\(881\) 1.07180 0.0361098 0.0180549 0.999837i \(-0.494253\pi\)
0.0180549 + 0.999837i \(0.494253\pi\)
\(882\) 2.00000 0.0673435
\(883\) 9.51666 0.320261 0.160131 0.987096i \(-0.448808\pi\)
0.160131 + 0.987096i \(0.448808\pi\)
\(884\) −8.19615 −0.275666
\(885\) 10.6077 0.356574
\(886\) 25.1769 0.845835
\(887\) −15.4641 −0.519234 −0.259617 0.965712i \(-0.583596\pi\)
−0.259617 + 0.965712i \(0.583596\pi\)
\(888\) −7.19615 −0.241487
\(889\) 13.6077 0.456387
\(890\) −16.3923 −0.549471
\(891\) −2.73205 −0.0915271
\(892\) 8.00000 0.267860
\(893\) 28.0718 0.939387
\(894\) 5.00000 0.167225
\(895\) −31.1769 −1.04213
\(896\) 3.00000 0.100223
\(897\) 1.26795 0.0423356
\(898\) 8.66025 0.288996
\(899\) −0.732051 −0.0244153
\(900\) 4.00000 0.133333
\(901\) −61.1769 −2.03810
\(902\) −33.1244 −1.10292
\(903\) 5.78461 0.192500
\(904\) −9.39230 −0.312383
\(905\) −15.3731 −0.511018
\(906\) −10.1244 −0.336359
\(907\) −51.8564 −1.72186 −0.860932 0.508720i \(-0.830119\pi\)
−0.860932 + 0.508720i \(0.830119\pi\)
\(908\) 5.58846 0.185459
\(909\) 3.07180 0.101885
\(910\) 11.4115 0.378289
\(911\) −16.0000 −0.530104 −0.265052 0.964234i \(-0.585389\pi\)
−0.265052 + 0.964234i \(0.585389\pi\)
\(912\) 2.46410 0.0815946
\(913\) 12.3923 0.410125
\(914\) 30.9090 1.02238
\(915\) 19.1769 0.633969
\(916\) 2.80385 0.0926417
\(917\) −23.4115 −0.773117
\(918\) −6.46410 −0.213347
\(919\) 53.3923 1.76125 0.880625 0.473814i \(-0.157123\pi\)
0.880625 + 0.473814i \(0.157123\pi\)
\(920\) 3.00000 0.0989071
\(921\) −22.9282 −0.755510
\(922\) −8.05256 −0.265197
\(923\) 7.17691 0.236231
\(924\) −8.19615 −0.269634
\(925\) −28.7846 −0.946432
\(926\) −31.1769 −1.02454
\(927\) 14.8564 0.487948
\(928\) −1.00000 −0.0328266
\(929\) 42.0000 1.37798 0.688988 0.724773i \(-0.258055\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(930\) 2.19615 0.0720147
\(931\) 4.92820 0.161515
\(932\) −11.3205 −0.370816
\(933\) 28.3205 0.927172
\(934\) 22.1962 0.726280
\(935\) 52.9808 1.73266
\(936\) 1.26795 0.0414442
\(937\) −24.4115 −0.797490 −0.398745 0.917062i \(-0.630554\pi\)
−0.398745 + 0.917062i \(0.630554\pi\)
\(938\) −28.3923 −0.927042
\(939\) 4.12436 0.134593
\(940\) 34.1769 1.11473
\(941\) 25.1769 0.820744 0.410372 0.911918i \(-0.365399\pi\)
0.410372 + 0.911918i \(0.365399\pi\)
\(942\) −3.73205 −0.121597
\(943\) 12.1244 0.394823
\(944\) 3.53590 0.115084
\(945\) 9.00000 0.292770
\(946\) −5.26795 −0.171276
\(947\) 10.0526 0.326664 0.163332 0.986571i \(-0.447776\pi\)
0.163332 + 0.986571i \(0.447776\pi\)
\(948\) −17.1244 −0.556173
\(949\) −16.3923 −0.532117
\(950\) 9.85641 0.319784
\(951\) 27.6603 0.896945
\(952\) −19.3923 −0.628508
\(953\) −45.4641 −1.47273 −0.736363 0.676586i \(-0.763459\pi\)
−0.736363 + 0.676586i \(0.763459\pi\)
\(954\) 9.46410 0.306412
\(955\) −78.3731 −2.53609
\(956\) 19.8564 0.642202
\(957\) 2.73205 0.0883147
\(958\) −1.85641 −0.0599778
\(959\) 2.78461 0.0899197
\(960\) 3.00000 0.0968246
\(961\) −30.4641 −0.982713
\(962\) −9.12436 −0.294181
\(963\) −1.19615 −0.0385455
\(964\) 10.2679 0.330708
\(965\) 7.60770 0.244900
\(966\) 3.00000 0.0965234
\(967\) −14.8756 −0.478368 −0.239184 0.970974i \(-0.576880\pi\)
−0.239184 + 0.970974i \(0.576880\pi\)
\(968\) −3.53590 −0.113648
\(969\) −15.9282 −0.511688
\(970\) 12.0000 0.385297
\(971\) −40.5885 −1.30255 −0.651273 0.758844i \(-0.725765\pi\)
−0.651273 + 0.758844i \(0.725765\pi\)
\(972\) 1.00000 0.0320750
\(973\) 23.5692 0.755594
\(974\) 12.5167 0.401060
\(975\) 5.07180 0.162427
\(976\) 6.39230 0.204613
\(977\) −32.9808 −1.05515 −0.527574 0.849509i \(-0.676898\pi\)
−0.527574 + 0.849509i \(0.676898\pi\)
\(978\) −23.7321 −0.758867
\(979\) 14.9282 0.477107
\(980\) 6.00000 0.191663
\(981\) −8.00000 −0.255420
\(982\) −23.6603 −0.755029
\(983\) 50.1051 1.59811 0.799053 0.601261i \(-0.205335\pi\)
0.799053 + 0.601261i \(0.205335\pi\)
\(984\) 12.1244 0.386510
\(985\) 42.8038 1.36384
\(986\) 6.46410 0.205859
\(987\) 34.1769 1.08786
\(988\) 3.12436 0.0993990
\(989\) 1.92820 0.0613133
\(990\) −8.19615 −0.260491
\(991\) 45.4449 1.44360 0.721802 0.692100i \(-0.243314\pi\)
0.721802 + 0.692100i \(0.243314\pi\)
\(992\) 0.732051 0.0232426
\(993\) −29.4449 −0.934405
\(994\) 16.9808 0.538597
\(995\) −51.9615 −1.64729
\(996\) −4.53590 −0.143725
\(997\) 43.4974 1.37758 0.688789 0.724962i \(-0.258143\pi\)
0.688789 + 0.724962i \(0.258143\pi\)
\(998\) −18.0526 −0.571444
\(999\) −7.19615 −0.227676
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 \(a_p\))