Properties

Label 8043.2.a.t.1.20
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.837626 q^{2}\) \(-1.00000 q^{3}\) \(-1.29838 q^{4}\) \(+2.34855 q^{5}\) \(+0.837626 q^{6}\) \(+1.00000 q^{7}\) \(+2.76281 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.837626 q^{2}\) \(-1.00000 q^{3}\) \(-1.29838 q^{4}\) \(+2.34855 q^{5}\) \(+0.837626 q^{6}\) \(+1.00000 q^{7}\) \(+2.76281 q^{8}\) \(+1.00000 q^{9}\) \(-1.96721 q^{10}\) \(+2.64878 q^{11}\) \(+1.29838 q^{12}\) \(-4.81100 q^{13}\) \(-0.837626 q^{14}\) \(-2.34855 q^{15}\) \(+0.282564 q^{16}\) \(-7.16278 q^{17}\) \(-0.837626 q^{18}\) \(+4.98734 q^{19}\) \(-3.04932 q^{20}\) \(-1.00000 q^{21}\) \(-2.21869 q^{22}\) \(+3.89405 q^{23}\) \(-2.76281 q^{24}\) \(+0.515710 q^{25}\) \(+4.02981 q^{26}\) \(-1.00000 q^{27}\) \(-1.29838 q^{28}\) \(-9.78351 q^{29}\) \(+1.96721 q^{30}\) \(-7.90929 q^{31}\) \(-5.76230 q^{32}\) \(-2.64878 q^{33}\) \(+5.99973 q^{34}\) \(+2.34855 q^{35}\) \(-1.29838 q^{36}\) \(+3.14302 q^{37}\) \(-4.17752 q^{38}\) \(+4.81100 q^{39}\) \(+6.48861 q^{40}\) \(-4.49750 q^{41}\) \(+0.837626 q^{42}\) \(+3.34830 q^{43}\) \(-3.43914 q^{44}\) \(+2.34855 q^{45}\) \(-3.26176 q^{46}\) \(+4.41618 q^{47}\) \(-0.282564 q^{48}\) \(+1.00000 q^{49}\) \(-0.431972 q^{50}\) \(+7.16278 q^{51}\) \(+6.24652 q^{52}\) \(+7.48954 q^{53}\) \(+0.837626 q^{54}\) \(+6.22082 q^{55}\) \(+2.76281 q^{56}\) \(-4.98734 q^{57}\) \(+8.19492 q^{58}\) \(+4.10404 q^{59}\) \(+3.04932 q^{60}\) \(-0.167344 q^{61}\) \(+6.62503 q^{62}\) \(+1.00000 q^{63}\) \(+4.26153 q^{64}\) \(-11.2989 q^{65}\) \(+2.21869 q^{66}\) \(-13.3627 q^{67}\) \(+9.30003 q^{68}\) \(-3.89405 q^{69}\) \(-1.96721 q^{70}\) \(+15.3017 q^{71}\) \(+2.76281 q^{72}\) \(-8.69102 q^{73}\) \(-2.63268 q^{74}\) \(-0.515710 q^{75}\) \(-6.47548 q^{76}\) \(+2.64878 q^{77}\) \(-4.02981 q^{78}\) \(+12.2587 q^{79}\) \(+0.663618 q^{80}\) \(+1.00000 q^{81}\) \(+3.76723 q^{82}\) \(+15.2779 q^{83}\) \(+1.29838 q^{84}\) \(-16.8222 q^{85}\) \(-2.80462 q^{86}\) \(+9.78351 q^{87}\) \(+7.31809 q^{88}\) \(+8.16472 q^{89}\) \(-1.96721 q^{90}\) \(-4.81100 q^{91}\) \(-5.05597 q^{92}\) \(+7.90929 q^{93}\) \(-3.69910 q^{94}\) \(+11.7130 q^{95}\) \(+5.76230 q^{96}\) \(+8.35604 q^{97}\) \(-0.837626 q^{98}\) \(+2.64878 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.837626 −0.592291 −0.296145 0.955143i \(-0.595701\pi\)
−0.296145 + 0.955143i \(0.595701\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.29838 −0.649192
\(5\) 2.34855 1.05031 0.525153 0.851008i \(-0.324008\pi\)
0.525153 + 0.851008i \(0.324008\pi\)
\(6\) 0.837626 0.341959
\(7\) 1.00000 0.377964
\(8\) 2.76281 0.976801
\(9\) 1.00000 0.333333
\(10\) −1.96721 −0.622086
\(11\) 2.64878 0.798639 0.399319 0.916812i \(-0.369246\pi\)
0.399319 + 0.916812i \(0.369246\pi\)
\(12\) 1.29838 0.374811
\(13\) −4.81100 −1.33433 −0.667165 0.744910i \(-0.732492\pi\)
−0.667165 + 0.744910i \(0.732492\pi\)
\(14\) −0.837626 −0.223865
\(15\) −2.34855 −0.606394
\(16\) 0.282564 0.0706411
\(17\) −7.16278 −1.73723 −0.868614 0.495489i \(-0.834989\pi\)
−0.868614 + 0.495489i \(0.834989\pi\)
\(18\) −0.837626 −0.197430
\(19\) 4.98734 1.14417 0.572087 0.820193i \(-0.306134\pi\)
0.572087 + 0.820193i \(0.306134\pi\)
\(20\) −3.04932 −0.681849
\(21\) −1.00000 −0.218218
\(22\) −2.21869 −0.473026
\(23\) 3.89405 0.811966 0.405983 0.913881i \(-0.366929\pi\)
0.405983 + 0.913881i \(0.366929\pi\)
\(24\) −2.76281 −0.563956
\(25\) 0.515710 0.103142
\(26\) 4.02981 0.790312
\(27\) −1.00000 −0.192450
\(28\) −1.29838 −0.245371
\(29\) −9.78351 −1.81675 −0.908376 0.418153i \(-0.862677\pi\)
−0.908376 + 0.418153i \(0.862677\pi\)
\(30\) 1.96721 0.359162
\(31\) −7.90929 −1.42055 −0.710276 0.703924i \(-0.751430\pi\)
−0.710276 + 0.703924i \(0.751430\pi\)
\(32\) −5.76230 −1.01864
\(33\) −2.64878 −0.461094
\(34\) 5.99973 1.02894
\(35\) 2.34855 0.396978
\(36\) −1.29838 −0.216397
\(37\) 3.14302 0.516709 0.258355 0.966050i \(-0.416820\pi\)
0.258355 + 0.966050i \(0.416820\pi\)
\(38\) −4.17752 −0.677684
\(39\) 4.81100 0.770376
\(40\) 6.48861 1.02594
\(41\) −4.49750 −0.702392 −0.351196 0.936302i \(-0.614225\pi\)
−0.351196 + 0.936302i \(0.614225\pi\)
\(42\) 0.837626 0.129248
\(43\) 3.34830 0.510611 0.255305 0.966860i \(-0.417824\pi\)
0.255305 + 0.966860i \(0.417824\pi\)
\(44\) −3.43914 −0.518469
\(45\) 2.34855 0.350102
\(46\) −3.26176 −0.480920
\(47\) 4.41618 0.644166 0.322083 0.946711i \(-0.395617\pi\)
0.322083 + 0.946711i \(0.395617\pi\)
\(48\) −0.282564 −0.0407847
\(49\) 1.00000 0.142857
\(50\) −0.431972 −0.0610900
\(51\) 7.16278 1.00299
\(52\) 6.24652 0.866236
\(53\) 7.48954 1.02877 0.514384 0.857560i \(-0.328021\pi\)
0.514384 + 0.857560i \(0.328021\pi\)
\(54\) 0.837626 0.113986
\(55\) 6.22082 0.838815
\(56\) 2.76281 0.369196
\(57\) −4.98734 −0.660589
\(58\) 8.19492 1.07605
\(59\) 4.10404 0.534300 0.267150 0.963655i \(-0.413918\pi\)
0.267150 + 0.963655i \(0.413918\pi\)
\(60\) 3.04932 0.393666
\(61\) −0.167344 −0.0214262 −0.0107131 0.999943i \(-0.503410\pi\)
−0.0107131 + 0.999943i \(0.503410\pi\)
\(62\) 6.62503 0.841379
\(63\) 1.00000 0.125988
\(64\) 4.26153 0.532691
\(65\) −11.2989 −1.40145
\(66\) 2.21869 0.273102
\(67\) −13.3627 −1.63252 −0.816259 0.577686i \(-0.803956\pi\)
−0.816259 + 0.577686i \(0.803956\pi\)
\(68\) 9.30003 1.12779
\(69\) −3.89405 −0.468789
\(70\) −1.96721 −0.235127
\(71\) 15.3017 1.81597 0.907986 0.419000i \(-0.137619\pi\)
0.907986 + 0.419000i \(0.137619\pi\)
\(72\) 2.76281 0.325600
\(73\) −8.69102 −1.01721 −0.508604 0.861001i \(-0.669838\pi\)
−0.508604 + 0.861001i \(0.669838\pi\)
\(74\) −2.63268 −0.306042
\(75\) −0.515710 −0.0595490
\(76\) −6.47548 −0.742788
\(77\) 2.64878 0.301857
\(78\) −4.02981 −0.456287
\(79\) 12.2587 1.37921 0.689606 0.724185i \(-0.257784\pi\)
0.689606 + 0.724185i \(0.257784\pi\)
\(80\) 0.663618 0.0741948
\(81\) 1.00000 0.111111
\(82\) 3.76723 0.416021
\(83\) 15.2779 1.67697 0.838485 0.544925i \(-0.183442\pi\)
0.838485 + 0.544925i \(0.183442\pi\)
\(84\) 1.29838 0.141665
\(85\) −16.8222 −1.82462
\(86\) −2.80462 −0.302430
\(87\) 9.78351 1.04890
\(88\) 7.31809 0.780111
\(89\) 8.16472 0.865459 0.432729 0.901524i \(-0.357551\pi\)
0.432729 + 0.901524i \(0.357551\pi\)
\(90\) −1.96721 −0.207362
\(91\) −4.81100 −0.504329
\(92\) −5.05597 −0.527121
\(93\) 7.90929 0.820156
\(94\) −3.69910 −0.381534
\(95\) 11.7130 1.20173
\(96\) 5.76230 0.588113
\(97\) 8.35604 0.848427 0.424213 0.905562i \(-0.360551\pi\)
0.424213 + 0.905562i \(0.360551\pi\)
\(98\) −0.837626 −0.0846130
\(99\) 2.64878 0.266213
\(100\) −0.669589 −0.0669589
\(101\) −8.56358 −0.852108 −0.426054 0.904698i \(-0.640097\pi\)
−0.426054 + 0.904698i \(0.640097\pi\)
\(102\) −5.99973 −0.594061
\(103\) 8.28638 0.816481 0.408241 0.912874i \(-0.366142\pi\)
0.408241 + 0.912874i \(0.366142\pi\)
\(104\) −13.2919 −1.30338
\(105\) −2.34855 −0.229195
\(106\) −6.27343 −0.609330
\(107\) 13.1463 1.27090 0.635449 0.772143i \(-0.280815\pi\)
0.635449 + 0.772143i \(0.280815\pi\)
\(108\) 1.29838 0.124937
\(109\) −4.71131 −0.451262 −0.225631 0.974213i \(-0.572444\pi\)
−0.225631 + 0.974213i \(0.572444\pi\)
\(110\) −5.21072 −0.496822
\(111\) −3.14302 −0.298322
\(112\) 0.282564 0.0266998
\(113\) −17.2264 −1.62052 −0.810261 0.586070i \(-0.800674\pi\)
−0.810261 + 0.586070i \(0.800674\pi\)
\(114\) 4.17752 0.391261
\(115\) 9.14539 0.852812
\(116\) 12.7027 1.17942
\(117\) −4.81100 −0.444777
\(118\) −3.43765 −0.316461
\(119\) −7.16278 −0.656611
\(120\) −6.48861 −0.592327
\(121\) −3.98394 −0.362176
\(122\) 0.140172 0.0126905
\(123\) 4.49750 0.405526
\(124\) 10.2693 0.922210
\(125\) −10.5316 −0.941975
\(126\) −0.837626 −0.0746216
\(127\) 4.63437 0.411233 0.205617 0.978633i \(-0.434080\pi\)
0.205617 + 0.978633i \(0.434080\pi\)
\(128\) 7.95505 0.703133
\(129\) −3.34830 −0.294801
\(130\) 9.46424 0.830069
\(131\) 9.28952 0.811629 0.405815 0.913955i \(-0.366988\pi\)
0.405815 + 0.913955i \(0.366988\pi\)
\(132\) 3.43914 0.299338
\(133\) 4.98734 0.432457
\(134\) 11.1930 0.966926
\(135\) −2.34855 −0.202131
\(136\) −19.7894 −1.69693
\(137\) 9.31778 0.796072 0.398036 0.917370i \(-0.369692\pi\)
0.398036 + 0.917370i \(0.369692\pi\)
\(138\) 3.26176 0.277659
\(139\) −14.0412 −1.19095 −0.595477 0.803372i \(-0.703037\pi\)
−0.595477 + 0.803372i \(0.703037\pi\)
\(140\) −3.04932 −0.257715
\(141\) −4.41618 −0.371909
\(142\) −12.8171 −1.07558
\(143\) −12.7433 −1.06565
\(144\) 0.282564 0.0235470
\(145\) −22.9771 −1.90815
\(146\) 7.27982 0.602482
\(147\) −1.00000 −0.0824786
\(148\) −4.08084 −0.335443
\(149\) 10.7903 0.883979 0.441989 0.897020i \(-0.354273\pi\)
0.441989 + 0.897020i \(0.354273\pi\)
\(150\) 0.431972 0.0352703
\(151\) 16.9627 1.38041 0.690203 0.723616i \(-0.257521\pi\)
0.690203 + 0.723616i \(0.257521\pi\)
\(152\) 13.7791 1.11763
\(153\) −7.16278 −0.579076
\(154\) −2.21869 −0.178787
\(155\) −18.5754 −1.49201
\(156\) −6.24652 −0.500122
\(157\) −12.1546 −0.970044 −0.485022 0.874502i \(-0.661188\pi\)
−0.485022 + 0.874502i \(0.661188\pi\)
\(158\) −10.2682 −0.816895
\(159\) −7.48954 −0.593959
\(160\) −13.5331 −1.06988
\(161\) 3.89405 0.306894
\(162\) −0.837626 −0.0658101
\(163\) 2.60894 0.204348 0.102174 0.994767i \(-0.467420\pi\)
0.102174 + 0.994767i \(0.467420\pi\)
\(164\) 5.83948 0.455987
\(165\) −6.22082 −0.484290
\(166\) −12.7972 −0.993254
\(167\) 4.36606 0.337856 0.168928 0.985628i \(-0.445969\pi\)
0.168928 + 0.985628i \(0.445969\pi\)
\(168\) −2.76281 −0.213155
\(169\) 10.1457 0.780437
\(170\) 14.0907 1.08071
\(171\) 4.98734 0.381391
\(172\) −4.34737 −0.331484
\(173\) −10.7265 −0.815520 −0.407760 0.913089i \(-0.633690\pi\)
−0.407760 + 0.913089i \(0.633690\pi\)
\(174\) −8.19492 −0.621256
\(175\) 0.515710 0.0389840
\(176\) 0.748452 0.0564167
\(177\) −4.10404 −0.308478
\(178\) −6.83898 −0.512603
\(179\) 15.2824 1.14226 0.571129 0.820860i \(-0.306506\pi\)
0.571129 + 0.820860i \(0.306506\pi\)
\(180\) −3.04932 −0.227283
\(181\) 6.31187 0.469157 0.234579 0.972097i \(-0.424629\pi\)
0.234579 + 0.972097i \(0.424629\pi\)
\(182\) 4.02981 0.298710
\(183\) 0.167344 0.0123704
\(184\) 10.7585 0.793129
\(185\) 7.38156 0.542703
\(186\) −6.62503 −0.485771
\(187\) −18.9727 −1.38742
\(188\) −5.73389 −0.418187
\(189\) −1.00000 −0.0727393
\(190\) −9.81114 −0.711775
\(191\) −1.99011 −0.144000 −0.0719998 0.997405i \(-0.522938\pi\)
−0.0719998 + 0.997405i \(0.522938\pi\)
\(192\) −4.26153 −0.307549
\(193\) −1.32056 −0.0950559 −0.0475280 0.998870i \(-0.515134\pi\)
−0.0475280 + 0.998870i \(0.515134\pi\)
\(194\) −6.99923 −0.502516
\(195\) 11.2989 0.809130
\(196\) −1.29838 −0.0927416
\(197\) 22.2380 1.58439 0.792196 0.610267i \(-0.208938\pi\)
0.792196 + 0.610267i \(0.208938\pi\)
\(198\) −2.21869 −0.157675
\(199\) −7.77181 −0.550929 −0.275464 0.961311i \(-0.588832\pi\)
−0.275464 + 0.961311i \(0.588832\pi\)
\(200\) 1.42481 0.100749
\(201\) 13.3627 0.942535
\(202\) 7.17308 0.504696
\(203\) −9.78351 −0.686668
\(204\) −9.30003 −0.651132
\(205\) −10.5626 −0.737727
\(206\) −6.94089 −0.483594
\(207\) 3.89405 0.270655
\(208\) −1.35942 −0.0942586
\(209\) 13.2104 0.913782
\(210\) 1.96721 0.135750
\(211\) 17.7994 1.22536 0.612680 0.790331i \(-0.290092\pi\)
0.612680 + 0.790331i \(0.290092\pi\)
\(212\) −9.72429 −0.667867
\(213\) −15.3017 −1.04845
\(214\) −11.0116 −0.752741
\(215\) 7.86366 0.536297
\(216\) −2.76281 −0.187985
\(217\) −7.90929 −0.536918
\(218\) 3.94632 0.267278
\(219\) 8.69102 0.587285
\(220\) −8.07700 −0.544551
\(221\) 34.4601 2.31804
\(222\) 2.63268 0.176694
\(223\) 27.3971 1.83464 0.917322 0.398146i \(-0.130346\pi\)
0.917322 + 0.398146i \(0.130346\pi\)
\(224\) −5.76230 −0.385010
\(225\) 0.515710 0.0343806
\(226\) 14.4293 0.959820
\(227\) −17.0761 −1.13338 −0.566692 0.823930i \(-0.691777\pi\)
−0.566692 + 0.823930i \(0.691777\pi\)
\(228\) 6.47548 0.428849
\(229\) 11.6393 0.769146 0.384573 0.923095i \(-0.374349\pi\)
0.384573 + 0.923095i \(0.374349\pi\)
\(230\) −7.66042 −0.505113
\(231\) −2.64878 −0.174277
\(232\) −27.0300 −1.77461
\(233\) 22.6650 1.48484 0.742418 0.669937i \(-0.233679\pi\)
0.742418 + 0.669937i \(0.233679\pi\)
\(234\) 4.02981 0.263437
\(235\) 10.3716 0.676571
\(236\) −5.32861 −0.346863
\(237\) −12.2587 −0.796288
\(238\) 5.99973 0.388904
\(239\) −19.9399 −1.28981 −0.644903 0.764264i \(-0.723102\pi\)
−0.644903 + 0.764264i \(0.723102\pi\)
\(240\) −0.663618 −0.0428364
\(241\) −15.5798 −1.00358 −0.501791 0.864989i \(-0.667325\pi\)
−0.501791 + 0.864989i \(0.667325\pi\)
\(242\) 3.33705 0.214514
\(243\) −1.00000 −0.0641500
\(244\) 0.217277 0.0139097
\(245\) 2.34855 0.150044
\(246\) −3.76723 −0.240190
\(247\) −23.9941 −1.52671
\(248\) −21.8519 −1.38760
\(249\) −15.2779 −0.968199
\(250\) 8.82154 0.557923
\(251\) −18.9220 −1.19435 −0.597173 0.802112i \(-0.703709\pi\)
−0.597173 + 0.802112i \(0.703709\pi\)
\(252\) −1.29838 −0.0817904
\(253\) 10.3145 0.648467
\(254\) −3.88186 −0.243570
\(255\) 16.8222 1.05345
\(256\) −15.1864 −0.949150
\(257\) 17.2789 1.07783 0.538915 0.842360i \(-0.318834\pi\)
0.538915 + 0.842360i \(0.318834\pi\)
\(258\) 2.80462 0.174608
\(259\) 3.14302 0.195298
\(260\) 14.6703 0.909812
\(261\) −9.78351 −0.605584
\(262\) −7.78114 −0.480721
\(263\) −3.26425 −0.201282 −0.100641 0.994923i \(-0.532089\pi\)
−0.100641 + 0.994923i \(0.532089\pi\)
\(264\) −7.31809 −0.450397
\(265\) 17.5896 1.08052
\(266\) −4.17752 −0.256140
\(267\) −8.16472 −0.499673
\(268\) 17.3500 1.05982
\(269\) −2.18341 −0.133125 −0.0665623 0.997782i \(-0.521203\pi\)
−0.0665623 + 0.997782i \(0.521203\pi\)
\(270\) 1.96721 0.119721
\(271\) −19.2778 −1.17104 −0.585522 0.810656i \(-0.699111\pi\)
−0.585522 + 0.810656i \(0.699111\pi\)
\(272\) −2.02395 −0.122720
\(273\) 4.81100 0.291175
\(274\) −7.80481 −0.471506
\(275\) 1.36600 0.0823731
\(276\) 5.05597 0.304334
\(277\) 6.06900 0.364651 0.182325 0.983238i \(-0.441638\pi\)
0.182325 + 0.983238i \(0.441638\pi\)
\(278\) 11.7612 0.705392
\(279\) −7.90929 −0.473517
\(280\) 6.48861 0.387769
\(281\) 5.35034 0.319174 0.159587 0.987184i \(-0.448984\pi\)
0.159587 + 0.987184i \(0.448984\pi\)
\(282\) 3.69910 0.220278
\(283\) 30.4642 1.81091 0.905456 0.424441i \(-0.139529\pi\)
0.905456 + 0.424441i \(0.139529\pi\)
\(284\) −19.8674 −1.17891
\(285\) −11.7130 −0.693821
\(286\) 10.6741 0.631173
\(287\) −4.49750 −0.265479
\(288\) −5.76230 −0.339547
\(289\) 34.3054 2.01796
\(290\) 19.2462 1.13018
\(291\) −8.35604 −0.489840
\(292\) 11.2843 0.660362
\(293\) 15.3100 0.894422 0.447211 0.894429i \(-0.352417\pi\)
0.447211 + 0.894429i \(0.352417\pi\)
\(294\) 0.837626 0.0488513
\(295\) 9.63855 0.561178
\(296\) 8.68357 0.504722
\(297\) −2.64878 −0.153698
\(298\) −9.03826 −0.523573
\(299\) −18.7343 −1.08343
\(300\) 0.669589 0.0386587
\(301\) 3.34830 0.192993
\(302\) −14.2084 −0.817602
\(303\) 8.56358 0.491965
\(304\) 1.40924 0.0808257
\(305\) −0.393017 −0.0225041
\(306\) 5.99973 0.342982
\(307\) 11.6405 0.664360 0.332180 0.943216i \(-0.392216\pi\)
0.332180 + 0.943216i \(0.392216\pi\)
\(308\) −3.43914 −0.195963
\(309\) −8.28638 −0.471396
\(310\) 15.5592 0.883706
\(311\) −34.2209 −1.94049 −0.970244 0.242129i \(-0.922154\pi\)
−0.970244 + 0.242129i \(0.922154\pi\)
\(312\) 13.2919 0.752504
\(313\) −15.1728 −0.857616 −0.428808 0.903396i \(-0.641066\pi\)
−0.428808 + 0.903396i \(0.641066\pi\)
\(314\) 10.1810 0.574548
\(315\) 2.34855 0.132326
\(316\) −15.9165 −0.895373
\(317\) −2.64579 −0.148602 −0.0743011 0.997236i \(-0.523673\pi\)
−0.0743011 + 0.997236i \(0.523673\pi\)
\(318\) 6.27343 0.351797
\(319\) −25.9144 −1.45093
\(320\) 10.0084 0.559488
\(321\) −13.1463 −0.733753
\(322\) −3.26176 −0.181771
\(323\) −35.7232 −1.98769
\(324\) −1.29838 −0.0721324
\(325\) −2.48108 −0.137625
\(326\) −2.18532 −0.121033
\(327\) 4.71131 0.260536
\(328\) −12.4258 −0.686098
\(329\) 4.41618 0.243472
\(330\) 5.21072 0.286840
\(331\) 11.4480 0.629237 0.314618 0.949218i \(-0.398123\pi\)
0.314618 + 0.949218i \(0.398123\pi\)
\(332\) −19.8366 −1.08867
\(333\) 3.14302 0.172236
\(334\) −3.65712 −0.200109
\(335\) −31.3831 −1.71464
\(336\) −0.282564 −0.0154152
\(337\) 3.70485 0.201816 0.100908 0.994896i \(-0.467825\pi\)
0.100908 + 0.994896i \(0.467825\pi\)
\(338\) −8.49829 −0.462246
\(339\) 17.2264 0.935608
\(340\) 21.8416 1.18453
\(341\) −20.9500 −1.13451
\(342\) −4.17752 −0.225895
\(343\) 1.00000 0.0539949
\(344\) 9.25071 0.498765
\(345\) −9.14539 −0.492371
\(346\) 8.98479 0.483025
\(347\) −6.95866 −0.373560 −0.186780 0.982402i \(-0.559805\pi\)
−0.186780 + 0.982402i \(0.559805\pi\)
\(348\) −12.7027 −0.680939
\(349\) −4.96087 −0.265549 −0.132775 0.991146i \(-0.542389\pi\)
−0.132775 + 0.991146i \(0.542389\pi\)
\(350\) −0.431972 −0.0230899
\(351\) 4.81100 0.256792
\(352\) −15.2631 −0.813526
\(353\) 2.33459 0.124258 0.0621289 0.998068i \(-0.480211\pi\)
0.0621289 + 0.998068i \(0.480211\pi\)
\(354\) 3.43765 0.182709
\(355\) 35.9368 1.90733
\(356\) −10.6009 −0.561848
\(357\) 7.16278 0.379094
\(358\) −12.8009 −0.676549
\(359\) −23.8904 −1.26089 −0.630444 0.776235i \(-0.717127\pi\)
−0.630444 + 0.776235i \(0.717127\pi\)
\(360\) 6.48861 0.341980
\(361\) 5.87355 0.309134
\(362\) −5.28698 −0.277878
\(363\) 3.98394 0.209103
\(364\) 6.24652 0.327406
\(365\) −20.4113 −1.06838
\(366\) −0.140172 −0.00732689
\(367\) 7.68336 0.401068 0.200534 0.979687i \(-0.435732\pi\)
0.200534 + 0.979687i \(0.435732\pi\)
\(368\) 1.10032 0.0573582
\(369\) −4.49750 −0.234131
\(370\) −6.18298 −0.321438
\(371\) 7.48954 0.388838
\(372\) −10.2693 −0.532438
\(373\) −4.55697 −0.235951 −0.117975 0.993017i \(-0.537640\pi\)
−0.117975 + 0.993017i \(0.537640\pi\)
\(374\) 15.8920 0.821755
\(375\) 10.5316 0.543850
\(376\) 12.2011 0.629222
\(377\) 47.0684 2.42415
\(378\) 0.837626 0.0430828
\(379\) 15.2378 0.782714 0.391357 0.920239i \(-0.372006\pi\)
0.391357 + 0.920239i \(0.372006\pi\)
\(380\) −15.2080 −0.780154
\(381\) −4.63437 −0.237426
\(382\) 1.66697 0.0852897
\(383\) −1.00000 −0.0510976
\(384\) −7.95505 −0.405954
\(385\) 6.22082 0.317042
\(386\) 1.10613 0.0563008
\(387\) 3.34830 0.170204
\(388\) −10.8493 −0.550792
\(389\) −0.845771 −0.0428823 −0.0214412 0.999770i \(-0.506825\pi\)
−0.0214412 + 0.999770i \(0.506825\pi\)
\(390\) −9.46424 −0.479240
\(391\) −27.8922 −1.41057
\(392\) 2.76281 0.139543
\(393\) −9.28952 −0.468594
\(394\) −18.6271 −0.938421
\(395\) 28.7902 1.44859
\(396\) −3.43914 −0.172823
\(397\) −5.44659 −0.273357 −0.136678 0.990615i \(-0.543643\pi\)
−0.136678 + 0.990615i \(0.543643\pi\)
\(398\) 6.50987 0.326310
\(399\) −4.98734 −0.249679
\(400\) 0.145721 0.00728606
\(401\) −37.3410 −1.86472 −0.932360 0.361532i \(-0.882254\pi\)
−0.932360 + 0.361532i \(0.882254\pi\)
\(402\) −11.1930 −0.558255
\(403\) 38.0516 1.89548
\(404\) 11.1188 0.553182
\(405\) 2.34855 0.116701
\(406\) 8.19492 0.406707
\(407\) 8.32519 0.412664
\(408\) 19.7894 0.979721
\(409\) 17.0992 0.845500 0.422750 0.906246i \(-0.361065\pi\)
0.422750 + 0.906246i \(0.361065\pi\)
\(410\) 8.84754 0.436949
\(411\) −9.31778 −0.459612
\(412\) −10.7589 −0.530053
\(413\) 4.10404 0.201946
\(414\) −3.26176 −0.160307
\(415\) 35.8810 1.76133
\(416\) 27.7224 1.35920
\(417\) 14.0412 0.687598
\(418\) −11.0654 −0.541225
\(419\) 6.48552 0.316838 0.158419 0.987372i \(-0.449360\pi\)
0.158419 + 0.987372i \(0.449360\pi\)
\(420\) 3.04932 0.148792
\(421\) 2.53483 0.123540 0.0617700 0.998090i \(-0.480325\pi\)
0.0617700 + 0.998090i \(0.480325\pi\)
\(422\) −14.9092 −0.725769
\(423\) 4.41618 0.214722
\(424\) 20.6922 1.00490
\(425\) −3.69391 −0.179181
\(426\) 12.8171 0.620989
\(427\) −0.167344 −0.00809834
\(428\) −17.0689 −0.825056
\(429\) 12.7433 0.615252
\(430\) −6.58681 −0.317644
\(431\) −26.6193 −1.28220 −0.641102 0.767455i \(-0.721523\pi\)
−0.641102 + 0.767455i \(0.721523\pi\)
\(432\) −0.282564 −0.0135949
\(433\) 21.2305 1.02027 0.510135 0.860094i \(-0.329595\pi\)
0.510135 + 0.860094i \(0.329595\pi\)
\(434\) 6.62503 0.318012
\(435\) 22.9771 1.10167
\(436\) 6.11709 0.292955
\(437\) 19.4209 0.929030
\(438\) −7.27982 −0.347843
\(439\) −4.56215 −0.217740 −0.108870 0.994056i \(-0.534723\pi\)
−0.108870 + 0.994056i \(0.534723\pi\)
\(440\) 17.1869 0.819355
\(441\) 1.00000 0.0476190
\(442\) −28.8647 −1.37295
\(443\) 11.6793 0.554899 0.277450 0.960740i \(-0.410511\pi\)
0.277450 + 0.960740i \(0.410511\pi\)
\(444\) 4.08084 0.193668
\(445\) 19.1753 0.908996
\(446\) −22.9485 −1.08664
\(447\) −10.7903 −0.510365
\(448\) 4.26153 0.201338
\(449\) 7.88702 0.372212 0.186106 0.982530i \(-0.440413\pi\)
0.186106 + 0.982530i \(0.440413\pi\)
\(450\) −0.431972 −0.0203633
\(451\) −11.9129 −0.560958
\(452\) 22.3664 1.05203
\(453\) −16.9627 −0.796978
\(454\) 14.3034 0.671293
\(455\) −11.2989 −0.529700
\(456\) −13.7791 −0.645264
\(457\) 27.9515 1.30752 0.653759 0.756703i \(-0.273191\pi\)
0.653759 + 0.756703i \(0.273191\pi\)
\(458\) −9.74937 −0.455558
\(459\) 7.16278 0.334330
\(460\) −11.8742 −0.553638
\(461\) 38.3961 1.78828 0.894142 0.447784i \(-0.147787\pi\)
0.894142 + 0.447784i \(0.147787\pi\)
\(462\) 2.21869 0.103223
\(463\) −1.00827 −0.0468585 −0.0234292 0.999725i \(-0.507458\pi\)
−0.0234292 + 0.999725i \(0.507458\pi\)
\(464\) −2.76447 −0.128337
\(465\) 18.5754 0.861414
\(466\) −18.9848 −0.879455
\(467\) −6.73587 −0.311699 −0.155849 0.987781i \(-0.549811\pi\)
−0.155849 + 0.987781i \(0.549811\pi\)
\(468\) 6.24652 0.288745
\(469\) −13.3627 −0.617034
\(470\) −8.68755 −0.400727
\(471\) 12.1546 0.560055
\(472\) 11.3387 0.521905
\(473\) 8.86892 0.407793
\(474\) 10.2682 0.471634
\(475\) 2.57202 0.118012
\(476\) 9.30003 0.426266
\(477\) 7.48954 0.342923
\(478\) 16.7022 0.763940
\(479\) 29.9094 1.36660 0.683298 0.730139i \(-0.260545\pi\)
0.683298 + 0.730139i \(0.260545\pi\)
\(480\) 13.5331 0.617698
\(481\) −15.1211 −0.689461
\(482\) 13.0500 0.594412
\(483\) −3.89405 −0.177185
\(484\) 5.17268 0.235122
\(485\) 19.6246 0.891108
\(486\) 0.837626 0.0379955
\(487\) 33.0486 1.49758 0.748788 0.662809i \(-0.230636\pi\)
0.748788 + 0.662809i \(0.230636\pi\)
\(488\) −0.462340 −0.0209291
\(489\) −2.60894 −0.117980
\(490\) −1.96721 −0.0888695
\(491\) 6.79917 0.306842 0.153421 0.988161i \(-0.450971\pi\)
0.153421 + 0.988161i \(0.450971\pi\)
\(492\) −5.83948 −0.263264
\(493\) 70.0771 3.15611
\(494\) 20.0981 0.904254
\(495\) 6.22082 0.279605
\(496\) −2.23489 −0.100349
\(497\) 15.3017 0.686373
\(498\) 12.7972 0.573455
\(499\) 4.92460 0.220455 0.110228 0.993906i \(-0.464842\pi\)
0.110228 + 0.993906i \(0.464842\pi\)
\(500\) 13.6741 0.611522
\(501\) −4.36606 −0.195061
\(502\) 15.8496 0.707400
\(503\) 16.5025 0.735812 0.367906 0.929863i \(-0.380075\pi\)
0.367906 + 0.929863i \(0.380075\pi\)
\(504\) 2.76281 0.123065
\(505\) −20.1120 −0.894974
\(506\) −8.63969 −0.384081
\(507\) −10.1457 −0.450586
\(508\) −6.01718 −0.266969
\(509\) −24.4469 −1.08359 −0.541794 0.840511i \(-0.682255\pi\)
−0.541794 + 0.840511i \(0.682255\pi\)
\(510\) −14.0907 −0.623946
\(511\) −8.69102 −0.384468
\(512\) −3.18957 −0.140960
\(513\) −4.98734 −0.220196
\(514\) −14.4733 −0.638389
\(515\) 19.4610 0.857555
\(516\) 4.34737 0.191382
\(517\) 11.6975 0.514456
\(518\) −2.63268 −0.115673
\(519\) 10.7265 0.470841
\(520\) −31.2167 −1.36894
\(521\) 34.1206 1.49485 0.747426 0.664345i \(-0.231289\pi\)
0.747426 + 0.664345i \(0.231289\pi\)
\(522\) 8.19492 0.358682
\(523\) 3.62918 0.158693 0.0793464 0.996847i \(-0.474717\pi\)
0.0793464 + 0.996847i \(0.474717\pi\)
\(524\) −12.0614 −0.526903
\(525\) −0.515710 −0.0225074
\(526\) 2.73422 0.119218
\(527\) 56.6525 2.46782
\(528\) −0.748452 −0.0325722
\(529\) −7.83637 −0.340712
\(530\) −14.7335 −0.639982
\(531\) 4.10404 0.178100
\(532\) −6.47548 −0.280747
\(533\) 21.6375 0.937223
\(534\) 6.83898 0.295952
\(535\) 30.8747 1.33483
\(536\) −36.9187 −1.59465
\(537\) −15.2824 −0.659483
\(538\) 1.82888 0.0788485
\(539\) 2.64878 0.114091
\(540\) 3.04932 0.131222
\(541\) −8.60482 −0.369950 −0.184975 0.982743i \(-0.559220\pi\)
−0.184975 + 0.982743i \(0.559220\pi\)
\(542\) 16.1476 0.693599
\(543\) −6.31187 −0.270868
\(544\) 41.2741 1.76961
\(545\) −11.0648 −0.473963
\(546\) −4.02981 −0.172460
\(547\) −26.6304 −1.13864 −0.569318 0.822118i \(-0.692793\pi\)
−0.569318 + 0.822118i \(0.692793\pi\)
\(548\) −12.0980 −0.516803
\(549\) −0.167344 −0.00714207
\(550\) −1.14420 −0.0487889
\(551\) −48.7937 −2.07868
\(552\) −10.7585 −0.457913
\(553\) 12.2587 0.521293
\(554\) −5.08355 −0.215979
\(555\) −7.38156 −0.313330
\(556\) 18.2308 0.773158
\(557\) −37.8231 −1.60262 −0.801308 0.598252i \(-0.795862\pi\)
−0.801308 + 0.598252i \(0.795862\pi\)
\(558\) 6.62503 0.280460
\(559\) −16.1087 −0.681323
\(560\) 0.663618 0.0280430
\(561\) 18.9727 0.801026
\(562\) −4.48158 −0.189044
\(563\) −3.49391 −0.147251 −0.0736254 0.997286i \(-0.523457\pi\)
−0.0736254 + 0.997286i \(0.523457\pi\)
\(564\) 5.73389 0.241440
\(565\) −40.4571 −1.70204
\(566\) −25.5176 −1.07259
\(567\) 1.00000 0.0419961
\(568\) 42.2756 1.77384
\(569\) 9.86383 0.413513 0.206757 0.978392i \(-0.433709\pi\)
0.206757 + 0.978392i \(0.433709\pi\)
\(570\) 9.81114 0.410944
\(571\) 45.2735 1.89464 0.947318 0.320293i \(-0.103781\pi\)
0.947318 + 0.320293i \(0.103781\pi\)
\(572\) 16.5457 0.691809
\(573\) 1.99011 0.0831382
\(574\) 3.76723 0.157241
\(575\) 2.00820 0.0837477
\(576\) 4.26153 0.177564
\(577\) 6.72576 0.279997 0.139998 0.990152i \(-0.455290\pi\)
0.139998 + 0.990152i \(0.455290\pi\)
\(578\) −28.7351 −1.19522
\(579\) 1.32056 0.0548806
\(580\) 29.8331 1.23875
\(581\) 15.2779 0.633835
\(582\) 6.99923 0.290128
\(583\) 19.8382 0.821614
\(584\) −24.0116 −0.993609
\(585\) −11.2989 −0.467152
\(586\) −12.8241 −0.529758
\(587\) −11.9195 −0.491972 −0.245986 0.969273i \(-0.579112\pi\)
−0.245986 + 0.969273i \(0.579112\pi\)
\(588\) 1.29838 0.0535444
\(589\) −39.4463 −1.62536
\(590\) −8.07350 −0.332381
\(591\) −22.2380 −0.914749
\(592\) 0.888106 0.0365009
\(593\) −8.73816 −0.358833 −0.179417 0.983773i \(-0.557421\pi\)
−0.179417 + 0.983773i \(0.557421\pi\)
\(594\) 2.21869 0.0910340
\(595\) −16.8222 −0.689642
\(596\) −14.0100 −0.573872
\(597\) 7.77181 0.318079
\(598\) 15.6923 0.641706
\(599\) 30.6671 1.25302 0.626512 0.779412i \(-0.284482\pi\)
0.626512 + 0.779412i \(0.284482\pi\)
\(600\) −1.42481 −0.0581676
\(601\) 21.9578 0.895677 0.447838 0.894115i \(-0.352194\pi\)
0.447838 + 0.894115i \(0.352194\pi\)
\(602\) −2.80462 −0.114308
\(603\) −13.3627 −0.544173
\(604\) −22.0241 −0.896148
\(605\) −9.35650 −0.380396
\(606\) −7.17308 −0.291386
\(607\) 45.8303 1.86019 0.930097 0.367313i \(-0.119722\pi\)
0.930097 + 0.367313i \(0.119722\pi\)
\(608\) −28.7386 −1.16550
\(609\) 9.78351 0.396448
\(610\) 0.329201 0.0133290
\(611\) −21.2462 −0.859530
\(612\) 9.30003 0.375931
\(613\) 38.0357 1.53625 0.768124 0.640302i \(-0.221191\pi\)
0.768124 + 0.640302i \(0.221191\pi\)
\(614\) −9.75040 −0.393494
\(615\) 10.5626 0.425927
\(616\) 7.31809 0.294854
\(617\) 37.9265 1.52686 0.763431 0.645889i \(-0.223513\pi\)
0.763431 + 0.645889i \(0.223513\pi\)
\(618\) 6.94089 0.279203
\(619\) 15.4194 0.619759 0.309880 0.950776i \(-0.399711\pi\)
0.309880 + 0.950776i \(0.399711\pi\)
\(620\) 24.1180 0.968602
\(621\) −3.89405 −0.156263
\(622\) 28.6643 1.14933
\(623\) 8.16472 0.327113
\(624\) 1.35942 0.0544202
\(625\) −27.3126 −1.09250
\(626\) 12.7091 0.507958
\(627\) −13.2104 −0.527572
\(628\) 15.7814 0.629745
\(629\) −22.5128 −0.897642
\(630\) −1.96721 −0.0783755
\(631\) 37.8063 1.50504 0.752522 0.658567i \(-0.228837\pi\)
0.752522 + 0.658567i \(0.228837\pi\)
\(632\) 33.8685 1.34722
\(633\) −17.7994 −0.707462
\(634\) 2.21618 0.0880157
\(635\) 10.8841 0.431921
\(636\) 9.72429 0.385593
\(637\) −4.81100 −0.190619
\(638\) 21.7066 0.859372
\(639\) 15.3017 0.605324
\(640\) 18.6829 0.738505
\(641\) 19.6878 0.777622 0.388811 0.921317i \(-0.372886\pi\)
0.388811 + 0.921317i \(0.372886\pi\)
\(642\) 11.0116 0.434595
\(643\) 35.8761 1.41482 0.707408 0.706806i \(-0.249864\pi\)
0.707408 + 0.706806i \(0.249864\pi\)
\(644\) −5.05597 −0.199233
\(645\) −7.86366 −0.309631
\(646\) 29.9227 1.17729
\(647\) 34.8738 1.37103 0.685515 0.728058i \(-0.259577\pi\)
0.685515 + 0.728058i \(0.259577\pi\)
\(648\) 2.76281 0.108533
\(649\) 10.8707 0.426713
\(650\) 2.07821 0.0815143
\(651\) 7.90929 0.309990
\(652\) −3.38740 −0.132661
\(653\) 18.8728 0.738549 0.369275 0.929320i \(-0.379606\pi\)
0.369275 + 0.929320i \(0.379606\pi\)
\(654\) −3.94632 −0.154313
\(655\) 21.8170 0.852459
\(656\) −1.27083 −0.0496178
\(657\) −8.69102 −0.339069
\(658\) −3.69910 −0.144206
\(659\) 7.13241 0.277839 0.138920 0.990304i \(-0.455637\pi\)
0.138920 + 0.990304i \(0.455637\pi\)
\(660\) 8.07700 0.314397
\(661\) −20.9940 −0.816571 −0.408285 0.912854i \(-0.633873\pi\)
−0.408285 + 0.912854i \(0.633873\pi\)
\(662\) −9.58910 −0.372691
\(663\) −34.4601 −1.33832
\(664\) 42.2100 1.63807
\(665\) 11.7130 0.454212
\(666\) −2.63268 −0.102014
\(667\) −38.0975 −1.47514
\(668\) −5.66882 −0.219333
\(669\) −27.3971 −1.05923
\(670\) 26.2873 1.01557
\(671\) −0.443258 −0.0171118
\(672\) 5.76230 0.222286
\(673\) −17.0045 −0.655476 −0.327738 0.944769i \(-0.606286\pi\)
−0.327738 + 0.944769i \(0.606286\pi\)
\(674\) −3.10328 −0.119534
\(675\) −0.515710 −0.0198497
\(676\) −13.1730 −0.506653
\(677\) 35.1770 1.35196 0.675982 0.736918i \(-0.263720\pi\)
0.675982 + 0.736918i \(0.263720\pi\)
\(678\) −14.4293 −0.554152
\(679\) 8.35604 0.320675
\(680\) −46.4765 −1.78229
\(681\) 17.0761 0.654359
\(682\) 17.5483 0.671958
\(683\) −15.8819 −0.607703 −0.303852 0.952719i \(-0.598273\pi\)
−0.303852 + 0.952719i \(0.598273\pi\)
\(684\) −6.47548 −0.247596
\(685\) 21.8833 0.836119
\(686\) −0.837626 −0.0319807
\(687\) −11.6393 −0.444067
\(688\) 0.946110 0.0360701
\(689\) −36.0322 −1.37272
\(690\) 7.66042 0.291627
\(691\) −27.3079 −1.03884 −0.519421 0.854519i \(-0.673852\pi\)
−0.519421 + 0.854519i \(0.673852\pi\)
\(692\) 13.9271 0.529429
\(693\) 2.64878 0.100619
\(694\) 5.82875 0.221256
\(695\) −32.9764 −1.25087
\(696\) 27.0300 1.02457
\(697\) 32.2146 1.22022
\(698\) 4.15535 0.157282
\(699\) −22.6650 −0.857271
\(700\) −0.669589 −0.0253081
\(701\) −9.45633 −0.357161 −0.178580 0.983925i \(-0.557150\pi\)
−0.178580 + 0.983925i \(0.557150\pi\)
\(702\) −4.02981 −0.152096
\(703\) 15.6753 0.591206
\(704\) 11.2879 0.425427
\(705\) −10.3716 −0.390618
\(706\) −1.95552 −0.0735968
\(707\) −8.56358 −0.322067
\(708\) 5.32861 0.200261
\(709\) 12.6737 0.475970 0.237985 0.971269i \(-0.423513\pi\)
0.237985 + 0.971269i \(0.423513\pi\)
\(710\) −30.1016 −1.12969
\(711\) 12.2587 0.459737
\(712\) 22.5576 0.845381
\(713\) −30.7992 −1.15344
\(714\) −5.99973 −0.224534
\(715\) −29.9283 −1.11926
\(716\) −19.8424 −0.741544
\(717\) 19.9399 0.744670
\(718\) 20.0112 0.746812
\(719\) 5.48988 0.204738 0.102369 0.994746i \(-0.467358\pi\)
0.102369 + 0.994746i \(0.467358\pi\)
\(720\) 0.663618 0.0247316
\(721\) 8.28638 0.308601
\(722\) −4.91984 −0.183097
\(723\) 15.5798 0.579418
\(724\) −8.19522 −0.304573
\(725\) −5.04545 −0.187383
\(726\) −3.33705 −0.123850
\(727\) −1.41600 −0.0525167 −0.0262583 0.999655i \(-0.508359\pi\)
−0.0262583 + 0.999655i \(0.508359\pi\)
\(728\) −13.2919 −0.492630
\(729\) 1.00000 0.0370370
\(730\) 17.0971 0.632791
\(731\) −23.9831 −0.887047
\(732\) −0.217277 −0.00803077
\(733\) −13.2592 −0.489739 −0.244869 0.969556i \(-0.578745\pi\)
−0.244869 + 0.969556i \(0.578745\pi\)
\(734\) −6.43578 −0.237549
\(735\) −2.34855 −0.0866277
\(736\) −22.4387 −0.827102
\(737\) −35.3950 −1.30379
\(738\) 3.76723 0.138674
\(739\) −8.96306 −0.329711 −0.164856 0.986318i \(-0.552716\pi\)
−0.164856 + 0.986318i \(0.552716\pi\)
\(740\) −9.58409 −0.352318
\(741\) 23.9941 0.881444
\(742\) −6.27343 −0.230305
\(743\) −7.29561 −0.267650 −0.133825 0.991005i \(-0.542726\pi\)
−0.133825 + 0.991005i \(0.542726\pi\)
\(744\) 21.8519 0.801129
\(745\) 25.3417 0.928448
\(746\) 3.81703 0.139751
\(747\) 15.2779 0.558990
\(748\) 24.6338 0.900700
\(749\) 13.1463 0.480354
\(750\) −8.82154 −0.322117
\(751\) 8.92028 0.325506 0.162753 0.986667i \(-0.447963\pi\)
0.162753 + 0.986667i \(0.447963\pi\)
\(752\) 1.24785 0.0455046
\(753\) 18.9220 0.689556
\(754\) −39.4257 −1.43580
\(755\) 39.8379 1.44985
\(756\) 1.29838 0.0472217
\(757\) 8.89494 0.323292 0.161646 0.986849i \(-0.448320\pi\)
0.161646 + 0.986849i \(0.448320\pi\)
\(758\) −12.7636 −0.463594
\(759\) −10.3145 −0.374393
\(760\) 32.3609 1.17385
\(761\) −37.4227 −1.35657 −0.678286 0.734798i \(-0.737277\pi\)
−0.678286 + 0.734798i \(0.737277\pi\)
\(762\) 3.88186 0.140625
\(763\) −4.71131 −0.170561
\(764\) 2.58393 0.0934834
\(765\) −16.8222 −0.608207
\(766\) 0.837626 0.0302647
\(767\) −19.7445 −0.712933
\(768\) 15.1864 0.547992
\(769\) −11.5675 −0.417133 −0.208566 0.978008i \(-0.566880\pi\)
−0.208566 + 0.978008i \(0.566880\pi\)
\(770\) −5.21072 −0.187781
\(771\) −17.2789 −0.622286
\(772\) 1.71459 0.0617095
\(773\) −30.3031 −1.08993 −0.544963 0.838460i \(-0.683456\pi\)
−0.544963 + 0.838460i \(0.683456\pi\)
\(774\) −2.80462 −0.100810
\(775\) −4.07890 −0.146518
\(776\) 23.0861 0.828744
\(777\) −3.14302 −0.112755
\(778\) 0.708440 0.0253988
\(779\) −22.4306 −0.803659
\(780\) −14.6703 −0.525280
\(781\) 40.5308 1.45031
\(782\) 23.3632 0.835468
\(783\) 9.78351 0.349634
\(784\) 0.282564 0.0100916
\(785\) −28.5458 −1.01884
\(786\) 7.78114 0.277544
\(787\) −33.5523 −1.19601 −0.598006 0.801492i \(-0.704040\pi\)
−0.598006 + 0.801492i \(0.704040\pi\)
\(788\) −28.8734 −1.02857
\(789\) 3.26425 0.116210
\(790\) −24.1154 −0.857989
\(791\) −17.2264 −0.612499
\(792\) 7.31809 0.260037
\(793\) 0.805091 0.0285896
\(794\) 4.56220 0.161907
\(795\) −17.5896 −0.623839
\(796\) 10.0908 0.357658
\(797\) 34.7862 1.23219 0.616096 0.787671i \(-0.288713\pi\)
0.616096 + 0.787671i \(0.288713\pi\)
\(798\) 4.17752 0.147883
\(799\) −31.6321 −1.11906
\(800\) −2.97168 −0.105065
\(801\) 8.16472 0.288486
\(802\) 31.2778 1.10446
\(803\) −23.0206 −0.812381
\(804\) −17.3500 −0.611886
\(805\) 9.14539 0.322333
\(806\) −31.8730 −1.12268
\(807\) 2.18341 0.0768595
\(808\) −23.6596 −0.832340
\(809\) 15.7501 0.553746 0.276873 0.960907i \(-0.410702\pi\)
0.276873 + 0.960907i \(0.410702\pi\)
\(810\) −1.96721 −0.0691207
\(811\) −37.8786 −1.33010 −0.665049 0.746800i \(-0.731589\pi\)
−0.665049 + 0.746800i \(0.731589\pi\)
\(812\) 12.7027 0.445779
\(813\) 19.2778 0.676103
\(814\) −6.97339 −0.244417
\(815\) 6.12724 0.214628
\(816\) 2.02395 0.0708523
\(817\) 16.6991 0.584227
\(818\) −14.3227 −0.500782
\(819\) −4.81100 −0.168110
\(820\) 13.7143 0.478926
\(821\) −43.1350 −1.50542 −0.752711 0.658351i \(-0.771254\pi\)
−0.752711 + 0.658351i \(0.771254\pi\)
\(822\) 7.80481 0.272224
\(823\) −45.1329 −1.57324 −0.786618 0.617441i \(-0.788170\pi\)
−0.786618 + 0.617441i \(0.788170\pi\)
\(824\) 22.8937 0.797540
\(825\) −1.36600 −0.0475582
\(826\) −3.43765 −0.119611
\(827\) 15.3556 0.533967 0.266984 0.963701i \(-0.413973\pi\)
0.266984 + 0.963701i \(0.413973\pi\)
\(828\) −5.05597 −0.175707
\(829\) −12.0825 −0.419643 −0.209822 0.977740i \(-0.567288\pi\)
−0.209822 + 0.977740i \(0.567288\pi\)
\(830\) −30.0549 −1.04322
\(831\) −6.06900 −0.210531
\(832\) −20.5022 −0.710785
\(833\) −7.16278 −0.248175
\(834\) −11.7612 −0.407258
\(835\) 10.2539 0.354852
\(836\) −17.1521 −0.593219
\(837\) 7.90929 0.273385
\(838\) −5.43244 −0.187660
\(839\) 26.0001 0.897623 0.448812 0.893626i \(-0.351847\pi\)
0.448812 + 0.893626i \(0.351847\pi\)
\(840\) −6.48861 −0.223878
\(841\) 66.7171 2.30059
\(842\) −2.12324 −0.0731717
\(843\) −5.35034 −0.184275
\(844\) −23.1104 −0.795493
\(845\) 23.8277 0.819698
\(846\) −3.69910 −0.127178
\(847\) −3.98394 −0.136890
\(848\) 2.11628 0.0726733
\(849\) −30.4642 −1.04553
\(850\) 3.09412 0.106127
\(851\) 12.2391 0.419550
\(852\) 19.8674 0.680646
\(853\) −18.8302 −0.644735 −0.322367 0.946615i \(-0.604479\pi\)
−0.322367 + 0.946615i \(0.604479\pi\)
\(854\) 0.140172 0.00479658
\(855\) 11.7130 0.400577
\(856\) 36.3206 1.24141
\(857\) 9.65738 0.329890 0.164945 0.986303i \(-0.447255\pi\)
0.164945 + 0.986303i \(0.447255\pi\)
\(858\) −10.6741 −0.364408
\(859\) 42.9535 1.46556 0.732778 0.680468i \(-0.238223\pi\)
0.732778 + 0.680468i \(0.238223\pi\)
\(860\) −10.2100 −0.348160
\(861\) 4.49750 0.153275
\(862\) 22.2970 0.759438
\(863\) 27.3304 0.930338 0.465169 0.885222i \(-0.345994\pi\)
0.465169 + 0.885222i \(0.345994\pi\)
\(864\) 5.76230 0.196038
\(865\) −25.1918 −0.856545
\(866\) −17.7832 −0.604297
\(867\) −34.3054 −1.16507
\(868\) 10.2693 0.348563
\(869\) 32.4707 1.10149
\(870\) −19.2462 −0.652508
\(871\) 64.2881 2.17832
\(872\) −13.0165 −0.440793
\(873\) 8.35604 0.282809
\(874\) −16.2675 −0.550256
\(875\) −10.5316 −0.356033
\(876\) −11.2843 −0.381260
\(877\) −37.9119 −1.28019 −0.640096 0.768295i \(-0.721106\pi\)
−0.640096 + 0.768295i \(0.721106\pi\)
\(878\) 3.82138 0.128965
\(879\) −15.3100 −0.516395
\(880\) 1.75778 0.0592548
\(881\) −25.3289 −0.853351 −0.426675 0.904405i \(-0.640315\pi\)
−0.426675 + 0.904405i \(0.640315\pi\)
\(882\) −0.837626 −0.0282043
\(883\) −35.1092 −1.18152 −0.590760 0.806847i \(-0.701172\pi\)
−0.590760 + 0.806847i \(0.701172\pi\)
\(884\) −44.7424 −1.50485
\(885\) −9.63855 −0.323996
\(886\) −9.78287 −0.328662
\(887\) 40.3424 1.35456 0.677282 0.735724i \(-0.263158\pi\)
0.677282 + 0.735724i \(0.263158\pi\)
\(888\) −8.68357 −0.291402
\(889\) 4.63437 0.155432
\(890\) −16.0617 −0.538390
\(891\) 2.64878 0.0887376
\(892\) −35.5719 −1.19104
\(893\) 22.0250 0.737038
\(894\) 9.03826 0.302285
\(895\) 35.8915 1.19972
\(896\) 7.95505 0.265759
\(897\) 18.7343 0.625519
\(898\) −6.60637 −0.220458
\(899\) 77.3807 2.58079
\(900\) −0.669589 −0.0223196
\(901\) −53.6459 −1.78720
\(902\) 9.97857 0.332250
\(903\) −3.34830 −0.111424
\(904\) −47.5932 −1.58293
\(905\) 14.8238 0.492759
\(906\) 14.2084 0.472043
\(907\) −36.1674 −1.20092 −0.600459 0.799656i \(-0.705015\pi\)
−0.600459 + 0.799656i \(0.705015\pi\)
\(908\) 22.1714 0.735783
\(909\) −8.56358 −0.284036
\(910\) 9.46424 0.313737
\(911\) −48.1370 −1.59485 −0.797425 0.603418i \(-0.793805\pi\)
−0.797425 + 0.603418i \(0.793805\pi\)
\(912\) −1.40924 −0.0466648
\(913\) 40.4679 1.33929
\(914\) −23.4129 −0.774431
\(915\) 0.393017 0.0129927
\(916\) −15.1123 −0.499323
\(917\) 9.28952 0.306767
\(918\) −5.99973 −0.198020
\(919\) 22.3951 0.738745 0.369372 0.929282i \(-0.379573\pi\)
0.369372 + 0.929282i \(0.379573\pi\)
\(920\) 25.2670 0.833028
\(921\) −11.6405 −0.383568
\(922\) −32.1615 −1.05918
\(923\) −73.6162 −2.42311
\(924\) 3.43914 0.113139
\(925\) 1.62089 0.0532944
\(926\) 0.844557 0.0277539
\(927\) 8.28638 0.272160
\(928\) 56.3756 1.85062
\(929\) −47.3719 −1.55422 −0.777111 0.629364i \(-0.783315\pi\)
−0.777111 + 0.629364i \(0.783315\pi\)
\(930\) −15.5592 −0.510208
\(931\) 4.98734 0.163453
\(932\) −29.4279 −0.963943
\(933\) 34.2209 1.12034
\(934\) 5.64214 0.184616
\(935\) −44.5583 −1.45721
\(936\) −13.2919 −0.434458
\(937\) 19.8073 0.647078 0.323539 0.946215i \(-0.395127\pi\)
0.323539 + 0.946215i \(0.395127\pi\)
\(938\) 11.1930 0.365464
\(939\) 15.1728 0.495145
\(940\) −13.4664 −0.439224
\(941\) −22.6040 −0.736871 −0.368435 0.929653i \(-0.620106\pi\)
−0.368435 + 0.929653i \(0.620106\pi\)
\(942\) −10.1810 −0.331716
\(943\) −17.5135 −0.570318
\(944\) 1.15965 0.0377435
\(945\) −2.34855 −0.0763985
\(946\) −7.42884 −0.241532
\(947\) −33.4604 −1.08732 −0.543658 0.839307i \(-0.682961\pi\)
−0.543658 + 0.839307i \(0.682961\pi\)
\(948\) 15.9165 0.516944
\(949\) 41.8125 1.35729
\(950\) −2.15439 −0.0698976
\(951\) 2.64579 0.0857955
\(952\) −19.7894 −0.641378
\(953\) 4.65073 0.150652 0.0753260 0.997159i \(-0.476000\pi\)
0.0753260 + 0.997159i \(0.476000\pi\)
\(954\) −6.27343 −0.203110
\(955\) −4.67389 −0.151244
\(956\) 25.8896 0.837331
\(957\) 25.9144 0.837694
\(958\) −25.0529 −0.809423
\(959\) 9.31778 0.300887
\(960\) −10.0084 −0.323021
\(961\) 31.5569 1.01797
\(962\) 12.6658 0.408362
\(963\) 13.1463 0.423632
\(964\) 20.2285 0.651516
\(965\) −3.10141 −0.0998378
\(966\) 3.26176 0.104945
\(967\) 56.5439 1.81833 0.909164 0.416438i \(-0.136722\pi\)
0.909164 + 0.416438i \(0.136722\pi\)
\(968\) −11.0069 −0.353774
\(969\) 35.7232 1.14759
\(970\) −16.4381 −0.527795
\(971\) 50.9483 1.63501 0.817504 0.575922i \(-0.195357\pi\)
0.817504 + 0.575922i \(0.195357\pi\)
\(972\) 1.29838 0.0416457
\(973\) −14.0412 −0.450139
\(974\) −27.6824 −0.887001
\(975\) 2.48108 0.0794581
\(976\) −0.0472855 −0.00151357
\(977\) −10.1428 −0.324497 −0.162248 0.986750i \(-0.551875\pi\)
−0.162248 + 0.986750i \(0.551875\pi\)
\(978\) 2.18532 0.0698787
\(979\) 21.6266 0.691189
\(980\) −3.04932 −0.0974071
\(981\) −4.71131 −0.150421
\(982\) −5.69516 −0.181740
\(983\) −62.2972 −1.98697 −0.993486 0.113957i \(-0.963647\pi\)
−0.993486 + 0.113957i \(0.963647\pi\)
\(984\) 12.4258 0.396119
\(985\) 52.2272 1.66410
\(986\) −58.6984 −1.86934
\(987\) −4.41618 −0.140568
\(988\) 31.1535 0.991125
\(989\) 13.0384 0.414598
\(990\) −5.21072 −0.165607
\(991\) 33.3558 1.05958 0.529791 0.848128i \(-0.322270\pi\)
0.529791 + 0.848128i \(0.322270\pi\)
\(992\) 45.5758 1.44703
\(993\) −11.4480 −0.363290
\(994\) −12.8171 −0.406533
\(995\) −18.2525 −0.578644
\(996\) 19.8366 0.628547
\(997\) −7.15965 −0.226748 −0.113374 0.993552i \(-0.536166\pi\)
−0.113374 + 0.993552i \(0.536166\pi\)
\(998\) −4.12497 −0.130574
\(999\) −3.14302 −0.0994408
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 \(a_p\))