Properties

Label 4015.2.a.h.1.15
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.446590 q^{2}\) \(+1.08482 q^{3}\) \(-1.80056 q^{4}\) \(+1.00000 q^{5}\) \(-0.484472 q^{6}\) \(+4.20380 q^{7}\) \(+1.69729 q^{8}\) \(-1.82316 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.446590 q^{2}\) \(+1.08482 q^{3}\) \(-1.80056 q^{4}\) \(+1.00000 q^{5}\) \(-0.484472 q^{6}\) \(+4.20380 q^{7}\) \(+1.69729 q^{8}\) \(-1.82316 q^{9}\) \(-0.446590 q^{10}\) \(+1.00000 q^{11}\) \(-1.95329 q^{12}\) \(-2.82350 q^{13}\) \(-1.87738 q^{14}\) \(+1.08482 q^{15}\) \(+2.84312 q^{16}\) \(+4.54365 q^{17}\) \(+0.814205 q^{18}\) \(-4.76704 q^{19}\) \(-1.80056 q^{20}\) \(+4.56039 q^{21}\) \(-0.446590 q^{22}\) \(+2.76248 q^{23}\) \(+1.84126 q^{24}\) \(+1.00000 q^{25}\) \(+1.26095 q^{26}\) \(-5.23228 q^{27}\) \(-7.56919 q^{28}\) \(-2.06610 q^{29}\) \(-0.484472 q^{30}\) \(+7.10845 q^{31}\) \(-4.66429 q^{32}\) \(+1.08482 q^{33}\) \(-2.02915 q^{34}\) \(+4.20380 q^{35}\) \(+3.28270 q^{36}\) \(-5.06844 q^{37}\) \(+2.12892 q^{38}\) \(-3.06299 q^{39}\) \(+1.69729 q^{40}\) \(+9.63406 q^{41}\) \(-2.03662 q^{42}\) \(+11.0577 q^{43}\) \(-1.80056 q^{44}\) \(-1.82316 q^{45}\) \(-1.23370 q^{46}\) \(-0.673225 q^{47}\) \(+3.08428 q^{48}\) \(+10.6720 q^{49}\) \(-0.446590 q^{50}\) \(+4.92906 q^{51}\) \(+5.08386 q^{52}\) \(+12.9970 q^{53}\) \(+2.33668 q^{54}\) \(+1.00000 q^{55}\) \(+7.13508 q^{56}\) \(-5.17140 q^{57}\) \(+0.922700 q^{58}\) \(-14.0926 q^{59}\) \(-1.95329 q^{60}\) \(+1.12602 q^{61}\) \(-3.17457 q^{62}\) \(-7.66420 q^{63}\) \(-3.60321 q^{64}\) \(-2.82350 q^{65}\) \(-0.484472 q^{66}\) \(+7.73434 q^{67}\) \(-8.18111 q^{68}\) \(+2.99680 q^{69}\) \(-1.87738 q^{70}\) \(-15.4056 q^{71}\) \(-3.09443 q^{72}\) \(+1.00000 q^{73}\) \(+2.26352 q^{74}\) \(+1.08482 q^{75}\) \(+8.58334 q^{76}\) \(+4.20380 q^{77}\) \(+1.36790 q^{78}\) \(-3.88009 q^{79}\) \(+2.84312 q^{80}\) \(-0.206625 q^{81}\) \(-4.30248 q^{82}\) \(+3.76371 q^{83}\) \(-8.21123 q^{84}\) \(+4.54365 q^{85}\) \(-4.93826 q^{86}\) \(-2.24135 q^{87}\) \(+1.69729 q^{88}\) \(+3.77803 q^{89}\) \(+0.814205 q^{90}\) \(-11.8694 q^{91}\) \(-4.97400 q^{92}\) \(+7.71142 q^{93}\) \(+0.300656 q^{94}\) \(-4.76704 q^{95}\) \(-5.05994 q^{96}\) \(+14.3786 q^{97}\) \(-4.76600 q^{98}\) \(-1.82316 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.446590 −0.315787 −0.157894 0.987456i \(-0.550470\pi\)
−0.157894 + 0.987456i \(0.550470\pi\)
\(3\) 1.08482 0.626323 0.313162 0.949700i \(-0.398612\pi\)
0.313162 + 0.949700i \(0.398612\pi\)
\(4\) −1.80056 −0.900279
\(5\) 1.00000 0.447214
\(6\) −0.484472 −0.197785
\(7\) 4.20380 1.58889 0.794444 0.607337i \(-0.207762\pi\)
0.794444 + 0.607337i \(0.207762\pi\)
\(8\) 1.69729 0.600083
\(9\) −1.82316 −0.607719
\(10\) −0.446590 −0.141224
\(11\) 1.00000 0.301511
\(12\) −1.95329 −0.563865
\(13\) −2.82350 −0.783097 −0.391548 0.920158i \(-0.628060\pi\)
−0.391548 + 0.920158i \(0.628060\pi\)
\(14\) −1.87738 −0.501750
\(15\) 1.08482 0.280100
\(16\) 2.84312 0.710780
\(17\) 4.54365 1.10200 0.550999 0.834506i \(-0.314247\pi\)
0.550999 + 0.834506i \(0.314247\pi\)
\(18\) 0.814205 0.191910
\(19\) −4.76704 −1.09364 −0.546818 0.837252i \(-0.684161\pi\)
−0.546818 + 0.837252i \(0.684161\pi\)
\(20\) −1.80056 −0.402617
\(21\) 4.56039 0.995158
\(22\) −0.446590 −0.0952134
\(23\) 2.76248 0.576017 0.288008 0.957628i \(-0.407007\pi\)
0.288008 + 0.957628i \(0.407007\pi\)
\(24\) 1.84126 0.375846
\(25\) 1.00000 0.200000
\(26\) 1.26095 0.247292
\(27\) −5.23228 −1.00695
\(28\) −7.56919 −1.43044
\(29\) −2.06610 −0.383665 −0.191832 0.981428i \(-0.561443\pi\)
−0.191832 + 0.981428i \(0.561443\pi\)
\(30\) −0.484472 −0.0884521
\(31\) 7.10845 1.27672 0.638358 0.769740i \(-0.279614\pi\)
0.638358 + 0.769740i \(0.279614\pi\)
\(32\) −4.66429 −0.824539
\(33\) 1.08482 0.188844
\(34\) −2.02915 −0.347997
\(35\) 4.20380 0.710572
\(36\) 3.28270 0.547116
\(37\) −5.06844 −0.833247 −0.416624 0.909079i \(-0.636787\pi\)
−0.416624 + 0.909079i \(0.636787\pi\)
\(38\) 2.12892 0.345356
\(39\) −3.06299 −0.490472
\(40\) 1.69729 0.268365
\(41\) 9.63406 1.50459 0.752294 0.658828i \(-0.228947\pi\)
0.752294 + 0.658828i \(0.228947\pi\)
\(42\) −2.03662 −0.314258
\(43\) 11.0577 1.68628 0.843141 0.537693i \(-0.180704\pi\)
0.843141 + 0.537693i \(0.180704\pi\)
\(44\) −1.80056 −0.271444
\(45\) −1.82316 −0.271780
\(46\) −1.23370 −0.181899
\(47\) −0.673225 −0.0981999 −0.0491000 0.998794i \(-0.515635\pi\)
−0.0491000 + 0.998794i \(0.515635\pi\)
\(48\) 3.08428 0.445178
\(49\) 10.6720 1.52457
\(50\) −0.446590 −0.0631574
\(51\) 4.92906 0.690207
\(52\) 5.08386 0.705005
\(53\) 12.9970 1.78528 0.892639 0.450772i \(-0.148851\pi\)
0.892639 + 0.450772i \(0.148851\pi\)
\(54\) 2.33668 0.317982
\(55\) 1.00000 0.134840
\(56\) 7.13508 0.953466
\(57\) −5.17140 −0.684969
\(58\) 0.922700 0.121156
\(59\) −14.0926 −1.83471 −0.917353 0.398076i \(-0.869678\pi\)
−0.917353 + 0.398076i \(0.869678\pi\)
\(60\) −1.95329 −0.252168
\(61\) 1.12602 0.144172 0.0720858 0.997398i \(-0.477034\pi\)
0.0720858 + 0.997398i \(0.477034\pi\)
\(62\) −3.17457 −0.403170
\(63\) −7.66420 −0.965598
\(64\) −3.60321 −0.450401
\(65\) −2.82350 −0.350212
\(66\) −0.484472 −0.0596344
\(67\) 7.73434 0.944900 0.472450 0.881358i \(-0.343370\pi\)
0.472450 + 0.881358i \(0.343370\pi\)
\(68\) −8.18111 −0.992105
\(69\) 2.99680 0.360773
\(70\) −1.87738 −0.224390
\(71\) −15.4056 −1.82831 −0.914155 0.405364i \(-0.867145\pi\)
−0.914155 + 0.405364i \(0.867145\pi\)
\(72\) −3.09443 −0.364682
\(73\) 1.00000 0.117041
\(74\) 2.26352 0.263129
\(75\) 1.08482 0.125265
\(76\) 8.58334 0.984576
\(77\) 4.20380 0.479068
\(78\) 1.36790 0.154885
\(79\) −3.88009 −0.436544 −0.218272 0.975888i \(-0.570042\pi\)
−0.218272 + 0.975888i \(0.570042\pi\)
\(80\) 2.84312 0.317870
\(81\) −0.206625 −0.0229583
\(82\) −4.30248 −0.475129
\(83\) 3.76371 0.413121 0.206560 0.978434i \(-0.433773\pi\)
0.206560 + 0.978434i \(0.433773\pi\)
\(84\) −8.21123 −0.895919
\(85\) 4.54365 0.492829
\(86\) −4.93826 −0.532506
\(87\) −2.24135 −0.240298
\(88\) 1.69729 0.180932
\(89\) 3.77803 0.400470 0.200235 0.979748i \(-0.435829\pi\)
0.200235 + 0.979748i \(0.435829\pi\)
\(90\) 0.814205 0.0858247
\(91\) −11.8694 −1.24425
\(92\) −4.97400 −0.518576
\(93\) 7.71142 0.799637
\(94\) 0.300656 0.0310103
\(95\) −4.76704 −0.489088
\(96\) −5.05994 −0.516428
\(97\) 14.3786 1.45992 0.729961 0.683489i \(-0.239538\pi\)
0.729961 + 0.683489i \(0.239538\pi\)
\(98\) −4.76600 −0.481438
\(99\) −1.82316 −0.183234
\(100\) −1.80056 −0.180056
\(101\) −13.3707 −1.33044 −0.665219 0.746649i \(-0.731662\pi\)
−0.665219 + 0.746649i \(0.731662\pi\)
\(102\) −2.20127 −0.217958
\(103\) 14.1322 1.39249 0.696244 0.717805i \(-0.254853\pi\)
0.696244 + 0.717805i \(0.254853\pi\)
\(104\) −4.79230 −0.469923
\(105\) 4.56039 0.445048
\(106\) −5.80434 −0.563768
\(107\) 6.98899 0.675651 0.337826 0.941209i \(-0.390309\pi\)
0.337826 + 0.941209i \(0.390309\pi\)
\(108\) 9.42101 0.906537
\(109\) −6.80765 −0.652054 −0.326027 0.945360i \(-0.605710\pi\)
−0.326027 + 0.945360i \(0.605710\pi\)
\(110\) −0.446590 −0.0425807
\(111\) −5.49837 −0.521882
\(112\) 11.9519 1.12935
\(113\) 18.0038 1.69366 0.846829 0.531865i \(-0.178509\pi\)
0.846829 + 0.531865i \(0.178509\pi\)
\(114\) 2.30950 0.216304
\(115\) 2.76248 0.257603
\(116\) 3.72013 0.345405
\(117\) 5.14768 0.475903
\(118\) 6.29364 0.579376
\(119\) 19.1006 1.75095
\(120\) 1.84126 0.168084
\(121\) 1.00000 0.0909091
\(122\) −0.502868 −0.0455275
\(123\) 10.4513 0.942358
\(124\) −12.7992 −1.14940
\(125\) 1.00000 0.0894427
\(126\) 3.42276 0.304923
\(127\) 6.65081 0.590164 0.295082 0.955472i \(-0.404653\pi\)
0.295082 + 0.955472i \(0.404653\pi\)
\(128\) 10.9377 0.966769
\(129\) 11.9956 1.05616
\(130\) 1.26095 0.110592
\(131\) −15.2775 −1.33480 −0.667401 0.744698i \(-0.732593\pi\)
−0.667401 + 0.744698i \(0.732593\pi\)
\(132\) −1.95329 −0.170012
\(133\) −20.0397 −1.73766
\(134\) −3.45408 −0.298387
\(135\) −5.23228 −0.450323
\(136\) 7.71191 0.661291
\(137\) −12.9074 −1.10275 −0.551375 0.834257i \(-0.685897\pi\)
−0.551375 + 0.834257i \(0.685897\pi\)
\(138\) −1.33834 −0.113927
\(139\) −1.39769 −0.118551 −0.0592753 0.998242i \(-0.518879\pi\)
−0.0592753 + 0.998242i \(0.518879\pi\)
\(140\) −7.56919 −0.639713
\(141\) −0.730330 −0.0615049
\(142\) 6.88000 0.577357
\(143\) −2.82350 −0.236113
\(144\) −5.18345 −0.431955
\(145\) −2.06610 −0.171580
\(146\) −0.446590 −0.0369601
\(147\) 11.5772 0.954871
\(148\) 9.12602 0.750155
\(149\) −3.27780 −0.268528 −0.134264 0.990946i \(-0.542867\pi\)
−0.134264 + 0.990946i \(0.542867\pi\)
\(150\) −0.484472 −0.0395570
\(151\) −6.18263 −0.503135 −0.251568 0.967840i \(-0.580946\pi\)
−0.251568 + 0.967840i \(0.580946\pi\)
\(152\) −8.09107 −0.656272
\(153\) −8.28380 −0.669705
\(154\) −1.87738 −0.151283
\(155\) 7.10845 0.570965
\(156\) 5.51510 0.441561
\(157\) −8.67135 −0.692049 −0.346024 0.938226i \(-0.612469\pi\)
−0.346024 + 0.938226i \(0.612469\pi\)
\(158\) 1.73281 0.137855
\(159\) 14.0995 1.11816
\(160\) −4.66429 −0.368745
\(161\) 11.6129 0.915227
\(162\) 0.0922767 0.00724994
\(163\) 17.7477 1.39011 0.695055 0.718957i \(-0.255380\pi\)
0.695055 + 0.718957i \(0.255380\pi\)
\(164\) −17.3467 −1.35455
\(165\) 1.08482 0.0844534
\(166\) −1.68084 −0.130458
\(167\) 20.4600 1.58324 0.791621 0.611012i \(-0.209237\pi\)
0.791621 + 0.611012i \(0.209237\pi\)
\(168\) 7.74031 0.597178
\(169\) −5.02787 −0.386759
\(170\) −2.02915 −0.155629
\(171\) 8.69107 0.664623
\(172\) −19.9100 −1.51812
\(173\) −22.2156 −1.68902 −0.844510 0.535540i \(-0.820108\pi\)
−0.844510 + 0.535540i \(0.820108\pi\)
\(174\) 1.00097 0.0758831
\(175\) 4.20380 0.317778
\(176\) 2.84312 0.214308
\(177\) −15.2880 −1.14912
\(178\) −1.68723 −0.126463
\(179\) 5.94621 0.444440 0.222220 0.974997i \(-0.428670\pi\)
0.222220 + 0.974997i \(0.428670\pi\)
\(180\) 3.28270 0.244678
\(181\) 4.15122 0.308558 0.154279 0.988027i \(-0.450695\pi\)
0.154279 + 0.988027i \(0.450695\pi\)
\(182\) 5.30077 0.392919
\(183\) 1.22153 0.0902980
\(184\) 4.68874 0.345658
\(185\) −5.06844 −0.372639
\(186\) −3.44385 −0.252515
\(187\) 4.54365 0.332265
\(188\) 1.21218 0.0884073
\(189\) −21.9955 −1.59993
\(190\) 2.12892 0.154448
\(191\) 8.77712 0.635090 0.317545 0.948243i \(-0.397142\pi\)
0.317545 + 0.948243i \(0.397142\pi\)
\(192\) −3.90885 −0.282097
\(193\) −12.5672 −0.904608 −0.452304 0.891864i \(-0.649398\pi\)
−0.452304 + 0.891864i \(0.649398\pi\)
\(194\) −6.42132 −0.461024
\(195\) −3.06299 −0.219346
\(196\) −19.2155 −1.37253
\(197\) −4.61568 −0.328853 −0.164427 0.986389i \(-0.552577\pi\)
−0.164427 + 0.986389i \(0.552577\pi\)
\(198\) 0.814205 0.0578630
\(199\) 9.01902 0.639341 0.319671 0.947529i \(-0.396428\pi\)
0.319671 + 0.947529i \(0.396428\pi\)
\(200\) 1.69729 0.120017
\(201\) 8.39039 0.591813
\(202\) 5.97124 0.420135
\(203\) −8.68547 −0.609601
\(204\) −8.87506 −0.621379
\(205\) 9.63406 0.672872
\(206\) −6.31131 −0.439730
\(207\) −5.03644 −0.350057
\(208\) −8.02754 −0.556609
\(209\) −4.76704 −0.329743
\(210\) −2.03662 −0.140540
\(211\) 14.9813 1.03135 0.515676 0.856783i \(-0.327541\pi\)
0.515676 + 0.856783i \(0.327541\pi\)
\(212\) −23.4019 −1.60725
\(213\) −16.7124 −1.14511
\(214\) −3.12122 −0.213362
\(215\) 11.0577 0.754128
\(216\) −8.88070 −0.604255
\(217\) 29.8825 2.02856
\(218\) 3.04023 0.205910
\(219\) 1.08482 0.0733056
\(220\) −1.80056 −0.121394
\(221\) −12.8290 −0.862971
\(222\) 2.45552 0.164804
\(223\) −11.7986 −0.790094 −0.395047 0.918661i \(-0.629272\pi\)
−0.395047 + 0.918661i \(0.629272\pi\)
\(224\) −19.6078 −1.31010
\(225\) −1.82316 −0.121544
\(226\) −8.04034 −0.534836
\(227\) 23.0051 1.52690 0.763451 0.645865i \(-0.223503\pi\)
0.763451 + 0.645865i \(0.223503\pi\)
\(228\) 9.31141 0.616663
\(229\) 18.0829 1.19495 0.597476 0.801887i \(-0.296170\pi\)
0.597476 + 0.801887i \(0.296170\pi\)
\(230\) −1.23370 −0.0813476
\(231\) 4.56039 0.300051
\(232\) −3.50677 −0.230231
\(233\) 20.0859 1.31587 0.657935 0.753075i \(-0.271430\pi\)
0.657935 + 0.753075i \(0.271430\pi\)
\(234\) −2.29890 −0.150284
\(235\) −0.673225 −0.0439163
\(236\) 25.3746 1.65175
\(237\) −4.20921 −0.273418
\(238\) −8.53016 −0.552928
\(239\) 16.4634 1.06493 0.532464 0.846453i \(-0.321266\pi\)
0.532464 + 0.846453i \(0.321266\pi\)
\(240\) 3.08428 0.199090
\(241\) 11.6755 0.752085 0.376042 0.926602i \(-0.377285\pi\)
0.376042 + 0.926602i \(0.377285\pi\)
\(242\) −0.446590 −0.0287079
\(243\) 15.4727 0.992573
\(244\) −2.02746 −0.129795
\(245\) 10.6720 0.681807
\(246\) −4.66743 −0.297585
\(247\) 13.4597 0.856422
\(248\) 12.0651 0.766136
\(249\) 4.08296 0.258747
\(250\) −0.446590 −0.0282449
\(251\) 30.0465 1.89652 0.948260 0.317496i \(-0.102842\pi\)
0.948260 + 0.317496i \(0.102842\pi\)
\(252\) 13.7998 0.869307
\(253\) 2.76248 0.173676
\(254\) −2.97019 −0.186366
\(255\) 4.92906 0.308670
\(256\) 2.32173 0.145108
\(257\) 12.6649 0.790013 0.395007 0.918678i \(-0.370742\pi\)
0.395007 + 0.918678i \(0.370742\pi\)
\(258\) −5.35714 −0.333521
\(259\) −21.3067 −1.32394
\(260\) 5.08386 0.315288
\(261\) 3.76682 0.233161
\(262\) 6.82279 0.421513
\(263\) 23.5086 1.44960 0.724801 0.688958i \(-0.241932\pi\)
0.724801 + 0.688958i \(0.241932\pi\)
\(264\) 1.84126 0.113322
\(265\) 12.9970 0.798401
\(266\) 8.94955 0.548732
\(267\) 4.09850 0.250824
\(268\) −13.9261 −0.850673
\(269\) −8.05493 −0.491118 −0.245559 0.969382i \(-0.578971\pi\)
−0.245559 + 0.969382i \(0.578971\pi\)
\(270\) 2.33668 0.142206
\(271\) −3.40895 −0.207079 −0.103539 0.994625i \(-0.533017\pi\)
−0.103539 + 0.994625i \(0.533017\pi\)
\(272\) 12.9182 0.783278
\(273\) −12.8762 −0.779305
\(274\) 5.76430 0.348234
\(275\) 1.00000 0.0603023
\(276\) −5.39592 −0.324796
\(277\) −13.0712 −0.785374 −0.392687 0.919672i \(-0.628454\pi\)
−0.392687 + 0.919672i \(0.628454\pi\)
\(278\) 0.624196 0.0374368
\(279\) −12.9598 −0.775885
\(280\) 7.13508 0.426403
\(281\) −24.9860 −1.49054 −0.745270 0.666763i \(-0.767679\pi\)
−0.745270 + 0.666763i \(0.767679\pi\)
\(282\) 0.326158 0.0194225
\(283\) −28.4917 −1.69366 −0.846829 0.531866i \(-0.821491\pi\)
−0.846829 + 0.531866i \(0.821491\pi\)
\(284\) 27.7387 1.64599
\(285\) −5.17140 −0.306328
\(286\) 1.26095 0.0745613
\(287\) 40.4997 2.39062
\(288\) 8.50374 0.501088
\(289\) 3.64479 0.214400
\(290\) 0.922700 0.0541828
\(291\) 15.5982 0.914383
\(292\) −1.80056 −0.105370
\(293\) 19.5783 1.14378 0.571889 0.820331i \(-0.306211\pi\)
0.571889 + 0.820331i \(0.306211\pi\)
\(294\) −5.17027 −0.301536
\(295\) −14.0926 −0.820505
\(296\) −8.60263 −0.500018
\(297\) −5.23228 −0.303607
\(298\) 1.46384 0.0847977
\(299\) −7.79985 −0.451077
\(300\) −1.95329 −0.112773
\(301\) 46.4843 2.67931
\(302\) 2.76110 0.158884
\(303\) −14.5049 −0.833284
\(304\) −13.5533 −0.777334
\(305\) 1.12602 0.0644755
\(306\) 3.69946 0.211484
\(307\) 3.33865 0.190547 0.0952733 0.995451i \(-0.469627\pi\)
0.0952733 + 0.995451i \(0.469627\pi\)
\(308\) −7.56919 −0.431295
\(309\) 15.3310 0.872148
\(310\) −3.17457 −0.180303
\(311\) −25.6738 −1.45583 −0.727913 0.685669i \(-0.759510\pi\)
−0.727913 + 0.685669i \(0.759510\pi\)
\(312\) −5.19880 −0.294324
\(313\) −32.0967 −1.81421 −0.907107 0.420901i \(-0.861714\pi\)
−0.907107 + 0.420901i \(0.861714\pi\)
\(314\) 3.87254 0.218540
\(315\) −7.66420 −0.431828
\(316\) 6.98632 0.393011
\(317\) 18.3511 1.03070 0.515349 0.856980i \(-0.327662\pi\)
0.515349 + 0.856980i \(0.327662\pi\)
\(318\) −6.29669 −0.353101
\(319\) −2.06610 −0.115679
\(320\) −3.60321 −0.201426
\(321\) 7.58182 0.423176
\(322\) −5.18622 −0.289017
\(323\) −21.6598 −1.20518
\(324\) 0.372040 0.0206689
\(325\) −2.82350 −0.156619
\(326\) −7.92597 −0.438979
\(327\) −7.38510 −0.408397
\(328\) 16.3518 0.902878
\(329\) −2.83010 −0.156029
\(330\) −0.484472 −0.0266693
\(331\) −0.948328 −0.0521248 −0.0260624 0.999660i \(-0.508297\pi\)
−0.0260624 + 0.999660i \(0.508297\pi\)
\(332\) −6.77677 −0.371924
\(333\) 9.24057 0.506380
\(334\) −9.13724 −0.499967
\(335\) 7.73434 0.422572
\(336\) 12.9657 0.707338
\(337\) 0.499871 0.0272297 0.0136149 0.999907i \(-0.495666\pi\)
0.0136149 + 0.999907i \(0.495666\pi\)
\(338\) 2.24540 0.122134
\(339\) 19.5310 1.06078
\(340\) −8.18111 −0.443683
\(341\) 7.10845 0.384944
\(342\) −3.88135 −0.209879
\(343\) 15.4362 0.833477
\(344\) 18.7681 1.01191
\(345\) 2.99680 0.161343
\(346\) 9.92127 0.533371
\(347\) −18.3938 −0.987431 −0.493716 0.869623i \(-0.664362\pi\)
−0.493716 + 0.869623i \(0.664362\pi\)
\(348\) 4.03568 0.216335
\(349\) 25.8683 1.38470 0.692350 0.721562i \(-0.256576\pi\)
0.692350 + 0.721562i \(0.256576\pi\)
\(350\) −1.87738 −0.100350
\(351\) 14.7733 0.788541
\(352\) −4.66429 −0.248608
\(353\) 11.5289 0.613622 0.306811 0.951770i \(-0.400738\pi\)
0.306811 + 0.951770i \(0.400738\pi\)
\(354\) 6.82749 0.362877
\(355\) −15.4056 −0.817645
\(356\) −6.80256 −0.360535
\(357\) 20.7208 1.09666
\(358\) −2.65552 −0.140349
\(359\) −13.3461 −0.704378 −0.352189 0.935929i \(-0.614563\pi\)
−0.352189 + 0.935929i \(0.614563\pi\)
\(360\) −3.09443 −0.163091
\(361\) 3.72472 0.196038
\(362\) −1.85389 −0.0974385
\(363\) 1.08482 0.0569385
\(364\) 21.3716 1.12017
\(365\) 1.00000 0.0523424
\(366\) −0.545523 −0.0285149
\(367\) −4.94953 −0.258364 −0.129182 0.991621i \(-0.541235\pi\)
−0.129182 + 0.991621i \(0.541235\pi\)
\(368\) 7.85406 0.409421
\(369\) −17.5644 −0.914367
\(370\) 2.26352 0.117675
\(371\) 54.6369 2.83661
\(372\) −13.8848 −0.719896
\(373\) 35.8998 1.85882 0.929411 0.369046i \(-0.120315\pi\)
0.929411 + 0.369046i \(0.120315\pi\)
\(374\) −2.02915 −0.104925
\(375\) 1.08482 0.0560201
\(376\) −1.14266 −0.0589281
\(377\) 5.83362 0.300447
\(378\) 9.82296 0.505239
\(379\) −24.6918 −1.26833 −0.634165 0.773197i \(-0.718656\pi\)
−0.634165 + 0.773197i \(0.718656\pi\)
\(380\) 8.58334 0.440316
\(381\) 7.21496 0.369634
\(382\) −3.91978 −0.200553
\(383\) 17.0405 0.870729 0.435364 0.900254i \(-0.356620\pi\)
0.435364 + 0.900254i \(0.356620\pi\)
\(384\) 11.8655 0.605510
\(385\) 4.20380 0.214246
\(386\) 5.61240 0.285664
\(387\) −20.1599 −1.02479
\(388\) −25.8894 −1.31434
\(389\) −12.6850 −0.643155 −0.321578 0.946883i \(-0.604213\pi\)
−0.321578 + 0.946883i \(0.604213\pi\)
\(390\) 1.36790 0.0692665
\(391\) 12.5518 0.634770
\(392\) 18.1134 0.914867
\(393\) −16.5734 −0.836018
\(394\) 2.06132 0.103848
\(395\) −3.88009 −0.195229
\(396\) 3.28270 0.164962
\(397\) 2.35417 0.118152 0.0590762 0.998253i \(-0.481185\pi\)
0.0590762 + 0.998253i \(0.481185\pi\)
\(398\) −4.02781 −0.201896
\(399\) −21.7396 −1.08834
\(400\) 2.84312 0.142156
\(401\) −26.1284 −1.30479 −0.652396 0.757878i \(-0.726236\pi\)
−0.652396 + 0.757878i \(0.726236\pi\)
\(402\) −3.74707 −0.186887
\(403\) −20.0707 −0.999792
\(404\) 24.0748 1.19776
\(405\) −0.206625 −0.0102673
\(406\) 3.87885 0.192504
\(407\) −5.06844 −0.251233
\(408\) 8.36606 0.414182
\(409\) −6.17352 −0.305261 −0.152630 0.988283i \(-0.548774\pi\)
−0.152630 + 0.988283i \(0.548774\pi\)
\(410\) −4.30248 −0.212484
\(411\) −14.0022 −0.690678
\(412\) −25.4458 −1.25363
\(413\) −59.2427 −2.91514
\(414\) 2.24922 0.110543
\(415\) 3.76371 0.184753
\(416\) 13.1696 0.645693
\(417\) −1.51625 −0.0742511
\(418\) 2.12892 0.104129
\(419\) −12.6796 −0.619437 −0.309718 0.950828i \(-0.600235\pi\)
−0.309718 + 0.950828i \(0.600235\pi\)
\(420\) −8.21123 −0.400667
\(421\) −9.82317 −0.478752 −0.239376 0.970927i \(-0.576943\pi\)
−0.239376 + 0.970927i \(0.576943\pi\)
\(422\) −6.69049 −0.325688
\(423\) 1.22739 0.0596780
\(424\) 22.0597 1.07132
\(425\) 4.54365 0.220400
\(426\) 7.46359 0.361612
\(427\) 4.73355 0.229072
\(428\) −12.5841 −0.608274
\(429\) −3.06299 −0.147883
\(430\) −4.93826 −0.238144
\(431\) 27.8242 1.34024 0.670122 0.742251i \(-0.266242\pi\)
0.670122 + 0.742251i \(0.266242\pi\)
\(432\) −14.8760 −0.715721
\(433\) 1.89166 0.0909074 0.0454537 0.998966i \(-0.485527\pi\)
0.0454537 + 0.998966i \(0.485527\pi\)
\(434\) −13.3453 −0.640593
\(435\) −2.24135 −0.107465
\(436\) 12.2576 0.587030
\(437\) −13.1689 −0.629952
\(438\) −0.484472 −0.0231490
\(439\) −12.7924 −0.610547 −0.305274 0.952265i \(-0.598748\pi\)
−0.305274 + 0.952265i \(0.598748\pi\)
\(440\) 1.69729 0.0809152
\(441\) −19.4567 −0.926508
\(442\) 5.72930 0.272515
\(443\) 21.6744 1.02978 0.514891 0.857256i \(-0.327832\pi\)
0.514891 + 0.857256i \(0.327832\pi\)
\(444\) 9.90013 0.469839
\(445\) 3.77803 0.179096
\(446\) 5.26915 0.249502
\(447\) −3.55584 −0.168185
\(448\) −15.1472 −0.715637
\(449\) 21.0784 0.994750 0.497375 0.867536i \(-0.334297\pi\)
0.497375 + 0.867536i \(0.334297\pi\)
\(450\) 0.814205 0.0383820
\(451\) 9.63406 0.453650
\(452\) −32.4169 −1.52476
\(453\) −6.70706 −0.315125
\(454\) −10.2739 −0.482176
\(455\) −11.8694 −0.556447
\(456\) −8.77738 −0.411039
\(457\) 24.7637 1.15839 0.579197 0.815187i \(-0.303366\pi\)
0.579197 + 0.815187i \(0.303366\pi\)
\(458\) −8.07565 −0.377350
\(459\) −23.7737 −1.10966
\(460\) −4.97400 −0.231914
\(461\) −10.2398 −0.476913 −0.238457 0.971153i \(-0.576641\pi\)
−0.238457 + 0.971153i \(0.576641\pi\)
\(462\) −2.03662 −0.0947524
\(463\) −3.21796 −0.149551 −0.0747756 0.997200i \(-0.523824\pi\)
−0.0747756 + 0.997200i \(0.523824\pi\)
\(464\) −5.87417 −0.272701
\(465\) 7.71142 0.357608
\(466\) −8.97016 −0.415535
\(467\) 18.9161 0.875331 0.437665 0.899138i \(-0.355805\pi\)
0.437665 + 0.899138i \(0.355805\pi\)
\(468\) −9.26869 −0.428445
\(469\) 32.5136 1.50134
\(470\) 0.300656 0.0138682
\(471\) −9.40688 −0.433446
\(472\) −23.9193 −1.10098
\(473\) 11.0577 0.508433
\(474\) 1.87979 0.0863418
\(475\) −4.76704 −0.218727
\(476\) −34.3918 −1.57634
\(477\) −23.6956 −1.08495
\(478\) −7.35239 −0.336290
\(479\) 2.25652 0.103103 0.0515515 0.998670i \(-0.483583\pi\)
0.0515515 + 0.998670i \(0.483583\pi\)
\(480\) −5.05994 −0.230953
\(481\) 14.3107 0.652513
\(482\) −5.21416 −0.237499
\(483\) 12.5980 0.573228
\(484\) −1.80056 −0.0818435
\(485\) 14.3786 0.652897
\(486\) −6.90995 −0.313442
\(487\) 10.7332 0.486367 0.243183 0.969980i \(-0.421808\pi\)
0.243183 + 0.969980i \(0.421808\pi\)
\(488\) 1.91118 0.0865149
\(489\) 19.2532 0.870658
\(490\) −4.76600 −0.215306
\(491\) −9.76040 −0.440481 −0.220240 0.975446i \(-0.570684\pi\)
−0.220240 + 0.975446i \(0.570684\pi\)
\(492\) −18.8181 −0.848385
\(493\) −9.38764 −0.422798
\(494\) −6.01099 −0.270447
\(495\) −1.82316 −0.0819448
\(496\) 20.2102 0.907464
\(497\) −64.7622 −2.90498
\(498\) −1.82341 −0.0817090
\(499\) −8.19839 −0.367010 −0.183505 0.983019i \(-0.558744\pi\)
−0.183505 + 0.983019i \(0.558744\pi\)
\(500\) −1.80056 −0.0805234
\(501\) 22.1955 0.991621
\(502\) −13.4185 −0.598896
\(503\) 28.8451 1.28614 0.643071 0.765807i \(-0.277660\pi\)
0.643071 + 0.765807i \(0.277660\pi\)
\(504\) −13.0084 −0.579439
\(505\) −13.3707 −0.594990
\(506\) −1.23370 −0.0548445
\(507\) −5.45436 −0.242236
\(508\) −11.9752 −0.531312
\(509\) −12.9788 −0.575276 −0.287638 0.957739i \(-0.592870\pi\)
−0.287638 + 0.957739i \(0.592870\pi\)
\(510\) −2.20127 −0.0974740
\(511\) 4.20380 0.185965
\(512\) −22.9124 −1.01259
\(513\) 24.9425 1.10124
\(514\) −5.65601 −0.249476
\(515\) 14.1322 0.622739
\(516\) −21.5988 −0.950836
\(517\) −0.673225 −0.0296084
\(518\) 9.51539 0.418082
\(519\) −24.1000 −1.05787
\(520\) −4.79230 −0.210156
\(521\) −11.3429 −0.496941 −0.248470 0.968639i \(-0.579928\pi\)
−0.248470 + 0.968639i \(0.579928\pi\)
\(522\) −1.68223 −0.0736291
\(523\) −22.7127 −0.993159 −0.496579 0.867991i \(-0.665411\pi\)
−0.496579 + 0.867991i \(0.665411\pi\)
\(524\) 27.5080 1.20169
\(525\) 4.56039 0.199032
\(526\) −10.4987 −0.457766
\(527\) 32.2984 1.40694
\(528\) 3.08428 0.134226
\(529\) −15.3687 −0.668204
\(530\) −5.80434 −0.252125
\(531\) 25.6931 1.11499
\(532\) 36.0827 1.56438
\(533\) −27.2017 −1.17824
\(534\) −1.83035 −0.0792069
\(535\) 6.98899 0.302160
\(536\) 13.1274 0.567019
\(537\) 6.45059 0.278363
\(538\) 3.59725 0.155089
\(539\) 10.6720 0.459674
\(540\) 9.42101 0.405416
\(541\) −33.8790 −1.45657 −0.728287 0.685273i \(-0.759683\pi\)
−0.728287 + 0.685273i \(0.759683\pi\)
\(542\) 1.52240 0.0653929
\(543\) 4.50334 0.193257
\(544\) −21.1929 −0.908640
\(545\) −6.80765 −0.291608
\(546\) 5.75040 0.246094
\(547\) −21.2530 −0.908713 −0.454357 0.890820i \(-0.650131\pi\)
−0.454357 + 0.890820i \(0.650131\pi\)
\(548\) 23.2404 0.992782
\(549\) −2.05290 −0.0876158
\(550\) −0.446590 −0.0190427
\(551\) 9.84919 0.419589
\(552\) 5.08645 0.216494
\(553\) −16.3111 −0.693620
\(554\) 5.83749 0.248011
\(555\) −5.49837 −0.233393
\(556\) 2.51662 0.106729
\(557\) 38.7154 1.64043 0.820213 0.572059i \(-0.193855\pi\)
0.820213 + 0.572059i \(0.193855\pi\)
\(558\) 5.78773 0.245014
\(559\) −31.2213 −1.32052
\(560\) 11.9519 0.505061
\(561\) 4.92906 0.208105
\(562\) 11.1585 0.470693
\(563\) −29.8386 −1.25755 −0.628774 0.777588i \(-0.716443\pi\)
−0.628774 + 0.777588i \(0.716443\pi\)
\(564\) 1.31500 0.0553715
\(565\) 18.0038 0.757427
\(566\) 12.7241 0.534835
\(567\) −0.868610 −0.0364782
\(568\) −26.1478 −1.09714
\(569\) 3.16612 0.132731 0.0663654 0.997795i \(-0.478860\pi\)
0.0663654 + 0.997795i \(0.478860\pi\)
\(570\) 2.30950 0.0967343
\(571\) −6.67544 −0.279359 −0.139679 0.990197i \(-0.544607\pi\)
−0.139679 + 0.990197i \(0.544607\pi\)
\(572\) 5.08386 0.212567
\(573\) 9.52163 0.397772
\(574\) −18.0868 −0.754928
\(575\) 2.76248 0.115203
\(576\) 6.56922 0.273717
\(577\) 24.4553 1.01809 0.509043 0.860741i \(-0.329999\pi\)
0.509043 + 0.860741i \(0.329999\pi\)
\(578\) −1.62773 −0.0677047
\(579\) −13.6332 −0.566577
\(580\) 3.72013 0.154470
\(581\) 15.8219 0.656403
\(582\) −6.96601 −0.288750
\(583\) 12.9970 0.538282
\(584\) 1.69729 0.0702345
\(585\) 5.14768 0.212830
\(586\) −8.74350 −0.361191
\(587\) −18.3362 −0.756815 −0.378408 0.925639i \(-0.623528\pi\)
−0.378408 + 0.925639i \(0.623528\pi\)
\(588\) −20.8454 −0.859650
\(589\) −33.8863 −1.39626
\(590\) 6.29364 0.259105
\(591\) −5.00719 −0.205968
\(592\) −14.4102 −0.592255
\(593\) −41.7703 −1.71530 −0.857650 0.514233i \(-0.828077\pi\)
−0.857650 + 0.514233i \(0.828077\pi\)
\(594\) 2.33668 0.0958753
\(595\) 19.1006 0.783049
\(596\) 5.90187 0.241750
\(597\) 9.78404 0.400434
\(598\) 3.48334 0.142444
\(599\) −17.8542 −0.729501 −0.364751 0.931105i \(-0.618846\pi\)
−0.364751 + 0.931105i \(0.618846\pi\)
\(600\) 1.84126 0.0751692
\(601\) 31.6467 1.29090 0.645448 0.763804i \(-0.276671\pi\)
0.645448 + 0.763804i \(0.276671\pi\)
\(602\) −20.7595 −0.846093
\(603\) −14.1009 −0.574234
\(604\) 11.1322 0.452962
\(605\) 1.00000 0.0406558
\(606\) 6.47774 0.263140
\(607\) 39.3323 1.59645 0.798224 0.602361i \(-0.205773\pi\)
0.798224 + 0.602361i \(0.205773\pi\)
\(608\) 22.2349 0.901744
\(609\) −9.42221 −0.381807
\(610\) −0.502868 −0.0203605
\(611\) 1.90085 0.0769000
\(612\) 14.9154 0.602921
\(613\) −20.4924 −0.827679 −0.413839 0.910350i \(-0.635812\pi\)
−0.413839 + 0.910350i \(0.635812\pi\)
\(614\) −1.49101 −0.0601722
\(615\) 10.4513 0.421435
\(616\) 7.13508 0.287481
\(617\) 16.7332 0.673654 0.336827 0.941567i \(-0.390646\pi\)
0.336827 + 0.941567i \(0.390646\pi\)
\(618\) −6.84666 −0.275413
\(619\) 28.4818 1.14478 0.572390 0.819982i \(-0.306016\pi\)
0.572390 + 0.819982i \(0.306016\pi\)
\(620\) −12.7992 −0.514027
\(621\) −14.4541 −0.580021
\(622\) 11.4657 0.459731
\(623\) 15.8821 0.636302
\(624\) −8.70846 −0.348617
\(625\) 1.00000 0.0400000
\(626\) 14.3341 0.572905
\(627\) −5.17140 −0.206526
\(628\) 15.6133 0.623037
\(629\) −23.0293 −0.918237
\(630\) 3.42276 0.136366
\(631\) −33.8003 −1.34557 −0.672784 0.739839i \(-0.734902\pi\)
−0.672784 + 0.739839i \(0.734902\pi\)
\(632\) −6.58565 −0.261963
\(633\) 16.2520 0.645960
\(634\) −8.19541 −0.325481
\(635\) 6.65081 0.263929
\(636\) −25.3869 −1.00666
\(637\) −30.1322 −1.19388
\(638\) 0.922700 0.0365300
\(639\) 28.0869 1.11110
\(640\) 10.9377 0.432352
\(641\) −24.2574 −0.958109 −0.479054 0.877785i \(-0.659020\pi\)
−0.479054 + 0.877785i \(0.659020\pi\)
\(642\) −3.38597 −0.133634
\(643\) −20.4656 −0.807086 −0.403543 0.914961i \(-0.632221\pi\)
−0.403543 + 0.914961i \(0.632221\pi\)
\(644\) −20.9097 −0.823959
\(645\) 11.9956 0.472328
\(646\) 9.67306 0.380581
\(647\) −26.6310 −1.04697 −0.523486 0.852034i \(-0.675369\pi\)
−0.523486 + 0.852034i \(0.675369\pi\)
\(648\) −0.350703 −0.0137769
\(649\) −14.0926 −0.553184
\(650\) 1.26095 0.0494584
\(651\) 32.4173 1.27053
\(652\) −31.9558 −1.25149
\(653\) 4.56814 0.178765 0.0893825 0.995997i \(-0.471511\pi\)
0.0893825 + 0.995997i \(0.471511\pi\)
\(654\) 3.29811 0.128966
\(655\) −15.2775 −0.596942
\(656\) 27.3908 1.06943
\(657\) −1.82316 −0.0711281
\(658\) 1.26390 0.0492718
\(659\) 1.77338 0.0690811 0.0345405 0.999403i \(-0.489003\pi\)
0.0345405 + 0.999403i \(0.489003\pi\)
\(660\) −1.95329 −0.0760316
\(661\) −25.9729 −1.01023 −0.505114 0.863053i \(-0.668550\pi\)
−0.505114 + 0.863053i \(0.668550\pi\)
\(662\) 0.423514 0.0164603
\(663\) −13.9172 −0.540499
\(664\) 6.38811 0.247907
\(665\) −20.0397 −0.777107
\(666\) −4.12675 −0.159908
\(667\) −5.70756 −0.220998
\(668\) −36.8394 −1.42536
\(669\) −12.7994 −0.494854
\(670\) −3.45408 −0.133443
\(671\) 1.12602 0.0434693
\(672\) −21.2710 −0.820546
\(673\) −19.3947 −0.747610 −0.373805 0.927507i \(-0.621947\pi\)
−0.373805 + 0.927507i \(0.621947\pi\)
\(674\) −0.223238 −0.00859879
\(675\) −5.23228 −0.201390
\(676\) 9.05297 0.348191
\(677\) −38.8712 −1.49394 −0.746970 0.664858i \(-0.768492\pi\)
−0.746970 + 0.664858i \(0.768492\pi\)
\(678\) −8.72235 −0.334980
\(679\) 60.4446 2.31965
\(680\) 7.71191 0.295738
\(681\) 24.9565 0.956335
\(682\) −3.17457 −0.121560
\(683\) −35.1512 −1.34502 −0.672512 0.740086i \(-0.734785\pi\)
−0.672512 + 0.740086i \(0.734785\pi\)
\(684\) −15.6488 −0.598346
\(685\) −12.9074 −0.493165
\(686\) −6.89366 −0.263201
\(687\) 19.6168 0.748426
\(688\) 31.4383 1.19858
\(689\) −36.6970 −1.39805
\(690\) −1.33834 −0.0509499
\(691\) −32.5538 −1.23841 −0.619203 0.785231i \(-0.712544\pi\)
−0.619203 + 0.785231i \(0.712544\pi\)
\(692\) 40.0004 1.52059
\(693\) −7.66420 −0.291139
\(694\) 8.21450 0.311818
\(695\) −1.39769 −0.0530175
\(696\) −3.80423 −0.144199
\(697\) 43.7738 1.65805
\(698\) −11.5525 −0.437270
\(699\) 21.7896 0.824160
\(700\) −7.56919 −0.286088
\(701\) 19.3571 0.731109 0.365554 0.930790i \(-0.380879\pi\)
0.365554 + 0.930790i \(0.380879\pi\)
\(702\) −6.59762 −0.249011
\(703\) 24.1615 0.911268
\(704\) −3.60321 −0.135801
\(705\) −0.730330 −0.0275058
\(706\) −5.14870 −0.193774
\(707\) −56.2079 −2.11392
\(708\) 27.5270 1.03453
\(709\) −28.2575 −1.06123 −0.530616 0.847612i \(-0.678039\pi\)
−0.530616 + 0.847612i \(0.678039\pi\)
\(710\) 6.88000 0.258202
\(711\) 7.07401 0.265296
\(712\) 6.41242 0.240316
\(713\) 19.6370 0.735410
\(714\) −9.25372 −0.346312
\(715\) −2.82350 −0.105593
\(716\) −10.7065 −0.400120
\(717\) 17.8599 0.666989
\(718\) 5.96022 0.222433
\(719\) 13.7927 0.514382 0.257191 0.966361i \(-0.417203\pi\)
0.257191 + 0.966361i \(0.417203\pi\)
\(720\) −5.18345 −0.193176
\(721\) 59.4090 2.21251
\(722\) −1.66342 −0.0619062
\(723\) 12.6659 0.471048
\(724\) −7.47450 −0.277788
\(725\) −2.06610 −0.0767330
\(726\) −0.484472 −0.0179804
\(727\) 2.82936 0.104935 0.0524676 0.998623i \(-0.483291\pi\)
0.0524676 + 0.998623i \(0.483291\pi\)
\(728\) −20.1459 −0.746656
\(729\) 17.4050 0.644630
\(730\) −0.446590 −0.0165291
\(731\) 50.2423 1.85828
\(732\) −2.19943 −0.0812933
\(733\) −47.5696 −1.75702 −0.878511 0.477722i \(-0.841463\pi\)
−0.878511 + 0.477722i \(0.841463\pi\)
\(734\) 2.21041 0.0815879
\(735\) 11.5772 0.427031
\(736\) −12.8850 −0.474948
\(737\) 7.73434 0.284898
\(738\) 7.84410 0.288745
\(739\) 17.2405 0.634203 0.317101 0.948392i \(-0.397290\pi\)
0.317101 + 0.948392i \(0.397290\pi\)
\(740\) 9.12602 0.335479
\(741\) 14.6014 0.536397
\(742\) −24.4003 −0.895764
\(743\) −31.7628 −1.16527 −0.582633 0.812736i \(-0.697977\pi\)
−0.582633 + 0.812736i \(0.697977\pi\)
\(744\) 13.0885 0.479849
\(745\) −3.27780 −0.120089
\(746\) −16.0325 −0.586992
\(747\) −6.86183 −0.251061
\(748\) −8.18111 −0.299131
\(749\) 29.3803 1.07353
\(750\) −0.484472 −0.0176904
\(751\) −40.7925 −1.48854 −0.744271 0.667878i \(-0.767203\pi\)
−0.744271 + 0.667878i \(0.767203\pi\)
\(752\) −1.91406 −0.0697985
\(753\) 32.5952 1.18783
\(754\) −2.60524 −0.0948772
\(755\) −6.18263 −0.225009
\(756\) 39.6041 1.44039
\(757\) −39.6054 −1.43948 −0.719742 0.694242i \(-0.755740\pi\)
−0.719742 + 0.694242i \(0.755740\pi\)
\(758\) 11.0271 0.400523
\(759\) 2.99680 0.108777
\(760\) −8.09107 −0.293494
\(761\) 1.53536 0.0556566 0.0278283 0.999613i \(-0.491141\pi\)
0.0278283 + 0.999613i \(0.491141\pi\)
\(762\) −3.22213 −0.116726
\(763\) −28.6180 −1.03604
\(764\) −15.8037 −0.571758
\(765\) −8.28380 −0.299501
\(766\) −7.61012 −0.274965
\(767\) 39.7905 1.43675
\(768\) 2.51866 0.0908845
\(769\) 26.4808 0.954923 0.477461 0.878653i \(-0.341557\pi\)
0.477461 + 0.878653i \(0.341557\pi\)
\(770\) −1.87738 −0.0676560
\(771\) 13.7392 0.494804
\(772\) 22.6280 0.814399
\(773\) 14.5416 0.523024 0.261512 0.965200i \(-0.415779\pi\)
0.261512 + 0.965200i \(0.415779\pi\)
\(774\) 9.00322 0.323614
\(775\) 7.10845 0.255343
\(776\) 24.4046 0.876074
\(777\) −23.1141 −0.829212
\(778\) 5.66500 0.203100
\(779\) −45.9260 −1.64547
\(780\) 5.51510 0.197472
\(781\) −15.4056 −0.551256
\(782\) −5.60549 −0.200452
\(783\) 10.8104 0.386332
\(784\) 30.3417 1.08363
\(785\) −8.67135 −0.309494
\(786\) 7.40153 0.264004
\(787\) 24.9365 0.888889 0.444444 0.895806i \(-0.353401\pi\)
0.444444 + 0.895806i \(0.353401\pi\)
\(788\) 8.31079 0.296060
\(789\) 25.5027 0.907919
\(790\) 1.73281 0.0616506
\(791\) 75.6846 2.69103
\(792\) −3.09443 −0.109956
\(793\) −3.17930 −0.112900
\(794\) −1.05135 −0.0373110
\(795\) 14.0995 0.500057
\(796\) −16.2393 −0.575585
\(797\) −18.9986 −0.672964 −0.336482 0.941690i \(-0.609237\pi\)
−0.336482 + 0.941690i \(0.609237\pi\)
\(798\) 9.70868 0.343684
\(799\) −3.05890 −0.108216
\(800\) −4.66429 −0.164908
\(801\) −6.88794 −0.243373
\(802\) 11.6687 0.412037
\(803\) 1.00000 0.0352892
\(804\) −15.1074 −0.532796
\(805\) 11.6129 0.409302
\(806\) 8.96337 0.315721
\(807\) −8.73818 −0.307598
\(808\) −22.6940 −0.798373
\(809\) −14.7798 −0.519629 −0.259815 0.965659i \(-0.583661\pi\)
−0.259815 + 0.965659i \(0.583661\pi\)
\(810\) 0.0922767 0.00324227
\(811\) 31.0921 1.09179 0.545896 0.837853i \(-0.316189\pi\)
0.545896 + 0.837853i \(0.316189\pi\)
\(812\) 15.6387 0.548810
\(813\) −3.69811 −0.129698
\(814\) 2.26352 0.0793363
\(815\) 17.7477 0.621676
\(816\) 14.0139 0.490585
\(817\) −52.7125 −1.84418
\(818\) 2.75703 0.0963974
\(819\) 21.6398 0.756157
\(820\) −17.3467 −0.605772
\(821\) −11.3198 −0.395064 −0.197532 0.980296i \(-0.563293\pi\)
−0.197532 + 0.980296i \(0.563293\pi\)
\(822\) 6.25325 0.218107
\(823\) −40.2698 −1.40372 −0.701859 0.712316i \(-0.747646\pi\)
−0.701859 + 0.712316i \(0.747646\pi\)
\(824\) 23.9865 0.835609
\(825\) 1.08482 0.0377687
\(826\) 26.4572 0.920564
\(827\) −7.73425 −0.268946 −0.134473 0.990917i \(-0.542934\pi\)
−0.134473 + 0.990917i \(0.542934\pi\)
\(828\) 9.06839 0.315148
\(829\) −3.54130 −0.122994 −0.0614972 0.998107i \(-0.519588\pi\)
−0.0614972 + 0.998107i \(0.519588\pi\)
\(830\) −1.68084 −0.0583427
\(831\) −14.1800 −0.491898
\(832\) 10.1736 0.352708
\(833\) 48.4897 1.68007
\(834\) 0.677142 0.0234475
\(835\) 20.4600 0.708047
\(836\) 8.58334 0.296861
\(837\) −37.1934 −1.28559
\(838\) 5.66257 0.195610
\(839\) 31.3132 1.08105 0.540526 0.841327i \(-0.318225\pi\)
0.540526 + 0.841327i \(0.318225\pi\)
\(840\) 7.74031 0.267066
\(841\) −24.7312 −0.852801
\(842\) 4.38693 0.151184
\(843\) −27.1054 −0.933560
\(844\) −26.9746 −0.928505
\(845\) −5.02787 −0.172964
\(846\) −0.548143 −0.0188455
\(847\) 4.20380 0.144444
\(848\) 36.9521 1.26894
\(849\) −30.9085 −1.06078
\(850\) −2.02915 −0.0695994
\(851\) −14.0015 −0.479965
\(852\) 30.0916 1.03092
\(853\) 17.8102 0.609809 0.304905 0.952383i \(-0.401375\pi\)
0.304905 + 0.952383i \(0.401375\pi\)
\(854\) −2.11396 −0.0723381
\(855\) 8.69107 0.297228
\(856\) 11.8624 0.405447
\(857\) −4.76167 −0.162656 −0.0813278 0.996687i \(-0.525916\pi\)
−0.0813278 + 0.996687i \(0.525916\pi\)
\(858\) 1.36790 0.0466995
\(859\) −54.5172 −1.86010 −0.930051 0.367431i \(-0.880237\pi\)
−0.930051 + 0.367431i \(0.880237\pi\)
\(860\) −19.9100 −0.678925
\(861\) 43.9350 1.49730
\(862\) −12.4260 −0.423232
\(863\) −50.5845 −1.72192 −0.860959 0.508675i \(-0.830136\pi\)
−0.860959 + 0.508675i \(0.830136\pi\)
\(864\) 24.4049 0.830271
\(865\) −22.2156 −0.755353
\(866\) −0.844797 −0.0287074
\(867\) 3.95396 0.134284
\(868\) −53.8052 −1.82627
\(869\) −3.88009 −0.131623
\(870\) 1.00097 0.0339360
\(871\) −21.8379 −0.739948
\(872\) −11.5546 −0.391287
\(873\) −26.2144 −0.887222
\(874\) 5.88109 0.198931
\(875\) 4.20380 0.142114
\(876\) −1.95329 −0.0659955
\(877\) −0.191186 −0.00645590 −0.00322795 0.999995i \(-0.501027\pi\)
−0.00322795 + 0.999995i \(0.501027\pi\)
\(878\) 5.71296 0.192803
\(879\) 21.2390 0.716375
\(880\) 2.84312 0.0958415
\(881\) 32.7952 1.10490 0.552450 0.833546i \(-0.313693\pi\)
0.552450 + 0.833546i \(0.313693\pi\)
\(882\) 8.68916 0.292579
\(883\) 0.495202 0.0166649 0.00833244 0.999965i \(-0.497348\pi\)
0.00833244 + 0.999965i \(0.497348\pi\)
\(884\) 23.0993 0.776914
\(885\) −15.2880 −0.513901
\(886\) −9.67958 −0.325192
\(887\) −30.3178 −1.01797 −0.508986 0.860775i \(-0.669979\pi\)
−0.508986 + 0.860775i \(0.669979\pi\)
\(888\) −9.33234 −0.313173
\(889\) 27.9587 0.937705
\(890\) −1.68723 −0.0565561
\(891\) −0.206625 −0.00692219
\(892\) 21.2441 0.711305
\(893\) 3.20929 0.107395
\(894\) 1.58800 0.0531108
\(895\) 5.94621 0.198760
\(896\) 45.9801 1.53609
\(897\) −8.46146 −0.282520
\(898\) −9.41340 −0.314129
\(899\) −14.6868 −0.489831
\(900\) 3.28270 0.109423
\(901\) 59.0540 1.96737
\(902\) −4.30248 −0.143257
\(903\) 50.4273 1.67812
\(904\) 30.5578 1.01634
\(905\) 4.15122 0.137991
\(906\) 2.99531 0.0995125
\(907\) −29.1269 −0.967142 −0.483571 0.875305i \(-0.660661\pi\)
−0.483571 + 0.875305i \(0.660661\pi\)
\(908\) −41.4220 −1.37464
\(909\) 24.3769 0.808532
\(910\) 5.30077 0.175719
\(911\) −25.3571 −0.840119 −0.420060 0.907497i \(-0.637991\pi\)
−0.420060 + 0.907497i \(0.637991\pi\)
\(912\) −14.7029 −0.486862
\(913\) 3.76371 0.124561
\(914\) −11.0592 −0.365806
\(915\) 1.22153 0.0403825
\(916\) −32.5593 −1.07579
\(917\) −64.2237 −2.12085
\(918\) 10.6171 0.350416
\(919\) −14.1662 −0.467299 −0.233649 0.972321i \(-0.575067\pi\)
−0.233649 + 0.972321i \(0.575067\pi\)
\(920\) 4.68874 0.154583
\(921\) 3.62184 0.119344
\(922\) 4.57298 0.150603
\(923\) 43.4977 1.43174
\(924\) −8.21123 −0.270130
\(925\) −5.06844 −0.166649
\(926\) 1.43711 0.0472263
\(927\) −25.7652 −0.846241
\(928\) 9.63689 0.316347
\(929\) 47.3845 1.55464 0.777318 0.629108i \(-0.216580\pi\)
0.777318 + 0.629108i \(0.216580\pi\)
\(930\) −3.44385 −0.112928
\(931\) −50.8737 −1.66732
\(932\) −36.1658 −1.18465
\(933\) −27.8515 −0.911818
\(934\) −8.44773 −0.276418
\(935\) 4.54365 0.148593
\(936\) 8.73711 0.285581
\(937\) 28.4129 0.928209 0.464104 0.885781i \(-0.346376\pi\)
0.464104 + 0.885781i \(0.346376\pi\)
\(938\) −14.5203 −0.474104
\(939\) −34.8193 −1.13628
\(940\) 1.21218 0.0395369
\(941\) −2.83238 −0.0923328 −0.0461664 0.998934i \(-0.514700\pi\)
−0.0461664 + 0.998934i \(0.514700\pi\)
\(942\) 4.20102 0.136877
\(943\) 26.6139 0.866668
\(944\) −40.0671 −1.30407
\(945\) −21.9955 −0.715512
\(946\) −4.93826 −0.160557
\(947\) 38.7106 1.25792 0.628962 0.777436i \(-0.283480\pi\)
0.628962 + 0.777436i \(0.283480\pi\)
\(948\) 7.57893 0.246152
\(949\) −2.82350 −0.0916545
\(950\) 2.12892 0.0690712
\(951\) 19.9077 0.645550
\(952\) 32.4194 1.05072
\(953\) 30.4692 0.986994 0.493497 0.869747i \(-0.335718\pi\)
0.493497 + 0.869747i \(0.335718\pi\)
\(954\) 10.5822 0.342612
\(955\) 8.77712 0.284021
\(956\) −29.6432 −0.958731
\(957\) −2.24135 −0.0724527
\(958\) −1.00774 −0.0325586
\(959\) −54.2600 −1.75215
\(960\) −3.90885 −0.126158
\(961\) 19.5301 0.630003
\(962\) −6.39104 −0.206055
\(963\) −12.7420 −0.410606
\(964\) −21.0224 −0.677086
\(965\) −12.5672 −0.404553
\(966\) −5.62614 −0.181018
\(967\) 21.5064 0.691600 0.345800 0.938308i \(-0.387608\pi\)
0.345800 + 0.938308i \(0.387608\pi\)
\(968\) 1.69729 0.0545530
\(969\) −23.4971 −0.754835
\(970\) −6.42132 −0.206176
\(971\) −1.68790 −0.0541673 −0.0270837 0.999633i \(-0.508622\pi\)
−0.0270837 + 0.999633i \(0.508622\pi\)
\(972\) −27.8594 −0.893592
\(973\) −5.87562 −0.188364
\(974\) −4.79334 −0.153588
\(975\) −3.06299 −0.0980943
\(976\) 3.20140 0.102474
\(977\) 8.68726 0.277930 0.138965 0.990297i \(-0.455622\pi\)
0.138965 + 0.990297i \(0.455622\pi\)
\(978\) −8.59828 −0.274943
\(979\) 3.77803 0.120746
\(980\) −19.2155 −0.613816
\(981\) 12.4114 0.396266
\(982\) 4.35890 0.139098
\(983\) 47.5368 1.51619 0.758095 0.652144i \(-0.226130\pi\)
0.758095 + 0.652144i \(0.226130\pi\)
\(984\) 17.7388 0.565494
\(985\) −4.61568 −0.147068
\(986\) 4.19243 0.133514
\(987\) −3.07016 −0.0977244
\(988\) −24.2350 −0.771018
\(989\) 30.5466 0.971327
\(990\) 0.814205 0.0258771
\(991\) −19.6531 −0.624301 −0.312150 0.950033i \(-0.601049\pi\)
−0.312150 + 0.950033i \(0.601049\pi\)
\(992\) −33.1559 −1.05270
\(993\) −1.02877 −0.0326470
\(994\) 28.9222 0.917356
\(995\) 9.01902 0.285922
\(996\) −7.35160 −0.232944
\(997\) −6.91185 −0.218900 −0.109450 0.993992i \(-0.534909\pi\)
−0.109450 + 0.993992i \(0.534909\pi\)
\(998\) 3.66132 0.115897
\(999\) 26.5195 0.839040
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 \(a_p\))