Properties

Label 4031.2.a.c.1.19
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.19064 q^{2}\) \(-0.642478 q^{3}\) \(-0.582384 q^{4}\) \(-0.355693 q^{5}\) \(+0.764958 q^{6}\) \(+0.205071 q^{7}\) \(+3.07468 q^{8}\) \(-2.58722 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.19064 q^{2}\) \(-0.642478 q^{3}\) \(-0.582384 q^{4}\) \(-0.355693 q^{5}\) \(+0.764958 q^{6}\) \(+0.205071 q^{7}\) \(+3.07468 q^{8}\) \(-2.58722 q^{9}\) \(+0.423501 q^{10}\) \(-1.45264 q^{11}\) \(+0.374169 q^{12}\) \(+5.41909 q^{13}\) \(-0.244165 q^{14}\) \(+0.228525 q^{15}\) \(-2.49606 q^{16}\) \(+4.41807 q^{17}\) \(+3.08044 q^{18}\) \(-2.06625 q^{19}\) \(+0.207150 q^{20}\) \(-0.131754 q^{21}\) \(+1.72957 q^{22}\) \(-8.86978 q^{23}\) \(-1.97542 q^{24}\) \(-4.87348 q^{25}\) \(-6.45217 q^{26}\) \(+3.58967 q^{27}\) \(-0.119430 q^{28}\) \(-1.00000 q^{29}\) \(-0.272090 q^{30}\) \(+3.96844 q^{31}\) \(-3.17746 q^{32}\) \(+0.933291 q^{33}\) \(-5.26032 q^{34}\) \(-0.0729423 q^{35}\) \(+1.50676 q^{36}\) \(+4.45603 q^{37}\) \(+2.46016 q^{38}\) \(-3.48165 q^{39}\) \(-1.09364 q^{40}\) \(+0.903757 q^{41}\) \(+0.156871 q^{42}\) \(-7.33633 q^{43}\) \(+0.845996 q^{44}\) \(+0.920257 q^{45}\) \(+10.5607 q^{46}\) \(+4.59729 q^{47}\) \(+1.60366 q^{48}\) \(-6.95795 q^{49}\) \(+5.80255 q^{50}\) \(-2.83852 q^{51}\) \(-3.15600 q^{52}\) \(+5.01563 q^{53}\) \(-4.27399 q^{54}\) \(+0.516695 q^{55}\) \(+0.630528 q^{56}\) \(+1.32752 q^{57}\) \(+1.19064 q^{58}\) \(+14.0025 q^{59}\) \(-0.133089 q^{60}\) \(-8.00492 q^{61}\) \(-4.72497 q^{62}\) \(-0.530564 q^{63}\) \(+8.77532 q^{64}\) \(-1.92753 q^{65}\) \(-1.11121 q^{66}\) \(+2.21279 q^{67}\) \(-2.57302 q^{68}\) \(+5.69864 q^{69}\) \(+0.0868478 q^{70}\) \(+14.1001 q^{71}\) \(-7.95488 q^{72}\) \(+7.81827 q^{73}\) \(-5.30551 q^{74}\) \(+3.13111 q^{75}\) \(+1.20335 q^{76}\) \(-0.297895 q^{77}\) \(+4.14538 q^{78}\) \(+4.40777 q^{79}\) \(+0.887831 q^{80}\) \(+5.45538 q^{81}\) \(-1.07605 q^{82}\) \(-12.1163 q^{83}\) \(+0.0767313 q^{84}\) \(-1.57148 q^{85}\) \(+8.73490 q^{86}\) \(+0.642478 q^{87}\) \(-4.46641 q^{88}\) \(+0.417775 q^{89}\) \(-1.09569 q^{90}\) \(+1.11130 q^{91}\) \(+5.16562 q^{92}\) \(-2.54964 q^{93}\) \(-5.47371 q^{94}\) \(+0.734952 q^{95}\) \(+2.04145 q^{96}\) \(-4.93875 q^{97}\) \(+8.28439 q^{98}\) \(+3.75831 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19064 −0.841907 −0.420954 0.907082i \(-0.638304\pi\)
−0.420954 + 0.907082i \(0.638304\pi\)
\(3\) −0.642478 −0.370935 −0.185468 0.982650i \(-0.559380\pi\)
−0.185468 + 0.982650i \(0.559380\pi\)
\(4\) −0.582384 −0.291192
\(5\) −0.355693 −0.159071 −0.0795354 0.996832i \(-0.525344\pi\)
−0.0795354 + 0.996832i \(0.525344\pi\)
\(6\) 0.764958 0.312293
\(7\) 0.205071 0.0775096 0.0387548 0.999249i \(-0.487661\pi\)
0.0387548 + 0.999249i \(0.487661\pi\)
\(8\) 3.07468 1.08706
\(9\) −2.58722 −0.862407
\(10\) 0.423501 0.133923
\(11\) −1.45264 −0.437988 −0.218994 0.975726i \(-0.570278\pi\)
−0.218994 + 0.975726i \(0.570278\pi\)
\(12\) 0.374169 0.108013
\(13\) 5.41909 1.50299 0.751493 0.659741i \(-0.229334\pi\)
0.751493 + 0.659741i \(0.229334\pi\)
\(14\) −0.244165 −0.0652559
\(15\) 0.228525 0.0590049
\(16\) −2.49606 −0.624015
\(17\) 4.41807 1.07154 0.535770 0.844364i \(-0.320021\pi\)
0.535770 + 0.844364i \(0.320021\pi\)
\(18\) 3.08044 0.726067
\(19\) −2.06625 −0.474031 −0.237016 0.971506i \(-0.576169\pi\)
−0.237016 + 0.971506i \(0.576169\pi\)
\(20\) 0.207150 0.0463202
\(21\) −0.131754 −0.0287510
\(22\) 1.72957 0.368745
\(23\) −8.86978 −1.84948 −0.924738 0.380604i \(-0.875716\pi\)
−0.924738 + 0.380604i \(0.875716\pi\)
\(24\) −1.97542 −0.403230
\(25\) −4.87348 −0.974696
\(26\) −6.45217 −1.26537
\(27\) 3.58967 0.690832
\(28\) −0.119430 −0.0225702
\(29\) −1.00000 −0.185695
\(30\) −0.272090 −0.0496767
\(31\) 3.96844 0.712752 0.356376 0.934343i \(-0.384012\pi\)
0.356376 + 0.934343i \(0.384012\pi\)
\(32\) −3.17746 −0.561701
\(33\) 0.933291 0.162465
\(34\) −5.26032 −0.902137
\(35\) −0.0729423 −0.0123295
\(36\) 1.50676 0.251126
\(37\) 4.45603 0.732566 0.366283 0.930503i \(-0.380630\pi\)
0.366283 + 0.930503i \(0.380630\pi\)
\(38\) 2.46016 0.399090
\(39\) −3.48165 −0.557510
\(40\) −1.09364 −0.172920
\(41\) 0.903757 0.141143 0.0705716 0.997507i \(-0.477518\pi\)
0.0705716 + 0.997507i \(0.477518\pi\)
\(42\) 0.156871 0.0242057
\(43\) −7.33633 −1.11878 −0.559390 0.828905i \(-0.688965\pi\)
−0.559390 + 0.828905i \(0.688965\pi\)
\(44\) 0.845996 0.127539
\(45\) 0.920257 0.137184
\(46\) 10.5607 1.55709
\(47\) 4.59729 0.670584 0.335292 0.942114i \(-0.391165\pi\)
0.335292 + 0.942114i \(0.391165\pi\)
\(48\) 1.60366 0.231469
\(49\) −6.95795 −0.993992
\(50\) 5.80255 0.820604
\(51\) −2.83852 −0.397472
\(52\) −3.15600 −0.437658
\(53\) 5.01563 0.688949 0.344475 0.938796i \(-0.388057\pi\)
0.344475 + 0.938796i \(0.388057\pi\)
\(54\) −4.27399 −0.581617
\(55\) 0.516695 0.0696711
\(56\) 0.630528 0.0842579
\(57\) 1.32752 0.175835
\(58\) 1.19064 0.156338
\(59\) 14.0025 1.82297 0.911486 0.411330i \(-0.134936\pi\)
0.911486 + 0.411330i \(0.134936\pi\)
\(60\) −0.133089 −0.0171818
\(61\) −8.00492 −1.02492 −0.512462 0.858710i \(-0.671267\pi\)
−0.512462 + 0.858710i \(0.671267\pi\)
\(62\) −4.72497 −0.600071
\(63\) −0.530564 −0.0668448
\(64\) 8.77532 1.09692
\(65\) −1.92753 −0.239081
\(66\) −1.11121 −0.136781
\(67\) 2.21279 0.270335 0.135168 0.990823i \(-0.456843\pi\)
0.135168 + 0.990823i \(0.456843\pi\)
\(68\) −2.57302 −0.312024
\(69\) 5.69864 0.686036
\(70\) 0.0868478 0.0103803
\(71\) 14.1001 1.67338 0.836688 0.547680i \(-0.184489\pi\)
0.836688 + 0.547680i \(0.184489\pi\)
\(72\) −7.95488 −0.937492
\(73\) 7.81827 0.915060 0.457530 0.889194i \(-0.348734\pi\)
0.457530 + 0.889194i \(0.348734\pi\)
\(74\) −5.30551 −0.616753
\(75\) 3.13111 0.361549
\(76\) 1.20335 0.138034
\(77\) −0.297895 −0.0339483
\(78\) 4.14538 0.469372
\(79\) 4.40777 0.495913 0.247957 0.968771i \(-0.420241\pi\)
0.247957 + 0.968771i \(0.420241\pi\)
\(80\) 0.887831 0.0992625
\(81\) 5.45538 0.606153
\(82\) −1.07605 −0.118829
\(83\) −12.1163 −1.32994 −0.664970 0.746870i \(-0.731556\pi\)
−0.664970 + 0.746870i \(0.731556\pi\)
\(84\) 0.0767313 0.00837207
\(85\) −1.57148 −0.170451
\(86\) 8.73490 0.941909
\(87\) 0.642478 0.0688809
\(88\) −4.46641 −0.476121
\(89\) 0.417775 0.0442841 0.0221420 0.999755i \(-0.492951\pi\)
0.0221420 + 0.999755i \(0.492951\pi\)
\(90\) −1.09569 −0.115496
\(91\) 1.11130 0.116496
\(92\) 5.16562 0.538553
\(93\) −2.54964 −0.264385
\(94\) −5.47371 −0.564570
\(95\) 0.734952 0.0754045
\(96\) 2.04145 0.208355
\(97\) −4.93875 −0.501454 −0.250727 0.968058i \(-0.580670\pi\)
−0.250727 + 0.968058i \(0.580670\pi\)
\(98\) 8.28439 0.836849
\(99\) 3.75831 0.377724
\(100\) 2.83824 0.283824
\(101\) −17.1886 −1.71033 −0.855167 0.518353i \(-0.826545\pi\)
−0.855167 + 0.518353i \(0.826545\pi\)
\(102\) 3.37964 0.334634
\(103\) 12.3007 1.21203 0.606013 0.795455i \(-0.292768\pi\)
0.606013 + 0.795455i \(0.292768\pi\)
\(104\) 16.6620 1.63384
\(105\) 0.0468639 0.00457345
\(106\) −5.97179 −0.580031
\(107\) 9.54320 0.922576 0.461288 0.887250i \(-0.347387\pi\)
0.461288 + 0.887250i \(0.347387\pi\)
\(108\) −2.09057 −0.201165
\(109\) 0.0890247 0.00852702 0.00426351 0.999991i \(-0.498643\pi\)
0.00426351 + 0.999991i \(0.498643\pi\)
\(110\) −0.615195 −0.0586566
\(111\) −2.86290 −0.271735
\(112\) −0.511870 −0.0483671
\(113\) −17.4313 −1.63979 −0.819897 0.572511i \(-0.805970\pi\)
−0.819897 + 0.572511i \(0.805970\pi\)
\(114\) −1.58060 −0.148037
\(115\) 3.15492 0.294198
\(116\) 0.582384 0.0540730
\(117\) −14.0204 −1.29619
\(118\) −16.6719 −1.53477
\(119\) 0.906019 0.0830546
\(120\) 0.702642 0.0641421
\(121\) −8.88983 −0.808167
\(122\) 9.53095 0.862891
\(123\) −0.580644 −0.0523549
\(124\) −2.31116 −0.207548
\(125\) 3.51193 0.314116
\(126\) 0.631709 0.0562771
\(127\) −15.6074 −1.38494 −0.692468 0.721449i \(-0.743476\pi\)
−0.692468 + 0.721449i \(0.743476\pi\)
\(128\) −4.09329 −0.361800
\(129\) 4.71343 0.414995
\(130\) 2.29499 0.201284
\(131\) 14.2133 1.24182 0.620912 0.783880i \(-0.286762\pi\)
0.620912 + 0.783880i \(0.286762\pi\)
\(132\) −0.543534 −0.0473086
\(133\) −0.423729 −0.0367420
\(134\) −2.63463 −0.227597
\(135\) −1.27682 −0.109891
\(136\) 13.5842 1.16483
\(137\) 5.70508 0.487418 0.243709 0.969848i \(-0.421636\pi\)
0.243709 + 0.969848i \(0.421636\pi\)
\(138\) −6.78501 −0.577578
\(139\) −1.00000 −0.0848189
\(140\) 0.0424805 0.00359026
\(141\) −2.95366 −0.248743
\(142\) −16.7881 −1.40883
\(143\) −7.87200 −0.658290
\(144\) 6.45786 0.538155
\(145\) 0.355693 0.0295387
\(146\) −9.30872 −0.770395
\(147\) 4.47033 0.368707
\(148\) −2.59512 −0.213318
\(149\) −9.98175 −0.817737 −0.408869 0.912593i \(-0.634077\pi\)
−0.408869 + 0.912593i \(0.634077\pi\)
\(150\) −3.72801 −0.304391
\(151\) 7.35339 0.598410 0.299205 0.954189i \(-0.403278\pi\)
0.299205 + 0.954189i \(0.403278\pi\)
\(152\) −6.35307 −0.515302
\(153\) −11.4305 −0.924104
\(154\) 0.354684 0.0285813
\(155\) −1.41155 −0.113378
\(156\) 2.02766 0.162343
\(157\) −16.5721 −1.32259 −0.661297 0.750124i \(-0.729994\pi\)
−0.661297 + 0.750124i \(0.729994\pi\)
\(158\) −5.24806 −0.417513
\(159\) −3.22243 −0.255555
\(160\) 1.13020 0.0893503
\(161\) −1.81893 −0.143352
\(162\) −6.49537 −0.510325
\(163\) −15.6672 −1.22715 −0.613575 0.789636i \(-0.710269\pi\)
−0.613575 + 0.789636i \(0.710269\pi\)
\(164\) −0.526334 −0.0410998
\(165\) −0.331965 −0.0258434
\(166\) 14.4262 1.11969
\(167\) 5.65637 0.437703 0.218852 0.975758i \(-0.429769\pi\)
0.218852 + 0.975758i \(0.429769\pi\)
\(168\) −0.405101 −0.0312542
\(169\) 16.3666 1.25897
\(170\) 1.87106 0.143504
\(171\) 5.34586 0.408808
\(172\) 4.27256 0.325780
\(173\) −7.61704 −0.579113 −0.289556 0.957161i \(-0.593508\pi\)
−0.289556 + 0.957161i \(0.593508\pi\)
\(174\) −0.764958 −0.0579913
\(175\) −0.999410 −0.0755483
\(176\) 3.62588 0.273311
\(177\) −8.99632 −0.676205
\(178\) −0.497418 −0.0372831
\(179\) 13.4824 1.00772 0.503862 0.863784i \(-0.331912\pi\)
0.503862 + 0.863784i \(0.331912\pi\)
\(180\) −0.535943 −0.0399468
\(181\) −0.207060 −0.0153906 −0.00769531 0.999970i \(-0.502450\pi\)
−0.00769531 + 0.999970i \(0.502450\pi\)
\(182\) −1.32315 −0.0980786
\(183\) 5.14299 0.380180
\(184\) −27.2717 −2.01050
\(185\) −1.58498 −0.116530
\(186\) 3.03569 0.222588
\(187\) −6.41788 −0.469322
\(188\) −2.67739 −0.195269
\(189\) 0.736137 0.0535461
\(190\) −0.875061 −0.0634836
\(191\) −12.5549 −0.908440 −0.454220 0.890890i \(-0.650082\pi\)
−0.454220 + 0.890890i \(0.650082\pi\)
\(192\) −5.63796 −0.406884
\(193\) −11.6429 −0.838071 −0.419035 0.907970i \(-0.637632\pi\)
−0.419035 + 0.907970i \(0.637632\pi\)
\(194\) 5.88026 0.422178
\(195\) 1.23840 0.0886836
\(196\) 4.05220 0.289443
\(197\) −2.51796 −0.179397 −0.0896985 0.995969i \(-0.528590\pi\)
−0.0896985 + 0.995969i \(0.528590\pi\)
\(198\) −4.47478 −0.318009
\(199\) 9.26997 0.657130 0.328565 0.944481i \(-0.393435\pi\)
0.328565 + 0.944481i \(0.393435\pi\)
\(200\) −14.9844 −1.05956
\(201\) −1.42167 −0.100277
\(202\) 20.4654 1.43994
\(203\) −0.205071 −0.0143932
\(204\) 1.65311 0.115741
\(205\) −0.321460 −0.0224517
\(206\) −14.6457 −1.02041
\(207\) 22.9481 1.59500
\(208\) −13.5264 −0.937886
\(209\) 3.00153 0.207620
\(210\) −0.0557979 −0.00385042
\(211\) 22.0221 1.51606 0.758031 0.652219i \(-0.226162\pi\)
0.758031 + 0.652219i \(0.226162\pi\)
\(212\) −2.92102 −0.200617
\(213\) −9.05902 −0.620714
\(214\) −11.3625 −0.776724
\(215\) 2.60948 0.177965
\(216\) 11.0371 0.750979
\(217\) 0.813812 0.0552451
\(218\) −0.105996 −0.00717896
\(219\) −5.02307 −0.339428
\(220\) −0.300915 −0.0202877
\(221\) 23.9419 1.61051
\(222\) 3.40868 0.228775
\(223\) −10.0768 −0.674792 −0.337396 0.941363i \(-0.609546\pi\)
−0.337396 + 0.941363i \(0.609546\pi\)
\(224\) −0.651606 −0.0435372
\(225\) 12.6088 0.840585
\(226\) 20.7543 1.38055
\(227\) −28.4152 −1.88598 −0.942992 0.332815i \(-0.892001\pi\)
−0.942992 + 0.332815i \(0.892001\pi\)
\(228\) −0.773129 −0.0512017
\(229\) −1.53508 −0.101441 −0.0507205 0.998713i \(-0.516152\pi\)
−0.0507205 + 0.998713i \(0.516152\pi\)
\(230\) −3.75636 −0.247687
\(231\) 0.191391 0.0125926
\(232\) −3.07468 −0.201863
\(233\) −14.7123 −0.963833 −0.481917 0.876217i \(-0.660059\pi\)
−0.481917 + 0.876217i \(0.660059\pi\)
\(234\) 16.6932 1.09127
\(235\) −1.63523 −0.106670
\(236\) −8.15485 −0.530836
\(237\) −2.83190 −0.183952
\(238\) −1.07874 −0.0699243
\(239\) −9.57934 −0.619636 −0.309818 0.950796i \(-0.600268\pi\)
−0.309818 + 0.950796i \(0.600268\pi\)
\(240\) −0.570412 −0.0368200
\(241\) −24.9634 −1.60803 −0.804017 0.594607i \(-0.797308\pi\)
−0.804017 + 0.594607i \(0.797308\pi\)
\(242\) 10.5846 0.680401
\(243\) −14.2740 −0.915676
\(244\) 4.66194 0.298450
\(245\) 2.47489 0.158115
\(246\) 0.691336 0.0440780
\(247\) −11.1972 −0.712462
\(248\) 12.2017 0.774808
\(249\) 7.78448 0.493322
\(250\) −4.18143 −0.264457
\(251\) 16.7502 1.05726 0.528630 0.848852i \(-0.322706\pi\)
0.528630 + 0.848852i \(0.322706\pi\)
\(252\) 0.308992 0.0194647
\(253\) 12.8846 0.810048
\(254\) 18.5828 1.16599
\(255\) 1.00964 0.0632262
\(256\) −12.6770 −0.792314
\(257\) 29.4059 1.83429 0.917143 0.398557i \(-0.130489\pi\)
0.917143 + 0.398557i \(0.130489\pi\)
\(258\) −5.61199 −0.349387
\(259\) 0.913802 0.0567809
\(260\) 1.12257 0.0696186
\(261\) 2.58722 0.160145
\(262\) −16.9229 −1.04550
\(263\) 11.5930 0.714854 0.357427 0.933941i \(-0.383654\pi\)
0.357427 + 0.933941i \(0.383654\pi\)
\(264\) 2.86957 0.176610
\(265\) −1.78402 −0.109592
\(266\) 0.504507 0.0309333
\(267\) −0.268412 −0.0164265
\(268\) −1.28869 −0.0787195
\(269\) −0.906001 −0.0552398 −0.0276199 0.999618i \(-0.508793\pi\)
−0.0276199 + 0.999618i \(0.508793\pi\)
\(270\) 1.52023 0.0925182
\(271\) −21.1256 −1.28329 −0.641644 0.767003i \(-0.721747\pi\)
−0.641644 + 0.767003i \(0.721747\pi\)
\(272\) −11.0278 −0.668657
\(273\) −0.713986 −0.0432124
\(274\) −6.79268 −0.410361
\(275\) 7.07942 0.426905
\(276\) −3.31880 −0.199768
\(277\) 3.59494 0.215999 0.108000 0.994151i \(-0.465555\pi\)
0.108000 + 0.994151i \(0.465555\pi\)
\(278\) 1.19064 0.0714096
\(279\) −10.2672 −0.614683
\(280\) −0.224274 −0.0134030
\(281\) −22.2466 −1.32712 −0.663562 0.748122i \(-0.730956\pi\)
−0.663562 + 0.748122i \(0.730956\pi\)
\(282\) 3.51674 0.209419
\(283\) 7.67119 0.456005 0.228003 0.973661i \(-0.426781\pi\)
0.228003 + 0.973661i \(0.426781\pi\)
\(284\) −8.21168 −0.487274
\(285\) −0.472191 −0.0279702
\(286\) 9.37269 0.554219
\(287\) 0.185334 0.0109399
\(288\) 8.22080 0.484415
\(289\) 2.51937 0.148198
\(290\) −0.423501 −0.0248688
\(291\) 3.17304 0.186007
\(292\) −4.55324 −0.266458
\(293\) −26.0696 −1.52300 −0.761500 0.648164i \(-0.775537\pi\)
−0.761500 + 0.648164i \(0.775537\pi\)
\(294\) −5.32254 −0.310417
\(295\) −4.98060 −0.289982
\(296\) 13.7009 0.796347
\(297\) −5.21450 −0.302576
\(298\) 11.8846 0.688459
\(299\) −48.0661 −2.77974
\(300\) −1.82351 −0.105280
\(301\) −1.50447 −0.0867161
\(302\) −8.75521 −0.503806
\(303\) 11.0433 0.634423
\(304\) 5.15749 0.295803
\(305\) 2.84729 0.163036
\(306\) 13.6096 0.778010
\(307\) 12.6116 0.719785 0.359892 0.932994i \(-0.382813\pi\)
0.359892 + 0.932994i \(0.382813\pi\)
\(308\) 0.173489 0.00988547
\(309\) −7.90295 −0.449583
\(310\) 1.68064 0.0954538
\(311\) −10.1650 −0.576404 −0.288202 0.957570i \(-0.593057\pi\)
−0.288202 + 0.957570i \(0.593057\pi\)
\(312\) −10.7050 −0.606049
\(313\) −12.1093 −0.684458 −0.342229 0.939617i \(-0.611182\pi\)
−0.342229 + 0.939617i \(0.611182\pi\)
\(314\) 19.7313 1.11350
\(315\) 0.188718 0.0106331
\(316\) −2.56702 −0.144406
\(317\) −8.74270 −0.491039 −0.245519 0.969392i \(-0.578958\pi\)
−0.245519 + 0.969392i \(0.578958\pi\)
\(318\) 3.83675 0.215154
\(319\) 1.45264 0.0813323
\(320\) −3.12132 −0.174487
\(321\) −6.13130 −0.342216
\(322\) 2.16569 0.120689
\(323\) −9.12886 −0.507944
\(324\) −3.17713 −0.176507
\(325\) −26.4099 −1.46496
\(326\) 18.6540 1.03315
\(327\) −0.0571965 −0.00316297
\(328\) 2.77876 0.153432
\(329\) 0.942772 0.0519767
\(330\) 0.395250 0.0217578
\(331\) −30.2894 −1.66486 −0.832428 0.554133i \(-0.813050\pi\)
−0.832428 + 0.554133i \(0.813050\pi\)
\(332\) 7.05637 0.387268
\(333\) −11.5287 −0.631771
\(334\) −6.73469 −0.368506
\(335\) −0.787074 −0.0430024
\(336\) 0.328865 0.0179411
\(337\) 6.26840 0.341462 0.170731 0.985318i \(-0.445387\pi\)
0.170731 + 0.985318i \(0.445387\pi\)
\(338\) −19.4866 −1.05993
\(339\) 11.1992 0.608257
\(340\) 0.915204 0.0496339
\(341\) −5.76472 −0.312177
\(342\) −6.36497 −0.344178
\(343\) −2.86237 −0.154553
\(344\) −22.5569 −1.21619
\(345\) −2.02697 −0.109128
\(346\) 9.06912 0.487559
\(347\) −17.0573 −0.915683 −0.457842 0.889034i \(-0.651377\pi\)
−0.457842 + 0.889034i \(0.651377\pi\)
\(348\) −0.374169 −0.0200576
\(349\) −14.9784 −0.801778 −0.400889 0.916127i \(-0.631299\pi\)
−0.400889 + 0.916127i \(0.631299\pi\)
\(350\) 1.18993 0.0636047
\(351\) 19.4528 1.03831
\(352\) 4.61572 0.246018
\(353\) 25.5484 1.35980 0.679902 0.733303i \(-0.262022\pi\)
0.679902 + 0.733303i \(0.262022\pi\)
\(354\) 10.7113 0.569302
\(355\) −5.01531 −0.266185
\(356\) −0.243306 −0.0128952
\(357\) −0.582098 −0.0308079
\(358\) −16.0527 −0.848410
\(359\) −12.2029 −0.644044 −0.322022 0.946732i \(-0.604363\pi\)
−0.322022 + 0.946732i \(0.604363\pi\)
\(360\) 2.82950 0.149128
\(361\) −14.7306 −0.775294
\(362\) 0.246533 0.0129575
\(363\) 5.71153 0.299777
\(364\) −0.647203 −0.0339227
\(365\) −2.78091 −0.145559
\(366\) −6.12343 −0.320077
\(367\) 20.3731 1.06347 0.531733 0.846912i \(-0.321541\pi\)
0.531733 + 0.846912i \(0.321541\pi\)
\(368\) 22.1395 1.15410
\(369\) −2.33822 −0.121723
\(370\) 1.88713 0.0981074
\(371\) 1.02856 0.0534002
\(372\) 1.48487 0.0769868
\(373\) −8.01136 −0.414813 −0.207406 0.978255i \(-0.566502\pi\)
−0.207406 + 0.978255i \(0.566502\pi\)
\(374\) 7.64136 0.395125
\(375\) −2.25634 −0.116517
\(376\) 14.1352 0.728968
\(377\) −5.41909 −0.279097
\(378\) −0.876472 −0.0450809
\(379\) −18.3147 −0.940765 −0.470383 0.882463i \(-0.655884\pi\)
−0.470383 + 0.882463i \(0.655884\pi\)
\(380\) −0.428025 −0.0219572
\(381\) 10.0274 0.513721
\(382\) 14.9483 0.764822
\(383\) −28.7048 −1.46674 −0.733372 0.679827i \(-0.762055\pi\)
−0.733372 + 0.679827i \(0.762055\pi\)
\(384\) 2.62985 0.134204
\(385\) 0.105959 0.00540018
\(386\) 13.8624 0.705578
\(387\) 18.9807 0.964844
\(388\) 2.87625 0.146020
\(389\) 8.10744 0.411063 0.205532 0.978650i \(-0.434108\pi\)
0.205532 + 0.978650i \(0.434108\pi\)
\(390\) −1.47448 −0.0746633
\(391\) −39.1873 −1.98179
\(392\) −21.3935 −1.08053
\(393\) −9.13176 −0.460636
\(394\) 2.99797 0.151036
\(395\) −1.56781 −0.0788853
\(396\) −2.18878 −0.109990
\(397\) −33.1119 −1.66184 −0.830918 0.556395i \(-0.812184\pi\)
−0.830918 + 0.556395i \(0.812184\pi\)
\(398\) −11.0372 −0.553243
\(399\) 0.272237 0.0136289
\(400\) 12.1645 0.608225
\(401\) −12.0019 −0.599345 −0.299673 0.954042i \(-0.596877\pi\)
−0.299673 + 0.954042i \(0.596877\pi\)
\(402\) 1.69269 0.0844238
\(403\) 21.5053 1.07126
\(404\) 10.0104 0.498036
\(405\) −1.94044 −0.0964213
\(406\) 0.244165 0.0121177
\(407\) −6.47301 −0.320855
\(408\) −8.72754 −0.432077
\(409\) 7.36671 0.364260 0.182130 0.983274i \(-0.441701\pi\)
0.182130 + 0.983274i \(0.441701\pi\)
\(410\) 0.382742 0.0189023
\(411\) −3.66539 −0.180800
\(412\) −7.16375 −0.352932
\(413\) 2.87151 0.141298
\(414\) −27.3228 −1.34284
\(415\) 4.30970 0.211555
\(416\) −17.2190 −0.844229
\(417\) 0.642478 0.0314623
\(418\) −3.57373 −0.174797
\(419\) −26.2137 −1.28062 −0.640312 0.768115i \(-0.721195\pi\)
−0.640312 + 0.768115i \(0.721195\pi\)
\(420\) −0.0272928 −0.00133175
\(421\) −2.44758 −0.119288 −0.0596439 0.998220i \(-0.518997\pi\)
−0.0596439 + 0.998220i \(0.518997\pi\)
\(422\) −26.2203 −1.27638
\(423\) −11.8942 −0.578317
\(424\) 15.4215 0.748932
\(425\) −21.5314 −1.04443
\(426\) 10.7860 0.522583
\(427\) −1.64158 −0.0794414
\(428\) −5.55781 −0.268647
\(429\) 5.05759 0.244183
\(430\) −3.10694 −0.149830
\(431\) −29.3222 −1.41240 −0.706200 0.708012i \(-0.749592\pi\)
−0.706200 + 0.708012i \(0.749592\pi\)
\(432\) −8.96003 −0.431090
\(433\) −15.6425 −0.751729 −0.375865 0.926675i \(-0.622654\pi\)
−0.375865 + 0.926675i \(0.622654\pi\)
\(434\) −0.968954 −0.0465113
\(435\) −0.228525 −0.0109569
\(436\) −0.0518466 −0.00248300
\(437\) 18.3272 0.876710
\(438\) 5.98065 0.285767
\(439\) 22.0197 1.05094 0.525472 0.850811i \(-0.323889\pi\)
0.525472 + 0.850811i \(0.323889\pi\)
\(440\) 1.58867 0.0757369
\(441\) 18.0017 0.857226
\(442\) −28.5062 −1.35590
\(443\) −5.85508 −0.278183 −0.139092 0.990280i \(-0.544418\pi\)
−0.139092 + 0.990280i \(0.544418\pi\)
\(444\) 1.66731 0.0791270
\(445\) −0.148600 −0.00704430
\(446\) 11.9978 0.568112
\(447\) 6.41306 0.303327
\(448\) 1.79956 0.0850214
\(449\) 27.0739 1.27770 0.638849 0.769332i \(-0.279411\pi\)
0.638849 + 0.769332i \(0.279411\pi\)
\(450\) −15.0125 −0.707695
\(451\) −1.31283 −0.0618190
\(452\) 10.1517 0.477495
\(453\) −4.72439 −0.221971
\(454\) 33.8322 1.58782
\(455\) −0.395281 −0.0185311
\(456\) 4.08171 0.191144
\(457\) −20.5286 −0.960287 −0.480143 0.877190i \(-0.659415\pi\)
−0.480143 + 0.877190i \(0.659415\pi\)
\(458\) 1.82772 0.0854039
\(459\) 15.8594 0.740254
\(460\) −1.83738 −0.0856681
\(461\) −10.2320 −0.476554 −0.238277 0.971197i \(-0.576583\pi\)
−0.238277 + 0.971197i \(0.576583\pi\)
\(462\) −0.227877 −0.0106018
\(463\) 12.9004 0.599534 0.299767 0.954012i \(-0.403091\pi\)
0.299767 + 0.954012i \(0.403091\pi\)
\(464\) 2.49606 0.115877
\(465\) 0.906888 0.0420559
\(466\) 17.5170 0.811458
\(467\) 34.2076 1.58294 0.791468 0.611210i \(-0.209317\pi\)
0.791468 + 0.611210i \(0.209317\pi\)
\(468\) 8.16526 0.377439
\(469\) 0.453779 0.0209536
\(470\) 1.94696 0.0898065
\(471\) 10.6472 0.490597
\(472\) 43.0533 1.98169
\(473\) 10.6571 0.490012
\(474\) 3.37176 0.154870
\(475\) 10.0699 0.462037
\(476\) −0.527651 −0.0241849
\(477\) −12.9765 −0.594155
\(478\) 11.4055 0.521676
\(479\) 23.8492 1.08970 0.544848 0.838535i \(-0.316587\pi\)
0.544848 + 0.838535i \(0.316587\pi\)
\(480\) −0.726130 −0.0331432
\(481\) 24.1476 1.10104
\(482\) 29.7223 1.35382
\(483\) 1.16863 0.0531743
\(484\) 5.17730 0.235332
\(485\) 1.75668 0.0797667
\(486\) 16.9951 0.770914
\(487\) −9.80750 −0.444420 −0.222210 0.974999i \(-0.571327\pi\)
−0.222210 + 0.974999i \(0.571327\pi\)
\(488\) −24.6126 −1.11416
\(489\) 10.0658 0.455193
\(490\) −2.94670 −0.133118
\(491\) 24.9459 1.12579 0.562897 0.826527i \(-0.309687\pi\)
0.562897 + 0.826527i \(0.309687\pi\)
\(492\) 0.338158 0.0152453
\(493\) −4.41807 −0.198980
\(494\) 13.3318 0.599827
\(495\) −1.33680 −0.0600848
\(496\) −9.90546 −0.444768
\(497\) 2.89152 0.129703
\(498\) −9.26849 −0.415331
\(499\) 25.9373 1.16111 0.580557 0.814220i \(-0.302835\pi\)
0.580557 + 0.814220i \(0.302835\pi\)
\(500\) −2.04529 −0.0914683
\(501\) −3.63410 −0.162360
\(502\) −19.9434 −0.890115
\(503\) −29.5903 −1.31937 −0.659683 0.751544i \(-0.729309\pi\)
−0.659683 + 0.751544i \(0.729309\pi\)
\(504\) −1.63132 −0.0726646
\(505\) 6.11388 0.272064
\(506\) −15.3409 −0.681986
\(507\) −10.5152 −0.466995
\(508\) 9.08952 0.403282
\(509\) 1.26580 0.0561056 0.0280528 0.999606i \(-0.491069\pi\)
0.0280528 + 0.999606i \(0.491069\pi\)
\(510\) −1.20212 −0.0532306
\(511\) 1.60330 0.0709259
\(512\) 23.2803 1.02885
\(513\) −7.41717 −0.327476
\(514\) −35.0117 −1.54430
\(515\) −4.37528 −0.192798
\(516\) −2.74503 −0.120843
\(517\) −6.67822 −0.293708
\(518\) −1.08801 −0.0478043
\(519\) 4.89378 0.214813
\(520\) −5.92655 −0.259896
\(521\) 14.7646 0.646851 0.323425 0.946254i \(-0.395166\pi\)
0.323425 + 0.946254i \(0.395166\pi\)
\(522\) −3.08044 −0.134827
\(523\) −8.03979 −0.351556 −0.175778 0.984430i \(-0.556244\pi\)
−0.175778 + 0.984430i \(0.556244\pi\)
\(524\) −8.27762 −0.361610
\(525\) 0.642099 0.0280235
\(526\) −13.8030 −0.601841
\(527\) 17.5328 0.763743
\(528\) −2.32955 −0.101381
\(529\) 55.6730 2.42056
\(530\) 2.12412 0.0922660
\(531\) −36.2276 −1.57214
\(532\) 0.246773 0.0106990
\(533\) 4.89754 0.212136
\(534\) 0.319581 0.0138296
\(535\) −3.39445 −0.146755
\(536\) 6.80362 0.293872
\(537\) −8.66217 −0.373800
\(538\) 1.07872 0.0465068
\(539\) 10.1074 0.435357
\(540\) 0.743600 0.0319995
\(541\) −26.5059 −1.13958 −0.569788 0.821792i \(-0.692975\pi\)
−0.569788 + 0.821792i \(0.692975\pi\)
\(542\) 25.1529 1.08041
\(543\) 0.133031 0.00570892
\(544\) −14.0383 −0.601886
\(545\) −0.0316655 −0.00135640
\(546\) 0.850097 0.0363808
\(547\) −11.2535 −0.481164 −0.240582 0.970629i \(-0.577338\pi\)
−0.240582 + 0.970629i \(0.577338\pi\)
\(548\) −3.32255 −0.141932
\(549\) 20.7105 0.883902
\(550\) −8.42902 −0.359415
\(551\) 2.06625 0.0880254
\(552\) 17.5215 0.745765
\(553\) 0.903906 0.0384380
\(554\) −4.28027 −0.181851
\(555\) 1.01831 0.0432250
\(556\) 0.582384 0.0246986
\(557\) −2.55814 −0.108392 −0.0541959 0.998530i \(-0.517260\pi\)
−0.0541959 + 0.998530i \(0.517260\pi\)
\(558\) 12.2245 0.517506
\(559\) −39.7563 −1.68151
\(560\) 0.182068 0.00769380
\(561\) 4.12335 0.174088
\(562\) 26.4877 1.11731
\(563\) 4.62470 0.194908 0.0974539 0.995240i \(-0.468930\pi\)
0.0974539 + 0.995240i \(0.468930\pi\)
\(564\) 1.72017 0.0724321
\(565\) 6.20018 0.260843
\(566\) −9.13361 −0.383914
\(567\) 1.11874 0.0469827
\(568\) 43.3533 1.81907
\(569\) 14.2623 0.597908 0.298954 0.954268i \(-0.403362\pi\)
0.298954 + 0.954268i \(0.403362\pi\)
\(570\) 0.562208 0.0235483
\(571\) −17.1570 −0.717998 −0.358999 0.933338i \(-0.616882\pi\)
−0.358999 + 0.933338i \(0.616882\pi\)
\(572\) 4.58453 0.191689
\(573\) 8.06625 0.336972
\(574\) −0.220666 −0.00921042
\(575\) 43.2267 1.80268
\(576\) −22.7037 −0.945988
\(577\) −33.3203 −1.38714 −0.693570 0.720389i \(-0.743963\pi\)
−0.693570 + 0.720389i \(0.743963\pi\)
\(578\) −2.99966 −0.124769
\(579\) 7.48028 0.310870
\(580\) −0.207150 −0.00860144
\(581\) −2.48471 −0.103083
\(582\) −3.77794 −0.156601
\(583\) −7.28591 −0.301752
\(584\) 24.0387 0.994729
\(585\) 4.98696 0.206185
\(586\) 31.0394 1.28223
\(587\) −2.03049 −0.0838074 −0.0419037 0.999122i \(-0.513342\pi\)
−0.0419037 + 0.999122i \(0.513342\pi\)
\(588\) −2.60345 −0.107364
\(589\) −8.19980 −0.337867
\(590\) 5.93008 0.244138
\(591\) 1.61773 0.0665447
\(592\) −11.1225 −0.457132
\(593\) −17.4811 −0.717865 −0.358932 0.933364i \(-0.616859\pi\)
−0.358932 + 0.933364i \(0.616859\pi\)
\(594\) 6.20858 0.254741
\(595\) −0.322265 −0.0132116
\(596\) 5.81322 0.238119
\(597\) −5.95575 −0.243753
\(598\) 57.2293 2.34028
\(599\) 22.3362 0.912633 0.456317 0.889817i \(-0.349168\pi\)
0.456317 + 0.889817i \(0.349168\pi\)
\(600\) 9.62716 0.393027
\(601\) −15.8799 −0.647755 −0.323878 0.946099i \(-0.604987\pi\)
−0.323878 + 0.946099i \(0.604987\pi\)
\(602\) 1.79128 0.0730070
\(603\) −5.72498 −0.233139
\(604\) −4.28250 −0.174252
\(605\) 3.16205 0.128556
\(606\) −13.1486 −0.534125
\(607\) −47.5812 −1.93126 −0.965631 0.259917i \(-0.916305\pi\)
−0.965631 + 0.259917i \(0.916305\pi\)
\(608\) 6.56545 0.266264
\(609\) 0.131754 0.00533893
\(610\) −3.39009 −0.137261
\(611\) 24.9132 1.00788
\(612\) 6.65697 0.269092
\(613\) −19.8166 −0.800384 −0.400192 0.916431i \(-0.631057\pi\)
−0.400192 + 0.916431i \(0.631057\pi\)
\(614\) −15.0159 −0.605992
\(615\) 0.206531 0.00832814
\(616\) −0.915931 −0.0369039
\(617\) 29.1135 1.17207 0.586033 0.810287i \(-0.300689\pi\)
0.586033 + 0.810287i \(0.300689\pi\)
\(618\) 9.40954 0.378507
\(619\) −3.48859 −0.140218 −0.0701092 0.997539i \(-0.522335\pi\)
−0.0701092 + 0.997539i \(0.522335\pi\)
\(620\) 0.822062 0.0330148
\(621\) −31.8396 −1.27768
\(622\) 12.1028 0.485279
\(623\) 0.0856736 0.00343244
\(624\) 8.69041 0.347895
\(625\) 23.1182 0.924730
\(626\) 14.4178 0.576250
\(627\) −1.92842 −0.0770135
\(628\) 9.65131 0.385129
\(629\) 19.6871 0.784974
\(630\) −0.224695 −0.00895205
\(631\) 5.68558 0.226339 0.113170 0.993576i \(-0.463900\pi\)
0.113170 + 0.993576i \(0.463900\pi\)
\(632\) 13.5525 0.539089
\(633\) −14.1487 −0.562361
\(634\) 10.4094 0.413409
\(635\) 5.55145 0.220303
\(636\) 1.87669 0.0744158
\(637\) −37.7058 −1.49396
\(638\) −1.72957 −0.0684743
\(639\) −36.4801 −1.44313
\(640\) 1.45596 0.0575517
\(641\) −10.6836 −0.421976 −0.210988 0.977489i \(-0.567668\pi\)
−0.210988 + 0.977489i \(0.567668\pi\)
\(642\) 7.30015 0.288114
\(643\) −42.6495 −1.68193 −0.840966 0.541089i \(-0.818012\pi\)
−0.840966 + 0.541089i \(0.818012\pi\)
\(644\) 1.05932 0.0417430
\(645\) −1.67654 −0.0660135
\(646\) 10.8692 0.427641
\(647\) 12.1181 0.476413 0.238207 0.971214i \(-0.423440\pi\)
0.238207 + 0.971214i \(0.423440\pi\)
\(648\) 16.7736 0.658927
\(649\) −20.3406 −0.798440
\(650\) 31.4445 1.23336
\(651\) −0.522856 −0.0204924
\(652\) 9.12434 0.357337
\(653\) 8.05822 0.315342 0.157671 0.987492i \(-0.449601\pi\)
0.157671 + 0.987492i \(0.449601\pi\)
\(654\) 0.0681002 0.00266293
\(655\) −5.05558 −0.197538
\(656\) −2.25583 −0.0880754
\(657\) −20.2276 −0.789154
\(658\) −1.12250 −0.0437596
\(659\) −14.1844 −0.552546 −0.276273 0.961079i \(-0.589099\pi\)
−0.276273 + 0.961079i \(0.589099\pi\)
\(660\) 0.193331 0.00752541
\(661\) 4.22367 0.164282 0.0821409 0.996621i \(-0.473824\pi\)
0.0821409 + 0.996621i \(0.473824\pi\)
\(662\) 36.0637 1.40165
\(663\) −15.3822 −0.597395
\(664\) −37.2539 −1.44573
\(665\) 0.150717 0.00584457
\(666\) 13.7265 0.531892
\(667\) 8.86978 0.343439
\(668\) −3.29418 −0.127456
\(669\) 6.47412 0.250304
\(670\) 0.937119 0.0362041
\(671\) 11.6283 0.448905
\(672\) 0.418643 0.0161495
\(673\) 20.8298 0.802931 0.401466 0.915874i \(-0.368501\pi\)
0.401466 + 0.915874i \(0.368501\pi\)
\(674\) −7.46339 −0.287479
\(675\) −17.4942 −0.673352
\(676\) −9.53163 −0.366601
\(677\) −33.4563 −1.28583 −0.642914 0.765938i \(-0.722275\pi\)
−0.642914 + 0.765938i \(0.722275\pi\)
\(678\) −13.3342 −0.512096
\(679\) −1.01280 −0.0388675
\(680\) −4.83179 −0.185291
\(681\) 18.2562 0.699578
\(682\) 6.86368 0.262824
\(683\) 26.1033 0.998814 0.499407 0.866368i \(-0.333551\pi\)
0.499407 + 0.866368i \(0.333551\pi\)
\(684\) −3.11334 −0.119042
\(685\) −2.02926 −0.0775339
\(686\) 3.40804 0.130120
\(687\) 0.986257 0.0376280
\(688\) 18.3119 0.698135
\(689\) 27.1801 1.03548
\(690\) 2.41338 0.0918758
\(691\) −51.1642 −1.94638 −0.973188 0.230010i \(-0.926124\pi\)
−0.973188 + 0.230010i \(0.926124\pi\)
\(692\) 4.43604 0.168633
\(693\) 0.770720 0.0292772
\(694\) 20.3090 0.770920
\(695\) 0.355693 0.0134922
\(696\) 1.97542 0.0748780
\(697\) 3.99286 0.151241
\(698\) 17.8339 0.675023
\(699\) 9.45232 0.357519
\(700\) 0.582041 0.0219991
\(701\) 4.35600 0.164524 0.0822618 0.996611i \(-0.473786\pi\)
0.0822618 + 0.996611i \(0.473786\pi\)
\(702\) −23.1612 −0.874162
\(703\) −9.20729 −0.347259
\(704\) −12.7474 −0.480436
\(705\) 1.05060 0.0395678
\(706\) −30.4189 −1.14483
\(707\) −3.52489 −0.132567
\(708\) 5.23932 0.196906
\(709\) 21.2807 0.799212 0.399606 0.916687i \(-0.369147\pi\)
0.399606 + 0.916687i \(0.369147\pi\)
\(710\) 5.97141 0.224103
\(711\) −11.4039 −0.427679
\(712\) 1.28453 0.0481396
\(713\) −35.1992 −1.31822
\(714\) 0.693067 0.0259374
\(715\) 2.80002 0.104715
\(716\) −7.85196 −0.293441
\(717\) 6.15452 0.229845
\(718\) 14.5292 0.542225
\(719\) 10.9571 0.408631 0.204315 0.978905i \(-0.434503\pi\)
0.204315 + 0.978905i \(0.434503\pi\)
\(720\) −2.29702 −0.0856047
\(721\) 2.52252 0.0939436
\(722\) 17.5388 0.652726
\(723\) 16.0384 0.596476
\(724\) 0.120588 0.00448163
\(725\) 4.87348 0.180997
\(726\) −6.80035 −0.252385
\(727\) 13.3017 0.493333 0.246666 0.969100i \(-0.420665\pi\)
0.246666 + 0.969100i \(0.420665\pi\)
\(728\) 3.41689 0.126638
\(729\) −7.19542 −0.266497
\(730\) 3.31105 0.122547
\(731\) −32.4124 −1.19882
\(732\) −2.99519 −0.110706
\(733\) −19.3193 −0.713574 −0.356787 0.934186i \(-0.616128\pi\)
−0.356787 + 0.934186i \(0.616128\pi\)
\(734\) −24.2569 −0.895339
\(735\) −1.59007 −0.0586504
\(736\) 28.1834 1.03885
\(737\) −3.21439 −0.118404
\(738\) 2.78397 0.102479
\(739\) 34.2719 1.26071 0.630356 0.776306i \(-0.282909\pi\)
0.630356 + 0.776306i \(0.282909\pi\)
\(740\) 0.923067 0.0339326
\(741\) 7.19398 0.264277
\(742\) −1.22464 −0.0449580
\(743\) 45.8795 1.68316 0.841578 0.540135i \(-0.181627\pi\)
0.841578 + 0.540135i \(0.181627\pi\)
\(744\) −7.83932 −0.287403
\(745\) 3.55044 0.130078
\(746\) 9.53862 0.349234
\(747\) 31.3476 1.14695
\(748\) 3.73767 0.136663
\(749\) 1.95703 0.0715085
\(750\) 2.68648 0.0980964
\(751\) −29.2344 −1.06678 −0.533389 0.845870i \(-0.679082\pi\)
−0.533389 + 0.845870i \(0.679082\pi\)
\(752\) −11.4751 −0.418455
\(753\) −10.7616 −0.392175
\(754\) 6.45217 0.234974
\(755\) −2.61555 −0.0951896
\(756\) −0.428715 −0.0155922
\(757\) −2.24805 −0.0817067 −0.0408533 0.999165i \(-0.513008\pi\)
−0.0408533 + 0.999165i \(0.513008\pi\)
\(758\) 21.8062 0.792037
\(759\) −8.27808 −0.300475
\(760\) 2.25974 0.0819695
\(761\) −30.9130 −1.12059 −0.560297 0.828292i \(-0.689313\pi\)
−0.560297 + 0.828292i \(0.689313\pi\)
\(762\) −11.9390 −0.432505
\(763\) 0.0182564 0.000660926 0
\(764\) 7.31177 0.264531
\(765\) 4.06576 0.146998
\(766\) 34.1769 1.23486
\(767\) 75.8810 2.73990
\(768\) 8.14471 0.293897
\(769\) 23.7353 0.855918 0.427959 0.903798i \(-0.359233\pi\)
0.427959 + 0.903798i \(0.359233\pi\)
\(770\) −0.126159 −0.00454645
\(771\) −18.8926 −0.680401
\(772\) 6.78062 0.244040
\(773\) 16.1748 0.581767 0.290883 0.956759i \(-0.406051\pi\)
0.290883 + 0.956759i \(0.406051\pi\)
\(774\) −22.5991 −0.812309
\(775\) −19.3401 −0.694717
\(776\) −15.1851 −0.545113
\(777\) −0.587098 −0.0210620
\(778\) −9.65301 −0.346077
\(779\) −1.86739 −0.0669063
\(780\) −0.721224 −0.0258240
\(781\) −20.4824 −0.732918
\(782\) 46.6579 1.66848
\(783\) −3.58967 −0.128284
\(784\) 17.3674 0.620266
\(785\) 5.89457 0.210386
\(786\) 10.8726 0.387813
\(787\) 10.7081 0.381704 0.190852 0.981619i \(-0.438875\pi\)
0.190852 + 0.981619i \(0.438875\pi\)
\(788\) 1.46642 0.0522390
\(789\) −7.44824 −0.265164
\(790\) 1.86670 0.0664141
\(791\) −3.57465 −0.127100
\(792\) 11.5556 0.410610
\(793\) −43.3794 −1.54045
\(794\) 39.4242 1.39911
\(795\) 1.14620 0.0406514
\(796\) −5.39868 −0.191351
\(797\) 35.3402 1.25181 0.625907 0.779898i \(-0.284729\pi\)
0.625907 + 0.779898i \(0.284729\pi\)
\(798\) −0.324135 −0.0114743
\(799\) 20.3112 0.718558
\(800\) 15.4853 0.547488
\(801\) −1.08088 −0.0381909
\(802\) 14.2899 0.504593
\(803\) −11.3572 −0.400785
\(804\) 0.827958 0.0291998
\(805\) 0.646982 0.0228031
\(806\) −25.6050 −0.901899
\(807\) 0.582086 0.0204904
\(808\) −52.8496 −1.85924
\(809\) 17.6977 0.622219 0.311110 0.950374i \(-0.399299\pi\)
0.311110 + 0.950374i \(0.399299\pi\)
\(810\) 2.31036 0.0811778
\(811\) −13.9831 −0.491014 −0.245507 0.969395i \(-0.578954\pi\)
−0.245507 + 0.969395i \(0.578954\pi\)
\(812\) 0.119430 0.00419118
\(813\) 13.5727 0.476016
\(814\) 7.70700 0.270130
\(815\) 5.57272 0.195204
\(816\) 7.08511 0.248028
\(817\) 15.1587 0.530337
\(818\) −8.77108 −0.306674
\(819\) −2.87518 −0.100467
\(820\) 0.187213 0.00653777
\(821\) 23.4837 0.819587 0.409794 0.912178i \(-0.365601\pi\)
0.409794 + 0.912178i \(0.365601\pi\)
\(822\) 4.36415 0.152217
\(823\) −28.7877 −1.00348 −0.501738 0.865019i \(-0.667306\pi\)
−0.501738 + 0.865019i \(0.667306\pi\)
\(824\) 37.8208 1.31755
\(825\) −4.54838 −0.158354
\(826\) −3.41893 −0.118960
\(827\) −5.66883 −0.197124 −0.0985622 0.995131i \(-0.531424\pi\)
−0.0985622 + 0.995131i \(0.531424\pi\)
\(828\) −13.3646 −0.464452
\(829\) −54.0910 −1.87866 −0.939328 0.343019i \(-0.888550\pi\)
−0.939328 + 0.343019i \(0.888550\pi\)
\(830\) −5.13128 −0.178109
\(831\) −2.30967 −0.0801216
\(832\) 47.5543 1.64865
\(833\) −30.7407 −1.06510
\(834\) −0.764958 −0.0264883
\(835\) −2.01193 −0.0696258
\(836\) −1.74804 −0.0604573
\(837\) 14.2454 0.492392
\(838\) 31.2110 1.07817
\(839\) 11.5242 0.397860 0.198930 0.980014i \(-0.436253\pi\)
0.198930 + 0.980014i \(0.436253\pi\)
\(840\) 0.144092 0.00497163
\(841\) 1.00000 0.0344828
\(842\) 2.91418 0.100429
\(843\) 14.2930 0.492277
\(844\) −12.8253 −0.441465
\(845\) −5.82147 −0.200265
\(846\) 14.1617 0.486889
\(847\) −1.82305 −0.0626406
\(848\) −12.5193 −0.429915
\(849\) −4.92858 −0.169148
\(850\) 25.6361 0.879310
\(851\) −39.5240 −1.35486
\(852\) 5.27583 0.180747
\(853\) 12.5581 0.429983 0.214991 0.976616i \(-0.431028\pi\)
0.214991 + 0.976616i \(0.431028\pi\)
\(854\) 1.95452 0.0668823
\(855\) −1.90148 −0.0650294
\(856\) 29.3423 1.00290
\(857\) 7.46078 0.254855 0.127428 0.991848i \(-0.459328\pi\)
0.127428 + 0.991848i \(0.459328\pi\)
\(858\) −6.02175 −0.205579
\(859\) −46.2580 −1.57830 −0.789151 0.614199i \(-0.789479\pi\)
−0.789151 + 0.614199i \(0.789479\pi\)
\(860\) −1.51972 −0.0518221
\(861\) −0.119073 −0.00405801
\(862\) 34.9121 1.18911
\(863\) 19.8442 0.675506 0.337753 0.941235i \(-0.390333\pi\)
0.337753 + 0.941235i \(0.390333\pi\)
\(864\) −11.4060 −0.388041
\(865\) 2.70933 0.0921199
\(866\) 18.6245 0.632886
\(867\) −1.61864 −0.0549720
\(868\) −0.473951 −0.0160870
\(869\) −6.40291 −0.217204
\(870\) 0.272090 0.00922473
\(871\) 11.9913 0.406310
\(872\) 0.273723 0.00926942
\(873\) 12.7776 0.432458
\(874\) −21.8211 −0.738108
\(875\) 0.720195 0.0243470
\(876\) 2.92536 0.0988387
\(877\) −16.0313 −0.541338 −0.270669 0.962673i \(-0.587245\pi\)
−0.270669 + 0.962673i \(0.587245\pi\)
\(878\) −26.2175 −0.884798
\(879\) 16.7491 0.564934
\(880\) −1.28970 −0.0434758
\(881\) 17.5709 0.591979 0.295989 0.955191i \(-0.404351\pi\)
0.295989 + 0.955191i \(0.404351\pi\)
\(882\) −21.4335 −0.721705
\(883\) −1.81821 −0.0611876 −0.0305938 0.999532i \(-0.509740\pi\)
−0.0305938 + 0.999532i \(0.509740\pi\)
\(884\) −13.9434 −0.468968
\(885\) 3.19993 0.107564
\(886\) 6.97128 0.234205
\(887\) 17.5395 0.588918 0.294459 0.955664i \(-0.404861\pi\)
0.294459 + 0.955664i \(0.404861\pi\)
\(888\) −8.80251 −0.295393
\(889\) −3.20063 −0.107346
\(890\) 0.176928 0.00593065
\(891\) −7.92471 −0.265488
\(892\) 5.86856 0.196494
\(893\) −9.49918 −0.317878
\(894\) −7.63563 −0.255374
\(895\) −4.79561 −0.160299
\(896\) −0.839416 −0.0280429
\(897\) 30.8815 1.03110
\(898\) −32.2352 −1.07570
\(899\) −3.96844 −0.132355
\(900\) −7.34316 −0.244772
\(901\) 22.1594 0.738237
\(902\) 1.56311 0.0520458
\(903\) 0.966589 0.0321661
\(904\) −53.5956 −1.78256
\(905\) 0.0736496 0.00244820
\(906\) 5.62504 0.186879
\(907\) −7.75346 −0.257449 −0.128725 0.991680i \(-0.541088\pi\)
−0.128725 + 0.991680i \(0.541088\pi\)
\(908\) 16.5486 0.549184
\(909\) 44.4708 1.47500
\(910\) 0.470636 0.0156014
\(911\) 57.4872 1.90464 0.952318 0.305107i \(-0.0986923\pi\)
0.952318 + 0.305107i \(0.0986923\pi\)
\(912\) −3.31358 −0.109724
\(913\) 17.6007 0.582498
\(914\) 24.4421 0.808472
\(915\) −1.82932 −0.0604756
\(916\) 0.894008 0.0295388
\(917\) 2.91474 0.0962533
\(918\) −18.8828 −0.623226
\(919\) −3.08439 −0.101745 −0.0508723 0.998705i \(-0.516200\pi\)
−0.0508723 + 0.998705i \(0.516200\pi\)
\(920\) 9.70037 0.319812
\(921\) −8.10271 −0.266993
\(922\) 12.1826 0.401214
\(923\) 76.4098 2.51506
\(924\) −0.111463 −0.00366687
\(925\) −21.7164 −0.714030
\(926\) −15.3597 −0.504752
\(927\) −31.8247 −1.04526
\(928\) 3.17746 0.104305
\(929\) −26.2372 −0.860814 −0.430407 0.902635i \(-0.641630\pi\)
−0.430407 + 0.902635i \(0.641630\pi\)
\(930\) −1.07977 −0.0354072
\(931\) 14.3769 0.471183
\(932\) 8.56820 0.280661
\(933\) 6.53079 0.213808
\(934\) −40.7288 −1.33269
\(935\) 2.28279 0.0746554
\(936\) −43.1082 −1.40904
\(937\) 12.3864 0.404648 0.202324 0.979319i \(-0.435151\pi\)
0.202324 + 0.979319i \(0.435151\pi\)
\(938\) −0.540286 −0.0176410
\(939\) 7.77996 0.253889
\(940\) 0.952330 0.0310616
\(941\) −47.8943 −1.56131 −0.780655 0.624962i \(-0.785115\pi\)
−0.780655 + 0.624962i \(0.785115\pi\)
\(942\) −12.6769 −0.413037
\(943\) −8.01612 −0.261041
\(944\) −34.9511 −1.13756
\(945\) −0.261839 −0.00851762
\(946\) −12.6887 −0.412545
\(947\) 36.5231 1.18684 0.593421 0.804892i \(-0.297777\pi\)
0.593421 + 0.804892i \(0.297777\pi\)
\(948\) 1.64925 0.0535653
\(949\) 42.3680 1.37532
\(950\) −11.9895 −0.388992
\(951\) 5.61699 0.182144
\(952\) 2.78572 0.0902857
\(953\) 44.0856 1.42807 0.714037 0.700108i \(-0.246865\pi\)
0.714037 + 0.700108i \(0.246865\pi\)
\(954\) 15.4503 0.500223
\(955\) 4.46569 0.144506
\(956\) 5.57886 0.180433
\(957\) −0.933291 −0.0301690
\(958\) −28.3957 −0.917423
\(959\) 1.16995 0.0377795
\(960\) 2.00538 0.0647234
\(961\) −15.2515 −0.491984
\(962\) −28.7510 −0.926971
\(963\) −24.6904 −0.795636
\(964\) 14.5383 0.468247
\(965\) 4.14128 0.133313
\(966\) −1.39141 −0.0447679
\(967\) −30.2021 −0.971235 −0.485618 0.874171i \(-0.661405\pi\)
−0.485618 + 0.874171i \(0.661405\pi\)
\(968\) −27.3334 −0.878529
\(969\) 5.86510 0.188414
\(970\) −2.09157 −0.0671562
\(971\) −13.0542 −0.418928 −0.209464 0.977816i \(-0.567172\pi\)
−0.209464 + 0.977816i \(0.567172\pi\)
\(972\) 8.31294 0.266638
\(973\) −0.205071 −0.00657428
\(974\) 11.6772 0.374161
\(975\) 16.9678 0.543403
\(976\) 19.9807 0.639568
\(977\) 8.03930 0.257200 0.128600 0.991697i \(-0.458952\pi\)
0.128600 + 0.991697i \(0.458952\pi\)
\(978\) −11.9848 −0.383231
\(979\) −0.606878 −0.0193959
\(980\) −1.44134 −0.0460419
\(981\) −0.230327 −0.00735377
\(982\) −29.7015 −0.947815
\(983\) 23.5683 0.751713 0.375857 0.926678i \(-0.377348\pi\)
0.375857 + 0.926678i \(0.377348\pi\)
\(984\) −1.78530 −0.0569132
\(985\) 0.895620 0.0285368
\(986\) 5.26032 0.167523
\(987\) −0.605711 −0.0192800
\(988\) 6.52109 0.207463
\(989\) 65.0716 2.06916
\(990\) 1.59165 0.0505859
\(991\) −21.7888 −0.692143 −0.346071 0.938208i \(-0.612484\pi\)
−0.346071 + 0.938208i \(0.612484\pi\)
\(992\) −12.6096 −0.400354
\(993\) 19.4603 0.617554
\(994\) −3.44275 −0.109198
\(995\) −3.29726 −0.104530
\(996\) −4.53356 −0.143651
\(997\) 54.9267 1.73955 0.869773 0.493452i \(-0.164265\pi\)
0.869773 + 0.493452i \(0.164265\pi\)
\(998\) −30.8819 −0.977549
\(999\) 15.9957 0.506080
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 \(a_p\))