Properties

Label 4019.2.a.b.1.16
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.43886 q^{2}\) \(-0.628245 q^{3}\) \(+3.94805 q^{4}\) \(+3.87591 q^{5}\) \(+1.53220 q^{6}\) \(-4.09962 q^{7}\) \(-4.75103 q^{8}\) \(-2.60531 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.43886 q^{2}\) \(-0.628245 q^{3}\) \(+3.94805 q^{4}\) \(+3.87591 q^{5}\) \(+1.53220 q^{6}\) \(-4.09962 q^{7}\) \(-4.75103 q^{8}\) \(-2.60531 q^{9}\) \(-9.45281 q^{10}\) \(-2.21292 q^{11}\) \(-2.48034 q^{12}\) \(+1.62769 q^{13}\) \(+9.99840 q^{14}\) \(-2.43502 q^{15}\) \(+3.69100 q^{16}\) \(+6.22231 q^{17}\) \(+6.35399 q^{18}\) \(+2.20181 q^{19}\) \(+15.3023 q^{20}\) \(+2.57556 q^{21}\) \(+5.39702 q^{22}\) \(+3.51792 q^{23}\) \(+2.98481 q^{24}\) \(+10.0227 q^{25}\) \(-3.96970 q^{26}\) \(+3.52150 q^{27}\) \(-16.1855 q^{28}\) \(-1.15470 q^{29}\) \(+5.93868 q^{30}\) \(+5.67640 q^{31}\) \(+0.500206 q^{32}\) \(+1.39026 q^{33}\) \(-15.1754 q^{34}\) \(-15.8897 q^{35}\) \(-10.2859 q^{36}\) \(-11.2931 q^{37}\) \(-5.36992 q^{38}\) \(-1.02259 q^{39}\) \(-18.4146 q^{40}\) \(+6.68311 q^{41}\) \(-6.28144 q^{42}\) \(-4.36322 q^{43}\) \(-8.73674 q^{44}\) \(-10.0979 q^{45}\) \(-8.57973 q^{46}\) \(-5.80689 q^{47}\) \(-2.31885 q^{48}\) \(+9.80686 q^{49}\) \(-24.4439 q^{50}\) \(-3.90913 q^{51}\) \(+6.42619 q^{52}\) \(+8.19329 q^{53}\) \(-8.58847 q^{54}\) \(-8.57709 q^{55}\) \(+19.4774 q^{56}\) \(-1.38328 q^{57}\) \(+2.81617 q^{58}\) \(+2.69786 q^{59}\) \(-9.61358 q^{60}\) \(-9.72805 q^{61}\) \(-13.8440 q^{62}\) \(+10.6808 q^{63}\) \(-8.60194 q^{64}\) \(+6.30877 q^{65}\) \(-3.39065 q^{66}\) \(-8.40586 q^{67}\) \(+24.5660 q^{68}\) \(-2.21012 q^{69}\) \(+38.7529 q^{70}\) \(-15.5834 q^{71}\) \(+12.3779 q^{72}\) \(+11.0703 q^{73}\) \(+27.5424 q^{74}\) \(-6.29669 q^{75}\) \(+8.69287 q^{76}\) \(+9.07214 q^{77}\) \(+2.49394 q^{78}\) \(-5.03435 q^{79}\) \(+14.3060 q^{80}\) \(+5.60356 q^{81}\) \(-16.2992 q^{82}\) \(-9.40283 q^{83}\) \(+10.1685 q^{84}\) \(+24.1171 q^{85}\) \(+10.6413 q^{86}\) \(+0.725437 q^{87}\) \(+10.5137 q^{88}\) \(+11.8335 q^{89}\) \(+24.6275 q^{90}\) \(-6.67289 q^{91}\) \(+13.8889 q^{92}\) \(-3.56617 q^{93}\) \(+14.1622 q^{94}\) \(+8.53402 q^{95}\) \(-0.314252 q^{96}\) \(-6.70100 q^{97}\) \(-23.9176 q^{98}\) \(+5.76535 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43886 −1.72454 −0.862268 0.506452i \(-0.830957\pi\)
−0.862268 + 0.506452i \(0.830957\pi\)
\(3\) −0.628245 −0.362717 −0.181359 0.983417i \(-0.558049\pi\)
−0.181359 + 0.983417i \(0.558049\pi\)
\(4\) 3.94805 1.97403
\(5\) 3.87591 1.73336 0.866680 0.498865i \(-0.166250\pi\)
0.866680 + 0.498865i \(0.166250\pi\)
\(6\) 1.53220 0.625519
\(7\) −4.09962 −1.54951 −0.774755 0.632262i \(-0.782127\pi\)
−0.774755 + 0.632262i \(0.782127\pi\)
\(8\) −4.75103 −1.67974
\(9\) −2.60531 −0.868436
\(10\) −9.45281 −2.98924
\(11\) −2.21292 −0.667222 −0.333611 0.942711i \(-0.608267\pi\)
−0.333611 + 0.942711i \(0.608267\pi\)
\(12\) −2.48034 −0.716013
\(13\) 1.62769 0.451439 0.225720 0.974192i \(-0.427527\pi\)
0.225720 + 0.974192i \(0.427527\pi\)
\(14\) 9.99840 2.67219
\(15\) −2.43502 −0.628719
\(16\) 3.69100 0.922751
\(17\) 6.22231 1.50913 0.754566 0.656224i \(-0.227847\pi\)
0.754566 + 0.656224i \(0.227847\pi\)
\(18\) 6.35399 1.49765
\(19\) 2.20181 0.505130 0.252565 0.967580i \(-0.418726\pi\)
0.252565 + 0.967580i \(0.418726\pi\)
\(20\) 15.3023 3.42170
\(21\) 2.57556 0.562034
\(22\) 5.39702 1.15065
\(23\) 3.51792 0.733537 0.366769 0.930312i \(-0.380464\pi\)
0.366769 + 0.930312i \(0.380464\pi\)
\(24\) 2.98481 0.609271
\(25\) 10.0227 2.00453
\(26\) −3.96970 −0.778523
\(27\) 3.52150 0.677714
\(28\) −16.1855 −3.05877
\(29\) −1.15470 −0.214423 −0.107212 0.994236i \(-0.534192\pi\)
−0.107212 + 0.994236i \(0.534192\pi\)
\(30\) 5.93868 1.08425
\(31\) 5.67640 1.01951 0.509756 0.860319i \(-0.329736\pi\)
0.509756 + 0.860319i \(0.329736\pi\)
\(32\) 0.500206 0.0884247
\(33\) 1.39026 0.242013
\(34\) −15.1754 −2.60255
\(35\) −15.8897 −2.68586
\(36\) −10.2859 −1.71432
\(37\) −11.2931 −1.85658 −0.928291 0.371855i \(-0.878722\pi\)
−0.928291 + 0.371855i \(0.878722\pi\)
\(38\) −5.36992 −0.871116
\(39\) −1.02259 −0.163745
\(40\) −18.4146 −2.91160
\(41\) 6.68311 1.04373 0.521863 0.853029i \(-0.325237\pi\)
0.521863 + 0.853029i \(0.325237\pi\)
\(42\) −6.28144 −0.969248
\(43\) −4.36322 −0.665385 −0.332693 0.943035i \(-0.607957\pi\)
−0.332693 + 0.943035i \(0.607957\pi\)
\(44\) −8.73674 −1.31711
\(45\) −10.0979 −1.50531
\(46\) −8.57973 −1.26501
\(47\) −5.80689 −0.847021 −0.423511 0.905891i \(-0.639202\pi\)
−0.423511 + 0.905891i \(0.639202\pi\)
\(48\) −2.31885 −0.334698
\(49\) 9.80686 1.40098
\(50\) −24.4439 −3.45689
\(51\) −3.90913 −0.547388
\(52\) 6.42619 0.891152
\(53\) 8.19329 1.12543 0.562717 0.826649i \(-0.309756\pi\)
0.562717 + 0.826649i \(0.309756\pi\)
\(54\) −8.58847 −1.16874
\(55\) −8.57709 −1.15654
\(56\) 19.4774 2.60278
\(57\) −1.38328 −0.183219
\(58\) 2.81617 0.369781
\(59\) 2.69786 0.351232 0.175616 0.984459i \(-0.443808\pi\)
0.175616 + 0.984459i \(0.443808\pi\)
\(60\) −9.61358 −1.24111
\(61\) −9.72805 −1.24555 −0.622775 0.782401i \(-0.713995\pi\)
−0.622775 + 0.782401i \(0.713995\pi\)
\(62\) −13.8440 −1.75818
\(63\) 10.6808 1.34565
\(64\) −8.60194 −1.07524
\(65\) 6.30877 0.782506
\(66\) −3.39065 −0.417360
\(67\) −8.40586 −1.02694 −0.513470 0.858108i \(-0.671640\pi\)
−0.513470 + 0.858108i \(0.671640\pi\)
\(68\) 24.5660 2.97907
\(69\) −2.21012 −0.266067
\(70\) 38.7529 4.63186
\(71\) −15.5834 −1.84941 −0.924705 0.380684i \(-0.875689\pi\)
−0.924705 + 0.380684i \(0.875689\pi\)
\(72\) 12.3779 1.45875
\(73\) 11.0703 1.29568 0.647839 0.761777i \(-0.275673\pi\)
0.647839 + 0.761777i \(0.275673\pi\)
\(74\) 27.5424 3.20174
\(75\) −6.29669 −0.727079
\(76\) 8.69287 0.997140
\(77\) 9.07214 1.03387
\(78\) 2.49394 0.282384
\(79\) −5.03435 −0.566409 −0.283204 0.959060i \(-0.591398\pi\)
−0.283204 + 0.959060i \(0.591398\pi\)
\(80\) 14.3060 1.59946
\(81\) 5.60356 0.622618
\(82\) −16.2992 −1.79994
\(83\) −9.40283 −1.03209 −0.516047 0.856560i \(-0.672597\pi\)
−0.516047 + 0.856560i \(0.672597\pi\)
\(84\) 10.1685 1.10947
\(85\) 24.1171 2.61587
\(86\) 10.6413 1.14748
\(87\) 0.725437 0.0777750
\(88\) 10.5137 1.12076
\(89\) 11.8335 1.25435 0.627174 0.778879i \(-0.284212\pi\)
0.627174 + 0.778879i \(0.284212\pi\)
\(90\) 24.6275 2.59597
\(91\) −6.67289 −0.699509
\(92\) 13.8889 1.44802
\(93\) −3.56617 −0.369794
\(94\) 14.1622 1.46072
\(95\) 8.53402 0.875572
\(96\) −0.314252 −0.0320732
\(97\) −6.70100 −0.680383 −0.340192 0.940356i \(-0.610492\pi\)
−0.340192 + 0.940356i \(0.610492\pi\)
\(98\) −23.9176 −2.41604
\(99\) 5.76535 0.579440
\(100\) 39.5700 3.95700
\(101\) 13.5965 1.35290 0.676450 0.736489i \(-0.263518\pi\)
0.676450 + 0.736489i \(0.263518\pi\)
\(102\) 9.53384 0.943991
\(103\) 1.60985 0.158624 0.0793119 0.996850i \(-0.474728\pi\)
0.0793119 + 0.996850i \(0.474728\pi\)
\(104\) −7.73319 −0.758301
\(105\) 9.98264 0.974206
\(106\) −19.9823 −1.94085
\(107\) 0.759987 0.0734708 0.0367354 0.999325i \(-0.488304\pi\)
0.0367354 + 0.999325i \(0.488304\pi\)
\(108\) 13.9031 1.33782
\(109\) 13.3165 1.27549 0.637744 0.770248i \(-0.279868\pi\)
0.637744 + 0.770248i \(0.279868\pi\)
\(110\) 20.9184 1.99449
\(111\) 7.09486 0.673414
\(112\) −15.1317 −1.42981
\(113\) −8.56360 −0.805596 −0.402798 0.915289i \(-0.631962\pi\)
−0.402798 + 0.915289i \(0.631962\pi\)
\(114\) 3.37362 0.315969
\(115\) 13.6351 1.27148
\(116\) −4.55883 −0.423277
\(117\) −4.24063 −0.392046
\(118\) −6.57971 −0.605712
\(119\) −25.5091 −2.33842
\(120\) 11.5688 1.05609
\(121\) −6.10297 −0.554815
\(122\) 23.7254 2.14799
\(123\) −4.19863 −0.378578
\(124\) 22.4107 2.01254
\(125\) 19.4674 1.74122
\(126\) −26.0489 −2.32062
\(127\) −20.8677 −1.85171 −0.925854 0.377882i \(-0.876652\pi\)
−0.925854 + 0.377882i \(0.876652\pi\)
\(128\) 19.9785 1.76587
\(129\) 2.74117 0.241347
\(130\) −15.3862 −1.34946
\(131\) 10.0230 0.875715 0.437857 0.899044i \(-0.355737\pi\)
0.437857 + 0.899044i \(0.355737\pi\)
\(132\) 5.48881 0.477739
\(133\) −9.02659 −0.782704
\(134\) 20.5007 1.77099
\(135\) 13.6490 1.17472
\(136\) −29.5624 −2.53495
\(137\) −3.80142 −0.324777 −0.162389 0.986727i \(-0.551920\pi\)
−0.162389 + 0.986727i \(0.551920\pi\)
\(138\) 5.39017 0.458842
\(139\) 5.68409 0.482119 0.241059 0.970510i \(-0.422505\pi\)
0.241059 + 0.970510i \(0.422505\pi\)
\(140\) −62.7335 −5.30195
\(141\) 3.64814 0.307229
\(142\) 38.0058 3.18938
\(143\) −3.60195 −0.301210
\(144\) −9.61620 −0.801350
\(145\) −4.47553 −0.371673
\(146\) −26.9989 −2.23444
\(147\) −6.16111 −0.508160
\(148\) −44.5859 −3.66494
\(149\) −9.66764 −0.792004 −0.396002 0.918250i \(-0.629603\pi\)
−0.396002 + 0.918250i \(0.629603\pi\)
\(150\) 15.3568 1.25387
\(151\) 19.4769 1.58500 0.792502 0.609869i \(-0.208778\pi\)
0.792502 + 0.609869i \(0.208778\pi\)
\(152\) −10.4609 −0.848489
\(153\) −16.2110 −1.31059
\(154\) −22.1257 −1.78294
\(155\) 22.0012 1.76718
\(156\) −4.03722 −0.323236
\(157\) 1.76005 0.140467 0.0702334 0.997531i \(-0.477626\pi\)
0.0702334 + 0.997531i \(0.477626\pi\)
\(158\) 12.2781 0.976793
\(159\) −5.14739 −0.408215
\(160\) 1.93875 0.153272
\(161\) −14.4221 −1.13662
\(162\) −13.6663 −1.07373
\(163\) 8.12353 0.636284 0.318142 0.948043i \(-0.396941\pi\)
0.318142 + 0.948043i \(0.396941\pi\)
\(164\) 26.3853 2.06034
\(165\) 5.38851 0.419495
\(166\) 22.9322 1.77988
\(167\) 22.1876 1.71693 0.858464 0.512873i \(-0.171419\pi\)
0.858464 + 0.512873i \(0.171419\pi\)
\(168\) −12.2366 −0.944072
\(169\) −10.3506 −0.796203
\(170\) −58.8183 −4.51116
\(171\) −5.73640 −0.438673
\(172\) −17.2262 −1.31349
\(173\) −9.30584 −0.707510 −0.353755 0.935338i \(-0.615095\pi\)
−0.353755 + 0.935338i \(0.615095\pi\)
\(174\) −1.76924 −0.134126
\(175\) −41.0891 −3.10605
\(176\) −8.16791 −0.615680
\(177\) −1.69492 −0.127398
\(178\) −28.8603 −2.16317
\(179\) 1.19714 0.0894786 0.0447393 0.998999i \(-0.485754\pi\)
0.0447393 + 0.998999i \(0.485754\pi\)
\(180\) −39.8672 −2.97152
\(181\) 20.4926 1.52321 0.761603 0.648044i \(-0.224413\pi\)
0.761603 + 0.648044i \(0.224413\pi\)
\(182\) 16.2743 1.20633
\(183\) 6.11159 0.451782
\(184\) −16.7137 −1.23215
\(185\) −43.7712 −3.21812
\(186\) 8.69739 0.637723
\(187\) −13.7695 −1.00693
\(188\) −22.9259 −1.67204
\(189\) −14.4368 −1.05012
\(190\) −20.8133 −1.50996
\(191\) 11.0771 0.801509 0.400754 0.916186i \(-0.368748\pi\)
0.400754 + 0.916186i \(0.368748\pi\)
\(192\) 5.40412 0.390009
\(193\) 19.4580 1.40061 0.700307 0.713841i \(-0.253046\pi\)
0.700307 + 0.713841i \(0.253046\pi\)
\(194\) 16.3428 1.17335
\(195\) −3.96345 −0.283828
\(196\) 38.7180 2.76557
\(197\) 11.4181 0.813503 0.406752 0.913539i \(-0.366661\pi\)
0.406752 + 0.913539i \(0.366661\pi\)
\(198\) −14.0609 −0.999265
\(199\) 20.0999 1.42485 0.712423 0.701751i \(-0.247598\pi\)
0.712423 + 0.701751i \(0.247598\pi\)
\(200\) −47.6180 −3.36710
\(201\) 5.28094 0.372489
\(202\) −33.1599 −2.33312
\(203\) 4.73385 0.332251
\(204\) −15.4335 −1.08056
\(205\) 25.9031 1.80915
\(206\) −3.92621 −0.273552
\(207\) −9.16527 −0.637031
\(208\) 6.00780 0.416566
\(209\) −4.87244 −0.337034
\(210\) −24.3463 −1.68005
\(211\) 21.0824 1.45137 0.725685 0.688027i \(-0.241523\pi\)
0.725685 + 0.688027i \(0.241523\pi\)
\(212\) 32.3475 2.22164
\(213\) 9.79019 0.670813
\(214\) −1.85350 −0.126703
\(215\) −16.9115 −1.15335
\(216\) −16.7308 −1.13838
\(217\) −23.2711 −1.57974
\(218\) −32.4771 −2.19963
\(219\) −6.95484 −0.469965
\(220\) −33.8628 −2.28303
\(221\) 10.1280 0.681281
\(222\) −17.3034 −1.16133
\(223\) 12.6501 0.847111 0.423555 0.905870i \(-0.360782\pi\)
0.423555 + 0.905870i \(0.360782\pi\)
\(224\) −2.05065 −0.137015
\(225\) −26.1122 −1.74081
\(226\) 20.8855 1.38928
\(227\) 0.455889 0.0302584 0.0151292 0.999886i \(-0.495184\pi\)
0.0151292 + 0.999886i \(0.495184\pi\)
\(228\) −5.46125 −0.361680
\(229\) 4.05325 0.267846 0.133923 0.990992i \(-0.457242\pi\)
0.133923 + 0.990992i \(0.457242\pi\)
\(230\) −33.2542 −2.19272
\(231\) −5.69952 −0.375001
\(232\) 5.48604 0.360176
\(233\) 2.02974 0.132973 0.0664865 0.997787i \(-0.478821\pi\)
0.0664865 + 0.997787i \(0.478821\pi\)
\(234\) 10.3423 0.676098
\(235\) −22.5070 −1.46819
\(236\) 10.6513 0.693340
\(237\) 3.16280 0.205446
\(238\) 62.2132 4.03268
\(239\) −2.94077 −0.190223 −0.0951114 0.995467i \(-0.530321\pi\)
−0.0951114 + 0.995467i \(0.530321\pi\)
\(240\) −8.98766 −0.580151
\(241\) −1.99108 −0.128257 −0.0641285 0.997942i \(-0.520427\pi\)
−0.0641285 + 0.997942i \(0.520427\pi\)
\(242\) 14.8843 0.956799
\(243\) −14.0849 −0.903548
\(244\) −38.4068 −2.45875
\(245\) 38.0105 2.42840
\(246\) 10.2399 0.652871
\(247\) 3.58386 0.228036
\(248\) −26.9687 −1.71252
\(249\) 5.90728 0.374358
\(250\) −47.4784 −3.00280
\(251\) 22.2070 1.40170 0.700848 0.713311i \(-0.252805\pi\)
0.700848 + 0.713311i \(0.252805\pi\)
\(252\) 42.1682 2.65635
\(253\) −7.78490 −0.489432
\(254\) 50.8934 3.19334
\(255\) −15.1514 −0.948821
\(256\) −31.5210 −1.97006
\(257\) −10.2911 −0.641943 −0.320971 0.947089i \(-0.604009\pi\)
−0.320971 + 0.947089i \(0.604009\pi\)
\(258\) −6.68534 −0.416211
\(259\) 46.2976 2.87679
\(260\) 24.9073 1.54469
\(261\) 3.00836 0.186213
\(262\) −24.4448 −1.51020
\(263\) −11.3371 −0.699076 −0.349538 0.936922i \(-0.613661\pi\)
−0.349538 + 0.936922i \(0.613661\pi\)
\(264\) −6.60515 −0.406519
\(265\) 31.7564 1.95078
\(266\) 22.0146 1.34980
\(267\) −7.43432 −0.454973
\(268\) −33.1868 −2.02720
\(269\) −18.4372 −1.12414 −0.562068 0.827091i \(-0.689994\pi\)
−0.562068 + 0.827091i \(0.689994\pi\)
\(270\) −33.2881 −2.02585
\(271\) 28.4641 1.72907 0.864534 0.502574i \(-0.167614\pi\)
0.864534 + 0.502574i \(0.167614\pi\)
\(272\) 22.9666 1.39255
\(273\) 4.19221 0.253724
\(274\) 9.27115 0.560090
\(275\) −22.1794 −1.33747
\(276\) −8.72565 −0.525222
\(277\) 1.83137 0.110036 0.0550182 0.998485i \(-0.482478\pi\)
0.0550182 + 0.998485i \(0.482478\pi\)
\(278\) −13.8627 −0.831431
\(279\) −14.7888 −0.885380
\(280\) 75.4926 4.51155
\(281\) 5.63789 0.336328 0.168164 0.985759i \(-0.446216\pi\)
0.168164 + 0.985759i \(0.446216\pi\)
\(282\) −8.89732 −0.529828
\(283\) 12.8735 0.765248 0.382624 0.923904i \(-0.375020\pi\)
0.382624 + 0.923904i \(0.375020\pi\)
\(284\) −61.5241 −3.65078
\(285\) −5.36145 −0.317585
\(286\) 8.78466 0.519448
\(287\) −27.3982 −1.61726
\(288\) −1.30319 −0.0767912
\(289\) 21.7172 1.27748
\(290\) 10.9152 0.640963
\(291\) 4.20986 0.246787
\(292\) 43.7060 2.55770
\(293\) 14.1162 0.824679 0.412340 0.911030i \(-0.364712\pi\)
0.412340 + 0.911030i \(0.364712\pi\)
\(294\) 15.0261 0.876340
\(295\) 10.4567 0.608810
\(296\) 53.6541 3.11858
\(297\) −7.79282 −0.452185
\(298\) 23.5780 1.36584
\(299\) 5.72607 0.331147
\(300\) −24.8596 −1.43527
\(301\) 17.8875 1.03102
\(302\) −47.5014 −2.73340
\(303\) −8.54191 −0.490720
\(304\) 8.12690 0.466109
\(305\) −37.7050 −2.15898
\(306\) 39.5365 2.26015
\(307\) −21.9501 −1.25276 −0.626380 0.779517i \(-0.715464\pi\)
−0.626380 + 0.779517i \(0.715464\pi\)
\(308\) 35.8173 2.04088
\(309\) −1.01138 −0.0575355
\(310\) −53.6579 −3.04756
\(311\) −25.2490 −1.43174 −0.715871 0.698233i \(-0.753970\pi\)
−0.715871 + 0.698233i \(0.753970\pi\)
\(312\) 4.85833 0.275049
\(313\) 8.19362 0.463131 0.231565 0.972819i \(-0.425615\pi\)
0.231565 + 0.972819i \(0.425615\pi\)
\(314\) −4.29251 −0.242240
\(315\) 41.3977 2.33250
\(316\) −19.8759 −1.11811
\(317\) 31.9121 1.79236 0.896180 0.443691i \(-0.146331\pi\)
0.896180 + 0.443691i \(0.146331\pi\)
\(318\) 12.5538 0.703981
\(319\) 2.55527 0.143068
\(320\) −33.3403 −1.86378
\(321\) −0.477458 −0.0266491
\(322\) 35.1736 1.96015
\(323\) 13.7004 0.762309
\(324\) 22.1231 1.22906
\(325\) 16.3138 0.904925
\(326\) −19.8122 −1.09729
\(327\) −8.36602 −0.462642
\(328\) −31.7517 −1.75319
\(329\) 23.8060 1.31247
\(330\) −13.1418 −0.723435
\(331\) 11.6244 0.638933 0.319466 0.947598i \(-0.396496\pi\)
0.319466 + 0.947598i \(0.396496\pi\)
\(332\) −37.1228 −2.03738
\(333\) 29.4221 1.61232
\(334\) −54.1125 −2.96091
\(335\) −32.5804 −1.78005
\(336\) 9.50641 0.518617
\(337\) −27.7217 −1.51010 −0.755049 0.655668i \(-0.772387\pi\)
−0.755049 + 0.655668i \(0.772387\pi\)
\(338\) 25.2438 1.37308
\(339\) 5.38004 0.292203
\(340\) 95.2156 5.16379
\(341\) −12.5614 −0.680240
\(342\) 13.9903 0.756508
\(343\) −11.5071 −0.621323
\(344\) 20.7298 1.11768
\(345\) −8.56621 −0.461189
\(346\) 22.6957 1.22013
\(347\) −26.5737 −1.42655 −0.713276 0.700883i \(-0.752789\pi\)
−0.713276 + 0.700883i \(0.752789\pi\)
\(348\) 2.86406 0.153530
\(349\) 17.4443 0.933772 0.466886 0.884317i \(-0.345376\pi\)
0.466886 + 0.884317i \(0.345376\pi\)
\(350\) 100.211 5.35649
\(351\) 5.73191 0.305947
\(352\) −1.10692 −0.0589989
\(353\) 30.8824 1.64371 0.821853 0.569699i \(-0.192940\pi\)
0.821853 + 0.569699i \(0.192940\pi\)
\(354\) 4.13367 0.219702
\(355\) −60.3999 −3.20569
\(356\) 46.7192 2.47611
\(357\) 16.0260 0.848183
\(358\) −2.91967 −0.154309
\(359\) 23.4050 1.23527 0.617633 0.786466i \(-0.288092\pi\)
0.617633 + 0.786466i \(0.288092\pi\)
\(360\) 47.9756 2.52854
\(361\) −14.1520 −0.744843
\(362\) −49.9787 −2.62682
\(363\) 3.83415 0.201241
\(364\) −26.3449 −1.38085
\(365\) 42.9074 2.24588
\(366\) −14.9053 −0.779114
\(367\) 28.3927 1.48209 0.741043 0.671458i \(-0.234332\pi\)
0.741043 + 0.671458i \(0.234332\pi\)
\(368\) 12.9847 0.676872
\(369\) −17.4116 −0.906410
\(370\) 106.752 5.54977
\(371\) −33.5894 −1.74387
\(372\) −14.0794 −0.729983
\(373\) 13.6212 0.705281 0.352640 0.935759i \(-0.385284\pi\)
0.352640 + 0.935759i \(0.385284\pi\)
\(374\) 33.5819 1.73648
\(375\) −12.2303 −0.631570
\(376\) 27.5887 1.42278
\(377\) −1.87950 −0.0967991
\(378\) 35.2094 1.81098
\(379\) −3.96826 −0.203836 −0.101918 0.994793i \(-0.532498\pi\)
−0.101918 + 0.994793i \(0.532498\pi\)
\(380\) 33.6928 1.72840
\(381\) 13.1100 0.671646
\(382\) −27.0155 −1.38223
\(383\) 2.84868 0.145561 0.0727804 0.997348i \(-0.476813\pi\)
0.0727804 + 0.997348i \(0.476813\pi\)
\(384\) −12.5514 −0.640511
\(385\) 35.1628 1.79206
\(386\) −47.4553 −2.41541
\(387\) 11.3675 0.577845
\(388\) −26.4559 −1.34309
\(389\) 0.863906 0.0438018 0.0219009 0.999760i \(-0.493028\pi\)
0.0219009 + 0.999760i \(0.493028\pi\)
\(390\) 9.66630 0.489472
\(391\) 21.8896 1.10701
\(392\) −46.5927 −2.35329
\(393\) −6.29690 −0.317637
\(394\) −27.8471 −1.40292
\(395\) −19.5127 −0.981790
\(396\) 22.7619 1.14383
\(397\) 14.8634 0.745973 0.372986 0.927837i \(-0.378334\pi\)
0.372986 + 0.927837i \(0.378334\pi\)
\(398\) −49.0209 −2.45720
\(399\) 5.67090 0.283900
\(400\) 36.9937 1.84969
\(401\) 28.9868 1.44753 0.723767 0.690045i \(-0.242409\pi\)
0.723767 + 0.690045i \(0.242409\pi\)
\(402\) −12.8795 −0.642370
\(403\) 9.23940 0.460247
\(404\) 53.6796 2.67066
\(405\) 21.7189 1.07922
\(406\) −11.5452 −0.572979
\(407\) 24.9909 1.23875
\(408\) 18.5724 0.919471
\(409\) 33.9530 1.67887 0.839434 0.543462i \(-0.182887\pi\)
0.839434 + 0.543462i \(0.182887\pi\)
\(410\) −63.1742 −3.11995
\(411\) 2.38822 0.117802
\(412\) 6.35579 0.313127
\(413\) −11.0602 −0.544237
\(414\) 22.3528 1.09858
\(415\) −36.4445 −1.78899
\(416\) 0.814178 0.0399184
\(417\) −3.57100 −0.174873
\(418\) 11.8832 0.581227
\(419\) −2.04520 −0.0999148 −0.0499574 0.998751i \(-0.515909\pi\)
−0.0499574 + 0.998751i \(0.515909\pi\)
\(420\) 39.4120 1.92311
\(421\) 16.2367 0.791329 0.395665 0.918395i \(-0.370514\pi\)
0.395665 + 0.918395i \(0.370514\pi\)
\(422\) −51.4170 −2.50294
\(423\) 15.1287 0.735584
\(424\) −38.9266 −1.89044
\(425\) 62.3642 3.02511
\(426\) −23.8769 −1.15684
\(427\) 39.8813 1.92999
\(428\) 3.00047 0.145033
\(429\) 2.26290 0.109254
\(430\) 41.2447 1.98900
\(431\) 8.97949 0.432527 0.216263 0.976335i \(-0.430613\pi\)
0.216263 + 0.976335i \(0.430613\pi\)
\(432\) 12.9979 0.625361
\(433\) −9.54993 −0.458940 −0.229470 0.973316i \(-0.573699\pi\)
−0.229470 + 0.973316i \(0.573699\pi\)
\(434\) 56.7549 2.72432
\(435\) 2.81173 0.134812
\(436\) 52.5742 2.51785
\(437\) 7.74580 0.370532
\(438\) 16.9619 0.810471
\(439\) 35.2852 1.68407 0.842036 0.539422i \(-0.181357\pi\)
0.842036 + 0.539422i \(0.181357\pi\)
\(440\) 40.7500 1.94268
\(441\) −25.5499 −1.21666
\(442\) −24.7007 −1.17489
\(443\) −11.0824 −0.526542 −0.263271 0.964722i \(-0.584801\pi\)
−0.263271 + 0.964722i \(0.584801\pi\)
\(444\) 28.0109 1.32934
\(445\) 45.8655 2.17423
\(446\) −30.8518 −1.46087
\(447\) 6.07364 0.287273
\(448\) 35.2647 1.66610
\(449\) 0.709031 0.0334613 0.0167306 0.999860i \(-0.494674\pi\)
0.0167306 + 0.999860i \(0.494674\pi\)
\(450\) 63.6840 3.00209
\(451\) −14.7892 −0.696397
\(452\) −33.8095 −1.59027
\(453\) −12.2362 −0.574908
\(454\) −1.11185 −0.0521817
\(455\) −25.8635 −1.21250
\(456\) 6.57198 0.307761
\(457\) −27.5148 −1.28709 −0.643545 0.765408i \(-0.722537\pi\)
−0.643545 + 0.765408i \(0.722537\pi\)
\(458\) −9.88532 −0.461911
\(459\) 21.9119 1.02276
\(460\) 53.8322 2.50994
\(461\) 4.35888 0.203013 0.101507 0.994835i \(-0.467634\pi\)
0.101507 + 0.994835i \(0.467634\pi\)
\(462\) 13.9004 0.646703
\(463\) 2.30016 0.106898 0.0534488 0.998571i \(-0.482979\pi\)
0.0534488 + 0.998571i \(0.482979\pi\)
\(464\) −4.26202 −0.197859
\(465\) −13.8221 −0.640986
\(466\) −4.95027 −0.229317
\(467\) −0.847476 −0.0392165 −0.0196083 0.999808i \(-0.506242\pi\)
−0.0196083 + 0.999808i \(0.506242\pi\)
\(468\) −16.7422 −0.773909
\(469\) 34.4608 1.59125
\(470\) 54.8914 2.53195
\(471\) −1.10574 −0.0509497
\(472\) −12.8176 −0.589978
\(473\) 9.65548 0.443960
\(474\) −7.71365 −0.354299
\(475\) 22.0680 1.01255
\(476\) −100.711 −4.61609
\(477\) −21.3461 −0.977369
\(478\) 7.17214 0.328046
\(479\) −34.9972 −1.59906 −0.799530 0.600626i \(-0.794918\pi\)
−0.799530 + 0.600626i \(0.794918\pi\)
\(480\) −1.21801 −0.0555943
\(481\) −18.3817 −0.838134
\(482\) 4.85598 0.221184
\(483\) 9.06063 0.412273
\(484\) −24.0948 −1.09522
\(485\) −25.9725 −1.17935
\(486\) 34.3512 1.55820
\(487\) −42.1102 −1.90819 −0.954097 0.299498i \(-0.903181\pi\)
−0.954097 + 0.299498i \(0.903181\pi\)
\(488\) 46.2182 2.09220
\(489\) −5.10356 −0.230791
\(490\) −92.7024 −4.18787
\(491\) −34.7830 −1.56973 −0.784866 0.619665i \(-0.787268\pi\)
−0.784866 + 0.619665i \(0.787268\pi\)
\(492\) −16.5764 −0.747322
\(493\) −7.18494 −0.323593
\(494\) −8.74054 −0.393256
\(495\) 22.3460 1.00438
\(496\) 20.9516 0.940755
\(497\) 63.8860 2.86568
\(498\) −14.4070 −0.645595
\(499\) 13.9032 0.622391 0.311195 0.950346i \(-0.399271\pi\)
0.311195 + 0.950346i \(0.399271\pi\)
\(500\) 76.8584 3.43721
\(501\) −13.9392 −0.622759
\(502\) −54.1599 −2.41728
\(503\) −21.4824 −0.957855 −0.478927 0.877855i \(-0.658974\pi\)
−0.478927 + 0.877855i \(0.658974\pi\)
\(504\) −50.7446 −2.26035
\(505\) 52.6987 2.34506
\(506\) 18.9863 0.844044
\(507\) 6.50273 0.288796
\(508\) −82.3867 −3.65532
\(509\) −38.1621 −1.69151 −0.845753 0.533574i \(-0.820848\pi\)
−0.845753 + 0.533574i \(0.820848\pi\)
\(510\) 36.9523 1.63628
\(511\) −45.3839 −2.00767
\(512\) 36.9184 1.63158
\(513\) 7.75369 0.342334
\(514\) 25.0986 1.10705
\(515\) 6.23965 0.274952
\(516\) 10.8223 0.476424
\(517\) 12.8502 0.565151
\(518\) −112.913 −4.96113
\(519\) 5.84634 0.256626
\(520\) −29.9731 −1.31441
\(521\) −30.1596 −1.32132 −0.660658 0.750687i \(-0.729723\pi\)
−0.660658 + 0.750687i \(0.729723\pi\)
\(522\) −7.33698 −0.321131
\(523\) 30.6838 1.34171 0.670854 0.741589i \(-0.265928\pi\)
0.670854 + 0.741589i \(0.265928\pi\)
\(524\) 39.5714 1.72868
\(525\) 25.8140 1.12662
\(526\) 27.6496 1.20558
\(527\) 35.3203 1.53858
\(528\) 5.13145 0.223318
\(529\) −10.6242 −0.461923
\(530\) −77.4496 −3.36420
\(531\) −7.02876 −0.305022
\(532\) −35.6374 −1.54508
\(533\) 10.8780 0.471179
\(534\) 18.1313 0.784618
\(535\) 2.94564 0.127351
\(536\) 39.9365 1.72499
\(537\) −0.752098 −0.0324554
\(538\) 44.9658 1.93861
\(539\) −21.7018 −0.934765
\(540\) 53.8871 2.31893
\(541\) 37.6465 1.61855 0.809275 0.587430i \(-0.199860\pi\)
0.809275 + 0.587430i \(0.199860\pi\)
\(542\) −69.4199 −2.98184
\(543\) −12.8744 −0.552493
\(544\) 3.11244 0.133445
\(545\) 51.6135 2.21088
\(546\) −10.2242 −0.437556
\(547\) 17.9264 0.766477 0.383238 0.923650i \(-0.374809\pi\)
0.383238 + 0.923650i \(0.374809\pi\)
\(548\) −15.0082 −0.641119
\(549\) 25.3446 1.08168
\(550\) 54.0925 2.30651
\(551\) −2.54244 −0.108312
\(552\) 10.5003 0.446923
\(553\) 20.6389 0.877656
\(554\) −4.46646 −0.189762
\(555\) 27.4990 1.16727
\(556\) 22.4411 0.951714
\(557\) −5.15105 −0.218257 −0.109128 0.994028i \(-0.534806\pi\)
−0.109128 + 0.994028i \(0.534806\pi\)
\(558\) 36.0678 1.52687
\(559\) −7.10196 −0.300381
\(560\) −58.6491 −2.47838
\(561\) 8.65062 0.365229
\(562\) −13.7500 −0.580010
\(563\) 8.56675 0.361045 0.180523 0.983571i \(-0.442221\pi\)
0.180523 + 0.983571i \(0.442221\pi\)
\(564\) 14.4031 0.606478
\(565\) −33.1917 −1.39639
\(566\) −31.3966 −1.31970
\(567\) −22.9725 −0.964752
\(568\) 74.0372 3.10653
\(569\) 26.3362 1.10407 0.552036 0.833820i \(-0.313851\pi\)
0.552036 + 0.833820i \(0.313851\pi\)
\(570\) 13.0758 0.547687
\(571\) 34.1341 1.42847 0.714233 0.699908i \(-0.246776\pi\)
0.714233 + 0.699908i \(0.246776\pi\)
\(572\) −14.2207 −0.594596
\(573\) −6.95911 −0.290721
\(574\) 66.8204 2.78903
\(575\) 35.2590 1.47040
\(576\) 22.4107 0.933780
\(577\) −17.0854 −0.711276 −0.355638 0.934624i \(-0.615736\pi\)
−0.355638 + 0.934624i \(0.615736\pi\)
\(578\) −52.9652 −2.20306
\(579\) −12.2244 −0.508027
\(580\) −17.6696 −0.733691
\(581\) 38.5480 1.59924
\(582\) −10.2673 −0.425592
\(583\) −18.1311 −0.750915
\(584\) −52.5952 −2.17641
\(585\) −16.4363 −0.679557
\(586\) −34.4276 −1.42219
\(587\) 26.8654 1.10886 0.554428 0.832232i \(-0.312937\pi\)
0.554428 + 0.832232i \(0.312937\pi\)
\(588\) −24.3244 −1.00312
\(589\) 12.4984 0.514986
\(590\) −25.5024 −1.04992
\(591\) −7.17334 −0.295072
\(592\) −41.6830 −1.71316
\(593\) −3.42519 −0.140656 −0.0703278 0.997524i \(-0.522405\pi\)
−0.0703278 + 0.997524i \(0.522405\pi\)
\(594\) 19.0056 0.779810
\(595\) −98.8710 −4.05331
\(596\) −38.1683 −1.56344
\(597\) −12.6277 −0.516816
\(598\) −13.9651 −0.571076
\(599\) 2.91800 0.119226 0.0596131 0.998222i \(-0.481013\pi\)
0.0596131 + 0.998222i \(0.481013\pi\)
\(600\) 29.9157 1.22131
\(601\) 4.93129 0.201152 0.100576 0.994929i \(-0.467931\pi\)
0.100576 + 0.994929i \(0.467931\pi\)
\(602\) −43.6253 −1.77803
\(603\) 21.8999 0.891831
\(604\) 76.8956 3.12884
\(605\) −23.6545 −0.961694
\(606\) 20.8325 0.846264
\(607\) 11.4106 0.463144 0.231572 0.972818i \(-0.425613\pi\)
0.231572 + 0.972818i \(0.425613\pi\)
\(608\) 1.10136 0.0446660
\(609\) −2.97401 −0.120513
\(610\) 91.9574 3.72325
\(611\) −9.45179 −0.382379
\(612\) −64.0020 −2.58713
\(613\) −46.8967 −1.89414 −0.947070 0.321026i \(-0.895972\pi\)
−0.947070 + 0.321026i \(0.895972\pi\)
\(614\) 53.5334 2.16043
\(615\) −16.2735 −0.656211
\(616\) −43.1020 −1.73663
\(617\) −38.5838 −1.55332 −0.776662 0.629917i \(-0.783089\pi\)
−0.776662 + 0.629917i \(0.783089\pi\)
\(618\) 2.46662 0.0992221
\(619\) 8.36777 0.336329 0.168165 0.985759i \(-0.446216\pi\)
0.168165 + 0.985759i \(0.446216\pi\)
\(620\) 86.8619 3.48846
\(621\) 12.3884 0.497128
\(622\) 61.5790 2.46909
\(623\) −48.5128 −1.94362
\(624\) −3.77437 −0.151096
\(625\) 25.3406 1.01362
\(626\) −19.9831 −0.798686
\(627\) 3.06109 0.122248
\(628\) 6.94875 0.277285
\(629\) −70.2695 −2.80183
\(630\) −100.963 −4.02247
\(631\) 36.2698 1.44388 0.721939 0.691957i \(-0.243251\pi\)
0.721939 + 0.691957i \(0.243251\pi\)
\(632\) 23.9184 0.951421
\(633\) −13.2449 −0.526437
\(634\) −77.8291 −3.09099
\(635\) −80.8812 −3.20967
\(636\) −20.3222 −0.805826
\(637\) 15.9625 0.632457
\(638\) −6.23196 −0.246726
\(639\) 40.5996 1.60610
\(640\) 77.4350 3.06089
\(641\) −27.1168 −1.07105 −0.535525 0.844520i \(-0.679886\pi\)
−0.535525 + 0.844520i \(0.679886\pi\)
\(642\) 1.16445 0.0459573
\(643\) −28.3221 −1.11691 −0.558457 0.829534i \(-0.688606\pi\)
−0.558457 + 0.829534i \(0.688606\pi\)
\(644\) −56.9393 −2.24372
\(645\) 10.6245 0.418341
\(646\) −33.4133 −1.31463
\(647\) −2.15649 −0.0847804 −0.0423902 0.999101i \(-0.513497\pi\)
−0.0423902 + 0.999101i \(0.513497\pi\)
\(648\) −26.6227 −1.04584
\(649\) −5.97016 −0.234349
\(650\) −39.7870 −1.56058
\(651\) 14.6199 0.573000
\(652\) 32.0721 1.25604
\(653\) 6.52339 0.255280 0.127640 0.991821i \(-0.459260\pi\)
0.127640 + 0.991821i \(0.459260\pi\)
\(654\) 20.4036 0.797842
\(655\) 38.8483 1.51793
\(656\) 24.6674 0.963100
\(657\) −28.8415 −1.12521
\(658\) −58.0596 −2.26340
\(659\) −16.7915 −0.654105 −0.327052 0.945006i \(-0.606055\pi\)
−0.327052 + 0.945006i \(0.606055\pi\)
\(660\) 21.2741 0.828094
\(661\) −20.6732 −0.804093 −0.402047 0.915619i \(-0.631701\pi\)
−0.402047 + 0.915619i \(0.631701\pi\)
\(662\) −28.3502 −1.10186
\(663\) −6.36285 −0.247112
\(664\) 44.6731 1.73365
\(665\) −34.9862 −1.35671
\(666\) −71.7565 −2.78051
\(667\) −4.06216 −0.157288
\(668\) 87.5978 3.38926
\(669\) −7.94733 −0.307262
\(670\) 79.4590 3.06977
\(671\) 21.5274 0.831058
\(672\) 1.28831 0.0496977
\(673\) −20.3307 −0.783691 −0.391846 0.920031i \(-0.628163\pi\)
−0.391846 + 0.920031i \(0.628163\pi\)
\(674\) 67.6095 2.60422
\(675\) 35.2949 1.35850
\(676\) −40.8648 −1.57172
\(677\) −29.8163 −1.14593 −0.572967 0.819578i \(-0.694208\pi\)
−0.572967 + 0.819578i \(0.694208\pi\)
\(678\) −13.1212 −0.503915
\(679\) 27.4715 1.05426
\(680\) −114.581 −4.39399
\(681\) −0.286410 −0.0109752
\(682\) 30.6356 1.17310
\(683\) −2.96283 −0.113369 −0.0566847 0.998392i \(-0.518053\pi\)
−0.0566847 + 0.998392i \(0.518053\pi\)
\(684\) −22.6476 −0.865953
\(685\) −14.7340 −0.562956
\(686\) 28.0641 1.07149
\(687\) −2.54643 −0.0971525
\(688\) −16.1047 −0.613985
\(689\) 13.3361 0.508065
\(690\) 20.8918 0.795337
\(691\) −1.29240 −0.0491651 −0.0245825 0.999698i \(-0.507826\pi\)
−0.0245825 + 0.999698i \(0.507826\pi\)
\(692\) −36.7399 −1.39664
\(693\) −23.6357 −0.897847
\(694\) 64.8097 2.46014
\(695\) 22.0310 0.835685
\(696\) −3.44657 −0.130642
\(697\) 41.5844 1.57512
\(698\) −42.5443 −1.61032
\(699\) −1.27518 −0.0482316
\(700\) −162.222 −6.13141
\(701\) 40.9042 1.54493 0.772464 0.635058i \(-0.219024\pi\)
0.772464 + 0.635058i \(0.219024\pi\)
\(702\) −13.9793 −0.527616
\(703\) −24.8654 −0.937816
\(704\) 19.0354 0.717425
\(705\) 14.1399 0.532539
\(706\) −75.3180 −2.83463
\(707\) −55.7403 −2.09633
\(708\) −6.69162 −0.251486
\(709\) −12.9779 −0.487396 −0.243698 0.969851i \(-0.578361\pi\)
−0.243698 + 0.969851i \(0.578361\pi\)
\(710\) 147.307 5.52833
\(711\) 13.1160 0.491890
\(712\) −56.2212 −2.10698
\(713\) 19.9691 0.747850
\(714\) −39.0851 −1.46272
\(715\) −13.9608 −0.522105
\(716\) 4.72638 0.176633
\(717\) 1.84752 0.0689971
\(718\) −57.0815 −2.13026
\(719\) −39.4615 −1.47166 −0.735832 0.677164i \(-0.763209\pi\)
−0.735832 + 0.677164i \(0.763209\pi\)
\(720\) −37.2715 −1.38903
\(721\) −6.59979 −0.245789
\(722\) 34.5148 1.28451
\(723\) 1.25089 0.0465210
\(724\) 80.9059 3.00685
\(725\) −11.5732 −0.429819
\(726\) −9.35098 −0.347047
\(727\) −14.2405 −0.528151 −0.264075 0.964502i \(-0.585067\pi\)
−0.264075 + 0.964502i \(0.585067\pi\)
\(728\) 31.7031 1.17500
\(729\) −7.96191 −0.294885
\(730\) −104.645 −3.87309
\(731\) −27.1493 −1.00415
\(732\) 24.1289 0.891829
\(733\) 23.5915 0.871374 0.435687 0.900098i \(-0.356506\pi\)
0.435687 + 0.900098i \(0.356506\pi\)
\(734\) −69.2458 −2.55591
\(735\) −23.8799 −0.880823
\(736\) 1.75969 0.0648629
\(737\) 18.6015 0.685196
\(738\) 42.4644 1.56314
\(739\) 25.2279 0.928025 0.464013 0.885829i \(-0.346409\pi\)
0.464013 + 0.885829i \(0.346409\pi\)
\(740\) −172.811 −6.35266
\(741\) −2.25154 −0.0827124
\(742\) 81.9198 3.00737
\(743\) 21.3735 0.784117 0.392059 0.919940i \(-0.371763\pi\)
0.392059 + 0.919940i \(0.371763\pi\)
\(744\) 16.9430 0.621159
\(745\) −37.4709 −1.37283
\(746\) −33.2203 −1.21628
\(747\) 24.4973 0.896308
\(748\) −54.3627 −1.98770
\(749\) −3.11566 −0.113844
\(750\) 29.8280 1.08917
\(751\) −14.4616 −0.527713 −0.263856 0.964562i \(-0.584994\pi\)
−0.263856 + 0.964562i \(0.584994\pi\)
\(752\) −21.4332 −0.781590
\(753\) −13.9514 −0.508419
\(754\) 4.58384 0.166933
\(755\) 75.4905 2.74738
\(756\) −56.9973 −2.07297
\(757\) 6.16797 0.224179 0.112089 0.993698i \(-0.464246\pi\)
0.112089 + 0.993698i \(0.464246\pi\)
\(758\) 9.67803 0.351522
\(759\) 4.89082 0.177525
\(760\) −40.5454 −1.47074
\(761\) 17.5936 0.637768 0.318884 0.947794i \(-0.396692\pi\)
0.318884 + 0.947794i \(0.396692\pi\)
\(762\) −31.9735 −1.15828
\(763\) −54.5925 −1.97638
\(764\) 43.7328 1.58220
\(765\) −62.8325 −2.27172
\(766\) −6.94754 −0.251025
\(767\) 4.39127 0.158560
\(768\) 19.8029 0.714576
\(769\) 33.4473 1.20614 0.603070 0.797689i \(-0.293944\pi\)
0.603070 + 0.797689i \(0.293944\pi\)
\(770\) −85.7572 −3.09048
\(771\) 6.46535 0.232844
\(772\) 76.8210 2.76485
\(773\) −2.14793 −0.0772557 −0.0386279 0.999254i \(-0.512299\pi\)
−0.0386279 + 0.999254i \(0.512299\pi\)
\(774\) −27.7239 −0.996514
\(775\) 56.8927 2.04364
\(776\) 31.8366 1.14287
\(777\) −29.0862 −1.04346
\(778\) −2.10695 −0.0755377
\(779\) 14.7150 0.527218
\(780\) −15.6479 −0.560284
\(781\) 34.4849 1.23397
\(782\) −53.3858 −1.90907
\(783\) −4.06630 −0.145318
\(784\) 36.1972 1.29276
\(785\) 6.82177 0.243480
\(786\) 15.3573 0.547776
\(787\) −28.2561 −1.00722 −0.503611 0.863931i \(-0.667995\pi\)
−0.503611 + 0.863931i \(0.667995\pi\)
\(788\) 45.0791 1.60588
\(789\) 7.12247 0.253567
\(790\) 47.5888 1.69313
\(791\) 35.1075 1.24828
\(792\) −27.3913 −0.973309
\(793\) −15.8342 −0.562290
\(794\) −36.2498 −1.28646
\(795\) −19.9508 −0.707582
\(796\) 79.3555 2.81268
\(797\) 49.1722 1.74177 0.870885 0.491487i \(-0.163547\pi\)
0.870885 + 0.491487i \(0.163547\pi\)
\(798\) −13.8306 −0.489596
\(799\) −36.1323 −1.27827
\(800\) 5.01340 0.177250
\(801\) −30.8299 −1.08932
\(802\) −70.6949 −2.49632
\(803\) −24.4977 −0.864505
\(804\) 20.8494 0.735302
\(805\) −55.8989 −1.97018
\(806\) −22.5336 −0.793713
\(807\) 11.5831 0.407744
\(808\) −64.5972 −2.27252
\(809\) 48.3023 1.69822 0.849109 0.528217i \(-0.177139\pi\)
0.849109 + 0.528217i \(0.177139\pi\)
\(810\) −52.9694 −1.86115
\(811\) −23.2458 −0.816271 −0.408135 0.912921i \(-0.633821\pi\)
−0.408135 + 0.912921i \(0.633821\pi\)
\(812\) 18.6895 0.655872
\(813\) −17.8824 −0.627163
\(814\) −60.9493 −2.13627
\(815\) 31.4861 1.10291
\(816\) −14.4286 −0.505103
\(817\) −9.60700 −0.336106
\(818\) −82.8067 −2.89527
\(819\) 17.3849 0.607479
\(820\) 102.267 3.57131
\(821\) 41.4282 1.44586 0.722928 0.690923i \(-0.242796\pi\)
0.722928 + 0.690923i \(0.242796\pi\)
\(822\) −5.82455 −0.203154
\(823\) 13.4994 0.470560 0.235280 0.971928i \(-0.424399\pi\)
0.235280 + 0.971928i \(0.424399\pi\)
\(824\) −7.64847 −0.266447
\(825\) 13.9341 0.485123
\(826\) 26.9743 0.938556
\(827\) −12.3354 −0.428943 −0.214471 0.976730i \(-0.568803\pi\)
−0.214471 + 0.976730i \(0.568803\pi\)
\(828\) −36.1850 −1.25751
\(829\) 32.9824 1.14553 0.572764 0.819720i \(-0.305871\pi\)
0.572764 + 0.819720i \(0.305871\pi\)
\(830\) 88.8831 3.08518
\(831\) −1.15055 −0.0399121
\(832\) −14.0013 −0.485407
\(833\) 61.0214 2.11427
\(834\) 8.70918 0.301574
\(835\) 85.9971 2.97605
\(836\) −19.2367 −0.665314
\(837\) 19.9895 0.690937
\(838\) 4.98797 0.172307
\(839\) 37.3200 1.28843 0.644214 0.764845i \(-0.277184\pi\)
0.644214 + 0.764845i \(0.277184\pi\)
\(840\) −47.4278 −1.63642
\(841\) −27.6667 −0.954023
\(842\) −39.5991 −1.36468
\(843\) −3.54197 −0.121992
\(844\) 83.2342 2.86504
\(845\) −40.1181 −1.38011
\(846\) −36.8969 −1.26854
\(847\) 25.0198 0.859691
\(848\) 30.2415 1.03850
\(849\) −8.08769 −0.277569
\(850\) −152.098 −5.21691
\(851\) −39.7284 −1.36187
\(852\) 38.6522 1.32420
\(853\) 37.3887 1.28017 0.640083 0.768306i \(-0.278900\pi\)
0.640083 + 0.768306i \(0.278900\pi\)
\(854\) −97.2650 −3.32834
\(855\) −22.2338 −0.760379
\(856\) −3.61072 −0.123412
\(857\) 40.6864 1.38982 0.694911 0.719095i \(-0.255444\pi\)
0.694911 + 0.719095i \(0.255444\pi\)
\(858\) −5.51891 −0.188413
\(859\) 16.1103 0.549676 0.274838 0.961491i \(-0.411376\pi\)
0.274838 + 0.961491i \(0.411376\pi\)
\(860\) −66.7673 −2.27675
\(861\) 17.2128 0.586610
\(862\) −21.8997 −0.745908
\(863\) −37.9883 −1.29314 −0.646569 0.762855i \(-0.723797\pi\)
−0.646569 + 0.762855i \(0.723797\pi\)
\(864\) 1.76148 0.0599267
\(865\) −36.0686 −1.22637
\(866\) 23.2910 0.791459
\(867\) −13.6437 −0.463364
\(868\) −91.8753 −3.11845
\(869\) 11.1406 0.377920
\(870\) −6.85742 −0.232488
\(871\) −13.6821 −0.463601
\(872\) −63.2670 −2.14249
\(873\) 17.4582 0.590869
\(874\) −18.8909 −0.638996
\(875\) −79.8090 −2.69804
\(876\) −27.4581 −0.927722
\(877\) −3.73410 −0.126092 −0.0630458 0.998011i \(-0.520081\pi\)
−0.0630458 + 0.998011i \(0.520081\pi\)
\(878\) −86.0558 −2.90424
\(879\) −8.86845 −0.299125
\(880\) −31.6581 −1.06719
\(881\) 0.934871 0.0314966 0.0157483 0.999876i \(-0.494987\pi\)
0.0157483 + 0.999876i \(0.494987\pi\)
\(882\) 62.3127 2.09818
\(883\) 19.9915 0.672768 0.336384 0.941725i \(-0.390796\pi\)
0.336384 + 0.941725i \(0.390796\pi\)
\(884\) 39.9858 1.34487
\(885\) −6.56934 −0.220826
\(886\) 27.0285 0.908041
\(887\) 7.01024 0.235381 0.117690 0.993050i \(-0.462451\pi\)
0.117690 + 0.993050i \(0.462451\pi\)
\(888\) −33.7079 −1.13116
\(889\) 85.5495 2.86924
\(890\) −111.860 −3.74955
\(891\) −12.4003 −0.415424
\(892\) 49.9431 1.67222
\(893\) −12.7857 −0.427856
\(894\) −14.8128 −0.495413
\(895\) 4.64001 0.155099
\(896\) −81.9044 −2.73623
\(897\) −3.59738 −0.120113
\(898\) −1.72923 −0.0577051
\(899\) −6.55456 −0.218607
\(900\) −103.092 −3.43640
\(901\) 50.9812 1.69843
\(902\) 36.0689 1.20096
\(903\) −11.2378 −0.373969
\(904\) 40.6859 1.35319
\(905\) 79.4276 2.64026
\(906\) 29.8425 0.991450
\(907\) 43.6889 1.45066 0.725332 0.688399i \(-0.241686\pi\)
0.725332 + 0.688399i \(0.241686\pi\)
\(908\) 1.79987 0.0597308
\(909\) −35.4230 −1.17491
\(910\) 63.0776 2.09100
\(911\) −36.8510 −1.22093 −0.610464 0.792044i \(-0.709017\pi\)
−0.610464 + 0.792044i \(0.709017\pi\)
\(912\) −5.10568 −0.169066
\(913\) 20.8077 0.688636
\(914\) 67.1049 2.21963
\(915\) 23.6880 0.783101
\(916\) 16.0024 0.528736
\(917\) −41.0905 −1.35693
\(918\) −53.4401 −1.76379
\(919\) 35.8749 1.18340 0.591702 0.806157i \(-0.298456\pi\)
0.591702 + 0.806157i \(0.298456\pi\)
\(920\) −64.7810 −2.13577
\(921\) 13.7901 0.454398
\(922\) −10.6307 −0.350103
\(923\) −25.3649 −0.834896
\(924\) −22.5020 −0.740262
\(925\) −113.188 −3.72158
\(926\) −5.60978 −0.184349
\(927\) −4.19417 −0.137755
\(928\) −0.577590 −0.0189603
\(929\) 19.9934 0.655961 0.327980 0.944685i \(-0.393632\pi\)
0.327980 + 0.944685i \(0.393632\pi\)
\(930\) 33.7103 1.10540
\(931\) 21.5929 0.707678
\(932\) 8.01354 0.262492
\(933\) 15.8626 0.519317
\(934\) 2.06688 0.0676303
\(935\) −53.3694 −1.74536
\(936\) 20.1473 0.658536
\(937\) −2.82509 −0.0922918 −0.0461459 0.998935i \(-0.514694\pi\)
−0.0461459 + 0.998935i \(0.514694\pi\)
\(938\) −84.0452 −2.74417
\(939\) −5.14760 −0.167985
\(940\) −88.8586 −2.89825
\(941\) 5.68873 0.185447 0.0927236 0.995692i \(-0.470443\pi\)
0.0927236 + 0.995692i \(0.470443\pi\)
\(942\) 2.69674 0.0878647
\(943\) 23.5107 0.765613
\(944\) 9.95781 0.324099
\(945\) −55.9558 −1.82024
\(946\) −23.5484 −0.765625
\(947\) −41.8313 −1.35933 −0.679667 0.733521i \(-0.737876\pi\)
−0.679667 + 0.733521i \(0.737876\pi\)
\(948\) 12.4869 0.405556
\(949\) 18.0189 0.584920
\(950\) −53.8209 −1.74618
\(951\) −20.0486 −0.650119
\(952\) 121.194 3.92794
\(953\) 57.6205 1.86651 0.933256 0.359211i \(-0.116954\pi\)
0.933256 + 0.359211i \(0.116954\pi\)
\(954\) 52.0601 1.68551
\(955\) 42.9337 1.38930
\(956\) −11.6103 −0.375505
\(957\) −1.60534 −0.0518932
\(958\) 85.3533 2.75764
\(959\) 15.5844 0.503246
\(960\) 20.9459 0.676026
\(961\) 1.22149 0.0394028
\(962\) 44.8305 1.44539
\(963\) −1.98000 −0.0638047
\(964\) −7.86090 −0.253182
\(965\) 75.4173 2.42777
\(966\) −22.0976 −0.710979
\(967\) 30.5409 0.982128 0.491064 0.871124i \(-0.336608\pi\)
0.491064 + 0.871124i \(0.336608\pi\)
\(968\) 28.9954 0.931946
\(969\) −8.60718 −0.276502
\(970\) 63.3432 2.03383
\(971\) −22.4503 −0.720465 −0.360233 0.932863i \(-0.617303\pi\)
−0.360233 + 0.932863i \(0.617303\pi\)
\(972\) −55.6080 −1.78363
\(973\) −23.3026 −0.747047
\(974\) 102.701 3.29075
\(975\) −10.2490 −0.328232
\(976\) −35.9063 −1.14933
\(977\) −1.42834 −0.0456966 −0.0228483 0.999739i \(-0.507273\pi\)
−0.0228483 + 0.999739i \(0.507273\pi\)
\(978\) 12.4469 0.398008
\(979\) −26.1866 −0.836928
\(980\) 150.067 4.79373
\(981\) −34.6936 −1.10768
\(982\) 84.8309 2.70706
\(983\) −42.0376 −1.34079 −0.670396 0.742004i \(-0.733876\pi\)
−0.670396 + 0.742004i \(0.733876\pi\)
\(984\) 19.9478 0.635913
\(985\) 44.2554 1.41009
\(986\) 17.5231 0.558048
\(987\) −14.9560 −0.476055
\(988\) 14.1493 0.450148
\(989\) −15.3495 −0.488085
\(990\) −54.4988 −1.73208
\(991\) −28.6001 −0.908513 −0.454257 0.890871i \(-0.650095\pi\)
−0.454257 + 0.890871i \(0.650095\pi\)
\(992\) 2.83937 0.0901500
\(993\) −7.30294 −0.231752
\(994\) −155.809 −4.94197
\(995\) 77.9055 2.46977
\(996\) 23.3222 0.738993
\(997\) −1.34132 −0.0424802 −0.0212401 0.999774i \(-0.506761\pi\)
−0.0212401 + 0.999774i \(0.506761\pi\)
\(998\) −33.9079 −1.07334
\(999\) −39.7689 −1.25823
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 \(a_p\))