Properties

Label 4033.2.a.d.1.5
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.66315 q^{2}\) \(+1.52081 q^{3}\) \(+5.09239 q^{4}\) \(+1.90830 q^{5}\) \(-4.05016 q^{6}\) \(-2.83326 q^{7}\) \(-8.23552 q^{8}\) \(-0.687131 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.66315 q^{2}\) \(+1.52081 q^{3}\) \(+5.09239 q^{4}\) \(+1.90830 q^{5}\) \(-4.05016 q^{6}\) \(-2.83326 q^{7}\) \(-8.23552 q^{8}\) \(-0.687131 q^{9}\) \(-5.08211 q^{10}\) \(+5.75810 q^{11}\) \(+7.74457 q^{12}\) \(-5.75389 q^{13}\) \(+7.54541 q^{14}\) \(+2.90217 q^{15}\) \(+11.7477 q^{16}\) \(+3.64029 q^{17}\) \(+1.82994 q^{18}\) \(+3.29429 q^{19}\) \(+9.71784 q^{20}\) \(-4.30886 q^{21}\) \(-15.3347 q^{22}\) \(-8.81520 q^{23}\) \(-12.5247 q^{24}\) \(-1.35837 q^{25}\) \(+15.3235 q^{26}\) \(-5.60743 q^{27}\) \(-14.4281 q^{28}\) \(+8.25297 q^{29}\) \(-7.72893 q^{30}\) \(-4.72730 q^{31}\) \(-14.8149 q^{32}\) \(+8.75699 q^{33}\) \(-9.69467 q^{34}\) \(-5.40672 q^{35}\) \(-3.49914 q^{36}\) \(-1.00000 q^{37}\) \(-8.77320 q^{38}\) \(-8.75059 q^{39}\) \(-15.7159 q^{40}\) \(-8.22487 q^{41}\) \(+11.4752 q^{42}\) \(+4.70090 q^{43}\) \(+29.3225 q^{44}\) \(-1.31125 q^{45}\) \(+23.4762 q^{46}\) \(-8.06805 q^{47}\) \(+17.8660 q^{48}\) \(+1.02737 q^{49}\) \(+3.61756 q^{50}\) \(+5.53620 q^{51}\) \(-29.3011 q^{52}\) \(+5.50423 q^{53}\) \(+14.9335 q^{54}\) \(+10.9882 q^{55}\) \(+23.3334 q^{56}\) \(+5.01000 q^{57}\) \(-21.9789 q^{58}\) \(+1.01395 q^{59}\) \(+14.7790 q^{60}\) \(-6.58289 q^{61}\) \(+12.5895 q^{62}\) \(+1.94682 q^{63}\) \(+15.9589 q^{64}\) \(-10.9802 q^{65}\) \(-23.3212 q^{66}\) \(+9.17431 q^{67}\) \(+18.5378 q^{68}\) \(-13.4063 q^{69}\) \(+14.3989 q^{70}\) \(+1.49410 q^{71}\) \(+5.65888 q^{72}\) \(+8.25195 q^{73}\) \(+2.66315 q^{74}\) \(-2.06583 q^{75}\) \(+16.7758 q^{76}\) \(-16.3142 q^{77}\) \(+23.3042 q^{78}\) \(-11.6914 q^{79}\) \(+22.4182 q^{80}\) \(-6.46646 q^{81}\) \(+21.9041 q^{82}\) \(-3.02745 q^{83}\) \(-21.9424 q^{84}\) \(+6.94679 q^{85}\) \(-12.5192 q^{86}\) \(+12.5512 q^{87}\) \(-47.4210 q^{88}\) \(-2.08727 q^{89}\) \(+3.49207 q^{90}\) \(+16.3023 q^{91}\) \(-44.8905 q^{92}\) \(-7.18933 q^{93}\) \(+21.4865 q^{94}\) \(+6.28651 q^{95}\) \(-22.5306 q^{96}\) \(-12.6361 q^{97}\) \(-2.73604 q^{98}\) \(-3.95657 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66315 −1.88313 −0.941567 0.336825i \(-0.890647\pi\)
−0.941567 + 0.336825i \(0.890647\pi\)
\(3\) 1.52081 0.878041 0.439021 0.898477i \(-0.355326\pi\)
0.439021 + 0.898477i \(0.355326\pi\)
\(4\) 5.09239 2.54620
\(5\) 1.90830 0.853420 0.426710 0.904389i \(-0.359673\pi\)
0.426710 + 0.904389i \(0.359673\pi\)
\(6\) −4.05016 −1.65347
\(7\) −2.83326 −1.07087 −0.535436 0.844576i \(-0.679853\pi\)
−0.535436 + 0.844576i \(0.679853\pi\)
\(8\) −8.23552 −2.91170
\(9\) −0.687131 −0.229044
\(10\) −5.08211 −1.60710
\(11\) 5.75810 1.73613 0.868067 0.496448i \(-0.165363\pi\)
0.868067 + 0.496448i \(0.165363\pi\)
\(12\) 7.74457 2.23567
\(13\) −5.75389 −1.59584 −0.797921 0.602762i \(-0.794067\pi\)
−0.797921 + 0.602762i \(0.794067\pi\)
\(14\) 7.54541 2.01660
\(15\) 2.90217 0.749338
\(16\) 11.7477 2.93692
\(17\) 3.64029 0.882901 0.441451 0.897286i \(-0.354464\pi\)
0.441451 + 0.897286i \(0.354464\pi\)
\(18\) 1.82994 0.431320
\(19\) 3.29429 0.755762 0.377881 0.925854i \(-0.376653\pi\)
0.377881 + 0.925854i \(0.376653\pi\)
\(20\) 9.71784 2.17297
\(21\) −4.30886 −0.940270
\(22\) −15.3347 −3.26937
\(23\) −8.81520 −1.83810 −0.919048 0.394146i \(-0.871041\pi\)
−0.919048 + 0.394146i \(0.871041\pi\)
\(24\) −12.5247 −2.55659
\(25\) −1.35837 −0.271675
\(26\) 15.3235 3.00519
\(27\) −5.60743 −1.07915
\(28\) −14.4281 −2.72665
\(29\) 8.25297 1.53254 0.766269 0.642520i \(-0.222111\pi\)
0.766269 + 0.642520i \(0.222111\pi\)
\(30\) −7.72893 −1.41110
\(31\) −4.72730 −0.849048 −0.424524 0.905417i \(-0.639559\pi\)
−0.424524 + 0.905417i \(0.639559\pi\)
\(32\) −14.8149 −2.61892
\(33\) 8.75699 1.52440
\(34\) −9.69467 −1.66262
\(35\) −5.40672 −0.913903
\(36\) −3.49914 −0.583190
\(37\) −1.00000 −0.164399
\(38\) −8.77320 −1.42320
\(39\) −8.75059 −1.40122
\(40\) −15.7159 −2.48490
\(41\) −8.22487 −1.28451 −0.642255 0.766491i \(-0.722001\pi\)
−0.642255 + 0.766491i \(0.722001\pi\)
\(42\) 11.4752 1.77065
\(43\) 4.70090 0.716881 0.358440 0.933553i \(-0.383309\pi\)
0.358440 + 0.933553i \(0.383309\pi\)
\(44\) 29.3225 4.42054
\(45\) −1.31125 −0.195470
\(46\) 23.4762 3.46138
\(47\) −8.06805 −1.17685 −0.588423 0.808553i \(-0.700251\pi\)
−0.588423 + 0.808553i \(0.700251\pi\)
\(48\) 17.8660 2.57874
\(49\) 1.02737 0.146767
\(50\) 3.61756 0.511600
\(51\) 5.53620 0.775224
\(52\) −29.3011 −4.06333
\(53\) 5.50423 0.756063 0.378032 0.925793i \(-0.376601\pi\)
0.378032 + 0.925793i \(0.376601\pi\)
\(54\) 14.9335 2.03219
\(55\) 10.9882 1.48165
\(56\) 23.3334 3.11805
\(57\) 5.01000 0.663590
\(58\) −21.9789 −2.88598
\(59\) 1.01395 0.132005 0.0660026 0.997819i \(-0.478975\pi\)
0.0660026 + 0.997819i \(0.478975\pi\)
\(60\) 14.7790 1.90796
\(61\) −6.58289 −0.842852 −0.421426 0.906863i \(-0.638470\pi\)
−0.421426 + 0.906863i \(0.638470\pi\)
\(62\) 12.5895 1.59887
\(63\) 1.94682 0.245276
\(64\) 15.9589 1.99486
\(65\) −10.9802 −1.36192
\(66\) −23.3212 −2.87064
\(67\) 9.17431 1.12082 0.560410 0.828215i \(-0.310643\pi\)
0.560410 + 0.828215i \(0.310643\pi\)
\(68\) 18.5378 2.24804
\(69\) −13.4063 −1.61392
\(70\) 14.3989 1.72100
\(71\) 1.49410 0.177317 0.0886583 0.996062i \(-0.471742\pi\)
0.0886583 + 0.996062i \(0.471742\pi\)
\(72\) 5.65888 0.666905
\(73\) 8.25195 0.965818 0.482909 0.875671i \(-0.339580\pi\)
0.482909 + 0.875671i \(0.339580\pi\)
\(74\) 2.66315 0.309585
\(75\) −2.06583 −0.238542
\(76\) 16.7758 1.92432
\(77\) −16.3142 −1.85918
\(78\) 23.3042 2.63868
\(79\) −11.6914 −1.31539 −0.657693 0.753286i \(-0.728468\pi\)
−0.657693 + 0.753286i \(0.728468\pi\)
\(80\) 22.4182 2.50643
\(81\) −6.46646 −0.718495
\(82\) 21.9041 2.41890
\(83\) −3.02745 −0.332306 −0.166153 0.986100i \(-0.553135\pi\)
−0.166153 + 0.986100i \(0.553135\pi\)
\(84\) −21.9424 −2.39411
\(85\) 6.94679 0.753485
\(86\) −12.5192 −1.34998
\(87\) 12.5512 1.34563
\(88\) −47.4210 −5.05509
\(89\) −2.08727 −0.221250 −0.110625 0.993862i \(-0.535285\pi\)
−0.110625 + 0.993862i \(0.535285\pi\)
\(90\) 3.49207 0.368097
\(91\) 16.3023 1.70894
\(92\) −44.8905 −4.68015
\(93\) −7.18933 −0.745499
\(94\) 21.4865 2.21616
\(95\) 6.28651 0.644982
\(96\) −22.5306 −2.29952
\(97\) −12.6361 −1.28300 −0.641500 0.767123i \(-0.721687\pi\)
−0.641500 + 0.767123i \(0.721687\pi\)
\(98\) −2.73604 −0.276382
\(99\) −3.95657 −0.397650
\(100\) −6.91737 −0.691737
\(101\) 4.57400 0.455130 0.227565 0.973763i \(-0.426924\pi\)
0.227565 + 0.973763i \(0.426924\pi\)
\(102\) −14.7438 −1.45985
\(103\) −11.1248 −1.09615 −0.548077 0.836428i \(-0.684640\pi\)
−0.548077 + 0.836428i \(0.684640\pi\)
\(104\) 47.3863 4.64661
\(105\) −8.22261 −0.802445
\(106\) −14.6586 −1.42377
\(107\) 7.82188 0.756169 0.378085 0.925771i \(-0.376583\pi\)
0.378085 + 0.925771i \(0.376583\pi\)
\(108\) −28.5553 −2.74773
\(109\) −1.00000 −0.0957826
\(110\) −29.2633 −2.79015
\(111\) −1.52081 −0.144349
\(112\) −33.2842 −3.14507
\(113\) −13.2684 −1.24819 −0.624094 0.781349i \(-0.714532\pi\)
−0.624094 + 0.781349i \(0.714532\pi\)
\(114\) −13.3424 −1.24963
\(115\) −16.8221 −1.56867
\(116\) 42.0274 3.90214
\(117\) 3.95368 0.365517
\(118\) −2.70031 −0.248584
\(119\) −10.3139 −0.945474
\(120\) −23.9009 −2.18184
\(121\) 22.1557 2.01416
\(122\) 17.5312 1.58720
\(123\) −12.5085 −1.12785
\(124\) −24.0733 −2.16184
\(125\) −12.1337 −1.08527
\(126\) −5.18469 −0.461888
\(127\) −14.3285 −1.27145 −0.635724 0.771916i \(-0.719298\pi\)
−0.635724 + 0.771916i \(0.719298\pi\)
\(128\) −12.8713 −1.13767
\(129\) 7.14919 0.629451
\(130\) 29.2419 2.56469
\(131\) 11.2001 0.978561 0.489280 0.872127i \(-0.337259\pi\)
0.489280 + 0.872127i \(0.337259\pi\)
\(132\) 44.5940 3.88141
\(133\) −9.33358 −0.809324
\(134\) −24.4326 −2.11066
\(135\) −10.7007 −0.920969
\(136\) −29.9797 −2.57074
\(137\) −19.1308 −1.63445 −0.817227 0.576316i \(-0.804490\pi\)
−0.817227 + 0.576316i \(0.804490\pi\)
\(138\) 35.7029 3.03924
\(139\) −4.18201 −0.354713 −0.177357 0.984147i \(-0.556755\pi\)
−0.177357 + 0.984147i \(0.556755\pi\)
\(140\) −27.5332 −2.32698
\(141\) −12.2700 −1.03332
\(142\) −3.97901 −0.333911
\(143\) −33.1315 −2.77060
\(144\) −8.07219 −0.672683
\(145\) 15.7492 1.30790
\(146\) −21.9762 −1.81876
\(147\) 1.56243 0.128867
\(148\) −5.09239 −0.418592
\(149\) −20.3468 −1.66687 −0.833436 0.552616i \(-0.813630\pi\)
−0.833436 + 0.552616i \(0.813630\pi\)
\(150\) 5.50163 0.449206
\(151\) 15.7402 1.28092 0.640461 0.767991i \(-0.278743\pi\)
0.640461 + 0.767991i \(0.278743\pi\)
\(152\) −27.1302 −2.20055
\(153\) −2.50136 −0.202223
\(154\) 43.4473 3.50108
\(155\) −9.02113 −0.724594
\(156\) −44.5614 −3.56777
\(157\) 11.7702 0.939366 0.469683 0.882835i \(-0.344368\pi\)
0.469683 + 0.882835i \(0.344368\pi\)
\(158\) 31.1360 2.47705
\(159\) 8.37089 0.663855
\(160\) −28.2712 −2.23504
\(161\) 24.9758 1.96837
\(162\) 17.2212 1.35302
\(163\) −10.9306 −0.856151 −0.428075 0.903743i \(-0.640808\pi\)
−0.428075 + 0.903743i \(0.640808\pi\)
\(164\) −41.8843 −3.27061
\(165\) 16.7110 1.30095
\(166\) 8.06257 0.625777
\(167\) −21.3050 −1.64863 −0.824316 0.566130i \(-0.808440\pi\)
−0.824316 + 0.566130i \(0.808440\pi\)
\(168\) 35.4857 2.73778
\(169\) 20.1073 1.54671
\(170\) −18.5004 −1.41891
\(171\) −2.26361 −0.173102
\(172\) 23.9388 1.82532
\(173\) −2.83316 −0.215401 −0.107701 0.994183i \(-0.534349\pi\)
−0.107701 + 0.994183i \(0.534349\pi\)
\(174\) −33.4258 −2.53401
\(175\) 3.84863 0.290929
\(176\) 67.6444 5.09889
\(177\) 1.54203 0.115906
\(178\) 5.55872 0.416644
\(179\) −11.3486 −0.848232 −0.424116 0.905608i \(-0.639415\pi\)
−0.424116 + 0.905608i \(0.639415\pi\)
\(180\) −6.67742 −0.497706
\(181\) −2.17518 −0.161680 −0.0808401 0.996727i \(-0.525760\pi\)
−0.0808401 + 0.996727i \(0.525760\pi\)
\(182\) −43.4155 −3.21817
\(183\) −10.0113 −0.740059
\(184\) 72.5978 5.35198
\(185\) −1.90830 −0.140301
\(186\) 19.1463 1.40388
\(187\) 20.9612 1.53283
\(188\) −41.0857 −2.99648
\(189\) 15.8873 1.15563
\(190\) −16.7419 −1.21459
\(191\) 5.11864 0.370372 0.185186 0.982704i \(-0.440711\pi\)
0.185186 + 0.982704i \(0.440711\pi\)
\(192\) 24.2705 1.75157
\(193\) 12.6350 0.909486 0.454743 0.890623i \(-0.349731\pi\)
0.454743 + 0.890623i \(0.349731\pi\)
\(194\) 33.6518 2.41606
\(195\) −16.6988 −1.19582
\(196\) 5.23176 0.373697
\(197\) 24.2001 1.72419 0.862094 0.506748i \(-0.169153\pi\)
0.862094 + 0.506748i \(0.169153\pi\)
\(198\) 10.5370 0.748829
\(199\) 14.6004 1.03500 0.517499 0.855684i \(-0.326863\pi\)
0.517499 + 0.855684i \(0.326863\pi\)
\(200\) 11.1869 0.791034
\(201\) 13.9524 0.984127
\(202\) −12.1813 −0.857070
\(203\) −23.3828 −1.64115
\(204\) 28.1925 1.97387
\(205\) −15.6956 −1.09623
\(206\) 29.6269 2.06421
\(207\) 6.05719 0.421004
\(208\) −67.5949 −4.68686
\(209\) 18.9689 1.31210
\(210\) 21.8981 1.51111
\(211\) −22.0729 −1.51956 −0.759779 0.650181i \(-0.774693\pi\)
−0.759779 + 0.650181i \(0.774693\pi\)
\(212\) 28.0297 1.92509
\(213\) 2.27224 0.155691
\(214\) −20.8309 −1.42397
\(215\) 8.97075 0.611800
\(216\) 46.1801 3.14216
\(217\) 13.3937 0.909222
\(218\) 2.66315 0.180372
\(219\) 12.5497 0.848028
\(220\) 55.9563 3.77257
\(221\) −20.9459 −1.40897
\(222\) 4.05016 0.271829
\(223\) −4.55927 −0.305311 −0.152656 0.988279i \(-0.548783\pi\)
−0.152656 + 0.988279i \(0.548783\pi\)
\(224\) 41.9743 2.80453
\(225\) 0.933380 0.0622254
\(226\) 35.3359 2.35051
\(227\) −13.5291 −0.897959 −0.448980 0.893542i \(-0.648212\pi\)
−0.448980 + 0.893542i \(0.648212\pi\)
\(228\) 25.5129 1.68963
\(229\) 17.6423 1.16584 0.582919 0.812530i \(-0.301910\pi\)
0.582919 + 0.812530i \(0.301910\pi\)
\(230\) 44.7998 2.95401
\(231\) −24.8108 −1.63243
\(232\) −67.9675 −4.46229
\(233\) 14.8513 0.972942 0.486471 0.873697i \(-0.338284\pi\)
0.486471 + 0.873697i \(0.338284\pi\)
\(234\) −10.5293 −0.688319
\(235\) −15.3963 −1.00434
\(236\) 5.16344 0.336111
\(237\) −17.7804 −1.15496
\(238\) 27.4675 1.78046
\(239\) 0.431188 0.0278912 0.0139456 0.999903i \(-0.495561\pi\)
0.0139456 + 0.999903i \(0.495561\pi\)
\(240\) 34.0938 2.20075
\(241\) −0.533625 −0.0343738 −0.0171869 0.999852i \(-0.505471\pi\)
−0.0171869 + 0.999852i \(0.505471\pi\)
\(242\) −59.0042 −3.79293
\(243\) 6.98803 0.448282
\(244\) −33.5227 −2.14607
\(245\) 1.96053 0.125254
\(246\) 33.3120 2.12390
\(247\) −18.9550 −1.20608
\(248\) 38.9318 2.47217
\(249\) −4.60418 −0.291778
\(250\) 32.3140 2.04371
\(251\) −3.74928 −0.236652 −0.118326 0.992975i \(-0.537753\pi\)
−0.118326 + 0.992975i \(0.537753\pi\)
\(252\) 9.91398 0.624522
\(253\) −50.7588 −3.19118
\(254\) 38.1590 2.39431
\(255\) 10.5648 0.661591
\(256\) 2.36040 0.147525
\(257\) −13.7054 −0.854917 −0.427459 0.904035i \(-0.640591\pi\)
−0.427459 + 0.904035i \(0.640591\pi\)
\(258\) −19.0394 −1.18534
\(259\) 2.83326 0.176050
\(260\) −55.9154 −3.46772
\(261\) −5.67087 −0.351018
\(262\) −29.8277 −1.84276
\(263\) 4.91308 0.302954 0.151477 0.988461i \(-0.451597\pi\)
0.151477 + 0.988461i \(0.451597\pi\)
\(264\) −72.1184 −4.43858
\(265\) 10.5037 0.645239
\(266\) 24.8568 1.52407
\(267\) −3.17434 −0.194267
\(268\) 46.7192 2.85383
\(269\) −24.9090 −1.51873 −0.759363 0.650667i \(-0.774489\pi\)
−0.759363 + 0.650667i \(0.774489\pi\)
\(270\) 28.4976 1.73431
\(271\) 19.9588 1.21241 0.606205 0.795308i \(-0.292691\pi\)
0.606205 + 0.795308i \(0.292691\pi\)
\(272\) 42.7650 2.59301
\(273\) 24.7927 1.50052
\(274\) 50.9482 3.07790
\(275\) −7.82166 −0.471664
\(276\) −68.2700 −4.10937
\(277\) −7.27225 −0.436947 −0.218474 0.975843i \(-0.570108\pi\)
−0.218474 + 0.975843i \(0.570108\pi\)
\(278\) 11.1373 0.667973
\(279\) 3.24827 0.194469
\(280\) 44.5272 2.66101
\(281\) −16.4327 −0.980293 −0.490147 0.871640i \(-0.663057\pi\)
−0.490147 + 0.871640i \(0.663057\pi\)
\(282\) 32.6769 1.94588
\(283\) −1.52497 −0.0906503 −0.0453251 0.998972i \(-0.514432\pi\)
−0.0453251 + 0.998972i \(0.514432\pi\)
\(284\) 7.60853 0.451483
\(285\) 9.56060 0.566321
\(286\) 88.2343 5.21740
\(287\) 23.3032 1.37555
\(288\) 10.1797 0.599847
\(289\) −3.74826 −0.220486
\(290\) −41.9425 −2.46295
\(291\) −19.2171 −1.12653
\(292\) 42.0222 2.45916
\(293\) −10.1968 −0.595706 −0.297853 0.954612i \(-0.596270\pi\)
−0.297853 + 0.954612i \(0.596270\pi\)
\(294\) −4.16100 −0.242675
\(295\) 1.93493 0.112656
\(296\) 8.23552 0.478680
\(297\) −32.2882 −1.87355
\(298\) 54.1866 3.13895
\(299\) 50.7217 2.93331
\(300\) −10.5200 −0.607374
\(301\) −13.3189 −0.767687
\(302\) −41.9187 −2.41215
\(303\) 6.95619 0.399623
\(304\) 38.7003 2.21961
\(305\) −12.5622 −0.719307
\(306\) 6.66150 0.380813
\(307\) 24.9669 1.42494 0.712468 0.701704i \(-0.247577\pi\)
0.712468 + 0.701704i \(0.247577\pi\)
\(308\) −83.0784 −4.73383
\(309\) −16.9187 −0.962469
\(310\) 24.0247 1.36451
\(311\) −29.8480 −1.69252 −0.846262 0.532767i \(-0.821152\pi\)
−0.846262 + 0.532767i \(0.821152\pi\)
\(312\) 72.0657 4.07991
\(313\) −17.2799 −0.976716 −0.488358 0.872643i \(-0.662404\pi\)
−0.488358 + 0.872643i \(0.662404\pi\)
\(314\) −31.3459 −1.76895
\(315\) 3.71513 0.209324
\(316\) −59.5373 −3.34923
\(317\) −3.26515 −0.183389 −0.0916946 0.995787i \(-0.529228\pi\)
−0.0916946 + 0.995787i \(0.529228\pi\)
\(318\) −22.2930 −1.25013
\(319\) 47.5215 2.66069
\(320\) 30.4544 1.70245
\(321\) 11.8956 0.663948
\(322\) −66.5143 −3.70670
\(323\) 11.9922 0.667263
\(324\) −32.9298 −1.82943
\(325\) 7.81594 0.433550
\(326\) 29.1099 1.61225
\(327\) −1.52081 −0.0841011
\(328\) 67.7361 3.74010
\(329\) 22.8589 1.26025
\(330\) −44.5040 −2.44986
\(331\) 16.6989 0.917854 0.458927 0.888474i \(-0.348234\pi\)
0.458927 + 0.888474i \(0.348234\pi\)
\(332\) −15.4170 −0.846116
\(333\) 0.687131 0.0376545
\(334\) 56.7386 3.10460
\(335\) 17.5074 0.956531
\(336\) −50.6191 −2.76150
\(337\) 3.01315 0.164137 0.0820685 0.996627i \(-0.473847\pi\)
0.0820685 + 0.996627i \(0.473847\pi\)
\(338\) −53.5488 −2.91267
\(339\) −20.1788 −1.09596
\(340\) 35.3758 1.91852
\(341\) −27.2203 −1.47406
\(342\) 6.02834 0.325975
\(343\) 16.9220 0.913703
\(344\) −38.7144 −2.08734
\(345\) −25.5832 −1.37735
\(346\) 7.54516 0.405630
\(347\) 17.9732 0.964850 0.482425 0.875937i \(-0.339756\pi\)
0.482425 + 0.875937i \(0.339756\pi\)
\(348\) 63.9157 3.42624
\(349\) 10.3890 0.556112 0.278056 0.960565i \(-0.410310\pi\)
0.278056 + 0.960565i \(0.410310\pi\)
\(350\) −10.2495 −0.547858
\(351\) 32.2646 1.72215
\(352\) −85.3054 −4.54680
\(353\) −10.8775 −0.578948 −0.289474 0.957186i \(-0.593480\pi\)
−0.289474 + 0.957186i \(0.593480\pi\)
\(354\) −4.10666 −0.218267
\(355\) 2.85119 0.151326
\(356\) −10.6292 −0.563346
\(357\) −15.6855 −0.830165
\(358\) 30.2230 1.59734
\(359\) 5.63415 0.297359 0.148679 0.988885i \(-0.452498\pi\)
0.148679 + 0.988885i \(0.452498\pi\)
\(360\) 10.7989 0.569150
\(361\) −8.14765 −0.428824
\(362\) 5.79285 0.304465
\(363\) 33.6947 1.76851
\(364\) 83.0176 4.35130
\(365\) 15.7472 0.824248
\(366\) 26.6617 1.39363
\(367\) −17.1351 −0.894444 −0.447222 0.894423i \(-0.647587\pi\)
−0.447222 + 0.894423i \(0.647587\pi\)
\(368\) −103.558 −5.39834
\(369\) 5.65156 0.294209
\(370\) 5.08211 0.264206
\(371\) −15.5949 −0.809647
\(372\) −36.6109 −1.89819
\(373\) 22.0572 1.14208 0.571039 0.820923i \(-0.306541\pi\)
0.571039 + 0.820923i \(0.306541\pi\)
\(374\) −55.8229 −2.88653
\(375\) −18.4531 −0.952914
\(376\) 66.4446 3.42662
\(377\) −47.4867 −2.44569
\(378\) −42.3104 −2.17621
\(379\) −3.63517 −0.186726 −0.0933631 0.995632i \(-0.529762\pi\)
−0.0933631 + 0.995632i \(0.529762\pi\)
\(380\) 32.0134 1.64225
\(381\) −21.7910 −1.11638
\(382\) −13.6317 −0.697460
\(383\) −25.5162 −1.30382 −0.651909 0.758297i \(-0.726032\pi\)
−0.651909 + 0.758297i \(0.726032\pi\)
\(384\) −19.5748 −0.998921
\(385\) −31.1325 −1.58666
\(386\) −33.6489 −1.71269
\(387\) −3.23013 −0.164197
\(388\) −64.3479 −3.26677
\(389\) −4.22127 −0.214027 −0.107013 0.994258i \(-0.534129\pi\)
−0.107013 + 0.994258i \(0.534129\pi\)
\(390\) 44.4715 2.25190
\(391\) −32.0899 −1.62286
\(392\) −8.46091 −0.427341
\(393\) 17.0333 0.859217
\(394\) −64.4487 −3.24688
\(395\) −22.3108 −1.12258
\(396\) −20.1484 −1.01250
\(397\) −15.3456 −0.770171 −0.385086 0.922881i \(-0.625828\pi\)
−0.385086 + 0.922881i \(0.625828\pi\)
\(398\) −38.8832 −1.94904
\(399\) −14.1946 −0.710620
\(400\) −15.9577 −0.797887
\(401\) 22.0609 1.10167 0.550833 0.834615i \(-0.314310\pi\)
0.550833 + 0.834615i \(0.314310\pi\)
\(402\) −37.1574 −1.85324
\(403\) 27.2004 1.35495
\(404\) 23.2926 1.15885
\(405\) −12.3400 −0.613178
\(406\) 62.2721 3.09051
\(407\) −5.75810 −0.285419
\(408\) −45.5935 −2.25722
\(409\) −8.89558 −0.439858 −0.219929 0.975516i \(-0.570583\pi\)
−0.219929 + 0.975516i \(0.570583\pi\)
\(410\) 41.7997 2.06434
\(411\) −29.0943 −1.43512
\(412\) −56.6516 −2.79102
\(413\) −2.87279 −0.141361
\(414\) −16.1312 −0.792807
\(415\) −5.77730 −0.283596
\(416\) 85.2431 4.17938
\(417\) −6.36005 −0.311453
\(418\) −50.5170 −2.47087
\(419\) −15.8380 −0.773735 −0.386867 0.922135i \(-0.626443\pi\)
−0.386867 + 0.922135i \(0.626443\pi\)
\(420\) −41.8728 −2.04318
\(421\) −8.13430 −0.396442 −0.198221 0.980157i \(-0.563516\pi\)
−0.198221 + 0.980157i \(0.563516\pi\)
\(422\) 58.7834 2.86153
\(423\) 5.54381 0.269549
\(424\) −45.3302 −2.20143
\(425\) −4.94488 −0.239862
\(426\) −6.05133 −0.293188
\(427\) 18.6510 0.902587
\(428\) 39.8321 1.92536
\(429\) −50.3868 −2.43270
\(430\) −23.8905 −1.15210
\(431\) −36.1977 −1.74358 −0.871790 0.489880i \(-0.837041\pi\)
−0.871790 + 0.489880i \(0.837041\pi\)
\(432\) −65.8743 −3.16938
\(433\) 24.8649 1.19493 0.597464 0.801895i \(-0.296175\pi\)
0.597464 + 0.801895i \(0.296175\pi\)
\(434\) −35.6694 −1.71219
\(435\) 23.9515 1.14839
\(436\) −5.09239 −0.243881
\(437\) −29.0398 −1.38916
\(438\) −33.4217 −1.59695
\(439\) 15.9773 0.762557 0.381278 0.924460i \(-0.375484\pi\)
0.381278 + 0.924460i \(0.375484\pi\)
\(440\) −90.4937 −4.31412
\(441\) −0.705936 −0.0336160
\(442\) 55.7821 2.65328
\(443\) 33.2803 1.58119 0.790596 0.612338i \(-0.209771\pi\)
0.790596 + 0.612338i \(0.209771\pi\)
\(444\) −7.74457 −0.367541
\(445\) −3.98314 −0.188819
\(446\) 12.1420 0.574943
\(447\) −30.9436 −1.46358
\(448\) −45.2157 −2.13624
\(449\) 12.6454 0.596772 0.298386 0.954445i \(-0.403552\pi\)
0.298386 + 0.954445i \(0.403552\pi\)
\(450\) −2.48574 −0.117179
\(451\) −47.3597 −2.23008
\(452\) −67.5681 −3.17813
\(453\) 23.9379 1.12470
\(454\) 36.0301 1.69098
\(455\) 31.1097 1.45845
\(456\) −41.2599 −1.93217
\(457\) −24.7432 −1.15744 −0.578719 0.815527i \(-0.696447\pi\)
−0.578719 + 0.815527i \(0.696447\pi\)
\(458\) −46.9843 −2.19543
\(459\) −20.4127 −0.952784
\(460\) −85.6647 −3.99414
\(461\) −27.1233 −1.26326 −0.631629 0.775271i \(-0.717614\pi\)
−0.631629 + 0.775271i \(0.717614\pi\)
\(462\) 66.0751 3.07409
\(463\) 27.2321 1.26558 0.632792 0.774322i \(-0.281909\pi\)
0.632792 + 0.774322i \(0.281909\pi\)
\(464\) 96.9533 4.50094
\(465\) −13.7194 −0.636224
\(466\) −39.5513 −1.83218
\(467\) 24.5842 1.13762 0.568812 0.822468i \(-0.307403\pi\)
0.568812 + 0.822468i \(0.307403\pi\)
\(468\) 20.1337 0.930679
\(469\) −25.9932 −1.20026
\(470\) 41.0027 1.89132
\(471\) 17.9003 0.824802
\(472\) −8.35042 −0.384359
\(473\) 27.0683 1.24460
\(474\) 47.3521 2.17495
\(475\) −4.47488 −0.205321
\(476\) −52.5225 −2.40736
\(477\) −3.78212 −0.173171
\(478\) −1.14832 −0.0525230
\(479\) −27.9236 −1.27586 −0.637931 0.770093i \(-0.720210\pi\)
−0.637931 + 0.770093i \(0.720210\pi\)
\(480\) −42.9953 −1.96246
\(481\) 5.75389 0.262355
\(482\) 1.42113 0.0647305
\(483\) 37.9834 1.72831
\(484\) 112.826 5.12844
\(485\) −24.1135 −1.09494
\(486\) −18.6102 −0.844176
\(487\) 18.2310 0.826126 0.413063 0.910702i \(-0.364459\pi\)
0.413063 + 0.910702i \(0.364459\pi\)
\(488\) 54.2135 2.45413
\(489\) −16.6234 −0.751735
\(490\) −5.22120 −0.235870
\(491\) 1.54878 0.0698956 0.0349478 0.999389i \(-0.488874\pi\)
0.0349478 + 0.999389i \(0.488874\pi\)
\(492\) −63.6981 −2.87173
\(493\) 30.0432 1.35308
\(494\) 50.4801 2.27121
\(495\) −7.55034 −0.339363
\(496\) −55.5348 −2.49359
\(497\) −4.23317 −0.189883
\(498\) 12.2616 0.549458
\(499\) −33.1204 −1.48267 −0.741336 0.671134i \(-0.765807\pi\)
−0.741336 + 0.671134i \(0.765807\pi\)
\(500\) −61.7896 −2.76332
\(501\) −32.4009 −1.44757
\(502\) 9.98491 0.445648
\(503\) −17.1074 −0.762782 −0.381391 0.924414i \(-0.624555\pi\)
−0.381391 + 0.924414i \(0.624555\pi\)
\(504\) −16.0331 −0.714170
\(505\) 8.72858 0.388417
\(506\) 135.179 6.00942
\(507\) 30.5794 1.35808
\(508\) −72.9663 −3.23736
\(509\) −1.12345 −0.0497962 −0.0248981 0.999690i \(-0.507926\pi\)
−0.0248981 + 0.999690i \(0.507926\pi\)
\(510\) −28.1356 −1.24587
\(511\) −23.3799 −1.03427
\(512\) 19.4564 0.859860
\(513\) −18.4725 −0.815581
\(514\) 36.4995 1.60992
\(515\) −21.2294 −0.935480
\(516\) 36.4065 1.60271
\(517\) −46.4567 −2.04316
\(518\) −7.54541 −0.331526
\(519\) −4.30871 −0.189131
\(520\) 90.4275 3.96551
\(521\) −17.0720 −0.747940 −0.373970 0.927441i \(-0.622004\pi\)
−0.373970 + 0.927441i \(0.622004\pi\)
\(522\) 15.1024 0.661014
\(523\) −23.4283 −1.02445 −0.512224 0.858852i \(-0.671178\pi\)
−0.512224 + 0.858852i \(0.671178\pi\)
\(524\) 57.0355 2.49161
\(525\) 5.85304 0.255448
\(526\) −13.0843 −0.570503
\(527\) −17.2088 −0.749625
\(528\) 102.874 4.47703
\(529\) 54.7077 2.37860
\(530\) −27.9731 −1.21507
\(531\) −0.696717 −0.0302350
\(532\) −47.5303 −2.06070
\(533\) 47.3250 2.04987
\(534\) 8.45377 0.365830
\(535\) 14.9265 0.645330
\(536\) −75.5553 −3.26349
\(537\) −17.2590 −0.744783
\(538\) 66.3364 2.85997
\(539\) 5.91569 0.254807
\(540\) −54.4921 −2.34497
\(541\) 18.1283 0.779398 0.389699 0.920942i \(-0.372579\pi\)
0.389699 + 0.920942i \(0.372579\pi\)
\(542\) −53.1533 −2.28313
\(543\) −3.30805 −0.141962
\(544\) −53.9304 −2.31225
\(545\) −1.90830 −0.0817428
\(546\) −66.0268 −2.82569
\(547\) 35.7185 1.52721 0.763606 0.645682i \(-0.223427\pi\)
0.763606 + 0.645682i \(0.223427\pi\)
\(548\) −97.4215 −4.16164
\(549\) 4.52330 0.193050
\(550\) 20.8303 0.888206
\(551\) 27.1877 1.15823
\(552\) 110.408 4.69926
\(553\) 33.1248 1.40861
\(554\) 19.3671 0.822831
\(555\) −2.90217 −0.123190
\(556\) −21.2964 −0.903170
\(557\) 41.7699 1.76985 0.884924 0.465735i \(-0.154210\pi\)
0.884924 + 0.465735i \(0.154210\pi\)
\(558\) −8.65065 −0.366211
\(559\) −27.0485 −1.14403
\(560\) −63.5165 −2.68406
\(561\) 31.8780 1.34589
\(562\) 43.7628 1.84602
\(563\) 10.5338 0.443945 0.221973 0.975053i \(-0.428750\pi\)
0.221973 + 0.975053i \(0.428750\pi\)
\(564\) −62.4836 −2.63104
\(565\) −25.3202 −1.06523
\(566\) 4.06124 0.170707
\(567\) 18.3212 0.769417
\(568\) −12.3047 −0.516292
\(569\) 1.77931 0.0745925 0.0372963 0.999304i \(-0.488125\pi\)
0.0372963 + 0.999304i \(0.488125\pi\)
\(570\) −25.4614 −1.06646
\(571\) −47.2598 −1.97776 −0.988880 0.148713i \(-0.952487\pi\)
−0.988880 + 0.148713i \(0.952487\pi\)
\(572\) −168.719 −7.05448
\(573\) 7.78449 0.325202
\(574\) −62.0601 −2.59034
\(575\) 11.9743 0.499364
\(576\) −10.9658 −0.456910
\(577\) 23.5199 0.979146 0.489573 0.871962i \(-0.337153\pi\)
0.489573 + 0.871962i \(0.337153\pi\)
\(578\) 9.98219 0.415204
\(579\) 19.2154 0.798566
\(580\) 80.2010 3.33017
\(581\) 8.57756 0.355857
\(582\) 51.1781 2.12140
\(583\) 31.6939 1.31263
\(584\) −67.9591 −2.81217
\(585\) 7.54482 0.311940
\(586\) 27.1558 1.12179
\(587\) 17.7788 0.733810 0.366905 0.930258i \(-0.380417\pi\)
0.366905 + 0.930258i \(0.380417\pi\)
\(588\) 7.95653 0.328122
\(589\) −15.5731 −0.641678
\(590\) −5.15301 −0.212146
\(591\) 36.8039 1.51391
\(592\) −11.7477 −0.482827
\(593\) −0.568642 −0.0233513 −0.0116757 0.999932i \(-0.503717\pi\)
−0.0116757 + 0.999932i \(0.503717\pi\)
\(594\) 85.9884 3.52815
\(595\) −19.6821 −0.806886
\(596\) −103.614 −4.24419
\(597\) 22.2045 0.908771
\(598\) −135.080 −5.52382
\(599\) 1.98833 0.0812411 0.0406206 0.999175i \(-0.487067\pi\)
0.0406206 + 0.999175i \(0.487067\pi\)
\(600\) 17.0132 0.694561
\(601\) −11.0555 −0.450964 −0.225482 0.974247i \(-0.572396\pi\)
−0.225482 + 0.974247i \(0.572396\pi\)
\(602\) 35.4702 1.44566
\(603\) −6.30395 −0.256717
\(604\) 80.1554 3.26148
\(605\) 42.2799 1.71892
\(606\) −18.5254 −0.752543
\(607\) −16.8242 −0.682871 −0.341436 0.939905i \(-0.610913\pi\)
−0.341436 + 0.939905i \(0.610913\pi\)
\(608\) −48.8044 −1.97928
\(609\) −35.5609 −1.44100
\(610\) 33.4550 1.35455
\(611\) 46.4227 1.87806
\(612\) −12.7379 −0.514899
\(613\) 8.00862 0.323465 0.161733 0.986835i \(-0.448292\pi\)
0.161733 + 0.986835i \(0.448292\pi\)
\(614\) −66.4907 −2.68335
\(615\) −23.8700 −0.962531
\(616\) 134.356 5.41336
\(617\) 20.1860 0.812659 0.406330 0.913727i \(-0.366808\pi\)
0.406330 + 0.913727i \(0.366808\pi\)
\(618\) 45.0570 1.81246
\(619\) 22.0187 0.885004 0.442502 0.896767i \(-0.354091\pi\)
0.442502 + 0.896767i \(0.354091\pi\)
\(620\) −45.9391 −1.84496
\(621\) 49.4306 1.98358
\(622\) 79.4898 3.18725
\(623\) 5.91378 0.236930
\(624\) −102.799 −4.11526
\(625\) −16.3630 −0.654518
\(626\) 46.0190 1.83929
\(627\) 28.8481 1.15208
\(628\) 59.9386 2.39181
\(629\) −3.64029 −0.145148
\(630\) −9.89396 −0.394185
\(631\) −44.6918 −1.77915 −0.889576 0.456788i \(-0.849000\pi\)
−0.889576 + 0.456788i \(0.849000\pi\)
\(632\) 96.2849 3.83001
\(633\) −33.5687 −1.33423
\(634\) 8.69560 0.345346
\(635\) −27.3431 −1.08508
\(636\) 42.6279 1.69031
\(637\) −5.91136 −0.234217
\(638\) −126.557 −5.01044
\(639\) −1.02664 −0.0406132
\(640\) −24.5623 −0.970909
\(641\) −34.4436 −1.36044 −0.680220 0.733008i \(-0.738116\pi\)
−0.680220 + 0.733008i \(0.738116\pi\)
\(642\) −31.6798 −1.25030
\(643\) 3.99052 0.157371 0.0786855 0.996899i \(-0.474928\pi\)
0.0786855 + 0.996899i \(0.474928\pi\)
\(644\) 127.186 5.01185
\(645\) 13.6428 0.537186
\(646\) −31.9370 −1.25655
\(647\) −10.2354 −0.402394 −0.201197 0.979551i \(-0.564483\pi\)
−0.201197 + 0.979551i \(0.564483\pi\)
\(648\) 53.2547 2.09204
\(649\) 5.83844 0.229179
\(650\) −20.8150 −0.816433
\(651\) 20.3693 0.798334
\(652\) −55.6629 −2.17993
\(653\) −36.1716 −1.41550 −0.707751 0.706462i \(-0.750290\pi\)
−0.707751 + 0.706462i \(0.750290\pi\)
\(654\) 4.05016 0.158374
\(655\) 21.3733 0.835123
\(656\) −96.6232 −3.77250
\(657\) −5.67017 −0.221214
\(658\) −60.8768 −2.37322
\(659\) 21.7418 0.846939 0.423470 0.905910i \(-0.360812\pi\)
0.423470 + 0.905910i \(0.360812\pi\)
\(660\) 85.0990 3.31247
\(661\) 22.5901 0.878653 0.439327 0.898327i \(-0.355217\pi\)
0.439327 + 0.898327i \(0.355217\pi\)
\(662\) −44.4717 −1.72844
\(663\) −31.8547 −1.23713
\(664\) 24.9326 0.967574
\(665\) −17.8113 −0.690693
\(666\) −1.82994 −0.0709086
\(667\) −72.7516 −2.81695
\(668\) −108.494 −4.19774
\(669\) −6.93380 −0.268076
\(670\) −46.6249 −1.80128
\(671\) −37.9049 −1.46330
\(672\) 63.8351 2.46249
\(673\) −11.8697 −0.457544 −0.228772 0.973480i \(-0.573471\pi\)
−0.228772 + 0.973480i \(0.573471\pi\)
\(674\) −8.02449 −0.309092
\(675\) 7.61699 0.293178
\(676\) 102.394 3.93824
\(677\) −10.5098 −0.403925 −0.201962 0.979393i \(-0.564732\pi\)
−0.201962 + 0.979393i \(0.564732\pi\)
\(678\) 53.7392 2.06384
\(679\) 35.8013 1.37393
\(680\) −57.2104 −2.19392
\(681\) −20.5752 −0.788445
\(682\) 72.4918 2.77585
\(683\) −20.1156 −0.769703 −0.384852 0.922978i \(-0.625747\pi\)
−0.384852 + 0.922978i \(0.625747\pi\)
\(684\) −11.5272 −0.440753
\(685\) −36.5074 −1.39487
\(686\) −45.0660 −1.72063
\(687\) 26.8307 1.02365
\(688\) 55.2247 2.10542
\(689\) −31.6707 −1.20656
\(690\) 68.1321 2.59374
\(691\) 35.6081 1.35460 0.677298 0.735709i \(-0.263151\pi\)
0.677298 + 0.735709i \(0.263151\pi\)
\(692\) −14.4276 −0.548455
\(693\) 11.2100 0.425832
\(694\) −47.8653 −1.81694
\(695\) −7.98054 −0.302719
\(696\) −103.366 −3.91807
\(697\) −29.9410 −1.13409
\(698\) −27.6676 −1.04723
\(699\) 22.5861 0.854283
\(700\) 19.5987 0.740762
\(701\) −21.9323 −0.828373 −0.414186 0.910192i \(-0.635934\pi\)
−0.414186 + 0.910192i \(0.635934\pi\)
\(702\) −85.9255 −3.24305
\(703\) −3.29429 −0.124247
\(704\) 91.8929 3.46334
\(705\) −23.4149 −0.881856
\(706\) 28.9683 1.09024
\(707\) −12.9593 −0.487386
\(708\) 7.85262 0.295120
\(709\) 30.0018 1.12674 0.563371 0.826204i \(-0.309504\pi\)
0.563371 + 0.826204i \(0.309504\pi\)
\(710\) −7.59316 −0.284966
\(711\) 8.03353 0.301281
\(712\) 17.1897 0.644213
\(713\) 41.6721 1.56063
\(714\) 41.7729 1.56331
\(715\) −63.2250 −2.36448
\(716\) −57.7914 −2.15977
\(717\) 0.655756 0.0244897
\(718\) −15.0046 −0.559967
\(719\) 44.7603 1.66928 0.834639 0.550798i \(-0.185676\pi\)
0.834639 + 0.550798i \(0.185676\pi\)
\(720\) −15.4042 −0.574081
\(721\) 31.5193 1.17384
\(722\) 21.6985 0.807533
\(723\) −0.811543 −0.0301816
\(724\) −11.0769 −0.411669
\(725\) −11.2106 −0.416352
\(726\) −89.7343 −3.33035
\(727\) −43.8411 −1.62598 −0.812988 0.582281i \(-0.802161\pi\)
−0.812988 + 0.582281i \(0.802161\pi\)
\(728\) −134.258 −4.97592
\(729\) 30.0269 1.11211
\(730\) −41.9373 −1.55217
\(731\) 17.1127 0.632935
\(732\) −50.9817 −1.88434
\(733\) −28.7311 −1.06121 −0.530603 0.847620i \(-0.678034\pi\)
−0.530603 + 0.847620i \(0.678034\pi\)
\(734\) 45.6334 1.68436
\(735\) 2.98160 0.109978
\(736\) 130.596 4.81383
\(737\) 52.8266 1.94589
\(738\) −15.0510 −0.554034
\(739\) −52.3300 −1.92499 −0.962495 0.271300i \(-0.912546\pi\)
−0.962495 + 0.271300i \(0.912546\pi\)
\(740\) −9.71784 −0.357235
\(741\) −28.8270 −1.05899
\(742\) 41.5316 1.52467
\(743\) 6.84981 0.251295 0.125648 0.992075i \(-0.459899\pi\)
0.125648 + 0.992075i \(0.459899\pi\)
\(744\) 59.2079 2.17067
\(745\) −38.8278 −1.42254
\(746\) −58.7417 −2.15069
\(747\) 2.08025 0.0761125
\(748\) 106.743 3.90290
\(749\) −22.1614 −0.809761
\(750\) 49.1435 1.79447
\(751\) −24.5586 −0.896157 −0.448078 0.893994i \(-0.647891\pi\)
−0.448078 + 0.893994i \(0.647891\pi\)
\(752\) −94.7809 −3.45631
\(753\) −5.70195 −0.207790
\(754\) 126.464 4.60556
\(755\) 30.0371 1.09316
\(756\) 80.9045 2.94247
\(757\) −14.1443 −0.514082 −0.257041 0.966401i \(-0.582747\pi\)
−0.257041 + 0.966401i \(0.582747\pi\)
\(758\) 9.68102 0.351631
\(759\) −77.1946 −2.80199
\(760\) −51.7727 −1.87799
\(761\) 17.3055 0.627325 0.313662 0.949535i \(-0.398444\pi\)
0.313662 + 0.949535i \(0.398444\pi\)
\(762\) 58.0327 2.10230
\(763\) 2.83326 0.102571
\(764\) 26.0661 0.943039
\(765\) −4.77335 −0.172581
\(766\) 67.9537 2.45527
\(767\) −5.83417 −0.210660
\(768\) 3.58972 0.129533
\(769\) 25.4240 0.916812 0.458406 0.888743i \(-0.348421\pi\)
0.458406 + 0.888743i \(0.348421\pi\)
\(770\) 82.9106 2.98789
\(771\) −20.8433 −0.750653
\(772\) 64.3423 2.31573
\(773\) 31.3428 1.12732 0.563660 0.826007i \(-0.309393\pi\)
0.563660 + 0.826007i \(0.309393\pi\)
\(774\) 8.60234 0.309205
\(775\) 6.42144 0.230665
\(776\) 104.065 3.73570
\(777\) 4.30886 0.154579
\(778\) 11.2419 0.403041
\(779\) −27.0951 −0.970783
\(780\) −85.0368 −3.04481
\(781\) 8.60316 0.307845
\(782\) 85.4604 3.05606
\(783\) −46.2780 −1.65384
\(784\) 12.0692 0.431043
\(785\) 22.4612 0.801673
\(786\) −45.3623 −1.61802
\(787\) −9.60509 −0.342385 −0.171192 0.985238i \(-0.554762\pi\)
−0.171192 + 0.985238i \(0.554762\pi\)
\(788\) 123.237 4.39012
\(789\) 7.47188 0.266006
\(790\) 59.4170 2.11396
\(791\) 37.5929 1.33665
\(792\) 32.5844 1.15784
\(793\) 37.8772 1.34506
\(794\) 40.8676 1.45034
\(795\) 15.9742 0.566547
\(796\) 74.3512 2.63531
\(797\) 6.23595 0.220889 0.110444 0.993882i \(-0.464773\pi\)
0.110444 + 0.993882i \(0.464773\pi\)
\(798\) 37.8025 1.33819
\(799\) −29.3701 −1.03904
\(800\) 20.1241 0.711495
\(801\) 1.43423 0.0506759
\(802\) −58.7515 −2.07459
\(803\) 47.5156 1.67679
\(804\) 71.0511 2.50578
\(805\) 47.6614 1.67984
\(806\) −72.4388 −2.55155
\(807\) −37.8818 −1.33350
\(808\) −37.6692 −1.32520
\(809\) 34.1747 1.20152 0.600759 0.799430i \(-0.294865\pi\)
0.600759 + 0.799430i \(0.294865\pi\)
\(810\) 32.8633 1.15470
\(811\) 16.4495 0.577620 0.288810 0.957386i \(-0.406740\pi\)
0.288810 + 0.957386i \(0.406740\pi\)
\(812\) −119.075 −4.17870
\(813\) 30.3536 1.06455
\(814\) 15.3347 0.537482
\(815\) −20.8589 −0.730656
\(816\) 65.0376 2.27677
\(817\) 15.4861 0.541791
\(818\) 23.6903 0.828312
\(819\) −11.2018 −0.391422
\(820\) −79.9280 −2.79121
\(821\) −32.7513 −1.14303 −0.571515 0.820592i \(-0.693644\pi\)
−0.571515 + 0.820592i \(0.693644\pi\)
\(822\) 77.4827 2.70252
\(823\) −3.80651 −0.132687 −0.0663434 0.997797i \(-0.521133\pi\)
−0.0663434 + 0.997797i \(0.521133\pi\)
\(824\) 91.6181 3.19167
\(825\) −11.8953 −0.414140
\(826\) 7.65068 0.266201
\(827\) 45.8443 1.59416 0.797081 0.603872i \(-0.206376\pi\)
0.797081 + 0.603872i \(0.206376\pi\)
\(828\) 30.8456 1.07196
\(829\) −14.4902 −0.503265 −0.251633 0.967823i \(-0.580968\pi\)
−0.251633 + 0.967823i \(0.580968\pi\)
\(830\) 15.3858 0.534050
\(831\) −11.0597 −0.383658
\(832\) −91.8257 −3.18348
\(833\) 3.73992 0.129581
\(834\) 16.9378 0.586508
\(835\) −40.6565 −1.40698
\(836\) 96.5969 3.34087
\(837\) 26.5080 0.916251
\(838\) 42.1789 1.45705
\(839\) −5.23388 −0.180694 −0.0903468 0.995910i \(-0.528798\pi\)
−0.0903468 + 0.995910i \(0.528798\pi\)
\(840\) 67.7175 2.33648
\(841\) 39.1115 1.34867
\(842\) 21.6629 0.746553
\(843\) −24.9911 −0.860738
\(844\) −112.404 −3.86909
\(845\) 38.3708 1.32000
\(846\) −14.7640 −0.507597
\(847\) −62.7730 −2.15691
\(848\) 64.6619 2.22050
\(849\) −2.31920 −0.0795947
\(850\) 13.1690 0.451692
\(851\) 8.81520 0.302181
\(852\) 11.5711 0.396421
\(853\) −26.0613 −0.892321 −0.446161 0.894953i \(-0.647209\pi\)
−0.446161 + 0.894953i \(0.647209\pi\)
\(854\) −49.6706 −1.69969
\(855\) −4.31965 −0.147729
\(856\) −64.4172 −2.20174
\(857\) 42.7655 1.46084 0.730421 0.682997i \(-0.239324\pi\)
0.730421 + 0.682997i \(0.239324\pi\)
\(858\) 134.188 4.58110
\(859\) −44.0380 −1.50256 −0.751279 0.659985i \(-0.770563\pi\)
−0.751279 + 0.659985i \(0.770563\pi\)
\(860\) 45.6826 1.55776
\(861\) 35.4398 1.20779
\(862\) 96.4000 3.28340
\(863\) −33.5392 −1.14169 −0.570844 0.821059i \(-0.693384\pi\)
−0.570844 + 0.821059i \(0.693384\pi\)
\(864\) 83.0733 2.82621
\(865\) −5.40654 −0.183828
\(866\) −66.2190 −2.25021
\(867\) −5.70039 −0.193596
\(868\) 68.2058 2.31506
\(869\) −67.3203 −2.28369
\(870\) −63.7867 −2.16257
\(871\) −52.7880 −1.78865
\(872\) 8.23552 0.278890
\(873\) 8.68264 0.293863
\(874\) 77.3375 2.61598
\(875\) 34.3780 1.16219
\(876\) 63.9078 2.15924
\(877\) 33.4114 1.12822 0.564111 0.825699i \(-0.309219\pi\)
0.564111 + 0.825699i \(0.309219\pi\)
\(878\) −42.5501 −1.43600
\(879\) −15.5075 −0.523054
\(880\) 129.086 4.35149
\(881\) 31.5381 1.06255 0.531273 0.847201i \(-0.321714\pi\)
0.531273 + 0.847201i \(0.321714\pi\)
\(882\) 1.88002 0.0633035
\(883\) −28.4668 −0.957984 −0.478992 0.877819i \(-0.658998\pi\)
−0.478992 + 0.877819i \(0.658998\pi\)
\(884\) −106.665 −3.58752
\(885\) 2.94266 0.0989165
\(886\) −88.6305 −2.97760
\(887\) −3.30601 −0.111005 −0.0555025 0.998459i \(-0.517676\pi\)
−0.0555025 + 0.998459i \(0.517676\pi\)
\(888\) 12.5247 0.420301
\(889\) 40.5964 1.36156
\(890\) 10.6077 0.355572
\(891\) −37.2345 −1.24740
\(892\) −23.2176 −0.777383
\(893\) −26.5785 −0.889416
\(894\) 82.4076 2.75612
\(895\) −21.6565 −0.723898
\(896\) 36.4676 1.21830
\(897\) 77.1382 2.57557
\(898\) −33.6766 −1.12380
\(899\) −39.0143 −1.30120
\(900\) 4.75314 0.158438
\(901\) 20.0370 0.667529
\(902\) 126.126 4.19954
\(903\) −20.2555 −0.674061
\(904\) 109.272 3.63435
\(905\) −4.15091 −0.137981
\(906\) −63.7504 −2.11797
\(907\) 46.6008 1.54735 0.773677 0.633581i \(-0.218416\pi\)
0.773677 + 0.633581i \(0.218416\pi\)
\(908\) −68.8956 −2.28638
\(909\) −3.14293 −0.104245
\(910\) −82.8500 −2.74645
\(911\) −2.14302 −0.0710013 −0.0355007 0.999370i \(-0.511303\pi\)
−0.0355007 + 0.999370i \(0.511303\pi\)
\(912\) 58.8558 1.94891
\(913\) −17.4324 −0.576927
\(914\) 65.8950 2.17961
\(915\) −19.1047 −0.631581
\(916\) 89.8418 2.96845
\(917\) −31.7329 −1.04791
\(918\) 54.3622 1.79422
\(919\) −21.3235 −0.703397 −0.351699 0.936113i \(-0.614396\pi\)
−0.351699 + 0.936113i \(0.614396\pi\)
\(920\) 138.539 4.56748
\(921\) 37.9700 1.25115
\(922\) 72.2336 2.37889
\(923\) −8.59687 −0.282969
\(924\) −126.347 −4.15650
\(925\) 1.35837 0.0446631
\(926\) −72.5234 −2.38327
\(927\) 7.64416 0.251067
\(928\) −122.267 −4.01360
\(929\) −22.6739 −0.743906 −0.371953 0.928252i \(-0.621312\pi\)
−0.371953 + 0.928252i \(0.621312\pi\)
\(930\) 36.5370 1.19809
\(931\) 3.38445 0.110921
\(932\) 75.6287 2.47730
\(933\) −45.3932 −1.48611
\(934\) −65.4716 −2.14230
\(935\) 40.0003 1.30815
\(936\) −32.5606 −1.06428
\(937\) −53.2629 −1.74002 −0.870012 0.493031i \(-0.835889\pi\)
−0.870012 + 0.493031i \(0.835889\pi\)
\(938\) 69.2240 2.26024
\(939\) −26.2794 −0.857597
\(940\) −78.4040 −2.55726
\(941\) −16.7386 −0.545662 −0.272831 0.962062i \(-0.587960\pi\)
−0.272831 + 0.962062i \(0.587960\pi\)
\(942\) −47.6713 −1.55321
\(943\) 72.5039 2.36105
\(944\) 11.9116 0.387689
\(945\) 30.3178 0.986240
\(946\) −72.0870 −2.34375
\(947\) 49.5960 1.61165 0.805826 0.592152i \(-0.201722\pi\)
0.805826 + 0.592152i \(0.201722\pi\)
\(948\) −90.5450 −2.94076
\(949\) −47.4808 −1.54129
\(950\) 11.9173 0.386648
\(951\) −4.96568 −0.161023
\(952\) 84.9404 2.75293
\(953\) −31.5258 −1.02122 −0.510610 0.859812i \(-0.670580\pi\)
−0.510610 + 0.859812i \(0.670580\pi\)
\(954\) 10.0724 0.326105
\(955\) 9.76792 0.316083
\(956\) 2.19578 0.0710166
\(957\) 72.2712 2.33620
\(958\) 74.3649 2.40262
\(959\) 54.2025 1.75029
\(960\) 46.3154 1.49482
\(961\) −8.65264 −0.279118
\(962\) −15.3235 −0.494050
\(963\) −5.37465 −0.173196
\(964\) −2.71743 −0.0875225
\(965\) 24.1114 0.776174
\(966\) −101.156 −3.25463
\(967\) −7.84754 −0.252360 −0.126180 0.992007i \(-0.540272\pi\)
−0.126180 + 0.992007i \(0.540272\pi\)
\(968\) −182.464 −5.86462
\(969\) 18.2379 0.585885
\(970\) 64.2179 2.06191
\(971\) −39.9194 −1.28107 −0.640537 0.767927i \(-0.721288\pi\)
−0.640537 + 0.767927i \(0.721288\pi\)
\(972\) 35.5858 1.14141
\(973\) 11.8487 0.379853
\(974\) −48.5520 −1.55571
\(975\) 11.8866 0.380675
\(976\) −77.3337 −2.47539
\(977\) −18.3445 −0.586893 −0.293446 0.955976i \(-0.594802\pi\)
−0.293446 + 0.955976i \(0.594802\pi\)
\(978\) 44.2706 1.41562
\(979\) −12.0187 −0.384120
\(980\) 9.98380 0.318921
\(981\) 0.687131 0.0219384
\(982\) −4.12465 −0.131623
\(983\) −6.75594 −0.215481 −0.107740 0.994179i \(-0.534362\pi\)
−0.107740 + 0.994179i \(0.534362\pi\)
\(984\) 103.014 3.28396
\(985\) 46.1812 1.47146
\(986\) −80.0098 −2.54803
\(987\) 34.7641 1.10655
\(988\) −96.5263 −3.07091
\(989\) −41.4394 −1.31770
\(990\) 20.1077 0.639065
\(991\) −3.59126 −0.114080 −0.0570401 0.998372i \(-0.518166\pi\)
−0.0570401 + 0.998372i \(0.518166\pi\)
\(992\) 70.0342 2.22359
\(993\) 25.3959 0.805913
\(994\) 11.2736 0.357576
\(995\) 27.8621 0.883288
\(996\) −23.4463 −0.742925
\(997\) −4.54488 −0.143938 −0.0719689 0.997407i \(-0.522928\pi\)
−0.0719689 + 0.997407i \(0.522928\pi\)
\(998\) 88.2047 2.79207
\(999\) 5.60743 0.177411
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 \(a_p\))