Properties

Label 690.3.f.a.229.9
Level $690$
Weight $3$
Character 690.229
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.9
Character \(\chi\) \(=\) 690.229
Dual form 690.3.f.a.229.11

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.91938 + 0.894267i) q^{5} -2.44949 q^{6} +6.65471 q^{7} +2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.91938 + 0.894267i) q^{5} -2.44949 q^{6} +6.65471 q^{7} +2.82843i q^{8} -3.00000 q^{9} +(1.26468 + 6.95705i) q^{10} +10.9802i q^{11} +3.46410i q^{12} +2.68725i q^{13} -9.41118i q^{14} +(1.54892 + 8.52061i) q^{15} +4.00000 q^{16} +26.7003 q^{17} +4.24264i q^{18} -21.8613i q^{19} +(9.83876 - 1.78853i) q^{20} -11.5263i q^{21} +15.5283 q^{22} +(7.63499 - 21.6958i) q^{23} +4.89898 q^{24} +(23.4006 - 8.79847i) q^{25} +3.80034 q^{26} +5.19615i q^{27} -13.3094 q^{28} -24.5688 q^{29} +(12.0500 - 2.19050i) q^{30} +19.2480 q^{31} -5.65685i q^{32} +19.0182 q^{33} -37.7600i q^{34} +(-32.7370 + 5.95108i) q^{35} +6.00000 q^{36} +22.7782 q^{37} -30.9165 q^{38} +4.65445 q^{39} +(-2.52937 - 13.9141i) q^{40} -66.8030 q^{41} -16.3006 q^{42} +41.3259 q^{43} -21.9604i q^{44} +(14.7581 - 2.68280i) q^{45} +(-30.6825 - 10.7975i) q^{46} +3.50098i q^{47} -6.92820i q^{48} -4.71486 q^{49} +(-12.4429 - 33.0934i) q^{50} -46.2463i q^{51} -5.37449i q^{52} +18.9181 q^{53} +7.34847 q^{54} +(-9.81922 - 54.0157i) q^{55} +18.8224i q^{56} -37.8649 q^{57} +34.7456i q^{58} +62.7409 q^{59} +(-3.09783 - 17.0412i) q^{60} -77.7774i q^{61} -27.2207i q^{62} -19.9641 q^{63} -8.00000 q^{64} +(-2.40311 - 13.2196i) q^{65} -26.8959i q^{66} -7.04561 q^{67} -53.4007 q^{68} +(-37.5782 - 13.2242i) q^{69} +(8.41610 + 46.2972i) q^{70} +104.609 q^{71} -8.48528i q^{72} -111.643i q^{73} -32.2132i q^{74} +(-15.2394 - 40.5310i) q^{75} +43.7226i q^{76} +73.0700i q^{77} -6.58238i q^{78} -111.861i q^{79} +(-19.6775 + 3.57707i) q^{80} +9.00000 q^{81} +94.4737i q^{82} -13.4125 q^{83} +23.0526i q^{84} +(-131.349 + 23.8772i) q^{85} -58.4436i q^{86} +42.5545i q^{87} -31.0567 q^{88} +55.4626i q^{89} +(-3.79405 - 20.8712i) q^{90} +17.8828i q^{91} +(-15.2700 + 43.3916i) q^{92} -33.3385i q^{93} +4.95113 q^{94} +(19.5498 + 107.544i) q^{95} -9.79796 q^{96} +61.5740 q^{97} +6.66782i q^{98} -32.9406i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 96q^{4} - 144q^{9} + O(q^{10}) \) \( 48q - 96q^{4} - 144q^{9} + 192q^{16} + 96q^{25} + 64q^{26} - 152q^{29} - 8q^{31} + 56q^{35} + 288q^{36} - 48q^{39} + 40q^{41} - 160q^{46} + 424q^{49} + 96q^{50} + 32q^{55} + 360q^{59} - 384q^{64} + 192q^{69} - 496q^{70} - 152q^{71} + 144q^{75} + 432q^{81} - 136q^{85} + 256q^{94} + 496q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 1.73205i 0.577350i
\(4\) −2.00000 −0.500000
\(5\) −4.91938 + 0.894267i −0.983876 + 0.178853i
\(6\) −2.44949 −0.408248
\(7\) 6.65471 0.950673 0.475336 0.879804i \(-0.342326\pi\)
0.475336 + 0.879804i \(0.342326\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −3.00000 −0.333333
\(10\) 1.26468 + 6.95705i 0.126468 + 0.695705i
\(11\) 10.9802i 0.998199i 0.866545 + 0.499100i \(0.166336\pi\)
−0.866545 + 0.499100i \(0.833664\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 2.68725i 0.206711i 0.994644 + 0.103356i \(0.0329580\pi\)
−0.994644 + 0.103356i \(0.967042\pi\)
\(14\) 9.41118i 0.672227i
\(15\) 1.54892 + 8.52061i 0.103261 + 0.568041i
\(16\) 4.00000 0.250000
\(17\) 26.7003 1.57061 0.785304 0.619111i \(-0.212507\pi\)
0.785304 + 0.619111i \(0.212507\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 21.8613i 1.15059i −0.817944 0.575297i \(-0.804886\pi\)
0.817944 0.575297i \(-0.195114\pi\)
\(20\) 9.83876 1.78853i 0.491938 0.0894267i
\(21\) 11.5263i 0.548871i
\(22\) 15.5283 0.705833
\(23\) 7.63499 21.6958i 0.331956 0.943295i
\(24\) 4.89898 0.204124
\(25\) 23.4006 8.79847i 0.936023 0.351939i
\(26\) 3.80034 0.146167
\(27\) 5.19615i 0.192450i
\(28\) −13.3094 −0.475336
\(29\) −24.5688 −0.847202 −0.423601 0.905849i \(-0.639234\pi\)
−0.423601 + 0.905849i \(0.639234\pi\)
\(30\) 12.0500 2.19050i 0.401666 0.0730166i
\(31\) 19.2480 0.620902 0.310451 0.950589i \(-0.399520\pi\)
0.310451 + 0.950589i \(0.399520\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 19.0182 0.576310
\(34\) 37.7600i 1.11059i
\(35\) −32.7370 + 5.95108i −0.935344 + 0.170031i
\(36\) 6.00000 0.166667
\(37\) 22.7782 0.615627 0.307814 0.951447i \(-0.400403\pi\)
0.307814 + 0.951447i \(0.400403\pi\)
\(38\) −30.9165 −0.813593
\(39\) 4.65445 0.119345
\(40\) −2.52937 13.9141i −0.0632342 0.347853i
\(41\) −66.8030 −1.62934 −0.814671 0.579924i \(-0.803082\pi\)
−0.814671 + 0.579924i \(0.803082\pi\)
\(42\) −16.3006 −0.388110
\(43\) 41.3259 0.961067 0.480534 0.876976i \(-0.340443\pi\)
0.480534 + 0.876976i \(0.340443\pi\)
\(44\) 21.9604i 0.499100i
\(45\) 14.7581 2.68280i 0.327959 0.0596178i
\(46\) −30.6825 10.7975i −0.667010 0.234728i
\(47\) 3.50098i 0.0744889i 0.999306 + 0.0372445i \(0.0118580\pi\)
−0.999306 + 0.0372445i \(0.988142\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −4.71486 −0.0962216
\(50\) −12.4429 33.0934i −0.248858 0.661868i
\(51\) 46.2463i 0.906791i
\(52\) 5.37449i 0.103356i
\(53\) 18.9181 0.356946 0.178473 0.983945i \(-0.442884\pi\)
0.178473 + 0.983945i \(0.442884\pi\)
\(54\) 7.34847 0.136083
\(55\) −9.81922 54.0157i −0.178531 0.982104i
\(56\) 18.8224i 0.336114i
\(57\) −37.8649 −0.664296
\(58\) 34.7456i 0.599062i
\(59\) 62.7409 1.06341 0.531703 0.846931i \(-0.321552\pi\)
0.531703 + 0.846931i \(0.321552\pi\)
\(60\) −3.09783 17.0412i −0.0516305 0.284020i
\(61\) 77.7774i 1.27504i −0.770434 0.637520i \(-0.779960\pi\)
0.770434 0.637520i \(-0.220040\pi\)
\(62\) 27.2207i 0.439044i
\(63\) −19.9641 −0.316891
\(64\) −8.00000 −0.125000
\(65\) −2.40311 13.2196i −0.0369710 0.203378i
\(66\) 26.8959i 0.407513i
\(67\) −7.04561 −0.105158 −0.0525791 0.998617i \(-0.516744\pi\)
−0.0525791 + 0.998617i \(0.516744\pi\)
\(68\) −53.4007 −0.785304
\(69\) −37.5782 13.2242i −0.544612 0.191655i
\(70\) 8.41610 + 46.2972i 0.120230 + 0.661388i
\(71\) 104.609 1.47337 0.736685 0.676236i \(-0.236390\pi\)
0.736685 + 0.676236i \(0.236390\pi\)
\(72\) 8.48528i 0.117851i
\(73\) 111.643i 1.52935i −0.644414 0.764677i \(-0.722899\pi\)
0.644414 0.764677i \(-0.277101\pi\)
\(74\) 32.2132i 0.435314i
\(75\) −15.2394 40.5310i −0.203192 0.540413i
\(76\) 43.7226i 0.575297i
\(77\) 73.0700i 0.948960i
\(78\) 6.58238i 0.0843895i
\(79\) 111.861i 1.41596i −0.706232 0.707980i \(-0.749607\pi\)
0.706232 0.707980i \(-0.250393\pi\)
\(80\) −19.6775 + 3.57707i −0.245969 + 0.0447133i
\(81\) 9.00000 0.111111
\(82\) 94.4737i 1.15212i
\(83\) −13.4125 −0.161596 −0.0807982 0.996730i \(-0.525747\pi\)
−0.0807982 + 0.996730i \(0.525747\pi\)
\(84\) 23.0526i 0.274436i
\(85\) −131.349 + 23.8772i −1.54528 + 0.280908i
\(86\) 58.4436i 0.679577i
\(87\) 42.5545i 0.489132i
\(88\) −31.0567 −0.352917
\(89\) 55.4626i 0.623175i 0.950217 + 0.311588i \(0.100861\pi\)
−0.950217 + 0.311588i \(0.899139\pi\)
\(90\) −3.79405 20.8712i −0.0421561 0.231902i
\(91\) 17.8828i 0.196515i
\(92\) −15.2700 + 43.3916i −0.165978 + 0.471647i
\(93\) 33.3385i 0.358478i
\(94\) 4.95113 0.0526716
\(95\) 19.5498 + 107.544i 0.205788 + 1.13204i
\(96\) −9.79796 −0.102062
\(97\) 61.5740 0.634783 0.317392 0.948295i \(-0.397193\pi\)
0.317392 + 0.948295i \(0.397193\pi\)
\(98\) 6.66782i 0.0680389i
\(99\) 32.9406i 0.332733i
\(100\) −46.8011 + 17.5969i −0.468011 + 0.175969i
\(101\) −56.2343 −0.556776 −0.278388 0.960469i \(-0.589800\pi\)
−0.278388 + 0.960469i \(0.589800\pi\)
\(102\) −65.4022 −0.641198
\(103\) 127.954 1.24227 0.621136 0.783702i \(-0.286671\pi\)
0.621136 + 0.783702i \(0.286671\pi\)
\(104\) −7.60068 −0.0730834
\(105\) 10.3076 + 56.7022i 0.0981674 + 0.540021i
\(106\) 26.7543i 0.252399i
\(107\) −60.7658 −0.567905 −0.283952 0.958838i \(-0.591646\pi\)
−0.283952 + 0.958838i \(0.591646\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 14.0645i 0.129032i −0.997917 0.0645162i \(-0.979450\pi\)
0.997917 0.0645162i \(-0.0205504\pi\)
\(110\) −76.3897 + 13.8865i −0.694452 + 0.126241i
\(111\) 39.4530i 0.355432i
\(112\) 26.6188 0.237668
\(113\) 1.76140 0.0155876 0.00779382 0.999970i \(-0.497519\pi\)
0.00779382 + 0.999970i \(0.497519\pi\)
\(114\) 53.5490i 0.469728i
\(115\) −18.1576 + 113.557i −0.157892 + 0.987456i
\(116\) 49.1377 0.423601
\(117\) 8.06174i 0.0689037i
\(118\) 88.7291i 0.751941i
\(119\) 177.683 1.49313
\(120\) −24.0999 + 4.38099i −0.200833 + 0.0365083i
\(121\) 0.435445 0.00359872
\(122\) −109.994 −0.901589
\(123\) 115.706i 0.940701i
\(124\) −38.4959 −0.310451
\(125\) −107.248 + 64.2094i −0.857985 + 0.513675i
\(126\) 28.2335i 0.224076i
\(127\) 60.2924i 0.474743i 0.971419 + 0.237371i \(0.0762859\pi\)
−0.971419 + 0.237371i \(0.923714\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 71.5785i 0.554872i
\(130\) −18.6953 + 3.39852i −0.143810 + 0.0261424i
\(131\) −18.3256 −0.139890 −0.0699449 0.997551i \(-0.522282\pi\)
−0.0699449 + 0.997551i \(0.522282\pi\)
\(132\) −38.0365 −0.288155
\(133\) 145.481i 1.09384i
\(134\) 9.96399i 0.0743581i
\(135\) −4.64675 25.5618i −0.0344203 0.189347i
\(136\) 75.5199i 0.555294i
\(137\) 134.685 0.983105 0.491552 0.870848i \(-0.336430\pi\)
0.491552 + 0.870848i \(0.336430\pi\)
\(138\) −18.7018 + 53.1436i −0.135520 + 0.385099i
\(139\) −184.379 −1.32647 −0.663233 0.748413i \(-0.730816\pi\)
−0.663233 + 0.748413i \(0.730816\pi\)
\(140\) 65.4741 11.9022i 0.467672 0.0850155i
\(141\) 6.06388 0.0430062
\(142\) 147.940i 1.04183i
\(143\) −29.5065 −0.206339
\(144\) −12.0000 −0.0833333
\(145\) 120.863 21.9711i 0.833541 0.151525i
\(146\) −157.887 −1.08142
\(147\) 8.16637i 0.0555536i
\(148\) −45.5564 −0.307814
\(149\) 124.082i 0.832766i 0.909189 + 0.416383i \(0.136702\pi\)
−0.909189 + 0.416383i \(0.863298\pi\)
\(150\) −57.3195 + 21.5518i −0.382130 + 0.143678i
\(151\) 295.727 1.95846 0.979229 0.202759i \(-0.0649907\pi\)
0.979229 + 0.202759i \(0.0649907\pi\)
\(152\) 61.8331 0.406797
\(153\) −80.1010 −0.523536
\(154\) 103.337 0.671016
\(155\) −94.6880 + 17.2128i −0.610891 + 0.111050i
\(156\) −9.30889 −0.0596724
\(157\) 235.853 1.50225 0.751125 0.660160i \(-0.229511\pi\)
0.751125 + 0.660160i \(0.229511\pi\)
\(158\) −158.195 −1.00124
\(159\) 32.7672i 0.206083i
\(160\) 5.05874 + 27.8282i 0.0316171 + 0.173926i
\(161\) 50.8086 144.379i 0.315581 0.896765i
\(162\) 12.7279i 0.0785674i
\(163\) 241.368i 1.48079i −0.672174 0.740393i \(-0.734639\pi\)
0.672174 0.740393i \(-0.265361\pi\)
\(164\) 133.606 0.814671
\(165\) −93.5580 + 17.0074i −0.567018 + 0.103075i
\(166\) 18.9681i 0.114266i
\(167\) 108.519i 0.649816i −0.945746 0.324908i \(-0.894667\pi\)
0.945746 0.324908i \(-0.105333\pi\)
\(168\) 32.6013 0.194055
\(169\) 161.779 0.957270
\(170\) 33.7675 + 185.756i 0.198632 + 1.09268i
\(171\) 65.5839i 0.383532i
\(172\) −82.6518 −0.480534
\(173\) 275.166i 1.59055i −0.606247 0.795276i \(-0.707326\pi\)
0.606247 0.795276i \(-0.292674\pi\)
\(174\) 60.1811 0.345869
\(175\) 155.724 58.5513i 0.889851 0.334579i
\(176\) 43.9208i 0.249550i
\(177\) 108.670i 0.613957i
\(178\) 78.4360 0.440652
\(179\) 90.2015 0.503919 0.251959 0.967738i \(-0.418925\pi\)
0.251959 + 0.967738i \(0.418925\pi\)
\(180\) −29.5163 + 5.36560i −0.163979 + 0.0298089i
\(181\) 50.3982i 0.278443i 0.990261 + 0.139222i \(0.0444600\pi\)
−0.990261 + 0.139222i \(0.955540\pi\)
\(182\) 25.2901 0.138957
\(183\) −134.714 −0.736144
\(184\) 61.3649 + 21.5950i 0.333505 + 0.117364i
\(185\) −112.055 + 20.3698i −0.605700 + 0.110107i
\(186\) −47.1477 −0.253482
\(187\) 293.175i 1.56778i
\(188\) 7.00196i 0.0372445i
\(189\) 34.5789i 0.182957i
\(190\) 152.090 27.6476i 0.800475 0.145514i
\(191\) 326.515i 1.70950i 0.519039 + 0.854750i \(0.326290\pi\)
−0.519039 + 0.854750i \(0.673710\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 96.3354i 0.499147i −0.968356 0.249574i \(-0.919710\pi\)
0.968356 0.249574i \(-0.0802905\pi\)
\(194\) 87.0788i 0.448860i
\(195\) −22.8970 + 4.16231i −0.117420 + 0.0213452i
\(196\) 9.42972 0.0481108
\(197\) 3.71172i 0.0188412i −0.999956 0.00942062i \(-0.997001\pi\)
0.999956 0.00942062i \(-0.00299872\pi\)
\(198\) −46.5850 −0.235278
\(199\) 291.255i 1.46359i 0.681524 + 0.731796i \(0.261317\pi\)
−0.681524 + 0.731796i \(0.738683\pi\)
\(200\) 24.8858 + 66.1868i 0.124429 + 0.330934i
\(201\) 12.2033i 0.0607132i
\(202\) 79.5274i 0.393700i
\(203\) −163.498 −0.805411
\(204\) 92.4927i 0.453395i
\(205\) 328.629 59.7397i 1.60307 0.291413i
\(206\) 180.954i 0.878420i
\(207\) −22.9050 + 65.0873i −0.110652 + 0.314432i
\(208\) 10.7490i 0.0516778i
\(209\) 240.041 1.14852
\(210\) 80.1890 14.5771i 0.381852 0.0694148i
\(211\) −302.726 −1.43472 −0.717361 0.696702i \(-0.754650\pi\)
−0.717361 + 0.696702i \(0.754650\pi\)
\(212\) −37.8363 −0.178473
\(213\) 181.189i 0.850650i
\(214\) 85.9358i 0.401569i
\(215\) −203.298 + 36.9564i −0.945571 + 0.171890i
\(216\) −14.6969 −0.0680414
\(217\) 128.090 0.590275
\(218\) −19.8903 −0.0912397
\(219\) −193.371 −0.882973
\(220\) 19.6384 + 108.031i 0.0892656 + 0.491052i
\(221\) 71.7503i 0.324662i
\(222\) −55.7950 −0.251329
\(223\) 92.7845i 0.416074i −0.978121 0.208037i \(-0.933293\pi\)
0.978121 0.208037i \(-0.0667074\pi\)
\(224\) 37.6447i 0.168057i
\(225\) −70.2017 + 26.3954i −0.312008 + 0.117313i
\(226\) 2.49100i 0.0110221i
\(227\) 142.941 0.629695 0.314848 0.949142i \(-0.398047\pi\)
0.314848 + 0.949142i \(0.398047\pi\)
\(228\) 75.7298 0.332148
\(229\) 350.149i 1.52904i 0.644603 + 0.764518i \(0.277023\pi\)
−0.644603 + 0.764518i \(0.722977\pi\)
\(230\) 160.595 + 25.6787i 0.698237 + 0.111647i
\(231\) 126.561 0.547883
\(232\) 69.4912i 0.299531i
\(233\) 67.8477i 0.291192i 0.989344 + 0.145596i \(0.0465099\pi\)
−0.989344 + 0.145596i \(0.953490\pi\)
\(234\) −11.4010 −0.0487223
\(235\) −3.13081 17.2226i −0.0133226 0.0732879i
\(236\) −125.482 −0.531703
\(237\) −193.749 −0.817505
\(238\) 251.282i 1.05580i
\(239\) −334.991 −1.40164 −0.700818 0.713340i \(-0.747182\pi\)
−0.700818 + 0.713340i \(0.747182\pi\)
\(240\) 6.19566 + 34.0825i 0.0258153 + 0.142010i
\(241\) 53.0754i 0.220230i −0.993919 0.110115i \(-0.964878\pi\)
0.993919 0.110115i \(-0.0351219\pi\)
\(242\) 0.615812i 0.00254468i
\(243\) 15.5885i 0.0641500i
\(244\) 155.555i 0.637520i
\(245\) 23.1942 4.21634i 0.0946701 0.0172095i
\(246\) 163.633 0.665176
\(247\) 58.7467 0.237841
\(248\) 54.4415i 0.219522i
\(249\) 23.2311i 0.0932977i
\(250\) 90.8058 + 151.672i 0.363223 + 0.606687i
\(251\) 287.306i 1.14464i 0.820029 + 0.572322i \(0.193957\pi\)
−0.820029 + 0.572322i \(0.806043\pi\)
\(252\) 39.9282 0.158445
\(253\) 238.224 + 83.8336i 0.941596 + 0.331358i
\(254\) 85.2663 0.335694
\(255\) 41.3565 + 227.503i 0.162183 + 0.892169i
\(256\) 16.0000 0.0625000
\(257\) 304.797i 1.18598i 0.805210 + 0.592990i \(0.202053\pi\)
−0.805210 + 0.592990i \(0.797947\pi\)
\(258\) −101.227 −0.392354
\(259\) 151.582 0.585260
\(260\) 4.80623 + 26.4392i 0.0184855 + 0.101689i
\(261\) 73.7065 0.282401
\(262\) 25.9163i 0.0989171i
\(263\) −167.430 −0.636617 −0.318308 0.947987i \(-0.603115\pi\)
−0.318308 + 0.947987i \(0.603115\pi\)
\(264\) 53.7917i 0.203757i
\(265\) −93.0655 + 16.9179i −0.351191 + 0.0638410i
\(266\) −205.741 −0.773461
\(267\) 96.0641 0.359791
\(268\) 14.0912 0.0525791
\(269\) 293.666 1.09170 0.545848 0.837884i \(-0.316208\pi\)
0.545848 + 0.837884i \(0.316208\pi\)
\(270\) −36.1499 + 6.57149i −0.133889 + 0.0243389i
\(271\) 145.730 0.537750 0.268875 0.963175i \(-0.413348\pi\)
0.268875 + 0.963175i \(0.413348\pi\)
\(272\) 106.801 0.392652
\(273\) 30.9740 0.113458
\(274\) 190.474i 0.695160i
\(275\) 96.6089 + 256.943i 0.351305 + 0.934337i
\(276\) 75.1564 + 26.4484i 0.272306 + 0.0958274i
\(277\) 395.777i 1.42880i 0.699738 + 0.714399i \(0.253300\pi\)
−0.699738 + 0.714399i \(0.746700\pi\)
\(278\) 260.751i 0.937953i
\(279\) −57.7439 −0.206967
\(280\) −16.8322 92.5943i −0.0601150 0.330694i
\(281\) 26.8272i 0.0954704i −0.998860 0.0477352i \(-0.984800\pi\)
0.998860 0.0477352i \(-0.0152004\pi\)
\(282\) 8.57562i 0.0304100i
\(283\) −213.545 −0.754576 −0.377288 0.926096i \(-0.623143\pi\)
−0.377288 + 0.926096i \(0.623143\pi\)
\(284\) −209.218 −0.736685
\(285\) 186.272 33.8613i 0.653585 0.118812i
\(286\) 41.7284i 0.145904i
\(287\) −444.554 −1.54897
\(288\) 16.9706i 0.0589256i
\(289\) 423.908 1.46681
\(290\) −31.0718 170.927i −0.107144 0.589403i
\(291\) 106.649i 0.366492i
\(292\) 223.286i 0.764677i
\(293\) −64.7200 −0.220887 −0.110444 0.993882i \(-0.535227\pi\)
−0.110444 + 0.993882i \(0.535227\pi\)
\(294\) 11.5490 0.0392823
\(295\) −308.646 + 56.1071i −1.04626 + 0.190194i
\(296\) 64.4265i 0.217657i
\(297\) −57.0547 −0.192103
\(298\) 175.479 0.588854
\(299\) 58.3019 + 20.5171i 0.194990 + 0.0686190i
\(300\) 30.4788 + 81.0620i 0.101596 + 0.270207i
\(301\) 275.012 0.913660
\(302\) 418.221i 1.38484i
\(303\) 97.4007i 0.321455i
\(304\) 87.4452i 0.287649i
\(305\) 69.5537 + 382.616i 0.228045 + 1.25448i
\(306\) 113.280i 0.370196i
\(307\) 401.291i 1.30714i −0.756868 0.653568i \(-0.773271\pi\)
0.756868 0.653568i \(-0.226729\pi\)
\(308\) 146.140i 0.474480i
\(309\) 221.623i 0.717227i
\(310\) 24.3426 + 133.909i 0.0785245 + 0.431965i
\(311\) −177.603 −0.571069 −0.285535 0.958368i \(-0.592171\pi\)
−0.285535 + 0.958368i \(0.592171\pi\)
\(312\) 13.1648i 0.0421947i
\(313\) 254.363 0.812661 0.406331 0.913726i \(-0.366808\pi\)
0.406331 + 0.913726i \(0.366808\pi\)
\(314\) 333.547i 1.06225i
\(315\) 98.2111 17.8533i 0.311781 0.0566770i
\(316\) 223.722i 0.707980i
\(317\) 353.112i 1.11392i −0.830540 0.556959i \(-0.811968\pi\)
0.830540 0.556959i \(-0.188032\pi\)
\(318\) −46.3398 −0.145723
\(319\) 269.771i 0.845676i
\(320\) 39.3550 7.15413i 0.122984 0.0223567i
\(321\) 105.249i 0.327880i
\(322\) −204.183 71.8542i −0.634108 0.223150i
\(323\) 583.704i 1.80713i
\(324\) −18.0000 −0.0555556
\(325\) 23.6437 + 62.8831i 0.0727497 + 0.193486i
\(326\) −341.346 −1.04707
\(327\) −24.3605 −0.0744969
\(328\) 188.947i 0.576059i
\(329\) 23.2980i 0.0708146i
\(330\) 24.0521 + 132.311i 0.0728851 + 0.400942i
\(331\) −120.997 −0.365549 −0.182774 0.983155i \(-0.558508\pi\)
−0.182774 + 0.983155i \(0.558508\pi\)
\(332\) 26.8250 0.0807982
\(333\) −68.3346 −0.205209
\(334\) −153.469 −0.459489
\(335\) 34.6600 6.30065i 0.103463 0.0188079i
\(336\) 46.1052i 0.137218i
\(337\) −110.729 −0.328573 −0.164286 0.986413i \(-0.552532\pi\)
−0.164286 + 0.986413i \(0.552532\pi\)
\(338\) 228.790i 0.676892i
\(339\) 3.05084i 0.00899953i
\(340\) 262.698 47.7544i 0.772641 0.140454i
\(341\) 211.346i 0.619784i
\(342\) 92.7496 0.271198
\(343\) −357.457 −1.04215
\(344\) 116.887i 0.339789i
\(345\) 196.687 + 31.4499i 0.570108 + 0.0911590i
\(346\) −389.143 −1.12469
\(347\) 334.500i 0.963978i 0.876177 + 0.481989i \(0.160086\pi\)
−0.876177 + 0.481989i \(0.839914\pi\)
\(348\) 85.1090i 0.244566i
\(349\) −550.891 −1.57848 −0.789242 0.614083i \(-0.789526\pi\)
−0.789242 + 0.614083i \(0.789526\pi\)
\(350\) −82.8040 220.227i −0.236583 0.629220i
\(351\) −13.9633 −0.0397816
\(352\) 62.1133 0.176458
\(353\) 406.298i 1.15099i −0.817807 0.575493i \(-0.804810\pi\)
0.817807 0.575493i \(-0.195190\pi\)
\(354\) −153.683 −0.434133
\(355\) −514.612 + 93.5486i −1.44961 + 0.263517i
\(356\) 110.925i 0.311588i
\(357\) 307.756i 0.862061i
\(358\) 127.564i 0.356324i
\(359\) 377.504i 1.05154i −0.850626 0.525771i \(-0.823777\pi\)
0.850626 0.525771i \(-0.176223\pi\)
\(360\) 7.58810 + 41.7423i 0.0210781 + 0.115951i
\(361\) −116.917 −0.323868
\(362\) 71.2739 0.196889
\(363\) 0.754212i 0.00207772i
\(364\) 35.7657i 0.0982573i
\(365\) 99.8385 + 549.213i 0.273530 + 1.50469i
\(366\) 190.515i 0.520533i
\(367\) 345.082 0.940279 0.470139 0.882592i \(-0.344204\pi\)
0.470139 + 0.882592i \(0.344204\pi\)
\(368\) 30.5400 86.7831i 0.0829890 0.235824i
\(369\) 200.409 0.543114
\(370\) 28.8072 + 158.469i 0.0778574 + 0.428295i
\(371\) 125.895 0.339339
\(372\) 66.6769i 0.179239i
\(373\) −91.3305 −0.244854 −0.122427 0.992478i \(-0.539068\pi\)
−0.122427 + 0.992478i \(0.539068\pi\)
\(374\) 414.612 1.10859
\(375\) 111.214 + 185.759i 0.296570 + 0.495358i
\(376\) −9.90227 −0.0263358
\(377\) 66.0225i 0.175126i
\(378\) 48.9019 0.129370
\(379\) 424.858i 1.12100i 0.828155 + 0.560499i \(0.189391\pi\)
−0.828155 + 0.560499i \(0.810609\pi\)
\(380\) −39.0997 215.088i −0.102894 0.566021i
\(381\) 104.429 0.274093
\(382\) 461.761 1.20880
\(383\) −535.544 −1.39829 −0.699143 0.714982i \(-0.746435\pi\)
−0.699143 + 0.714982i \(0.746435\pi\)
\(384\) 19.5959 0.0510310
\(385\) −65.3440 359.459i −0.169725 0.933659i
\(386\) −136.239 −0.352950
\(387\) −123.978 −0.320356
\(388\) −123.148 −0.317392
\(389\) 725.538i 1.86514i −0.360993 0.932568i \(-0.617562\pi\)
0.360993 0.932568i \(-0.382438\pi\)
\(390\) 5.88640 + 32.3812i 0.0150933 + 0.0830288i
\(391\) 203.857 579.285i 0.521373 1.48155i
\(392\) 13.3356i 0.0340195i
\(393\) 31.7408i 0.0807655i
\(394\) −5.24917 −0.0133228
\(395\) 100.033 + 550.286i 0.253249 + 1.39313i
\(396\) 65.8811i 0.166367i
\(397\) 721.320i 1.81693i 0.417964 + 0.908463i \(0.362744\pi\)
−0.417964 + 0.908463i \(0.637256\pi\)
\(398\) 411.896 1.03492
\(399\) −251.980 −0.631528
\(400\) 93.6023 35.1939i 0.234006 0.0879847i
\(401\) 458.171i 1.14257i −0.820751 0.571286i \(-0.806445\pi\)
0.820751 0.571286i \(-0.193555\pi\)
\(402\) 17.2581 0.0429307
\(403\) 51.7240i 0.128347i
\(404\) 112.469 0.278388
\(405\) −44.2744 + 8.04840i −0.109320 + 0.0198726i
\(406\) 231.222i 0.569512i
\(407\) 250.109i 0.614518i
\(408\) 130.804 0.320599
\(409\) −499.936 −1.22234 −0.611169 0.791500i \(-0.709301\pi\)
−0.611169 + 0.791500i \(0.709301\pi\)
\(410\) −84.4847 464.752i −0.206060 1.13354i
\(411\) 233.282i 0.567596i
\(412\) −255.908 −0.621136
\(413\) 417.523 1.01095
\(414\) 92.0474 + 32.3925i 0.222337 + 0.0782428i
\(415\) 65.9811 11.9943i 0.158991 0.0289020i
\(416\) 15.2014 0.0365417
\(417\) 319.353i 0.765836i
\(418\) 339.470i 0.812128i
\(419\) 413.532i 0.986950i −0.869760 0.493475i \(-0.835726\pi\)
0.869760 0.493475i \(-0.164274\pi\)
\(420\) −20.6152 113.404i −0.0490837 0.270010i
\(421\) 523.778i 1.24413i 0.782966 + 0.622064i \(0.213706\pi\)
−0.782966 + 0.622064i \(0.786294\pi\)
\(422\) 428.120i 1.01450i
\(423\) 10.5029i 0.0248296i
\(424\) 53.5086i 0.126200i
\(425\) 624.803 234.922i 1.47012 0.552758i
\(426\) −256.239 −0.601501
\(427\) 517.586i 1.21215i
\(428\) 121.532 0.283952
\(429\) 51.1067i 0.119130i
\(430\) 52.2642 + 287.506i 0.121545 + 0.668620i
\(431\) 129.957i 0.301523i 0.988570 + 0.150762i \(0.0481726\pi\)
−0.988570 + 0.150762i \(0.951827\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) −302.337 −0.698239 −0.349119 0.937078i \(-0.613519\pi\)
−0.349119 + 0.937078i \(0.613519\pi\)
\(434\) 181.146i 0.417387i
\(435\) −38.0551 209.342i −0.0874829 0.481245i
\(436\) 28.1291i 0.0645162i
\(437\) −474.298 166.911i −1.08535 0.381947i
\(438\) 273.468i 0.624356i
\(439\) −124.955 −0.284634 −0.142317 0.989821i \(-0.545455\pi\)
−0.142317 + 0.989821i \(0.545455\pi\)
\(440\) 152.779 27.7729i 0.347226 0.0631203i
\(441\) 14.1446 0.0320739
\(442\) 101.470 0.229571
\(443\) 516.339i 1.16555i 0.812633 + 0.582776i \(0.198033\pi\)
−0.812633 + 0.582776i \(0.801967\pi\)
\(444\) 78.9060i 0.177716i
\(445\) −49.5984 272.842i −0.111457 0.613127i
\(446\) −131.217 −0.294209
\(447\) 214.917 0.480798
\(448\) −53.2377 −0.118834
\(449\) 45.4215 0.101162 0.0505808 0.998720i \(-0.483893\pi\)
0.0505808 + 0.998720i \(0.483893\pi\)
\(450\) 37.3288 + 99.2802i 0.0829528 + 0.220623i
\(451\) 733.510i 1.62641i
\(452\) −3.52281 −0.00779382
\(453\) 512.214i 1.13072i
\(454\) 202.149i 0.445262i
\(455\) −15.9920 87.9724i −0.0351473 0.193346i
\(456\) 107.098i 0.234864i
\(457\) 102.958 0.225290 0.112645 0.993635i \(-0.464068\pi\)
0.112645 + 0.993635i \(0.464068\pi\)
\(458\) 495.186 1.08119
\(459\) 138.739i 0.302264i
\(460\) 36.3152 227.115i 0.0789460 0.493728i
\(461\) 110.027 0.238669 0.119335 0.992854i \(-0.461924\pi\)
0.119335 + 0.992854i \(0.461924\pi\)
\(462\) 178.984i 0.387411i
\(463\) 81.3171i 0.175631i 0.996137 + 0.0878154i \(0.0279886\pi\)
−0.996137 + 0.0878154i \(0.972011\pi\)
\(464\) −98.2754 −0.211800
\(465\) 29.8135 + 164.005i 0.0641150 + 0.352698i
\(466\) 95.9511 0.205904
\(467\) −807.265 −1.72862 −0.864309 0.502961i \(-0.832244\pi\)
−0.864309 + 0.502961i \(0.832244\pi\)
\(468\) 16.1235i 0.0344519i
\(469\) −46.8864 −0.0999711
\(470\) −24.3565 + 4.42763i −0.0518223 + 0.00942050i
\(471\) 408.510i 0.867325i
\(472\) 177.458i 0.375971i
\(473\) 453.766i 0.959336i
\(474\) 274.002i 0.578063i
\(475\) −192.346 511.567i −0.404939 1.07698i
\(476\) −355.366 −0.746567
\(477\) −56.7544 −0.118982
\(478\) 473.749i 0.991107i
\(479\) 496.522i 1.03658i 0.855205 + 0.518290i \(0.173431\pi\)
−0.855205 + 0.518290i \(0.826569\pi\)
\(480\) 48.1999 8.76199i 0.100416 0.0182541i
\(481\) 61.2106i 0.127257i
\(482\) −75.0600 −0.155726
\(483\) −250.072 88.0031i −0.517747 0.182201i
\(484\) −0.870889 −0.00179936
\(485\) −302.906 + 55.0636i −0.624548 + 0.113533i
\(486\) −22.0454 −0.0453609
\(487\) 196.039i 0.402543i 0.979535 + 0.201272i \(0.0645074\pi\)
−0.979535 + 0.201272i \(0.935493\pi\)
\(488\) 219.988 0.450794
\(489\) −418.062 −0.854932
\(490\) −5.96280 32.8015i −0.0121690 0.0669419i
\(491\) 103.195 0.210173 0.105086 0.994463i \(-0.466488\pi\)
0.105086 + 0.994463i \(0.466488\pi\)
\(492\) 231.412i 0.470350i
\(493\) −655.996 −1.33062
\(494\) 83.0803i 0.168179i
\(495\) 29.4577 + 162.047i 0.0595104 + 0.327368i
\(496\) 76.9919 0.155226
\(497\) 696.144 1.40069
\(498\) 32.8538 0.0659714
\(499\) −820.456 −1.64420 −0.822101 0.569342i \(-0.807198\pi\)
−0.822101 + 0.569342i \(0.807198\pi\)
\(500\) 214.496 128.419i 0.428992 0.256837i
\(501\) −187.961 −0.375171
\(502\) 406.312 0.809386
\(503\) 146.500 0.291253 0.145627 0.989340i \(-0.453480\pi\)
0.145627 + 0.989340i \(0.453480\pi\)
\(504\) 56.4671i 0.112038i
\(505\) 276.638 50.2885i 0.547798 0.0995812i
\(506\) 118.559 336.899i 0.234306 0.665809i
\(507\) 280.209i 0.552680i
\(508\) 120.585i 0.237371i
\(509\) −138.422 −0.271949 −0.135974 0.990712i \(-0.543416\pi\)
−0.135974 + 0.990712i \(0.543416\pi\)
\(510\) 321.738 58.4870i 0.630859 0.114680i
\(511\) 742.950i 1.45391i
\(512\) 22.6274i 0.0441942i
\(513\) 113.595 0.221432
\(514\) 431.048 0.838615
\(515\) −629.455 + 114.425i −1.22224 + 0.222185i
\(516\) 143.157i 0.277436i
\(517\) −38.4414 −0.0743548
\(518\) 214.370i 0.413841i
\(519\) −476.601 −0.918306
\(520\) 37.3906 6.79703i 0.0719050 0.0130712i
\(521\) 833.697i 1.60019i −0.599876 0.800093i \(-0.704783\pi\)
0.599876 0.800093i \(-0.295217\pi\)
\(522\) 104.237i 0.199687i
\(523\) −747.765 −1.42976 −0.714881 0.699247i \(-0.753519\pi\)
−0.714881 + 0.699247i \(0.753519\pi\)
\(524\) 36.6511 0.0699449
\(525\) −101.414 269.722i −0.193169 0.513756i
\(526\) 236.782i 0.450156i
\(527\) 513.927 0.975194
\(528\) 76.0730 0.144078
\(529\) −412.414 331.294i −0.779610 0.626265i
\(530\) 23.9255 + 131.615i 0.0451424 + 0.248329i
\(531\) −188.223 −0.354468
\(532\) 290.961i 0.546919i
\(533\) 179.516i 0.336803i
\(534\) 135.855i 0.254410i
\(535\) 298.930 54.3408i 0.558748 0.101572i
\(536\) 19.9280i 0.0371791i
\(537\) 156.234i 0.290938i
\(538\) 415.307i 0.771945i
\(539\) 51.7700i 0.0960483i
\(540\) 9.29349 + 51.1237i 0.0172102 + 0.0946735i
\(541\) 295.029 0.545340 0.272670 0.962108i \(-0.412093\pi\)
0.272670 + 0.962108i \(0.412093\pi\)
\(542\) 206.094i 0.380246i
\(543\) 87.2923 0.160759
\(544\) 151.040i 0.277647i
\(545\) 12.5774 + 69.1888i 0.0230779 + 0.126952i
\(546\) 43.8038i 0.0802268i
\(547\) 491.725i 0.898948i 0.893293 + 0.449474i \(0.148389\pi\)
−0.893293 + 0.449474i \(0.851611\pi\)
\(548\) −269.371 −0.491552
\(549\) 233.332i 0.425013i
\(550\) 363.372 136.626i 0.660676 0.248410i
\(551\) 537.107i 0.974786i
\(552\) 37.4036 106.287i 0.0677602 0.192549i
\(553\) 744.401i 1.34611i
\(554\) 559.713 1.01031
\(555\) 35.2815 + 194.084i 0.0635703 + 0.349701i
\(556\) 368.758 0.663233
\(557\) −510.871 −0.917183 −0.458592 0.888647i \(-0.651646\pi\)
−0.458592 + 0.888647i \(0.651646\pi\)
\(558\) 81.6622i 0.146348i
\(559\) 111.053i 0.198663i
\(560\) −130.948 + 23.8043i −0.233836 + 0.0425077i
\(561\) 507.793 0.905158
\(562\) −37.9394 −0.0675078
\(563\) −243.665 −0.432797 −0.216398 0.976305i \(-0.569431\pi\)
−0.216398 + 0.976305i \(0.569431\pi\)
\(564\) −12.1278 −0.0215031
\(565\) −8.66501 + 1.57517i −0.0153363 + 0.00278790i
\(566\) 301.998i 0.533566i
\(567\) 59.8924 0.105630
\(568\) 295.880i 0.520915i
\(569\) 971.291i 1.70701i 0.521081 + 0.853507i \(0.325529\pi\)
−0.521081 + 0.853507i \(0.674471\pi\)
\(570\) −47.8871 263.428i −0.0840125 0.462154i
\(571\) 179.364i 0.314123i −0.987589 0.157062i \(-0.949798\pi\)
0.987589 0.157062i \(-0.0502022\pi\)
\(572\) 59.0129 0.103169
\(573\) 565.540 0.986981
\(574\) 628.695i 1.09529i
\(575\) −12.2266 574.870i −0.0212637 0.999774i
\(576\) 24.0000 0.0416667
\(577\) 339.485i 0.588363i −0.955750 0.294181i \(-0.904953\pi\)
0.955750 0.294181i \(-0.0950470\pi\)
\(578\) 599.496i 1.03719i
\(579\) −166.858 −0.288183
\(580\) −241.727 + 43.9422i −0.416771 + 0.0757624i
\(581\) −89.2562 −0.153625
\(582\) −150.825 −0.259149
\(583\) 207.725i 0.356303i
\(584\) 315.774 0.540708
\(585\) 7.20934 + 39.6587i 0.0123237 + 0.0677927i
\(586\) 91.5279i 0.156191i
\(587\) 798.800i 1.36082i 0.732832 + 0.680409i \(0.238198\pi\)
−0.732832 + 0.680409i \(0.761802\pi\)
\(588\) 16.3327i 0.0277768i
\(589\) 420.786i 0.714407i
\(590\) 79.3474 + 436.492i 0.134487 + 0.739817i
\(591\) −6.42889 −0.0108780
\(592\) 91.1128 0.153907
\(593\) 1121.35i 1.89098i −0.325657 0.945488i \(-0.605585\pi\)
0.325657 0.945488i \(-0.394415\pi\)
\(594\) 80.6876i 0.135838i
\(595\) −874.090 + 158.896i −1.46906 + 0.267052i
\(596\) 248.164i 0.416383i
\(597\) 504.468 0.845005
\(598\) 29.0155 82.4513i 0.0485210 0.137878i
\(599\) 1047.06 1.74801 0.874004 0.485919i \(-0.161515\pi\)
0.874004 + 0.485919i \(0.161515\pi\)
\(600\) 114.639 43.1035i 0.191065 0.0718392i
\(601\) 329.240 0.547820 0.273910 0.961755i \(-0.411683\pi\)
0.273910 + 0.961755i \(0.411683\pi\)
\(602\) 388.925i 0.646055i
\(603\) 21.1368 0.0350528
\(604\) −591.454 −0.979229
\(605\) −2.14212 + 0.389404i −0.00354069 + 0.000643642i
\(606\) 137.745 0.227303
\(607\) 524.433i 0.863976i 0.901879 + 0.431988i \(0.142188\pi\)
−0.901879 + 0.431988i \(0.857812\pi\)
\(608\) −123.666 −0.203398
\(609\) 283.188i 0.465004i
\(610\) 541.101 98.3638i 0.887052 0.161252i
\(611\) −9.40799 −0.0153977
\(612\) 160.202 0.261768
\(613\) 233.266 0.380532 0.190266 0.981733i \(-0.439065\pi\)
0.190266 + 0.981733i \(0.439065\pi\)
\(614\) −567.511 −0.924285
\(615\) −103.472 569.203i −0.168247 0.925533i
\(616\) −206.673 −0.335508
\(617\) −280.650 −0.454863 −0.227431 0.973794i \(-0.573033\pi\)
−0.227431 + 0.973794i \(0.573033\pi\)
\(618\) −313.422 −0.507156
\(619\) 613.679i 0.991405i −0.868492 0.495702i \(-0.834911\pi\)
0.868492 0.495702i \(-0.165089\pi\)
\(620\) 189.376 34.4256i 0.305445 0.0555252i
\(621\) 112.735 + 39.6726i 0.181537 + 0.0638850i
\(622\) 251.168i 0.403807i
\(623\) 369.088i 0.592436i
\(624\) 18.6178 0.0298362
\(625\) 470.174 411.779i 0.752278 0.658846i
\(626\) 359.724i 0.574638i
\(627\) 415.764i 0.663100i
\(628\) −471.707 −0.751125
\(629\) 608.185 0.966909
\(630\) −25.2483 138.891i −0.0400767 0.220463i
\(631\) 102.785i 0.162893i 0.996678 + 0.0814464i \(0.0259539\pi\)
−0.996678 + 0.0814464i \(0.974046\pi\)
\(632\) 316.390 0.500618
\(633\) 524.337i 0.828337i
\(634\) −499.376 −0.787660
\(635\) −53.9174 296.601i −0.0849094 0.467088i
\(636\) 65.5344i 0.103041i
\(637\) 12.6700i 0.0198901i
\(638\) −381.513 −0.597983
\(639\) −313.828 −0.491123
\(640\) −10.1175 55.6564i −0.0158085 0.0869632i
\(641\) 96.0151i 0.149790i −0.997191 0.0748948i \(-0.976138\pi\)
0.997191 0.0748948i \(-0.0238621\pi\)
\(642\) 148.845 0.231846
\(643\) 620.769 0.965427 0.482713 0.875778i \(-0.339651\pi\)
0.482713 + 0.875778i \(0.339651\pi\)
\(644\) −101.617 + 288.758i −0.157791 + 0.448382i
\(645\) 64.0103 + 352.122i 0.0992408 + 0.545926i
\(646\) −825.482 −1.27784
\(647\) 1267.27i 1.95869i −0.202193 0.979346i \(-0.564807\pi\)
0.202193 0.979346i \(-0.435193\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 688.907i 1.06149i
\(650\) 88.9301 33.4372i 0.136816 0.0514418i
\(651\) 221.858i 0.340795i
\(652\) 482.736i 0.740393i
\(653\) 27.5591i 0.0422038i 0.999777 + 0.0211019i \(0.00671744\pi\)
−0.999777 + 0.0211019i \(0.993283\pi\)
\(654\) 34.4509i 0.0526773i
\(655\) 90.1504 16.3879i 0.137634 0.0250198i
\(656\) −267.212 −0.407335
\(657\) 334.928i 0.509785i
\(658\) 32.9484 0.0500735
\(659\) 575.719i 0.873626i 0.899552 + 0.436813i \(0.143893\pi\)
−0.899552 + 0.436813i \(0.856107\pi\)
\(660\) 187.116 34.0148i 0.283509 0.0515375i
\(661\) 556.994i 0.842653i 0.906909 + 0.421327i \(0.138435\pi\)
−0.906909 + 0.421327i \(0.861565\pi\)
\(662\) 171.115i 0.258482i
\(663\) 124.275 0.187444
\(664\) 37.9363i 0.0571329i
\(665\) 130.098 + 715.674i 0.195637 + 1.07620i
\(666\) 96.6397i 0.145105i
\(667\) −187.583 + 533.040i −0.281234 + 0.799161i
\(668\) 217.038i 0.324908i
\(669\) −160.707 −0.240220
\(670\) −8.91046 49.0166i −0.0132992 0.0731592i
\(671\) 854.011 1.27274
\(672\) −65.2026 −0.0970276
\(673\) 644.574i 0.957762i 0.877880 + 0.478881i \(0.158957\pi\)
−0.877880 + 0.478881i \(0.841043\pi\)
\(674\) 156.594i 0.232336i
\(675\) 45.7182 + 121.593i 0.0677307 + 0.180138i
\(676\) −323.557 −0.478635
\(677\) 1135.00 1.67652 0.838260 0.545270i \(-0.183573\pi\)
0.838260 + 0.545270i \(0.183573\pi\)
\(678\) −4.31454 −0.00636363
\(679\) 409.757 0.603471
\(680\) −67.5350 371.511i −0.0993161 0.546340i
\(681\) 247.581i 0.363555i
\(682\) 298.889 0.438253
\(683\) 336.175i 0.492203i 0.969244 + 0.246101i \(0.0791496\pi\)
−0.969244 + 0.246101i \(0.920850\pi\)
\(684\) 131.168i 0.191766i
\(685\) −662.568 + 120.445i −0.967253 + 0.175832i
\(686\) 505.520i 0.736910i
\(687\) 606.476 0.882789
\(688\) 165.304 0.240267
\(689\) 50.8377i 0.0737848i
\(690\) 44.4768 278.158i 0.0644591 0.403127i
\(691\) 876.008 1.26774 0.633870 0.773440i \(-0.281465\pi\)
0.633870 + 0.773440i \(0.281465\pi\)
\(692\) 550.331i 0.795276i
\(693\) 219.210i 0.316320i
\(694\) 473.055 0.681636
\(695\) 907.029 164.884i 1.30508 0.237243i
\(696\) −120.362 −0.172934
\(697\) −1783.66 −2.55906
\(698\) 779.077i 1.11616i
\(699\) 117.516 0.168120
\(700\) −311.448 + 117.103i −0.444926 + 0.167289i
\(701\) 1042.02i 1.48647i 0.669029 + 0.743236i \(0.266710\pi\)
−0.669029 + 0.743236i \(0.733290\pi\)
\(702\) 19.7471i 0.0281298i
\(703\) 497.961i 0.708337i
\(704\) 87.8415i 0.124775i
\(705\) −29.8305 + 5.42272i −0.0423128 + 0.00769180i
\(706\) −574.592 −0.813869
\(707\) −374.223 −0.529311
\(708\) 217.341i 0.306979i
\(709\) 284.090i 0.400692i −0.979725 0.200346i \(-0.935793\pi\)
0.979725 0.200346i \(-0.0642066\pi\)
\(710\) 132.298 + 727.772i 0.186335 + 1.02503i
\(711\) 335.583i 0.471987i
\(712\) −156.872 −0.220326
\(713\) 146.958 417.600i 0.206112 0.585694i
\(714\) −435.232 −0.609569
\(715\) 145.153 26.3866i 0.203012 0.0369044i
\(716\) −180.403 −0.251959
\(717\) 580.222i 0.809235i
\(718\) −533.871 −0.743553
\(719\) −354.612 −0.493202 −0.246601 0.969117i \(-0.579314\pi\)
−0.246601 + 0.969117i \(0.579314\pi\)
\(720\) 59.0325 10.7312i 0.0819896 0.0149044i
\(721\) 851.497 1.18099
\(722\) 165.345i 0.229010i
\(723\) −91.9293 −0.127150
\(724\) 100.796i 0.139222i
\(725\) −574.925 + 216.168i −0.793000 + 0.298163i
\(726\) −1.06662 −0.00146917
\(727\) 75.5220 0.103882 0.0519408 0.998650i \(-0.483459\pi\)
0.0519408 + 0.998650i \(0.483459\pi\)
\(728\) −50.5803 −0.0694784
\(729\) −27.0000 −0.0370370
\(730\) 776.705 141.193i 1.06398 0.193415i
\(731\) 1103.42 1.50946
\(732\) 269.429 0.368072
\(733\) 1193.82 1.62868 0.814338 0.580390i \(-0.197100\pi\)
0.814338 + 0.580390i \(0.197100\pi\)
\(734\) 488.020i 0.664878i
\(735\) −7.30291 40.1735i −0.00993594 0.0546578i
\(736\) −122.730 43.1900i −0.166753 0.0586821i
\(737\) 77.3621i 0.104969i
\(738\) 283.421i 0.384039i
\(739\) −1258.10 −1.70243 −0.851216 0.524815i \(-0.824134\pi\)
−0.851216 + 0.524815i \(0.824134\pi\)
\(740\) 224.109 40.7396i 0.302850 0.0550535i
\(741\) 101.752i 0.137317i
\(742\) 178.042i 0.239949i
\(743\) −670.264 −0.902105 −0.451052 0.892497i \(-0.648951\pi\)
−0.451052 + 0.892497i \(0.648951\pi\)
\(744\) 94.2954 0.126741
\(745\) −110.963 610.407i −0.148943 0.819338i
\(746\) 129.161i 0.173138i
\(747\) 40.2375 0.0538654
\(748\) 586.349i 0.783890i
\(749\) −404.379 −0.539891
\(750\) 262.703 157.280i 0.350271 0.209707i
\(751\) 567.949i 0.756257i −0.925753 0.378129i \(-0.876568\pi\)
0.925753 0.378129i \(-0.123432\pi\)
\(752\) 14.0039i 0.0186222i
\(753\) 497.628 0.660861
\(754\) −93.3699 −0.123833
\(755\) −1454.79 + 264.459i −1.92688 + 0.350277i
\(756\) 69.1578i 0.0914785i
\(757\) 335.085 0.442648 0.221324 0.975200i \(-0.428962\pi\)
0.221324 + 0.975200i \(0.428962\pi\)
\(758\) 600.840 0.792665
\(759\) 145.204 412.616i 0.191310 0.543631i
\(760\) −304.180 + 55.2953i −0.400237 + 0.0727569i
\(761\) −1035.35 −1.36051 −0.680255 0.732976i \(-0.738131\pi\)
−0.680255 + 0.732976i \(0.738131\pi\)
\(762\) 147.686i 0.193813i
\(763\) 93.5954i 0.122668i
\(764\) 653.029i 0.854750i
\(765\) 394.047 71.6316i 0.515094 0.0936361i
\(766\) 757.373i 0.988738i
\(767\) 168.600i 0.219818i
\(768\) 27.7128i 0.0360844i
\(769\) 691.450i 0.899155i −0.893241 0.449577i \(-0.851575\pi\)
0.893241 0.449577i \(-0.148425\pi\)
\(770\) −508.351 + 92.4104i −0.660197 + 0.120014i
\(771\) 527.924 0.684726
\(772\) 192.671i 0.249574i
\(773\) 739.787 0.957033 0.478517 0.878079i \(-0.341175\pi\)
0.478517 + 0.878079i \(0.341175\pi\)
\(774\) 175.331i 0.226526i
\(775\) 450.413 169.353i 0.581179 0.218520i
\(776\) 174.158i 0.224430i
\(777\) 262.548i 0.337900i
\(778\) −1026.07 −1.31885
\(779\) 1460.40i 1.87471i
\(780\) 45.7940 8.32463i 0.0587102 0.0106726i
\(781\) 1148.63i 1.47072i
\(782\) −819.232 288.297i −1.04761 0.368666i
\(783\) 127.663i 0.163044i
\(784\) −18.8594 −0.0240554
\(785\) −1160.25 + 210.916i −1.47803 + 0.268682i
\(786\) 44.8883 0.0571098
\(787\) −1337.12 −1.69901 −0.849503 0.527583i \(-0.823098\pi\)
−0.849503 + 0.527583i \(0.823098\pi\)
\(788\)