Properties

Label 177.3.b.a.119.34
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.34
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.5

$q$-expansion

\(f(q)\) \(=\) \(q+3.18759i q^{2} +(2.94308 - 0.581607i) q^{3} -6.16073 q^{4} -2.91835i q^{5} +(1.85393 + 9.38134i) q^{6} +12.1837 q^{7} -6.88752i q^{8} +(8.32347 - 3.42344i) q^{9} +O(q^{10})\) \(q+3.18759i q^{2} +(2.94308 - 0.581607i) q^{3} -6.16073 q^{4} -2.91835i q^{5} +(1.85393 + 9.38134i) q^{6} +12.1837 q^{7} -6.88752i q^{8} +(8.32347 - 3.42344i) q^{9} +9.30252 q^{10} +13.3732i q^{11} +(-18.1315 + 3.58312i) q^{12} -12.2071 q^{13} +38.8366i q^{14} +(-1.69734 - 8.58896i) q^{15} -2.68834 q^{16} +2.10350i q^{17} +(10.9125 + 26.5318i) q^{18} -3.44330 q^{19} +17.9792i q^{20} +(35.8576 - 7.08611i) q^{21} -42.6282 q^{22} -44.1928i q^{23} +(-4.00583 - 20.2705i) q^{24} +16.4832 q^{25} -38.9112i q^{26} +(22.5056 - 14.9164i) q^{27} -75.0603 q^{28} +41.6037i q^{29} +(27.3781 - 5.41041i) q^{30} -28.5455 q^{31} -36.1194i q^{32} +(7.77793 + 39.3583i) q^{33} -6.70509 q^{34} -35.5563i q^{35} +(-51.2786 + 21.0909i) q^{36} -16.7372 q^{37} -10.9758i q^{38} +(-35.9264 + 7.09973i) q^{39} -20.1002 q^{40} -7.60876i q^{41} +(22.5876 + 114.299i) q^{42} -46.0831 q^{43} -82.3884i q^{44} +(-9.99080 - 24.2908i) q^{45} +140.869 q^{46} +1.11928i q^{47} +(-7.91200 + 1.56356i) q^{48} +99.4419 q^{49} +52.5417i q^{50} +(1.22341 + 6.19077i) q^{51} +75.2045 q^{52} -30.2820i q^{53} +(47.5475 + 71.7385i) q^{54} +39.0276 q^{55} -83.9152i q^{56} +(-10.1339 + 2.00265i) q^{57} -132.616 q^{58} +7.68115i q^{59} +(10.4568 + 52.9142i) q^{60} -46.1565 q^{61} -90.9915i q^{62} +(101.410 - 41.7100i) q^{63} +104.380 q^{64} +35.6246i q^{65} +(-125.458 + 24.7928i) q^{66} +66.4936 q^{67} -12.9591i q^{68} +(-25.7029 - 130.063i) q^{69} +113.339 q^{70} -99.7802i q^{71} +(-23.5790 - 57.3280i) q^{72} -129.745 q^{73} -53.3515i q^{74} +(48.5114 - 9.58675i) q^{75} +21.2133 q^{76} +162.934i q^{77} +(-22.6310 - 114.519i) q^{78} +12.2886 q^{79} +7.84553i q^{80} +(57.5602 - 56.9897i) q^{81} +24.2536 q^{82} -41.1271i q^{83} +(-220.909 + 43.6556i) q^{84} +6.13875 q^{85} -146.894i q^{86} +(24.1970 + 122.443i) q^{87} +92.1079 q^{88} -75.0603i q^{89} +(77.4292 - 31.8466i) q^{90} -148.727 q^{91} +272.260i q^{92} +(-84.0119 + 16.6023i) q^{93} -3.56781 q^{94} +10.0488i q^{95} +(-21.0073 - 106.302i) q^{96} +186.423 q^{97} +316.980i q^{98} +(45.7822 + 111.311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.18759i 1.59379i 0.604115 + 0.796897i \(0.293527\pi\)
−0.604115 + 0.796897i \(0.706473\pi\)
\(3\) 2.94308 0.581607i 0.981027 0.193869i
\(4\) −6.16073 −1.54018
\(5\) 2.91835i 0.583671i −0.956469 0.291835i \(-0.905734\pi\)
0.956469 0.291835i \(-0.0942660\pi\)
\(6\) 1.85393 + 9.38134i 0.308988 + 1.56356i
\(7\) 12.1837 1.74052 0.870262 0.492588i \(-0.163949\pi\)
0.870262 + 0.492588i \(0.163949\pi\)
\(8\) 6.88752i 0.860939i
\(9\) 8.32347 3.42344i 0.924830 0.380382i
\(10\) 9.30252 0.930252
\(11\) 13.3732i 1.21574i 0.794036 + 0.607871i \(0.207976\pi\)
−0.794036 + 0.607871i \(0.792024\pi\)
\(12\) −18.1315 + 3.58312i −1.51096 + 0.298594i
\(13\) −12.2071 −0.939006 −0.469503 0.882931i \(-0.655567\pi\)
−0.469503 + 0.882931i \(0.655567\pi\)
\(14\) 38.8366i 2.77404i
\(15\) −1.69734 8.58896i −0.113156 0.572597i
\(16\) −2.68834 −0.168021
\(17\) 2.10350i 0.123735i 0.998084 + 0.0618676i \(0.0197057\pi\)
−0.998084 + 0.0618676i \(0.980294\pi\)
\(18\) 10.9125 + 26.5318i 0.606250 + 1.47399i
\(19\) −3.44330 −0.181227 −0.0906133 0.995886i \(-0.528883\pi\)
−0.0906133 + 0.995886i \(0.528883\pi\)
\(20\) 17.9792i 0.898960i
\(21\) 35.8576 7.08611i 1.70750 0.337434i
\(22\) −42.6282 −1.93764
\(23\) 44.1928i 1.92143i −0.277540 0.960714i \(-0.589519\pi\)
0.277540 0.960714i \(-0.410481\pi\)
\(24\) −4.00583 20.2705i −0.166910 0.844605i
\(25\) 16.4832 0.659328
\(26\) 38.9112i 1.49658i
\(27\) 22.5056 14.9164i 0.833539 0.552461i
\(28\) −75.0603 −2.68073
\(29\) 41.6037i 1.43461i 0.696759 + 0.717305i \(0.254625\pi\)
−0.696759 + 0.717305i \(0.745375\pi\)
\(30\) 27.3781 5.41041i 0.912603 0.180347i
\(31\) −28.5455 −0.920824 −0.460412 0.887705i \(-0.652298\pi\)
−0.460412 + 0.887705i \(0.652298\pi\)
\(32\) 36.1194i 1.12873i
\(33\) 7.77793 + 39.3583i 0.235695 + 1.19268i
\(34\) −6.70509 −0.197209
\(35\) 35.5563i 1.01589i
\(36\) −51.2786 + 21.0909i −1.42441 + 0.585857i
\(37\) −16.7372 −0.452358 −0.226179 0.974086i \(-0.572623\pi\)
−0.226179 + 0.974086i \(0.572623\pi\)
\(38\) 10.9758i 0.288838i
\(39\) −35.9264 + 7.09973i −0.921191 + 0.182044i
\(40\) −20.1002 −0.502505
\(41\) 7.60876i 0.185580i −0.995686 0.0927898i \(-0.970422\pi\)
0.995686 0.0927898i \(-0.0295785\pi\)
\(42\) 22.5876 + 114.299i 0.537800 + 2.72141i
\(43\) −46.0831 −1.07170 −0.535850 0.844313i \(-0.680009\pi\)
−0.535850 + 0.844313i \(0.680009\pi\)
\(44\) 82.3884i 1.87246i
\(45\) −9.99080 24.2908i −0.222018 0.539796i
\(46\) 140.869 3.06236
\(47\) 1.11928i 0.0238145i 0.999929 + 0.0119072i \(0.00379028\pi\)
−0.999929 + 0.0119072i \(0.996210\pi\)
\(48\) −7.91200 + 1.56356i −0.164833 + 0.0325741i
\(49\) 99.4419 2.02943
\(50\) 52.5417i 1.05083i
\(51\) 1.22341 + 6.19077i 0.0239884 + 0.121388i
\(52\) 75.2045 1.44624
\(53\) 30.2820i 0.571358i −0.958325 0.285679i \(-0.907781\pi\)
0.958325 0.285679i \(-0.0922191\pi\)
\(54\) 47.5475 + 71.7385i 0.880509 + 1.32849i
\(55\) 39.0276 0.709593
\(56\) 83.9152i 1.49849i
\(57\) −10.1339 + 2.00265i −0.177788 + 0.0351342i
\(58\) −132.616 −2.28648
\(59\) 7.68115i 0.130189i
\(60\) 10.4568 + 52.9142i 0.174280 + 0.881904i
\(61\) −46.1565 −0.756664 −0.378332 0.925670i \(-0.623502\pi\)
−0.378332 + 0.925670i \(0.623502\pi\)
\(62\) 90.9915i 1.46760i
\(63\) 101.410 41.7100i 1.60969 0.662064i
\(64\) 104.380 1.63094
\(65\) 35.6246i 0.548071i
\(66\) −125.458 + 24.7928i −1.90088 + 0.375649i
\(67\) 66.4936 0.992442 0.496221 0.868196i \(-0.334721\pi\)
0.496221 + 0.868196i \(0.334721\pi\)
\(68\) 12.9591i 0.190575i
\(69\) −25.7029 130.063i −0.372505 1.88497i
\(70\) 113.339 1.61913
\(71\) 99.7802i 1.40535i −0.711509 0.702677i \(-0.751988\pi\)
0.711509 0.702677i \(-0.248012\pi\)
\(72\) −23.5790 57.3280i −0.327486 0.796222i
\(73\) −129.745 −1.77733 −0.888663 0.458561i \(-0.848365\pi\)
−0.888663 + 0.458561i \(0.848365\pi\)
\(74\) 53.3515i 0.720966i
\(75\) 48.5114 9.58675i 0.646819 0.127823i
\(76\) 21.2133 0.279122
\(77\) 162.934i 2.11603i
\(78\) −22.6310 114.519i −0.290141 1.46819i
\(79\) 12.2886 0.155551 0.0777757 0.996971i \(-0.475218\pi\)
0.0777757 + 0.996971i \(0.475218\pi\)
\(80\) 7.84553i 0.0980691i
\(81\) 57.5602 56.9897i 0.710619 0.703577i
\(82\) 24.2536 0.295776
\(83\) 41.1271i 0.495507i −0.968823 0.247754i \(-0.920308\pi\)
0.968823 0.247754i \(-0.0796923\pi\)
\(84\) −220.909 + 43.6556i −2.62986 + 0.519710i
\(85\) 6.13875 0.0722206
\(86\) 146.894i 1.70807i
\(87\) 24.1970 + 122.443i 0.278127 + 1.40739i
\(88\) 92.1079 1.04668
\(89\) 75.0603i 0.843374i −0.906741 0.421687i \(-0.861438\pi\)
0.906741 0.421687i \(-0.138562\pi\)
\(90\) 77.4292 31.8466i 0.860324 0.353851i
\(91\) −148.727 −1.63436
\(92\) 272.260i 2.95935i
\(93\) −84.0119 + 16.6023i −0.903354 + 0.178519i
\(94\) −3.56781 −0.0379554
\(95\) 10.0488i 0.105777i
\(96\) −21.0073 106.302i −0.218826 1.10732i
\(97\) 186.423 1.92189 0.960943 0.276747i \(-0.0892564\pi\)
0.960943 + 0.276747i \(0.0892564\pi\)
\(98\) 316.980i 3.23449i
\(99\) 45.7822 + 111.311i 0.462446 + 1.12435i
\(100\) −101.549 −1.01549
\(101\) 40.4331i 0.400328i 0.979762 + 0.200164i \(0.0641474\pi\)
−0.979762 + 0.200164i \(0.935853\pi\)
\(102\) −19.7336 + 3.89973i −0.193467 + 0.0382326i
\(103\) −43.2601 −0.420001 −0.210001 0.977701i \(-0.567347\pi\)
−0.210001 + 0.977701i \(0.567347\pi\)
\(104\) 84.0765i 0.808428i
\(105\) −20.6798 104.645i −0.196950 0.996620i
\(106\) 96.5265 0.910627
\(107\) 105.027i 0.981557i 0.871284 + 0.490779i \(0.163288\pi\)
−0.871284 + 0.490779i \(0.836712\pi\)
\(108\) −138.651 + 91.8961i −1.28380 + 0.850890i
\(109\) −87.1490 −0.799532 −0.399766 0.916617i \(-0.630909\pi\)
−0.399766 + 0.916617i \(0.630909\pi\)
\(110\) 124.404i 1.13095i
\(111\) −49.2591 + 9.73450i −0.443775 + 0.0876982i
\(112\) −32.7539 −0.292445
\(113\) 119.661i 1.05894i −0.848328 0.529472i \(-0.822390\pi\)
0.848328 0.529472i \(-0.177610\pi\)
\(114\) −6.38363 32.3028i −0.0559967 0.283358i
\(115\) −128.970 −1.12148
\(116\) 256.309i 2.20956i
\(117\) −101.605 + 41.7902i −0.868421 + 0.357181i
\(118\) −24.4843 −0.207494
\(119\) 25.6283i 0.215364i
\(120\) −59.1566 + 11.6904i −0.492972 + 0.0974202i
\(121\) −57.8415 −0.478029
\(122\) 147.128i 1.20597i
\(123\) −4.42531 22.3932i −0.0359781 0.182059i
\(124\) 175.861 1.41824
\(125\) 121.063i 0.968502i
\(126\) 132.954 + 323.255i 1.05519 + 2.56551i
\(127\) −197.855 −1.55791 −0.778955 0.627080i \(-0.784250\pi\)
−0.778955 + 0.627080i \(0.784250\pi\)
\(128\) 188.244i 1.47066i
\(129\) −135.626 + 26.8022i −1.05137 + 0.207769i
\(130\) −113.557 −0.873512
\(131\) 120.820i 0.922292i 0.887324 + 0.461146i \(0.152562\pi\)
−0.887324 + 0.461146i \(0.847438\pi\)
\(132\) −47.9177 242.476i −0.363013 1.83694i
\(133\) −41.9521 −0.315429
\(134\) 211.954i 1.58175i
\(135\) −43.5315 65.6792i −0.322455 0.486512i
\(136\) 14.4879 0.106529
\(137\) 174.325i 1.27244i 0.771506 + 0.636222i \(0.219504\pi\)
−0.771506 + 0.636222i \(0.780496\pi\)
\(138\) 414.588 81.9302i 3.00426 0.593697i
\(139\) 1.76171 0.0126742 0.00633709 0.999980i \(-0.497983\pi\)
0.00633709 + 0.999980i \(0.497983\pi\)
\(140\) 219.053i 1.56466i
\(141\) 0.650981 + 3.29413i 0.00461689 + 0.0233626i
\(142\) 318.058 2.23985
\(143\) 163.247i 1.14159i
\(144\) −22.3763 + 9.20336i −0.155391 + 0.0639122i
\(145\) 121.414 0.837341
\(146\) 413.573i 2.83269i
\(147\) 292.666 57.8361i 1.99092 0.393443i
\(148\) 103.114 0.696713
\(149\) 88.4441i 0.593584i 0.954942 + 0.296792i \(0.0959169\pi\)
−0.954942 + 0.296792i \(0.904083\pi\)
\(150\) 30.5586 + 154.635i 0.203724 + 1.03090i
\(151\) 79.9437 0.529428 0.264714 0.964327i \(-0.414722\pi\)
0.264714 + 0.964327i \(0.414722\pi\)
\(152\) 23.7158i 0.156025i
\(153\) 7.20119 + 17.5084i 0.0470666 + 0.114434i
\(154\) −519.368 −3.37252
\(155\) 83.3060i 0.537458i
\(156\) 221.333 43.7395i 1.41880 0.280381i
\(157\) 71.8100 0.457388 0.228694 0.973498i \(-0.426554\pi\)
0.228694 + 0.973498i \(0.426554\pi\)
\(158\) 39.1709i 0.247917i
\(159\) −17.6122 89.1223i −0.110769 0.560518i
\(160\) −105.409 −0.658807
\(161\) 538.431i 3.34429i
\(162\) 181.660 + 183.478i 1.12136 + 1.13258i
\(163\) 43.7644 0.268493 0.134247 0.990948i \(-0.457139\pi\)
0.134247 + 0.990948i \(0.457139\pi\)
\(164\) 46.8755i 0.285826i
\(165\) 114.862 22.6988i 0.696131 0.137568i
\(166\) 131.096 0.789737
\(167\) 97.8528i 0.585945i −0.956121 0.292973i \(-0.905356\pi\)
0.956121 0.292973i \(-0.0946445\pi\)
\(168\) −48.8057 246.969i −0.290510 1.47006i
\(169\) −19.9871 −0.118267
\(170\) 19.5678i 0.115105i
\(171\) −28.6602 + 11.7879i −0.167604 + 0.0689353i
\(172\) 283.905 1.65061
\(173\) 67.8975i 0.392471i 0.980557 + 0.196235i \(0.0628717\pi\)
−0.980557 + 0.196235i \(0.937128\pi\)
\(174\) −390.299 + 77.1302i −2.24310 + 0.443277i
\(175\) 200.826 1.14758
\(176\) 35.9516i 0.204270i
\(177\) 4.46741 + 22.6062i 0.0252396 + 0.127719i
\(178\) 239.261 1.34417
\(179\) 290.963i 1.62549i 0.582620 + 0.812745i \(0.302028\pi\)
−0.582620 + 0.812745i \(0.697972\pi\)
\(180\) 61.5506 + 149.649i 0.341948 + 0.831384i
\(181\) 63.7495 0.352207 0.176104 0.984372i \(-0.443651\pi\)
0.176104 + 0.984372i \(0.443651\pi\)
\(182\) 474.081i 2.60484i
\(183\) −135.842 + 26.8450i −0.742308 + 0.146694i
\(184\) −304.379 −1.65423
\(185\) 48.8452i 0.264028i
\(186\) −52.9213 267.795i −0.284523 1.43976i
\(187\) −28.1304 −0.150430
\(188\) 6.89558i 0.0366786i
\(189\) 274.200 181.737i 1.45080 0.961572i
\(190\) −32.0314 −0.168586
\(191\) 181.224i 0.948818i 0.880305 + 0.474409i \(0.157338\pi\)
−0.880305 + 0.474409i \(0.842662\pi\)
\(192\) 307.200 60.7084i 1.60000 0.316190i
\(193\) −267.431 −1.38565 −0.692826 0.721104i \(-0.743635\pi\)
−0.692826 + 0.721104i \(0.743635\pi\)
\(194\) 594.240i 3.06309i
\(195\) 20.7195 + 104.846i 0.106254 + 0.537672i
\(196\) −612.635 −3.12569
\(197\) 187.173i 0.950115i 0.879955 + 0.475058i \(0.157573\pi\)
−0.879955 + 0.475058i \(0.842427\pi\)
\(198\) −354.814 + 145.935i −1.79199 + 0.737044i
\(199\) −43.9546 −0.220877 −0.110439 0.993883i \(-0.535226\pi\)
−0.110439 + 0.993883i \(0.535226\pi\)
\(200\) 113.528i 0.567642i
\(201\) 195.696 38.6732i 0.973613 0.192404i
\(202\) −128.884 −0.638040
\(203\) 506.886i 2.49698i
\(204\) −7.53709 38.1396i −0.0369465 0.186959i
\(205\) −22.2051 −0.108317
\(206\) 137.895i 0.669395i
\(207\) −151.291 367.838i −0.730876 1.77699i
\(208\) 32.8168 0.157773
\(209\) 46.0479i 0.220325i
\(210\) 333.566 65.9187i 1.58841 0.313899i
\(211\) −153.458 −0.727291 −0.363645 0.931537i \(-0.618468\pi\)
−0.363645 + 0.931537i \(0.618468\pi\)
\(212\) 186.559i 0.879995i
\(213\) −58.0329 293.661i −0.272455 1.37869i
\(214\) −334.782 −1.56440
\(215\) 134.487i 0.625520i
\(216\) −102.737 155.007i −0.475635 0.717627i
\(217\) −347.790 −1.60272
\(218\) 277.795i 1.27429i
\(219\) −381.850 + 75.4605i −1.74361 + 0.344568i
\(220\) −240.439 −1.09290
\(221\) 25.6776i 0.116188i
\(222\) −31.0296 157.018i −0.139773 0.707287i
\(223\) 348.282 1.56180 0.780901 0.624654i \(-0.214760\pi\)
0.780901 + 0.624654i \(0.214760\pi\)
\(224\) 440.067i 1.96458i
\(225\) 137.197 56.4292i 0.609766 0.250796i
\(226\) 381.429 1.68774
\(227\) 135.891i 0.598641i −0.954153 0.299320i \(-0.903240\pi\)
0.954153 0.299320i \(-0.0967599\pi\)
\(228\) 62.4324 12.3378i 0.273826 0.0541131i
\(229\) 243.213 1.06207 0.531033 0.847351i \(-0.321804\pi\)
0.531033 + 0.847351i \(0.321804\pi\)
\(230\) 411.105i 1.78741i
\(231\) 94.7637 + 479.529i 0.410233 + 2.07588i
\(232\) 286.546 1.23511
\(233\) 455.367i 1.95436i 0.212406 + 0.977181i \(0.431870\pi\)
−0.212406 + 0.977181i \(0.568130\pi\)
\(234\) −133.210 323.876i −0.569273 1.38408i
\(235\) 3.26646 0.0138998
\(236\) 47.3215i 0.200515i
\(237\) 36.1662 7.14711i 0.152600 0.0301566i
\(238\) −81.6926 −0.343246
\(239\) 195.311i 0.817199i 0.912714 + 0.408600i \(0.133983\pi\)
−0.912714 + 0.408600i \(0.866017\pi\)
\(240\) 4.56302 + 23.0900i 0.0190126 + 0.0962085i
\(241\) 27.4728 0.113995 0.0569976 0.998374i \(-0.481847\pi\)
0.0569976 + 0.998374i \(0.481847\pi\)
\(242\) 184.375i 0.761880i
\(243\) 136.259 201.203i 0.560735 0.827995i
\(244\) 284.358 1.16540
\(245\) 290.207i 1.18452i
\(246\) 71.3804 14.1061i 0.290164 0.0573418i
\(247\) 42.0327 0.170173
\(248\) 196.608i 0.792774i
\(249\) −23.9198 121.040i −0.0960635 0.486106i
\(250\) 385.898 1.54359
\(251\) 239.932i 0.955903i 0.878386 + 0.477952i \(0.158621\pi\)
−0.878386 + 0.477952i \(0.841379\pi\)
\(252\) −624.762 + 256.964i −2.47921 + 1.01970i
\(253\) 590.998 2.33596
\(254\) 630.679i 2.48299i
\(255\) 18.0669 3.57034i 0.0708504 0.0140013i
\(256\) −182.524 −0.712986
\(257\) 334.481i 1.30148i −0.759300 0.650741i \(-0.774458\pi\)
0.759300 0.650741i \(-0.225542\pi\)
\(258\) −85.4346 432.321i −0.331142 1.67566i
\(259\) −203.921 −0.787340
\(260\) 219.473i 0.844129i
\(261\) 142.428 + 346.287i 0.545700 + 1.32677i
\(262\) −385.125 −1.46994
\(263\) 351.568i 1.33676i 0.743820 + 0.668380i \(0.233012\pi\)
−0.743820 + 0.668380i \(0.766988\pi\)
\(264\) 271.081 53.5706i 1.02682 0.202919i
\(265\) −88.3735 −0.333485
\(266\) 133.726i 0.502730i
\(267\) −43.6556 220.909i −0.163504 0.827373i
\(268\) −409.649 −1.52854
\(269\) 243.044i 0.903508i −0.892143 0.451754i \(-0.850798\pi\)
0.892143 0.451754i \(-0.149202\pi\)
\(270\) 209.358 138.760i 0.775401 0.513928i
\(271\) −69.7893 −0.257525 −0.128763 0.991675i \(-0.541101\pi\)
−0.128763 + 0.991675i \(0.541101\pi\)
\(272\) 5.65492i 0.0207901i
\(273\) −437.716 + 86.5008i −1.60336 + 0.316853i
\(274\) −555.676 −2.02801
\(275\) 220.433i 0.801573i
\(276\) 158.348 + 801.284i 0.573726 + 2.90320i
\(277\) 74.2229 0.267953 0.133976 0.990985i \(-0.457225\pi\)
0.133976 + 0.990985i \(0.457225\pi\)
\(278\) 5.61561i 0.0202000i
\(279\) −237.598 + 97.7238i −0.851605 + 0.350265i
\(280\) −244.894 −0.874623
\(281\) 342.390i 1.21847i 0.792990 + 0.609235i \(0.208524\pi\)
−0.792990 + 0.609235i \(0.791476\pi\)
\(282\) −10.5003 + 2.07506i −0.0372353 + 0.00735837i
\(283\) 490.428 1.73296 0.866481 0.499209i \(-0.166376\pi\)
0.866481 + 0.499209i \(0.166376\pi\)
\(284\) 614.719i 2.16450i
\(285\) 5.84445 + 29.5744i 0.0205068 + 0.103770i
\(286\) 520.365 1.81946
\(287\) 92.7027i 0.323006i
\(288\) −123.652 300.638i −0.429349 1.04388i
\(289\) 284.575 0.984690
\(290\) 387.019i 1.33455i
\(291\) 548.658 108.425i 1.88542 0.372594i
\(292\) 799.322 2.73741
\(293\) 400.366i 1.36644i −0.730214 0.683219i \(-0.760579\pi\)
0.730214 0.683219i \(-0.239421\pi\)
\(294\) 184.358 + 932.898i 0.627068 + 3.17312i
\(295\) 22.4163 0.0759875
\(296\) 115.278i 0.389453i
\(297\) 199.480 + 300.970i 0.671650 + 1.01337i
\(298\) −281.923 −0.946052
\(299\) 539.466i 1.80423i
\(300\) −298.866 + 59.0614i −0.996219 + 0.196871i
\(301\) −561.461 −1.86532
\(302\) 254.828i 0.843800i
\(303\) 23.5162 + 118.998i 0.0776111 + 0.392732i
\(304\) 9.25677 0.0304499
\(305\) 134.701i 0.441643i
\(306\) −55.8096 + 22.9544i −0.182384 + 0.0750145i
\(307\) 209.512 0.682450 0.341225 0.939982i \(-0.389158\pi\)
0.341225 + 0.939982i \(0.389158\pi\)
\(308\) 1003.79i 3.25907i
\(309\) −127.318 + 25.1604i −0.412033 + 0.0814252i
\(310\) −265.545 −0.856598
\(311\) 383.028i 1.23160i 0.787902 + 0.615801i \(0.211167\pi\)
−0.787902 + 0.615801i \(0.788833\pi\)
\(312\) 48.8995 + 247.444i 0.156729 + 0.793090i
\(313\) 28.8222 0.0920837 0.0460418 0.998940i \(-0.485339\pi\)
0.0460418 + 0.998940i \(0.485339\pi\)
\(314\) 228.901i 0.728983i
\(315\) −121.725 295.952i −0.386427 0.939529i
\(316\) −75.7065 −0.239577
\(317\) 357.739i 1.12851i −0.825599 0.564257i \(-0.809163\pi\)
0.825599 0.564257i \(-0.190837\pi\)
\(318\) 284.085 56.1405i 0.893350 0.176542i
\(319\) −556.373 −1.74412
\(320\) 304.619i 0.951935i
\(321\) 61.0842 + 309.102i 0.190294 + 0.962935i
\(322\) 1716.30 5.33012
\(323\) 7.24298i 0.0224241i
\(324\) −354.613 + 351.098i −1.09448 + 1.08364i
\(325\) −201.212 −0.619113
\(326\) 139.503i 0.427923i
\(327\) −256.487 + 50.6865i −0.784363 + 0.155004i
\(328\) −52.4055 −0.159773
\(329\) 13.6369i 0.0414497i
\(330\) 72.3543 + 366.131i 0.219255 + 1.10949i
\(331\) −132.781 −0.401152 −0.200576 0.979678i \(-0.564281\pi\)
−0.200576 + 0.979678i \(0.564281\pi\)
\(332\) 253.373i 0.763171i
\(333\) −139.312 + 57.2989i −0.418354 + 0.172069i
\(334\) 311.915 0.933876
\(335\) 194.052i 0.579260i
\(336\) −96.3973 + 19.0499i −0.286897 + 0.0566961i
\(337\) 203.625 0.604228 0.302114 0.953272i \(-0.402308\pi\)
0.302114 + 0.953272i \(0.402308\pi\)
\(338\) 63.7108i 0.188493i
\(339\) −69.5955 352.171i −0.205296 1.03885i
\(340\) −37.8192 −0.111233
\(341\) 381.744i 1.11948i
\(342\) −37.5751 91.3571i −0.109869 0.267126i
\(343\) 614.568 1.79174
\(344\) 317.398i 0.922668i
\(345\) −379.570 + 75.0101i −1.10020 + 0.217421i
\(346\) −216.429 −0.625518
\(347\) 191.457i 0.551750i −0.961194 0.275875i \(-0.911032\pi\)
0.961194 0.275875i \(-0.0889676\pi\)
\(348\) −149.071 754.339i −0.428366 2.16764i
\(349\) 376.372 1.07843 0.539215 0.842168i \(-0.318721\pi\)
0.539215 + 0.842168i \(0.318721\pi\)
\(350\) 640.151i 1.82900i
\(351\) −274.727 + 182.086i −0.782698 + 0.518764i
\(352\) 483.030 1.37225
\(353\) 514.841i 1.45847i −0.684261 0.729237i \(-0.739875\pi\)
0.684261 0.729237i \(-0.260125\pi\)
\(354\) −72.0594 + 14.2403i −0.203558 + 0.0402267i
\(355\) −291.194 −0.820265
\(356\) 462.426i 1.29895i
\(357\) 14.9056 + 75.4263i 0.0417525 + 0.211278i
\(358\) −927.469 −2.59070
\(359\) 204.536i 0.569738i −0.958566 0.284869i \(-0.908050\pi\)
0.958566 0.284869i \(-0.0919501\pi\)
\(360\) −167.303 + 68.8118i −0.464732 + 0.191144i
\(361\) −349.144 −0.967157
\(362\) 203.207i 0.561346i
\(363\) −170.232 + 33.6410i −0.468959 + 0.0926750i
\(364\) 916.267 2.51722
\(365\) 378.641i 1.03737i
\(366\) −85.5707 433.010i −0.233800 1.18309i
\(367\) 72.5182 0.197597 0.0987986 0.995107i \(-0.468500\pi\)
0.0987986 + 0.995107i \(0.468500\pi\)
\(368\) 118.805i 0.322841i
\(369\) −26.0481 63.3313i −0.0705911 0.171629i
\(370\) −155.698 −0.420807
\(371\) 368.946i 0.994463i
\(372\) 517.574 102.282i 1.39133 0.274952i
\(373\) 33.8148 0.0906563 0.0453282 0.998972i \(-0.485567\pi\)
0.0453282 + 0.998972i \(0.485567\pi\)
\(374\) 89.6683i 0.239755i
\(375\) −70.4109 356.298i −0.187763 0.950127i
\(376\) 7.70906 0.0205028
\(377\) 507.860i 1.34711i
\(378\) 579.303 + 874.038i 1.53255 + 2.31227i
\(379\) 70.9565 0.187220 0.0936102 0.995609i \(-0.470159\pi\)
0.0936102 + 0.995609i \(0.470159\pi\)
\(380\) 61.9078i 0.162915i
\(381\) −582.302 + 115.074i −1.52835 + 0.302031i
\(382\) −577.668 −1.51222
\(383\) 152.819i 0.399006i −0.979897 0.199503i \(-0.936067\pi\)
0.979897 0.199503i \(-0.0639328\pi\)
\(384\) 109.484 + 554.019i 0.285115 + 1.44276i
\(385\) 475.500 1.23506
\(386\) 852.460i 2.20845i
\(387\) −383.571 + 157.762i −0.991139 + 0.407655i
\(388\) −1148.50 −2.96005
\(389\) 448.180i 1.15213i −0.817403 0.576067i \(-0.804587\pi\)
0.817403 0.576067i \(-0.195413\pi\)
\(390\) −334.206 + 66.0453i −0.856940 + 0.169347i
\(391\) 92.9596 0.237748
\(392\) 684.908i 1.74721i
\(393\) 70.2699 + 355.584i 0.178804 + 0.904794i
\(394\) −596.630 −1.51429
\(395\) 35.8624i 0.0907908i
\(396\) −282.051 685.757i −0.712251 1.73171i
\(397\) 244.470 0.615795 0.307897 0.951420i \(-0.400375\pi\)
0.307897 + 0.951420i \(0.400375\pi\)
\(398\) 140.109i 0.352033i
\(399\) −123.468 + 24.3996i −0.309445 + 0.0611520i
\(400\) −44.3124 −0.110781
\(401\) 3.27174i 0.00815896i −0.999992 0.00407948i \(-0.998701\pi\)
0.999992 0.00407948i \(-0.00129854\pi\)
\(402\) 123.274 + 623.799i 0.306652 + 1.55174i
\(403\) 348.458 0.864660
\(404\) 249.097i 0.616577i
\(405\) −166.316 167.981i −0.410657 0.414768i
\(406\) −1615.75 −3.97967
\(407\) 223.830i 0.549951i
\(408\) 42.6390 8.42625i 0.104507 0.0206526i
\(409\) −523.908 −1.28095 −0.640474 0.767980i \(-0.721262\pi\)
−0.640474 + 0.767980i \(0.721262\pi\)
\(410\) 70.7806i 0.172636i
\(411\) 101.389 + 513.052i 0.246687 + 1.24830i
\(412\) 266.514 0.646878
\(413\) 93.5846i 0.226597i
\(414\) 1172.52 482.255i 2.83216 1.16487i
\(415\) −120.023 −0.289213
\(416\) 440.912i 1.05989i
\(417\) 5.18486 1.02462i 0.0124337 0.00245713i
\(418\) 146.782 0.351152
\(419\) 596.864i 1.42450i 0.701928 + 0.712248i \(0.252323\pi\)
−0.701928 + 0.712248i \(0.747677\pi\)
\(420\) 127.403 + 644.690i 0.303339 + 1.53498i
\(421\) 745.944 1.77184 0.885919 0.463839i \(-0.153529\pi\)
0.885919 + 0.463839i \(0.153529\pi\)
\(422\) 489.162i 1.15915i
\(423\) 3.83178 + 9.31629i 0.00905859 + 0.0220243i
\(424\) −208.568 −0.491905
\(425\) 34.6724i 0.0815821i
\(426\) 936.072 184.985i 2.19735 0.434237i
\(427\) −562.356 −1.31699
\(428\) 647.041i 1.51178i
\(429\) −94.9458 480.450i −0.221319 1.11993i
\(430\) −428.689 −0.996950
\(431\) 514.240i 1.19313i −0.802564 0.596566i \(-0.796531\pi\)
0.802564 0.596566i \(-0.203469\pi\)
\(432\) −60.5026 + 40.1005i −0.140052 + 0.0928251i
\(433\) 94.8594 0.219075 0.109537 0.993983i \(-0.465063\pi\)
0.109537 + 0.993983i \(0.465063\pi\)
\(434\) 1108.61i 2.55440i
\(435\) 357.333 70.6155i 0.821454 0.162334i
\(436\) 536.901 1.23142
\(437\) 152.169i 0.348214i
\(438\) −240.537 1217.18i −0.549172 2.77895i
\(439\) −229.998 −0.523912 −0.261956 0.965080i \(-0.584368\pi\)
−0.261956 + 0.965080i \(0.584368\pi\)
\(440\) 268.803i 0.610917i
\(441\) 827.701 340.433i 1.87687 0.771957i
\(442\) 81.8496 0.185180
\(443\) 567.587i 1.28123i 0.767860 + 0.640617i \(0.221321\pi\)
−0.767860 + 0.640617i \(0.778679\pi\)
\(444\) 303.472 59.9716i 0.683495 0.135071i
\(445\) −219.053 −0.492253
\(446\) 1110.18i 2.48919i
\(447\) 51.4397 + 260.298i 0.115078 + 0.582323i
\(448\) 1271.74 2.83870
\(449\) 718.237i 1.59964i 0.600242 + 0.799819i \(0.295071\pi\)
−0.600242 + 0.799819i \(0.704929\pi\)
\(450\) 179.873 + 437.329i 0.399718 + 0.971842i
\(451\) 101.753 0.225617
\(452\) 737.196i 1.63097i
\(453\) 235.281 46.4958i 0.519384 0.102640i
\(454\) 433.166 0.954110
\(455\) 434.039i 0.953931i
\(456\) 13.7933 + 69.7976i 0.0302484 + 0.153065i
\(457\) −649.904 −1.42211 −0.711055 0.703137i \(-0.751782\pi\)
−0.711055 + 0.703137i \(0.751782\pi\)
\(458\) 775.263i 1.69271i
\(459\) 31.3767 + 47.3404i 0.0683588 + 0.103138i
\(460\) 794.552 1.72729
\(461\) 657.743i 1.42677i −0.700771 0.713387i \(-0.747160\pi\)
0.700771 0.713387i \(-0.252840\pi\)
\(462\) −1528.54 + 302.068i −3.30853 + 0.653827i
\(463\) 46.1887 0.0997597 0.0498798 0.998755i \(-0.484116\pi\)
0.0498798 + 0.998755i \(0.484116\pi\)
\(464\) 111.845i 0.241045i
\(465\) 48.4514 + 245.177i 0.104197 + 0.527261i
\(466\) −1451.52 −3.11485
\(467\) 406.250i 0.869914i 0.900451 + 0.434957i \(0.143236\pi\)
−0.900451 + 0.434957i \(0.856764\pi\)
\(468\) 625.962 257.458i 1.33753 0.550124i
\(469\) 810.137 1.72737
\(470\) 10.4121i 0.0221535i
\(471\) 211.343 41.7652i 0.448711 0.0886735i
\(472\) 52.9040 0.112085
\(473\) 616.276i 1.30291i
\(474\) 22.7821 + 115.283i 0.0480634 + 0.243213i
\(475\) −56.7567 −0.119488
\(476\) 157.889i 0.331700i
\(477\) −103.668 252.051i −0.217334 0.528409i
\(478\) −622.570 −1.30245
\(479\) 569.676i 1.18930i 0.803984 + 0.594651i \(0.202710\pi\)
−0.803984 + 0.594651i \(0.797290\pi\)
\(480\) −310.228 + 61.3067i −0.646308 + 0.127722i
\(481\) 204.313 0.424767
\(482\) 87.5721i 0.181685i
\(483\) −313.155 1584.65i −0.648355 3.28084i
\(484\) 356.346 0.736252
\(485\) 544.048i 1.12175i
\(486\) 641.352 + 434.337i 1.31965 + 0.893697i
\(487\) −478.590 −0.982731 −0.491366 0.870953i \(-0.663502\pi\)
−0.491366 + 0.870953i \(0.663502\pi\)
\(488\) 317.904i 0.651442i
\(489\) 128.802 25.4537i 0.263399 0.0520525i
\(490\) 925.060 1.88788
\(491\) 454.446i 0.925552i −0.886475 0.462776i \(-0.846853\pi\)
0.886475 0.462776i \(-0.153147\pi\)
\(492\) 27.2631 + 137.958i 0.0554129 + 0.280403i
\(493\) −87.5133 −0.177512
\(494\) 133.983i 0.271221i
\(495\) 324.845 133.609i 0.656253 0.269916i
\(496\) 76.7401 0.154718
\(497\) 1215.69i 2.44605i
\(498\) 385.827 76.2465i 0.774753 0.153105i
\(499\) −158.942 −0.318520 −0.159260 0.987237i \(-0.550911\pi\)
−0.159260 + 0.987237i \(0.550911\pi\)
\(500\) 745.834i 1.49167i
\(501\) −56.9119 287.989i −0.113597 0.574828i
\(502\) −764.804 −1.52351
\(503\) 455.984i 0.906529i −0.891376 0.453265i \(-0.850259\pi\)
0.891376 0.453265i \(-0.149741\pi\)
\(504\) −287.278 698.466i −0.569997 1.38584i
\(505\) 117.998 0.233660
\(506\) 1883.86i 3.72304i
\(507\) −58.8238 + 11.6247i −0.116023 + 0.0229283i
\(508\) 1218.93 2.39947
\(509\) 831.857i 1.63430i −0.576428 0.817148i \(-0.695554\pi\)
0.576428 0.817148i \(-0.304446\pi\)
\(510\) 11.3808 + 57.5897i 0.0223153 + 0.112921i
\(511\) −1580.77 −3.09348
\(512\) 171.165i 0.334307i
\(513\) −77.4935 + 51.3618i −0.151059 + 0.100121i
\(514\) 1066.19 2.07430
\(515\) 126.248i 0.245142i
\(516\) 835.557 165.121i 1.61930 0.320003i
\(517\) −14.9683 −0.0289523
\(518\) 650.017i 1.25486i
\(519\) 39.4896 + 199.828i 0.0760880 + 0.385025i
\(520\) 245.365 0.471856
\(521\) 886.146i 1.70086i 0.526091 + 0.850428i \(0.323657\pi\)
−0.526091 + 0.850428i \(0.676343\pi\)
\(522\) −1103.82 + 454.001i −2.11460 + 0.869734i
\(523\) −116.013 −0.221823 −0.110912 0.993830i \(-0.535377\pi\)
−0.110912 + 0.993830i \(0.535377\pi\)
\(524\) 744.341i 1.42050i
\(525\) 591.047 116.802i 1.12580 0.222480i
\(526\) −1120.65 −2.13052
\(527\) 60.0455i 0.113938i
\(528\) −20.9097 105.809i −0.0396017 0.200395i
\(529\) −1424.01 −2.69189
\(530\) 281.699i 0.531507i
\(531\) 26.2959 + 63.9338i 0.0495215 + 0.120403i
\(532\) 258.455 0.485819
\(533\) 92.8808i 0.174260i
\(534\) 704.166 139.156i 1.31866 0.260592i
\(535\) 306.505 0.572906
\(536\) 457.976i 0.854433i
\(537\) 169.226 + 856.327i 0.315132 + 1.59465i
\(538\) 774.723 1.44001
\(539\) 1329.85i 2.46726i
\(540\) 268.186 + 404.632i 0.496640 + 0.749318i
\(541\) 391.559 0.723769 0.361885 0.932223i \(-0.382133\pi\)
0.361885 + 0.932223i \(0.382133\pi\)
\(542\) 222.460i 0.410442i
\(543\) 187.620 37.0772i 0.345525 0.0682821i
\(544\) 75.9771 0.139664
\(545\) 254.332i 0.466664i
\(546\) −275.729 1395.26i −0.504998 2.55542i
\(547\) 390.455 0.713812 0.356906 0.934140i \(-0.383832\pi\)
0.356906 + 0.934140i \(0.383832\pi\)
\(548\) 1073.97i 1.95979i
\(549\) −384.182 + 158.014i −0.699785 + 0.287821i
\(550\) −702.649 −1.27754
\(551\) 143.254i 0.259990i
\(552\) −895.812 + 177.029i −1.62285 + 0.320705i
\(553\) 149.720 0.270741
\(554\) 236.592i 0.427062i
\(555\) 28.4087 + 143.755i 0.0511869 + 0.259019i
\(556\) −10.8534 −0.0195205
\(557\) 417.528i 0.749602i 0.927105 + 0.374801i \(0.122289\pi\)
−0.927105 + 0.374801i \(0.877711\pi\)
\(558\) −311.503 757.365i −0.558250 1.35728i
\(559\) 562.540 1.00633
\(560\) 95.5874i 0.170692i
\(561\) −82.7902 + 16.3609i −0.147576 + 0.0291637i
\(562\) −1091.40 −1.94199
\(563\) 142.520i 0.253144i −0.991957 0.126572i \(-0.959602\pi\)
0.991957 0.126572i \(-0.0403975\pi\)
\(564\) −4.01052 20.2943i −0.00711085 0.0359827i
\(565\) −349.212 −0.618074
\(566\) 1563.28i 2.76199i
\(567\) 701.294 694.344i 1.23685 1.22459i
\(568\) −687.238 −1.20993
\(569\) 441.466i 0.775863i −0.921688 0.387932i \(-0.873190\pi\)
0.921688 0.387932i \(-0.126810\pi\)
\(570\) −94.2711 + 18.6297i −0.165388 + 0.0326837i
\(571\) 560.119 0.980943 0.490472 0.871457i \(-0.336825\pi\)
0.490472 + 0.871457i \(0.336825\pi\)
\(572\) 1005.72i 1.75826i
\(573\) 105.401 + 533.358i 0.183946 + 0.930816i
\(574\) 295.498 0.514805
\(575\) 728.440i 1.26685i
\(576\) 868.807 357.340i 1.50835 0.620381i
\(577\) 521.847 0.904414 0.452207 0.891913i \(-0.350637\pi\)
0.452207 + 0.891913i \(0.350637\pi\)
\(578\) 907.109i 1.56939i
\(579\) −787.071 + 155.540i −1.35936 + 0.268635i
\(580\) −748.001 −1.28966
\(581\) 501.079i 0.862442i
\(582\) 345.614 + 1748.90i 0.593839 + 3.00498i
\(583\) 404.966 0.694624
\(584\) 893.619i 1.53017i
\(585\) 121.959 + 296.520i 0.208476 + 0.506872i
\(586\) 1276.20 2.17782
\(587\) 393.477i 0.670319i 0.942161 + 0.335160i \(0.108790\pi\)
−0.942161 + 0.335160i \(0.891210\pi\)
\(588\) −1803.03 + 356.313i −3.06638 + 0.605974i
\(589\) 98.2910 0.166878
\(590\) 71.4540i 0.121108i
\(591\) 108.861 + 550.865i 0.184198 + 0.932089i
\(592\) 44.9954 0.0760057
\(593\) 815.002i 1.37437i 0.726482 + 0.687185i \(0.241154\pi\)
−0.726482 + 0.687185i \(0.758846\pi\)
\(594\) −959.370 + 635.860i −1.61510 + 1.07047i
\(595\) 74.7926 0.125702
\(596\) 544.880i 0.914228i
\(597\) −129.362 + 25.5643i −0.216687 + 0.0428213i
\(598\) −1719.60 −2.87558
\(599\) 248.629i 0.415074i −0.978227 0.207537i \(-0.933455\pi\)
0.978227 0.207537i \(-0.0665447\pi\)
\(600\) −66.0289 334.123i −0.110048 0.556872i
\(601\) 463.227 0.770761 0.385381 0.922758i \(-0.374070\pi\)
0.385381 + 0.922758i \(0.374070\pi\)
\(602\) 1789.71i 2.97294i
\(603\) 553.457 227.637i 0.917840 0.377507i
\(604\) −492.511 −0.815416
\(605\) 168.802i 0.279012i
\(606\) −379.316 + 74.9599i −0.625935 + 0.123696i
\(607\) 61.8284 0.101859 0.0509295 0.998702i \(-0.483782\pi\)
0.0509295 + 0.998702i \(0.483782\pi\)
\(608\) 124.370i 0.204556i
\(609\) 294.809 + 1491.81i 0.484086 + 2.44960i
\(610\) −429.372 −0.703888
\(611\) 13.6631i 0.0223619i
\(612\) −44.3646 107.864i −0.0724911 0.176249i
\(613\) 356.755 0.581981 0.290991 0.956726i \(-0.406015\pi\)
0.290991 + 0.956726i \(0.406015\pi\)
\(614\) 667.839i 1.08769i
\(615\) −65.3513 + 12.9146i −0.106262 + 0.0209994i
\(616\) 1122.21 1.82177
\(617\) 225.517i 0.365506i −0.983159 0.182753i \(-0.941499\pi\)
0.983159 0.182753i \(-0.0585008\pi\)
\(618\) −80.2010 405.838i −0.129775 0.656695i
\(619\) −1105.63 −1.78616 −0.893080 0.449898i \(-0.851460\pi\)
−0.893080 + 0.449898i \(0.851460\pi\)
\(620\) 513.226i 0.827784i
\(621\) −659.200 994.584i −1.06151 1.60158i
\(622\) −1220.94 −1.96292
\(623\) 914.510i 1.46791i
\(624\) 96.5825 19.0865i 0.154780 0.0305873i
\(625\) 58.7762 0.0940419
\(626\) 91.8733i 0.146763i
\(627\) −26.7818 135.523i −0.0427142 0.216145i
\(628\) −442.402 −0.704462
\(629\) 35.2068i 0.0559726i
\(630\) 943.372 388.008i 1.49742 0.615886i
\(631\) 130.411 0.206674 0.103337 0.994646i \(-0.467048\pi\)
0.103337 + 0.994646i \(0.467048\pi\)
\(632\) 84.6376i 0.133920i
\(633\) −451.641 + 89.2525i −0.713492 + 0.140999i
\(634\) 1140.33 1.79862
\(635\) 577.410i 0.909307i
\(636\) 108.504 + 549.058i 0.170604 + 0.863299i
\(637\) −1213.90 −1.90564
\(638\) 1773.49i 2.77976i
\(639\) −341.591 830.517i −0.534571 1.29971i
\(640\) 549.364 0.858381
\(641\) 19.7410i 0.0307972i −0.999881 0.0153986i \(-0.995098\pi\)
0.999881 0.0153986i \(-0.00490172\pi\)
\(642\) −985.290 + 194.711i −1.53472 + 0.303289i
\(643\) 879.551 1.36789 0.683943 0.729535i \(-0.260263\pi\)
0.683943 + 0.729535i \(0.260263\pi\)
\(644\) 3317.13i 5.15082i
\(645\) 78.2185 + 395.806i 0.121269 + 0.613652i
\(646\) 23.0877 0.0357394
\(647\) 611.023i 0.944394i −0.881493 0.472197i \(-0.843461\pi\)
0.881493 0.472197i \(-0.156539\pi\)
\(648\) −392.517 396.447i −0.605737 0.611800i
\(649\) −102.721 −0.158276
\(650\) 641.381i 0.986740i
\(651\) −1023.57 + 202.277i −1.57231 + 0.310717i
\(652\) −269.620 −0.413528
\(653\) 441.041i 0.675407i 0.941253 + 0.337704i \(0.109650\pi\)
−0.941253 + 0.337704i \(0.890350\pi\)
\(654\) −161.568 817.574i −0.247045 1.25011i
\(655\) 352.596 0.538315
\(656\) 20.4549i 0.0311813i
\(657\) −1079.93 + 444.173i −1.64372 + 0.676062i
\(658\) −43.4690 −0.0660623
\(659\) 38.8201i 0.0589076i −0.999566 0.0294538i \(-0.990623\pi\)
0.999566 0.0294538i \(-0.00937680\pi\)
\(660\) −707.631 + 139.841i −1.07217 + 0.211880i
\(661\) −951.942 −1.44016 −0.720078 0.693894i \(-0.755894\pi\)
−0.720078 + 0.693894i \(0.755894\pi\)
\(662\) 423.252i 0.639354i
\(663\) −14.9343 75.5712i −0.0225253 0.113984i
\(664\) −283.263 −0.426602
\(665\) 122.431i 0.184107i
\(666\) −182.645 444.069i −0.274242 0.666770i
\(667\) 1838.59 2.75650
\(668\) 602.845i 0.902462i
\(669\) 1025.02 202.563i 1.53217 0.302785i
\(670\) 618.558 0.923221
\(671\) 617.259i 0.919909i
\(672\) −255.946 1295.15i −0.380872 1.92731i
\(673\) −435.673 −0.647360 −0.323680 0.946167i \(-0.604920\pi\)
−0.323680 + 0.946167i \(0.604920\pi\)
\(674\) 649.073i 0.963016i
\(675\) 370.964 245.871i 0.549576 0.364253i
\(676\) 123.135 0.182153
\(677\) 138.438i 0.204488i −0.994759 0.102244i \(-0.967398\pi\)
0.994759 0.102244i \(-0.0326022\pi\)
\(678\) 1122.58 221.842i 1.65572 0.327200i
\(679\) 2271.32 3.34509
\(680\) 42.2808i 0.0621776i
\(681\) −79.0354 399.940i −0.116058 0.587283i
\(682\) 1216.84 1.78423
\(683\) 610.846i 0.894358i 0.894445 + 0.447179i \(0.147571\pi\)
−0.894445 + 0.447179i \(0.852429\pi\)
\(684\) 176.568 72.6222i 0.258140 0.106173i
\(685\) 508.741 0.742688
\(686\) 1958.99i 2.85567i
\(687\) 715.796 141.454i 1.04192 0.205902i
\(688\) 123.887 0.180068
\(689\) 369.654i 0.536509i
\(690\) −239.101 1209.91i −0.346524 1.75350i
\(691\) 150.187 0.217347 0.108674 0.994077i \(-0.465340\pi\)
0.108674 + 0.994077i \(0.465340\pi\)
\(692\) 418.298i 0.604477i
\(693\) 557.795 + 1356.18i 0.804899 + 1.95697i
\(694\) 610.287 0.879376
\(695\) 5.14130i 0.00739755i
\(696\) 843.329 166.657i 1.21168 0.239450i
\(697\) 16.0050 0.0229627
\(698\) 1199.72i 1.71880i
\(699\) 264.844 + 1340.18i 0.378891 + 1.91728i
\(700\) −1237.23 −1.76748
\(701\) 484.616i 0.691321i −0.938360 0.345661i \(-0.887655\pi\)
0.938360 0.345661i \(-0.112345\pi\)
\(702\) −580.416 875.717i −0.826804 1.24746i
\(703\) 57.6314 0.0819793
\(704\) 1395.90i 1.98281i
\(705\) 9.61345 1.89979i 0.0136361 0.00269474i
\(706\) 1641.10 2.32451
\(707\) 492.624i 0.696780i
\(708\) −27.5225 139.271i −0.0388736 0.196710i
\(709\) −626.486 −0.883619 −0.441809 0.897109i \(-0.645663\pi\)
−0.441809 + 0.897109i \(0.645663\pi\)
\(710\) 928.207i 1.30733i
\(711\) 102.283 42.0691i 0.143858 0.0591689i
\(712\) −516.979 −0.726094
\(713\) 1261.51i 1.76930i
\(714\) −240.428 + 47.5130i −0.336734 + 0.0665448i
\(715\) −476.414 −0.666313
\(716\) 1792.54i 2.50355i
\(717\) 113.594 + 574.815i 0.158430 + 0.801695i
\(718\) 651.977 0.908045
\(719\) 1027.95i 1.42969i −0.699284 0.714844i \(-0.746498\pi\)
0.699284 0.714844i \(-0.253502\pi\)
\(720\) 26.8587 + 65.3020i 0.0373037 + 0.0906972i
\(721\) −527.067 −0.731022
\(722\) 1112.93i 1.54145i
\(723\) 80.8548 15.9784i 0.111832 0.0221001i
\(724\) −392.743 −0.542463
\(725\) 685.763i 0.945879i
\(726\) −107.234 542.631i −0.147705 0.747425i
\(727\) −554.861 −0.763220 −0.381610 0.924323i \(-0.624630\pi\)
−0.381610 + 0.924323i \(0.624630\pi\)
\(728\) 1024.36i 1.40709i
\(729\) 284.000 671.405i 0.389574 0.920995i
\(730\) −1206.95 −1.65336
\(731\) 96.9357i 0.132607i
\(732\) 836.888 165.385i 1.14329 0.225935i
\(733\) 175.837 0.239886 0.119943 0.992781i \(-0.461729\pi\)
0.119943 + 0.992781i \(0.461729\pi\)
\(734\) 231.158i 0.314929i
\(735\) −168.786 854.102i −0.229641 1.16204i
\(736\) −1596.22 −2.16877
\(737\) 889.230i 1.20655i
\(738\) 201.874 83.0307i 0.273542 0.112508i
\(739\) −139.389 −0.188618 −0.0943090 0.995543i \(-0.530064\pi\)
−0.0943090 + 0.995543i \(0.530064\pi\)
\(740\) 300.922i 0.406651i
\(741\) 123.706 24.4465i 0.166944 0.0329913i
\(742\) 1176.05 1.58497
\(743\) 100.461i 0.135210i 0.997712 + 0.0676048i \(0.0215357\pi\)
−0.997712 + 0.0676048i \(0.978464\pi\)
\(744\) 114.349 + 578.633i 0.153694 + 0.777733i
\(745\) 258.111 0.346458
\(746\) 107.788i 0.144488i
\(747\) −140.796 342.320i −0.188482 0.458260i
\(748\) 173.304 0.231690
\(749\) 1279.61i 1.70842i
\(750\) 1135.73 224.441i 1.51431 0.299255i
\(751\) −153.159 −0.203940 −0.101970 0.994787i \(-0.532515\pi\)
−0.101970 + 0.994787i \(0.532515\pi\)
\(752\) 3.00900i 0.00400134i
\(753\) 139.546 + 706.139i 0.185320 + 0.937767i
\(754\) 1618.85 2.14702
\(755\) 233.304i 0.309012i
\(756\) −1689.27 + 1119.63i −2.23449 + 1.48100i
\(757\) −947.893 −1.25217 −0.626085 0.779755i \(-0.715344\pi\)
−0.626085 + 0.779755i \(0.715344\pi\)
\(758\) 226.180i 0.298391i
\(759\) 1739.36 343.729i 2.29164 0.452871i
\(760\) 69.2112 0.0910673
\(761\) 1068.30i 1.40381i −0.712272 0.701904i \(-0.752334\pi\)
0.712272 0.701904i \(-0.247666\pi\)
\(762\) −366.808 1856.14i −0.481375 2.43588i
\(763\) −1061.79 −1.39161
\(764\) 1116.47i 1.46135i
\(765\) 51.0957 21.0156i 0.0667918 0.0274714i
\(766\) 487.125 0.635934
\(767\) 93.7644i 0.122248i
\(768\) −537.184 + 106.157i −0.699458 + 0.138226i
\(769\) 908.642 1.18159 0.590795 0.806822i \(-0.298814\pi\)
0.590795 + 0.806822i \(0.298814\pi\)
\(770\) 1515.70i 1.96844i
\(771\) −194.536 984.405i −0.252317 1.27679i
\(772\) 1647.57 2.13416
\(773\) 606.118i 0.784112i −0.919941 0.392056i \(-0.871764\pi\)
0.919941 0.392056i \(-0.128236\pi\)
\(774\) −502.882 1222.67i −0.649718 1.57967i
\(775\) −470.522 −0.607125
\(776\) 1283.99i 1.65463i
\(777\) −600.157 + 118.602i −0.772402 + 0.152641i
\(778\) 1428.61 1.83626
\(779\) 26.1993i 0.0336319i
\(780\) −127.647 645.928i −0.163650 0.828113i
\(781\) 1334.38 1.70855
\(782\) 296.317i 0.378922i
\(783\) 620.579 + 936.315i 0.792566 + 1.19580i
\(784\) −267.334 −0.340987
\(785\) 209.567i 0.266964i
\(786\) −1133.46