Properties

Label 177.3.b.a.119.13
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 119.13
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.26

$q$-expansion

\(f(q)\) \(=\) \(q-1.50450i q^{2} +(2.07476 - 2.16688i) q^{3} +1.73647 q^{4} +9.35091i q^{5} +(-3.26008 - 3.12148i) q^{6} +7.09053 q^{7} -8.63054i q^{8} +(-0.390753 - 8.99151i) q^{9} +O(q^{10})\) \(q-1.50450i q^{2} +(2.07476 - 2.16688i) q^{3} +1.73647 q^{4} +9.35091i q^{5} +(-3.26008 - 3.12148i) q^{6} +7.09053 q^{7} -8.63054i q^{8} +(-0.390753 - 8.99151i) q^{9} +14.0685 q^{10} +19.6440i q^{11} +(3.60276 - 3.76273i) q^{12} +5.28870 q^{13} -10.6677i q^{14} +(20.2623 + 19.4009i) q^{15} -6.03878 q^{16} -18.6801i q^{17} +(-13.5278 + 0.587888i) q^{18} -28.5841 q^{19} +16.2376i q^{20} +(14.7111 - 15.3643i) q^{21} +29.5544 q^{22} -22.2573i q^{23} +(-18.7014 - 17.9063i) q^{24} -62.4396 q^{25} -7.95686i q^{26} +(-20.2943 - 17.8085i) q^{27} +12.3125 q^{28} -17.6355i q^{29} +(29.1887 - 30.4847i) q^{30} -8.65134 q^{31} -25.4368i q^{32} +(42.5662 + 40.7565i) q^{33} -28.1042 q^{34} +66.3029i q^{35} +(-0.678531 - 15.6135i) q^{36} -2.64085 q^{37} +43.0049i q^{38} +(10.9728 - 11.4600i) q^{39} +80.7034 q^{40} +43.6618i q^{41} +(-23.1157 - 22.1329i) q^{42} +14.7841 q^{43} +34.1112i q^{44} +(84.0789 - 3.65389i) q^{45} -33.4861 q^{46} -43.3598i q^{47} +(-12.5290 + 13.0853i) q^{48} +1.27559 q^{49} +93.9405i q^{50} +(-40.4775 - 38.7567i) q^{51} +9.18367 q^{52} +30.3805i q^{53} +(-26.7929 + 30.5328i) q^{54} -183.689 q^{55} -61.1951i q^{56} +(-59.3051 + 61.9384i) q^{57} -26.5327 q^{58} -7.68115i q^{59} +(35.1849 + 33.6891i) q^{60} +67.1584 q^{61} +13.0160i q^{62} +(-2.77064 - 63.7546i) q^{63} -62.4248 q^{64} +49.4541i q^{65} +(61.3183 - 64.0409i) q^{66} +33.3864 q^{67} -32.4374i q^{68} +(-48.2289 - 46.1785i) q^{69} +99.7529 q^{70} +61.7198i q^{71} +(-77.6016 + 3.37240i) q^{72} +41.7753 q^{73} +3.97316i q^{74} +(-129.547 + 135.299i) q^{75} -49.6355 q^{76} +139.286i q^{77} +(-17.2416 - 16.5086i) q^{78} -16.0603 q^{79} -56.4681i q^{80} +(-80.6946 + 7.02691i) q^{81} +65.6893 q^{82} -50.6679i q^{83} +(25.5455 - 26.6797i) q^{84} +174.676 q^{85} -22.2427i q^{86} +(-38.2141 - 36.5894i) q^{87} +169.538 q^{88} +119.246i q^{89} +(-5.49729 - 126.497i) q^{90} +37.4996 q^{91} -38.6491i q^{92} +(-17.9494 + 18.7464i) q^{93} -65.2349 q^{94} -267.287i q^{95} +(-55.1185 - 52.7752i) q^{96} +58.4958 q^{97} -1.91912i q^{98} +(176.629 - 7.67594i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50450i 0.752251i −0.926569 0.376126i \(-0.877256\pi\)
0.926569 0.376126i \(-0.122744\pi\)
\(3\) 2.07476 2.16688i 0.691586 0.722294i
\(4\) 1.73647 0.434118
\(5\) 9.35091i 1.87018i 0.354407 + 0.935091i \(0.384683\pi\)
−0.354407 + 0.935091i \(0.615317\pi\)
\(6\) −3.26008 3.12148i −0.543347 0.520247i
\(7\) 7.09053 1.01293 0.506466 0.862260i \(-0.330951\pi\)
0.506466 + 0.862260i \(0.330951\pi\)
\(8\) 8.63054i 1.07882i
\(9\) −0.390753 8.99151i −0.0434170 0.999057i
\(10\) 14.0685 1.40685
\(11\) 19.6440i 1.78582i 0.450239 + 0.892908i \(0.351339\pi\)
−0.450239 + 0.892908i \(0.648661\pi\)
\(12\) 3.60276 3.76273i 0.300230 0.313561i
\(13\) 5.28870 0.406823 0.203411 0.979093i \(-0.434797\pi\)
0.203411 + 0.979093i \(0.434797\pi\)
\(14\) 10.6677i 0.761980i
\(15\) 20.2623 + 19.4009i 1.35082 + 1.29339i
\(16\) −6.03878 −0.377424
\(17\) 18.6801i 1.09883i −0.835550 0.549414i \(-0.814851\pi\)
0.835550 0.549414i \(-0.185149\pi\)
\(18\) −13.5278 + 0.587888i −0.751542 + 0.0326605i
\(19\) −28.5841 −1.50443 −0.752213 0.658920i \(-0.771014\pi\)
−0.752213 + 0.658920i \(0.771014\pi\)
\(20\) 16.2376i 0.811880i
\(21\) 14.7111 15.3643i 0.700530 0.731635i
\(22\) 29.5544 1.34338
\(23\) 22.2573i 0.967708i −0.875149 0.483854i \(-0.839237\pi\)
0.875149 0.483854i \(-0.160763\pi\)
\(24\) −18.7014 17.9063i −0.779223 0.746095i
\(25\) −62.4396 −2.49758
\(26\) 7.95686i 0.306033i
\(27\) −20.2943 17.8085i −0.751639 0.659574i
\(28\) 12.3125 0.439732
\(29\) 17.6355i 0.608121i −0.952653 0.304061i \(-0.901657\pi\)
0.952653 0.304061i \(-0.0983426\pi\)
\(30\) 29.1887 30.4847i 0.972956 1.01616i
\(31\) −8.65134 −0.279075 −0.139538 0.990217i \(-0.544562\pi\)
−0.139538 + 0.990217i \(0.544562\pi\)
\(32\) 25.4368i 0.794900i
\(33\) 42.5662 + 40.7565i 1.28988 + 1.23505i
\(34\) −28.1042 −0.826595
\(35\) 66.3029i 1.89437i
\(36\) −0.678531 15.6135i −0.0188481 0.433708i
\(37\) −2.64085 −0.0713742 −0.0356871 0.999363i \(-0.511362\pi\)
−0.0356871 + 0.999363i \(0.511362\pi\)
\(38\) 43.0049i 1.13171i
\(39\) 10.9728 11.4600i 0.281353 0.293846i
\(40\) 80.7034 2.01758
\(41\) 43.6618i 1.06492i 0.846454 + 0.532461i \(0.178733\pi\)
−0.846454 + 0.532461i \(0.821267\pi\)
\(42\) −23.1157 22.1329i −0.550373 0.526975i
\(43\) 14.7841 0.343817 0.171908 0.985113i \(-0.445007\pi\)
0.171908 + 0.985113i \(0.445007\pi\)
\(44\) 34.1112i 0.775255i
\(45\) 84.0789 3.65389i 1.86842 0.0811976i
\(46\) −33.4861 −0.727959
\(47\) 43.3598i 0.922549i −0.887258 0.461274i \(-0.847392\pi\)
0.887258 0.461274i \(-0.152608\pi\)
\(48\) −12.5290 + 13.0853i −0.261021 + 0.272611i
\(49\) 1.27559 0.0260324
\(50\) 93.9405i 1.87881i
\(51\) −40.4775 38.7567i −0.793677 0.759935i
\(52\) 9.18367 0.176609
\(53\) 30.3805i 0.573217i 0.958048 + 0.286608i \(0.0925279\pi\)
−0.958048 + 0.286608i \(0.907472\pi\)
\(54\) −26.7929 + 30.5328i −0.496166 + 0.565422i
\(55\) −183.689 −3.33980
\(56\) 61.1951i 1.09277i
\(57\) −59.3051 + 61.9384i −1.04044 + 1.08664i
\(58\) −26.5327 −0.457460
\(59\) 7.68115i 0.130189i
\(60\) 35.1849 + 33.6891i 0.586416 + 0.561485i
\(61\) 67.1584 1.10096 0.550479 0.834849i \(-0.314445\pi\)
0.550479 + 0.834849i \(0.314445\pi\)
\(62\) 13.0160i 0.209935i
\(63\) −2.77064 63.7546i −0.0439784 1.01198i
\(64\) −62.4248 −0.975388
\(65\) 49.4541i 0.760833i
\(66\) 61.3183 64.0409i 0.929065 0.970317i
\(67\) 33.3864 0.498304 0.249152 0.968464i \(-0.419848\pi\)
0.249152 + 0.968464i \(0.419848\pi\)
\(68\) 32.4374i 0.477021i
\(69\) −48.2289 46.1785i −0.698969 0.669253i
\(70\) 99.7529 1.42504
\(71\) 61.7198i 0.869293i 0.900601 + 0.434647i \(0.143127\pi\)
−0.900601 + 0.434647i \(0.856873\pi\)
\(72\) −77.6016 + 3.37240i −1.07780 + 0.0468390i
\(73\) 41.7753 0.572264 0.286132 0.958190i \(-0.407630\pi\)
0.286132 + 0.958190i \(0.407630\pi\)
\(74\) 3.97316i 0.0536914i
\(75\) −129.547 + 135.299i −1.72729 + 1.80399i
\(76\) −49.6355 −0.653098
\(77\) 139.286i 1.80891i
\(78\) −17.2416 16.5086i −0.221046 0.211648i
\(79\) −16.0603 −0.203294 −0.101647 0.994821i \(-0.532411\pi\)
−0.101647 + 0.994821i \(0.532411\pi\)
\(80\) 56.4681i 0.705852i
\(81\) −80.6946 + 7.02691i −0.996230 + 0.0867520i
\(82\) 65.6893 0.801089
\(83\) 50.6679i 0.610456i −0.952279 0.305228i \(-0.901267\pi\)
0.952279 0.305228i \(-0.0987327\pi\)
\(84\) 25.5455 26.6797i 0.304113 0.317616i
\(85\) 174.676 2.05501
\(86\) 22.2427i 0.258637i
\(87\) −38.2141 36.5894i −0.439242 0.420568i
\(88\) 169.538 1.92657
\(89\) 119.246i 1.33984i 0.742434 + 0.669919i \(0.233671\pi\)
−0.742434 + 0.669919i \(0.766329\pi\)
\(90\) −5.49729 126.497i −0.0610810 1.40552i
\(91\) 37.4996 0.412084
\(92\) 38.6491i 0.420099i
\(93\) −17.9494 + 18.7464i −0.193005 + 0.201574i
\(94\) −65.2349 −0.693989
\(95\) 267.287i 2.81355i
\(96\) −55.1185 52.7752i −0.574151 0.549742i
\(97\) 58.4958 0.603050 0.301525 0.953458i \(-0.402504\pi\)
0.301525 + 0.953458i \(0.402504\pi\)
\(98\) 1.91912i 0.0195829i
\(99\) 176.629 7.67594i 1.78413 0.0775347i
\(100\) −108.425 −1.08425
\(101\) 65.7293i 0.650785i 0.945579 + 0.325393i \(0.105496\pi\)
−0.945579 + 0.325393i \(0.894504\pi\)
\(102\) −58.3095 + 60.8986i −0.571662 + 0.597045i
\(103\) −107.070 −1.03951 −0.519756 0.854315i \(-0.673977\pi\)
−0.519756 + 0.854315i \(0.673977\pi\)
\(104\) 45.6443i 0.438887i
\(105\) 143.671 + 137.563i 1.36829 + 1.31012i
\(106\) 45.7075 0.431203
\(107\) 24.7229i 0.231055i 0.993304 + 0.115528i \(0.0368559\pi\)
−0.993304 + 0.115528i \(0.963144\pi\)
\(108\) −35.2404 30.9240i −0.326300 0.286333i
\(109\) −54.3272 −0.498414 −0.249207 0.968450i \(-0.580170\pi\)
−0.249207 + 0.968450i \(0.580170\pi\)
\(110\) 276.361i 2.51237i
\(111\) −5.47912 + 5.72240i −0.0493614 + 0.0515532i
\(112\) −42.8182 −0.382305
\(113\) 89.2190i 0.789549i −0.918778 0.394774i \(-0.870823\pi\)
0.918778 0.394774i \(-0.129177\pi\)
\(114\) 93.1864 + 89.2247i 0.817425 + 0.782673i
\(115\) 208.126 1.80979
\(116\) 30.6236i 0.263996i
\(117\) −2.06657 47.5534i −0.0176630 0.406439i
\(118\) −11.5563 −0.0979348
\(119\) 132.452i 1.11304i
\(120\) 167.440 174.875i 1.39533 1.45729i
\(121\) −264.886 −2.18914
\(122\) 101.040i 0.828197i
\(123\) 94.6100 + 90.5877i 0.769187 + 0.736486i
\(124\) −15.0228 −0.121152
\(125\) 350.094i 2.80075i
\(126\) −95.9189 + 4.16844i −0.761261 + 0.0330828i
\(127\) −185.143 −1.45782 −0.728908 0.684612i \(-0.759972\pi\)
−0.728908 + 0.684612i \(0.759972\pi\)
\(128\) 7.82879i 0.0611624i
\(129\) 30.6735 32.0354i 0.237779 0.248337i
\(130\) 74.4039 0.572338
\(131\) 23.1778i 0.176929i 0.996079 + 0.0884647i \(0.0281960\pi\)
−0.996079 + 0.0884647i \(0.971804\pi\)
\(132\) 73.9150 + 70.7725i 0.559962 + 0.536156i
\(133\) −202.676 −1.52388
\(134\) 50.2299i 0.374850i
\(135\) 166.526 189.770i 1.23352 1.40570i
\(136\) −161.219 −1.18543
\(137\) 152.484i 1.11302i −0.830840 0.556512i \(-0.812139\pi\)
0.830840 0.556512i \(-0.187861\pi\)
\(138\) −69.4756 + 72.5605i −0.503447 + 0.525801i
\(139\) 147.205 1.05903 0.529513 0.848302i \(-0.322375\pi\)
0.529513 + 0.848302i \(0.322375\pi\)
\(140\) 115.133i 0.822379i
\(141\) −93.9555 89.9611i −0.666351 0.638022i
\(142\) 92.8576 0.653927
\(143\) 103.891i 0.726511i
\(144\) 2.35967 + 54.2978i 0.0163866 + 0.377068i
\(145\) 164.908 1.13730
\(146\) 62.8510i 0.430486i
\(147\) 2.64653 2.76405i 0.0180036 0.0188030i
\(148\) −4.58576 −0.0309848
\(149\) 32.7895i 0.220064i 0.993928 + 0.110032i \(0.0350953\pi\)
−0.993928 + 0.110032i \(0.964905\pi\)
\(150\) 203.558 + 194.904i 1.35705 + 1.29936i
\(151\) 122.450 0.810928 0.405464 0.914111i \(-0.367110\pi\)
0.405464 + 0.914111i \(0.367110\pi\)
\(152\) 246.696i 1.62300i
\(153\) −167.962 + 7.29929i −1.09779 + 0.0477078i
\(154\) 209.556 1.36076
\(155\) 80.8979i 0.521922i
\(156\) 19.0539 19.8999i 0.122140 0.127564i
\(157\) 154.489 0.984006 0.492003 0.870594i \(-0.336265\pi\)
0.492003 + 0.870594i \(0.336265\pi\)
\(158\) 24.1627i 0.152928i
\(159\) 65.8309 + 63.0322i 0.414031 + 0.396429i
\(160\) 237.857 1.48661
\(161\) 157.816i 0.980223i
\(162\) 10.5720 + 121.405i 0.0652593 + 0.749415i
\(163\) −90.2530 −0.553700 −0.276850 0.960913i \(-0.589290\pi\)
−0.276850 + 0.960913i \(0.589290\pi\)
\(164\) 75.8175i 0.462302i
\(165\) −381.111 + 398.033i −2.30976 + 2.41232i
\(166\) −76.2300 −0.459217
\(167\) 256.147i 1.53381i 0.641758 + 0.766907i \(0.278205\pi\)
−0.641758 + 0.766907i \(0.721795\pi\)
\(168\) −132.602 126.965i −0.789300 0.755744i
\(169\) −141.030 −0.834495
\(170\) 262.800i 1.54588i
\(171\) 11.1693 + 257.014i 0.0653176 + 1.50301i
\(172\) 25.6722 0.149257
\(173\) 231.773i 1.33973i 0.742484 + 0.669864i \(0.233647\pi\)
−0.742484 + 0.669864i \(0.766353\pi\)
\(174\) −55.0489 + 57.4932i −0.316373 + 0.330421i
\(175\) −442.729 −2.52988
\(176\) 118.626i 0.674010i
\(177\) −16.6441 15.9365i −0.0940347 0.0900369i
\(178\) 179.405 1.00790
\(179\) 269.568i 1.50597i −0.658039 0.752984i \(-0.728614\pi\)
0.658039 0.752984i \(-0.271386\pi\)
\(180\) 146.001 6.34488i 0.811114 0.0352493i
\(181\) −36.1729 −0.199850 −0.0999251 0.994995i \(-0.531860\pi\)
−0.0999251 + 0.994995i \(0.531860\pi\)
\(182\) 56.4183i 0.309991i
\(183\) 139.338 145.524i 0.761407 0.795215i
\(184\) −192.092 −1.04398
\(185\) 24.6943i 0.133483i
\(186\) 28.2041 + 27.0050i 0.151635 + 0.145188i
\(187\) 366.951 1.96231
\(188\) 75.2930i 0.400495i
\(189\) −143.897 126.272i −0.761360 0.668104i
\(190\) −402.135 −2.11650
\(191\) 29.5445i 0.154683i 0.997005 + 0.0773417i \(0.0246432\pi\)
−0.997005 + 0.0773417i \(0.975357\pi\)
\(192\) −129.516 + 135.267i −0.674565 + 0.704517i
\(193\) 142.657 0.739156 0.369578 0.929200i \(-0.379502\pi\)
0.369578 + 0.929200i \(0.379502\pi\)
\(194\) 88.0072i 0.453645i
\(195\) 107.161 + 102.605i 0.549545 + 0.526182i
\(196\) 2.21502 0.0113011
\(197\) 8.10839i 0.0411593i 0.999788 + 0.0205797i \(0.00655118\pi\)
−0.999788 + 0.0205797i \(0.993449\pi\)
\(198\) −11.5485 265.739i −0.0583256 1.34212i
\(199\) 192.191 0.965786 0.482893 0.875679i \(-0.339586\pi\)
0.482893 + 0.875679i \(0.339586\pi\)
\(200\) 538.887i 2.69443i
\(201\) 69.2687 72.3443i 0.344620 0.359922i
\(202\) 98.8899 0.489554
\(203\) 125.045i 0.615986i
\(204\) −70.2881 67.2998i −0.344549 0.329901i
\(205\) −408.278 −1.99160
\(206\) 161.087i 0.781975i
\(207\) −200.127 + 8.69709i −0.966795 + 0.0420149i
\(208\) −31.9373 −0.153545
\(209\) 561.506i 2.68663i
\(210\) 206.963 216.153i 0.985539 1.02930i
\(211\) 124.794 0.591439 0.295720 0.955275i \(-0.404441\pi\)
0.295720 + 0.955275i \(0.404441\pi\)
\(212\) 52.7548i 0.248844i
\(213\) 133.740 + 128.054i 0.627885 + 0.601191i
\(214\) 37.1957 0.173812
\(215\) 138.245i 0.643000i
\(216\) −153.697 + 175.150i −0.711560 + 0.810881i
\(217\) −61.3426 −0.282685
\(218\) 81.7354i 0.374933i
\(219\) 86.6736 90.5220i 0.395770 0.413343i
\(220\) −318.971 −1.44987
\(221\) 98.7933i 0.447028i
\(222\) 8.60937 + 8.24335i 0.0387810 + 0.0371322i
\(223\) −265.562 −1.19086 −0.595430 0.803407i \(-0.703018\pi\)
−0.595430 + 0.803407i \(0.703018\pi\)
\(224\) 180.360i 0.805180i
\(225\) 24.3984 + 561.426i 0.108437 + 2.49523i
\(226\) −134.230 −0.593939
\(227\) 22.3352i 0.0983931i 0.998789 + 0.0491966i \(0.0156661\pi\)
−0.998789 + 0.0491966i \(0.984334\pi\)
\(228\) −102.982 + 107.554i −0.451674 + 0.471729i
\(229\) 189.051 0.825551 0.412775 0.910833i \(-0.364559\pi\)
0.412775 + 0.910833i \(0.364559\pi\)
\(230\) 313.126i 1.36142i
\(231\) 301.817 + 288.985i 1.30657 + 1.25102i
\(232\) −152.204 −0.656052
\(233\) 222.374i 0.954396i 0.878796 + 0.477198i \(0.158348\pi\)
−0.878796 + 0.477198i \(0.841652\pi\)
\(234\) −71.5442 + 3.10916i −0.305744 + 0.0132870i
\(235\) 405.454 1.72533
\(236\) 13.3381i 0.0565173i
\(237\) −33.3212 + 34.8007i −0.140596 + 0.146838i
\(238\) −199.274 −0.837285
\(239\) 195.861i 0.819501i −0.912198 0.409751i \(-0.865616\pi\)
0.912198 0.409751i \(-0.134384\pi\)
\(240\) −122.360 117.158i −0.509832 0.488157i
\(241\) 26.5673 0.110238 0.0551189 0.998480i \(-0.482446\pi\)
0.0551189 + 0.998480i \(0.482446\pi\)
\(242\) 398.522i 1.64678i
\(243\) −152.195 + 189.435i −0.626318 + 0.779567i
\(244\) 116.619 0.477945
\(245\) 11.9279i 0.0486853i
\(246\) 136.290 142.341i 0.554022 0.578622i
\(247\) −151.173 −0.612035
\(248\) 74.6657i 0.301071i
\(249\) −109.791 105.124i −0.440929 0.422183i
\(250\) −526.717 −2.10687
\(251\) 358.916i 1.42994i 0.699154 + 0.714971i \(0.253560\pi\)
−0.699154 + 0.714971i \(0.746440\pi\)
\(252\) −4.81114 110.708i −0.0190918 0.439317i
\(253\) 437.221 1.72815
\(254\) 278.548i 1.09664i
\(255\) 362.410 378.502i 1.42122 1.48432i
\(256\) −261.478 −1.02140
\(257\) 18.4478i 0.0717814i 0.999356 + 0.0358907i \(0.0114268\pi\)
−0.999356 + 0.0358907i \(0.988573\pi\)
\(258\) −48.1974 46.1483i −0.186812 0.178870i
\(259\) −18.7250 −0.0722973
\(260\) 85.8757i 0.330291i
\(261\) −158.570 + 6.89112i −0.607548 + 0.0264028i
\(262\) 34.8710 0.133095
\(263\) 170.772i 0.649322i −0.945831 0.324661i \(-0.894750\pi\)
0.945831 0.324661i \(-0.105250\pi\)
\(264\) 351.751 367.369i 1.33239 1.39155i
\(265\) −284.085 −1.07202
\(266\) 304.927i 1.14634i
\(267\) 258.391 + 247.406i 0.967757 + 0.926614i
\(268\) 57.9745 0.216323
\(269\) 113.815i 0.423105i −0.977367 0.211552i \(-0.932148\pi\)
0.977367 0.211552i \(-0.0678519\pi\)
\(270\) −285.509 250.539i −1.05744 0.927920i
\(271\) 285.172 1.05230 0.526148 0.850393i \(-0.323636\pi\)
0.526148 + 0.850393i \(0.323636\pi\)
\(272\) 112.805i 0.414724i
\(273\) 77.8027 81.2573i 0.284992 0.297646i
\(274\) −229.413 −0.837274
\(275\) 1226.56i 4.46022i
\(276\) −83.7481 80.1876i −0.303435 0.290535i
\(277\) 14.4234 0.0520702 0.0260351 0.999661i \(-0.491712\pi\)
0.0260351 + 0.999661i \(0.491712\pi\)
\(278\) 221.470i 0.796654i
\(279\) 3.38053 + 77.7886i 0.0121166 + 0.278812i
\(280\) 572.230 2.04368
\(281\) 378.218i 1.34597i 0.739655 + 0.672987i \(0.234989\pi\)
−0.739655 + 0.672987i \(0.765011\pi\)
\(282\) −135.347 + 141.356i −0.479953 + 0.501264i
\(283\) 190.998 0.674903 0.337452 0.941343i \(-0.390435\pi\)
0.337452 + 0.941343i \(0.390435\pi\)
\(284\) 107.175i 0.377376i
\(285\) −579.180 554.557i −2.03221 1.94581i
\(286\) 156.304 0.546519
\(287\) 309.585i 1.07869i
\(288\) −228.715 + 9.93949i −0.794150 + 0.0345121i
\(289\) −59.9455 −0.207424
\(290\) 248.105i 0.855534i
\(291\) 121.365 126.754i 0.417061 0.435579i
\(292\) 72.5415 0.248430
\(293\) 450.672i 1.53813i 0.639171 + 0.769065i \(0.279278\pi\)
−0.639171 + 0.769065i \(0.720722\pi\)
\(294\) −4.15851 3.98172i −0.0141446 0.0135433i
\(295\) 71.8257 0.243477
\(296\) 22.7919i 0.0769998i
\(297\) 349.830 398.660i 1.17788 1.34229i
\(298\) 49.3320 0.165543
\(299\) 117.712i 0.393686i
\(300\) −224.955 + 234.943i −0.749849 + 0.783144i
\(301\) 104.827 0.348263
\(302\) 184.227i 0.610022i
\(303\) 142.428 + 136.372i 0.470058 + 0.450074i
\(304\) 172.613 0.567806
\(305\) 627.993i 2.05899i
\(306\) 10.9818 + 252.700i 0.0358882 + 0.825816i
\(307\) −165.062 −0.537662 −0.268831 0.963187i \(-0.586637\pi\)
−0.268831 + 0.963187i \(0.586637\pi\)
\(308\) 241.866i 0.785281i
\(309\) −222.144 + 232.007i −0.718912 + 0.750833i
\(310\) −121.711 −0.392617
\(311\) 591.518i 1.90199i −0.309212 0.950993i \(-0.600065\pi\)
0.309212 0.950993i \(-0.399935\pi\)
\(312\) −98.9058 94.7009i −0.317006 0.303528i
\(313\) 350.121 1.11860 0.559298 0.828966i \(-0.311071\pi\)
0.559298 + 0.828966i \(0.311071\pi\)
\(314\) 232.429i 0.740220i
\(315\) 596.163 25.9080i 1.89258 0.0822477i
\(316\) −27.8882 −0.0882537
\(317\) 2.33568i 0.00736808i −0.999993 0.00368404i \(-0.998827\pi\)
0.999993 0.00368404i \(-0.00117267\pi\)
\(318\) 94.8321 99.0428i 0.298214 0.311455i
\(319\) 346.432 1.08599
\(320\) 583.729i 1.82415i
\(321\) 53.5717 + 51.2941i 0.166890 + 0.159795i
\(322\) −237.434 −0.737374
\(323\) 533.953i 1.65311i
\(324\) −140.124 + 12.2020i −0.432481 + 0.0376606i
\(325\) −330.224 −1.01607
\(326\) 135.786i 0.416521i
\(327\) −112.716 + 117.721i −0.344696 + 0.360002i
\(328\) 376.825 1.14886
\(329\) 307.444i 0.934480i
\(330\) 598.841 + 573.382i 1.81467 + 1.73752i
\(331\) −37.9525 −0.114660 −0.0573301 0.998355i \(-0.518259\pi\)
−0.0573301 + 0.998355i \(0.518259\pi\)
\(332\) 87.9833i 0.265010i
\(333\) 1.03192 + 23.7452i 0.00309885 + 0.0713069i
\(334\) 385.374 1.15381
\(335\) 312.193i 0.931919i
\(336\) −88.8373 + 92.7819i −0.264397 + 0.276137i
\(337\) 340.605 1.01070 0.505349 0.862915i \(-0.331364\pi\)
0.505349 + 0.862915i \(0.331364\pi\)
\(338\) 212.180i 0.627750i
\(339\) −193.327 185.108i −0.570286 0.546041i
\(340\) 303.320 0.892116
\(341\) 169.947i 0.498377i
\(342\) 386.679 16.8043i 1.13064 0.0491353i
\(343\) −338.391 −0.986564
\(344\) 127.595i 0.370915i
\(345\) 431.811 450.984i 1.25163 1.30720i
\(346\) 348.703 1.00781
\(347\) 647.225i 1.86520i −0.360911 0.932600i \(-0.617534\pi\)
0.360911 0.932600i \(-0.382466\pi\)
\(348\) −66.3577 63.5365i −0.190683 0.182576i
\(349\) 384.765 1.10248 0.551239 0.834348i \(-0.314155\pi\)
0.551239 + 0.834348i \(0.314155\pi\)
\(350\) 666.088i 1.90311i
\(351\) −107.330 94.1838i −0.305784 0.268330i
\(352\) 499.680 1.41954
\(353\) 537.674i 1.52316i 0.648074 + 0.761578i \(0.275575\pi\)
−0.648074 + 0.761578i \(0.724425\pi\)
\(354\) −23.9765 + 25.0411i −0.0677304 + 0.0707377i
\(355\) −577.137 −1.62574
\(356\) 207.067i 0.581648i
\(357\) −287.007 274.805i −0.803941 0.769763i
\(358\) −405.566 −1.13287
\(359\) 61.1053i 0.170210i −0.996372 0.0851048i \(-0.972877\pi\)
0.996372 0.0851048i \(-0.0271225\pi\)
\(360\) −31.5351 725.646i −0.0875974 2.01568i
\(361\) 456.051 1.26330
\(362\) 54.4222i 0.150338i
\(363\) −549.575 + 573.977i −1.51398 + 1.58120i
\(364\) 65.1171 0.178893
\(365\) 390.637i 1.07024i
\(366\) −218.942 209.634i −0.598202 0.572770i
\(367\) 444.355 1.21078 0.605388 0.795931i \(-0.293018\pi\)
0.605388 + 0.795931i \(0.293018\pi\)
\(368\) 134.407i 0.365236i
\(369\) 392.586 17.0610i 1.06392 0.0462357i
\(370\) −37.1527 −0.100413
\(371\) 215.414i 0.580630i
\(372\) −31.1687 + 32.5526i −0.0837868 + 0.0875071i
\(373\) −8.79441 −0.0235775 −0.0117888 0.999931i \(-0.503753\pi\)
−0.0117888 + 0.999931i \(0.503753\pi\)
\(374\) 552.079i 1.47615i
\(375\) −758.612 726.361i −2.02297 1.93696i
\(376\) −374.218 −0.995261
\(377\) 93.2689i 0.247398i
\(378\) −189.976 + 216.493i −0.502582 + 0.572734i
\(379\) −133.349 −0.351844 −0.175922 0.984404i \(-0.556291\pi\)
−0.175922 + 0.984404i \(0.556291\pi\)
\(380\) 464.137i 1.22141i
\(381\) −384.126 + 401.182i −1.00821 + 1.05297i
\(382\) 44.4498 0.116361
\(383\) 612.768i 1.59992i −0.600056 0.799958i \(-0.704855\pi\)
0.600056 0.799958i \(-0.295145\pi\)
\(384\) −16.9641 16.2428i −0.0441772 0.0422991i
\(385\) −1302.45 −3.38299
\(386\) 214.628i 0.556031i
\(387\) −5.77693 132.932i −0.0149275 0.343493i
\(388\) 101.576 0.261795
\(389\) 225.199i 0.578918i −0.957190 0.289459i \(-0.906525\pi\)
0.957190 0.289459i \(-0.0934754\pi\)
\(390\) 154.370 161.224i 0.395821 0.413396i
\(391\) −415.768 −1.06334
\(392\) 11.0090i 0.0280842i
\(393\) 50.2234 + 48.0882i 0.127795 + 0.122362i
\(394\) 12.1991 0.0309622
\(395\) 150.178i 0.380198i
\(396\) 306.711 13.3290i 0.774524 0.0336592i
\(397\) −455.986 −1.14858 −0.574289 0.818652i \(-0.694722\pi\)
−0.574289 + 0.818652i \(0.694722\pi\)
\(398\) 289.153i 0.726514i
\(399\) −420.505 + 439.176i −1.05390 + 1.10069i
\(400\) 377.059 0.942647
\(401\) 398.057i 0.992661i 0.868134 + 0.496331i \(0.165320\pi\)
−0.868134 + 0.496331i \(0.834680\pi\)
\(402\) −108.842 104.215i −0.270752 0.259241i
\(403\) −45.7543 −0.113534
\(404\) 114.137i 0.282518i
\(405\) −65.7081 754.568i −0.162242 1.86313i
\(406\) −188.131 −0.463376
\(407\) 51.8767i 0.127461i
\(408\) −334.491 + 349.343i −0.819831 + 0.856232i
\(409\) 786.441 1.92284 0.961419 0.275089i \(-0.0887073\pi\)
0.961419 + 0.275089i \(0.0887073\pi\)
\(410\) 614.255i 1.49818i
\(411\) −330.415 316.368i −0.803930 0.769752i
\(412\) −185.924 −0.451271
\(413\) 54.4634i 0.131873i
\(414\) 13.0848 + 301.091i 0.0316058 + 0.727273i
\(415\) 473.791 1.14166
\(416\) 134.527i 0.323383i
\(417\) 305.414 318.975i 0.732408 0.764929i
\(418\) −844.787 −2.02102
\(419\) 152.439i 0.363817i 0.983315 + 0.181908i \(0.0582275\pi\)
−0.983315 + 0.181908i \(0.941773\pi\)
\(420\) 249.480 + 238.873i 0.594000 + 0.568746i
\(421\) −442.750 −1.05166 −0.525832 0.850589i \(-0.676246\pi\)
−0.525832 + 0.850589i \(0.676246\pi\)
\(422\) 187.753i 0.444911i
\(423\) −389.870 + 16.9429i −0.921679 + 0.0400543i
\(424\) 262.200 0.618396
\(425\) 1166.38i 2.74441i
\(426\) 192.657 201.212i 0.452247 0.472327i
\(427\) 476.189 1.11520
\(428\) 42.9307i 0.100305i
\(429\) 225.120 + 215.549i 0.524754 + 0.502445i
\(430\) 207.990 0.483698
\(431\) 38.8281i 0.0900885i 0.998985 + 0.0450442i \(0.0143429\pi\)
−0.998985 + 0.0450442i \(0.985657\pi\)
\(432\) 122.553 + 107.542i 0.283687 + 0.248939i
\(433\) −491.902 −1.13603 −0.568016 0.823018i \(-0.692289\pi\)
−0.568016 + 0.823018i \(0.692289\pi\)
\(434\) 92.2900i 0.212650i
\(435\) 342.145 357.337i 0.786540 0.821463i
\(436\) −94.3375 −0.216371
\(437\) 636.204i 1.45584i
\(438\) −136.191 130.401i −0.310938 0.297718i
\(439\) 164.965 0.375775 0.187887 0.982191i \(-0.439836\pi\)
0.187887 + 0.982191i \(0.439836\pi\)
\(440\) 1585.34i 3.60304i
\(441\) −0.498439 11.4695i −0.00113025 0.0260078i
\(442\) −148.635 −0.336278
\(443\) 243.990i 0.550768i 0.961334 + 0.275384i \(0.0888050\pi\)
−0.961334 + 0.275384i \(0.911195\pi\)
\(444\) −9.51434 + 9.93679i −0.0214287 + 0.0223802i
\(445\) −1115.06 −2.50574
\(446\) 399.538i 0.895826i
\(447\) 71.0511 + 68.0304i 0.158951 + 0.152193i
\(448\) −442.625 −0.988002
\(449\) 484.609i 1.07931i 0.841887 + 0.539654i \(0.181445\pi\)
−0.841887 + 0.539654i \(0.818555\pi\)
\(450\) 844.667 36.7075i 1.87704 0.0815722i
\(451\) −857.692 −1.90176
\(452\) 154.926i 0.342757i
\(453\) 254.054 265.335i 0.560827 0.585728i
\(454\) 33.6034 0.0740163
\(455\) 350.656i 0.770672i
\(456\) 534.561 + 511.835i 1.17228 + 1.12245i
\(457\) −744.037 −1.62809 −0.814045 0.580802i \(-0.802739\pi\)
−0.814045 + 0.580802i \(0.802739\pi\)
\(458\) 284.428i 0.621022i
\(459\) −332.664 + 379.099i −0.724759 + 0.825923i
\(460\) 361.405 0.785662
\(461\) 185.525i 0.402441i −0.979546 0.201220i \(-0.935509\pi\)
0.979546 0.201220i \(-0.0644907\pi\)
\(462\) 434.779 454.084i 0.941080 0.982866i
\(463\) 141.705 0.306058 0.153029 0.988222i \(-0.451097\pi\)
0.153029 + 0.988222i \(0.451097\pi\)
\(464\) 106.497i 0.229520i
\(465\) −175.296 167.844i −0.376981 0.360954i
\(466\) 334.563 0.717946
\(467\) 205.961i 0.441031i −0.975383 0.220515i \(-0.929226\pi\)
0.975383 0.220515i \(-0.0707739\pi\)
\(468\) −3.58854 82.5751i −0.00766783 0.176442i
\(469\) 236.727 0.504748
\(470\) 610.006i 1.29789i
\(471\) 320.527 334.759i 0.680525 0.710741i
\(472\) −66.2924 −0.140450
\(473\) 290.419i 0.613994i
\(474\) 52.3577 + 50.1318i 0.110459 + 0.105763i
\(475\) 1784.78 3.75743
\(476\) 229.998i 0.483190i
\(477\) 273.167 11.8713i 0.572676 0.0248873i
\(478\) −294.673 −0.616471
\(479\) 285.339i 0.595697i −0.954613 0.297849i \(-0.903731\pi\)
0.954613 0.297849i \(-0.0962691\pi\)
\(480\) 493.496 515.408i 1.02812 1.07377i
\(481\) −13.9666 −0.0290367
\(482\) 39.9706i 0.0829266i
\(483\) −341.968 327.430i −0.708009 0.677908i
\(484\) −459.967 −0.950345
\(485\) 546.990i 1.12781i
\(486\) 285.005 + 228.978i 0.586431 + 0.471149i
\(487\) −507.398 −1.04188 −0.520942 0.853592i \(-0.674419\pi\)
−0.520942 + 0.853592i \(0.674419\pi\)
\(488\) 579.613i 1.18773i
\(489\) −187.253 + 195.568i −0.382931 + 0.399934i
\(490\) 17.9456 0.0366236
\(491\) 158.306i 0.322416i −0.986920 0.161208i \(-0.948461\pi\)
0.986920 0.161208i \(-0.0515390\pi\)
\(492\) 164.288 + 157.303i 0.333918 + 0.319722i
\(493\) −329.433 −0.668221
\(494\) 227.440i 0.460404i
\(495\) 71.7770 + 1651.64i 0.145004 + 3.33665i
\(496\) 52.2435 0.105330
\(497\) 437.626i 0.880535i
\(498\) −158.159 + 165.181i −0.317588 + 0.331689i
\(499\) 703.877 1.41058 0.705288 0.708921i \(-0.250818\pi\)
0.705288 + 0.708921i \(0.250818\pi\)
\(500\) 607.928i 1.21586i
\(501\) 555.040 + 531.443i 1.10786 + 1.06076i
\(502\) 539.989 1.07568
\(503\) 785.933i 1.56249i −0.624224 0.781245i \(-0.714585\pi\)
0.624224 0.781245i \(-0.285415\pi\)
\(504\) −550.236 + 23.9121i −1.09174 + 0.0474447i
\(505\) −614.629 −1.21709
\(506\) 657.801i 1.30000i
\(507\) −292.603 + 305.595i −0.577125 + 0.602751i
\(508\) −321.495 −0.632864
\(509\) 705.767i 1.38658i −0.720661 0.693288i \(-0.756161\pi\)
0.720661 0.693288i \(-0.243839\pi\)
\(510\) −569.457 545.247i −1.11658 1.06911i
\(511\) 296.209 0.579665
\(512\) 362.079i 0.707185i
\(513\) 580.093 + 509.040i 1.13079 + 0.992281i
\(514\) 27.7548 0.0539977
\(515\) 1001.20i 1.94408i
\(516\) 53.2636 55.6286i 0.103224 0.107807i
\(517\) 851.759 1.64750
\(518\) 28.1718i 0.0543857i
\(519\) 502.224 + 480.873i 0.967677 + 0.926537i
\(520\) 426.816 0.820800
\(521\) 8.30979i 0.0159497i −0.999968 0.00797485i \(-0.997462\pi\)
0.999968 0.00797485i \(-0.00253850\pi\)
\(522\) 10.3677 + 238.569i 0.0198615 + 0.457029i
\(523\) 535.808 1.02449 0.512245 0.858840i \(-0.328814\pi\)
0.512245 + 0.858840i \(0.328814\pi\)
\(524\) 40.2475i 0.0768082i
\(525\) −918.557 + 959.342i −1.74963 + 1.82732i
\(526\) −256.926 −0.488453
\(527\) 161.608i 0.306656i
\(528\) −257.048 246.120i −0.486833 0.466136i
\(529\) 33.6137 0.0635420
\(530\) 427.407i 0.806429i
\(531\) −69.0651 + 3.00143i −0.130066 + 0.00565241i
\(532\) −351.942 −0.661545
\(533\) 230.914i 0.433235i
\(534\) 372.223 388.750i 0.697047 0.727997i
\(535\) −231.182 −0.432116
\(536\) 288.142i 0.537579i
\(537\) −584.123 559.289i −1.08775 1.04151i
\(538\) −171.235 −0.318281
\(539\) 25.0576i 0.0464891i
\(540\) 289.167 329.530i 0.535495 0.610241i
\(541\) −957.545 −1.76995 −0.884977 0.465635i \(-0.845826\pi\)
−0.884977 + 0.465635i \(0.845826\pi\)
\(542\) 429.042i 0.791591i
\(543\) −75.0500 + 78.3823i −0.138214 + 0.144351i
\(544\) −475.161 −0.873458
\(545\) 508.008i 0.932126i
\(546\) −122.252 117.054i −0.223904 0.214385i
\(547\) −106.032 −0.193843 −0.0969214 0.995292i \(-0.530900\pi\)
−0.0969214 + 0.995292i \(0.530900\pi\)
\(548\) 264.785i 0.483184i
\(549\) −26.2423 603.856i −0.0478002 1.09992i
\(550\) −1845.37 −3.35521
\(551\) 504.095i 0.914874i
\(552\) −398.545 + 416.241i −0.722002 + 0.754060i
\(553\) −113.876 −0.205924
\(554\) 21.7001i 0.0391699i
\(555\) −53.5097 51.2348i −0.0964139 0.0923149i
\(556\) 255.617 0.459742
\(557\) 2.19030i 0.00393232i 0.999998 + 0.00196616i \(0.000625849\pi\)
−0.999998 + 0.00196616i \(0.999374\pi\)
\(558\) 117.033 5.08602i 0.209737 0.00911473i
\(559\) 78.1887 0.139872
\(560\) 400.389i 0.714980i
\(561\) 761.335 795.140i 1.35710 1.41736i
\(562\) 569.031 1.01251
\(563\) 488.602i 0.867855i −0.900948 0.433927i \(-0.857127\pi\)
0.900948 0.433927i \(-0.142873\pi\)
\(564\) −163.151 156.215i −0.289275 0.276977i
\(565\) 834.279 1.47660
\(566\) 287.356i 0.507697i
\(567\) −572.167 + 49.8245i −1.00911 + 0.0878740i
\(568\) 532.675 0.937808
\(569\) 389.337i 0.684248i 0.939655 + 0.342124i \(0.111146\pi\)
−0.939655 + 0.342124i \(0.888854\pi\)
\(570\) −834.332 + 871.378i −1.46374 + 1.52873i
\(571\) −522.297 −0.914706 −0.457353 0.889285i \(-0.651202\pi\)
−0.457353 + 0.889285i \(0.651202\pi\)
\(572\) 180.404i 0.315391i
\(573\) 64.0195 + 61.2978i 0.111727 + 0.106977i
\(574\) 465.772 0.811450
\(575\) 1389.73i 2.41693i
\(576\) 24.3927 + 561.294i 0.0423484 + 0.974468i
\(577\) 867.206 1.50296 0.751478 0.659758i \(-0.229341\pi\)
0.751478 + 0.659758i \(0.229341\pi\)
\(578\) 90.1882i 0.156035i
\(579\) 295.979 309.121i 0.511190 0.533888i
\(580\) 286.358 0.493721
\(581\) 359.262i 0.618351i
\(582\) −190.701 182.594i −0.327665 0.313735i
\(583\) −596.794 −1.02366
\(584\) 360.543i 0.617368i
\(585\) 444.668 19.3243i 0.760115 0.0330330i
\(586\) 678.037 1.15706
\(587\) 698.172i 1.18939i 0.803951 + 0.594695i \(0.202727\pi\)
−0.803951 + 0.594695i \(0.797273\pi\)
\(588\) 4.59563 4.79969i 0.00781570 0.00816273i
\(589\) 247.291 0.419848
\(590\) 108.062i 0.183156i
\(591\) 17.5699 + 16.8230i 0.0297291 + 0.0284652i
\(592\) 15.9475 0.0269383
\(593\) 227.806i 0.384158i −0.981379 0.192079i \(-0.938477\pi\)
0.981379 0.192079i \(-0.0615230\pi\)
\(594\) −599.785 526.320i −1.00974 0.886061i
\(595\) 1238.54 2.08159
\(596\) 56.9381i 0.0955337i
\(597\) 398.751 416.456i 0.667924 0.697582i
\(598\) −177.098 −0.296150
\(599\) 304.030i 0.507562i 0.967262 + 0.253781i \(0.0816742\pi\)
−0.967262 + 0.253781i \(0.918326\pi\)
\(600\) 1167.70 + 1118.06i 1.94617 + 1.86343i
\(601\) −939.805 −1.56374 −0.781868 0.623445i \(-0.785733\pi\)
−0.781868 + 0.623445i \(0.785733\pi\)
\(602\) 157.713i 0.261981i
\(603\) −13.0458 300.194i −0.0216348 0.497834i
\(604\) 212.631 0.352038
\(605\) 2476.93i 4.09409i
\(606\) 205.173 214.283i 0.338569 0.353602i
\(607\) −918.465 −1.51312 −0.756561 0.653923i \(-0.773122\pi\)
−0.756561 + 0.653923i \(0.773122\pi\)
\(608\) 727.088i 1.19587i
\(609\) −270.958 259.438i −0.444923 0.426007i
\(610\) 944.817 1.54888
\(611\) 229.317i 0.375314i
\(612\) −291.662 + 12.6750i −0.476571 + 0.0207108i
\(613\) −328.504 −0.535895 −0.267947 0.963434i \(-0.586345\pi\)
−0.267947 + 0.963434i \(0.586345\pi\)
\(614\) 248.337i 0.404457i
\(615\) −847.078 + 884.690i −1.37736 + 1.43852i
\(616\) 1202.11 1.95148
\(617\) 968.760i 1.57011i −0.619424 0.785057i \(-0.712634\pi\)
0.619424 0.785057i \(-0.287366\pi\)
\(618\) 349.056 + 334.216i 0.564815 + 0.540803i
\(619\) 812.768 1.31303 0.656517 0.754311i \(-0.272029\pi\)
0.656517 + 0.754311i \(0.272029\pi\)
\(620\) 140.477i 0.226576i
\(621\) −396.369 + 451.695i −0.638275 + 0.727367i
\(622\) −889.940 −1.43077
\(623\) 845.514i 1.35717i
\(624\) −66.2622 + 69.2043i −0.106189 + 0.110904i
\(625\) 1712.71 2.74034
\(626\) 526.758i 0.841466i
\(627\) −1216.72 1164.99i −1.94054 1.85804i
\(628\) 268.265 0.427174
\(629\) 49.3312i 0.0784281i
\(630\) −38.9787 896.930i −0.0618710 1.42370i
\(631\) −22.1005 −0.0350246 −0.0175123 0.999847i \(-0.505575\pi\)
−0.0175123 + 0.999847i \(0.505575\pi\)
\(632\) 138.609i 0.219317i
\(633\) 258.917 270.413i 0.409031 0.427193i
\(634\) −3.51404 −0.00554265
\(635\) 1731.25i 2.72638i
\(636\) 114.314 + 109.454i 0.179738 + 0.172097i
\(637\) 6.74619 0.0105906
\(638\) 521.208i 0.816940i
\(639\) 554.955 24.1172i 0.868473 0.0377421i
\(640\) 73.2063 0.114385
\(641\) 482.527i 0.752772i −0.926463 0.376386i \(-0.877167\pi\)
0.926463 0.376386i \(-0.122833\pi\)
\(642\) 77.1722 80.5987i 0.120206 0.125543i
\(643\) −1172.14 −1.82292 −0.911462 0.411384i \(-0.865045\pi\)
−0.911462 + 0.411384i \(0.865045\pi\)
\(644\) 274.043i 0.425532i
\(645\) 299.561 + 286.825i 0.464435 + 0.444690i
\(646\) 803.334 1.24355
\(647\) 212.268i 0.328080i 0.986454 + 0.164040i \(0.0524526\pi\)
−0.986454 + 0.164040i \(0.947547\pi\)
\(648\) 60.6460 + 696.438i 0.0935896 + 1.07475i
\(649\) 150.888 0.232493
\(650\) 496.823i 0.764343i
\(651\) −127.271 + 132.922i −0.195501 + 0.204181i
\(652\) −156.722 −0.240371
\(653\) 370.397i 0.567224i 0.958939 + 0.283612i \(0.0915327\pi\)
−0.958939 + 0.283612i \(0.908467\pi\)
\(654\) 177.111 + 169.581i 0.270812 + 0.259298i
\(655\) −216.733 −0.330890
\(656\) 263.664i 0.401927i
\(657\) −16.3238 375.623i −0.0248460 0.571724i
\(658\) −462.550 −0.702964
\(659\) 1206.27i 1.83046i 0.402931 + 0.915230i \(0.367991\pi\)
−0.402931 + 0.915230i \(0.632009\pi\)
\(660\) −661.788 + 691.172i −1.00271 + 1.04723i
\(661\) 279.734 0.423198 0.211599 0.977357i \(-0.432133\pi\)
0.211599 + 0.977357i \(0.432133\pi\)
\(662\) 57.0996i 0.0862532i
\(663\) −214.073 204.972i −0.322886 0.309159i
\(664\) −437.291 −0.658571
\(665\) 1895.21i 2.84994i
\(666\) 35.7247 1.55252i 0.0536407 0.00233112i
\(667\) −392.519 −0.588484
\(668\) 444.792i 0.665856i
\(669\) −550.976 + 575.441i −0.823582 + 0.860151i
\(670\) 469.695 0.701038
\(671\) 1319.26i 1.96611i
\(672\) −390.819 374.204i −0.581576 0.556851i
\(673\) −72.6008 −0.107876 −0.0539382 0.998544i \(-0.517177\pi\)
−0.0539382 + 0.998544i \(0.517177\pi\)
\(674\) 512.441i 0.760299i
\(675\) 1267.16 + 1111.96i 1.87728 + 1.64734i
\(676\) −244.894 −0.362269
\(677\) 1191.38i 1.75979i 0.475172 + 0.879893i \(0.342386\pi\)
−0.475172 + 0.879893i \(0.657614\pi\)
\(678\) −278.495 + 290.861i −0.410760 + 0.428999i
\(679\) 414.766 0.610849
\(680\) 1507.55i 2.21698i
\(681\) 48.3978 + 46.3402i 0.0710687 + 0.0680473i
\(682\) −255.685 −0.374905
\(683\) 1224.58i 1.79295i −0.443094 0.896475i \(-0.646119\pi\)
0.443094 0.896475i \(-0.353881\pi\)
\(684\) 19.3952 + 446.298i 0.0283555 + 0.652482i
\(685\) 1425.87 2.08156
\(686\) 509.111i 0.742144i
\(687\) 392.235 409.651i 0.570939 0.596290i
\(688\) −89.2781 −0.129765
\(689\) 160.673i 0.233198i
\(690\) −678.507 649.661i −0.983343 0.941537i
\(691\) −1352.87 −1.95785 −0.978923 0.204229i \(-0.934531\pi\)
−0.978923 + 0.204229i \(0.934531\pi\)
\(692\) 402.467i 0.581600i
\(693\) 1252.39 54.4264i 1.80721 0.0785374i
\(694\) −973.751 −1.40310
\(695\) 1376.50i 1.98057i
\(696\) −315.787 + 329.808i −0.453716 + 0.473862i
\(697\) 815.606 1.17017
\(698\) 578.879i 0.829340i
\(699\) 481.859 + 461.373i 0.689355 + 0.660047i
\(700\) −768.787 −1.09827
\(701\) 799.448i 1.14044i 0.821492 + 0.570220i \(0.193142\pi\)
−0.821492 + 0.570220i \(0.806858\pi\)
\(702\) −141.700 + 161.479i −0.201852 + 0.230026i
\(703\) 75.4862 0.107377
\(704\) 1226.27i 1.74186i
\(705\) 841.218 878.570i 1.19322 1.24620i
\(706\) 808.932 1.14580
\(707\) 466.056i 0.659202i
\(708\) −28.9021 27.6733i −0.0408221 0.0390866i
\(709\) 437.816 0.617512 0.308756 0.951141i \(-0.400087\pi\)
0.308756 + 0.951141i \(0.400087\pi\)
\(710\) 868.304i 1.22296i
\(711\) 6.27559 + 144.406i 0.00882642 + 0.203103i
\(712\) 1029.15 1.44544
\(713\) 192.555i 0.270063i
\(714\) −413.445 + 431.803i −0.579055 + 0.604766i
\(715\) −971.476 −1.35871
\(716\) 468.098i 0.653768i
\(717\) −424.407 406.364i −0.591921 0.566756i
\(718\) −91.9330 −0.128040
\(719\) 995.948i 1.38519i −0.721329 0.692593i \(-0.756468\pi\)
0.721329 0.692593i \(-0.243532\pi\)
\(720\) −507.734 + 22.0651i −0.705186 + 0.0306459i
\(721\) −759.181 −1.05296
\(722\) 686.130i 0.950318i
\(723\) 55.1208 57.5682i 0.0762390 0.0796241i
\(724\) −62.8132 −0.0867585
\(725\) 1101.15i 1.51883i
\(726\) 863.549 + 826.836i 1.18946 + 1.13889i
\(727\) 810.654 1.11507 0.557533 0.830155i \(-0.311748\pi\)
0.557533 + 0.830155i \(0.311748\pi\)
\(728\) 323.642i 0.444563i
\(729\) 94.7142 + 722.821i 0.129923 + 0.991524i
\(730\) 587.714 0.805088
\(731\) 276.169i 0.377796i
\(732\) 241.956 252.699i 0.330541 0.345217i
\(733\) −753.454 −1.02790 −0.513952 0.857819i \(-0.671819\pi\)
−0.513952 + 0.857819i \(0.671819\pi\)
\(734\) 668.533i 0.910807i
\(735\) 25.8463 + 24.7475i 0.0351651 + 0.0336701i
\(736\) −566.153 −0.769230
\(737\) 655.841i 0.889879i
\(738\) −25.6683 590.646i −0.0347809 0.800334i
\(739\) 536.212 0.725592 0.362796 0.931869i \(-0.381822\pi\)
0.362796 + 0.931869i \(0.381822\pi\)
\(740\) 42.8810i 0.0579473i
\(741\) −313.647 + 327.573i −0.423275 + 0.442069i
\(742\) 324.091 0.436780
\(743\) 329.135i 0.442981i 0.975163 + 0.221490i \(0.0710922\pi\)
−0.975163 + 0.221490i \(0.928908\pi\)
\(744\) 161.792 + 154.913i 0.217462 + 0.208217i
\(745\) −306.612 −0.411560
\(746\) 13.2312i 0.0177362i
\(747\) −455.581 + 19.7986i −0.609881 + 0.0265042i
\(748\) 637.200 0.851872
\(749\) 175.299i 0.234044i
\(750\) −1092.81 + 1141.33i −1.45708 + 1.52178i
\(751\) 152.366 0.202884 0.101442 0.994841i \(-0.467654\pi\)
0.101442 + 0.994841i \(0.467654\pi\)
\(752\) 261.840i 0.348192i
\(753\) 777.728 + 744.663i 1.03284 + 0.988929i
\(754\) −140.323 −0.186105
\(755\) 1145.02i 1.51658i
\(756\) −249.873 219.267i −0.330520 0.290036i
\(757\) −1062.25 −1.40324 −0.701618 0.712554i \(-0.747539\pi\)
−0.701618 + 0.712554i \(0.747539\pi\)
\(758\) 200.624i 0.264675i
\(759\) 907.129 947.407i 1.19516 1.24823i
\(760\) −2306.83 −3.03531
\(761\) 347.069i 0.456069i −0.973653 0.228035i \(-0.926770\pi\)
0.973653 0.228035i \(-0.0732299\pi\)
\(762\) 603.580 + 577.919i 0.792099 + 0.758424i
\(763\) −385.208 −0.504860
\(764\) 51.3032i 0.0671508i
\(765\) −68.2550 1570.60i −0.0892223 2.05307i
\(766\) −921.911 −1.20354
\(767\) 40.6232i 0.0529638i
\(768\) −542.503 + 566.591i −0.706385 + 0.737749i
\(769\) −599.875 −0.780071 −0.390036 0.920800i \(-0.627537\pi\)
−0.390036 + 0.920800i \(0.627537\pi\)
\(770\) 1959.54i 2.54486i
\(771\) 39.9742 + 38.2748i 0.0518473 + 0.0496430i
\(772\) 247.720 0.320881
\(773\) 915.795i 1.18473i 0.805670 + 0.592364i \(0.201805\pi\)
−0.805670 + 0.592364i \(0.798195\pi\)
\(774\) −199.996 + 8.69141i −0.258393 + 0.0112292i
\(775\) 540.186 0.697014
\(776\) 504.851i 0.650581i
\(777\) −38.8499 + 40.5749i −0.0499998 + 0.0522199i
\(778\) −338.813 −0.435492
\(779\) 1248.03i 1.60210i
\(780\) 186.082 + 178.171i 0.238567 + 0.228425i
\(781\) −1212.42 −1.55240
\(782\) 625.524i 0.799902i
\(783\) −314.062 + 357.900i −0.401101 + 0.457088i
\(784\) −7.70299 −0.00982524
\(785\) 1444.61i 1.84027i
\(786\) 72.3489 75.5613i 0.0920469