Properties

Label 21.3.b.a.8.4
Level 21
Weight 3
Character 21.8
Analytic conductor 0.572
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 21.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.572208555157\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.65856.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 8.4
Root \(3.50592i\)
Character \(\chi\) = 21.8
Dual form 21.3.b.a.8.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.50592i q^{2} +(0.822876 - 2.88494i) q^{3} -8.29150 q^{4} -1.24197i q^{5} +(10.1144 + 2.88494i) q^{6} +2.64575 q^{7} -15.0457i q^{8} +(-7.64575 - 4.74789i) q^{9} +O(q^{10})\) \(q+3.50592i q^{2} +(0.822876 - 2.88494i) q^{3} -8.29150 q^{4} -1.24197i q^{5} +(10.1144 + 2.88494i) q^{6} +2.64575 q^{7} -15.0457i q^{8} +(-7.64575 - 4.74789i) q^{9} +4.35425 q^{10} +7.01185i q^{11} +(-6.82288 + 23.9205i) q^{12} -11.6458 q^{13} +9.27580i q^{14} +(-3.58301 - 1.02199i) q^{15} +19.5830 q^{16} -4.52791i q^{17} +(16.6458 - 26.8054i) q^{18} +16.2288 q^{19} +10.2978i q^{20} +(2.17712 - 7.63283i) q^{21} -24.5830 q^{22} +25.5635i q^{23} +(-43.4059 - 12.3807i) q^{24} +23.4575 q^{25} -40.8291i q^{26} +(-19.9889 + 18.1506i) q^{27} -21.9373 q^{28} -9.49579i q^{29} +(3.58301 - 12.5617i) q^{30} +28.7085 q^{31} +8.47380i q^{32} +(20.2288 + 5.76988i) q^{33} +15.8745 q^{34} -3.28594i q^{35} +(63.3948 + 39.3672i) q^{36} -33.0405 q^{37} +56.8968i q^{38} +(-9.58301 + 33.5973i) q^{39} -18.6863 q^{40} -67.1946i q^{41} +(26.7601 + 7.63283i) q^{42} -24.1255 q^{43} -58.1388i q^{44} +(-5.89674 + 9.49579i) q^{45} -89.6235 q^{46} +33.0153i q^{47} +(16.1144 - 56.4958i) q^{48} +7.00000 q^{49} +82.2403i q^{50} +(-13.0627 - 3.72591i) q^{51} +96.5608 q^{52} +15.1877i q^{53} +(-63.6346 - 70.0795i) q^{54} +8.70850 q^{55} -39.8071i q^{56} +(13.3542 - 46.8190i) q^{57} +33.2915 q^{58} -92.3960i q^{59} +(29.7085 + 8.47380i) q^{60} -57.5203 q^{61} +100.650i q^{62} +(-20.2288 - 12.5617i) q^{63} +48.6235 q^{64} +14.4637i q^{65} +(-20.2288 + 70.9205i) q^{66} +15.1660 q^{67} +37.5432i q^{68} +(73.7490 + 21.0355i) q^{69} +11.5203 q^{70} +70.5584i q^{71} +(-71.4353 + 115.036i) q^{72} -76.7895 q^{73} -115.838i q^{74} +(19.3026 - 67.6735i) q^{75} -134.561 q^{76} +18.5516i q^{77} +(-117.790 - 33.5973i) q^{78} +127.247 q^{79} -24.3215i q^{80} +(35.9150 + 72.6024i) q^{81} +235.579 q^{82} -74.2844i q^{83} +(-18.0516 + 63.2876i) q^{84} -5.62352 q^{85} -84.5821i q^{86} +(-27.3948 - 7.81385i) q^{87} +105.498 q^{88} +127.377i q^{89} +(-33.2915 - 20.6735i) q^{90} -30.8118 q^{91} -211.959i q^{92} +(23.6235 - 82.8223i) q^{93} -115.749 q^{94} -20.1556i q^{95} +(24.4464 + 6.97288i) q^{96} -23.1660 q^{97} +24.5415i q^{98} +(33.2915 - 53.6108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 12q^{4} + 14q^{6} - 20q^{9} + O(q^{10}) \) \( 4q - 2q^{3} - 12q^{4} + 14q^{6} - 20q^{9} + 28q^{10} - 22q^{12} - 36q^{13} + 28q^{15} + 36q^{16} + 56q^{18} + 12q^{19} + 14q^{21} - 56q^{22} - 126q^{24} - 12q^{25} + 10q^{27} - 56q^{28} - 28q^{30} + 136q^{31} + 28q^{33} + 116q^{36} + 16q^{37} + 4q^{39} + 84q^{40} + 70q^{42} - 160q^{43} - 140q^{45} - 168q^{46} + 38q^{48} + 28q^{49} - 84q^{51} + 164q^{52} - 154q^{54} + 56q^{55} + 64q^{57} + 112q^{58} + 140q^{60} - 156q^{61} - 28q^{63} + 4q^{64} - 28q^{66} - 24q^{67} + 168q^{69} - 28q^{70} - 32q^{73} + 146q^{75} - 316q^{76} - 196q^{78} + 128q^{79} - 68q^{81} + 392q^{82} - 14q^{84} + 168q^{85} + 28q^{87} + 168q^{88} - 112q^{90} - 28q^{91} - 96q^{93} - 336q^{94} - 98q^{96} - 8q^{97} + 112q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.50592i 1.75296i 0.481436 + 0.876481i \(0.340115\pi\)
−0.481436 + 0.876481i \(0.659885\pi\)
\(3\) 0.822876 2.88494i 0.274292 0.961646i
\(4\) −8.29150 −2.07288
\(5\) 1.24197i 0.248394i −0.992258 0.124197i \(-0.960365\pi\)
0.992258 0.124197i \(-0.0396354\pi\)
\(6\) 10.1144 + 2.88494i 1.68573 + 0.480823i
\(7\) 2.64575 0.377964
\(8\) 15.0457i 1.88071i
\(9\) −7.64575 4.74789i −0.849528 0.527544i
\(10\) 4.35425 0.435425
\(11\) 7.01185i 0.637441i 0.947849 + 0.318720i \(0.103253\pi\)
−0.947849 + 0.318720i \(0.896747\pi\)
\(12\) −6.82288 + 23.9205i −0.568573 + 1.99337i
\(13\) −11.6458 −0.895827 −0.447914 0.894077i \(-0.647833\pi\)
−0.447914 + 0.894077i \(0.647833\pi\)
\(14\) 9.27580i 0.662557i
\(15\) −3.58301 1.02199i −0.238867 0.0681324i
\(16\) 19.5830 1.22394
\(17\) 4.52791i 0.266348i −0.991093 0.133174i \(-0.957483\pi\)
0.991093 0.133174i \(-0.0425169\pi\)
\(18\) 16.6458 26.8054i 0.924764 1.48919i
\(19\) 16.2288 0.854145 0.427073 0.904217i \(-0.359545\pi\)
0.427073 + 0.904217i \(0.359545\pi\)
\(20\) 10.2978i 0.514889i
\(21\) 2.17712 7.63283i 0.103673 0.363468i
\(22\) −24.5830 −1.11741
\(23\) 25.5635i 1.11145i 0.831365 + 0.555727i \(0.187560\pi\)
−0.831365 + 0.555727i \(0.812440\pi\)
\(24\) −43.4059 12.3807i −1.80858 0.515864i
\(25\) 23.4575 0.938301
\(26\) 40.8291i 1.57035i
\(27\) −19.9889 + 18.1506i −0.740329 + 0.672245i
\(28\) −21.9373 −0.783473
\(29\) 9.49579i 0.327441i −0.986507 0.163720i \(-0.947650\pi\)
0.986507 0.163720i \(-0.0523495\pi\)
\(30\) 3.58301 12.5617i 0.119434 0.418725i
\(31\) 28.7085 0.926081 0.463040 0.886337i \(-0.346759\pi\)
0.463040 + 0.886337i \(0.346759\pi\)
\(32\) 8.47380i 0.264806i
\(33\) 20.2288 + 5.76988i 0.612993 + 0.174845i
\(34\) 15.8745 0.466897
\(35\) 3.28594i 0.0938840i
\(36\) 63.3948 + 39.3672i 1.76097 + 1.09353i
\(37\) −33.0405 −0.892987 −0.446493 0.894787i \(-0.647327\pi\)
−0.446493 + 0.894787i \(0.647327\pi\)
\(38\) 56.8968i 1.49728i
\(39\) −9.58301 + 33.5973i −0.245718 + 0.861469i
\(40\) −18.6863 −0.467157
\(41\) 67.1946i 1.63889i −0.573156 0.819446i \(-0.694281\pi\)
0.573156 0.819446i \(-0.305719\pi\)
\(42\) 26.7601 + 7.63283i 0.637146 + 0.181734i
\(43\) −24.1255 −0.561058 −0.280529 0.959846i \(-0.590510\pi\)
−0.280529 + 0.959846i \(0.590510\pi\)
\(44\) 58.1388i 1.32134i
\(45\) −5.89674 + 9.49579i −0.131039 + 0.211017i
\(46\) −89.6235 −1.94834
\(47\) 33.0153i 0.702452i 0.936291 + 0.351226i \(0.114235\pi\)
−0.936291 + 0.351226i \(0.885765\pi\)
\(48\) 16.1144 56.4958i 0.335716 1.17700i
\(49\) 7.00000 0.142857
\(50\) 82.2403i 1.64481i
\(51\) −13.0627 3.72591i −0.256132 0.0730570i
\(52\) 96.5608 1.85694
\(53\) 15.1877i 0.286561i 0.989682 + 0.143281i \(0.0457651\pi\)
−0.989682 + 0.143281i \(0.954235\pi\)
\(54\) −63.6346 70.0795i −1.17842 1.29777i
\(55\) 8.70850 0.158336
\(56\) 39.8071i 0.710842i
\(57\) 13.3542 46.8190i 0.234285 0.821386i
\(58\) 33.2915 0.573991
\(59\) 92.3960i 1.56603i −0.622000 0.783017i \(-0.713680\pi\)
0.622000 0.783017i \(-0.286320\pi\)
\(60\) 29.7085 + 8.47380i 0.495142 + 0.141230i
\(61\) −57.5203 −0.942955 −0.471478 0.881878i \(-0.656279\pi\)
−0.471478 + 0.881878i \(0.656279\pi\)
\(62\) 100.650i 1.62338i
\(63\) −20.2288 12.5617i −0.321091 0.199393i
\(64\) 48.6235 0.759743
\(65\) 14.4637i 0.222518i
\(66\) −20.2288 + 70.9205i −0.306496 + 1.07455i
\(67\) 15.1660 0.226358 0.113179 0.993575i \(-0.463897\pi\)
0.113179 + 0.993575i \(0.463897\pi\)
\(68\) 37.5432i 0.552106i
\(69\) 73.7490 + 21.0355i 1.06883 + 0.304863i
\(70\) 11.5203 0.164575
\(71\) 70.5584i 0.993781i 0.867813 + 0.496890i \(0.165525\pi\)
−0.867813 + 0.496890i \(0.834475\pi\)
\(72\) −71.4353 + 115.036i −0.992157 + 1.59772i
\(73\) −76.7895 −1.05191 −0.525956 0.850512i \(-0.676292\pi\)
−0.525956 + 0.850512i \(0.676292\pi\)
\(74\) 115.838i 1.56537i
\(75\) 19.3026 67.6735i 0.257368 0.902313i
\(76\) −134.561 −1.77054
\(77\) 18.5516i 0.240930i
\(78\) −117.790 33.5973i −1.51012 0.430734i
\(79\) 127.247 1.61072 0.805361 0.592785i \(-0.201971\pi\)
0.805361 + 0.592785i \(0.201971\pi\)
\(80\) 24.3215i 0.304019i
\(81\) 35.9150 + 72.6024i 0.443395 + 0.896326i
\(82\) 235.579 2.87292
\(83\) 74.2844i 0.894992i −0.894286 0.447496i \(-0.852316\pi\)
0.894286 0.447496i \(-0.147684\pi\)
\(84\) −18.0516 + 63.2876i −0.214900 + 0.753424i
\(85\) −5.62352 −0.0661591
\(86\) 84.5821i 0.983513i
\(87\) −27.3948 7.81385i −0.314882 0.0898144i
\(88\) 105.498 1.19884
\(89\) 127.377i 1.43121i 0.698507 + 0.715603i \(0.253848\pi\)
−0.698507 + 0.715603i \(0.746152\pi\)
\(90\) −33.2915 20.6735i −0.369906 0.229706i
\(91\) −30.8118 −0.338591
\(92\) 211.959i 2.30391i
\(93\) 23.6235 82.8223i 0.254016 0.890562i
\(94\) −115.749 −1.23137
\(95\) 20.1556i 0.212164i
\(96\) 24.4464 + 6.97288i 0.254650 + 0.0726342i
\(97\) −23.1660 −0.238825 −0.119412 0.992845i \(-0.538101\pi\)
−0.119412 + 0.992845i \(0.538101\pi\)
\(98\) 24.5415i 0.250423i
\(99\) 33.2915 53.6108i 0.336278 0.541524i
\(100\) −194.498 −1.94498
\(101\) 134.907i 1.33571i 0.744290 + 0.667857i \(0.232788\pi\)
−0.744290 + 0.667857i \(0.767212\pi\)
\(102\) 13.0627 45.7970i 0.128066 0.448990i
\(103\) −119.749 −1.16261 −0.581306 0.813685i \(-0.697458\pi\)
−0.581306 + 0.813685i \(0.697458\pi\)
\(104\) 175.218i 1.68479i
\(105\) −9.47974 2.70392i −0.0902832 0.0257516i
\(106\) −53.2470 −0.502331
\(107\) 77.8544i 0.727611i 0.931475 + 0.363806i \(0.118523\pi\)
−0.931475 + 0.363806i \(0.881477\pi\)
\(108\) 165.738 150.496i 1.53461 1.39348i
\(109\) −36.5385 −0.335216 −0.167608 0.985854i \(-0.553604\pi\)
−0.167608 + 0.985854i \(0.553604\pi\)
\(110\) 30.5313i 0.277558i
\(111\) −27.1882 + 95.3199i −0.244939 + 0.858738i
\(112\) 51.8118 0.462605
\(113\) 21.7596i 0.192563i −0.995354 0.0962815i \(-0.969305\pi\)
0.995354 0.0962815i \(-0.0306949\pi\)
\(114\) 164.144 + 46.8190i 1.43986 + 0.410693i
\(115\) 31.7490 0.276078
\(116\) 78.7343i 0.678744i
\(117\) 89.0405 + 55.2928i 0.761030 + 0.472588i
\(118\) 323.933 2.74520
\(119\) 11.9797i 0.100670i
\(120\) −15.3765 + 53.9088i −0.128137 + 0.449240i
\(121\) 71.8340 0.593669
\(122\) 201.662i 1.65296i
\(123\) −193.852 55.2928i −1.57603 0.449535i
\(124\) −238.037 −1.91965
\(125\) 60.1827i 0.481462i
\(126\) 44.0405 70.9205i 0.349528 0.562861i
\(127\) −15.4170 −0.121394 −0.0606968 0.998156i \(-0.519332\pi\)
−0.0606968 + 0.998156i \(0.519332\pi\)
\(128\) 204.366i 1.59661i
\(129\) −19.8523 + 69.6006i −0.153894 + 0.539539i
\(130\) −50.7085 −0.390065
\(131\) 183.110i 1.39779i −0.715226 0.698893i \(-0.753676\pi\)
0.715226 0.698893i \(-0.246324\pi\)
\(132\) −167.727 47.8410i −1.27066 0.362432i
\(133\) 42.9373 0.322836
\(134\) 53.1709i 0.396798i
\(135\) 22.5425 + 24.8256i 0.166981 + 0.183893i
\(136\) −68.1255 −0.500923
\(137\) 33.0153i 0.240987i −0.992714 0.120494i \(-0.961552\pi\)
0.992714 0.120494i \(-0.0384477\pi\)
\(138\) −73.7490 + 258.558i −0.534413 + 1.87361i
\(139\) 64.6418 0.465049 0.232525 0.972591i \(-0.425301\pi\)
0.232525 + 0.972591i \(0.425301\pi\)
\(140\) 27.2454i 0.194610i
\(141\) 95.2470 + 27.1675i 0.675511 + 0.192677i
\(142\) −247.373 −1.74206
\(143\) 81.6582i 0.571037i
\(144\) −149.727 92.9780i −1.03977 0.645681i
\(145\) −11.7935 −0.0813343
\(146\) 269.218i 1.84396i
\(147\) 5.76013 20.1946i 0.0391846 0.137378i
\(148\) 273.956 1.85105
\(149\) 195.736i 1.31366i −0.754037 0.656832i \(-0.771896\pi\)
0.754037 0.656832i \(-0.228104\pi\)
\(150\) 237.258 + 67.6735i 1.58172 + 0.451157i
\(151\) 102.251 0.677159 0.338579 0.940938i \(-0.390054\pi\)
0.338579 + 0.940938i \(0.390054\pi\)
\(152\) 244.173i 1.60640i
\(153\) −21.4980 + 34.6193i −0.140510 + 0.226270i
\(154\) −65.0405 −0.422341
\(155\) 35.6551i 0.230033i
\(156\) 79.4575 278.572i 0.509343 1.78572i
\(157\) 104.723 0.667025 0.333512 0.942746i \(-0.391766\pi\)
0.333512 + 0.942746i \(0.391766\pi\)
\(158\) 446.118i 2.82353i
\(159\) 43.8157 + 12.4976i 0.275570 + 0.0786014i
\(160\) 10.5242 0.0657762
\(161\) 67.6345i 0.420090i
\(162\) −254.539 + 125.915i −1.57123 + 0.777255i
\(163\) −70.9595 −0.435334 −0.217667 0.976023i \(-0.569845\pi\)
−0.217667 + 0.976023i \(0.569845\pi\)
\(164\) 557.144i 3.39722i
\(165\) 7.16601 25.1235i 0.0434304 0.152264i
\(166\) 260.435 1.56889
\(167\) 206.992i 1.23947i 0.784811 + 0.619735i \(0.212760\pi\)
−0.784811 + 0.619735i \(0.787240\pi\)
\(168\) −114.841 32.7563i −0.683578 0.194978i
\(169\) −33.3765 −0.197494
\(170\) 19.7156i 0.115974i
\(171\) −124.081 77.0524i −0.725620 0.450599i
\(172\) 200.037 1.16300
\(173\) 108.464i 0.626958i −0.949595 0.313479i \(-0.898506\pi\)
0.949595 0.313479i \(-0.101494\pi\)
\(174\) 27.3948 96.0440i 0.157441 0.551977i
\(175\) 62.0627 0.354644
\(176\) 137.313i 0.780188i
\(177\) −266.557 76.0304i −1.50597 0.429550i
\(178\) −446.575 −2.50885
\(179\) 159.357i 0.890261i −0.895466 0.445131i \(-0.853157\pi\)
0.895466 0.445131i \(-0.146843\pi\)
\(180\) 48.8928 78.7343i 0.271627 0.437413i
\(181\) −233.889 −1.29220 −0.646102 0.763251i \(-0.723602\pi\)
−0.646102 + 0.763251i \(0.723602\pi\)
\(182\) 108.024i 0.593537i
\(183\) −47.3320 + 165.942i −0.258645 + 0.906789i
\(184\) 384.620 2.09032
\(185\) 41.0353i 0.221812i
\(186\) 290.369 + 82.8223i 1.56112 + 0.445281i
\(187\) 31.7490 0.169781
\(188\) 273.746i 1.45610i
\(189\) −52.8856 + 48.0220i −0.279818 + 0.254085i
\(190\) 70.6640 0.371916
\(191\) 288.210i 1.50895i 0.656328 + 0.754476i \(0.272109\pi\)
−0.656328 + 0.754476i \(0.727891\pi\)
\(192\) 40.0111 140.276i 0.208391 0.730604i
\(193\) 77.1216 0.399594 0.199797 0.979837i \(-0.435972\pi\)
0.199797 + 0.979837i \(0.435972\pi\)
\(194\) 81.2183i 0.418651i
\(195\) 41.7268 + 11.9018i 0.213984 + 0.0610348i
\(196\) −58.0405 −0.296125
\(197\) 136.433i 0.692554i 0.938132 + 0.346277i \(0.112554\pi\)
−0.938132 + 0.346277i \(0.887446\pi\)
\(198\) 187.956 + 116.717i 0.949270 + 0.589482i
\(199\) 86.5830 0.435090 0.217545 0.976050i \(-0.430195\pi\)
0.217545 + 0.976050i \(0.430195\pi\)
\(200\) 352.934i 1.76467i
\(201\) 12.4797 43.7530i 0.0620883 0.217677i
\(202\) −472.974 −2.34145
\(203\) 25.1235i 0.123761i
\(204\) 108.310 + 30.8934i 0.530930 + 0.151438i
\(205\) −83.4536 −0.407091
\(206\) 419.831i 2.03801i
\(207\) 121.373 195.452i 0.586341 0.944212i
\(208\) −228.059 −1.09644
\(209\) 113.794i 0.544467i
\(210\) 9.47974 33.2353i 0.0451416 0.158263i
\(211\) 19.4170 0.0920237 0.0460118 0.998941i \(-0.485349\pi\)
0.0460118 + 0.998941i \(0.485349\pi\)
\(212\) 125.929i 0.594005i
\(213\) 203.557 + 58.0608i 0.955666 + 0.272586i
\(214\) −272.952 −1.27547
\(215\) 29.9631i 0.139363i
\(216\) 273.088 + 300.746i 1.26430 + 1.39234i
\(217\) 75.9555 0.350026
\(218\) 128.101i 0.587621i
\(219\) −63.1882 + 221.533i −0.288531 + 1.01157i
\(220\) −72.2065 −0.328211
\(221\) 52.7309i 0.238601i
\(222\) −334.184 95.3199i −1.50533 0.429369i
\(223\) 175.041 0.784935 0.392468 0.919766i \(-0.371622\pi\)
0.392468 + 0.919766i \(0.371622\pi\)
\(224\) 22.4196i 0.100087i
\(225\) −179.350 111.374i −0.797112 0.494994i
\(226\) 76.2876 0.337556
\(227\) 177.574i 0.782264i 0.920335 + 0.391132i \(0.127916\pi\)
−0.920335 + 0.391132i \(0.872084\pi\)
\(228\) −110.727 + 388.200i −0.485644 + 1.70263i
\(229\) 40.8118 0.178217 0.0891087 0.996022i \(-0.471598\pi\)
0.0891087 + 0.996022i \(0.471598\pi\)
\(230\) 111.310i 0.483955i
\(231\) 53.5203 + 15.2657i 0.231689 + 0.0660851i
\(232\) −142.871 −0.615821
\(233\) 387.696i 1.66393i −0.554828 0.831965i \(-0.687216\pi\)
0.554828 0.831965i \(-0.312784\pi\)
\(234\) −193.852 + 312.169i −0.828429 + 1.33406i
\(235\) 41.0039 0.174485
\(236\) 766.102i 3.24619i
\(237\) 104.708 367.100i 0.441808 1.54895i
\(238\) 42.0000 0.176471
\(239\) 49.5229i 0.207209i 0.994619 + 0.103604i \(0.0330376\pi\)
−0.994619 + 0.103604i \(0.966962\pi\)
\(240\) −70.1660 20.0136i −0.292358 0.0833898i
\(241\) 325.247 1.34957 0.674786 0.738013i \(-0.264236\pi\)
0.674786 + 0.738013i \(0.264236\pi\)
\(242\) 251.845i 1.04068i
\(243\) 239.007 43.8699i 0.983569 0.180535i
\(244\) 476.929 1.95463
\(245\) 8.69378i 0.0354848i
\(246\) 193.852 679.631i 0.788017 2.76273i
\(247\) −188.996 −0.765166
\(248\) 431.939i 1.74169i
\(249\) −214.306 61.1268i −0.860666 0.245489i
\(250\) 210.996 0.843984
\(251\) 263.732i 1.05073i 0.850878 + 0.525364i \(0.176071\pi\)
−0.850878 + 0.525364i \(0.823929\pi\)
\(252\) 167.727 + 104.156i 0.665582 + 0.413316i
\(253\) −179.247 −0.708486
\(254\) 54.0508i 0.212798i
\(255\) −4.62746 + 16.2235i −0.0181469 + 0.0636217i
\(256\) −521.996 −2.03905
\(257\) 151.181i 0.588252i 0.955767 + 0.294126i \(0.0950286\pi\)
−0.955767 + 0.294126i \(0.904971\pi\)
\(258\) −244.014 69.6006i −0.945792 0.269770i
\(259\) −87.4170 −0.337517
\(260\) 119.925i 0.461252i
\(261\) −45.0850 + 72.6024i −0.172739 + 0.278170i
\(262\) 641.970 2.45027
\(263\) 114.389i 0.434941i −0.976067 0.217470i \(-0.930219\pi\)
0.976067 0.217470i \(-0.0697805\pi\)
\(264\) 86.8118 304.355i 0.328832 1.15286i
\(265\) 18.8627 0.0711800
\(266\) 150.535i 0.565920i
\(267\) 367.476 + 104.816i 1.37631 + 0.392568i
\(268\) −125.749 −0.469213
\(269\) 4.76170i 0.0177015i −0.999961 0.00885074i \(-0.997183\pi\)
0.999961 0.00885074i \(-0.00281731\pi\)
\(270\) −87.0366 + 79.0322i −0.322358 + 0.292712i
\(271\) −518.701 −1.91402 −0.957012 0.290048i \(-0.906329\pi\)
−0.957012 + 0.290048i \(0.906329\pi\)
\(272\) 88.6701i 0.325993i
\(273\) −25.3542 + 88.8901i −0.0928727 + 0.325605i
\(274\) 115.749 0.422442
\(275\) 164.481i 0.598111i
\(276\) −611.490 174.416i −2.21554 0.631943i
\(277\) −121.085 −0.437130 −0.218565 0.975822i \(-0.570138\pi\)
−0.218565 + 0.975822i \(0.570138\pi\)
\(278\) 226.629i 0.815213i
\(279\) −219.498 136.305i −0.786731 0.488548i
\(280\) −49.4392 −0.176569
\(281\) 407.255i 1.44931i −0.689113 0.724654i \(-0.742000\pi\)
0.689113 0.724654i \(-0.258000\pi\)
\(282\) −95.2470 + 333.929i −0.337755 + 1.18415i
\(283\) −398.634 −1.40860 −0.704300 0.709902i \(-0.748739\pi\)
−0.704300 + 0.709902i \(0.748739\pi\)
\(284\) 585.036i 2.05998i
\(285\) −58.1477 16.5856i −0.204027 0.0581950i
\(286\) 286.288 1.00101
\(287\) 177.780i 0.619443i
\(288\) 40.2327 64.7886i 0.139697 0.224960i
\(289\) 268.498 0.929059
\(290\) 41.3470i 0.142576i
\(291\) −19.0627 + 66.8325i −0.0655077 + 0.229665i
\(292\) 636.701 2.18048
\(293\) 2.53426i 0.00864935i −0.999991 0.00432468i \(-0.998623\pi\)
0.999991 0.00432468i \(-0.00137659\pi\)
\(294\) 70.8006 + 20.1946i 0.240819 + 0.0686890i
\(295\) −114.753 −0.388993
\(296\) 497.117i 1.67945i
\(297\) −127.269 140.159i −0.428516 0.471916i
\(298\) 686.235 2.30280
\(299\) 297.706i 0.995671i
\(300\) −160.048 + 561.115i −0.533492 + 1.87038i
\(301\) −63.8301 −0.212060
\(302\) 358.484i 1.18703i
\(303\) 389.199 + 111.012i 1.28448 + 0.366375i
\(304\) 317.808 1.04542
\(305\) 71.4384i 0.234224i
\(306\) −121.373 75.3705i −0.396642 0.246309i
\(307\) 86.2366 0.280901 0.140451 0.990088i \(-0.455145\pi\)
0.140451 + 0.990088i \(0.455145\pi\)
\(308\) 153.821i 0.499418i
\(309\) −98.5385 + 345.469i −0.318895 + 1.11802i
\(310\) 125.004 0.403239
\(311\) 151.777i 0.488028i −0.969772 0.244014i \(-0.921536\pi\)
0.969772 0.244014i \(-0.0784643\pi\)
\(312\) 505.494 + 144.183i 1.62017 + 0.462125i
\(313\) 318.118 1.01635 0.508175 0.861254i \(-0.330320\pi\)
0.508175 + 0.861254i \(0.330320\pi\)
\(314\) 367.150i 1.16927i
\(315\) −15.6013 + 25.1235i −0.0495279 + 0.0797571i
\(316\) −1055.07 −3.33883
\(317\) 364.020i 1.14833i −0.818740 0.574164i \(-0.805327\pi\)
0.818740 0.574164i \(-0.194673\pi\)
\(318\) −43.8157 + 153.615i −0.137785 + 0.483064i
\(319\) 66.5830 0.208724
\(320\) 60.3889i 0.188715i
\(321\) 224.605 + 64.0645i 0.699705 + 0.199578i
\(322\) −237.122 −0.736402
\(323\) 73.4823i 0.227500i
\(324\) −297.790 601.983i −0.919104 1.85797i
\(325\) −273.180 −0.840555
\(326\) 248.779i 0.763124i
\(327\) −30.0667 + 105.412i −0.0919470 + 0.322359i
\(328\) −1010.99 −3.08228
\(329\) 87.3502i 0.265502i
\(330\) 88.0810 + 25.1235i 0.266912 + 0.0761318i
\(331\) 154.369 0.466370 0.233185 0.972432i \(-0.425085\pi\)
0.233185 + 0.972432i \(0.425085\pi\)
\(332\) 615.929i 1.85521i
\(333\) 252.620 + 156.873i 0.758617 + 0.471090i
\(334\) −725.697 −2.17274
\(335\) 18.8357i 0.0562260i
\(336\) 42.6346 149.474i 0.126889 0.444862i
\(337\) 403.041 1.19597 0.597983 0.801509i \(-0.295969\pi\)
0.597983 + 0.801509i \(0.295969\pi\)
\(338\) 117.015i 0.346199i
\(339\) −62.7752 17.9055i −0.185178 0.0528185i
\(340\) 46.6275 0.137140
\(341\) 201.300i 0.590321i
\(342\) 270.140 435.019i 0.789883 1.27198i
\(343\) 18.5203 0.0539949
\(344\) 362.984i 1.05519i
\(345\) 26.1255 91.5940i 0.0757261 0.265490i
\(346\) 380.265 1.09903
\(347\) 471.242i 1.35805i 0.734117 + 0.679023i \(0.237596\pi\)
−0.734117 + 0.679023i \(0.762404\pi\)
\(348\) 227.144 + 64.7886i 0.652712 + 0.186174i
\(349\) −364.516 −1.04446 −0.522230 0.852805i \(-0.674900\pi\)
−0.522230 + 0.852805i \(0.674900\pi\)
\(350\) 217.587i 0.621678i
\(351\) 232.786 211.377i 0.663207 0.602215i
\(352\) −59.4170 −0.168798
\(353\) 86.3420i 0.244595i 0.992493 + 0.122297i \(0.0390262\pi\)
−0.992493 + 0.122297i \(0.960974\pi\)
\(354\) 266.557 934.528i 0.752985 2.63991i
\(355\) 87.6314 0.246849
\(356\) 1056.15i 2.96671i
\(357\) −34.5608 9.85782i −0.0968089 0.0276129i
\(358\) 558.693 1.56059
\(359\) 372.068i 1.03640i −0.855259 0.518200i \(-0.826602\pi\)
0.855259 0.518200i \(-0.173398\pi\)
\(360\) 142.871 + 88.7204i 0.396863 + 0.246446i
\(361\) −97.6275 −0.270436
\(362\) 819.997i 2.26518i
\(363\) 59.1104 207.237i 0.162839 0.570900i
\(364\) 255.476 0.701857
\(365\) 95.3702i 0.261288i
\(366\) −581.782 165.942i −1.58957 0.453395i
\(367\) −161.786 −0.440833 −0.220416 0.975406i \(-0.570742\pi\)
−0.220416 + 0.975406i \(0.570742\pi\)
\(368\) 500.609i 1.36035i
\(369\) −319.033 + 513.753i −0.864587 + 1.39228i
\(370\) −143.867 −0.388829
\(371\) 40.1830i 0.108310i
\(372\) −195.875 + 686.721i −0.526544 + 1.84602i
\(373\) 378.251 1.01408 0.507039 0.861923i \(-0.330740\pi\)
0.507039 + 0.861923i \(0.330740\pi\)
\(374\) 111.310i 0.297619i
\(375\) −173.624 49.5229i −0.462996 0.132061i
\(376\) 496.737 1.32111
\(377\) 110.586i 0.293330i
\(378\) −168.361 185.413i −0.445401 0.490510i
\(379\) −50.7974 −0.134030 −0.0670151 0.997752i \(-0.521348\pi\)
−0.0670151 + 0.997752i \(0.521348\pi\)
\(380\) 167.120i 0.439790i
\(381\) −12.6863 + 44.4771i −0.0332973 + 0.116738i
\(382\) −1010.44 −2.64514
\(383\) 113.381i 0.296034i −0.988985 0.148017i \(-0.952711\pi\)
0.988985 0.148017i \(-0.0472891\pi\)
\(384\) 589.582 + 168.167i 1.53537 + 0.437936i
\(385\) 23.0405 0.0598455
\(386\) 270.382i 0.700472i
\(387\) 184.458 + 114.545i 0.476634 + 0.295983i
\(388\) 192.081 0.495054
\(389\) 725.584i 1.86526i 0.360841 + 0.932628i \(0.382490\pi\)
−0.360841 + 0.932628i \(0.617510\pi\)
\(390\) −41.7268 + 146.291i −0.106992 + 0.375105i
\(391\) 115.749 0.296033
\(392\) 105.320i 0.268673i
\(393\) −528.261 150.677i −1.34418 0.383402i
\(394\) −478.324 −1.21402
\(395\) 158.037i 0.400093i
\(396\) −276.037 + 444.514i −0.697062 + 1.12251i
\(397\) −94.3464 −0.237648 −0.118824 0.992915i \(-0.537912\pi\)
−0.118824 + 0.992915i \(0.537912\pi\)
\(398\) 303.553i 0.762697i
\(399\) 35.3320 123.871i 0.0885514 0.310455i
\(400\) 459.369 1.14842
\(401\) 677.665i 1.68994i 0.534815 + 0.844969i \(0.320381\pi\)
−0.534815 + 0.844969i \(0.679619\pi\)
\(402\) 153.395 + 43.7530i 0.381579 + 0.108838i
\(403\) −334.332 −0.829608
\(404\) 1118.58i 2.76877i
\(405\) 90.1699 44.6053i 0.222642 0.110137i
\(406\) 88.0810 0.216948
\(407\) 231.675i 0.569226i
\(408\) −56.0588 + 196.538i −0.137399 + 0.481711i
\(409\) 17.3647 0.0424564 0.0212282 0.999775i \(-0.493242\pi\)
0.0212282 + 0.999775i \(0.493242\pi\)
\(410\) 292.582i 0.713614i
\(411\) −95.2470 27.1675i −0.231745 0.0661009i
\(412\) 992.899 2.40995
\(413\) 244.457i 0.591905i
\(414\) 685.239 + 425.523i 1.65517 + 1.02783i
\(415\) −92.2589 −0.222311
\(416\) 98.6838i 0.237221i
\(417\) 53.1922 186.488i 0.127559 0.447213i
\(418\) −398.952 −0.954430
\(419\) 136.071i 0.324752i −0.986729 0.162376i \(-0.948084\pi\)
0.986729 0.162376i \(-0.0519157\pi\)
\(420\) 78.6013 + 22.4196i 0.187146 + 0.0533799i
\(421\) 423.992 1.00711 0.503554 0.863964i \(-0.332026\pi\)
0.503554 + 0.863964i \(0.332026\pi\)
\(422\) 68.0745i 0.161314i
\(423\) 156.753 252.427i 0.370574 0.596753i
\(424\) 228.510 0.538938
\(425\) 106.214i 0.249914i
\(426\) −203.557 + 713.655i −0.477833 + 1.67525i
\(427\) −152.184 −0.356404
\(428\) 645.530i 1.50825i
\(429\) −235.579 67.1946i −0.549135 0.156631i
\(430\) −105.048 −0.244299
\(431\) 340.244i 0.789430i −0.918804 0.394715i \(-0.870843\pi\)
0.918804 0.394715i \(-0.129157\pi\)
\(432\) −391.442 + 355.443i −0.906117 + 0.822786i
\(433\) 159.166 0.367589 0.183794 0.982965i \(-0.441162\pi\)
0.183794 + 0.982965i \(0.441162\pi\)
\(434\) 266.294i 0.613581i
\(435\) −9.70456 + 34.0235i −0.0223093 + 0.0782148i
\(436\) 302.959 0.694861
\(437\) 414.863i 0.949343i
\(438\) −776.678 221.533i −1.77324 0.505783i
\(439\) 128.073 0.291738 0.145869 0.989304i \(-0.453402\pi\)
0.145869 + 0.989304i \(0.453402\pi\)
\(440\) 131.025i 0.297785i
\(441\) −53.5203 33.2353i −0.121361 0.0753634i
\(442\) −184.871 −0.418259
\(443\) 197.340i 0.445463i 0.974880 + 0.222731i \(0.0714973\pi\)
−0.974880 + 0.222731i \(0.928503\pi\)
\(444\) 225.431 790.345i 0.507728 1.78006i
\(445\) 158.199 0.355503
\(446\) 613.679i 1.37596i
\(447\) −564.686 161.066i −1.26328 0.360327i
\(448\) 128.646 0.287156
\(449\) 148.101i 0.329847i −0.986306 0.164923i \(-0.947262\pi\)
0.986306 0.164923i \(-0.0527377\pi\)
\(450\) 390.468 628.789i 0.867707 1.39731i
\(451\) 471.158 1.04470
\(452\) 180.420i 0.399159i
\(453\) 84.1398 294.988i 0.185739 0.651187i
\(454\) −622.561 −1.37128
\(455\) 38.2673i 0.0841038i
\(456\) −704.423 200.924i −1.54479 0.440622i
\(457\) −122.214 −0.267428 −0.133714 0.991020i \(-0.542690\pi\)
−0.133714 + 0.991020i \(0.542690\pi\)
\(458\) 143.083i 0.312408i
\(459\) 82.1843 + 90.5079i 0.179051 + 0.197185i
\(460\) −263.247 −0.572276
\(461\) 602.089i 1.30605i −0.757337 0.653025i \(-0.773500\pi\)
0.757337 0.653025i \(-0.226500\pi\)
\(462\) −53.5203 + 187.638i −0.115845 + 0.406143i
\(463\) −637.061 −1.37594 −0.687971 0.725738i \(-0.741498\pi\)
−0.687971 + 0.725738i \(0.741498\pi\)
\(464\) 185.956i 0.400767i
\(465\) −102.863 29.3397i −0.221210 0.0630961i
\(466\) 1359.23 2.91681
\(467\) 767.706i 1.64391i 0.569553 + 0.821955i \(0.307116\pi\)
−0.569553 + 0.821955i \(0.692884\pi\)
\(468\) −738.280 458.460i −1.57752 0.979616i
\(469\) 40.1255 0.0855554
\(470\) 143.757i 0.305865i
\(471\) 86.1739 302.119i 0.182959 0.641442i
\(472\) −1390.16 −2.94526
\(473\) 169.164i 0.357641i
\(474\) 1287.02 + 367.100i 2.71524 + 0.774473i
\(475\) 380.686 0.801445
\(476\) 99.3299i 0.208676i
\(477\) 72.1097 116.122i 0.151173 0.243442i
\(478\) −173.624 −0.363229
\(479\) 393.855i 0.822245i −0.911580 0.411122i \(-0.865137\pi\)
0.911580 0.411122i \(-0.134863\pi\)
\(480\) 8.66010 30.3617i 0.0180419 0.0632535i
\(481\) 384.782 0.799962
\(482\) 1140.29i 2.36575i
\(483\) 195.122 + 55.6548i 0.403978 + 0.115227i
\(484\) −595.612 −1.23060
\(485\) 28.7715i 0.0593226i
\(486\) 153.805 + 837.941i 0.316470 + 1.72416i
\(487\) 573.409 1.17743 0.588716 0.808340i \(-0.299634\pi\)
0.588716 + 0.808340i \(0.299634\pi\)
\(488\) 865.432i 1.77343i
\(489\) −58.3908 + 204.714i −0.119409 + 0.418638i
\(490\) 30.4797 0.0622036
\(491\) 170.796i 0.347853i 0.984759 + 0.173927i \(0.0556455\pi\)
−0.984759 + 0.173927i \(0.944354\pi\)
\(492\) 1607.33 + 458.460i 3.26692 + 0.931830i
\(493\) −42.9961 −0.0872131
\(494\) 662.606i 1.34131i
\(495\) −66.5830 41.3470i −0.134511 0.0835293i
\(496\) 562.199 1.13347
\(497\) 186.680i 0.375614i
\(498\) 214.306 751.340i 0.430333 1.50871i
\(499\) −847.814 −1.69903 −0.849513 0.527567i \(-0.823104\pi\)
−0.849513 + 0.527567i \(0.823104\pi\)
\(500\) 499.005i 0.998010i
\(501\) 597.158 + 170.328i 1.19193 + 0.339977i
\(502\) −924.626 −1.84188
\(503\) 197.624i 0.392891i −0.980515 0.196445i \(-0.937060\pi\)
0.980515 0.196445i \(-0.0629398\pi\)
\(504\) −189.000 + 304.355i −0.375000 + 0.603880i
\(505\) 167.550 0.331783
\(506\) 628.427i 1.24195i
\(507\) −27.4647 + 96.2891i −0.0541710 + 0.189919i
\(508\) 127.830 0.251634
\(509\) 491.448i 0.965516i −0.875754 0.482758i \(-0.839635\pi\)
0.875754 0.482758i \(-0.160365\pi\)
\(510\) −56.8784 16.2235i −0.111526 0.0318108i
\(511\) −203.166 −0.397585
\(512\) 1012.62i 1.97777i
\(513\) −324.395 + 294.562i −0.632348 + 0.574194i
\(514\) −530.029 −1.03118
\(515\) 148.725i 0.288786i
\(516\) 164.605 577.093i 0.319002 1.11840i
\(517\) −231.498 −0.447772
\(518\) 306.477i 0.591655i
\(519\) −312.911 89.2521i −0.602912 0.171969i
\(520\) 217.616 0.418492
\(521\) 870.010i 1.66988i −0.550338 0.834942i \(-0.685501\pi\)
0.550338 0.834942i \(-0.314499\pi\)
\(522\) −254.539 158.064i −0.487622 0.302806i
\(523\) 798.707 1.52716 0.763582 0.645710i \(-0.223439\pi\)
0.763582 + 0.645710i \(0.223439\pi\)
\(524\) 1518.26i 2.89744i
\(525\) 51.0699 179.047i 0.0972760 0.341042i
\(526\) 401.041 0.762434
\(527\) 129.989i 0.246659i
\(528\) 396.140 + 112.992i 0.750265 + 0.213999i
\(529\) −124.490 −0.235331
\(530\) 66.1312i 0.124776i
\(531\) −438.686 + 706.437i −0.826151 + 1.33039i
\(532\) −356.014 −0.669200
\(533\) 782.531i 1.46816i
\(534\) −367.476 + 1288.34i −0.688157 + 2.41263i
\(535\) 96.6927 0.180734
\(536\) 228.183i 0.425714i
\(537\) −459.735 131.131i −0.856117 0.244191i
\(538\) 16.6941 0.0310300
\(539\) 49.0829i 0.0910630i
\(540\) −186.911 205.841i −0.346132 0.381188i
\(541\) −736.243 −1.36089 −0.680446 0.732798i \(-0.738214\pi\)
−0.680446 + 0.732798i \(0.738214\pi\)
\(542\) 1818.52i 3.35521i
\(543\) −192.461 + 674.755i −0.354441 + 1.24264i
\(544\) 38.3686 0.0705305
\(545\) 45.3797i 0.0832656i
\(546\) −311.642 88.8901i −0.570773 0.162802i
\(547\) −228.952 −0.418559 −0.209279 0.977856i \(-0.567112\pi\)
−0.209279 + 0.977856i \(0.567112\pi\)
\(548\) 273.746i 0.499537i
\(549\) 439.786 + 273.100i 0.801067 + 0.497450i
\(550\) −576.656 −1.04847
\(551\) 154.105i 0.279682i
\(552\) 316.494 1109.60i 0.573359 2.01015i
\(553\) 336.664 0.608796
\(554\) 424.515i 0.766272i
\(555\) 118.384 + 33.7669i 0.213305 + 0.0608413i
\(556\) −535.978 −0.963989
\(557\) 906.288i 1.62709i −0.581503 0.813544i \(-0.697535\pi\)
0.581503 0.813544i \(-0.302465\pi\)
\(558\) 477.875 769.543i 0.856406 1.37911i
\(559\) 280.959 0.502611
\(560\) 64.3486i 0.114908i
\(561\) 26.1255 91.5940i 0.0465695 0.163269i
\(562\) 1427.81 2.54058
\(563\) 458.616i 0.814593i 0.913296 + 0.407297i \(0.133529\pi\)
−0.913296 + 0.407297i \(0.866471\pi\)
\(564\) −789.741 225.259i −1.40025 0.399396i
\(565\) −27.0248 −0.0478315
\(566\) 1397.58i 2.46922i
\(567\) 95.0222 + 192.088i 0.167588 + 0.338779i
\(568\) 1061.60 1.86901
\(569\) 577.428i 1.01481i 0.861707 + 0.507406i \(0.169395\pi\)
−0.861707 + 0.507406i \(0.830605\pi\)
\(570\) 58.1477 203.861i 0.102014 0.357652i
\(571\) −103.122 −0.180598 −0.0902991 0.995915i \(-0.528782\pi\)
−0.0902991 + 0.995915i \(0.528782\pi\)
\(572\) 677.069i 1.18369i
\(573\) 831.468 + 237.161i 1.45108 + 0.413893i
\(574\) 623.284 1.08586
\(575\) 599.655i 1.04288i
\(576\) −371.763 230.859i −0.645423 0.400797i
\(577\) −676.583 −1.17259 −0.586294 0.810099i \(-0.699414\pi\)
−0.586294 + 0.810099i \(0.699414\pi\)
\(578\) 941.334i 1.62860i
\(579\) 63.4615 222.491i 0.109605 0.384268i
\(580\) 97.7856 0.168596
\(581\) 196.538i 0.338275i
\(582\) −234.310 66.8325i −0.402594 0.114833i
\(583\) −106.494 −0.182666
\(584\) 1155.35i 1.97834i
\(585\) 68.6719 110.586i 0.117388 0.189035i
\(586\) 8.88492 0.0151620
\(587\) 158.683i 0.270329i −0.990823 0.135164i \(-0.956844\pi\)
0.990823 0.135164i \(-0.0431563\pi\)
\(588\) −47.7601 + 167.443i −0.0812247 + 0.284768i
\(589\) 465.903 0.791007
\(590\) 402.315i 0.681890i
\(591\) 393.601 + 112.267i 0.665992 + 0.189962i
\(592\) −647.033 −1.09296
\(593\) 935.371i 1.57735i 0.614807 + 0.788677i \(0.289234\pi\)
−0.614807 + 0.788677i \(0.710766\pi\)
\(594\) 491.387 446.196i 0.827251 0.751172i
\(595\) −14.8784 −0.0250058
\(596\) 1622.94i 2.72306i
\(597\) 71.2470 249.787i 0.119342 0.418403i
\(598\) 1043.73 1.74537
\(599\) 73.7665i 0.123149i −0.998102 0.0615747i \(-0.980388\pi\)
0.998102 0.0615747i \(-0.0196122\pi\)
\(600\) −1018.19 290.421i −1.69699 0.484035i
\(601\) −934.280 −1.55454 −0.777271 0.629166i \(-0.783397\pi\)
−0.777271 + 0.629166i \(0.783397\pi\)
\(602\) 223.783i 0.371733i
\(603\) −115.956 72.0066i −0.192298 0.119414i
\(604\) −847.814 −1.40367
\(605\) 89.2156i 0.147464i
\(606\) −389.199 + 1364.50i −0.642242 + 2.25165i
\(607\) −181.608 −0.299189 −0.149595 0.988747i \(-0.547797\pi\)
−0.149595 + 0.988747i \(0.547797\pi\)
\(608\) 137.519i 0.226183i
\(609\) −72.4797 20.6735i −0.119014 0.0339466i
\(610\) −250.458 −0.410586
\(611\) 384.488i 0.629276i
\(612\) 178.251 287.046i 0.291260 0.469029i
\(613\) −897.940 −1.46483 −0.732414 0.680859i \(-0.761606\pi\)
−0.732414 + 0.680859i \(0.761606\pi\)
\(614\) 302.339i 0.492409i
\(615\) −68.6719 + 240.759i −0.111662 + 0.391477i
\(616\) 279.122 0.453119
\(617\) 1169.69i 1.89576i −0.318622 0.947882i \(-0.603220\pi\)
0.318622 0.947882i \(-0.396780\pi\)
\(618\) −1211.19 345.469i −1.95985 0.559011i
\(619\) 1208.97 1.95310 0.976548 0.215301i \(-0.0690734\pi\)
0.976548 + 0.215301i \(0.0690734\pi\)
\(620\) 295.634i 0.476829i
\(621\) −463.992 510.985i −0.747169 0.822842i
\(622\) 532.118 0.855495
\(623\) 337.009i 0.540945i
\(624\) −187.664 + 657.936i −0.300744 + 1.05438i
\(625\) 511.693 0.818708
\(626\) 1115.30i 1.78162i
\(627\) 328.288 + 93.6380i 0.523585 + 0.149343i
\(628\) −868.310 −1.38266
\(629\) 149.604i 0.237845i
\(630\) −88.0810 54.6970i −0.139811 0.0868206i
\(631\) 901.223 1.42825 0.714123 0.700020i \(-0.246826\pi\)
0.714123 + 0.700020i \(0.246826\pi\)
\(632\) 1914.52i 3.02930i
\(633\) 15.9778 56.0169i 0.0252413 0.0884942i
\(634\) 1276.23 2.01298
\(635\) 19.1474i 0.0301534i
\(636\) −363.298 103.624i −0.571223 0.162931i
\(637\) −81.5203 −0.127975
\(638\) 233.435i 0.365886i
\(639\) 335.004 539.472i 0.524263 0.844245i
\(640\) 253.816 0.396587
\(641\) 528.629i 0.824694i −0.911027 0.412347i \(-0.864709\pi\)
0.911027 0.412347i \(-0.135291\pi\)
\(642\) −224.605 + 787.449i −0.349852 + 1.22656i
\(643\) 33.4392 0.0520050 0.0260025 0.999662i \(-0.491722\pi\)
0.0260025 + 0.999662i \(0.491722\pi\)
\(644\) 560.792i 0.870795i
\(645\) 86.4418 + 24.6559i 0.134018 + 0.0382262i
\(646\) 257.624 0.398798
\(647\) 786.308i 1.21531i 0.794200 + 0.607657i \(0.207890\pi\)
−0.794200 + 0.607657i \(0.792110\pi\)
\(648\) 1092.35 540.366i 1.68573 0.833898i
\(649\) 647.867 0.998254
\(650\) 957.750i 1.47346i
\(651\) 62.5020 219.127i 0.0960092 0.336601i
\(652\) 588.361 0.902394
\(653\) 385.807i 0.590823i 0.955370 + 0.295412i \(0.0954568\pi\)
−0.955370 + 0.295412i \(0.904543\pi\)
\(654\) −369.565 105.412i −0.565084 0.161180i
\(655\) −227.417 −0.347202
\(656\) 1315.87i 2.00590i
\(657\) 587.114 + 364.588i 0.893628 + 0.554929i
\(658\) −306.243 −0.465415
\(659\) 97.2583i 0.147585i 0.997274 + 0.0737924i \(0.0235102\pi\)
−0.997274 + 0.0737924i \(0.976490\pi\)
\(660\) −59.4170 + 208.311i −0.0900257 + 0.315623i
\(661\) −961.505 −1.45462 −0.727311 0.686309i \(-0.759230\pi\)
−0.727311 + 0.686309i \(0.759230\pi\)
\(662\) 541.205i 0.817530i
\(663\) 152.125 + 43.3910i 0.229450 + 0.0654464i
\(664\) −1117.66 −1.68322
\(665\) 53.3267i 0.0801906i
\(666\) −549.984 + 885.665i −0.825802 + 1.32983i
\(667\) 242.745 0.363936
\(668\) 1716.27i 2.56927i
\(669\) 144.037 504.981i 0.215301 0.754830i
\(670\) 66.0366 0.0985621
\(671\) 403.323i 0.601078i
\(672\) 64.6791 + 18.4485i 0.0962487 + 0.0274531i
\(673\) −1089.81 −1.61933 −0.809663 0.586895i \(-0.800350\pi\)
−0.809663 + 0.586895i \(0.800350\pi\)
\(674\) 1413.03i 2.09648i
\(675\) −468.890 + 425.768i −0.694651 + 0.630767i
\(676\) 276.741 0.409380
\(677\) 1252.56i 1.85016i −0.379771 0.925080i \(-0.623997\pi\)
0.379771 0.925080i \(-0.376003\pi\)
\(678\) 62.7752 220.085i 0.0925888 0.324609i
\(679\) −61.2915 −0.0902673
\(680\) 84.6097i 0.124426i
\(681\) 512.290 + 146.121i 0.752262 + 0.214569i
\(682\) −705.741 −1.03481
\(683\) 341.097i 0.499409i −0.968322 0.249705i \(-0.919666\pi\)
0.968322 0.249705i \(-0.0803335\pi\)
\(684\) 1028.82 + 638.880i 1.50412 + 0.934035i
\(685\) −41.0039 −0.0598598
\(686\) 64.9306i 0.0946510i
\(687\) 33.5830 117.739i 0.0488836 0.171382i
\(688\) −472.450 −0.686700
\(689\) 176.873i 0.256709i
\(690\) 321.122 + 91.5940i 0.465394 + 0.132745i
\(691\) −783.667 −1.13411 −0.567053 0.823682i \(-0.691916\pi\)
−0.567053 + 0.823682i \(0.691916\pi\)
\(692\) 899.327i 1.29961i
\(693\) 88.0810 141.841i 0.127101 0.204677i
\(694\) −1652.14 −2.38060
\(695\) 80.2831i 0.115515i
\(696\) −117.565 + 412.173i −0.168915 + 0.592203i
\(697\) −304.251 −0.436515
\(698\) 1277.97i 1.83090i
\(699\) −1118.48 319.025i −1.60011 0.456402i
\(700\) −514.593 −0.735133
\(701\) 1331.76i 1.89979i 0.312562 + 0.949897i \(0.398813\pi\)
−0.312562 + 0.949897i \(0.601187\pi\)
\(702\) 741.073 + 816.129i 1.05566 + 1.16258i
\(703\) −536.207 −0.762740
\(704\) 340.941i 0.484291i
\(705\) 33.7411 118.294i 0.0478598 0.167793i
\(706\) −302.708 −0.428766
\(707\) 356.930i 0.504852i
\(708\) 2210.16 + 630.406i 3.12169 + 0.890404i
\(709\) 763.963 1.07752 0.538761 0.842459i \(-0.318893\pi\)
0.538761 + 0.842459i \(0.318893\pi\)
\(710\) 307.229i 0.432717i
\(711\) −972.899 604.155i −1.36835 0.849726i
\(712\) 1916.48 2.69168
\(713\) 733.888i 1.02930i
\(714\) 34.5608 121.167i 0.0484045 0.169702i
\(715\) −101.417 −0.141842
\(716\) 1321.31i 1.84540i
\(717\) 142.871 + 40.7512i 0.199262 + 0.0568357i
\(718\) 1304.44 1.81677
\(719\) 623.715i 0.867476i 0.901039 + 0.433738i \(0.142806\pi\)
−0.901039 + 0.433738i \(0.857194\pi\)
\(720\) −115.476 + 185.956i −0.160383 + 0.258272i
\(721\) −316.826 −0.439426
\(722\) 342.274i 0.474064i
\(723\) 267.638 938.318i 0.370177 1.29781i
\(724\) 1939.29 2.67858
\(725\) 222.748i 0.307238i
\(726\) 726.556 + 207.237i 1.00077 + 0.285450i
\(727\) 678.494 0.933279 0.466640 0.884448i \(-0.345464\pi\)
0.466640 + 0.884448i \(0.345464\pi\)
\(728\) 463.584i 0.636791i
\(729\) 70.1111 725.621i 0.0961744 0.995364i
\(730\) −334.361 −0.458028
\(731\) 109.238i 0.149436i
\(732\) 392.454 1375.91i 0.536139 1.87966i
\(733\) −394.966 −0.538835 −0.269417 0.963023i \(-0.586831\pi\)
−0.269417 + 0.963023i \(0.586831\pi\)
\(734\) 567.208i 0.772763i
\(735\) −25.0810 7.15390i −0.0341239 0.00973320i
\(736\) −216.620 −0.294320
\(737\) 106.342i 0.144290i
\(738\) −1801.18 1118.50i −2.44062 1.51559i
\(739\) 292.199 0.395397 0.197699 0.980263i \(-0.436653\pi\)
0.197699 + 0.980263i \(0.436653\pi\)
\(740\) 340.244i 0.459790i
\(741\) −155.520 + 545.242i −0.209879 + 0.735819i
\(742\) −140.878 −0.189863
\(743\) 383.452i 0.516086i −0.966133 0.258043i \(-0.916922\pi\)
0.966133 0.258043i \(-0.0830776\pi\)
\(744\) −1246.12 355.432i −1.67489 0.477731i
\(745\) −243.098 −0.326306
\(746\) 1326.12i 1.77764i
\(747\) −352.694 + 567.960i −0.472147 + 0.760321i
\(748\) −263.247 −0.351935
\(749\) 205.983i 0.275011i
\(750\) 173.624 608.711i 0.231498 0.811614i
\(751\) −696.332 −0.927206 −0.463603 0.886043i \(-0.653444\pi\)
−0.463603 + 0.886043i \(0.653444\pi\)
\(752\) 646.538i 0.859758i
\(753\) 760.852 + 217.019i 1.01043 + 0.288206i
\(754\) −387.705 −0.514197
\(755\) 126.993i 0.168202i
\(756\) 438.501 398.174i 0.580028 0.526686i
\(757\) 967.357 1.27788 0.638941 0.769256i \(-0.279373\pi\)
0.638941 + 0.769256i \(0.279373\pi\)
\(758\) 178.092i 0.234950i
\(759\) −147.498 + 517.117i −0.194332 + 0.681313i
\(760\) −303.255 −0.399020
\(761\) 89.7059i 0.117879i −0.998262 0.0589395i \(-0.981228\pi\)
0.998262 0.0589395i \(-0.0187719\pi\)
\(762\) −155.933 44.4771i −0.204637 0.0583689i
\(763\) −96.6719 −0.126700
\(764\) 2389.69i 3.12787i
\(765\) 42.9961 + 26.6999i 0.0562040 + 0.0349018i
\(766\) 397.506 0.518937
\(767\) 1076.02i 1.40290i
\(768\) −429.538 + 1505.93i −0.559294 + 1.96084i
\(769\) 926.219 1.20445 0.602223 0.798328i \(-0.294282\pi\)
0.602223 + 0.798328i \(0.294282\pi\)
\(770\) 80.7783i 0.104907i
\(771\) 436.148 + 124.403i 0.565691 + 0.161353i
\(772\) −639.454 −0.828308
\(773\) 424.125i 0.548674i 0.961634 + 0.274337i \(0.0884584\pi\)
−0.961634 + 0.274337i \(0.911542\pi\)
\(774\) −401.587 + 646.694i −0.518846 + 0.835522i
\(775\) 673.430 0.868942
\(776\) 348.548i 0.449160i
\(777\) −71.9333 + 252.193i −0.0925783 + 0.324572i
\(778\) −2543.84 −3.26972
\(779\) 1090.48i 1.39985i
\(780\) −345.978 98.6838i −0.443561 0.126518i
\(781\) −494.745 −0.633476
\(782\) 405.807i 0.518935i
\(783\) 172.354 + 189.810i 0.220120 + 0.242414i
\(784\) 137.081 0.174848
\(785\) 130.063i 0.165685i
\(786\) 528.261 1852.04i 0.672088 2.35629i
\(787\) −155.889 −0.198080 −0.0990399 0.995083i \(-0.531577\pi\)
−0.0990399 + 0.995083i \(0.531577\pi\)
\(788\) 1131.24i 1.43558i
\(789\) −330.006 94.1282i −0.418259 0.119301i
\(790\) 554.065 0.701348