Properties

Label 230.3.d.a.91.15
Level $230$
Weight $3$
Character 230.91
Analytic conductor $6.267$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.15
Root \(-1.00527i\) of defining polynomial
Character \(\chi\) \(=\) 230.91
Dual form 230.3.d.a.91.16

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} +4.30716 q^{3} +2.00000 q^{4} -2.23607i q^{5} +6.09125 q^{6} +1.47532i q^{7} +2.82843 q^{8} +9.55167 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} +4.30716 q^{3} +2.00000 q^{4} -2.23607i q^{5} +6.09125 q^{6} +1.47532i q^{7} +2.82843 q^{8} +9.55167 q^{9} -3.16228i q^{10} +6.04959i q^{11} +8.61433 q^{12} -5.21324 q^{13} +2.08642i q^{14} -9.63111i q^{15} +4.00000 q^{16} -15.7063i q^{17} +13.5081 q^{18} -4.82663i q^{19} -4.47214i q^{20} +6.35447i q^{21} +8.55541i q^{22} +(-2.58013 + 22.8548i) q^{23} +12.1825 q^{24} -5.00000 q^{25} -7.37263 q^{26} +2.37613 q^{27} +2.95065i q^{28} -23.4711 q^{29} -13.6205i q^{30} -20.4887 q^{31} +5.65685 q^{32} +26.0566i q^{33} -22.2121i q^{34} +3.29893 q^{35} +19.1033 q^{36} -15.5248i q^{37} -6.82589i q^{38} -22.4543 q^{39} -6.32456i q^{40} +20.3093 q^{41} +8.98657i q^{42} +38.1696i q^{43} +12.0992i q^{44} -21.3582i q^{45} +(-3.64885 + 32.3216i) q^{46} -13.8273 q^{47} +17.2287 q^{48} +46.8234 q^{49} -7.07107 q^{50} -67.6497i q^{51} -10.4265 q^{52} +38.2742i q^{53} +3.36035 q^{54} +13.5273 q^{55} +4.17285i q^{56} -20.7891i q^{57} -33.1932 q^{58} -33.5696 q^{59} -19.2622i q^{60} -100.567i q^{61} -28.9753 q^{62} +14.0918i q^{63} +8.00000 q^{64} +11.6572i q^{65} +36.8496i q^{66} +32.4469i q^{67} -31.4126i q^{68} +(-11.1130 + 98.4395i) q^{69} +4.66539 q^{70} -24.1306 q^{71} +27.0162 q^{72} +15.1818 q^{73} -21.9554i q^{74} -21.5358 q^{75} -9.65326i q^{76} -8.92511 q^{77} -31.7552 q^{78} +11.2095i q^{79} -8.94427i q^{80} -75.7306 q^{81} +28.7216 q^{82} -44.1310i q^{83} +12.7089i q^{84} -35.1204 q^{85} +53.9800i q^{86} -101.094 q^{87} +17.1108i q^{88} +111.039i q^{89} -30.2050i q^{90} -7.69122i q^{91} +(-5.16026 + 45.7096i) q^{92} -88.2480 q^{93} -19.5547 q^{94} -10.7927 q^{95} +24.3650 q^{96} -154.126i q^{97} +66.2183 q^{98} +57.7837i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) 4.30716 1.43572 0.717861 0.696187i \(-0.245121\pi\)
0.717861 + 0.696187i \(0.245121\pi\)
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) 6.09125 1.01521
\(7\) 1.47532i 0.210761i 0.994432 + 0.105380i \(0.0336060\pi\)
−0.994432 + 0.105380i \(0.966394\pi\)
\(8\) 2.82843 0.353553
\(9\) 9.55167 1.06130
\(10\) 3.16228i 0.316228i
\(11\) 6.04959i 0.549963i 0.961450 + 0.274981i \(0.0886717\pi\)
−0.961450 + 0.274981i \(0.911328\pi\)
\(12\) 8.61433 0.717861
\(13\) −5.21324 −0.401018 −0.200509 0.979692i \(-0.564260\pi\)
−0.200509 + 0.979692i \(0.564260\pi\)
\(14\) 2.08642i 0.149030i
\(15\) 9.63111i 0.642074i
\(16\) 4.00000 0.250000
\(17\) 15.7063i 0.923901i −0.886906 0.461951i \(-0.847150\pi\)
0.886906 0.461951i \(-0.152850\pi\)
\(18\) 13.5081 0.750450
\(19\) 4.82663i 0.254033i −0.991901 0.127017i \(-0.959460\pi\)
0.991901 0.127017i \(-0.0405402\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 6.35447i 0.302594i
\(22\) 8.55541i 0.388882i
\(23\) −2.58013 + 22.8548i −0.112180 + 0.993688i
\(24\) 12.1825 0.507604
\(25\) −5.00000 −0.200000
\(26\) −7.37263 −0.283563
\(27\) 2.37613 0.0880047
\(28\) 2.95065i 0.105380i
\(29\) −23.4711 −0.809349 −0.404674 0.914461i \(-0.632615\pi\)
−0.404674 + 0.914461i \(0.632615\pi\)
\(30\) 13.6205i 0.454015i
\(31\) −20.4887 −0.660924 −0.330462 0.943819i \(-0.607205\pi\)
−0.330462 + 0.943819i \(0.607205\pi\)
\(32\) 5.65685 0.176777
\(33\) 26.0566i 0.789593i
\(34\) 22.2121i 0.653297i
\(35\) 3.29893 0.0942550
\(36\) 19.1033 0.530648
\(37\) 15.5248i 0.419589i −0.977746 0.209794i \(-0.932721\pi\)
0.977746 0.209794i \(-0.0672795\pi\)
\(38\) 6.82589i 0.179629i
\(39\) −22.4543 −0.575751
\(40\) 6.32456i 0.158114i
\(41\) 20.3093 0.495348 0.247674 0.968843i \(-0.420334\pi\)
0.247674 + 0.968843i \(0.420334\pi\)
\(42\) 8.98657i 0.213966i
\(43\) 38.1696i 0.887666i 0.896109 + 0.443833i \(0.146382\pi\)
−0.896109 + 0.443833i \(0.853618\pi\)
\(44\) 12.0992i 0.274981i
\(45\) 21.3582i 0.474626i
\(46\) −3.64885 + 32.3216i −0.0793229 + 0.702643i
\(47\) −13.8273 −0.294198 −0.147099 0.989122i \(-0.546994\pi\)
−0.147099 + 0.989122i \(0.546994\pi\)
\(48\) 17.2287 0.358930
\(49\) 46.8234 0.955580
\(50\) −7.07107 −0.141421
\(51\) 67.6497i 1.32647i
\(52\) −10.4265 −0.200509
\(53\) 38.2742i 0.722154i 0.932536 + 0.361077i \(0.117591\pi\)
−0.932536 + 0.361077i \(0.882409\pi\)
\(54\) 3.36035 0.0622287
\(55\) 13.5273 0.245951
\(56\) 4.17285i 0.0745152i
\(57\) 20.7891i 0.364721i
\(58\) −33.1932 −0.572296
\(59\) −33.5696 −0.568977 −0.284488 0.958679i \(-0.591824\pi\)
−0.284488 + 0.958679i \(0.591824\pi\)
\(60\) 19.2622i 0.321037i
\(61\) 100.567i 1.64864i −0.566124 0.824320i \(-0.691558\pi\)
0.566124 0.824320i \(-0.308442\pi\)
\(62\) −28.9753 −0.467344
\(63\) 14.0918i 0.223680i
\(64\) 8.00000 0.125000
\(65\) 11.6572i 0.179341i
\(66\) 36.8496i 0.558327i
\(67\) 32.4469i 0.484282i 0.970241 + 0.242141i \(0.0778497\pi\)
−0.970241 + 0.242141i \(0.922150\pi\)
\(68\) 31.4126i 0.461951i
\(69\) −11.1130 + 98.4395i −0.161059 + 1.42666i
\(70\) 4.66539 0.0666484
\(71\) −24.1306 −0.339868 −0.169934 0.985455i \(-0.554355\pi\)
−0.169934 + 0.985455i \(0.554355\pi\)
\(72\) 27.0162 0.375225
\(73\) 15.1818 0.207969 0.103985 0.994579i \(-0.466841\pi\)
0.103985 + 0.994579i \(0.466841\pi\)
\(74\) 21.9554i 0.296694i
\(75\) −21.5358 −0.287144
\(76\) 9.65326i 0.127017i
\(77\) −8.92511 −0.115910
\(78\) −31.7552 −0.407117
\(79\) 11.2095i 0.141893i 0.997480 + 0.0709463i \(0.0226019\pi\)
−0.997480 + 0.0709463i \(0.977398\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −75.7306 −0.934946
\(82\) 28.7216 0.350264
\(83\) 44.1310i 0.531698i −0.964015 0.265849i \(-0.914348\pi\)
0.964015 0.265849i \(-0.0856523\pi\)
\(84\) 12.7089i 0.151297i
\(85\) −35.1204 −0.413181
\(86\) 53.9800i 0.627675i
\(87\) −101.094 −1.16200
\(88\) 17.1108i 0.194441i
\(89\) 111.039i 1.24763i 0.781572 + 0.623815i \(0.214418\pi\)
−0.781572 + 0.623815i \(0.785582\pi\)
\(90\) 30.2050i 0.335611i
\(91\) 7.69122i 0.0845189i
\(92\) −5.16026 + 45.7096i −0.0560898 + 0.496844i
\(93\) −88.2480 −0.948903
\(94\) −19.5547 −0.208029
\(95\) −10.7927 −0.113607
\(96\) 24.3650 0.253802
\(97\) 154.126i 1.58893i −0.607312 0.794463i \(-0.707752\pi\)
0.607312 0.794463i \(-0.292248\pi\)
\(98\) 66.2183 0.675697
\(99\) 57.7837i 0.583673i
\(100\) −10.0000 −0.100000
\(101\) −58.8607 −0.582779 −0.291390 0.956604i \(-0.594118\pi\)
−0.291390 + 0.956604i \(0.594118\pi\)
\(102\) 95.6712i 0.937952i
\(103\) 54.2662i 0.526856i 0.964679 + 0.263428i \(0.0848531\pi\)
−0.964679 + 0.263428i \(0.915147\pi\)
\(104\) −14.7453 −0.141781
\(105\) 14.2090 0.135324
\(106\) 54.1279i 0.510640i
\(107\) 119.124i 1.11331i −0.830745 0.556653i \(-0.812085\pi\)
0.830745 0.556653i \(-0.187915\pi\)
\(108\) 4.75225 0.0440023
\(109\) 149.223i 1.36902i 0.729003 + 0.684510i \(0.239984\pi\)
−0.729003 + 0.684510i \(0.760016\pi\)
\(110\) 19.1305 0.173913
\(111\) 66.8678i 0.602413i
\(112\) 5.90130i 0.0526902i
\(113\) 35.3339i 0.312690i −0.987703 0.156345i \(-0.950029\pi\)
0.987703 0.156345i \(-0.0499711\pi\)
\(114\) 29.4002i 0.257897i
\(115\) 51.1049 + 5.76935i 0.444391 + 0.0501682i
\(116\) −46.9422 −0.404674
\(117\) −49.7951 −0.425599
\(118\) −47.4746 −0.402327
\(119\) 23.1719 0.194722
\(120\) 27.2409i 0.227008i
\(121\) 84.4025 0.697541
\(122\) 142.223i 1.16576i
\(123\) 87.4753 0.711181
\(124\) −40.9773 −0.330462
\(125\) 11.1803i 0.0894427i
\(126\) 19.9288i 0.158165i
\(127\) 92.8398 0.731022 0.365511 0.930807i \(-0.380894\pi\)
0.365511 + 0.930807i \(0.380894\pi\)
\(128\) 11.3137 0.0883883
\(129\) 164.403i 1.27444i
\(130\) 16.4857i 0.126813i
\(131\) 151.709 1.15808 0.579042 0.815297i \(-0.303427\pi\)
0.579042 + 0.815297i \(0.303427\pi\)
\(132\) 52.1131i 0.394797i
\(133\) 7.12085 0.0535402
\(134\) 45.8869i 0.342439i
\(135\) 5.31318i 0.0393569i
\(136\) 44.4242i 0.326648i
\(137\) 267.464i 1.95229i −0.217121 0.976145i \(-0.569667\pi\)
0.217121 0.976145i \(-0.430333\pi\)
\(138\) −15.7162 + 139.214i −0.113886 + 1.00880i
\(139\) 239.779 1.72503 0.862516 0.506030i \(-0.168888\pi\)
0.862516 + 0.506030i \(0.168888\pi\)
\(140\) 6.59785 0.0471275
\(141\) −59.5564 −0.422386
\(142\) −34.1258 −0.240323
\(143\) 31.5380i 0.220545i
\(144\) 38.2067 0.265324
\(145\) 52.4830i 0.361952i
\(146\) 21.4703 0.147057
\(147\) 201.676 1.37195
\(148\) 31.0496i 0.209794i
\(149\) 201.647i 1.35333i 0.736290 + 0.676667i \(0.236576\pi\)
−0.736290 + 0.676667i \(0.763424\pi\)
\(150\) −30.4563 −0.203042
\(151\) 120.787 0.799912 0.399956 0.916534i \(-0.369025\pi\)
0.399956 + 0.916534i \(0.369025\pi\)
\(152\) 13.6518i 0.0898143i
\(153\) 150.022i 0.980533i
\(154\) −12.6220 −0.0819611
\(155\) 45.8140i 0.295574i
\(156\) −44.9086 −0.287875
\(157\) 194.897i 1.24138i −0.784055 0.620692i \(-0.786852\pi\)
0.784055 0.620692i \(-0.213148\pi\)
\(158\) 15.8526i 0.100333i
\(159\) 164.853i 1.03681i
\(160\) 12.6491i 0.0790569i
\(161\) −33.7183 3.80653i −0.209430 0.0236430i
\(162\) −107.099 −0.661107
\(163\) 153.813 0.943635 0.471817 0.881696i \(-0.343598\pi\)
0.471817 + 0.881696i \(0.343598\pi\)
\(164\) 40.6185 0.247674
\(165\) 58.2643 0.353117
\(166\) 62.4106i 0.375967i
\(167\) 48.4949 0.290389 0.145194 0.989403i \(-0.453619\pi\)
0.145194 + 0.989403i \(0.453619\pi\)
\(168\) 17.9731i 0.106983i
\(169\) −141.822 −0.839184
\(170\) −49.6678 −0.292163
\(171\) 46.1024i 0.269605i
\(172\) 76.3393i 0.443833i
\(173\) −111.269 −0.643174 −0.321587 0.946880i \(-0.604216\pi\)
−0.321587 + 0.946880i \(0.604216\pi\)
\(174\) −142.968 −0.821658
\(175\) 7.37662i 0.0421521i
\(176\) 24.1984i 0.137491i
\(177\) −144.590 −0.816892
\(178\) 157.033i 0.882207i
\(179\) 262.590 1.46698 0.733492 0.679698i \(-0.237889\pi\)
0.733492 + 0.679698i \(0.237889\pi\)
\(180\) 42.7164i 0.237313i
\(181\) 211.167i 1.16667i 0.812231 + 0.583335i \(0.198253\pi\)
−0.812231 + 0.583335i \(0.801747\pi\)
\(182\) 10.8770i 0.0597639i
\(183\) 433.159i 2.36699i
\(184\) −7.29771 + 64.6432i −0.0396615 + 0.351322i
\(185\) −34.7145 −0.187646
\(186\) −124.802 −0.670976
\(187\) 95.0168 0.508111
\(188\) −27.6546 −0.147099
\(189\) 3.50556i 0.0185479i
\(190\) −15.2631 −0.0803324
\(191\) 72.8209i 0.381261i 0.981662 + 0.190631i \(0.0610533\pi\)
−0.981662 + 0.190631i \(0.938947\pi\)
\(192\) 34.4573 0.179465
\(193\) 198.550 1.02875 0.514377 0.857564i \(-0.328023\pi\)
0.514377 + 0.857564i \(0.328023\pi\)
\(194\) 217.967i 1.12354i
\(195\) 50.2093i 0.257484i
\(196\) 93.6468 0.477790
\(197\) 28.2055 0.143175 0.0715876 0.997434i \(-0.477193\pi\)
0.0715876 + 0.997434i \(0.477193\pi\)
\(198\) 81.7184i 0.412719i
\(199\) 214.499i 1.07788i −0.842343 0.538941i \(-0.818825\pi\)
0.842343 0.538941i \(-0.181175\pi\)
\(200\) −14.1421 −0.0707107
\(201\) 139.754i 0.695295i
\(202\) −83.2416 −0.412087
\(203\) 34.6275i 0.170579i
\(204\) 135.299i 0.663233i
\(205\) 45.4129i 0.221526i
\(206\) 76.7439i 0.372543i
\(207\) −24.6445 + 218.302i −0.119056 + 1.05460i
\(208\) −20.8530 −0.100255
\(209\) 29.1991 0.139709
\(210\) 20.0946 0.0956885
\(211\) 240.262 1.13868 0.569340 0.822102i \(-0.307199\pi\)
0.569340 + 0.822102i \(0.307199\pi\)
\(212\) 76.5483i 0.361077i
\(213\) −103.935 −0.487956
\(214\) 168.466i 0.787226i
\(215\) 85.3499 0.396976
\(216\) 6.72070 0.0311144
\(217\) 30.2274i 0.139297i
\(218\) 211.034i 0.968044i
\(219\) 65.3904 0.298586
\(220\) 27.0546 0.122975
\(221\) 81.8808i 0.370501i
\(222\) 94.5654i 0.425970i
\(223\) 257.402 1.15427 0.577136 0.816648i \(-0.304170\pi\)
0.577136 + 0.816648i \(0.304170\pi\)
\(224\) 8.34570i 0.0372576i
\(225\) −47.7583 −0.212259
\(226\) 49.9697i 0.221105i
\(227\) 106.401i 0.468727i 0.972149 + 0.234363i \(0.0753005\pi\)
−0.972149 + 0.234363i \(0.924699\pi\)
\(228\) 41.5782i 0.182360i
\(229\) 328.507i 1.43453i −0.696801 0.717265i \(-0.745394\pi\)
0.696801 0.717265i \(-0.254606\pi\)
\(230\) 72.2733 + 8.15909i 0.314232 + 0.0354743i
\(231\) −38.4419 −0.166415
\(232\) −66.3863 −0.286148
\(233\) −149.213 −0.640400 −0.320200 0.947350i \(-0.603750\pi\)
−0.320200 + 0.947350i \(0.603750\pi\)
\(234\) −70.4210 −0.300944
\(235\) 30.9187i 0.131569i
\(236\) −67.1393 −0.284488
\(237\) 48.2812i 0.203718i
\(238\) 32.7701 0.137689
\(239\) −343.168 −1.43585 −0.717925 0.696121i \(-0.754908\pi\)
−0.717925 + 0.696121i \(0.754908\pi\)
\(240\) 38.5245i 0.160519i
\(241\) 348.748i 1.44709i 0.690278 + 0.723544i \(0.257488\pi\)
−0.690278 + 0.723544i \(0.742512\pi\)
\(242\) 119.363 0.493236
\(243\) −347.570 −1.43033
\(244\) 201.134i 0.824320i
\(245\) 104.700i 0.427348i
\(246\) 123.709 0.502881
\(247\) 25.1624i 0.101872i
\(248\) −57.9507 −0.233672
\(249\) 190.079i 0.763371i
\(250\) 15.8114i 0.0632456i
\(251\) 225.099i 0.896809i 0.893831 + 0.448405i \(0.148008\pi\)
−0.893831 + 0.448405i \(0.851992\pi\)
\(252\) 28.1836i 0.111840i
\(253\) −138.262 15.6087i −0.546491 0.0616946i
\(254\) 131.295 0.516911
\(255\) −151.269 −0.593213
\(256\) 16.0000 0.0625000
\(257\) −393.632 −1.53164 −0.765821 0.643054i \(-0.777667\pi\)
−0.765821 + 0.643054i \(0.777667\pi\)
\(258\) 232.501i 0.901166i
\(259\) 22.9041 0.0884328
\(260\) 23.3143i 0.0896704i
\(261\) −224.188 −0.858959
\(262\) 214.549 0.818890
\(263\) 132.720i 0.504640i −0.967644 0.252320i \(-0.918806\pi\)
0.967644 0.252320i \(-0.0811935\pi\)
\(264\) 73.6991i 0.279163i
\(265\) 85.5836 0.322957
\(266\) 10.0704 0.0378586
\(267\) 478.263i 1.79125i
\(268\) 64.8938i 0.242141i
\(269\) −438.116 −1.62868 −0.814341 0.580386i \(-0.802902\pi\)
−0.814341 + 0.580386i \(0.802902\pi\)
\(270\) 7.51397i 0.0278295i
\(271\) −204.698 −0.755342 −0.377671 0.925940i \(-0.623275\pi\)
−0.377671 + 0.925940i \(0.623275\pi\)
\(272\) 62.8253i 0.230975i
\(273\) 33.1274i 0.121346i
\(274\) 378.251i 1.38048i
\(275\) 30.2479i 0.109993i
\(276\) −22.2261 + 196.879i −0.0805293 + 0.713330i
\(277\) 173.804 0.627452 0.313726 0.949514i \(-0.398423\pi\)
0.313726 + 0.949514i \(0.398423\pi\)
\(278\) 339.099 1.21978
\(279\) −195.701 −0.701437
\(280\) 9.33077 0.0333242
\(281\) 143.605i 0.511051i 0.966802 + 0.255526i \(0.0822485\pi\)
−0.966802 + 0.255526i \(0.917752\pi\)
\(282\) −84.2255 −0.298672
\(283\) 72.1714i 0.255023i −0.991837 0.127511i \(-0.959301\pi\)
0.991837 0.127511i \(-0.0406989\pi\)
\(284\) −48.2612 −0.169934
\(285\) −46.4858 −0.163108
\(286\) 44.6014i 0.155949i
\(287\) 29.9627i 0.104400i
\(288\) 54.0324 0.187612
\(289\) 42.3114 0.146406
\(290\) 74.2222i 0.255939i
\(291\) 663.845i 2.28126i
\(292\) 30.3635 0.103985
\(293\) 124.199i 0.423889i −0.977282 0.211944i \(-0.932020\pi\)
0.977282 0.211944i \(-0.0679796\pi\)
\(294\) 285.213 0.970113
\(295\) 75.0640i 0.254454i
\(296\) 43.9107i 0.148347i
\(297\) 14.3746i 0.0483993i
\(298\) 285.171i 0.956951i
\(299\) 13.4508 119.148i 0.0449861 0.398487i
\(300\) −43.0716 −0.143572
\(301\) −56.3126 −0.187085
\(302\) 170.818 0.565623
\(303\) −253.523 −0.836709
\(304\) 19.3065i 0.0635083i
\(305\) −224.875 −0.737294
\(306\) 212.163i 0.693342i
\(307\) 219.717 0.715690 0.357845 0.933781i \(-0.383512\pi\)
0.357845 + 0.933781i \(0.383512\pi\)
\(308\) −17.8502 −0.0579552
\(309\) 233.733i 0.756418i
\(310\) 64.7908i 0.209003i
\(311\) −317.069 −1.01951 −0.509757 0.860319i \(-0.670265\pi\)
−0.509757 + 0.860319i \(0.670265\pi\)
\(312\) −63.5103 −0.203559
\(313\) 484.654i 1.54841i 0.632932 + 0.774207i \(0.281851\pi\)
−0.632932 + 0.774207i \(0.718149\pi\)
\(314\) 275.626i 0.877791i
\(315\) 31.5103 0.100033
\(316\) 22.4190i 0.0709463i
\(317\) −521.910 −1.64640 −0.823202 0.567748i \(-0.807815\pi\)
−0.823202 + 0.567748i \(0.807815\pi\)
\(318\) 233.138i 0.733137i
\(319\) 141.991i 0.445111i
\(320\) 17.8885i 0.0559017i
\(321\) 513.086i 1.59840i
\(322\) −47.6849 5.38325i −0.148090 0.0167182i
\(323\) −75.8086 −0.234702
\(324\) −151.461 −0.467473
\(325\) 26.0662 0.0802037
\(326\) 217.524 0.667251
\(327\) 642.729i 1.96553i
\(328\) 57.4432 0.175132
\(329\) 20.3997i 0.0620053i
\(330\) 82.3981 0.249691
\(331\) −318.270 −0.961540 −0.480770 0.876847i \(-0.659643\pi\)
−0.480770 + 0.876847i \(0.659643\pi\)
\(332\) 88.2619i 0.265849i
\(333\) 148.288i 0.445308i
\(334\) 68.5822 0.205336
\(335\) 72.5535 0.216578
\(336\) 25.4179i 0.0756484i
\(337\) 116.539i 0.345812i −0.984938 0.172906i \(-0.944684\pi\)
0.984938 0.172906i \(-0.0553156\pi\)
\(338\) −200.567 −0.593393
\(339\) 152.189i 0.448935i
\(340\) −70.2408 −0.206591
\(341\) 123.948i 0.363484i
\(342\) 65.1986i 0.190639i
\(343\) 141.371i 0.412159i
\(344\) 107.960i 0.313837i
\(345\) 220.117 + 24.8495i 0.638021 + 0.0720276i
\(346\) −157.358 −0.454793
\(347\) −100.715 −0.290245 −0.145122 0.989414i \(-0.546358\pi\)
−0.145122 + 0.989414i \(0.546358\pi\)
\(348\) −202.188 −0.581000
\(349\) 143.476 0.411106 0.205553 0.978646i \(-0.434101\pi\)
0.205553 + 0.978646i \(0.434101\pi\)
\(350\) 10.4321i 0.0298061i
\(351\) −12.3873 −0.0352915
\(352\) 34.2216i 0.0972206i
\(353\) −274.394 −0.777320 −0.388660 0.921381i \(-0.627062\pi\)
−0.388660 + 0.921381i \(0.627062\pi\)
\(354\) −204.481 −0.577630
\(355\) 53.9577i 0.151994i
\(356\) 222.078i 0.623815i
\(357\) 99.8053 0.279567
\(358\) 371.358 1.03731
\(359\) 476.871i 1.32833i 0.747586 + 0.664166i \(0.231213\pi\)
−0.747586 + 0.664166i \(0.768787\pi\)
\(360\) 60.4101i 0.167806i
\(361\) 337.704 0.935467
\(362\) 298.636i 0.824961i
\(363\) 363.535 1.00147
\(364\) 15.3824i 0.0422595i
\(365\) 33.9475i 0.0930067i
\(366\) 612.579i 1.67371i
\(367\) 14.0319i 0.0382340i 0.999817 + 0.0191170i \(0.00608551\pi\)
−0.999817 + 0.0191170i \(0.993914\pi\)
\(368\) −10.3205 + 91.4193i −0.0280449 + 0.248422i
\(369\) 193.987 0.525711
\(370\) −49.0937 −0.132686
\(371\) −56.4668 −0.152202
\(372\) −176.496 −0.474452
\(373\) 105.662i 0.283277i 0.989918 + 0.141639i \(0.0452371\pi\)
−0.989918 + 0.141639i \(0.954763\pi\)
\(374\) 134.374 0.359289
\(375\) 48.1556i 0.128415i
\(376\) −39.1095 −0.104015
\(377\) 122.361 0.324564
\(378\) 4.95761i 0.0131154i
\(379\) 339.983i 0.897053i −0.893770 0.448527i \(-0.851949\pi\)
0.893770 0.448527i \(-0.148051\pi\)
\(380\) −21.5854 −0.0568036
\(381\) 399.876 1.04954
\(382\) 102.984i 0.269592i
\(383\) 699.796i 1.82714i −0.406676 0.913572i \(-0.633312\pi\)
0.406676 0.913572i \(-0.366688\pi\)
\(384\) 48.7300 0.126901
\(385\) 19.9571i 0.0518367i
\(386\) 280.792 0.727439
\(387\) 364.584i 0.942077i
\(388\) 308.252i 0.794463i
\(389\) 124.817i 0.320867i 0.987047 + 0.160433i \(0.0512892\pi\)
−0.987047 + 0.160433i \(0.948711\pi\)
\(390\) 71.0067i 0.182068i
\(391\) 358.965 + 40.5244i 0.918070 + 0.103643i
\(392\) 132.437 0.337849
\(393\) 653.436 1.66269
\(394\) 39.8886 0.101240
\(395\) 25.0652 0.0634563
\(396\) 115.567i 0.291837i
\(397\) −149.557 −0.376719 −0.188360 0.982100i \(-0.560317\pi\)
−0.188360 + 0.982100i \(0.560317\pi\)
\(398\) 303.347i 0.762178i
\(399\) 30.6707 0.0768688
\(400\) −20.0000 −0.0500000
\(401\) 426.696i 1.06408i 0.846719 + 0.532040i \(0.178574\pi\)
−0.846719 + 0.532040i \(0.821426\pi\)
\(402\) 197.642i 0.491647i
\(403\) 106.812 0.265043
\(404\) −117.721 −0.291390
\(405\) 169.339i 0.418121i
\(406\) 48.9707i 0.120617i
\(407\) 93.9186 0.230758
\(408\) 191.342i 0.468976i
\(409\) 346.263 0.846610 0.423305 0.905987i \(-0.360870\pi\)
0.423305 + 0.905987i \(0.360870\pi\)
\(410\) 64.2235i 0.156643i
\(411\) 1152.01i 2.80294i
\(412\) 108.532i 0.263428i
\(413\) 49.5261i 0.119918i
\(414\) −34.8527 + 308.725i −0.0841852 + 0.745713i
\(415\) −98.6798 −0.237783
\(416\) −29.4905 −0.0708907
\(417\) 1032.77 2.47667
\(418\) 41.2938 0.0987890
\(419\) 158.433i 0.378121i 0.981965 + 0.189060i \(0.0605442\pi\)
−0.981965 + 0.189060i \(0.939456\pi\)
\(420\) 28.4180 0.0676620
\(421\) 18.0568i 0.0428902i 0.999770 + 0.0214451i \(0.00682671\pi\)
−0.999770 + 0.0214451i \(0.993173\pi\)
\(422\) 339.781 0.805169
\(423\) −132.074 −0.312231
\(424\) 108.256i 0.255320i
\(425\) 78.5316i 0.184780i
\(426\) −146.986 −0.345037
\(427\) 148.369 0.347469
\(428\) 238.247i 0.556653i
\(429\) 135.839i 0.316641i
\(430\) 120.703 0.280705
\(431\) 151.730i 0.352041i 0.984387 + 0.176020i \(0.0563225\pi\)
−0.984387 + 0.176020i \(0.943678\pi\)
\(432\) 9.50451 0.0220012
\(433\) 625.471i 1.44451i −0.691629 0.722253i \(-0.743106\pi\)
0.691629 0.722253i \(-0.256894\pi\)
\(434\) 42.7480i 0.0984978i
\(435\) 226.053i 0.519662i
\(436\) 298.447i 0.684510i
\(437\) 110.312 + 12.4533i 0.252430 + 0.0284973i
\(438\) 92.4759 0.211132
\(439\) 272.842 0.621509 0.310755 0.950490i \(-0.399418\pi\)
0.310755 + 0.950490i \(0.399418\pi\)
\(440\) 38.2610 0.0869567
\(441\) 447.242 1.01415
\(442\) 115.797i 0.261984i
\(443\) 5.57528 0.0125853 0.00629264 0.999980i \(-0.497997\pi\)
0.00629264 + 0.999980i \(0.497997\pi\)
\(444\) 133.736i 0.301206i
\(445\) 248.291 0.557957
\(446\) 364.022 0.816193
\(447\) 868.525i 1.94301i
\(448\) 11.8026i 0.0263451i
\(449\) 455.331 1.01410 0.507050 0.861916i \(-0.330736\pi\)
0.507050 + 0.861916i \(0.330736\pi\)
\(450\) −67.5405 −0.150090
\(451\) 122.863i 0.272423i
\(452\) 70.6679i 0.156345i
\(453\) 520.248 1.14845
\(454\) 150.474i 0.331440i
\(455\) −17.1981 −0.0377980
\(456\) 58.8004i 0.128948i
\(457\) 597.785i 1.30806i −0.756467 0.654032i \(-0.773076\pi\)
0.756467 0.654032i \(-0.226924\pi\)
\(458\) 464.579i 1.01437i
\(459\) 37.3202i 0.0813077i
\(460\) 102.210 + 11.5387i 0.222195 + 0.0250841i
\(461\) −340.556 −0.738734 −0.369367 0.929284i \(-0.620425\pi\)
−0.369367 + 0.929284i \(0.620425\pi\)
\(462\) −54.3651 −0.117673
\(463\) −471.395 −1.01813 −0.509066 0.860727i \(-0.670009\pi\)
−0.509066 + 0.860727i \(0.670009\pi\)
\(464\) −93.8844 −0.202337
\(465\) 197.329i 0.424362i
\(466\) −211.019 −0.452831
\(467\) 245.681i 0.526084i 0.964784 + 0.263042i \(0.0847257\pi\)
−0.964784 + 0.263042i \(0.915274\pi\)
\(468\) −99.5903 −0.212800
\(469\) −47.8697 −0.102068
\(470\) 43.7257i 0.0930334i
\(471\) 839.455i 1.78228i
\(472\) −94.9493 −0.201164
\(473\) −230.911 −0.488183
\(474\) 68.2800i 0.144051i
\(475\) 24.1332i 0.0508066i
\(476\) 46.3439 0.0973610
\(477\) 365.582i 0.766420i
\(478\) −485.313 −1.01530
\(479\) 203.940i 0.425763i −0.977078 0.212881i \(-0.931715\pi\)
0.977078 0.212881i \(-0.0682848\pi\)
\(480\) 54.4818i 0.113504i
\(481\) 80.9345i 0.168263i
\(482\) 493.205i 1.02325i
\(483\) −145.230 16.3954i −0.300684 0.0339448i
\(484\) 168.805 0.348771
\(485\) −344.636 −0.710589
\(486\) −491.538 −1.01139
\(487\) −681.456 −1.39929 −0.699647 0.714489i \(-0.746659\pi\)
−0.699647 + 0.714489i \(0.746659\pi\)
\(488\) 284.447i 0.582882i
\(489\) 662.496 1.35480
\(490\) 148.069i 0.302181i
\(491\) −329.666 −0.671417 −0.335709 0.941966i \(-0.608976\pi\)
−0.335709 + 0.941966i \(0.608976\pi\)
\(492\) 174.951 0.355591
\(493\) 368.645i 0.747758i
\(494\) 35.5850i 0.0720344i
\(495\) 129.208 0.261027
\(496\) −81.9546 −0.165231
\(497\) 35.6005i 0.0716308i
\(498\) 268.813i 0.539785i
\(499\) −993.708 −1.99140 −0.995700 0.0926377i \(-0.970470\pi\)
−0.995700 + 0.0926377i \(0.970470\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 208.876 0.416918
\(502\) 318.338i 0.634140i
\(503\) 880.515i 1.75053i −0.483646 0.875264i \(-0.660688\pi\)
0.483646 0.875264i \(-0.339312\pi\)
\(504\) 39.8577i 0.0790827i
\(505\) 131.617i 0.260627i
\(506\) −195.532 22.0741i −0.386428 0.0436246i
\(507\) −610.851 −1.20483
\(508\) 185.680 0.365511
\(509\) −689.907 −1.35542 −0.677708 0.735331i \(-0.737027\pi\)
−0.677708 + 0.735331i \(0.737027\pi\)
\(510\) −213.927 −0.419465
\(511\) 22.3980i 0.0438318i
\(512\) 22.6274 0.0441942
\(513\) 11.4687i 0.0223561i
\(514\) −556.680 −1.08303
\(515\) 121.343 0.235617
\(516\) 328.806i 0.637221i
\(517\) 83.6494i 0.161798i
\(518\) 32.3913 0.0625315
\(519\) −479.255 −0.923419
\(520\) 32.9714i 0.0634066i
\(521\) 408.559i 0.784183i 0.919926 + 0.392092i \(0.128248\pi\)
−0.919926 + 0.392092i \(0.871752\pi\)
\(522\) −317.050 −0.607376
\(523\) 516.837i 0.988216i 0.869400 + 0.494108i \(0.164505\pi\)
−0.869400 + 0.494108i \(0.835495\pi\)
\(524\) 303.418 0.579042
\(525\) 31.7723i 0.0605187i
\(526\) 187.695i 0.356834i
\(527\) 321.801i 0.610629i
\(528\) 104.226i 0.197398i
\(529\) −515.686 117.937i −0.974831 0.222943i
\(530\) 121.034 0.228365
\(531\) −320.646 −0.603853
\(532\) 14.2417 0.0267701
\(533\) −105.877 −0.198644
\(534\) 676.367i 1.26660i
\(535\) −266.369 −0.497886
\(536\) 91.7737i 0.171220i
\(537\) 1131.02 2.10618
\(538\) −619.589 −1.15165
\(539\) 283.262i 0.525533i
\(540\) 10.6264i 0.0196784i
\(541\) −825.026 −1.52500 −0.762501 0.646987i \(-0.776029\pi\)
−0.762501 + 0.646987i \(0.776029\pi\)
\(542\) −289.486 −0.534107
\(543\) 909.533i 1.67501i
\(544\) 88.8484i 0.163324i
\(545\) 333.673 0.612245
\(546\) 46.8492i 0.0858043i
\(547\) −749.566 −1.37032 −0.685161 0.728392i \(-0.740268\pi\)
−0.685161 + 0.728392i \(0.740268\pi\)
\(548\) 534.927i 0.976145i
\(549\) 960.583i 1.74970i
\(550\) 42.7770i 0.0777765i
\(551\) 113.286i 0.205601i
\(552\) −31.4324 + 278.429i −0.0569428 + 0.504400i
\(553\) −16.5377 −0.0299054
\(554\) 245.796 0.443675
\(555\) −149.521 −0.269407
\(556\) 479.559 0.862516
\(557\) 406.149i 0.729173i −0.931170 0.364586i \(-0.881210\pi\)
0.931170 0.364586i \(-0.118790\pi\)
\(558\) −276.763 −0.495991
\(559\) 198.988i 0.355971i
\(560\) 13.1957 0.0235638
\(561\) 409.253 0.729506
\(562\) 203.089i 0.361368i
\(563\) 285.771i 0.507587i 0.967258 + 0.253793i \(0.0816784\pi\)
−0.967258 + 0.253793i \(0.918322\pi\)
\(564\) −119.113 −0.211193
\(565\) −79.0091 −0.139839
\(566\) 102.066i 0.180328i
\(567\) 111.727i 0.197050i
\(568\) −68.2517 −0.120161
\(569\) 315.624i 0.554699i 0.960769 + 0.277349i \(0.0894560\pi\)
−0.960769 + 0.277349i \(0.910544\pi\)
\(570\) −65.7409 −0.115335
\(571\) 383.907i 0.672342i −0.941801 0.336171i \(-0.890868\pi\)
0.941801 0.336171i \(-0.109132\pi\)
\(572\) 63.0759i 0.110273i
\(573\) 313.652i 0.547385i
\(574\) 42.3737i 0.0738218i
\(575\) 12.9007 114.274i 0.0224359 0.198738i
\(576\) 76.4133 0.132662
\(577\) −717.832 −1.24408 −0.622038 0.782987i \(-0.713695\pi\)
−0.622038 + 0.782987i \(0.713695\pi\)
\(578\) 59.8374 0.103525
\(579\) 855.186 1.47701
\(580\) 104.966i 0.180976i
\(581\) 65.1075 0.112061
\(582\) 938.819i 1.61309i
\(583\) −231.543 −0.397158
\(584\) 42.9405 0.0735283
\(585\) 111.345i 0.190334i
\(586\) 175.644i 0.299735i
\(587\) −296.393 −0.504928 −0.252464 0.967606i \(-0.581241\pi\)
−0.252464 + 0.967606i \(0.581241\pi\)
\(588\) 403.352 0.685973
\(589\) 98.8912i 0.167897i
\(590\) 106.157i 0.179926i
\(591\) 121.486 0.205560
\(592\) 62.0992i 0.104897i
\(593\) 654.259 1.10330 0.551652 0.834075i \(-0.313998\pi\)
0.551652 + 0.834075i \(0.313998\pi\)
\(594\) 20.3287i 0.0342235i
\(595\) 51.8140i 0.0870824i
\(596\) 403.293i 0.676667i
\(597\) 923.881i 1.54754i
\(598\) 19.0224 168.500i 0.0318100 0.281773i
\(599\) 368.673 0.615480 0.307740 0.951470i \(-0.400427\pi\)
0.307740 + 0.951470i \(0.400427\pi\)
\(600\) −60.9125 −0.101521
\(601\) 148.316 0.246782 0.123391 0.992358i \(-0.460623\pi\)
0.123391 + 0.992358i \(0.460623\pi\)
\(602\) −79.6381 −0.132289
\(603\) 309.922i 0.513967i
\(604\) 241.573 0.399956
\(605\) 188.730i 0.311950i
\(606\) −358.535 −0.591643
\(607\) 939.932 1.54849 0.774244 0.632887i \(-0.218130\pi\)
0.774244 + 0.632887i \(0.218130\pi\)
\(608\) 27.3036i 0.0449072i
\(609\) 149.146i 0.244904i
\(610\) −318.021 −0.521346
\(611\) 72.0850 0.117979
\(612\) 300.043i 0.490267i
\(613\) 602.963i 0.983626i 0.870701 + 0.491813i \(0.163666\pi\)
−0.870701 + 0.491813i \(0.836334\pi\)
\(614\) 310.727 0.506069
\(615\) 195.601i 0.318050i
\(616\) −25.2440 −0.0409805
\(617\) 885.697i 1.43549i −0.696306 0.717745i \(-0.745174\pi\)
0.696306 0.717745i \(-0.254826\pi\)
\(618\) 330.549i 0.534869i
\(619\) 85.9838i 0.138908i −0.997585 0.0694538i \(-0.977874\pi\)
0.997585 0.0694538i \(-0.0221257\pi\)
\(620\) 91.6280i 0.147787i
\(621\) −6.13072 + 54.3060i −0.00987233 + 0.0874492i
\(622\) −448.403 −0.720905
\(623\) −163.819 −0.262951
\(624\) −89.8171 −0.143938
\(625\) 25.0000 0.0400000
\(626\) 685.404i 1.09489i
\(627\) 125.765 0.200583
\(628\) 389.794i 0.620692i
\(629\) −243.837 −0.387659
\(630\) 44.5622 0.0707337
\(631\) 645.385i 1.02280i 0.859344 + 0.511398i \(0.170872\pi\)
−0.859344 + 0.511398i \(0.829128\pi\)
\(632\) 31.7053i 0.0501666i
\(633\) 1034.85 1.63483
\(634\) −738.092 −1.16418
\(635\) 207.596i 0.326923i
\(636\) 329.706i 0.518406i
\(637\) −244.102 −0.383205
\(638\) 200.805i 0.314741i
\(639\) −230.488 −0.360701
\(640\) 25.2982i 0.0395285i
\(641\) 140.119i 0.218594i 0.994009 + 0.109297i \(0.0348599\pi\)
−0.994009 + 0.109297i \(0.965140\pi\)
\(642\) 725.613i 1.13024i
\(643\) 1028.11i 1.59892i 0.600718 + 0.799461i \(0.294882\pi\)
−0.600718 + 0.799461i \(0.705118\pi\)
\(644\) −67.4366 7.61306i −0.104715 0.0118215i
\(645\) 367.616 0.569948
\(646\) −107.210 −0.165959
\(647\) 1248.29 1.92934 0.964672 0.263455i \(-0.0848621\pi\)
0.964672 + 0.263455i \(0.0848621\pi\)
\(648\) −214.199 −0.330553
\(649\) 203.082i 0.312916i
\(650\) 36.8632 0.0567126
\(651\) 130.194i 0.199992i
\(652\) 307.625 0.471817
\(653\) −457.504 −0.700618 −0.350309 0.936634i \(-0.613923\pi\)
−0.350309 + 0.936634i \(0.613923\pi\)
\(654\) 908.956i 1.38984i
\(655\) 339.232i 0.517911i
\(656\) 81.2370 0.123837
\(657\) 145.011 0.220717
\(658\) 28.8496i 0.0438444i
\(659\) 173.014i 0.262540i −0.991347 0.131270i \(-0.958095\pi\)
0.991347 0.131270i \(-0.0419055\pi\)
\(660\) 116.529 0.176558
\(661\) 582.673i 0.881502i 0.897629 + 0.440751i \(0.145288\pi\)
−0.897629 + 0.440751i \(0.854712\pi\)
\(662\) −450.101 −0.679911
\(663\) 352.674i 0.531937i
\(664\) 124.821i 0.187984i
\(665\) 15.9227i 0.0239439i
\(666\) 209.710i 0.314880i
\(667\) 60.5585 536.428i 0.0907924 0.804240i
\(668\) 96.9899 0.145194
\(669\) 1108.67 1.65721
\(670\) 102.606 0.153144
\(671\) 608.389 0.906690
\(672\) 35.9463i 0.0534915i
\(673\) −390.678 −0.580502 −0.290251 0.956951i \(-0.593739\pi\)
−0.290251 + 0.956951i \(0.593739\pi\)
\(674\) 164.810i 0.244526i
\(675\) −11.8806 −0.0176009
\(676\) −283.644 −0.419592
\(677\) 952.947i 1.40760i 0.710397 + 0.703801i \(0.248515\pi\)
−0.710397 + 0.703801i \(0.751485\pi\)
\(678\) 215.228i 0.317445i
\(679\) 227.386 0.334883
\(680\) −99.3355 −0.146082
\(681\) 458.286i 0.672961i
\(682\) 175.289i 0.257022i
\(683\) 299.732 0.438847 0.219423 0.975630i \(-0.429582\pi\)
0.219423 + 0.975630i \(0.429582\pi\)
\(684\) 92.2048i 0.134802i
\(685\) −598.067 −0.873090
\(686\) 199.928i 0.291441i
\(687\) 1414.93i 2.05958i
\(688\) 152.679i 0.221917i
\(689\) 199.532i 0.289597i
\(690\) 311.293 + 35.1425i 0.451149 + 0.0509312i
\(691\) 165.585 0.239631 0.119815 0.992796i \(-0.461770\pi\)
0.119815 + 0.992796i \(0.461770\pi\)
\(692\) −222.538 −0.321587
\(693\) −85.2497 −0.123015
\(694\) −142.432 −0.205234
\(695\) 536.163i 0.771458i
\(696\) −285.937 −0.410829
\(697\) 318.984i 0.457652i
\(698\) 202.906 0.290696
\(699\) −642.685 −0.919436
\(700\) 14.7532i 0.0210761i
\(701\) 831.750i 1.18652i 0.805011 + 0.593260i \(0.202159\pi\)
−0.805011 + 0.593260i \(0.797841\pi\)
\(702\) −17.5183 −0.0249549
\(703\) −74.9324 −0.106590
\(704\) 48.3967i 0.0687453i
\(705\) 133.172i 0.188897i
\(706\) −388.052 −0.549649
\(707\) 86.8387i 0.122827i
\(708\) −289.180 −0.408446
\(709\) 835.784i 1.17882i −0.807834 0.589410i \(-0.799360\pi\)
0.807834 0.589410i \(-0.200640\pi\)
\(710\) 76.3077i 0.107476i
\(711\) 107.070i 0.150590i
\(712\) 314.066i 0.441104i
\(713\) 52.8634 468.265i 0.0741422 0.656753i
\(714\) 141.146 0.197683
\(715\) −70.5210 −0.0986308
\(716\) 525.180 0.733492
\(717\) −1478.08 −2.06148
\(718\) 674.397i 0.939272i
\(719\) 881.656 1.22623 0.613113 0.789996i \(-0.289917\pi\)
0.613113 + 0.789996i \(0.289917\pi\)
\(720\) 85.4327i 0.118657i
\(721\) −80.0602 −0.111041
\(722\) 477.585 0.661475
\(723\) 1502.12i 2.07762i
\(724\) 422.335i 0.583335i
\(725\) 117.356 0.161870
\(726\) 514.117 0.708150
\(727\) 531.577i 0.731193i 0.930774 + 0.365596i \(0.119135\pi\)
−0.930774 + 0.365596i \(0.880865\pi\)
\(728\) 21.7541i 0.0298820i
\(729\) −815.463 −1.11861
\(730\) 48.0090i 0.0657657i
\(731\) 599.505 0.820116
\(732\) 866.318i 1.18349i
\(733\) 18.4847i 0.0252178i 0.999921 + 0.0126089i \(0.00401364\pi\)
−0.999921 + 0.0126089i \(0.995986\pi\)
\(734\) 19.8441i 0.0270356i
\(735\) 450.962i 0.613553i
\(736\) −14.5954 + 129.286i −0.0198307 + 0.175661i
\(737\) −196.290 −0.266337
\(738\) 274.339 0.371734
\(739\) −960.371 −1.29955 −0.649777 0.760125i \(-0.725138\pi\)
−0.649777 + 0.760125i \(0.725138\pi\)
\(740\) −69.4290 −0.0938229
\(741\) 108.379i 0.146260i
\(742\) −79.8562 −0.107623
\(743\) 248.966i 0.335082i −0.985865 0.167541i \(-0.946417\pi\)
0.985865 0.167541i \(-0.0535826\pi\)
\(744\) −249.603 −0.335488
\(745\) 450.896 0.605229
\(746\) 149.429i 0.200307i
\(747\) 421.524i 0.564289i
\(748\) 190.034 0.254056
\(749\) 175.746 0.234641
\(750\) 68.1023i 0.0908030i
\(751\) 24.0757i 0.0320582i −0.999872 0.0160291i \(-0.994898\pi\)
0.999872 0.0160291i \(-0.00510244\pi\)
\(752\) −55.3091 −0.0735494
\(753\) 969.539i 1.28757i
\(754\) 173.044 0.229501
\(755\) 270.087i 0.357731i
\(756\) 7.01112i 0.00927396i
\(757\) 914.334i 1.20784i −0.797045 0.603920i \(-0.793605\pi\)
0.797045 0.603920i \(-0.206395\pi\)
\(758\) 480.809i 0.634312i
\(759\) −595.518 67.2294i −0.784609 0.0885762i
\(760\) −30.5263 −0.0401662
\(761\) 313.770 0.412312 0.206156 0.978519i \(-0.433905\pi\)
0.206156 + 0.978519i \(0.433905\pi\)
\(762\) 565.511 0.742140
\(763\) −220.153 −0.288536
\(764\) 145.642i 0.190631i
\(765\) −335.458 −0.438508
\(766\) 989.662i 1.29199i
\(767\) 175.007 0.228170
\(768\) 68.9146 0.0897326
\(769\) 309.335i 0.402257i 0.979565 + 0.201128i \(0.0644608\pi\)
−0.979565 + 0.201128i \(0.935539\pi\)
\(770\) 28.2237i 0.0366541i
\(771\) −1695.44 −2.19901
\(772\) 397.099 0.514377
\(773\) 233.356i 0.301884i −0.988543 0.150942i \(-0.951769\pi\)
0.988543 0.150942i \(-0.0482306\pi\)
\(774\) 515.599i 0.666149i
\(775\) 102.443 0.132185
\(776\) 435.934i 0.561770i
\(777\) 98.6518 0.126965
\(778\) 176.518i 0.226887i
\(779\) 98.0253i 0.125835i
\(780\) 100.419i 0.128742i
\(781\) 145.980i 0.186915i
\(782\) 507.653 + 57.3101i 0.649173 + 0.0732866i
\(783\) −55.7703 −0.0712265
\(784\) 187.294 0.238895
\(785\) −435.803 −0.555164
\(786\) 924.098 1.17570
\(787\) 690.751i 0.877702i −0.898560 0.438851i \(-0.855386\pi\)
0.898560 0.438851i