Properties

Label 690.3.f.a.229.16
Level $690$
Weight $3$
Character 690.229
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 229.16
Character \(\chi\) \(=\) 690.229
Dual form 690.3.f.a.229.14

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(4.27075 - 2.60014i) q^{5} +2.44949 q^{6} +3.19570 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(4.27075 - 2.60014i) q^{5} +2.44949 q^{6} +3.19570 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(3.67715 + 6.03975i) q^{10} +11.2032i q^{11} +3.46410i q^{12} +14.7022i q^{13} +4.51940i q^{14} +(-4.50357 - 7.39715i) q^{15} +4.00000 q^{16} +10.6897 q^{17} -4.24264i q^{18} +9.81553i q^{19} +(-8.54150 + 5.20027i) q^{20} -5.53511i q^{21} -15.8437 q^{22} +(-22.2781 + 5.71720i) q^{23} -4.89898 q^{24} +(11.4786 - 22.2091i) q^{25} -20.7920 q^{26} +5.19615i q^{27} -6.39140 q^{28} +24.7684 q^{29} +(10.4612 - 6.36901i) q^{30} +37.7890 q^{31} +5.65685i q^{32} +19.4044 q^{33} +15.1176i q^{34} +(13.6480 - 8.30925i) q^{35} +6.00000 q^{36} +45.5299 q^{37} -13.8813 q^{38} +25.4649 q^{39} +(-7.35430 - 12.0795i) q^{40} +57.0782 q^{41} +7.82783 q^{42} -15.9581 q^{43} -22.4063i q^{44} +(-12.8122 + 7.80041i) q^{45} +(-8.08534 - 31.5060i) q^{46} -12.7398i q^{47} -6.92820i q^{48} -38.7875 q^{49} +(31.4083 + 16.2332i) q^{50} -18.5152i q^{51} -29.4043i q^{52} -62.0971 q^{53} -7.34847 q^{54} +(29.1297 + 47.8459i) q^{55} -9.03880i q^{56} +17.0010 q^{57} +35.0278i q^{58} +76.6723 q^{59} +(9.00714 + 14.7943i) q^{60} -39.0469i q^{61} +53.4418i q^{62} -9.58710 q^{63} -8.00000 q^{64} +(38.2276 + 62.7892i) q^{65} +27.4420i q^{66} +18.2212 q^{67} -21.3795 q^{68} +(9.90248 + 38.5868i) q^{69} +(11.7511 + 19.3012i) q^{70} +94.9316 q^{71} +8.48528i q^{72} -8.59349i q^{73} +64.3891i q^{74} +(-38.4672 - 19.8815i) q^{75} -19.6311i q^{76} +35.8019i q^{77} +36.0128i q^{78} +96.9457i q^{79} +(17.0830 - 10.4005i) q^{80} +9.00000 q^{81} +80.7208i q^{82} -69.0270 q^{83} +11.0702i q^{84} +(45.6532 - 27.7948i) q^{85} -22.5682i q^{86} -42.9001i q^{87} +31.6873 q^{88} +91.6181i q^{89} +(-11.0314 - 18.1193i) q^{90} +46.9837i q^{91} +(44.5562 - 11.4344i) q^{92} -65.4525i q^{93} +18.0168 q^{94} +(25.5217 + 41.9196i) q^{95} +9.79796 q^{96} -99.7353 q^{97} -54.8538i q^{98} -33.6095i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 96q^{4} - 144q^{9} + O(q^{10}) \) \( 48q - 96q^{4} - 144q^{9} + 192q^{16} + 96q^{25} + 64q^{26} - 152q^{29} - 8q^{31} + 56q^{35} + 288q^{36} - 48q^{39} + 40q^{41} - 160q^{46} + 424q^{49} + 96q^{50} + 32q^{55} + 360q^{59} - 384q^{64} + 192q^{69} - 496q^{70} - 152q^{71} + 144q^{75} + 432q^{81} - 136q^{85} + 256q^{94} + 496q^{95} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 1.73205i 0.577350i
\(4\) −2.00000 −0.500000
\(5\) 4.27075 2.60014i 0.854150 0.520027i
\(6\) 2.44949 0.408248
\(7\) 3.19570 0.456529 0.228264 0.973599i \(-0.426695\pi\)
0.228264 + 0.973599i \(0.426695\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −3.00000 −0.333333
\(10\) 3.67715 + 6.03975i 0.367715 + 0.603975i
\(11\) 11.2032i 1.01847i 0.860628 + 0.509234i \(0.170071\pi\)
−0.860628 + 0.509234i \(0.829929\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 14.7022i 1.13094i 0.824771 + 0.565468i \(0.191304\pi\)
−0.824771 + 0.565468i \(0.808696\pi\)
\(14\) 4.51940i 0.322814i
\(15\) −4.50357 7.39715i −0.300238 0.493144i
\(16\) 4.00000 0.250000
\(17\) 10.6897 0.628808 0.314404 0.949289i \(-0.398195\pi\)
0.314404 + 0.949289i \(0.398195\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 9.81553i 0.516607i 0.966064 + 0.258303i \(0.0831634\pi\)
−0.966064 + 0.258303i \(0.916837\pi\)
\(20\) −8.54150 + 5.20027i −0.427075 + 0.260014i
\(21\) 5.53511i 0.263577i
\(22\) −15.8437 −0.720166
\(23\) −22.2781 + 5.71720i −0.968613 + 0.248574i
\(24\) −4.89898 −0.204124
\(25\) 11.4786 22.2091i 0.459143 0.888362i
\(26\) −20.7920 −0.799692
\(27\) 5.19615i 0.192450i
\(28\) −6.39140 −0.228264
\(29\) 24.7684 0.854083 0.427042 0.904232i \(-0.359556\pi\)
0.427042 + 0.904232i \(0.359556\pi\)
\(30\) 10.4612 6.36901i 0.348705 0.212300i
\(31\) 37.7890 1.21900 0.609501 0.792786i \(-0.291370\pi\)
0.609501 + 0.792786i \(0.291370\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 19.4044 0.588013
\(34\) 15.1176i 0.444635i
\(35\) 13.6480 8.30925i 0.389944 0.237407i
\(36\) 6.00000 0.166667
\(37\) 45.5299 1.23054 0.615269 0.788317i \(-0.289047\pi\)
0.615269 + 0.788317i \(0.289047\pi\)
\(38\) −13.8813 −0.365296
\(39\) 25.4649 0.652946
\(40\) −7.35430 12.0795i −0.183857 0.301988i
\(41\) 57.0782 1.39215 0.696076 0.717968i \(-0.254928\pi\)
0.696076 + 0.717968i \(0.254928\pi\)
\(42\) 7.82783 0.186377
\(43\) −15.9581 −0.371119 −0.185560 0.982633i \(-0.559410\pi\)
−0.185560 + 0.982633i \(0.559410\pi\)
\(44\) 22.4063i 0.509234i
\(45\) −12.8122 + 7.80041i −0.284717 + 0.173342i
\(46\) −8.08534 31.5060i −0.175768 0.684913i
\(47\) 12.7398i 0.271060i −0.990773 0.135530i \(-0.956726\pi\)
0.990773 0.135530i \(-0.0432737\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −38.7875 −0.791582
\(50\) 31.4083 + 16.2332i 0.628167 + 0.324663i
\(51\) 18.5152i 0.363043i
\(52\) 29.4043i 0.565468i
\(53\) −62.0971 −1.17164 −0.585822 0.810440i \(-0.699228\pi\)
−0.585822 + 0.810440i \(0.699228\pi\)
\(54\) −7.34847 −0.136083
\(55\) 29.1297 + 47.8459i 0.529632 + 0.869925i
\(56\) 9.03880i 0.161407i
\(57\) 17.0010 0.298263
\(58\) 35.0278i 0.603928i
\(59\) 76.6723 1.29953 0.649765 0.760135i \(-0.274867\pi\)
0.649765 + 0.760135i \(0.274867\pi\)
\(60\) 9.00714 + 14.7943i 0.150119 + 0.246572i
\(61\) 39.0469i 0.640113i −0.947398 0.320057i \(-0.896298\pi\)
0.947398 0.320057i \(-0.103702\pi\)
\(62\) 53.4418i 0.861964i
\(63\) −9.58710 −0.152176
\(64\) −8.00000 −0.125000
\(65\) 38.2276 + 62.7892i 0.588117 + 0.965988i
\(66\) 27.4420i 0.415788i
\(67\) 18.2212 0.271958 0.135979 0.990712i \(-0.456582\pi\)
0.135979 + 0.990712i \(0.456582\pi\)
\(68\) −21.3795 −0.314404
\(69\) 9.90248 + 38.5868i 0.143514 + 0.559229i
\(70\) 11.7511 + 19.3012i 0.167872 + 0.275732i
\(71\) 94.9316 1.33707 0.668533 0.743683i \(-0.266923\pi\)
0.668533 + 0.743683i \(0.266923\pi\)
\(72\) 8.48528i 0.117851i
\(73\) 8.59349i 0.117719i −0.998266 0.0588595i \(-0.981254\pi\)
0.998266 0.0588595i \(-0.0187464\pi\)
\(74\) 64.3891i 0.870122i
\(75\) −38.4672 19.8815i −0.512896 0.265087i
\(76\) 19.6311i 0.258303i
\(77\) 35.8019i 0.464960i
\(78\) 36.0128i 0.461702i
\(79\) 96.9457i 1.22716i 0.789632 + 0.613580i \(0.210271\pi\)
−0.789632 + 0.613580i \(0.789729\pi\)
\(80\) 17.0830 10.4005i 0.213537 0.130007i
\(81\) 9.00000 0.111111
\(82\) 80.7208i 0.984400i
\(83\) −69.0270 −0.831651 −0.415825 0.909444i \(-0.636507\pi\)
−0.415825 + 0.909444i \(0.636507\pi\)
\(84\) 11.0702i 0.131788i
\(85\) 45.6532 27.7948i 0.537096 0.326997i
\(86\) 22.5682i 0.262421i
\(87\) 42.9001i 0.493105i
\(88\) 31.6873 0.360083
\(89\) 91.6181i 1.02942i 0.857365 + 0.514708i \(0.172100\pi\)
−0.857365 + 0.514708i \(0.827900\pi\)
\(90\) −11.0314 18.1193i −0.122572 0.201325i
\(91\) 46.9837i 0.516304i
\(92\) 44.5562 11.4344i 0.484306 0.124287i
\(93\) 65.4525i 0.703791i
\(94\) 18.0168 0.191668
\(95\) 25.5217 + 41.9196i 0.268650 + 0.441259i
\(96\) 9.79796 0.102062
\(97\) −99.7353 −1.02820 −0.514099 0.857731i \(-0.671874\pi\)
−0.514099 + 0.857731i \(0.671874\pi\)
\(98\) 54.8538i 0.559733i
\(99\) 33.6095i 0.339490i
\(100\) −22.9572 + 44.4181i −0.229572 + 0.444181i
\(101\) 24.8729 0.246267 0.123133 0.992390i \(-0.460706\pi\)
0.123133 + 0.992390i \(0.460706\pi\)
\(102\) 26.1844 0.256710
\(103\) −40.9185 −0.397267 −0.198633 0.980074i \(-0.563650\pi\)
−0.198633 + 0.980074i \(0.563650\pi\)
\(104\) 41.5840 0.399846
\(105\) −14.3921 23.6391i −0.137067 0.225134i
\(106\) 87.8185i 0.828477i
\(107\) 17.8171 0.166515 0.0832575 0.996528i \(-0.473468\pi\)
0.0832575 + 0.996528i \(0.473468\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 73.8190i 0.677239i −0.940923 0.338619i \(-0.890040\pi\)
0.940923 0.338619i \(-0.109960\pi\)
\(110\) −67.6643 + 41.1957i −0.615130 + 0.374506i
\(111\) 78.8602i 0.710452i
\(112\) 12.7828 0.114132
\(113\) 118.752 1.05090 0.525450 0.850824i \(-0.323897\pi\)
0.525450 + 0.850824i \(0.323897\pi\)
\(114\) 24.0430i 0.210904i
\(115\) −80.2786 + 82.3428i −0.698075 + 0.716024i
\(116\) −49.5368 −0.427042
\(117\) 44.1065i 0.376978i
\(118\) 108.431i 0.918906i
\(119\) 34.1612 0.287069
\(120\) −20.9223 + 12.7380i −0.174353 + 0.106150i
\(121\) −4.51074 −0.0372788
\(122\) 55.2207 0.452628
\(123\) 98.8624i 0.803759i
\(124\) −75.5781 −0.609501
\(125\) −8.72443 124.695i −0.0697955 0.997561i
\(126\) 13.5582i 0.107605i
\(127\) 137.061i 1.07922i 0.841916 + 0.539609i \(0.181428\pi\)
−0.841916 + 0.539609i \(0.818572\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 27.6403i 0.214266i
\(130\) −88.7973 + 54.0620i −0.683057 + 0.415862i
\(131\) 56.4354 0.430805 0.215402 0.976525i \(-0.430894\pi\)
0.215402 + 0.976525i \(0.430894\pi\)
\(132\) −38.8089 −0.294007
\(133\) 31.3675i 0.235846i
\(134\) 25.7686i 0.192303i
\(135\) 13.5107 + 22.1915i 0.100079 + 0.164381i
\(136\) 30.2352i 0.222317i
\(137\) 185.263 1.35228 0.676141 0.736772i \(-0.263651\pi\)
0.676141 + 0.736772i \(0.263651\pi\)
\(138\) −54.5700 + 14.0042i −0.395435 + 0.101480i
\(139\) −216.501 −1.55756 −0.778780 0.627297i \(-0.784161\pi\)
−0.778780 + 0.627297i \(0.784161\pi\)
\(140\) −27.2961 + 16.6185i −0.194972 + 0.118704i
\(141\) −22.0660 −0.156496
\(142\) 134.254i 0.945448i
\(143\) −164.711 −1.15182
\(144\) −12.0000 −0.0833333
\(145\) 105.780 64.4012i 0.729515 0.444147i
\(146\) 12.1530 0.0832399
\(147\) 67.1819i 0.457020i
\(148\) −91.0599 −0.615269
\(149\) 42.7648i 0.287012i −0.989649 0.143506i \(-0.954162\pi\)
0.989649 0.143506i \(-0.0458377\pi\)
\(150\) 28.1167 54.4009i 0.187444 0.362672i
\(151\) −232.802 −1.54173 −0.770867 0.636996i \(-0.780177\pi\)
−0.770867 + 0.636996i \(0.780177\pi\)
\(152\) 27.7625 0.182648
\(153\) −32.0692 −0.209603
\(154\) −50.6316 −0.328776
\(155\) 161.387 98.2566i 1.04121 0.633914i
\(156\) −50.9298 −0.326473
\(157\) −225.331 −1.43523 −0.717613 0.696442i \(-0.754765\pi\)
−0.717613 + 0.696442i \(0.754765\pi\)
\(158\) −137.102 −0.867733
\(159\) 107.555i 0.676448i
\(160\) 14.7086 + 24.1590i 0.0919287 + 0.150994i
\(161\) −71.1941 + 18.2705i −0.442199 + 0.113481i
\(162\) 12.7279i 0.0785674i
\(163\) 160.569i 0.985086i −0.870288 0.492543i \(-0.836067\pi\)
0.870288 0.492543i \(-0.163933\pi\)
\(164\) −114.156 −0.696076
\(165\) 82.8715 50.4542i 0.502251 0.305783i
\(166\) 97.6189i 0.588066i
\(167\) 168.699i 1.01017i −0.863069 0.505086i \(-0.831461\pi\)
0.863069 0.505086i \(-0.168539\pi\)
\(168\) −15.6557 −0.0931885
\(169\) −47.1534 −0.279014
\(170\) 39.3078 + 64.5634i 0.231222 + 0.379784i
\(171\) 29.4466i 0.172202i
\(172\) 31.9162 0.185560
\(173\) 48.8655i 0.282460i 0.989977 + 0.141230i \(0.0451057\pi\)
−0.989977 + 0.141230i \(0.954894\pi\)
\(174\) 60.6700 0.348678
\(175\) 36.6821 70.9735i 0.209612 0.405563i
\(176\) 44.8126i 0.254617i
\(177\) 132.800i 0.750284i
\(178\) −129.568 −0.727908
\(179\) 141.731 0.791794 0.395897 0.918295i \(-0.370434\pi\)
0.395897 + 0.918295i \(0.370434\pi\)
\(180\) 25.6245 15.6008i 0.142358 0.0866712i
\(181\) 97.7581i 0.540100i 0.962846 + 0.270050i \(0.0870402\pi\)
−0.962846 + 0.270050i \(0.912960\pi\)
\(182\) −66.4449 −0.365082
\(183\) −67.6312 −0.369570
\(184\) 16.1707 + 63.0120i 0.0878841 + 0.342456i
\(185\) 194.447 118.384i 1.05106 0.639914i
\(186\) 92.5639 0.497655
\(187\) 119.759i 0.640422i
\(188\) 25.4796i 0.135530i
\(189\) 16.6053i 0.0878590i
\(190\) −59.2833 + 36.0931i −0.312018 + 0.189964i
\(191\) 93.5071i 0.489566i −0.969578 0.244783i \(-0.921283\pi\)
0.969578 0.244783i \(-0.0787167\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 39.3466i 0.203869i 0.994791 + 0.101934i \(0.0325031\pi\)
−0.994791 + 0.101934i \(0.967497\pi\)
\(194\) 141.047i 0.727046i
\(195\) 108.754 66.2122i 0.557713 0.339550i
\(196\) 77.5750 0.395791
\(197\) 327.431i 1.66209i −0.556208 0.831043i \(-0.687744\pi\)
0.556208 0.831043i \(-0.312256\pi\)
\(198\) 47.5310 0.240055
\(199\) 174.324i 0.876001i 0.898975 + 0.438000i \(0.144313\pi\)
−0.898975 + 0.438000i \(0.855687\pi\)
\(200\) −62.8167 32.4663i −0.314083 0.162332i
\(201\) 31.5600i 0.157015i
\(202\) 35.1756i 0.174137i
\(203\) 79.1524 0.389913
\(204\) 37.0303i 0.181521i
\(205\) 243.767 148.411i 1.18911 0.723957i
\(206\) 57.8674i 0.280910i
\(207\) 66.8343 17.1516i 0.322871 0.0828580i
\(208\) 58.8086i 0.282734i
\(209\) −109.965 −0.526148
\(210\) 33.4307 20.3534i 0.159194 0.0969211i
\(211\) −276.060 −1.30834 −0.654170 0.756348i \(-0.726982\pi\)
−0.654170 + 0.756348i \(0.726982\pi\)
\(212\) 124.194 0.585822
\(213\) 164.426i 0.771955i
\(214\) 25.1972i 0.117744i
\(215\) −68.1531 + 41.4933i −0.316991 + 0.192992i
\(216\) 14.6969 0.0680414
\(217\) 120.762 0.556509
\(218\) 104.396 0.478880
\(219\) −14.8844 −0.0679651
\(220\) −58.2595 95.6917i −0.264816 0.434962i
\(221\) 157.162i 0.711141i
\(222\) 111.525 0.502365
\(223\) 239.528i 1.07412i 0.843545 + 0.537059i \(0.180465\pi\)
−0.843545 + 0.537059i \(0.819535\pi\)
\(224\) 18.0776i 0.0807036i
\(225\) −34.4357 + 66.6272i −0.153048 + 0.296121i
\(226\) 167.940i 0.743099i
\(227\) −164.561 −0.724936 −0.362468 0.931996i \(-0.618066\pi\)
−0.362468 + 0.931996i \(0.618066\pi\)
\(228\) −34.0020 −0.149132
\(229\) 88.8399i 0.387947i −0.981007 0.193974i \(-0.937862\pi\)
0.981007 0.193974i \(-0.0621376\pi\)
\(230\) −116.450 113.531i −0.506306 0.493614i
\(231\) 62.0108 0.268445
\(232\) 70.0557i 0.301964i
\(233\) 206.041i 0.884296i −0.896942 0.442148i \(-0.854217\pi\)
0.896942 0.442148i \(-0.145783\pi\)
\(234\) 62.3760 0.266564
\(235\) −33.1252 54.4085i −0.140958 0.231526i
\(236\) −153.345 −0.649765
\(237\) 167.915 0.708501
\(238\) 48.3112i 0.202988i
\(239\) 153.776 0.643413 0.321706 0.946839i \(-0.395744\pi\)
0.321706 + 0.946839i \(0.395744\pi\)
\(240\) −18.0143 29.5886i −0.0750595 0.123286i
\(241\) 390.573i 1.62063i −0.585991 0.810317i \(-0.699295\pi\)
0.585991 0.810317i \(-0.300705\pi\)
\(242\) 6.37914i 0.0263601i
\(243\) 15.5885i 0.0641500i
\(244\) 78.0938i 0.320057i
\(245\) −165.652 + 100.853i −0.676129 + 0.411644i
\(246\) 139.813 0.568344
\(247\) −144.309 −0.584249
\(248\) 106.884i 0.430982i
\(249\) 119.558i 0.480154i
\(250\) 176.346 12.3382i 0.705382 0.0493529i
\(251\) 403.416i 1.60723i 0.595147 + 0.803617i \(0.297094\pi\)
−0.595147 + 0.803617i \(0.702906\pi\)
\(252\) 19.1742 0.0760881
\(253\) −64.0507 249.585i −0.253165 0.986502i
\(254\) −193.833 −0.763122
\(255\) −48.1420 79.0736i −0.188792 0.310093i
\(256\) 16.0000 0.0625000
\(257\) 310.575i 1.20846i −0.796809 0.604231i \(-0.793480\pi\)
0.796809 0.604231i \(-0.206520\pi\)
\(258\) −39.0893 −0.151509
\(259\) 145.500 0.561776
\(260\) −76.4552 125.578i −0.294059 0.482994i
\(261\) −74.3052 −0.284694
\(262\) 79.8117i 0.304625i
\(263\) −222.756 −0.846980 −0.423490 0.905901i \(-0.639195\pi\)
−0.423490 + 0.905901i \(0.639195\pi\)
\(264\) 54.8840i 0.207894i
\(265\) −265.201 + 161.461i −1.00076 + 0.609286i
\(266\) −44.3603 −0.166768
\(267\) 158.687 0.594334
\(268\) −36.4423 −0.135979
\(269\) 42.0265 0.156232 0.0781161 0.996944i \(-0.475110\pi\)
0.0781161 + 0.996944i \(0.475110\pi\)
\(270\) −31.3835 + 19.1070i −0.116235 + 0.0707667i
\(271\) 170.649 0.629700 0.314850 0.949141i \(-0.398046\pi\)
0.314850 + 0.949141i \(0.398046\pi\)
\(272\) 42.7590 0.157202
\(273\) 81.3781 0.298088
\(274\) 262.001i 0.956208i
\(275\) 248.812 + 128.596i 0.904769 + 0.467623i
\(276\) −19.8050 77.1736i −0.0717571 0.279614i
\(277\) 412.691i 1.48986i −0.667143 0.744930i \(-0.732483\pi\)
0.667143 0.744930i \(-0.267517\pi\)
\(278\) 306.178i 1.10136i
\(279\) −113.367 −0.406334
\(280\) −23.5021 38.6025i −0.0839361 0.137866i
\(281\) 20.8145i 0.0740729i 0.999314 + 0.0370364i \(0.0117918\pi\)
−0.999314 + 0.0370364i \(0.988208\pi\)
\(282\) 31.2060i 0.110660i
\(283\) −402.588 −1.42257 −0.711286 0.702903i \(-0.751887\pi\)
−0.711286 + 0.702903i \(0.751887\pi\)
\(284\) −189.863 −0.668533
\(285\) 72.6070 44.2049i 0.254761 0.155105i
\(286\) 232.936i 0.814461i
\(287\) 182.405 0.635557
\(288\) 16.9706i 0.0589256i
\(289\) −174.729 −0.604600
\(290\) 91.0771 + 149.595i 0.314059 + 0.515845i
\(291\) 172.747i 0.593631i
\(292\) 17.1870i 0.0588595i
\(293\) −107.231 −0.365977 −0.182988 0.983115i \(-0.558577\pi\)
−0.182988 + 0.983115i \(0.558577\pi\)
\(294\) −95.0096 −0.323162
\(295\) 327.448 199.358i 1.10999 0.675791i
\(296\) 128.778i 0.435061i
\(297\) −58.2133 −0.196004
\(298\) 60.4786 0.202948
\(299\) −84.0552 327.536i −0.281121 1.09544i
\(300\) 76.9344 + 39.7630i 0.256448 + 0.132543i
\(301\) −50.9974 −0.169426
\(302\) 329.231i 1.09017i
\(303\) 43.0812i 0.142182i
\(304\) 39.2621i 0.129152i
\(305\) −101.527 166.760i −0.332876 0.546753i
\(306\) 45.3527i 0.148212i
\(307\) 225.517i 0.734582i 0.930106 + 0.367291i \(0.119715\pi\)
−0.930106 + 0.367291i \(0.880285\pi\)
\(308\) 71.6039i 0.232480i
\(309\) 70.8729i 0.229362i
\(310\) 138.956 + 228.236i 0.448245 + 0.736246i
\(311\) −284.663 −0.915314 −0.457657 0.889129i \(-0.651311\pi\)
−0.457657 + 0.889129i \(0.651311\pi\)
\(312\) 72.0256i 0.230851i
\(313\) 152.480 0.487158 0.243579 0.969881i \(-0.421679\pi\)
0.243579 + 0.969881i \(0.421679\pi\)
\(314\) 318.665i 1.01486i
\(315\) −40.9441 + 24.9278i −0.129981 + 0.0791358i
\(316\) 193.891i 0.613580i
\(317\) 570.042i 1.79824i 0.437704 + 0.899119i \(0.355792\pi\)
−0.437704 + 0.899119i \(0.644208\pi\)
\(318\) −152.106 −0.478321
\(319\) 277.484i 0.869857i
\(320\) −34.1660 + 20.8011i −0.106769 + 0.0650034i
\(321\) 30.8601i 0.0961375i
\(322\) −25.8383 100.684i −0.0802432 0.312682i
\(323\) 104.925i 0.324847i
\(324\) −18.0000 −0.0555556
\(325\) 326.521 + 168.760i 1.00468 + 0.519261i
\(326\) 227.079 0.696561
\(327\) −127.858 −0.391004
\(328\) 161.442i 0.492200i
\(329\) 40.7126i 0.123747i
\(330\) 71.3530 + 117.198i 0.216221 + 0.355145i
\(331\) 124.401 0.375835 0.187917 0.982185i \(-0.439826\pi\)
0.187917 + 0.982185i \(0.439826\pi\)
\(332\) 138.054 0.415825
\(333\) −136.590 −0.410180
\(334\) 238.576 0.714300
\(335\) 77.8180 47.3775i 0.232292 0.141425i
\(336\) 22.1405i 0.0658942i
\(337\) −214.663 −0.636983 −0.318491 0.947926i \(-0.603176\pi\)
−0.318491 + 0.947926i \(0.603176\pi\)
\(338\) 66.6849i 0.197293i
\(339\) 205.684i 0.606738i
\(340\) −91.3064 + 55.5896i −0.268548 + 0.163499i
\(341\) 423.356i 1.24151i
\(342\) 41.6438 0.121765
\(343\) −280.542 −0.817908
\(344\) 45.1364i 0.131210i
\(345\) 142.622 + 139.047i 0.413397 + 0.403034i
\(346\) −69.1063 −0.199729
\(347\) 550.835i 1.58742i 0.608296 + 0.793710i \(0.291853\pi\)
−0.608296 + 0.793710i \(0.708147\pi\)
\(348\) 85.8003i 0.246553i
\(349\) −369.105 −1.05761 −0.528804 0.848744i \(-0.677359\pi\)
−0.528804 + 0.848744i \(0.677359\pi\)
\(350\) 100.372 + 51.8763i 0.286776 + 0.148218i
\(351\) −76.3946 −0.217649
\(352\) −63.3746 −0.180042
\(353\) 414.260i 1.17354i −0.809753 0.586770i \(-0.800399\pi\)
0.809753 0.586770i \(-0.199601\pi\)
\(354\) 187.808 0.530531
\(355\) 405.429 246.835i 1.14205 0.695311i
\(356\) 183.236i 0.514708i
\(357\) 59.1689i 0.165739i
\(358\) 200.438i 0.559883i
\(359\) 285.478i 0.795202i −0.917558 0.397601i \(-0.869843\pi\)
0.917558 0.397601i \(-0.130157\pi\)
\(360\) 22.0629 + 36.2385i 0.0612858 + 0.100663i
\(361\) 264.655 0.733118
\(362\) −138.251 −0.381908
\(363\) 7.81282i 0.0215229i
\(364\) 93.9673i 0.258152i
\(365\) −22.3442 36.7006i −0.0612171 0.100550i
\(366\) 95.6450i 0.261325i
\(367\) 273.124 0.744208 0.372104 0.928191i \(-0.378637\pi\)
0.372104 + 0.928191i \(0.378637\pi\)
\(368\) −89.1124 + 22.8688i −0.242153 + 0.0621435i
\(369\) −171.235 −0.464051
\(370\) 167.420 + 274.989i 0.452487 + 0.743215i
\(371\) −198.444 −0.534888
\(372\) 130.905i 0.351895i
\(373\) −481.201 −1.29008 −0.645042 0.764147i \(-0.723160\pi\)
−0.645042 + 0.764147i \(0.723160\pi\)
\(374\) −169.365 −0.452846
\(375\) −215.978 + 15.1112i −0.575942 + 0.0402964i
\(376\) −36.0336 −0.0958341
\(377\) 364.149i 0.965913i
\(378\) −23.4835 −0.0621257
\(379\) 502.144i 1.32492i −0.749098 0.662459i \(-0.769513\pi\)
0.749098 0.662459i \(-0.230487\pi\)
\(380\) −51.0434 83.8393i −0.134325 0.220630i
\(381\) 237.396 0.623087
\(382\) 132.239 0.346175
\(383\) −579.743 −1.51369 −0.756844 0.653595i \(-0.773260\pi\)
−0.756844 + 0.653595i \(0.773260\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 93.0899 + 152.901i 0.241792 + 0.397145i
\(386\) −55.6445 −0.144157
\(387\) 47.8744 0.123706
\(388\) 199.471 0.514099
\(389\) 282.311i 0.725736i 0.931841 + 0.362868i \(0.118202\pi\)
−0.931841 + 0.362868i \(0.881798\pi\)
\(390\) 93.6381 + 153.802i 0.240098 + 0.394363i
\(391\) −238.147 + 61.1154i −0.609072 + 0.156305i
\(392\) 109.708i 0.279866i
\(393\) 97.7490i 0.248725i
\(394\) 463.057 1.17527
\(395\) 252.072 + 414.031i 0.638157 + 1.04818i
\(396\) 67.2189i 0.169745i
\(397\) 44.7863i 0.112812i −0.998408 0.0564059i \(-0.982036\pi\)
0.998408 0.0564059i \(-0.0179641\pi\)
\(398\) −246.532 −0.619426
\(399\) 54.3301 0.136166
\(400\) 45.9143 88.8362i 0.114786 0.222091i
\(401\) 176.453i 0.440032i −0.975496 0.220016i \(-0.929389\pi\)
0.975496 0.220016i \(-0.0706110\pi\)
\(402\) 44.6325 0.111026
\(403\) 555.580i 1.37861i
\(404\) −49.7459 −0.123133
\(405\) 38.4367 23.4012i 0.0949055 0.0577808i
\(406\) 111.938i 0.275710i
\(407\) 510.079i 1.25327i
\(408\) −52.3688 −0.128355
\(409\) 546.610 1.33645 0.668227 0.743957i \(-0.267053\pi\)
0.668227 + 0.743957i \(0.267053\pi\)
\(410\) 209.885 + 344.738i 0.511915 + 0.840825i
\(411\) 320.884i 0.780741i
\(412\) 81.8369 0.198633
\(413\) 245.021 0.593272
\(414\) 24.2560 + 94.5180i 0.0585894 + 0.228304i
\(415\) −294.797 + 179.480i −0.710354 + 0.432481i
\(416\) −83.1679 −0.199923
\(417\) 374.990i 0.899258i
\(418\) 155.514i 0.372043i
\(419\) 695.370i 1.65959i −0.558066 0.829797i \(-0.688456\pi\)
0.558066 0.829797i \(-0.311544\pi\)
\(420\) 28.7841 + 47.2782i 0.0685336 + 0.112567i
\(421\) 376.599i 0.894534i 0.894400 + 0.447267i \(0.147603\pi\)
−0.894400 + 0.447267i \(0.852397\pi\)
\(422\) 390.407i 0.925136i
\(423\) 38.2194i 0.0903533i
\(424\) 175.637i 0.414238i
\(425\) 122.703 237.409i 0.288713 0.558609i
\(426\) 232.534 0.545855
\(427\) 124.782i 0.292230i
\(428\) −35.6342 −0.0832575
\(429\) 285.287i 0.665005i
\(430\) −58.6804 96.3831i −0.136466 0.224147i
\(431\) 717.791i 1.66541i 0.553718 + 0.832704i \(0.313208\pi\)
−0.553718 + 0.832704i \(0.686792\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) −426.428 −0.984823 −0.492411 0.870363i \(-0.663884\pi\)
−0.492411 + 0.870363i \(0.663884\pi\)
\(434\) 170.784i 0.393511i
\(435\) −111.546 183.216i −0.256428 0.421186i
\(436\) 147.638i 0.338619i
\(437\) −56.1173 218.671i −0.128415 0.500392i
\(438\) 21.0497i 0.0480586i
\(439\) −454.954 −1.03634 −0.518171 0.855277i \(-0.673387\pi\)
−0.518171 + 0.855277i \(0.673387\pi\)
\(440\) 135.329 82.3913i 0.307565 0.187253i
\(441\) 116.363 0.263861
\(442\) −222.261 −0.502853
\(443\) 745.667i 1.68322i 0.540085 + 0.841611i \(0.318392\pi\)
−0.540085 + 0.841611i \(0.681608\pi\)
\(444\) 157.720i 0.355226i
\(445\) 238.220 + 391.278i 0.535325 + 0.879276i
\(446\) −338.744 −0.759516
\(447\) −74.0708 −0.165707
\(448\) −25.5656 −0.0570661
\(449\) 504.255 1.12306 0.561532 0.827455i \(-0.310212\pi\)
0.561532 + 0.827455i \(0.310212\pi\)
\(450\) −94.2250 48.6995i −0.209389 0.108221i
\(451\) 639.457i 1.41786i
\(452\) −237.503 −0.525450
\(453\) 403.225i 0.890120i
\(454\) 232.724i 0.512607i
\(455\) 122.164 + 200.655i 0.268492 + 0.441001i
\(456\) 48.0861i 0.105452i
\(457\) −290.397 −0.635443 −0.317721 0.948184i \(-0.602918\pi\)
−0.317721 + 0.948184i \(0.602918\pi\)
\(458\) 125.639 0.274320
\(459\) 55.5455i 0.121014i
\(460\) 160.557 164.686i 0.349038 0.358012i
\(461\) 537.525 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(462\) 87.6964i 0.189819i
\(463\) 604.525i 1.30567i −0.757500 0.652835i \(-0.773580\pi\)
0.757500 0.652835i \(-0.226420\pi\)
\(464\) 99.0737 0.213521
\(465\) −170.185 279.531i −0.365990 0.601143i
\(466\) 291.386 0.625292
\(467\) −42.4654 −0.0909323 −0.0454661 0.998966i \(-0.514477\pi\)
−0.0454661 + 0.998966i \(0.514477\pi\)
\(468\) 88.2129i 0.188489i
\(469\) 58.2293 0.124156
\(470\) 76.9453 46.8462i 0.163713 0.0996727i
\(471\) 390.284i 0.828628i
\(472\) 216.862i 0.459453i
\(473\) 178.781i 0.377973i
\(474\) 237.467i 0.500986i
\(475\) 217.994 + 112.668i 0.458934 + 0.237196i
\(476\) −68.3224 −0.143534
\(477\) 186.291 0.390548
\(478\) 217.472i 0.454961i
\(479\) 411.978i 0.860079i −0.902810 0.430039i \(-0.858500\pi\)
0.902810 0.430039i \(-0.141500\pi\)
\(480\) 41.8446 25.4760i 0.0871763 0.0530751i
\(481\) 669.388i 1.39166i
\(482\) 552.353 1.14596
\(483\) 31.6454 + 123.312i 0.0655183 + 0.255304i
\(484\) 9.02147 0.0186394
\(485\) −425.944 + 259.325i −0.878235 + 0.534691i
\(486\) 22.0454 0.0453609
\(487\) 593.535i 1.21876i 0.792879 + 0.609379i \(0.208581\pi\)
−0.792879 + 0.609379i \(0.791419\pi\)
\(488\) −110.441 −0.226314
\(489\) −278.114 −0.568740
\(490\) −142.627 234.267i −0.291076 0.478096i
\(491\) −155.028 −0.315739 −0.157869 0.987460i \(-0.550462\pi\)
−0.157869 + 0.987460i \(0.550462\pi\)
\(492\) 197.725i 0.401880i
\(493\) 264.768 0.537055
\(494\) 204.084i 0.413126i
\(495\) −87.3892 143.538i −0.176544 0.289975i
\(496\) 151.156 0.304750
\(497\) 303.373 0.610409
\(498\) −169.081 −0.339520
\(499\) −4.87786 −0.00977527 −0.00488764 0.999988i \(-0.501556\pi\)
−0.00488764 + 0.999988i \(0.501556\pi\)
\(500\) 17.4489 + 249.390i 0.0348977 + 0.498781i
\(501\) −292.195 −0.583224
\(502\) −570.516 −1.13649
\(503\) −385.678 −0.766756 −0.383378 0.923592i \(-0.625239\pi\)
−0.383378 + 0.923592i \(0.625239\pi\)
\(504\) 27.1164i 0.0538024i
\(505\) 106.226 64.6730i 0.210349 0.128065i
\(506\) 352.967 90.5814i 0.697562 0.179015i
\(507\) 81.6720i 0.161089i
\(508\) 274.121i 0.539609i
\(509\) 406.891 0.799392 0.399696 0.916648i \(-0.369116\pi\)
0.399696 + 0.916648i \(0.369116\pi\)
\(510\) 111.827 68.0830i 0.219269 0.133496i
\(511\) 27.4622i 0.0537421i
\(512\) 22.6274i 0.0441942i
\(513\) −51.0030 −0.0994210
\(514\) 439.219 0.854511
\(515\) −174.752 + 106.394i −0.339325 + 0.206589i
\(516\) 55.2805i 0.107133i
\(517\) 142.726 0.276066
\(518\) 205.768i 0.397236i
\(519\) 84.6376 0.163078
\(520\) 177.595 108.124i 0.341528 0.207931i
\(521\) 501.963i 0.963461i 0.876320 + 0.481730i \(0.159991\pi\)
−0.876320 + 0.481730i \(0.840009\pi\)
\(522\) 105.083i 0.201309i
\(523\) 217.341 0.415565 0.207783 0.978175i \(-0.433375\pi\)
0.207783 + 0.978175i \(0.433375\pi\)
\(524\) −112.871 −0.215402
\(525\) −122.930 63.5353i −0.234152 0.121020i
\(526\) 315.024i 0.598905i
\(527\) 403.955 0.766518
\(528\) 77.6178 0.147003
\(529\) 463.627 254.737i 0.876422 0.481544i
\(530\) −228.340 375.051i −0.430830 0.707643i
\(531\) −230.017 −0.433177
\(532\) 62.7350i 0.117923i
\(533\) 839.173i 1.57443i
\(534\) 224.418i 0.420258i
\(535\) 76.0924 46.3269i 0.142229 0.0865923i
\(536\) 51.5372i 0.0961515i
\(537\) 245.486i 0.457143i
\(538\) 59.4344i 0.110473i
\(539\) 434.543i 0.806201i
\(540\) −27.0214 44.3829i −0.0500396 0.0821906i
\(541\) 140.244 0.259231 0.129616 0.991564i \(-0.458626\pi\)
0.129616 + 0.991564i \(0.458626\pi\)
\(542\) 241.334i 0.445265i
\(543\) 169.322 0.311827
\(544\) 60.4703i 0.111159i
\(545\) −191.939 315.262i −0.352183 0.578463i
\(546\) 115.086i 0.210780i
\(547\) 83.5353i 0.152715i 0.997080 + 0.0763577i \(0.0243291\pi\)
−0.997080 + 0.0763577i \(0.975671\pi\)
\(548\) −370.525 −0.676141
\(549\) 117.141i 0.213371i
\(550\) −181.863 + 351.873i −0.330660 + 0.639768i
\(551\) 243.115i 0.441225i
\(552\) 109.140 28.0084i 0.197717 0.0507399i
\(553\) 309.809i 0.560234i
\(554\) 583.633 1.05349
\(555\) −205.047 336.792i −0.369454 0.606832i
\(556\) 433.002 0.778780
\(557\) 900.002 1.61580 0.807901 0.589318i \(-0.200604\pi\)
0.807901 + 0.589318i \(0.200604\pi\)
\(558\) 160.325i 0.287321i
\(559\) 234.619i 0.419712i
\(560\) 54.5921 33.2370i 0.0974859 0.0593518i
\(561\) 207.428 0.369748
\(562\) −29.4361 −0.0523774
\(563\) −1.27327 −0.00226159 −0.00113079 0.999999i \(-0.500360\pi\)
−0.00113079 + 0.999999i \(0.500360\pi\)
\(564\) 44.1320 0.0782482
\(565\) 507.159 308.771i 0.897626 0.546497i
\(566\) 569.345i 1.00591i
\(567\) 28.7613 0.0507254
\(568\) 268.507i 0.472724i
\(569\) 1129.75i 1.98550i −0.120191 0.992751i \(-0.538351\pi\)
0.120191 0.992751i \(-0.461649\pi\)
\(570\) 62.5152 + 102.682i 0.109676 + 0.180143i
\(571\) 153.556i 0.268925i −0.990919 0.134462i \(-0.957069\pi\)
0.990919 0.134462i \(-0.0429307\pi\)
\(572\) 329.421 0.575911
\(573\) −161.959 −0.282651
\(574\) 257.959i 0.449407i
\(575\) −128.747 + 560.401i −0.223908 + 0.974610i
\(576\) 24.0000 0.0416667
\(577\) 602.704i 1.04455i −0.852778 0.522274i \(-0.825084\pi\)
0.852778 0.522274i \(-0.174916\pi\)
\(578\) 247.105i 0.427517i
\(579\) 68.1504 0.117704
\(580\) −211.559 + 128.802i −0.364757 + 0.222073i
\(581\) −220.590 −0.379672
\(582\) −244.300 −0.419760
\(583\) 695.683i 1.19328i
\(584\) −24.3060 −0.0416199
\(585\) −114.683 188.368i −0.196039 0.321996i
\(586\) 151.648i 0.258785i
\(587\) 163.210i 0.278042i 0.990289 + 0.139021i \(0.0443955\pi\)
−0.990289 + 0.139021i \(0.955605\pi\)
\(588\) 134.364i 0.228510i
\(589\) 370.919i 0.629744i
\(590\) 281.935 + 463.081i 0.477856 + 0.784883i
\(591\) −567.127 −0.959606
\(592\) 182.120 0.307635
\(593\) 890.275i 1.50131i −0.660696 0.750653i \(-0.729739\pi\)
0.660696 0.750653i \(-0.270261\pi\)
\(594\) 82.3261i 0.138596i
\(595\) 145.894 88.8238i 0.245200 0.149284i
\(596\) 85.5296i 0.143506i
\(597\) 301.938 0.505759
\(598\) 463.206 118.872i 0.774592 0.198783i
\(599\) 643.232 1.07384 0.536921 0.843632i \(-0.319587\pi\)
0.536921 + 0.843632i \(0.319587\pi\)
\(600\) −56.2333 + 108.802i −0.0937222 + 0.181336i
\(601\) −185.138 −0.308050 −0.154025 0.988067i \(-0.549224\pi\)
−0.154025 + 0.988067i \(0.549224\pi\)
\(602\) 72.1212i 0.119803i
\(603\) −54.6635 −0.0906525
\(604\) 465.604 0.770867
\(605\) −19.2642 + 11.7285i −0.0318417 + 0.0193860i
\(606\) 60.9260 0.100538
\(607\) 722.082i 1.18959i −0.803877 0.594796i \(-0.797233\pi\)
0.803877 0.594796i \(-0.202767\pi\)
\(608\) −55.5250 −0.0913240
\(609\) 137.096i 0.225117i
\(610\) 235.834 143.581i 0.386612 0.235379i
\(611\) 187.303 0.306551
\(612\) 64.1384 0.104801
\(613\) −779.332 −1.27134 −0.635671 0.771960i \(-0.719276\pi\)
−0.635671 + 0.771960i \(0.719276\pi\)
\(614\) −318.929 −0.519428
\(615\) −257.056 422.216i −0.417977 0.686531i
\(616\) 101.263 0.164388
\(617\) −906.051 −1.46848 −0.734239 0.678891i \(-0.762461\pi\)
−0.734239 + 0.678891i \(0.762461\pi\)
\(618\) −100.229 −0.162183
\(619\) 829.532i 1.34012i 0.742308 + 0.670058i \(0.233731\pi\)
−0.742308 + 0.670058i \(0.766269\pi\)
\(620\) −322.775 + 196.513i −0.520605 + 0.316957i
\(621\) −29.7074 115.760i −0.0478381 0.186410i
\(622\) 402.574i 0.647225i
\(623\) 292.784i 0.469958i
\(624\) 101.860 0.163236
\(625\) −361.484 509.857i −0.578375 0.815771i
\(626\) 215.640i 0.344473i
\(627\) 190.465i 0.303772i
\(628\) 450.661 0.717613
\(629\) 486.703 0.773773
\(630\) −35.2532 57.9037i −0.0559574 0.0919106i
\(631\) 1078.38i 1.70900i −0.519451 0.854500i \(-0.673864\pi\)
0.519451 0.854500i \(-0.326136\pi\)
\(632\) 274.204 0.433867
\(633\) 478.150i 0.755370i
\(634\) −806.161 −1.27155
\(635\) 356.377 + 585.352i 0.561223 + 0.921814i
\(636\) 215.111i 0.338224i
\(637\) 570.260i 0.895227i
\(638\) −392.422 −0.615082
\(639\) −284.795 −0.445688
\(640\) −29.4172 48.3180i −0.0459644 0.0754969i
\(641\) 744.723i 1.16182i 0.813970 + 0.580908i \(0.197302\pi\)
−0.813970 + 0.580908i \(0.802698\pi\)
\(642\) 43.6428 0.0679795
\(643\) 373.410 0.580731 0.290365 0.956916i \(-0.406223\pi\)
0.290365 + 0.956916i \(0.406223\pi\)
\(644\) 142.388 36.5409i 0.221100 0.0567405i
\(645\) 71.8685 + 118.045i 0.111424 + 0.183015i
\(646\) −148.387 −0.229701
\(647\) 174.894i 0.270315i −0.990824 0.135157i \(-0.956846\pi\)
0.990824 0.135157i \(-0.0431540\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 858.971i 1.32353i
\(650\) −238.663 + 461.770i −0.367173 + 0.710416i
\(651\) 209.167i 0.321300i
\(652\) 321.138i 0.492543i
\(653\) 343.261i 0.525668i −0.964841 0.262834i \(-0.915343\pi\)
0.964841 0.262834i \(-0.0846572\pi\)
\(654\) 180.819i 0.276481i
\(655\) 241.021 146.740i 0.367972 0.224030i
\(656\) 228.313 0.348038
\(657\) 25.7805i 0.0392397i
\(658\) 57.5763 0.0875020
\(659\) 206.113i 0.312766i −0.987696 0.156383i \(-0.950017\pi\)
0.987696 0.156383i \(-0.0499834\pi\)
\(660\) −165.743 + 100.908i −0.251126 + 0.152891i
\(661\) 876.964i 1.32672i −0.748299 0.663362i \(-0.769129\pi\)
0.748299 0.663362i \(-0.230871\pi\)
\(662\) 175.930i 0.265755i
\(663\) 272.213 0.410578
\(664\) 195.238i 0.294033i
\(665\) 81.5597 + 133.963i 0.122646 + 0.201448i
\(666\) 193.167i 0.290041i
\(667\) −551.793 + 141.606i −0.827276 + 0.212303i
\(668\) 337.398i 0.505086i
\(669\) 414.875 0.620142
\(670\) 67.0019 + 110.051i 0.100003 + 0.164256i
\(671\) 437.449 0.651935
\(672\) 31.3113 0.0465942
\(673\) 434.411i 0.645485i −0.946487 0.322743i \(-0.895395\pi\)
0.946487 0.322743i \(-0.104605\pi\)
\(674\) 303.580i 0.450415i
\(675\) 115.402 + 59.6445i 0.170965 + 0.0883622i
\(676\) 94.3067 0.139507
\(677\) −665.420 −0.982895 −0.491447 0.870907i \(-0.663532\pi\)
−0.491447 + 0.870907i \(0.663532\pi\)
\(678\) 290.881 0.429028
\(679\) −318.724 −0.469402
\(680\) −78.6155 129.127i −0.115611 0.189892i
\(681\) 285.027i 0.418542i
\(682\) −598.716 −0.877883
\(683\) 513.018i 0.751124i 0.926797 + 0.375562i \(0.122550\pi\)
−0.926797 + 0.375562i \(0.877450\pi\)
\(684\) 58.8932i 0.0861011i
\(685\) 791.210 481.708i 1.15505 0.703224i
\(686\) 396.747i 0.578348i
\(687\) −153.875 −0.223981
\(688\) −63.8325 −0.0927798
\(689\) 912.961i 1.32505i
\(690\) −196.642 + 201.698i −0.284988 + 0.292316i
\(691\) −521.187 −0.754251 −0.377125 0.926162i \(-0.623087\pi\)
−0.377125 + 0.926162i \(0.623087\pi\)
\(692\) 97.7311i 0.141230i
\(693\) 107.406i 0.154987i
\(694\) −778.998 −1.12248
\(695\) −924.620 + 562.932i −1.33039 + 0.809973i
\(696\) −121.340 −0.174339
\(697\) 610.152 0.875397
\(698\) 521.993i 0.747841i
\(699\) −356.874 −0.510549
\(700\) −73.3642 + 141.947i −0.104806 + 0.202781i
\(701\) 148.024i 0.211161i −0.994411 0.105580i \(-0.966330\pi\)
0.994411 0.105580i \(-0.0336700\pi\)
\(702\) 108.038i 0.153901i
\(703\) 446.900i 0.635705i
\(704\) 89.6253i 0.127309i
\(705\) −94.2383 + 57.3746i −0.133671 + 0.0813824i
\(706\) 585.852 0.829819
\(707\) 79.4864 0.112428
\(708\) 265.600i 0.375142i
\(709\) 1053.52i 1.48592i −0.669336 0.742960i \(-0.733421\pi\)
0.669336 0.742960i \(-0.266579\pi\)
\(710\) 349.078 + 573.363i 0.491659 + 0.807554i
\(711\) 290.837i 0.409053i
\(712\) 259.135 0.363954
\(713\) −841.868 + 216.047i −1.18074 + 0.303012i
\(714\) 83.6775 0.117195
\(715\) −703.437 + 428.270i −0.983828 + 0.598979i
\(716\) −283.462 −0.395897
\(717\) 266.347i 0.371474i
\(718\) 403.726 0.562293
\(719\) −516.738 −0.718689 −0.359345 0.933205i \(-0.617000\pi\)
−0.359345 + 0.933205i \(0.617000\pi\)
\(720\) −51.2490 + 31.2016i −0.0711791 + 0.0433356i
\(721\) −130.763 −0.181364
\(722\) 374.279i 0.518392i
\(723\) −676.492 −0.935674
\(724\) 195.516i 0.270050i
\(725\) 284.306 550.083i 0.392147 0.758735i
\(726\) −11.0490 −0.0152190
\(727\) 348.090 0.478803 0.239401 0.970921i \(-0.423049\pi\)
0.239401 + 0.970921i \(0.423049\pi\)
\(728\) 132.890 0.182541
\(729\) −27.0000 −0.0370370
\(730\) 51.9025 31.5995i 0.0710993 0.0432870i
\(731\) −170.588 −0.233363
\(732\) 135.262 0.184785
\(733\) 1172.59 1.59972 0.799858 0.600189i \(-0.204908\pi\)
0.799858 + 0.600189i \(0.204908\pi\)
\(734\) 386.256i 0.526234i
\(735\) 174.682 + 286.917i 0.237663 + 0.390363i
\(736\) −32.3414 126.024i −0.0439421 0.171228i
\(737\) 204.134i 0.276980i
\(738\) 242.162i 0.328133i
\(739\) −586.911 −0.794196 −0.397098 0.917776i \(-0.629983\pi\)
−0.397098 + 0.917776i \(0.629983\pi\)
\(740\) −388.894 + 236.768i −0.525532 + 0.319957i
\(741\) 249.951i 0.337316i
\(742\) 280.642i 0.378223i
\(743\) 256.074 0.344648 0.172324 0.985040i \(-0.444872\pi\)
0.172324 + 0.985040i \(0.444872\pi\)
\(744\) −185.128 −0.248828
\(745\) −111.194 182.638i −0.149254 0.245151i
\(746\) 680.521i 0.912227i
\(747\) 207.081 0.277217
\(748\) 239.518i 0.320211i
\(749\) 56.9381 0.0760188
\(750\) −21.3704 305.440i −0.0284939 0.407253i
\(751\) 839.297i 1.11757i 0.829312 + 0.558786i \(0.188733\pi\)
−0.829312 + 0.558786i \(0.811267\pi\)
\(752\) 50.9592i 0.0677650i
\(753\) 698.736 0.927937
\(754\) −514.985 −0.683003
\(755\) −994.238 + 605.316i −1.31687 + 0.801744i
\(756\) 33.2107i 0.0439295i
\(757\) 979.027 1.29330 0.646649 0.762788i \(-0.276170\pi\)
0.646649 + 0.762788i \(0.276170\pi\)
\(758\) 710.139 0.936858
\(759\) −432.294 + 110.939i −0.569557 + 0.146165i
\(760\) 118.567 72.1863i 0.156009 0.0949820i
\(761\) 419.697 0.551507 0.275753 0.961228i \(-0.411073\pi\)
0.275753 + 0.961228i \(0.411073\pi\)
\(762\) 335.729i 0.440589i
\(763\) 235.903i 0.309179i
\(764\) 187.014i 0.244783i
\(765\) −136.960 + 83.3843i −0.179032 + 0.108999i
\(766\) 819.880i 1.07034i
\(767\) 1127.25i 1.46968i
\(768\) 27.7128i 0.0360844i
\(769\) 215.482i 0.280211i 0.990137 + 0.140105i \(0.0447442\pi\)
−0.990137 + 0.140105i \(0.955256\pi\)
\(770\) −216.235 + 131.649i −0.280824 + 0.170973i
\(771\) −537.931 −0.697706
\(772\) 78.6932i 0.101934i
\(773\) 1480.63 1.91543 0.957716 0.287715i \(-0.0928956\pi\)
0.957716 + 0.287715i \(0.0928956\pi\)
\(774\) 67.7046i 0.0874736i
\(775\) 433.765 839.259i 0.559696 1.08291i
\(776\) 282.094i 0.363523i
\(777\) 252.013i 0.324342i
\(778\) −399.249 −0.513173
\(779\) 560.253i 0.719195i
\(780\) −217.508 + 132.424i −0.278857 + 0.169775i
\(781\) 1063.53i 1.36176i
\(782\) −86.4302 336.791i −0.110525 0.430679i
\(783\) 128.700i 0.164368i
\(784\) −155.150 −0.197895
\(785\) −962.330 + 585.890i −1.22590 + 0.746357i
\(786\) 138.238 0.175875
\(787\) −464.168 −0.589795 −0.294897 0.955529i \(-0.595285\pi\)
−0.294897 + 0.955529i \(0.595285\pi\)