Properties

Label 91.2.c.a.64.5
Level $91$
Weight $2$
Character 91.64
Analytic conductor $0.727$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.5
Root \(-0.854638 - 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 91.64
Dual form 91.2.c.a.64.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.17009i q^{2} +0.539189 q^{3} +0.630898 q^{4} -0.460811i q^{5} +0.630898i q^{6} -1.00000i q^{7} +3.07838i q^{8} -2.70928 q^{9} +O(q^{10})\) \(q+1.17009i q^{2} +0.539189 q^{3} +0.630898 q^{4} -0.460811i q^{5} +0.630898i q^{6} -1.00000i q^{7} +3.07838i q^{8} -2.70928 q^{9} +0.539189 q^{10} +0.829914i q^{11} +0.340173 q^{12} +(-2.87936 - 2.17009i) q^{13} +1.17009 q^{14} -0.248464i q^{15} -2.34017 q^{16} +2.87936 q^{17} -3.17009i q^{18} -4.32684i q^{19} -0.290725i q^{20} -0.539189i q^{21} -0.971071 q^{22} -5.04945 q^{23} +1.65983i q^{24} +4.78765 q^{25} +(2.53919 - 3.36910i) q^{26} -3.07838 q^{27} -0.630898i q^{28} +0.261795 q^{29} +0.290725 q^{30} -6.80098i q^{31} +3.41855i q^{32} +0.447480i q^{33} +3.36910i q^{34} -0.460811 q^{35} -1.70928 q^{36} +9.51026i q^{37} +5.06278 q^{38} +(-1.55252 - 1.17009i) q^{39} +1.41855 q^{40} +6.68035i q^{41} +0.630898 q^{42} +0.418551 q^{43} +0.523590i q^{44} +1.24846i q^{45} -5.90829i q^{46} +9.24846i q^{47} -1.26180 q^{48} -1.00000 q^{49} +5.60197i q^{50} +1.55252 q^{51} +(-1.81658 - 1.36910i) q^{52} +1.63090 q^{53} -3.60197i q^{54} +0.382433 q^{55} +3.07838 q^{56} -2.33299i q^{57} +0.306323i q^{58} -2.78765i q^{59} -0.156755i q^{60} +7.26180 q^{61} +7.95774 q^{62} +2.70928i q^{63} -8.68035 q^{64} +(-1.00000 + 1.32684i) q^{65} -0.523590 q^{66} +5.07838i q^{67} +1.81658 q^{68} -2.72261 q^{69} -0.539189i q^{70} -12.7721i q^{71} -8.34017i q^{72} +0.353504i q^{73} -11.1278 q^{74} +2.58145 q^{75} -2.72979i q^{76} +0.829914 q^{77} +(1.36910 - 1.81658i) q^{78} +2.81658 q^{79} +1.07838i q^{80} +6.46800 q^{81} -7.81658 q^{82} -10.3763i q^{83} -0.340173i q^{84} -1.32684i q^{85} +0.489741i q^{86} +0.141157 q^{87} -2.55479 q^{88} +5.43188i q^{89} -1.46081 q^{90} +(-2.17009 + 2.87936i) q^{91} -3.18568 q^{92} -3.66701i q^{93} -10.8215 q^{94} -1.99386 q^{95} +1.84324i q^{96} +12.6092i q^{97} -1.17009i q^{98} -2.24846i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 4q^{4} - 2q^{9} + O(q^{10}) \) \( 6q - 4q^{4} - 2q^{9} - 20q^{12} + 8q^{13} - 4q^{14} + 8q^{16} - 8q^{17} + 24q^{22} + 6q^{23} + 8q^{25} + 12q^{26} - 12q^{27} - 14q^{29} + 16q^{30} - 6q^{35} + 4q^{36} - 4q^{38} - 8q^{39} - 20q^{40} - 4q^{42} - 26q^{43} + 8q^{48} - 6q^{49} + 8q^{51} - 20q^{52} + 2q^{53} + 12q^{55} + 12q^{56} + 28q^{61} + 16q^{62} - 8q^{64} - 6q^{65} + 28q^{66} + 20q^{68} - 4q^{69} - 24q^{74} + 44q^{75} + 16q^{77} + 16q^{78} + 26q^{79} - 26q^{81} - 56q^{82} - 40q^{87} - 40q^{88} - 12q^{90} - 2q^{91} - 36q^{92} + 20q^{94} + 58q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.17009i 0.827376i 0.910419 + 0.413688i \(0.135760\pi\)
−0.910419 + 0.413688i \(0.864240\pi\)
\(3\) 0.539189 0.311301 0.155650 0.987812i \(-0.450253\pi\)
0.155650 + 0.987812i \(0.450253\pi\)
\(4\) 0.630898 0.315449
\(5\) 0.460811i 0.206081i −0.994677 0.103041i \(-0.967143\pi\)
0.994677 0.103041i \(-0.0328571\pi\)
\(6\) 0.630898i 0.257563i
\(7\) 1.00000i 0.377964i
\(8\) 3.07838i 1.08837i
\(9\) −2.70928 −0.903092
\(10\) 0.539189 0.170506
\(11\) 0.829914i 0.250228i 0.992142 + 0.125114i \(0.0399297\pi\)
−0.992142 + 0.125114i \(0.960070\pi\)
\(12\) 0.340173 0.0981995
\(13\) −2.87936 2.17009i −0.798591 0.601874i
\(14\) 1.17009 0.312719
\(15\) 0.248464i 0.0641532i
\(16\) −2.34017 −0.585043
\(17\) 2.87936 0.698348 0.349174 0.937058i \(-0.386462\pi\)
0.349174 + 0.937058i \(0.386462\pi\)
\(18\) 3.17009i 0.747197i
\(19\) 4.32684i 0.992646i −0.868138 0.496323i \(-0.834683\pi\)
0.868138 0.496323i \(-0.165317\pi\)
\(20\) 0.290725i 0.0650080i
\(21\) 0.539189i 0.117661i
\(22\) −0.971071 −0.207033
\(23\) −5.04945 −1.05288 −0.526441 0.850211i \(-0.676474\pi\)
−0.526441 + 0.850211i \(0.676474\pi\)
\(24\) 1.65983i 0.338811i
\(25\) 4.78765 0.957531
\(26\) 2.53919 3.36910i 0.497976 0.660735i
\(27\) −3.07838 −0.592434
\(28\) 0.630898i 0.119228i
\(29\) 0.261795 0.0486142 0.0243071 0.999705i \(-0.492262\pi\)
0.0243071 + 0.999705i \(0.492262\pi\)
\(30\) 0.290725 0.0530788
\(31\) 6.80098i 1.22149i −0.791826 0.610746i \(-0.790869\pi\)
0.791826 0.610746i \(-0.209131\pi\)
\(32\) 3.41855i 0.604320i
\(33\) 0.447480i 0.0778963i
\(34\) 3.36910i 0.577796i
\(35\) −0.460811 −0.0778913
\(36\) −1.70928 −0.284879
\(37\) 9.51026i 1.56348i 0.623606 + 0.781739i \(0.285667\pi\)
−0.623606 + 0.781739i \(0.714333\pi\)
\(38\) 5.06278 0.821291
\(39\) −1.55252 1.17009i −0.248602 0.187364i
\(40\) 1.41855 0.224293
\(41\) 6.68035i 1.04329i 0.853161 + 0.521647i \(0.174682\pi\)
−0.853161 + 0.521647i \(0.825318\pi\)
\(42\) 0.630898 0.0973496
\(43\) 0.418551 0.0638284 0.0319142 0.999491i \(-0.489840\pi\)
0.0319142 + 0.999491i \(0.489840\pi\)
\(44\) 0.523590i 0.0789342i
\(45\) 1.24846i 0.186110i
\(46\) 5.90829i 0.871130i
\(47\) 9.24846i 1.34903i 0.738262 + 0.674514i \(0.235647\pi\)
−0.738262 + 0.674514i \(0.764353\pi\)
\(48\) −1.26180 −0.182124
\(49\) −1.00000 −0.142857
\(50\) 5.60197i 0.792238i
\(51\) 1.55252 0.217396
\(52\) −1.81658 1.36910i −0.251915 0.189860i
\(53\) 1.63090 0.224021 0.112011 0.993707i \(-0.464271\pi\)
0.112011 + 0.993707i \(0.464271\pi\)
\(54\) 3.60197i 0.490166i
\(55\) 0.382433 0.0515673
\(56\) 3.07838 0.411366
\(57\) 2.33299i 0.309011i
\(58\) 0.306323i 0.0402222i
\(59\) 2.78765i 0.362922i −0.983398 0.181461i \(-0.941917\pi\)
0.983398 0.181461i \(-0.0580825\pi\)
\(60\) 0.156755i 0.0202370i
\(61\) 7.26180 0.929778 0.464889 0.885369i \(-0.346094\pi\)
0.464889 + 0.885369i \(0.346094\pi\)
\(62\) 7.95774 1.01063
\(63\) 2.70928i 0.341337i
\(64\) −8.68035 −1.08504
\(65\) −1.00000 + 1.32684i −0.124035 + 0.164574i
\(66\) −0.523590 −0.0644495
\(67\) 5.07838i 0.620423i 0.950668 + 0.310211i \(0.100400\pi\)
−0.950668 + 0.310211i \(0.899600\pi\)
\(68\) 1.81658 0.220293
\(69\) −2.72261 −0.327763
\(70\) 0.539189i 0.0644454i
\(71\) 12.7721i 1.51576i −0.652392 0.757882i \(-0.726234\pi\)
0.652392 0.757882i \(-0.273766\pi\)
\(72\) 8.34017i 0.982899i
\(73\) 0.353504i 0.0413745i 0.999786 + 0.0206873i \(0.00658543\pi\)
−0.999786 + 0.0206873i \(0.993415\pi\)
\(74\) −11.1278 −1.29358
\(75\) 2.58145 0.298080
\(76\) 2.72979i 0.313129i
\(77\) 0.829914 0.0945774
\(78\) 1.36910 1.81658i 0.155020 0.205687i
\(79\) 2.81658 0.316890 0.158445 0.987368i \(-0.449352\pi\)
0.158445 + 0.987368i \(0.449352\pi\)
\(80\) 1.07838i 0.120566i
\(81\) 6.46800 0.718667
\(82\) −7.81658 −0.863197
\(83\) 10.3763i 1.13895i −0.822010 0.569473i \(-0.807147\pi\)
0.822010 0.569473i \(-0.192853\pi\)
\(84\) 0.340173i 0.0371159i
\(85\) 1.32684i 0.143916i
\(86\) 0.489741i 0.0528101i
\(87\) 0.141157 0.0151336
\(88\) −2.55479 −0.272341
\(89\) 5.43188i 0.575778i 0.957664 + 0.287889i \(0.0929535\pi\)
−0.957664 + 0.287889i \(0.907047\pi\)
\(90\) −1.46081 −0.153983
\(91\) −2.17009 + 2.87936i −0.227487 + 0.301839i
\(92\) −3.18568 −0.332131
\(93\) 3.66701i 0.380252i
\(94\) −10.8215 −1.11615
\(95\) −1.99386 −0.204565
\(96\) 1.84324i 0.188125i
\(97\) 12.6092i 1.28027i 0.768264 + 0.640133i \(0.221121\pi\)
−0.768264 + 0.640133i \(0.778879\pi\)
\(98\) 1.17009i 0.118197i
\(99\) 2.24846i 0.225979i
\(100\) 3.02052 0.302052
\(101\) −3.64423 −0.362614 −0.181307 0.983427i \(-0.558033\pi\)
−0.181307 + 0.983427i \(0.558033\pi\)
\(102\) 1.81658i 0.179868i
\(103\) −17.9421 −1.76789 −0.883946 0.467589i \(-0.845123\pi\)
−0.883946 + 0.467589i \(0.845123\pi\)
\(104\) 6.68035 8.86376i 0.655062 0.869164i
\(105\) −0.248464 −0.0242476
\(106\) 1.90829i 0.185350i
\(107\) 2.94441 0.284647 0.142323 0.989820i \(-0.454543\pi\)
0.142323 + 0.989820i \(0.454543\pi\)
\(108\) −1.94214 −0.186883
\(109\) 8.43188i 0.807628i −0.914841 0.403814i \(-0.867684\pi\)
0.914841 0.403814i \(-0.132316\pi\)
\(110\) 0.447480i 0.0426656i
\(111\) 5.12783i 0.486712i
\(112\) 2.34017i 0.221126i
\(113\) 12.8082 1.20489 0.602446 0.798160i \(-0.294193\pi\)
0.602446 + 0.798160i \(0.294193\pi\)
\(114\) 2.72979 0.255669
\(115\) 2.32684i 0.216979i
\(116\) 0.165166 0.0153353
\(117\) 7.80098 + 5.87936i 0.721201 + 0.543547i
\(118\) 3.26180 0.300273
\(119\) 2.87936i 0.263951i
\(120\) 0.764867 0.0698225
\(121\) 10.3112 0.937386
\(122\) 8.49693i 0.769276i
\(123\) 3.60197i 0.324779i
\(124\) 4.29072i 0.385318i
\(125\) 4.51026i 0.403410i
\(126\) −3.17009 −0.282414
\(127\) 13.4680 1.19509 0.597546 0.801835i \(-0.296143\pi\)
0.597546 + 0.801835i \(0.296143\pi\)
\(128\) 3.31965i 0.293419i
\(129\) 0.225678 0.0198698
\(130\) −1.55252 1.17009i −0.136165 0.102623i
\(131\) −14.4391 −1.26155 −0.630774 0.775967i \(-0.717262\pi\)
−0.630774 + 0.775967i \(0.717262\pi\)
\(132\) 0.282314i 0.0245723i
\(133\) −4.32684 −0.375185
\(134\) −5.94214 −0.513323
\(135\) 1.41855i 0.122089i
\(136\) 8.86376i 0.760061i
\(137\) 16.4319i 1.40387i 0.712241 + 0.701935i \(0.247680\pi\)
−0.712241 + 0.701935i \(0.752320\pi\)
\(138\) 3.18568i 0.271184i
\(139\) 13.2195 1.12127 0.560633 0.828064i \(-0.310558\pi\)
0.560633 + 0.828064i \(0.310558\pi\)
\(140\) −0.290725 −0.0245707
\(141\) 4.98667i 0.419953i
\(142\) 14.9444 1.25411
\(143\) 1.80098 2.38962i 0.150606 0.199830i
\(144\) 6.34017 0.528348
\(145\) 0.120638i 0.0100185i
\(146\) −0.413630 −0.0342323
\(147\) −0.539189 −0.0444715
\(148\) 6.00000i 0.493197i
\(149\) 20.5041i 1.67976i −0.542770 0.839881i \(-0.682624\pi\)
0.542770 0.839881i \(-0.317376\pi\)
\(150\) 3.02052i 0.246624i
\(151\) 1.59478i 0.129781i −0.997892 0.0648907i \(-0.979330\pi\)
0.997892 0.0648907i \(-0.0206699\pi\)
\(152\) 13.3197 1.08037
\(153\) −7.80098 −0.630672
\(154\) 0.971071i 0.0782511i
\(155\) −3.13397 −0.251726
\(156\) −0.979481 0.738205i −0.0784212 0.0591037i
\(157\) −8.29791 −0.662246 −0.331123 0.943588i \(-0.607427\pi\)
−0.331123 + 0.943588i \(0.607427\pi\)
\(158\) 3.29565i 0.262187i
\(159\) 0.879362 0.0697379
\(160\) 1.57531 0.124539
\(161\) 5.04945i 0.397952i
\(162\) 7.56812i 0.594608i
\(163\) 0.398032i 0.0311763i 0.999878 + 0.0155881i \(0.00496206\pi\)
−0.999878 + 0.0155881i \(0.995038\pi\)
\(164\) 4.21461i 0.329106i
\(165\) 0.206204 0.0160529
\(166\) 12.1412 0.942337
\(167\) 23.8710i 1.84719i −0.383370 0.923595i \(-0.625237\pi\)
0.383370 0.923595i \(-0.374763\pi\)
\(168\) 1.65983 0.128058
\(169\) 3.58145 + 12.4969i 0.275496 + 0.961302i
\(170\) 1.55252 0.119073
\(171\) 11.7226i 0.896450i
\(172\) 0.264063 0.0201346
\(173\) −25.8999 −1.96913 −0.984566 0.175015i \(-0.944003\pi\)
−0.984566 + 0.175015i \(0.944003\pi\)
\(174\) 0.165166i 0.0125212i
\(175\) 4.78765i 0.361913i
\(176\) 1.94214i 0.146394i
\(177\) 1.50307i 0.112978i
\(178\) −6.35577 −0.476385
\(179\) −20.6742 −1.54526 −0.772631 0.634855i \(-0.781060\pi\)
−0.772631 + 0.634855i \(0.781060\pi\)
\(180\) 0.787653i 0.0587082i
\(181\) −15.7165 −1.16820 −0.584098 0.811683i \(-0.698552\pi\)
−0.584098 + 0.811683i \(0.698552\pi\)
\(182\) −3.36910 2.53919i −0.249734 0.188217i
\(183\) 3.91548 0.289441
\(184\) 15.5441i 1.14593i
\(185\) 4.38243 0.322203
\(186\) 4.29072 0.314611
\(187\) 2.38962i 0.174746i
\(188\) 5.83483i 0.425549i
\(189\) 3.07838i 0.223919i
\(190\) 2.33299i 0.169253i
\(191\) −16.7877 −1.21471 −0.607356 0.794430i \(-0.707770\pi\)
−0.607356 + 0.794430i \(0.707770\pi\)
\(192\) −4.68035 −0.337775
\(193\) 20.0144i 1.44067i −0.693628 0.720333i \(-0.743989\pi\)
0.693628 0.720333i \(-0.256011\pi\)
\(194\) −14.7538 −1.05926
\(195\) −0.539189 + 0.715418i −0.0386121 + 0.0512322i
\(196\) −0.630898 −0.0450641
\(197\) 17.5174i 1.24807i −0.781398 0.624033i \(-0.785493\pi\)
0.781398 0.624033i \(-0.214507\pi\)
\(198\) 2.63090 0.186970
\(199\) 16.2979 1.15533 0.577664 0.816275i \(-0.303964\pi\)
0.577664 + 0.816275i \(0.303964\pi\)
\(200\) 14.7382i 1.04215i
\(201\) 2.73820i 0.193138i
\(202\) 4.26406i 0.300018i
\(203\) 0.261795i 0.0183744i
\(204\) 0.979481 0.0685774
\(205\) 3.07838 0.215003
\(206\) 20.9939i 1.46271i
\(207\) 13.6803 0.950850
\(208\) 6.73820 + 5.07838i 0.467210 + 0.352122i
\(209\) 3.59090 0.248388
\(210\) 0.290725i 0.0200619i
\(211\) 2.70928 0.186514 0.0932571 0.995642i \(-0.470272\pi\)
0.0932571 + 0.995642i \(0.470272\pi\)
\(212\) 1.02893 0.0706672
\(213\) 6.88655i 0.471859i
\(214\) 3.44521i 0.235510i
\(215\) 0.192873i 0.0131538i
\(216\) 9.47641i 0.644788i
\(217\) −6.80098 −0.461681
\(218\) 9.86603 0.668212
\(219\) 0.190605i 0.0128799i
\(220\) 0.241276 0.0162668
\(221\) −8.29072 6.24846i −0.557694 0.420317i
\(222\) −6.00000 −0.402694
\(223\) 19.7948i 1.32556i 0.748814 + 0.662780i \(0.230624\pi\)
−0.748814 + 0.662780i \(0.769376\pi\)
\(224\) 3.41855 0.228412
\(225\) −12.9711 −0.864738
\(226\) 14.9867i 0.996898i
\(227\) 13.2618i 0.880216i −0.897945 0.440108i \(-0.854940\pi\)
0.897945 0.440108i \(-0.145060\pi\)
\(228\) 1.47187i 0.0974773i
\(229\) 27.8082i 1.83762i −0.394705 0.918808i \(-0.629153\pi\)
0.394705 0.918808i \(-0.370847\pi\)
\(230\) −2.72261 −0.179523
\(231\) 0.447480 0.0294420
\(232\) 0.805905i 0.0529102i
\(233\) 13.3668 0.875690 0.437845 0.899050i \(-0.355742\pi\)
0.437845 + 0.899050i \(0.355742\pi\)
\(234\) −6.87936 + 9.12783i −0.449718 + 0.596705i
\(235\) 4.26180 0.278009
\(236\) 1.75872i 0.114483i
\(237\) 1.51867 0.0986482
\(238\) 3.36910 0.218386
\(239\) 8.70701i 0.563210i 0.959530 + 0.281605i \(0.0908667\pi\)
−0.959530 + 0.281605i \(0.909133\pi\)
\(240\) 0.581449i 0.0375324i
\(241\) 16.9311i 1.09063i 0.838232 + 0.545313i \(0.183589\pi\)
−0.838232 + 0.545313i \(0.816411\pi\)
\(242\) 12.0650i 0.775571i
\(243\) 12.7226 0.816156
\(244\) 4.58145 0.293297
\(245\) 0.460811i 0.0294401i
\(246\) −4.21461 −0.268714
\(247\) −9.38962 + 12.4585i −0.597447 + 0.792718i
\(248\) 20.9360 1.32944
\(249\) 5.59478i 0.354555i
\(250\) 5.27739 0.333772
\(251\) 8.82150 0.556808 0.278404 0.960464i \(-0.410195\pi\)
0.278404 + 0.960464i \(0.410195\pi\)
\(252\) 1.70928i 0.107674i
\(253\) 4.19061i 0.263461i
\(254\) 15.7587i 0.988790i
\(255\) 0.715418i 0.0448012i
\(256\) −13.4764 −0.842276
\(257\) 13.6442 0.851104 0.425552 0.904934i \(-0.360080\pi\)
0.425552 + 0.904934i \(0.360080\pi\)
\(258\) 0.264063i 0.0164398i
\(259\) 9.51026 0.590939
\(260\) −0.630898 + 0.837101i −0.0391266 + 0.0519148i
\(261\) −0.709275 −0.0439030
\(262\) 16.8950i 1.04377i
\(263\) −12.1773 −0.750883 −0.375441 0.926846i \(-0.622509\pi\)
−0.375441 + 0.926846i \(0.622509\pi\)
\(264\) −1.37751 −0.0847801
\(265\) 0.751536i 0.0461665i
\(266\) 5.06278i 0.310419i
\(267\) 2.92881i 0.179240i
\(268\) 3.20394i 0.195712i
\(269\) −11.0472 −0.673559 −0.336779 0.941584i \(-0.609338\pi\)
−0.336779 + 0.941584i \(0.609338\pi\)
\(270\) −1.65983 −0.101014
\(271\) 10.9360i 0.664315i 0.943224 + 0.332157i \(0.107776\pi\)
−0.943224 + 0.332157i \(0.892224\pi\)
\(272\) −6.73820 −0.408564
\(273\) −1.17009 + 1.55252i −0.0708169 + 0.0939628i
\(274\) −19.2267 −1.16153
\(275\) 3.97334i 0.239601i
\(276\) −1.71769 −0.103393
\(277\) 26.1194 1.56936 0.784682 0.619899i \(-0.212826\pi\)
0.784682 + 0.619899i \(0.212826\pi\)
\(278\) 15.4680i 0.927709i
\(279\) 18.4257i 1.10312i
\(280\) 1.41855i 0.0847746i
\(281\) 4.80325i 0.286538i −0.989684 0.143269i \(-0.954239\pi\)
0.989684 0.143269i \(-0.0457614\pi\)
\(282\) −5.83483 −0.347459
\(283\) −0.979481 −0.0582241 −0.0291121 0.999576i \(-0.509268\pi\)
−0.0291121 + 0.999576i \(0.509268\pi\)
\(284\) 8.05786i 0.478146i
\(285\) −1.07507 −0.0636814
\(286\) 2.79606 + 2.10731i 0.165335 + 0.124608i
\(287\) 6.68035 0.394328
\(288\) 9.26180i 0.545757i
\(289\) −8.70928 −0.512310
\(290\) 0.141157 0.00828903
\(291\) 6.79872i 0.398548i
\(292\) 0.223025i 0.0130515i
\(293\) 24.3268i 1.42119i 0.703602 + 0.710595i \(0.251574\pi\)
−0.703602 + 0.710595i \(0.748426\pi\)
\(294\) 0.630898i 0.0367947i
\(295\) −1.28458 −0.0747912
\(296\) −29.2762 −1.70164
\(297\) 2.55479i 0.148244i
\(298\) 23.9916 1.38980
\(299\) 14.5392 + 10.9577i 0.840823 + 0.633702i
\(300\) 1.62863 0.0940290
\(301\) 0.418551i 0.0241249i
\(302\) 1.86603 0.107378
\(303\) −1.96493 −0.112882
\(304\) 10.1256i 0.580741i
\(305\) 3.34632i 0.191609i
\(306\) 9.12783i 0.521803i
\(307\) 6.21953i 0.354968i −0.984124 0.177484i \(-0.943204\pi\)
0.984124 0.177484i \(-0.0567957\pi\)
\(308\) 0.523590 0.0298343
\(309\) −9.67420 −0.550346
\(310\) 3.66701i 0.208272i
\(311\) 25.1084 1.42376 0.711882 0.702299i \(-0.247843\pi\)
0.711882 + 0.702299i \(0.247843\pi\)
\(312\) 3.60197 4.77924i 0.203921 0.270571i
\(313\) 2.24005 0.126615 0.0633077 0.997994i \(-0.479835\pi\)
0.0633077 + 0.997994i \(0.479835\pi\)
\(314\) 9.70928i 0.547926i
\(315\) 1.24846 0.0703430
\(316\) 1.77698 0.0999627
\(317\) 2.89496i 0.162597i 0.996690 + 0.0812986i \(0.0259067\pi\)
−0.996690 + 0.0812986i \(0.974093\pi\)
\(318\) 1.02893i 0.0576995i
\(319\) 0.217267i 0.0121646i
\(320\) 4.00000i 0.223607i
\(321\) 1.58759 0.0886108
\(322\) −5.90829 −0.329256
\(323\) 12.4585i 0.693212i
\(324\) 4.08065 0.226703
\(325\) −13.7854 10.3896i −0.764676 0.576312i
\(326\) −0.465732 −0.0257945
\(327\) 4.54638i 0.251415i
\(328\) −20.5646 −1.13549
\(329\) 9.24846 0.509884
\(330\) 0.241276i 0.0132818i
\(331\) 4.25565i 0.233912i 0.993137 + 0.116956i \(0.0373136\pi\)
−0.993137 + 0.116956i \(0.962686\pi\)
\(332\) 6.54638i 0.359279i
\(333\) 25.7659i 1.41196i
\(334\) 27.9311 1.52832
\(335\) 2.34017 0.127857
\(336\) 1.26180i 0.0688366i
\(337\) −15.5464 −0.846865 −0.423433 0.905928i \(-0.639175\pi\)
−0.423433 + 0.905928i \(0.639175\pi\)
\(338\) −14.6225 + 4.19061i −0.795358 + 0.227939i
\(339\) 6.90602 0.375084
\(340\) 0.837101i 0.0453982i
\(341\) 5.64423 0.305652
\(342\) −13.7165 −0.741701
\(343\) 1.00000i 0.0539949i
\(344\) 1.28846i 0.0694690i
\(345\) 1.25461i 0.0675458i
\(346\) 30.3051i 1.62921i
\(347\) −20.3812 −1.09412 −0.547060 0.837093i \(-0.684253\pi\)
−0.547060 + 0.837093i \(0.684253\pi\)
\(348\) 0.0890557 0.00477388
\(349\) 7.16394i 0.383477i −0.981446 0.191739i \(-0.938587\pi\)
0.981446 0.191739i \(-0.0614126\pi\)
\(350\) 5.60197 0.299438
\(351\) 8.86376 + 6.68035i 0.473113 + 0.356570i
\(352\) −2.83710 −0.151218
\(353\) 5.38348i 0.286534i 0.989684 + 0.143267i \(0.0457607\pi\)
−0.989684 + 0.143267i \(0.954239\pi\)
\(354\) 1.75872 0.0934751
\(355\) −5.88550 −0.312370
\(356\) 3.42696i 0.181629i
\(357\) 1.55252i 0.0821681i
\(358\) 24.1906i 1.27851i
\(359\) 15.6937i 0.828281i 0.910213 + 0.414140i \(0.135918\pi\)
−0.910213 + 0.414140i \(0.864082\pi\)
\(360\) −3.84324 −0.202557
\(361\) 0.278438 0.0146547
\(362\) 18.3896i 0.966537i
\(363\) 5.55971 0.291809
\(364\) −1.36910 + 1.81658i −0.0717605 + 0.0952148i
\(365\) 0.162899 0.00852650
\(366\) 4.58145i 0.239476i
\(367\) 0.324575 0.0169427 0.00847133 0.999964i \(-0.497303\pi\)
0.00847133 + 0.999964i \(0.497303\pi\)
\(368\) 11.8166 0.615982
\(369\) 18.0989i 0.942191i
\(370\) 5.12783i 0.266583i
\(371\) 1.63090i 0.0846720i
\(372\) 2.31351i 0.119950i
\(373\) −25.3112 −1.31057 −0.655283 0.755383i \(-0.727451\pi\)
−0.655283 + 0.755383i \(0.727451\pi\)
\(374\) −2.79606 −0.144581
\(375\) 2.43188i 0.125582i
\(376\) −28.4703 −1.46824
\(377\) −0.753803 0.568118i −0.0388228 0.0292596i
\(378\) −3.60197 −0.185265
\(379\) 16.7187i 0.858784i 0.903118 + 0.429392i \(0.141272\pi\)
−0.903118 + 0.429392i \(0.858728\pi\)
\(380\) −1.25792 −0.0645299
\(381\) 7.26180 0.372033
\(382\) 19.6430i 1.00502i
\(383\) 13.1629i 0.672593i −0.941756 0.336296i \(-0.890826\pi\)
0.941756 0.336296i \(-0.109174\pi\)
\(384\) 1.78992i 0.0913415i
\(385\) 0.382433i 0.0194906i
\(386\) 23.4186 1.19197
\(387\) −1.13397 −0.0576429
\(388\) 7.95509i 0.403858i
\(389\) 10.0761 0.510879 0.255440 0.966825i \(-0.417780\pi\)
0.255440 + 0.966825i \(0.417780\pi\)
\(390\) −0.837101 0.630898i −0.0423883 0.0319467i
\(391\) −14.5392 −0.735278
\(392\) 3.07838i 0.155482i
\(393\) −7.78539 −0.392721
\(394\) 20.4969 1.03262
\(395\) 1.29791i 0.0653051i
\(396\) 1.41855i 0.0712849i
\(397\) 8.07119i 0.405081i 0.979274 + 0.202541i \(0.0649198\pi\)
−0.979274 + 0.202541i \(0.935080\pi\)
\(398\) 19.0700i 0.955891i
\(399\) −2.33299 −0.116795
\(400\) −11.2039 −0.560197
\(401\) 12.8371i 0.641054i 0.947239 + 0.320527i \(0.103860\pi\)
−0.947239 + 0.320527i \(0.896140\pi\)
\(402\) −3.20394 −0.159798
\(403\) −14.7587 + 19.5825i −0.735184 + 0.975474i
\(404\) −2.29914 −0.114386
\(405\) 2.98053i 0.148104i
\(406\) 0.306323 0.0152026
\(407\) −7.89269 −0.391226
\(408\) 4.77924i 0.236608i
\(409\) 18.7515i 0.927204i 0.886044 + 0.463602i \(0.153443\pi\)
−0.886044 + 0.463602i \(0.846557\pi\)
\(410\) 3.60197i 0.177889i
\(411\) 8.85989i 0.437026i
\(412\) −11.3197 −0.557679
\(413\) −2.78765 −0.137171
\(414\) 16.0072i 0.786710i
\(415\) −4.78151 −0.234715
\(416\) 7.41855 9.84324i 0.363724 0.482605i
\(417\) 7.12783 0.349051
\(418\) 4.20167i 0.205510i
\(419\) 23.6319 1.15450 0.577248 0.816569i \(-0.304127\pi\)
0.577248 + 0.816569i \(0.304127\pi\)
\(420\) −0.156755 −0.00764888
\(421\) 19.4524i 0.948052i 0.880511 + 0.474026i \(0.157200\pi\)
−0.880511 + 0.474026i \(0.842800\pi\)
\(422\) 3.17009i 0.154317i
\(423\) 25.0566i 1.21830i
\(424\) 5.02052i 0.243818i
\(425\) 13.7854 0.668689
\(426\) 8.05786 0.390405
\(427\) 7.26180i 0.351423i
\(428\) 1.85762 0.0897915
\(429\) 0.971071 1.28846i 0.0468837 0.0622073i
\(430\) 0.225678 0.0108832
\(431\) 18.0989i 0.871793i 0.899997 + 0.435897i \(0.143569\pi\)
−0.899997 + 0.435897i \(0.856431\pi\)
\(432\) 7.20394 0.346600
\(433\) −20.5380 −0.986992 −0.493496 0.869748i \(-0.664281\pi\)
−0.493496 + 0.869748i \(0.664281\pi\)
\(434\) 7.95774i 0.381984i
\(435\) 0.0650468i 0.00311875i
\(436\) 5.31965i 0.254765i
\(437\) 21.8482i 1.04514i
\(438\) −0.223025 −0.0106565
\(439\) 26.9627 1.28686 0.643429 0.765506i \(-0.277511\pi\)
0.643429 + 0.765506i \(0.277511\pi\)
\(440\) 1.17727i 0.0561244i
\(441\) 2.70928 0.129013
\(442\) 7.31124 9.70086i 0.347760 0.461423i
\(443\) 26.4101 1.25478 0.627392 0.778704i \(-0.284122\pi\)
0.627392 + 0.778704i \(0.284122\pi\)
\(444\) 3.23513i 0.153533i
\(445\) 2.50307 0.118657
\(446\) −23.1617 −1.09674
\(447\) 11.0556i 0.522912i
\(448\) 8.68035i 0.410108i
\(449\) 31.4329i 1.48341i 0.670725 + 0.741706i \(0.265983\pi\)
−0.670725 + 0.741706i \(0.734017\pi\)
\(450\) 15.1773i 0.715464i
\(451\) −5.54411 −0.261062
\(452\) 8.08065 0.380082
\(453\) 0.859888i 0.0404011i
\(454\) 15.5174 0.728270
\(455\) 1.32684 + 1.00000i 0.0622033 + 0.0468807i
\(456\) 7.18181 0.336319
\(457\) 18.0650i 0.845047i −0.906352 0.422524i \(-0.861144\pi\)
0.906352 0.422524i \(-0.138856\pi\)
\(458\) 32.5380 1.52040
\(459\) −8.86376 −0.413725
\(460\) 1.46800i 0.0684458i
\(461\) 23.0784i 1.07487i −0.843306 0.537434i \(-0.819394\pi\)
0.843306 0.537434i \(-0.180606\pi\)
\(462\) 0.523590i 0.0243596i
\(463\) 4.54760i 0.211345i 0.994401 + 0.105672i \(0.0336995\pi\)
−0.994401 + 0.105672i \(0.966301\pi\)
\(464\) −0.612646 −0.0284414
\(465\) −1.68980 −0.0783627
\(466\) 15.6404i 0.724525i
\(467\) −37.8154 −1.74989 −0.874943 0.484226i \(-0.839101\pi\)
−0.874943 + 0.484226i \(0.839101\pi\)
\(468\) 4.92162 + 3.70928i 0.227502 + 0.171461i
\(469\) 5.07838 0.234498
\(470\) 4.98667i 0.230018i
\(471\) −4.47414 −0.206158
\(472\) 8.58145 0.394993
\(473\) 0.347361i 0.0159717i
\(474\) 1.77698i 0.0816192i
\(475\) 20.7154i 0.950489i
\(476\) 1.81658i 0.0832629i
\(477\) −4.41855 −0.202312
\(478\) −10.1880 −0.465986
\(479\) 9.24005i 0.422189i 0.977466 + 0.211094i \(0.0677028\pi\)
−0.977466 + 0.211094i \(0.932297\pi\)
\(480\) 0.849388 0.0387691
\(481\) 20.6381 27.3835i 0.941016 1.24858i
\(482\) −19.8108 −0.902358
\(483\) 2.72261i 0.123883i
\(484\) 6.50534 0.295697
\(485\) 5.81044 0.263838
\(486\) 14.8865i 0.675268i
\(487\) 13.6598i 0.618986i 0.950902 + 0.309493i \(0.100159\pi\)
−0.950902 + 0.309493i \(0.899841\pi\)
\(488\) 22.3545i 1.01194i
\(489\) 0.214614i 0.00970519i
\(490\) −0.539189 −0.0243581
\(491\) 29.6514 1.33815 0.669075 0.743195i \(-0.266691\pi\)
0.669075 + 0.743195i \(0.266691\pi\)
\(492\) 2.27247i 0.102451i
\(493\) 0.753803 0.0339496
\(494\) −14.5776 10.9867i −0.655876 0.494314i
\(495\) −1.03612 −0.0465700
\(496\) 15.9155i 0.714626i
\(497\) −12.7721 −0.572905
\(498\) 6.54638 0.293350
\(499\) 35.5246i 1.59030i −0.606412 0.795151i \(-0.707392\pi\)
0.606412 0.795151i \(-0.292608\pi\)
\(500\) 2.84551i 0.127255i
\(501\) 12.8710i 0.575032i
\(502\) 10.3219i 0.460690i
\(503\) 34.4124 1.53437 0.767187 0.641424i \(-0.221656\pi\)
0.767187 + 0.641424i \(0.221656\pi\)
\(504\) −8.34017 −0.371501
\(505\) 1.67930i 0.0747279i
\(506\) 4.90337 0.217981
\(507\) 1.93108 + 6.73820i 0.0857622 + 0.299254i
\(508\) 8.49693 0.376990
\(509\) 11.1184i 0.492813i −0.969167 0.246407i \(-0.920750\pi\)
0.969167 0.246407i \(-0.0792498\pi\)
\(510\) 0.837101 0.0370675
\(511\) 0.353504 0.0156381
\(512\) 22.4079i 0.990297i
\(513\) 13.3197i 0.588077i
\(514\) 15.9649i 0.704183i
\(515\) 8.26794i 0.364329i
\(516\) 0.142380 0.00626791
\(517\) −7.67543 −0.337565
\(518\) 11.1278i 0.488929i
\(519\) −13.9649 −0.612992
\(520\) −4.08452 3.07838i −0.179118 0.134996i
\(521\) −17.8888 −0.783723 −0.391862 0.920024i \(-0.628169\pi\)
−0.391862 + 0.920024i \(0.628169\pi\)
\(522\) 0.829914i 0.0363243i
\(523\) −23.9877 −1.04891 −0.524455 0.851438i \(-0.675731\pi\)
−0.524455 + 0.851438i \(0.675731\pi\)
\(524\) −9.10957 −0.397954
\(525\) 2.58145i 0.112664i
\(526\) 14.2485i 0.621263i
\(527\) 19.5825i 0.853027i
\(528\) 1.04718i 0.0455727i
\(529\) 2.49693 0.108562
\(530\) 0.879362 0.0381970
\(531\) 7.55252i 0.327751i
\(532\) −2.72979 −0.118352
\(533\) 14.4969 19.2351i 0.627932 0.833166i
\(534\) −3.42696 −0.148299
\(535\) 1.35682i 0.0586603i
\(536\) −15.6332 −0.675250
\(537\) −11.1473 −0.481042
\(538\) 12.9262i 0.557286i
\(539\) 0.829914i 0.0357469i
\(540\) 0.894960i 0.0385130i
\(541\) 19.4114i 0.834560i −0.908778 0.417280i \(-0.862983\pi\)
0.908778 0.417280i \(-0.137017\pi\)
\(542\) −12.7961 −0.549638
\(543\) −8.47414 −0.363660
\(544\) 9.84324i 0.422026i
\(545\) −3.88550 −0.166437
\(546\) −1.81658 1.36910i −0.0777426 0.0585922i
\(547\) −1.81432 −0.0775745 −0.0387873 0.999247i \(-0.512349\pi\)
−0.0387873 + 0.999247i \(0.512349\pi\)
\(548\) 10.3668i 0.442849i
\(549\) −19.6742 −0.839675
\(550\) −4.64915 −0.198240
\(551\) 1.13275i 0.0482566i
\(552\) 8.38121i 0.356728i
\(553\) 2.81658i 0.119773i
\(554\) 30.5620i 1.29845i
\(555\) 2.36296 0.100302
\(556\) 8.34017 0.353702
\(557\) 23.4186i 0.992276i 0.868244 + 0.496138i \(0.165249\pi\)
−0.868244 + 0.496138i \(0.834751\pi\)
\(558\) −21.5597 −0.912695
\(559\) −1.20516 0.908291i −0.0509728 0.0384166i
\(560\) 1.07838 0.0455698
\(561\) 1.28846i 0.0543987i
\(562\) 5.62022 0.237075
\(563\) −26.6947 −1.12505 −0.562524 0.826781i \(-0.690170\pi\)
−0.562524 + 0.826781i \(0.690170\pi\)
\(564\) 3.14608i 0.132474i
\(565\) 5.90215i 0.248305i
\(566\) 1.14608i 0.0481732i
\(567\) 6.46800i 0.271630i
\(568\) 39.3172 1.64971
\(569\) 26.5897 1.11470 0.557349 0.830279i \(-0.311819\pi\)
0.557349 + 0.830279i \(0.311819\pi\)
\(570\) 1.25792i 0.0526885i
\(571\) 3.43310 0.143671 0.0718355 0.997416i \(-0.477114\pi\)
0.0718355 + 0.997416i \(0.477114\pi\)
\(572\) 1.13624 1.50761i 0.0475084 0.0630362i
\(573\) −9.05172 −0.378141
\(574\) 7.81658i 0.326258i
\(575\) −24.1750 −1.00817
\(576\) 23.5174 0.979894
\(577\) 30.4657i 1.26831i −0.773208 0.634153i \(-0.781349\pi\)
0.773208 0.634153i \(-0.218651\pi\)
\(578\) 10.1906i 0.423873i
\(579\) 10.7915i 0.448481i
\(580\) 0.0761103i 0.00316031i
\(581\) −10.3763 −0.430481
\(582\) −7.95509 −0.329749
\(583\) 1.35350i 0.0560564i
\(584\) −1.08822 −0.0450308
\(585\) 2.70928 3.59478i 0.112015 0.148626i
\(586\) −28.4645 −1.17586
\(587\) 26.2606i 1.08389i −0.840414 0.541945i \(-0.817688\pi\)
0.840414 0.541945i \(-0.182312\pi\)
\(588\) −0.340173 −0.0140285
\(589\) −29.4268 −1.21251
\(590\) 1.50307i 0.0618805i
\(591\) 9.44521i 0.388524i
\(592\) 22.2557i 0.914702i
\(593\) 40.8420i 1.67718i 0.544762 + 0.838590i \(0.316620\pi\)
−0.544762 + 0.838590i \(0.683380\pi\)
\(594\) 2.98932 0.122653
\(595\) −1.32684 −0.0543952
\(596\) 12.9360i 0.529879i
\(597\) 8.78765 0.359655
\(598\) −12.8215 + 17.0121i −0.524310 + 0.695677i
\(599\) −27.3545 −1.11768 −0.558838 0.829277i \(-0.688753\pi\)
−0.558838 + 0.829277i \(0.688753\pi\)
\(600\) 7.94668i 0.324422i
\(601\) 25.4908 1.03979 0.519895 0.854230i \(-0.325971\pi\)
0.519895 + 0.854230i \(0.325971\pi\)
\(602\) 0.489741 0.0199603
\(603\) 13.7587i 0.560299i
\(604\) 1.00614i 0.0409394i
\(605\) 4.75154i 0.193177i
\(606\) 2.29914i 0.0933960i
\(607\) 19.9311 0.808977 0.404489 0.914543i \(-0.367449\pi\)
0.404489 + 0.914543i \(0.367449\pi\)
\(608\) 14.7915 0.599876
\(609\) 0.141157i 0.00571997i
\(610\) 3.91548 0.158533
\(611\) 20.0700 26.6297i 0.811944 1.07732i
\(612\) −4.92162 −0.198945
\(613\) 22.7214i 0.917708i −0.888512 0.458854i \(-0.848260\pi\)
0.888512 0.458854i \(-0.151740\pi\)
\(614\) 7.27739 0.293692
\(615\) 1.65983 0.0669307
\(616\) 2.55479i 0.102935i
\(617\) 14.3545i 0.577892i 0.957345 + 0.288946i \(0.0933049\pi\)
−0.957345 + 0.288946i \(0.906695\pi\)
\(618\) 11.3197i 0.455343i
\(619\) 27.9832i 1.12474i 0.826886 + 0.562369i \(0.190110\pi\)
−0.826886 + 0.562369i \(0.809890\pi\)
\(620\) −1.97721 −0.0794068
\(621\) 15.5441 0.623764
\(622\) 29.3789i 1.17799i
\(623\) 5.43188 0.217624
\(624\) 3.63317 + 2.73820i 0.145443 + 0.109616i
\(625\) 21.8599 0.874396
\(626\) 2.62106i 0.104758i
\(627\) 1.93618 0.0773234
\(628\) −5.23513 −0.208905
\(629\) 27.3835i 1.09185i
\(630\) 1.46081i 0.0582001i
\(631\) 21.4186i 0.852659i −0.904568 0.426330i \(-0.859806\pi\)
0.904568 0.426330i \(-0.140194\pi\)
\(632\) 8.67050i 0.344894i
\(633\) 1.46081 0.0580620
\(634\) −3.38735 −0.134529
\(635\) 6.20620i 0.246286i
\(636\) 0.554787 0.0219987
\(637\) 2.87936 + 2.17009i 0.114084 + 0.0859820i
\(638\) −0.254222 −0.0100647
\(639\) 34.6030i 1.36887i
\(640\) −1.52973 −0.0604680
\(641\) 37.9360 1.49838 0.749191 0.662354i \(-0.230443\pi\)
0.749191 + 0.662354i \(0.230443\pi\)
\(642\) 1.85762i 0.0733144i
\(643\) 36.2122i 1.42807i −0.700111 0.714034i \(-0.746866\pi\)
0.700111 0.714034i \(-0.253134\pi\)
\(644\) 3.18568i 0.125534i
\(645\) 0.103995i 0.00409479i
\(646\) 14.5776 0.573547
\(647\) −42.7948 −1.68244 −0.841219 0.540694i \(-0.818162\pi\)
−0.841219 + 0.540694i \(0.818162\pi\)
\(648\) 19.9109i 0.782176i
\(649\) 2.31351 0.0908132
\(650\) 12.1568 16.1301i 0.476827 0.632674i
\(651\) −3.66701 −0.143722
\(652\) 0.251117i 0.00983451i
\(653\) 5.54864 0.217135 0.108568 0.994089i \(-0.465374\pi\)
0.108568 + 0.994089i \(0.465374\pi\)
\(654\) 5.31965 0.208015
\(655\) 6.65368i 0.259981i
\(656\) 15.6332i 0.610373i
\(657\) 0.957740i 0.0373650i
\(658\) 10.8215i 0.421866i
\(659\) −23.1529 −0.901908 −0.450954 0.892547i \(-0.648916\pi\)
−0.450954 + 0.892547i \(0.648916\pi\)
\(660\) 0.130094 0.00506388
\(661\) 47.2544i 1.83798i 0.394276 + 0.918992i \(0.370995\pi\)
−0.394276 + 0.918992i \(0.629005\pi\)
\(662\) −4.97948 −0.193533
\(663\) −4.47027 3.36910i −0.173611 0.130845i
\(664\) 31.9421 1.23960
\(665\) 1.99386i 0.0773185i
\(666\) 30.1483 1.16822
\(667\) −1.32192 −0.0511850
\(668\) 15.0601i 0.582694i
\(669\) 10.6732i 0.412648i
\(670\) 2.73820i 0.105786i
\(671\) 6.02666i 0.232657i
\(672\) 1.84324 0.0711047
\(673\) 3.42082 0.131863 0.0659314 0.997824i \(-0.478998\pi\)
0.0659314 + 0.997824i \(0.478998\pi\)
\(674\) 18.1906i 0.700676i
\(675\) −14.7382 −0.567274
\(676\) 2.25953 + 7.88428i 0.0869049 + 0.303242i
\(677\) 10.6959 0.411079 0.205539 0.978649i \(-0.434105\pi\)
0.205539 + 0.978649i \(0.434105\pi\)
\(678\) 8.08065i 0.310335i
\(679\) 12.6092 0.483895
\(680\) 4.08452 0.156634
\(681\) 7.15061i 0.274012i
\(682\) 6.60424i 0.252889i
\(683\) 6.59583i 0.252382i 0.992006 + 0.126191i \(0.0402753\pi\)
−0.992006 + 0.126191i \(0.959725\pi\)
\(684\) 7.39576i 0.282784i
\(685\) 7.57199 0.289311
\(686\) −1.17009 −0.0446741
\(687\) 14.9939i 0.572051i
\(688\) −0.979481 −0.0373424
\(689\) −4.69594 3.53919i −0.178901 0.134832i
\(690\) −1.46800 −0.0558858
\(691\) 49.4729i 1.88204i 0.338353 + 0.941019i \(0.390130\pi\)
−0.338353 + 0.941019i \(0.609870\pi\)
\(692\) −16.3402 −0.621160
\(693\) −2.24846 −0.0854121
\(694\) 23.8478i 0.905249i
\(695\) 6.09171i 0.231072i
\(696\) 0.434535i 0.0164710i
\(697\) 19.2351i 0.728583i
\(698\) 8.38243 0.317280
\(699\) 7.20725 0.272603
\(700\) 3.02052i 0.114165i
\(701\) −20.8166 −0.786231 −0.393116 0.919489i \(-0.628603\pi\)
−0.393116 + 0.919489i \(0.628603\pi\)
\(702\) −7.81658 + 10.3714i −0.295018 + 0.391442i
\(703\) 41.1494 1.55198
\(704\) 7.20394i 0.271509i
\(705\) 2.29791 0.0865444
\(706\) −6.29914 −0.237071
\(707\) 3.64423i 0.137055i
\(708\) 0.948284i 0.0356387i
\(709\) 5.95386i 0.223602i 0.993731 + 0.111801i \(0.0356619\pi\)
−0.993731 + 0.111801i \(0.964338\pi\)
\(710\) 6.88655i 0.258448i
\(711\) −7.63090 −0.286181
\(712\) −16.7214 −0.626660
\(713\) 34.3412i 1.28609i
\(714\) 1.81658 0.0679839
\(715\) −1.10116 0.829914i −0.0411812 0.0310370i
\(716\) −13.0433 −0.487451
\(717\) 4.69472i 0.175328i
\(718\) −18.3630 −0.685300
\(719\) 1.68980 0.0630190 0.0315095 0.999503i \(-0.489969\pi\)
0.0315095 + 0.999503i \(0.489969\pi\)
\(720\) 2.92162i 0.108882i
\(721\) 17.9421i 0.668200i
\(722\) 0.325797i 0.0121249i
\(723\) 9.12905i 0.339513i
\(724\) −9.91548 −0.368506
\(725\) 1.25338 0.0465495
\(726\) 6.50534i 0.241436i
\(727\) −14.0722 −0.521910 −0.260955 0.965351i \(-0.584037\pi\)
−0.260955 + 0.965351i \(0.584037\pi\)
\(728\) −8.86376 6.68035i −0.328513 0.247590i
\(729\) −12.5441 −0.464597
\(730\) 0.190605i 0.00705462i
\(731\) 1.20516 0.0445744
\(732\) 2.47027 0.0913037
\(733\) 10.9311i 0.403749i 0.979411 + 0.201874i \(0.0647032\pi\)
−0.979411 + 0.201874i \(0.935297\pi\)
\(734\) 0.379780i 0.0140179i
\(735\) 0.248464i 0.00916474i
\(736\) 17.2618i 0.636278i
\(737\) −4.21461 −0.155247
\(738\) 21.1773 0.779546
\(739\) 3.17009i 0.116614i −0.998299 0.0583068i \(-0.981430\pi\)
0.998299 0.0583068i \(-0.0185701\pi\)
\(740\) 2.76487 0.101639
\(741\) −5.06278 + 6.71751i −0.185986 + 0.246774i
\(742\) 1.90829 0.0700556
\(743\) 9.73206i 0.357035i −0.983937 0.178517i \(-0.942870\pi\)
0.983937 0.178517i \(-0.0571301\pi\)
\(744\) 11.2885 0.413855
\(745\) −9.44852 −0.346167
\(746\) 29.6163i 1.08433i
\(747\) 28.1122i 1.02857i
\(748\) 1.50761i 0.0551235i
\(749\) 2.94441i 0.107586i
\(750\) 2.84551 0.103903
\(751\) −7.77924 −0.283869 −0.141934 0.989876i \(-0.545332\pi\)
−0.141934 + 0.989876i \(0.545332\pi\)
\(752\) 21.6430i 0.789239i
\(753\) 4.75646 0.173335
\(754\) 0.664748 0.882015i 0.0242087 0.0321211i
\(755\) −0.734892 −0.0267455
\(756\) 1.94214i 0.0706350i
\(757\) 10.8576 0.394627 0.197313 0.980340i \(-0.436778\pi\)
0.197313 + 0.980340i \(0.436778\pi\)
\(758\) −19.5624 −0.710537
\(759\) 2.25953i 0.0820157i
\(760\) 6.13784i 0.222643i
\(761\) 1.82150i 0.0660294i 0.999455 + 0.0330147i \(0.0105108\pi\)
−0.999455 + 0.0330147i \(0.989489\pi\)
\(762\) 8.49693i 0.307811i
\(763\) −8.43188 −0.305255
\(764\) −10.5913 −0.383179
\(765\) 3.59478i 0.129970i
\(766\) 15.4017 0.556487
\(767\) −6.04945 + 8.02666i −0.218433 + 0.289826i
\(768\) −7.26633 −0.262201
\(769\) 39.7948i 1.43504i −0.696539 0.717519i \(-0.745277\pi\)
0.696539 0.717519i \(-0.254723\pi\)
\(770\) 0.447480 0.0161261
\(771\) 7.35682 0.264949
\(772\) 12.6270i 0.454456i
\(773\) 18.3135i 0.658691i −0.944209 0.329346i \(-0.893172\pi\)
0.944209 0.329346i \(-0.106828\pi\)
\(774\) 1.32684i 0.0476924i
\(775\) 32.5608i 1.16962i
\(776\) −38.8157 −1.39340
\(777\) 5.12783 0.183960
\(778\) 11.7899i 0.422689i
\(779\) 28.9048 1.03562
\(780\) −0.340173 + 0.451356i −0.0121801 + 0.0161611i
\(781\) 10.5997 0.379287
\(782\) 17.0121i 0.608352i
\(783\) −0.805905 −0.0288007
\(784\) 2.34017 0.0835776
\(785\) 3.82377i 0.136476i
\(786\) 9.10957i 0.324928i
\(787\) 26.2606i 0.936088i −0.883705 0.468044i \(-0.844959\pi\)
0.883705 0.468044i \(-0.155041\pi\)
\(788\) 11.0517i 0.393701i
\(789\) −6.56585 −0.233750
\(790\) 1.51867 0.0540319
\(791\) 12.8082i