Properties

Label 637.2.f.g.393.3
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.1485512441856.7
Defining polynomial: \(x^{8} + 24 x^{6} + 455 x^{4} + 2904 x^{2} + 14641\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.3
Root \(-2.04914 + 3.54921i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.g.295.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.09827 q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.09827 q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.04914 + 3.54921i) q^{10} +(1.89792 + 3.28729i) q^{11} +1.41421 q^{12} +(0.634922 + 3.54921i) q^{13} +(-2.89792 - 5.01934i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.634922 + 1.09972i) q^{17} -1.00000 q^{18} +(-1.41421 + 2.44949i) q^{19} +(-2.04914 + 3.54921i) q^{20} +(1.89792 - 3.28729i) q^{22} +(3.89792 + 6.75139i) q^{23} +(-2.12132 - 3.67423i) q^{24} +11.7958 q^{25} +(2.75624 - 2.32446i) q^{26} +5.65685 q^{27} +(-0.397916 - 0.689210i) q^{29} +(-2.89792 + 5.01934i) q^{30} +1.41421 q^{31} +(-2.50000 + 4.33013i) q^{32} +(-2.68406 + 4.64893i) q^{33} +1.26984 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-1.39792 - 2.42126i) q^{37} +2.82843 q^{38} +(-3.89792 + 3.28729i) q^{39} +12.2948 q^{40} +(1.48640 + 2.57452i) q^{41} +(-3.89792 + 6.75139i) q^{43} +3.79583 q^{44} +(-2.04914 + 3.54921i) q^{45} +(3.89792 - 6.75139i) q^{46} -2.82843 q^{47} +(-0.707107 + 1.22474i) q^{48} +(-5.89792 - 10.2155i) q^{50} -1.79583 q^{51} +(3.39116 + 1.22474i) q^{52} -12.5917 q^{53} +(-2.82843 - 4.89898i) q^{54} +(-7.77817 - 13.4722i) q^{55} -4.00000 q^{57} +(-0.397916 + 0.689210i) q^{58} +(-6.21959 + 10.7726i) q^{59} -5.79583 q^{60} +(4.17046 - 7.22344i) q^{61} +(-0.707107 - 1.22474i) q^{62} +7.00000 q^{64} +(-2.60208 - 14.5456i) q^{65} +5.36812 q^{66} +(1.89792 + 3.28729i) q^{67} +(0.634922 + 1.09972i) q^{68} +(-5.51249 + 9.54790i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +12.5836 q^{73} +(-1.39792 + 2.42126i) q^{74} +(8.34091 + 14.4469i) q^{75} +(1.41421 + 2.44949i) q^{76} +(4.79583 + 1.73205i) q^{78} -2.20417 q^{79} +(-2.04914 - 3.54921i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.48640 - 2.57452i) q^{82} +9.89949 q^{83} +(2.60208 - 4.50694i) q^{85} +7.79583 q^{86} +(0.562738 - 0.974691i) q^{87} +(-5.69375 - 9.86186i) q^{88} +(-7.48944 - 12.9721i) q^{89} +4.09827 q^{90} +7.79583 q^{92} +(1.00000 + 1.73205i) q^{93} +(1.41421 + 2.44949i) q^{94} +(5.79583 - 10.0387i) q^{95} -7.07107 q^{96} +(-2.12132 + 3.67423i) q^{97} +3.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + 4q^{4} - 24q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + 4q^{4} - 24q^{8} + 4q^{9} - 4q^{11} - 4q^{15} + 4q^{16} - 8q^{18} - 4q^{22} + 12q^{23} + 56q^{25} + 16q^{29} - 4q^{30} - 20q^{32} - 4q^{36} + 8q^{37} - 12q^{39} - 12q^{43} - 8q^{44} + 12q^{46} - 28q^{50} + 24q^{51} - 24q^{53} - 32q^{57} + 16q^{58} - 8q^{60} + 56q^{64} - 40q^{65} - 4q^{67} - 24q^{71} - 12q^{72} + 8q^{74} - 56q^{79} + 20q^{81} + 40q^{85} + 24q^{86} + 12q^{88} + 24q^{92} + 8q^{93} + 8q^{95} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 0.707107 + 1.22474i 0.408248 + 0.707107i 0.994694 0.102882i \(-0.0328064\pi\)
−0.586445 + 0.809989i \(0.699473\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −4.09827 −1.83280 −0.916401 0.400260i \(-0.868920\pi\)
−0.916401 + 0.400260i \(0.868920\pi\)
\(6\) 0.707107 1.22474i 0.288675 0.500000i
\(7\) 0 0
\(8\) −3.00000 −1.06066
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 2.04914 + 3.54921i 0.647994 + 1.12236i
\(11\) 1.89792 + 3.28729i 0.572243 + 0.991154i 0.996335 + 0.0855351i \(0.0272600\pi\)
−0.424092 + 0.905619i \(0.639407\pi\)
\(12\) 1.41421 0.408248
\(13\) 0.634922 + 3.54921i 0.176096 + 0.984373i
\(14\) 0 0
\(15\) −2.89792 5.01934i −0.748239 1.29599i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −0.634922 + 1.09972i −0.153991 + 0.266721i −0.932691 0.360676i \(-0.882546\pi\)
0.778700 + 0.627396i \(0.215879\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.41421 + 2.44949i −0.324443 + 0.561951i −0.981399 0.191977i \(-0.938510\pi\)
0.656957 + 0.753928i \(0.271843\pi\)
\(20\) −2.04914 + 3.54921i −0.458201 + 0.793627i
\(21\) 0 0
\(22\) 1.89792 3.28729i 0.404637 0.700852i
\(23\) 3.89792 + 6.75139i 0.812772 + 1.40776i 0.910917 + 0.412590i \(0.135376\pi\)
−0.0981454 + 0.995172i \(0.531291\pi\)
\(24\) −2.12132 3.67423i −0.433013 0.750000i
\(25\) 11.7958 2.35917
\(26\) 2.75624 2.32446i 0.540544 0.455865i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) −0.397916 0.689210i −0.0738911 0.127983i 0.826712 0.562625i \(-0.190208\pi\)
−0.900604 + 0.434642i \(0.856875\pi\)
\(30\) −2.89792 + 5.01934i −0.529085 + 0.916401i
\(31\) 1.41421 0.254000 0.127000 0.991903i \(-0.459465\pi\)
0.127000 + 0.991903i \(0.459465\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) −2.68406 + 4.64893i −0.467235 + 0.809274i
\(34\) 1.26984 0.217777
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −1.39792 2.42126i −0.229816 0.398053i 0.727937 0.685643i \(-0.240479\pi\)
−0.957753 + 0.287591i \(0.907146\pi\)
\(38\) 2.82843 0.458831
\(39\) −3.89792 + 3.28729i −0.624166 + 0.526387i
\(40\) 12.2948 1.94398
\(41\) 1.48640 + 2.57452i 0.232136 + 0.402072i 0.958437 0.285306i \(-0.0920951\pi\)
−0.726300 + 0.687378i \(0.758762\pi\)
\(42\) 0 0
\(43\) −3.89792 + 6.75139i −0.594427 + 1.02958i 0.399201 + 0.916863i \(0.369288\pi\)
−0.993628 + 0.112714i \(0.964046\pi\)
\(44\) 3.79583 0.572243
\(45\) −2.04914 + 3.54921i −0.305467 + 0.529085i
\(46\) 3.89792 6.75139i 0.574716 0.995438i
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) −0.707107 + 1.22474i −0.102062 + 0.176777i
\(49\) 0 0
\(50\) −5.89792 10.2155i −0.834091 1.44469i
\(51\) −1.79583 −0.251467
\(52\) 3.39116 + 1.22474i 0.470270 + 0.169842i
\(53\) −12.5917 −1.72960 −0.864799 0.502118i \(-0.832554\pi\)
−0.864799 + 0.502118i \(0.832554\pi\)
\(54\) −2.82843 4.89898i −0.384900 0.666667i
\(55\) −7.77817 13.4722i −1.04881 1.81659i
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) −0.397916 + 0.689210i −0.0522489 + 0.0904977i
\(59\) −6.21959 + 10.7726i −0.809722 + 1.40248i 0.103335 + 0.994647i \(0.467049\pi\)
−0.913057 + 0.407833i \(0.866285\pi\)
\(60\) −5.79583 −0.748239
\(61\) 4.17046 7.22344i 0.533972 0.924867i −0.465240 0.885185i \(-0.654032\pi\)
0.999212 0.0396825i \(-0.0126346\pi\)
\(62\) −0.707107 1.22474i −0.0898027 0.155543i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −2.60208 14.5456i −0.322749 1.80416i
\(66\) 5.36812 0.660769
\(67\) 1.89792 + 3.28729i 0.231867 + 0.401606i 0.958358 0.285571i \(-0.0921831\pi\)
−0.726490 + 0.687177i \(0.758850\pi\)
\(68\) 0.634922 + 1.09972i 0.0769956 + 0.133360i
\(69\) −5.51249 + 9.54790i −0.663625 + 1.14943i
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) 12.5836 1.47279 0.736397 0.676550i \(-0.236526\pi\)
0.736397 + 0.676550i \(0.236526\pi\)
\(74\) −1.39792 + 2.42126i −0.162504 + 0.281466i
\(75\) 8.34091 + 14.4469i 0.963126 + 1.66818i
\(76\) 1.41421 + 2.44949i 0.162221 + 0.280976i
\(77\) 0 0
\(78\) 4.79583 + 1.73205i 0.543021 + 0.196116i
\(79\) −2.20417 −0.247988 −0.123994 0.992283i \(-0.539570\pi\)
−0.123994 + 0.992283i \(0.539570\pi\)
\(80\) −2.04914 3.54921i −0.229100 0.396813i
\(81\) 2.50000 + 4.33013i 0.277778 + 0.481125i
\(82\) 1.48640 2.57452i 0.164145 0.284308i
\(83\) 9.89949 1.08661 0.543305 0.839535i \(-0.317173\pi\)
0.543305 + 0.839535i \(0.317173\pi\)
\(84\) 0 0
\(85\) 2.60208 4.50694i 0.282236 0.488847i
\(86\) 7.79583 0.840646
\(87\) 0.562738 0.974691i 0.0603318 0.104498i
\(88\) −5.69375 9.86186i −0.606955 1.05128i
\(89\) −7.48944 12.9721i −0.793879 1.37504i −0.923549 0.383481i \(-0.874725\pi\)
0.129670 0.991557i \(-0.458608\pi\)
\(90\) 4.09827 0.431996
\(91\) 0 0
\(92\) 7.79583 0.812772
\(93\) 1.00000 + 1.73205i 0.103695 + 0.179605i
\(94\) 1.41421 + 2.44949i 0.145865 + 0.252646i
\(95\) 5.79583 10.0387i 0.594640 1.02995i
\(96\) −7.07107 −0.721688
\(97\) −2.12132 + 3.67423i −0.215387 + 0.373062i −0.953392 0.301733i \(-0.902435\pi\)
0.738005 + 0.674795i \(0.235768\pi\)
\(98\) 0 0
\(99\) 3.79583 0.381495
\(100\) 5.89792 10.2155i 0.589792 1.02155i
\(101\) −4.87756 8.44819i −0.485336 0.840626i 0.514522 0.857477i \(-0.327969\pi\)
−0.999858 + 0.0168509i \(0.994636\pi\)
\(102\) 0.897916 + 1.55524i 0.0889069 + 0.153991i
\(103\) −5.36812 −0.528936 −0.264468 0.964394i \(-0.585196\pi\)
−0.264468 + 0.964394i \(0.585196\pi\)
\(104\) −1.90477 10.6476i −0.186778 1.04409i
\(105\) 0 0
\(106\) 6.29583 + 10.9047i 0.611505 + 1.05916i
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) 2.82843 4.89898i 0.272166 0.471405i
\(109\) 1.59166 0.152454 0.0762268 0.997091i \(-0.475713\pi\)
0.0762268 + 0.997091i \(0.475713\pi\)
\(110\) −7.77817 + 13.4722i −0.741620 + 1.28452i
\(111\) 1.97695 3.42418i 0.187644 0.325009i
\(112\) 0 0
\(113\) −1.29583 + 2.24445i −0.121902 + 0.211140i −0.920518 0.390701i \(-0.872233\pi\)
0.798616 + 0.601841i \(0.205566\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) −15.9747 27.6690i −1.48965 2.58015i
\(116\) −0.795832 −0.0738911
\(117\) 3.39116 + 1.22474i 0.313513 + 0.113228i
\(118\) 12.4392 1.14512
\(119\) 0 0
\(120\) 8.69375 + 15.0580i 0.793627 + 1.37460i
\(121\) −1.70417 + 2.95171i −0.154924 + 0.268337i
\(122\) −8.34091 −0.755151
\(123\) −2.10208 + 3.64092i −0.189539 + 0.328290i
\(124\) 0.707107 1.22474i 0.0635001 0.109985i
\(125\) −27.8512 −2.49108
\(126\) 0 0
\(127\) 5.79583 + 10.0387i 0.514297 + 0.890788i 0.999862 + 0.0165881i \(0.00528038\pi\)
−0.485566 + 0.874200i \(0.661386\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) −11.0250 −0.970695
\(130\) −11.2958 + 9.52628i −0.990710 + 0.835510i
\(131\) −5.36812 −0.469015 −0.234507 0.972114i \(-0.575348\pi\)
−0.234507 + 0.972114i \(0.575348\pi\)
\(132\) 2.68406 + 4.64893i 0.233617 + 0.404637i
\(133\) 0 0
\(134\) 1.89792 3.28729i 0.163955 0.283978i
\(135\) −23.1833 −1.99530
\(136\) 1.90477 3.29915i 0.163332 0.282900i
\(137\) 9.39792 16.2777i 0.802918 1.39069i −0.114769 0.993392i \(-0.536613\pi\)
0.917688 0.397303i \(-0.130054\pi\)
\(138\) 11.0250 0.938508
\(139\) −0.851476 + 1.47480i −0.0722212 + 0.125091i −0.899875 0.436149i \(-0.856342\pi\)
0.827653 + 0.561240i \(0.189675\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) 6.00000 0.503509
\(143\) −10.4622 + 8.82327i −0.874896 + 0.737839i
\(144\) 1.00000 0.0833333
\(145\) 1.63077 + 2.82457i 0.135428 + 0.234568i
\(146\) −6.29178 10.8977i −0.520711 0.901898i
\(147\) 0 0
\(148\) −2.79583 −0.229816
\(149\) 7.29583 12.6368i 0.597698 1.03524i −0.395462 0.918482i \(-0.629416\pi\)
0.993160 0.116761i \(-0.0372511\pi\)
\(150\) 8.34091 14.4469i 0.681033 1.17958i
\(151\) 1.59166 0.129528 0.0647639 0.997901i \(-0.479371\pi\)
0.0647639 + 0.997901i \(0.479371\pi\)
\(152\) 4.24264 7.34847i 0.344124 0.596040i
\(153\) 0.634922 + 1.09972i 0.0513304 + 0.0889069i
\(154\) 0 0
\(155\) −5.79583 −0.465532
\(156\) 0.897916 + 5.01934i 0.0718908 + 0.401869i
\(157\) 0.144369 0.0115219 0.00576095 0.999983i \(-0.498166\pi\)
0.00576095 + 0.999983i \(0.498166\pi\)
\(158\) 1.10208 + 1.90887i 0.0876771 + 0.151861i
\(159\) −8.90365 15.4216i −0.706105 1.22301i
\(160\) 10.2457 17.7460i 0.809992 1.40295i
\(161\) 0 0
\(162\) 2.50000 4.33013i 0.196419 0.340207i
\(163\) −7.69375 + 13.3260i −0.602621 + 1.04377i 0.389802 + 0.920899i \(0.372543\pi\)
−0.992423 + 0.122871i \(0.960790\pi\)
\(164\) 2.97280 0.232136
\(165\) 11.0000 19.0526i 0.856349 1.48324i
\(166\) −4.94975 8.57321i −0.384175 0.665410i
\(167\) 0.851476 + 1.47480i 0.0658892 + 0.114123i 0.897088 0.441852i \(-0.145678\pi\)
−0.831199 + 0.555975i \(0.812345\pi\)
\(168\) 0 0
\(169\) −12.1937 + 4.50694i −0.937981 + 0.346688i
\(170\) −5.20417 −0.399142
\(171\) 1.41421 + 2.44949i 0.108148 + 0.187317i
\(172\) 3.89792 + 6.75139i 0.297213 + 0.514789i
\(173\) −8.90365 + 15.4216i −0.676932 + 1.17248i 0.298968 + 0.954263i \(0.403358\pi\)
−0.975900 + 0.218218i \(0.929976\pi\)
\(174\) −1.12548 −0.0853221
\(175\) 0 0
\(176\) −1.89792 + 3.28729i −0.143061 + 0.247789i
\(177\) −17.5917 −1.32227
\(178\) −7.48944 + 12.9721i −0.561357 + 0.972299i
\(179\) 9.79583 + 16.9669i 0.732175 + 1.26816i 0.955952 + 0.293524i \(0.0948279\pi\)
−0.223777 + 0.974640i \(0.571839\pi\)
\(180\) 2.04914 + 3.54921i 0.152734 + 0.264542i
\(181\) −3.80953 −0.283160 −0.141580 0.989927i \(-0.545218\pi\)
−0.141580 + 0.989927i \(0.545218\pi\)
\(182\) 0 0
\(183\) 11.7958 0.871973
\(184\) −11.6937 20.2542i −0.862074 1.49316i
\(185\) 5.72904 + 9.92299i 0.421207 + 0.729552i
\(186\) 1.00000 1.73205i 0.0733236 0.127000i
\(187\) −4.82012 −0.352482
\(188\) −1.41421 + 2.44949i −0.103142 + 0.178647i
\(189\) 0 0
\(190\) −11.5917 −0.840948
\(191\) 8.10208 14.0332i 0.586246 1.01541i −0.408473 0.912771i \(-0.633938\pi\)
0.994719 0.102638i \(-0.0327282\pi\)
\(192\) 4.94975 + 8.57321i 0.357217 + 0.618718i
\(193\) −11.2958 19.5650i −0.813092 1.40832i −0.910690 0.413090i \(-0.864449\pi\)
0.0975983 0.995226i \(-0.468884\pi\)
\(194\) 4.24264 0.304604
\(195\) 15.9747 13.4722i 1.14397 0.964764i
\(196\) 0 0
\(197\) 4.00000 + 6.92820i 0.284988 + 0.493614i 0.972606 0.232458i \(-0.0746770\pi\)
−0.687618 + 0.726073i \(0.741344\pi\)
\(198\) −1.89792 3.28729i −0.134879 0.233617i
\(199\) 2.53969 4.39887i 0.180034 0.311828i −0.761858 0.647744i \(-0.775713\pi\)
0.941892 + 0.335916i \(0.109046\pi\)
\(200\) −35.3875 −2.50227
\(201\) −2.68406 + 4.64893i −0.189319 + 0.327910i
\(202\) −4.87756 + 8.44819i −0.343184 + 0.594412i
\(203\) 0 0
\(204\) −0.897916 + 1.55524i −0.0628667 + 0.108888i
\(205\) −6.09166 10.5511i −0.425460 0.736919i
\(206\) 2.68406 + 4.64893i 0.187007 + 0.323906i
\(207\) 7.79583 0.541848
\(208\) −2.75624 + 2.32446i −0.191111 + 0.161172i
\(209\) −10.7362 −0.742641
\(210\) 0 0
\(211\) −3.89792 6.75139i −0.268344 0.464785i 0.700091 0.714054i \(-0.253143\pi\)
−0.968434 + 0.249269i \(0.919810\pi\)
\(212\) −6.29583 + 10.9047i −0.432399 + 0.748938i
\(213\) −8.48528 −0.581402
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 15.9747 27.6690i 1.08947 1.88701i
\(216\) −16.9706 −1.15470
\(217\) 0 0
\(218\) −0.795832 1.37842i −0.0539005 0.0933584i
\(219\) 8.89792 + 15.4116i 0.601265 + 1.04142i
\(220\) −15.5563 −1.04881
\(221\) −4.30625 1.55524i −0.289670 0.104616i
\(222\) −3.95390 −0.265369
\(223\) −2.82843 4.89898i −0.189405 0.328060i 0.755647 0.654979i \(-0.227323\pi\)
−0.945052 + 0.326920i \(0.893989\pi\)
\(224\) 0 0
\(225\) 5.89792 10.2155i 0.393194 0.681033i
\(226\) 2.59166 0.172395
\(227\) 3.67990 6.37378i 0.244244 0.423043i −0.717675 0.696378i \(-0.754794\pi\)
0.961919 + 0.273336i \(0.0881270\pi\)
\(228\) −2.00000 + 3.46410i −0.132453 + 0.229416i
\(229\) −12.7279 −0.841085 −0.420542 0.907273i \(-0.638160\pi\)
−0.420542 + 0.907273i \(0.638160\pi\)
\(230\) −15.9747 + 27.6690i −1.05334 + 1.82444i
\(231\) 0 0
\(232\) 1.19375 + 2.06763i 0.0783733 + 0.135747i
\(233\) 17.1833 1.12572 0.562859 0.826553i \(-0.309702\pi\)
0.562859 + 0.826553i \(0.309702\pi\)
\(234\) −0.634922 3.54921i −0.0415062 0.232019i
\(235\) 11.5917 0.756157
\(236\) 6.21959 + 10.7726i 0.404861 + 0.701240i
\(237\) −1.55858 2.69954i −0.101241 0.175354i
\(238\) 0 0
\(239\) −10.2042 −0.660053 −0.330026 0.943972i \(-0.607058\pi\)
−0.330026 + 0.943972i \(0.607058\pi\)
\(240\) 2.89792 5.01934i 0.187060 0.323997i
\(241\) 5.58467 9.67293i 0.359740 0.623088i −0.628177 0.778070i \(-0.716199\pi\)
0.987917 + 0.154982i \(0.0495320\pi\)
\(242\) 3.40834 0.219096
\(243\) 4.94975 8.57321i 0.317526 0.549972i
\(244\) −4.17046 7.22344i −0.266986 0.462433i
\(245\) 0 0
\(246\) 4.20417 0.268048
\(247\) −9.59166 3.46410i −0.610303 0.220416i
\(248\) −4.24264 −0.269408
\(249\) 7.00000 + 12.1244i 0.443607 + 0.768350i
\(250\) 13.9256 + 24.1198i 0.880731 + 1.52547i
\(251\) −8.34091 + 14.4469i −0.526474 + 0.911879i 0.473050 + 0.881035i \(0.343153\pi\)
−0.999524 + 0.0308439i \(0.990181\pi\)
\(252\) 0 0
\(253\) −14.7958 + 25.6271i −0.930206 + 1.61116i
\(254\) 5.79583 10.0387i 0.363663 0.629882i
\(255\) 7.35981 0.460889
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 4.31483 + 7.47350i 0.269151 + 0.466184i 0.968643 0.248457i \(-0.0799235\pi\)
−0.699492 + 0.714641i \(0.746590\pi\)
\(258\) 5.51249 + 9.54790i 0.343192 + 0.594427i
\(259\) 0 0
\(260\) −13.8979 5.01934i −0.861912 0.311286i
\(261\) −0.795832 −0.0492607
\(262\) 2.68406 + 4.64893i 0.165822 + 0.287212i
\(263\) −1.69375 2.93366i −0.104441 0.180897i 0.809069 0.587714i \(-0.199972\pi\)
−0.913510 + 0.406817i \(0.866639\pi\)
\(264\) 8.05217 13.9468i 0.495577 0.858365i
\(265\) 51.6041 3.17001
\(266\) 0 0
\(267\) 10.5917 18.3453i 0.648199 1.12271i
\(268\) 3.79583 0.231867
\(269\) 6.21959 10.7726i 0.379215 0.656820i −0.611733 0.791064i \(-0.709527\pi\)
0.990948 + 0.134244i \(0.0428607\pi\)
\(270\) 11.5917 + 20.0773i 0.705446 + 1.22187i
\(271\) 8.75928 + 15.1715i 0.532088 + 0.921604i 0.999298 + 0.0374577i \(0.0119260\pi\)
−0.467210 + 0.884147i \(0.654741\pi\)
\(272\) −1.26984 −0.0769956
\(273\) 0 0
\(274\) −18.7958 −1.13550
\(275\) 22.3875 + 38.7763i 1.35002 + 2.33830i
\(276\) 5.51249 + 9.54790i 0.331813 + 0.574716i
\(277\) −16.0917 + 27.8716i −0.966854 + 1.67464i −0.262306 + 0.964985i \(0.584483\pi\)
−0.704548 + 0.709656i \(0.748850\pi\)
\(278\) 1.70295 0.102136
\(279\) 0.707107 1.22474i 0.0423334 0.0733236i
\(280\) 0 0
\(281\) 24.7958 1.47920 0.739598 0.673049i \(-0.235016\pi\)
0.739598 + 0.673049i \(0.235016\pi\)
\(282\) −2.00000 + 3.46410i −0.119098 + 0.206284i
\(283\) −7.92254 13.7222i −0.470946 0.815703i 0.528501 0.848932i \(-0.322754\pi\)
−0.999448 + 0.0332294i \(0.989421\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 16.3931 0.971043
\(286\) 12.8723 + 4.64893i 0.761155 + 0.274897i
\(287\) 0 0
\(288\) 2.50000 + 4.33013i 0.147314 + 0.255155i
\(289\) 7.69375 + 13.3260i 0.452573 + 0.783880i
\(290\) 1.63077 2.82457i 0.0957619 0.165865i
\(291\) −6.00000 −0.351726
\(292\) 6.29178 10.8977i 0.368198 0.637738i
\(293\) −1.48640 + 2.57452i −0.0868363 + 0.150405i −0.906172 0.422909i \(-0.861009\pi\)
0.819336 + 0.573314i \(0.194342\pi\)
\(294\) 0 0
\(295\) 25.4896 44.1492i 1.48406 2.57047i
\(296\) 4.19375 + 7.26378i 0.243757 + 0.422199i
\(297\) 10.7362 + 18.5957i 0.622979 + 1.07903i
\(298\) −14.5917 −0.845272
\(299\) −21.4872 + 18.1211i −1.24264 + 1.04797i
\(300\) 16.6818 0.963126
\(301\) 0 0
\(302\) −0.795832 1.37842i −0.0457950 0.0793192i
\(303\) 6.89792 11.9475i 0.396275 0.686368i
\(304\) −2.82843 −0.162221
\(305\) −17.0917 + 29.6036i −0.978666 + 1.69510i
\(306\) 0.634922 1.09972i 0.0362961 0.0628667i
\(307\) 20.0583 1.14478 0.572392 0.819980i \(-0.306015\pi\)
0.572392 + 0.819980i \(0.306015\pi\)
\(308\) 0 0
\(309\) −3.79583 6.57457i −0.215937 0.374014i
\(310\) 2.89792 + 5.01934i 0.164591 + 0.285079i
\(311\) 28.8323 1.63493 0.817464 0.575980i \(-0.195379\pi\)
0.817464 + 0.575980i \(0.195379\pi\)
\(312\) 11.6937 9.86186i 0.662028 0.558318i
\(313\) −15.2676 −0.862976 −0.431488 0.902119i \(-0.642011\pi\)
−0.431488 + 0.902119i \(0.642011\pi\)
\(314\) −0.0721845 0.125027i −0.00407360 0.00705569i
\(315\) 0 0
\(316\) −1.10208 + 1.90887i −0.0619971 + 0.107382i
\(317\) 6.59166 0.370225 0.185112 0.982717i \(-0.440735\pi\)
0.185112 + 0.982717i \(0.440735\pi\)
\(318\) −8.90365 + 15.4216i −0.499292 + 0.864799i
\(319\) 1.51042 2.61613i 0.0845674 0.146475i
\(320\) −28.6879 −1.60370
\(321\) −4.24264 + 7.34847i −0.236801 + 0.410152i
\(322\) 0 0
\(323\) −1.79583 3.11047i −0.0999227 0.173071i
\(324\) 5.00000 0.277778
\(325\) 7.48944 + 41.8659i 0.415439 + 2.32230i
\(326\) 15.3875 0.852235
\(327\) 1.12548 + 1.94938i 0.0622390 + 0.107801i
\(328\) −4.45919 7.72355i −0.246218 0.426462i
\(329\) 0 0
\(330\) −22.0000 −1.21106
\(331\) −14.6937 + 25.4503i −0.807641 + 1.39888i 0.106852 + 0.994275i \(0.465923\pi\)
−0.914493 + 0.404601i \(0.867410\pi\)
\(332\) 4.94975 8.57321i 0.271653 0.470516i
\(333\) −2.79583 −0.153211
\(334\) 0.851476 1.47480i 0.0465907 0.0806974i
\(335\) −7.77817 13.4722i −0.424967 0.736065i
\(336\) 0 0
\(337\) 17.9792 0.979387 0.489694 0.871895i \(-0.337109\pi\)
0.489694 + 0.871895i \(0.337109\pi\)
\(338\) 10.0000 + 8.30662i 0.543928 + 0.451821i
\(339\) −3.66517 −0.199064
\(340\) −2.60208 4.50694i −0.141118 0.244423i
\(341\) 2.68406 + 4.64893i 0.145350 + 0.251753i
\(342\) 1.41421 2.44949i 0.0764719 0.132453i
\(343\) 0 0
\(344\) 11.6937 20.2542i 0.630485 1.09203i
\(345\) 22.5917 39.1299i 1.21629 2.10668i
\(346\) 17.8073 0.957326
\(347\) 16.4896 28.5608i 0.885207 1.53322i 0.0397307 0.999210i \(-0.487350\pi\)
0.845476 0.534013i \(-0.179317\pi\)
\(348\) −0.562738 0.974691i −0.0301659 0.0522489i
\(349\) 13.2907 + 23.0201i 0.711433 + 1.23224i 0.964319 + 0.264742i \(0.0852867\pi\)
−0.252887 + 0.967496i \(0.581380\pi\)
\(350\) 0 0
\(351\) 3.59166 + 20.0773i 0.191709 + 1.07165i
\(352\) −18.9792 −1.01159
\(353\) 2.61187 + 4.52390i 0.139016 + 0.240783i 0.927124 0.374754i \(-0.122273\pi\)
−0.788108 + 0.615536i \(0.788939\pi\)
\(354\) 8.79583 + 15.2348i 0.467493 + 0.809722i
\(355\) 12.2948 21.2952i 0.652541 1.13023i
\(356\) −14.9789 −0.793879
\(357\) 0 0
\(358\) 9.79583 16.9669i 0.517726 0.896727i
\(359\) −4.00000 −0.211112 −0.105556 0.994413i \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) 6.14741 10.6476i 0.323997 0.561179i
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) 1.90477 + 3.29915i 0.100112 + 0.173400i
\(363\) −4.82012 −0.252990
\(364\) 0 0
\(365\) −51.5708 −2.69934
\(366\) −5.89792 10.2155i −0.308289 0.533972i
\(367\) 10.6066 + 18.3712i 0.553660 + 0.958967i 0.998006 + 0.0631123i \(0.0201026\pi\)
−0.444346 + 0.895855i \(0.646564\pi\)
\(368\) −3.89792 + 6.75139i −0.203193 + 0.351940i
\(369\) 2.97280 0.154758
\(370\) 5.72904 9.92299i 0.297839 0.515871i
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) −3.29583 + 5.70855i −0.170652 + 0.295577i −0.938648 0.344877i \(-0.887921\pi\)
0.767996 + 0.640454i \(0.221254\pi\)
\(374\) 2.41006 + 4.17434i 0.124621 + 0.215850i
\(375\) −19.6937 34.1106i −1.01698 1.76146i
\(376\) 8.48528 0.437595
\(377\) 2.19350 1.84988i 0.112971 0.0952737i
\(378\) 0 0
\(379\) −12.6937 21.9862i −0.652034 1.12936i −0.982629 0.185583i \(-0.940583\pi\)
0.330595 0.943773i \(-0.392751\pi\)
\(380\) −5.79583 10.0387i −0.297320 0.514973i
\(381\) −8.19654 + 14.1968i −0.419922 + 0.727326i
\(382\) −16.2042 −0.829077
\(383\) 6.07522 10.5226i 0.310429 0.537680i −0.668026 0.744138i \(-0.732860\pi\)
0.978455 + 0.206458i \(0.0661938\pi\)
\(384\) −2.12132 + 3.67423i −0.108253 + 0.187500i
\(385\) 0 0
\(386\) −11.2958 + 19.5650i −0.574943 + 0.995830i
\(387\) 3.89792 + 6.75139i 0.198142 + 0.343192i
\(388\) 2.12132 + 3.67423i 0.107694 + 0.186531i
\(389\) −0.387495 −0.0196468 −0.00982338 0.999952i \(-0.503127\pi\)
−0.00982338 + 0.999952i \(0.503127\pi\)
\(390\) −19.6546 7.09841i −0.995250 0.359442i
\(391\) −9.89949 −0.500639
\(392\) 0 0
\(393\) −3.79583 6.57457i −0.191474 0.331643i
\(394\) 4.00000 6.92820i 0.201517 0.349038i
\(395\) 9.03328 0.454514
\(396\) 1.89792 3.28729i 0.0953739 0.165192i
\(397\) 3.53553 6.12372i 0.177443 0.307341i −0.763561 0.645736i \(-0.776551\pi\)
0.941004 + 0.338395i \(0.109884\pi\)
\(398\) −5.07938 −0.254606
\(399\) 0 0
\(400\) 5.89792 + 10.2155i 0.294896 + 0.510774i
\(401\) 2.19375 + 3.79968i 0.109551 + 0.189747i 0.915588 0.402117i \(-0.131726\pi\)
−0.806038 + 0.591864i \(0.798392\pi\)
\(402\) 5.36812 0.267737
\(403\) 0.897916 + 5.01934i 0.0447284 + 0.250031i
\(404\) −9.75513 −0.485336
\(405\) −10.2457 17.7460i −0.509112 0.881808i
\(406\) 0 0
\(407\) 5.30625 9.19070i 0.263021 0.455566i
\(408\) 5.38749 0.266721
\(409\) 9.39420 16.2712i 0.464513 0.804561i −0.534666 0.845063i \(-0.679563\pi\)
0.999179 + 0.0405026i \(0.0128959\pi\)
\(410\) −6.09166 + 10.5511i −0.300846 + 0.521080i
\(411\) 26.5813 1.31116
\(412\) −2.68406 + 4.64893i −0.132234 + 0.229036i
\(413\) 0 0
\(414\) −3.89792 6.75139i −0.191572 0.331813i
\(415\) −40.5708 −1.99154
\(416\) −16.9558 6.12372i −0.831328 0.300240i
\(417\) −2.40834 −0.117937
\(418\) 5.36812 + 9.29785i 0.262563 + 0.454773i
\(419\) −12.8576 22.2699i −0.628133 1.08796i −0.987926 0.154926i \(-0.950486\pi\)
0.359794 0.933032i \(-0.382847\pi\)
\(420\) 0 0
\(421\) 12.5917 0.613680 0.306840 0.951761i \(-0.400728\pi\)
0.306840 + 0.951761i \(0.400728\pi\)
\(422\) −3.89792 + 6.75139i −0.189748 + 0.328652i
\(423\) −1.41421 + 2.44949i −0.0687614 + 0.119098i
\(424\) 37.7750 1.83452
\(425\) −7.48944 + 12.9721i −0.363291 + 0.629239i
\(426\) 4.24264 + 7.34847i 0.205557 + 0.356034i
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) −18.2042 6.57457i −0.878906 0.317423i
\(430\) −31.9494 −1.54074
\(431\) −16.5917 28.7376i −0.799192 1.38424i −0.920143 0.391583i \(-0.871928\pi\)
0.120950 0.992659i \(-0.461406\pi\)
\(432\) 2.82843 + 4.89898i 0.136083 + 0.235702i
\(433\) −10.2457 + 17.7460i −0.492376 + 0.852820i −0.999961 0.00878126i \(-0.997205\pi\)
0.507586 + 0.861601i \(0.330538\pi\)
\(434\) 0 0
\(435\) −2.30625 + 3.99455i −0.110576 + 0.191524i
\(436\) 0.795832 1.37842i 0.0381134 0.0660144i
\(437\) −22.0499 −1.05479
\(438\) 8.89792 15.4116i 0.425159 0.736397i
\(439\) −10.0291 17.3710i −0.478664 0.829070i 0.521037 0.853534i \(-0.325545\pi\)
−0.999701 + 0.0244638i \(0.992212\pi\)
\(440\) 23.3345 + 40.4166i 1.11243 + 1.92678i
\(441\) 0 0
\(442\) 0.806253 + 4.50694i 0.0383495 + 0.214373i
\(443\) 10.0000 0.475114 0.237557 0.971374i \(-0.423653\pi\)
0.237557 + 0.971374i \(0.423653\pi\)
\(444\) −1.97695 3.42418i −0.0938220 0.162504i
\(445\) 30.6937 + 53.1631i 1.45502 + 2.52017i
\(446\) −2.82843 + 4.89898i −0.133930 + 0.231973i
\(447\) 20.6357 0.976036
\(448\) 0 0
\(449\) −11.7958 + 20.4310i −0.556680 + 0.964198i 0.441091 + 0.897462i \(0.354592\pi\)
−0.997771 + 0.0667352i \(0.978742\pi\)
\(450\) −11.7958 −0.556061
\(451\) −5.64212 + 9.77243i −0.265677 + 0.460166i
\(452\) 1.29583 + 2.24445i 0.0609508 + 0.105570i
\(453\) 1.12548 + 1.94938i 0.0528795 + 0.0915899i
\(454\) −7.35981 −0.345413
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −2.29583 3.97650i −0.107394 0.186013i 0.807320 0.590115i \(-0.200917\pi\)
−0.914714 + 0.404102i \(0.867584\pi\)
\(458\) 6.36396 + 11.0227i 0.297368 + 0.515057i
\(459\) −3.59166 + 6.22094i −0.167644 + 0.290369i
\(460\) −31.9494 −1.48965
\(461\) 12.0930 20.9457i 0.563227 0.975538i −0.433985 0.900920i \(-0.642893\pi\)
0.997212 0.0746180i \(-0.0237737\pi\)
\(462\) 0 0
\(463\) −17.3875 −0.808065 −0.404033 0.914745i \(-0.632392\pi\)
−0.404033 + 0.914745i \(0.632392\pi\)
\(464\) 0.397916 0.689210i 0.0184728 0.0319958i
\(465\) −4.09827 7.09841i −0.190053 0.329181i
\(466\) −8.59166 14.8812i −0.398001 0.689358i
\(467\) 31.9494 1.47844 0.739222 0.673462i \(-0.235194\pi\)
0.739222 + 0.673462i \(0.235194\pi\)
\(468\) 2.75624 2.32446i 0.127407 0.107448i
\(469\) 0 0
\(470\) −5.79583 10.0387i −0.267342 0.463050i
\(471\) 0.102084 + 0.176815i 0.00470379 + 0.00814721i
\(472\) 18.6588 32.3179i 0.858840 1.48755i
\(473\) −29.5917 −1.36063
\(474\) −1.55858 + 2.69954i −0.0715881 + 0.123994i
\(475\) −16.6818 + 28.8938i −0.765415 + 1.32574i
\(476\) 0 0
\(477\) −6.29583 + 10.9047i −0.288266 + 0.499292i
\(478\) 5.10208 + 8.83707i 0.233364 + 0.404198i
\(479\) −10.4622 18.1211i −0.478032 0.827975i 0.521651 0.853159i \(-0.325316\pi\)
−0.999683 + 0.0251838i \(0.991983\pi\)
\(480\) 28.9792 1.32271
\(481\) 7.70599 6.49881i 0.351363 0.296320i
\(482\) −11.1693 −0.508749
\(483\) 0 0
\(484\) 1.70417 + 2.95171i 0.0774622 + 0.134168i
\(485\) 8.69375 15.0580i 0.394763 0.683749i
\(486\) −9.89949 −0.449050
\(487\) −0.204168 + 0.353630i −0.00925176 + 0.0160245i −0.870614 0.491966i \(-0.836278\pi\)
0.861362 + 0.507991i \(0.169612\pi\)
\(488\) −12.5114 + 21.6703i −0.566363 + 0.980970i
\(489\) −21.7612 −0.984076
\(490\) 0 0
\(491\) −4.79583 8.30662i −0.216433 0.374873i 0.737282 0.675585i \(-0.236109\pi\)
−0.953715 + 0.300712i \(0.902776\pi\)
\(492\) 2.10208 + 3.64092i 0.0947693 + 0.164145i
\(493\) 1.01058 0.0455143
\(494\) 1.79583 + 10.0387i 0.0807983 + 0.451661i
\(495\) −15.5563 −0.699206
\(496\) 0.707107 + 1.22474i 0.0317500 + 0.0549927i
\(497\) 0 0
\(498\) 7.00000 12.1244i 0.313678 0.543305i
\(499\) 25.7958 1.15478 0.577390 0.816468i \(-0.304071\pi\)
0.577390 + 0.816468i \(0.304071\pi\)
\(500\) −13.9256 + 24.1198i −0.622771 + 1.07867i
\(501\) −1.20417 + 2.08568i −0.0537983 + 0.0931814i
\(502\) 16.6818 0.744546
\(503\) 12.8576 22.2699i 0.573290 0.992967i −0.422935 0.906160i \(-0.639000\pi\)
0.996225 0.0868074i \(-0.0276665\pi\)
\(504\) 0 0
\(505\) 19.9896 + 34.6230i 0.889525 + 1.54070i
\(506\) 29.5917 1.31551
\(507\) −14.1421 11.7473i −0.628074 0.521718i
\(508\) 11.5917 0.514297
\(509\) 3.04498 + 5.27406i 0.134966 + 0.233769i 0.925585 0.378541i \(-0.123574\pi\)
−0.790618 + 0.612309i \(0.790241\pi\)
\(510\) −3.67990 6.37378i −0.162949 0.282236i
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) −8.00000 + 13.8564i −0.353209 + 0.611775i
\(514\) 4.31483 7.47350i 0.190319 0.329642i
\(515\) 22.0000 0.969436
\(516\) −5.51249 + 9.54790i −0.242674 + 0.420323i
\(517\) −5.36812 9.29785i −0.236089 0.408919i
\(518\) 0 0
\(519\) −25.1833 −1.10543
\(520\) 7.80625 + 43.6369i 0.342327 + 1.91360i
\(521\) −4.67575 −0.204848 −0.102424 0.994741i \(-0.532660\pi\)
−0.102424 + 0.994741i \(0.532660\pi\)
\(522\) 0.397916 + 0.689210i 0.0174163 + 0.0301659i
\(523\) 21.0688 + 36.4923i 0.921276 + 1.59570i 0.797444 + 0.603393i \(0.206185\pi\)
0.123832 + 0.992303i \(0.460482\pi\)
\(524\) −2.68406 + 4.64893i −0.117254 + 0.203089i
\(525\) 0 0
\(526\) −1.69375 + 2.93366i −0.0738509 + 0.127913i
\(527\) −0.897916 + 1.55524i −0.0391138 + 0.0677471i
\(528\) −5.36812 −0.233617
\(529\) −18.8875 + 32.7141i −0.821195 + 1.42235i
\(530\) −25.8020 44.6904i −1.12077 1.94123i
\(531\) 6.21959 + 10.7726i 0.269907 + 0.467493i
\(532\) 0 0
\(533\) −8.19375 + 6.91015i −0.354911 + 0.299312i
\(534\) −21.1833 −0.916692
\(535\) −12.2948 21.2952i −0.531551 0.920674i
\(536\) −5.69375 9.86186i −0.245932 0.425967i
\(537\) −13.8534 + 23.9948i −0.597818 + 1.03545i
\(538\) −12.4392 −0.536291
\(539\) 0 0
\(540\) −11.5917 + 20.0773i −0.498826 + 0.863992i
\(541\) 6.59166 0.283398 0.141699 0.989910i \(-0.454744\pi\)
0.141699 + 0.989910i \(0.454744\pi\)
\(542\) 8.75928 15.1715i 0.376243 0.651673i
\(543\) −2.69375 4.66571i −0.115600 0.200225i
\(544\) −3.17461 5.49859i −0.136110 0.235750i
\(545\) −6.52307 −0.279418
\(546\) 0 0
\(547\) 10.9792 0.469435 0.234717 0.972064i \(-0.424584\pi\)
0.234717 + 0.972064i \(0.424584\pi\)
\(548\) −9.39792 16.2777i −0.401459 0.695347i
\(549\) −4.17046 7.22344i −0.177991 0.308289i
\(550\) 22.3875 38.7763i 0.954606 1.65343i
\(551\) 2.25095 0.0958938
\(552\) 16.5375 28.6437i 0.703881 1.21916i
\(553\) 0 0
\(554\) 32.1833 1.36734
\(555\) −8.10208 + 14.0332i −0.343914 + 0.595677i
\(556\) 0.851476 + 1.47480i 0.0361106 + 0.0625454i
\(557\) −0.704168 1.21966i −0.0298366 0.0516785i 0.850722 0.525617i \(-0.176165\pi\)
−0.880558 + 0.473938i \(0.842832\pi\)
\(558\) −1.41421 −0.0598684
\(559\) −26.4370 9.54790i −1.11816 0.403833i
\(560\) 0 0
\(561\) −3.40834 5.90341i −0.143900 0.249242i
\(562\) −12.3979 21.4738i −0.522975 0.905818i
\(563\) 6.21959 10.7726i 0.262125 0.454013i −0.704682 0.709524i \(-0.748910\pi\)
0.966806 + 0.255511i \(0.0822435\pi\)
\(564\) −4.00000 −0.168430
\(565\) 5.31067 9.19835i 0.223422 0.386977i
\(566\) −7.92254 + 13.7222i −0.333009 + 0.576789i
\(567\) 0 0
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) −12.7958 22.1630i −0.536429 0.929123i −0.999093 0.0425886i \(-0.986440\pi\)
0.462664 0.886534i \(-0.346894\pi\)
\(570\) −8.19654 14.1968i −0.343315 0.594640i
\(571\) −23.1833 −0.970192 −0.485096 0.874461i \(-0.661215\pi\)
−0.485096 + 0.874461i \(0.661215\pi\)
\(572\) 2.41006 + 13.4722i 0.100770 + 0.563301i
\(573\) 22.9162 0.957336
\(574\) 0 0
\(575\) 45.9792 + 79.6382i 1.91746 + 3.32114i
\(576\) 3.50000 6.06218i 0.145833 0.252591i
\(577\) −24.7340 −1.02969 −0.514845 0.857283i \(-0.672151\pi\)
−0.514845 + 0.857283i \(0.672151\pi\)
\(578\) 7.69375 13.3260i 0.320018 0.554287i
\(579\) 15.9747 27.6690i 0.663887 1.14989i
\(580\) 3.26153 0.135428
\(581\) 0 0
\(582\) 3.00000 + 5.19615i 0.124354 + 0.215387i
\(583\) −23.8979 41.3924i −0.989751 1.71430i
\(584\) −37.7507 −1.56213
\(585\) −13.8979 5.01934i −0.574608 0.207524i
\(586\) 2.97280 0.122805
\(587\) 8.34091 + 14.4469i 0.344266 + 0.596287i 0.985220 0.171293i \(-0.0547944\pi\)
−0.640954 + 0.767579i \(0.721461\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) −50.9792 −2.09878
\(591\) −5.65685 + 9.79796i −0.232692 + 0.403034i
\(592\) 1.39792 2.42126i 0.0574540 0.0995132i
\(593\) 8.34091 0.342520 0.171260 0.985226i \(-0.445216\pi\)
0.171260 + 0.985226i \(0.445216\pi\)
\(594\) 10.7362 18.5957i 0.440513 0.762991i
\(595\) 0 0
\(596\) −7.29583 12.6368i −0.298849 0.517621i
\(597\) 7.18333 0.293994
\(598\) 26.4370 + 9.54790i 1.08109 + 0.390443i
\(599\) −33.5917 −1.37252 −0.686259 0.727357i \(-0.740748\pi\)
−0.686259 + 0.727357i \(0.740748\pi\)
\(600\) −25.0227 43.3407i −1.02155 1.76937i
\(601\) −12.0930 20.9457i −0.493284 0.854393i 0.506686 0.862130i \(-0.330870\pi\)
−0.999970 + 0.00773797i \(0.997537\pi\)
\(602\) 0 0
\(603\) 3.79583 0.154578
\(604\) 0.795832 1.37842i 0.0323819 0.0560871i
\(605\) 6.98415 12.0969i 0.283946 0.491809i
\(606\) −13.7958 −0.560417
\(607\) 2.39532 4.14882i 0.0972231 0.168395i −0.813311 0.581829i \(-0.802337\pi\)
0.910534 + 0.413434i \(0.135671\pi\)
\(608\) −7.07107 12.2474i −0.286770 0.496700i
\(609\) 0 0
\(610\) 34.1833 1.38404
\(611\) −1.79583 10.0387i −0.0726516 0.406121i
\(612\) 1.26984 0.0513304
\(613\) −20.9896 36.3550i −0.847761 1.46837i −0.883202 0.468994i \(-0.844617\pi\)
0.0354405 0.999372i \(-0.488717\pi\)
\(614\) −10.0291 17.3710i −0.404743 0.701035i
\(615\) 8.61491 14.9215i 0.347387 0.601692i
\(616\) 0 0
\(617\) −2.19375 + 3.79968i −0.0883169 + 0.152969i −0.906800 0.421561i \(-0.861482\pi\)
0.818483 + 0.574531i \(0.194815\pi\)
\(618\) −3.79583 + 6.57457i −0.152691 + 0.264468i
\(619\) 33.9116 1.36302 0.681512 0.731807i \(-0.261323\pi\)
0.681512 + 0.731807i \(0.261323\pi\)
\(620\) −2.89792 + 5.01934i −0.116383 + 0.201581i
\(621\) 22.0499 + 38.1916i 0.884834 + 1.53258i
\(622\) −14.4161 24.9695i −0.578034 1.00118i
\(623\) 0 0
\(624\) −4.79583 1.73205i −0.191987 0.0693375i
\(625\) 55.1625 2.20650
\(626\) 7.63381 + 13.2221i 0.305108 + 0.528463i
\(627\) −7.59166 13.1491i −0.303182 0.525126i
\(628\) 0.0721845 0.125027i 0.00288047 0.00498913i
\(629\) 3.55027 0.141559
\(630\) 0 0
\(631\) 19.7958 34.2874i 0.788060 1.36496i −0.139095 0.990279i \(-0.544419\pi\)
0.927154 0.374680i \(-0.122247\pi\)
\(632\) 6.61251 0.263031
\(633\) 5.51249 9.54790i 0.219102 0.379495i
\(634\) −3.29583 5.70855i −0.130894 0.226715i
\(635\) −23.7529 41.1412i −0.942605 1.63264i
\(636\) −17.8073 −0.706105
\(637\) 0 0
\(638\) −3.02084 −0.119596
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) −6.14741 10.6476i −0.242998 0.420884i
\(641\) 2.39792 4.15331i 0.0947120 0.164046i −0.814776 0.579775i \(-0.803140\pi\)
0.909488 + 0.415729i \(0.136474\pi\)
\(642\) 8.48528 0.334887
\(643\) 2.82843 4.89898i 0.111542 0.193197i −0.804850 0.593478i \(-0.797754\pi\)
0.916392 + 0.400281i \(0.131088\pi\)
\(644\) 0 0
\(645\) 45.1833 1.77909
\(646\) −1.79583 + 3.11047i −0.0706560 + 0.122380i
\(647\) 19.3659 + 33.5427i 0.761351 + 1.31870i 0.942154 + 0.335180i \(0.108797\pi\)
−0.180803 + 0.983519i \(0.557870\pi\)
\(648\) −7.50000 12.9904i −0.294628 0.510310i
\(649\) −47.2170 −1.85343
\(650\) 32.5122 27.4190i 1.27523 1.07546i
\(651\) 0 0
\(652\) 7.69375 + 13.3260i 0.301310 + 0.521885i
\(653\) 6.59166 + 11.4171i 0.257952 + 0.446785i 0.965693 0.259686i \(-0.0836191\pi\)
−0.707741 + 0.706472i \(0.750286\pi\)
\(654\) 1.12548 1.94938i 0.0440096 0.0762268i
\(655\) 22.0000 0.859611
\(656\) −1.48640 + 2.57452i −0.0580341 + 0.100518i
\(657\) 6.29178 10.8977i 0.245466 0.425159i
\(658\) 0 0
\(659\) 9.20417 15.9421i 0.358543 0.621016i −0.629174 0.777264i \(-0.716607\pi\)
0.987718 + 0.156249i \(0.0499401\pi\)
\(660\) −11.0000 19.0526i −0.428174 0.741620i
\(661\) 3.75209 + 6.49881i 0.145939 + 0.252774i 0.929723 0.368260i \(-0.120046\pi\)
−0.783784 + 0.621034i \(0.786713\pi\)
\(662\) 29.3875 1.14218
\(663\) −1.14021 6.37378i −0.0442822 0.247537i
\(664\) −29.6985 −1.15252
\(665\) 0 0
\(666\) 1.39792 + 2.42126i 0.0541681 + 0.0938220i
\(667\) 3.10208 5.37297i 0.120113 0.208042i
\(668\) 1.70295 0.0658892
\(669\) 4.00000 6.92820i 0.154649 0.267860i
\(670\) −7.77817 + 13.4722i −0.300497 + 0.520476i
\(671\) 31.6607 1.22225
\(672\) 0 0
\(673\) 11.9896 + 20.7666i 0.462164 + 0.800492i 0.999069 0.0431511i \(-0.0137397\pi\)
−0.536904 + 0.843643i \(0.680406\pi\)
\(674\) −8.98958 15.5704i −0.346266 0.599750i
\(675\) 66.7273 2.56833
\(676\) −2.19375 + 12.8136i −0.0843749 + 0.492829i
\(677\) −7.64854 −0.293957 −0.146979 0.989140i \(-0.546955\pi\)
−0.146979 + 0.989140i \(0.546955\pi\)
\(678\) 1.83258 + 3.17413i 0.0703799 + 0.121902i
\(679\) 0 0
\(680\) −7.80625 + 13.5208i −0.299356 + 0.518500i
\(681\) 10.4083 0.398848
\(682\) 2.68406 4.64893i 0.102778 0.178017i
\(683\) 3.38749 5.86731i 0.129619 0.224506i −0.793910 0.608035i \(-0.791958\pi\)
0.923529 + 0.383529i \(0.125291\pi\)
\(684\) 2.82843 0.108148
\(685\) −38.5152 + 66.7103i −1.47159 + 2.54887i
\(686\) 0 0
\(687\) −9.00000 15.5885i −0.343371 0.594737i
\(688\) −7.79583 −0.297213
\(689\) −7.99473 44.6904i −0.304575 1.70257i
\(690\) −45.1833 −1.72010
\(691\) −1.26984 2.19944i −0.0483072 0.0836705i 0.840861 0.541251i \(-0.182049\pi\)
−0.889168 + 0.457581i \(0.848716\pi\)
\(692\) 8.90365 + 15.4216i 0.338466 + 0.586240i
\(693\) 0 0
\(694\) −32.9792 −1.25187
\(695\) 3.48958 6.04413i 0.132367 0.229267i
\(696\) −1.68821 + 2.92407i −0.0639916 + 0.110837i
\(697\) −3.77499 −0.142988
\(698\) 13.2907 23.0201i 0.503059 0.871324i
\(699\) 12.1504 + 21.0452i 0.459572 + 0.796002i
\(700\) 0 0
\(701\) −29.5917 −1.11766 −0.558831 0.829282i \(-0.688750\pi\)
−0.558831 + 0.829282i \(0.688750\pi\)
\(702\) 15.5917 13.1491i 0.588469 0.496283i
\(703\) 7.90781 0.298249
\(704\) 13.2854 + 23.0110i 0.500713 + 0.867260i
\(705\) 8.19654 + 14.1968i 0.308700 + 0.534684i
\(706\) 2.61187 4.52390i 0.0982992 0.170259i
\(707\) 0 0
\(708\) −8.79583 + 15.2348i −0.330568 + 0.572560i
\(709\) 4.60208 7.97104i 0.172835 0.299359i −0.766575 0.642155i \(-0.778041\pi\)
0.939410 + 0.342796i \(0.111374\pi\)
\(710\) −24.5896 −0.922832
\(711\) −1.10208 + 1.90887i −0.0413314 + 0.0715881i
\(712\) 22.4683 + 38.9163i 0.842036 + 1.45845i
\(713\) 5.51249 + 9.54790i 0.206444 + 0.357572i
\(714\) 0 0
\(715\) 42.8771 36.1602i 1.60351 1.35231i
\(716\) 19.5917 0.732175
\(717\) −7.21544 12.4975i −0.269465 0.466728i
\(718\) 2.00000 + 3.46410i 0.0746393 + 0.129279i
\(719\) 0.995845 1.72485i 0.0371387 0.0643262i −0.846859 0.531818i \(-0.821509\pi\)
0.883997 + 0.467492i \(0.154842\pi\)
\(720\) −4.09827 −0.152734
\(721\) 0 0
\(722\) 5.50000 9.52628i 0.204689 0.354531i
\(723\) 15.7958 0.587453
\(724\) −1.90477 + 3.29915i −0.0707901 + 0.122612i
\(725\) −4.69375 8.12981i −0.174321 0.301934i
\(726\) 2.41006 + 4.17434i 0.0894456 + 0.154924i
\(727\) −32.4974 −1.20526 −0.602632 0.798020i \(-0.705881\pi\)
−0.602632 + 0.798020i \(0.705881\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 25.7854 + 44.6616i 0.954361 + 1.65300i
\(731\) −4.94975 8.57321i −0.183073 0.317092i
\(732\) 5.89792 10.2155i 0.217993 0.377575i
\(733\) 33.2193 1.22698 0.613491 0.789702i \(-0.289765\pi\)
0.613491 + 0.789702i \(0.289765\pi\)
\(734\) 10.6066 18.3712i 0.391497 0.678092i
\(735\) 0 0
\(736\) −38.9792 −1.43679
\(737\) −7.20417 + 12.4780i −0.265369 + 0.459633i
\(738\) −1.48640 2.57452i −0.0547151 0.0947693i
\(739\) 11.5917 + 20.0773i 0.426406 + 0.738557i 0.996551 0.0829873i \(-0.0264461\pi\)
−0.570144 + 0.821545i \(0.693113\pi\)
\(740\) 11.4581 0.421207
\(741\) −2.53969 14.1968i −0.0932978 0.521534i
\(742\) 0 0
\(743\) 14.5917 + 25.2735i 0.535316 + 0.927195i 0.999148 + 0.0412716i \(0.0131409\pi\)
−0.463832 + 0.885923i \(0.653526\pi\)
\(744\) −3.00000 5.19615i −0.109985 0.190500i
\(745\) −29.9003 + 51.7888i −1.09546 + 1.89740i
\(746\) 6.59166 0.241338
\(747\) 4.94975 8.57321i 0.181102 0.313678i
\(748\) −2.41006 + 4.17434i −0.0881205 + 0.152629i
\(749\) 0 0
\(750\) −19.6937 + 34.1106i −0.719114 + 1.24554i
\(751\) 3.89792 + 6.75139i 0.142237 + 0.246362i 0.928339 0.371735i \(-0.121237\pi\)
−0.786102 + 0.618097i \(0.787904\pi\)
\(752\) −1.41421 2.44949i −0.0515711 0.0893237i
\(753\) −23.5917 −0.859728
\(754\) −2.69880 0.974691i −0.0982844 0.0354961i
\(755\) −6.52307 −0.237399
\(756\) 0 0
\(757\) −6.59166 11.4171i −0.239578 0.414961i 0.721015 0.692919i \(-0.243676\pi\)
−0.960593 + 0.277958i \(0.910342\pi\)
\(758\) −12.6937 + 21.9862i −0.461058 + 0.798575i
\(759\) −41.8489 −1.51902
\(760\) −17.3875 + 30.1160i −0.630711 + 1.09242i
\(761\) −8.90365 + 15.4216i −0.322757 + 0.559032i −0.981056 0.193725i \(-0.937943\pi\)
0.658299 + 0.752757i \(0.271276\pi\)
\(762\) 16.3931 0.593859
\(763\) 0 0
\(764\) −8.10208 14.0332i −0.293123 0.507704i
\(765\) −2.60208 4.50694i −0.0940786 0.162949i
\(766\) −12.1504 −0.439013
\(767\) −42.1833 15.2348i −1.52315 0.550098i
\(768\) 24.0416 0.867528
\(769\) 2.12132 + 3.67423i 0.0764968 + 0.132496i 0.901736 0.432287i \(-0.142293\pi\)
−0.825239 + 0.564783i \(0.808960\pi\)
\(770\) 0 0
\(771\) −6.10208 + 10.5691i −0.219761 + 0.380638i
\(772\) −22.5917 −0.813092
\(773\) 17.3889 30.1185i 0.625436 1.08329i −0.363020 0.931781i \(-0.618254\pi\)
0.988456 0.151506i \(-0.0484124\pi\)
\(774\) 3.89792 6.75139i 0.140108 0.242674i
\(775\) 16.6818 0.599229
\(776\) 6.36396 11.0227i 0.228453 0.395692i
\(777\) 0 0
\(778\) 0.193747 + 0.335580i 0.00694618 + 0.0120311i
\(779\) −8.40834 −0.301260
\(780\) −3.67990 20.5706i −0.131762 0.736546i
\(781\) −22.7750 −0.814953
\(782\) 4.94975 + 8.57321i 0.177003 + 0.306578i
\(783\) −2.25095 3.89876i −0.0804424