Properties

Label 637.2.h.k.471.1
Level $637$
Weight $2$
Character 637.471
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.h (of order \(3\), degree \(2\), not 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 471.1
Root \(-2.04914 + 3.54921i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.k.165.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.707107 + 1.22474i) q^{3} -1.00000 q^{4} +(-2.04914 + 3.54921i) q^{5} +(-0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.707107 + 1.22474i) q^{3} -1.00000 q^{4} +(-2.04914 + 3.54921i) 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} +(0.707107 - 1.22474i) q^{12} +(-0.634922 - 3.54921i) q^{13} +(-2.89792 - 5.01934i) q^{15} -1.00000 q^{16} -1.26984 q^{17} +(0.500000 + 0.866025i) q^{18} +(1.41421 + 2.44949i) q^{19} +(2.04914 - 3.54921i) q^{20} +(1.89792 - 3.28729i) q^{22} -7.79583 q^{23} +(2.12132 - 3.67423i) q^{24} +(-5.89792 - 10.2155i) q^{25} +(-0.634922 - 3.54921i) q^{26} -5.65685 q^{27} +(-0.397916 - 0.689210i) q^{29} +(-2.89792 - 5.01934i) q^{30} +(0.707107 + 1.22474i) q^{31} +5.00000 q^{32} +(2.68406 + 4.64893i) q^{33} -1.26984 q^{34} +(-0.500000 - 0.866025i) q^{36} +2.79583 q^{37} +(1.41421 + 2.44949i) q^{38} +(4.79583 + 1.73205i) q^{39} +(6.14741 - 10.6476i) q^{40} +(-1.48640 - 2.57452i) q^{41} +(-3.89792 + 6.75139i) q^{43} +(-1.89792 + 3.28729i) q^{44} -4.09827 q^{45} -7.79583 q^{46} +(-1.41421 + 2.44949i) q^{47} +(0.707107 - 1.22474i) q^{48} +(-5.89792 - 10.2155i) q^{50} +(0.897916 - 1.55524i) q^{51} +(0.634922 + 3.54921i) q^{52} +(6.29583 + 10.9047i) q^{53} -5.65685 q^{54} +(7.77817 + 13.4722i) q^{55} -4.00000 q^{57} +(-0.397916 - 0.689210i) q^{58} -12.4392 q^{59} +(2.89792 + 5.01934i) q^{60} +(-4.17046 - 7.22344i) q^{61} +(0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(13.8979 + 5.01934i) q^{65} +(2.68406 + 4.64893i) q^{66} +(1.89792 - 3.28729i) q^{67} +1.26984 q^{68} +(5.51249 - 9.54790i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +(6.29178 + 10.8977i) q^{73} +2.79583 q^{74} +16.6818 q^{75} +(-1.41421 - 2.44949i) q^{76} +(4.79583 + 1.73205i) q^{78} +(1.10208 - 1.90887i) 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} +(-3.89792 + 6.75139i) q^{86} +1.12548 q^{87} +(-5.69375 + 9.86186i) q^{88} -14.9789 q^{89} -4.09827 q^{90} +7.79583 q^{92} -2.00000 q^{93} +(-1.41421 + 2.44949i) q^{94} -11.5917 q^{95} +(-3.53553 + 6.12372i) q^{96} +(2.12132 - 3.67423i) q^{97} +3.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 8 q^{4} - 24 q^{8} + 4 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{2} - 8 q^{4} - 24 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{22} - 24 q^{23} - 28 q^{25} + 16 q^{29} - 4 q^{30} + 40 q^{32} - 4 q^{36} - 16 q^{37} - 12 q^{43} + 4 q^{44} - 24 q^{46} - 28 q^{50} - 12 q^{51} + 12 q^{53} - 32 q^{57} + 16 q^{58} + 4 q^{60} + 56 q^{64} + 92 q^{65} - 4 q^{67} - 24 q^{71} - 12 q^{72} - 16 q^{74} + 28 q^{79} + 20 q^{81} + 40 q^{85} - 12 q^{86} + 12 q^{88} + 24 q^{92} - 16 q^{93} - 16 q^{95} - 8 q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) −0.707107 + 1.22474i −0.408248 + 0.707107i −0.994694 0.102882i \(-0.967194\pi\)
0.586445 + 0.809989i \(0.300527\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.04914 + 3.54921i −0.916401 + 1.58725i −0.111565 + 0.993757i \(0.535586\pi\)
−0.804836 + 0.593497i \(0.797747\pi\)
\(6\) −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 −0.424092 0.905619i \(-0.639407\pi\)
0.996335 0.0855351i \(-0.0272600\pi\)
\(12\) 0.707107 1.22474i 0.204124 0.353553i
\(13\) −0.634922 3.54921i −0.176096 0.984373i
\(14\) 0 0
\(15\) −2.89792 5.01934i −0.748239 1.29599i
\(16\) −1.00000 −0.250000
\(17\) −1.26984 −0.307983 −0.153991 0.988072i \(-0.549213\pi\)
−0.153991 + 0.988072i \(0.549213\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 1.41421 + 2.44949i 0.324443 + 0.561951i 0.981399 0.191977i \(-0.0614899\pi\)
−0.656957 + 0.753928i \(0.728157\pi\)
\(20\) 2.04914 3.54921i 0.458201 0.793627i
\(21\) 0 0
\(22\) 1.89792 3.28729i 0.404637 0.700852i
\(23\) −7.79583 −1.62554 −0.812772 0.582582i \(-0.802042\pi\)
−0.812772 + 0.582582i \(0.802042\pi\)
\(24\) 2.12132 3.67423i 0.433013 0.750000i
\(25\) −5.89792 10.2155i −1.17958 2.04310i
\(26\) −0.634922 3.54921i −0.124519 0.696057i
\(27\) −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
\(31\) 0.707107 + 1.22474i 0.127000 + 0.219971i 0.922513 0.385966i \(-0.126132\pi\)
−0.795513 + 0.605937i \(0.792798\pi\)
\(32\) 5.00000 0.883883
\(33\) 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
\(37\) 2.79583 0.459632 0.229816 0.973234i \(-0.426188\pi\)
0.229816 + 0.973234i \(0.426188\pi\)
\(38\) 1.41421 + 2.44949i 0.229416 + 0.397360i
\(39\) 4.79583 + 1.73205i 0.767948 + 0.277350i
\(40\) 6.14741 10.6476i 0.971990 1.68354i
\(41\) −1.48640 2.57452i −0.232136 0.402072i 0.726300 0.687378i \(-0.241238\pi\)
−0.958437 + 0.285306i \(0.907905\pi\)
\(42\) 0 0
\(43\) −3.89792 + 6.75139i −0.594427 + 1.02958i 0.399201 + 0.916863i \(0.369288\pi\)
−0.993628 + 0.112714i \(0.964046\pi\)
\(44\) −1.89792 + 3.28729i −0.286122 + 0.495577i
\(45\) −4.09827 −0.610934
\(46\) −7.79583 −1.14943
\(47\) −1.41421 + 2.44949i −0.206284 + 0.357295i −0.950541 0.310599i \(-0.899470\pi\)
0.744257 + 0.667893i \(0.232804\pi\)
\(48\) 0.707107 1.22474i 0.102062 0.176777i
\(49\) 0 0
\(50\) −5.89792 10.2155i −0.834091 1.44469i
\(51\) 0.897916 1.55524i 0.125733 0.217777i
\(52\) 0.634922 + 3.54921i 0.0880479 + 0.492187i
\(53\) 6.29583 + 10.9047i 0.864799 + 1.49788i 0.867247 + 0.497879i \(0.165888\pi\)
−0.00244768 + 0.999997i \(0.500779\pi\)
\(54\) −5.65685 −0.769800
\(55\) 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
\(59\) −12.4392 −1.61944 −0.809722 0.586814i \(-0.800382\pi\)
−0.809722 + 0.586814i \(0.800382\pi\)
\(60\) 2.89792 + 5.01934i 0.374119 + 0.647994i
\(61\) −4.17046 7.22344i −0.533972 0.924867i −0.999212 0.0396825i \(-0.987365\pi\)
0.465240 0.885185i \(-0.345968\pi\)
\(62\) 0.707107 + 1.22474i 0.0898027 + 0.155543i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 13.8979 + 5.01934i 1.72382 + 0.622572i
\(66\) 2.68406 + 4.64893i 0.330385 + 0.572243i
\(67\) 1.89792 3.28729i 0.231867 0.401606i −0.726490 0.687177i \(-0.758850\pi\)
0.958358 + 0.285571i \(0.0921831\pi\)
\(68\) 1.26984 0.153991
\(69\) 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
\(73\) 6.29178 + 10.8977i 0.736397 + 1.27548i 0.954108 + 0.299463i \(0.0968076\pi\)
−0.217711 + 0.976013i \(0.569859\pi\)
\(74\) 2.79583 0.325009
\(75\) 16.6818 1.92625
\(76\) −1.41421 2.44949i −0.162221 0.280976i
\(77\) 0 0
\(78\) 4.79583 + 1.73205i 0.543021 + 0.196116i
\(79\) 1.10208 1.90887i 0.123994 0.214764i −0.797345 0.603524i \(-0.793763\pi\)
0.921339 + 0.388759i \(0.127096\pi\)
\(80\) 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 \(-0.682827\pi\)
−0.543305 + 0.839535i \(0.682827\pi\)
\(84\) 0 0
\(85\) 2.60208 4.50694i 0.282236 0.488847i
\(86\) −3.89792 + 6.75139i −0.420323 + 0.728021i
\(87\) 1.12548 0.120664
\(88\) −5.69375 + 9.86186i −0.606955 + 1.05128i
\(89\) −14.9789 −1.58776 −0.793879 0.608076i \(-0.791942\pi\)
−0.793879 + 0.608076i \(0.791942\pi\)
\(90\) −4.09827 −0.431996
\(91\) 0 0
\(92\) 7.79583 0.812772
\(93\) −2.00000 −0.207390
\(94\) −1.41421 + 2.44949i −0.145865 + 0.252646i
\(95\) −11.5917 −1.18928
\(96\) −3.53553 + 6.12372i −0.360844 + 0.625000i
\(97\) 2.12132 3.67423i 0.215387 0.373062i −0.738005 0.674795i \(-0.764232\pi\)
0.953392 + 0.301733i \(0.0975652\pi\)
\(98\) 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 \(-0.672031\pi\)
0.999858 + 0.0168509i \(0.00536408\pi\)
\(102\) 0.897916 1.55524i 0.0889069 0.153991i
\(103\) −2.68406 + 4.64893i −0.264468 + 0.458072i −0.967424 0.253161i \(-0.918530\pi\)
0.702956 + 0.711233i \(0.251863\pi\)
\(104\) 1.90477 + 10.6476i 0.186778 + 1.04409i
\(105\) 0 0
\(106\) 6.29583 + 10.9047i 0.611505 + 1.05916i
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 5.65685 0.544331
\(109\) −0.795832 1.37842i −0.0762268 0.132029i 0.825392 0.564560i \(-0.190954\pi\)
−0.901619 + 0.432531i \(0.857621\pi\)
\(110\) 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 \(0.205566\pi\)
\(114\) −4.00000 −0.374634
\(115\) 15.9747 27.6690i 1.48965 2.58015i
\(116\) 0.397916 + 0.689210i 0.0369456 + 0.0639916i
\(117\) 2.75624 2.32446i 0.254815 0.214897i
\(118\) −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
\(122\) −4.17046 7.22344i −0.377575 0.653980i
\(123\) 4.20417 0.379077
\(124\) −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 \(0.661386\pi\)
\(128\) −3.00000 −0.265165
\(129\) −5.51249 9.54790i −0.485347 0.840646i
\(130\) 13.8979 + 5.01934i 1.21893 + 0.440225i
\(131\) −2.68406 + 4.64893i −0.234507 + 0.406178i −0.959129 0.282968i \(-0.908681\pi\)
0.724622 + 0.689146i \(0.242014\pi\)
\(132\) −2.68406 4.64893i −0.233617 0.404637i
\(133\) 0 0
\(134\) 1.89792 3.28729i 0.163955 0.283978i
\(135\) 11.5917 20.0773i 0.997652 1.72798i
\(136\) 3.80953 0.326665
\(137\) −18.7958 −1.60584 −0.802918 0.596089i \(-0.796720\pi\)
−0.802918 + 0.596089i \(0.796720\pi\)
\(138\) 5.51249 9.54790i 0.469254 0.812772i
\(139\) 0.851476 1.47480i 0.0722212 0.125091i −0.827653 0.561240i \(-0.810325\pi\)
0.899875 + 0.436149i \(0.143658\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −12.8723 4.64893i −1.07644 0.388763i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 3.26153 0.270856
\(146\) 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 0.993160 + 0.116761i \(0.0372511\pi\)
−0.395462 + 0.918482i \(0.629416\pi\)
\(150\) 16.6818 1.36207
\(151\) −0.795832 1.37842i −0.0647639 0.112174i 0.831825 0.555037i \(-0.187296\pi\)
−0.896589 + 0.442863i \(0.853963\pi\)
\(152\) −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
\(156\) −4.79583 1.73205i −0.383974 0.138675i
\(157\) 0.0721845 + 0.125027i 0.00576095 + 0.00997825i 0.868892 0.495003i \(-0.164833\pi\)
−0.863131 + 0.504981i \(0.831500\pi\)
\(158\) 1.10208 1.90887i 0.0876771 0.151861i
\(159\) −17.8073 −1.41221
\(160\) −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 −0.992423 0.122871i \(-0.960790\pi\)
0.389802 0.920899i \(-0.372543\pi\)
\(164\) 1.48640 + 2.57452i 0.116068 + 0.201036i
\(165\) −22.0000 −1.71270
\(166\) −9.89949 −0.768350
\(167\) −0.851476 1.47480i −0.0658892 0.114123i 0.831199 0.555975i \(-0.187655\pi\)
−0.897088 + 0.441852i \(0.854322\pi\)
\(168\) 0 0
\(169\) −12.1937 + 4.50694i −0.937981 + 0.346688i
\(170\) 2.60208 4.50694i 0.199571 0.345667i
\(171\) −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 0.975900 + 0.218218i \(0.0700242\pi\)
−0.298968 + 0.954263i \(0.596642\pi\)
\(174\) 1.12548 0.0853221
\(175\) 0 0
\(176\) −1.89792 + 3.28729i −0.143061 + 0.247789i
\(177\) 8.79583 15.2348i 0.661135 1.14512i
\(178\) −14.9789 −1.12271
\(179\) 9.79583 16.9669i 0.732175 1.26816i −0.223777 0.974640i \(-0.571839\pi\)
0.955952 0.293524i \(-0.0948279\pi\)
\(180\) 4.09827 0.305467
\(181\) 3.80953 0.283160 0.141580 0.989927i \(-0.454782\pi\)
0.141580 + 0.989927i \(0.454782\pi\)
\(182\) 0 0
\(183\) 11.7958 0.871973
\(184\) 23.3875 1.72415
\(185\) −5.72904 + 9.92299i −0.421207 + 0.729552i
\(186\) −2.00000 −0.146647
\(187\) −2.41006 + 4.17434i −0.176241 + 0.305258i
\(188\) 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 0.994719 + 0.102638i \(0.0327282\pi\)
−0.408473 + 0.912771i \(0.633938\pi\)
\(192\) −4.94975 + 8.57321i −0.357217 + 0.618718i
\(193\) −11.2958 + 19.5650i −0.813092 + 1.40832i 0.0975983 + 0.995226i \(0.468884\pi\)
−0.910690 + 0.413090i \(0.864449\pi\)
\(194\) 2.12132 3.67423i 0.152302 0.263795i
\(195\) −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 \(0.741344\pi\)
\(198\) 3.79583 0.269758
\(199\) 5.07938 0.360068 0.180034 0.983660i \(-0.442379\pi\)
0.180034 + 0.983660i \(0.442379\pi\)
\(200\) 17.6937 + 30.6465i 1.25114 + 2.16703i
\(201\) 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
\(205\) 12.1833 0.850920
\(206\) −2.68406 + 4.64893i −0.187007 + 0.323906i
\(207\) −3.89792 6.75139i −0.270924 0.469254i
\(208\) 0.634922 + 3.54921i 0.0440239 + 0.246093i
\(209\) 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
\(213\) −4.24264 7.34847i −0.290701 0.503509i
\(214\) −6.00000 −0.410152
\(215\) −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
\(219\) −17.7958 −1.20253
\(220\) −7.77817 13.4722i −0.524404 0.908295i
\(221\) 0.806253 + 4.50694i 0.0542344 + 0.303170i
\(222\) −1.97695 + 3.42418i −0.132684 + 0.229816i
\(223\) 2.82843 + 4.89898i 0.189405 + 0.328060i 0.945052 0.326920i \(-0.106011\pi\)
−0.755647 + 0.654979i \(0.772677\pi\)
\(224\) 0 0
\(225\) 5.89792 10.2155i 0.393194 0.681033i
\(226\) −1.29583 + 2.24445i −0.0861974 + 0.149298i
\(227\) 7.35981 0.488487 0.244244 0.969714i \(-0.421460\pi\)
0.244244 + 0.969714i \(0.421460\pi\)
\(228\) 4.00000 0.264906
\(229\) −6.36396 + 11.0227i −0.420542 + 0.728401i −0.995993 0.0894361i \(-0.971494\pi\)
0.575450 + 0.817837i \(0.304827\pi\)
\(230\) 15.9747 27.6690i 1.05334 1.82444i
\(231\) 0 0
\(232\) 1.19375 + 2.06763i 0.0783733 + 0.135747i
\(233\) −8.59166 + 14.8812i −0.562859 + 0.974900i 0.434387 + 0.900726i \(0.356965\pi\)
−0.997245 + 0.0741732i \(0.976368\pi\)
\(234\) 2.75624 2.32446i 0.180181 0.151955i
\(235\) −5.79583 10.0387i −0.378078 0.654851i
\(236\) 12.4392 0.809722
\(237\) 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
\(241\) 11.1693 0.719480 0.359740 0.933053i \(-0.382865\pi\)
0.359740 + 0.933053i \(0.382865\pi\)
\(242\) −1.70417 2.95171i −0.109548 0.189743i
\(243\) −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
\(247\) 7.79583 6.57457i 0.496037 0.418330i
\(248\) −2.12132 3.67423i −0.134704 0.233314i
\(249\) 7.00000 12.1244i 0.443607 0.768350i
\(250\) 27.8512 1.76146
\(251\) 8.34091 14.4469i 0.526474 0.911879i −0.473050 0.881035i \(-0.656847\pi\)
0.999524 0.0308439i \(-0.00981948\pi\)
\(252\) 0 0
\(253\) −14.7958 + 25.6271i −0.930206 + 1.61116i
\(254\) 5.79583 + 10.0387i 0.363663 + 0.629882i
\(255\) 3.67990 + 6.37378i 0.230444 + 0.399142i
\(256\) −17.0000 −1.06250
\(257\) 8.62965 0.538303 0.269151 0.963098i \(-0.413257\pi\)
0.269151 + 0.963098i \(0.413257\pi\)
\(258\) −5.51249 9.54790i −0.343192 0.594427i
\(259\) 0 0
\(260\) −13.8979 5.01934i −0.861912 0.311286i
\(261\) 0.397916 0.689210i 0.0246304 0.0426610i
\(262\) −2.68406 + 4.64893i −0.165822 + 0.287212i
\(263\) −1.69375 + 2.93366i −0.104441 + 0.180897i −0.913510 0.406817i \(-0.866639\pi\)
0.809069 + 0.587714i \(0.199972\pi\)
\(264\) −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
\(268\) −1.89792 + 3.28729i −0.115934 + 0.200803i
\(269\) 12.4392 0.758430 0.379215 0.925308i \(-0.376194\pi\)
0.379215 + 0.925308i \(0.376194\pi\)
\(270\) 11.5917 20.0773i 0.705446 1.22187i
\(271\) 17.5186 1.06418 0.532088 0.846689i \(-0.321407\pi\)
0.532088 + 0.846689i \(0.321407\pi\)
\(272\) 1.26984 0.0769956
\(273\) 0 0
\(274\) −18.7958 −1.13550
\(275\) −44.7750 −2.70003
\(276\) −5.51249 + 9.54790i −0.331813 + 0.574716i
\(277\) 32.1833 1.93371 0.966854 0.255329i \(-0.0821837\pi\)
0.966854 + 0.255329i \(0.0821837\pi\)
\(278\) 0.851476 1.47480i 0.0510681 0.0884526i
\(279\) −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 \(-0.677246\pi\)
0.999448 + 0.0332294i \(0.0105792\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) 8.19654 14.1968i 0.485521 0.840948i
\(286\) −12.8723 4.64893i −0.761155 0.274897i
\(287\) 0 0
\(288\) 2.50000 + 4.33013i 0.147314 + 0.255155i
\(289\) −15.3875 −0.905147
\(290\) 3.26153 0.191524
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) −6.29178 10.8977i −0.368198 0.637738i
\(293\) 1.48640 2.57452i 0.0868363 0.150405i −0.819336 0.573314i \(-0.805658\pi\)
0.906172 + 0.422909i \(0.138991\pi\)
\(294\) 0 0
\(295\) 25.4896 44.1492i 1.48406 2.57047i
\(296\) −8.38749 −0.487513
\(297\) −10.7362 + 18.5957i −0.622979 + 1.07903i
\(298\) 7.29583 + 12.6368i 0.422636 + 0.732027i
\(299\) 4.94975 + 27.6690i 0.286251 + 1.60014i
\(300\) −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
\(304\) −1.41421 2.44949i −0.0811107 0.140488i
\(305\) 34.1833 1.95733
\(306\) −0.634922 1.09972i −0.0362961 0.0628667i
\(307\) −20.0583 −1.14478 −0.572392 0.819980i \(-0.693985\pi\)
−0.572392 + 0.819980i \(0.693985\pi\)
\(308\) 0 0
\(309\) −3.79583 6.57457i −0.215937 0.374014i
\(310\) −5.79583 −0.329181
\(311\) 14.4161 + 24.9695i 0.817464 + 1.41589i 0.907545 + 0.419955i \(0.137954\pi\)
−0.0900809 + 0.995934i \(0.528713\pi\)
\(312\) −14.3875 5.19615i −0.814531 0.294174i
\(313\) −7.63381 + 13.2221i −0.431488 + 0.747359i −0.997002 0.0773795i \(-0.975345\pi\)
0.565514 + 0.824739i \(0.308678\pi\)
\(314\) 0.0721845 + 0.125027i 0.00407360 + 0.00705569i
\(315\) 0 0
\(316\) −1.10208 + 1.90887i −0.0619971 + 0.107382i
\(317\) −3.29583 + 5.70855i −0.185112 + 0.320624i −0.943614 0.331047i \(-0.892598\pi\)
0.758502 + 0.651671i \(0.225932\pi\)
\(318\) −17.8073 −0.998584
\(319\) −3.02084 −0.169135
\(320\) −14.3440 + 24.8445i −0.801851 + 1.38885i
\(321\) 4.24264 7.34847i 0.236801 0.410152i
\(322\) 0 0
\(323\) −1.79583 3.11047i −0.0999227 0.173071i
\(324\) −2.50000 + 4.33013i −0.138889 + 0.240563i
\(325\) −32.5122 + 27.4190i −1.80345 + 1.52093i
\(326\) −7.69375 13.3260i −0.426117 0.738057i
\(327\) 2.25095 0.124478
\(328\) 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 −0.914493 0.404601i \(-0.867410\pi\)
0.106852 0.994275i \(-0.465923\pi\)
\(332\) 9.89949 0.543305
\(333\) 1.39792 + 2.42126i 0.0766053 + 0.132684i
\(334\) −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 \(0.337109\pi\)
\(338\) −12.1937 + 4.50694i −0.663252 + 0.245145i
\(339\) −1.83258 3.17413i −0.0995322 0.172395i
\(340\) −2.60208 + 4.50694i −0.141118 + 0.244423i
\(341\) 5.36812 0.290700
\(342\) −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
\(346\) 8.90365 + 15.4216i 0.478663 + 0.829069i
\(347\) −32.9792 −1.77041 −0.885207 0.465197i \(-0.845983\pi\)
−0.885207 + 0.465197i \(0.845983\pi\)
\(348\) −1.12548 −0.0603318
\(349\) −13.2907 23.0201i −0.711433 1.23224i −0.964319 0.264742i \(-0.914713\pi\)
0.252887 0.967496i \(-0.418620\pi\)
\(350\) 0 0
\(351\) 3.59166 + 20.0773i 0.191709 + 1.07165i
\(352\) 9.48958 16.4364i 0.505796 0.876065i
\(353\) −2.61187 + 4.52390i −0.139016 + 0.240783i −0.927124 0.374754i \(-0.877727\pi\)
0.788108 + 0.615536i \(0.211061\pi\)
\(354\) 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
\(359\) 2.00000 3.46410i 0.105556 0.182828i −0.808409 0.588621i \(-0.799671\pi\)
0.913965 + 0.405793i \(0.133004\pi\)
\(360\) 12.2948 0.647994
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) 3.80953 0.200225
\(363\) 4.82012 0.252990
\(364\) 0 0
\(365\) −51.5708 −2.69934
\(366\) 11.7958 0.616578
\(367\) −10.6066 + 18.3712i −0.553660 + 0.958967i 0.444346 + 0.895855i \(0.353436\pi\)
−0.998006 + 0.0631123i \(0.979897\pi\)
\(368\) 7.79583 0.406386
\(369\) 1.48640 2.57452i 0.0773788 0.134024i
\(370\) −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 0.767996 0.640454i \(-0.221254\pi\)
−0.938648 + 0.344877i \(0.887921\pi\)
\(374\) −2.41006 + 4.17434i −0.124621 + 0.215850i
\(375\) −19.6937 + 34.1106i −1.01698 + 1.76146i
\(376\) 4.24264 7.34847i 0.218797 0.378968i
\(377\) −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 \(-0.392751\pi\)
\(380\) 11.5917 0.594640
\(381\) −16.3931 −0.839843
\(382\) 8.10208 + 14.0332i 0.414539 + 0.718002i
\(383\) −6.07522 10.5226i −0.310429 0.537680i 0.668026 0.744138i \(-0.267140\pi\)
−0.978455 + 0.206458i \(0.933806\pi\)
\(384\) 2.12132 3.67423i 0.108253 0.187500i
\(385\) 0 0
\(386\) −11.2958 + 19.5650i −0.574943 + 0.995830i
\(387\) −7.79583 −0.396284
\(388\) −2.12132 + 3.67423i −0.107694 + 0.186531i
\(389\) 0.193747 + 0.335580i 0.00982338 + 0.0170146i 0.870895 0.491469i \(-0.163540\pi\)
−0.861072 + 0.508483i \(0.830206\pi\)
\(390\) −15.9747 + 13.4722i −0.808911 + 0.682191i
\(391\) 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
\(395\) 4.51664 + 7.82305i 0.227257 + 0.393620i
\(396\) −3.79583 −0.190748
\(397\) −3.53553 6.12372i −0.177443 0.307341i 0.763561 0.645736i \(-0.223449\pi\)
−0.941004 + 0.338395i \(0.890116\pi\)
\(398\) 5.07938 0.254606
\(399\) 0 0
\(400\) 5.89792 + 10.2155i 0.294896 + 0.510774i
\(401\) −4.38749 −0.219101 −0.109551 0.993981i \(-0.534941\pi\)
−0.109551 + 0.993981i \(0.534941\pi\)
\(402\) 2.68406 + 4.64893i 0.133869 + 0.231867i
\(403\) 3.89792 3.28729i 0.194169 0.163751i
\(404\) −4.87756 + 8.44819i −0.242668 + 0.420313i
\(405\) 10.2457 + 17.7460i 0.509112 + 0.881808i
\(406\) 0 0
\(407\) 5.30625 9.19070i 0.263021 0.455566i
\(408\) −2.69375 + 4.66571i −0.133360 + 0.230987i
\(409\) 18.7884 0.929027 0.464513 0.885566i \(-0.346229\pi\)
0.464513 + 0.885566i \(0.346229\pi\)
\(410\) 12.1833 0.601692
\(411\) 13.2907 23.0201i 0.655580 1.13550i
\(412\) 2.68406 4.64893i 0.132234 0.229036i
\(413\) 0 0
\(414\) −3.89792 6.75139i −0.191572 0.331813i
\(415\) 20.2854 35.1354i 0.995772 1.72473i
\(416\) −3.17461 17.7460i −0.155648 0.870071i
\(417\) 1.20417 + 2.08568i 0.0589684 + 0.102136i
\(418\) 10.7362 0.525126
\(419\) 12.8576 + 22.2699i 0.628133 + 1.08796i 0.987926 + 0.154926i \(0.0495138\pi\)
−0.359794 + 0.933032i \(0.617153\pi\)
\(420\) 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
\(423\) −2.82843 −0.137523
\(424\) −18.8875 32.7141i −0.917258 1.58874i
\(425\) 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
\(429\) 14.7958 12.4780i 0.714349 0.602443i
\(430\) −15.9747 27.6690i −0.770369 1.33432i
\(431\) −16.5917 + 28.7376i −0.799192 + 1.38424i 0.120950 + 0.992659i \(0.461406\pi\)
−0.920143 + 0.391583i \(0.871928\pi\)
\(432\) 5.65685 0.272166
\(433\) 10.2457 17.7460i 0.492376 0.852820i −0.507586 0.861601i \(-0.669462\pi\)
0.999961 + 0.00878126i \(0.00279520\pi\)
\(434\) 0 0
\(435\) −2.30625 + 3.99455i −0.110576 + 0.191524i
\(436\) 0.795832 + 1.37842i 0.0381134 + 0.0660144i
\(437\) −11.0250 19.0958i −0.527396 0.913476i
\(438\) −17.7958 −0.850318
\(439\) −20.0583 −0.957328 −0.478664 0.877998i \(-0.658879\pi\)
−0.478664 + 0.877998i \(0.658879\pi\)
\(440\) −23.3345 40.4166i −1.11243 1.92678i
\(441\) 0 0
\(442\) 0.806253 + 4.50694i 0.0383495 + 0.214373i
\(443\) −5.00000 + 8.66025i −0.237557 + 0.411461i −0.960013 0.279956i \(-0.909680\pi\)
0.722456 + 0.691417i \(0.243013\pi\)
\(444\) 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 \(0.978742\pi\)
\(450\) 5.89792 10.2155i 0.278030 0.481563i
\(451\) −11.2842 −0.531354
\(452\) 1.29583 2.24445i 0.0609508 0.105570i
\(453\) 2.25095 0.105759
\(454\) 7.35981 0.345413
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) 4.59166 0.214789 0.107394 0.994216i \(-0.465749\pi\)
0.107394 + 0.994216i \(0.465749\pi\)
\(458\) −6.36396 + 11.0227i −0.297368 + 0.515057i
\(459\) 7.18333 0.335289
\(460\) −15.9747 + 27.6690i −0.744825 + 1.29007i
\(461\) −12.0930 + 20.9457i −0.563227 + 0.975538i 0.433985 + 0.900920i \(0.357107\pi\)
−0.997212 + 0.0746180i \(0.976226\pi\)
\(462\) 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
\(467\) 15.9747 27.6690i 0.739222 1.28037i −0.213624 0.976916i \(-0.568527\pi\)
0.952846 0.303454i \(-0.0981398\pi\)
\(468\) −2.75624 + 2.32446i −0.127407 + 0.107448i
\(469\) 0 0
\(470\) −5.79583 10.0387i −0.267342 0.463050i
\(471\) −0.204168 −0.00940759
\(472\) 37.3176 1.71768
\(473\) 14.7958 + 25.6271i 0.680313 + 1.17834i
\(474\) 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
\(478\) −10.2042 −0.466728
\(479\) 10.4622 18.1211i 0.478032 0.827975i −0.521651 0.853159i \(-0.674684\pi\)
0.999683 + 0.0251838i \(0.00801710\pi\)
\(480\) −14.4896 25.0967i −0.661356 1.14550i
\(481\) −1.77514 9.92299i −0.0809392 0.452449i
\(482\) 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
\(486\) −4.94975 8.57321i −0.224525 0.388889i
\(487\) 0.408337 0.0185035 0.00925176 0.999957i \(-0.497055\pi\)
0.00925176 + 0.999957i \(0.497055\pi\)
\(488\) 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 \(0.902776\pi\)
\(492\) −4.20417 −0.189539
\(493\) 0.505291 + 0.875190i 0.0227572 + 0.0394166i
\(494\) 7.79583 6.57457i 0.350751 0.295804i
\(495\) −7.77817 + 13.4722i −0.349603 + 0.605530i
\(496\) −0.707107 1.22474i −0.0317500 0.0549927i
\(497\) 0 0
\(498\) 7.00000 12.1244i 0.313678 0.543305i
\(499\) −12.8979 + 22.3398i −0.577390 + 1.00007i 0.418387 + 0.908269i \(0.362595\pi\)
−0.995777 + 0.0918002i \(0.970738\pi\)
\(500\) −27.8512 −1.24554
\(501\) 2.40834 0.107597
\(502\) 8.34091 14.4469i 0.372273 0.644796i
\(503\) −12.8576 + 22.2699i −0.573290 + 0.992967i 0.422935 + 0.906160i \(0.361000\pi\)
−0.996225 + 0.0868074i \(0.972334\pi\)
\(504\) 0 0
\(505\) 19.9896 + 34.6230i 0.889525 + 1.54070i
\(506\) −14.7958 + 25.6271i −0.657755 + 1.13926i
\(507\) 3.10243 18.1211i 0.137784 0.804787i
\(508\) −5.79583 10.0387i −0.257148 0.445394i
\(509\) 6.08996 0.269933 0.134966 0.990850i \(-0.456907\pi\)
0.134966 + 0.990850i \(0.456907\pi\)
\(510\) 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
\(514\) 8.62965 0.380638
\(515\) −11.0000 19.0526i −0.484718 0.839556i
\(516\) 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
\(520\) −41.6937 15.0580i −1.82839 0.660338i
\(521\) −2.33787 4.04932i −0.102424 0.177404i 0.810259 0.586072i \(-0.199327\pi\)
−0.912683 + 0.408669i \(0.865993\pi\)
\(522\) 0.397916 0.689210i 0.0174163 0.0301659i
\(523\) 42.1377 1.84255 0.921276 0.388910i \(-0.127148\pi\)
0.921276 + 0.388910i \(0.127148\pi\)
\(524\) 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
\(528\) −2.68406 4.64893i −0.116809 0.202318i
\(529\) 37.7750 1.64239
\(530\) −51.6041 −2.24154
\(531\) −6.21959 10.7726i −0.269907 0.467493i
\(532\) 0 0
\(533\) −8.19375 + 6.91015i −0.354911 + 0.299312i
\(534\) 10.5917 18.3453i 0.458346 0.793879i
\(535\) 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
\(541\) −3.29583 + 5.70855i −0.141699 + 0.245430i −0.928136 0.372240i \(-0.878590\pi\)
0.786438 + 0.617670i \(0.211923\pi\)
\(542\) 17.5186 0.752487
\(543\) −2.69375 + 4.66571i −0.115600 + 0.200225i
\(544\) −6.34922 −0.272221
\(545\) 6.52307 0.279418
\(546\) 0 0
\(547\) 10.9792 0.469435 0.234717 0.972064i \(-0.424584\pi\)
0.234717 + 0.972064i \(0.424584\pi\)
\(548\) 18.7958 0.802918
\(549\) 4.17046 7.22344i 0.177991 0.308289i
\(550\) −44.7750 −1.90921
\(551\) 1.12548 1.94938i 0.0479469 0.0830464i
\(552\) −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 −0.880558 0.473938i \(-0.842832\pi\)
0.850722 + 0.525617i \(0.176165\pi\)
\(558\) −0.707107 + 1.22474i −0.0299342 + 0.0518476i
\(559\) 26.4370 + 9.54790i 1.11816 + 0.403833i
\(560\) 0 0
\(561\) −3.40834 5.90341i −0.143900 0.249242i
\(562\) 24.7958 1.04595
\(563\) 12.4392 0.524249 0.262125 0.965034i \(-0.415577\pi\)
0.262125 + 0.965034i \(0.415577\pi\)
\(564\) 2.00000 + 3.46410i 0.0842152 + 0.145865i
\(565\) −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
\(569\) 25.5917 1.07286 0.536429 0.843945i \(-0.319773\pi\)
0.536429 + 0.843945i \(0.319773\pi\)
\(570\) 8.19654 14.1968i 0.343315 0.594640i
\(571\) 11.5917 + 20.0773i 0.485096 + 0.840211i 0.999853 0.0171250i \(-0.00545132\pi\)
−0.514757 + 0.857336i \(0.672118\pi\)
\(572\) 12.8723 + 4.64893i 0.538218 + 0.194381i
\(573\) −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
\(577\) −12.3670 21.4203i −0.514845 0.891738i −0.999852 0.0172271i \(-0.994516\pi\)
0.485007 0.874510i \(-0.338817\pi\)
\(578\) −15.3875 −0.640035
\(579\) −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
\(583\) 47.7958 1.97950
\(584\) −18.8753 32.6930i −0.781067 1.35285i
\(585\) 2.60208 + 14.5456i 0.107583 + 0.601387i
\(586\) 1.48640 2.57452i 0.0614025 0.106352i
\(587\) −8.34091 14.4469i −0.344266 0.596287i 0.640954 0.767579i \(-0.278539\pi\)
−0.985220 + 0.171293i \(0.945206\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 25.4896 44.1492i 1.04939 1.81760i
\(591\) −11.3137 −0.465384
\(592\) −2.79583 −0.114908
\(593\) 4.17046 7.22344i 0.171260 0.296631i −0.767601 0.640929i \(-0.778549\pi\)
0.938861 + 0.344297i \(0.111883\pi\)
\(594\) −10.7362 + 18.5957i −0.440513 + 0.762991i
\(595\) 0 0
\(596\) −7.29583 12.6368i −0.298849 0.517621i
\(597\) −3.59166 + 6.22094i −0.146997 + 0.254606i
\(598\) 4.94975 + 27.6690i 0.202410 + 1.13147i
\(599\) 16.7958 + 29.0912i 0.686259 + 1.18864i 0.973039 + 0.230639i \(0.0740817\pi\)
−0.286780 + 0.957996i \(0.592585\pi\)
\(600\) −50.0455 −2.04310
\(601\) 12.0930 + 20.9457i 0.493284 + 0.854393i 0.999970 0.00773797i \(-0.00246310\pi\)
−0.506686 + 0.862130i \(0.669130\pi\)
\(602\) 0 0
\(603\) 3.79583 0.154578
\(604\) 0.795832 + 1.37842i 0.0323819 + 0.0560871i
\(605\) 13.9683 0.567892
\(606\) 6.89792 + 11.9475i 0.280209 + 0.485336i
\(607\) −2.39532 4.14882i −0.0972231 0.168395i 0.813311 0.581829i \(-0.197663\pi\)
−0.910534 + 0.413434i \(0.864329\pi\)
\(608\) 7.07107 + 12.2474i 0.286770 + 0.496700i
\(609\) 0 0
\(610\) 34.1833 1.38404
\(611\) 9.59166 + 3.46410i 0.388037 + 0.140143i
\(612\) 0.634922 + 1.09972i 0.0256652 + 0.0444535i
\(613\) −20.9896 + 36.3550i −0.847761 + 1.46837i 0.0354405 + 0.999372i \(0.488717\pi\)
−0.883202 + 0.468994i \(0.844617\pi\)
\(614\) −20.0583 −0.809485
\(615\) −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
\(619\) 16.9558 + 29.3684i 0.681512 + 1.18041i 0.974519 + 0.224303i \(0.0720107\pi\)
−0.293007 + 0.956110i \(0.594656\pi\)
\(620\) 5.79583 0.232766
\(621\) 44.0999 1.76967
\(622\) 14.4161 + 24.9695i 0.578034 + 1.00118i
\(623\) 0 0
\(624\) −4.79583 1.73205i −0.191987 0.0693375i
\(625\) −27.5812 + 47.7721i −1.10325 + 1.91088i
\(626\) −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 \(-0.122247\pi\)
\(632\) −3.30625 + 5.72660i −0.131516 + 0.227792i
\(633\) 11.0250 0.438203
\(634\) −3.29583 + 5.70855i −0.130894 + 0.226715i
\(635\) −47.5058 −1.88521
\(636\) 17.8073 0.706105
\(637\) 0 0
\(638\) −3.02084 −0.119596
\(639\) −6.00000 −0.237356
\(640\) 6.14741 10.6476i 0.242998 0.420884i
\(641\) −4.79583 −0.189424 −0.0947120 0.995505i \(-0.530193\pi\)
−0.0947120 + 0.995505i \(0.530193\pi\)
\(642\) 4.24264 7.34847i 0.167444 0.290021i
\(643\) −2.82843 + 4.89898i −0.111542 + 0.193197i −0.916392 0.400281i \(-0.868912\pi\)
0.804850 + 0.593478i \(0.202246\pi\)
\(644\) 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 0.180803 + 0.983519i \(0.442130\pi\)
−0.942154 + 0.335180i \(0.891203\pi\)
\(648\) −7.50000 + 12.9904i −0.294628 + 0.510310i
\(649\) −23.6085 + 40.8912i −0.926716 + 1.60512i
\(650\) −32.5122 + 27.4190i −1.27523 + 1.07546i
\(651\) 0 0
\(652\) 7.69375 + 13.3260i 0.301310 + 0.521885i
\(653\) −13.1833 −0.515903 −0.257952 0.966158i \(-0.583048\pi\)
−0.257952 + 0.966158i \(0.583048\pi\)
\(654\) 2.25095 0.0880192
\(655\) −11.0000 19.0526i −0.429806 0.744445i
\(656\) 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 \(0.0499401\pi\)
\(660\) 22.0000 0.856349
\(661\) −3.75209 + 6.49881i −0.145939 + 0.252774i −0.929723 0.368260i \(-0.879954\pi\)
0.783784 + 0.621034i \(0.213287\pi\)
\(662\) −14.6937 25.4503i −0.571089 0.989155i
\(663\) −6.08996 2.19944i −0.236514 0.0854190i
\(664\) 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
\(668\) 0.851476 + 1.47480i 0.0329446 + 0.0570617i
\(669\) −8.00000 −0.309298
\(670\) 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 \(0.680406\pi\)
\(674\) 17.9792 0.692531
\(675\) 33.3636 + 57.7875i 1.28417 + 2.22424i
\(676\) 12.1937 4.50694i 0.468990 0.173344i
\(677\) −3.82427 + 6.62383i −0.146979 + 0.254575i −0.930109 0.367283i \(-0.880288\pi\)
0.783131 + 0.621857i \(0.213622\pi\)
\(678\) −1.83258 3.17413i −0.0703799 0.121902i
\(679\) 0 0
\(680\) −7.80625 + 13.5208i −0.299356 + 0.518500i
\(681\) −5.20417 + 9.01388i −0.199424 + 0.345413i
\(682\) 5.36812 0.205556
\(683\) −6.77499 −0.259238 −0.129619 0.991564i \(-0.541375\pi\)
−0.129619 + 0.991564i \(0.541375\pi\)
\(684\) 1.41421 2.44949i 0.0540738 0.0936586i
\(685\) 38.5152 66.7103i 1.47159 2.54887i
\(686\) 0 0
\(687\) −9.00000 15.5885i −0.343371 0.594737i
\(688\) 3.89792 6.75139i 0.148607 0.257394i
\(689\) 34.7057 29.2688i 1.32218 1.11505i
\(690\) 22.5917 + 39.1299i 0.860050 + 1.48965i
\(691\) −2.53969 −0.0966143 −0.0483072 0.998833i \(-0.515383\pi\)
−0.0483072 + 0.998833i \(0.515383\pi\)
\(692\) −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
\(696\) −3.37643 −0.127983
\(697\) 1.88749 + 3.26924i 0.0714940 + 0.123831i
\(698\) −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 \(0.688750\pi\)
\(702\) 3.59166 + 20.0773i 0.135559 + 0.757771i
\(703\) 3.95390 + 6.84836i 0.149124 + 0.258291i
\(704\) 13.2854 23.0110i 0.500713 0.867260i
\(705\) 16.3931 0.617399
\(706\) −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 0.939410 0.342796i \(-0.111374\pi\)
−0.766575 + 0.642155i \(0.778041\pi\)
\(710\) −12.2948 21.2952i −0.461416 0.799196i
\(711\) 2.20417 0.0826628
\(712\) 44.9366 1.68407
\(713\) −5.51249 9.54790i −0.206444 0.357572i
\(714\) 0 0
\(715\) 42.8771 36.1602i 1.60351 1.35231i
\(716\) −9.79583 + 16.9669i −0.366087 + 0.634082i
\(717\) 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 \(-0.178491\pi\)
−0.883997 + 0.467492i \(0.845158\pi\)
\(720\) 4.09827 0.152734
\(721\) 0 0
\(722\) 5.50000 9.52628i 0.204689 0.354531i
\(723\) −7.89792 + 13.6796i −0.293727 + 0.508749i
\(724\) −3.80953 −0.141580
\(725\) −4.69375 + 8.12981i −0.174321 + 0.301934i
\(726\) 4.82012 0.178891
\(727\) 32.4974 1.20526 0.602632 0.798020i \(-0.294119\pi\)
0.602632 + 0.798020i \(0.294119\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) −51.5708 −1.90872
\(731\) 4.94975 8.57321i 0.183073 0.317092i
\(732\) −11.7958 −0.435986
\(733\) 16.6096 28.7687i 0.613491 1.06260i −0.377156 0.926150i \(-0.623098\pi\)
0.990647 0.136448i \(-0.0435687\pi\)
\(734\) −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 −0.570144 0.821545i \(-0.693113\pi\)
0.996551 + 0.0829873i \(0.0264461\pi\)
\(740\) 5.72904 9.92299i 0.210604 0.364776i
\(741\) 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 \(0.653526\pi\)
\(744\) 6.00000 0.219971
\(745\) −59.8006 −2.19092
\(746\) −3.29583 5.70855i −0.120669 0.209005i
\(747\) −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
\(751\) −7.79583 −0.284474 −0.142237 0.989833i \(-0.545430\pi\)
−0.142237 + 0.989833i \(0.545430\pi\)
\(752\) 1.41421 2.44949i 0.0515711 0.0893237i
\(753\) 11.7958 + 20.4310i 0.429864 + 0.744546i
\(754\) −2.19350 + 1.84988i −0.0798827 + 0.0673687i
\(755\) 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
\(759\) −20.9245 36.2422i −0.759510 1.31551i
\(760\) 34.7750 1.26142
\(761\) 8.90365 + 15.4216i 0.322757 + 0.559032i 0.981056 0.193725i \(-0.0620570\pi\)
−0.658299 + 0.752757i \(0.728724\pi\)
\(762\) −16.3931 −0.593859
\(763\) 0 0
\(764\) −8.10208 14.0332i −0.293123 0.507704i
\(765\) 5.20417 0.188157
\(766\) −6.07522 10.5226i −0.219507 0.380197i
\(767\) 7.89792 + 44.1492i 0.285177 + 1.59414i
\(768\) 12.0208 20.8207i 0.433764 0.751301i
\(769\) −2.12132 3.67423i −0.0764968 0.132496i 0.825239 0.564783i \(-0.191040\pi\)
−0.901736 + 0.432287i \(0.857707\pi\)
\(770\) 0 0
\(771\) −6.10208 + 10.5691i −0.219761 + 0.380638i
\(772\) 11.2958 19.5650i 0.406546 0.704158i
\(773\) 34.7779 1.25087 0.625436 0.780275i \(-0.284921\pi\)
0.625436 + 0.780275i \(0.284921\pi\)
\(774\) −7.79583 −0.280215
\(775\) 8.34091 14.4469i 0.299614 0.518947i
\(776\) −6.36396 + 11.0227i −0.228453 + 0.395692i
\(777\) 0 0
\(778\) 0.193747 + 0.335580i 0.00694618 + 0.0120311i
\(779\) 4.20417 7.28183i 0.150630 0.260899i
\(780\) 15.9747 13.4722i 0.571987 0.482382i
\(781\) 11.3875 + 19.7237i 0.407477 + 0.705770i
\(782\) 9.89949 0.354005
\(783\) 2.25095