Properties

Label 637.2.h.k.471.2
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 471.2
Root \(1.34203 - 2.32446i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.k.165.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.707107 + 1.22474i) q^{3} -1.00000 q^{4} +(1.34203 - 2.32446i) q^{5} +(-0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.707107 + 1.22474i) q^{3} -1.00000 q^{4} +(1.34203 - 2.32446i) q^{5} +(-0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.34203 - 2.32446i) q^{10} +(-2.89792 + 5.01934i) q^{11} +(0.707107 - 1.22474i) q^{12} +(2.75624 + 2.32446i) q^{13} +(1.89792 + 3.28729i) q^{15} -1.00000 q^{16} +5.51249 q^{17} +(0.500000 + 0.866025i) q^{18} +(1.41421 + 2.44949i) q^{19} +(-1.34203 + 2.32446i) q^{20} +(-2.89792 + 5.01934i) q^{22} +1.79583 q^{23} +(2.12132 - 3.67423i) q^{24} +(-1.10208 - 1.90887i) q^{25} +(2.75624 + 2.32446i) q^{26} -5.65685 q^{27} +(4.39792 + 7.61741i) q^{29} +(1.89792 + 3.28729i) q^{30} +(0.707107 + 1.22474i) q^{31} +5.00000 q^{32} +(-4.09827 - 7.09841i) q^{33} +5.51249 q^{34} +(-0.500000 - 0.866025i) q^{36} -6.79583 q^{37} +(1.41421 + 2.44949i) q^{38} +(-4.79583 + 1.73205i) q^{39} +(-4.02609 + 6.97339i) q^{40} +(-4.87756 - 8.44819i) q^{41} +(0.897916 - 1.55524i) q^{43} +(2.89792 - 5.01934i) q^{44} +2.68406 q^{45} +1.79583 q^{46} +(-1.41421 + 2.44949i) q^{47} +(0.707107 - 1.22474i) q^{48} +(-1.10208 - 1.90887i) q^{50} +(-3.89792 + 6.75139i) q^{51} +(-2.75624 - 2.32446i) q^{52} +(-3.29583 - 5.70855i) q^{53} -5.65685 q^{54} +(7.77817 + 13.4722i) q^{55} -4.00000 q^{57} +(4.39792 + 7.61741i) q^{58} +1.12548 q^{59} +(-1.89792 - 3.28729i) q^{60} +(-0.779291 - 1.34977i) q^{61} +(0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(9.10208 - 3.28729i) q^{65} +(-4.09827 - 7.09841i) q^{66} +(-2.89792 + 5.01934i) q^{67} -5.51249 q^{68} +(-1.26984 + 2.19944i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +(2.90061 + 5.02401i) q^{73} -6.79583 q^{74} +3.11716 q^{75} +(-1.41421 - 2.44949i) q^{76} +(-4.79583 + 1.73205i) q^{78} +(5.89792 - 10.2155i) q^{79} +(-1.34203 + 2.32446i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-4.87756 - 8.44819i) q^{82} -9.89949 q^{83} +(7.39792 - 12.8136i) q^{85} +(0.897916 - 1.55524i) q^{86} -12.4392 q^{87} +(8.69375 - 15.0580i) q^{88} +12.1504 q^{89} +2.68406 q^{90} -1.79583 q^{92} -2.00000 q^{93} +(-1.41421 + 2.44949i) q^{94} +7.59166 q^{95} +(-3.53553 + 6.12372i) q^{96} +(2.12132 - 3.67423i) q^{97} -5.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 8q^{4} - 24q^{8} + 4q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - 8q^{4} - 24q^{8} + 4q^{9} - 4q^{11} - 4q^{15} - 8q^{16} + 4q^{18} - 4q^{22} - 24q^{23} - 28q^{25} + 16q^{29} - 4q^{30} + 40q^{32} - 4q^{36} - 16q^{37} - 12q^{43} + 4q^{44} - 24q^{46} - 28q^{50} - 12q^{51} + 12q^{53} - 32q^{57} + 16q^{58} + 4q^{60} + 56q^{64} + 92q^{65} - 4q^{67} - 24q^{71} - 12q^{72} - 16q^{74} + 28q^{79} + 20q^{81} + 40q^{85} - 12q^{86} + 12q^{88} + 24q^{92} - 16q^{93} - 16q^{95} - 8q^{99} + O(q^{100}) \)

Character values

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

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

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
\(5\) 1.34203 2.32446i 0.600174 1.03953i −0.392621 0.919700i \(-0.628431\pi\)
0.992794 0.119831i \(-0.0382352\pi\)
\(6\) −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
\(10\) 1.34203 2.32446i 0.424387 0.735060i
\(11\) −2.89792 + 5.01934i −0.873754 + 1.51339i −0.0156708 + 0.999877i \(0.504988\pi\)
−0.858084 + 0.513510i \(0.828345\pi\)
\(12\) 0.707107 1.22474i 0.204124 0.353553i
\(13\) 2.75624 + 2.32446i 0.764444 + 0.644690i
\(14\) 0 0
\(15\) 1.89792 + 3.28729i 0.490040 + 0.848774i
\(16\) −1.00000 −0.250000
\(17\) 5.51249 1.33697 0.668487 0.743724i \(-0.266942\pi\)
0.668487 + 0.743724i \(0.266942\pi\)
\(18\) 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 \(0.728157\pi\)
\(20\) −1.34203 + 2.32446i −0.300087 + 0.519766i
\(21\) 0 0
\(22\) −2.89792 + 5.01934i −0.617838 + 1.07013i
\(23\) 1.79583 0.374457 0.187228 0.982316i \(-0.440050\pi\)
0.187228 + 0.982316i \(0.440050\pi\)
\(24\) 2.12132 3.67423i 0.433013 0.750000i
\(25\) −1.10208 1.90887i −0.220417 0.381773i
\(26\) 2.75624 + 2.32446i 0.540544 + 0.455865i
\(27\) −5.65685 −1.08866
\(28\) 0 0
\(29\) 4.39792 + 7.61741i 0.816672 + 1.41452i 0.908121 + 0.418708i \(0.137517\pi\)
−0.0914483 + 0.995810i \(0.529150\pi\)
\(30\) 1.89792 + 3.28729i 0.346510 + 0.600174i
\(31\) 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
\(33\) −4.09827 7.09841i −0.713418 1.23568i
\(34\) 5.51249 0.945383
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −6.79583 −1.11723 −0.558614 0.829428i \(-0.688667\pi\)
−0.558614 + 0.829428i \(0.688667\pi\)
\(38\) 1.41421 + 2.44949i 0.229416 + 0.397360i
\(39\) −4.79583 + 1.73205i −0.767948 + 0.277350i
\(40\) −4.02609 + 6.97339i −0.636580 + 1.10259i
\(41\) −4.87756 8.44819i −0.761747 1.31939i −0.941949 0.335755i \(-0.891008\pi\)
0.180202 0.983630i \(-0.442325\pi\)
\(42\) 0 0
\(43\) 0.897916 1.55524i 0.136931 0.237171i −0.789403 0.613876i \(-0.789610\pi\)
0.926333 + 0.376705i \(0.122943\pi\)
\(44\) 2.89792 5.01934i 0.436877 0.756694i
\(45\) 2.68406 0.400116
\(46\) 1.79583 0.264781
\(47\) −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
\(50\) −1.10208 1.90887i −0.155858 0.269954i
\(51\) −3.89792 + 6.75139i −0.545817 + 0.945383i
\(52\) −2.75624 2.32446i −0.382222 0.322345i
\(53\) −3.29583 5.70855i −0.452717 0.784129i 0.545836 0.837892i \(-0.316212\pi\)
−0.998554 + 0.0537624i \(0.982879\pi\)
\(54\) −5.65685 −0.769800
\(55\) 7.77817 + 13.4722i 1.04881 + 1.81659i
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 4.39792 + 7.61741i 0.577475 + 1.00022i
\(59\) 1.12548 0.146524 0.0732622 0.997313i \(-0.476659\pi\)
0.0732622 + 0.997313i \(0.476659\pi\)
\(60\) −1.89792 3.28729i −0.245020 0.424387i
\(61\) −0.779291 1.34977i −0.0997780 0.172821i 0.811815 0.583915i \(-0.198480\pi\)
−0.911593 + 0.411095i \(0.865147\pi\)
\(62\) 0.707107 + 1.22474i 0.0898027 + 0.155543i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 9.10208 3.28729i 1.12897 0.407738i
\(66\) −4.09827 7.09841i −0.504462 0.873754i
\(67\) −2.89792 + 5.01934i −0.354037 + 0.613210i −0.986953 0.161011i \(-0.948525\pi\)
0.632916 + 0.774221i \(0.281858\pi\)
\(68\) −5.51249 −0.668487
\(69\) −1.26984 + 2.19944i −0.152871 + 0.264781i
\(70\) 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
\(73\) 2.90061 + 5.02401i 0.339491 + 0.588015i 0.984337 0.176297i \(-0.0564119\pi\)
−0.644846 + 0.764312i \(0.723079\pi\)
\(74\) −6.79583 −0.789999
\(75\) 3.11716 0.359939
\(76\) −1.41421 2.44949i −0.162221 0.280976i
\(77\) 0 0
\(78\) −4.79583 + 1.73205i −0.543021 + 0.196116i
\(79\) 5.89792 10.2155i 0.663567 1.14933i −0.316104 0.948724i \(-0.602375\pi\)
0.979672 0.200608i \(-0.0642917\pi\)
\(80\) −1.34203 + 2.32446i −0.150043 + 0.259883i
\(81\) 2.50000 4.33013i 0.277778 0.481125i
\(82\) −4.87756 8.44819i −0.538637 0.932946i
\(83\) −9.89949 −1.08661 −0.543305 0.839535i \(-0.682827\pi\)
−0.543305 + 0.839535i \(0.682827\pi\)
\(84\) 0 0
\(85\) 7.39792 12.8136i 0.802417 1.38983i
\(86\) 0.897916 1.55524i 0.0968247 0.167705i
\(87\) −12.4392 −1.33362
\(88\) 8.69375 15.0580i 0.926757 1.60519i
\(89\) 12.1504 1.28794 0.643972 0.765049i \(-0.277285\pi\)
0.643972 + 0.765049i \(0.277285\pi\)
\(90\) 2.68406 0.282925
\(91\) 0 0
\(92\) −1.79583 −0.187228
\(93\) −2.00000 −0.207390
\(94\) −1.41421 + 2.44949i −0.145865 + 0.252646i
\(95\) 7.59166 0.778888
\(96\) −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
\(99\) −5.79583 −0.582503
\(100\) 1.10208 + 1.90887i 0.110208 + 0.190887i
\(101\) 1.48640 2.57452i 0.147902 0.256174i −0.782550 0.622588i \(-0.786081\pi\)
0.930452 + 0.366414i \(0.119415\pi\)
\(102\) −3.89792 + 6.75139i −0.385951 + 0.668487i
\(103\) 4.09827 7.09841i 0.403815 0.699428i −0.590368 0.807134i \(-0.701017\pi\)
0.994183 + 0.107707i \(0.0343507\pi\)
\(104\) −8.26873 6.97339i −0.810815 0.683797i
\(105\) 0 0
\(106\) −3.29583 5.70855i −0.320119 0.554463i
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 5.65685 0.544331
\(109\) 8.79583 + 15.2348i 0.842488 + 1.45923i 0.887785 + 0.460258i \(0.152243\pi\)
−0.0452972 + 0.998974i \(0.514423\pi\)
\(110\) 7.77817 + 13.4722i 0.741620 + 1.28452i
\(111\) 4.80538 8.32316i 0.456106 0.789999i
\(112\) 0 0
\(113\) 8.29583 14.3688i 0.780406 1.35170i −0.151299 0.988488i \(-0.548346\pi\)
0.931705 0.363215i \(-0.118321\pi\)
\(114\) −4.00000 −0.374634
\(115\) 2.41006 4.17434i 0.224739 0.389260i
\(116\) −4.39792 7.61741i −0.408336 0.707259i
\(117\) −0.634922 + 3.54921i −0.0586986 + 0.328124i
\(118\) 1.12548 0.103608
\(119\) 0 0
\(120\) −5.69375 9.86186i −0.519766 0.900260i
\(121\) −11.2958 19.5650i −1.02689 1.77863i
\(122\) −0.779291 1.34977i −0.0705537 0.122203i
\(123\) 13.7958 1.24393
\(124\) −0.707107 1.22474i −0.0635001 0.109985i
\(125\) 7.50417 0.671194
\(126\) 0 0
\(127\) −3.79583 6.57457i −0.336826 0.583399i 0.647008 0.762483i \(-0.276020\pi\)
−0.983834 + 0.179084i \(0.942687\pi\)
\(128\) −3.00000 −0.265165
\(129\) 1.26984 + 2.19944i 0.111804 + 0.193649i
\(130\) 9.10208 3.28729i 0.798306 0.288314i
\(131\) 4.09827 7.09841i 0.358068 0.620191i −0.629570 0.776944i \(-0.716769\pi\)
0.987638 + 0.156752i \(0.0501024\pi\)
\(132\) 4.09827 + 7.09841i 0.356709 + 0.617838i
\(133\) 0 0
\(134\) −2.89792 + 5.01934i −0.250342 + 0.433605i
\(135\) −7.59166 + 13.1491i −0.653386 + 1.13170i
\(136\) −16.5375 −1.41808
\(137\) −9.20417 −0.786365 −0.393183 0.919460i \(-0.628626\pi\)
−0.393183 + 0.919460i \(0.628626\pi\)
\(138\) −1.26984 + 2.19944i −0.108096 + 0.187228i
\(139\) 7.63381 13.2221i 0.647491 1.12149i −0.336229 0.941780i \(-0.609152\pi\)
0.983720 0.179707i \(-0.0575150\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −19.6546 + 7.09841i −1.64360 + 0.593599i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 23.6085 1.96058
\(146\) 2.90061 + 5.02401i 0.240056 + 0.415790i
\(147\) 0 0
\(148\) 6.79583 0.558614
\(149\) −2.29583 3.97650i −0.188082 0.325767i 0.756529 0.653960i \(-0.226894\pi\)
−0.944611 + 0.328193i \(0.893560\pi\)
\(150\) 3.11716 0.254515
\(151\) 8.79583 + 15.2348i 0.715795 + 1.23979i 0.962652 + 0.270741i \(0.0872687\pi\)
−0.246858 + 0.969052i \(0.579398\pi\)
\(152\) −4.24264 7.34847i −0.344124 0.596040i
\(153\) 2.75624 + 4.77395i 0.222829 + 0.385951i
\(154\) 0 0
\(155\) 3.79583 0.304889
\(156\) 4.79583 1.73205i 0.383974 0.138675i
\(157\) 3.46335 + 5.99870i 0.276405 + 0.478748i 0.970489 0.241146i \(-0.0775234\pi\)
−0.694083 + 0.719895i \(0.744190\pi\)
\(158\) 5.89792 10.2155i 0.469213 0.812701i
\(159\) 9.32202 0.739284
\(160\) 6.71015 11.6223i 0.530484 0.918825i
\(161\) 0 0
\(162\) 2.50000 4.33013i 0.196419 0.340207i
\(163\) 6.69375 + 11.5939i 0.524295 + 0.908105i 0.999600 + 0.0282841i \(0.00900432\pi\)
−0.475305 + 0.879821i \(0.657662\pi\)
\(164\) 4.87756 + 8.44819i 0.380874 + 0.659693i
\(165\) −22.0000 −1.71270
\(166\) −9.89949 −0.768350
\(167\) −7.63381 13.2221i −0.590722 1.02316i −0.994135 0.108142i \(-0.965510\pi\)
0.403414 0.915018i \(-0.367824\pi\)
\(168\) 0 0
\(169\) 2.19375 + 12.8136i 0.168750 + 0.985659i
\(170\) 7.39792 12.8136i 0.567394 0.982756i
\(171\) −1.41421 + 2.44949i −0.108148 + 0.187317i
\(172\) −0.897916 + 1.55524i −0.0684654 + 0.118586i
\(173\) −4.66101 8.07311i −0.354370 0.613787i 0.632640 0.774446i \(-0.281971\pi\)
−0.987010 + 0.160659i \(0.948638\pi\)
\(174\) −12.4392 −0.943012
\(175\) 0 0
\(176\) 2.89792 5.01934i 0.218439 0.378347i
\(177\) −0.795832 + 1.37842i −0.0598184 + 0.103608i
\(178\) 12.1504 0.910714
\(179\) 0.204168 0.353630i 0.0152603 0.0264316i −0.858294 0.513158i \(-0.828476\pi\)
0.873555 + 0.486726i \(0.161809\pi\)
\(180\) −2.68406 −0.200058
\(181\) −16.5375 −1.22922 −0.614610 0.788831i \(-0.710686\pi\)
−0.614610 + 0.788831i \(0.710686\pi\)
\(182\) 0 0
\(183\) 2.20417 0.162937
\(184\) −5.38749 −0.397171
\(185\) −9.12020 + 15.7967i −0.670531 + 1.16139i
\(186\) −2.00000 −0.146647
\(187\) −15.9747 + 27.6690i −1.16819 + 2.02336i
\(188\) 1.41421 2.44949i 0.103142 0.178647i
\(189\) 0 0
\(190\) 7.59166 0.550757
\(191\) 12.8979 + 22.3398i 0.933260 + 1.61645i 0.777707 + 0.628627i \(0.216383\pi\)
0.155553 + 0.987827i \(0.450284\pi\)
\(192\) −4.94975 + 8.57321i −0.357217 + 0.618718i
\(193\) −1.70417 + 2.95171i −0.122669 + 0.212468i −0.920819 0.389990i \(-0.872479\pi\)
0.798151 + 0.602458i \(0.205812\pi\)
\(194\) 2.12132 3.67423i 0.152302 0.263795i
\(195\) −2.41006 + 13.4722i −0.172588 + 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 \(0.741344\pi\)
\(198\) −5.79583 −0.411892
\(199\) −22.0499 −1.56308 −0.781539 0.623856i \(-0.785565\pi\)
−0.781539 + 0.623856i \(0.785565\pi\)
\(200\) 3.30625 + 5.72660i 0.233787 + 0.404932i
\(201\) −4.09827 7.09841i −0.289070 0.500684i
\(202\) 1.48640 2.57452i 0.104583 0.181142i
\(203\) 0 0
\(204\) 3.89792 6.75139i 0.272909 0.472692i
\(205\) −26.1833 −1.82872
\(206\) 4.09827 7.09841i 0.285540 0.494570i
\(207\) 0.897916 + 1.55524i 0.0624095 + 0.108096i
\(208\) −2.75624 2.32446i −0.191111 0.161172i
\(209\) −16.3931 −1.13393
\(210\) 0 0
\(211\) 0.897916 + 1.55524i 0.0618151 + 0.107067i 0.895277 0.445510i \(-0.146978\pi\)
−0.833462 + 0.552577i \(0.813644\pi\)
\(212\) 3.29583 + 5.70855i 0.226359 + 0.392065i
\(213\) −4.24264 7.34847i −0.290701 0.503509i
\(214\) −6.00000 −0.410152
\(215\) −2.41006 4.17434i −0.164365 0.284688i
\(216\) 16.9706 1.15470
\(217\) 0 0
\(218\) 8.79583 + 15.2348i 0.595729 + 1.03183i
\(219\) −8.20417 −0.554386
\(220\) −7.77817 13.4722i −0.524404 0.908295i
\(221\) 15.1937 + 12.8136i 1.02204 + 0.861934i
\(222\) 4.80538 8.32316i 0.322516 0.558614i
\(223\) 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
\(225\) 1.10208 1.90887i 0.0734723 0.127258i
\(226\) 8.29583 14.3688i 0.551831 0.955798i
\(227\) 20.9245 1.38881 0.694403 0.719587i \(-0.255669\pi\)
0.694403 + 0.719587i \(0.255669\pi\)
\(228\) 4.00000 0.264906
\(229\) −6.36396 + 11.0227i −0.420542 + 0.728401i −0.995993 0.0894361i \(-0.971494\pi\)
0.575450 + 0.817837i \(0.304827\pi\)
\(230\) 2.41006 4.17434i 0.158915 0.275248i
\(231\) 0 0
\(232\) −13.1937 22.8522i −0.866212 1.50032i
\(233\) 10.5917 18.3453i 0.693883 1.20184i −0.276673 0.960964i \(-0.589232\pi\)
0.970556 0.240876i \(-0.0774348\pi\)
\(234\) −0.634922 + 3.54921i −0.0415062 + 0.232019i
\(235\) 3.79583 + 6.57457i 0.247613 + 0.428878i
\(236\) −1.12548 −0.0732622
\(237\) 8.34091 + 14.4469i 0.541800 + 0.938426i
\(238\) 0 0
\(239\) −19.7958 −1.28049 −0.640243 0.768172i \(-0.721166\pi\)
−0.640243 + 0.768172i \(0.721166\pi\)
\(240\) −1.89792 3.28729i −0.122510 0.212193i
\(241\) 4.38701 0.282592 0.141296 0.989967i \(-0.454873\pi\)
0.141296 + 0.989967i \(0.454873\pi\)
\(242\) −11.2958 19.5650i −0.726124 1.25768i
\(243\) −4.94975 8.57321i −0.317526 0.549972i
\(244\) 0.779291 + 1.34977i 0.0498890 + 0.0864103i
\(245\) 0 0
\(246\) 13.7958 0.879590
\(247\) −1.79583 + 10.0387i −0.114266 + 0.638746i
\(248\) −2.12132 3.67423i −0.134704 0.233314i
\(249\) 7.00000 12.1244i 0.443607 0.768350i
\(250\) 7.50417 0.474606
\(251\) 1.55858 2.69954i 0.0983769 0.170394i −0.812636 0.582771i \(-0.801968\pi\)
0.911013 + 0.412378i \(0.135302\pi\)
\(252\) 0 0
\(253\) −5.20417 + 9.01388i −0.327183 + 0.566698i
\(254\) −3.79583 6.57457i −0.238172 0.412525i
\(255\) 10.4622 + 18.1211i 0.655170 + 1.13479i
\(256\) −17.0000 −1.06250
\(257\) 15.4120 0.961373 0.480686 0.876893i \(-0.340388\pi\)
0.480686 + 0.876893i \(0.340388\pi\)
\(258\) 1.26984 + 2.19944i 0.0790571 + 0.136931i
\(259\) 0 0
\(260\) −9.10208 + 3.28729i −0.564487 + 0.203869i
\(261\) −4.39792 + 7.61741i −0.272224 + 0.471506i
\(262\) 4.09827 7.09841i 0.253192 0.438542i
\(263\) 12.6937 21.9862i 0.782730 1.35573i −0.147616 0.989045i \(-0.547160\pi\)
0.930346 0.366683i \(-0.119507\pi\)
\(264\) 12.2948 + 21.2952i 0.756694 + 1.31063i
\(265\) −17.6924 −1.08684
\(266\) 0 0
\(267\) −8.59166 + 14.8812i −0.525801 + 0.910714i
\(268\) 2.89792 5.01934i 0.177018 0.306605i
\(269\) −1.12548 −0.0686215 −0.0343107 0.999411i \(-0.510924\pi\)
−0.0343107 + 0.999411i \(0.510924\pi\)
\(270\) −7.59166 + 13.1491i −0.462014 + 0.800232i
\(271\) −23.1754 −1.40781 −0.703903 0.710296i \(-0.748561\pi\)
−0.703903 + 0.710296i \(0.748561\pi\)
\(272\) −5.51249 −0.334244
\(273\) 0 0
\(274\) −9.20417 −0.556044
\(275\) 12.7750 0.770361
\(276\) 1.26984 2.19944i 0.0764357 0.132390i
\(277\) −6.18333 −0.371520 −0.185760 0.982595i \(-0.559475\pi\)
−0.185760 + 0.982595i \(0.559475\pi\)
\(278\) 7.63381 13.2221i 0.457845 0.793011i
\(279\) −0.707107 + 1.22474i −0.0423334 + 0.0733236i
\(280\) 0 0
\(281\) 15.2042 0.907005 0.453502 0.891255i \(-0.350174\pi\)
0.453502 + 0.891255i \(0.350174\pi\)
\(282\) −2.00000 3.46410i −0.119098 0.206284i
\(283\) 14.7049 25.4696i 0.874114 1.51401i 0.0164104 0.999865i \(-0.494776\pi\)
0.857704 0.514145i \(-0.171891\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) −5.36812 + 9.29785i −0.317980 + 0.550757i
\(286\) −19.6546 + 7.09841i −1.16220 + 0.419738i
\(287\) 0 0
\(288\) 2.50000 + 4.33013i 0.147314 + 0.255155i
\(289\) 13.3875 0.787500
\(290\) 23.6085 1.38634
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) −2.90061 5.02401i −0.169745 0.294008i
\(293\) 4.87756 8.44819i 0.284950 0.493548i −0.687647 0.726045i \(-0.741356\pi\)
0.972597 + 0.232497i \(0.0746896\pi\)
\(294\) 0 0
\(295\) 1.51042 2.61613i 0.0879401 0.152317i
\(296\) 20.3875 1.18500
\(297\) 16.3931 28.3937i 0.951223 1.64757i
\(298\) −2.29583 3.97650i −0.132994 0.230352i
\(299\) 4.94975 + 4.17434i 0.286251 + 0.241409i
\(300\) −3.11716 −0.179970
\(301\) 0 0
\(302\) 8.79583 + 15.2348i 0.506143 + 0.876666i
\(303\) 2.10208 + 3.64092i 0.120762 + 0.209165i
\(304\) −1.41421 2.44949i −0.0811107 0.140488i
\(305\) −4.18333 −0.239537
\(306\) 2.75624 + 4.77395i 0.157564 + 0.272909i
\(307\) 34.2004 1.95192 0.975960 0.217951i \(-0.0699374\pi\)
0.975960 + 0.217951i \(0.0699374\pi\)
\(308\) 0 0
\(309\) 5.79583 + 10.0387i 0.329713 + 0.571080i
\(310\) 3.79583 0.215589
\(311\) −5.93085 10.2725i −0.336308 0.582502i 0.647427 0.762127i \(-0.275845\pi\)
−0.983735 + 0.179625i \(0.942512\pi\)
\(312\) 14.3875 5.19615i 0.814531 0.294174i
\(313\) −0.851476 + 1.47480i −0.0481283 + 0.0833606i −0.889086 0.457740i \(-0.848659\pi\)
0.840958 + 0.541101i \(0.181992\pi\)
\(314\) 3.46335 + 5.99870i 0.195448 + 0.338526i
\(315\) 0 0
\(316\) −5.89792 + 10.2155i −0.331784 + 0.574666i
\(317\) 6.29583 10.9047i 0.353609 0.612469i −0.633270 0.773931i \(-0.718288\pi\)
0.986879 + 0.161462i \(0.0516210\pi\)
\(318\) 9.32202 0.522753
\(319\) −50.9792 −2.85428
\(320\) 9.39420 16.2712i 0.525152 0.909590i
\(321\) 4.24264 7.34847i 0.236801 0.410152i
\(322\) 0 0
\(323\) 7.79583 + 13.5028i 0.433772 + 0.751315i
\(324\) −2.50000 + 4.33013i −0.138889 + 0.240563i
\(325\) 1.39948 7.82305i 0.0776289 0.433945i
\(326\) 6.69375 + 11.5939i 0.370732 + 0.642127i
\(327\) −24.8784 −1.37578
\(328\) 14.6327 + 25.3446i 0.807955 + 1.39942i
\(329\) 0 0
\(330\) −22.0000 −1.21106
\(331\) −0.306253 0.530445i −0.0168332 0.0291559i 0.857486 0.514507i \(-0.172025\pi\)
−0.874319 + 0.485351i \(0.838692\pi\)
\(332\) 9.89949 0.543305
\(333\) −3.39792 5.88536i −0.186205 0.322516i
\(334\) −7.63381 13.2221i −0.417703 0.723483i
\(335\) 7.77817 + 13.4722i 0.424967 + 0.736065i
\(336\) 0 0
\(337\) −29.9792 −1.63307 −0.816534 0.577297i \(-0.804108\pi\)
−0.816534 + 0.577297i \(0.804108\pi\)
\(338\) 2.19375 + 12.8136i 0.119324 + 0.696966i
\(339\) 11.7321 + 20.3206i 0.637199 + 1.10366i
\(340\) −7.39792 + 12.8136i −0.401208 + 0.694913i
\(341\) −8.19654 −0.443868
\(342\) −1.41421 + 2.44949i −0.0764719 + 0.132453i
\(343\) 0 0
\(344\) −2.69375 + 4.66571i −0.145237 + 0.251558i
\(345\) 3.40834 + 5.90341i 0.183499 + 0.317829i
\(346\) −4.66101 8.07311i −0.250577 0.434013i
\(347\) 14.9792 0.804123 0.402062 0.915613i \(-0.368294\pi\)
0.402062 + 0.915613i \(0.368294\pi\)
\(348\) 12.4392 0.666810
\(349\) −6.50833 11.2728i −0.348383 0.603417i 0.637579 0.770385i \(-0.279936\pi\)
−0.985962 + 0.166968i \(0.946602\pi\)
\(350\) 0 0
\(351\) −15.5917 13.1491i −0.832221 0.701849i
\(352\) −14.4896 + 25.0967i −0.772297 + 1.33766i
\(353\) 7.56162 13.0971i 0.402464 0.697089i −0.591558 0.806262i \(-0.701487\pi\)
0.994023 + 0.109173i \(0.0348204\pi\)
\(354\) −0.795832 + 1.37842i −0.0422980 + 0.0732622i
\(355\) 8.05217 + 13.9468i 0.427365 + 0.740218i
\(356\) −12.1504 −0.643972
\(357\) 0 0
\(358\) 0.204168 0.353630i 0.0107906 0.0186899i
\(359\) 2.00000 3.46410i 0.105556 0.182828i −0.808409 0.588621i \(-0.799671\pi\)
0.913965 + 0.405793i \(0.133004\pi\)
\(360\) −8.05217 −0.424387
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) −16.5375 −0.869189
\(363\) 31.9494 1.67691
\(364\) 0 0
\(365\) 15.5708 0.815014
\(366\) 2.20417 0.115214
\(367\) −10.6066 + 18.3712i −0.553660 + 0.958967i 0.444346 + 0.895855i \(0.353436\pi\)
−0.998006 + 0.0631123i \(0.979897\pi\)
\(368\) −1.79583 −0.0936142
\(369\) 4.87756 8.44819i 0.253916 0.439795i
\(370\) −9.12020 + 15.7967i −0.474137 + 0.821229i
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 6.29583 + 10.9047i 0.325986 + 0.564624i 0.981711 0.190375i \(-0.0609705\pi\)
−0.655726 + 0.754999i \(0.727637\pi\)
\(374\) −15.9747 + 27.6690i −0.826033 + 1.43073i
\(375\) −5.30625 + 9.19070i −0.274014 + 0.474606i
\(376\) 4.24264 7.34847i 0.218797 0.378968i
\(377\) −5.58467 + 31.2182i −0.287625 + 1.60782i
\(378\) 0 0
\(379\) 1.69375 + 2.93366i 0.0870020 + 0.150692i 0.906243 0.422758i \(-0.138938\pi\)
−0.819241 + 0.573450i \(0.805605\pi\)
\(380\) −7.59166 −0.389444
\(381\) 10.7362 0.550034
\(382\) 12.8979 + 22.3398i 0.659915 + 1.14301i
\(383\) 7.48944 + 12.9721i 0.382692 + 0.662843i 0.991446 0.130517i \(-0.0416636\pi\)
−0.608754 + 0.793359i \(0.708330\pi\)
\(384\) 2.12132 3.67423i 0.108253 0.187500i
\(385\) 0 0
\(386\) −1.70417 + 2.95171i −0.0867399 + 0.150238i
\(387\) 1.79583 0.0912872
\(388\) −2.12132 + 3.67423i −0.107694 + 0.186531i
\(389\) −14.1937 24.5843i −0.719652 1.24647i −0.961138 0.276069i \(-0.910968\pi\)
0.241486 0.970404i \(-0.422365\pi\)
\(390\) −2.41006 + 13.4722i −0.122038 + 0.682191i
\(391\) 9.89949 0.500639
\(392\) 0 0
\(393\) 5.79583 + 10.0387i 0.292361 + 0.506384i
\(394\) 4.00000 + 6.92820i 0.201517 + 0.349038i
\(395\) −15.8303 27.4190i −0.796511 1.37960i
\(396\) 5.79583 0.291251
\(397\) −3.53553 6.12372i −0.177443 0.307341i 0.763561 0.645736i \(-0.223449\pi\)
−0.941004 + 0.338395i \(0.890116\pi\)
\(398\) −22.0499 −1.10526
\(399\) 0 0
\(400\) 1.10208 + 1.90887i 0.0551042 + 0.0954433i
\(401\) 24.3875 1.21785 0.608927 0.793227i \(-0.291600\pi\)
0.608927 + 0.793227i \(0.291600\pi\)
\(402\) −4.09827 7.09841i −0.204403 0.354037i
\(403\) −0.897916 + 5.01934i −0.0447284 + 0.250031i
\(404\) −1.48640 + 2.57452i −0.0739511 + 0.128087i
\(405\) −6.71015 11.6223i −0.333430 0.577517i
\(406\) 0 0
\(407\) 19.6937 34.1106i 0.976183 1.69080i
\(408\) 11.6937 20.2542i 0.578927 1.00273i
\(409\) −28.6879 −1.41853 −0.709263 0.704944i \(-0.750972\pi\)
−0.709263 + 0.704944i \(0.750972\pi\)
\(410\) −26.1833 −1.29310
\(411\) 6.50833 11.2728i 0.321032 0.556044i
\(412\) −4.09827 + 7.09841i −0.201907 + 0.349714i
\(413\) 0 0
\(414\) 0.897916 + 1.55524i 0.0441302 + 0.0764357i
\(415\) −13.2854 + 23.0110i −0.652155 + 1.12957i
\(416\) 13.7812 + 11.6223i 0.675680 + 0.569831i
\(417\) 10.7958 + 18.6989i 0.528674 + 0.915690i
\(418\) −16.3931 −0.801812
\(419\) −14.2718 24.7194i −0.697221 1.20762i −0.969426 0.245384i \(-0.921086\pi\)
0.272205 0.962239i \(-0.412247\pi\)
\(420\) 0 0
\(421\) −6.59166 −0.321258 −0.160629 0.987015i \(-0.551352\pi\)
−0.160629 + 0.987015i \(0.551352\pi\)
\(422\) 0.897916 + 1.55524i 0.0437099 + 0.0757077i
\(423\) −2.82843 −0.137523
\(424\) 9.88749 + 17.1256i 0.480179 + 0.831695i
\(425\) −6.07522 10.5226i −0.294692 0.510421i
\(426\) −4.24264 7.34847i −0.205557 0.356034i
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) 5.20417 29.0912i 0.251260 1.40454i
\(430\) −2.41006 4.17434i −0.116223 0.201305i
\(431\) 2.59166 4.48889i 0.124836 0.216222i −0.796833 0.604200i \(-0.793493\pi\)
0.921669 + 0.387978i \(0.126826\pi\)
\(432\) 5.65685 0.272166
\(433\) −6.71015 + 11.6223i −0.322469 + 0.558533i −0.980997 0.194024i \(-0.937846\pi\)
0.658528 + 0.752556i \(0.271179\pi\)
\(434\) 0 0
\(435\) −16.6937 + 28.9144i −0.800404 + 1.38634i
\(436\) −8.79583 15.2348i −0.421244 0.729616i
\(437\) 2.53969 + 4.39887i 0.121490 + 0.210427i
\(438\) −8.20417 −0.392010
\(439\) 34.2004 1.63230 0.816148 0.577843i \(-0.196106\pi\)
0.816148 + 0.577843i \(0.196106\pi\)
\(440\) −23.3345 40.4166i −1.11243 1.92678i
\(441\) 0 0
\(442\) 15.1937 + 12.8136i 0.722693 + 0.609479i
\(443\) −5.00000 + 8.66025i −0.237557 + 0.411461i −0.960013 0.279956i \(-0.909680\pi\)
0.722456 + 0.691417i \(0.243013\pi\)
\(444\) −4.80538 + 8.32316i −0.228053 + 0.395000i
\(445\) 16.3063 28.2433i 0.772991 1.33886i
\(446\) 2.82843 + 4.89898i 0.133930 + 0.231973i
\(447\) 6.49359 0.307136
\(448\) 0 0
\(449\) −2.20417 + 3.81773i −0.104021 + 0.180170i −0.913338 0.407203i \(-0.866504\pi\)
0.809317 + 0.587372i \(0.199838\pi\)
\(450\) 1.10208 1.90887i 0.0519527 0.0899848i
\(451\) 56.5391 2.66232
\(452\) −8.29583 + 14.3688i −0.390203 + 0.675852i
\(453\) −24.8784 −1.16889
\(454\) 20.9245 0.982034
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −14.5917 −0.682569 −0.341285 0.939960i \(-0.610862\pi\)
−0.341285 + 0.939960i \(0.610862\pi\)
\(458\) −6.36396 + 11.0227i −0.297368 + 0.515057i
\(459\) −31.1833 −1.45551
\(460\) −2.41006 + 4.17434i −0.112370 + 0.194630i
\(461\) −15.4842 + 26.8194i −0.721169 + 1.24910i 0.239362 + 0.970930i \(0.423062\pi\)
−0.960531 + 0.278172i \(0.910272\pi\)
\(462\) 0 0
\(463\) 11.3875 0.529222 0.264611 0.964355i \(-0.414756\pi\)
0.264611 + 0.964355i \(0.414756\pi\)
\(464\) −4.39792 7.61741i −0.204168 0.353630i
\(465\) −2.68406 + 4.64893i −0.124470 + 0.215589i
\(466\) 10.5917 18.3453i 0.490649 0.849830i
\(467\) 2.41006 4.17434i 0.111524 0.193166i −0.804861 0.593464i \(-0.797760\pi\)
0.916385 + 0.400298i \(0.131093\pi\)
\(468\) 0.634922 3.54921i 0.0293493 0.164062i
\(469\) 0 0
\(470\) 3.79583 + 6.57457i 0.175089 + 0.303262i
\(471\) −9.79583 −0.451368
\(472\) −3.37643 −0.155413
\(473\) 5.20417 + 9.01388i 0.239288 + 0.414459i
\(474\) 8.34091 + 14.4469i 0.383111 + 0.663567i
\(475\) 3.11716 5.39909i 0.143025 0.247727i
\(476\) 0 0
\(477\) 3.29583 5.70855i 0.150906 0.261376i
\(478\) −19.7958 −0.905440
\(479\) 3.67990 6.37378i 0.168139 0.291225i −0.769627 0.638494i \(-0.779558\pi\)
0.937766 + 0.347269i \(0.112891\pi\)
\(480\) 9.48958 + 16.4364i 0.433138 + 0.750217i
\(481\) −18.7310 15.7967i −0.854058 0.720266i
\(482\) 4.38701 0.199823
\(483\) 0 0
\(484\) 11.2958 + 19.5650i 0.513447 + 0.889316i
\(485\) −5.69375 9.86186i −0.258540 0.447804i
\(486\) −4.94975 8.57321i −0.224525 0.388889i
\(487\) 19.5917 0.887783 0.443891 0.896081i \(-0.353598\pi\)
0.443891 + 0.896081i \(0.353598\pi\)
\(488\) 2.33787 + 4.04932i 0.105831 + 0.183304i
\(489\) −18.9328 −0.856170
\(490\) 0 0
\(491\) 4.79583 + 8.30662i 0.216433 + 0.374873i 0.953715 0.300712i \(-0.0972244\pi\)
−0.737282 + 0.675585i \(0.763891\pi\)
\(492\) −13.7958 −0.621964
\(493\) 24.2434 + 41.9909i 1.09187 + 1.89117i
\(494\) −1.79583 + 10.0387i −0.0807983 + 0.451661i
\(495\) −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
\(499\) −8.10208 + 14.0332i −0.362699 + 0.628213i −0.988404 0.151847i \(-0.951478\pi\)
0.625705 + 0.780060i \(0.284811\pi\)
\(500\) −7.50417 −0.335597
\(501\) 21.5917 0.964644
\(502\) 1.55858 2.69954i 0.0695629 0.120487i
\(503\) 14.2718 24.7194i 0.636347 1.10218i −0.349881 0.936794i \(-0.613778\pi\)
0.986228 0.165391i \(-0.0528885\pi\)
\(504\) 0 0
\(505\) −3.98958 6.91015i −0.177534 0.307498i
\(506\) −5.20417 + 9.01388i −0.231354 + 0.400716i
\(507\) −17.2446 6.37378i −0.765858 0.283069i
\(508\) 3.79583 + 6.57457i 0.168413 + 0.291700i
\(509\) 26.4370 1.17180 0.585899 0.810384i \(-0.300742\pi\)
0.585899 + 0.810384i \(0.300742\pi\)
\(510\) 10.4622 + 18.1211i 0.463275 + 0.802417i
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) −8.00000 13.8564i −0.353209 0.611775i
\(514\) 15.4120 0.679793
\(515\) −11.0000 19.0526i −0.484718 0.839556i
\(516\) −1.26984 2.19944i −0.0559018 0.0968247i
\(517\) −8.19654 14.1968i −0.360484 0.624376i
\(518\) 0 0
\(519\) 13.1833 0.578684
\(520\) −27.3063 + 9.86186i −1.19746 + 0.432471i
\(521\) −12.5114 21.6703i −0.548133 0.949394i −0.998403 0.0565015i \(-0.982005\pi\)
0.450269 0.892893i \(-0.351328\pi\)
\(522\) −4.39792 + 7.61741i −0.192492 + 0.333405i
\(523\) 28.5730 1.24941 0.624705 0.780861i \(-0.285219\pi\)
0.624705 + 0.780861i \(0.285219\pi\)
\(524\) −4.09827 + 7.09841i −0.179034 + 0.310096i
\(525\) 0 0
\(526\) 12.6937 21.9862i 0.553474 0.958645i
\(527\) 3.89792 + 6.75139i 0.169796 + 0.294095i
\(528\) 4.09827 + 7.09841i 0.178354 + 0.308919i
\(529\) −19.7750 −0.859782
\(530\) −17.6924 −0.768509
\(531\) 0.562738 + 0.974691i 0.0244207 + 0.0422980i
\(532\) 0 0
\(533\) 6.19375 34.6230i 0.268281 1.49969i
\(534\) −8.59166 + 14.8812i −0.371798 + 0.643972i
\(535\) −8.05217 + 13.9468i −0.348126 + 0.602972i
\(536\) 8.69375 15.0580i 0.375513 0.650407i
\(537\) 0.288738 + 0.500109i 0.0124600 + 0.0215813i
\(538\) −1.12548 −0.0485227
\(539\) 0 0
\(540\) 7.59166 13.1491i 0.326693 0.565849i
\(541\) 6.29583 10.9047i 0.270679 0.468830i −0.698357 0.715750i \(-0.746085\pi\)
0.969036 + 0.246920i \(0.0794185\pi\)
\(542\) −23.1754 −0.995469
\(543\) 11.6937 20.2542i 0.501827 0.869189i
\(544\) 27.5624 1.18173
\(545\) 47.2170 2.02256
\(546\) 0 0
\(547\) −36.9792 −1.58111 −0.790557 0.612388i \(-0.790209\pi\)
−0.790557 + 0.612388i \(0.790209\pi\)
\(548\) 9.20417 0.393183
\(549\) 0.779291 1.34977i 0.0332593 0.0576069i
\(550\) 12.7750 0.544727
\(551\) −12.4392 + 21.5453i −0.529927 + 0.917861i
\(552\) 3.80953 6.59831i 0.162145 0.280843i
\(553\) 0 0
\(554\) −6.18333 −0.262704
\(555\) −12.8979 22.3398i −0.547486 0.948274i
\(556\) −7.63381 + 13.2221i −0.323745 + 0.560744i
\(557\) −10.2958 + 17.8329i −0.436248 + 0.755604i −0.997397 0.0721110i \(-0.977026\pi\)
0.561148 + 0.827715i \(0.310360\pi\)
\(558\) −0.707107 + 1.22474i −0.0299342 + 0.0518476i
\(559\) 6.08996 2.19944i 0.257578 0.0930262i
\(560\) 0 0
\(561\) −22.5917 39.1299i −0.953821 1.65207i
\(562\) 15.2042 0.641349
\(563\) −1.12548 −0.0474331 −0.0237166 0.999719i \(-0.507550\pi\)
−0.0237166 + 0.999719i \(0.507550\pi\)
\(564\) 2.00000 + 3.46410i 0.0842152 + 0.145865i
\(565\) −22.2665 38.5667i −0.936758 1.62251i
\(566\) 14.7049 25.4696i 0.618092 1.07057i
\(567\) 0 0
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) 6.40834 0.268651 0.134326 0.990937i \(-0.457113\pi\)
0.134326 + 0.990937i \(0.457113\pi\)
\(570\) −5.36812 + 9.29785i −0.224846 + 0.389444i
\(571\) −7.59166 13.1491i −0.317701 0.550275i 0.662307 0.749233i \(-0.269578\pi\)
−0.980008 + 0.198958i \(0.936244\pi\)
\(572\) 19.6546 7.09841i 0.821801 0.296800i
\(573\) −36.4808 −1.52401
\(574\) 0 0
\(575\) −1.97916 3.42800i −0.0825366 0.142958i
\(576\) 3.50000 + 6.06218i 0.145833 + 0.252591i
\(577\) 4.58883 + 7.94808i 0.191035 + 0.330883i 0.945594 0.325350i \(-0.105482\pi\)
−0.754558 + 0.656233i \(0.772149\pi\)
\(578\) 13.3875 0.556846
\(579\) −2.41006 4.17434i −0.100159 0.173480i
\(580\) −23.6085 −0.980291
\(581\) 0 0
\(582\) 3.00000 + 5.19615i 0.124354 + 0.215387i
\(583\) 38.2042 1.58225
\(584\) −8.70183 15.0720i −0.360084 0.623685i
\(585\) 7.39792 + 6.23899i 0.305866 + 0.257951i
\(586\) 4.87756 8.44819i 0.201490 0.348991i
\(587\) −1.55858 2.69954i −0.0643296 0.111422i 0.832067 0.554675i \(-0.187158\pi\)
−0.896396 + 0.443253i \(0.853824\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 1.51042 2.61613i 0.0621831 0.107704i
\(591\) −11.3137 −0.465384
\(592\) 6.79583 0.279307
\(593\) 0.779291 1.34977i 0.0320017 0.0554285i −0.849581 0.527458i \(-0.823145\pi\)
0.881583 + 0.472030i \(0.156478\pi\)
\(594\) 16.3931 28.3937i 0.672617 1.16501i
\(595\) 0 0
\(596\) 2.29583 + 3.97650i 0.0940409 + 0.162884i
\(597\) 15.5917 27.0056i 0.638124 1.10526i
\(598\) 4.94975 + 4.17434i 0.202410 + 0.170702i
\(599\) 7.20417 + 12.4780i 0.294354 + 0.509837i 0.974834 0.222930i \(-0.0715621\pi\)
−0.680480 + 0.732767i \(0.738229\pi\)
\(600\) −9.35149 −0.381773
\(601\) 15.4842 + 26.8194i 0.631612 + 1.09398i 0.987222 + 0.159350i \(0.0509398\pi\)
−0.355610 + 0.934634i \(0.615727\pi\)
\(602\) 0 0
\(603\) −5.79583 −0.236025
\(604\) −8.79583 15.2348i −0.357897 0.619896i
\(605\) −60.6373 −2.46526
\(606\) 2.10208 + 3.64092i 0.0853913 + 0.147902i
\(607\) 17.9517 + 31.0932i 0.728636 + 1.26203i 0.957460 + 0.288566i \(0.0931786\pi\)
−0.228824 + 0.973468i \(0.573488\pi\)
\(608\) 7.07107 + 12.2474i 0.286770 + 0.496700i
\(609\) 0 0
\(610\) −4.18333 −0.169378
\(611\) −9.59166 + 3.46410i −0.388037 + 0.140143i
\(612\) −2.75624 4.77395i −0.111415 0.192976i
\(613\) 2.98958 5.17810i 0.120748 0.209142i −0.799315 0.600912i \(-0.794804\pi\)
0.920063 + 0.391771i \(0.128137\pi\)
\(614\) 34.2004 1.38022
\(615\) 18.5144 32.0679i 0.746573 1.29310i
\(616\) 0 0
\(617\) 12.1937 21.1202i 0.490902 0.850267i −0.509043 0.860741i \(-0.670001\pi\)
0.999945 + 0.0104740i \(0.00333405\pi\)
\(618\) 5.79583 + 10.0387i 0.233143 + 0.403815i
\(619\) −16.9558 29.3684i −0.681512 1.18041i −0.974519 0.224303i \(-0.927989\pi\)
0.293007 0.956110i \(-0.405344\pi\)
\(620\) −3.79583 −0.152444
\(621\) −10.1588 −0.407657
\(622\) −5.93085 10.2725i −0.237806 0.411891i
\(623\) 0 0
\(624\) 4.79583 1.73205i 0.191987 0.0693375i
\(625\) 15.5812 26.9875i 0.623250 1.07950i
\(626\) −0.851476 + 1.47480i −0.0340318 + 0.0589448i
\(627\) 11.5917 20.0773i 0.462926 0.801812i
\(628\) −3.46335 5.99870i −0.138203 0.239374i
\(629\) −37.4619 −1.49370
\(630\) 0 0
\(631\) 10.2042 17.6741i 0.406222 0.703596i −0.588241 0.808685i \(-0.700179\pi\)
0.994463 + 0.105089i \(0.0335128\pi\)
\(632\) −17.6937 + 30.6465i −0.703819 + 1.21905i
\(633\) −2.53969 −0.100944
\(634\) 6.29583 10.9047i 0.250039 0.433081i
\(635\) −20.3765 −0.808615
\(636\) −9.32202 −0.369642
\(637\) 0 0
\(638\) −50.9792 −2.01828
\(639\) −6.00000 −0.237356
\(640\) −4.02609 + 6.97339i −0.159145 + 0.275647i
\(641\) 4.79583 0.189424 0.0947120 0.995505i \(-0.469807\pi\)
0.0947120 + 0.995505i \(0.469807\pi\)
\(642\) 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
\(645\) 6.81667 0.268406
\(646\) 7.79583 + 13.5028i 0.306723 + 0.531260i
\(647\) 0.981107 1.69933i 0.0385713 0.0668074i −0.846095 0.533032i \(-0.821053\pi\)
0.884667 + 0.466224i \(0.154386\pi\)
\(648\) −7.50000 + 12.9904i −0.294628 + 0.510310i
\(649\) −3.26153 + 5.64914i −0.128026 + 0.221748i
\(650\) 1.39948 7.82305i 0.0548920 0.306845i
\(651\) 0 0
\(652\) −6.69375 11.5939i −0.262147 0.454053i
\(653\) 25.1833 0.985500 0.492750 0.870171i \(-0.335992\pi\)
0.492750 + 0.870171i \(0.335992\pi\)
\(654\) −24.8784 −0.972821
\(655\) −11.0000 19.0526i −0.429806 0.744445i
\(656\) 4.87756 + 8.44819i 0.190437 + 0.329846i
\(657\) −2.90061 + 5.02401i −0.113164 + 0.196005i
\(658\) 0 0
\(659\) 18.7958 32.5553i 0.732182 1.26818i −0.223767 0.974643i \(-0.571836\pi\)
0.955949 0.293533i \(-0.0948311\pi\)
\(660\) 22.0000 0.856349
\(661\) −13.9256 + 24.1198i −0.541642 + 0.938152i 0.457168 + 0.889381i \(0.348864\pi\)
−0.998810 + 0.0487715i \(0.984469\pi\)
\(662\) −0.306253 0.530445i −0.0119028 0.0206163i
\(663\) −26.4370 + 9.54790i −1.02673 + 0.370810i
\(664\) 29.6985 1.15252
\(665\) 0 0
\(666\) −3.39792 5.88536i −0.131667 0.228053i
\(667\) 7.89792 + 13.6796i 0.305809 + 0.529676i
\(668\) 7.63381 + 13.2221i 0.295361 + 0.511580i
\(669\) −8.00000 −0.309298
\(670\) 7.77817 + 13.4722i 0.300497 + 0.520476i
\(671\) 9.03328 0.348726
\(672\) 0 0
\(673\) −11.9896 20.7666i −0.462164 0.800492i 0.536904 0.843643i \(-0.319594\pi\)
−0.999069 + 0.0431511i \(0.986260\pi\)
\(674\) −29.9792 −1.15475
\(675\) 6.23433 + 10.7982i 0.239959 + 0.415622i
\(676\) −2.19375 12.8136i −0.0843749 0.492829i
\(677\) −17.3889 + 30.1185i −0.668311 + 1.15755i 0.310065 + 0.950715i \(0.399649\pi\)
−0.978376 + 0.206833i \(0.933684\pi\)
\(678\) 11.7321 + 20.3206i 0.450568 + 0.780406i
\(679\) 0 0
\(680\) −22.1937 + 38.4407i −0.851091 + 1.47413i
\(681\) −14.7958 + 25.6271i −0.566977 + 0.982034i
\(682\) −8.19654 −0.313862
\(683\) 50.7750 1.94285 0.971425 0.237345i \(-0.0762771\pi\)
0.971425 + 0.237345i \(0.0762771\pi\)
\(684\) 1.41421 2.44949i 0.0540738 0.0936586i
\(685\) −12.3523 + 21.3947i −0.471956 + 0.817451i
\(686\) 0 0
\(687\) −9.00000 15.5885i −0.343371 0.594737i
\(688\) −0.897916 + 1.55524i −0.0342327 + 0.0592928i
\(689\) 4.18519 23.3952i 0.159443 0.891285i
\(690\) 3.40834 + 5.90341i 0.129753 + 0.224739i
\(691\) 11.0250 0.419410 0.209705 0.977765i \(-0.432750\pi\)
0.209705 + 0.977765i \(0.432750\pi\)
\(692\) 4.66101 + 8.07311i 0.177185 + 0.306893i
\(693\) 0 0
\(694\) 14.9792 0.568601
\(695\) −20.4896 35.4890i −0.777214 1.34617i
\(696\) 37.3176 1.41452
\(697\) −26.8875 46.5705i −1.01844 1.76398i
\(698\) −6.50833 11.2728i −0.246344 0.426680i
\(699\) 14.9789 + 25.9442i 0.566553 + 0.981299i
\(700\) 0 0
\(701\) −10.4083 −0.393117 −0.196559 0.980492i \(-0.562977\pi\)
−0.196559 + 0.980492i \(0.562977\pi\)
\(702\) −15.5917 13.1491i −0.588469 0.496283i
\(703\) −9.61076 16.6463i −0.362477 0.627828i
\(704\) −20.2854 + 35.1354i −0.764535 + 1.32421i
\(705\) −10.7362 −0.404350
\(706\) 7.56162 13.0971i 0.284585 0.492916i
\(707\) 0 0
\(708\) 0.795832 1.37842i 0.0299092 0.0518042i
\(709\) 9.39792 + 16.2777i 0.352946 + 0.611321i 0.986764 0.162162i \(-0.0518466\pi\)
−0.633818 + 0.773482i \(0.718513\pi\)
\(710\) 8.05217 + 13.9468i 0.302193 + 0.523413i
\(711\) 11.7958 0.442378
\(712\) −36.4513 −1.36607
\(713\) 1.26984 + 2.19944i 0.0475561 + 0.0823695i
\(714\) 0 0
\(715\) −9.87707 + 55.2127i −0.369382 + 2.06484i
\(716\) −0.204168 + 0.353630i −0.00763013 + 0.0132158i
\(717\) 13.9978 24.2448i 0.522756 0.905440i
\(718\) 2.00000 3.46410i 0.0746393 0.129279i
\(719\) −14.5605 25.2195i −0.543015 0.940530i −0.998729 0.0504035i \(-0.983949\pi\)
0.455714 0.890126i \(-0.349384\pi\)
\(720\) −2.68406 −0.100029
\(721\) 0 0
\(722\) 5.50000 9.52628i 0.204689 0.354531i
\(723\) −3.10208 + 5.37297i −0.115368 + 0.199823i
\(724\) 16.5375 0.614610
\(725\) 9.69375 16.7901i 0.360017 0.623567i
\(726\) 31.9494 1.18575
\(727\) −35.3259 −1.31016 −0.655082 0.755558i \(-0.727366\pi\)
−0.655082 + 0.755558i \(0.727366\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 15.5708 0.576302
\(731\) 4.94975 8.57321i 0.183073 0.317092i
\(732\) −2.20417 −0.0814684
\(733\) −0.346184 + 0.599609i −0.0127866 + 0.0221471i −0.872348 0.488886i \(-0.837404\pi\)
0.859561 + 0.511033i \(0.170737\pi\)
\(734\) −10.6066 + 18.3712i −0.391497 + 0.678092i
\(735\) 0 0
\(736\) 8.97916 0.330976
\(737\) −16.7958 29.0912i −0.618682 1.07159i
\(738\) 4.87756 8.44819i 0.179546 0.310982i
\(739\) −7.59166 + 13.1491i −0.279264 + 0.483699i −0.971202 0.238258i \(-0.923424\pi\)
0.691938 + 0.721957i \(0.256757\pi\)
\(740\) 9.12020 15.7967i 0.335265 0.580697i
\(741\) −11.0250 9.29785i −0.405012 0.341565i
\(742\) 0 0
\(743\) −4.59166 7.95299i −0.168452 0.291767i 0.769424 0.638738i \(-0.220543\pi\)
−0.937876 + 0.346971i \(0.887210\pi\)
\(744\) 6.00000 0.219971
\(745\) −12.3243 −0.451527
\(746\) 6.29583 + 10.9047i 0.230507 + 0.399249i
\(747\) −4.94975 8.57321i −0.181102 0.313678i
\(748\) 15.9747 27.6690i 0.584094 1.01168i
\(749\) 0 0
\(750\) −5.30625 + 9.19070i −0.193757 + 0.335597i
\(751\) 1.79583 0.0655308 0.0327654 0.999463i \(-0.489569\pi\)
0.0327654 + 0.999463i \(0.489569\pi\)
\(752\) 1.41421 2.44949i 0.0515711 0.0893237i
\(753\) 2.20417 + 3.81773i 0.0803244 + 0.139126i
\(754\) −5.58467 + 31.2182i −0.203382 + 1.13690i
\(755\) 47.2170 1.71840
\(756\) 0 0
\(757\) 12.5917 + 21.8094i 0.457652 + 0.792676i 0.998836 0.0482277i \(-0.0153573\pi\)
−0.541185 + 0.840904i \(0.682024\pi\)
\(758\) 1.69375 + 2.93366i 0.0615197 + 0.106555i
\(759\) −7.35981 12.7476i −0.267144 0.462707i
\(760\) −22.7750 −0.826136
\(761\) −4.66101 8.07311i −0.168961 0.292650i 0.769094 0.639136i \(-0.220708\pi\)
−0.938055 + 0.346486i \(0.887375\pi\)
\(762\) 10.7362 0.388933
\(763\) 0 0
\(764\) −12.8979 22.3398i −0.466630 0.808227i
\(765\) 14.7958 0.534944
\(766\) 7.48944 + 12.9721i 0.270604 + 0.468700i
\(767\) 3.10208 + 2.61613i 0.112010 + 0.0944628i
\(768\) 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
\(771\) −10.8979 + 18.8757i −0.392479 + 0.679793i
\(772\) 1.70417 2.95171i 0.0613344 0.106234i
\(773\) 7.64854 0.275099 0.137549 0.990495i \(-0.456077\pi\)
0.137549 + 0.990495i \(0.456077\pi\)
\(774\) 1.79583 0.0645498
\(775\) 1.55858 2.69954i 0.0559859 0.0969705i
\(776\) −6.36396 + 11.0227i −0.228453 + 0.395692i
\(777\) 0 0
\(778\) −14.1937 24.5843i −0.508870 0.881390i
\(779\) 13.7958 23.8951i 0.494287 0.856130i
\(780\) 2.41006 13.4722i 0.0862939 0.482382i
\(781\) −17.3875 30.1160i −0.622173 1.07764i
\(782\) 9.89949 0.354005
\(783\) −24.8784 43.0906i −0.889080