Properties

Label 637.2.h.k.471.4
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 471.4
Root \(2.04914 - 3.54921i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.k.165.4

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 8q^{4} - 24q^{8} + 4q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - 8q^{4} - 24q^{8} + 4q^{9} - 4q^{11} - 4q^{15} - 8q^{16} + 4q^{18} - 4q^{22} - 24q^{23} - 28q^{25} + 16q^{29} - 4q^{30} + 40q^{32} - 4q^{36} - 16q^{37} - 12q^{43} + 4q^{44} - 24q^{46} - 28q^{50} - 12q^{51} + 12q^{53} - 32q^{57} + 16q^{58} + 4q^{60} + 56q^{64} + 92q^{65} - 4q^{67} - 24q^{71} - 12q^{72} - 16q^{74} + 28q^{79} + 20q^{81} + 40q^{85} - 12q^{86} + 12q^{88} + 24q^{92} - 16q^{93} - 16q^{95} - 8q^{99} + O(q^{100}) \)

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 −0.586445 0.809989i \(-0.699473\pi\)
0.994694 + 0.102882i \(0.0328064\pi\)
\(4\) −1.00000 −0.500000
\(5\) 2.04914 3.54921i 0.916401 1.58725i 0.111565 0.993757i \(-0.464414\pi\)
0.804836 0.593497i \(-0.202253\pi\)
\(6\) 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 \(-0.450787\pi\)
0.153991 + 0.988072i \(0.450787\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −1.41421 2.44949i −0.324443 0.561951i 0.656957 0.753928i \(-0.271843\pi\)
−0.981399 + 0.191977i \(0.938510\pi\)
\(20\) −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 0.795513 0.605937i \(-0.207202\pi\)
−0.922513 + 0.385966i \(0.873868\pi\)
\(32\) 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 0.958437 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 \(0.964046\pi\)
\(44\) −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 −0.744257 0.667893i \(-0.767196\pi\)
0.950541 + 0.310599i \(0.100530\pi\)
\(48\) −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 \(-0.199618\pi\)
0.809722 + 0.586814i \(0.199618\pi\)
\(60\) 2.89792 + 5.01934i 0.374119 + 0.647994i
\(61\) 4.17046 + 7.22344i 0.533972 + 0.924867i 0.999212 + 0.0396825i \(0.0126346\pi\)
−0.465240 + 0.885185i \(0.654032\pi\)
\(62\) −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 \(-0.903192\pi\)
0.217711 0.976013i \(-0.430141\pi\)
\(74\) 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 \(-0.317173\pi\)
0.543305 + 0.839535i \(0.317173\pi\)
\(84\) 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 \(-0.208058\pi\)
0.793879 + 0.608076i \(0.208058\pi\)
\(90\) 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 −0.953392 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 −0.999858 0.0168509i \(-0.994636\pi\)
0.514522 + 0.857477i \(0.327969\pi\)
\(102\) 0.897916 1.55524i 0.0889069 0.153991i
\(103\) 2.68406 4.64893i 0.264468 0.458072i −0.702956 0.711233i \(-0.748137\pi\)
0.967424 + 0.253161i \(0.0814703\pi\)
\(104\) −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 −0.724622 0.689146i \(-0.757986\pi\)
0.959129 + 0.282968i \(0.0913190\pi\)
\(132\) 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 −0.899875 0.436149i \(-0.856342\pi\)
0.827653 + 0.561240i \(0.189675\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) −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 0.863131 0.504981i \(-0.168500\pi\)
−0.868892 + 0.495003i \(0.835167\pi\)
\(158\) 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 0.897088 0.441852i \(-0.145678\pi\)
−0.831199 + 0.555975i \(0.812345\pi\)
\(168\) 0 0
\(169\) −12.1937 + 4.50694i −0.937981 + 0.346688i
\(170\) 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 \(-0.929976\pi\)
0.298968 0.954263i \(-0.403358\pi\)
\(174\) −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 \(-0.545218\pi\)
−0.141580 + 0.989927i \(0.545218\pi\)
\(182\) 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 \(-0.557621\pi\)
−0.180034 + 0.983660i \(0.557621\pi\)
\(200\) 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 0.755647 0.654979i \(-0.227323\pi\)
−0.945052 + 0.326920i \(0.893989\pi\)
\(224\) 0 0
\(225\) 5.89792 10.2155i 0.393194 0.681033i
\(226\) −1.29583 + 2.24445i −0.0861974 + 0.149298i
\(227\) −7.35981 −0.488487 −0.244244 0.969714i \(-0.578540\pi\)
−0.244244 + 0.969714i \(0.578540\pi\)
\(228\) 4.00000 0.264906
\(229\) 6.36396 11.0227i 0.420542 0.728401i −0.575450 0.817837i \(-0.695173\pi\)
0.995993 + 0.0894361i \(0.0285065\pi\)
\(230\) −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 \(-0.617135\pi\)
−0.359740 + 0.933053i \(0.617135\pi\)
\(242\) −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 \(0.343153\pi\)
−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
\(255\) −3.67990 6.37378i −0.230444 0.399142i
\(256\) −17.0000 −1.06250
\(257\) −8.62965 −0.538303 −0.269151 0.963098i \(-0.586743\pi\)
−0.269151 + 0.963098i \(0.586743\pi\)
\(258\) 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 \(-0.623806\pi\)
−0.379215 + 0.925308i \(0.623806\pi\)
\(270\) 11.5917 20.0773i 0.705446 1.22187i
\(271\) −17.5186 −1.06418 −0.532088 0.846689i \(-0.678593\pi\)
−0.532088 + 0.846689i \(0.678593\pi\)
\(272\) −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 −0.999448 0.0332294i \(-0.989421\pi\)
0.528501 + 0.848932i \(0.322754\pi\)
\(284\) 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 −0.906172 0.422909i \(-0.861009\pi\)
0.819336 + 0.573314i \(0.194342\pi\)
\(294\) 0 0
\(295\) 25.4896 44.1492i 1.48406 2.57047i
\(296\) −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 \(-0.306015\pi\)
0.572392 + 0.819980i \(0.306015\pi\)
\(308\) 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 \(-0.862046\pi\)
0.0900809 0.995934i \(-0.471287\pi\)
\(312\) −14.3875 5.19615i −0.814531 0.294174i
\(313\) 7.63381 13.2221i 0.431488 0.747359i −0.565514 0.824739i \(-0.691322\pi\)
0.997002 + 0.0773795i \(0.0246553\pi\)
\(314\) −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 \(0.0852867\pi\)
−0.252887 + 0.967496i \(0.581380\pi\)
\(350\) 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 −0.788108 0.615536i \(-0.788939\pi\)
0.927124 + 0.374754i \(0.122273\pi\)
\(354\) 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 \(-0.646564\pi\)
0.998006 0.0631123i \(-0.0201026\pi\)
\(368\) 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 0.978455 0.206458i \(-0.0661938\pi\)
−0.668026 + 0.744138i \(0.732860\pi\)
\(384\) −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 0.941004 0.338395i \(-0.109884\pi\)
−0.763561 + 0.645736i \(0.776551\pi\)
\(398\) −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 \(-0.653771\pi\)
−0.464513 + 0.885566i \(0.653771\pi\)
\(410\) 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 \(-0.950486\pi\)
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
\(423\) 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 −0.999961 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
\(437\) 11.0250 + 19.0958i 0.527396 + 0.913476i
\(438\) −17.7958 −0.850318
\(439\) 20.0583 0.957328 0.478664 0.877998i \(-0.341121\pi\)
0.478664 + 0.877998i \(0.341121\pi\)
\(440\) 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 \(-0.642893\pi\)
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
\(467\) −15.9747 + 27.6690i −0.739222 + 1.28037i 0.213624 + 0.976916i \(0.431473\pi\)
−0.952846 + 0.303454i \(0.901860\pi\)
\(468\) 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 −0.999683 0.0251838i \(-0.991983\pi\)
0.521651 + 0.853159i \(0.325316\pi\)
\(480\) −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 \(-0.639000\pi\)
0.996225 0.0868074i \(-0.0276665\pi\)
\(504\) 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 \(-0.543093\pi\)
−0.134966 + 0.990850i \(0.543093\pi\)
\(510\) −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 0.912683 0.408669i \(-0.134007\pi\)
−0.810259 + 0.586072i \(0.800673\pi\)
\(522\) 0.397916 0.689210i 0.0174163 0.0301659i
\(523\) −42.1377 −1.84255 −0.921276 0.388910i \(-0.872852\pi\)
−0.921276 + 0.388910i \(0.872852\pi\)
\(524\) −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 \(-0.584423\pi\)
−0.262125 + 0.965034i \(0.584423\pi\)
\(564\) 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 \(0.00548384\pi\)
−0.485007 + 0.874510i \(0.661183\pi\)
\(578\) −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 0.985220 0.171293i \(-0.0547944\pi\)
−0.640954 + 0.767579i \(0.721461\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 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 −0.938861 0.344297i \(-0.888117\pi\)
0.767601 + 0.640929i \(0.221451\pi\)
\(594\) 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 0.506686 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
\(605\) −13.9683 −0.567892
\(606\) 6.89792 + 11.9475i 0.280209 + 0.485336i
\(607\) 2.39532 + 4.14882i 0.0972231 + 0.168395i 0.910534 0.413434i \(-0.135671\pi\)
−0.813311 + 0.581829i \(0.802337\pi\)
\(608\) −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 \(-0.927989\pi\)
0.293007 0.956110i \(-0.405344\pi\)
\(620\) 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 −0.804850 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 −0.180803 0.983519i \(-0.557870\pi\)
0.942154 0.335180i \(-0.108797\pi\)
\(648\) −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 −0.783784 0.621034i \(-0.786713\pi\)
0.929723 + 0.368260i \(0.120046\pi\)
\(662\) −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 −0.783131 0.621857i \(-0.786378\pi\)
0.930109 + 0.367283i \(0.119712\pi\)
\(678\) 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 \(-0.484617\pi\)
0.0483072 + 0.998833i \(0.484617\pi\)
\(692\) 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 0.883997 0.467492i \(-0.154842\pi\)
−0.846859 + 0.531818i \(0.821509\pi\)
\(720\) −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 \(-0.705881\pi\)
−0.602632 + 0.798020i \(0.705881\pi\)
\(728\) 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 \(0.376902\pi\)
−0.990647 + 0.136448i \(0.956431\pi\)
\(734\) 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 0.658299 0.752757i \(-0.271276\pi\)
−0.981056 + 0.193725i \(0.937943\pi\)
\(762\) 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 0.901736 0.432287i \(-0.142293\pi\)
−0.825239 + 0.564783i \(0.808960\pi\)
\(770\) 0 0
\(771\) −6.10208 + 10.5691i −0.219761 + 0.380638i
\(772\) 11.2958 19.5650i 0.406546 0.704158i
\(773\) −34.7779 −1.25087 −0.625436 0.780275i \(-0.715079\pi\)
−0.625436 + 0.780275i \(0.715079\pi\)
\(774\) −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