Properties

Label 507.2.k.f.80.1
Level $507$
Weight $2$
Character 507.80
Analytic conductor $4.048$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.k (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: 8.0.56070144.2
Defining polynomial: \(x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 63 x^{4} - 74 x^{3} + 70 x^{2} - 38 x + 13\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 80.1
Root \(0.500000 - 0.564882i\) of defining polynomial
Character \(\chi\) \(=\) 507.80
Dual form 507.2.k.f.488.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.389774 + 1.45466i) q^{2} +(-1.60523 - 0.650571i) q^{3} +(-0.232051 - 0.133975i) q^{4} +(-1.06488 - 1.06488i) q^{5} +(1.57203 - 2.08148i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(2.15351 + 2.08863i) q^{9} +O(q^{10})\) \(q+(-0.389774 + 1.45466i) q^{2} +(-1.60523 - 0.650571i) q^{3} +(-0.232051 - 0.133975i) q^{4} +(-1.06488 - 1.06488i) q^{5} +(1.57203 - 2.08148i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(2.15351 + 2.08863i) q^{9} +(1.96410 - 1.13397i) q^{10} +(-3.97420 - 1.06488i) q^{11} +(0.285334 + 0.366025i) q^{12} +2.12976i q^{14} +(1.01660 + 2.40216i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(2.51954 - 4.36397i) q^{17} +(-3.87762 + 2.31853i) q^{18} +(-1.00000 - 3.73205i) q^{19} +(0.104440 + 0.389774i) q^{20} +(-2.43091 - 0.301143i) q^{21} +(3.09808 - 5.36603i) q^{22} +(4.16067 - 1.76080i) q^{24} -2.73205i q^{25} +(-2.09808 - 4.75374i) q^{27} +(-0.366025 - 0.0980762i) q^{28} +(6.20840 - 3.58442i) q^{29} +(-3.89056 + 0.542499i) q^{30} +(2.46410 - 2.46410i) q^{31} +(1.45466 - 0.389774i) q^{32} +(5.68671 + 4.29488i) q^{33} +(5.36603 + 5.36603i) q^{34} +(-1.84443 - 1.06488i) q^{35} +(-0.219901 - 0.773185i) q^{36} +(-1.40192 + 5.23205i) q^{37} +5.81863 q^{38} +3.92820 q^{40} +(1.45466 - 5.42885i) q^{41} +(1.38556 - 3.41876i) q^{42} +(-1.90192 - 1.09808i) q^{43} +(0.779548 + 0.779548i) q^{44} +(-0.0690922 - 4.51739i) q^{45} +(4.25953 - 4.25953i) q^{47} +(1.06782 + 7.65796i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(3.97420 + 1.06488i) q^{50} +(-6.88351 + 5.36603i) q^{51} +0.779548i q^{53} +(7.73284 - 1.19909i) q^{54} +(3.09808 + 5.36603i) q^{55} +(-1.84443 + 3.19465i) q^{56} +(-0.822738 + 6.64136i) q^{57} +(2.79423 + 10.4282i) q^{58} +(-0.779548 - 2.90931i) q^{59} +(0.0859264 - 0.693622i) q^{60} +(3.50000 - 6.06218i) q^{61} +(2.62398 + 4.54486i) q^{62} +(3.70625 + 2.06488i) q^{63} -6.66025i q^{64} +(-8.46410 + 6.59817i) q^{66} +(-5.73205 - 1.53590i) q^{67} +(-1.16932 + 0.675108i) q^{68} +(2.26795 - 2.26795i) q^{70} +(-2.90931 + 0.779548i) q^{71} +(-7.82434 + 0.119671i) q^{72} +(0.901924 + 0.901924i) q^{73} +(-7.06440 - 4.07863i) q^{74} +(-1.77739 + 4.38556i) q^{75} +(-0.267949 + 1.00000i) q^{76} -5.81863 q^{77} +2.00000 q^{79} +(-1.73999 + 6.49373i) q^{80} +(0.275241 + 8.99579i) q^{81} +(7.33013 + 4.23205i) q^{82} +(-2.90931 - 2.90931i) q^{83} +(0.523749 + 0.395560i) q^{84} +(-7.33013 + 1.96410i) q^{85} +(2.33864 - 2.33864i) q^{86} +(-12.2978 + 1.71481i) q^{87} +(9.29423 - 5.36603i) q^{88} +(-9.01327 - 2.41510i) q^{89} +(6.59817 + 1.66025i) q^{90} +(-5.55852 + 2.35237i) q^{93} +(4.53590 + 7.85641i) q^{94} +(-2.90931 + 5.03908i) q^{95} +(-2.58863 - 0.320682i) q^{96} +(0.437822 + 1.63397i) q^{97} +(-1.94887 - 7.27328i) q^{98} +(-6.33434 - 10.5939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} + 12q^{4} + 14q^{6} + 4q^{7} + 4q^{9} + O(q^{10}) \) \( 8q - 2q^{3} + 12q^{4} + 14q^{6} + 4q^{7} + 4q^{9} - 12q^{10} + 2q^{15} - 4q^{16} - 4q^{18} - 8q^{19} - 4q^{21} + 4q^{22} + 30q^{24} + 4q^{27} + 4q^{28} - 18q^{30} - 8q^{31} + 20q^{33} + 36q^{34} + 36q^{36} - 32q^{37} - 24q^{40} - 16q^{42} - 36q^{43} - 16q^{45} - 14q^{48} + 38q^{54} + 4q^{55} - 16q^{57} - 40q^{58} - 44q^{60} + 28q^{61} - 16q^{63} - 40q^{66} - 32q^{67} + 32q^{70} - 24q^{72} + 28q^{73} - 12q^{75} - 16q^{76} + 16q^{79} + 4q^{81} + 24q^{82} + 8q^{84} - 24q^{85} - 34q^{87} + 12q^{88} - 16q^{93} + 64q^{94} - 16q^{96} + 52q^{97} - 40q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.389774 + 1.45466i −0.275612 + 1.02860i 0.679818 + 0.733380i \(0.262059\pi\)
−0.955430 + 0.295217i \(0.904608\pi\)
\(3\) −1.60523 0.650571i −0.926779 0.375608i
\(4\) −0.232051 0.133975i −0.116025 0.0669873i
\(5\) −1.06488 1.06488i −0.476230 0.476230i 0.427694 0.903924i \(-0.359326\pi\)
−0.903924 + 0.427694i \(0.859326\pi\)
\(6\) 1.57203 2.08148i 0.641780 0.849760i
\(7\) 1.36603 0.366025i 0.516309 0.138345i 0.00875026 0.999962i \(-0.497215\pi\)
0.507559 + 0.861617i \(0.330548\pi\)
\(8\) −1.84443 + 1.84443i −0.652105 + 0.652105i
\(9\) 2.15351 + 2.08863i 0.717838 + 0.696210i
\(10\) 1.96410 1.13397i 0.621103 0.358594i
\(11\) −3.97420 1.06488i −1.19826 0.321074i −0.396117 0.918200i \(-0.629643\pi\)
−0.802148 + 0.597126i \(0.796309\pi\)
\(12\) 0.285334 + 0.366025i 0.0823689 + 0.105662i
\(13\) 0 0
\(14\) 2.12976i 0.569204i
\(15\) 1.01660 + 2.40216i 0.262484 + 0.620235i
\(16\) −2.23205 3.86603i −0.558013 0.966506i
\(17\) 2.51954 4.36397i 0.611078 1.05842i −0.379981 0.924994i \(-0.624070\pi\)
0.991059 0.133424i \(-0.0425971\pi\)
\(18\) −3.87762 + 2.31853i −0.913965 + 0.546482i
\(19\) −1.00000 3.73205i −0.229416 0.856191i −0.980587 0.196084i \(-0.937177\pi\)
0.751171 0.660107i \(-0.229489\pi\)
\(20\) 0.104440 + 0.389774i 0.0233534 + 0.0871561i
\(21\) −2.43091 0.301143i −0.530468 0.0657148i
\(22\) 3.09808 5.36603i 0.660512 1.14404i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 4.16067 1.76080i 0.849292 0.359421i
\(25\) 2.73205i 0.546410i
\(26\) 0 0
\(27\) −2.09808 4.75374i −0.403775 0.914858i
\(28\) −0.366025 0.0980762i −0.0691723 0.0185347i
\(29\) 6.20840 3.58442i 1.15287 0.665610i 0.203286 0.979119i \(-0.434838\pi\)
0.949585 + 0.313509i \(0.101505\pi\)
\(30\) −3.89056 + 0.542499i −0.710316 + 0.0990463i
\(31\) 2.46410 2.46410i 0.442566 0.442566i −0.450308 0.892873i \(-0.648686\pi\)
0.892873 + 0.450308i \(0.148686\pi\)
\(32\) 1.45466 0.389774i 0.257149 0.0689030i
\(33\) 5.68671 + 4.29488i 0.989929 + 0.747642i
\(34\) 5.36603 + 5.36603i 0.920266 + 0.920266i
\(35\) −1.84443 1.06488i −0.311766 0.179998i
\(36\) −0.219901 0.773185i −0.0366502 0.128864i
\(37\) −1.40192 + 5.23205i −0.230475 + 0.860144i 0.749662 + 0.661821i \(0.230216\pi\)
−0.980137 + 0.198323i \(0.936451\pi\)
\(38\) 5.81863 0.943906
\(39\) 0 0
\(40\) 3.92820 0.621103
\(41\) 1.45466 5.42885i 0.227179 0.847844i −0.754341 0.656483i \(-0.772043\pi\)
0.981520 0.191361i \(-0.0612901\pi\)
\(42\) 1.38556 3.41876i 0.213797 0.527526i
\(43\) −1.90192 1.09808i −0.290041 0.167455i 0.347920 0.937524i \(-0.386888\pi\)
−0.637960 + 0.770069i \(0.720222\pi\)
\(44\) 0.779548 + 0.779548i 0.117521 + 0.117521i
\(45\) −0.0690922 4.51739i −0.0102997 0.673412i
\(46\) 0 0
\(47\) 4.25953 4.25953i 0.621316 0.621316i −0.324552 0.945868i \(-0.605213\pi\)
0.945868 + 0.324552i \(0.105213\pi\)
\(48\) 1.06782 + 7.65796i 0.154127 + 1.10533i
\(49\) −4.33013 + 2.50000i −0.618590 + 0.357143i
\(50\) 3.97420 + 1.06488i 0.562036 + 0.150597i
\(51\) −6.88351 + 5.36603i −0.963884 + 0.751394i
\(52\) 0 0
\(53\) 0.779548i 0.107079i 0.998566 + 0.0535396i \(0.0170503\pi\)
−0.998566 + 0.0535396i \(0.982950\pi\)
\(54\) 7.73284 1.19909i 1.05231 0.163176i
\(55\) 3.09808 + 5.36603i 0.417745 + 0.723555i
\(56\) −1.84443 + 3.19465i −0.246472 + 0.426903i
\(57\) −0.822738 + 6.64136i −0.108974 + 0.879670i
\(58\) 2.79423 + 10.4282i 0.366900 + 1.36929i
\(59\) −0.779548 2.90931i −0.101489 0.378760i 0.896435 0.443176i \(-0.146148\pi\)
−0.997923 + 0.0644157i \(0.979482\pi\)
\(60\) 0.0859264 0.693622i 0.0110931 0.0895462i
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 2.62398 + 4.54486i 0.333246 + 0.577198i
\(63\) 3.70625 + 2.06488i 0.466943 + 0.260151i
\(64\) 6.66025i 0.832532i
\(65\) 0 0
\(66\) −8.46410 + 6.59817i −1.04186 + 0.812179i
\(67\) −5.73205 1.53590i −0.700281 0.187640i −0.108925 0.994050i \(-0.534741\pi\)
−0.591357 + 0.806410i \(0.701407\pi\)
\(68\) −1.16932 + 0.675108i −0.141801 + 0.0818689i
\(69\) 0 0
\(70\) 2.26795 2.26795i 0.271072 0.271072i
\(71\) −2.90931 + 0.779548i −0.345272 + 0.0925153i −0.427288 0.904116i \(-0.640531\pi\)
0.0820158 + 0.996631i \(0.473864\pi\)
\(72\) −7.82434 + 0.119671i −0.922107 + 0.0141034i
\(73\) 0.901924 + 0.901924i 0.105562 + 0.105562i 0.757915 0.652353i \(-0.226218\pi\)
−0.652353 + 0.757915i \(0.726218\pi\)
\(74\) −7.06440 4.07863i −0.821220 0.474132i
\(75\) −1.77739 + 4.38556i −0.205236 + 0.506401i
\(76\) −0.267949 + 1.00000i −0.0307359 + 0.114708i
\(77\) −5.81863 −0.663094
\(78\) 0 0
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) −1.73999 + 6.49373i −0.194537 + 0.726022i
\(81\) 0.275241 + 8.99579i 0.0305823 + 0.999532i
\(82\) 7.33013 + 4.23205i 0.809477 + 0.467352i
\(83\) −2.90931 2.90931i −0.319339 0.319339i 0.529174 0.848513i \(-0.322502\pi\)
−0.848513 + 0.529174i \(0.822502\pi\)
\(84\) 0.523749 + 0.395560i 0.0571457 + 0.0431592i
\(85\) −7.33013 + 1.96410i −0.795064 + 0.213037i
\(86\) 2.33864 2.33864i 0.252182 0.252182i
\(87\) −12.2978 + 1.71481i −1.31846 + 0.183846i
\(88\) 9.29423 5.36603i 0.990768 0.572020i
\(89\) −9.01327 2.41510i −0.955405 0.256000i −0.252751 0.967531i \(-0.581335\pi\)
−0.702654 + 0.711531i \(0.748002\pi\)
\(90\) 6.59817 + 1.66025i 0.695509 + 0.175006i
\(91\) 0 0
\(92\) 0 0
\(93\) −5.55852 + 2.35237i −0.576392 + 0.243929i
\(94\) 4.53590 + 7.85641i 0.467842 + 0.810326i
\(95\) −2.90931 + 5.03908i −0.298489 + 0.516998i
\(96\) −2.58863 0.320682i −0.264201 0.0327295i
\(97\) 0.437822 + 1.63397i 0.0444541 + 0.165905i 0.984584 0.174910i \(-0.0559636\pi\)
−0.940130 + 0.340815i \(0.889297\pi\)
\(98\) −1.94887 7.27328i −0.196866 0.734712i
\(99\) −6.33434 10.5939i −0.636625 1.06472i
\(100\) −0.366025 + 0.633975i −0.0366025 + 0.0633975i
\(101\) −3.01375 5.21997i −0.299880 0.519407i 0.676229 0.736692i \(-0.263613\pi\)
−0.976108 + 0.217285i \(0.930280\pi\)
\(102\) −5.12271 12.1047i −0.507224 1.19854i
\(103\) 6.92820i 0.682656i 0.939944 + 0.341328i \(0.110877\pi\)
−0.939944 + 0.341328i \(0.889123\pi\)
\(104\) 0 0
\(105\) 2.26795 + 2.90931i 0.221329 + 0.283920i
\(106\) −1.13397 0.303848i −0.110141 0.0295123i
\(107\) −16.4675 + 9.50749i −1.59197 + 0.919123i −0.598999 + 0.800749i \(0.704435\pi\)
−0.992969 + 0.118374i \(0.962232\pi\)
\(108\) −0.150021 + 1.38420i −0.0144357 + 0.133195i
\(109\) 13.1962 13.1962i 1.26396 1.26396i 0.314806 0.949156i \(-0.398060\pi\)
0.949156 0.314806i \(-0.101940\pi\)
\(110\) −9.01327 + 2.41510i −0.859382 + 0.230271i
\(111\) 5.65423 7.48658i 0.536676 0.710595i
\(112\) −4.46410 4.46410i −0.421818 0.421818i
\(113\) 8.90883 + 5.14352i 0.838073 + 0.483861i 0.856609 0.515967i \(-0.172567\pi\)
−0.0185360 + 0.999828i \(0.505901\pi\)
\(114\) −9.34022 3.78543i −0.874792 0.354538i
\(115\) 0 0
\(116\) −1.92089 −0.178350
\(117\) 0 0
\(118\) 4.53590 0.417563
\(119\) 1.84443 6.88351i 0.169079 0.631010i
\(120\) −6.30566 2.55558i −0.575626 0.233291i
\(121\) 5.13397 + 2.96410i 0.466725 + 0.269464i
\(122\) 7.45418 + 7.45418i 0.674869 + 0.674869i
\(123\) −5.86691 + 7.76819i −0.529002 + 0.700434i
\(124\) −0.901924 + 0.241670i −0.0809951 + 0.0217026i
\(125\) −8.23373 + 8.23373i −0.736447 + 0.736447i
\(126\) −4.44829 + 4.58648i −0.396285 + 0.408596i
\(127\) −7.90192 + 4.56218i −0.701182 + 0.404828i −0.807788 0.589474i \(-0.799335\pi\)
0.106605 + 0.994301i \(0.466002\pi\)
\(128\) 12.5977 + 3.37554i 1.11349 + 0.298359i
\(129\) 2.33864 + 3.00000i 0.205906 + 0.264135i
\(130\) 0 0
\(131\) 7.94839i 0.694454i −0.937781 0.347227i \(-0.887123\pi\)
0.937781 0.347227i \(-0.112877\pi\)
\(132\) −0.744201 1.75850i −0.0647743 0.153058i
\(133\) −2.73205 4.73205i −0.236899 0.410321i
\(134\) 4.46841 7.73951i 0.386012 0.668592i
\(135\) −2.82797 + 7.29638i −0.243393 + 0.627973i
\(136\) 3.40192 + 12.6962i 0.291713 + 1.08869i
\(137\) 1.73999 + 6.49373i 0.148657 + 0.554797i 0.999565 + 0.0294822i \(0.00938583\pi\)
−0.850908 + 0.525315i \(0.823948\pi\)
\(138\) 0 0
\(139\) −9.19615 + 15.9282i −0.780007 + 1.35101i 0.151929 + 0.988391i \(0.451451\pi\)
−0.931937 + 0.362621i \(0.881882\pi\)
\(140\) 0.285334 + 0.494214i 0.0241152 + 0.0417687i
\(141\) −9.60864 + 4.06639i −0.809194 + 0.342452i
\(142\) 4.53590i 0.380644i
\(143\) 0 0
\(144\) 3.26795 12.9875i 0.272329 1.08229i
\(145\) −10.4282 2.79423i −0.866015 0.232048i
\(146\) −1.66354 + 0.960443i −0.137675 + 0.0794868i
\(147\) 8.57727 1.19601i 0.707441 0.0986455i
\(148\) 1.02628 1.02628i 0.0843597 0.0843597i
\(149\) 8.33816 2.23420i 0.683089 0.183033i 0.0994454 0.995043i \(-0.468293\pi\)
0.583644 + 0.812010i \(0.301626\pi\)
\(150\) −5.68671 4.29488i −0.464318 0.350675i
\(151\) −0.535898 0.535898i −0.0436108 0.0436108i 0.684965 0.728576i \(-0.259817\pi\)
−0.728576 + 0.684965i \(0.759817\pi\)
\(152\) 8.72794 + 5.03908i 0.707929 + 0.408723i
\(153\) 14.5406 4.13548i 1.17554 0.334334i
\(154\) 2.26795 8.46410i 0.182757 0.682057i
\(155\) −5.24796 −0.421526
\(156\) 0 0
\(157\) −4.80385 −0.383389 −0.191694 0.981455i \(-0.561398\pi\)
−0.191694 + 0.981455i \(0.561398\pi\)
\(158\) −0.779548 + 2.90931i −0.0620175 + 0.231453i
\(159\) 0.507152 1.25135i 0.0402197 0.0992387i
\(160\) −1.96410 1.13397i −0.155276 0.0896486i
\(161\) 0 0
\(162\) −13.1931 3.10594i −1.03655 0.244026i
\(163\) −4.00000 + 1.07180i −0.313304 + 0.0839496i −0.412045 0.911164i \(-0.635185\pi\)
0.0987406 + 0.995113i \(0.468519\pi\)
\(164\) −1.06488 + 1.06488i −0.0831533 + 0.0831533i
\(165\) −1.48214 10.6292i −0.115384 0.827483i
\(166\) 5.36603 3.09808i 0.416484 0.240457i
\(167\) 12.9875 + 3.47998i 1.00500 + 0.269289i 0.723539 0.690283i \(-0.242514\pi\)
0.281461 + 0.959573i \(0.409181\pi\)
\(168\) 5.03908 3.92820i 0.388773 0.303067i
\(169\) 0 0
\(170\) 11.4284i 0.876516i
\(171\) 5.64136 10.1257i 0.431406 0.774328i
\(172\) 0.294229 + 0.509619i 0.0224347 + 0.0388581i
\(173\) −8.72794 + 15.1172i −0.663573 + 1.14934i 0.316097 + 0.948727i \(0.397627\pi\)
−0.979670 + 0.200615i \(0.935706\pi\)
\(174\) 2.29892 18.5575i 0.174281 1.40684i
\(175\) −1.00000 3.73205i −0.0755929 0.282117i
\(176\) 4.75374 + 17.7412i 0.358327 + 1.33729i
\(177\) −0.641364 + 5.17726i −0.0482078 + 0.389147i
\(178\) 7.02628 12.1699i 0.526642 0.912171i
\(179\) −13.2728 22.9892i −0.992056 1.71829i −0.604972 0.796247i \(-0.706816\pi\)
−0.387084 0.922045i \(-0.626518\pi\)
\(180\) −0.589182 + 1.05752i −0.0439150 + 0.0788228i
\(181\) 3.00000i 0.222988i 0.993765 + 0.111494i \(0.0355636\pi\)
−0.993765 + 0.111494i \(0.964436\pi\)
\(182\) 0 0
\(183\) −9.56218 + 7.45418i −0.706857 + 0.551029i
\(184\) 0 0
\(185\) 7.06440 4.07863i 0.519385 0.299867i
\(186\) −1.25532 9.00263i −0.0920449 0.660105i
\(187\) −14.6603 + 14.6603i −1.07206 + 1.07206i
\(188\) −1.55910 + 0.417759i −0.113709 + 0.0304682i
\(189\) −4.60602 5.72579i −0.335038 0.416490i
\(190\) −6.19615 6.19615i −0.449516 0.449516i
\(191\) −4.18307 2.41510i −0.302677 0.174750i 0.340968 0.940075i \(-0.389245\pi\)
−0.643645 + 0.765324i \(0.722579\pi\)
\(192\) −4.33297 + 10.6912i −0.312705 + 0.771573i
\(193\) 0.0358984 0.133975i 0.00258402 0.00964370i −0.964622 0.263638i \(-0.915078\pi\)
0.967206 + 0.253994i \(0.0817443\pi\)
\(194\) −2.54752 −0.182902
\(195\) 0 0
\(196\) 1.33975 0.0956961
\(197\) −1.06488 + 3.97420i −0.0758697 + 0.283150i −0.993429 0.114449i \(-0.963490\pi\)
0.917559 + 0.397599i \(0.130156\pi\)
\(198\) 17.8794 5.08507i 1.27063 0.361380i
\(199\) −11.1962 6.46410i −0.793674 0.458228i 0.0475802 0.998867i \(-0.484849\pi\)
−0.841254 + 0.540639i \(0.818182\pi\)
\(200\) 5.03908 + 5.03908i 0.356317 + 0.356317i
\(201\) 8.20204 + 6.19458i 0.578527 + 0.436932i
\(202\) 8.76795 2.34936i 0.616911 0.165301i
\(203\) 7.16884 7.16884i 0.503154 0.503154i
\(204\) 2.31623 0.322975i 0.162169 0.0226128i
\(205\) −7.33013 + 4.23205i −0.511958 + 0.295579i
\(206\) −10.0782 2.70043i −0.702178 0.188148i
\(207\) 0 0
\(208\) 0 0
\(209\) 15.8968i 1.09960i
\(210\) −5.11604 + 2.16511i −0.353040 + 0.149407i
\(211\) 0.901924 + 1.56218i 0.0620910 + 0.107545i 0.895400 0.445263i \(-0.146890\pi\)
−0.833309 + 0.552808i \(0.813556\pi\)
\(212\) 0.104440 0.180895i 0.00717294 0.0124239i
\(213\) 5.17726 + 0.641364i 0.354740 + 0.0439455i
\(214\) −7.41154 27.6603i −0.506643 1.89082i
\(215\) 0.856003 + 3.19465i 0.0583789 + 0.217873i
\(216\) 12.6377 + 4.89819i 0.859887 + 0.333280i
\(217\) 2.46410 4.26795i 0.167274 0.289727i
\(218\) 14.0524 + 24.3394i 0.951745 + 1.64847i
\(219\) −0.861027 2.03456i −0.0581828 0.137483i
\(220\) 1.66025i 0.111934i
\(221\) 0 0
\(222\) 8.68653 + 11.1430i 0.583002 + 0.747872i
\(223\) 25.0263 + 6.70577i 1.67588 + 0.449052i 0.966687 0.255960i \(-0.0823914\pi\)
0.709196 + 0.705011i \(0.249058\pi\)
\(224\) 1.84443 1.06488i 0.123236 0.0711505i
\(225\) 5.70625 5.88351i 0.380416 0.392234i
\(226\) −10.9545 + 10.9545i −0.728681 + 0.728681i
\(227\) 19.5856 5.24796i 1.29994 0.348319i 0.458515 0.888686i \(-0.348381\pi\)
0.841429 + 0.540367i \(0.181715\pi\)
\(228\) 1.08069 1.43091i 0.0715705 0.0947642i
\(229\) 14.1244 + 14.1244i 0.933364 + 0.933364i 0.997914 0.0645507i \(-0.0205614\pi\)
−0.0645507 + 0.997914i \(0.520561\pi\)
\(230\) 0 0
\(231\) 9.34022 + 3.78543i 0.614541 + 0.249063i
\(232\) −4.83975 + 18.0622i −0.317745 + 1.18584i
\(233\) 17.4559 1.14357 0.571786 0.820403i \(-0.306251\pi\)
0.571786 + 0.820403i \(0.306251\pi\)
\(234\) 0 0
\(235\) −9.07180 −0.591779
\(236\) −0.208879 + 0.779548i −0.0135969 + 0.0507443i
\(237\) −3.21046 1.30114i −0.208542 0.0845183i
\(238\) 9.29423 + 5.36603i 0.602455 + 0.347828i
\(239\) −6.59817 6.59817i −0.426800 0.426800i 0.460737 0.887537i \(-0.347585\pi\)
−0.887537 + 0.460737i \(0.847585\pi\)
\(240\) 7.01772 9.29194i 0.452992 0.599792i
\(241\) 14.0622 3.76795i 0.905825 0.242715i 0.224309 0.974518i \(-0.427988\pi\)
0.681516 + 0.731803i \(0.261321\pi\)
\(242\) −6.31284 + 6.31284i −0.405805 + 0.405805i
\(243\) 5.41058 14.6194i 0.347089 0.937832i
\(244\) −1.62436 + 0.937822i −0.103989 + 0.0600379i
\(245\) 7.27328 + 1.94887i 0.464673 + 0.124509i
\(246\) −9.01327 11.5622i −0.574665 0.737178i
\(247\) 0 0
\(248\) 9.08973i 0.577198i
\(249\) 2.77739 + 6.56283i 0.176010 + 0.415902i
\(250\) −8.76795 15.1865i −0.554534 0.960481i
\(251\) 0.494214 0.856003i 0.0311945 0.0540304i −0.850007 0.526772i \(-0.823402\pi\)
0.881201 + 0.472741i \(0.156736\pi\)
\(252\) −0.583396 0.975700i −0.0367505 0.0614634i
\(253\) 0 0
\(254\) −3.55644 13.2728i −0.223151 0.832810i
\(255\) 13.0443 + 1.61594i 0.816867 + 0.101194i
\(256\) −3.16025 + 5.47372i −0.197516 + 0.342108i
\(257\) 10.7533 + 18.6252i 0.670770 + 1.16181i 0.977686 + 0.210071i \(0.0673696\pi\)
−0.306916 + 0.951737i \(0.599297\pi\)
\(258\) −5.27551 + 2.23260i −0.328439 + 0.138996i
\(259\) 7.66025i 0.475985i
\(260\) 0 0
\(261\) 20.8564 + 5.24796i 1.29098 + 0.324840i
\(262\) 11.5622 + 3.09808i 0.714314 + 0.191400i
\(263\) 19.3003 11.1430i 1.19011 0.687109i 0.231777 0.972769i \(-0.425546\pi\)
0.958331 + 0.285660i \(0.0922127\pi\)
\(264\) −18.4103 + 2.56713i −1.13308 + 0.157996i
\(265\) 0.830127 0.830127i 0.0509943 0.0509943i
\(266\) 7.94839 2.12976i 0.487347 0.130584i
\(267\) 12.8972 + 9.74056i 0.789294 + 0.596113i
\(268\) 1.12436 + 1.12436i 0.0686810 + 0.0686810i
\(269\) 12.4168 + 7.16884i 0.757066 + 0.437092i 0.828241 0.560372i \(-0.189342\pi\)
−0.0711756 + 0.997464i \(0.522675\pi\)
\(270\) −9.51146 6.95767i −0.578849 0.423430i
\(271\) 2.00000 7.46410i 0.121491 0.453412i −0.878199 0.478295i \(-0.841255\pi\)
0.999690 + 0.0248835i \(0.00792149\pi\)
\(272\) −22.4950 −1.36396
\(273\) 0 0
\(274\) −10.1244 −0.611635
\(275\) −2.90931 + 10.8577i −0.175438 + 0.654744i
\(276\) 0 0
\(277\) −23.8923 13.7942i −1.43555 0.828815i −0.438013 0.898969i \(-0.644318\pi\)
−0.997536 + 0.0701536i \(0.977651\pi\)
\(278\) −19.5856 19.5856i −1.17467 1.17467i
\(279\) 10.4531 0.159877i 0.625809 0.00957158i
\(280\) 5.36603 1.43782i 0.320681 0.0859263i
\(281\) 12.1315 12.1315i 0.723703 0.723703i −0.245655 0.969357i \(-0.579003\pi\)
0.969357 + 0.245655i \(0.0790030\pi\)
\(282\) −2.17000 15.5622i −0.129221 0.926718i
\(283\) 5.70577 3.29423i 0.339173 0.195822i −0.320733 0.947170i \(-0.603929\pi\)
0.659906 + 0.751348i \(0.270596\pi\)
\(284\) 0.779548 + 0.208879i 0.0462577 + 0.0123947i
\(285\) 7.94839 6.19615i 0.470822 0.367028i
\(286\) 0 0
\(287\) 7.94839i 0.469179i
\(288\) 3.94672 + 2.19886i 0.232562 + 0.129569i
\(289\) −4.19615 7.26795i −0.246832 0.427526i
\(290\) 8.12929 14.0803i 0.477368 0.826826i
\(291\) 0.360213 2.90774i 0.0211161 0.170455i
\(292\) −0.0884573 0.330127i −0.00517657 0.0193192i
\(293\) −0.466229 1.73999i −0.0272374 0.101651i 0.950969 0.309286i \(-0.100090\pi\)
−0.978206 + 0.207635i \(0.933423\pi\)
\(294\) −1.60341 + 12.9432i −0.0935127 + 0.754860i
\(295\) −2.26795 + 3.92820i −0.132045 + 0.228709i
\(296\) −7.06440 12.2359i −0.410610 0.711198i
\(297\) 3.27599 + 21.1265i 0.190092 + 1.22588i
\(298\) 13.0000i 0.753070i
\(299\) 0 0
\(300\) 1.00000 0.779548i 0.0577350 0.0450072i
\(301\) −3.00000 0.803848i −0.172917 0.0463330i
\(302\) 0.988427 0.570669i 0.0568776 0.0328383i
\(303\) 1.44179 + 10.3399i 0.0828289 + 0.594012i
\(304\) −12.1962 + 12.1962i −0.699497 + 0.699497i
\(305\) −10.1826 + 2.72842i −0.583054 + 0.156229i
\(306\) 0.348161 + 22.7635i 0.0199030 + 1.30130i
\(307\) −8.39230 8.39230i −0.478974 0.478974i 0.425829 0.904803i \(-0.359982\pi\)
−0.904803 + 0.425829i \(0.859982\pi\)
\(308\) 1.35022 + 0.779548i 0.0769357 + 0.0444189i
\(309\) 4.50729 11.1213i 0.256411 0.632671i
\(310\) 2.04552 7.63397i 0.116178 0.433581i
\(311\) 10.0782 0.571480 0.285740 0.958307i \(-0.407761\pi\)
0.285740 + 0.958307i \(0.407761\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 1.87241 6.98795i 0.105666 0.394353i
\(315\) −1.74786 6.14557i −0.0984807 0.346264i
\(316\) −0.464102 0.267949i −0.0261078 0.0150733i
\(317\) 11.3519 + 11.3519i 0.637587 + 0.637587i 0.949960 0.312373i \(-0.101124\pi\)
−0.312373 + 0.949960i \(0.601124\pi\)
\(318\) 1.62261 + 1.22548i 0.0909916 + 0.0687213i
\(319\) −28.4904 + 7.63397i −1.59516 + 0.427421i
\(320\) −7.09239 + 7.09239i −0.396477 + 0.396477i
\(321\) 32.6193 4.54843i 1.82063 0.253869i
\(322\) 0 0
\(323\) −18.8061 5.03908i −1.04640 0.280382i
\(324\) 1.14134 2.12436i 0.0634076 0.118020i
\(325\) 0 0
\(326\) 6.23638i 0.345401i
\(327\) −29.7679 + 12.5978i −1.64617 + 0.696659i
\(328\) 7.33013 + 12.6962i 0.404739 + 0.701028i
\(329\) 4.25953 7.37772i 0.234835 0.406747i
\(330\) 16.0396 + 1.98699i 0.882948 + 0.109380i
\(331\) −8.85641 33.0526i −0.486792 1.81673i −0.571852 0.820357i \(-0.693775\pi\)
0.0850595 0.996376i \(-0.472892\pi\)
\(332\) 0.285334 + 1.06488i 0.0156598 + 0.0584430i
\(333\) −13.9469 + 8.33919i −0.764285 + 0.456985i
\(334\) −10.1244 + 17.5359i −0.553980 + 0.959522i
\(335\) 4.46841 + 7.73951i 0.244135 + 0.422855i
\(336\) 4.26168 + 10.0701i 0.232494 + 0.549370i
\(337\) 18.4641i 1.00580i −0.864344 0.502902i \(-0.832266\pi\)
0.864344 0.502902i \(-0.167734\pi\)
\(338\) 0 0
\(339\) −10.9545 14.0524i −0.594966 0.763219i
\(340\) 1.96410 + 0.526279i 0.106518 + 0.0285415i
\(341\) −12.4168 + 7.16884i −0.672407 + 0.388215i
\(342\) 12.5305 + 12.1530i 0.677571 + 0.657157i
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 5.53329 1.48264i 0.298335 0.0799386i
\(345\) 0 0
\(346\) −18.5885 18.5885i −0.999322 0.999322i
\(347\) −17.8177 10.2870i −0.956502 0.552237i −0.0614076 0.998113i \(-0.519559\pi\)
−0.895095 + 0.445876i \(0.852892\pi\)
\(348\) 3.08346 + 1.24967i 0.165291 + 0.0669895i
\(349\) 7.36603 27.4904i 0.394294 1.47153i −0.428684 0.903454i \(-0.641023\pi\)
0.822979 0.568072i \(-0.192311\pi\)
\(350\) 5.81863 0.311019
\(351\) 0 0
\(352\) −6.19615 −0.330256
\(353\) 3.66088 13.6626i 0.194849 0.727186i −0.797457 0.603376i \(-0.793822\pi\)
0.992306 0.123810i \(-0.0395113\pi\)
\(354\) −7.28115 2.95093i −0.386989 0.156840i
\(355\) 3.92820 + 2.26795i 0.208487 + 0.120370i
\(356\) 1.76798 + 1.76798i 0.0937025 + 0.0937025i
\(357\) −7.43895 + 9.84967i −0.393711 + 0.521300i
\(358\) 38.6147 10.3468i 2.04085 0.546845i
\(359\) −18.2354 + 18.2354i −0.962429 + 0.962429i −0.999319 0.0368904i \(-0.988255\pi\)
0.0368904 + 0.999319i \(0.488255\pi\)
\(360\) 8.45944 + 8.20457i 0.445852 + 0.432419i
\(361\) 3.52628 2.03590i 0.185594 0.107153i
\(362\) −4.36397 1.16932i −0.229365 0.0614582i
\(363\) −6.31284 8.09808i −0.331338 0.425039i
\(364\) 0 0
\(365\) 1.92089i 0.100544i
\(366\) −7.11618 16.8151i −0.371969 0.878941i
\(367\) −15.1962 26.3205i −0.793233 1.37392i −0.923955 0.382500i \(-0.875063\pi\)
0.130723 0.991419i \(-0.458270\pi\)
\(368\) 0 0
\(369\) 14.4715 8.65286i 0.753356 0.450450i
\(370\) 3.17949 + 11.8660i 0.165294 + 0.616885i
\(371\) 0.285334 + 1.06488i 0.0148138 + 0.0552859i
\(372\) 1.60502 + 0.198831i 0.0832162 + 0.0103089i
\(373\) −5.79423 + 10.0359i −0.300014 + 0.519639i −0.976139 0.217148i \(-0.930325\pi\)
0.676125 + 0.736787i \(0.263658\pi\)
\(374\) −15.6114 27.0398i −0.807249 1.39820i
\(375\) 18.5736 7.86038i 0.959138 0.405908i
\(376\) 15.7128i 0.810326i
\(377\) 0 0
\(378\) 10.1244 4.46841i 0.520741 0.229830i
\(379\) 14.2942 + 3.83013i 0.734245 + 0.196740i 0.606519 0.795069i \(-0.292565\pi\)
0.127726 + 0.991809i \(0.459232\pi\)
\(380\) 1.35022 0.779548i 0.0692647 0.0399900i
\(381\) 15.6524 2.18257i 0.801897 0.111816i
\(382\) 5.14359 5.14359i 0.263169 0.263169i
\(383\) −31.7936 + 8.51906i −1.62458 + 0.435304i −0.952341 0.305035i \(-0.901332\pi\)
−0.672234 + 0.740339i \(0.734665\pi\)
\(384\) −18.0261 13.6142i −0.919893 0.694748i
\(385\) 6.19615 + 6.19615i 0.315785 + 0.315785i
\(386\) 0.180895 + 0.104440i 0.00920730 + 0.00531584i
\(387\) −1.80234 6.33714i −0.0916182 0.322135i
\(388\) 0.117314 0.437822i 0.00595572 0.0222271i
\(389\) 22.4950 1.14054 0.570270 0.821457i \(-0.306839\pi\)
0.570270 + 0.821457i \(0.306839\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.37554 12.5977i 0.170491 0.636280i
\(393\) −5.17100 + 12.7590i −0.260842 + 0.643605i
\(394\) −5.36603 3.09808i −0.270336 0.156079i
\(395\) −2.12976 2.12976i −0.107160 0.107160i
\(396\) 0.0505790 + 3.30696i 0.00254169 + 0.166181i
\(397\) −13.2942 + 3.56218i −0.667218 + 0.178781i −0.576501 0.817096i \(-0.695582\pi\)
−0.0907168 + 0.995877i \(0.528916\pi\)
\(398\) 13.7670 13.7670i 0.690078 0.690078i
\(399\) 1.30703 + 9.37341i 0.0654332 + 0.469258i
\(400\) −10.5622 + 6.09808i −0.528109 + 0.304904i
\(401\) −12.0270 3.22263i −0.600601 0.160931i −0.0543073 0.998524i \(-0.517295\pi\)
−0.546294 + 0.837594i \(0.683962\pi\)
\(402\) −12.2079 + 9.51666i −0.608876 + 0.474648i
\(403\) 0 0
\(404\) 1.61507i 0.0803525i
\(405\) 9.28636 9.87256i 0.461443 0.490571i
\(406\) 7.63397 + 13.2224i 0.378868 + 0.656218i
\(407\) 11.1430 19.3003i 0.552340 0.956681i
\(408\) 2.79889 22.5934i 0.138566 1.11854i
\(409\) 7.76795 + 28.9904i 0.384100 + 1.43348i 0.839580 + 0.543236i \(0.182801\pi\)
−0.455480 + 0.890246i \(0.650532\pi\)
\(410\) −3.29909 12.3124i −0.162930 0.608064i
\(411\) 1.43156 11.5559i 0.0706135 0.570011i
\(412\) 0.928203 1.60770i 0.0457293 0.0792055i
\(413\) −2.12976 3.68886i −0.104799 0.181517i
\(414\) 0 0
\(415\) 6.19615i 0.304157i
\(416\) 0 0
\(417\) 25.1244 19.5856i 1.23034 0.959113i
\(418\) −23.1244 6.19615i −1.13105 0.303064i
\(419\) 8.23373 4.75374i 0.402244 0.232236i −0.285208 0.958466i \(-0.592063\pi\)
0.687452 + 0.726230i \(0.258729\pi\)
\(420\) −0.136505 0.978956i −0.00666078 0.0477682i
\(421\) 7.83013 7.83013i 0.381617 0.381617i −0.490067 0.871685i \(-0.663028\pi\)
0.871685 + 0.490067i \(0.163028\pi\)
\(422\) −2.62398 + 0.703093i −0.127733 + 0.0342260i
\(423\) 18.0695 0.276369i 0.878571 0.0134375i
\(424\) −1.43782 1.43782i −0.0698268 0.0698268i
\(425\) −11.9226 6.88351i −0.578330 0.333899i
\(426\) −2.95093 + 7.28115i −0.142973 + 0.352773i
\(427\) 2.56218 9.56218i 0.123992 0.462746i
\(428\) 5.09505 0.246278
\(429\) 0 0
\(430\) −4.98076 −0.240194
\(431\) −9.79282 + 36.5473i −0.471704 + 1.76042i 0.161944 + 0.986800i \(0.448224\pi\)
−0.633648 + 0.773622i \(0.718443\pi\)
\(432\) −13.6951 + 18.7218i −0.658905 + 0.900754i
\(433\) 26.8923 + 15.5263i 1.29236 + 0.746145i 0.979072 0.203512i \(-0.0652357\pi\)
0.313289 + 0.949658i \(0.398569\pi\)
\(434\) 5.24796 + 5.24796i 0.251910 + 0.251910i
\(435\) 14.9218 + 11.2697i 0.715445 + 0.540339i
\(436\) −4.83013 + 1.29423i −0.231321 + 0.0619823i
\(437\) 0 0
\(438\) 3.29519 0.459481i 0.157450 0.0219548i
\(439\) −1.09808 + 0.633975i −0.0524083 + 0.0302580i −0.525975 0.850500i \(-0.676300\pi\)
0.473567 + 0.880758i \(0.342966\pi\)
\(440\) −15.6114 4.18307i −0.744247 0.199420i
\(441\) −14.5466 3.66025i −0.692694 0.174298i
\(442\) 0 0
\(443\) 11.2195i 0.533054i 0.963827 + 0.266527i \(0.0858762\pi\)
−0.963827 + 0.266527i \(0.914124\pi\)
\(444\) −2.31508 + 0.979744i −0.109869 + 0.0464966i
\(445\) 7.02628 + 12.1699i 0.333078 + 0.576907i
\(446\) −19.5092 + 33.7909i −0.923787 + 1.60005i
\(447\) −14.8382 1.83816i −0.701821 0.0869422i
\(448\) −2.43782 9.09808i −0.115176 0.429844i
\(449\) −5.32441 19.8710i −0.251275 0.937769i −0.970125 0.242605i \(-0.921998\pi\)
0.718851 0.695165i \(-0.244669\pi\)
\(450\) 6.33434 + 10.5939i 0.298603 + 0.499400i
\(451\) −11.5622 + 20.0263i −0.544442 + 0.943001i
\(452\) −1.37820 2.38711i −0.0648251 0.112280i
\(453\) 0.511599 + 1.20888i 0.0240370 + 0.0567981i
\(454\) 30.5359i 1.43312i
\(455\) 0 0
\(456\) −10.7321 13.7670i −0.502574 0.644700i
\(457\) −3.76795 1.00962i −0.176257 0.0472280i 0.169611 0.985511i \(-0.445749\pi\)
−0.345868 + 0.938283i \(0.612416\pi\)
\(458\) −26.0514 + 15.0408i −1.21730 + 0.702809i
\(459\) −26.0314 2.82130i −1.21504 0.131687i
\(460\) 0 0
\(461\) −20.5461 + 5.50531i −0.956927 + 0.256408i −0.703299 0.710894i \(-0.748290\pi\)
−0.253628 + 0.967302i \(0.581624\pi\)
\(462\) −9.14708 + 12.1113i −0.425561 + 0.563471i
\(463\) −23.0526 23.0526i −1.07134 1.07134i −0.997251 0.0740918i \(-0.976394\pi\)
−0.0740918 0.997251i \(-0.523606\pi\)
\(464\) −27.7149 16.0012i −1.28663 0.742838i
\(465\) 8.42417 + 3.41417i 0.390661 + 0.158328i
\(466\) −6.80385 + 25.3923i −0.315182 + 1.17628i
\(467\) −19.1679 −0.886984 −0.443492 0.896278i \(-0.646261\pi\)
−0.443492 + 0.896278i \(0.646261\pi\)
\(468\) 0 0
\(469\) −8.39230 −0.387521
\(470\) 3.53595 13.1963i 0.163101 0.608702i
\(471\) 7.71127 + 3.12525i 0.355317 + 0.144004i
\(472\) 6.80385 + 3.92820i 0.313172 + 0.180810i
\(473\) 6.38929 + 6.38929i 0.293780 + 0.293780i
\(474\) 3.14407 4.16296i 0.144412 0.191211i
\(475\) −10.1962 + 2.73205i −0.467832 + 0.125355i
\(476\) −1.35022 + 1.35022i −0.0618871 + 0.0618871i
\(477\) −1.62819 + 1.67877i −0.0745496 + 0.0768655i
\(478\) 12.1699 7.02628i 0.556637 0.321375i
\(479\) 19.8710 + 5.32441i 0.907928 + 0.243279i 0.682418 0.730962i \(-0.260928\pi\)
0.225510 + 0.974241i \(0.427595\pi\)
\(480\) 2.41510 + 3.09808i 0.110234 + 0.141407i
\(481\) 0 0
\(482\) 21.9243i 0.998624i
\(483\) 0 0
\(484\) −0.794229 1.37564i −0.0361013 0.0625293i
\(485\) 1.27376 2.20622i 0.0578385 0.100179i
\(486\) 19.1572 + 13.5688i 0.868990 + 0.615492i
\(487\) 1.49038 + 5.56218i 0.0675356 + 0.252046i 0.991437 0.130584i \(-0.0416851\pi\)
−0.923902 + 0.382630i \(0.875018\pi\)
\(488\) 4.72576 + 17.6368i 0.213925 + 0.798379i
\(489\) 7.11819 + 0.881808i 0.321896 + 0.0398767i
\(490\) −5.66987 + 9.82051i −0.256139 + 0.443645i
\(491\) 14.2612 + 24.7012i 0.643600 + 1.11475i 0.984623 + 0.174693i \(0.0558934\pi\)
−0.341023 + 0.940055i \(0.610773\pi\)
\(492\) 2.40216 1.01660i 0.108298 0.0458317i
\(493\) 36.1244i 1.62696i
\(494\) 0 0
\(495\) −4.53590 + 18.0265i −0.203873 + 0.810233i
\(496\) −15.0263 4.02628i −0.674700 0.180785i
\(497\) −3.68886 + 2.12976i −0.165468 + 0.0955330i
\(498\) −10.6292 + 1.48214i −0.476306 + 0.0664161i
\(499\) 2.46410 2.46410i 0.110308 0.110308i −0.649798 0.760107i \(-0.725147\pi\)
0.760107 + 0.649798i \(0.225147\pi\)
\(500\) 3.01375 0.807533i 0.134779 0.0361140i
\(501\) −18.5839 14.0354i −0.830266 0.627057i
\(502\) 1.05256 + 1.05256i 0.0469780 + 0.0469780i
\(503\) 2.83286 + 1.63555i 0.126311 + 0.0729256i 0.561824 0.827257i \(-0.310100\pi\)
−0.435513 + 0.900182i \(0.643433\pi\)
\(504\) −10.6444 + 3.02738i −0.474141 + 0.134850i
\(505\) −2.34936 + 8.76795i −0.104545 + 0.390169i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.44486 0.108473
\(509\) 3.79330 14.1568i 0.168135 0.627489i −0.829484 0.558530i \(-0.811366\pi\)
0.997620 0.0689588i \(-0.0219677\pi\)
\(510\) −7.43497 + 18.3451i −0.329226 + 0.812337i
\(511\) 1.56218 + 0.901924i 0.0691067 + 0.0398988i
\(512\) 11.7137 + 11.7137i 0.517678 + 0.517678i
\(513\) −15.6431 + 12.5839i −0.690661 + 0.555591i
\(514\) −31.2846 + 8.38269i −1.37990 + 0.369744i
\(515\) 7.37772 7.37772i 0.325101 0.325101i
\(516\) −0.140760 1.00947i −0.00619663 0.0444395i
\(517\) −21.4641 + 12.3923i −0.943990 + 0.545013i
\(518\) −11.1430 2.98577i −0.489597 0.131187i
\(519\) 23.8452 18.5885i 1.04669 0.815943i
\(520\) 0 0
\(521\) 2.49155i 0.109157i 0.998509 + 0.0545785i \(0.0173815\pi\)
−0.998509 + 0.0545785i \(0.982618\pi\)
\(522\) −15.7633 + 28.2934i −0.689939 + 1.23837i
\(523\) 19.4904 + 33.7583i 0.852255 + 1.47615i 0.879169 + 0.476511i \(0.158099\pi\)
−0.0269137 + 0.999638i \(0.508568\pi\)
\(524\) −1.06488 + 1.84443i −0.0465196 + 0.0805743i
\(525\) −0.822738 + 6.64136i −0.0359072 + 0.289853i
\(526\) 8.68653 + 32.4186i 0.378751 + 1.41352i
\(527\) −4.54486 16.9617i −0.197977 0.738862i
\(528\) 3.91108 31.5713i 0.170208 1.37397i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 0.883988 + 1.53111i 0.0383980 + 0.0665072i
\(531\) 4.39771 7.89343i 0.190845 0.342546i
\(532\) 1.46410i 0.0634769i
\(533\) 0 0
\(534\) −19.1962 + 14.9643i −0.830699 + 0.647570i
\(535\) 27.6603 + 7.41154i 1.19586 + 0.320429i
\(536\) 13.4052 7.73951i 0.579018 0.334296i
\(537\) 6.34978 + 45.5378i 0.274013 + 1.96510i
\(538\) −15.2679 + 15.2679i −0.658248 + 0.658248i
\(539\) 19.8710 5.32441i 0.855904 0.229339i
\(540\) 1.63376 1.31425i 0.0703060 0.0565565i
\(541\) 12.6865 + 12.6865i 0.545437 + 0.545437i 0.925118 0.379681i \(-0.123966\pi\)
−0.379681 + 0.925118i \(0.623966\pi\)
\(542\) 10.0782 + 5.81863i 0.432894 + 0.249931i
\(543\) 1.95171 4.81568i 0.0837561 0.206661i
\(544\) 1.96410 7.33013i 0.0842102 0.314277i
\(545\) −28.1047 −1.20387
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 0.466229 1.73999i 0.0199163 0.0743287i
\(549\) 20.1990 5.74477i 0.862070 0.245181i
\(550\) −14.6603 8.46410i −0.625115 0.360911i
\(551\) −19.5856 19.5856i −0.834376 0.834376i
\(552\) 0 0
\(553\) 2.73205 0.732051i 0.116179 0.0311300i
\(554\) 29.3785 29.3785i 1.24817 1.24817i
\(555\) −13.9934 + 1.95124i −0.593988 + 0.0828255i
\(556\) 4.26795 2.46410i 0.181001 0.104501i
\(557\) 24.7292 + 6.62616i 1.04781 + 0.280759i 0.741346 0.671123i \(-0.234188\pi\)
0.306462 + 0.951883i \(0.400855\pi\)
\(558\) −3.84177 + 15.2679i −0.162635 + 0.646344i
\(559\) 0 0
\(560\) 9.50749i 0.401765i
\(561\) 33.0706 13.9955i 1.39624 0.590891i
\(562\) 12.9186 + 22.3756i 0.544938 + 0.943860i
\(563\) 5.03908 8.72794i 0.212372 0.367839i −0.740085 0.672514i \(-0.765215\pi\)
0.952456 + 0.304675i \(0.0985479\pi\)
\(564\) 2.77449 + 0.343706i 0.116827 + 0.0144726i
\(565\) −4.00962 14.9641i −0.168686 0.629544i
\(566\) 2.56801 + 9.58394i 0.107941 + 0.402843i
\(567\) 3.66867 + 12.1877i 0.154070 + 0.511837i
\(568\) 3.92820 6.80385i 0.164824 0.285483i
\(569\) 1.35022 + 2.33864i 0.0566040 + 0.0980411i 0.892939 0.450178i \(-0.148639\pi\)
−0.836335 + 0.548219i \(0.815306\pi\)
\(570\) 5.91520 + 13.9773i 0.247760 + 0.585444i
\(571\) 1.94744i 0.0814979i 0.999169 + 0.0407489i \(0.0129744\pi\)
−0.999169 + 0.0407489i \(0.987026\pi\)
\(572\) 0 0
\(573\) 5.14359 + 6.59817i 0.214877 + 0.275643i
\(574\) 11.5622 + 3.09808i 0.482596 + 0.129311i
\(575\) 0 0
\(576\) 13.9108 14.3429i 0.579617 0.597623i
\(577\) 22.4904 22.4904i 0.936287 0.936287i −0.0618016 0.998088i \(-0.519685\pi\)
0.998088 + 0.0618016i \(0.0196846\pi\)
\(578\) 12.2079 3.27110i 0.507783 0.136060i
\(579\) −0.144785 + 0.191705i −0.00601707 + 0.00796700i
\(580\) 2.04552 + 2.04552i 0.0849355 + 0.0849355i
\(581\) −5.03908 2.90931i −0.209056 0.120699i
\(582\) 4.08936 + 1.65735i 0.169509 + 0.0686992i
\(583\) 0.830127 3.09808i 0.0343803 0.128309i
\(584\) −3.32707 −0.137675
\(585\) 0 0
\(586\) 2.71281 0.112065
\(587\) 4.83020 18.0265i 0.199364 0.744035i −0.791730 0.610871i \(-0.790819\pi\)
0.991094 0.133164i \(-0.0425138\pi\)
\(588\) −2.15060 0.871601i −0.0886892 0.0359442i
\(589\) −11.6603 6.73205i −0.480452 0.277389i
\(590\) −4.83020 4.83020i −0.198856 0.198856i
\(591\) 4.29488 5.68671i 0.176668 0.233920i
\(592\) 23.3564 6.25833i 0.959942 0.257216i
\(593\) −10.3635 + 10.3635i −0.425578 + 0.425578i −0.887119 0.461541i \(-0.847297\pi\)
0.461541 + 0.887119i \(0.347297\pi\)
\(594\) −32.0087 3.46913i −1.31333 0.142340i
\(595\) −9.29423 + 5.36603i −0.381026 + 0.219986i
\(596\) −2.23420 0.598653i −0.0915166 0.0245218i
\(597\) 13.7670 + 17.6603i 0.563446 + 0.722786i
\(598\) 0 0
\(599\) 20.7270i 0.846881i −0.905924 0.423441i \(-0.860822\pi\)
0.905924 0.423441i \(-0.139178\pi\)
\(600\) −4.81059 11.3671i −0.196391 0.464062i
\(601\) −11.7942 20.4282i −0.481097 0.833284i 0.518668 0.854976i \(-0.326428\pi\)
−0.999765 + 0.0216919i \(0.993095\pi\)
\(602\) 2.33864 4.05065i 0.0953160 0.165092i
\(603\) −9.13612 15.2797i −0.372052 0.622238i
\(604\) 0.0525589 + 0.196152i 0.00213859 + 0.00798133i
\(605\) −2.31066 8.62350i −0.0939417 0.350595i
\(606\) −15.6030 1.93291i −0.633828 0.0785192i
\(607\) 0.0980762 0.169873i 0.00398079 0.00689493i −0.864028 0.503444i \(-0.832066\pi\)
0.868009 + 0.496549i \(0.165400\pi\)
\(608\) −2.90931 5.03908i −0.117988 0.204362i
\(609\) −16.1715 + 6.84378i −0.655301 + 0.277324i
\(610\) 15.8756i 0.642786i
\(611\) 0 0
\(612\) −3.92820 0.988427i −0.158788 0.0399548i
\(613\) −42.3827 11.3564i −1.71182 0.458681i −0.735951 0.677035i \(-0.763265\pi\)
−0.975870 + 0.218354i \(0.929931\pi\)
\(614\) 15.4790 8.93682i 0.624683 0.360661i
\(615\) 14.5198 2.02463i 0.585494 0.0816411i
\(616\) 10.7321 10.7321i 0.432407 0.432407i
\(617\) −17.8457 + 4.78173i −0.718439 + 0.192505i −0.599475 0.800393i \(-0.704624\pi\)
−0.118964 + 0.992899i \(0.537957\pi\)
\(618\) 14.4209 + 10.8914i 0.580094 + 0.438115i
\(619\) 31.6603 + 31.6603i 1.27253 + 1.27253i 0.944755 + 0.327778i \(0.106300\pi\)
0.327778 + 0.944755i \(0.393700\pi\)
\(620\) 1.21779 + 0.703093i 0.0489077 + 0.0282369i
\(621\) 0 0
\(622\) −3.92820 + 14.6603i −0.157507 + 0.587823i
\(623\) −13.1963 −0.528701
\(624\) 0 0
\(625\) 3.87564 0.155026
\(626\) −0.779548 + 2.90931i −0.0311570 + 0.116280i
\(627\) 10.3420 25.5180i 0.413019 1.01909i
\(628\) 1.11474 + 0.643594i 0.0444828 + 0.0256822i
\(629\) 19.3003 + 19.3003i 0.769554 + 0.769554i
\(630\) 9.62097 0.147150i 0.383309 0.00586260i
\(631\) 21.3923 5.73205i 0.851614 0.228189i 0.193493 0.981102i \(-0.438018\pi\)
0.658121 + 0.752912i \(0.271352\pi\)
\(632\) −3.68886 + 3.68886i −0.146735 + 0.146735i
\(633\) −0.431485 3.09442i −0.0171500 0.122992i
\(634\) −20.9378 + 12.0885i −0.831547 + 0.480094i
\(635\) 13.2728 + 3.55644i 0.526715 + 0.141133i
\(636\) −0.285334 + 0.222432i −0.0113142 + 0.00882000i
\(637\) 0 0
\(638\) 44.4192i 1.75857i
\(639\) −7.89343 4.39771i −0.312259 0.173971i
\(640\) −9.82051 17.0096i −0.388190 0.672364i
\(641\) −22.6758 + 39.2757i −0.895642 + 1.55130i −0.0626345 + 0.998037i \(0.519950\pi\)
−0.833008 + 0.553261i \(0.813383\pi\)
\(642\) −6.09776 + 49.2228i −0.240659 + 1.94267i
\(643\) 1.87564 + 7.00000i 0.0739682 + 0.276053i 0.992997 0.118136i \(-0.0376920\pi\)
−0.919029 + 0.394190i \(0.871025\pi\)
\(644\) 0 0
\(645\) 0.704266 5.68503i 0.0277305 0.223848i
\(646\) 14.6603 25.3923i 0.576800 0.999047i
\(647\) 8.23373 + 14.2612i 0.323701 + 0.560667i 0.981249 0.192746i \(-0.0617394\pi\)
−0.657547 + 0.753413i \(0.728406\pi\)
\(648\) −17.0998 16.0844i −0.671742 0.631857i
\(649\) 12.3923i 0.486441i
\(650\) 0 0
\(651\) −6.73205 + 5.24796i −0.263850 + 0.205684i
\(652\) 1.07180 + 0.287187i 0.0419748 + 0.0112471i
\(653\) −8.36615 + 4.83020i −0.327393 + 0.189020i −0.654683 0.755904i \(-0.727198\pi\)
0.327290 + 0.944924i \(0.393865\pi\)
\(654\) −6.72272 48.2123i −0.262879 1.88525i
\(655\) −8.46410 + 8.46410i −0.330720 + 0.330720i
\(656\) −24.2349 + 6.49373i −0.946216 + 0.253538i
\(657\) 0.0585190 + 3.82609i 0.00228304 + 0.149270i
\(658\) 9.07180 + 9.07180i 0.353655 + 0.353655i
\(659\) 23.4834 + 13.5581i 0.914783 + 0.528150i 0.881967 0.471311i \(-0.156219\pi\)
0.0328158 + 0.999461i \(0.489553\pi\)
\(660\) −1.08011 + 2.66509i −0.0420434 + 0.103738i
\(661\) 2.52628 9.42820i 0.0982609 0.366715i −0.899233 0.437470i \(-0.855874\pi\)
0.997494 + 0.0707559i \(0.0225411\pi\)
\(662\) 51.5321 2.00285
\(663\) 0 0
\(664\) 10.7321 0.416484
\(665\) −2.12976 + 7.94839i −0.0825887 + 0.308225i
\(666\) −6.69452 23.5383i −0.259408 0.912092i
\(667\) 0 0
\(668\) −2.54752 2.54752i −0.0985666 0.0985666i
\(669\) −35.8103 27.0457i −1.38451 1.04565i
\(670\) −13.0000 + 3.48334i −0.502234 + 0.134573i
\(671\) −20.3652 + 20.3652i −0.786189 + 0.786189i
\(672\) −3.65351 + 0.509445i −0.140937 + 0.0196523i
\(673\) 36.9904 21.3564i 1.42587 0.823229i 0.429082 0.903265i \(-0.358837\pi\)
0.996792 + 0.0800364i \(0.0255036\pi\)
\(674\) 26.8589 + 7.19683i 1.03457 + 0.277211i
\(675\) −12.9875 + 5.73205i −0.499888 + 0.220627i
\(676\) 0 0
\(677\) 9.66040i 0.371279i −0.982618 0.185640i \(-0.940564\pi\)
0.982618 0.185640i \(-0.0594357\pi\)
\(678\) 24.7111 10.4578i 0.949025 0.401628i
\(679\) 1.19615 + 2.07180i 0.0459041 + 0.0795083i
\(680\) 9.89726 17.1426i 0.379543 0.657387i
\(681\) −34.8536 4.31769i −1.33559 0.165454i
\(682\) −5.58846 20.8564i −0.213993 0.798633i
\(683\) 12.1315 + 45.2752i 0.464198 + 1.73241i 0.659536 + 0.751673i \(0.270753\pi\)
−0.195338 + 0.980736i \(0.562580\pi\)
\(684\) −2.66566 + 1.59387i −0.101924 + 0.0609430i
\(685\) 5.06218 8.76795i 0.193416 0.335006i
\(686\) −12.7786 22.1332i −0.487889 0.845048i
\(687\) −13.4839 31.8617i −0.514443 1.21560i
\(688\) 9.80385i 0.373768i
\(689\) 0 0
\(690\) 0 0
\(691\) 18.2224 + 4.88269i 0.693214 + 0.185746i 0.588189 0.808723i \(-0.299841\pi\)
0.105025 + 0.994470i \(0.466508\pi\)
\(692\) 4.05065 2.33864i 0.153983 0.0889019i
\(693\) −12.5305 12.1530i −0.475994 0.461653i
\(694\) 21.9090 21.9090i 0.831653 0.831653i
\(695\) 26.7545 7.16884i 1.01486 0.271930i
\(696\) 19.5196 25.8453i 0.739890 0.979664i
\(697\) −20.0263 20.0263i −0.758549 0.758549i
\(698\) 37.1180 + 21.4301i 1.40494 + 0.811140i
\(699\) −28.0207 11.3563i −1.05984 0.429535i
\(700\) −0.267949 + 1.00000i −0.0101275 + 0.0377964i
\(701\) 12.7786 0.482641 0.241320 0.970446i \(-0.422420\pi\)
0.241320 + 0.970446i \(0.422420\pi\)
\(702\) 0 0
\(703\) 20.9282 0.789322
\(704\) −7.09239 + 26.4692i −0.267304 + 0.997594i
\(705\) 14.5623 + 5.90185i 0.548448 + 0.222277i
\(706\) 18.4474 + 10.6506i 0.694279 + 0.400842i
\(707\) −6.02751 6.02751i −0.226688 0.226688i
\(708\) 0.842451 1.11546i 0.0316612 0.0419216i
\(709\) −11.3301 + 3.03590i −0.425512 + 0.114016i −0.465219 0.885196i \(-0.654024\pi\)
0.0397068 + 0.999211i \(0.487358\pi\)
\(710\) −4.83020 + 4.83020i −0.181274 + 0.181274i
\(711\) 4.30703 + 4.17726i 0.161526 + 0.156660i
\(712\) 21.0788 12.1699i 0.789963 0.456085i
\(713\) 0 0
\(714\) −11.4284 14.6603i −0.427696 0.548646i
\(715\) 0 0
\(716\) 7.11287i 0.265821i
\(717\) 6.29899 + 14.8842i 0.235240 + 0.555859i
\(718\) −19.4186 33.6340i −0.724695 1.25521i
\(719\) 3.68886 6.38929i 0.137571 0.238280i −0.789005 0.614386i \(-0.789404\pi\)
0.926577 + 0.376106i \(0.122737\pi\)
\(720\) −17.3101 + 10.3501i −0.645110 + 0.385727i
\(721\) 2.53590 + 9.46410i 0.0944418 + 0.352462i
\(722\) 1.58708 + 5.92307i 0.0590650 + 0.220434i
\(723\) −25.0243 3.10003i −0.930665 0.115292i
\(724\) 0.401924 0.696152i 0.0149374 0.0258723i
\(725\) −9.79282 16.9617i −0.363696 0.629940i
\(726\) 14.2405 6.02659i 0.528515 0.223668i
\(727\) 19.5167i 0.723833i −0.932211 0.361916i \(-0.882123\pi\)
0.932211 0.361916i \(-0.117877\pi\)
\(728\) 0 0
\(729\) −18.1962 + 19.9474i −0.673932 + 0.738794i
\(730\) 2.79423 + 0.748711i 0.103419 + 0.0277110i
\(731\) −9.58394 + 5.53329i −0.354475 + 0.204656i
\(732\) 3.21758 0.448659i 0.118925 0.0165829i
\(733\) 6.77757 6.77757i 0.250335 0.250335i −0.570773 0.821108i \(-0.693356\pi\)
0.821108 + 0.570773i \(0.193356\pi\)
\(734\) 44.2104 11.8461i 1.63183 0.437249i
\(735\) −10.4074 7.86017i −0.383883 0.289927i
\(736\) 0 0
\(737\) 21.1447 + 12.2079i 0.778876 + 0.449685i
\(738\) 6.94633 + 24.4237i 0.255698 + 0.899049i
\(739\) −2.98076 + 11.1244i −0.109649 + 0.409216i −0.998831 0.0483378i \(-0.984608\pi\)
0.889182 + 0.457554i \(0.151274\pi\)
\(740\) −2.18573 −0.0803492
\(741\) 0 0
\(742\) −1.66025 −0.0609498
\(743\) −2.28268 + 8.51906i −0.0837432 + 0.312534i −0.995073 0.0991426i \(-0.968390\pi\)
0.911330 + 0.411677i \(0.135057\pi\)
\(744\) 5.91352 14.5911i 0.216800 0.534935i
\(745\) −11.2583 6.50000i −0.412473 0.238142i
\(746\) −12.3403 12.3403i −0.451812 0.451812i
\(747\) −0.188763 12.3417i −0.00690649 0.451560i
\(748\) 5.36603 1.43782i 0.196201 0.0525720i
\(749\) −19.0150 + 19.0150i −0.694792 + 0.694792i
\(750\) 4.19463 + 30.0820i 0.153166 + 1.09844i
\(751\) 29.2750 16.9019i 1.06826 0.616760i 0.140554 0.990073i \(-0.455112\pi\)
0.927705 + 0.373313i \(0.121778\pi\)
\(752\) −25.9749 6.95996i −0.947208 0.253804i
\(753\) −1.35022 + 1.05256i −0.0492046 + 0.0383574i
\(754\) 0 0
\(755\) 1.14134i 0.0415375i
\(756\) 0.301720 + 1.94576i 0.0109735 + 0.0707667i
\(757\) −8.39230 14.5359i −0.305024 0.528316i 0.672243 0.740331i \(-0.265331\pi\)
−0.977267 + 0.212014i \(0.931998\pi\)
\(758\) −11.1430 + 19.3003i −0.404733 + 0.701019i
\(759\) 0 0
\(760\) −3.92820 14.6603i −0.142491 0.531783i
\(761\) 4.75374 + 17.7412i 0.172323 + 0.643118i 0.996992 + 0.0775029i \(0.0246947\pi\)
−0.824669 + 0.565616i \(0.808639\pi\)
\(762\) −2.92602 + 23.6196i −0.105998 + 0.855647i
\(763\) 13.1962 22.8564i 0.477733 0.827457i
\(764\) 0.647124 + 1.12085i 0.0234121 + 0.0405510i
\(765\) −19.8878 11.0802i −0.719045 0.400606i
\(766\) 49.5692i 1.79101i
\(767\) 0 0
\(768\) 8.63397 6.73060i 0.311552 0.242870i
\(769\) −40.4186 10.8301i −1.45753 0.390544i −0.558895 0.829238i \(-0.688775\pi\)
−0.898636 + 0.438694i \(0.855441\pi\)
\(770\) −11.4284 + 6.59817i −0.411850 + 0.237782i
\(771\) −5.14442 36.8935i −0.185272 1.32869i
\(772\) −0.0262794 + 0.0262794i −0.000945818 + 0.000945818i
\(773\) 41.5864 11.1430i 1.49576 0.400787i 0.584081 0.811695i \(-0.301455\pi\)
0.911677 + 0.410908i \(0.134788\pi\)
\(774\) 9.92087 0.151737i 0.356598 0.00545407i
\(775\) −6.73205 6.73205i −0.241822 0.241822i