Properties

Label 507.2.k.f.488.1
Level $507$
Weight $2$
Character 507.488
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 488.1
Root \(0.500000 + 0.564882i\) of defining polynomial
Character \(\chi\) \(=\) 507.488
Dual form 507.2.k.f.80.1

$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{12}\right)\)

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 −0.955430 0.295217i \(-0.904608\pi\)
0.679818 0.733380i \(-0.262059\pi\)
\(3\) −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 −0.903924 0.427694i \(-0.859326\pi\)
0.427694 + 0.903924i \(0.359326\pi\)
\(6\) 1.57203 + 2.08148i 0.641780 + 0.849760i
\(7\) 1.36603 + 0.366025i 0.516309 + 0.138345i 0.507559 0.861617i \(-0.330548\pi\)
0.00875026 + 0.999962i \(0.497215\pi\)
\(8\) −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 −0.802148 0.597126i \(-0.796309\pi\)
−0.396117 + 0.918200i \(0.629643\pi\)
\(12\) 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 0.991059 + 0.133424i \(0.0425971\pi\)
−0.379981 + 0.924994i \(0.624070\pi\)
\(18\) −3.87762 2.31853i −0.913965 0.546482i
\(19\) −1.00000 + 3.73205i −0.229416 + 0.856191i 0.751171 + 0.660107i \(0.229489\pi\)
−0.980587 + 0.196084i \(0.937177\pi\)
\(20\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 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 0.949585 0.313509i \(-0.101505\pi\)
0.203286 + 0.979119i \(0.434838\pi\)
\(30\) −3.89056 0.542499i −0.710316 0.0990463i
\(31\) 2.46410 + 2.46410i 0.442566 + 0.442566i 0.892873 0.450308i \(-0.148686\pi\)
−0.450308 + 0.892873i \(0.648686\pi\)
\(32\) 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 −0.980137 0.198323i \(-0.936451\pi\)
0.749662 0.661821i \(-0.230216\pi\)
\(38\) 5.81863 0.943906
\(39\) 0 0
\(40\) 3.92820 0.621103
\(41\) 1.45466 + 5.42885i 0.227179 + 0.847844i 0.981520 + 0.191361i \(0.0612901\pi\)
−0.754341 + 0.656483i \(0.772043\pi\)
\(42\) 1.38556 + 3.41876i 0.213797 + 0.527526i
\(43\) −1.90192 + 1.09808i −0.290041 + 0.167455i −0.637960 0.770069i \(-0.720222\pi\)
0.347920 + 0.937524i \(0.386888\pi\)
\(44\) 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 0.945868 0.324552i \(-0.105213\pi\)
−0.324552 + 0.945868i \(0.605213\pi\)
\(48\) 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 \(-0.982950\pi\)
0.998566 0.0535396i \(-0.0170503\pi\)
\(54\) 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 −0.997923 0.0644157i \(-0.979482\pi\)
0.896435 + 0.443176i \(0.146148\pi\)
\(60\) 0.0859264 + 0.693622i 0.0110931 + 0.0895462i
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 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 −0.591357 0.806410i \(-0.701407\pi\)
−0.108925 + 0.994050i \(0.534741\pi\)
\(68\) −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 0.0820158 0.996631i \(-0.473864\pi\)
−0.427288 + 0.904116i \(0.640531\pi\)
\(72\) −7.82434 0.119671i −0.922107 0.0141034i
\(73\) 0.901924 0.901924i 0.105562 0.105562i −0.652353 0.757915i \(-0.726218\pi\)
0.757915 + 0.652353i \(0.226218\pi\)
\(74\) −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 −0.848513 0.529174i \(-0.822502\pi\)
0.529174 + 0.848513i \(0.322502\pi\)
\(84\) 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 −0.702654 0.711531i \(-0.748002\pi\)
−0.252751 + 0.967531i \(0.581335\pi\)
\(90\) 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 −0.940130 0.340815i \(-0.889297\pi\)
0.984584 + 0.174910i \(0.0559636\pi\)
\(98\) −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 −0.976108 0.217285i \(-0.930280\pi\)
0.676229 + 0.736692i \(0.263613\pi\)
\(102\) −5.12271 + 12.1047i −0.507224 + 1.19854i
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) 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 −0.992969 0.118374i \(-0.962232\pi\)
−0.598999 0.800749i \(-0.704435\pi\)
\(108\) −0.150021 1.38420i −0.0144357 0.133195i
\(109\) 13.1962 + 13.1962i 1.26396 + 1.26396i 0.949156 + 0.314806i \(0.101940\pi\)
0.314806 + 0.949156i \(0.398060\pi\)
\(110\) −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 −0.0185360 0.999828i \(-0.505901\pi\)
0.856609 + 0.515967i \(0.172567\pi\)
\(114\) −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 0.106605 0.994301i \(-0.466002\pi\)
−0.807788 + 0.589474i \(0.799335\pi\)
\(128\) 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 \(0.112877\pi\)
−0.937781 + 0.347227i \(0.887123\pi\)
\(132\) −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 −0.850908 0.525315i \(-0.823948\pi\)
0.999565 0.0294822i \(-0.00938583\pi\)
\(138\) 0 0
\(139\) −9.19615 15.9282i −0.780007 1.35101i −0.931937 0.362621i \(-0.881882\pi\)
0.151929 0.988391i \(-0.451451\pi\)
\(140\) 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 0.583644 0.812010i \(-0.301626\pi\)
0.0994454 + 0.995043i \(0.468293\pi\)
\(150\) −5.68671 + 4.29488i −0.464318 + 0.350675i
\(151\) −0.535898 + 0.535898i −0.0436108 + 0.0436108i −0.728576 0.684965i \(-0.759817\pi\)
0.684965 + 0.728576i \(0.259817\pi\)
\(152\) 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 0.0987406 0.995113i \(-0.468519\pi\)
−0.412045 + 0.911164i \(0.635185\pi\)
\(164\) −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 0.281461 0.959573i \(-0.409181\pi\)
0.723539 + 0.690283i \(0.242514\pi\)
\(168\) 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 −0.979670 0.200615i \(-0.935706\pi\)
0.316097 0.948727i \(-0.397627\pi\)
\(174\) 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 −0.387084 + 0.922045i \(0.626518\pi\)
−0.604972 + 0.796247i \(0.706816\pi\)
\(180\) −0.589182 1.05752i −0.0439150 0.0788228i
\(181\) 3.00000i 0.222988i −0.993765 0.111494i \(-0.964436\pi\)
0.993765 0.111494i \(-0.0355636\pi\)
\(182\) 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 −0.643645 0.765324i \(-0.722579\pi\)
0.340968 + 0.940075i \(0.389245\pi\)
\(192\) −4.33297 10.6912i −0.312705 0.771573i
\(193\) 0.0358984 + 0.133975i 0.00258402 + 0.00964370i 0.967206 0.253994i \(-0.0817443\pi\)
−0.964622 + 0.263638i \(0.915078\pi\)
\(194\) −2.54752 −0.182902
\(195\) 0 0
\(196\) 1.33975 0.0956961
\(197\) −1.06488 3.97420i −0.0758697 0.283150i 0.917559 0.397599i \(-0.130156\pi\)
−0.993429 + 0.114449i \(0.963490\pi\)
\(198\) 17.8794 + 5.08507i 1.27063 + 0.361380i
\(199\) −11.1962 + 6.46410i −0.793674 + 0.458228i −0.841254 0.540639i \(-0.818182\pi\)
0.0475802 + 0.998867i \(0.484849\pi\)
\(200\) 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 −0.833309 0.552808i \(-0.813556\pi\)
0.895400 + 0.445263i \(0.146890\pi\)
\(212\) 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 0.709196 0.705011i \(-0.249058\pi\)
0.966687 + 0.255960i \(0.0823914\pi\)
\(224\) 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 0.841429 0.540367i \(-0.181715\pi\)
0.458515 + 0.888686i \(0.348381\pi\)
\(228\) 1.08069 + 1.43091i 0.0715705 + 0.0947642i
\(229\) 14.1244 14.1244i 0.933364 0.933364i −0.0645507 0.997914i \(-0.520561\pi\)
0.997914 + 0.0645507i \(0.0205614\pi\)
\(230\) 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 −0.887537 0.460737i \(-0.847585\pi\)
0.460737 + 0.887537i \(0.347585\pi\)
\(240\) 7.01772 + 9.29194i 0.452992 + 0.599792i
\(241\) 14.0622 + 3.76795i 0.905825 + 0.242715i 0.681516 0.731803i \(-0.261321\pi\)
0.224309 + 0.974518i \(0.427988\pi\)
\(242\) −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 0.881201 0.472741i \(-0.156736\pi\)
−0.850007 + 0.526772i \(0.823402\pi\)
\(252\) −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 −0.306916 0.951737i \(-0.599297\pi\)
0.977686 0.210071i \(-0.0673696\pi\)
\(258\) −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 0.958331 0.285660i \(-0.0922127\pi\)
0.231777 + 0.972769i \(0.425546\pi\)
\(264\) −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 −0.0711756 0.997464i \(-0.522675\pi\)
0.828241 + 0.560372i \(0.189342\pi\)
\(270\) −9.51146 + 6.95767i −0.578849 + 0.423430i
\(271\) 2.00000 + 7.46410i 0.121491 + 0.453412i 0.999690 0.0248835i \(-0.00792149\pi\)
−0.878199 + 0.478295i \(0.841255\pi\)
\(272\) −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 −0.997536 0.0701536i \(-0.977651\pi\)
−0.438013 + 0.898969i \(0.644318\pi\)
\(278\) −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 0.969357 0.245655i \(-0.0790030\pi\)
−0.245655 + 0.969357i \(0.579003\pi\)
\(282\) −2.17000 + 15.5622i −0.129221 + 0.926718i
\(283\) 5.70577 + 3.29423i 0.339173 + 0.195822i 0.659906 0.751348i \(-0.270596\pi\)
−0.320733 + 0.947170i \(0.603929\pi\)
\(284\) 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 −0.978206 0.207635i \(-0.933423\pi\)
0.950969 + 0.309286i \(0.100090\pi\)
\(294\) −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 −0.904803 0.425829i \(-0.859982\pi\)
0.425829 + 0.904803i \(0.359982\pi\)
\(308\) 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 −0.312373 0.949960i \(-0.601124\pi\)
0.949960 + 0.312373i \(0.101124\pi\)
\(318\) 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 0.0850595 + 0.996376i \(0.472892\pi\)
−0.571852 + 0.820357i \(0.693775\pi\)
\(332\) 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 \(0.167734\pi\)
−0.864344 + 0.502902i \(0.832266\pi\)
\(338\) 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 −0.895095 0.445876i \(-0.852892\pi\)
−0.0614076 + 0.998113i \(0.519559\pi\)
\(348\) 3.08346 1.24967i 0.165291 0.0669895i
\(349\) 7.36603 + 27.4904i 0.394294 + 1.47153i 0.822979 + 0.568072i \(0.192311\pi\)
−0.428684 + 0.903454i \(0.641023\pi\)
\(350\) 5.81863 0.311019
\(351\) 0 0
\(352\) −6.19615 −0.330256
\(353\) 3.66088 + 13.6626i 0.194849 + 0.727186i 0.992306 + 0.123810i \(0.0395113\pi\)
−0.797457 + 0.603376i \(0.793822\pi\)
\(354\) −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 0.0368904 0.999319i \(-0.488255\pi\)
−0.999319 + 0.0368904i \(0.988255\pi\)
\(360\) 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 0.130723 + 0.991419i \(0.458270\pi\)
−0.923955 + 0.382500i \(0.875063\pi\)
\(368\) 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 0.676125 0.736787i \(-0.263658\pi\)
−0.976139 + 0.217148i \(0.930325\pi\)
\(374\) −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 0.127726 0.991809i \(-0.459232\pi\)
0.606519 + 0.795069i \(0.292565\pi\)
\(380\) 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 −0.672234 0.740339i \(-0.734665\pi\)
−0.952341 + 0.305035i \(0.901332\pi\)
\(384\) −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 −0.0907168 0.995877i \(-0.528916\pi\)
−0.576501 + 0.817096i \(0.695582\pi\)
\(398\) 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 −0.546294 0.837594i \(-0.683962\pi\)
−0.0543073 + 0.998524i \(0.517295\pi\)
\(402\) −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 −0.455480 0.890246i \(-0.650532\pi\)
0.839580 0.543236i \(-0.182801\pi\)
\(410\) −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 0.687452 0.726230i \(-0.258729\pi\)
−0.285208 + 0.958466i \(0.592063\pi\)
\(420\) −0.136505 + 0.978956i −0.00666078 + 0.0477682i
\(421\) 7.83013 + 7.83013i 0.381617 + 0.381617i 0.871685 0.490067i \(-0.163028\pi\)
−0.490067 + 0.871685i \(0.663028\pi\)
\(422\) −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 −0.633648 0.773622i \(-0.718443\pi\)
0.161944 0.986800i \(-0.448224\pi\)
\(432\) −13.6951 18.7218i −0.658905 0.900754i
\(433\) 26.8923 15.5263i 1.29236 0.746145i 0.313289 0.949658i \(-0.398569\pi\)
0.979072 + 0.203512i \(0.0652357\pi\)
\(434\) 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 0.473567 0.880758i \(-0.342966\pi\)
−0.525975 + 0.850500i \(0.676300\pi\)
\(440\) −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 \(-0.914124\pi\)
0.963827 0.266527i \(-0.0858762\pi\)
\(444\) −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 0.718851 + 0.695165i \(0.244669\pi\)
−0.970125 + 0.242605i \(0.921998\pi\)
\(450\) 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 −0.345868 0.938283i \(-0.612416\pi\)
0.169611 + 0.985511i \(0.445749\pi\)
\(458\) −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 −0.253628 0.967302i \(-0.581624\pi\)
−0.703299 + 0.710894i \(0.748290\pi\)
\(462\) −9.14708 12.1113i −0.425561 0.563471i
\(463\) −23.0526 + 23.0526i −1.07134 + 1.07134i −0.0740918 + 0.997251i \(0.523606\pi\)
−0.997251 + 0.0740918i \(0.976394\pi\)
\(464\) −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 0.225510 0.974241i \(-0.427595\pi\)
0.682418 + 0.730962i \(0.260928\pi\)
\(480\) 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 −0.923902 0.382630i \(-0.875018\pi\)
0.991437 + 0.130584i \(0.0416851\pi\)
\(488\) 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 −0.341023 0.940055i \(-0.610773\pi\)
0.984623 0.174693i \(-0.0558934\pi\)
\(492\) 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 0.760107 0.649798i \(-0.225147\pi\)
−0.649798 + 0.760107i \(0.725147\pi\)
\(500\) 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 −0.435513 0.900182i \(-0.643433\pi\)
0.561824 + 0.827257i \(0.310100\pi\)
\(504\) −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 0.997620 + 0.0689588i \(0.0219677\pi\)
−0.829484 + 0.558530i \(0.811366\pi\)
\(510\) −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 \(-0.982618\pi\)
0.998509 0.0545785i \(-0.0173815\pi\)
\(522\) −15.7633 28.2934i −0.689939 1.23837i
\(523\) 19.4904 33.7583i 0.852255 1.47615i −0.0269137 0.999638i \(-0.508568\pi\)
0.879169 0.476511i \(-0.158099\pi\)
\(524\) −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 −0.379681 0.925118i \(-0.623966\pi\)
0.925118 + 0.379681i \(0.123966\pi\)
\(542\) 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 0.306462 0.951883i \(-0.400855\pi\)
0.741346 + 0.671123i \(0.234188\pi\)
\(558\) −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 0.952456 0.304675i \(-0.0985479\pi\)
−0.740085 + 0.672514i \(0.765215\pi\)
\(564\) 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 −0.836335 0.548219i \(-0.815306\pi\)
0.892939 + 0.450178i \(0.148639\pi\)
\(570\) 5.91520 13.9773i 0.247760 0.585444i
\(571\) 1.94744i 0.0814979i −0.999169 0.0407489i \(-0.987026\pi\)
0.999169 0.0407489i \(-0.0129744\pi\)
\(572\) 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 0.998088 0.0618016i \(-0.0196846\pi\)
−0.0618016 + 0.998088i \(0.519685\pi\)
\(578\) 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 0.991094 + 0.133164i \(0.0425138\pi\)
−0.791730 + 0.610871i \(0.790819\pi\)
\(588\) −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 0.461541 0.887119i \(-0.347297\pi\)
−0.887119 + 0.461541i \(0.847297\pi\)
\(594\) −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 \(0.139178\pi\)
−0.905924 + 0.423441i \(0.860822\pi\)
\(600\) −4.81059 + 11.3671i −0.196391 + 0.464062i
\(601\) −11.7942 + 20.4282i −0.481097 + 0.833284i −0.999765 0.0216919i \(-0.993095\pi\)
0.518668 + 0.854976i \(0.326428\pi\)
\(602\) 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 0.868009 0.496549i \(-0.165400\pi\)
−0.864028 + 0.503444i \(0.832066\pi\)
\(608\) −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 −0.975870 0.218354i \(-0.929931\pi\)
−0.735951 + 0.677035i \(0.763265\pi\)
\(614\) 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 −0.118964 0.992899i \(-0.537957\pi\)
−0.599475 + 0.800393i \(0.704624\pi\)
\(618\) 14.4209 10.8914i 0.580094 0.438115i
\(619\) 31.6603 31.6603i 1.27253 1.27253i 0.327778 0.944755i \(-0.393700\pi\)
0.944755 0.327778i \(-0.106300\pi\)
\(620\) 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 0.658121 0.752912i \(-0.271352\pi\)
0.193493 + 0.981102i \(0.438018\pi\)
\(632\) −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 −0.833008 0.553261i \(-0.813383\pi\)
−0.0626345 0.998037i \(-0.519950\pi\)
\(642\) −6.09776 49.2228i −0.240659 1.94267i
\(643\) 1.87564 7.00000i 0.0739682 0.276053i −0.919029 0.394190i \(-0.871025\pi\)
0.992997 + 0.118136i \(0.0376920\pi\)
\(644\) 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 −0.657547 0.753413i \(-0.728406\pi\)
0.981249 + 0.192746i \(0.0617394\pi\)
\(648\) −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 0.327290 0.944924i \(-0.393865\pi\)
−0.654683 + 0.755904i \(0.727198\pi\)
\(654\) −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 0.0328158 0.999461i \(-0.489553\pi\)
0.881967 + 0.471311i \(0.156219\pi\)
\(660\) −1.08011 2.66509i −0.0420434 0.103738i
\(661\) 2.52628 + 9.42820i 0.0982609 + 0.366715i 0.997494 0.0707559i \(-0.0225411\pi\)
−0.899233 + 0.437470i \(0.855874\pi\)
\(662\) 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 0.996792 0.0800364i \(-0.0255036\pi\)
0.429082 + 0.903265i \(0.358837\pi\)
\(674\) 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 \(0.0594357\pi\)
−0.982618 + 0.185640i \(0.940564\pi\)
\(678\) 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 −0.195338 0.980736i \(-0.562580\pi\)
0.659536 0.751673i \(-0.270753\pi\)
\(684\) −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 0.105025 0.994470i \(-0.466508\pi\)
0.588189 + 0.808723i \(0.299841\pi\)
\(692\) 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 0.0397068 0.999211i \(-0.487358\pi\)
−0.465219 + 0.885196i \(0.654024\pi\)
\(710\) −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 0.926577 0.376106i \(-0.122737\pi\)
−0.789005 + 0.614386i \(0.789404\pi\)
\(720\) −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 \(0.117877\pi\)
−0.932211 + 0.361916i \(0.882123\pi\)
\(728\) 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 0.821108 0.570773i \(-0.193356\pi\)
−0.570773 + 0.821108i \(0.693356\pi\)
\(734\) 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 0.889182 0.457554i \(-0.151274\pi\)
−0.998831 + 0.0483378i \(0.984608\pi\)
\(740\) −2.18573 −0.0803492
\(741\) 0 0
\(742\) −1.66025 −0.0609498
\(743\) −2.28268 8.51906i −0.0837432 0.312534i 0.911330 0.411677i \(-0.135057\pi\)
−0.995073 + 0.0991426i \(0.968390\pi\)
\(744\) 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 0.927705 0.373313i \(-0.121778\pi\)
0.140554 + 0.990073i \(0.455112\pi\)
\(752\) −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 −0.977267 0.212014i \(-0.931998\pi\)
0.672243 + 0.740331i \(0.265331\pi\)
\(758\) −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 −0.824669 0.565616i \(-0.808639\pi\)
0.996992 0.0775029i \(-0.0246947\pi\)
\(762\) −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 −0.898636 0.438694i \(-0.855441\pi\)
−0.558895 + 0.829238i \(0.688775\pi\)
\(770\) −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 0.911677 0.410908i \(-0.134788\pi\)
0.584081 + 0.811695i \(0.301455\pi\)
\(774\) 9.92087 + 0.151737i 0.356598 + 0.00545407i
\(775\) −6.73205 + 6.73205i −0.241822 + 0.241822i