Properties

Label 507.2.k.e.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.e.488.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.389774 + 1.45466i) q^{2} +(0.239203 - 1.71545i) q^{3} +(-0.232051 - 0.133975i) q^{4} +(-1.06488 - 1.06488i) q^{5} +(2.40216 + 1.01660i) q^{6} +(-1.36603 + 0.366025i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +O(q^{10})\) \(q+(-0.389774 + 1.45466i) q^{2} +(0.239203 - 1.71545i) q^{3} +(-0.232051 - 0.133975i) q^{4} +(-1.06488 - 1.06488i) q^{5} +(2.40216 + 1.01660i) q^{6} +(-1.36603 + 0.366025i) q^{7} +(-1.84443 + 1.84443i) q^{8} +(-2.88556 - 0.820682i) q^{9} +(1.96410 - 1.13397i) q^{10} +(-3.97420 - 1.06488i) q^{11} +(-0.285334 + 0.366025i) q^{12} -2.12976i q^{14} +(-2.08148 + 1.57203i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-2.51954 + 4.36397i) q^{17} +(2.31853 - 3.87762i) q^{18} +(1.00000 + 3.73205i) q^{19} +(0.104440 + 0.389774i) q^{20} +(0.301143 + 2.43091i) q^{21} +(3.09808 - 5.36603i) q^{22} +(2.72284 + 3.60523i) q^{24} -2.73205i q^{25} +(-2.09808 + 4.75374i) q^{27} +(0.366025 + 0.0980762i) q^{28} +(-6.20840 + 3.58442i) q^{29} +(-1.47546 - 3.64058i) q^{30} +(-2.46410 + 2.46410i) q^{31} +(1.45466 - 0.389774i) q^{32} +(-2.77739 + 6.56283i) q^{33} +(-5.36603 - 5.36603i) q^{34} +(1.84443 + 1.06488i) q^{35} +(0.559647 + 0.577032i) q^{36} +(1.40192 - 5.23205i) q^{37} -5.81863 q^{38} +3.92820 q^{40} +(1.45466 - 5.42885i) q^{41} +(-3.65351 - 0.509445i) q^{42} +(-1.90192 - 1.09808i) q^{43} +(0.779548 + 0.779548i) q^{44} +(2.19886 + 3.94672i) q^{45} +(4.25953 - 4.25953i) q^{47} +(-7.16590 + 2.90422i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(3.97420 + 1.06488i) q^{50} +(6.88351 + 5.36603i) q^{51} -0.779548i q^{53} +(-6.09729 - 4.90487i) q^{54} +(3.09808 + 5.36603i) q^{55} +(1.84443 - 3.19465i) q^{56} +(6.64136 - 0.822738i) q^{57} +(-2.79423 - 10.4282i) q^{58} +(-0.779548 - 2.90931i) q^{59} +(0.693622 - 0.0859264i) q^{60} +(3.50000 - 6.06218i) q^{61} +(-2.62398 - 4.54486i) q^{62} +(4.24214 + 0.0648824i) 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} +(6.83591 - 3.80853i) q^{72} +(-0.901924 - 0.901924i) q^{73} +(7.06440 + 4.07863i) q^{74} +(-4.68671 - 0.653513i) q^{75} +(0.267949 - 1.00000i) q^{76} +5.81863 q^{77} +2.00000 q^{79} +(-1.73999 + 6.49373i) q^{80} +(7.65296 + 4.73626i) q^{81} +(7.33013 + 4.23205i) q^{82} +(-2.90931 - 2.90931i) q^{83} +(0.255799 - 0.604440i) q^{84} +(7.33013 - 1.96410i) q^{85} +(2.33864 - 2.33864i) q^{86} +(4.66384 + 11.5076i) q^{87} +(9.29423 - 5.36603i) q^{88} +(-9.01327 - 2.41510i) q^{89} +(-6.59817 + 1.66025i) q^{90} +(3.63763 + 4.81647i) q^{93} +(4.53590 + 7.85641i) q^{94} +(2.90931 - 5.03908i) q^{95} +(-0.320682 - 2.58863i) q^{96} +(-0.437822 - 1.63397i) q^{97} +(-1.94887 - 7.27328i) q^{98} +(10.5939 + 6.33434i) 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 \(0.904608\pi\)
\(3\) 0.239203 1.71545i 0.138104 0.990418i
\(4\) −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 \(0.859326\pi\)
\(6\) 2.40216 + 1.01660i 0.980678 + 0.415024i
\(7\) −1.36603 + 0.366025i −0.516309 + 0.138345i −0.507559 0.861617i \(-0.669452\pi\)
−0.00875026 + 0.999962i \(0.502785\pi\)
\(8\) −1.84443 + 1.84443i −0.652105 + 0.652105i
\(9\) −2.88556 0.820682i −0.961855 0.273561i
\(10\) 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
\(15\) −2.08148 + 1.57203i −0.537436 + 0.405897i
\(16\) −2.23205 3.86603i −0.558013 0.966506i
\(17\) −2.51954 + 4.36397i −0.611078 + 1.05842i 0.379981 + 0.924994i \(0.375930\pi\)
−0.991059 + 0.133424i \(0.957403\pi\)
\(18\) 2.31853 3.87762i 0.546482 0.913965i
\(19\) 1.00000 + 3.73205i 0.229416 + 0.856191i 0.980587 + 0.196084i \(0.0628225\pi\)
−0.751171 + 0.660107i \(0.770511\pi\)
\(20\) 0.104440 + 0.389774i 0.0233534 + 0.0871561i
\(21\) 0.301143 + 2.43091i 0.0657148 + 0.530468i
\(22\) 3.09808 5.36603i 0.660512 1.14404i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 2.72284 + 3.60523i 0.555798 + 0.735914i
\(25\) 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 \(-0.898495\pi\)
−0.203286 + 0.979119i \(0.565162\pi\)
\(30\) −1.47546 3.64058i −0.269381 0.664675i
\(31\) −2.46410 + 2.46410i −0.442566 + 0.442566i −0.892873 0.450308i \(-0.851314\pi\)
0.450308 + 0.892873i \(0.351314\pi\)
\(32\) 1.45466 0.389774i 0.257149 0.0689030i
\(33\) −2.77739 + 6.56283i −0.483482 + 1.14244i
\(34\) −5.36603 5.36603i −0.920266 0.920266i
\(35\) 1.84443 + 1.06488i 0.311766 + 0.179998i
\(36\) 0.559647 + 0.577032i 0.0932745 + 0.0961720i
\(37\) 1.40192 5.23205i 0.230475 0.860144i −0.749662 0.661821i \(-0.769784\pi\)
0.980137 0.198323i \(-0.0635495\pi\)
\(38\) −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 \(-0.0612901\pi\)
\(42\) −3.65351 0.509445i −0.563749 0.0786091i
\(43\) −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
\(45\) 2.19886 + 3.94672i 0.327786 + 0.588342i
\(46\) 0 0
\(47\) 4.25953 4.25953i 0.621316 0.621316i −0.324552 0.945868i \(-0.605213\pi\)
0.945868 + 0.324552i \(0.105213\pi\)
\(48\) −7.16590 + 2.90422i −1.03431 + 0.419188i
\(49\) −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 \(-0.0170503\pi\)
\(54\) −6.09729 4.90487i −0.829736 0.667468i
\(55\) 3.09808 + 5.36603i 0.417745 + 0.723555i
\(56\) 1.84443 3.19465i 0.246472 0.426903i
\(57\) 6.64136 0.822738i 0.879670 0.108974i
\(58\) −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 \(0.979482\pi\)
\(60\) 0.693622 0.0859264i 0.0895462 0.0110931i
\(61\) 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
\(63\) 4.24214 + 0.0648824i 0.534460 + 0.00817442i
\(64\) 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 \(-0.298593\pi\)
0.108925 + 0.994050i \(0.465259\pi\)
\(68\) 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 \(0.473864\pi\)
\(72\) 6.83591 3.80853i 0.805620 0.448840i
\(73\) −0.901924 0.901924i −0.105562 0.105562i 0.652353 0.757915i \(-0.273782\pi\)
−0.757915 + 0.652353i \(0.773782\pi\)
\(74\) 7.06440 + 4.07863i 0.821220 + 0.474132i
\(75\) −4.68671 0.653513i −0.541174 0.0754612i
\(76\) 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
\(81\) 7.65296 + 4.73626i 0.850329 + 0.526251i
\(82\) 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 \(0.822502\pi\)
\(84\) 0.255799 0.604440i 0.0279100 0.0659498i
\(85\) 7.33013 1.96410i 0.795064 0.213037i
\(86\) 2.33864 2.33864i 0.252182 0.252182i
\(87\) 4.66384 + 11.5076i 0.500017 + 1.23375i
\(88\) 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
\(93\) 3.63763 + 4.81647i 0.377205 + 0.499445i
\(94\) 4.53590 + 7.85641i 0.467842 + 0.810326i
\(95\) 2.90931 5.03908i 0.298489 0.516998i
\(96\) −0.320682 2.58863i −0.0327295 0.264201i
\(97\) −0.437822 1.63397i −0.0444541 0.165905i 0.940130 0.340815i \(-0.110703\pi\)
−0.984584 + 0.174910i \(0.944036\pi\)
\(98\) −1.94887 7.27328i −0.196866 0.734712i
\(99\) 10.5939 + 6.33434i 1.06472 + 0.636625i
\(100\) −0.366025 + 0.633975i −0.0366025 + 0.0633975i
\(101\) 3.01375 + 5.21997i 0.299880 + 0.519407i 0.976108 0.217285i \(-0.0697202\pi\)
−0.676229 + 0.736692i \(0.736387\pi\)
\(102\) −10.4887 + 7.92160i −1.03854 + 0.784356i
\(103\) 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 \(-0.295565\pi\)
0.992969 0.118374i \(-0.0377682\pi\)
\(108\) 1.12374 0.822021i 0.108132 0.0790990i
\(109\) −13.1962 + 13.1962i −1.26396 + 1.26396i −0.314806 + 0.949156i \(0.601940\pi\)
−0.949156 + 0.314806i \(0.898060\pi\)
\(110\) −9.01327 + 2.41510i −0.859382 + 0.230271i
\(111\) −8.64000 3.65646i −0.820072 0.347055i
\(112\) 4.46410 + 4.46410i 0.421818 + 0.421818i
\(113\) −8.90883 5.14352i −0.838073 0.483861i 0.0185360 0.999828i \(-0.494099\pi\)
−0.856609 + 0.515967i \(0.827433\pi\)
\(114\) −1.39183 + 9.98158i −0.130357 + 0.934861i
\(115\) 0 0
\(116\) 1.92089 0.178350
\(117\) 0 0
\(118\) 4.53590 0.417563
\(119\) 1.84443 6.88351i 0.169079 0.631010i
\(120\) 0.939636 6.73865i 0.0857767 0.615152i
\(121\) 5.13397 + 2.96410i 0.466725 + 0.269464i
\(122\) 7.45418 + 7.45418i 0.674869 + 0.674869i
\(123\) −8.96499 3.79399i −0.808346 0.342093i
\(124\) 0.901924 0.241670i 0.0809951 0.0217026i
\(125\) −8.23373 + 8.23373i −0.736447 + 0.736447i
\(126\) −1.74786 + 6.14557i −0.155712 + 0.547491i
\(127\) −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 \(0.112877\pi\)
−0.937781 + 0.347227i \(0.887123\pi\)
\(132\) 1.52375 1.15081i 0.132625 0.100165i
\(133\) −2.73205 4.73205i −0.236899 0.410321i
\(134\) −4.46841 + 7.73951i −0.386012 + 0.668592i
\(135\) 7.29638 2.82797i 0.627973 0.243393i
\(136\) −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
\(141\) −6.28814 8.32592i −0.529557 0.701169i
\(142\) 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
\(147\) 3.25286 + 8.02614i 0.268291 + 0.661985i
\(148\) −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 \(0.301626\pi\)
\(150\) 2.77739 6.56283i 0.226773 0.535853i
\(151\) 0.535898 + 0.535898i 0.0436108 + 0.0436108i 0.728576 0.684965i \(-0.240183\pi\)
−0.684965 + 0.728576i \(0.740183\pi\)
\(152\) −8.72794 5.03908i −0.707929 0.408723i
\(153\) 10.8517 10.5248i 0.877310 0.850878i
\(154\) −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
\(159\) −1.33728 0.186470i −0.106053 0.0147880i
\(160\) −1.96410 1.13397i −0.155276 0.0896486i
\(161\) 0 0
\(162\) −9.87256 + 9.28636i −0.775661 + 0.729605i
\(163\) 4.00000 1.07180i 0.313304 0.0839496i −0.0987406 0.995113i \(-0.531481\pi\)
0.412045 + 0.911164i \(0.364815\pi\)
\(164\) −1.06488 + 1.06488i −0.0831533 + 0.0831533i
\(165\) 9.94624 4.03104i 0.774313 0.313816i
\(166\) 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
\(171\) 0.177262 11.5898i 0.0135556 0.886291i
\(172\) 0.294229 + 0.509619i 0.0224347 + 0.0388581i
\(173\) 8.72794 15.1172i 0.663573 1.14934i −0.316097 0.948727i \(-0.602373\pi\)
0.979670 0.200615i \(-0.0642941\pi\)
\(174\) −18.5575 + 2.29892i −1.40684 + 0.174281i
\(175\) 1.00000 + 3.73205i 0.0755929 + 0.282117i
\(176\) 4.75374 + 17.7412i 0.358327 + 1.33729i
\(177\) −5.17726 + 0.641364i −0.389147 + 0.0482078i
\(178\) 7.02628 12.1699i 0.526642 0.912171i
\(179\) 13.2728 + 22.9892i 0.992056 + 1.71829i 0.604972 + 0.796247i \(0.293184\pi\)
0.387084 + 0.922045i \(0.373482\pi\)
\(180\) 0.0185132 1.21043i 0.00137989 0.0902201i
\(181\) 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
\(186\) −8.42417 + 3.41417i −0.617690 + 0.250339i
\(187\) 14.6603 14.6603i 1.07206 1.07206i
\(188\) −1.55910 + 0.417759i −0.113709 + 0.0304682i
\(189\) 1.12603 7.26168i 0.0819070 0.528210i
\(190\) 6.19615 + 6.19615i 0.449516 + 0.449516i
\(191\) 4.18307 + 2.41510i 0.302677 + 0.174750i 0.643645 0.765324i \(-0.277421\pi\)
−0.340968 + 0.940075i \(0.610755\pi\)
\(192\) −11.4254 1.59315i −0.824554 0.114976i
\(193\) −0.0358984 + 0.133975i −0.00258402 + 0.00964370i −0.967206 0.253994i \(-0.918256\pi\)
0.964622 + 0.263638i \(0.0849223\pi\)
\(194\) 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 \(0.130156\pi\)
\(198\) −13.3435 + 12.9415i −0.948281 + 0.919711i
\(199\) −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
\(201\) 4.00588 9.46568i 0.282553 0.667657i
\(202\) −8.76795 + 2.34936i −0.616911 + 0.165301i
\(203\) 7.16884 7.16884i 0.503154 0.503154i
\(204\) −0.878413 2.16741i −0.0615012 0.151749i
\(205\) −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
\(210\) 3.34806 + 4.43306i 0.231038 + 0.305910i
\(211\) 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
\(213\) 0.641364 + 5.17726i 0.0439455 + 0.354740i
\(214\) 7.41154 + 27.6603i 0.506643 + 1.89082i
\(215\) 0.856003 + 3.19465i 0.0583789 + 0.217873i
\(216\) −4.89819 12.6377i −0.333280 0.859887i
\(217\) 2.46410 4.26795i 0.167274 0.289727i
\(218\) −14.0524 24.3394i −0.951745 1.64847i
\(219\) −1.76295 + 1.33147i −0.119129 + 0.0899722i
\(220\) 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 \(-0.750942\pi\)
−0.966687 + 0.255960i \(0.917609\pi\)
\(224\) −1.84443 + 1.06488i −0.123236 + 0.0711505i
\(225\) −2.24214 + 7.88351i −0.149476 + 0.525567i
\(226\) 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 \(0.181715\pi\)
\(228\) −1.65136 0.698857i −0.109364 0.0462829i
\(229\) −14.1244 14.1244i −0.933364 0.933364i 0.0645507 0.997914i \(-0.479439\pi\)
−0.997914 + 0.0645507i \(0.979439\pi\)
\(230\) 0 0
\(231\) 1.39183 9.98158i 0.0915757 0.656740i
\(232\) 4.83975 18.0622i 0.317745 1.18584i
\(233\) −17.4559 −1.14357 −0.571786 0.820403i \(-0.693749\pi\)
−0.571786 + 0.820403i \(0.693749\pi\)
\(234\) 0 0
\(235\) −9.07180 −0.591779
\(236\) −0.208879 + 0.779548i −0.0135969 + 0.0507443i
\(237\) 0.478405 3.43091i 0.0310757 0.222861i
\(238\) 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 \(0.847585\pi\)
\(240\) 10.7235 + 4.53819i 0.692198 + 0.292939i
\(241\) −14.0622 + 3.76795i −0.905825 + 0.242715i −0.681516 0.731803i \(-0.738679\pi\)
−0.224309 + 0.974518i \(0.572012\pi\)
\(242\) −6.31284 + 6.31284i −0.405805 + 0.405805i
\(243\) 9.95544 11.9954i 0.638642 0.769504i
\(244\) −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
\(249\) −5.68671 + 4.29488i −0.360380 + 0.272177i
\(250\) −8.76795 15.1865i −0.554534 0.960481i
\(251\) −0.494214 + 0.856003i −0.0311945 + 0.0540304i −0.881201 0.472741i \(-0.843264\pi\)
0.850007 + 0.526772i \(0.176598\pi\)
\(252\) −0.975700 0.583396i −0.0614634 0.0367505i
\(253\) 0 0
\(254\) −3.55644 13.2728i −0.223151 0.832810i
\(255\) −1.61594 13.0443i −0.101194 0.816867i
\(256\) −3.16025 + 5.47372i −0.197516 + 0.342108i
\(257\) −10.7533 18.6252i −0.670770 1.16181i −0.977686 0.210071i \(-0.932630\pi\)
0.306916 0.951737i \(-0.400703\pi\)
\(258\) −3.45243 4.57125i −0.214939 0.284593i
\(259\) 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 \(-0.907787\pi\)
−0.231777 + 0.972769i \(0.574454\pi\)
\(264\) −6.98197 17.2274i −0.429710 1.06027i
\(265\) −0.830127 + 0.830127i −0.0509943 + 0.0509943i
\(266\) 7.94839 2.12976i 0.487347 0.130584i
\(267\) −6.29899 + 14.8842i −0.385492 + 0.910896i
\(268\) −1.12436 1.12436i −0.0686810 0.0686810i
\(269\) −12.4168 7.16884i −0.757066 0.437092i 0.0711756 0.997464i \(-0.477325\pi\)
−0.828241 + 0.560372i \(0.810658\pi\)
\(270\) 1.26979 + 11.7160i 0.0772769 + 0.713013i
\(271\) −2.00000 + 7.46410i −0.121491 + 0.453412i −0.999690 0.0248835i \(-0.992079\pi\)
0.878199 + 0.478295i \(0.158745\pi\)
\(272\) 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
\(279\) 9.13257 5.08808i 0.546752 0.304615i
\(280\) −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 \(0.0790030\pi\)
\(282\) 14.5623 5.90185i 0.867172 0.351450i
\(283\) 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
\(288\) −4.51739 0.0690922i −0.266189 0.00407129i
\(289\) −4.19615 7.26795i −0.246832 0.427526i
\(290\) −8.12929 + 14.0803i −0.477368 + 0.826826i
\(291\) −2.90774 + 0.360213i −0.170455 + 0.0211161i
\(292\) 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 \(0.933423\pi\)
\(294\) −12.9432 + 1.60341i −0.754860 + 0.0935127i
\(295\) −2.26795 + 3.92820i −0.132045 + 0.228709i
\(296\) 7.06440 + 12.2359i 0.410610 + 0.711198i
\(297\) 13.4003 16.6581i 0.777567 0.966601i
\(298\) 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
\(303\) 9.67552 3.92132i 0.555844 0.225274i
\(304\) 12.1962 12.1962i 0.699497 0.699497i
\(305\) −10.1826 + 2.72842i −0.583054 + 0.156229i
\(306\) 11.0802 + 19.8878i 0.633414 + 1.13691i
\(307\) 8.39230 + 8.39230i 0.478974 + 0.478974i 0.904803 0.425829i \(-0.140018\pi\)
−0.425829 + 0.904803i \(0.640018\pi\)
\(308\) −1.35022 0.779548i −0.0769357 0.0444189i
\(309\) 11.8850 + 1.65724i 0.676115 + 0.0942773i
\(310\) −2.04552 + 7.63397i −0.116178 + 0.433581i
\(311\) −10.0782 −0.571480 −0.285740 0.958307i \(-0.592239\pi\)
−0.285740 + 0.958307i \(0.592239\pi\)
\(312\) 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
\(315\) −4.44829 4.58648i −0.250633 0.258419i
\(316\) −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 \(0.601124\pi\)
\(318\) 0.792486 1.87260i 0.0444404 0.105010i
\(319\) 28.4904 7.63397i 1.59516 0.427421i
\(320\) −7.09239 + 7.09239i −0.396477 + 0.396477i
\(321\) −12.3706 30.5234i −0.690460 1.70365i
\(322\) 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
\(327\) 19.4808 + 25.7939i 1.07729 + 1.42641i
\(328\) 7.33013 + 12.6962i 0.404739 + 0.701028i
\(329\) −4.25953 + 7.37772i −0.234835 + 0.406747i
\(330\) 1.98699 + 16.0396i 0.109380 + 0.882948i
\(331\) 8.85641 + 33.0526i 0.486792 + 1.81673i 0.571852 + 0.820357i \(0.306225\pi\)
−0.0850595 + 0.996376i \(0.527108\pi\)
\(332\) 0.285334 + 1.06488i 0.0156598 + 0.0584430i
\(333\) −8.33919 + 13.9469i −0.456985 + 0.764285i
\(334\) −10.1244 + 17.5359i −0.553980 + 0.959522i
\(335\) −4.46841 7.73951i −0.244135 0.422855i
\(336\) 8.72579 6.59014i 0.476031 0.359521i
\(337\) 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
\(342\) 16.7900 + 4.77524i 0.907900 + 0.258215i
\(343\) 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 \(-0.147108\pi\)
0.0614076 + 0.998113i \(0.480441\pi\)
\(348\) 0.459481 3.29519i 0.0246308 0.176641i
\(349\) −7.36603 + 27.4904i −0.394294 + 1.47153i 0.428684 + 0.903454i \(0.358977\pi\)
−0.822979 + 0.568072i \(0.807689\pi\)
\(350\) −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 \(-0.0395113\pi\)
\(354\) 1.08500 7.78112i 0.0576670 0.413562i
\(355\) 3.92820 + 2.26795i 0.208487 + 0.120370i
\(356\) 1.76798 + 1.76798i 0.0937025 + 0.0937025i
\(357\) −11.3671 4.81059i −0.601613 0.254603i
\(358\) −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 \(0.488255\pi\)
\(360\) −11.3351 3.22381i −0.597411 0.169909i
\(361\) 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
\(366\) 14.5704 11.0042i 0.761605 0.575201i
\(367\) −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
\(369\) −8.65286 + 14.4715i −0.450450 + 0.753356i
\(370\) −3.17949 11.8660i −0.165294 0.616885i
\(371\) 0.285334 + 1.06488i 0.0148138 + 0.0552859i
\(372\) −0.198831 1.60502i −0.0103089 0.0832162i
\(373\) −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
\(375\) 12.1550 + 16.0941i 0.627684 + 0.831096i
\(376\) 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 \(-0.540768\pi\)
−0.606519 + 0.795069i \(0.707435\pi\)
\(380\) −1.35022 + 0.779548i −0.0692647 + 0.0399900i
\(381\) 5.93605 + 14.6467i 0.304113 + 0.750372i
\(382\) −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 \(0.734665\pi\)
\(384\) 8.80399 20.8033i 0.449277 1.06162i
\(385\) −6.19615 6.19615i −0.315785 0.315785i
\(386\) −0.180895 0.104440i −0.00920730 0.00531584i
\(387\) 4.58695 + 4.72944i 0.233168 + 0.240411i
\(388\) −0.117314 + 0.437822i −0.00595572 + 0.0222271i
\(389\) −22.4950 −1.14054 −0.570270 0.821457i \(-0.693161\pi\)
−0.570270 + 0.821457i \(0.693161\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.37554 12.5977i 0.170491 0.636280i
\(393\) 13.6351 + 1.90128i 0.687800 + 0.0959066i
\(394\) −5.36603 3.09808i −0.270336 0.156079i
\(395\) −2.12976 2.12976i −0.107160 0.107160i
\(396\) −1.60968 2.88920i −0.0808892 0.145188i
\(397\) 13.2942 3.56218i 0.667218 0.178781i 0.0907168 0.995877i \(-0.471084\pi\)
0.576501 + 0.817096i \(0.304418\pi\)
\(398\) 13.7670 13.7670i 0.690078 0.690078i
\(399\) −8.77113 + 3.55479i −0.439106 + 0.177962i
\(400\) −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
\(405\) −3.10594 13.1931i −0.154336 0.655569i
\(406\) 7.63397 + 13.2224i 0.378868 + 0.656218i
\(407\) −11.1430 + 19.3003i −0.552340 + 0.956681i
\(408\) −22.5934 + 2.79889i −1.11854 + 0.138566i
\(409\) −7.76795 28.9904i −0.384100 1.43348i −0.839580 0.543236i \(-0.817199\pi\)
0.455480 0.890246i \(-0.349468\pi\)
\(410\) −3.29909 12.3124i −0.162930 0.608064i
\(411\) 11.5559 1.43156i 0.570011 0.0706135i
\(412\) 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 \(-0.741271\pi\)
0.285208 + 0.958466i \(0.407937\pi\)
\(420\) −0.916053 + 0.371261i −0.0446988 + 0.0181157i
\(421\) −7.83013 + 7.83013i −0.381617 + 0.381617i −0.871685 0.490067i \(-0.836972\pi\)
0.490067 + 0.871685i \(0.336972\pi\)
\(422\) −2.62398 + 0.703093i −0.127733 + 0.0342260i
\(423\) −15.7869 + 8.79543i −0.767584 + 0.427648i
\(424\) 1.43782 + 1.43782i 0.0698268 + 0.0698268i
\(425\) 11.9226 + 6.88351i 0.578330 + 0.333899i
\(426\) −7.78112 1.08500i −0.376997 0.0525683i
\(427\) −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 \(0.718443\pi\)
\(432\) 23.0611 2.49938i 1.10953 0.120252i
\(433\) 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
\(435\) 7.28782 17.2207i 0.349424 0.825670i
\(436\) 4.83013 1.29423i 0.231321 0.0619823i
\(437\) 0 0
\(438\) −1.24967 3.08346i −0.0597117 0.147333i
\(439\) −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 \(-0.914124\pi\)
0.963827 0.266527i \(-0.0858762\pi\)
\(444\) 1.51505 + 2.00602i 0.0719009 + 0.0952017i
\(445\) 7.02628 + 12.1699i 0.333078 + 0.576907i
\(446\) 19.5092 33.7909i 0.923787 1.60005i
\(447\) −1.83816 14.8382i −0.0869422 0.701821i
\(448\) 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 \(-0.244669\pi\)
\(450\) −10.5939 6.33434i −0.499400 0.298603i
\(451\) −11.5622 + 20.0263i −0.544442 + 0.943001i
\(452\) 1.37820 + 2.38711i 0.0648251 + 0.112280i
\(453\) 1.04750 0.791121i 0.0492157 0.0371701i
\(454\) 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 \(-0.387584\pi\)
−0.169611 + 0.985511i \(0.554251\pi\)
\(458\) 26.0514 15.0408i 1.21730 0.702809i
\(459\) −15.4590 21.1332i −0.721565 0.986412i
\(460\) 0 0
\(461\) −20.5461 + 5.50531i −0.956927 + 0.256408i −0.703299 0.710894i \(-0.748290\pi\)
−0.253628 + 0.967302i \(0.581624\pi\)
\(462\) 13.9773 + 5.91520i 0.650282 + 0.275200i
\(463\) 23.0526 + 23.0526i 1.07134 + 1.07134i 0.997251 + 0.0740918i \(0.0236058\pi\)
0.0740918 + 0.997251i \(0.476394\pi\)
\(464\) 27.7149 + 16.0012i 1.28663 + 0.742838i
\(465\) 1.25532 9.00263i 0.0582143 0.417487i
\(466\) 6.80385 25.3923i 0.315182 1.17628i
\(467\) 19.1679 0.886984 0.443492 0.896278i \(-0.353739\pi\)
0.443492 + 0.896278i \(0.353739\pi\)
\(468\) 0 0
\(469\) −8.39230 −0.387521
\(470\) 3.53595 13.1963i 0.163101 0.608702i
\(471\) −1.14909 + 8.24078i −0.0529474 + 0.379715i
\(472\) 6.80385 + 3.92820i 0.313172 + 0.180810i
\(473\) 6.38929 + 6.38929i 0.293780 + 0.293780i
\(474\) 4.80432 + 2.03319i 0.220670 + 0.0933877i
\(475\) 10.1962 2.73205i 0.467832 0.125355i
\(476\) −1.35022 + 1.35022i −0.0618871 + 0.0618871i
\(477\) −0.639761 + 2.24944i −0.0292926 + 0.102995i
\(478\) 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
\(486\) 13.5688 + 19.1572i 0.615492 + 0.868990i
\(487\) −1.49038 5.56218i −0.0675356 0.252046i 0.923902 0.382630i \(-0.124982\pi\)
−0.991437 + 0.130584i \(0.958315\pi\)
\(488\) 4.72576 + 17.6368i 0.213925 + 0.798379i
\(489\) −0.881808 7.11819i −0.0398767 0.321896i
\(490\) −5.66987 + 9.82051i −0.256139 + 0.443645i
\(491\) −14.2612 24.7012i −0.643600 1.11475i −0.984623 0.174693i \(-0.944107\pi\)
0.341023 0.940055i \(-0.389227\pi\)
\(492\) 1.57203 + 2.08148i 0.0708728 + 0.0938403i
\(493\) 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
\(498\) −4.03104 9.94624i −0.180635 0.445702i
\(499\) −2.46410 + 2.46410i −0.110308 + 0.110308i −0.760107 0.649798i \(-0.774853\pi\)
0.649798 + 0.760107i \(0.274853\pi\)
\(500\) 3.01375 0.807533i 0.134779 0.0361140i
\(501\) 9.07638 21.4470i 0.405503 0.958181i
\(502\) −1.05256 1.05256i −0.0469780 0.0469780i
\(503\) −2.83286 1.63555i −0.126311 0.0729256i 0.435513 0.900182i \(-0.356567\pi\)
−0.561824 + 0.827257i \(0.689900\pi\)
\(504\) −7.94401 + 7.70467i −0.353854 + 0.343193i
\(505\) 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 \(-0.0219677\pi\)
\(510\) 19.6048 + 2.73370i 0.868117 + 0.121050i
\(511\) 1.56218 + 0.901924i 0.0691067 + 0.0398988i
\(512\) 11.7137 + 11.7137i 0.517678 + 0.517678i
\(513\) −19.8393 3.07638i −0.875926 0.135826i
\(514\) 31.2846 8.38269i 1.37990 0.369744i
\(515\) 7.37772 7.37772i 0.325101 0.325101i
\(516\) 0.944608 0.382834i 0.0415841 0.0168533i
\(517\) −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 \(-0.0173815\pi\)
\(522\) −0.495311 + 32.3844i −0.0216792 + 1.41743i
\(523\) 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
\(525\) 6.64136 0.822738i 0.289853 0.0359072i
\(526\) −8.68653 32.4186i −0.378751 1.41352i
\(527\) −4.54486 16.9617i −0.197977 0.738862i
\(528\) 31.5713 3.91108i 1.37397 0.170208i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −0.883988 1.53111i −0.0383980 0.0665072i
\(531\) −0.138184 + 9.03477i −0.00599669 + 0.392076i
\(532\) 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
\(537\) 42.6117 17.2698i 1.83883 0.745247i
\(538\) 15.2679 15.2679i 0.658248 0.658248i
\(539\) 19.8710 5.32441i 0.855904 0.229339i
\(540\) −2.07201 0.321296i −0.0891650 0.0138264i
\(541\) −12.6865 12.6865i −0.545437 0.545437i 0.379681 0.925118i \(-0.376034\pi\)
−0.925118 + 0.379681i \(0.876034\pi\)
\(542\) −10.0782 5.81863i −0.432894 0.249931i
\(543\) 5.14636 + 0.717608i 0.220852 + 0.0307955i
\(544\) −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
\(549\) −15.0746 + 14.6204i −0.643368 + 0.623984i
\(550\) −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
\(555\) 5.30689 + 13.0943i 0.225265 + 0.555821i
\(556\) 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
\(561\) −21.6422 28.6558i −0.913735 1.20985i
\(562\) 12.9186 + 22.3756i 0.544938 + 0.943860i
\(563\) −5.03908 + 8.72794i −0.212372 + 0.367839i −0.952456 0.304675i \(-0.901452\pi\)
0.740085 + 0.672514i \(0.234785\pi\)
\(564\) 0.343706 + 2.77449i 0.0144726 + 0.116827i
\(565\) 4.00962 + 14.9641i 0.168686 + 0.629544i
\(566\) 2.56801 + 9.58394i 0.107941 + 0.402843i
\(567\) −12.1877 3.66867i −0.511837 0.154070i
\(568\) 3.92820 6.80385i 0.164824 0.285483i
\(569\) −1.35022 2.33864i −0.0566040 0.0980411i 0.836335 0.548219i \(-0.184694\pi\)
−0.892939 + 0.450178i \(0.851361\pi\)
\(570\) 12.1113 9.14708i 0.507289 0.383129i
\(571\) 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
\(576\) −5.46595 + 19.2186i −0.227748 + 0.800775i
\(577\) −22.4904 + 22.4904i −0.936287 + 0.936287i −0.998088 0.0618016i \(-0.980315\pi\)
0.0618016 + 0.998088i \(0.480315\pi\)
\(578\) 12.2079 3.27110i 0.507783 0.136060i
\(579\) 0.221240 + 0.0936291i 0.00919443 + 0.00389109i
\(580\) −2.04552 2.04552i −0.0849355 0.0849355i
\(581\) 5.03908 + 2.90931i 0.209056 + 0.120699i
\(582\) 0.609374 4.37016i 0.0252594 0.181149i
\(583\) −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 \(-0.0425138\pi\)
\(588\) 0.320471 2.29827i 0.0132160 0.0947792i
\(589\) −11.6603 6.73205i −0.480452 0.277389i
\(590\) −4.83020 4.83020i −0.198856 0.198856i
\(591\) 6.56283 + 2.77739i 0.269959 + 0.114247i
\(592\) −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 \(0.347297\pi\)
\(594\) 19.0087 + 25.9858i 0.779937 + 1.06621i
\(595\) −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 \(0.860822\pi\)
\(600\) 9.84967 7.43895i 0.402111 0.303694i
\(601\) −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
\(603\) −15.2797 9.13612i −0.622238 0.372052i
\(604\) −0.0525589 0.196152i −0.00213859 0.00798133i
\(605\) −2.31066 8.62350i −0.0939417 0.350595i
\(606\) 1.93291 + 15.6030i 0.0785192 + 0.633828i
\(607\) 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
\(609\) −10.5830 14.0126i −0.428845 0.567820i
\(610\) 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 \(-0.0700687\pi\)
0.735951 + 0.677035i \(0.236735\pi\)
\(614\) −15.4790 + 8.93682i −0.624683 + 0.360661i
\(615\) 5.50650 + 13.5868i 0.222044 + 0.547873i
\(616\) −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 \(0.537957\pi\)
\(618\) −7.04319 + 16.6427i −0.283319 + 0.669466i
\(619\) −31.6603 31.6603i −1.27253 1.27253i −0.944755 0.327778i \(-0.893700\pi\)
−0.327778 0.944755i \(-0.606300\pi\)
\(620\) −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
\(627\) −27.2702 3.80255i −1.08907 0.151859i
\(628\) 1.11474 + 0.643594i 0.0444828 + 0.0256822i
\(629\) 19.3003 + 19.3003i 0.769554 + 0.769554i
\(630\) 8.40558 4.68305i 0.334886 0.186577i
\(631\) −21.3923 + 5.73205i −0.851614 + 0.228189i −0.658121 0.752912i \(-0.728648\pi\)
−0.193493 + 0.981102i \(0.561982\pi\)
\(632\) −3.68886 + 3.68886i −0.146735 + 0.146735i
\(633\) 2.89559 1.17353i 0.115089 0.0466437i
\(634\) −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
\(639\) 9.03477 + 0.138184i 0.357410 + 0.00546649i
\(640\) −9.82051 17.0096i −0.388190 0.672364i
\(641\) 22.6758 39.2757i 0.895642 1.55130i 0.0626345 0.998037i \(-0.480050\pi\)
0.833008 0.553261i \(-0.186617\pi\)
\(642\) 49.2228 6.09776i 1.94267 0.240659i
\(643\) −1.87564 7.00000i −0.0739682 0.276053i 0.919029 0.394190i \(-0.128975\pi\)
−0.992997 + 0.118136i \(0.962308\pi\)
\(644\) 0 0
\(645\) 5.68503 0.704266i 0.223848 0.0277305i
\(646\) 14.6603 25.3923i 0.576800 0.999047i
\(647\) −8.23373 14.2612i −0.323701 0.560667i 0.657547 0.753413i \(-0.271594\pi\)
−0.981249 + 0.192746i \(0.938261\pi\)
\(648\) −22.8511 + 5.37965i −0.897674 + 0.211333i
\(649\) 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 \(-0.606135\pi\)
0.654683 + 0.755904i \(0.272802\pi\)
\(654\) −45.1145 + 18.2841i −1.76411 + 0.714966i
\(655\) 8.46410 8.46410i 0.330720 0.330720i
\(656\) −24.2349 + 6.49373i −0.946216 + 0.253538i
\(657\) 1.86237 + 3.34275i 0.0726578 + 0.130413i
\(658\) −9.07180 9.07180i −0.353655 0.353655i
\(659\) −23.4834 13.5581i −0.914783 0.528150i −0.0328158 0.999461i \(-0.510447\pi\)
−0.881967 + 0.471311i \(0.843781\pi\)
\(660\) −2.84809 0.397137i −0.110862 0.0154585i
\(661\) −2.52628 + 9.42820i −0.0982609 + 0.366715i −0.997494 0.0707559i \(-0.977459\pi\)
0.899233 + 0.437470i \(0.144126\pi\)
\(662\) −51.5321 −2.00285
\(663\) 0 0
\(664\) 10.7321 0.416484
\(665\) −2.12976 + 7.94839i −0.0825887 + 0.308225i
\(666\) −17.0375 17.5668i −0.660191 0.680699i
\(667\) 0 0
\(668\) −2.54752 2.54752i −0.0985666 0.0985666i
\(669\) −17.4898 + 41.3274i −0.676194 + 1.59781i
\(670\) 13.0000 3.48334i 0.502234 0.134573i
\(671\) −20.3652 + 20.3652i −0.786189 + 0.786189i
\(672\) 1.38556 + 3.41876i 0.0534493 + 0.131881i
\(673\) 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 \(0.0594357\pi\)
−0.982618 + 0.185640i \(0.940564\pi\)
\(678\) −16.1716 21.4123i −0.621065 0.822333i
\(679\) 1.19615 + 2.07180i 0.0459041 + 0.0795083i
\(680\) −9.89726 + 17.1426i −0.379543 + 0.657387i
\(681\) −4.31769 34.8536i −0.165454 1.33559i
\(682\) 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 \(0.562580\pi\)
\(684\) −1.59387 + 2.66566i −0.0609430 + 0.101924i
\(685\) 5.06218 8.76795i 0.193416 0.335006i
\(686\) 12.7786 + 22.1332i 0.487889 + 0.845048i
\(687\) −27.6083 + 20.8511i −1.05332 + 0.795519i
\(688\) 9.80385i 0.373768i
\(689\) 0 0
\(690\) 0 0
\(691\) −18.2224 4.88269i −0.693214 0.185746i −0.105025 0.994470i \(-0.533492\pi\)
−0.588189 + 0.808723i \(0.700159\pi\)
\(692\) −4.05065 + 2.33864i −0.153983 + 0.0889019i
\(693\) −16.7900 4.77524i −0.637800 0.181396i
\(694\) −21.9090 + 21.9090i −0.831653 + 0.831653i
\(695\) 26.7545 7.16884i 1.01486 0.271930i
\(696\) −29.8272 12.6229i −1.13060 0.478469i
\(697\) 20.0263 + 20.0263i 0.758549 + 0.758549i
\(698\) −37.1180 21.4301i −1.40494 0.811140i
\(699\) −4.17549 + 29.9448i −0.157932 + 1.13261i
\(700\) 0.267949 1.00000i 0.0101275 0.0377964i
\(701\) −12.7786 −0.482641 −0.241320 0.970446i \(-0.577580\pi\)
−0.241320 + 0.970446i \(0.577580\pi\)
\(702\) 0 0
\(703\) 20.9282 0.789322
\(704\) −7.09239 + 26.4692i −0.267304 + 0.997594i
\(705\) −2.17000 + 15.5622i −0.0817268 + 0.586108i
\(706\) 18.4474 + 10.6506i 0.694279 + 0.400842i
\(707\) −6.02751 6.02751i −0.226688 0.226688i
\(708\) 1.28731 + 0.544793i 0.0483802 + 0.0204746i
\(709\) 11.3301 3.03590i 0.425512 0.114016i −0.0397068 0.999211i \(-0.512642\pi\)
0.465219 + 0.885196i \(0.345976\pi\)
\(710\) −4.83020 + 4.83020i −0.181274 + 0.181274i
\(711\) −5.77113 1.64136i −0.216434 0.0615559i
\(712\) 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
\(717\) −12.8972 + 9.74056i −0.481653 + 0.363768i
\(718\) −19.4186 33.6340i −0.724695 1.25521i
\(719\) −3.68886 + 6.38929i −0.137571 + 0.238280i −0.926577 0.376106i \(-0.877263\pi\)
0.789005 + 0.614386i \(0.210596\pi\)
\(720\) 10.3501 17.3101i 0.385727 0.645110i
\(721\) −2.53590 9.46410i −0.0944418 0.352462i
\(722\) 1.58708 + 5.92307i 0.0590650 + 0.220434i
\(723\) 3.10003 + 25.0243i 0.115292 + 0.930665i
\(724\) 0.401924 0.696152i 0.0149374 0.0258723i
\(725\) 9.79282 + 16.9617i 0.363696 + 0.629940i
\(726\) 9.31934 + 12.3394i 0.345873 + 0.457959i
\(727\) 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
\(732\) 1.22024 + 3.01084i 0.0451014 + 0.111284i
\(733\) −6.77757 + 6.77757i −0.250335 + 0.250335i −0.821108 0.570773i \(-0.806644\pi\)
0.570773 + 0.821108i \(0.306644\pi\)
\(734\) 44.2104 11.8461i 1.63183 0.437249i
\(735\) 5.08298 12.0108i 0.187489 0.443025i
\(736\) 0 0
\(737\) −21.1447 12.2079i −0.778876 0.449685i
\(738\) −17.6784 18.2276i −0.650750 0.670966i
\(739\) 2.98076 11.1244i 0.109649 0.409216i −0.889182 0.457554i \(-0.848726\pi\)
0.998831 + 0.0483378i \(0.0153924\pi\)
\(740\) 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 \(0.135057\pi\)
\(744\) −15.5930 2.17429i −0.571667 0.0797132i
\(745\) −11.2583 6.50000i −0.412473 0.238142i
\(746\) −12.3403 12.3403i −0.451812 0.451812i
\(747\) 6.00739 + 10.7826i 0.219799 + 0.394516i
\(748\) −5.36603 + 1.43782i −0.196201 + 0.0525720i
\(749\) −19.0150 + 19.0150i −0.694792 + 0.694792i
\(750\) −28.1491 + 11.4084i −1.02786 + 0.416574i
\(751\) 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
\(756\) −1.23418 + 1.53422i −0.0448866 + 0.0557990i
\(757\) −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 \(0.808639\pi\)
\(762\) −23.6196 + 2.92602i −0.855647 + 0.105998i
\(763\) 13.1962 22.8564i 0.477733 0.827457i
\(764\) −0.647124 1.12085i −0.0234121 0.0405510i
\(765\) −22.7635 0.348161i −0.823014 0.0125878i
\(766\) 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 \(-0.144559\pi\)
0.558895 + 0.829238i \(0.311225\pi\)
\(770\) 11.4284 6.59817i 0.411850 0.237782i
\(771\) −34.5229 + 13.9915i −1.24331 + 0.503893i
\(772\) 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 \(0.134788\pi\)
\(774\) −8.66759 + 4.82903i −0.311550 + 0.173576i
\(775\) 6.73205 + 6.73205i