Properties

Label 507.2.k.e.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.e.80.1

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

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

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 \(-0.262059\pi\)
\(3\) 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 −0.903924 0.427694i \(-0.859326\pi\)
0.427694 + 0.903924i \(0.359326\pi\)
\(6\) 2.40216 1.01660i 0.980678 0.415024i
\(7\) −1.36603 0.366025i −0.516309 0.138345i −0.00875026 0.999962i \(-0.502785\pi\)
−0.507559 + 0.861617i \(0.669452\pi\)
\(8\) −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 −0.802148 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
\(15\) −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 −0.991059 0.133424i \(-0.957403\pi\)
0.379981 0.924994i \(-0.375930\pi\)
\(18\) 2.31853 + 3.87762i 0.546482 + 0.913965i
\(19\) 1.00000 3.73205i 0.229416 0.856191i −0.751171 0.660107i \(-0.770511\pi\)
0.980587 0.196084i \(-0.0628225\pi\)
\(20\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 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 −0.203286 0.979119i \(-0.565162\pi\)
−0.949585 + 0.313509i \(0.898495\pi\)
\(30\) −1.47546 + 3.64058i −0.269381 + 0.664675i
\(31\) −2.46410 2.46410i −0.442566 0.442566i 0.450308 0.892873i \(-0.351314\pi\)
−0.892873 + 0.450308i \(0.851314\pi\)
\(32\) 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 0.980137 + 0.198323i \(0.0635495\pi\)
−0.749662 + 0.661821i \(0.769784\pi\)
\(38\) −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 \(0.772043\pi\)
\(42\) −3.65351 + 0.509445i −0.563749 + 0.0786091i
\(43\) −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
\(45\) 2.19886 3.94672i 0.327786 0.588342i
\(46\) 0 0
\(47\) 4.25953 + 4.25953i 0.621316 + 0.621316i 0.945868 0.324552i \(-0.105213\pi\)
−0.324552 + 0.945868i \(0.605213\pi\)
\(48\) −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 \(0.0170503\pi\)
−0.998566 + 0.0535396i \(0.982950\pi\)
\(54\) −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 −0.997923 0.0644157i \(-0.979482\pi\)
0.896435 + 0.443176i \(0.146148\pi\)
\(60\) 0.693622 + 0.0859264i 0.0895462 + 0.0110931i
\(61\) 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
\(63\) 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 0.108925 0.994050i \(-0.465259\pi\)
0.591357 + 0.806410i \(0.298593\pi\)
\(68\) 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 \(0.640531\pi\)
\(72\) 6.83591 + 3.80853i 0.805620 + 0.448840i
\(73\) −0.901924 + 0.901924i −0.105562 + 0.105562i −0.757915 0.652353i \(-0.773782\pi\)
0.652353 + 0.757915i \(0.273782\pi\)
\(74\) 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 −0.848513 0.529174i \(-0.822502\pi\)
0.529174 + 0.848513i \(0.322502\pi\)
\(84\) 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 −0.702654 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
\(93\) 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 −0.984584 0.174910i \(-0.944036\pi\)
0.940130 + 0.340815i \(0.110703\pi\)
\(98\) −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 −0.676229 0.736692i \(-0.736387\pi\)
0.976108 + 0.217285i \(0.0697202\pi\)
\(102\) −10.4887 7.92160i −1.03854 0.784356i
\(103\) 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 \(0.0377682\pi\)
0.598999 + 0.800749i \(0.295565\pi\)
\(108\) 1.12374 + 0.822021i 0.108132 + 0.0790990i
\(109\) −13.1962 13.1962i −1.26396 1.26396i −0.949156 0.314806i \(-0.898060\pi\)
−0.314806 0.949156i \(-0.601940\pi\)
\(110\) −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 −0.856609 0.515967i \(-0.827433\pi\)
0.0185360 + 0.999828i \(0.494099\pi\)
\(114\) −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 0.106605 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 \(-0.887123\pi\)
0.937781 0.347227i \(-0.112877\pi\)
\(132\) 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 −0.850908 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
\(141\) −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 0.583644 0.812010i \(-0.301626\pi\)
0.0994454 + 0.995043i \(0.468293\pi\)
\(150\) 2.77739 + 6.56283i 0.226773 + 0.535853i
\(151\) 0.535898 0.535898i 0.0436108 0.0436108i −0.684965 0.728576i \(-0.740183\pi\)
0.728576 + 0.684965i \(0.240183\pi\)
\(152\) −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 0.412045 0.911164i \(-0.364815\pi\)
−0.0987406 + 0.995113i \(0.531481\pi\)
\(164\) −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 0.281461 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
\(171\) 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 0.979670 + 0.200615i \(0.0642941\pi\)
−0.316097 + 0.948727i \(0.602373\pi\)
\(174\) −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 0.387084 0.922045i \(-0.373482\pi\)
0.604972 0.796247i \(-0.293184\pi\)
\(180\) 0.0185132 + 1.21043i 0.00137989 + 0.0902201i
\(181\) 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
\(186\) −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 −0.340968 0.940075i \(-0.610755\pi\)
0.643645 + 0.765324i \(0.277421\pi\)
\(192\) −11.4254 + 1.59315i −0.824554 + 0.114976i
\(193\) −0.0358984 0.133975i −0.00258402 0.00964370i 0.964622 0.263638i \(-0.0849223\pi\)
−0.967206 + 0.253994i \(0.918256\pi\)
\(194\) 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 \(0.963490\pi\)
\(198\) −13.3435 12.9415i −0.948281 0.919711i
\(199\) −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
\(201\) 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 −0.833309 0.552808i \(-0.813556\pi\)
0.895400 + 0.445263i \(0.146890\pi\)
\(212\) −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 −0.966687 0.255960i \(-0.917609\pi\)
−0.709196 + 0.705011i \(0.750942\pi\)
\(224\) −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 0.841429 0.540367i \(-0.181715\pi\)
0.458515 + 0.888686i \(0.348381\pi\)
\(228\) −1.65136 + 0.698857i −0.109364 + 0.0462829i
\(229\) −14.1244 + 14.1244i −0.933364 + 0.933364i −0.997914 0.0645507i \(-0.979439\pi\)
0.0645507 + 0.997914i \(0.479439\pi\)
\(230\) 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 −0.887537 0.460737i \(-0.847585\pi\)
0.460737 + 0.887537i \(0.347585\pi\)
\(240\) 10.7235 4.53819i 0.692198 0.292939i
\(241\) −14.0622 3.76795i −0.905825 0.242715i −0.224309 0.974518i \(-0.572012\pi\)
−0.681516 + 0.731803i \(0.738679\pi\)
\(242\) −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 0.850007 0.526772i \(-0.176598\pi\)
−0.881201 + 0.472741i \(0.843264\pi\)
\(252\) −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 0.306916 + 0.951737i \(0.400703\pi\)
−0.977686 + 0.210071i \(0.932630\pi\)
\(258\) −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 −0.231777 0.972769i \(-0.574454\pi\)
−0.958331 + 0.285660i \(0.907787\pi\)
\(264\) −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 −0.828241 0.560372i \(-0.810658\pi\)
0.0711756 + 0.997464i \(0.477325\pi\)
\(270\) 1.26979 11.7160i 0.0772769 0.713013i
\(271\) −2.00000 7.46410i −0.121491 0.453412i 0.878199 0.478295i \(-0.158745\pi\)
−0.999690 + 0.0248835i \(0.992079\pi\)
\(272\) 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
\(279\) 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 0.969357 0.245655i \(-0.0790030\pi\)
−0.245655 + 0.969357i \(0.579003\pi\)
\(282\) 14.5623 + 5.90185i 0.867172 + 0.351450i
\(283\) 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
\(288\) −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 −0.978206 0.207635i \(-0.933423\pi\)
0.950969 + 0.309286i \(0.100090\pi\)
\(294\) −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 −0.425829 0.904803i \(-0.640018\pi\)
0.904803 + 0.425829i \(0.140018\pi\)
\(308\) −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 −0.312373 0.949960i \(-0.601124\pi\)
0.949960 + 0.312373i \(0.101124\pi\)
\(318\) 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 −0.0850595 0.996376i \(-0.527108\pi\)
0.571852 0.820357i \(-0.306225\pi\)
\(332\) 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 \(0.167734\pi\)
−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
\(342\) 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 0.0614076 0.998113i \(-0.480441\pi\)
0.895095 + 0.445876i \(0.147108\pi\)
\(348\) 0.459481 + 3.29519i 0.0246308 + 0.176641i
\(349\) −7.36603 27.4904i −0.394294 1.47153i −0.822979 0.568072i \(-0.807689\pi\)
0.428684 0.903454i \(-0.358977\pi\)
\(350\) −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 \(0.793822\pi\)
\(354\) 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 0.0368904 0.999319i \(-0.488255\pi\)
−0.999319 + 0.0368904i \(0.988255\pi\)
\(360\) −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 0.130723 + 0.991419i \(0.458270\pi\)
−0.923955 + 0.382500i \(0.875063\pi\)
\(368\) 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 0.676125 0.736787i \(-0.263658\pi\)
−0.976139 + 0.217148i \(0.930325\pi\)
\(374\) 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 −0.606519 0.795069i \(-0.707435\pi\)
−0.127726 + 0.991809i \(0.540768\pi\)
\(380\) −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 −0.672234 0.740339i \(-0.734665\pi\)
−0.952341 + 0.305035i \(0.901332\pi\)
\(384\) 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 0.576501 0.817096i \(-0.304418\pi\)
0.0907168 + 0.995877i \(0.471084\pi\)
\(398\) 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 −0.546294 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
\(405\) −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 0.455480 + 0.890246i \(0.349468\pi\)
−0.839580 + 0.543236i \(0.817199\pi\)
\(410\) −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 0.285208 0.958466i \(-0.407937\pi\)
−0.687452 + 0.726230i \(0.741271\pi\)
\(420\) −0.916053 0.371261i −0.0446988 0.0181157i
\(421\) −7.83013 7.83013i −0.381617 0.381617i 0.490067 0.871685i \(-0.336972\pi\)
−0.871685 + 0.490067i \(0.836972\pi\)
\(422\) −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 −0.633648 0.773622i \(-0.718443\pi\)
0.161944 0.986800i \(-0.448224\pi\)
\(432\) 23.0611 + 2.49938i 1.10953 + 0.120252i
\(433\) 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
\(435\) 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 0.473567 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 \(0.0858762\pi\)
−0.963827 + 0.266527i \(0.914124\pi\)
\(444\) 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 0.718851 + 0.695165i \(0.244669\pi\)
−0.970125 + 0.242605i \(0.921998\pi\)
\(450\) −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 −0.169611 0.985511i \(-0.554251\pi\)
0.345868 + 0.938283i \(0.387584\pi\)
\(458\) 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 −0.253628 0.967302i \(-0.581624\pi\)
−0.703299 + 0.710894i \(0.748290\pi\)
\(462\) 13.9773 5.91520i 0.650282 0.275200i
\(463\) 23.0526 23.0526i 1.07134 1.07134i 0.0740918 0.997251i \(-0.476394\pi\)
0.997251 0.0740918i \(-0.0236058\pi\)
\(464\) 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 0.225510 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
\(486\) 13.5688 19.1572i 0.615492 0.868990i
\(487\) −1.49038 + 5.56218i −0.0675356 + 0.252046i −0.991437 0.130584i \(-0.958315\pi\)
0.923902 + 0.382630i \(0.124982\pi\)
\(488\) 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 0.341023 + 0.940055i \(0.389227\pi\)
−0.984623 + 0.174693i \(0.944107\pi\)
\(492\) 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 0.649798 0.760107i \(-0.274853\pi\)
−0.760107 + 0.649798i \(0.774853\pi\)
\(500\) 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 −0.561824 0.827257i \(-0.689900\pi\)
0.435513 + 0.900182i \(0.356567\pi\)
\(504\) −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 0.997620 + 0.0689588i \(0.0219677\pi\)
−0.829484 + 0.558530i \(0.811366\pi\)
\(510\) 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 \(0.0173815\pi\)
−0.998509 + 0.0545785i \(0.982618\pi\)
\(522\) −0.495311 32.3844i −0.0216792 1.41743i
\(523\) 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
\(525\) 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 −0.925118 0.379681i \(-0.876034\pi\)
0.379681 + 0.925118i \(0.376034\pi\)
\(542\) −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 0.306462 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
\(561\) −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 0.740085 0.672514i \(-0.234785\pi\)
−0.952456 + 0.304675i \(0.901452\pi\)
\(564\) 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 −0.892939 0.450178i \(-0.851361\pi\)
0.836335 + 0.548219i \(0.184694\pi\)
\(570\) 12.1113 + 9.14708i 0.507289 + 0.383129i
\(571\) 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
\(576\) −5.46595 19.2186i −0.227748 0.800775i
\(577\) −22.4904 22.4904i −0.936287 0.936287i 0.0618016 0.998088i \(-0.480315\pi\)
−0.998088 + 0.0618016i \(0.980315\pi\)
\(578\) 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 0.991094 + 0.133164i \(0.0425138\pi\)
−0.791730 + 0.610871i \(0.790819\pi\)
\(588\) 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 0.461541 0.887119i \(-0.347297\pi\)
−0.887119 + 0.461541i \(0.847297\pi\)
\(594\) 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 \(-0.860822\pi\)
0.905924 0.423441i \(-0.139178\pi\)
\(600\) 9.84967 + 7.43895i 0.402111 + 0.303694i
\(601\) −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
\(603\) −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 0.868009 0.496549i \(-0.165400\pi\)
−0.864028 + 0.503444i \(0.832066\pi\)
\(608\) 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 0.735951 0.677035i \(-0.236735\pi\)
0.975870 + 0.218354i \(0.0700687\pi\)
\(614\) −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 −0.118964 0.992899i \(-0.537957\pi\)
−0.599475 + 0.800393i \(0.704624\pi\)
\(618\) −7.04319 16.6427i −0.283319 0.669466i
\(619\) −31.6603 + 31.6603i −1.27253 + 1.27253i −0.327778 + 0.944755i \(0.606300\pi\)
−0.944755 + 0.327778i \(0.893700\pi\)
\(620\) −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 −0.193493 0.981102i \(-0.561982\pi\)
−0.658121 + 0.752912i \(0.728648\pi\)
\(632\) −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 0.833008 + 0.553261i \(0.186617\pi\)
0.0626345 + 0.998037i \(0.480050\pi\)
\(642\) 49.2228 + 6.09776i 1.94267 + 0.240659i
\(643\) −1.87564 + 7.00000i −0.0739682 + 0.276053i −0.992997 0.118136i \(-0.962308\pi\)
0.919029 + 0.394190i \(0.128975\pi\)
\(644\) 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 −0.981249 0.192746i \(-0.938261\pi\)
0.657547 + 0.753413i \(0.271594\pi\)
\(648\) −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 0.654683 0.755904i \(-0.272802\pi\)
−0.327290 + 0.944924i \(0.606135\pi\)
\(654\) −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 −0.881967 0.471311i \(-0.843781\pi\)
−0.0328158 + 0.999461i \(0.510447\pi\)
\(660\) −2.84809 + 0.397137i −0.110862 + 0.0154585i
\(661\) −2.52628 9.42820i −0.0982609 0.366715i 0.899233 0.437470i \(-0.144126\pi\)
−0.997494 + 0.0707559i \(0.977459\pi\)
\(662\) −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 0.996792 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 \(-0.940564\pi\)
0.982618 0.185640i \(-0.0594357\pi\)
\(678\) −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 −0.195338 0.980736i \(-0.562580\pi\)
0.659536 0.751673i \(-0.270753\pi\)
\(684\) −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 −0.588189 0.808723i \(-0.700159\pi\)
−0.105025 + 0.994470i \(0.533492\pi\)
\(692\) −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 0.465219 0.885196i \(-0.345976\pi\)
−0.0397068 + 0.999211i \(0.512642\pi\)
\(710\) −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 0.789005 0.614386i \(-0.210596\pi\)
−0.926577 + 0.376106i \(0.877263\pi\)
\(720\) 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 \(0.117877\pi\)
−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
\(732\) 1.22024 3.01084i 0.0451014 0.111284i
\(733\) −6.77757 6.77757i −0.250335 0.250335i 0.570773 0.821108i \(-0.306644\pi\)
−0.821108 + 0.570773i \(0.806644\pi\)
\(734\) 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 0.998831 0.0483378i \(-0.0153924\pi\)
−0.889182 + 0.457554i \(0.848726\pi\)
\(740\) 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 \(0.968390\pi\)
\(744\) −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 0.927705 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
\(756\) −1.23418 1.53422i −0.0448866 0.0557990i
\(757\) −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 \(-0.0246947\pi\)
\(762\) −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 0.558895 0.829238i \(-0.311225\pi\)
0.898636 + 0.438694i \(0.144559\pi\)
\(770\) 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 0.911677 0.410908i \(-0.134788\pi\)
0.584081 + 0.811695i \(0.301455\pi\)
\(774\) −8.66759 4.82903i −0.311550 0.173576i
\(775\) 6.73205 6.73205i