Properties

Label 507.2.k.f.80.2
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 80.2
Root \(0.500000 + 1.56488i\) of defining polynomial
Character \(\chi\) \(=\) 507.80
Dual form 507.2.k.f.488.2

$q$-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 \(-0.737941\pi\)
0.955430 0.295217i \(-0.0953919\pi\)
\(3\) 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 \(-0.140674\pi\)
−0.427694 + 0.903924i \(0.640674\pi\)
\(6\) −2.40216 1.01660i −0.980678 0.415024i
\(7\) 1.36603 0.366025i 0.516309 0.138345i 0.00875026 0.999962i \(-0.497215\pi\)
0.507559 + 0.861617i \(0.330548\pi\)
\(8\) 1.84443 1.84443i 0.652105 0.652105i
\(9\) −2.88556 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 \(-0.203691\pi\)
0.396117 + 0.918200i \(0.370357\pi\)
\(12\) −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 \(-0.937177\pi\)
0.751171 0.660107i \(-0.229489\pi\)
\(20\) −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 −0.450308 0.892873i \(-0.648686\pi\)
0.892873 + 0.450308i \(0.148686\pi\)
\(32\) −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 \(0.230216\pi\)
−0.980137 + 0.198323i \(0.936451\pi\)
\(38\) −5.81863 −0.943906
\(39\) 0 0
\(40\) 3.92820 0.621103
\(41\) −1.45466 + 5.42885i −0.227179 + 0.847844i 0.754341 + 0.656483i \(0.227957\pi\)
−0.981520 + 0.191361i \(0.938710\pi\)
\(42\) −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 −0.945868 0.324552i \(-0.894787\pi\)
0.324552 + 0.945868i \(0.394787\pi\)
\(48\) −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 0.997923 0.0644157i \(-0.0205184\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(60\) −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 −0.108925 0.994050i \(-0.534741\pi\)
−0.591357 + 0.806410i \(0.701407\pi\)
\(68\) 1.16932 0.675108i 0.141801 0.0818689i
\(69\) 0 0
\(70\) 2.26795 2.26795i 0.271072 0.271072i
\(71\) 2.90931 0.779548i 0.345272 0.0925153i −0.0820158 0.996631i \(-0.526136\pi\)
0.427288 + 0.904116i \(0.359469\pi\)
\(72\) −6.83591 + 3.80853i −0.805620 + 0.448840i
\(73\) 0.901924 + 0.901924i 0.105562 + 0.105562i 0.757915 0.652353i \(-0.226218\pi\)
−0.652353 + 0.757915i \(0.726218\pi\)
\(74\) 7.06440 + 4.07863i 0.821220 + 0.474132i
\(75\) −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 \(-0.177498\pi\)
−0.529174 + 0.848513i \(0.677498\pi\)
\(84\) −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 \(-0.251998\pi\)
0.252751 + 0.967531i \(0.418665\pi\)
\(90\) −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 \(-0.0559636\pi\)
−0.940130 + 0.340815i \(0.889297\pi\)
\(98\) 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 \(-0.398060\pi\)
0.949156 0.314806i \(-0.101940\pi\)
\(110\) 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 \(-0.990614\pi\)
0.850908 0.525315i \(-0.176052\pi\)
\(138\) 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 −0.583644 0.812010i \(-0.698374\pi\)
−0.0994454 + 0.995043i \(0.531707\pi\)
\(150\) −2.77739 + 6.56283i −0.226773 + 0.535853i
\(151\) −0.535898 0.535898i −0.0436108 0.0436108i 0.684965 0.728576i \(-0.259817\pi\)
−0.728576 + 0.684965i \(0.759817\pi\)
\(152\) −8.72794 5.03908i −0.707929 0.408723i
\(153\) 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 \(-0.635185\pi\)
0.0987406 + 0.995113i \(0.468519\pi\)
\(164\) 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 \(-0.590819\pi\)
−0.723539 + 0.690283i \(0.757486\pi\)
\(168\) −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 −0.964622 0.263638i \(-0.915078\pi\)
0.967206 + 0.253994i \(0.0817443\pi\)
\(194\) 2.54752 0.182902
\(195\) 0 0
\(196\) 1.33975 0.0956961
\(197\) 1.06488 3.97420i 0.0758697 0.283150i −0.917559 0.397599i \(-0.869844\pi\)
0.993429 + 0.114449i \(0.0365103\pi\)
\(198\) −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 0.966687 0.255960i \(-0.0823914\pi\)
0.709196 + 0.705011i \(0.249058\pi\)
\(224\) −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 \(-0.818285\pi\)
−0.458515 + 0.888686i \(0.651619\pi\)
\(228\) 1.65136 + 0.698857i 0.109364 + 0.0462829i
\(229\) 14.1244 + 14.1244i 0.933364 + 0.933364i 0.997914 0.0645507i \(-0.0205614\pi\)
−0.0645507 + 0.997914i \(0.520561\pi\)
\(230\) 0 0
\(231\) 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 \(-0.152415\pi\)
−0.460737 + 0.887537i \(0.652415\pi\)
\(240\) −10.7235 4.53819i −0.692198 0.292939i
\(241\) 14.0622 3.76795i 0.905825 0.242715i 0.224309 0.974518i \(-0.427988\pi\)
0.681516 + 0.731803i \(0.261321\pi\)
\(242\) 6.31284 6.31284i 0.405805 0.405805i
\(243\) 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 −0.878199 0.478295i \(-0.841255\pi\)
0.999690 + 0.0248835i \(0.00792149\pi\)
\(272\) 22.4950 1.36396
\(273\) 0 0
\(274\) −10.1244 −0.611635
\(275\) 2.90931 10.8577i 0.175438 0.654744i
\(276\) 0 0
\(277\) −23.8923 13.7942i −1.43555 0.828815i −0.438013 0.898969i \(-0.644318\pi\)
−0.997536 + 0.0701536i \(0.977651\pi\)
\(278\) 19.5856 + 19.5856i 1.17467 + 1.17467i
\(279\) −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 \(-0.920997\pi\)
0.245655 + 0.969357i \(0.420997\pi\)
\(282\) 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 0.978206 0.207635i \(-0.0665766\pi\)
−0.950969 + 0.309286i \(0.899910\pi\)
\(294\) 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 \(-0.359982\pi\)
−0.904803 + 0.425829i \(0.859982\pi\)
\(308\) −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 \(-0.398876\pi\)
−0.949960 + 0.312373i \(0.898876\pi\)
\(318\) −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 \(-0.693775\pi\)
0.0850595 0.996376i \(-0.472892\pi\)
\(332\) −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 \(-0.641023\pi\)
0.822979 0.568072i \(-0.192311\pi\)
\(350\) −5.81863 −0.311019
\(351\) 0 0
\(352\) −6.19615 −0.330256
\(353\) −3.66088 + 13.6626i −0.194849 + 0.727186i 0.797457 + 0.603376i \(0.206178\pi\)
−0.992306 + 0.123810i \(0.960489\pi\)
\(354\) 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 \(-0.511745\pi\)
0.999319 + 0.0368904i \(0.0117452\pi\)
\(360\) −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 0.606519 0.795069i \(-0.292565\pi\)
0.127726 + 0.991809i \(0.459232\pi\)
\(380\) −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 \(-0.265335\pi\)
0.952341 + 0.305035i \(0.0986682\pi\)
\(384\) −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 \(-0.695582\pi\)
−0.0907168 + 0.995877i \(0.528916\pi\)
\(398\) −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 \(-0.316038\pi\)
0.0543073 + 0.998524i \(0.482705\pi\)
\(402\) 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 \(0.182801\pi\)
−0.455480 + 0.890246i \(0.650532\pi\)
\(410\) 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 −0.490067 0.871685i \(-0.663028\pi\)
0.871685 + 0.490067i \(0.163028\pi\)
\(422\) 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 \(-0.551776\pi\)
0.633648 0.773622i \(-0.281557\pi\)
\(432\) 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 \(0.0780018\pi\)
−0.718851 + 0.695165i \(0.755331\pi\)
\(450\) 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 \(-0.445749\pi\)
−0.345868 + 0.938283i \(0.612416\pi\)
\(458\) 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 \(-0.418376\pi\)
0.703299 + 0.710894i \(0.251710\pi\)
\(462\) −13.9773 5.91520i −0.650282 0.275200i
\(463\) −23.0526 23.0526i −1.07134 1.07134i −0.997251 0.0740918i \(-0.976394\pi\)
−0.0740918 0.997251i \(-0.523606\pi\)
\(464\) 27.7149 + 16.0012i 1.28663 + 0.742838i
\(465\) 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 \(-0.572405\pi\)
−0.682418 + 0.730962i \(0.739072\pi\)
\(480\) −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 \(-0.0416851\pi\)
−0.923902 + 0.382630i \(0.875018\pi\)
\(488\) −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 −0.649798 0.760107i \(-0.725147\pi\)
0.760107 + 0.649798i \(0.225147\pi\)
\(500\) −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 \(0.188634\pi\)
−0.997620 + 0.0689588i \(0.978032\pi\)
\(510\) 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 0.925118 0.379681i \(-0.123966\pi\)
−0.379681 + 0.925118i \(0.623966\pi\)
\(542\) −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 \(-0.599145\pi\)
−0.741346 + 0.671123i \(0.765812\pi\)
\(558\) 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 −0.0618016 0.998088i \(-0.519685\pi\)
0.998088 + 0.0618016i \(0.0196846\pi\)
\(578\) −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 \(0.209181\pi\)
−0.991094 + 0.133164i \(0.957486\pi\)
\(588\) 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 \(-0.652703\pi\)
0.887119 + 0.461541i \(0.152703\pi\)
\(594\) 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 −0.735951 0.677035i \(-0.763265\pi\)
−0.975870 + 0.218354i \(0.929931\pi\)
\(614\) −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 \(-0.462043\pi\)
0.599475 + 0.800393i \(0.295376\pi\)
\(618\) 7.04319 16.6427i 0.283319 0.669466i
\(619\) 31.6603 + 31.6603i 1.27253 + 1.27253i 0.944755 + 0.327778i \(0.106300\pi\)
0.327778 + 0.944755i \(0.393700\pi\)
\(620\) −1.21779 0.703093i −0.0489077 0.0282369i
\(621\) 0 0
\(622\) −3.92820 + 14.6603i −0.157507 + 0.587823i
\(623\) 13.1963 0.528701
\(624\) 0 0
\(625\) 3.87564 0.155026
\(626\) 0.779548 2.90931i 0.0311570 0.116280i
\(627\) −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 \(-0.438018\pi\)
0.658121 + 0.752912i \(0.271352\pi\)
\(632\) 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 0.992997 0.118136i \(-0.0376920\pi\)
−0.919029 + 0.394190i \(0.871025\pi\)
\(644\) 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 −0.899233 0.437470i \(-0.855874\pi\)
0.997494 + 0.0707559i \(0.0225411\pi\)
\(662\) −51.5321 −2.00285
\(663\) 0 0
\(664\) 10.7321 0.416484
\(665\) 2.12976 7.94839i 0.0825887 0.308225i
\(666\) −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 \(-0.729247\pi\)
0.195338 0.980736i \(-0.437420\pi\)
\(684\) 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 \(-0.299841\pi\)
0.105025 + 0.994470i \(0.466508\pi\)
\(692\) −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 \(-0.654024\pi\)
0.0397068 + 0.999211i \(0.487358\pi\)
\(710\) 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 −0.570773 0.821108i \(-0.693356\pi\)
0.821108 + 0.570773i \(0.193356\pi\)
\(734\) −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 \(-0.984608\pi\)
0.889182 + 0.457554i \(0.151274\pi\)
\(740\) 2.18573 0.0803492
\(741\) 0 0
\(742\) −1.66025 −0.0609498
\(743\) 2.28268 8.51906i 0.0837432 0.312534i −0.911330 0.411677i \(-0.864943\pi\)
0.995073 + 0.0991426i \(0.0316100\pi\)
\(744\) −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 \(-0.975305\pi\)
0.824669 0.565616i \(-0.191361\pi\)
\(762\) 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 \(-0.688775\pi\)
−0.898636 + 0.438694i \(0.855441\pi\)
\(770\) 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 \(-0.865212\pi\)
−0.584081 + 0.811695i \(0.698545\pi\)
\(774\) 8.66759 4.82903i 0.311550 0.173576i
\(775\) −6.73205 6.73205i