Properties

Label 20.4.e.b.7.4
Level 20
Weight 4
Character 20.7
Analytic conductor 1.180
Analytic rank 0
Dimension 12
CM No
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 20.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(1.18003820011\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{14} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.4
Root \(1.13579 + 1.64620i\)
Character \(\chi\) = 20.7
Dual form 20.4.e.b.3.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.510409 - 2.78199i) q^{2} +(-4.02923 - 4.02923i) q^{3} +(-7.47897 + 2.83991i) q^{4} +(10.9349 - 2.32970i) q^{5} +(-9.15273 + 13.2658i) q^{6} +(14.4440 - 14.4440i) q^{7} +(11.7179 + 19.3569i) q^{8} +5.46937i q^{9} +O(q^{10})\) \(q+(-0.510409 - 2.78199i) q^{2} +(-4.02923 - 4.02923i) q^{3} +(-7.47897 + 2.83991i) q^{4} +(10.9349 - 2.32970i) q^{5} +(-9.15273 + 13.2658i) q^{6} +(14.4440 - 14.4440i) q^{7} +(11.7179 + 19.3569i) q^{8} +5.46937i q^{9} +(-12.0625 - 29.2318i) q^{10} +47.0607i q^{11} +(41.5771 + 18.6918i) q^{12} +(-8.79525 + 8.79525i) q^{13} +(-47.5554 - 32.8107i) q^{14} +(-53.4462 - 34.6724i) q^{15} +(47.8698 - 42.4791i) q^{16} +(-26.4898 - 26.4898i) q^{17} +(15.2157 - 2.79162i) q^{18} +49.8054 q^{19} +(-75.1658 + 48.4779i) q^{20} -116.396 q^{21} +(130.922 - 24.0202i) q^{22} +(41.2762 + 41.2762i) q^{23} +(30.7792 - 125.208i) q^{24} +(114.145 - 50.9501i) q^{25} +(28.9575 + 19.9791i) q^{26} +(-86.7518 + 86.7518i) q^{27} +(-67.0065 + 149.046i) q^{28} +247.406i q^{29} +(-69.1790 + 166.384i) q^{30} -62.3240i q^{31} +(-142.610 - 111.492i) q^{32} +(189.618 - 189.618i) q^{33} +(-60.1738 + 87.2150i) q^{34} +(124.294 - 191.594i) q^{35} +(-15.5325 - 40.9052i) q^{36} +(-73.2182 - 73.2182i) q^{37} +(-25.4211 - 138.558i) q^{38} +70.8761 q^{39} +(173.230 + 184.367i) q^{40} +118.624 q^{41} +(59.4097 + 323.814i) q^{42} +(-245.335 - 245.335i) q^{43} +(-133.648 - 351.965i) q^{44} +(12.7420 + 59.8071i) q^{45} +(93.7624 - 135.898i) q^{46} +(-125.525 + 125.525i) q^{47} +(-364.037 - 21.7203i) q^{48} -74.2578i q^{49} +(-200.004 - 291.545i) q^{50} +213.467i q^{51} +(40.8017 - 90.7571i) q^{52} +(-326.574 + 326.574i) q^{53} +(285.622 + 197.064i) q^{54} +(109.637 + 514.605i) q^{55} +(448.845 + 110.337i) q^{56} +(-200.677 - 200.677i) q^{57} +(688.282 - 126.278i) q^{58} +365.123 q^{59} +(498.189 + 107.532i) q^{60} -268.160 q^{61} +(-173.385 + 31.8107i) q^{62} +(78.9995 + 78.9995i) q^{63} +(-237.380 + 453.646i) q^{64} +(-75.6851 + 116.666i) q^{65} +(-624.299 - 430.733i) q^{66} +(112.617 - 112.617i) q^{67} +(273.345 + 122.888i) q^{68} -332.623i q^{69} +(-596.454 - 247.993i) q^{70} -559.873i q^{71} +(-105.870 + 64.0897i) q^{72} +(215.825 - 215.825i) q^{73} +(-166.321 + 241.064i) q^{74} +(-665.206 - 254.627i) q^{75} +(-372.493 + 141.443i) q^{76} +(679.744 + 679.744i) q^{77} +(-36.1758 - 197.177i) q^{78} -1172.36 q^{79} +(424.489 - 576.028i) q^{80} +846.759 q^{81} +(-60.5470 - 330.012i) q^{82} +(592.561 + 592.561i) q^{83} +(870.524 - 330.555i) q^{84} +(-351.377 - 227.951i) q^{85} +(-557.299 + 807.742i) q^{86} +(996.857 - 996.857i) q^{87} +(-910.949 + 551.454i) q^{88} -552.071i q^{89} +(159.879 - 65.9742i) q^{90} +254.077i q^{91} +(-425.924 - 191.483i) q^{92} +(-251.118 + 251.118i) q^{93} +(413.277 + 285.139i) q^{94} +(544.618 - 116.032i) q^{95} +(125.382 + 1023.83i) q^{96} +(460.651 + 460.651i) q^{97} +(-206.585 + 37.9019i) q^{98} -257.392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{2} + 8q^{6} - 12q^{8} + O(q^{10}) \) \( 12q - 6q^{2} + 8q^{6} - 12q^{8} - 110q^{10} - 80q^{12} + 116q^{13} + 312q^{16} - 332q^{17} + 198q^{18} + 140q^{20} - 144q^{21} + 360q^{22} + 340q^{25} - 164q^{26} - 880q^{28} - 1240q^{30} - 376q^{32} + 80q^{33} + 460q^{36} + 508q^{37} + 1600q^{38} + 1420q^{40} - 656q^{41} + 1160q^{42} + 1180q^{45} - 1432q^{46} - 2720q^{48} - 1570q^{50} - 932q^{52} - 644q^{53} + 2048q^{56} - 960q^{57} + 1576q^{58} + 3280q^{60} - 896q^{61} + 2440q^{62} - 2740q^{65} - 1680q^{66} - 844q^{68} - 3040q^{70} - 3036q^{72} + 1436q^{73} + 800q^{76} + 3120q^{77} + 3720q^{78} + 1840q^{80} + 5988q^{81} - 1352q^{82} + 500q^{85} - 2552q^{86} - 2400q^{88} - 750q^{90} - 1840q^{92} - 3280q^{93} + 1088q^{96} - 4772q^{97} + 1698q^{98} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.510409 2.78199i −0.180457 0.983583i
\(3\) −4.02923 4.02923i −0.775425 0.775425i 0.203624 0.979049i \(-0.434728\pi\)
−0.979049 + 0.203624i \(0.934728\pi\)
\(4\) −7.47897 + 2.83991i −0.934871 + 0.354989i
\(5\) 10.9349 2.32970i 0.978049 0.208375i
\(6\) −9.15273 + 13.2658i −0.622764 + 0.902626i
\(7\) 14.4440 14.4440i 0.779902 0.779902i −0.199912 0.979814i \(-0.564066\pi\)
0.979814 + 0.199912i \(0.0640655\pi\)
\(8\) 11.7179 + 19.3569i 0.517864 + 0.855463i
\(9\) 5.46937i 0.202569i
\(10\) −12.0625 29.2318i −0.381449 0.924390i
\(11\) 47.0607i 1.28994i 0.764209 + 0.644969i \(0.223130\pi\)
−0.764209 + 0.644969i \(0.776870\pi\)
\(12\) 41.5771 + 18.6918i 1.00019 + 0.449655i
\(13\) −8.79525 + 8.79525i −0.187643 + 0.187643i −0.794676 0.607033i \(-0.792360\pi\)
0.607033 + 0.794676i \(0.292360\pi\)
\(14\) −47.5554 32.8107i −0.907837 0.626360i
\(15\) −53.4462 34.6724i −0.919983 0.596825i
\(16\) 47.8698 42.4791i 0.747966 0.663737i
\(17\) −26.4898 26.4898i −0.377925 0.377925i 0.492428 0.870353i \(-0.336109\pi\)
−0.870353 + 0.492428i \(0.836109\pi\)
\(18\) 15.2157 2.79162i 0.199244 0.0365550i
\(19\) 49.8054 0.601376 0.300688 0.953723i \(-0.402784\pi\)
0.300688 + 0.953723i \(0.402784\pi\)
\(20\) −75.1658 + 48.4779i −0.840379 + 0.541999i
\(21\) −116.396 −1.20951
\(22\) 130.922 24.0202i 1.26876 0.232778i
\(23\) 41.2762 + 41.2762i 0.374204 + 0.374204i 0.869006 0.494802i \(-0.164759\pi\)
−0.494802 + 0.869006i \(0.664759\pi\)
\(24\) 30.7792 125.208i 0.261782 1.06491i
\(25\) 114.145 50.9501i 0.913160 0.407601i
\(26\) 28.9575 + 19.9791i 0.218424 + 0.150701i
\(27\) −86.7518 + 86.7518i −0.618348 + 0.618348i
\(28\) −67.0065 + 149.046i −0.452251 + 1.00596i
\(29\) 247.406i 1.58421i 0.610382 + 0.792107i \(0.291016\pi\)
−0.610382 + 0.792107i \(0.708984\pi\)
\(30\) −69.1790 + 166.384i −0.421010 + 1.01258i
\(31\) 62.3240i 0.361088i −0.983567 0.180544i \(-0.942214\pi\)
0.983567 0.180544i \(-0.0577858\pi\)
\(32\) −142.610 111.492i −0.787816 0.615911i
\(33\) 189.618 189.618i 1.00025 1.00025i
\(34\) −60.1738 + 87.2150i −0.303521 + 0.439919i
\(35\) 124.294 191.594i 0.600271 0.925294i
\(36\) −15.5325 40.9052i −0.0719098 0.189376i
\(37\) −73.2182 73.2182i −0.325324 0.325324i 0.525481 0.850805i \(-0.323885\pi\)
−0.850805 + 0.525481i \(0.823885\pi\)
\(38\) −25.4211 138.558i −0.108522 0.591503i
\(39\) 70.8761 0.291007
\(40\) 173.230 + 184.367i 0.684754 + 0.728775i
\(41\) 118.624 0.451854 0.225927 0.974144i \(-0.427459\pi\)
0.225927 + 0.974144i \(0.427459\pi\)
\(42\) 59.4097 + 323.814i 0.218265 + 1.18966i
\(43\) −245.335 245.335i −0.870076 0.870076i 0.122404 0.992480i \(-0.460940\pi\)
−0.992480 + 0.122404i \(0.960940\pi\)
\(44\) −133.648 351.965i −0.457913 1.20593i
\(45\) 12.7420 + 59.8071i 0.0422103 + 0.198123i
\(46\) 93.7624 135.898i 0.300533 0.435588i
\(47\) −125.525 + 125.525i −0.389567 + 0.389567i −0.874533 0.484966i \(-0.838832\pi\)
0.484966 + 0.874533i \(0.338832\pi\)
\(48\) −364.037 21.7203i −1.09467 0.0653138i
\(49\) 74.2578i 0.216495i
\(50\) −200.004 291.545i −0.565695 0.824614i
\(51\) 213.467i 0.586105i
\(52\) 40.8017 90.7571i 0.108811 0.242033i
\(53\) −326.574 + 326.574i −0.846385 + 0.846385i −0.989680 0.143295i \(-0.954230\pi\)
0.143295 + 0.989680i \(0.454230\pi\)
\(54\) 285.622 + 197.064i 0.719782 + 0.496611i
\(55\) 109.637 + 514.605i 0.268790 + 1.26162i
\(56\) 448.845 + 110.337i 1.07106 + 0.263294i
\(57\) −200.677 200.677i −0.466322 0.466322i
\(58\) 688.282 126.278i 1.55821 0.285882i
\(59\) 365.123 0.805677 0.402839 0.915271i \(-0.368024\pi\)
0.402839 + 0.915271i \(0.368024\pi\)
\(60\) 498.189 + 107.532i 1.07193 + 0.231371i
\(61\) −268.160 −0.562858 −0.281429 0.959582i \(-0.590808\pi\)
−0.281429 + 0.959582i \(0.590808\pi\)
\(62\) −173.385 + 31.8107i −0.355160 + 0.0651608i
\(63\) 78.9995 + 78.9995i 0.157984 + 0.157984i
\(64\) −237.380 + 453.646i −0.463633 + 0.886027i
\(65\) −75.6851 + 116.666i −0.144424 + 0.222624i
\(66\) −624.299 430.733i −1.16433 0.803328i
\(67\) 112.617 112.617i 0.205349 0.205349i −0.596938 0.802287i \(-0.703616\pi\)
0.802287 + 0.596938i \(0.203616\pi\)
\(68\) 273.345 + 122.888i 0.487469 + 0.219152i
\(69\) 332.623i 0.580334i
\(70\) −596.454 247.993i −1.01843 0.423441i
\(71\) 559.873i 0.935841i −0.883771 0.467921i \(-0.845003\pi\)
0.883771 0.467921i \(-0.154997\pi\)
\(72\) −105.870 + 64.0897i −0.173290 + 0.104903i
\(73\) 215.825 215.825i 0.346033 0.346033i −0.512597 0.858629i \(-0.671316\pi\)
0.858629 + 0.512597i \(0.171316\pi\)
\(74\) −166.321 + 241.064i −0.261276 + 0.378690i
\(75\) −665.206 254.627i −1.02415 0.392023i
\(76\) −372.493 + 141.443i −0.562209 + 0.213482i
\(77\) 679.744 + 679.744i 1.00603 + 1.00603i
\(78\) −36.1758 197.177i −0.0525142 0.286229i
\(79\) −1172.36 −1.66963 −0.834816 0.550528i \(-0.814426\pi\)
−0.834816 + 0.550528i \(0.814426\pi\)
\(80\) 424.489 576.028i 0.593242 0.805024i
\(81\) 846.759 1.16153
\(82\) −60.5470 330.012i −0.0815402 0.444436i
\(83\) 592.561 + 592.561i 0.783639 + 0.783639i 0.980443 0.196804i \(-0.0630562\pi\)
−0.196804 + 0.980443i \(0.563056\pi\)
\(84\) 870.524 330.555i 1.13074 0.429363i
\(85\) −351.377 227.951i −0.448379 0.290879i
\(86\) −557.299 + 807.742i −0.698781 + 1.01280i
\(87\) 996.857 996.857i 1.22844 1.22844i
\(88\) −910.949 + 551.454i −1.10349 + 0.668013i
\(89\) 552.071i 0.657522i −0.944413 0.328761i \(-0.893369\pi\)
0.944413 0.328761i \(-0.106631\pi\)
\(90\) 159.879 65.9742i 0.187253 0.0772699i
\(91\) 254.077i 0.292687i
\(92\) −425.924 191.483i −0.482670 0.216994i
\(93\) −251.118 + 251.118i −0.279997 + 0.279997i
\(94\) 413.277 + 285.139i 0.453471 + 0.312871i
\(95\) 544.618 116.032i 0.588175 0.125311i
\(96\) 125.382 + 1023.83i 0.133299 + 1.08849i
\(97\) 460.651 + 460.651i 0.482186 + 0.482186i 0.905829 0.423643i \(-0.139249\pi\)
−0.423643 + 0.905829i \(0.639249\pi\)
\(98\) −206.585 + 37.9019i −0.212941 + 0.0390680i
\(99\) −257.392 −0.261302
\(100\) −708.993 + 705.216i −0.708993 + 0.705216i
\(101\) −5.97644 −0.00588790 −0.00294395 0.999996i \(-0.500937\pi\)
−0.00294395 + 0.999996i \(0.500937\pi\)
\(102\) 593.863 108.955i 0.576483 0.105767i
\(103\) 137.824 + 137.824i 0.131847 + 0.131847i 0.769951 0.638104i \(-0.220281\pi\)
−0.638104 + 0.769951i \(0.720281\pi\)
\(104\) −273.311 67.1867i −0.257696 0.0633481i
\(105\) −1272.78 + 271.168i −1.18296 + 0.252032i
\(106\) 1075.21 + 741.840i 0.985225 + 0.679754i
\(107\) −723.943 + 723.943i −0.654077 + 0.654077i −0.953972 0.299895i \(-0.903048\pi\)
0.299895 + 0.953972i \(0.403048\pi\)
\(108\) 402.447 895.181i 0.358569 0.797582i
\(109\) 896.758i 0.788017i −0.919107 0.394009i \(-0.871088\pi\)
0.919107 0.394009i \(-0.128912\pi\)
\(110\) 1375.67 567.668i 1.19241 0.492046i
\(111\) 590.026i 0.504530i
\(112\) 77.8631 1305.00i 0.0656908 1.10099i
\(113\) −525.727 + 525.727i −0.437665 + 0.437665i −0.891226 0.453560i \(-0.850154\pi\)
0.453560 + 0.891226i \(0.350154\pi\)
\(114\) −455.855 + 660.710i −0.374515 + 0.542817i
\(115\) 547.513 + 355.191i 0.443964 + 0.288015i
\(116\) −702.611 1850.34i −0.562378 1.48103i
\(117\) −48.1045 48.1045i −0.0380108 0.0380108i
\(118\) −186.362 1015.77i −0.145390 0.792450i
\(119\) −765.237 −0.589488
\(120\) 44.8719 1440.84i 0.0341352 1.09609i
\(121\) −883.705 −0.663941
\(122\) 136.871 + 746.019i 0.101572 + 0.553618i
\(123\) −477.965 477.965i −0.350379 0.350379i
\(124\) 176.995 + 466.119i 0.128182 + 0.337571i
\(125\) 1129.47 823.059i 0.808182 0.588933i
\(126\) 179.454 260.098i 0.126881 0.183900i
\(127\) 75.4237 75.4237i 0.0526990 0.0526990i −0.680266 0.732965i \(-0.738136\pi\)
0.732965 + 0.680266i \(0.238136\pi\)
\(128\) 1383.20 + 428.844i 0.955147 + 0.296132i
\(129\) 1977.02i 1.34936i
\(130\) 363.193 + 151.008i 0.245032 + 0.101879i
\(131\) 1374.47i 0.916701i −0.888771 0.458351i \(-0.848440\pi\)
0.888771 0.458351i \(-0.151560\pi\)
\(132\) −879.649 + 1956.65i −0.580028 + 1.29018i
\(133\) 719.389 719.389i 0.469014 0.469014i
\(134\) −370.782 255.820i −0.239035 0.164922i
\(135\) −746.519 + 1150.73i −0.475927 + 0.733623i
\(136\) 202.355 823.166i 0.127587 0.519014i
\(137\) −2002.37 2002.37i −1.24871 1.24871i −0.956289 0.292424i \(-0.905538\pi\)
−0.292424 0.956289i \(-0.594462\pi\)
\(138\) −925.354 + 169.774i −0.570807 + 0.104725i
\(139\) 2575.00 1.57129 0.785643 0.618679i \(-0.212332\pi\)
0.785643 + 0.618679i \(0.212332\pi\)
\(140\) −385.479 + 1785.91i −0.232707 + 1.07812i
\(141\) 1011.53 0.604160
\(142\) −1557.56 + 285.764i −0.920477 + 0.168879i
\(143\) −413.910 413.910i −0.242048 0.242048i
\(144\) 232.334 + 261.818i 0.134453 + 0.151515i
\(145\) 576.382 + 2705.37i 0.330110 + 1.54944i
\(146\) −710.582 490.264i −0.402796 0.277908i
\(147\) −299.202 + 299.202i −0.167876 + 0.167876i
\(148\) 755.529 + 339.663i 0.419623 + 0.188650i
\(149\) 1322.91i 0.727364i −0.931523 0.363682i \(-0.881519\pi\)
0.931523 0.363682i \(-0.118481\pi\)
\(150\) −368.842 + 1980.56i −0.200772 + 1.07808i
\(151\) 57.2419i 0.0308495i −0.999881 0.0154248i \(-0.995090\pi\)
0.999881 0.0154248i \(-0.00491005\pi\)
\(152\) 583.616 + 964.079i 0.311431 + 0.514455i
\(153\) 144.882 144.882i 0.0765559 0.0765559i
\(154\) 1544.09 2237.99i 0.807966 1.17105i
\(155\) −145.196 681.508i −0.0752415 0.353162i
\(156\) −530.080 + 201.282i −0.272054 + 0.103304i
\(157\) 1622.22 + 1622.22i 0.824634 + 0.824634i 0.986769 0.162134i \(-0.0518378\pi\)
−0.162134 + 0.986769i \(0.551838\pi\)
\(158\) 598.384 + 3261.50i 0.301297 + 1.64222i
\(159\) 2631.68 1.31262
\(160\) −1819.17 886.916i −0.898863 0.438230i
\(161\) 1192.39 0.583685
\(162\) −432.193 2355.68i −0.209607 1.14247i
\(163\) −1696.16 1696.16i −0.815052 0.815052i 0.170334 0.985386i \(-0.445515\pi\)
−0.985386 + 0.170334i \(0.945515\pi\)
\(164\) −887.188 + 336.882i −0.422425 + 0.160403i
\(165\) 1631.71 2515.21i 0.769868 1.18672i
\(166\) 1346.05 1950.95i 0.629361 0.912187i
\(167\) −2015.29 + 2015.29i −0.933819 + 0.933819i −0.997942 0.0641235i \(-0.979575\pi\)
0.0641235 + 0.997942i \(0.479575\pi\)
\(168\) −1363.92 2253.07i −0.626363 1.03469i
\(169\) 2042.29i 0.929580i
\(170\) −454.811 + 1093.88i −0.205191 + 0.493509i
\(171\) 272.404i 0.121820i
\(172\) 2531.58 + 1138.12i 1.12228 + 0.504542i
\(173\) 317.896 317.896i 0.139706 0.139706i −0.633795 0.773501i \(-0.718504\pi\)
0.773501 + 0.633795i \(0.218504\pi\)
\(174\) −3282.05 2264.44i −1.42995 0.986592i
\(175\) 912.786 2384.63i 0.394287 1.03006i
\(176\) 1999.10 + 2252.79i 0.856179 + 0.964830i
\(177\) −1471.16 1471.16i −0.624743 0.624743i
\(178\) −1535.86 + 281.782i −0.646727 + 0.118654i
\(179\) −3518.04 −1.46900 −0.734499 0.678610i \(-0.762583\pi\)
−0.734499 + 0.678610i \(0.762583\pi\)
\(180\) −265.144 411.109i −0.109792 0.170235i
\(181\) −4769.86 −1.95879 −0.979395 0.201955i \(-0.935271\pi\)
−0.979395 + 0.201955i \(0.935271\pi\)
\(182\) 706.840 129.683i 0.287882 0.0528174i
\(183\) 1080.48 + 1080.48i 0.436455 + 0.436455i
\(184\) −315.308 + 1282.65i −0.126331 + 0.513904i
\(185\) −971.212 630.059i −0.385972 0.250394i
\(186\) 826.781 + 570.435i 0.325927 + 0.224873i
\(187\) 1246.63 1246.63i 0.487499 0.487499i
\(188\) 582.316 1295.27i 0.225903 0.502486i
\(189\) 2506.09i 0.964502i
\(190\) −600.777 1455.90i −0.229394 0.555906i
\(191\) 1728.42i 0.654787i 0.944888 + 0.327393i \(0.106170\pi\)
−0.944888 + 0.327393i \(0.893830\pi\)
\(192\) 2784.30 871.385i 1.04656 0.327536i
\(193\) 1439.32 1439.32i 0.536813 0.536813i −0.385779 0.922591i \(-0.626067\pi\)
0.922591 + 0.385779i \(0.126067\pi\)
\(194\) 1046.41 1516.65i 0.387256 0.561283i
\(195\) 775.025 165.120i 0.284619 0.0606384i
\(196\) 210.885 + 555.372i 0.0768533 + 0.202395i
\(197\) −658.673 658.673i −0.238216 0.238216i 0.577895 0.816111i \(-0.303874\pi\)
−0.816111 + 0.577895i \(0.803874\pi\)
\(198\) 131.375 + 716.063i 0.0471537 + 0.257012i
\(199\) 658.733 0.234655 0.117327 0.993093i \(-0.462567\pi\)
0.117327 + 0.993093i \(0.462567\pi\)
\(200\) 2323.78 + 1612.46i 0.821581 + 0.570092i
\(201\) −907.523 −0.318466
\(202\) 3.05043 + 16.6264i 0.00106251 + 0.00579124i
\(203\) 3573.53 + 3573.53i 1.23553 + 1.23553i
\(204\) −606.226 1596.51i −0.208060 0.547932i
\(205\) 1297.15 276.359i 0.441935 0.0941549i
\(206\) 313.080 453.773i 0.105890 0.153475i
\(207\) −225.755 + 225.755i −0.0758022 + 0.0758022i
\(208\) −47.4125 + 794.642i −0.0158051 + 0.264897i
\(209\) 2343.87i 0.775738i
\(210\) 1404.03 + 3402.47i 0.461368 + 1.11806i
\(211\) 5821.53i 1.89939i 0.313182 + 0.949693i \(0.398605\pi\)
−0.313182 + 0.949693i \(0.601395\pi\)
\(212\) 1515.00 3369.88i 0.490803 1.09172i
\(213\) −2255.86 + 2255.86i −0.725675 + 0.725675i
\(214\) 2383.51 + 1644.50i 0.761371 + 0.525306i
\(215\) −3254.28 2111.16i −1.03228 0.669675i
\(216\) −2695.80 662.695i −0.849194 0.208753i
\(217\) −900.208 900.208i −0.281613 0.281613i
\(218\) −2494.77 + 457.714i −0.775080 + 0.142203i
\(219\) −1739.22 −0.536645
\(220\) −2281.40 3537.35i −0.699146 1.08404i
\(221\) 465.969 0.141830
\(222\) 1641.45 301.155i 0.496247 0.0910458i
\(223\) −2315.57 2315.57i −0.695347 0.695347i 0.268056 0.963403i \(-0.413619\pi\)
−0.963403 + 0.268056i \(0.913619\pi\)
\(224\) −3670.24 + 449.469i −1.09477 + 0.134069i
\(225\) 278.665 + 624.301i 0.0825674 + 0.184978i
\(226\) 1730.90 + 1194.23i 0.509460 + 0.351501i
\(227\) 2970.19 2970.19i 0.868450 0.868450i −0.123851 0.992301i \(-0.539524\pi\)
0.992301 + 0.123851i \(0.0395243\pi\)
\(228\) 2070.76 + 930.954i 0.601490 + 0.270412i
\(229\) 4981.25i 1.43742i −0.695308 0.718712i \(-0.744732\pi\)
0.695308 0.718712i \(-0.255268\pi\)
\(230\) 708.683 1704.47i 0.203170 0.488650i
\(231\) 5477.69i 1.56020i
\(232\) −4789.02 + 2899.09i −1.35524 + 0.820408i
\(233\) 1649.04 1649.04i 0.463659 0.463659i −0.436194 0.899853i \(-0.643674\pi\)
0.899853 + 0.436194i \(0.143674\pi\)
\(234\) −109.273 + 158.379i −0.0305274 + 0.0442460i
\(235\) −1080.17 + 1665.04i −0.299840 + 0.462191i
\(236\) −2730.74 + 1036.92i −0.753204 + 0.286006i
\(237\) 4723.71 + 4723.71i 1.29468 + 1.29468i
\(238\) 390.584 + 2128.88i 0.106377 + 0.579811i
\(239\) 3574.98 0.967558 0.483779 0.875190i \(-0.339264\pi\)
0.483779 + 0.875190i \(0.339264\pi\)
\(240\) −4031.32 + 610.586i −1.08425 + 0.164221i
\(241\) 5135.22 1.37257 0.686283 0.727334i \(-0.259241\pi\)
0.686283 + 0.727334i \(0.259241\pi\)
\(242\) 451.051 + 2458.46i 0.119813 + 0.653041i
\(243\) −1069.49 1069.49i −0.282336 0.282336i
\(244\) 2005.56 761.549i 0.526200 0.199808i
\(245\) −172.998 812.003i −0.0451121 0.211743i
\(246\) −1085.74 + 1573.65i −0.281399 + 0.407855i
\(247\) −438.051 + 438.051i −0.112844 + 0.112844i
\(248\) 1206.40 730.309i 0.308897 0.186995i
\(249\) 4775.13i 1.21531i
\(250\) −2866.24 2722.08i −0.725107 0.688637i
\(251\) 6648.06i 1.67180i −0.548882 0.835900i \(-0.684946\pi\)
0.548882 0.835900i \(-0.315054\pi\)
\(252\) −815.186 366.483i −0.203777 0.0916122i
\(253\) −1942.49 + 1942.49i −0.482700 + 0.482700i
\(254\) −248.325 171.331i −0.0613437 0.0423239i
\(255\) 497.313 + 2334.24i 0.122129 + 0.573239i
\(256\) 487.044 4066.94i 0.118907 0.992905i
\(257\) −448.260 448.260i −0.108800 0.108800i 0.650611 0.759411i \(-0.274513\pi\)
−0.759411 + 0.650611i \(0.774513\pi\)
\(258\) 5500.06 1009.09i 1.32721 0.243501i
\(259\) −2115.13 −0.507442
\(260\) 234.726 1087.48i 0.0559889 0.259394i
\(261\) −1353.16 −0.320913
\(262\) −3823.76 + 701.541i −0.901652 + 0.165425i
\(263\) 145.529 + 145.529i 0.0341205 + 0.0341205i 0.723961 0.689841i \(-0.242319\pi\)
−0.689841 + 0.723961i \(0.742319\pi\)
\(264\) 5892.35 + 1448.49i 1.37367 + 0.337683i
\(265\) −2810.24 + 4331.88i −0.651441 + 1.00417i
\(266\) −2368.52 1634.15i −0.545951 0.376678i
\(267\) −2224.42 + 2224.42i −0.509859 + 0.509859i
\(268\) −522.439 + 1162.09i −0.119078 + 0.264872i
\(269\) 2764.90i 0.626687i 0.949640 + 0.313344i \(0.101449\pi\)
−0.949640 + 0.313344i \(0.898551\pi\)
\(270\) 3582.35 + 1489.47i 0.807463 + 0.335726i
\(271\) 6372.29i 1.42837i 0.699955 + 0.714187i \(0.253203\pi\)
−0.699955 + 0.714187i \(0.746797\pi\)
\(272\) −2393.33 142.798i −0.533517 0.0318324i
\(273\) 1023.73 1023.73i 0.226957 0.226957i
\(274\) −4548.54 + 6592.59i −1.00287 + 1.45355i
\(275\) 2397.75 + 5371.74i 0.525780 + 1.17792i
\(276\) 944.618 + 2487.67i 0.206012 + 0.542538i
\(277\) −387.343 387.343i −0.0840187 0.0840187i 0.663848 0.747867i \(-0.268922\pi\)
−0.747867 + 0.663848i \(0.768922\pi\)
\(278\) −1314.30 7163.64i −0.283549 1.54549i
\(279\) 340.873 0.0731453
\(280\) 5165.14 + 160.857i 1.10241 + 0.0343323i
\(281\) 5284.49 1.12187 0.560936 0.827859i \(-0.310441\pi\)
0.560936 + 0.827859i \(0.310441\pi\)
\(282\) −516.296 2814.08i −0.109025 0.594241i
\(283\) 341.577 + 341.577i 0.0717479 + 0.0717479i 0.742070 0.670322i \(-0.233844\pi\)
−0.670322 + 0.742070i \(0.733844\pi\)
\(284\) 1589.99 + 4187.27i 0.332213 + 0.874890i
\(285\) −2661.91 1726.87i −0.553256 0.358916i
\(286\) −940.232 + 1362.76i −0.194395 + 0.281754i
\(287\) 1713.41 1713.41i 0.352402 0.352402i
\(288\) 609.790 779.986i 0.124765 0.159587i
\(289\) 3509.58i 0.714346i
\(290\) 7232.12 2984.33i 1.46443 0.604297i
\(291\) 3712.13i 0.747798i
\(292\) −1001.22 + 2227.07i −0.200658 + 0.446333i
\(293\) −6655.74 + 6655.74i −1.32707 + 1.32707i −0.419161 + 0.907912i \(0.637676\pi\)
−0.907912 + 0.419161i \(0.862324\pi\)
\(294\) 985.092 + 679.662i 0.195414 + 0.134825i
\(295\) 3992.59 850.626i 0.787992 0.167883i
\(296\) 559.312 2275.24i 0.109829 0.446777i
\(297\) −4082.60 4082.60i −0.797631 0.797631i
\(298\) −3680.33 + 675.227i −0.715423 + 0.131258i
\(299\) −726.069 −0.140434
\(300\) 5698.17 + 15.2195i 1.09661 + 0.00292899i
\(301\) −7087.24 −1.35715
\(302\) −159.247 + 29.2168i −0.0303431 + 0.00556701i
\(303\) 24.0804 + 24.0804i 0.00456563 + 0.00456563i
\(304\) 2384.18 2115.69i 0.449809 0.399155i
\(305\) −2932.31 + 624.732i −0.550503 + 0.117285i
\(306\) −477.011 329.113i −0.0891141 0.0614840i
\(307\) 535.672 535.672i 0.0995844 0.0995844i −0.655559 0.755144i \(-0.727567\pi\)
0.755144 + 0.655559i \(0.227567\pi\)
\(308\) −7014.19 3153.37i −1.29763 0.583376i
\(309\) 1110.65i 0.204475i
\(310\) −1821.84 + 751.783i −0.333786 + 0.137737i
\(311\) 3579.61i 0.652672i 0.945254 + 0.326336i \(0.105814\pi\)
−0.945254 + 0.326336i \(0.894186\pi\)
\(312\) 830.522 + 1371.94i 0.150702 + 0.248945i
\(313\) 6740.52 6740.52i 1.21724 1.21724i 0.248648 0.968594i \(-0.420014\pi\)
0.968594 0.248648i \(-0.0799861\pi\)
\(314\) 3685.02 5341.01i 0.662285 0.959907i
\(315\) 1047.90 + 679.809i 0.187436 + 0.121596i
\(316\) 8768.05 3329.40i 1.56089 0.592701i
\(317\) 4163.19 + 4163.19i 0.737628 + 0.737628i 0.972118 0.234490i \(-0.0753421\pi\)
−0.234490 + 0.972118i \(0.575342\pi\)
\(318\) −1343.23 7321.32i −0.236871 1.29107i
\(319\) −11643.1 −2.04354
\(320\) −1538.87 + 5513.61i −0.268830 + 0.963188i
\(321\) 5833.86 1.01438
\(322\) −608.605 3317.21i −0.105330 0.574102i
\(323\) −1319.33 1319.33i −0.227275 0.227275i
\(324\) −6332.88 + 2404.72i −1.08588 + 0.412332i
\(325\) −555.815 + 1452.05i −0.0948648 + 0.247832i
\(326\) −3852.97 + 5584.44i −0.654590 + 0.948753i
\(327\) −3613.24 + 3613.24i −0.611049 + 0.611049i
\(328\) 1390.03 + 2296.20i 0.233999 + 0.386544i
\(329\) 3626.15i 0.607648i
\(330\) −7830.14 3255.61i −1.30617 0.543077i
\(331\) 8821.65i 1.46490i −0.680821 0.732450i \(-0.738377\pi\)
0.680821 0.732450i \(-0.261623\pi\)
\(332\) −6114.57 2748.93i −1.01078 0.454418i
\(333\) 400.457 400.457i 0.0659007 0.0659007i
\(334\) 6635.14 + 4577.90i 1.08700 + 0.749974i
\(335\) 969.099 1493.83i 0.158052 0.243631i
\(336\) −5571.87 + 4944.42i −0.904674 + 0.802798i
\(337\) 3165.30 + 3165.30i 0.511647 + 0.511647i 0.915031 0.403384i \(-0.132166\pi\)
−0.403384 + 0.915031i \(0.632166\pi\)
\(338\) 5681.63 1042.40i 0.914319 0.167749i
\(339\) 4236.55 0.678754
\(340\) 3275.29 + 706.956i 0.522435 + 0.112765i
\(341\) 2933.01 0.465781
\(342\) 757.826 139.038i 0.119820 0.0219833i
\(343\) 3881.71 + 3881.71i 0.611057 + 0.611057i
\(344\) 1874.11 7623.75i 0.293736 1.19490i
\(345\) −774.910 3637.20i −0.120927 0.567595i
\(346\) −1046.64 722.128i −0.162624 0.112202i
\(347\) −856.765 + 856.765i −0.132546 + 0.132546i −0.770267 0.637721i \(-0.779877\pi\)
0.637721 + 0.770267i \(0.279877\pi\)
\(348\) −4624.47 + 10286.4i −0.712350 + 1.58451i
\(349\) 3731.17i 0.572278i −0.958188 0.286139i \(-0.907628\pi\)
0.958188 0.286139i \(-0.0923720\pi\)
\(350\) −7099.93 1322.23i −1.08431 0.201931i
\(351\) 1526.01i 0.232058i
\(352\) 5246.88 6711.31i 0.794487 1.01623i
\(353\) −1774.39 + 1774.39i −0.267539 + 0.267539i −0.828108 0.560569i \(-0.810583\pi\)
0.560569 + 0.828108i \(0.310583\pi\)
\(354\) −3341.87 + 4843.66i −0.501747 + 0.727225i
\(355\) −1304.34 6122.17i −0.195005 0.915298i
\(356\) 1567.83 + 4128.92i 0.233413 + 0.614698i
\(357\) 3083.31 + 3083.31i 0.457104 + 0.457104i
\(358\) 1795.64 + 9787.16i 0.265091 + 1.44488i
\(359\) 10477.6 1.54036 0.770178 0.637829i \(-0.220168\pi\)
0.770178 + 0.637829i \(0.220168\pi\)
\(360\) −1008.37 + 947.461i −0.147627 + 0.138710i
\(361\) −4378.42 −0.638347
\(362\) 2434.58 + 13269.7i 0.353477 + 1.92663i
\(363\) 3560.65 + 3560.65i 0.514837 + 0.514837i
\(364\) −721.555 1900.23i −0.103901 0.273624i
\(365\) 1857.22 2862.83i 0.266333 0.410541i
\(366\) 2454.39 3557.37i 0.350528 0.508051i
\(367\) 5250.87 5250.87i 0.746848 0.746848i −0.227038 0.973886i \(-0.572904\pi\)
0.973886 + 0.227038i \(0.0729040\pi\)
\(368\) 3729.27 + 222.507i 0.528265 + 0.0315190i
\(369\) 648.801i 0.0915317i
\(370\) −1257.10 + 3023.49i −0.176632 + 0.424821i
\(371\) 9434.06i 1.32019i
\(372\) 1164.95 2591.25i 0.162365 0.361156i
\(373\) 3349.09 3349.09i 0.464904 0.464904i −0.435355 0.900259i \(-0.643377\pi\)
0.900259 + 0.435355i \(0.143377\pi\)
\(374\) −4104.40 2831.82i −0.567469 0.391523i
\(375\) −7867.18 1234.59i −1.08336 0.170011i
\(376\) −3900.66 958.879i −0.535003 0.131517i
\(377\) −2176.00 2176.00i −0.297267 0.297267i
\(378\) 6971.91 1279.13i 0.948668 0.174051i
\(379\) −1701.61 −0.230622 −0.115311 0.993329i \(-0.536787\pi\)
−0.115311 + 0.993329i \(0.536787\pi\)
\(380\) −3743.66 + 2414.46i −0.505384 + 0.325945i
\(381\) −607.798 −0.0817282
\(382\) 4808.46 882.202i 0.644037 0.118161i
\(383\) −5674.07 5674.07i −0.757001 0.757001i 0.218775 0.975775i \(-0.429794\pi\)
−0.975775 + 0.218775i \(0.929794\pi\)
\(384\) −3845.32 7301.14i −0.511017 0.970273i
\(385\) 9016.54 + 5849.35i 1.19357 + 0.774312i
\(386\) −4738.83 3269.55i −0.624871 0.431128i
\(387\) 1341.83 1341.83i 0.176251 0.176251i
\(388\) −4753.40 2136.99i −0.621951 0.279611i
\(389\) 2301.42i 0.299965i 0.988689 + 0.149983i \(0.0479218\pi\)
−0.988689 + 0.149983i \(0.952078\pi\)
\(390\) −854.942 2071.84i −0.111004 0.269004i
\(391\) 2186.80i 0.282842i
\(392\) 1437.40 870.148i 0.185203 0.112115i
\(393\) −5538.05 + 5538.05i −0.710833 + 0.710833i
\(394\) −1496.23 + 2168.62i −0.191317 + 0.277293i
\(395\) −12819.7 + 2731.25i −1.63298 + 0.347909i
\(396\) 1925.03 730.970i 0.244283 0.0927592i
\(397\) −7499.18 7499.18i −0.948043 0.948043i 0.0506721 0.998715i \(-0.483864\pi\)
−0.998715 + 0.0506721i \(0.983864\pi\)
\(398\) −336.223 1832.59i −0.0423451 0.230803i
\(399\) −5797.16 −0.727371
\(400\) 3299.79 7287.76i 0.412473 0.910970i
\(401\) −9495.99 −1.18256 −0.591280 0.806466i \(-0.701377\pi\)
−0.591280 + 0.806466i \(0.701377\pi\)
\(402\) 463.208 + 2524.72i 0.0574694 + 0.313238i
\(403\) 548.155 + 548.155i 0.0677557 + 0.0677557i
\(404\) 44.6976 16.9725i 0.00550442 0.00209014i
\(405\) 9259.24 1972.69i 1.13604 0.242034i
\(406\) 8117.58 11765.5i 0.992288 1.43821i
\(407\) 3445.70 3445.70i 0.419648 0.419648i
\(408\) −4132.06 + 2501.39i −0.501391 + 0.303523i
\(409\) 10456.4i 1.26415i 0.774909 + 0.632073i \(0.217796\pi\)
−0.774909 + 0.632073i \(0.782204\pi\)
\(410\) −1430.90 3467.60i −0.172359 0.417689i
\(411\) 16136.0i 1.93657i
\(412\) −1422.19 639.375i −0.170064 0.0764557i
\(413\) 5273.83 5273.83i 0.628349 0.628349i
\(414\) 743.276 + 512.821i 0.0882368 + 0.0608787i
\(415\) 7860.10 + 5099.12i 0.929728 + 0.603147i
\(416\) 2234.89 273.691i 0.263400 0.0322568i
\(417\) −10375.3 10375.3i −1.21842 1.21842i
\(418\) 6520.64 1196.33i 0.763002 0.139987i
\(419\) 8542.91 0.996058 0.498029 0.867160i \(-0.334057\pi\)
0.498029 + 0.867160i \(0.334057\pi\)
\(420\) 8749.02 5642.65i 1.01645 0.655555i
\(421\) −3112.71 −0.360342 −0.180171 0.983635i \(-0.557665\pi\)
−0.180171 + 0.983635i \(0.557665\pi\)
\(422\) 16195.4 2971.36i 1.86820 0.342757i
\(423\) −686.540 686.540i −0.0789142 0.0789142i
\(424\) −10148.2 2494.69i −1.16236 0.285738i
\(425\) −4373.34 1674.02i −0.499148 0.191063i
\(426\) 7427.19 + 5124.37i 0.844714 + 0.582808i
\(427\) −3873.30 + 3873.30i −0.438974 + 0.438974i
\(428\) 3358.41 7470.28i 0.379287 0.843667i
\(429\) 3335.48i 0.375381i
\(430\) −4212.23 + 10130.9i −0.472399 + 1.13618i
\(431\) 1474.93i 0.164837i −0.996598 0.0824187i \(-0.973736\pi\)
0.996598 0.0824187i \(-0.0262645\pi\)
\(432\) −467.653 + 7837.94i −0.0520832 + 0.872924i
\(433\) −6196.57 + 6196.57i −0.687733 + 0.687733i −0.961730 0.273998i \(-0.911654\pi\)
0.273998 + 0.961730i \(0.411654\pi\)
\(434\) −2044.90 + 2963.85i −0.226171 + 0.327809i
\(435\) 8578.17 13222.9i 0.945499 1.45745i
\(436\) 2546.71 + 6706.82i 0.279737 + 0.736694i
\(437\) 2055.78 + 2055.78i 0.225037 + 0.225037i
\(438\) 887.711 + 4838.48i 0.0968413 + 0.527835i
\(439\) 4661.49 0.506790 0.253395 0.967363i \(-0.418453\pi\)
0.253395 + 0.967363i \(0.418453\pi\)
\(440\) −8676.43 + 8152.34i −0.940074 + 0.883290i
\(441\) 406.144 0.0438553
\(442\) −237.835 1296.32i −0.0255942 0.139502i
\(443\) −5250.61 5250.61i −0.563124 0.563124i 0.367069 0.930194i \(-0.380361\pi\)
−0.930194 + 0.367069i \(0.880361\pi\)
\(444\) −1675.62 4412.78i −0.179102 0.471670i
\(445\) −1286.16 6036.85i −0.137011 0.643088i
\(446\) −5260.02 + 7623.80i −0.558451 + 0.809411i
\(447\) −5330.32 + 5330.32i −0.564017 + 0.564017i
\(448\) 3123.74 + 9981.17i 0.329427 + 1.05260i
\(449\) 2992.06i 0.314485i −0.987560 0.157243i \(-0.949740\pi\)
0.987560 0.157243i \(-0.0502605\pi\)
\(450\) 1594.57 1093.89i 0.167041 0.114592i
\(451\) 5582.54i 0.582864i
\(452\) 2438.88 5424.91i 0.253794 0.564527i
\(453\) −230.641 + 230.641i −0.0239215 + 0.0239215i
\(454\) −9779.05 6747.03i −1.01091 0.697475i
\(455\) 591.923 + 2778.31i 0.0609885 + 0.286262i
\(456\) 1532.97 6236.02i 0.157430 0.640413i
\(457\) 13147.8 + 13147.8i 1.34579 + 1.34579i 0.890175 + 0.455619i \(0.150582\pi\)
0.455619 + 0.890175i \(0.349418\pi\)
\(458\) −13857.8 + 2542.47i −1.41383 + 0.259393i
\(459\) 4596.08 0.467378
\(460\) −5103.54 1101.57i −0.517291 0.111655i
\(461\) 3239.67 0.327302 0.163651 0.986518i \(-0.447673\pi\)
0.163651 + 0.986518i \(0.447673\pi\)
\(462\) −15238.9 + 2795.86i −1.53458 + 0.281548i
\(463\) 1552.82 + 1552.82i 0.155865 + 0.155865i 0.780732 0.624867i \(-0.214847\pi\)
−0.624867 + 0.780732i \(0.714847\pi\)
\(464\) 10509.6 + 11843.3i 1.05150 + 1.18494i
\(465\) −2160.92 + 3330.98i −0.215506 + 0.332195i
\(466\) −5429.32 3745.94i −0.539717 0.372377i
\(467\) −6322.16 + 6322.16i −0.626456 + 0.626456i −0.947174 0.320719i \(-0.896076\pi\)
0.320719 + 0.947174i \(0.396076\pi\)
\(468\) 496.384 + 223.159i 0.0490285 + 0.0220418i
\(469\) 3253.29i 0.320305i
\(470\) 5183.44 + 2155.17i 0.508711 + 0.211512i
\(471\) 13072.6i 1.27888i
\(472\) 4278.49 + 7067.65i 0.417232 + 0.689227i
\(473\) 11545.6 11545.6i 1.12234 1.12234i
\(474\) 10730.3 15552.4i 1.03979 1.50705i
\(475\) 5685.04 2537.59i 0.549152 0.245121i
\(476\) 5723.18 2173.20i 0.551095 0.209262i
\(477\) −1786.15 1786.15i −0.171451 0.171451i
\(478\) −1824.70 9945.57i −0.174602 0.951673i
\(479\) −7141.64 −0.681232 −0.340616 0.940203i \(-0.610636\pi\)
−0.340616 + 0.940203i \(0.610636\pi\)
\(480\) 3756.26 + 10903.4i 0.357186 + 1.03682i
\(481\) 1287.94 0.122090
\(482\) −2621.06 14286.1i −0.247689 1.35003i
\(483\) −4804.40 4804.40i −0.452604 0.452604i
\(484\) 6609.20 2509.64i 0.620699 0.235691i
\(485\) 6110.36 + 3964.00i 0.572076 + 0.371126i
\(486\) −2429.43 + 3521.18i −0.226751 + 0.328650i
\(487\) −3827.76 + 3827.76i −0.356165 + 0.356165i −0.862397 0.506232i \(-0.831038\pi\)
0.506232 + 0.862397i \(0.331038\pi\)
\(488\) −3142.28 5190.75i −0.291484 0.481504i
\(489\) 13668.4i 1.26402i
\(490\) −2170.69 + 895.734i −0.200126 + 0.0825819i
\(491\) 14943.2i 1.37348i −0.726904 0.686739i \(-0.759041\pi\)
0.726904 0.686739i \(-0.240959\pi\)
\(492\) 4932.06 + 2217.31i 0.451940 + 0.203179i
\(493\) 6553.74 6553.74i 0.598713 0.598713i
\(494\) 1442.24 + 995.069i 0.131355 + 0.0906281i
\(495\) −2814.56 + 599.646i −0.255566 + 0.0544486i
\(496\) −2647.47 2983.44i −0.239667 0.270082i
\(497\) −8086.80 8086.80i −0.729865 0.729865i
\(498\) −13284.4 + 2437.27i −1.19536 + 0.219311i
\(499\) −2324.51 −0.208535 −0.104268 0.994549i \(-0.533250\pi\)
−0.104268 + 0.994549i \(0.533250\pi\)
\(500\) −6109.84 + 9363.22i −0.546481 + 0.837472i
\(501\) 16240.1 1.44821
\(502\) −18494.8 + 3393.23i −1.64435 + 0.301688i
\(503\) 4791.06 + 4791.06i 0.424697 + 0.424697i 0.886817 0.462120i \(-0.152911\pi\)
−0.462120 + 0.886817i \(0.652911\pi\)
\(504\) −603.476 + 2454.90i −0.0533352 + 0.216964i
\(505\) −65.3519 + 13.9233i −0.00575865 + 0.00122689i
\(506\) 6395.44 + 4412.52i 0.561882 + 0.387669i
\(507\) 8228.84 8228.84i 0.720820 0.720820i
\(508\) −349.895 + 778.287i −0.0305592 + 0.0679742i
\(509\) 3391.52i 0.295337i −0.989037 0.147668i \(-0.952823\pi\)
0.989037 0.147668i \(-0.0471768\pi\)
\(510\) 6240.01 2574.94i 0.541789 0.223569i
\(511\) 6234.74i 0.539743i
\(512\) −11562.8 + 720.851i −0.998062 + 0.0622215i
\(513\) −4320.71 + 4320.71i −0.371860 + 0.371860i
\(514\) −1018.26 + 1475.85i −0.0873804 + 0.126648i
\(515\) 1828.19 + 1186.01i 0.156426 + 0.101479i
\(516\) −5614.56 14786.1i −0.479007 1.26148i
\(517\) −5907.27 5907.27i −0.502517 0.502517i
\(518\) 1079.58 + 5884.27i 0.0915714 + 0.499112i
\(519\) −2561.75 −0.216664
\(520\) −3145.16 97.9491i −0.265239 0.00826029i
\(521\) −10835.4 −0.911146 −0.455573 0.890198i \(-0.650566\pi\)
−0.455573 + 0.890198i \(0.650566\pi\)
\(522\) 690.663 + 3764.47i 0.0579109 + 0.315645i
\(523\) −1210.80 1210.80i −0.101233 0.101233i 0.654676 0.755909i \(-0.272805\pi\)
−0.755909 + 0.654676i \(0.772805\pi\)
\(524\) 3903.36 + 10279.6i 0.325418 + 0.856997i
\(525\) −13286.1 + 5930.41i −1.10448 + 0.492998i
\(526\) 330.581 479.139i 0.0274030 0.0397176i
\(527\) −1650.95 + 1650.95i −0.136464 + 0.136464i
\(528\) 1022.17 17131.8i 0.0842507 1.41206i
\(529\) 8759.55i 0.719943i
\(530\) 13485.6 + 5607.04i 1.10524 + 0.459536i
\(531\) 1996.99i 0.163205i
\(532\) −3337.29 + 7423.28i −0.271973 + 0.604963i
\(533\) −1043.33 + 1043.33i −0.0847874 + 0.0847874i
\(534\) 7323.69 + 5052.96i 0.593496 + 0.409481i
\(535\) −6229.69 + 9602.83i −0.503426 + 0.776012i
\(536\) 3499.57 + 860.282i 0.282012 + 0.0693256i
\(537\) 14175.0 + 14175.0i 1.13910 + 1.13910i
\(538\) 7691.93 1411.23i 0.616399 0.113090i
\(539\) 3494.62 0.279265
\(540\) 2315.22 10726.3i 0.184502 0.854791i
\(541\) −7014.81 −0.557468 −0.278734 0.960368i \(-0.589915\pi\)
−0.278734 + 0.960368i \(0.589915\pi\)
\(542\) 17727.7 3252.47i 1.40492 0.257760i
\(543\) 19218.9 + 19218.9i 1.51890 + 1.51890i
\(544\) 824.311 + 6731.10i 0.0649670 + 0.530503i
\(545\) −2089.18 9805.98i −0.164203 0.770719i
\(546\) −3370.55 2325.50i −0.264187 0.182275i
\(547\) −10104.9 + 10104.9i −0.789860 + 0.789860i −0.981471 0.191611i \(-0.938629\pi\)
0.191611 + 0.981471i \(0.438629\pi\)
\(548\) 20662.2 + 9289.09i 1.61066 + 0.724106i
\(549\) 1466.67i 0.114018i
\(550\) 13720.3 9412.30i 1.06370 0.729712i
\(551\) 12322.2i 0.952708i
\(552\) 6438.55 3897.65i 0.496454 0.300535i
\(553\) −16933.6 + 16933.6i −1.30215 + 1.30215i
\(554\) −879.882 + 1275.29i −0.0674776 + 0.0978011i
\(555\) 1374.58 + 6451.89i 0.105131 + 0.493455i
\(556\) −19258.4 + 7312.77i −1.46895 + 0.557789i
\(557\) 1950.22 + 1950.22i 0.148355 + 0.148355i 0.777383 0.629028i \(-0.216547\pi\)
−0.629028 + 0.777383i \(0.716547\pi\)
\(558\) −173.985 948.307i −0.0131996 0.0719445i
\(559\) 4315.57 0.326528
\(560\) −2188.83 14451.5i −0.165169 1.09051i
\(561\) −10045.9 −0.756039
\(562\) −2697.25 14701.4i −0.202450 1.10346i
\(563\) −4425.60 4425.60i −0.331291 0.331291i 0.521786 0.853077i \(-0.325266\pi\)
−0.853077 + 0.521786i \(0.825266\pi\)
\(564\) −7565.23 + 2872.66i −0.564811 + 0.214470i
\(565\) −4523.99 + 6973.56i −0.336860 + 0.519257i
\(566\) 775.921 1124.61i 0.0576226 0.0835174i
\(567\) 12230.6 12230.6i 0.905884 0.905884i
\(568\) 10837.4 6560.56i 0.800577 0.484639i
\(569\) 14666.9i 1.08061i −0.841469 0.540305i \(-0.818309\pi\)
0.841469 0.540305i \(-0.181691\pi\)
\(570\) −3445.49 + 8286.82i −0.253185 + 0.608942i
\(571\) 664.054i 0.0486686i 0.999704 + 0.0243343i \(0.00774662\pi\)
−0.999704 + 0.0243343i \(0.992253\pi\)
\(572\) 4271.09 + 1920.15i 0.312208 + 0.140359i
\(573\) 6964.21 6964.21i 0.507738 0.507738i
\(574\) −5641.23 3892.15i −0.410210 0.283023i
\(575\) 6814.50 + 2608.45i 0.494234 + 0.189182i
\(576\) −2481.16 1298.32i −0.179482 0.0939178i
\(577\) 583.058 + 583.058i 0.0420676 + 0.0420676i 0.727828 0.685760i \(-0.240530\pi\)
−0.685760 + 0.727828i \(0.740530\pi\)
\(578\) −9763.63 + 1791.32i −0.702619 + 0.128909i
\(579\) −11598.7 −0.832516
\(580\) −11993.7 18596.5i −0.858643 1.33134i
\(581\) 17117.9 1.22232
\(582\) −10327.1 + 1894.71i −0.735521 + 0.134945i
\(583\) −15368.8 15368.8i −1.09178 1.09178i
\(584\) 6706.72 + 1648.68i 0.475216 + 0.116820i
\(585\) −638.088 413.950i −0.0450969 0.0292559i
\(586\) 21913.4 + 15119.1i 1.54477 + 1.06581i
\(587\) 6911.99 6911.99i 0.486011 0.486011i −0.421034 0.907045i \(-0.638333\pi\)
0.907045 + 0.421034i \(0.138333\pi\)
\(588\) 1388.01 3087.43i 0.0973482 0.216536i
\(589\) 3104.07i 0.217150i
\(590\) −4404.29 10673.2i −0.307325 0.744760i
\(591\) 5307.89i 0.369437i
\(592\) −6615.19 394.697i −0.459261 0.0274019i
\(593\) −11384.8 + 11384.8i −0.788396 + 0.788396i −0.981231 0.192835i \(-0.938232\pi\)
0.192835 + 0.981231i \(0.438232\pi\)
\(594\) −9273.96 + 13441.6i −0.640598 + 0.928474i
\(595\) −8367.80 + 1782.77i −0.576549 + 0.122834i
\(596\) 3756.95 + 9894.02i 0.258206 + 0.679991i
\(597\) −2654.19 2654.19i −0.181957 0.181957i
\(598\) 370.592 + 2019.92i 0.0253422 + 0.138128i
\(599\) −25321.6 −1.72723 −0.863616 0.504151i \(-0.831806\pi\)
−0.863616 + 0.504151i \(0.831806\pi\)
\(600\) −2866.06 15860.0i −0.195010 1.07914i
\(601\) 27777.8 1.88533 0.942663 0.333746i \(-0.108313\pi\)
0.942663 + 0.333746i \(0.108313\pi\)
\(602\) 3617.39 + 19716.6i 0.244907 + 1.33487i
\(603\) 615.947 + 615.947i 0.0415975 + 0.0415975i
\(604\) 162.562 + 428.110i 0.0109512 + 0.0288403i
\(605\) −9663.25 + 2058.77i −0.649367 + 0.138348i
\(606\) 54.7007 79.2825i 0.00366677 0.00531457i
\(607\) 19575.7 19575.7i 1.30898 1.30898i 0.386833 0.922150i \(-0.373569\pi\)
0.922150 0.386833i \(-0.126431\pi\)
\(608\) −7102.74 5552.89i −0.473773 0.370394i
\(609\) 28797.2i 1.91613i
\(610\) 3234.67 + 7838.79i 0.214702 + 0.520300i
\(611\) 2208.04i 0.146199i
\(612\) −672.118 + 1495.02i −0.0443934 + 0.0987463i
\(613\) −12841.3 + 12841.3i −0.846091 + 0.846091i −0.989643 0.143552i \(-0.954147\pi\)
0.143552 + 0.989643i \(0.454147\pi\)
\(614\) −1763.65 1216.82i −0.115920 0.0799788i
\(615\) −6340.02 4112.99i −0.415698 0.269678i
\(616\) −5192.55 + 21122.9i −0.339633 + 1.38160i
\(617\) 15254.6 + 15254.6i 0.995346 + 0.995346i 0.999989 0.00464336i \(-0.00147803\pi\)
−0.00464336 + 0.999989i \(0.501478\pi\)
\(618\) −3089.83 + 566.887i −0.201118 + 0.0368989i
\(619\) 13042.3 0.846874 0.423437 0.905926i \(-0.360824\pi\)
0.423437 + 0.905926i \(0.360824\pi\)
\(620\) 3021.34 + 4684.63i 0.195709 + 0.303451i
\(621\) −7161.58 −0.462776
\(622\) 9958.45 1827.07i 0.641957 0.117779i
\(623\) −7974.11 7974.11i −0.512803 0.512803i
\(624\) 3392.83 3010.76i 0.217663 0.193152i
\(625\) 10433.2 11631.4i 0.667723 0.744410i
\(626\) −22192.5 15311.7i −1.41692 0.977599i
\(627\) 9444.01 9444.01i 0.601527 0.601527i
\(628\) −16739.5 7525.59i −1.06366 0.478191i
\(629\) 3879.07i 0.245896i
\(630\) 1356.37 3262.23i 0.0857760 0.206302i
\(631\) 6843.39i 0.431745i 0.976422 + 0.215872i \(0.0692595\pi\)
−0.976422 + 0.215872i \(0.930740\pi\)
\(632\) −13737.7 22693.3i −0.864644 1.42831i
\(633\) 23456.3 23456.3i 1.47283 1.47283i
\(634\) 9457.04 13706.9i 0.592409 0.858629i
\(635\) 649.038 1000.47i 0.0405611 0.0625233i
\(636\) −19682.3 + 7473.74i −1.22713 + 0.465964i
\(637\) 653.116 + 653.116i 0.0406239 + 0.0406239i
\(638\) 5942.74 + 32391.0i 0.368770 + 2.00999i
\(639\) 3062.15 0.189573
\(640\) 16124.3 + 1466.94i 0.995887 + 0.0906029i
\(641\) −2449.97 −0.150964 −0.0754820 0.997147i \(-0.524050\pi\)
−0.0754820 + 0.997147i \(0.524050\pi\)
\(642\) −2977.66 16229.8i −0.183051 0.997723i
\(643\) 22279.7 + 22279.7i 1.36645 + 1.36645i 0.865448 + 0.500999i \(0.167034\pi\)
0.500999 + 0.865448i \(0.332966\pi\)
\(644\) −8917.82 + 3386.27i −0.545670 + 0.207201i
\(645\) 4605.87 + 21618.6i 0.281172 + 1.31974i
\(646\) −2996.98 + 4343.78i −0.182530 + 0.264557i
\(647\) −5040.77 + 5040.77i −0.306295 + 0.306295i −0.843471 0.537175i \(-0.819491\pi\)
0.537175 + 0.843471i \(0.319491\pi\)
\(648\) 9922.27 + 16390.6i 0.601518 + 0.993650i
\(649\) 17182.9i 1.03927i
\(650\) 4323.29 + 805.132i 0.260882 + 0.0485844i
\(651\) 7254.29i 0.436740i
\(652\) 17502.5 + 7868.58i 1.05130 + 0.472634i
\(653\) −4532.72 + 4532.72i −0.271637 + 0.271637i −0.829759 0.558122i \(-0.811522\pi\)
0.558122 + 0.829759i \(0.311522\pi\)
\(654\) 11896.3 + 8207.79i 0.711285 + 0.490749i
\(655\) −3202.10 15029.7i −0.191017 0.896579i
\(656\) 5678.53 5039.06i 0.337972 0.299912i
\(657\) 1180.43 + 1180.43i 0.0700956 + 0.0700956i
\(658\) 10087.9 1850.82i 0.597672 0.109654i
\(659\) −12951.7 −0.765595 −0.382797 0.923832i \(-0.625039\pi\)
−0.382797 + 0.923832i \(0.625039\pi\)
\(660\) −5060.50 + 23445.1i −0.298454 + 1.38273i
\(661\) 6827.08 0.401729 0.200864 0.979619i \(-0.435625\pi\)
0.200864 + 0.979619i \(0.435625\pi\)
\(662\) −24541.8 + 4502.65i −1.44085 + 0.264351i
\(663\) −1877.49 1877.49i −0.109979 0.109979i
\(664\) −4526.56 + 18413.8i −0.264555 + 1.07619i
\(665\) 6190.50 9542.42i 0.360988 0.556450i
\(666\) −1318.47 909.673i −0.0767110 0.0529266i
\(667\) −10212.0 + 10212.0i −0.592819 + 0.592819i
\(668\) 9349.04 20795.5i 0.541505 1.20449i
\(669\) 18660.0i 1.07838i
\(670\) −4650.46 1933.56i −0.268153 0.111493i
\(671\) 12619.8i 0.726052i
\(672\) 16599.3 + 12977.2i 0.952873 + 0.744952i
\(673\) 9731.89 9731.89i 0.557410 0.557410i −0.371159 0.928569i \(-0.621040\pi\)
0.928569 + 0.371159i \(0.121040\pi\)
\(674\) 7190.25 10421.5i 0.410917 0.595578i
\(675\) −5482.27 + 14322.3i −0.312611 + 0.816690i
\(676\) −5799.91 15274.2i −0.329990 0.869037i
\(677\) −7885.88 7885.88i −0.447679 0.447679i 0.446903 0.894582i \(-0.352527\pi\)
−0.894582 + 0.446903i \(0.852527\pi\)
\(678\) −2162.37 11786.0i −0.122486 0.667611i
\(679\) 13307.3 0.752115
\(680\) 295.006 9472.68i 0.0166367 0.534207i
\(681\) −23935.1 −1.34684
\(682\) −1497.03 8159.61i −0.0840534 0.458134i
\(683\) 15861.8 + 15861.8i 0.888629 + 0.888629i 0.994391 0.105763i \(-0.0337284\pi\)
−0.105763 + 0.994391i \(0.533728\pi\)
\(684\) −773.603 2037.30i −0.0432448 0.113886i
\(685\) −26560.6 17230.8i −1.48150 0.961102i
\(686\) 8817.63 12780.1i 0.490756 0.711295i
\(687\) −20070.6 + 20070.6i −1.11462 + 1.11462i
\(688\) −22165.8 1322.53i −1.22829 0.0732861i
\(689\) 5744.60i 0.317637i
\(690\) −9723.15 + 4012.26i −0.536455 + 0.221368i
\(691\) 30100.7i 1.65714i −0.559883 0.828572i \(-0.689154\pi\)
0.559883 0.828572i \(-0.310846\pi\)
\(692\) −1474.74 + 3280.33i −0.0810132 + 0.180201i
\(693\) −3717.77 + 3717.77i −0.203790 + 0.203790i
\(694\) 2820.81 + 1946.21i 0.154289 + 0.106451i
\(695\) 28157.5 5998.98i 1.53680 0.327416i
\(696\) 30977.2 + 7614.96i 1.68705 + 0.414719i
\(697\) −3142.34 3142.34i −0.170767 0.170767i
\(698\) −10380.1 + 1904.43i −0.562883 + 0.103272i
\(699\) −13288.8 −0.719066
\(700\) −54.5587 + 20426.8i −0.00294590 + 1.10294i
\(701\) −20267.4 −1.09199 −0.545997 0.837787i \(-0.683849\pi\)
−0.545997 + 0.837787i \(0.683849\pi\)
\(702\) −4245.34 + 778.888i −0.228248 + 0.0418764i
\(703\) −3646.66 3646.66i −0.195642 0.195642i
\(704\) −21348.9 11171.3i −1.14292 0.598058i
\(705\) 11061.0 2356.57i 0.590898 0.125892i
\(706\) 5842.01 + 4030.68i 0.311426 + 0.214868i
\(707\) −86.3236 + 86.3236i −0.00459199 + 0.00459199i
\(708\) 15180.8 + 6824.81i 0.805830 + 0.362277i
\(709\) 18499.1i 0.979900i 0.871750 + 0.489950i \(0.162985\pi\)
−0.871750 + 0.489950i \(0.837015\pi\)
\(710\) −16366.1 + 6753.46i −0.865082 + 0.356976i
\(711\) 6412.08i 0.338216i
\(712\) 10686.4 6469.13i 0.562485 0.340507i
\(713\) 2572.50 2572.50i 0.135120 0.135120i
\(714\) 7004.00 10151.5i 0.367112 0.532088i
\(715\) −5490.36 3561.79i −0.287172 0.186298i
\(716\) 26311.3 9990.91i 1.37332 0.521478i
\(717\) −14404.4 14404.4i −0.750269 0.750269i
\(718\) −5347.87 29148.7i −0.277968 1.51507i
\(719\) 25990.9 1.34812 0.674060 0.738676i \(-0.264549\pi\)
0.674060 + 0.738676i \(0.264549\pi\)
\(720\) 3150.51 + 2321.69i 0.163073 + 0.120173i
\(721\) 3981.47 0.205656
\(722\) 2234.79 + 12180.7i 0.115194 + 0.627867i
\(723\) −20691.0 20691.0i −1.06432 1.06432i
\(724\) 35673.6 13546.0i 1.83122 0.695348i
\(725\) 12605.4 + 28240.2i 0.645727 + 1.44664i
\(726\) 8088.31 11723.1i 0.413479 0.599290i
\(727\) −23543.5 + 23543.5i −1.20107 + 1.20107i −0.227232 + 0.973841i \(0.572967\pi\)
−0.973841 + 0.227232i \(0.927033\pi\)
\(728\) −4918.15 + 2977.26i −0.250383 + 0.151572i
\(729\) 14244.1i 0.723674i
\(730\) −8912.33 3705.56i −0.451863 0.187875i
\(731\) 12997.8i 0.657646i
\(732\) −11149.3 5012.40i −0.562965 0.253092i
\(733\) 16546.7 16546.7i 0.833789 0.833789i −0.154244 0.988033i \(-0.549294\pi\)
0.988033 + 0.154244i \(0.0492942\pi\)
\(734\) −17288.0 11927.8i −0.869361 0.599813i
\(735\) −2574.70 + 3968.80i −0.129210 + 0.199172i
\(736\) −1284.44 10488.4i −0.0643274 0.525280i
\(737\) 5299.85 + 5299.85i 0.264888 + 0.264888i
\(738\) 1804.96 331.154i 0.0900291 0.0165175i
\(739\) 8124.95 0.404440 0.202220 0.979340i \(-0.435184\pi\)
0.202220 + 0.979340i \(0.435184\pi\)
\(740\) 9052.97 + 1954.04i 0.449721 + 0.0970701i
\(741\) 3530.01 0.175004
\(742\) 26245.5 4815.23i 1.29852 0.238238i
\(743\) 5222.62 + 5222.62i 0.257873 + 0.257873i 0.824188 0.566316i \(-0.191632\pi\)
−0.566316 + 0.824188i \(0.691632\pi\)
\(744\) −7803.45 1918.28i −0.384527 0.0945264i
\(745\) −3081.99 14465.9i −0.151564 0.711398i
\(746\) −11026.5 7607.73i −0.541167 0.373376i
\(747\) −3240.94 + 3240.94i −0.158741 + 0.158741i
\(748\) −5783.17 + 12863.8i −0.282692 + 0.628806i
\(749\) 20913.3i 1.02023i
\(750\) 580.852 + 22516.6i 0.0282796 + 1.09625i
\(751\) 27086.9i 1.31613i 0.752961 + 0.658066i \(0.228625\pi\)
−0.752961 + 0.658066i \(0.771375\pi\)
\(752\) −676.664 + 11341.0i −0.0328130 + 0.549953i
\(753\) −26786.5 + 26786.5i −1.29636 + 1.29636i
\(754\) −4942.97 + 7164.27i −0.238743 + 0.346031i
\(755\) −133.356 625.936i −0.00642826 0.0301724i
\(756\) −7117.05 18742.9i −0.342387 0.901685i
\(757\) −11094.6 11094.6i −0.532684 0.532684i 0.388686 0.921370i \(-0.372929\pi\)
−0.921370 + 0.388686i \(0.872929\pi\)
\(758\) 868.517 + 4733.87i 0.0416174 + 0.226836i
\(759\) 15653.4 0.748595
\(760\) 8627.81 + 9182.47i 0.411794 + 0.438268i
\(761\) −8006.53 −0.381388 −0.190694 0.981649i \(-0.561074\pi\)
−0.190694 + 0.981649i \(0.561074\pi\)
\(762\) 310.226 + 1690.89i 0.0147484 + 0.0803865i
\(763\) −12952.8 12952.8i −0.614576 0.614576i
\(764\) −4908.56 12926.8i −0.232442 0.612141i
\(765\) 1246.75 1921.81i 0.0589231 0.0908277i
\(766\) −12889.1 + 18681.3i −0.607967 + 0.881179i
\(767\) −3211.35 + 3211.35i −0.151180 + 0.151180i
\(768\) −18349.0 + 14424.2i −0.862128 + 0.677720i
\(769\) 5515.54i 0.258642i −0.991603 0.129321i \(-0.958720\pi\)
0.991603 0.129321i \(-0.0412797\pi\)
\(770\) 11670.7 28069.5i 0.546212 1.31371i
\(771\) 3612.28i