Properties

Label 20.4.e.b.7.1
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 7.1
Root \(-1.13579 + 1.64620i\)
Character \(\chi\) = 20.7
Dual form 20.4.e.b.3.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.78199 - 0.510409i) q^{2} +(4.02923 + 4.02923i) q^{3} +(7.47897 + 2.83991i) q^{4} +(10.9349 - 2.32970i) q^{5} +(-9.15273 - 13.2658i) q^{6} +(-14.4440 + 14.4440i) q^{7} +(-19.3569 - 11.7179i) q^{8} +5.46937i q^{9} +O(q^{10})\) \(q+(-2.78199 - 0.510409i) 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} +(-19.3569 - 11.7179i) q^{8} +5.46937i q^{9} +(-31.6100 + 0.899920i) q^{10} -47.0607i q^{11} +(18.6918 + 41.5771i) 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} +(2.79162 - 15.2157i) q^{18} -49.8054 q^{19} +(88.3980 + 13.6304i) q^{20} -116.396 q^{21} +(-24.0202 + 130.922i) 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} +(-149.046 + 67.0065i) q^{28} +247.406i q^{29} +(-130.990 - 123.738i) q^{30} +62.3240i q^{31} +(-111.492 - 142.610i) 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} +(138.558 + 25.4211i) q^{38} -70.8761 q^{39} +(-238.966 - 83.0389i) q^{40} +118.624 q^{41} +(323.814 + 59.4097i) 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} +(21.7203 + 364.037i) q^{48} -74.2578i q^{49} +(-343.556 + 83.4822i) q^{50} -213.467i q^{51} +(-90.7571 + 40.8017i) 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} +(126.278 - 688.282i) q^{58} -365.123 q^{59} +(301.256 + 411.096i) q^{60} -268.160 q^{61} +(31.8107 - 173.385i) 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} +(-122.888 - 273.345i) q^{68} -332.623i q^{69} +(443.576 - 469.573i) q^{70} +559.873i q^{71} +(64.0897 - 105.870i) 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} +(197.177 + 36.1758i) q^{78} +1172.36 q^{79} +(622.417 + 352.984i) q^{80} +846.759 q^{81} +(-330.012 - 60.5470i) 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} +(-551.454 + 910.949i) q^{88} -552.071i q^{89} +(-4.92200 - 172.887i) q^{90} -254.077i q^{91} +(-191.483 - 425.924i) 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} +(-37.9019 + 206.585i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78199 0.510409i −0.983583 0.180457i
\(3\) 4.02923 + 4.02923i 0.775425 + 0.775425i 0.979049 0.203624i \(-0.0652719\pi\)
−0.203624 + 0.979049i \(0.565272\pi\)
\(4\) 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 −0.979814 0.199912i \(-0.935934\pi\)
0.199912 + 0.979814i \(0.435934\pi\)
\(8\) −19.3569 11.7179i −0.855463 0.517864i
\(9\) 5.46937i 0.202569i
\(10\) −31.6100 + 0.899920i −0.999595 + 0.0284580i
\(11\) 47.0607i 1.28994i −0.764209 0.644969i \(-0.776870\pi\)
0.764209 0.644969i \(-0.223130\pi\)
\(12\) 18.6918 + 41.5771i 0.449655 + 1.00019i
\(13\) −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 \(0.836109\pi\)
\(18\) 2.79162 15.2157i 0.0365550 0.199244i
\(19\) −49.8054 −0.601376 −0.300688 0.953723i \(-0.597216\pi\)
−0.300688 + 0.953723i \(0.597216\pi\)
\(20\) 88.3980 + 13.6304i 0.988320 + 0.152393i
\(21\) −116.396 −1.20951
\(22\) −24.0202 + 130.922i −0.232778 + 1.26876i
\(23\) −41.2762 41.2762i −0.374204 0.374204i 0.494802 0.869006i \(-0.335241\pi\)
−0.869006 + 0.494802i \(0.835241\pi\)
\(24\) −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
\(28\) −149.046 + 67.0065i −1.00596 + 0.452251i
\(29\) 247.406i 1.58421i 0.610382 + 0.792107i \(0.291016\pi\)
−0.610382 + 0.792107i \(0.708984\pi\)
\(30\) −130.990 123.738i −0.797178 0.753044i
\(31\) 62.3240i 0.361088i 0.983567 + 0.180544i \(0.0577858\pi\)
−0.983567 + 0.180544i \(0.942214\pi\)
\(32\) −111.492 142.610i −0.615911 0.787816i
\(33\) 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 \(0.823885\pi\)
\(38\) 138.558 + 25.4211i 0.591503 + 0.108522i
\(39\) −70.8761 −0.291007
\(40\) −238.966 83.0389i −0.944594 0.328240i
\(41\) 118.624 0.451854 0.225927 0.974144i \(-0.427459\pi\)
0.225927 + 0.974144i \(0.427459\pi\)
\(42\) 323.814 + 59.4097i 1.18966 + 0.218265i
\(43\) 245.335 + 245.335i 0.870076 + 0.870076i 0.992480 0.122404i \(-0.0390605\pi\)
−0.122404 + 0.992480i \(0.539060\pi\)
\(44\) 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 −0.484966 0.874533i \(-0.661168\pi\)
0.874533 + 0.484966i \(0.161168\pi\)
\(48\) 21.7203 + 364.037i 0.0653138 + 1.09467i
\(49\) 74.2578i 0.216495i
\(50\) −343.556 + 83.4822i −0.971723 + 0.236123i
\(51\) 213.467i 0.586105i
\(52\) −90.7571 + 40.8017i −0.242033 + 0.108811i
\(53\) −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
\(58\) 126.278 688.282i 0.285882 1.55821i
\(59\) −365.123 −0.805677 −0.402839 0.915271i \(-0.631976\pi\)
−0.402839 + 0.915271i \(0.631976\pi\)
\(60\) 301.256 + 411.096i 0.648199 + 0.884538i
\(61\) −268.160 −0.562858 −0.281429 0.959582i \(-0.590808\pi\)
−0.281429 + 0.959582i \(0.590808\pi\)
\(62\) 31.8107 173.385i 0.0651608 0.355160i
\(63\) −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 −0.802287 0.596938i \(-0.796384\pi\)
0.596938 + 0.802287i \(0.296384\pi\)
\(68\) −122.888 273.345i −0.219152 0.487469i
\(69\) 332.623i 0.580334i
\(70\) 443.576 469.573i 0.757392 0.801781i
\(71\) 559.873i 0.935841i 0.883771 + 0.467921i \(0.154997\pi\)
−0.883771 + 0.467921i \(0.845003\pi\)
\(72\) 64.0897 105.870i 0.104903 0.173290i
\(73\) 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
\(78\) 197.177 + 36.1758i 0.286229 + 0.0525142i
\(79\) 1172.36 1.66963 0.834816 0.550528i \(-0.185574\pi\)
0.834816 + 0.550528i \(0.185574\pi\)
\(80\) 622.417 + 352.984i 0.869854 + 0.493310i
\(81\) 846.759 1.16153
\(82\) −330.012 60.5470i −0.444436 0.0815402i
\(83\) −592.561 592.561i −0.783639 0.783639i 0.196804 0.980443i \(-0.436944\pi\)
−0.980443 + 0.196804i \(0.936944\pi\)
\(84\) −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
\(88\) −551.454 + 910.949i −0.668013 + 1.10349i
\(89\) 552.071i 0.657522i −0.944413 0.328761i \(-0.893369\pi\)
0.944413 0.328761i \(-0.106631\pi\)
\(90\) −4.92200 172.887i −0.00576471 0.202487i
\(91\) 254.077i 0.292687i
\(92\) −191.483 425.924i −0.216994 0.482670i
\(93\) −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 \(0.639249\pi\)
\(98\) −37.9019 + 206.585i −0.0390680 + 0.212941i
\(99\) 257.392 0.261302
\(100\) 998.380 56.8929i 0.998380 0.0568929i
\(101\) −5.97644 −0.00588790 −0.00294395 0.999996i \(-0.500937\pi\)
−0.00294395 + 0.999996i \(0.500937\pi\)
\(102\) −108.955 + 593.863i −0.105767 + 0.576483i
\(103\) −137.824 137.824i −0.131847 0.131847i 0.638104 0.769951i \(-0.279719\pi\)
−0.769951 + 0.638104i \(0.779719\pi\)
\(104\) 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 −0.299895 0.953972i \(-0.596952\pi\)
0.953972 + 0.299895i \(0.0969518\pi\)
\(108\) 895.181 402.447i 0.797582 0.358569i
\(109\) 896.758i 0.788017i −0.919107 0.394009i \(-0.871088\pi\)
0.919107 0.394009i \(-0.128912\pi\)
\(110\) 42.3508 + 1487.59i 0.0367090 + 1.28942i
\(111\) 590.026i 0.504530i
\(112\) −1305.00 + 77.8631i −1.10099 + 0.0656908i
\(113\) −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
\(118\) 1015.77 + 186.362i 0.792450 + 0.145390i
\(119\) 765.237 0.589488
\(120\) −628.264 1297.43i −0.477937 0.986988i
\(121\) −883.705 −0.663941
\(122\) 746.019 + 136.871i 0.553618 + 0.101572i
\(123\) 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 −0.732965 0.680266i \(-0.761864\pi\)
0.680266 + 0.732965i \(0.261864\pi\)
\(128\) −428.844 1383.20i −0.296132 0.955147i
\(129\) 1977.02i 1.34936i
\(130\) 270.103 285.933i 0.182227 0.192907i
\(131\) 1374.47i 0.916701i 0.888771 + 0.458351i \(0.151560\pi\)
−0.888771 + 0.458351i \(0.848440\pi\)
\(132\) 1956.65 879.649i 1.29018 0.580028i
\(133\) 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 \(-0.594462\pi\)
\(138\) −169.774 + 925.354i −0.104725 + 0.570807i
\(139\) −2575.00 −1.57129 −0.785643 0.618679i \(-0.787668\pi\)
−0.785643 + 0.618679i \(0.787668\pi\)
\(140\) −1473.70 + 1079.94i −0.889645 + 0.651941i
\(141\) 1011.53 0.604160
\(142\) 285.764 1557.56i 0.168879 0.920477i
\(143\) 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
\(148\) −339.663 755.529i −0.188650 0.419623i
\(149\) 1322.91i 0.727364i −0.931523 0.363682i \(-0.881519\pi\)
0.931523 0.363682i \(-0.118481\pi\)
\(150\) −1720.63 1047.90i −0.936595 0.570403i
\(151\) 57.2419i 0.0308495i 0.999881 + 0.0154248i \(0.00491005\pi\)
−0.999881 + 0.0154248i \(0.995090\pi\)
\(152\) 964.079 + 583.616i 0.514455 + 0.311431i
\(153\) 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 \(0.551838\pi\)
\(158\) −3261.50 598.384i −1.64222 0.301297i
\(159\) −2631.68 −1.31262
\(160\) −1551.39 1299.69i −0.766552 0.642182i
\(161\) 1192.39 0.583685
\(162\) −2355.68 432.193i −1.14247 0.209607i
\(163\) 1696.16 + 1696.16i 0.815052 + 0.815052i 0.985386 0.170334i \(-0.0544847\pi\)
−0.170334 + 0.985386i \(0.554485\pi\)
\(164\) 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 −0.0641235 0.997942i \(-0.520425\pi\)
0.997942 + 0.0641235i \(0.0204251\pi\)
\(168\) 2253.07 + 1363.92i 1.03469 + 0.626363i
\(169\) 2042.29i 0.929580i
\(170\) 861.180 + 813.503i 0.388526 + 0.367017i
\(171\) 272.404i 0.121820i
\(172\) 1138.12 + 2531.58i 0.504542 + 1.12228i
\(173\) 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
\(178\) −281.782 + 1535.86i −0.118654 + 0.646727i
\(179\) 3518.04 1.46900 0.734499 0.678610i \(-0.237417\pi\)
0.734499 + 0.678610i \(0.237417\pi\)
\(180\) −74.5499 + 483.481i −0.0308701 + 0.200203i
\(181\) −4769.86 −1.95879 −0.979395 0.201955i \(-0.935271\pi\)
−0.979395 + 0.201955i \(0.935271\pi\)
\(182\) −129.683 + 706.840i −0.0528174 + 0.287882i
\(183\) −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
\(188\) 1295.27 582.316i 0.502486 0.225903i
\(189\) 2506.09i 0.964502i
\(190\) 1574.35 44.8209i 0.601132 0.0171139i
\(191\) 1728.42i 0.654787i −0.944888 0.327393i \(-0.893830\pi\)
0.944888 0.327393i \(-0.106170\pi\)
\(192\) −871.385 + 2784.30i −0.327536 + 1.04656i
\(193\) 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 \(0.803874\pi\)
\(198\) −716.063 131.375i −0.257012 0.0471537i
\(199\) −658.733 −0.234655 −0.117327 0.993093i \(-0.537433\pi\)
−0.117327 + 0.993093i \(0.537433\pi\)
\(200\) −2806.53 351.307i −0.992256 0.124206i
\(201\) −907.523 −0.318466
\(202\) 16.6264 + 3.05043i 0.00579124 + 0.00106251i
\(203\) −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
\(208\) −794.642 + 47.4125i −0.264897 + 0.0158051i
\(209\) 2343.87i 0.775738i
\(210\) 3679.28 104.747i 1.20902 0.0344203i
\(211\) 5821.53i 1.89939i −0.313182 0.949693i \(-0.601395\pi\)
0.313182 0.949693i \(-0.398605\pi\)
\(212\) −3369.88 + 1515.00i −1.09172 + 0.490803i
\(213\) −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
\(218\) −457.714 + 2494.77i −0.142203 + 0.775080i
\(219\) 1739.22 0.536645
\(220\) 641.457 4160.07i 0.196578 1.27487i
\(221\) 465.969 0.141830
\(222\) −301.155 + 1641.45i −0.0910458 + 0.496247i
\(223\) 2315.57 + 2315.57i 0.695347 + 0.695347i 0.963403 0.268056i \(-0.0863814\pi\)
−0.268056 + 0.963403i \(0.586381\pi\)
\(224\) 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 −0.992301 0.123851i \(-0.960476\pi\)
0.123851 + 0.992301i \(0.460476\pi\)
\(228\) −930.954 2070.76i −0.270412 0.601490i
\(229\) 4981.25i 1.43742i −0.695308 0.718712i \(-0.744732\pi\)
0.695308 0.718712i \(-0.255268\pi\)
\(230\) 1341.89 + 1267.59i 0.384701 + 0.363403i
\(231\) 5477.69i 1.56020i
\(232\) 2899.09 4789.02i 0.820408 1.35524i
\(233\) 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
\(238\) −2128.88 390.584i −0.579811 0.106377i
\(239\) −3574.98 −0.967558 −0.483779 0.875190i \(-0.660736\pi\)
−0.483779 + 0.875190i \(0.660736\pi\)
\(240\) 1085.61 + 3930.11i 0.291982 + 1.05703i
\(241\) 5135.22 1.37257 0.686283 0.727334i \(-0.259241\pi\)
0.686283 + 0.727334i \(0.259241\pi\)
\(242\) 2458.46 + 451.051i 0.653041 + 0.119813i
\(243\) 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
\(248\) 730.309 1206.40i 0.186995 0.308897i
\(249\) 4775.13i 1.21531i
\(250\) −3562.27 + 1713.25i −0.901191 + 0.433423i
\(251\) 6648.06i 1.67180i 0.548882 + 0.835900i \(0.315054\pi\)
−0.548882 + 0.835900i \(0.684946\pi\)
\(252\) −366.483 815.186i −0.0916122 0.203777i
\(253\) −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 \(0.774513\pi\)
\(258\) 1009.09 5500.06i 0.243501 1.32721i
\(259\) 2115.13 0.507442
\(260\) −897.366 + 657.600i −0.214047 + 0.156856i
\(261\) −1353.16 −0.320913
\(262\) 701.541 3823.76i 0.165425 0.901652i
\(263\) −145.529 145.529i −0.0341205 0.0341205i 0.689841 0.723961i \(-0.257681\pi\)
−0.723961 + 0.689841i \(0.757681\pi\)
\(264\) −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
\(268\) −1162.09 + 522.439i −0.264872 + 0.119078i
\(269\) 2764.90i 0.626687i 0.949640 + 0.313344i \(0.101449\pi\)
−0.949640 + 0.313344i \(0.898551\pi\)
\(270\) −2664.15 + 2820.29i −0.600501 + 0.635695i
\(271\) 6372.29i 1.42837i −0.699955 0.714187i \(-0.746797\pi\)
0.699955 0.714187i \(-0.253203\pi\)
\(272\) −142.798 2393.33i −0.0318324 0.533517i
\(273\) 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 \(0.768922\pi\)
\(278\) 7163.64 + 1314.30i 1.54549 + 0.283549i
\(279\) −340.873 −0.0731453
\(280\) 4651.03 2252.20i 0.992687 0.480696i
\(281\) 5284.49 1.12187 0.560936 0.827859i \(-0.310441\pi\)
0.560936 + 0.827859i \(0.310441\pi\)
\(282\) −2814.08 516.296i −0.594241 0.109025i
\(283\) −341.577 341.577i −0.0717479 0.0717479i 0.670322 0.742070i \(-0.266156\pi\)
−0.742070 + 0.670322i \(0.766156\pi\)
\(284\) −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
\(288\) 779.986 609.790i 0.159587 0.124765i
\(289\) 3509.58i 0.714346i
\(290\) −222.646 7820.51i −0.0450835 1.58357i
\(291\) 3712.13i 0.747798i
\(292\) 2227.07 1001.22i 0.446333 0.200658i
\(293\) −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
\(298\) −675.227 + 3680.33i −0.131258 + 0.715423i
\(299\) 726.069 0.140434
\(300\) 4251.94 + 3793.47i 0.818286 + 0.730053i
\(301\) −7087.24 −1.35715
\(302\) 29.2168 159.247i 0.00556701 0.0303431i
\(303\) −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 −0.755144 0.655559i \(-0.772433\pi\)
0.655559 + 0.755144i \(0.272433\pi\)
\(308\) 3153.37 + 7014.19i 0.583376 + 1.29763i
\(309\) 1110.65i 0.204475i
\(310\) −56.0867 1970.06i −0.0102758 0.360942i
\(311\) 3579.61i 0.652672i −0.945254 0.326336i \(-0.894186\pi\)
0.945254 0.326336i \(-0.105814\pi\)
\(312\) 1371.94 + 830.522i 0.248945 + 0.150702i
\(313\) 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 \(0.575342\pi\)
\(318\) 7321.32 + 1343.23i 1.29107 + 0.236871i
\(319\) 11643.1 2.04354
\(320\) 3652.59 + 4407.56i 0.638081 + 0.769969i
\(321\) 5833.86 1.01438
\(322\) −3317.21 608.605i −0.574102 0.105330i
\(323\) 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
\(328\) −2296.20 1390.03i −0.386544 0.233999i
\(329\) 3626.15i 0.607648i
\(330\) −5823.18 + 6164.46i −0.971381 + 1.02831i
\(331\) 8821.65i 1.46490i 0.680821 + 0.732450i \(0.261623\pi\)
−0.680821 + 0.732450i \(0.738377\pi\)
\(332\) −2748.93 6114.57i −0.454418 1.01078i
\(333\) 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 \(0.632166\pi\)
\(338\) 1042.40 5681.63i 0.167749 0.914319i
\(339\) −4236.55 −0.678754
\(340\) −1980.58 2702.71i −0.315917 0.431103i
\(341\) 2933.01 0.465781
\(342\) −139.038 + 757.826i −0.0219833 + 0.119820i
\(343\) −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 −0.637721 0.770267i \(-0.720123\pi\)
0.770267 + 0.637721i \(0.220123\pi\)
\(348\) −10286.4 + 4624.47i −1.58451 + 0.712350i
\(349\) 3731.17i 0.572278i −0.958188 0.286139i \(-0.907628\pi\)
0.958188 0.286139i \(-0.0923720\pi\)
\(350\) 3756.50 6168.14i 0.573696 0.942002i
\(351\) 1526.01i 0.232058i
\(352\) −6711.31 + 5246.88i −1.01623 + 0.794487i
\(353\) −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
\(358\) −9787.16 1795.64i −1.44488 0.265091i
\(359\) −10477.6 −1.54036 −0.770178 0.637829i \(-0.779832\pi\)
−0.770178 + 0.637829i \(0.779832\pi\)
\(360\) 454.171 1306.99i 0.0664914 0.191346i
\(361\) −4378.42 −0.638347
\(362\) 13269.7 + 2434.58i 1.92663 + 0.353477i
\(363\) −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 −0.973886 0.227038i \(-0.927096\pi\)
0.227038 + 0.973886i \(0.427096\pi\)
\(368\) −222.507 3729.27i −0.0315190 0.528265i
\(369\) 648.801i 0.0915317i
\(370\) 2380.32 + 2248.53i 0.334451 + 0.315935i
\(371\) 9434.06i 1.32019i
\(372\) −2591.25 + 1164.95i −0.361156 + 0.162365i
\(373\) 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
\(378\) 1279.13 6971.91i 0.174051 0.948668i
\(379\) 1701.61 0.230622 0.115311 0.993329i \(-0.463213\pi\)
0.115311 + 0.993329i \(0.463213\pi\)
\(380\) −4402.70 678.870i −0.594352 0.0916454i
\(381\) −607.798 −0.0817282
\(382\) −882.202 + 4808.46i −0.118161 + 0.644037i
\(383\) 5674.07 + 5674.07i 0.757001 + 0.757001i 0.975775 0.218775i \(-0.0702060\pi\)
−0.218775 + 0.975775i \(0.570206\pi\)
\(384\) 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
\(388\) 2136.99 + 4753.40i 0.279611 + 0.621951i
\(389\) 2301.42i 0.299965i 0.988689 + 0.149983i \(0.0479218\pi\)
−0.988689 + 0.149983i \(0.952078\pi\)
\(390\) 2240.39 63.7829i 0.290889 0.00828147i
\(391\) 2186.80i 0.282842i
\(392\) −870.148 + 1437.40i −0.112115 + 0.185203i
\(393\) −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 \(0.983864\pi\)
\(398\) 1832.59 + 336.223i 0.230803 + 0.0423451i
\(399\) 5797.16 0.727371
\(400\) 7628.42 + 2409.81i 0.953553 + 0.301226i
\(401\) −9495.99 −1.18256 −0.591280 0.806466i \(-0.701377\pi\)
−0.591280 + 0.806466i \(0.701377\pi\)
\(402\) 2524.72 + 463.208i 0.313238 + 0.0574694i
\(403\) −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
\(408\) −2501.39 + 4132.06i −0.303523 + 0.501391i
\(409\) 10456.4i 1.26415i 0.774909 + 0.632073i \(0.217796\pi\)
−0.774909 + 0.632073i \(0.782204\pi\)
\(410\) −3749.71 + 106.753i −0.451671 + 0.0128589i
\(411\) 16136.0i 1.93657i
\(412\) −639.375 1422.19i −0.0764557 0.170064i
\(413\) 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
\(418\) 1196.33 6520.64i 0.139987 0.763002i
\(419\) −8542.91 −0.996058 −0.498029 0.867160i \(-0.665943\pi\)
−0.498029 + 0.867160i \(0.665943\pi\)
\(420\) −10289.2 1586.53i −1.19539 0.184321i
\(421\) −3112.71 −0.360342 −0.180171 0.983635i \(-0.557665\pi\)
−0.180171 + 0.983635i \(0.557665\pi\)
\(422\) −2971.36 + 16195.4i −0.342757 + 1.86820i
\(423\) 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
\(428\) 7470.28 3358.41i 0.843667 0.379287i
\(429\) 3335.48i 0.375381i
\(430\) −7975.82 7534.26i −0.894484 0.844963i
\(431\) 1474.93i 0.164837i 0.996598 + 0.0824187i \(0.0262645\pi\)
−0.996598 + 0.0824187i \(0.973736\pi\)
\(432\) 7837.94 467.653i 0.872924 0.0520832i
\(433\) −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
\(438\) −4838.48 887.711i −0.527835 0.0968413i
\(439\) −4661.49 −0.506790 −0.253395 0.967363i \(-0.581547\pi\)
−0.253395 + 0.967363i \(0.581547\pi\)
\(440\) −3907.87 + 11245.9i −0.423410 + 1.21847i
\(441\) 406.144 0.0438553
\(442\) −1296.32 237.835i −0.139502 0.0255942i
\(443\) 5250.61 + 5250.61i 0.563124 + 0.563124i 0.930194 0.367069i \(-0.119639\pi\)
−0.367069 + 0.930194i \(0.619639\pi\)
\(444\) 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
\(448\) −9981.17 3123.74i −1.05260 0.329427i
\(449\) 2992.06i 0.314485i −0.987560 0.157243i \(-0.949740\pi\)
0.987560 0.157243i \(-0.0502605\pi\)
\(450\) −456.595 1879.03i −0.0478314 0.196841i
\(451\) 5582.54i 0.582864i
\(452\) −5424.91 + 2438.88i −0.564527 + 0.253794i
\(453\) −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 \(0.349418\pi\)
\(458\) −2542.47 + 13857.8i −0.259393 + 1.41383i
\(459\) −4596.08 −0.467378
\(460\) −3086.12 4211.35i −0.312807 0.426859i
\(461\) 3239.67 0.327302 0.163651 0.986518i \(-0.447673\pi\)
0.163651 + 0.986518i \(0.447673\pi\)
\(462\) 2795.86 15238.9i 0.281548 1.53458i
\(463\) −1552.82 1552.82i −0.155865 0.155865i 0.624867 0.780732i \(-0.285153\pi\)
−0.780732 + 0.624867i \(0.785153\pi\)
\(464\) −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 −0.320719 0.947174i \(-0.603924\pi\)
0.947174 + 0.320719i \(0.103924\pi\)
\(468\) −223.159 496.384i −0.0220418 0.0490285i
\(469\) 3253.29i 0.320305i
\(470\) −3854.86 + 4080.79i −0.378323 + 0.400495i
\(471\) 13072.6i 1.27888i
\(472\) 7067.65 + 4278.49i 0.689227 + 0.417232i
\(473\) 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
\(478\) 9945.57 + 1824.70i 0.951673 + 0.174602i
\(479\) 7141.64 0.681232 0.340616 0.940203i \(-0.389364\pi\)
0.340616 + 0.940203i \(0.389364\pi\)
\(480\) −1014.18 11487.6i −0.0964394 1.09237i
\(481\) 1287.94 0.122090
\(482\) −14286.1 2621.06i −1.35003 0.247689i
\(483\) 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 −0.506232 0.862397i \(-0.668962\pi\)
0.862397 + 0.506232i \(0.168962\pi\)
\(488\) 5190.75 + 3142.28i 0.481504 + 0.291484i
\(489\) 13668.4i 1.26402i
\(490\) 66.8261 + 2347.29i 0.00616101 + 0.216407i
\(491\) 14943.2i 1.37348i 0.726904 + 0.686739i \(0.240959\pi\)
−0.726904 + 0.686739i \(0.759041\pi\)
\(492\) 2217.31 + 4932.06i 0.203179 + 0.451940i
\(493\) 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
\(498\) −2437.27 + 13284.4i −0.219311 + 1.19536i
\(499\) 2324.51 0.208535 0.104268 0.994549i \(-0.466750\pi\)
0.104268 + 0.994549i \(0.466750\pi\)
\(500\) 10784.7 2948.04i 0.964610 0.263681i
\(501\) 16240.1 1.44821
\(502\) 3393.23 18494.8i 0.301688 1.64435i
\(503\) −4791.06 4791.06i −0.424697 0.424697i 0.462120 0.886817i \(-0.347089\pi\)
−0.886817 + 0.462120i \(0.847089\pi\)
\(504\) 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
\(508\) −778.287 + 349.895i −0.0679742 + 0.0305592i
\(509\) 3391.52i 0.295337i −0.989037 0.147668i \(-0.952823\pi\)
0.989037 0.147668i \(-0.0471768\pi\)
\(510\) 192.103 + 6747.68i 0.0166794 + 0.585867i
\(511\) 6234.74i 0.539743i
\(512\) 720.851 11562.8i 0.0622215 0.998062i
\(513\) −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
\(518\) −5884.27 1079.58i −0.499112 0.0915714i
\(519\) 2561.75 0.216664
\(520\) 2832.11 1371.41i 0.238839 0.115655i
\(521\) −10835.4 −0.911146 −0.455573 0.890198i \(-0.650566\pi\)
−0.455573 + 0.890198i \(0.650566\pi\)
\(522\) 3764.47 + 690.663i 0.315645 + 0.0579109i
\(523\) 1210.80 + 1210.80i 0.101233 + 0.101233i 0.755909 0.654676i \(-0.227195\pi\)
−0.654676 + 0.755909i \(0.727195\pi\)
\(524\) −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
\(528\) 17131.8 1022.17i 1.41206 0.0842507i
\(529\) 8759.55i 0.719943i
\(530\) 10029.1 10616.9i 0.821955 0.870128i
\(531\) 1996.99i 0.163205i
\(532\) 7423.28 3337.29i 0.604963 0.271973i
\(533\) −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
\(538\) 1411.23 7691.93i 0.113090 0.616399i
\(539\) −3494.62 −0.279265
\(540\) 8851.16 6486.23i 0.705358 0.516894i
\(541\) −7014.81 −0.557468 −0.278734 0.960368i \(-0.589915\pi\)
−0.278734 + 0.960368i \(0.589915\pi\)
\(542\) −3252.47 + 17727.7i −0.257760 + 1.40492i
\(543\) −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 −0.191611 0.981471i \(-0.561371\pi\)
0.981471 + 0.191611i \(0.0613711\pi\)
\(548\) −9289.09 20662.2i −0.724106 1.61066i
\(549\) 1466.67i 0.114018i
\(550\) 3928.73 + 16168.0i 0.304585 + 1.25346i
\(551\) 12322.2i 0.952708i
\(552\) −3897.65 + 6438.55i −0.300535 + 0.496454i
\(553\) −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 \(0.716547\pi\)
\(558\) 948.307 + 173.985i 0.0719445 + 0.0131996i
\(559\) −4315.57 −0.326528
\(560\) −14088.7 + 3891.68i −1.06313 + 0.293667i
\(561\) −10045.9 −0.756039
\(562\) −14701.4 2697.25i −1.10346 0.202450i
\(563\) 4425.60 + 4425.60i 0.331291 + 0.331291i 0.853077 0.521786i \(-0.174734\pi\)
−0.521786 + 0.853077i \(0.674734\pi\)
\(564\) 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
\(568\) 6560.56 10837.4i 0.484639 0.800577i
\(569\) 14666.9i 1.08061i −0.841469 0.540305i \(-0.818309\pi\)
0.841469 0.540305i \(-0.181691\pi\)
\(570\) 6524.00 + 6162.81i 0.479404 + 0.452863i
\(571\) 664.054i 0.0486686i −0.999704 0.0243343i \(-0.992253\pi\)
0.999704 0.0243343i \(-0.00774662\pi\)
\(572\) 1920.15 + 4271.09i 0.140359 + 0.312208i
\(573\) 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 \(0.740530\pi\)
\(578\) −1791.32 + 9763.63i −0.128909 + 0.702619i
\(579\) 11598.7 0.832516
\(580\) −3372.26 + 21870.2i −0.241423 + 1.56571i
\(581\) 17117.9 1.22232
\(582\) 1894.71 10327.1i 0.134945 0.735521i
\(583\) 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 −0.907045 0.421034i \(-0.861667\pi\)
0.421034 + 0.907045i \(0.361667\pi\)
\(588\) 3087.43 1388.01i 0.216536 0.0973482i
\(589\) 3104.07i 0.217150i
\(590\) 11541.5 328.582i 0.805351 0.0229279i
\(591\) 5307.89i 0.369437i
\(592\) −394.697 6615.19i −0.0274019 0.459261i
\(593\) −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
\(598\) −2019.92 370.592i −0.138128 0.0253422i
\(599\) 25321.6 1.72723 0.863616 0.504151i \(-0.168194\pi\)
0.863616 + 0.504151i \(0.168194\pi\)
\(600\) −9892.64 12723.6i −0.673109 0.865733i
\(601\) 27777.8 1.88533 0.942663 0.333746i \(-0.108313\pi\)
0.942663 + 0.333746i \(0.108313\pi\)
\(602\) 19716.6 + 3617.39i 1.33487 + 0.244907i
\(603\) −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 \(0.626431\pi\)
−0.922150 + 0.386833i \(0.873569\pi\)
\(608\) 5552.89 + 7102.74i 0.370394 + 0.473773i
\(609\) 28797.2i 1.91613i
\(610\) 8476.53 241.323i 0.562630 0.0160178i
\(611\) 2208.04i 0.146199i
\(612\) 1495.02 672.118i 0.0987463 0.0443934i
\(613\) −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 \(0.501478\pi\)
\(618\) −566.887 + 3089.83i −0.0368989 + 0.201118i
\(619\) −13042.3 −0.846874 −0.423437 0.905926i \(-0.639176\pi\)
−0.423437 + 0.905926i \(0.639176\pi\)
\(620\) −849.504 + 5509.32i −0.0550273 + 0.356870i
\(621\) −7161.58 −0.462776
\(622\) −1827.07 + 9958.45i −0.117779 + 0.641957i
\(623\) 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
\(628\) 7525.59 + 16739.5i 0.478191 + 1.06366i
\(629\) 3879.07i 0.245896i
\(630\) 2568.27 + 2426.08i 0.162416 + 0.153424i
\(631\) 6843.39i 0.431745i −0.976422 0.215872i \(-0.930740\pi\)
0.976422 0.215872i \(-0.0692595\pi\)
\(632\) −22693.3 13737.7i −1.42831 0.864644i
\(633\) 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
\(638\) −32391.0 5942.74i −2.00999 0.368770i
\(639\) −3062.15 −0.189573
\(640\) −7911.82 14126.1i −0.488660 0.872475i
\(641\) −2449.97 −0.150964 −0.0754820 0.997147i \(-0.524050\pi\)
−0.0754820 + 0.997147i \(0.524050\pi\)
\(642\) −16229.8 2977.66i −0.997723 0.183051i
\(643\) −22279.7 22279.7i −1.36645 1.36645i −0.865448 0.500999i \(-0.832966\pi\)
−0.500999 0.865448i \(1.33297\pi\)
\(644\) 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 −0.537175 0.843471i \(-0.680509\pi\)
0.843471 + 0.537175i \(0.180509\pi\)
\(648\) −16390.6 9922.27i −0.993650 0.601518i
\(649\) 17182.9i 1.03927i
\(650\) 2287.41 3755.91i 0.138030 0.226644i
\(651\) 7254.29i 0.436740i
\(652\) 7868.58 + 17502.5i 0.472634 + 1.05130i
\(653\) −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
\(658\) 1850.82 10087.9i 0.109654 0.597672i
\(659\) 12951.7 0.765595 0.382797 0.923832i \(-0.374961\pi\)
0.382797 + 0.923832i \(0.374961\pi\)
\(660\) 19346.4 14177.3i 1.14100 0.836137i
\(661\) 6827.08 0.401729 0.200864 0.979619i \(-0.435625\pi\)
0.200864 + 0.979619i \(0.435625\pi\)
\(662\) 4502.65 24541.8i 0.264351 1.44085i
\(663\) 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
\(668\) 20795.5 9349.04i 1.20449 0.541505i
\(669\) 18660.0i 1.07838i
\(670\) 3458.49 3661.18i 0.199422 0.211110i
\(671\) 12619.8i 0.726052i
\(672\) 12977.2 + 16599.3i 0.744952 + 0.952873i
\(673\) 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 \(0.852527\pi\)
\(678\) 11786.0 + 2162.37i 0.667611 + 0.122486i
\(679\) −13307.3 −0.752115
\(680\) 4130.46 + 8529.83i 0.232935 + 0.481035i
\(681\) −23935.1 −1.34684
\(682\) −8159.61 1497.03i −0.458134 0.0840534i
\(683\) −15861.8 15861.8i −0.888629 0.888629i 0.105763 0.994391i \(-0.466272\pi\)
−0.994391 + 0.105763i \(0.966272\pi\)
\(684\) 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
\(688\) 1322.53 + 22165.8i 0.0732861 + 1.22829i
\(689\) 5744.60i 0.317637i
\(690\) 299.334 + 10514.2i 0.0165151 + 0.580099i
\(691\) 30100.7i 1.65714i 0.559883 + 0.828572i \(0.310846\pi\)
−0.559883 + 0.828572i \(0.689154\pi\)
\(692\) 3280.33 1474.74i 0.180201 0.0810132i
\(693\) −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
\(698\) −1904.43 + 10380.1i −0.103272 + 0.562883i
\(699\) 13288.8 0.719066
\(700\) −13598.8 + 15242.4i −0.734268 + 0.823010i
\(701\) −20267.4 −1.09199 −0.545997 0.837787i \(-0.683849\pi\)
−0.545997 + 0.837787i \(0.683849\pi\)
\(702\) 778.888 4245.34i 0.0418764 0.228248i
\(703\) 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
\(708\) −6824.81 15180.8i −0.362277 0.805830i
\(709\) 18499.1i 0.979900i 0.871750 + 0.489950i \(0.162985\pi\)
−0.871750 + 0.489950i \(0.837015\pi\)
\(710\) −503.841 17697.6i −0.0266321 0.935462i
\(711\) 6412.08i 0.338216i
\(712\) −6469.13 + 10686.4i −0.340507 + 0.562485i
\(713\) 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
\(718\) 29148.7 + 5347.87i 1.51507 + 0.277968i
\(719\) −25990.9 −1.34812 −0.674060 0.738676i \(-0.735451\pi\)
−0.674060 + 0.738676i \(0.735451\pi\)
\(720\) −1930.60 + 3404.23i −0.0999294 + 0.176206i
\(721\) 3981.47 0.205656
\(722\) 12180.7 + 2234.79i 0.627867 + 0.115194i
\(723\) 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 \(-0.427033\pi\)
0.973841 0.227232i \(-0.0729675\pi\)
\(728\) −2977.26 + 4918.15i −0.151572 + 0.250383i
\(729\) 14244.1i 0.723674i
\(730\) −6627.99 + 7016.44i −0.336045 + 0.355740i
\(731\) 12997.8i 0.657646i
\(732\) −5012.40 11149.3i −0.253092 0.562965i
\(733\) 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
\(738\) 331.154 1804.96i 0.0165175 0.0900291i
\(739\) −8124.95 −0.404440 −0.202220 0.979340i \(-0.564816\pi\)
−0.202220 + 0.979340i \(0.564816\pi\)
\(740\) −5474.35 7470.34i −0.271947 0.371102i
\(741\) 3530.01 0.175004
\(742\) −4815.23 + 26245.5i −0.238238 + 1.29852i
\(743\) −5222.62 5222.62i −0.257873 0.257873i 0.566316 0.824188i \(-0.308368\pi\)
−0.824188 + 0.566316i \(0.808368\pi\)
\(744\) 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
\(748\) −12863.8 + 5783.17i −0.628806 + 0.282692i
\(749\) 20913.3i 1.02023i
\(750\) −21256.3 7450.11i −1.03489 0.362719i
\(751\) 27086.9i 1.31613i −0.752961 0.658066i \(-0.771375\pi\)
0.752961 0.658066i \(-0.228625\pi\)
\(752\) 11341.0 676.664i 0.549953 0.0328130i
\(753\) −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 \(0.872929\pi\)
\(758\) −4733.87 868.517i −0.226836 0.0416174i
\(759\) −15653.4 −0.748595
\(760\) 11901.8 + 4135.79i 0.568056 + 0.197396i
\(761\) −8006.53 −0.381388 −0.190694 0.981649i \(-0.561074\pi\)
−0.190694 + 0.981649i \(0.561074\pi\)
\(762\) 1690.89 + 310.226i 0.0803865 + 0.0147484i
\(763\) 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
\(768\) −14424.2 + 18349.0i −0.677720 + 0.862128i
\(769\) 5515.54i 0.258642i −0.991603 0.129321i \(-0.958720\pi\)
0.991603 0.129321i \(-0.0412797\pi\)
\(770\) −22098.4 20875.0i −1.03425 0.976989i
\(771\) 3612.28i