Properties

Label 20.4.e.b.3.4
Level 20
Weight 4
Character 20.3
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 3.4
Root \(1.13579 - 1.64620i\)
Character \(\chi\) = 20.3
Dual form 20.4.e.b.7.4

$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 −0.979049 0.203624i \(-0.934728\pi\)
0.203624 + 0.979049i \(0.434728\pi\)
\(4\) −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 \(-0.0640655\pi\)
−0.199912 + 0.979814i \(0.564066\pi\)
\(8\) 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 \(-0.776870\pi\)
0.764209 0.644969i \(-0.223130\pi\)
\(12\) 41.5771 18.6918i 1.00019 0.449655i
\(13\) −8.79525 8.79525i −0.187643 0.187643i 0.607033 0.794676i \(-0.292360\pi\)
−0.794676 + 0.607033i \(0.792360\pi\)
\(14\) −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 −0.870353 0.492428i \(-0.836109\pi\)
0.492428 + 0.870353i \(0.336109\pi\)
\(18\) 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 −0.494802 0.869006i \(-0.664759\pi\)
0.869006 + 0.494802i \(0.164759\pi\)
\(24\) 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 \(-0.708984\pi\)
0.610382 0.792107i \(-0.291016\pi\)
\(30\) −69.1790 166.384i −0.421010 1.01258i
\(31\) 62.3240i 0.361088i 0.983567 + 0.180544i \(0.0577858\pi\)
−0.983567 + 0.180544i \(0.942214\pi\)
\(32\) −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 −0.850805 0.525481i \(-0.823885\pi\)
0.525481 + 0.850805i \(0.323885\pi\)
\(38\) −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 −0.992480 0.122404i \(-0.960940\pi\)
0.122404 + 0.992480i \(0.460940\pi\)
\(44\) −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 \(-0.338832\pi\)
−0.874533 + 0.484966i \(0.838832\pi\)
\(48\) −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 0.143295 0.989680i \(-0.454230\pi\)
−0.989680 + 0.143295i \(0.954230\pi\)
\(54\) 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 0.802287 0.596938i \(-0.203616\pi\)
−0.596938 + 0.802287i \(0.703616\pi\)
\(68\) 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 \(0.154997\pi\)
−0.883771 + 0.467921i \(0.845003\pi\)
\(72\) −105.870 64.0897i −0.173290 0.104903i
\(73\) 215.825 + 215.825i 0.346033 + 0.346033i 0.858629 0.512597i \(-0.171316\pi\)
−0.512597 + 0.858629i \(0.671316\pi\)
\(74\) −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 −0.196804 0.980443i \(-0.563056\pi\)
0.980443 + 0.196804i \(0.0630562\pi\)
\(84\) 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 \(0.106631\pi\)
−0.944413 + 0.328761i \(0.893369\pi\)
\(90\) 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 −0.423643 0.905829i \(-0.639249\pi\)
0.905829 + 0.423643i \(0.139249\pi\)
\(98\) −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 −0.638104 0.769951i \(-0.720281\pi\)
0.769951 + 0.638104i \(0.220281\pi\)
\(104\) −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 \(-0.403048\pi\)
−0.953972 + 0.299895i \(0.903048\pi\)
\(108\) 402.447 + 895.181i 0.358569 + 0.797582i
\(109\) 896.758i 0.788017i 0.919107 + 0.394009i \(0.128912\pi\)
−0.919107 + 0.394009i \(0.871088\pi\)
\(110\) 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 0.453560 0.891226i \(-0.350154\pi\)
−0.891226 + 0.453560i \(0.850154\pi\)
\(114\) −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 0.732965 0.680266i \(-0.238136\pi\)
−0.680266 + 0.732965i \(0.738136\pi\)
\(128\) 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 \(0.151560\pi\)
−0.888771 + 0.458351i \(0.848440\pi\)
\(132\) −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 −0.292424 + 0.956289i \(0.594462\pi\)
−0.956289 + 0.292424i \(0.905538\pi\)
\(138\) −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 \(0.118481\pi\)
−0.931523 + 0.363682i \(0.881519\pi\)
\(150\) −368.842 1980.56i −0.200772 1.07808i
\(151\) 57.2419i 0.0308495i 0.999881 + 0.0154248i \(0.00491005\pi\)
−0.999881 + 0.0154248i \(0.995090\pi\)
\(152\) 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 −0.162134 0.986769i \(-0.551838\pi\)
0.986769 + 0.162134i \(0.0518378\pi\)
\(158\) 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 −0.985386 0.170334i \(-0.945515\pi\)
0.170334 + 0.985386i \(0.445515\pi\)
\(164\) −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 \(-0.479575\pi\)
−0.997942 + 0.0641235i \(0.979575\pi\)
\(168\) −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 0.773501 0.633795i \(-0.218504\pi\)
−0.633795 + 0.773501i \(0.718504\pi\)
\(174\) −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 \(-0.893830\pi\)
0.944888 0.327393i \(-0.106170\pi\)
\(192\) 2784.30 + 871.385i 1.04656 + 0.327536i
\(193\) 1439.32 + 1439.32i 0.536813 + 0.536813i 0.922591 0.385779i \(-0.126067\pi\)
−0.385779 + 0.922591i \(0.626067\pi\)
\(194\) 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 −0.816111 0.577895i \(-0.803874\pi\)
0.577895 + 0.816111i \(0.303874\pi\)
\(198\) 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 \(-0.601395\pi\)
0.313182 0.949693i \(-0.398605\pi\)
\(212\) 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 −0.963403 0.268056i \(-0.913619\pi\)
0.268056 + 0.963403i \(0.413619\pi\)
\(224\) −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 \(-0.0395243\pi\)
−0.123851 + 0.992301i \(0.539524\pi\)
\(228\) 2070.76 930.954i 0.601490 0.270412i
\(229\) 4981.25i 1.43742i 0.695308 + 0.718712i \(0.255268\pi\)
−0.695308 + 0.718712i \(0.744732\pi\)
\(230\) 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 0.899853 0.436194i \(-0.143674\pi\)
−0.436194 + 0.899853i \(0.643674\pi\)
\(234\) −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 \(0.315054\pi\)
−0.548882 + 0.835900i \(0.684946\pi\)
\(252\) −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 −0.759411 0.650611i \(-0.774513\pi\)
0.650611 + 0.759411i \(0.274513\pi\)
\(258\) 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 −0.689841 0.723961i \(-0.742319\pi\)
0.723961 + 0.689841i \(0.242319\pi\)
\(264\) 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 \(-0.898551\pi\)
0.949640 0.313344i \(-0.101449\pi\)
\(270\) 3582.35 1489.47i 0.807463 0.335726i
\(271\) 6372.29i 1.42837i −0.699955 0.714187i \(-0.746797\pi\)
0.699955 0.714187i \(-0.253203\pi\)
\(272\) −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 −0.747867 0.663848i \(-0.768922\pi\)
0.663848 + 0.747867i \(0.268922\pi\)
\(278\) −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 −0.670322 0.742070i \(-0.733844\pi\)
0.742070 + 0.670322i \(0.233844\pi\)
\(284\) 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 −0.907912 0.419161i \(-0.862324\pi\)
−0.419161 0.907912i \(-0.637676\pi\)
\(294\) 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 0.755144 0.655559i \(-0.227567\pi\)
−0.655559 + 0.755144i \(0.727567\pi\)
\(308\) −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 \(-0.894186\pi\)
0.945254 0.326336i \(-0.105814\pi\)
\(312\) 830.522 1371.94i 0.150702 0.248945i
\(313\) 6740.52 + 6740.52i 1.21724 + 1.21724i 0.968594 + 0.248648i \(0.0799861\pi\)
0.248648 + 0.968594i \(0.420014\pi\)
\(314\) 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 −0.234490 0.972118i \(-0.575342\pi\)
0.972118 + 0.234490i \(0.0753421\pi\)
\(318\) −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 \(0.261623\pi\)
−0.680821 + 0.732450i \(0.738377\pi\)
\(332\) −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 −0.403384 0.915031i \(-0.632166\pi\)
0.915031 + 0.403384i \(0.132166\pi\)
\(338\) 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 0.637721 0.770267i \(-0.279877\pi\)
−0.770267 + 0.637721i \(0.779877\pi\)
\(348\) −4624.47 10286.4i −0.712350 1.58451i
\(349\) 3731.17i 0.572278i 0.958188 + 0.286139i \(0.0923720\pi\)
−0.958188 + 0.286139i \(0.907628\pi\)
\(350\) −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 0.560569 0.828108i \(-0.310583\pi\)
−0.828108 + 0.560569i \(0.810583\pi\)
\(354\) −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 0.973886 0.227038i \(-0.0729040\pi\)
−0.227038 + 0.973886i \(0.572904\pi\)
\(368\) 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 0.900259 0.435355i \(-0.143377\pi\)
−0.435355 + 0.900259i \(0.643377\pi\)
\(374\) −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 −0.975775 0.218775i \(-0.929794\pi\)
0.218775 + 0.975775i \(0.429794\pi\)
\(384\) −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 \(-0.952078\pi\)
0.988689 0.149983i \(-0.0479218\pi\)
\(390\) −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 −0.998715 0.0506721i \(-0.983864\pi\)
0.0506721 + 0.998715i \(0.483864\pi\)
\(398\) −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 \(-0.782204\pi\)
0.774909 0.632073i \(-0.217796\pi\)
\(410\) −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 \(0.0262645\pi\)
−0.996598 + 0.0824187i \(0.973736\pi\)
\(432\) −467.653 7837.94i −0.0520832 0.872924i
\(433\) −6196.57 6196.57i −0.687733 0.687733i 0.273998 0.961730i \(-0.411654\pi\)
−0.961730 + 0.273998i \(0.911654\pi\)
\(434\) −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 −0.930194 0.367069i \(-0.880361\pi\)
0.367069 + 0.930194i \(0.380361\pi\)
\(444\) −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 \(0.0502605\pi\)
−0.987560 + 0.157243i \(0.949740\pi\)
\(450\) 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 0.455619 0.890175i \(-0.349418\pi\)
0.890175 0.455619i \(-0.150582\pi\)
\(458\) −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 −0.624867 0.780732i \(-0.714847\pi\)
0.780732 + 0.624867i \(0.214847\pi\)
\(464\) 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 \(-0.396076\pi\)
−0.947174 + 0.320719i \(0.896076\pi\)
\(468\) 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 0.506232 0.862397i \(-0.331038\pi\)
−0.862397 + 0.506232i \(0.831038\pi\)
\(488\) −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 \(0.240959\pi\)
−0.726904 + 0.686739i \(0.759041\pi\)
\(492\) 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 −0.462120 0.886817i \(-0.652911\pi\)
0.886817 + 0.462120i \(0.152911\pi\)
\(504\) −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 \(0.0471768\pi\)
−0.989037 + 0.147668i \(0.952823\pi\)
\(510\) 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 −0.755909 0.654676i \(-0.772805\pi\)
0.654676 + 0.755909i \(0.272805\pi\)
\(524\) 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 0.191611 0.981471i \(-0.438629\pi\)
−0.981471 + 0.191611i \(0.938629\pi\)
\(548\) 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 −0.629028 0.777383i \(-0.716547\pi\)
0.777383 + 0.629028i \(0.216547\pi\)
\(558\) −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 −0.853077 0.521786i \(-0.825266\pi\)
0.521786 + 0.853077i \(0.325266\pi\)
\(564\) −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 \(0.181691\pi\)
−0.841469 + 0.540305i \(0.818309\pi\)
\(570\) −3445.49 8286.82i −0.253185 0.608942i
\(571\) 664.054i 0.0486686i −0.999704 0.0243343i \(-0.992253\pi\)
0.999704 0.0243343i \(-0.00774662\pi\)
\(572\) 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 −0.685760 0.727828i \(-0.740530\pi\)
0.727828 + 0.685760i \(0.240530\pi\)
\(578\) −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 0.907045 0.421034i \(-0.138333\pi\)
−0.421034 + 0.907045i \(0.638333\pi\)
\(588\) 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 0.192835 0.981231i \(-0.438232\pi\)
−0.981231 + 0.192835i \(0.938232\pi\)
\(594\) −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 0.922150 + 0.386833i \(0.126431\pi\)
0.386833 + 0.922150i \(0.373569\pi\)
\(608\) −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 0.143552 0.989643i \(-0.454147\pi\)
−0.989643 + 0.143552i \(0.954147\pi\)
\(614\) −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 −0.00464336 0.999989i \(-0.501478\pi\)
0.999989 + 0.00464336i \(0.00147803\pi\)
\(618\) −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 \(-0.930740\pi\)
0.976422 0.215872i \(-0.0692595\pi\)
\(632\) −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 0.500999 0.865448i \(-0.332966\pi\)
0.865448 0.500999i \(-0.167034\pi\)
\(644\) −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 \(-0.319491\pi\)
−0.843471 + 0.537175i \(0.819491\pi\)
\(648\) 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 0.558122 0.829759i \(-0.311522\pi\)
−0.829759 + 0.558122i \(0.811522\pi\)
\(654\) 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 0.928569 0.371159i \(-0.121040\pi\)
−0.371159 + 0.928569i \(0.621040\pi\)
\(674\) 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 −0.894582 0.446903i \(-0.852527\pi\)
0.446903 + 0.894582i \(0.352527\pi\)
\(678\) −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 −0.105763 0.994391i \(-0.533728\pi\)
0.994391 + 0.105763i \(0.0337284\pi\)
\(684\) −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 \(0.310846\pi\)
−0.559883 + 0.828572i \(0.689154\pi\)
\(692\) −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 \(-0.837015\pi\)
0.871750 0.489950i \(-0.162985\pi\)
\(710\) −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 −0.973841 0.227232i \(-0.927033\pi\)
−0.227232 0.973841i \(1.42703\pi\)
\(728\) −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 0.988033 0.154244i \(-0.0492942\pi\)
−0.154244 + 0.988033i \(0.549294\pi\)
\(734\) −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 −0.566316 0.824188i \(-0.691632\pi\)
0.824188 + 0.566316i \(0.191632\pi\)
\(744\) −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 \(-0.771375\pi\)
0.752961 0.658066i \(-0.228625\pi\)
\(752\) −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 −0.921370 0.388686i \(-0.872929\pi\)
0.388686 + 0.921370i \(0.372929\pi\)
\(758\) 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 \(0.0412797\pi\)
−0.991603 + 0.129321i \(0.958720\pi\)
\(770\) 11670.7 + 28069.5i 0.546212 + 1.31371i
\(771\) 3612.28i