Properties

Label 63.4.e.d.37.1
Level $63$
Weight $4$
Character 63.37
Analytic conductor $3.717$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 19 x^{6} + 319 x^{4} + 798 x^{2} + 1764\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(2.02770 + 3.51207i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.4.e.d.46.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.02770 + 3.51207i) q^{2} +(-4.22311 - 7.31464i) q^{4} +(-4.96020 + 8.59131i) q^{5} +(-15.3924 - 10.2992i) q^{7} +1.80961 q^{8} +O(q^{10})\) \(q+(-2.02770 + 3.51207i) q^{2} +(-4.22311 - 7.31464i) q^{4} +(-4.96020 + 8.59131i) q^{5} +(-15.3924 - 10.2992i) q^{7} +1.80961 q^{8} +(-20.1156 - 34.8412i) q^{10} +(-6.76980 - 11.7256i) q^{11} +18.5538 q^{13} +(67.3826 - 33.1758i) q^{14} +(30.1156 - 52.1617i) q^{16} +(-46.8551 - 81.1555i) q^{17} +(-65.9542 + 114.236i) q^{19} +83.7899 q^{20} +54.9084 q^{22} +(-99.1391 + 171.714i) q^{23} +(13.2929 + 23.0240i) q^{25} +(-37.6214 + 65.1622i) q^{26} +(-10.3307 + 156.085i) q^{28} -188.358 q^{29} +(41.9622 + 72.6807i) q^{31} +(129.369 + 224.073i) q^{32} +380.032 q^{34} +(164.833 - 81.1555i) q^{35} +(-40.0778 + 69.4167i) q^{37} +(-267.470 - 463.272i) q^{38} +(-8.97600 + 15.5469i) q^{40} +385.828 q^{41} -397.048 q^{43} +(-57.1793 + 99.0374i) q^{44} +(-402.048 - 696.368i) q^{46} +(136.139 - 235.799i) q^{47} +(130.855 + 317.058i) q^{49} -107.816 q^{50} +(-78.3547 - 135.714i) q^{52} +(-18.4998 - 32.0426i) q^{53} +134.318 q^{55} +(-27.8543 - 18.6374i) q^{56} +(381.932 - 661.526i) q^{58} +(197.874 + 342.728i) q^{59} +(-6.73689 + 11.6686i) q^{61} -340.347 q^{62} -567.435 q^{64} +(-92.0304 + 159.401i) q^{65} +(-170.261 - 294.901i) q^{67} +(-395.749 + 685.457i) q^{68} +(-49.2071 + 743.464i) q^{70} +211.140 q^{71} +(-243.062 - 420.995i) q^{73} +(-162.531 - 281.512i) q^{74} +1114.13 q^{76} +(-16.5604 + 250.210i) q^{77} +(-146.871 + 254.387i) q^{79} +(298.758 + 517.464i) q^{80} +(-782.343 + 1355.06i) q^{82} -889.635 q^{83} +929.643 q^{85} +(805.093 - 1394.46i) q^{86} +(-12.2507 - 21.2188i) q^{88} +(572.182 - 991.048i) q^{89} +(-285.588 - 191.088i) q^{91} +1674.70 q^{92} +(552.096 + 956.258i) q^{94} +(-654.292 - 1133.27i) q^{95} +1384.61 q^{97} +(-1378.87 - 183.327i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{4} - 12q^{7} + O(q^{10}) \) \( 8q - 6q^{4} - 12q^{7} - 22q^{10} + 204q^{13} + 102q^{16} - 222q^{19} - 172q^{22} - 366q^{25} - 166q^{28} - 220q^{31} + 2040q^{34} + 374q^{37} - 822q^{40} - 1676q^{43} - 1716q^{46} + 380q^{49} + 40q^{52} + 5020q^{55} + 1694q^{58} - 1332q^{61} - 1372q^{64} - 1890q^{67} - 866q^{70} - 1750q^{73} + 4912q^{76} - 8q^{79} - 2480q^{82} - 2232q^{85} - 2682q^{88} + 466q^{91} + 1416q^{94} + 6020q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.02770 + 3.51207i −0.716899 + 1.24171i 0.245323 + 0.969441i \(0.421106\pi\)
−0.962222 + 0.272264i \(0.912227\pi\)
\(3\) 0 0
\(4\) −4.22311 7.31464i −0.527889 0.914330i
\(5\) −4.96020 + 8.59131i −0.443654 + 0.768430i −0.997957 0.0638840i \(-0.979651\pi\)
0.554304 + 0.832314i \(0.312985\pi\)
\(6\) 0 0
\(7\) −15.3924 10.2992i −0.831114 0.556102i
\(8\) 1.80961 0.0799740
\(9\) 0 0
\(10\) −20.1156 34.8412i −0.636110 1.10177i
\(11\) −6.76980 11.7256i −0.185561 0.321401i 0.758204 0.652017i \(-0.226077\pi\)
−0.943765 + 0.330616i \(0.892744\pi\)
\(12\) 0 0
\(13\) 18.5538 0.395838 0.197919 0.980218i \(-0.436582\pi\)
0.197919 + 0.980218i \(0.436582\pi\)
\(14\) 67.3826 33.1758i 1.28634 0.633330i
\(15\) 0 0
\(16\) 30.1156 52.1617i 0.470556 0.815026i
\(17\) −46.8551 81.1555i −0.668473 1.15783i −0.978331 0.207046i \(-0.933615\pi\)
0.309858 0.950783i \(-0.399718\pi\)
\(18\) 0 0
\(19\) −65.9542 + 114.236i −0.796365 + 1.37934i 0.125604 + 0.992080i \(0.459913\pi\)
−0.921969 + 0.387264i \(0.873420\pi\)
\(20\) 83.7899 0.936799
\(21\) 0 0
\(22\) 54.9084 0.532115
\(23\) −99.1391 + 171.714i −0.898779 + 1.55673i −0.0697230 + 0.997566i \(0.522212\pi\)
−0.829056 + 0.559165i \(0.811122\pi\)
\(24\) 0 0
\(25\) 13.2929 + 23.0240i 0.106343 + 0.184192i
\(26\) −37.6214 + 65.1622i −0.283776 + 0.491514i
\(27\) 0 0
\(28\) −10.3307 + 156.085i −0.0697254 + 1.05347i
\(29\) −188.358 −1.20611 −0.603054 0.797700i \(-0.706050\pi\)
−0.603054 + 0.797700i \(0.706050\pi\)
\(30\) 0 0
\(31\) 41.9622 + 72.6807i 0.243117 + 0.421092i 0.961601 0.274453i \(-0.0884967\pi\)
−0.718483 + 0.695544i \(0.755163\pi\)
\(32\) 129.369 + 224.073i 0.714669 + 1.23784i
\(33\) 0 0
\(34\) 380.032 1.91691
\(35\) 164.833 81.1555i 0.796053 0.391936i
\(36\) 0 0
\(37\) −40.0778 + 69.4167i −0.178074 + 0.308434i −0.941221 0.337792i \(-0.890320\pi\)
0.763147 + 0.646225i \(0.223653\pi\)
\(38\) −267.470 463.272i −1.14183 1.97770i
\(39\) 0 0
\(40\) −8.97600 + 15.5469i −0.0354808 + 0.0614545i
\(41\) 385.828 1.46967 0.734833 0.678249i \(-0.237261\pi\)
0.734833 + 0.678249i \(0.237261\pi\)
\(42\) 0 0
\(43\) −397.048 −1.40812 −0.704061 0.710139i \(-0.748632\pi\)
−0.704061 + 0.710139i \(0.748632\pi\)
\(44\) −57.1793 + 99.0374i −0.195911 + 0.339328i
\(45\) 0 0
\(46\) −402.048 696.368i −1.28867 2.23204i
\(47\) 136.139 235.799i 0.422508 0.731805i −0.573676 0.819082i \(-0.694483\pi\)
0.996184 + 0.0872772i \(0.0278166\pi\)
\(48\) 0 0
\(49\) 130.855 + 317.058i 0.381500 + 0.924369i
\(50\) −107.816 −0.304949
\(51\) 0 0
\(52\) −78.3547 135.714i −0.208958 0.361927i
\(53\) −18.4998 32.0426i −0.0479461 0.0830451i 0.841056 0.540948i \(-0.181934\pi\)
−0.889002 + 0.457902i \(0.848601\pi\)
\(54\) 0 0
\(55\) 134.318 0.329299
\(56\) −27.8543 18.6374i −0.0664675 0.0444738i
\(57\) 0 0
\(58\) 381.932 661.526i 0.864658 1.49763i
\(59\) 197.874 + 342.728i 0.436628 + 0.756262i 0.997427 0.0716901i \(-0.0228393\pi\)
−0.560799 + 0.827952i \(0.689506\pi\)
\(60\) 0 0
\(61\) −6.73689 + 11.6686i −0.0141405 + 0.0244921i −0.873009 0.487704i \(-0.837835\pi\)
0.858869 + 0.512196i \(0.171168\pi\)
\(62\) −340.347 −0.697162
\(63\) 0 0
\(64\) −567.435 −1.10827
\(65\) −92.0304 + 159.401i −0.175615 + 0.304174i
\(66\) 0 0
\(67\) −170.261 294.901i −0.310458 0.537729i 0.668004 0.744158i \(-0.267149\pi\)
−0.978462 + 0.206429i \(0.933816\pi\)
\(68\) −395.749 + 685.457i −0.705759 + 1.22241i
\(69\) 0 0
\(70\) −49.2071 + 743.464i −0.0840196 + 1.26944i
\(71\) 211.140 0.352925 0.176463 0.984307i \(-0.443534\pi\)
0.176463 + 0.984307i \(0.443534\pi\)
\(72\) 0 0
\(73\) −243.062 420.995i −0.389702 0.674983i 0.602708 0.797962i \(-0.294089\pi\)
−0.992409 + 0.122979i \(0.960755\pi\)
\(74\) −162.531 281.512i −0.255323 0.442232i
\(75\) 0 0
\(76\) 1114.13 1.68157
\(77\) −16.5604 + 250.210i −0.0245096 + 0.370312i
\(78\) 0 0
\(79\) −146.871 + 254.387i −0.209168 + 0.362289i −0.951453 0.307795i \(-0.900409\pi\)
0.742285 + 0.670084i \(0.233742\pi\)
\(80\) 298.758 + 517.464i 0.417527 + 0.723178i
\(81\) 0 0
\(82\) −782.343 + 1355.06i −1.05360 + 1.82489i
\(83\) −889.635 −1.17651 −0.588253 0.808677i \(-0.700184\pi\)
−0.588253 + 0.808677i \(0.700184\pi\)
\(84\) 0 0
\(85\) 929.643 1.18628
\(86\) 805.093 1394.46i 1.00948 1.74847i
\(87\) 0 0
\(88\) −12.2507 21.2188i −0.0148401 0.0257038i
\(89\) 572.182 991.048i 0.681474 1.18035i −0.293057 0.956095i \(-0.594673\pi\)
0.974531 0.224252i \(-0.0719939\pi\)
\(90\) 0 0
\(91\) −285.588 191.088i −0.328986 0.220126i
\(92\) 1674.70 1.89782
\(93\) 0 0
\(94\) 552.096 + 956.258i 0.605791 + 1.04926i
\(95\) −654.292 1133.27i −0.706620 1.22390i
\(96\) 0 0
\(97\) 1384.61 1.44933 0.724667 0.689099i \(-0.241993\pi\)
0.724667 + 0.689099i \(0.241993\pi\)
\(98\) −1378.87 183.327i −1.42129 0.188968i
\(99\) 0 0
\(100\) 112.275 194.465i 0.112275 0.194465i
\(101\) 892.994 + 1546.71i 0.879765 + 1.52380i 0.851599 + 0.524194i \(0.175633\pi\)
0.0281660 + 0.999603i \(0.491033\pi\)
\(102\) 0 0
\(103\) −244.831 + 424.059i −0.234212 + 0.405668i −0.959044 0.283259i \(-0.908584\pi\)
0.724831 + 0.688927i \(0.241918\pi\)
\(104\) 33.5750 0.0316568
\(105\) 0 0
\(106\) 150.048 0.137490
\(107\) 141.034 244.278i 0.127423 0.220703i −0.795254 0.606276i \(-0.792663\pi\)
0.922678 + 0.385573i \(0.125996\pi\)
\(108\) 0 0
\(109\) 143.616 + 248.749i 0.126201 + 0.218586i 0.922202 0.386709i \(-0.126388\pi\)
−0.796001 + 0.605295i \(0.793055\pi\)
\(110\) −272.357 + 471.736i −0.236074 + 0.408893i
\(111\) 0 0
\(112\) −1000.77 + 492.731i −0.844323 + 0.415702i
\(113\) −1895.21 −1.57776 −0.788879 0.614548i \(-0.789338\pi\)
−0.788879 + 0.614548i \(0.789338\pi\)
\(114\) 0 0
\(115\) −983.499 1703.47i −0.797493 1.38130i
\(116\) 795.456 + 1377.77i 0.636691 + 1.10278i
\(117\) 0 0
\(118\) −1604.92 −1.25207
\(119\) −114.618 + 1731.75i −0.0882943 + 1.33403i
\(120\) 0 0
\(121\) 573.840 993.919i 0.431134 0.746746i
\(122\) −27.3208 47.3209i −0.0202746 0.0351167i
\(123\) 0 0
\(124\) 354.422 613.877i 0.256678 0.444579i
\(125\) −1503.79 −1.07603
\(126\) 0 0
\(127\) −1222.92 −0.854463 −0.427231 0.904142i \(-0.640511\pi\)
−0.427231 + 0.904142i \(0.640511\pi\)
\(128\) 115.635 200.285i 0.0798496 0.138304i
\(129\) 0 0
\(130\) −373.220 646.435i −0.251796 0.436124i
\(131\) 595.303 1031.10i 0.397037 0.687689i −0.596322 0.802746i \(-0.703372\pi\)
0.993359 + 0.115057i \(0.0367051\pi\)
\(132\) 0 0
\(133\) 2191.73 1079.10i 1.42893 0.703532i
\(134\) 1380.95 0.890268
\(135\) 0 0
\(136\) −84.7893 146.859i −0.0534605 0.0925963i
\(137\) 53.4807 + 92.6313i 0.0333516 + 0.0577666i 0.882219 0.470839i \(-0.156049\pi\)
−0.848868 + 0.528605i \(0.822715\pi\)
\(138\) 0 0
\(139\) −1096.78 −0.669262 −0.334631 0.942349i \(-0.608612\pi\)
−0.334631 + 0.942349i \(0.608612\pi\)
\(140\) −1289.73 862.965i −0.778587 0.520956i
\(141\) 0 0
\(142\) −428.128 + 741.539i −0.253012 + 0.438230i
\(143\) −125.605 217.555i −0.0734521 0.127223i
\(144\) 0 0
\(145\) 934.292 1618.24i 0.535094 0.926811i
\(146\) 1971.42 1.11751
\(147\) 0 0
\(148\) 677.012 0.376014
\(149\) 358.331 620.647i 0.197018 0.341244i −0.750542 0.660822i \(-0.770208\pi\)
0.947560 + 0.319578i \(0.103541\pi\)
\(150\) 0 0
\(151\) −77.1840 133.687i −0.0415970 0.0720481i 0.844477 0.535591i \(-0.179911\pi\)
−0.886074 + 0.463543i \(0.846578\pi\)
\(152\) −119.351 + 206.722i −0.0636885 + 0.110312i
\(153\) 0 0
\(154\) −845.175 565.511i −0.442248 0.295910i
\(155\) −832.564 −0.431439
\(156\) 0 0
\(157\) 1046.87 + 1813.24i 0.532163 + 0.921734i 0.999295 + 0.0375459i \(0.0119541\pi\)
−0.467132 + 0.884188i \(0.654713\pi\)
\(158\) −595.618 1031.64i −0.299904 0.519449i
\(159\) 0 0
\(160\) −2566.78 −1.26826
\(161\) 3294.50 1622.05i 1.61269 0.794008i
\(162\) 0 0
\(163\) −1503.93 + 2604.88i −0.722680 + 1.25172i 0.237242 + 0.971451i \(0.423757\pi\)
−0.959922 + 0.280268i \(0.909577\pi\)
\(164\) −1629.40 2822.20i −0.775820 1.34376i
\(165\) 0 0
\(166\) 1803.91 3124.46i 0.843437 1.46088i
\(167\) 2230.43 1.03351 0.516754 0.856134i \(-0.327140\pi\)
0.516754 + 0.856134i \(0.327140\pi\)
\(168\) 0 0
\(169\) −1852.76 −0.843312
\(170\) −1885.03 + 3264.97i −0.850444 + 1.47301i
\(171\) 0 0
\(172\) 1676.78 + 2904.26i 0.743332 + 1.28749i
\(173\) −281.585 + 487.719i −0.123749 + 0.214339i −0.921243 0.388987i \(-0.872825\pi\)
0.797495 + 0.603326i \(0.206158\pi\)
\(174\) 0 0
\(175\) 32.5174 491.300i 0.0140462 0.212222i
\(176\) −815.506 −0.349267
\(177\) 0 0
\(178\) 2320.42 + 4019.09i 0.977096 + 1.69238i
\(179\) 919.749 + 1593.05i 0.384052 + 0.665197i 0.991637 0.129057i \(-0.0411951\pi\)
−0.607585 + 0.794254i \(0.707862\pi\)
\(180\) 0 0
\(181\) 2324.71 0.954664 0.477332 0.878723i \(-0.341604\pi\)
0.477332 + 0.878723i \(0.341604\pi\)
\(182\) 1250.20 615.537i 0.509182 0.250696i
\(183\) 0 0
\(184\) −179.403 + 310.735i −0.0718790 + 0.124498i
\(185\) −397.587 688.641i −0.158006 0.273675i
\(186\) 0 0
\(187\) −634.400 + 1098.81i −0.248085 + 0.429696i
\(188\) −2299.71 −0.892149
\(189\) 0 0
\(190\) 5306.82 2.02630
\(191\) −1563.64 + 2708.30i −0.592360 + 1.02600i 0.401553 + 0.915836i \(0.368470\pi\)
−0.993914 + 0.110163i \(0.964863\pi\)
\(192\) 0 0
\(193\) 1854.64 + 3212.34i 0.691711 + 1.19808i 0.971277 + 0.237952i \(0.0764761\pi\)
−0.279566 + 0.960126i \(0.590191\pi\)
\(194\) −2807.56 + 4862.84i −1.03903 + 1.79965i
\(195\) 0 0
\(196\) 1766.56 2296.13i 0.643788 0.836781i
\(197\) −851.150 −0.307827 −0.153913 0.988084i \(-0.549188\pi\)
−0.153913 + 0.988084i \(0.549188\pi\)
\(198\) 0 0
\(199\) −1698.89 2942.57i −0.605182 1.04821i −0.992023 0.126060i \(-0.959767\pi\)
0.386840 0.922147i \(-0.373566\pi\)
\(200\) 24.0549 + 41.6643i 0.00850469 + 0.0147306i
\(201\) 0 0
\(202\) −7242.89 −2.52281
\(203\) 2899.29 + 1939.93i 1.00241 + 0.670720i
\(204\) 0 0
\(205\) −1913.78 + 3314.77i −0.652022 + 1.12934i
\(206\) −992.885 1719.73i −0.335813 0.581646i
\(207\) 0 0
\(208\) 558.757 967.796i 0.186264 0.322618i
\(209\) 1785.99 0.591098
\(210\) 0 0
\(211\) 216.732 0.0707132 0.0353566 0.999375i \(-0.488743\pi\)
0.0353566 + 0.999375i \(0.488743\pi\)
\(212\) −156.253 + 270.639i −0.0506204 + 0.0876772i
\(213\) 0 0
\(214\) 571.948 + 990.644i 0.182699 + 0.316444i
\(215\) 1969.44 3411.16i 0.624718 1.08204i
\(216\) 0 0
\(217\) 102.649 1550.91i 0.0321118 0.485173i
\(218\) −1164.84 −0.361893
\(219\) 0 0
\(220\) −567.241 982.490i −0.173833 0.301088i
\(221\) −869.340 1505.74i −0.264607 0.458312i
\(222\) 0 0
\(223\) −2254.86 −0.677115 −0.338558 0.940946i \(-0.609939\pi\)
−0.338558 + 0.940946i \(0.609939\pi\)
\(224\) 316.465 4781.43i 0.0943960 1.42622i
\(225\) 0 0
\(226\) 3842.92 6656.13i 1.13109 1.95911i
\(227\) −1695.40 2936.52i −0.495716 0.858606i 0.504271 0.863545i \(-0.331761\pi\)
−0.999988 + 0.00493916i \(0.998428\pi\)
\(228\) 0 0
\(229\) −1293.92 + 2241.14i −0.373384 + 0.646720i −0.990084 0.140479i \(-0.955136\pi\)
0.616700 + 0.787198i \(0.288469\pi\)
\(230\) 7976.95 2.28689
\(231\) 0 0
\(232\) −340.853 −0.0964574
\(233\) −477.210 + 826.552i −0.134176 + 0.232400i −0.925282 0.379279i \(-0.876172\pi\)
0.791106 + 0.611679i \(0.209505\pi\)
\(234\) 0 0
\(235\) 1350.55 + 2339.22i 0.374894 + 0.649336i
\(236\) 1671.29 2894.76i 0.460982 0.798444i
\(237\) 0 0
\(238\) −5849.62 3914.01i −1.59317 1.06600i
\(239\) −199.504 −0.0539951 −0.0269976 0.999635i \(-0.508595\pi\)
−0.0269976 + 0.999635i \(0.508595\pi\)
\(240\) 0 0
\(241\) −2397.21 4152.10i −0.640739 1.10979i −0.985268 0.171017i \(-0.945295\pi\)
0.344529 0.938776i \(-0.388039\pi\)
\(242\) 2327.15 + 4030.73i 0.618159 + 1.07068i
\(243\) 0 0
\(244\) 113.803 0.0298585
\(245\) −3373.01 448.459i −0.879567 0.116943i
\(246\) 0 0
\(247\) −1223.70 + 2119.51i −0.315231 + 0.545997i
\(248\) 75.9351 + 131.523i 0.0194431 + 0.0336764i
\(249\) 0 0
\(250\) 3049.23 5281.42i 0.771401 1.33611i
\(251\) −6249.73 −1.57163 −0.785816 0.618460i \(-0.787757\pi\)
−0.785816 + 0.618460i \(0.787757\pi\)
\(252\) 0 0
\(253\) 2684.61 0.667114
\(254\) 2479.71 4294.99i 0.612564 1.06099i
\(255\) 0 0
\(256\) −1800.79 3119.07i −0.439647 0.761491i
\(257\) −1918.93 + 3323.68i −0.465756 + 0.806713i −0.999235 0.0390999i \(-0.987551\pi\)
0.533479 + 0.845813i \(0.320884\pi\)
\(258\) 0 0
\(259\) 1331.83 655.726i 0.319521 0.157316i
\(260\) 1554.62 0.370821
\(261\) 0 0
\(262\) 2414.19 + 4181.50i 0.569271 + 0.986007i
\(263\) 103.602 + 179.443i 0.0242903 + 0.0420721i 0.877915 0.478816i \(-0.158934\pi\)
−0.853625 + 0.520889i \(0.825601\pi\)
\(264\) 0 0
\(265\) 367.051 0.0850858
\(266\) −654.292 + 9885.61i −0.150817 + 2.27867i
\(267\) 0 0
\(268\) −1438.06 + 2490.80i −0.327775 + 0.567722i
\(269\) 2402.04 + 4160.46i 0.544442 + 0.943002i 0.998642 + 0.0521018i \(0.0165920\pi\)
−0.454199 + 0.890900i \(0.650075\pi\)
\(270\) 0 0
\(271\) −1607.88 + 2784.92i −0.360411 + 0.624251i −0.988029 0.154271i \(-0.950697\pi\)
0.627617 + 0.778522i \(0.284030\pi\)
\(272\) −5644.27 −1.25821
\(273\) 0 0
\(274\) −433.771 −0.0956388
\(275\) 179.980 311.735i 0.0394663 0.0683576i
\(276\) 0 0
\(277\) −1027.20 1779.16i −0.222810 0.385918i 0.732850 0.680390i \(-0.238190\pi\)
−0.955660 + 0.294472i \(0.904856\pi\)
\(278\) 2223.93 3851.97i 0.479794 0.831027i
\(279\) 0 0
\(280\) 298.283 146.859i 0.0636635 0.0313447i
\(281\) −1768.61 −0.375468 −0.187734 0.982220i \(-0.560114\pi\)
−0.187734 + 0.982220i \(0.560114\pi\)
\(282\) 0 0
\(283\) −1170.26 2026.96i −0.245813 0.425760i 0.716547 0.697539i \(-0.245721\pi\)
−0.962360 + 0.271779i \(0.912388\pi\)
\(284\) −891.668 1544.41i −0.186305 0.322690i
\(285\) 0 0
\(286\) 1018.76 0.210631
\(287\) −5938.84 3973.71i −1.22146 0.817284i
\(288\) 0 0
\(289\) −1934.31 + 3350.32i −0.393712 + 0.681929i
\(290\) 3788.92 + 6562.60i 0.767217 + 1.32886i
\(291\) 0 0
\(292\) −2052.95 + 3555.82i −0.411438 + 0.712632i
\(293\) 3633.47 0.724470 0.362235 0.932087i \(-0.382014\pi\)
0.362235 + 0.932087i \(0.382014\pi\)
\(294\) 0 0
\(295\) −3925.98 −0.774846
\(296\) −72.5250 + 125.617i −0.0142413 + 0.0246667i
\(297\) 0 0
\(298\) 1453.17 + 2516.97i 0.282483 + 0.489276i
\(299\) −1839.40 + 3185.94i −0.355771 + 0.616213i
\(300\) 0 0
\(301\) 6111.54 + 4089.26i 1.17031 + 0.783060i
\(302\) 626.023 0.119283
\(303\) 0 0
\(304\) 3972.50 + 6880.56i 0.749468 + 1.29812i
\(305\) −66.8326 115.758i −0.0125470 0.0217320i
\(306\) 0 0
\(307\) 5954.32 1.10694 0.553471 0.832868i \(-0.313303\pi\)
0.553471 + 0.832868i \(0.313303\pi\)
\(308\) 1900.13 935.529i 0.351526 0.173074i
\(309\) 0 0
\(310\) 1688.19 2924.03i 0.309299 0.535721i
\(311\) 590.047 + 1021.99i 0.107584 + 0.186340i 0.914791 0.403928i \(-0.132355\pi\)
−0.807207 + 0.590268i \(0.799022\pi\)
\(312\) 0 0
\(313\) 4873.12 8440.50i 0.880017 1.52423i 0.0286960 0.999588i \(-0.490865\pi\)
0.851321 0.524646i \(-0.175802\pi\)
\(314\) −8490.97 −1.52603
\(315\) 0 0
\(316\) 2481.00 0.441669
\(317\) 4295.96 7440.81i 0.761151 1.31835i −0.181106 0.983464i \(-0.557968\pi\)
0.942258 0.334889i \(-0.108699\pi\)
\(318\) 0 0
\(319\) 1275.14 + 2208.62i 0.223807 + 0.387645i
\(320\) 2814.59 4875.01i 0.491688 0.851629i
\(321\) 0 0
\(322\) −983.499 + 14859.6i −0.170212 + 2.57171i
\(323\) 12361.2 2.12939
\(324\) 0 0
\(325\) 246.633 + 427.181i 0.0420946 + 0.0729100i
\(326\) −6099.02 10563.8i −1.03618 1.79471i
\(327\) 0 0
\(328\) 698.197 0.117535
\(329\) −4524.04 + 2227.41i −0.758111 + 0.373256i
\(330\) 0 0
\(331\) 2625.60 4547.67i 0.436000 0.755174i −0.561377 0.827560i \(-0.689728\pi\)
0.997377 + 0.0723864i \(0.0230615\pi\)
\(332\) 3757.03 + 6507.36i 0.621065 + 1.07572i
\(333\) 0 0
\(334\) −4522.64 + 7833.44i −0.740921 + 1.28331i
\(335\) 3378.11 0.550943
\(336\) 0 0
\(337\) −8496.45 −1.37339 −0.686693 0.726947i \(-0.740938\pi\)
−0.686693 + 0.726947i \(0.740938\pi\)
\(338\) 3756.83 6507.02i 0.604570 1.04715i
\(339\) 0 0
\(340\) −3925.98 6800.00i −0.626225 1.08465i
\(341\) 568.152 984.068i 0.0902263 0.156276i
\(342\) 0 0
\(343\) 1251.26 6228.00i 0.196973 0.980409i
\(344\) −718.500 −0.112613
\(345\) 0 0
\(346\) −1141.94 1977.89i −0.177430 0.307319i
\(347\) −2915.07 5049.06i −0.450978 0.781117i 0.547469 0.836826i \(-0.315591\pi\)
−0.998447 + 0.0557090i \(0.982258\pi\)
\(348\) 0 0
\(349\) 1811.13 0.277786 0.138893 0.990307i \(-0.455646\pi\)
0.138893 + 0.990307i \(0.455646\pi\)
\(350\) 1659.55 + 1110.41i 0.253447 + 0.169583i
\(351\) 0 0
\(352\) 1751.60 3033.87i 0.265230 0.459391i
\(353\) 1663.88 + 2881.92i 0.250876 + 0.434531i 0.963767 0.266744i \(-0.0859479\pi\)
−0.712891 + 0.701275i \(0.752615\pi\)
\(354\) 0 0
\(355\) −1047.30 + 1813.97i −0.156577 + 0.271199i
\(356\) −9665.55 −1.43897
\(357\) 0 0
\(358\) −7459.89 −1.10131
\(359\) −435.430 + 754.188i −0.0640143 + 0.110876i −0.896256 0.443536i \(-0.853724\pi\)
0.832242 + 0.554413i \(0.187057\pi\)
\(360\) 0 0
\(361\) −5270.42 9128.63i −0.768395 1.33090i
\(362\) −4713.80 + 8164.55i −0.684398 + 1.18541i
\(363\) 0 0
\(364\) −191.673 + 2895.96i −0.0276000 + 0.417004i
\(365\) 4822.54 0.691570
\(366\) 0 0
\(367\) −587.358 1017.33i −0.0835418 0.144699i 0.821227 0.570601i \(-0.193290\pi\)
−0.904769 + 0.425903i \(0.859957\pi\)
\(368\) 5971.26 + 10342.5i 0.845851 + 1.46506i
\(369\) 0 0
\(370\) 3224.75 0.453099
\(371\) −45.2546 + 683.746i −0.00633289 + 0.0956829i
\(372\) 0 0
\(373\) −1814.17 + 3142.23i −0.251834 + 0.436189i −0.964031 0.265791i \(-0.914367\pi\)
0.712197 + 0.701980i \(0.247700\pi\)
\(374\) −2572.74 4456.12i −0.355704 0.616097i
\(375\) 0 0
\(376\) 246.357 426.703i 0.0337897 0.0585254i
\(377\) −3494.75 −0.477424
\(378\) 0 0
\(379\) 7321.99 0.992362 0.496181 0.868219i \(-0.334735\pi\)
0.496181 + 0.868219i \(0.334735\pi\)
\(380\) −5526.29 + 9571.82i −0.746034 + 1.29217i
\(381\) 0 0
\(382\) −6341.17 10983.2i −0.849325 1.47107i
\(383\) −3677.45 + 6369.52i −0.490623 + 0.849784i −0.999942 0.0107937i \(-0.996564\pi\)
0.509318 + 0.860578i \(0.329898\pi\)
\(384\) 0 0
\(385\) −2067.49 1383.36i −0.273685 0.183124i
\(386\) −15042.6 −1.98355
\(387\) 0 0
\(388\) −5847.35 10127.9i −0.765088 1.32517i
\(389\) 4534.81 + 7854.52i 0.591064 + 1.02375i 0.994089 + 0.108564i \(0.0346254\pi\)
−0.403025 + 0.915189i \(0.632041\pi\)
\(390\) 0 0
\(391\) 18580.7 2.40324
\(392\) 236.795 + 573.751i 0.0305101 + 0.0739255i
\(393\) 0 0
\(394\) 1725.87 2989.30i 0.220681 0.382230i
\(395\) −1457.01 2523.62i −0.185596 0.321462i
\(396\) 0 0
\(397\) −3688.41 + 6388.52i −0.466288 + 0.807634i −0.999259 0.0384997i \(-0.987742\pi\)
0.532971 + 0.846134i \(0.321075\pi\)
\(398\) 13779.4 1.73542
\(399\) 0 0
\(400\) 1601.29 0.200161
\(401\) −1426.76 + 2471.21i −0.177678 + 0.307747i −0.941085 0.338171i \(-0.890192\pi\)
0.763407 + 0.645918i \(0.223525\pi\)
\(402\) 0 0
\(403\) 778.558 + 1348.50i 0.0962350 + 0.166684i
\(404\) 7542.43 13063.9i 0.928836 1.60879i
\(405\) 0 0
\(406\) −12692.0 + 6248.93i −1.55147 + 0.763864i
\(407\) 1085.27 0.132175
\(408\) 0 0
\(409\) −5630.03 9751.49i −0.680652 1.17892i −0.974782 0.223159i \(-0.928363\pi\)
0.294130 0.955766i \(-0.404970\pi\)
\(410\) −7761.15 13442.7i −0.934868 1.61924i
\(411\) 0 0
\(412\) 4135.79 0.494553
\(413\) 484.045 7313.37i 0.0576714 0.871350i
\(414\) 0 0
\(415\) 4412.76 7643.13i 0.521961 0.904064i
\(416\) 2400.28 + 4157.41i 0.282893 + 0.489985i
\(417\) 0 0
\(418\) −3621.44 + 6272.52i −0.423757 + 0.733969i
\(419\) 9221.47 1.07517 0.537587 0.843208i \(-0.319336\pi\)
0.537587 + 0.843208i \(0.319336\pi\)
\(420\) 0 0
\(421\) −8520.28 −0.986349 −0.493175 0.869930i \(-0.664164\pi\)
−0.493175 + 0.869930i \(0.664164\pi\)
\(422\) −439.468 + 761.181i −0.0506942 + 0.0878049i
\(423\) 0 0
\(424\) −33.4774 57.9845i −0.00383444 0.00664145i
\(425\) 1245.68 2157.58i 0.142175 0.246254i
\(426\) 0 0
\(427\) 223.874 110.225i 0.0253725 0.0124921i
\(428\) −2382.41 −0.269061
\(429\) 0 0
\(430\) 7986.84 + 13833.6i 0.895720 + 1.55143i
\(431\) 4581.05 + 7934.62i 0.511976 + 0.886768i 0.999904 + 0.0138840i \(0.00441955\pi\)
−0.487928 + 0.872884i \(0.662247\pi\)
\(432\) 0 0
\(433\) −10976.2 −1.21820 −0.609100 0.793093i \(-0.708469\pi\)
−0.609100 + 0.793093i \(0.708469\pi\)
\(434\) 5238.77 + 3505.28i 0.579421 + 0.387694i
\(435\) 0 0
\(436\) 1213.01 2100.99i 0.133240 0.230778i
\(437\) −13077.3 22650.5i −1.43151 2.47945i
\(438\) 0 0
\(439\) −1991.59 + 3449.54i −0.216523 + 0.375028i −0.953743 0.300625i \(-0.902805\pi\)
0.737220 + 0.675653i \(0.236138\pi\)
\(440\) 243.063 0.0263354
\(441\) 0 0
\(442\) 7051.03 0.758786
\(443\) 2262.22 3918.29i 0.242622 0.420234i −0.718838 0.695177i \(-0.755326\pi\)
0.961460 + 0.274944i \(0.0886592\pi\)
\(444\) 0 0
\(445\) 5676.27 + 9831.59i 0.604676 + 1.04733i
\(446\) 4572.18 7919.24i 0.485423 0.840778i
\(447\) 0 0
\(448\) 8734.21 + 5844.10i 0.921099 + 0.616312i
\(449\) 2076.49 0.218253 0.109127 0.994028i \(-0.465195\pi\)
0.109127 + 0.994028i \(0.465195\pi\)
\(450\) 0 0
\(451\) −2611.98 4524.09i −0.272713 0.472352i
\(452\) 8003.70 + 13862.8i 0.832881 + 1.44259i
\(453\) 0 0
\(454\) 13751.0 1.42151
\(455\) 3058.27 1505.74i 0.315108 0.155143i
\(456\) 0 0
\(457\) 923.795 1600.06i 0.0945587 0.163780i −0.814866 0.579650i \(-0.803189\pi\)
0.909424 + 0.415869i \(0.136523\pi\)
\(458\) −5247.37 9088.71i −0.535357 0.927266i
\(459\) 0 0
\(460\) −8306.85 + 14387.9i −0.841976 + 1.45834i
\(461\) −876.945 −0.0885974 −0.0442987 0.999018i \(-0.514105\pi\)
−0.0442987 + 0.999018i \(0.514105\pi\)
\(462\) 0 0
\(463\) 16245.2 1.63062 0.815310 0.579025i \(-0.196566\pi\)
0.815310 + 0.579025i \(0.196566\pi\)
\(464\) −5672.50 + 9825.05i −0.567541 + 0.983010i
\(465\) 0 0
\(466\) −1935.27 3351.99i −0.192382 0.333215i
\(467\) −9480.88 + 16421.4i −0.939449 + 1.62717i −0.172947 + 0.984931i \(0.555329\pi\)
−0.766502 + 0.642242i \(0.778004\pi\)
\(468\) 0 0
\(469\) −416.496 + 6292.78i −0.0410064 + 0.619560i
\(470\) −10954.0 −1.07505
\(471\) 0 0
\(472\) 358.075 + 620.204i 0.0349189 + 0.0604813i
\(473\) 2687.94 + 4655.64i 0.261293 + 0.452572i
\(474\) 0 0
\(475\) −3506.89 −0.338752
\(476\) 13151.2 6474.98i 1.26635 0.623488i
\(477\) 0 0
\(478\) 404.533 700.672i 0.0387090 0.0670460i
\(479\) −4188.88 7255.35i −0.399572 0.692078i 0.594101 0.804390i \(-0.297508\pi\)
−0.993673 + 0.112312i \(0.964174\pi\)
\(480\) 0 0
\(481\) −743.594 + 1287.94i −0.0704885 + 0.122090i
\(482\) 19443.3 1.83738
\(483\) 0 0
\(484\) −9693.55 −0.910364
\(485\) −6867.92 + 11895.6i −0.643002 + 1.11371i
\(486\) 0 0
\(487\) 2279.42 + 3948.08i 0.212096 + 0.367360i 0.952370 0.304944i \(-0.0986378\pi\)
−0.740275 + 0.672305i \(0.765304\pi\)
\(488\) −12.1911 + 21.1156i −0.00113087 + 0.00195873i
\(489\) 0 0
\(490\) 8414.47 10936.9i 0.775769 1.00833i
\(491\) −15809.9 −1.45314 −0.726570 0.687092i \(-0.758887\pi\)
−0.726570 + 0.687092i \(0.758887\pi\)
\(492\) 0 0
\(493\) 8825.53 + 15286.3i 0.806251 + 1.39647i
\(494\) −4962.59 8595.45i −0.451978 0.782849i
\(495\) 0 0
\(496\) 5054.86 0.457601
\(497\) −3249.96 2174.56i −0.293321 0.196263i
\(498\) 0 0
\(499\) −6693.04 + 11592.7i −0.600444 + 1.04000i 0.392309 + 0.919833i \(0.371676\pi\)
−0.992754 + 0.120167i \(0.961657\pi\)
\(500\) 6350.67 + 10999.7i 0.568022 + 0.983842i
\(501\) 0 0
\(502\) 12672.6 21949.5i 1.12670 1.95150i
\(503\) −5720.55 −0.507091 −0.253545 0.967323i \(-0.581597\pi\)
−0.253545 + 0.967323i \(0.581597\pi\)
\(504\) 0 0
\(505\) −17717.7 −1.56124
\(506\) −5443.57 + 9428.54i −0.478254 + 0.828359i
\(507\) 0 0
\(508\) 5164.53 + 8945.24i 0.451061 + 0.781261i
\(509\) −7646.59 + 13244.3i −0.665873 + 1.15333i 0.313175 + 0.949695i \(0.398607\pi\)
−0.979048 + 0.203630i \(0.934726\pi\)
\(510\) 0 0
\(511\) −594.583 + 8983.48i −0.0514732 + 0.777702i
\(512\) 16456.0 1.42043
\(513\) 0 0
\(514\) −7782.00 13478.8i −0.667800 1.15666i
\(515\) −2428.82 4206.83i −0.207818 0.359952i
\(516\) 0 0
\(517\) −3686.53 −0.313604
\(518\) −397.587 + 6007.10i −0.0337239 + 0.509530i
\(519\) 0 0
\(520\) −166.539 + 288.454i −0.0140446 + 0.0243260i
\(521\) 2184.35 + 3783.40i 0.183681 + 0.318145i 0.943131 0.332420i \(-0.107865\pi\)
−0.759450 + 0.650566i \(0.774532\pi\)
\(522\) 0 0
\(523\) 1211.08 2097.66i 0.101256 0.175381i −0.810946 0.585121i \(-0.801047\pi\)
0.912202 + 0.409740i \(0.134381\pi\)
\(524\) −10056.1 −0.838366
\(525\) 0 0
\(526\) −840.291 −0.0696548
\(527\) 3932.29 6810.93i 0.325035 0.562976i
\(528\) 0 0
\(529\) −13573.6 23510.2i −1.11561 1.93229i
\(530\) −744.268 + 1289.11i −0.0609980 + 0.105652i
\(531\) 0 0
\(532\) −17149.2 11474.6i −1.39758 0.935124i
\(533\) 7158.57 0.581749
\(534\) 0 0
\(535\) 1399.11 + 2423.33i 0.113063 + 0.195832i
\(536\) −308.105 533.654i −0.0248286 0.0430044i
\(537\) 0 0
\(538\) −19482.4 −1.56124
\(539\) 2831.85 3680.78i 0.226302 0.294142i
\(540\) 0 0
\(541\) −6581.27 + 11399.1i −0.523014 + 0.905888i 0.476627 + 0.879106i \(0.341859\pi\)
−0.999641 + 0.0267819i \(0.991474\pi\)
\(542\) −6520.57 11294.0i −0.516757 0.895050i
\(543\) 0 0
\(544\) 12123.2 20998.0i 0.955473 1.65493i
\(545\) −2849.45 −0.223958
\(546\) 0 0
\(547\) 12112.4 0.946778 0.473389 0.880853i \(-0.343031\pi\)
0.473389 + 0.880853i \(0.343031\pi\)
\(548\) 451.710 782.384i 0.0352118 0.0609887i
\(549\) 0 0
\(550\) 729.892 + 1264.21i 0.0565867 + 0.0980110i
\(551\) 12423.0 21517.2i 0.960503 1.66364i
\(552\) 0 0
\(553\) 4880.68 2403.00i 0.375312 0.184785i
\(554\) 8331.38 0.638928
\(555\) 0 0
\(556\) 4631.81 + 8022.54i 0.353296 + 0.611927i
\(557\) −4179.82 7239.67i −0.317962 0.550726i 0.662101 0.749415i \(-0.269665\pi\)
−0.980063 + 0.198689i \(0.936332\pi\)
\(558\) 0 0
\(559\) −7366.74 −0.557388
\(560\) 730.829 11042.0i 0.0551485 0.833231i
\(561\) 0 0
\(562\) 3586.21 6211.50i 0.269173 0.466221i
\(563\) 6819.20 + 11811.2i 0.510471 + 0.884162i 0.999926 + 0.0121334i \(0.00386228\pi\)
−0.489455 + 0.872028i \(0.662804\pi\)
\(564\) 0 0
\(565\) 9400.63 16282.4i 0.699978 1.21240i
\(566\) 9491.76 0.704891
\(567\) 0 0
\(568\) 382.080 0.0282249
\(569\) 7745.67 13415.9i 0.570677 0.988442i −0.425820 0.904808i \(-0.640014\pi\)
0.996497 0.0836335i \(-0.0266525\pi\)
\(570\) 0 0
\(571\) 2324.08 + 4025.42i 0.170332 + 0.295024i 0.938536 0.345182i \(-0.112183\pi\)
−0.768204 + 0.640205i \(0.778849\pi\)
\(572\) −1060.89 + 1837.52i −0.0775491 + 0.134319i
\(573\) 0 0
\(574\) 25998.1 12800.2i 1.89049 0.930782i
\(575\) −5271.38 −0.382316
\(576\) 0 0
\(577\) 2739.53 + 4745.01i 0.197657 + 0.342352i 0.947768 0.318959i \(-0.103333\pi\)
−0.750111 + 0.661312i \(0.770000\pi\)
\(578\) −7844.37 13586.8i −0.564503 0.977748i
\(579\) 0 0
\(580\) −15782.5 −1.12988
\(581\) 13693.6 + 9162.49i 0.977811 + 0.654258i
\(582\) 0 0
\(583\) −250.480 + 433.844i −0.0177939 + 0.0308199i
\(584\) −439.846 761.836i −0.0311660 0.0539811i
\(585\) 0 0
\(586\) −7367.59 + 12761.0i −0.519372 + 0.899579i
\(587\) −4408.22 −0.309960 −0.154980 0.987918i \(-0.549531\pi\)
−0.154980 + 0.987918i \(0.549531\pi\)
\(588\) 0 0
\(589\) −11070.3 −0.774441
\(590\) 7960.71 13788.3i 0.555487 0.962131i
\(591\) 0 0
\(592\) 2413.93 + 4181.05i 0.167588 + 0.290270i
\(593\) 1407.63 2438.08i 0.0974779 0.168837i −0.813162 0.582037i \(-0.802256\pi\)
0.910640 + 0.413201i \(0.135589\pi\)
\(594\) 0 0
\(595\) −14309.5 9574.54i −0.985935 0.659694i
\(596\) −6053.09 −0.416014
\(597\) 0 0
\(598\) −7459.51 12920.2i −0.510104 0.883526i
\(599\) 9859.53 + 17077.2i 0.672537 + 1.16487i 0.977182 + 0.212402i \(0.0681287\pi\)
−0.304646 + 0.952466i \(0.598538\pi\)
\(600\) 0 0
\(601\) −13982.8 −0.949033 −0.474517 0.880247i \(-0.657377\pi\)
−0.474517 + 0.880247i \(0.657377\pi\)
\(602\) −26754.1 + 13172.4i −1.81132 + 0.891805i
\(603\) 0 0
\(604\) −651.913 + 1129.15i −0.0439172 + 0.0760667i
\(605\) 5692.71 + 9860.07i 0.382548 + 0.662593i
\(606\) 0 0
\(607\) −6694.14 + 11594.6i −0.447622 + 0.775305i −0.998231 0.0594590i \(-0.981062\pi\)
0.550608 + 0.834764i \(0.314396\pi\)
\(608\) −34129.7 −2.27655
\(609\) 0 0
\(610\) 542.065 0.0359797
\(611\) 2525.89 4374.96i 0.167245 0.289676i
\(612\) 0 0
\(613\) 13895.9 + 24068.5i 0.915582 + 1.58583i 0.806047 + 0.591852i \(0.201603\pi\)
0.109535 + 0.993983i \(0.465064\pi\)
\(614\) −12073.6 + 20912.0i −0.793566 + 1.37450i
\(615\) 0 0
\(616\) −29.9679 + 452.781i −0.00196013 + 0.0296154i
\(617\) 19107.2 1.24672 0.623361 0.781935i \(-0.285767\pi\)
0.623361 + 0.781935i \(0.285767\pi\)
\(618\) 0 0
\(619\) −546.469 946.512i −0.0354837 0.0614596i 0.847738 0.530415i \(-0.177964\pi\)
−0.883222 + 0.468955i \(0.844631\pi\)
\(620\) 3516.01 + 6089.90i 0.227752 + 0.394478i
\(621\) 0 0
\(622\) −4785.75 −0.308507
\(623\) −19014.2 + 9361.66i −1.22278 + 0.602034i
\(624\) 0 0
\(625\) 5797.49 10041.5i 0.371039 0.642659i
\(626\) 19762.4 + 34229.5i 1.26177 + 2.18544i
\(627\) 0 0
\(628\) 8842.13 15315.0i 0.561846 0.973146i
\(629\) 7511.40 0.476151
\(630\) 0 0
\(631\) 19235.2 1.21353 0.606767 0.794879i \(-0.292466\pi\)
0.606767 + 0.794879i \(0.292466\pi\)
\(632\) −265.778 + 460.341i −0.0167280 + 0.0289737i
\(633\) 0 0
\(634\) 17421.8 + 30175.4i 1.09134 + 1.89025i
\(635\) 6065.93 10506.5i 0.379085 0.656595i
\(636\) 0 0
\(637\) 2427.85 + 5882.63i 0.151012 + 0.365900i
\(638\) −10342.4 −0.641788
\(639\) 0 0
\(640\) 1147.14 + 1986.91i 0.0708511 + 0.122718i
\(641\) −9975.33 17277.8i −0.614667 1.06463i −0.990443 0.137924i \(-0.955957\pi\)
0.375776 0.926711i \(-0.377376\pi\)
\(642\) 0 0
\(643\) 688.125 0.0422037 0.0211019 0.999777i \(-0.493283\pi\)
0.0211019 + 0.999777i \(0.493283\pi\)
\(644\) −25777.7 17248.0i −1.57731 1.05538i
\(645\) 0 0
\(646\) −25064.7 + 43413.4i −1.52656 + 2.64408i
\(647\) 5483.09 + 9497.00i 0.333173 + 0.577072i 0.983132 0.182897i \(-0.0585475\pi\)
−0.649959 + 0.759969i \(0.725214\pi\)
\(648\) 0 0
\(649\) 2679.14 4640.41i 0.162042 0.280666i
\(650\) −2000.39 −0.120710
\(651\) 0 0
\(652\) 25405.0 1.52598
\(653\) −6462.54 + 11193.4i −0.387287 + 0.670802i −0.992084 0.125579i \(-0.959921\pi\)
0.604796 + 0.796380i \(0.293255\pi\)
\(654\) 0 0
\(655\) 5905.64 + 10228.9i 0.352294 + 0.610191i
\(656\) 11619.4 20125.5i 0.691559 1.19782i
\(657\) 0 0
\(658\) 1350.55 20405.3i 0.0800150 1.20894i
\(659\) 11779.0 0.696273 0.348137 0.937444i \(-0.386815\pi\)
0.348137 + 0.937444i \(0.386815\pi\)
\(660\) 0 0
\(661\) 12520.0 + 21685.3i 0.736721 + 1.27604i 0.953964 + 0.299921i \(0.0969604\pi\)
−0.217243 + 0.976118i \(0.569706\pi\)
\(662\) 10647.8 + 18442.6i 0.625136 + 1.08277i
\(663\) 0 0
\(664\) −1609.89 −0.0940900
\(665\) −1600.54 + 24182.4i −0.0933329 + 1.41016i
\(666\) 0 0
\(667\) 18673.6 32343.6i 1.08403 1.87759i
\(668\) −9419.36 16314.8i −0.545578 0.944968i
\(669\) 0 0
\(670\) −6849.78 + 11864.2i −0.394971 + 0.684109i
\(671\) 182.430 0.0104957
\(672\) 0 0
\(673\) 4104.64 0.235100 0.117550 0.993067i \(-0.462496\pi\)
0.117550 + 0.993067i \(0.462496\pi\)
\(674\) 17228.2 29840.2i 0.984580 1.70534i
\(675\) 0 0
\(676\) 7824.40 + 13552.3i 0.445175 + 0.771066i
\(677\) 6076.70 10525.1i 0.344973 0.597510i −0.640376 0.768061i \(-0.721222\pi\)
0.985349 + 0.170551i \(0.0545549\pi\)
\(678\) 0 0
\(679\) −21312.5 14260.3i −1.20456 0.805978i
\(680\) 1682.29 0.0948717
\(681\) 0 0
\(682\) 2304.08 + 3990.78i 0.129366 + 0.224069i
\(683\) −10207.0 17679.0i −0.571830 0.990438i −0.996378 0.0850328i \(-0.972900\pi\)
0.424549 0.905405i \(-0.360433\pi\)
\(684\) 0 0
\(685\) −1061.10 −0.0591862
\(686\) 19336.0 + 17023.0i 1.07617 + 0.947437i
\(687\) 0 0
\(688\) −11957.3 + 20710.7i −0.662600 + 1.14766i
\(689\) −343.241 594.511i −0.0189789 0.0328724i
\(690\) 0 0
\(691\) −8046.76 + 13937.4i −0.443000 + 0.767299i −0.997911 0.0646110i \(-0.979419\pi\)
0.554910 + 0.831910i \(0.312753\pi\)
\(692\) 4756.66 0.261302
\(693\) 0 0
\(694\) 23643.6 1.29322
\(695\) 5440.23 9422.76i 0.296921 0.514282i
\(696\) 0 0
\(697\) −18078.0 31312.1i −0.982431 1.70162i
\(698\) −3672.42 + 6360.81i −0.199145 + 0.344929i
\(699\) 0 0
\(700\) −3731.01 + 1836.96i −0.201456 + 0.0991867i
\(701\) −20803.0 −1.12085 −0.560426 0.828204i \(-0.689363\pi\)
−0.560426 + 0.828204i \(0.689363\pi\)
\(702\) 0 0
\(703\) −5286.60 9156.65i −0.283624 0.491251i
\(704\) 3841.42 + 6653.54i 0.205652 + 0.356200i
\(705\) 0 0
\(706\) −13495.4 −0.719412
\(707\) 2184.46 33004.8i 0.116202 1.75569i
\(708\) 0 0
\(709\) −70.7460 + 122.536i −0.00374742 + 0.00649073i −0.867893 0.496751i \(-0.834526\pi\)
0.864146 + 0.503242i \(0.167860\pi\)
\(710\) −4247.20 7356.36i −0.224499 0.388844i
\(711\) 0 0
\(712\) 1035.42 1793.41i 0.0545002 0.0943971i
\(713\) −16640.4 −0.874035
\(714\) 0 0
\(715\) 2492.11 0.130349
\(716\) 7768.40 13455.3i 0.405473 0.702300i
\(717\) 0 0
\(718\) −1765.84 3058.53i −0.0917836 0.158974i
\(719\) −3332.23 + 5771.59i −0.172839 + 0.299366i −0.939411 0.342792i \(-0.888627\pi\)
0.766572 + 0.642158i \(0.221961\pi\)
\(720\) 0 0
\(721\) 8135.99 4005.76i 0.420250 0.206910i
\(722\) 42747.2 2.20345
\(723\) 0 0
\(724\) −9817.50 17004.4i −0.503957 0.872878i
\(725\) −2503.82 4336.74i −0.128261 0.222155i
\(726\) 0 0
\(727\) −4837.23 −0.246772 −0.123386 0.992359i \(-0.539375\pi\)
−0.123386 + 0.992359i \(0.539375\pi\)
\(728\) −516.802 345.795i −0.0263104 0.0176044i
\(729\) 0 0
\(730\) −9778.65 + 16937.1i −0.495786 + 0.858727i
\(731\) 18603.7 + 32222.6i 0.941291 + 1.63036i
\(732\) 0 0
\(733\) 15801.3 27368.6i 0.796225 1.37910i −0.125834 0.992051i \(-0.540161\pi\)
0.922059 0.387050i \(-0.126506\pi\)
\(734\) 4763.93 0.239564
\(735\) 0 0
\(736\) −51302.0 −2.56932
\(737\) −2305.27 + 3992.84i −0.115218 + 0.199563i
\(738\) 0 0
\(739\) 4113.79 + 7125.30i 0.204774 + 0.354680i 0.950061 0.312065i \(-0.101021\pi\)
−0.745286 + 0.666744i \(0.767687\pi\)
\(740\) −3358.11 + 5816.42i −0.166820 + 0.288940i
\(741\) 0 0
\(742\) −2309.61 1545.37i −0.114270 0.0764586i
\(743\) −37020.3 −1.82792 −0.913959 0.405805i \(-0.866991\pi\)
−0.913959 + 0.405805i \(0.866991\pi\)
\(744\) 0 0
\(745\) 3554.78 + 6157.07i 0.174815 + 0.302789i
\(746\) −7357.16 12743.0i −0.361079 0.625407i
\(747\) 0 0
\(748\) 10716.6 0.523846
\(749\) −4686.72 + 2307.50i −0.228637 + 0.112569i
\(750\) 0 0
\(751\) 12575.0 21780.5i 0.611008 1.05830i −0.380063 0.924960i \(-0.624098\pi\)
0.991071 0.133336i \(-0.0425689\pi\)
\(752\) −8199.78 14202.4i −0.397627 0.688710i
\(753\) 0 0
\(754\) 7086.29 12273.8i 0.342265 0.592820i
\(755\) 1531.39 0.0738186
\(756\) 0 0
\(757\) 20460.8 0.982377 0.491189 0.871053i \(-0.336563\pi\)
0.491189 + 0.871053i \(0.336563\pi\)
\(758\) −14846.8 + 25715.4i −0.711424 + 1.23222i
\(759\) 0 0
\(760\) −1184.01 2050.77i −0.0565113 0.0978804i
\(761\) 16329.6 28283.6i 0.777853 1.34728i −0.155324 0.987864i \(-0.549642\pi\)
0.933177 0.359417i \(-0.117024\pi\)
\(762\) 0 0
\(763\) 351.316 5307.98i 0.0166690 0.251850i
\(764\) 26413.7 1.25080
\(765\) 0 0
\(766\) −14913.5 25830.9i −0.703455 1.21842i
\(767\) 3671.32 + 6358.91i 0.172834 + 0.299357i
\(768\) 0 0
\(769\) −11005.3 −0.516075 −0.258037 0.966135i \(-0.583076\pi\)
−0.258037 + 0.966135i \(0.583076\pi\)
\(770\) 9050.72 4456.12i 0.423591 0.208555i
\(771\) 0 0
\(772\) 15664.7 27132.1i 0.730293 1.26490i
\(773\) −1519.09 2631.14i −0.0706829 0.122426i 0.828518 0.559963i \(-0.189185\pi\)
−0.899201 + 0.437536i \(0.855851\pi\)
\(774\) 0 0
\(775\) −1115.60 + 1932.27i −0.0517077 + 0.0895604i
\(776\) 2505.59 0.115909
\(777\) 0 0
\(778\) −36780.9 −1.69493
\(779\) −25447.0 + 44075.5i −1.17039 + 2.02717i
\(780\) 0 0
\(781\) −1429.38 2475.75i −0.0654893 0.113431i
\(782\) −37676.0 + 65256.8i −1.72288 + 2.98411i
\(783\) 0 0
\(784\) 20479.1 + 2722.79i 0.932902 + 0.124034i
\(785\) −20770.8 −0.944384
\(786\) 0 0
\(787\) 6153.38 + 10658.0i 0.278710 + 0.482739i 0.971064 0.238818i \(-0.0767600\pi\)
−0.692355 + 0.721557i \(0.743427\pi\)