Properties

Label 252.4.x.a.41.2
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.2
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.09172 - 1.03651i) q^{3} +(-10.5571 + 18.2854i) q^{5} +(-4.11592 + 18.0571i) q^{7} +(24.8513 + 10.5552i) q^{9} +O(q^{10})\) \(q+(-5.09172 - 1.03651i) q^{3} +(-10.5571 + 18.2854i) q^{5} +(-4.11592 + 18.0571i) q^{7} +(24.8513 + 10.5552i) q^{9} +(-21.5235 + 12.4266i) q^{11} +(-52.5651 - 30.3485i) q^{13} +(72.7066 - 82.1615i) q^{15} +117.397 q^{17} +104.946i q^{19} +(39.6735 - 87.6756i) q^{21} +(-17.4885 - 10.0970i) q^{23} +(-160.403 - 277.826i) q^{25} +(-115.595 - 79.5029i) q^{27} +(-24.2671 + 14.0106i) q^{29} +(-216.679 - 125.100i) q^{31} +(122.472 - 40.9636i) q^{33} +(-286.729 - 265.891i) q^{35} +18.2279 q^{37} +(236.190 + 209.010i) q^{39} +(153.058 - 265.105i) q^{41} +(74.5402 + 129.107i) q^{43} +(-455.363 + 342.983i) q^{45} +(108.676 + 188.233i) q^{47} +(-309.118 - 148.643i) q^{49} +(-597.755 - 121.683i) q^{51} +116.324i q^{53} -524.754i q^{55} +(108.777 - 534.356i) q^{57} +(-38.3919 + 66.4967i) q^{59} +(493.712 - 285.045i) q^{61} +(-292.883 + 405.298i) q^{63} +(1109.87 - 640.781i) q^{65} +(-33.8430 + 58.6179i) q^{67} +(78.5811 + 69.5382i) q^{69} -796.967i q^{71} +710.481i q^{73} +(528.759 + 1580.87i) q^{75} +(-135.800 - 439.800i) q^{77} +(-40.0640 - 69.3928i) q^{79} +(506.174 + 524.622i) q^{81} +(-57.6203 - 99.8013i) q^{83} +(-1239.37 + 2146.65i) q^{85} +(138.084 - 46.1852i) q^{87} +1055.26 q^{89} +(764.359 - 824.261i) q^{91} +(973.605 + 861.564i) q^{93} +(-1918.98 - 1107.92i) q^{95} +(444.295 - 256.514i) q^{97} +(-666.054 + 81.6319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −5.09172 1.03651i −0.979903 0.199476i
\(4\) 0 0
\(5\) −10.5571 + 18.2854i −0.944252 + 1.63549i −0.187010 + 0.982358i \(0.559880\pi\)
−0.757242 + 0.653135i \(0.773454\pi\)
\(6\) 0 0
\(7\) −4.11592 + 18.0571i −0.222239 + 0.974992i
\(8\) 0 0
\(9\) 24.8513 + 10.5552i 0.920419 + 0.390934i
\(10\) 0 0
\(11\) −21.5235 + 12.4266i −0.589963 + 0.340615i −0.765083 0.643932i \(-0.777302\pi\)
0.175120 + 0.984547i \(0.443969\pi\)
\(12\) 0 0
\(13\) −52.5651 30.3485i −1.12146 0.647473i −0.179684 0.983724i \(-0.557507\pi\)
−0.941772 + 0.336251i \(0.890841\pi\)
\(14\) 0 0
\(15\) 72.7066 82.1615i 1.25152 1.41427i
\(16\) 0 0
\(17\) 117.397 1.67489 0.837443 0.546525i \(-0.184050\pi\)
0.837443 + 0.546525i \(0.184050\pi\)
\(18\) 0 0
\(19\) 104.946i 1.26717i 0.773672 + 0.633586i \(0.218418\pi\)
−0.773672 + 0.633586i \(0.781582\pi\)
\(20\) 0 0
\(21\) 39.6735 87.6756i 0.412260 0.911066i
\(22\) 0 0
\(23\) −17.4885 10.0970i −0.158548 0.0915379i 0.418627 0.908158i \(-0.362512\pi\)
−0.577175 + 0.816621i \(0.695845\pi\)
\(24\) 0 0
\(25\) −160.403 277.826i −1.28322 2.22261i
\(26\) 0 0
\(27\) −115.595 79.5029i −0.823939 0.566679i
\(28\) 0 0
\(29\) −24.2671 + 14.0106i −0.155390 + 0.0897142i −0.575679 0.817676i \(-0.695262\pi\)
0.420289 + 0.907390i \(0.361929\pi\)
\(30\) 0 0
\(31\) −216.679 125.100i −1.25538 0.724794i −0.283207 0.959059i \(-0.591398\pi\)
−0.972173 + 0.234265i \(0.924732\pi\)
\(32\) 0 0
\(33\) 122.472 40.9636i 0.646051 0.216086i
\(34\) 0 0
\(35\) −286.729 265.891i −1.38474 1.28411i
\(36\) 0 0
\(37\) 18.2279 0.0809904 0.0404952 0.999180i \(-0.487106\pi\)
0.0404952 + 0.999180i \(0.487106\pi\)
\(38\) 0 0
\(39\) 236.190 + 209.010i 0.969763 + 0.858164i
\(40\) 0 0
\(41\) 153.058 265.105i 0.583016 1.00981i −0.412103 0.911137i \(-0.635206\pi\)
0.995120 0.0986769i \(-0.0314610\pi\)
\(42\) 0 0
\(43\) 74.5402 + 129.107i 0.264355 + 0.457877i 0.967395 0.253274i \(-0.0815075\pi\)
−0.703039 + 0.711151i \(0.748174\pi\)
\(44\) 0 0
\(45\) −455.363 + 342.983i −1.50848 + 1.13620i
\(46\) 0 0
\(47\) 108.676 + 188.233i 0.337278 + 0.584182i 0.983920 0.178611i \(-0.0571605\pi\)
−0.646642 + 0.762794i \(0.723827\pi\)
\(48\) 0 0
\(49\) −309.118 148.643i −0.901220 0.433362i
\(50\) 0 0
\(51\) −597.755 121.683i −1.64122 0.334099i
\(52\) 0 0
\(53\) 116.324i 0.301479i 0.988574 + 0.150739i \(0.0481655\pi\)
−0.988574 + 0.150739i \(0.951835\pi\)
\(54\) 0 0
\(55\) 524.754i 1.28651i
\(56\) 0 0
\(57\) 108.777 534.356i 0.252770 1.24171i
\(58\) 0 0
\(59\) −38.3919 + 66.4967i −0.0847153 + 0.146731i −0.905270 0.424837i \(-0.860331\pi\)
0.820555 + 0.571568i \(0.193665\pi\)
\(60\) 0 0
\(61\) 493.712 285.045i 1.03629 0.598300i 0.117506 0.993072i \(-0.462510\pi\)
0.918779 + 0.394773i \(0.129177\pi\)
\(62\) 0 0
\(63\) −292.883 + 405.298i −0.585711 + 0.810520i
\(64\) 0 0
\(65\) 1109.87 640.781i 2.11787 1.22276i
\(66\) 0 0
\(67\) −33.8430 + 58.6179i −0.0617102 + 0.106885i −0.895230 0.445604i \(-0.852989\pi\)
0.833520 + 0.552490i \(0.186322\pi\)
\(68\) 0 0
\(69\) 78.5811 + 69.5382i 0.137102 + 0.121325i
\(70\) 0 0
\(71\) 796.967i 1.33215i −0.745886 0.666074i \(-0.767973\pi\)
0.745886 0.666074i \(-0.232027\pi\)
\(72\) 0 0
\(73\) 710.481i 1.13912i 0.821951 + 0.569558i \(0.192886\pi\)
−0.821951 + 0.569558i \(0.807114\pi\)
\(74\) 0 0
\(75\) 528.759 + 1580.87i 0.814077 + 2.43391i
\(76\) 0 0
\(77\) −135.800 439.800i −0.200984 0.650907i
\(78\) 0 0
\(79\) −40.0640 69.3928i −0.0570576 0.0988266i 0.836086 0.548599i \(-0.184839\pi\)
−0.893143 + 0.449772i \(0.851505\pi\)
\(80\) 0 0
\(81\) 506.174 + 524.622i 0.694341 + 0.719646i
\(82\) 0 0
\(83\) −57.6203 99.8013i −0.0762006 0.131983i 0.825407 0.564538i \(-0.190946\pi\)
−0.901608 + 0.432555i \(0.857612\pi\)
\(84\) 0 0
\(85\) −1239.37 + 2146.65i −1.58151 + 2.73926i
\(86\) 0 0
\(87\) 138.084 46.1852i 0.170162 0.0569147i
\(88\) 0 0
\(89\) 1055.26 1.25682 0.628409 0.777883i \(-0.283706\pi\)
0.628409 + 0.777883i \(0.283706\pi\)
\(90\) 0 0
\(91\) 764.359 824.261i 0.880512 0.949517i
\(92\) 0 0
\(93\) 973.605 + 861.564i 1.08557 + 0.960646i
\(94\) 0 0
\(95\) −1918.98 1107.92i −2.07245 1.19653i
\(96\) 0 0
\(97\) 444.295 256.514i 0.465065 0.268505i −0.249106 0.968476i \(-0.580137\pi\)
0.714172 + 0.699971i \(0.246804\pi\)
\(98\) 0 0
\(99\) −666.054 + 81.6319i −0.676171 + 0.0828719i
\(100\) 0 0
\(101\) −83.3542 144.374i −0.0821193 0.142235i 0.822041 0.569429i \(-0.192836\pi\)
−0.904160 + 0.427194i \(0.859502\pi\)
\(102\) 0 0
\(103\) −1304.16 752.955i −1.24760 0.720300i −0.276967 0.960879i \(-0.589329\pi\)
−0.970629 + 0.240579i \(0.922663\pi\)
\(104\) 0 0
\(105\) 1184.35 + 1651.04i 1.10076 + 1.53452i
\(106\) 0 0
\(107\) 776.966i 0.701983i 0.936379 + 0.350991i \(0.114155\pi\)
−0.936379 + 0.350991i \(0.885845\pi\)
\(108\) 0 0
\(109\) −562.383 −0.494189 −0.247094 0.968991i \(-0.579476\pi\)
−0.247094 + 0.968991i \(0.579476\pi\)
\(110\) 0 0
\(111\) −92.8114 18.8934i −0.0793628 0.0161557i
\(112\) 0 0
\(113\) 1648.89 + 951.987i 1.37270 + 0.792526i 0.991267 0.131872i \(-0.0420989\pi\)
0.381429 + 0.924398i \(0.375432\pi\)
\(114\) 0 0
\(115\) 369.255 213.189i 0.299419 0.172870i
\(116\) 0 0
\(117\) −985.976 1309.04i −0.779090 1.03436i
\(118\) 0 0
\(119\) −483.198 + 2119.86i −0.372225 + 1.63300i
\(120\) 0 0
\(121\) −356.658 + 617.750i −0.267963 + 0.464125i
\(122\) 0 0
\(123\) −1054.11 + 1191.19i −0.772733 + 0.873222i
\(124\) 0 0
\(125\) 4134.27 2.95824
\(126\) 0 0
\(127\) −2470.46 −1.72612 −0.863062 0.505098i \(-0.831456\pi\)
−0.863062 + 0.505098i \(0.831456\pi\)
\(128\) 0 0
\(129\) −245.717 734.641i −0.167707 0.501407i
\(130\) 0 0
\(131\) 199.978 346.373i 0.133375 0.231013i −0.791600 0.611039i \(-0.790752\pi\)
0.924976 + 0.380026i \(0.124085\pi\)
\(132\) 0 0
\(133\) −1895.02 431.950i −1.23548 0.281615i
\(134\) 0 0
\(135\) 2674.09 1274.39i 1.70481 0.812458i
\(136\) 0 0
\(137\) −2065.15 + 1192.31i −1.28787 + 0.743550i −0.978273 0.207320i \(-0.933526\pi\)
−0.309592 + 0.950869i \(0.600193\pi\)
\(138\) 0 0
\(139\) 570.066 + 329.128i 0.347859 + 0.200836i 0.663742 0.747962i \(-0.268967\pi\)
−0.315883 + 0.948798i \(0.602301\pi\)
\(140\) 0 0
\(141\) −358.245 1071.07i −0.213969 0.639721i
\(142\) 0 0
\(143\) 1508.52 0.882156
\(144\) 0 0
\(145\) 591.645i 0.338851i
\(146\) 0 0
\(147\) 1419.88 + 1077.25i 0.796662 + 0.604425i
\(148\) 0 0
\(149\) −1116.26 644.476i −0.613745 0.354346i 0.160685 0.987006i \(-0.448630\pi\)
−0.774430 + 0.632660i \(0.781963\pi\)
\(150\) 0 0
\(151\) −98.0311 169.795i −0.0528322 0.0915080i 0.838400 0.545056i \(-0.183492\pi\)
−0.891232 + 0.453548i \(0.850158\pi\)
\(152\) 0 0
\(153\) 2917.48 + 1239.16i 1.54160 + 0.654770i
\(154\) 0 0
\(155\) 4575.00 2641.38i 2.37079 1.36878i
\(156\) 0 0
\(157\) −2865.72 1654.52i −1.45675 0.841053i −0.457897 0.889005i \(-0.651397\pi\)
−0.998850 + 0.0479519i \(0.984731\pi\)
\(158\) 0 0
\(159\) 120.571 592.292i 0.0601378 0.295420i
\(160\) 0 0
\(161\) 254.304 274.234i 0.124484 0.134240i
\(162\) 0 0
\(163\) −1864.65 −0.896018 −0.448009 0.894029i \(-0.647867\pi\)
−0.448009 + 0.894029i \(0.647867\pi\)
\(164\) 0 0
\(165\) −543.912 + 2671.90i −0.256627 + 1.26065i
\(166\) 0 0
\(167\) −1863.24 + 3227.22i −0.863363 + 1.49539i 0.00530083 + 0.999986i \(0.498313\pi\)
−0.868664 + 0.495402i \(0.835021\pi\)
\(168\) 0 0
\(169\) 743.558 + 1287.88i 0.338443 + 0.586200i
\(170\) 0 0
\(171\) −1107.73 + 2608.04i −0.495381 + 1.16633i
\(172\) 0 0
\(173\) −1798.60 3115.26i −0.790432 1.36907i −0.925700 0.378259i \(-0.876523\pi\)
0.135268 0.990809i \(-0.456810\pi\)
\(174\) 0 0
\(175\) 5676.94 1752.90i 2.45221 0.757183i
\(176\) 0 0
\(177\) 264.405 298.790i 0.112282 0.126884i
\(178\) 0 0
\(179\) 598.233i 0.249799i −0.992169 0.124899i \(-0.960139\pi\)
0.992169 0.124899i \(-0.0398608\pi\)
\(180\) 0 0
\(181\) 1669.69i 0.685673i −0.939395 0.342837i \(-0.888612\pi\)
0.939395 0.342837i \(-0.111388\pi\)
\(182\) 0 0
\(183\) −2809.30 + 939.634i −1.13481 + 0.379561i
\(184\) 0 0
\(185\) −192.433 + 333.304i −0.0764754 + 0.132459i
\(186\) 0 0
\(187\) −2526.81 + 1458.85i −0.988120 + 0.570491i
\(188\) 0 0
\(189\) 1911.37 1760.09i 0.735619 0.677396i
\(190\) 0 0
\(191\) 2927.86 1690.40i 1.10918 0.640383i 0.170560 0.985347i \(-0.445442\pi\)
0.938616 + 0.344964i \(0.112109\pi\)
\(192\) 0 0
\(193\) 476.298 824.972i 0.177641 0.307683i −0.763431 0.645889i \(-0.776487\pi\)
0.941072 + 0.338206i \(0.109820\pi\)
\(194\) 0 0
\(195\) −6315.30 + 2112.30i −2.31922 + 0.775716i
\(196\) 0 0
\(197\) 2192.96i 0.793106i 0.918012 + 0.396553i \(0.129794\pi\)
−0.918012 + 0.396553i \(0.870206\pi\)
\(198\) 0 0
\(199\) 1581.79i 0.563469i −0.959492 0.281735i \(-0.909090\pi\)
0.959492 0.281735i \(-0.0909098\pi\)
\(200\) 0 0
\(201\) 233.077 263.387i 0.0817911 0.0924275i
\(202\) 0 0
\(203\) −153.110 495.861i −0.0529370 0.171442i
\(204\) 0 0
\(205\) 3231.69 + 5597.45i 1.10103 + 1.90704i
\(206\) 0 0
\(207\) −328.037 435.519i −0.110145 0.146235i
\(208\) 0 0
\(209\) −1304.12 2258.81i −0.431618 0.747584i
\(210\) 0 0
\(211\) −1547.26 + 2679.93i −0.504823 + 0.874379i 0.495161 + 0.868801i \(0.335109\pi\)
−0.999984 + 0.00557832i \(0.998224\pi\)
\(212\) 0 0
\(213\) −826.062 + 4057.93i −0.265732 + 1.30538i
\(214\) 0 0
\(215\) −3147.70 −0.998472
\(216\) 0 0
\(217\) 3150.78 3397.70i 0.985663 1.06291i
\(218\) 0 0
\(219\) 736.419 3617.57i 0.227226 1.11622i
\(220\) 0 0
\(221\) −6171.00 3562.83i −1.87831 1.08444i
\(222\) 0 0
\(223\) −1320.52 + 762.403i −0.396541 + 0.228943i −0.684990 0.728552i \(-0.740194\pi\)
0.288450 + 0.957495i \(0.406860\pi\)
\(224\) 0 0
\(225\) −1053.71 8597.43i −0.312209 2.54739i
\(226\) 0 0
\(227\) −836.909 1449.57i −0.244703 0.423838i 0.717345 0.696718i \(-0.245357\pi\)
−0.962048 + 0.272880i \(0.912024\pi\)
\(228\) 0 0
\(229\) 2751.35 + 1588.49i 0.793949 + 0.458387i 0.841351 0.540489i \(-0.181761\pi\)
−0.0474019 + 0.998876i \(0.515094\pi\)
\(230\) 0 0
\(231\) 235.598 + 2380.10i 0.0671049 + 0.677917i
\(232\) 0 0
\(233\) 3225.60i 0.906936i −0.891272 0.453468i \(-0.850187\pi\)
0.891272 0.453468i \(-0.149813\pi\)
\(234\) 0 0
\(235\) −4589.21 −1.27390
\(236\) 0 0
\(237\) 132.068 + 394.856i 0.0361973 + 0.108222i
\(238\) 0 0
\(239\) −1535.18 886.337i −0.415492 0.239884i 0.277655 0.960681i \(-0.410443\pi\)
−0.693147 + 0.720797i \(0.743776\pi\)
\(240\) 0 0
\(241\) 3202.47 1848.95i 0.855972 0.494196i −0.00668945 0.999978i \(-0.502129\pi\)
0.862661 + 0.505782i \(0.168796\pi\)
\(242\) 0 0
\(243\) −2033.53 3195.89i −0.536834 0.843688i
\(244\) 0 0
\(245\) 5981.38 4083.11i 1.55974 1.06473i
\(246\) 0 0
\(247\) 3184.95 5516.49i 0.820460 1.42108i
\(248\) 0 0
\(249\) 189.942 + 567.885i 0.0483417 + 0.144531i
\(250\) 0 0
\(251\) −2501.61 −0.629084 −0.314542 0.949244i \(-0.601851\pi\)
−0.314542 + 0.949244i \(0.601851\pi\)
\(252\) 0 0
\(253\) 501.887 0.124717
\(254\) 0 0
\(255\) 8535.56 9645.55i 2.09615 2.36874i
\(256\) 0 0
\(257\) 472.215 817.900i 0.114615 0.198518i −0.803011 0.595964i \(-0.796770\pi\)
0.917626 + 0.397446i \(0.130103\pi\)
\(258\) 0 0
\(259\) −75.0246 + 329.143i −0.0179992 + 0.0789651i
\(260\) 0 0
\(261\) −750.956 + 92.0376i −0.178096 + 0.0218275i
\(262\) 0 0
\(263\) −4896.74 + 2827.13i −1.14808 + 0.662846i −0.948420 0.317018i \(-0.897318\pi\)
−0.199664 + 0.979864i \(0.563985\pi\)
\(264\) 0 0
\(265\) −2127.03 1228.04i −0.493067 0.284672i
\(266\) 0 0
\(267\) −5373.07 1093.78i −1.23156 0.250705i
\(268\) 0 0
\(269\) −4010.37 −0.908983 −0.454491 0.890751i \(-0.650179\pi\)
−0.454491 + 0.890751i \(0.650179\pi\)
\(270\) 0 0
\(271\) 3596.81i 0.806239i 0.915147 + 0.403120i \(0.132074\pi\)
−0.915147 + 0.403120i \(0.867926\pi\)
\(272\) 0 0
\(273\) −4746.26 + 3404.65i −1.05222 + 0.754794i
\(274\) 0 0
\(275\) 6904.88 + 3986.53i 1.51411 + 0.874171i
\(276\) 0 0
\(277\) −3175.77 5500.59i −0.688856 1.19313i −0.972208 0.234118i \(-0.924780\pi\)
0.283352 0.959016i \(-0.408554\pi\)
\(278\) 0 0
\(279\) −4064.31 5396.00i −0.872128 1.15788i
\(280\) 0 0
\(281\) −1591.00 + 918.563i −0.337761 + 0.195007i −0.659282 0.751896i \(-0.729140\pi\)
0.321520 + 0.946903i \(0.395806\pi\)
\(282\) 0 0
\(283\) 2653.87 + 1532.21i 0.557442 + 0.321839i 0.752118 0.659028i \(-0.229032\pi\)
−0.194676 + 0.980868i \(0.562366\pi\)
\(284\) 0 0
\(285\) 8622.53 + 7630.26i 1.79212 + 1.58589i
\(286\) 0 0
\(287\) 4157.05 + 3854.94i 0.854992 + 0.792856i
\(288\) 0 0
\(289\) 8869.15 1.80524
\(290\) 0 0
\(291\) −2528.11 + 845.582i −0.509279 + 0.170340i
\(292\) 0 0
\(293\) −3473.03 + 6015.47i −0.692481 + 1.19941i 0.278542 + 0.960424i \(0.410149\pi\)
−0.971023 + 0.238988i \(0.923184\pi\)
\(294\) 0 0
\(295\) −810.611 1404.02i −0.159985 0.277102i
\(296\) 0 0
\(297\) 3475.97 + 274.723i 0.679112 + 0.0536735i
\(298\) 0 0
\(299\) 612.857 + 1061.50i 0.118537 + 0.205311i
\(300\) 0 0
\(301\) −2638.11 + 814.585i −0.505176 + 0.155986i
\(302\) 0 0
\(303\) 274.772 + 821.508i 0.0520965 + 0.155757i
\(304\) 0 0
\(305\) 12036.9i 2.25978i
\(306\) 0 0
\(307\) 2168.45i 0.403128i 0.979475 + 0.201564i \(0.0646023\pi\)
−0.979475 + 0.201564i \(0.935398\pi\)
\(308\) 0 0
\(309\) 5859.96 + 5185.61i 1.07884 + 0.954689i
\(310\) 0 0
\(311\) 142.507 246.830i 0.0259834 0.0450046i −0.852741 0.522333i \(-0.825062\pi\)
0.878725 + 0.477329i \(0.158395\pi\)
\(312\) 0 0
\(313\) −9429.66 + 5444.22i −1.70286 + 0.983148i −0.760025 + 0.649894i \(0.774813\pi\)
−0.942837 + 0.333253i \(0.891854\pi\)
\(314\) 0 0
\(315\) −4319.04 9634.23i −0.772541 1.72326i
\(316\) 0 0
\(317\) 598.240 345.394i 0.105995 0.0611964i −0.446065 0.895000i \(-0.647175\pi\)
0.552060 + 0.833804i \(0.313842\pi\)
\(318\) 0 0
\(319\) 348.210 603.117i 0.0611160 0.105856i
\(320\) 0 0
\(321\) 805.332 3956.10i 0.140029 0.687875i
\(322\) 0 0
\(323\) 12320.4i 2.12237i
\(324\) 0 0
\(325\) 19471.9i 3.32341i
\(326\) 0 0
\(327\) 2863.50 + 582.915i 0.484257 + 0.0985788i
\(328\) 0 0
\(329\) −3846.24 + 1187.63i −0.644529 + 0.199015i
\(330\) 0 0
\(331\) −4246.17 7354.58i −0.705108 1.22128i −0.966653 0.256091i \(-0.917565\pi\)
0.261545 0.965191i \(-0.415768\pi\)
\(332\) 0 0
\(333\) 452.987 + 192.399i 0.0745451 + 0.0316619i
\(334\) 0 0
\(335\) −714.566 1237.66i −0.116540 0.201853i
\(336\) 0 0
\(337\) 1799.53 3116.88i 0.290881 0.503820i −0.683138 0.730290i \(-0.739385\pi\)
0.974018 + 0.226470i \(0.0727184\pi\)
\(338\) 0 0
\(339\) −7408.95 6556.35i −1.18702 1.05042i
\(340\) 0 0
\(341\) 6218.28 0.987503
\(342\) 0 0
\(343\) 3956.38 4969.98i 0.622811 0.782372i
\(344\) 0 0
\(345\) −2101.12 + 702.766i −0.327885 + 0.109669i
\(346\) 0 0
\(347\) 5923.82 + 3420.12i 0.916448 + 0.529112i 0.882500 0.470312i \(-0.155859\pi\)
0.0339480 + 0.999424i \(0.489192\pi\)
\(348\) 0 0
\(349\) 5589.41 3227.04i 0.857289 0.494956i −0.00581419 0.999983i \(-0.501851\pi\)
0.863104 + 0.505027i \(0.168517\pi\)
\(350\) 0 0
\(351\) 3663.49 + 7687.22i 0.557102 + 1.16898i
\(352\) 0 0
\(353\) 294.916 + 510.809i 0.0444668 + 0.0770188i 0.887402 0.460996i \(-0.152508\pi\)
−0.842935 + 0.538015i \(0.819174\pi\)
\(354\) 0 0
\(355\) 14572.8 + 8413.62i 2.17872 + 1.25788i
\(356\) 0 0
\(357\) 4657.56 10292.9i 0.690488 1.52593i
\(358\) 0 0
\(359\) 8812.02i 1.29549i 0.761857 + 0.647745i \(0.224288\pi\)
−0.761857 + 0.647745i \(0.775712\pi\)
\(360\) 0 0
\(361\) −4154.66 −0.605724
\(362\) 0 0
\(363\) 2456.31 2775.73i 0.355159 0.401345i
\(364\) 0 0
\(365\) −12991.4 7500.59i −1.86302 1.07561i
\(366\) 0 0
\(367\) 9716.89 5610.05i 1.38206 0.797935i 0.389661 0.920958i \(-0.372592\pi\)
0.992404 + 0.123023i \(0.0392589\pi\)
\(368\) 0 0
\(369\) 6601.93 4972.63i 0.931390 0.701531i
\(370\) 0 0
\(371\) −2100.48 478.782i −0.293940 0.0670003i
\(372\) 0 0
\(373\) −403.305 + 698.546i −0.0559849 + 0.0969687i −0.892660 0.450731i \(-0.851163\pi\)
0.836675 + 0.547700i \(0.184497\pi\)
\(374\) 0 0
\(375\) −21050.6 4285.21i −2.89879 0.590099i
\(376\) 0 0
\(377\) 1700.81 0.232350
\(378\) 0 0
\(379\) 7667.10 1.03914 0.519568 0.854429i \(-0.326093\pi\)
0.519568 + 0.854429i \(0.326093\pi\)
\(380\) 0 0
\(381\) 12578.9 + 2560.65i 1.69143 + 0.344320i
\(382\) 0 0
\(383\) −5599.27 + 9698.23i −0.747022 + 1.29388i 0.202222 + 0.979340i \(0.435184\pi\)
−0.949244 + 0.314541i \(0.898149\pi\)
\(384\) 0 0
\(385\) 9475.54 + 2159.85i 1.25433 + 0.285912i
\(386\) 0 0
\(387\) 489.663 + 3995.28i 0.0643178 + 0.524784i
\(388\) 0 0
\(389\) 1300.72 750.970i 0.169535 0.0978810i −0.412832 0.910807i \(-0.635460\pi\)
0.582366 + 0.812926i \(0.302127\pi\)
\(390\) 0 0
\(391\) −2053.11 1185.36i −0.265550 0.153315i
\(392\) 0 0
\(393\) −1377.25 + 1556.35i −0.176777 + 0.199765i
\(394\) 0 0
\(395\) 1691.83 0.215507
\(396\) 0 0
\(397\) 1509.70i 0.190856i −0.995436 0.0954280i \(-0.969578\pi\)
0.995436 0.0954280i \(-0.0304220\pi\)
\(398\) 0 0
\(399\) 9201.21 + 4163.57i 1.15448 + 0.522404i
\(400\) 0 0
\(401\) −780.767 450.776i −0.0972311 0.0561364i 0.450596 0.892728i \(-0.351212\pi\)
−0.547827 + 0.836592i \(0.684545\pi\)
\(402\) 0 0
\(403\) 7593.18 + 13151.8i 0.938569 + 1.62565i
\(404\) 0 0
\(405\) −14936.6 + 3717.12i −1.83261 + 0.456062i
\(406\) 0 0
\(407\) −392.329 + 226.511i −0.0477813 + 0.0275866i
\(408\) 0 0
\(409\) −13891.4 8020.20i −1.67943 0.969617i −0.962027 0.272955i \(-0.911999\pi\)
−0.717399 0.696662i \(-0.754668\pi\)
\(410\) 0 0
\(411\) 11751.0 3930.39i 1.41030 0.471708i
\(412\) 0 0
\(413\) −1042.72 966.942i −0.124235 0.115206i
\(414\) 0 0
\(415\) 2433.20 0.287810
\(416\) 0 0
\(417\) −2561.48 2266.71i −0.300806 0.266190i
\(418\) 0 0
\(419\) 424.053 734.482i 0.0494424 0.0856367i −0.840245 0.542207i \(-0.817589\pi\)
0.889687 + 0.456570i \(0.150922\pi\)
\(420\) 0 0
\(421\) −3933.58 6813.16i −0.455370 0.788725i 0.543339 0.839513i \(-0.317160\pi\)
−0.998709 + 0.0507886i \(0.983827\pi\)
\(422\) 0 0
\(423\) 713.907 + 5824.93i 0.0820599 + 0.669546i
\(424\) 0 0
\(425\) −18830.9 32616.1i −2.14925 3.72262i
\(426\) 0 0
\(427\) 3115.01 + 10088.2i 0.353035 + 1.14334i
\(428\) 0 0
\(429\) −7680.94 1563.59i −0.864427 0.175969i
\(430\) 0 0
\(431\) 9164.19i 1.02418i −0.858930 0.512092i \(-0.828871\pi\)
0.858930 0.512092i \(-0.171129\pi\)
\(432\) 0 0
\(433\) 5634.15i 0.625312i 0.949866 + 0.312656i \(0.101219\pi\)
−0.949866 + 0.312656i \(0.898781\pi\)
\(434\) 0 0
\(435\) −613.245 + 3012.49i −0.0675927 + 0.332041i
\(436\) 0 0
\(437\) 1059.64 1835.35i 0.115994 0.200908i
\(438\) 0 0
\(439\) −11030.6 + 6368.50i −1.19923 + 0.692373i −0.960383 0.278685i \(-0.910101\pi\)
−0.238843 + 0.971058i \(0.576768\pi\)
\(440\) 0 0
\(441\) −6113.03 6956.79i −0.660083 0.751192i
\(442\) 0 0
\(443\) 1685.37 973.047i 0.180754 0.104359i −0.406893 0.913476i \(-0.633388\pi\)
0.587647 + 0.809117i \(0.300054\pi\)
\(444\) 0 0
\(445\) −11140.4 + 19295.7i −1.18675 + 2.05552i
\(446\) 0 0
\(447\) 5015.71 + 4438.51i 0.530727 + 0.469652i
\(448\) 0 0
\(449\) 7602.87i 0.799113i −0.916709 0.399556i \(-0.869164\pi\)
0.916709 0.399556i \(-0.130836\pi\)
\(450\) 0 0
\(451\) 7607.98i 0.794337i
\(452\) 0 0
\(453\) 323.154 + 966.159i 0.0335167 + 0.100208i
\(454\) 0 0
\(455\) 7002.53 + 22678.4i 0.721503 + 2.33666i
\(456\) 0 0
\(457\) −102.789 178.036i −0.0105214 0.0182236i 0.860717 0.509084i \(-0.170016\pi\)
−0.871238 + 0.490861i \(0.836682\pi\)
\(458\) 0 0
\(459\) −13570.6 9333.43i −1.38000 0.949122i
\(460\) 0 0
\(461\) 9165.82 + 15875.7i 0.926019 + 1.60391i 0.789914 + 0.613218i \(0.210125\pi\)
0.136105 + 0.990694i \(0.456542\pi\)
\(462\) 0 0
\(463\) 6817.76 11808.7i 0.684338 1.18531i −0.289307 0.957236i \(-0.593425\pi\)
0.973644 0.228071i \(-0.0732419\pi\)
\(464\) 0 0
\(465\) −26032.4 + 8707.13i −2.59618 + 0.868352i
\(466\) 0 0
\(467\) −15609.8 −1.54676 −0.773378 0.633946i \(-0.781434\pi\)
−0.773378 + 0.633946i \(0.781434\pi\)
\(468\) 0 0
\(469\) −919.174 852.374i −0.0904979 0.0839211i
\(470\) 0 0
\(471\) 12876.5 + 11394.7i 1.25970 + 1.11474i
\(472\) 0 0
\(473\) −3208.74 1852.57i −0.311920 0.180087i
\(474\) 0 0
\(475\) 29156.7 16833.7i 2.81643 1.62607i
\(476\) 0 0
\(477\) −1227.83 + 2890.81i −0.117858 + 0.277487i
\(478\) 0 0
\(479\) −7412.67 12839.1i −0.707084 1.22471i −0.965934 0.258788i \(-0.916677\pi\)
0.258850 0.965918i \(-0.416657\pi\)
\(480\) 0 0
\(481\) −958.150 553.188i −0.0908272 0.0524391i
\(482\) 0 0
\(483\) −1579.09 + 1132.73i −0.148760 + 0.106711i
\(484\) 0 0
\(485\) 10832.1i 1.01415i
\(486\) 0 0
\(487\) 12830.1 1.19381 0.596906 0.802311i \(-0.296396\pi\)
0.596906 + 0.802311i \(0.296396\pi\)
\(488\) 0 0
\(489\) 9494.30 + 1932.73i 0.878010 + 0.178734i
\(490\) 0 0
\(491\) −7054.53 4072.93i −0.648404 0.374356i 0.139441 0.990230i \(-0.455470\pi\)
−0.787844 + 0.615874i \(0.788803\pi\)
\(492\) 0 0
\(493\) −2848.90 + 1644.81i −0.260260 + 0.150261i
\(494\) 0 0
\(495\) 5538.90 13040.8i 0.502939 1.18412i
\(496\) 0 0
\(497\) 14390.9 + 3280.25i 1.29883 + 0.296055i
\(498\) 0 0
\(499\) 8727.94 15117.2i 0.782999 1.35619i −0.147189 0.989108i \(-0.547022\pi\)
0.930187 0.367085i \(-0.119644\pi\)
\(500\) 0 0
\(501\) 12832.1 14500.9i 1.14431 1.29311i
\(502\) 0 0
\(503\) 13372.9 1.18543 0.592714 0.805413i \(-0.298057\pi\)
0.592714 + 0.805413i \(0.298057\pi\)
\(504\) 0 0
\(505\) 3519.90 0.310165
\(506\) 0 0
\(507\) −2451.10 7328.24i −0.214708 0.641930i
\(508\) 0 0
\(509\) 2910.35 5040.87i 0.253436 0.438964i −0.711033 0.703158i \(-0.751773\pi\)
0.964470 + 0.264194i \(0.0851059\pi\)
\(510\) 0 0
\(511\) −12829.2 2924.28i −1.11063 0.253156i
\(512\) 0 0
\(513\) 8343.51 12131.3i 0.718080 1.04407i
\(514\) 0 0
\(515\) 27536.1 15898.0i 2.35609 1.36029i
\(516\) 0 0
\(517\) −4678.19 2700.96i −0.397963 0.229764i
\(518\) 0 0
\(519\) 5928.96 + 17726.3i 0.501450 + 1.49923i
\(520\) 0 0
\(521\) 6546.17 0.550466 0.275233 0.961378i \(-0.411245\pi\)
0.275233 + 0.961378i \(0.411245\pi\)
\(522\) 0 0
\(523\) 7475.29i 0.624994i −0.949919 0.312497i \(-0.898835\pi\)
0.949919 0.312497i \(-0.101165\pi\)
\(524\) 0 0
\(525\) −30722.3 + 3041.11i −2.55397 + 0.252809i
\(526\) 0 0
\(527\) −25437.6 14686.4i −2.10262 1.21395i
\(528\) 0 0
\(529\) −5879.60 10183.8i −0.483242 0.836999i
\(530\) 0 0
\(531\) −1655.98 + 1247.30i −0.135336 + 0.101936i
\(532\) 0 0
\(533\) −16091.0 + 9290.16i −1.30765 + 0.754975i
\(534\) 0 0
\(535\) −14207.1 8202.48i −1.14809 0.662849i
\(536\) 0 0
\(537\) −620.073 + 3046.03i −0.0498289 + 0.244779i
\(538\) 0 0
\(539\) 8500.45 641.967i 0.679296 0.0513014i
\(540\) 0 0
\(541\) −6578.64 −0.522806 −0.261403 0.965230i \(-0.584185\pi\)
−0.261403 + 0.965230i \(0.584185\pi\)
\(542\) 0 0
\(543\) −1730.64 + 8501.59i −0.136775 + 0.671893i
\(544\) 0 0
\(545\) 5937.11 10283.4i 0.466639 0.808242i
\(546\) 0 0
\(547\) −2357.36 4083.06i −0.184266 0.319158i 0.759063 0.651017i \(-0.225657\pi\)
−0.943329 + 0.331859i \(0.892324\pi\)
\(548\) 0 0
\(549\) 15278.1 1872.49i 1.18771 0.145567i
\(550\) 0 0
\(551\) −1470.36 2546.74i −0.113683 0.196905i
\(552\) 0 0
\(553\) 1417.93 437.824i 0.109036 0.0336676i
\(554\) 0 0
\(555\) 1325.29 1497.63i 0.101361 0.114542i
\(556\) 0 0
\(557\) 5985.03i 0.455286i 0.973745 + 0.227643i \(0.0731018\pi\)
−0.973745 + 0.227643i \(0.926898\pi\)
\(558\) 0 0
\(559\) 9048.73i 0.684652i
\(560\) 0 0
\(561\) 14377.9 4809.02i 1.08206 0.361920i
\(562\) 0 0
\(563\) −10574.8 + 18316.0i −0.791605 + 1.37110i 0.133368 + 0.991067i \(0.457421\pi\)
−0.924973 + 0.380033i \(0.875913\pi\)
\(564\) 0 0
\(565\) −34814.9 + 20100.4i −2.59234 + 1.49669i
\(566\) 0 0
\(567\) −11556.5 + 6980.74i −0.855959 + 0.517044i
\(568\) 0 0
\(569\) 9600.92 5543.09i 0.707366 0.408398i −0.102719 0.994710i \(-0.532754\pi\)
0.810085 + 0.586312i \(0.199421\pi\)
\(570\) 0 0
\(571\) −889.103 + 1539.97i −0.0651626 + 0.112865i −0.896766 0.442505i \(-0.854090\pi\)
0.831604 + 0.555370i \(0.187423\pi\)
\(572\) 0 0
\(573\) −16660.0 + 5572.31i −1.21463 + 0.406259i
\(574\) 0 0
\(575\) 6478.36i 0.469854i
\(576\) 0 0
\(577\) 9282.23i 0.669713i 0.942269 + 0.334856i \(0.108688\pi\)
−0.942269 + 0.334856i \(0.891312\pi\)
\(578\) 0 0
\(579\) −3280.27 + 3706.84i −0.235446 + 0.266064i
\(580\) 0 0
\(581\) 2039.28 629.682i 0.145617 0.0449632i
\(582\) 0 0
\(583\) −1445.52 2503.71i −0.102688 0.177861i
\(584\) 0 0
\(585\) 34345.2 4209.37i 2.42735 0.297497i
\(586\) 0 0
\(587\) 12177.5 + 21092.1i 0.856253 + 1.48307i 0.875477 + 0.483259i \(0.160547\pi\)
−0.0192240 + 0.999815i \(0.506120\pi\)
\(588\) 0 0
\(589\) 13128.7 22739.6i 0.918439 1.59078i
\(590\) 0 0
\(591\) 2273.02 11165.9i 0.158206 0.777167i
\(592\) 0 0
\(593\) 3634.37 0.251679 0.125840 0.992051i \(-0.459838\pi\)
0.125840 + 0.992051i \(0.459838\pi\)
\(594\) 0 0
\(595\) −33661.2 31214.9i −2.31929 2.15073i
\(596\) 0 0
\(597\) −1639.54 + 8054.06i −0.112399 + 0.552145i
\(598\) 0 0
\(599\) 16689.7 + 9635.82i 1.13844 + 0.657277i 0.946043 0.324041i \(-0.105041\pi\)
0.192394 + 0.981318i \(0.438375\pi\)
\(600\) 0 0
\(601\) −9993.33 + 5769.65i −0.678264 + 0.391596i −0.799201 0.601064i \(-0.794744\pi\)
0.120937 + 0.992660i \(0.461410\pi\)
\(602\) 0 0
\(603\) −1459.77 + 1099.51i −0.0985844 + 0.0742545i
\(604\) 0 0
\(605\) −7530.53 13043.3i −0.506049 0.876502i
\(606\) 0 0
\(607\) −3327.05 1920.88i −0.222473 0.128445i 0.384622 0.923074i \(-0.374332\pi\)
−0.607095 + 0.794629i \(0.707665\pi\)
\(608\) 0 0
\(609\) 265.630 + 2683.49i 0.0176747 + 0.178556i
\(610\) 0 0
\(611\) 13192.6i 0.873513i
\(612\) 0 0
\(613\) −26792.1 −1.76529 −0.882644 0.470043i \(-0.844238\pi\)
−0.882644 + 0.470043i \(0.844238\pi\)
\(614\) 0 0
\(615\) −10653.1 31850.3i −0.698493 2.08834i
\(616\) 0 0
\(617\) −2434.46 1405.54i −0.158846 0.0917095i 0.418470 0.908231i \(-0.362566\pi\)
−0.577316 + 0.816521i \(0.695900\pi\)
\(618\) 0 0
\(619\) −2964.61 + 1711.62i −0.192500 + 0.111140i −0.593152 0.805090i \(-0.702117\pi\)
0.400652 + 0.916230i \(0.368784\pi\)
\(620\) 0 0
\(621\) 1218.85 + 2557.56i 0.0787614 + 0.165268i
\(622\) 0 0
\(623\) −4343.35 + 19054.9i −0.279314 + 1.22539i
\(624\) 0 0
\(625\) −23595.4 + 40868.4i −1.51010 + 2.61558i
\(626\) 0 0
\(627\) 4298.97 + 12853.0i 0.273818 + 0.818657i
\(628\) 0 0
\(629\) 2139.91 0.135650
\(630\) 0 0
\(631\) −4476.28 −0.282406 −0.141203 0.989981i \(-0.545097\pi\)
−0.141203 + 0.989981i \(0.545097\pi\)
\(632\) 0 0
\(633\) 10656.0 12041.7i 0.669095 0.756107i
\(634\) 0 0
\(635\) 26080.8 45173.2i 1.62990 2.82306i
\(636\) 0 0
\(637\) 11737.7 + 17194.7i 0.730088 + 1.06951i
\(638\) 0 0
\(639\) 8412.16 19805.7i 0.520782 1.22613i
\(640\) 0 0
\(641\) −15150.6 + 8747.20i −0.933561 + 0.538992i −0.887936 0.459967i \(-0.847861\pi\)
−0.0456248 + 0.998959i \(0.514528\pi\)
\(642\) 0 0
\(643\) 4602.79 + 2657.42i 0.282296 + 0.162984i 0.634462 0.772954i \(-0.281222\pi\)
−0.352166 + 0.935937i \(0.614555\pi\)
\(644\) 0 0
\(645\) 16027.2 + 3262.62i 0.978406 + 0.199171i
\(646\) 0 0
\(647\) −4660.14 −0.283167 −0.141584 0.989926i \(-0.545219\pi\)
−0.141584 + 0.989926i \(0.545219\pi\)
\(648\) 0 0
\(649\) 1908.33i 0.115421i
\(650\) 0 0
\(651\) −19564.6 + 14034.4i −1.17788 + 0.844931i
\(652\) 0 0
\(653\) −16836.5 9720.58i −1.00898 0.582536i −0.0980880 0.995178i \(-0.531273\pi\)
−0.910893 + 0.412642i \(0.864606\pi\)
\(654\) 0 0
\(655\) 4222.36 + 7313.35i 0.251880 + 0.436269i
\(656\) 0 0
\(657\) −7499.29 + 17656.4i −0.445320 + 1.04846i
\(658\) 0 0
\(659\) 4244.21 2450.39i 0.250881 0.144846i −0.369286 0.929316i \(-0.620398\pi\)
0.620168 + 0.784469i \(0.287065\pi\)
\(660\) 0 0
\(661\) 6520.45 + 3764.58i 0.383685 + 0.221521i 0.679420 0.733749i \(-0.262231\pi\)
−0.295735 + 0.955270i \(0.595565\pi\)
\(662\) 0 0
\(663\) 27728.1 + 24537.2i 1.62424 + 1.43733i
\(664\) 0 0
\(665\) 27904.2 30091.0i 1.62719 1.75471i
\(666\) 0 0
\(667\) 565.862 0.0328490
\(668\) 0 0
\(669\) 7513.96 2513.21i 0.434240 0.145241i
\(670\) 0 0
\(671\) −7084.29 + 12270.4i −0.407580 + 0.705949i
\(672\) 0 0
\(673\) 5380.01 + 9318.45i 0.308149 + 0.533729i 0.977957 0.208804i \(-0.0669572\pi\)
−0.669809 + 0.742534i \(0.733624\pi\)
\(674\) 0 0
\(675\) −3546.13 + 44867.9i −0.202208 + 2.55847i
\(676\) 0 0
\(677\) 7477.31 + 12951.1i 0.424485 + 0.735230i 0.996372 0.0851025i \(-0.0271218\pi\)
−0.571887 + 0.820332i \(0.693788\pi\)
\(678\) 0 0
\(679\) 2803.21 + 9078.47i 0.158435 + 0.513107i
\(680\) 0 0
\(681\) 2758.82 + 8248.27i 0.155240 + 0.464133i
\(682\) 0 0
\(683\) 28835.1i 1.61544i −0.589566 0.807720i \(-0.700701\pi\)
0.589566 0.807720i \(-0.299299\pi\)
\(684\) 0 0
\(685\) 50349.3i 2.80839i
\(686\) 0 0
\(687\) −12362.6 10940.0i −0.686556 0.607548i
\(688\) 0 0
\(689\) 3530.27 6114.60i 0.195199 0.338095i
\(690\) 0 0
\(691\) −845.405 + 488.095i −0.0465423 + 0.0268712i −0.523091 0.852277i \(-0.675221\pi\)
0.476548 + 0.879148i \(0.341888\pi\)
\(692\) 0 0
\(693\) 1267.39 12363.0i 0.0694720 0.677679i
\(694\) 0 0
\(695\) −12036.4 + 6949.24i −0.656933 + 0.379280i
\(696\) 0 0
\(697\) 17968.6 31122.6i 0.976486 1.69132i
\(698\) 0 0
\(699\) −3343.36 + 16423.9i −0.180912 + 0.888709i
\(700\) 0 0
\(701\) 6963.25i 0.375176i −0.982248 0.187588i \(-0.939933\pi\)
0.982248 0.187588i \(-0.0600669\pi\)
\(702\) 0 0
\(703\) 1912.94i 0.102629i
\(704\) 0 0
\(705\) 23367.0 + 4756.75i 1.24830 + 0.254113i
\(706\) 0 0
\(707\) 2950.05 910.905i 0.156928 0.0484556i
\(708\) 0 0
\(709\) 14914.8 + 25833.2i 0.790039 + 1.36839i 0.925942 + 0.377665i \(0.123273\pi\)
−0.135903 + 0.990722i \(0.543394\pi\)
\(710\) 0 0
\(711\) −263.185 2147.39i −0.0138821 0.113268i
\(712\) 0 0
\(713\) 2526.27 + 4375.63i 0.132692 + 0.229830i
\(714\) 0 0
\(715\) −15925.5 + 27583.7i −0.832978 + 1.44276i
\(716\) 0 0
\(717\) 6898.02 + 6104.21i 0.359290 + 0.317944i
\(718\) 0 0
\(719\) −14089.4 −0.730803 −0.365402 0.930850i \(-0.619068\pi\)
−0.365402 + 0.930850i \(0.619068\pi\)
\(720\) 0 0
\(721\) 18964.0 20450.2i 0.979551 1.05632i
\(722\) 0 0
\(723\) −18222.5 + 6094.94i −0.937349 + 0.313518i
\(724\) 0 0
\(725\) 7785.05 + 4494.70i 0.398799 + 0.230247i
\(726\) 0 0
\(727\) 16592.3 9579.56i 0.846457 0.488702i −0.0129971 0.999916i \(-0.504137\pi\)
0.859454 + 0.511214i \(0.170804\pi\)
\(728\) 0 0
\(729\) 7041.59 + 18380.3i 0.357750 + 0.933817i
\(730\) 0 0
\(731\) 8750.83 + 15156.9i 0.442765 + 0.766891i
\(732\) 0 0
\(733\) 31099.2 + 17955.1i 1.56709 + 0.904757i 0.996507 + 0.0835145i \(0.0266145\pi\)
0.570579 + 0.821243i \(0.306719\pi\)
\(734\) 0 0
\(735\) −34687.7 + 14590.3i −1.74078 + 0.732206i
\(736\) 0 0
\(737\) 1682.22i 0.0840778i
\(738\) 0 0
\(739\) 15603.3 0.776694 0.388347 0.921513i \(-0.373046\pi\)
0.388347 + 0.921513i \(0.373046\pi\)
\(740\) 0 0
\(741\) −21934.8 + 24787.2i −1.08744 + 1.22886i
\(742\) 0 0
\(743\) 9187.85 + 5304.61i 0.453660 + 0.261921i 0.709375 0.704831i \(-0.248977\pi\)
−0.255715 + 0.966752i \(0.582311\pi\)
\(744\) 0 0
\(745\) 23569.0 13607.5i 1.15906 0.669183i
\(746\) 0 0
\(747\) −378.514 3088.39i −0.0185397 0.151269i
\(748\) 0 0
\(749\) −14029.8 3197.93i −0.684428 0.156008i
\(750\) 0 0
\(751\) −3593.39 + 6223.93i −0.174600 + 0.302416i −0.940023 0.341112i \(-0.889197\pi\)
0.765423 + 0.643528i \(0.222530\pi\)
\(752\) 0 0
\(753\) 12737.5 + 2592.94i 0.616441 + 0.125487i
\(754\) 0 0
\(755\) 4139.68 0.199548
\(756\) 0 0
\(757\) −30230.3 −1.45144 −0.725720 0.687990i \(-0.758493\pi\)
−0.725720 + 0.687990i \(0.758493\pi\)
\(758\) 0 0
\(759\) −2555.47 520.209i −0.122210 0.0248780i
\(760\) 0 0
\(761\) −4067.61 + 7045.32i −0.193759 + 0.335601i −0.946493 0.322724i \(-0.895401\pi\)
0.752734 + 0.658325i \(0.228735\pi\)
\(762\) 0 0
\(763\) 2314.73 10155.0i 0.109828 0.481830i
\(764\) 0 0
\(765\) −53458.4 + 40265.3i −2.52653 + 1.90300i
\(766\) 0 0
\(767\) 4036.15 2330.27i 0.190009 0.109702i
\(768\) 0 0
\(769\) −19458.9 11234.6i −0.912490 0.526826i −0.0312583 0.999511i \(-0.509951\pi\)
−0.881231 + 0.472685i \(0.843285\pi\)
\(770\) 0 0
\(771\) −3252.15 + 3675.07i −0.151911 + 0.171666i
\(772\) 0 0
\(773\) 18079.1 0.841217 0.420609 0.907242i \(-0.361817\pi\)
0.420609 + 0.907242i \(0.361817\pi\)
\(774\) 0 0
\(775\) 80265.6i 3.72029i
\(776\) 0 0
\(777\) 723.164 1598.14i 0.0333891 0.0737877i
\(778\) 0 0
\(779\) 27821.7 + 16062.8i 1.27961 + 0.738782i
\(780\) 0 0
\(781\) 9903.60 + 17153.5i 0.453750 + 0.785918i
\(782\) 0 0
\(783\) 3919.06 + 309.742i 0.178871 + 0.0141370i
\(784\) 0 0
\(785\) 60507.1 34933.8i 2.75107 1.58833i
\(786\) 0 0
\(787\) −24672.8 14244.8i −1.11752 0.645202i −0.176755 0.984255i \(-0.556560\pi\)
−0.940767 + 0.339053i \(0.889893\pi\)
\(788\) 0 0
\(789\) 27863.2 9319.48i 1.25723 0.420510i
\(790\) 0 0
\(791\) −23976.8 + 25855.9i −1.07777 + 1.16224i
\(792\) 0 0
\(793\) −34602.7 −1.54953
\(794\) 0 0
\(795\) 9557.39 + 8457.54i 0.426372 + 0.377306i