Properties

Label 252.4.x.a.41.9
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 41.9
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.29905 + 4.65987i) q^{3} +(-6.03570 + 10.4541i) q^{5} +(-16.9871 - 7.37834i) q^{7} +(-16.4287 - 21.4265i) q^{9} +O(q^{10})\) \(q+(-2.29905 + 4.65987i) q^{3} +(-6.03570 + 10.4541i) q^{5} +(-16.9871 - 7.37834i) q^{7} +(-16.4287 - 21.4265i) q^{9} +(0.00221312 - 0.00127775i) q^{11} +(-6.06841 - 3.50360i) q^{13} +(-34.8386 - 52.1602i) q^{15} +28.3143 q^{17} -49.1973i q^{19} +(73.4362 - 62.1943i) q^{21} +(44.4689 + 25.6741i) q^{23} +(-10.3594 - 17.9431i) q^{25} +(137.615 - 27.2951i) q^{27} +(97.9469 - 56.5497i) q^{29} +(28.4271 + 16.4124i) q^{31} +(0.000866054 + 0.0132505i) q^{33} +(179.663 - 133.052i) q^{35} -101.961 q^{37} +(30.2779 - 20.2230i) q^{39} +(11.2449 - 19.4767i) q^{41} +(-227.203 - 393.527i) q^{43} +(323.155 - 42.4243i) q^{45} +(-231.260 - 400.554i) q^{47} +(234.120 + 250.672i) q^{49} +(-65.0960 + 131.941i) q^{51} -567.586i q^{53} +0.0308484i q^{55} +(229.253 + 113.107i) q^{57} +(145.654 - 252.280i) q^{59} +(-592.003 + 341.793i) q^{61} +(120.984 + 485.191i) q^{63} +(73.2542 - 42.2933i) q^{65} +(269.780 - 467.273i) q^{67} +(-221.874 + 148.193i) q^{69} +307.517i q^{71} +495.192i q^{73} +(107.429 - 7.02162i) q^{75} +(-0.0470221 + 0.00537600i) q^{77} +(-324.865 - 562.683i) q^{79} +(-189.193 + 704.022i) q^{81} +(-565.581 - 979.615i) q^{83} +(-170.897 + 296.002i) q^{85} +(38.3293 + 586.430i) q^{87} -130.217 q^{89} +(77.2337 + 104.291i) q^{91} +(-141.835 + 94.7337i) q^{93} +(514.315 + 296.940i) q^{95} +(-1260.41 + 727.696i) q^{97} +(-0.0637365 - 0.0264277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

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
\(3\) −2.29905 + 4.65987i −0.442452 + 0.896792i
\(4\) 0 0
\(5\) −6.03570 + 10.4541i −0.539850 + 0.935047i 0.459062 + 0.888404i \(0.348186\pi\)
−0.998912 + 0.0466430i \(0.985148\pi\)
\(6\) 0 0
\(7\) −16.9871 7.37834i −0.917215 0.398393i
\(8\) 0 0
\(9\) −16.4287 21.4265i −0.608472 0.793575i
\(10\) 0 0
\(11\) 0.00221312 0.00127775i 6.06619e−5 3.50232e-5i −0.499970 0.866043i \(-0.666656\pi\)
0.500030 + 0.866008i \(0.333322\pi\)
\(12\) 0 0
\(13\) −6.06841 3.50360i −0.129467 0.0747479i 0.433868 0.900977i \(-0.357149\pi\)
−0.563335 + 0.826229i \(0.690482\pi\)
\(14\) 0 0
\(15\) −34.8386 52.1602i −0.599685 0.897847i
\(16\) 0 0
\(17\) 28.3143 0.403955 0.201977 0.979390i \(-0.435263\pi\)
0.201977 + 0.979390i \(0.435263\pi\)
\(18\) 0 0
\(19\) 49.1973i 0.594033i −0.954872 0.297016i \(-0.904008\pi\)
0.954872 0.297016i \(-0.0959916\pi\)
\(20\) 0 0
\(21\) 73.4362 62.1943i 0.763099 0.646281i
\(22\) 0 0
\(23\) 44.4689 + 25.6741i 0.403148 + 0.232758i 0.687841 0.725861i \(-0.258558\pi\)
−0.284693 + 0.958619i \(0.591892\pi\)
\(24\) 0 0
\(25\) −10.3594 17.9431i −0.0828756 0.143545i
\(26\) 0 0
\(27\) 137.615 27.2951i 0.980892 0.194554i
\(28\) 0 0
\(29\) 97.9469 56.5497i 0.627182 0.362104i −0.152478 0.988307i \(-0.548725\pi\)
0.779660 + 0.626203i \(0.215392\pi\)
\(30\) 0 0
\(31\) 28.4271 + 16.4124i 0.164699 + 0.0950889i 0.580084 0.814557i \(-0.303020\pi\)
−0.415385 + 0.909646i \(0.636353\pi\)
\(32\) 0 0
\(33\) 0.000866054 0.0132505i 4.56850e−6 6.98972e-5i
\(34\) 0 0
\(35\) 179.663 133.052i 0.867674 0.642567i
\(36\) 0 0
\(37\) −101.961 −0.453034 −0.226517 0.974007i \(-0.572734\pi\)
−0.226517 + 0.974007i \(0.572734\pi\)
\(38\) 0 0
\(39\) 30.2779 20.2230i 0.124316 0.0830328i
\(40\) 0 0
\(41\) 11.2449 19.4767i 0.0428331 0.0741891i −0.843814 0.536636i \(-0.819695\pi\)
0.886647 + 0.462447i \(0.153028\pi\)
\(42\) 0 0
\(43\) −227.203 393.527i −0.805771 1.39564i −0.915769 0.401705i \(-0.868418\pi\)
0.109998 0.993932i \(-0.464916\pi\)
\(44\) 0 0
\(45\) 323.155 42.4243i 1.07051 0.140539i
\(46\) 0 0
\(47\) −231.260 400.554i −0.717717 1.24312i −0.961902 0.273394i \(-0.911854\pi\)
0.244185 0.969729i \(-0.421480\pi\)
\(48\) 0 0
\(49\) 234.120 + 250.672i 0.682567 + 0.730823i
\(50\) 0 0
\(51\) −65.0960 + 131.941i −0.178731 + 0.362263i
\(52\) 0 0
\(53\) 567.586i 1.47102i −0.677515 0.735509i \(-0.736943\pi\)
0.677515 0.735509i \(-0.263057\pi\)
\(54\) 0 0
\(55\) 0.0308484i 7.56290e-5i
\(56\) 0 0
\(57\) 229.253 + 113.107i 0.532724 + 0.262831i
\(58\) 0 0
\(59\) 145.654 252.280i 0.321399 0.556680i −0.659378 0.751812i \(-0.729180\pi\)
0.980777 + 0.195132i \(0.0625136\pi\)
\(60\) 0 0
\(61\) −592.003 + 341.793i −1.24259 + 0.717412i −0.969621 0.244610i \(-0.921340\pi\)
−0.272972 + 0.962022i \(0.588007\pi\)
\(62\) 0 0
\(63\) 120.984 + 485.191i 0.241945 + 0.970290i
\(64\) 0 0
\(65\) 73.2542 42.2933i 0.139786 0.0807053i
\(66\) 0 0
\(67\) 269.780 467.273i 0.491924 0.852037i −0.508033 0.861338i \(-0.669627\pi\)
0.999957 + 0.00930051i \(0.00296049\pi\)
\(68\) 0 0
\(69\) −221.874 + 148.193i −0.387109 + 0.258556i
\(70\) 0 0
\(71\) 307.517i 0.514022i 0.966408 + 0.257011i \(0.0827377\pi\)
−0.966408 + 0.257011i \(0.917262\pi\)
\(72\) 0 0
\(73\) 495.192i 0.793943i 0.917831 + 0.396971i \(0.129939\pi\)
−0.917831 + 0.396971i \(0.870061\pi\)
\(74\) 0 0
\(75\) 107.429 7.02162i 0.165398 0.0108105i
\(76\) 0 0
\(77\) −0.0470221 + 0.00537600i −6.95930e−5 + 7.95652e-6i
\(78\) 0 0
\(79\) −324.865 562.683i −0.462661 0.801352i 0.536432 0.843944i \(-0.319772\pi\)
−0.999093 + 0.0425920i \(0.986438\pi\)
\(80\) 0 0
\(81\) −189.193 + 704.022i −0.259524 + 0.965737i
\(82\) 0 0
\(83\) −565.581 979.615i −0.747959 1.29550i −0.948800 0.315879i \(-0.897701\pi\)
0.200841 0.979624i \(-0.435633\pi\)
\(84\) 0 0
\(85\) −170.897 + 296.002i −0.218075 + 0.377717i
\(86\) 0 0
\(87\) 38.3293 + 586.430i 0.0472336 + 0.722665i
\(88\) 0 0
\(89\) −130.217 −0.155089 −0.0775447 0.996989i \(-0.524708\pi\)
−0.0775447 + 0.996989i \(0.524708\pi\)
\(90\) 0 0
\(91\) 77.2337 + 104.291i 0.0889702 + 0.120139i
\(92\) 0 0
\(93\) −141.835 + 94.7337i −0.158146 + 0.105628i
\(94\) 0 0
\(95\) 514.315 + 296.940i 0.555449 + 0.320688i
\(96\) 0 0
\(97\) −1260.41 + 727.696i −1.31933 + 0.761715i −0.983621 0.180251i \(-0.942309\pi\)
−0.335709 + 0.941966i \(0.608976\pi\)
\(98\) 0 0
\(99\) −0.0637365 0.0264277i −6.47046e−5 2.68292e-5i
\(100\) 0 0
\(101\) −197.600 342.254i −0.194673 0.337183i 0.752120 0.659026i \(-0.229031\pi\)
−0.946793 + 0.321842i \(0.895698\pi\)
\(102\) 0 0
\(103\) −545.260 314.806i −0.521612 0.301153i 0.215982 0.976397i \(-0.430705\pi\)
−0.737594 + 0.675244i \(0.764038\pi\)
\(104\) 0 0
\(105\) 206.949 + 1143.10i 0.192345 + 1.06243i
\(106\) 0 0
\(107\) 515.616i 0.465855i 0.972494 + 0.232927i \(0.0748305\pi\)
−0.972494 + 0.232927i \(0.925170\pi\)
\(108\) 0 0
\(109\) 794.011 0.697729 0.348864 0.937173i \(-0.386567\pi\)
0.348864 + 0.937173i \(0.386567\pi\)
\(110\) 0 0
\(111\) 234.413 475.124i 0.200446 0.406277i
\(112\) 0 0
\(113\) 1782.31 + 1029.02i 1.48377 + 0.856654i 0.999830 0.0184476i \(-0.00587238\pi\)
0.483939 + 0.875102i \(0.339206\pi\)
\(114\) 0 0
\(115\) −536.802 + 309.923i −0.435279 + 0.251308i
\(116\) 0 0
\(117\) 24.6264 + 187.585i 0.0194591 + 0.148224i
\(118\) 0 0
\(119\) −480.977 208.912i −0.370513 0.160933i
\(120\) 0 0
\(121\) −665.500 + 1152.68i −0.500000 + 0.866025i
\(122\) 0 0
\(123\) 64.9064 + 97.1776i 0.0475806 + 0.0712375i
\(124\) 0 0
\(125\) −1258.82 −0.900738
\(126\) 0 0
\(127\) −2071.63 −1.44746 −0.723729 0.690084i \(-0.757573\pi\)
−0.723729 + 0.690084i \(0.757573\pi\)
\(128\) 0 0
\(129\) 2356.14 153.998i 1.60811 0.105107i
\(130\) 0 0
\(131\) 467.210 809.232i 0.311606 0.539717i −0.667104 0.744964i \(-0.732467\pi\)
0.978710 + 0.205247i \(0.0657999\pi\)
\(132\) 0 0
\(133\) −362.994 + 835.717i −0.236658 + 0.544856i
\(134\) 0 0
\(135\) −545.258 + 1603.40i −0.347617 + 1.02221i
\(136\) 0 0
\(137\) 2320.59 1339.79i 1.44716 0.835521i 0.448853 0.893606i \(-0.351833\pi\)
0.998312 + 0.0580849i \(0.0184994\pi\)
\(138\) 0 0
\(139\) −794.727 458.836i −0.484949 0.279985i 0.237528 0.971381i \(-0.423663\pi\)
−0.722476 + 0.691395i \(0.756996\pi\)
\(140\) 0 0
\(141\) 2398.21 156.748i 1.43238 0.0936207i
\(142\) 0 0
\(143\) −0.0179068 −1.04716e−5
\(144\) 0 0
\(145\) 1365.27i 0.781926i
\(146\) 0 0
\(147\) −1706.35 + 514.662i −0.957400 + 0.288766i
\(148\) 0 0
\(149\) 1187.44 + 685.572i 0.652881 + 0.376941i 0.789559 0.613674i \(-0.210309\pi\)
−0.136678 + 0.990616i \(0.543643\pi\)
\(150\) 0 0
\(151\) 127.186 + 220.292i 0.0685445 + 0.118723i 0.898261 0.439463i \(-0.144831\pi\)
−0.829716 + 0.558185i \(0.811498\pi\)
\(152\) 0 0
\(153\) −465.169 606.678i −0.245795 0.320568i
\(154\) 0 0
\(155\) −343.155 + 198.121i −0.177825 + 0.102667i
\(156\) 0 0
\(157\) −511.747 295.457i −0.260139 0.150191i 0.364259 0.931298i \(-0.381322\pi\)
−0.624398 + 0.781106i \(0.714656\pi\)
\(158\) 0 0
\(159\) 2644.87 + 1304.91i 1.31920 + 0.650855i
\(160\) 0 0
\(161\) −565.963 764.234i −0.277044 0.374100i
\(162\) 0 0
\(163\) −2197.17 −1.05580 −0.527901 0.849306i \(-0.677021\pi\)
−0.527901 + 0.849306i \(0.677021\pi\)
\(164\) 0 0
\(165\) −0.143749 0.0709220i −6.78235e−5 3.34622e-5i
\(166\) 0 0
\(167\) −210.903 + 365.295i −0.0977256 + 0.169266i −0.910743 0.412974i \(-0.864490\pi\)
0.813017 + 0.582240i \(0.197823\pi\)
\(168\) 0 0
\(169\) −1073.95 1860.14i −0.488826 0.846671i
\(170\) 0 0
\(171\) −1054.13 + 808.249i −0.471410 + 0.361452i
\(172\) 0 0
\(173\) −872.428 1511.09i −0.383407 0.664081i 0.608139 0.793830i \(-0.291916\pi\)
−0.991547 + 0.129749i \(0.958583\pi\)
\(174\) 0 0
\(175\) 43.5864 + 381.236i 0.0188276 + 0.164678i
\(176\) 0 0
\(177\) 840.727 + 1258.73i 0.357022 + 0.534532i
\(178\) 0 0
\(179\) 4311.61i 1.80036i −0.435518 0.900180i \(-0.643435\pi\)
0.435518 0.900180i \(-0.356565\pi\)
\(180\) 0 0
\(181\) 1307.99i 0.537141i 0.963260 + 0.268570i \(0.0865512\pi\)
−0.963260 + 0.268570i \(0.913449\pi\)
\(182\) 0 0
\(183\) −231.667 3544.45i −0.0935808 1.43177i
\(184\) 0 0
\(185\) 615.405 1065.91i 0.244570 0.423608i
\(186\) 0 0
\(187\) 0.0626630 0.0361785i 2.45047e−5 1.41478e-5i
\(188\) 0 0
\(189\) −2539.07 551.708i −0.977197 0.212333i
\(190\) 0 0
\(191\) −3495.99 + 2018.41i −1.32440 + 0.764644i −0.984428 0.175791i \(-0.943752\pi\)
−0.339975 + 0.940435i \(0.610419\pi\)
\(192\) 0 0
\(193\) 2209.64 3827.21i 0.824112 1.42740i −0.0784849 0.996915i \(-0.525008\pi\)
0.902596 0.430488i \(-0.141658\pi\)
\(194\) 0 0
\(195\) 28.6663 + 438.589i 0.0105274 + 0.161067i
\(196\) 0 0
\(197\) 151.673i 0.0548540i −0.999624 0.0274270i \(-0.991269\pi\)
0.999624 0.0274270i \(-0.00873138\pi\)
\(198\) 0 0
\(199\) 1838.65i 0.654966i 0.944857 + 0.327483i \(0.106200\pi\)
−0.944857 + 0.327483i \(0.893800\pi\)
\(200\) 0 0
\(201\) 1557.19 + 2331.42i 0.546447 + 0.818139i
\(202\) 0 0
\(203\) −2081.07 + 237.927i −0.719520 + 0.0822622i
\(204\) 0 0
\(205\) 135.742 + 235.111i 0.0462468 + 0.0801019i
\(206\) 0 0
\(207\) −180.461 1374.61i −0.0605936 0.461555i
\(208\) 0 0
\(209\) −0.0628616 0.108879i −2.08049e−5 3.60352e-5i
\(210\) 0 0
\(211\) 1229.27 2129.15i 0.401072 0.694678i −0.592783 0.805362i \(-0.701971\pi\)
0.993856 + 0.110684i \(0.0353042\pi\)
\(212\) 0 0
\(213\) −1432.99 706.997i −0.460971 0.227430i
\(214\) 0 0
\(215\) 5485.32 1.73998
\(216\) 0 0
\(217\) −361.797 488.543i −0.113181 0.152832i
\(218\) 0 0
\(219\) −2307.53 1138.47i −0.712002 0.351282i
\(220\) 0 0
\(221\) −171.823 99.2019i −0.0522989 0.0301948i
\(222\) 0 0
\(223\) 4491.19 2592.99i 1.34867 0.778653i 0.360606 0.932718i \(-0.382570\pi\)
0.988061 + 0.154066i \(0.0492367\pi\)
\(224\) 0 0
\(225\) −214.266 + 516.750i −0.0634861 + 0.153111i
\(226\) 0 0
\(227\) −497.531 861.749i −0.145473 0.251966i 0.784077 0.620664i \(-0.213137\pi\)
−0.929549 + 0.368698i \(0.879804\pi\)
\(228\) 0 0
\(229\) −101.864 58.8111i −0.0293946 0.0169710i 0.485231 0.874386i \(-0.338736\pi\)
−0.514625 + 0.857415i \(0.672069\pi\)
\(230\) 0 0
\(231\) 0.0830546 0.231476i 2.36562e−5 6.59308e-5i
\(232\) 0 0
\(233\) 1484.08i 0.417276i −0.977993 0.208638i \(-0.933097\pi\)
0.977993 0.208638i \(-0.0669030\pi\)
\(234\) 0 0
\(235\) 5583.26 1.54984
\(236\) 0 0
\(237\) 3368.91 220.193i 0.923351 0.0603505i
\(238\) 0 0
\(239\) 2392.08 + 1381.07i 0.647409 + 0.373782i 0.787463 0.616362i \(-0.211394\pi\)
−0.140054 + 0.990144i \(0.544728\pi\)
\(240\) 0 0
\(241\) 3362.99 1941.62i 0.898877 0.518967i 0.0220413 0.999757i \(-0.492983\pi\)
0.876836 + 0.480790i \(0.159650\pi\)
\(242\) 0 0
\(243\) −2845.69 2500.19i −0.751238 0.660031i
\(244\) 0 0
\(245\) −4033.65 + 934.544i −1.05184 + 0.243697i
\(246\) 0 0
\(247\) −172.367 + 298.549i −0.0444027 + 0.0769078i
\(248\) 0 0
\(249\) 5865.18 383.350i 1.49273 0.0975655i
\(250\) 0 0
\(251\) 5549.57 1.39556 0.697780 0.716312i \(-0.254171\pi\)
0.697780 + 0.716312i \(0.254171\pi\)
\(252\) 0 0
\(253\) 0.131220 3.26076e−5
\(254\) 0 0
\(255\) −986.430 1476.88i −0.242246 0.362689i
\(256\) 0 0
\(257\) −809.585 + 1402.24i −0.196500 + 0.340348i −0.947391 0.320078i \(-0.896291\pi\)
0.750891 + 0.660426i \(0.229624\pi\)
\(258\) 0 0
\(259\) 1732.01 + 752.301i 0.415529 + 0.180485i
\(260\) 0 0
\(261\) −2820.81 1169.62i −0.668979 0.277386i
\(262\) 0 0
\(263\) −594.813 + 343.415i −0.139459 + 0.0805167i −0.568106 0.822955i \(-0.692324\pi\)
0.428647 + 0.903472i \(0.358990\pi\)
\(264\) 0 0
\(265\) 5933.62 + 3425.78i 1.37547 + 0.794128i
\(266\) 0 0
\(267\) 299.375 606.793i 0.0686196 0.139083i
\(268\) 0 0
\(269\) 1805.03 0.409124 0.204562 0.978854i \(-0.434423\pi\)
0.204562 + 0.978854i \(0.434423\pi\)
\(270\) 0 0
\(271\) 6726.19i 1.50770i −0.657046 0.753851i \(-0.728194\pi\)
0.657046 0.753851i \(-0.271806\pi\)
\(272\) 0 0
\(273\) −663.544 + 120.130i −0.147104 + 0.0266322i
\(274\) 0 0
\(275\) −0.0458534 0.0264735i −1.00548e−5 5.80513e-6i
\(276\) 0 0
\(277\) −336.124 582.184i −0.0729088 0.126282i 0.827266 0.561810i \(-0.189895\pi\)
−0.900175 + 0.435528i \(0.856562\pi\)
\(278\) 0 0
\(279\) −115.361 878.730i −0.0247544 0.188560i
\(280\) 0 0
\(281\) −2007.12 + 1158.81i −0.426102 + 0.246010i −0.697685 0.716405i \(-0.745786\pi\)
0.271583 + 0.962415i \(0.412453\pi\)
\(282\) 0 0
\(283\) −8014.87 4627.39i −1.68352 0.971978i −0.959294 0.282411i \(-0.908866\pi\)
−0.724222 0.689567i \(-0.757801\pi\)
\(284\) 0 0
\(285\) −2566.14 + 1713.96i −0.533350 + 0.356233i
\(286\) 0 0
\(287\) −334.723 + 247.883i −0.0688435 + 0.0509829i
\(288\) 0 0
\(289\) −4111.30 −0.836821
\(290\) 0 0
\(291\) −493.231 7546.34i −0.0993599 1.52019i
\(292\) 0 0
\(293\) −4392.72 + 7608.42i −0.875855 + 1.51703i −0.0200056 + 0.999800i \(0.506368\pi\)
−0.855849 + 0.517225i \(0.826965\pi\)
\(294\) 0 0
\(295\) 1758.25 + 3045.38i 0.347015 + 0.601047i
\(296\) 0 0
\(297\) 0.269683 0.236245i 5.26889e−5 4.61559e-5i
\(298\) 0 0
\(299\) −179.904 311.602i −0.0347963 0.0602689i
\(300\) 0 0
\(301\) 955.936 + 8361.25i 0.183054 + 1.60111i
\(302\) 0 0
\(303\) 2049.15 133.933i 0.388517 0.0253936i
\(304\) 0 0
\(305\) 8251.85i 1.54918i
\(306\) 0 0
\(307\) 599.516i 0.111453i 0.998446 + 0.0557267i \(0.0177476\pi\)
−0.998446 + 0.0557267i \(0.982252\pi\)
\(308\) 0 0
\(309\) 2720.53 1817.08i 0.500860 0.334532i
\(310\) 0 0
\(311\) −4494.29 + 7784.34i −0.819447 + 1.41932i 0.0866437 + 0.996239i \(0.472386\pi\)
−0.906090 + 0.423084i \(0.860948\pi\)
\(312\) 0 0
\(313\) −7102.69 + 4100.74i −1.28264 + 0.740535i −0.977331 0.211717i \(-0.932095\pi\)
−0.305314 + 0.952252i \(0.598761\pi\)
\(314\) 0 0
\(315\) −5802.48 1663.68i −1.03788 0.297581i
\(316\) 0 0
\(317\) −5894.42 + 3403.15i −1.04436 + 0.602964i −0.921066 0.389405i \(-0.872681\pi\)
−0.123298 + 0.992370i \(0.539347\pi\)
\(318\) 0 0
\(319\) 0.144512 0.250302i 2.53640e−5 4.39318e-5i
\(320\) 0 0
\(321\) −2402.70 1185.43i −0.417775 0.206118i
\(322\) 0 0
\(323\) 1392.99i 0.239962i
\(324\) 0 0
\(325\) 145.181i 0.0247791i
\(326\) 0 0
\(327\) −1825.47 + 3699.99i −0.308712 + 0.625718i
\(328\) 0 0
\(329\) 973.004 + 8510.54i 0.163050 + 1.42614i
\(330\) 0 0
\(331\) 3875.41 + 6712.41i 0.643540 + 1.11464i 0.984637 + 0.174616i \(0.0558684\pi\)
−0.341097 + 0.940028i \(0.610798\pi\)
\(332\) 0 0
\(333\) 1675.09 + 2184.67i 0.275658 + 0.359517i
\(334\) 0 0
\(335\) 3256.63 + 5640.64i 0.531130 + 0.919944i
\(336\) 0 0
\(337\) −1544.24 + 2674.70i −0.249614 + 0.432344i −0.963419 0.268001i \(-0.913637\pi\)
0.713805 + 0.700345i \(0.246970\pi\)
\(338\) 0 0
\(339\) −8892.72 + 5939.58i −1.42474 + 0.951603i
\(340\) 0 0
\(341\) 0.0838835 1.33213e−5
\(342\) 0 0
\(343\) −2127.47 5985.61i −0.334906 0.942252i
\(344\) 0 0
\(345\) −210.065 3213.95i −0.0327812 0.501546i
\(346\) 0 0
\(347\) 10112.9 + 5838.71i 1.56453 + 0.903281i 0.996789 + 0.0800721i \(0.0255151\pi\)
0.567739 + 0.823209i \(0.307818\pi\)
\(348\) 0 0
\(349\) 6683.19 3858.54i 1.02505 0.591814i 0.109489 0.993988i \(-0.465079\pi\)
0.915563 + 0.402174i \(0.131745\pi\)
\(350\) 0 0
\(351\) −930.737 316.511i −0.141536 0.0481313i
\(352\) 0 0
\(353\) −2760.12 4780.66i −0.416165 0.720818i 0.579385 0.815054i \(-0.303293\pi\)
−0.995550 + 0.0942355i \(0.969959\pi\)
\(354\) 0 0
\(355\) −3214.83 1856.08i −0.480635 0.277495i
\(356\) 0 0
\(357\) 2079.29 1760.99i 0.308257 0.261068i
\(358\) 0 0
\(359\) 6290.95i 0.924857i 0.886657 + 0.462429i \(0.153022\pi\)
−0.886657 + 0.462429i \(0.846978\pi\)
\(360\) 0 0
\(361\) 4438.63 0.647125
\(362\) 0 0
\(363\) −3841.32 5751.21i −0.555419 0.831571i
\(364\) 0 0
\(365\) −5176.81 2988.83i −0.742374 0.428610i
\(366\) 0 0
\(367\) 3342.42 1929.75i 0.475404 0.274474i −0.243095 0.970002i \(-0.578163\pi\)
0.718499 + 0.695528i \(0.244829\pi\)
\(368\) 0 0
\(369\) −602.058 + 79.0390i −0.0849373 + 0.0111507i
\(370\) 0 0
\(371\) −4187.84 + 9641.61i −0.586042 + 1.34924i
\(372\) 0 0
\(373\) −4308.29 + 7462.17i −0.598055 + 1.03586i 0.395052 + 0.918659i \(0.370726\pi\)
−0.993108 + 0.117204i \(0.962607\pi\)
\(374\) 0 0
\(375\) 2894.09 5865.93i 0.398534 0.807775i
\(376\) 0 0
\(377\) −792.509 −0.108266
\(378\) 0 0
\(379\) 11100.5 1.50447 0.752237 0.658893i \(-0.228975\pi\)
0.752237 + 0.658893i \(0.228975\pi\)
\(380\) 0 0
\(381\) 4762.77 9653.51i 0.640431 1.29807i
\(382\) 0 0
\(383\) 3294.29 5705.87i 0.439505 0.761244i −0.558147 0.829742i \(-0.688487\pi\)
0.997651 + 0.0684980i \(0.0218207\pi\)
\(384\) 0 0
\(385\) 0.227610 0.524023i 3.01300e−5 6.93681e-5i
\(386\) 0 0
\(387\) −4699.27 + 11333.3i −0.617253 + 1.48865i
\(388\) 0 0
\(389\) −6913.20 + 3991.34i −0.901062 + 0.520228i −0.877545 0.479495i \(-0.840820\pi\)
−0.0235174 + 0.999723i \(0.507487\pi\)
\(390\) 0 0
\(391\) 1259.11 + 726.945i 0.162854 + 0.0940235i
\(392\) 0 0
\(393\) 2696.77 + 4037.60i 0.346143 + 0.518245i
\(394\) 0 0
\(395\) 7843.16 0.999069
\(396\) 0 0
\(397\) 9040.06i 1.14284i −0.820658 0.571420i \(-0.806393\pi\)
0.820658 0.571420i \(-0.193607\pi\)
\(398\) 0 0
\(399\) −3059.79 3612.86i −0.383912 0.453306i
\(400\) 0 0
\(401\) −836.173 482.765i −0.104131 0.0601200i 0.447030 0.894519i \(-0.352482\pi\)
−0.551161 + 0.834399i \(0.685815\pi\)
\(402\) 0 0
\(403\) −115.005 199.194i −0.0142154 0.0246218i
\(404\) 0 0
\(405\) −6218.04 6227.12i −0.762906 0.764020i
\(406\) 0 0
\(407\) −0.225652 + 0.130280i −2.74819e−5 + 1.58667e-5i
\(408\) 0 0
\(409\) 2868.77 + 1656.28i 0.346825 + 0.200240i 0.663286 0.748366i \(-0.269161\pi\)
−0.316461 + 0.948606i \(0.602495\pi\)
\(410\) 0 0
\(411\) 908.110 + 13893.9i 0.108987 + 1.66748i
\(412\) 0 0
\(413\) −4335.64 + 3210.82i −0.516569 + 0.382552i
\(414\) 0 0
\(415\) 13654.7 1.61514
\(416\) 0 0
\(417\) 3965.23 2648.44i 0.465655 0.311018i
\(418\) 0 0
\(419\) −4172.32 + 7226.67i −0.486470 + 0.842591i −0.999879 0.0155530i \(-0.995049\pi\)
0.513409 + 0.858144i \(0.328382\pi\)
\(420\) 0 0
\(421\) 3350.59 + 5803.38i 0.387880 + 0.671828i 0.992164 0.124941i \(-0.0398741\pi\)
−0.604284 + 0.796769i \(0.706541\pi\)
\(422\) 0 0
\(423\) −4783.17 + 11535.7i −0.549801 + 1.32597i
\(424\) 0 0
\(425\) −293.321 508.046i −0.0334780 0.0579856i
\(426\) 0 0
\(427\) 12578.2 1438.06i 1.42554 0.162981i
\(428\) 0 0
\(429\) 0.0411687 0.0834434i 4.63320e−6 9.39088e-6i
\(430\) 0 0
\(431\) 9168.55i 1.02467i 0.858785 + 0.512336i \(0.171220\pi\)
−0.858785 + 0.512336i \(0.828780\pi\)
\(432\) 0 0
\(433\) 1346.90i 0.149487i −0.997203 0.0747436i \(-0.976186\pi\)
0.997203 0.0747436i \(-0.0238138\pi\)
\(434\) 0 0
\(435\) −6361.97 3138.82i −0.701225 0.345965i
\(436\) 0 0
\(437\) 1263.10 2187.75i 0.138266 0.239483i
\(438\) 0 0
\(439\) −4892.07 + 2824.44i −0.531858 + 0.307069i −0.741773 0.670651i \(-0.766015\pi\)
0.209914 + 0.977720i \(0.432681\pi\)
\(440\) 0 0
\(441\) 1524.74 9134.62i 0.164641 0.986354i
\(442\) 0 0
\(443\) −7525.68 + 4344.95i −0.807124 + 0.465993i −0.845956 0.533253i \(-0.820970\pi\)
0.0388322 + 0.999246i \(0.487636\pi\)
\(444\) 0 0
\(445\) 785.950 1361.31i 0.0837249 0.145016i
\(446\) 0 0
\(447\) −5924.67 + 3957.17i −0.626906 + 0.418720i
\(448\) 0 0
\(449\) 14492.3i 1.52324i −0.648026 0.761618i \(-0.724405\pi\)
0.648026 0.761618i \(-0.275595\pi\)
\(450\) 0 0
\(451\) 0.0574724i 6.00060e-6i
\(452\) 0 0
\(453\) −1318.94 + 86.2062i −0.136797 + 0.00894111i
\(454\) 0 0
\(455\) −1556.43 + 177.945i −0.160366 + 0.0183345i
\(456\) 0 0
\(457\) −4131.68 7156.27i −0.422914 0.732508i 0.573309 0.819339i \(-0.305659\pi\)
−0.996223 + 0.0868308i \(0.972326\pi\)
\(458\) 0 0
\(459\) 3896.48 772.843i 0.396236 0.0785909i
\(460\) 0 0
\(461\) −4948.33 8570.75i −0.499928 0.865900i 0.500072 0.865984i \(-0.333307\pi\)
−1.00000 8.36677e-5i \(0.999973\pi\)
\(462\) 0 0
\(463\) 1987.79 3442.95i 0.199525 0.345588i −0.748849 0.662740i \(-0.769393\pi\)
0.948375 + 0.317152i \(0.102727\pi\)
\(464\) 0 0
\(465\) −134.286 2054.55i −0.0133922 0.204898i
\(466\) 0 0
\(467\) 17044.5 1.68892 0.844460 0.535619i \(-0.179921\pi\)
0.844460 + 0.535619i \(0.179921\pi\)
\(468\) 0 0
\(469\) −8030.47 + 5947.07i −0.790645 + 0.585522i
\(470\) 0 0
\(471\) 2553.32 1705.40i 0.249790 0.166838i
\(472\) 0 0
\(473\) −1.00566 0.580616i −9.77592e−5 5.64413e-5i
\(474\) 0 0
\(475\) −882.751 + 509.656i −0.0852703 + 0.0492308i
\(476\) 0 0
\(477\) −12161.4 + 9324.72i −1.16736 + 0.895073i
\(478\) 0 0
\(479\) 5364.93 + 9292.33i 0.511753 + 0.886383i 0.999907 + 0.0136250i \(0.00433712\pi\)
−0.488154 + 0.872758i \(0.662330\pi\)
\(480\) 0 0
\(481\) 618.740 + 357.230i 0.0586530 + 0.0338633i
\(482\) 0 0
\(483\) 4862.41 880.302i 0.458069 0.0829299i
\(484\) 0 0
\(485\) 17568.6i 1.64485i
\(486\) 0 0
\(487\) −12461.1 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(488\) 0 0
\(489\) 5051.40 10238.5i 0.467142 0.946834i
\(490\) 0 0
\(491\) −4052.21 2339.55i −0.372452 0.215035i 0.302077 0.953283i \(-0.402320\pi\)
−0.674529 + 0.738248i \(0.735653\pi\)
\(492\) 0 0
\(493\) 2773.30 1601.16i 0.253353 0.146273i
\(494\) 0 0
\(495\) 0.660974 0.506800i 6.00173e−5 4.60181e-5i
\(496\) 0 0
\(497\) 2268.96 5223.81i 0.204783 0.471469i
\(498\) 0 0
\(499\) 2685.54 4651.49i 0.240924 0.417293i −0.720054 0.693918i \(-0.755883\pi\)
0.960978 + 0.276625i \(0.0892161\pi\)
\(500\) 0 0
\(501\) −1217.35 1822.61i −0.108557 0.162532i
\(502\) 0 0
\(503\) −22263.9 −1.97355 −0.986777 0.162086i \(-0.948178\pi\)
−0.986777 + 0.162086i \(0.948178\pi\)
\(504\) 0 0
\(505\) 4770.63 0.420376
\(506\) 0 0
\(507\) 11137.0 727.921i 0.975569 0.0637635i
\(508\) 0 0
\(509\) 7249.76 12556.9i 0.631316 1.09347i −0.355967 0.934498i \(-0.615848\pi\)
0.987283 0.158973i \(-0.0508182\pi\)
\(510\) 0 0
\(511\) 3653.69 8411.85i 0.316301 0.728216i
\(512\) 0 0
\(513\) −1342.85 6770.30i −0.115571 0.582682i
\(514\) 0 0
\(515\) 6582.05 3800.15i 0.563184 0.325155i
\(516\) 0 0
\(517\) −1.02361 0.590983i −8.70762e−5 5.02735e-5i
\(518\) 0 0
\(519\) 9047.24 591.330i 0.765182 0.0500126i
\(520\) 0 0
\(521\) 7009.79 0.589452 0.294726 0.955582i \(-0.404772\pi\)
0.294726 + 0.955582i \(0.404772\pi\)
\(522\) 0 0
\(523\) 3631.76i 0.303644i −0.988408 0.151822i \(-0.951486\pi\)
0.988408 0.151822i \(-0.0485141\pi\)
\(524\) 0 0
\(525\) −1876.72 673.373i −0.156013 0.0559779i
\(526\) 0 0
\(527\) 804.894 + 464.706i 0.0665308 + 0.0384116i
\(528\) 0 0
\(529\) −4765.18 8253.53i −0.391648 0.678354i
\(530\) 0 0
\(531\) −7798.41 + 1023.79i −0.637330 + 0.0836696i
\(532\) 0 0
\(533\) −136.477 + 78.7951i −0.0110910 + 0.00640336i
\(534\) 0 0
\(535\) −5390.32 3112.10i −0.435596 0.251492i
\(536\) 0 0
\(537\) 20091.5 + 9912.59i 1.61455 + 0.796573i
\(538\) 0 0
\(539\) 0.838432 + 0.255622i 6.70015e−5 + 2.04275e-5i
\(540\) 0 0
\(541\) −12760.4 −1.01407 −0.507037 0.861925i \(-0.669259\pi\)
−0.507037 + 0.861925i \(0.669259\pi\)
\(542\) 0 0
\(543\) −6095.08 3007.14i −0.481704 0.237659i
\(544\) 0 0
\(545\) −4792.42 + 8300.71i −0.376669 + 0.652410i
\(546\) 0 0
\(547\) −3919.62 6788.98i −0.306382 0.530669i 0.671186 0.741289i \(-0.265785\pi\)
−0.977568 + 0.210620i \(0.932452\pi\)
\(548\) 0 0
\(549\) 17049.3 + 7069.34i 1.32540 + 0.549566i
\(550\) 0 0
\(551\) −2782.09 4818.72i −0.215101 0.372567i
\(552\) 0 0
\(553\) 1366.84 + 11955.3i 0.105107 + 0.919332i
\(554\) 0 0
\(555\) 3552.17 + 5318.29i 0.271678 + 0.406755i
\(556\) 0 0
\(557\) 9443.19i 0.718350i −0.933270 0.359175i \(-0.883058\pi\)
0.933270 0.359175i \(-0.116942\pi\)
\(558\) 0 0
\(559\) 3184.11i 0.240919i
\(560\) 0 0
\(561\) 0.0245217 + 0.375177i 1.84547e−6 + 2.82353e-5i
\(562\) 0 0
\(563\) 8022.13 13894.7i 0.600519 1.04013i −0.392223 0.919870i \(-0.628294\pi\)
0.992742 0.120260i \(-0.0383728\pi\)
\(564\) 0 0
\(565\) −21515.0 + 12421.7i −1.60202 + 0.924929i
\(566\) 0 0
\(567\) 8408.34 10563.3i 0.622781 0.782396i
\(568\) 0 0
\(569\) 19213.9 11093.2i 1.41562 0.817310i 0.419712 0.907657i \(-0.362131\pi\)
0.995910 + 0.0903469i \(0.0287976\pi\)
\(570\) 0 0
\(571\) −3211.11 + 5561.80i −0.235343 + 0.407625i −0.959372 0.282144i \(-0.908955\pi\)
0.724030 + 0.689769i \(0.242288\pi\)
\(572\) 0 0
\(573\) −1368.07 20931.3i −0.0997419 1.52603i
\(574\) 0 0
\(575\) 1063.88i 0.0771597i
\(576\) 0 0
\(577\) 21441.1i 1.54697i 0.633813 + 0.773486i \(0.281489\pi\)
−0.633813 + 0.773486i \(0.718511\pi\)
\(578\) 0 0
\(579\) 12754.2 + 19095.6i 0.915454 + 1.37061i
\(580\) 0 0
\(581\) 2379.63 + 20813.8i 0.169920 + 1.48624i
\(582\) 0 0
\(583\) −0.725230 1.25614i −5.15197e−5 8.92347e-5i
\(584\) 0 0
\(585\) −2109.67 874.757i −0.149101 0.0618235i
\(586\) 0 0
\(587\) −342.762 593.681i −0.0241010 0.0417442i 0.853723 0.520727i \(-0.174339\pi\)
−0.877824 + 0.478983i \(0.841006\pi\)
\(588\) 0 0
\(589\) 807.445 1398.54i 0.0564859 0.0978365i
\(590\) 0 0
\(591\) 706.775 + 348.703i 0.0491926 + 0.0242703i
\(592\) 0 0
\(593\) 11503.8 0.796635 0.398317 0.917248i \(-0.369594\pi\)
0.398317 + 0.917248i \(0.369594\pi\)
\(594\) 0 0
\(595\) 5087.04 3767.27i 0.350501 0.259568i
\(596\) 0 0
\(597\) −8567.85 4227.14i −0.587368 0.289791i
\(598\) 0 0
\(599\) 5124.45 + 2958.60i 0.349548 + 0.201812i 0.664486 0.747300i \(-0.268650\pi\)
−0.314938 + 0.949112i \(0.601984\pi\)
\(600\) 0 0
\(601\) 10168.3 5870.67i 0.690139 0.398452i −0.113525 0.993535i \(-0.536214\pi\)
0.803664 + 0.595083i \(0.202881\pi\)
\(602\) 0 0
\(603\) −14444.2 + 1896.25i −0.975478 + 0.128062i
\(604\) 0 0
\(605\) −8033.52 13914.5i −0.539850 0.935047i
\(606\) 0 0
\(607\) −24018.0 13866.8i −1.60603 0.927241i −0.990247 0.139325i \(-0.955507\pi\)
−0.615782 0.787916i \(-0.711160\pi\)
\(608\) 0 0
\(609\) 3675.78 10244.5i 0.244581 0.681657i
\(610\) 0 0
\(611\) 3240.96i 0.214592i
\(612\) 0 0
\(613\) −19338.2 −1.27416 −0.637081 0.770797i \(-0.719858\pi\)
−0.637081 + 0.770797i \(0.719858\pi\)
\(614\) 0 0
\(615\) −1407.66 + 92.0054i −0.0922968 + 0.00603255i
\(616\) 0 0
\(617\) 9927.33 + 5731.55i 0.647746 + 0.373976i 0.787592 0.616197i \(-0.211327\pi\)
−0.139846 + 0.990173i \(0.544661\pi\)
\(618\) 0 0
\(619\) 3429.59 1980.07i 0.222693 0.128572i −0.384504 0.923123i \(-0.625627\pi\)
0.607196 + 0.794552i \(0.292294\pi\)
\(620\) 0 0
\(621\) 6820.38 + 2319.37i 0.440728 + 0.149876i
\(622\) 0 0
\(623\) 2212.00 + 960.783i 0.142250 + 0.0617865i
\(624\) 0 0
\(625\) 8892.79 15402.8i 0.569139 0.985777i
\(626\) 0 0
\(627\) 0.651886 0.0426075i 4.15212e−5 2.71384e-6i
\(628\) 0 0
\(629\) −2886.95 −0.183005
\(630\) 0 0
\(631\) −5409.20 −0.341263 −0.170631 0.985335i \(-0.554581\pi\)
−0.170631 + 0.985335i \(0.554581\pi\)
\(632\) 0 0
\(633\) 7095.43 + 10623.3i 0.445526 + 0.667040i
\(634\) 0 0
\(635\) 12503.7 21657.1i 0.781410 1.35344i
\(636\) 0 0
\(637\) −542.482 2341.45i −0.0337424 0.145638i
\(638\) 0 0
\(639\) 6589.02 5052.12i 0.407915 0.312768i
\(640\) 0 0
\(641\) −20809.6 + 12014.4i −1.28226 + 0.740313i −0.977261 0.212040i \(-0.931989\pi\)
−0.304999 + 0.952353i \(0.598656\pi\)
\(642\) 0 0
\(643\) 3581.87 + 2068.00i 0.219682 + 0.126833i 0.605803 0.795615i \(-0.292852\pi\)
−0.386121 + 0.922448i \(0.626185\pi\)
\(644\) 0 0
\(645\) −12611.0 + 25560.9i −0.769859 + 1.56040i
\(646\) 0 0
\(647\) −1393.75 −0.0846895 −0.0423447 0.999103i \(-0.513483\pi\)
−0.0423447 + 0.999103i \(0.513483\pi\)
\(648\) 0 0
\(649\) 0.744436i 4.50257e-5i
\(650\) 0 0
\(651\) 3108.34 562.741i 0.187136 0.0338795i
\(652\) 0 0
\(653\) 7846.10 + 4529.95i 0.470202 + 0.271471i 0.716324 0.697768i \(-0.245823\pi\)
−0.246122 + 0.969239i \(0.579157\pi\)
\(654\) 0 0
\(655\) 5639.89 + 9768.57i 0.336441 + 0.582732i
\(656\) 0 0
\(657\) 10610.2 8135.38i 0.630053 0.483092i
\(658\) 0 0
\(659\) 14018.1 8093.34i 0.828629 0.478409i −0.0247539 0.999694i \(-0.507880\pi\)
0.853383 + 0.521284i \(0.174547\pi\)
\(660\) 0 0
\(661\) −24821.5 14330.7i −1.46058 0.843269i −0.461546 0.887116i \(-0.652705\pi\)
−0.999038 + 0.0438473i \(0.986038\pi\)
\(662\) 0 0
\(663\) 857.297 572.601i 0.0502182 0.0335415i
\(664\) 0 0
\(665\) −6545.78 8838.93i −0.381706 0.515427i
\(666\) 0 0
\(667\) 5807.45 0.337130
\(668\) 0 0
\(669\) 1757.53 + 26889.8i 0.101569 + 1.55399i
\(670\) 0 0
\(671\) −0.873449 + 1.51286i −5.02521e−5 + 8.70391e-5i
\(672\) 0 0
\(673\) 3670.88 + 6358.15i 0.210255 + 0.364173i 0.951794 0.306737i \(-0.0992371\pi\)
−0.741539 + 0.670910i \(0.765904\pi\)
\(674\) 0 0
\(675\) −1915.38 2186.48i −0.109219 0.124678i
\(676\) 0 0
\(677\) −16478.4 28541.4i −0.935474 1.62029i −0.773787 0.633446i \(-0.781640\pi\)
−0.161687 0.986842i \(-0.551693\pi\)
\(678\) 0 0
\(679\) 26779.8 3061.71i 1.51357 0.173045i
\(680\) 0 0
\(681\) 5159.48 337.226i 0.290326 0.0189758i
\(682\) 0 0
\(683\) 22213.0i 1.24444i 0.782841 + 0.622222i \(0.213770\pi\)
−0.782841 + 0.622222i \(0.786230\pi\)
\(684\) 0 0
\(685\) 32346.4i 1.80422i
\(686\) 0 0
\(687\) 508.242 339.463i 0.0282251 0.0188520i
\(688\) 0 0
\(689\) −1988.59 + 3444.34i −0.109955 + 0.190448i
\(690\) 0 0
\(691\) −22072.1 + 12743.3i −1.21514 + 0.701563i −0.963875 0.266355i \(-0.914181\pi\)
−0.251267 + 0.967918i \(0.580847\pi\)
\(692\) 0 0
\(693\) 0.887702 + 0.919199i 4.86595e−5 + 5.03860e-5i
\(694\) 0 0
\(695\) 9593.47 5538.79i 0.523599 0.302300i
\(696\) 0 0
\(697\) 318.391 551.470i 0.0173026 0.0299690i
\(698\) 0 0
\(699\) 6915.61 + 3411.97i 0.374209 + 0.184625i
\(700\) 0 0
\(701\) 22316.4i 1.20239i 0.799101 + 0.601197i \(0.205309\pi\)
−0.799101 + 0.601197i \(0.794691\pi\)
\(702\) 0 0
\(703\) 5016.19i 0.269117i
\(704\) 0 0
\(705\) −12836.2 + 26017.3i −0.685729 + 1.38988i
\(706\) 0 0
\(707\) 831.385 + 7271.84i 0.0442255 + 0.386826i
\(708\) 0 0
\(709\) −620.251 1074.31i −0.0328547 0.0569061i 0.849130 0.528183i \(-0.177127\pi\)
−0.881985 + 0.471277i \(0.843793\pi\)
\(710\) 0 0
\(711\) −6719.22 + 16204.9i −0.354417 + 0.854756i
\(712\) 0 0
\(713\) 842.748 + 1459.68i 0.0442653 + 0.0766698i
\(714\) 0 0
\(715\) 0.108080 0.187201i 5.65311e−6 9.79147e-6i
\(716\) 0 0
\(717\) −11935.1 + 7971.63i −0.621652 + 0.415211i
\(718\) 0 0
\(719\) −1718.52 −0.0891374 −0.0445687 0.999006i \(-0.514191\pi\)
−0.0445687 + 0.999006i \(0.514191\pi\)
\(720\) 0 0
\(721\) 6939.62 + 9370.74i 0.358453 + 0.484028i
\(722\) 0 0
\(723\) 1316.03 + 20135.0i 0.0676952 + 1.03572i
\(724\) 0 0
\(725\) −2029.35 1171.65i −0.103956 0.0600191i
\(726\) 0 0
\(727\) −2204.74 + 1272.91i −0.112475 + 0.0649376i −0.555182 0.831729i \(-0.687351\pi\)
0.442707 + 0.896666i \(0.354018\pi\)
\(728\) 0 0
\(729\) 18193.0 7512.46i 0.924298 0.381672i
\(730\) 0 0
\(731\) −6433.10 11142.5i −0.325495 0.563774i
\(732\) 0 0
\(733\) −19126.0 11042.4i −0.963761 0.556427i −0.0664323 0.997791i \(-0.521162\pi\)
−0.897328 + 0.441363i \(0.854495\pi\)
\(734\) 0 0
\(735\) 4918.70 20944.8i 0.246842 1.05110i
\(736\) 0 0
\(737\) 1.37884i 6.89149e-5i
\(738\) 0 0
\(739\) −5401.50 −0.268873 −0.134437 0.990922i \(-0.542922\pi\)
−0.134437 + 0.990922i \(0.542922\pi\)
\(740\) 0 0
\(741\) −994.918 1489.59i −0.0493242 0.0738480i
\(742\) 0 0
\(743\) −26971.1 15571.7i −1.33173 0.768872i −0.346161 0.938175i \(-0.612515\pi\)
−0.985564 + 0.169303i \(0.945848\pi\)
\(744\) 0 0
\(745\) −14334.1 + 8275.82i −0.704915 + 0.406983i
\(746\) 0 0
\(747\) −11698.0 + 28212.3i −0.572967 + 1.38184i
\(748\) 0 0
\(749\) 3804.39 8758.80i 0.185593 0.427289i
\(750\) 0 0
\(751\) −2644.61 + 4580.61i −0.128500 + 0.222568i −0.923096 0.384571i \(-0.874350\pi\)
0.794596 + 0.607139i \(0.207683\pi\)
\(752\) 0 0
\(753\) −12758.7 + 25860.2i −0.617468 + 1.25153i
\(754\) 0 0
\(755\) −3070.62 −0.148015
\(756\) 0 0
\(757\) −20794.2 −0.998384 −0.499192 0.866491i \(-0.666370\pi\)
−0.499192 + 0.866491i \(0.666370\pi\)
\(758\) 0 0
\(759\) −0.301681 + 0.611468i −1.44273e−5 + 2.92423e-5i
\(760\) 0 0
\(761\) 9126.94 15808.3i 0.434759 0.753024i −0.562517 0.826785i \(-0.690167\pi\)
0.997276 + 0.0737616i \(0.0235004\pi\)
\(762\) 0 0
\(763\) −13487.9 5858.48i −0.639967 0.277970i
\(764\) 0 0
\(765\) 9149.92 1201.21i 0.432439 0.0567712i
\(766\) 0 0
\(767\) −1767.78 + 1020.63i −0.0832213 + 0.0480478i
\(768\) 0 0
\(769\) 28098.3 + 16222.6i 1.31762 + 0.760730i 0.983346 0.181745i \(-0.0581744\pi\)
0.334278 + 0.942475i \(0.391508\pi\)
\(770\) 0 0
\(771\) −4672.99 6996.39i −0.218280 0.326808i
\(772\) 0 0
\(773\) −20600.1 −0.958519 −0.479259 0.877673i \(-0.659095\pi\)
−0.479259 + 0.877673i \(0.659095\pi\)
\(774\) 0 0
\(775\) 680.094i 0.0315222i
\(776\) 0 0
\(777\) −7487.61 + 6341.38i −0.345710 + 0.292787i
\(778\) 0 0
\(779\) −958.201 553.217i −0.0440707 0.0254442i
\(780\) 0 0
\(781\) 0.392929 + 0.680572i 1.80027e−5 + 3.11816e-5i
\(782\) 0 0
\(783\) 11935.5 10455.6i 0.544749 0.477205i
\(784\) 0 0
\(785\) 6177.51 3566.59i 0.280872 0.162162i
\(786\) 0 0
\(787\) −12253.1 7074.35i −0.554990 0.320424i 0.196142 0.980575i \(-0.437159\pi\)
−0.751132 + 0.660152i \(0.770492\pi\)
\(788\) 0 0
\(789\) −232.766 3561.28i −0.0105028 0.160691i
\(790\) 0 0
\(791\) −22683.8 30630.5i −1.01965 1.37686i
\(792\) 0 0
\(793\) 4790.02 0.214500
\(794\) 0 0
\(795\)