Properties

Label 252.4.x.a.41.7
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 41.7
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.07854 - 3.21955i) q^{3} +(0.330097 - 0.571745i) q^{5} +(-15.6440 - 9.91296i) q^{7} +(6.26899 + 26.2621i) q^{9} +O(q^{10})\) \(q+(-4.07854 - 3.21955i) q^{3} +(0.330097 - 0.571745i) q^{5} +(-15.6440 - 9.91296i) q^{7} +(6.26899 + 26.2621i) q^{9} +(21.4150 - 12.3640i) q^{11} +(-43.5283 - 25.1311i) q^{13} +(-3.18708 + 1.26912i) q^{15} -67.5530 q^{17} +62.9647i q^{19} +(31.8892 + 90.7969i) q^{21} +(135.811 + 78.4107i) q^{23} +(62.2821 + 107.876i) q^{25} +(58.9839 - 127.295i) q^{27} +(-129.859 + 74.9743i) q^{29} +(139.518 + 80.5507i) q^{31} +(-127.149 - 18.5198i) q^{33} +(-10.8317 + 5.67211i) q^{35} -16.2664 q^{37} +(96.6211 + 242.639i) q^{39} +(-134.901 + 233.655i) q^{41} +(188.088 + 325.779i) q^{43} +(17.0846 + 5.08479i) q^{45} +(-31.3735 - 54.3405i) q^{47} +(146.467 + 310.156i) q^{49} +(275.518 + 217.490i) q^{51} -136.820i q^{53} -16.3253i q^{55} +(202.718 - 256.804i) q^{57} +(-358.829 + 621.509i) q^{59} +(23.9682 - 13.8380i) q^{61} +(162.264 - 472.988i) q^{63} +(-28.7371 + 16.5914i) q^{65} +(-163.773 + 283.664i) q^{67} +(-301.465 - 757.052i) q^{69} -246.304i q^{71} +261.253i q^{73} +(93.2913 - 640.496i) q^{75} +(-457.579 - 18.8649i) q^{77} +(-391.980 - 678.930i) q^{79} +(-650.399 + 329.274i) q^{81} +(-599.424 - 1038.23i) q^{83} +(-22.2990 + 38.6231i) q^{85} +(771.020 + 112.303i) q^{87} -968.771 q^{89} +(431.831 + 824.643i) q^{91} +(-309.692 - 777.714i) q^{93} +(35.9997 + 20.7845i) q^{95} +(1106.79 - 639.005i) q^{97} +(458.955 + 484.895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

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
\(3\) −4.07854 3.21955i −0.784916 0.619603i
\(4\) 0 0
\(5\) 0.330097 0.571745i 0.0295248 0.0511384i −0.850885 0.525351i \(-0.823934\pi\)
0.880410 + 0.474213i \(0.157267\pi\)
\(6\) 0 0
\(7\) −15.6440 9.91296i −0.844694 0.535249i
\(8\) 0 0
\(9\) 6.26899 + 26.2621i 0.232185 + 0.972672i
\(10\) 0 0
\(11\) 21.4150 12.3640i 0.586989 0.338898i −0.176917 0.984226i \(-0.556612\pi\)
0.763906 + 0.645328i \(0.223279\pi\)
\(12\) 0 0
\(13\) −43.5283 25.1311i −0.928659 0.536162i −0.0422718 0.999106i \(-0.513460\pi\)
−0.886387 + 0.462945i \(0.846793\pi\)
\(14\) 0 0
\(15\) −3.18708 + 1.26912i −0.0548600 + 0.0218457i
\(16\) 0 0
\(17\) −67.5530 −0.963765 −0.481882 0.876236i \(-0.660047\pi\)
−0.481882 + 0.876236i \(0.660047\pi\)
\(18\) 0 0
\(19\) 62.9647i 0.760268i 0.924932 + 0.380134i \(0.124122\pi\)
−0.924932 + 0.380134i \(0.875878\pi\)
\(20\) 0 0
\(21\) 31.8892 + 90.7969i 0.331372 + 0.943500i
\(22\) 0 0
\(23\) 135.811 + 78.4107i 1.23124 + 0.710859i 0.967289 0.253676i \(-0.0816398\pi\)
0.263954 + 0.964535i \(0.414973\pi\)
\(24\) 0 0
\(25\) 62.2821 + 107.876i 0.498257 + 0.863006i
\(26\) 0 0
\(27\) 58.9839 127.295i 0.420424 0.907328i
\(28\) 0 0
\(29\) −129.859 + 74.9743i −0.831527 + 0.480082i −0.854375 0.519657i \(-0.826060\pi\)
0.0228484 + 0.999739i \(0.492727\pi\)
\(30\) 0 0
\(31\) 139.518 + 80.5507i 0.808327 + 0.466688i 0.846375 0.532588i \(-0.178780\pi\)
−0.0380475 + 0.999276i \(0.512114\pi\)
\(32\) 0 0
\(33\) −127.149 18.5198i −0.670719 0.0976934i
\(34\) 0 0
\(35\) −10.8317 + 5.67211i −0.0523112 + 0.0273932i
\(36\) 0 0
\(37\) −16.2664 −0.0722753 −0.0361377 0.999347i \(-0.511505\pi\)
−0.0361377 + 0.999347i \(0.511505\pi\)
\(38\) 0 0
\(39\) 96.6211 + 242.639i 0.396712 + 0.996241i
\(40\) 0 0
\(41\) −134.901 + 233.655i −0.513853 + 0.890019i 0.486018 + 0.873949i \(0.338449\pi\)
−0.999871 + 0.0160703i \(0.994884\pi\)
\(42\) 0 0
\(43\) 188.088 + 325.779i 0.667051 + 1.15537i 0.978725 + 0.205178i \(0.0657772\pi\)
−0.311673 + 0.950189i \(0.600889\pi\)
\(44\) 0 0
\(45\) 17.0846 + 5.08479i 0.0565961 + 0.0168444i
\(46\) 0 0
\(47\) −31.3735 54.3405i −0.0973679 0.168646i 0.813226 0.581947i \(-0.197709\pi\)
−0.910594 + 0.413301i \(0.864376\pi\)
\(48\) 0 0
\(49\) 146.467 + 310.156i 0.427016 + 0.904244i
\(50\) 0 0
\(51\) 275.518 + 217.490i 0.756474 + 0.597151i
\(52\) 0 0
\(53\) 136.820i 0.354597i −0.984157 0.177299i \(-0.943264\pi\)
0.984157 0.177299i \(-0.0567358\pi\)
\(54\) 0 0
\(55\) 16.3253i 0.0400236i
\(56\) 0 0
\(57\) 202.718 256.804i 0.471064 0.596746i
\(58\) 0 0
\(59\) −358.829 + 621.509i −0.791788 + 1.37142i 0.133070 + 0.991107i \(0.457516\pi\)
−0.924859 + 0.380311i \(0.875817\pi\)
\(60\) 0 0
\(61\) 23.9682 13.8380i 0.0503083 0.0290455i −0.474635 0.880183i \(-0.657420\pi\)
0.524943 + 0.851137i \(0.324087\pi\)
\(62\) 0 0
\(63\) 162.264 472.988i 0.324497 0.945887i
\(64\) 0 0
\(65\) −28.7371 + 16.5914i −0.0548369 + 0.0316601i
\(66\) 0 0
\(67\) −163.773 + 283.664i −0.298628 + 0.517239i −0.975822 0.218565i \(-0.929862\pi\)
0.677194 + 0.735804i \(0.263196\pi\)
\(68\) 0 0
\(69\) −301.465 757.052i −0.525972 1.32085i
\(70\) 0 0
\(71\) 246.304i 0.411703i −0.978583 0.205852i \(-0.934004\pi\)
0.978583 0.205852i \(-0.0659965\pi\)
\(72\) 0 0
\(73\) 261.253i 0.418868i 0.977823 + 0.209434i \(0.0671622\pi\)
−0.977823 + 0.209434i \(0.932838\pi\)
\(74\) 0 0
\(75\) 93.2913 640.496i 0.143631 0.986108i
\(76\) 0 0
\(77\) −457.579 18.8649i −0.677221 0.0279201i
\(78\) 0 0
\(79\) −391.980 678.930i −0.558244 0.966906i −0.997643 0.0686145i \(-0.978142\pi\)
0.439400 0.898292i \(-0.355191\pi\)
\(80\) 0 0
\(81\) −650.399 + 329.274i −0.892180 + 0.451679i
\(82\) 0 0
\(83\) −599.424 1038.23i −0.792715 1.37302i −0.924280 0.381715i \(-0.875334\pi\)
0.131565 0.991308i \(-0.458000\pi\)
\(84\) 0 0
\(85\) −22.2990 + 38.6231i −0.0284550 + 0.0492854i
\(86\) 0 0
\(87\) 771.020 + 112.303i 0.950139 + 0.138392i
\(88\) 0 0
\(89\) −968.771 −1.15381 −0.576907 0.816810i \(-0.695741\pi\)
−0.576907 + 0.816810i \(0.695741\pi\)
\(90\) 0 0
\(91\) 431.831 + 824.643i 0.497453 + 0.949957i
\(92\) 0 0
\(93\) −309.692 777.714i −0.345307 0.867152i
\(94\) 0 0
\(95\) 35.9997 + 20.7845i 0.0388789 + 0.0224467i
\(96\) 0 0
\(97\) 1106.79 639.005i 1.15853 0.668878i 0.207579 0.978218i \(-0.433442\pi\)
0.950951 + 0.309340i \(0.100108\pi\)
\(98\) 0 0
\(99\) 458.955 + 484.895i 0.465927 + 0.492260i
\(100\) 0 0
\(101\) 285.125 + 493.852i 0.280901 + 0.486535i 0.971607 0.236601i \(-0.0760333\pi\)
−0.690706 + 0.723136i \(0.742700\pi\)
\(102\) 0 0
\(103\) 1559.24 + 900.228i 1.49162 + 0.861186i 0.999954 0.00959990i \(-0.00305579\pi\)
0.491663 + 0.870785i \(0.336389\pi\)
\(104\) 0 0
\(105\) 62.4392 + 11.7393i 0.0580328 + 0.0109108i
\(106\) 0 0
\(107\) 2038.95i 1.84218i −0.389350 0.921090i \(-0.627300\pi\)
0.389350 0.921090i \(-0.372700\pi\)
\(108\) 0 0
\(109\) −1189.58 −1.04533 −0.522666 0.852538i \(-0.675062\pi\)
−0.522666 + 0.852538i \(0.675062\pi\)
\(110\) 0 0
\(111\) 66.3434 + 52.3706i 0.0567300 + 0.0447820i
\(112\) 0 0
\(113\) −646.454 373.230i −0.538171 0.310713i 0.206167 0.978517i \(-0.433901\pi\)
−0.744337 + 0.667804i \(0.767234\pi\)
\(114\) 0 0
\(115\) 89.6618 51.7663i 0.0727044 0.0419759i
\(116\) 0 0
\(117\) 387.117 1300.69i 0.305889 1.02777i
\(118\) 0 0
\(119\) 1056.80 + 669.650i 0.814086 + 0.515854i
\(120\) 0 0
\(121\) −359.764 + 623.130i −0.270296 + 0.468167i
\(122\) 0 0
\(123\) 1302.46 518.652i 0.954789 0.380205i
\(124\) 0 0
\(125\) 164.761 0.117893
\(126\) 0 0
\(127\) −1832.75 −1.28055 −0.640277 0.768144i \(-0.721180\pi\)
−0.640277 + 0.768144i \(0.721180\pi\)
\(128\) 0 0
\(129\) 281.735 1934.26i 0.192289 1.32017i
\(130\) 0 0
\(131\) −235.639 + 408.138i −0.157159 + 0.272208i −0.933843 0.357683i \(-0.883567\pi\)
0.776684 + 0.629890i \(0.216900\pi\)
\(132\) 0 0
\(133\) 624.166 985.016i 0.406933 0.642194i
\(134\) 0 0
\(135\) −53.3096 75.7433i −0.0339864 0.0482885i
\(136\) 0 0
\(137\) −2271.58 + 1311.50i −1.41660 + 0.817874i −0.995998 0.0893720i \(-0.971514\pi\)
−0.420601 + 0.907246i \(0.638181\pi\)
\(138\) 0 0
\(139\) 164.415 + 94.9252i 0.100328 + 0.0579241i 0.549324 0.835609i \(-0.314885\pi\)
−0.448997 + 0.893533i \(0.648219\pi\)
\(140\) 0 0
\(141\) −46.9938 + 322.638i −0.0280680 + 0.192702i
\(142\) 0 0
\(143\) −1242.88 −0.726817
\(144\) 0 0
\(145\) 98.9953i 0.0566973i
\(146\) 0 0
\(147\) 401.192 1736.54i 0.225100 0.974336i
\(148\) 0 0
\(149\) −383.974 221.687i −0.211117 0.121888i 0.390714 0.920512i \(-0.372228\pi\)
−0.601830 + 0.798624i \(0.705562\pi\)
\(150\) 0 0
\(151\) 943.459 + 1634.12i 0.508461 + 0.880680i 0.999952 + 0.00979739i \(0.00311865\pi\)
−0.491491 + 0.870883i \(0.663548\pi\)
\(152\) 0 0
\(153\) −423.489 1774.09i −0.223772 0.937427i
\(154\) 0 0
\(155\) 92.1089 53.1791i 0.0477314 0.0275577i
\(156\) 0 0
\(157\) 2133.22 + 1231.62i 1.08439 + 0.626075i 0.932078 0.362257i \(-0.117994\pi\)
0.152316 + 0.988332i \(0.451327\pi\)
\(158\) 0 0
\(159\) −440.498 + 558.025i −0.219709 + 0.278329i
\(160\) 0 0
\(161\) −1347.34 2572.94i −0.659537 1.25948i
\(162\) 0 0
\(163\) 2514.36 1.20822 0.604111 0.796900i \(-0.293528\pi\)
0.604111 + 0.796900i \(0.293528\pi\)
\(164\) 0 0
\(165\) −52.5600 + 66.5832i −0.0247987 + 0.0314151i
\(166\) 0 0
\(167\) −1415.81 + 2452.25i −0.656038 + 1.13629i 0.325594 + 0.945510i \(0.394436\pi\)
−0.981632 + 0.190782i \(0.938898\pi\)
\(168\) 0 0
\(169\) 164.640 + 285.164i 0.0749385 + 0.129797i
\(170\) 0 0
\(171\) −1653.59 + 394.725i −0.739491 + 0.176523i
\(172\) 0 0
\(173\) −667.439 1156.04i −0.293320 0.508046i 0.681272 0.732030i \(-0.261427\pi\)
−0.974593 + 0.223984i \(0.928094\pi\)
\(174\) 0 0
\(175\) 95.0295 2305.00i 0.0410489 0.995667i
\(176\) 0 0
\(177\) 3464.48 1379.58i 1.47122 0.585853i
\(178\) 0 0
\(179\) 1431.23i 0.597626i 0.954312 + 0.298813i \(0.0965907\pi\)
−0.954312 + 0.298813i \(0.903409\pi\)
\(180\) 0 0
\(181\) 262.769i 0.107909i 0.998543 + 0.0539543i \(0.0171825\pi\)
−0.998543 + 0.0539543i \(0.982817\pi\)
\(182\) 0 0
\(183\) −142.307 20.7278i −0.0574845 0.00837289i
\(184\) 0 0
\(185\) −5.36951 + 9.30026i −0.00213391 + 0.00369605i
\(186\) 0 0
\(187\) −1446.65 + 835.223i −0.565719 + 0.326618i
\(188\) 0 0
\(189\) −2184.61 + 1406.68i −0.840777 + 0.541382i
\(190\) 0 0
\(191\) −97.8990 + 56.5220i −0.0370876 + 0.0214125i −0.518429 0.855121i \(-0.673483\pi\)
0.481342 + 0.876533i \(0.340150\pi\)
\(192\) 0 0
\(193\) −2091.54 + 3622.65i −0.780063 + 1.35111i 0.151842 + 0.988405i \(0.451480\pi\)
−0.931905 + 0.362704i \(0.881854\pi\)
\(194\) 0 0
\(195\) 170.622 + 24.8520i 0.0626591 + 0.00912659i
\(196\) 0 0
\(197\) 314.320i 0.113677i 0.998383 + 0.0568385i \(0.0181020\pi\)
−0.998383 + 0.0568385i \(0.981898\pi\)
\(198\) 0 0
\(199\) 1407.97i 0.501550i 0.968045 + 0.250775i \(0.0806855\pi\)
−0.968045 + 0.250775i \(0.919314\pi\)
\(200\) 0 0
\(201\) 1581.23 629.658i 0.554881 0.220958i
\(202\) 0 0
\(203\) 2774.73 + 114.395i 0.959349 + 0.0395516i
\(204\) 0 0
\(205\) 89.0607 + 154.258i 0.0303428 + 0.0525552i
\(206\) 0 0
\(207\) −1207.83 + 4058.25i −0.405556 + 1.36265i
\(208\) 0 0
\(209\) 778.494 + 1348.39i 0.257653 + 0.446269i
\(210\) 0 0
\(211\) −73.9358 + 128.061i −0.0241230 + 0.0417822i −0.877835 0.478963i \(-0.841013\pi\)
0.853712 + 0.520746i \(0.174346\pi\)
\(212\) 0 0
\(213\) −792.989 + 1004.56i −0.255093 + 0.323152i
\(214\) 0 0
\(215\) 248.350 0.0787782
\(216\) 0 0
\(217\) −1384.12 2643.16i −0.432995 0.826865i
\(218\) 0 0
\(219\) 841.118 1065.53i 0.259532 0.328776i
\(220\) 0 0
\(221\) 2940.46 + 1697.68i 0.895009 + 0.516734i
\(222\) 0 0
\(223\) −2005.48 + 1157.86i −0.602228 + 0.347696i −0.769917 0.638143i \(-0.779703\pi\)
0.167690 + 0.985840i \(0.446369\pi\)
\(224\) 0 0
\(225\) −2442.60 + 2311.93i −0.723734 + 0.685017i
\(226\) 0 0
\(227\) −2233.35 3868.27i −0.653006 1.13104i −0.982390 0.186843i \(-0.940174\pi\)
0.329384 0.944196i \(-0.393159\pi\)
\(228\) 0 0
\(229\) −1016.15 586.677i −0.293229 0.169296i 0.346168 0.938172i \(-0.387483\pi\)
−0.639397 + 0.768877i \(0.720816\pi\)
\(230\) 0 0
\(231\) 1805.52 + 1550.14i 0.514262 + 0.441523i
\(232\) 0 0
\(233\) 1751.08i 0.492347i −0.969226 0.246173i \(-0.920827\pi\)
0.969226 0.246173i \(-0.0791733\pi\)
\(234\) 0 0
\(235\) −41.4252 −0.0114991
\(236\) 0 0
\(237\) −587.141 + 4031.04i −0.160924 + 1.10483i
\(238\) 0 0
\(239\) 5007.40 + 2891.03i 1.35524 + 0.782447i 0.988978 0.148065i \(-0.0473045\pi\)
0.366261 + 0.930512i \(0.380638\pi\)
\(240\) 0 0
\(241\) 230.468 133.061i 0.0616005 0.0355651i −0.468883 0.883260i \(-0.655344\pi\)
0.530484 + 0.847695i \(0.322010\pi\)
\(242\) 0 0
\(243\) 3712.80 + 751.035i 0.980148 + 0.198267i
\(244\) 0 0
\(245\) 225.678 + 18.6400i 0.0588492 + 0.00486067i
\(246\) 0 0
\(247\) 1582.37 2740.74i 0.407626 0.706029i
\(248\) 0 0
\(249\) −897.867 + 6164.35i −0.228514 + 1.56887i
\(250\) 0 0
\(251\) 7212.14 1.81365 0.906826 0.421506i \(-0.138498\pi\)
0.906826 + 0.421506i \(0.138498\pi\)
\(252\) 0 0
\(253\) 3877.87 0.963635
\(254\) 0 0
\(255\) 215.297 85.7329i 0.0528721 0.0210541i
\(256\) 0 0
\(257\) −2752.31 + 4767.14i −0.668033 + 1.15707i 0.310421 + 0.950599i \(0.399530\pi\)
−0.978453 + 0.206468i \(0.933803\pi\)
\(258\) 0 0
\(259\) 254.471 + 161.249i 0.0610505 + 0.0386853i
\(260\) 0 0
\(261\) −2783.07 2940.37i −0.660030 0.697335i
\(262\) 0 0
\(263\) −4088.19 + 2360.32i −0.958511 + 0.553396i −0.895714 0.444630i \(-0.853335\pi\)
−0.0627964 + 0.998026i \(0.520002\pi\)
\(264\) 0 0
\(265\) −78.2261 45.1639i −0.0181336 0.0104694i
\(266\) 0 0
\(267\) 3951.17 + 3119.01i 0.905647 + 0.714907i
\(268\) 0 0
\(269\) 3595.18 0.814877 0.407439 0.913233i \(-0.366422\pi\)
0.407439 + 0.913233i \(0.366422\pi\)
\(270\) 0 0
\(271\) 3673.66i 0.823466i 0.911305 + 0.411733i \(0.135076\pi\)
−0.911305 + 0.411733i \(0.864924\pi\)
\(272\) 0 0
\(273\) 893.739 4753.64i 0.198137 1.05386i
\(274\) 0 0
\(275\) 2667.55 + 1540.11i 0.584942 + 0.337716i
\(276\) 0 0
\(277\) 880.297 + 1524.72i 0.190946 + 0.330727i 0.945564 0.325437i \(-0.105511\pi\)
−0.754618 + 0.656164i \(0.772178\pi\)
\(278\) 0 0
\(279\) −1240.80 + 4169.01i −0.266253 + 0.894595i
\(280\) 0 0
\(281\) −6960.95 + 4018.91i −1.47778 + 0.853195i −0.999685 0.0251141i \(-0.992005\pi\)
−0.478093 + 0.878309i \(0.658672\pi\)
\(282\) 0 0
\(283\) −6519.11 3763.81i −1.36933 0.790584i −0.378488 0.925606i \(-0.623556\pi\)
−0.990843 + 0.135022i \(0.956889\pi\)
\(284\) 0 0
\(285\) −79.9098 200.673i −0.0166086 0.0417083i
\(286\) 0 0
\(287\) 4426.59 2318.02i 0.910430 0.476754i
\(288\) 0 0
\(289\) −349.597 −0.0711575
\(290\) 0 0
\(291\) −6571.40 957.156i −1.32379 0.192816i
\(292\) 0 0
\(293\) −105.807 + 183.262i −0.0210965 + 0.0365403i −0.876381 0.481619i \(-0.840049\pi\)
0.855284 + 0.518159i \(0.173382\pi\)
\(294\) 0 0
\(295\) 236.897 + 410.317i 0.0467548 + 0.0809816i
\(296\) 0 0
\(297\) −310.724 3455.29i −0.0607072 0.675072i
\(298\) 0 0
\(299\) −3941.08 6826.16i −0.762270 1.32029i
\(300\) 0 0
\(301\) 286.984 6960.98i 0.0549551 1.33297i
\(302\) 0 0
\(303\) 427.085 2932.17i 0.0809748 0.555937i
\(304\) 0 0
\(305\) 18.2716i 0.00343025i
\(306\) 0 0
\(307\) 2701.00i 0.502131i −0.967970 0.251065i \(-0.919219\pi\)
0.967970 0.251065i \(-0.0807809\pi\)
\(308\) 0 0
\(309\) −3461.10 8691.67i −0.637201 1.60017i
\(310\) 0 0
\(311\) 3234.86 5602.95i 0.589815 1.02159i −0.404442 0.914564i \(-0.632534\pi\)
0.994256 0.107025i \(-0.0341325\pi\)
\(312\) 0 0
\(313\) −1476.26 + 852.319i −0.266592 + 0.153917i −0.627338 0.778747i \(-0.715855\pi\)
0.360746 + 0.932664i \(0.382522\pi\)
\(314\) 0 0
\(315\) −216.866 248.905i −0.0387905 0.0445214i
\(316\) 0 0
\(317\) 1247.17 720.056i 0.220972 0.127578i −0.385428 0.922738i \(-0.625946\pi\)
0.606400 + 0.795159i \(0.292613\pi\)
\(318\) 0 0
\(319\) −1853.96 + 3211.16i −0.325398 + 0.563606i
\(320\) 0 0
\(321\) −6564.52 + 8315.96i −1.14142 + 1.44596i
\(322\) 0 0
\(323\) 4253.45i 0.732719i
\(324\) 0 0
\(325\) 6260.86i 1.06858i
\(326\) 0 0
\(327\) 4851.75 + 3829.91i 0.820497 + 0.647690i
\(328\) 0 0
\(329\) −47.8694 + 1161.10i −0.00802166 + 0.194571i
\(330\) 0 0
\(331\) −5661.53 9806.05i −0.940138 1.62837i −0.765205 0.643786i \(-0.777363\pi\)
−0.174932 0.984580i \(-0.555971\pi\)
\(332\) 0 0
\(333\) −101.974 427.191i −0.0167812 0.0703002i
\(334\) 0 0
\(335\) 108.122 + 187.273i 0.0176339 + 0.0305428i
\(336\) 0 0
\(337\) −1069.77 + 1852.89i −0.172920 + 0.299505i −0.939439 0.342715i \(-0.888653\pi\)
0.766520 + 0.642221i \(0.221987\pi\)
\(338\) 0 0
\(339\) 1434.96 + 3603.53i 0.229900 + 0.577335i
\(340\) 0 0
\(341\) 3983.71 0.632639
\(342\) 0 0
\(343\) 783.244 6303.98i 0.123298 0.992370i
\(344\) 0 0
\(345\) −532.354 77.5399i −0.0830752 0.0121003i
\(346\) 0 0
\(347\) 3237.97 + 1869.44i 0.500931 + 0.289213i 0.729098 0.684409i \(-0.239940\pi\)
−0.228167 + 0.973622i \(0.573273\pi\)
\(348\) 0 0
\(349\) 5644.28 3258.72i 0.865705 0.499815i −0.000213394 1.00000i \(-0.500068\pi\)
0.865919 + 0.500185i \(0.166735\pi\)
\(350\) 0 0
\(351\) −5766.51 + 4058.58i −0.876905 + 0.617183i
\(352\) 0 0
\(353\) 1772.88 + 3070.72i 0.267312 + 0.462998i 0.968167 0.250306i \(-0.0805313\pi\)
−0.700855 + 0.713304i \(0.747198\pi\)
\(354\) 0 0
\(355\) −140.823 81.3044i −0.0210539 0.0121555i
\(356\) 0 0
\(357\) −2154.21 6133.60i −0.319364 0.909312i
\(358\) 0 0
\(359\) 6414.84i 0.943071i −0.881847 0.471535i \(-0.843700\pi\)
0.881847 0.471535i \(-0.156300\pi\)
\(360\) 0 0
\(361\) 2894.45 0.421993
\(362\) 0 0
\(363\) 3473.51 1383.18i 0.502237 0.199995i
\(364\) 0 0
\(365\) 149.370 + 86.2390i 0.0214203 + 0.0123670i
\(366\) 0 0
\(367\) −6771.55 + 3909.55i −0.963139 + 0.556068i −0.897138 0.441751i \(-0.854357\pi\)
−0.0660011 + 0.997820i \(0.521024\pi\)
\(368\) 0 0
\(369\) −6981.97 2078.00i −0.985005 0.293161i
\(370\) 0 0
\(371\) −1356.29 + 2140.40i −0.189798 + 0.299526i
\(372\) 0 0
\(373\) 5548.13 9609.65i 0.770165 1.33396i −0.167307 0.985905i \(-0.553507\pi\)
0.937472 0.348060i \(-0.113159\pi\)
\(374\) 0 0
\(375\) −671.984 530.456i −0.0925363 0.0730470i
\(376\) 0 0
\(377\) 7536.74 1.02961
\(378\) 0 0
\(379\) −5192.03 −0.703686 −0.351843 0.936059i \(-0.614445\pi\)
−0.351843 + 0.936059i \(0.614445\pi\)
\(380\) 0 0
\(381\) 7474.95 + 5900.63i 1.00513 + 0.793435i
\(382\) 0 0
\(383\) 6875.13 11908.1i 0.917240 1.58871i 0.113652 0.993521i \(-0.463745\pi\)
0.803588 0.595186i \(-0.202922\pi\)
\(384\) 0 0
\(385\) −161.832 + 255.392i −0.0214226 + 0.0338077i
\(386\) 0 0
\(387\) −7376.52 + 6981.91i −0.968913 + 0.917081i
\(388\) 0 0
\(389\) −8425.29 + 4864.34i −1.09815 + 0.634016i −0.935734 0.352707i \(-0.885261\pi\)
−0.162413 + 0.986723i \(0.551928\pi\)
\(390\) 0 0
\(391\) −9174.45 5296.87i −1.18663 0.685101i
\(392\) 0 0
\(393\) 2275.08 905.958i 0.292017 0.116284i
\(394\) 0 0
\(395\) −517.567 −0.0659281
\(396\) 0 0
\(397\) 9192.44i 1.16210i 0.813866 + 0.581052i \(0.197359\pi\)
−0.813866 + 0.581052i \(0.802641\pi\)
\(398\) 0 0
\(399\) −5717.00 + 2007.90i −0.717313 + 0.251931i
\(400\) 0 0
\(401\) 7796.50 + 4501.31i 0.970919 + 0.560560i 0.899516 0.436887i \(-0.143919\pi\)
0.0714027 + 0.997448i \(0.477252\pi\)
\(402\) 0 0
\(403\) −4048.65 7012.46i −0.500440 0.866788i
\(404\) 0 0
\(405\) −26.4341 + 480.555i −0.00324326 + 0.0589604i
\(406\) 0 0
\(407\) −348.346 + 201.118i −0.0424248 + 0.0244940i
\(408\) 0 0
\(409\) 4580.39 + 2644.49i 0.553755 + 0.319711i 0.750635 0.660717i \(-0.229748\pi\)
−0.196880 + 0.980428i \(0.563081\pi\)
\(410\) 0 0
\(411\) 13487.2 + 1964.47i 1.61867 + 0.235767i
\(412\) 0 0
\(413\) 11774.5 6165.81i 1.40287 0.734624i
\(414\) 0 0
\(415\) −791.473 −0.0936190
\(416\) 0 0
\(417\) −364.958 916.500i −0.0428587 0.107629i
\(418\) 0 0
\(419\) 2805.44 4859.17i 0.327100 0.566554i −0.654835 0.755772i \(-0.727262\pi\)
0.981935 + 0.189218i \(0.0605953\pi\)
\(420\) 0 0
\(421\) −641.365 1110.88i −0.0742475 0.128600i 0.826511 0.562920i \(-0.190322\pi\)
−0.900759 + 0.434320i \(0.856989\pi\)
\(422\) 0 0
\(423\) 1230.42 1164.59i 0.141430 0.133864i
\(424\) 0 0
\(425\) −4207.34 7287.32i −0.480202 0.831734i
\(426\) 0 0
\(427\) −512.133 21.1140i −0.0580418 0.00239292i
\(428\) 0 0
\(429\) 5069.13 + 4001.51i 0.570490 + 0.450338i
\(430\) 0 0
\(431\) 7183.17i 0.802787i 0.915906 + 0.401393i \(0.131474\pi\)
−0.915906 + 0.401393i \(0.868526\pi\)
\(432\) 0 0
\(433\) 15271.9i 1.69497i −0.530820 0.847485i \(-0.678116\pi\)
0.530820 0.847485i \(-0.321884\pi\)
\(434\) 0 0
\(435\) 318.720 403.756i 0.0351298 0.0445026i
\(436\) 0 0
\(437\) −4937.10 + 8551.31i −0.540443 + 0.936075i
\(438\) 0 0
\(439\) −5050.88 + 2916.13i −0.549123 + 0.317037i −0.748768 0.662832i \(-0.769354\pi\)
0.199645 + 0.979868i \(0.436021\pi\)
\(440\) 0 0
\(441\) −7227.15 + 5790.89i −0.780386 + 0.625298i
\(442\) 0 0
\(443\) 2636.52 1522.20i 0.282765 0.163255i −0.351909 0.936034i \(-0.614467\pi\)
0.634675 + 0.772780i \(0.281134\pi\)
\(444\) 0 0
\(445\) −319.788 + 553.890i −0.0340661 + 0.0590043i
\(446\) 0 0
\(447\) 852.319 + 2140.38i 0.0901864 + 0.226480i
\(448\) 0 0
\(449\) 1445.89i 0.151973i 0.997109 + 0.0759863i \(0.0242105\pi\)
−0.997109 + 0.0759863i \(0.975789\pi\)
\(450\) 0 0
\(451\) 6671.64i 0.696575i
\(452\) 0 0
\(453\) 1413.19 9702.33i 0.146573 1.00630i
\(454\) 0 0
\(455\) 614.032 + 25.3150i 0.0632665 + 0.00260832i
\(456\) 0 0
\(457\) 8001.23 + 13858.5i 0.818998 + 1.41855i 0.906422 + 0.422374i \(0.138803\pi\)
−0.0874239 + 0.996171i \(0.527863\pi\)
\(458\) 0 0
\(459\) −3984.54 + 8599.12i −0.405190 + 0.874450i
\(460\) 0 0
\(461\) 6375.19 + 11042.2i 0.644083 + 1.11559i 0.984512 + 0.175315i \(0.0560943\pi\)
−0.340429 + 0.940270i \(0.610572\pi\)
\(462\) 0 0
\(463\) 3779.86 6546.91i 0.379406 0.657151i −0.611570 0.791191i \(-0.709462\pi\)
0.990976 + 0.134040i \(0.0427949\pi\)
\(464\) 0 0
\(465\) −546.883 79.6561i −0.0545399 0.00794401i
\(466\) 0 0
\(467\) −15808.4 −1.56643 −0.783217 0.621749i \(-0.786423\pi\)
−0.783217 + 0.621749i \(0.786423\pi\)
\(468\) 0 0
\(469\) 5374.01 2814.14i 0.529102 0.277068i
\(470\) 0 0
\(471\) −4735.19 11891.2i −0.463240 1.16331i
\(472\) 0 0
\(473\) 8055.84 + 4651.04i 0.783103 + 0.452125i
\(474\) 0 0
\(475\) −6792.36 + 3921.57i −0.656115 + 0.378808i
\(476\) 0 0
\(477\) 3593.18 857.723i 0.344907 0.0823321i
\(478\) 0 0
\(479\) −4236.78 7338.32i −0.404141 0.699992i 0.590080 0.807345i \(-0.299096\pi\)
−0.994221 + 0.107352i \(0.965763\pi\)
\(480\) 0 0
\(481\) 708.050 + 408.793i 0.0671191 + 0.0387512i
\(482\) 0 0
\(483\) −2788.53 + 14831.7i −0.262696 + 1.39724i
\(484\) 0 0
\(485\) 843.735i 0.0789939i
\(486\) 0 0
\(487\) −5933.46 −0.552096 −0.276048 0.961144i \(-0.589025\pi\)
−0.276048 + 0.961144i \(0.589025\pi\)
\(488\) 0 0
\(489\) −10254.9 8095.12i −0.948352 0.748618i
\(490\) 0 0
\(491\) 232.094 + 133.999i 0.0213325 + 0.0123163i 0.510628 0.859802i \(-0.329413\pi\)
−0.489296 + 0.872118i \(0.662746\pi\)
\(492\) 0 0
\(493\) 8772.38 5064.74i 0.801396 0.462686i
\(494\) 0 0
\(495\) 428.736 102.343i 0.0389298 0.00929287i
\(496\) 0 0
\(497\) −2441.60 + 3853.17i −0.220364 + 0.347763i
\(498\) 0 0
\(499\) −5365.31 + 9292.98i −0.481331 + 0.833689i −0.999770 0.0214248i \(-0.993180\pi\)
0.518440 + 0.855114i \(0.326513\pi\)
\(500\) 0 0
\(501\) 13669.6 5443.34i 1.21898 0.485410i
\(502\) 0 0
\(503\) −1490.98 −0.132166 −0.0660830 0.997814i \(-0.521050\pi\)
−0.0660830 + 0.997814i \(0.521050\pi\)
\(504\) 0 0
\(505\) 376.476 0.0331742
\(506\) 0 0
\(507\) 246.611 1693.12i 0.0216023 0.148312i
\(508\) 0 0
\(509\) −5918.88 + 10251.8i −0.515422 + 0.892736i 0.484418 + 0.874837i \(0.339031\pi\)
−0.999840 + 0.0178998i \(0.994302\pi\)
\(510\) 0 0
\(511\) 2589.79 4087.04i 0.224199 0.353816i
\(512\) 0 0
\(513\) 8015.06 + 3713.90i 0.689812 + 0.319635i
\(514\) 0 0
\(515\) 1029.40 594.326i 0.0880794 0.0508526i
\(516\) 0 0
\(517\) −1343.73 775.802i −0.114308 0.0659956i
\(518\) 0 0
\(519\) −999.746 + 6863.80i −0.0845549 + 0.580515i
\(520\) 0 0
\(521\) −5868.12 −0.493449 −0.246724 0.969086i \(-0.579354\pi\)
−0.246724 + 0.969086i \(0.579354\pi\)
\(522\) 0 0
\(523\) 20680.0i 1.72901i 0.502622 + 0.864507i \(0.332369\pi\)
−0.502622 + 0.864507i \(0.667631\pi\)
\(524\) 0 0
\(525\) −7808.65 + 9095.09i −0.649138 + 0.756081i
\(526\) 0 0
\(527\) −9424.84 5441.44i −0.779037 0.449777i
\(528\) 0 0
\(529\) 6212.96 + 10761.2i 0.510640 + 0.884455i
\(530\) 0 0
\(531\) −18571.7 5527.37i −1.51778 0.451728i
\(532\) 0 0
\(533\) 11744.0 6780.40i 0.954388 0.551016i
\(534\) 0 0
\(535\) −1165.76 673.053i −0.0942062 0.0543900i
\(536\) 0 0
\(537\) 4607.91 5837.33i 0.370291 0.469086i
\(538\) 0 0
\(539\) 6971.35 + 4831.09i 0.557100 + 0.386066i
\(540\) 0 0
\(541\) 7401.95 0.588234 0.294117 0.955769i \(-0.404974\pi\)
0.294117 + 0.955769i \(0.404974\pi\)
\(542\) 0 0
\(543\) 845.997 1071.71i 0.0668604 0.0846991i
\(544\) 0 0
\(545\) −392.677 + 680.137i −0.0308632 + 0.0534566i
\(546\) 0 0
\(547\) 5185.72 + 8981.93i 0.405348 + 0.702083i 0.994362 0.106040i \(-0.0338171\pi\)
−0.589014 + 0.808123i \(0.700484\pi\)
\(548\) 0 0
\(549\) 513.672 + 542.705i 0.0399326 + 0.0421896i
\(550\) 0 0
\(551\) −4720.73 8176.55i −0.364991 0.632183i
\(552\) 0 0
\(553\) −598.081 + 14506.8i −0.0459909 + 1.11554i
\(554\) 0 0
\(555\) 51.8424 20.6441i 0.00396502 0.00157891i
\(556\) 0 0
\(557\) 23317.1i 1.77375i −0.462014 0.886873i \(-0.652873\pi\)
0.462014 0.886873i \(-0.347127\pi\)
\(558\) 0 0
\(559\) 18907.4i 1.43059i
\(560\) 0 0
\(561\) 8589.26 + 1251.07i 0.646415 + 0.0941535i
\(562\) 0 0
\(563\) −4168.16 + 7219.47i −0.312020 + 0.540434i −0.978799 0.204821i \(-0.934339\pi\)
0.666780 + 0.745255i \(0.267672\pi\)
\(564\) 0 0
\(565\) −426.785 + 246.405i −0.0317788 + 0.0183475i
\(566\) 0 0
\(567\) 13438.9 + 1296.23i 0.995381 + 0.0960081i
\(568\) 0 0
\(569\) −19760.4 + 11408.7i −1.45589 + 0.840556i −0.998805 0.0488697i \(-0.984438\pi\)
−0.457080 + 0.889425i \(0.651105\pi\)
\(570\) 0 0
\(571\) 4072.82 7054.34i 0.298498 0.517014i −0.677295 0.735712i \(-0.736848\pi\)
0.975793 + 0.218698i \(0.0701810\pi\)
\(572\) 0 0
\(573\) 581.261 + 84.6634i 0.0423779 + 0.00617254i
\(574\) 0 0
\(575\) 19534.3i 1.41676i
\(576\) 0 0
\(577\) 19823.7i 1.43028i 0.698982 + 0.715140i \(0.253637\pi\)
−0.698982 + 0.715140i \(0.746363\pi\)
\(578\) 0 0
\(579\) 20193.7 8041.31i 1.44943 0.577177i
\(580\) 0 0
\(581\) −914.597 + 22184.1i −0.0653079 + 1.58408i
\(582\) 0 0
\(583\) −1691.64 2930.00i −0.120172 0.208145i
\(584\) 0 0
\(585\) −615.878 650.687i −0.0435272 0.0459873i
\(586\) 0 0
\(587\) −349.569 605.472i −0.0245797 0.0425732i 0.853474 0.521136i \(-0.174491\pi\)
−0.878054 + 0.478562i \(0.841158\pi\)
\(588\) 0 0
\(589\) −5071.84 + 8784.69i −0.354808 + 0.614545i
\(590\) 0 0
\(591\) 1011.97 1281.97i 0.0704345 0.0892268i
\(592\) 0 0
\(593\) −22770.8 −1.57687 −0.788434 0.615119i \(-0.789108\pi\)
−0.788434 + 0.615119i \(0.789108\pi\)
\(594\) 0 0
\(595\) 731.714 383.168i 0.0504157 0.0264006i
\(596\) 0 0
\(597\) 4533.04 5742.47i 0.310762 0.393675i
\(598\) 0 0
\(599\) −1737.23 1002.99i −0.118500 0.0684159i 0.439579 0.898204i \(-0.355128\pi\)
−0.558078 + 0.829788i \(0.688461\pi\)
\(600\) 0 0
\(601\) 12437.9 7181.05i 0.844184 0.487390i −0.0145004 0.999895i \(-0.504616\pi\)
0.858684 + 0.512505i \(0.171282\pi\)
\(602\) 0 0
\(603\) −8476.31 2522.75i −0.572441 0.170372i
\(604\) 0 0
\(605\) 237.514 + 411.387i 0.0159609 + 0.0276450i
\(606\) 0 0
\(607\) 13864.4 + 8004.64i 0.927085 + 0.535253i 0.885888 0.463898i \(-0.153550\pi\)
0.0411965 + 0.999151i \(0.486883\pi\)
\(608\) 0 0
\(609\) −10948.6 9399.95i −0.728502 0.625460i
\(610\) 0 0
\(611\) 3153.79i 0.208820i
\(612\) 0 0
\(613\) 721.073 0.0475104 0.0237552 0.999718i \(-0.492438\pi\)
0.0237552 + 0.999718i \(0.492438\pi\)
\(614\) 0 0
\(615\) 133.403 915.882i 0.00874685 0.0600519i
\(616\) 0 0
\(617\) −7798.16 4502.27i −0.508820 0.293767i 0.223528 0.974697i \(-0.428242\pi\)
−0.732349 + 0.680930i \(0.761576\pi\)
\(618\) 0 0
\(619\) −9685.79 + 5592.09i −0.628925 + 0.363110i −0.780336 0.625361i \(-0.784952\pi\)
0.151411 + 0.988471i \(0.451618\pi\)
\(620\) 0 0
\(621\) 17991.9 12663.1i 1.16263 0.818279i
\(622\) 0 0
\(623\) 15155.4 + 9603.38i 0.974620 + 0.617578i
\(624\) 0 0
\(625\) −7730.87 + 13390.3i −0.494776 + 0.856977i
\(626\) 0 0
\(627\) 1166.09 8005.87i 0.0742732 0.509926i
\(628\) 0 0
\(629\) 1098.85 0.0696564
\(630\) 0 0
\(631\) 8969.76 0.565897 0.282948 0.959135i \(-0.408688\pi\)
0.282948 + 0.959135i \(0.408688\pi\)
\(632\) 0 0
\(633\) 713.847 284.260i 0.0448229 0.0178489i
\(634\) 0 0
\(635\) −604.986 + 1047.87i −0.0378081 + 0.0654855i
\(636\) 0 0
\(637\) 1419.11 17181.4i 0.0882684 1.06868i
\(638\) 0 0
\(639\) 6468.48 1544.08i 0.400452 0.0955913i
\(640\) 0 0
\(641\) −1495.77 + 863.586i −0.0921678 + 0.0532131i −0.545375 0.838192i \(-0.683613\pi\)
0.453208 + 0.891405i \(0.350280\pi\)
\(642\) 0 0
\(643\) 15392.5 + 8886.86i 0.944045 + 0.545045i 0.891226 0.453560i \(-0.149846\pi\)
0.0528189 + 0.998604i \(0.483179\pi\)
\(644\) 0 0
\(645\) −1012.90 799.575i −0.0618342 0.0488112i
\(646\) 0 0
\(647\) 7518.12 0.456828 0.228414 0.973564i \(-0.426646\pi\)
0.228414 + 0.973564i \(0.426646\pi\)
\(648\) 0 0
\(649\) 17746.2i 1.07334i
\(650\) 0 0
\(651\) −2864.63 + 15236.5i −0.172464 + 0.917304i
\(652\) 0 0
\(653\) 5483.68 + 3166.00i 0.328626 + 0.189732i 0.655231 0.755429i \(-0.272571\pi\)
−0.326605 + 0.945161i \(0.605905\pi\)
\(654\) 0 0
\(655\) 155.567 + 269.451i 0.00928018 + 0.0160737i
\(656\) 0 0
\(657\) −6861.07 + 1637.80i −0.407421 + 0.0972549i
\(658\) 0 0
\(659\) 5478.28 3162.89i 0.323829 0.186963i −0.329269 0.944236i \(-0.606802\pi\)
0.653098 + 0.757273i \(0.273469\pi\)
\(660\) 0 0
\(661\) 18882.2 + 10901.7i 1.11110 + 0.641491i 0.939113 0.343608i \(-0.111649\pi\)
0.171983 + 0.985100i \(0.444983\pi\)
\(662\) 0 0
\(663\) −6527.04 16391.0i −0.382337 0.960142i
\(664\) 0 0
\(665\) −357.143 682.015i −0.0208262 0.0397705i
\(666\) 0 0
\(667\) −23515.1 −1.36508
\(668\) 0 0
\(669\) 11907.2 + 1734.35i 0.688132 + 0.100230i
\(670\) 0 0
\(671\) 342.186 592.684i 0.0196870 0.0340988i
\(672\) 0 0
\(673\) −12150.3 21044.9i −0.695926 1.20538i −0.969868 0.243632i \(-0.921661\pi\)
0.273942 0.961746i \(-0.411672\pi\)
\(674\) 0 0
\(675\) 17405.6 1565.23i 0.992508 0.0892532i
\(676\) 0 0
\(677\) −15606.5 27031.3i −0.885979 1.53456i −0.844587 0.535418i \(-0.820154\pi\)
−0.0413922 0.999143i \(-0.513179\pi\)
\(678\) 0 0
\(679\) −23649.0 974.990i −1.33662 0.0551056i
\(680\) 0 0
\(681\) −3345.29 + 22967.3i −0.188241 + 1.29237i
\(682\) 0 0
\(683\) 32330.6i 1.81127i −0.424063 0.905633i \(-0.639397\pi\)
0.424063 0.905633i \(-0.360603\pi\)
\(684\) 0 0
\(685\) 1731.69i 0.0965902i
\(686\) 0 0
\(687\) 2255.59 + 5664.35i 0.125264 + 0.314568i
\(688\) 0 0
\(689\) −3438.43 + 5955.53i −0.190121 + 0.329300i
\(690\) 0 0
\(691\) −10098.5 + 5830.40i −0.555958 + 0.320982i −0.751521 0.659709i \(-0.770680\pi\)
0.195564 + 0.980691i \(0.437346\pi\)
\(692\) 0 0
\(693\) −2373.13 12135.3i −0.130083 0.665196i
\(694\) 0 0
\(695\) 108.546 62.6691i 0.00592430 0.00342040i
\(696\) 0 0
\(697\) 9112.95 15784.1i 0.495233 0.857769i
\(698\) 0 0
\(699\) −5637.68 + 7141.84i −0.305060 + 0.386451i
\(700\) 0 0
\(701\) 35502.0i 1.91283i −0.292015 0.956414i \(-0.594326\pi\)
0.292015 0.956414i \(-0.405674\pi\)
\(702\) 0 0
\(703\) 1024.21i 0.0549486i
\(704\) 0 0
\(705\) 168.954 + 133.370i 0.00902580 + 0.00712485i
\(706\) 0 0
\(707\) 435.042 10552.2i 0.0231421 0.561326i
\(708\) 0 0
\(709\) 6912.86 + 11973.4i 0.366175 + 0.634233i 0.988964 0.148156i \(-0.0473339\pi\)
−0.622789 + 0.782390i \(0.714001\pi\)
\(710\) 0 0
\(711\) 15372.8 14550.4i 0.810867 0.767489i
\(712\) 0 0
\(713\) 12632.1 + 21879.4i 0.663498 + 1.14921i
\(714\) 0 0
\(715\) −410.271 + 710.610i −0.0214591 + 0.0371683i
\(716\) 0 0
\(717\) −11115.1 27912.8i −0.578941 1.45386i
\(718\) 0 0
\(719\) −35196.0 −1.82558 −0.912788 0.408434i \(-0.866075\pi\)
−0.912788 + 0.408434i \(0.866075\pi\)
\(720\) 0 0
\(721\) −15468.8 29539.8i −0.799011 1.52583i
\(722\) 0 0
\(723\) −1368.37 199.309i −0.0703874 0.0102523i
\(724\) 0 0
\(725\) −16175.8 9339.11i −0.828627 0.478408i
\(726\) 0 0
\(727\) 27427.8 15835.4i 1.39923 0.807846i 0.404918 0.914353i \(-0.367300\pi\)
0.994312 + 0.106507i \(0.0339667\pi\)
\(728\) 0 0
\(729\) −12724.8 15016.7i −0.646487 0.762925i
\(730\) 0 0
\(731\) −12705.9 22007.3i −0.642881 1.11350i
\(732\) 0 0
\(733\) 33629.6 + 19416.1i 1.69460 + 0.978375i 0.950717 + 0.310060i \(0.100349\pi\)
0.743878 + 0.668315i \(0.232984\pi\)
\(734\) 0 0
\(735\) −860.425 802.606i −0.0431800 0.0402783i
\(736\) 0 0
\(737\) 8099.56i 0.404818i
\(738\) 0 0
\(739\) −63.2905 −0.00315044 −0.00157522 0.999999i \(-0.500501\pi\)
−0.00157522 + 0.999999i \(0.500501\pi\)
\(740\) 0 0
\(741\) −15277.7 + 6083.72i −0.757410 + 0.301607i
\(742\) 0 0
\(743\) −17506.0 10107.1i −0.864376 0.499048i 0.00109946 0.999999i \(-0.499650\pi\)
−0.865475 + 0.500952i \(0.832983\pi\)
\(744\) 0 0
\(745\) −253.497 + 146.357i −0.0124663 + 0.00719745i
\(746\) 0 0
\(747\) 23508.4 22250.8i 1.15144 1.08985i
\(748\) 0 0
\(749\) −20212.1 + 31897.3i −0.986025 + 1.55608i
\(750\) 0 0
\(751\) 2887.55 5001.39i 0.140304 0.243014i −0.787307 0.616561i \(-0.788525\pi\)
0.927611 + 0.373547i \(0.121859\pi\)
\(752\) 0 0
\(753\) −29415.0 23219.9i −1.42356 1.12374i
\(754\) 0 0
\(755\) 1245.73 0.0600488
\(756\) 0 0
\(757\) −10392.0 −0.498949 −0.249474 0.968381i \(-0.580258\pi\)
−0.249474 + 0.968381i \(0.580258\pi\)
\(758\) 0 0
\(759\) −15816.1 12485.0i −0.756372 0.597071i
\(760\) 0 0
\(761\) −4343.28 + 7522.79i −0.206891 + 0.358345i −0.950733 0.310009i \(-0.899668\pi\)
0.743843 + 0.668355i \(0.233001\pi\)
\(762\) 0 0
\(763\) 18609.7 + 11792.3i 0.882985 + 0.559513i
\(764\) 0 0
\(765\) −1154.12 343.493i −0.0545453 0.0162340i
\(766\) 0 0
\(767\) 31238.4 18035.5i 1.47060 0.849053i
\(768\) 0 0
\(769\) −24932.6 14394.8i −1.16917 0.675021i −0.215687 0.976463i \(-0.569199\pi\)
−0.953485 + 0.301441i \(0.902532\pi\)
\(770\) 0 0
\(771\) 26573.5 10581.8i 1.24127 0.494285i
\(772\) 0 0
\(773\) −12521.5 −0.582622 −0.291311 0.956628i \(-0.594091\pi\)
−0.291311 + 0.956628i \(0.594091\pi\)
\(774\) 0 0
\(775\) 20067.4i 0.930121i
\(776\) 0 0
\(777\) −518.724 1476.94i −0.0239500 0.0681918i
\(778\) 0 0
\(779\) −14712.0 8493.98i −0.676653 0.390666i
\(780\) 0 0
\(781\) −3045.30 5274.62i −0.139526 0.241665i
\(782\) 0 0
\(783\) 1884.21 + 20952.7i 0.0859976 + 0.956305i
\(784\) 0 0
\(785\) 1408.34 813.107i 0.0640330 0.0369695i
\(786\) 0 0
\(787\) 15973.1 + 9222.08i 0.723482 + 0.417702i 0.816033 0.578006i \(-0.196169\pi\)
−0.0925512 + 0.995708i \(0.529502\pi\)
\(788\) 0 0
\(789\) 24273.0 + 3535.48i 1.09524 + 0.159526i
\(790\) 0 0
\(791\) 6413.28 + 12247.1i 0.288281 + 0.550513i
\(792\) 0 0
\(793\) −1391.06 −0.0622924
\(794\) 0 0
\(795\) 173.641 + 436.056i 0.00774643 + 0.0194532i