Properties

Label 108.4.h.b.71.3
Level 108
Weight 4
Character 108.71
Analytic conductor 6.372
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.3
Character \(\chi\) \(=\) 108.71
Dual form 108.4.h.b.35.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.15223 + 1.83518i) q^{2} +(1.26420 - 7.89948i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(-2.30362 + 1.33000i) q^{7} +(11.7761 + 19.3216i) q^{8} +O(q^{10})\) \(q+(-2.15223 + 1.83518i) q^{2} +(1.26420 - 7.89948i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(-2.30362 + 1.33000i) q^{7} +(11.7761 + 19.3216i) q^{8} +(6.70190 - 1.23654i) q^{10} +(24.1428 + 41.8166i) q^{11} +(-20.3570 + 35.2594i) q^{13} +(2.51714 - 7.09003i) q^{14} +(-60.8036 - 19.9731i) q^{16} -36.3729i q^{17} +125.173i q^{19} +(-12.1548 + 14.9605i) q^{20} +(-128.702 - 45.6925i) q^{22} +(-97.0560 + 168.106i) q^{23} +(-59.5972 - 103.225i) q^{25} +(-20.8944 - 113.245i) q^{26} +(7.59405 + 19.8788i) q^{28} +(-153.593 + 88.6772i) q^{29} +(152.058 + 87.7909i) q^{31} +(167.518 - 68.5991i) q^{32} +(66.7510 + 78.2830i) q^{34} +6.40918 q^{35} +199.364 q^{37} +(-229.716 - 269.402i) q^{38} +(-1.29548 - 54.5047i) q^{40} +(201.816 + 116.518i) q^{41} +(252.553 - 145.812i) q^{43} +(360.851 - 137.851i) q^{44} +(-99.6182 - 539.918i) q^{46} +(-30.9476 - 53.6029i) q^{47} +(-167.962 + 290.919i) q^{49} +(317.705 + 112.793i) q^{50} +(252.795 + 205.385i) q^{52} -352.175i q^{53} -116.343i q^{55} +(-52.8254 - 28.8473i) q^{56} +(167.830 - 472.726i) q^{58} +(70.7911 - 122.614i) q^{59} +(-7.71518 - 13.3631i) q^{61} +(-488.377 + 90.1086i) q^{62} +(-234.645 + 455.067i) q^{64} +(84.9565 - 49.0496i) q^{65} +(-131.657 - 76.0120i) q^{67} +(-287.327 - 45.9827i) q^{68} +(-13.7940 + 11.7620i) q^{70} +28.0331 q^{71} +124.499 q^{73} +(-429.078 + 365.870i) q^{74} +(988.804 + 158.244i) q^{76} +(-111.232 - 64.2199i) q^{77} +(-648.411 + 374.360i) q^{79} +(102.814 + 114.929i) q^{80} +(-648.187 + 119.595i) q^{82} +(-174.444 - 302.146i) q^{83} +(-43.8198 + 75.8981i) q^{85} +(-275.962 + 777.302i) q^{86} +(-523.653 + 958.916i) q^{88} +416.864i q^{89} -108.299i q^{91} +(1205.25 + 979.212i) q^{92} +(164.978 + 58.5712i) q^{94} +(150.801 - 261.195i) q^{95} +(-752.565 - 1303.48i) q^{97} +(-172.396 - 934.367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.15223 + 1.83518i −0.760929 + 0.648835i
\(3\) 0 0
\(4\) 1.26420 7.89948i 0.158025 0.987435i
\(5\) −2.08666 1.20474i −0.186637 0.107755i 0.403770 0.914860i \(-0.367699\pi\)
−0.590407 + 0.807106i \(0.701033\pi\)
\(6\) 0 0
\(7\) −2.30362 + 1.33000i −0.124384 + 0.0718131i −0.560901 0.827883i \(-0.689545\pi\)
0.436517 + 0.899696i \(0.356212\pi\)
\(8\) 11.7761 + 19.3216i 0.520437 + 0.853900i
\(9\) 0 0
\(10\) 6.70190 1.23654i 0.211933 0.0391029i
\(11\) 24.1428 + 41.8166i 0.661758 + 1.14620i 0.980153 + 0.198241i \(0.0635229\pi\)
−0.318395 + 0.947958i \(0.603144\pi\)
\(12\) 0 0
\(13\) −20.3570 + 35.2594i −0.434309 + 0.752245i −0.997239 0.0742593i \(-0.976341\pi\)
0.562930 + 0.826505i \(0.309674\pi\)
\(14\) 2.51714 7.09003i 0.0480524 0.135349i
\(15\) 0 0
\(16\) −60.8036 19.9731i −0.950056 0.312079i
\(17\) 36.3729i 0.518925i −0.965753 0.259463i \(-0.916455\pi\)
0.965753 0.259463i \(-0.0835455\pi\)
\(18\) 0 0
\(19\) 125.173i 1.51141i 0.654914 + 0.755703i \(0.272705\pi\)
−0.654914 + 0.755703i \(0.727295\pi\)
\(20\) −12.1548 + 14.9605i −0.135894 + 0.167264i
\(21\) 0 0
\(22\) −128.702 45.6925i −1.24725 0.442804i
\(23\) −97.0560 + 168.106i −0.879894 + 1.52402i −0.0284384 + 0.999596i \(0.509053\pi\)
−0.851456 + 0.524426i \(0.824280\pi\)
\(24\) 0 0
\(25\) −59.5972 103.225i −0.476778 0.825803i
\(26\) −20.8944 113.245i −0.157605 0.854200i
\(27\) 0 0
\(28\) 7.59405 + 19.8788i 0.0512550 + 0.134169i
\(29\) −153.593 + 88.6772i −0.983503 + 0.567826i −0.903326 0.428955i \(-0.858882\pi\)
−0.0801773 + 0.996781i \(0.525549\pi\)
\(30\) 0 0
\(31\) 152.058 + 87.7909i 0.880983 + 0.508636i 0.870982 0.491314i \(-0.163483\pi\)
0.0100006 + 0.999950i \(0.496817\pi\)
\(32\) 167.518 68.5991i 0.925413 0.378960i
\(33\) 0 0
\(34\) 66.7510 + 78.2830i 0.336697 + 0.394865i
\(35\) 6.40918 0.0309529
\(36\) 0 0
\(37\) 199.364 0.885818 0.442909 0.896566i \(-0.353946\pi\)
0.442909 + 0.896566i \(0.353946\pi\)
\(38\) −229.716 269.402i −0.980654 1.15007i
\(39\) 0 0
\(40\) −1.29548 54.5047i −0.00512084 0.215449i
\(41\) 201.816 + 116.518i 0.768740 + 0.443832i 0.832425 0.554138i \(-0.186952\pi\)
−0.0636849 + 0.997970i \(0.520285\pi\)
\(42\) 0 0
\(43\) 252.553 145.812i 0.895674 0.517118i 0.0198798 0.999802i \(-0.493672\pi\)
0.875794 + 0.482685i \(0.160338\pi\)
\(44\) 360.851 137.851i 1.23637 0.472315i
\(45\) 0 0
\(46\) −99.6182 539.918i −0.319302 1.73058i
\(47\) −30.9476 53.6029i −0.0960463 0.166357i 0.813998 0.580867i \(-0.197286\pi\)
−0.910045 + 0.414510i \(0.863953\pi\)
\(48\) 0 0
\(49\) −167.962 + 290.919i −0.489686 + 0.848161i
\(50\) 317.705 + 112.793i 0.898604 + 0.319027i
\(51\) 0 0
\(52\) 252.795 + 205.385i 0.674162 + 0.547726i
\(53\) 352.175i 0.912735i −0.889791 0.456367i \(-0.849150\pi\)
0.889791 0.456367i \(-0.150850\pi\)
\(54\) 0 0
\(55\) 116.343i 0.285231i
\(56\) −52.8254 28.8473i −0.126055 0.0688373i
\(57\) 0 0
\(58\) 167.830 472.726i 0.379950 1.07021i
\(59\) 70.7911 122.614i 0.156207 0.270559i −0.777291 0.629141i \(-0.783407\pi\)
0.933498 + 0.358583i \(0.116740\pi\)
\(60\) 0 0
\(61\) −7.71518 13.3631i −0.0161939 0.0280486i 0.857815 0.513959i \(-0.171822\pi\)
−0.874009 + 0.485910i \(0.838488\pi\)
\(62\) −488.377 + 90.1086i −1.00039 + 0.184577i
\(63\) 0 0
\(64\) −234.645 + 455.067i −0.458291 + 0.888802i
\(65\) 84.9565 49.0496i 0.162116 0.0935978i
\(66\) 0 0
\(67\) −131.657 76.0120i −0.240066 0.138602i 0.375141 0.926968i \(-0.377594\pi\)
−0.615207 + 0.788366i \(0.710928\pi\)
\(68\) −287.327 45.9827i −0.512405 0.0820033i
\(69\) 0 0
\(70\) −13.7940 + 11.7620i −0.0235529 + 0.0200833i
\(71\) 28.0331 0.0468580 0.0234290 0.999726i \(-0.492542\pi\)
0.0234290 + 0.999726i \(0.492542\pi\)
\(72\) 0 0
\(73\) 124.499 0.199609 0.0998047 0.995007i \(-0.468178\pi\)
0.0998047 + 0.995007i \(0.468178\pi\)
\(74\) −429.078 + 365.870i −0.674045 + 0.574750i
\(75\) 0 0
\(76\) 988.804 + 158.244i 1.49242 + 0.238840i
\(77\) −111.232 64.2199i −0.164624 0.0950459i
\(78\) 0 0
\(79\) −648.411 + 374.360i −0.923443 + 0.533150i −0.884732 0.466101i \(-0.845658\pi\)
−0.0387108 + 0.999250i \(0.512325\pi\)
\(80\) 102.814 + 114.929i 0.143687 + 0.160619i
\(81\) 0 0
\(82\) −648.187 + 119.595i −0.872931 + 0.161061i
\(83\) −174.444 302.146i −0.230695 0.399576i 0.727318 0.686301i \(-0.240767\pi\)
−0.958013 + 0.286725i \(0.907433\pi\)
\(84\) 0 0
\(85\) −43.8198 + 75.8981i −0.0559167 + 0.0968506i
\(86\) −275.962 + 777.302i −0.346020 + 0.974635i
\(87\) 0 0
\(88\) −523.653 + 958.916i −0.634336 + 1.16160i
\(89\) 416.864i 0.496488i 0.968698 + 0.248244i \(0.0798535\pi\)
−0.968698 + 0.248244i \(0.920146\pi\)
\(90\) 0 0
\(91\) 108.299i 0.124756i
\(92\) 1205.25 + 979.212i 1.36583 + 1.10967i
\(93\) 0 0
\(94\) 164.978 + 58.5712i 0.181023 + 0.0642677i
\(95\) 150.801 261.195i 0.162861 0.282084i
\(96\) 0 0
\(97\) −752.565 1303.48i −0.787747 1.36442i −0.927344 0.374209i \(-0.877914\pi\)
0.139598 0.990208i \(-0.455419\pi\)
\(98\) −172.396 934.367i −0.177701 0.963115i
\(99\) 0 0
\(100\) −890.770 + 340.289i −0.890770 + 0.340289i
\(101\) −377.088 + 217.712i −0.371502 + 0.214487i −0.674114 0.738627i \(-0.735474\pi\)
0.302613 + 0.953114i \(0.402141\pi\)
\(102\) 0 0
\(103\) −1511.52 872.679i −1.44597 0.834831i −0.447732 0.894168i \(-0.647768\pi\)
−0.998238 + 0.0593366i \(0.981101\pi\)
\(104\) −920.993 + 21.8904i −0.868373 + 0.0206397i
\(105\) 0 0
\(106\) 646.306 + 757.962i 0.592215 + 0.694526i
\(107\) 783.805 0.708161 0.354081 0.935215i \(-0.384794\pi\)
0.354081 + 0.935215i \(0.384794\pi\)
\(108\) 0 0
\(109\) 1581.89 1.39007 0.695035 0.718976i \(-0.255389\pi\)
0.695035 + 0.718976i \(0.255389\pi\)
\(110\) 213.511 + 250.397i 0.185068 + 0.217040i
\(111\) 0 0
\(112\) 166.633 34.8582i 0.140583 0.0294088i
\(113\) 384.367 + 221.914i 0.319984 + 0.184743i 0.651386 0.758747i \(-0.274188\pi\)
−0.331401 + 0.943490i \(0.607521\pi\)
\(114\) 0 0
\(115\) 405.046 233.854i 0.328442 0.189626i
\(116\) 506.331 + 1325.41i 0.405273 + 1.06088i
\(117\) 0 0
\(118\) 72.6600 + 393.808i 0.0566855 + 0.307228i
\(119\) 48.3759 + 83.7895i 0.0372657 + 0.0645460i
\(120\) 0 0
\(121\) −500.254 + 866.466i −0.375848 + 0.650989i
\(122\) 41.1286 + 14.6017i 0.0305214 + 0.0108359i
\(123\) 0 0
\(124\) 885.735 1090.20i 0.641462 0.789536i
\(125\) 588.380i 0.421010i
\(126\) 0 0
\(127\) 425.829i 0.297529i −0.988873 0.148765i \(-0.952470\pi\)
0.988873 0.148765i \(-0.0475297\pi\)
\(128\) −330.121 1410.03i −0.227960 0.973671i
\(129\) 0 0
\(130\) −92.8309 + 261.477i −0.0626293 + 0.176408i
\(131\) 871.836 1510.06i 0.581471 1.00714i −0.413835 0.910352i \(-0.635811\pi\)
0.995305 0.0967846i \(-0.0308558\pi\)
\(132\) 0 0
\(133\) −166.480 288.352i −0.108539 0.187995i
\(134\) 422.851 78.0187i 0.272603 0.0502969i
\(135\) 0 0
\(136\) 702.782 428.333i 0.443110 0.270068i
\(137\) 1274.32 735.731i 0.794692 0.458816i −0.0469195 0.998899i \(-0.514940\pi\)
0.841612 + 0.540083i \(0.181607\pi\)
\(138\) 0 0
\(139\) 1107.04 + 639.151i 0.675526 + 0.390015i 0.798167 0.602436i \(-0.205803\pi\)
−0.122641 + 0.992451i \(0.539136\pi\)
\(140\) 8.10250 50.6292i 0.00489133 0.0305639i
\(141\) 0 0
\(142\) −60.3338 + 51.4459i −0.0356556 + 0.0304031i
\(143\) −1965.90 −1.14963
\(144\) 0 0
\(145\) 427.331 0.244744
\(146\) −267.950 + 228.478i −0.151889 + 0.129514i
\(147\) 0 0
\(148\) 252.037 1574.87i 0.139982 0.874688i
\(149\) −1861.15 1074.53i −1.02330 0.590800i −0.108239 0.994125i \(-0.534521\pi\)
−0.915057 + 0.403325i \(0.867854\pi\)
\(150\) 0 0
\(151\) 828.626 478.407i 0.446574 0.257829i −0.259808 0.965660i \(-0.583659\pi\)
0.706382 + 0.707831i \(0.250326\pi\)
\(152\) −2418.54 + 1474.06i −1.29059 + 0.786592i
\(153\) 0 0
\(154\) 357.252 65.9152i 0.186936 0.0344909i
\(155\) −211.530 366.380i −0.109616 0.189860i
\(156\) 0 0
\(157\) −1046.60 + 1812.77i −0.532024 + 0.921493i 0.467277 + 0.884111i \(0.345235\pi\)
−0.999301 + 0.0373822i \(0.988098\pi\)
\(158\) 708.511 1995.66i 0.356748 1.00485i
\(159\) 0 0
\(160\) −432.197 58.6713i −0.213551 0.0289899i
\(161\) 516.337i 0.252752i
\(162\) 0 0
\(163\) 1468.60i 0.705703i 0.935679 + 0.352851i \(0.114788\pi\)
−0.935679 + 0.352851i \(0.885212\pi\)
\(164\) 1175.57 1446.94i 0.559736 0.688944i
\(165\) 0 0
\(166\) 929.936 + 330.151i 0.434801 + 0.154365i
\(167\) −1524.19 + 2639.98i −0.706261 + 1.22328i 0.259974 + 0.965616i \(0.416286\pi\)
−0.966235 + 0.257664i \(0.917047\pi\)
\(168\) 0 0
\(169\) 269.685 + 467.108i 0.122751 + 0.212612i
\(170\) −44.9766 243.768i −0.0202915 0.109977i
\(171\) 0 0
\(172\) −832.558 2179.37i −0.369081 0.966137i
\(173\) 2403.71 1387.79i 1.05636 0.609892i 0.131940 0.991258i \(-0.457879\pi\)
0.924424 + 0.381365i \(0.124546\pi\)
\(174\) 0 0
\(175\) 274.579 + 158.528i 0.118607 + 0.0684778i
\(176\) −632.765 3024.81i −0.271003 1.29547i
\(177\) 0 0
\(178\) −765.021 897.187i −0.322139 0.377792i
\(179\) 477.618 0.199435 0.0997174 0.995016i \(-0.468206\pi\)
0.0997174 + 0.995016i \(0.468206\pi\)
\(180\) 0 0
\(181\) −732.350 −0.300747 −0.150373 0.988629i \(-0.548048\pi\)
−0.150373 + 0.988629i \(0.548048\pi\)
\(182\) 198.749 + 233.085i 0.0809463 + 0.0949307i
\(183\) 0 0
\(184\) −4391.01 + 104.367i −1.75929 + 0.0418153i
\(185\) −416.006 240.181i −0.165326 0.0954512i
\(186\) 0 0
\(187\) 1520.99 878.146i 0.594792 0.343403i
\(188\) −462.559 + 176.705i −0.179445 + 0.0685509i
\(189\) 0 0
\(190\) 154.782 + 838.898i 0.0591003 + 0.320316i
\(191\) 1543.00 + 2672.55i 0.584542 + 1.01246i 0.994932 + 0.100546i \(0.0320590\pi\)
−0.410391 + 0.911910i \(0.634608\pi\)
\(192\) 0 0
\(193\) 817.160 1415.36i 0.304769 0.527876i −0.672441 0.740151i \(-0.734754\pi\)
0.977210 + 0.212275i \(0.0680873\pi\)
\(194\) 4011.82 + 1424.30i 1.48470 + 0.527106i
\(195\) 0 0
\(196\) 2085.77 + 1694.59i 0.760121 + 0.617564i
\(197\) 3350.67i 1.21181i 0.795539 + 0.605903i \(0.207188\pi\)
−0.795539 + 0.605903i \(0.792812\pi\)
\(198\) 0 0
\(199\) 1046.61i 0.372826i 0.982471 + 0.186413i \(0.0596863\pi\)
−0.982471 + 0.186413i \(0.940314\pi\)
\(200\) 1292.65 2367.11i 0.457021 0.836899i
\(201\) 0 0
\(202\) 412.040 1160.59i 0.143520 0.404252i
\(203\) 235.881 408.558i 0.0815547 0.141257i
\(204\) 0 0
\(205\) −280.748 486.270i −0.0956502 0.165671i
\(206\) 4854.68 895.718i 1.64195 0.302950i
\(207\) 0 0
\(208\) 1942.02 1737.30i 0.647378 0.579136i
\(209\) −5234.33 + 3022.04i −1.73237 + 1.00019i
\(210\) 0 0
\(211\) 4570.77 + 2638.94i 1.49130 + 0.861004i 0.999950 0.00995667i \(-0.00316936\pi\)
0.491352 + 0.870961i \(0.336503\pi\)
\(212\) −2782.00 445.220i −0.901266 0.144235i
\(213\) 0 0
\(214\) −1686.93 + 1438.43i −0.538860 + 0.459480i
\(215\) −702.658 −0.222888
\(216\) 0 0
\(217\) −467.047 −0.146107
\(218\) −3404.60 + 2903.06i −1.05774 + 0.901927i
\(219\) 0 0
\(220\) −919.050 147.081i −0.281647 0.0450737i
\(221\) 1282.49 + 740.444i 0.390359 + 0.225374i
\(222\) 0 0
\(223\) −4122.02 + 2379.85i −1.23781 + 0.714648i −0.968645 0.248447i \(-0.920080\pi\)
−0.269161 + 0.963095i \(0.586746\pi\)
\(224\) −294.661 + 380.824i −0.0878923 + 0.113593i
\(225\) 0 0
\(226\) −1234.50 + 227.773i −0.363353 + 0.0670409i
\(227\) 1115.23 + 1931.63i 0.326080 + 0.564788i 0.981730 0.190277i \(-0.0609387\pi\)
−0.655650 + 0.755065i \(0.727605\pi\)
\(228\) 0 0
\(229\) 2917.29 5052.89i 0.841833 1.45810i −0.0465095 0.998918i \(-0.514810\pi\)
0.888343 0.459181i \(-0.151857\pi\)
\(230\) −442.589 + 1246.64i −0.126885 + 0.357396i
\(231\) 0 0
\(232\) −3522.12 1923.39i −0.996718 0.544296i
\(233\) 3080.09i 0.866022i −0.901389 0.433011i \(-0.857451\pi\)
0.901389 0.433011i \(-0.142549\pi\)
\(234\) 0 0
\(235\) 149.135i 0.0413978i
\(236\) −879.091 714.221i −0.242474 0.196999i
\(237\) 0 0
\(238\) −257.885 91.5558i −0.0702362 0.0249356i
\(239\) −2645.73 + 4582.53i −0.716058 + 1.24025i 0.246492 + 0.969145i \(0.420722\pi\)
−0.962550 + 0.271104i \(0.912611\pi\)
\(240\) 0 0
\(241\) 2501.61 + 4332.91i 0.668642 + 1.15812i 0.978284 + 0.207268i \(0.0664573\pi\)
−0.309642 + 0.950853i \(0.600209\pi\)
\(242\) −513.461 2782.89i −0.136391 0.739220i
\(243\) 0 0
\(244\) −115.315 + 44.0523i −0.0302553 + 0.0115580i
\(245\) 700.961 404.700i 0.182787 0.105532i
\(246\) 0 0
\(247\) −4413.53 2548.15i −1.13695 0.656417i
\(248\) 94.4037 + 3971.84i 0.0241719 + 1.01698i
\(249\) 0 0
\(250\) −1079.78 1266.33i −0.273166 0.320359i
\(251\) 2577.68 0.648215 0.324107 0.946020i \(-0.394936\pi\)
0.324107 + 0.946020i \(0.394936\pi\)
\(252\) 0 0
\(253\) −9372.83 −2.32911
\(254\) 781.475 + 916.483i 0.193048 + 0.226399i
\(255\) 0 0
\(256\) 3298.15 + 2428.87i 0.805213 + 0.592986i
\(257\) 753.933 + 435.283i 0.182992 + 0.105651i 0.588698 0.808353i \(-0.299641\pi\)
−0.405705 + 0.914004i \(0.632974\pi\)
\(258\) 0 0
\(259\) −459.260 + 265.154i −0.110182 + 0.0636134i
\(260\) −280.065 733.121i −0.0668033 0.174870i
\(261\) 0 0
\(262\) 894.852 + 4849.99i 0.211008 + 1.14364i
\(263\) −2155.19 3732.90i −0.505304 0.875212i −0.999981 0.00613515i \(-0.998047\pi\)
0.494677 0.869077i \(1.66471\pi\)
\(264\) 0 0
\(265\) −424.278 + 734.871i −0.0983516 + 0.170350i
\(266\) 887.483 + 315.079i 0.204568 + 0.0726268i
\(267\) 0 0
\(268\) −766.896 + 943.924i −0.174797 + 0.215147i
\(269\) 5603.52i 1.27008i −0.772478 0.635042i \(-0.780983\pi\)
0.772478 0.635042i \(-0.219017\pi\)
\(270\) 0 0
\(271\) 2149.22i 0.481756i −0.970555 0.240878i \(-0.922565\pi\)
0.970555 0.240878i \(-0.0774353\pi\)
\(272\) −726.479 + 2211.60i −0.161946 + 0.493008i
\(273\) 0 0
\(274\) −1392.44 + 3922.08i −0.307008 + 0.864751i
\(275\) 2877.69 4984.31i 0.631023 1.09296i
\(276\) 0 0
\(277\) 1604.99 + 2779.93i 0.348140 + 0.602995i 0.985919 0.167224i \(-0.0534802\pi\)
−0.637779 + 0.770219i \(0.720147\pi\)
\(278\) −3555.57 + 656.025i −0.767083 + 0.141531i
\(279\) 0 0
\(280\) 75.4755 + 123.835i 0.0161090 + 0.0264306i
\(281\) 814.389 470.188i 0.172891 0.0998187i −0.411057 0.911610i \(-0.634840\pi\)
0.583948 + 0.811791i \(0.301507\pi\)
\(282\) 0 0
\(283\) 1775.44 + 1025.05i 0.372929 + 0.215310i 0.674737 0.738058i \(-0.264257\pi\)
−0.301809 + 0.953369i \(0.597590\pi\)
\(284\) 35.4395 221.447i 0.00740475 0.0462693i
\(285\) 0 0
\(286\) 4231.08 3607.80i 0.874787 0.745921i
\(287\) −619.877 −0.127492
\(288\) 0 0
\(289\) 3590.01 0.730716
\(290\) −919.715 + 784.230i −0.186233 + 0.158799i
\(291\) 0 0
\(292\) 157.392 983.476i 0.0315433 0.197101i
\(293\) 3842.30 + 2218.35i 0.766108 + 0.442312i 0.831484 0.555548i \(-0.187492\pi\)
−0.0653767 + 0.997861i \(0.520825\pi\)
\(294\) 0 0
\(295\) −295.434 + 170.569i −0.0583080 + 0.0336641i
\(296\) 2347.74 + 3852.03i 0.461013 + 0.756400i
\(297\) 0 0
\(298\) 5977.58 1102.90i 1.16199 0.214394i
\(299\) −3951.54 6844.26i −0.764292 1.32379i
\(300\) 0 0
\(301\) −387.858 + 671.790i −0.0742716 + 0.128642i
\(302\) −905.429 + 2550.32i −0.172522 + 0.485943i
\(303\) 0 0
\(304\) 2500.09 7610.98i 0.471678 1.43592i
\(305\) 37.1790i 0.00697988i
\(306\) 0 0
\(307\) 7392.80i 1.37436i −0.726486 0.687181i \(-0.758848\pi\)
0.726486 0.687181i \(-0.241152\pi\)
\(308\) −647.923 + 797.489i −0.119866 + 0.147536i
\(309\) 0 0
\(310\) 1127.64 + 400.339i 0.206598 + 0.0733475i
\(311\) 2448.25 4240.50i 0.446391 0.773172i −0.551757 0.834005i \(-0.686042\pi\)
0.998148 + 0.0608332i \(0.0193758\pi\)
\(312\) 0 0
\(313\) −340.861 590.388i −0.0615546 0.106616i 0.833606 0.552360i \(-0.186273\pi\)
−0.895160 + 0.445744i \(0.852939\pi\)
\(314\) −1074.23 5822.20i −0.193065 1.04639i
\(315\) 0 0
\(316\) 2137.53 + 5595.38i 0.380524 + 0.996091i
\(317\) −1344.13 + 776.034i −0.238151 + 0.137497i −0.614327 0.789052i \(-0.710572\pi\)
0.376176 + 0.926548i \(0.377239\pi\)
\(318\) 0 0
\(319\) −7416.37 4281.84i −1.30168 0.751527i
\(320\) 1037.86 666.886i 0.181307 0.116500i
\(321\) 0 0
\(322\) 947.573 + 1111.28i 0.163994 + 0.192326i
\(323\) 4552.92 0.784307
\(324\) 0 0
\(325\) 4852.88 0.828276
\(326\) −2695.15 3160.76i −0.457885 0.536990i
\(327\) 0 0
\(328\) 125.295 + 5271.53i 0.0210923 + 0.887414i
\(329\) 142.583 + 82.3206i 0.0238932 + 0.0137948i
\(330\) 0 0
\(331\) 6410.22 3700.94i 1.06446 0.614569i 0.137801 0.990460i \(-0.455997\pi\)
0.926664 + 0.375891i \(0.122663\pi\)
\(332\) −2607.33 + 996.043i −0.431011 + 0.164653i
\(333\) 0 0
\(334\) −1564.43 8479.02i −0.256293 1.38908i
\(335\) 183.149 + 317.223i 0.0298701 + 0.0517365i
\(336\) 0 0
\(337\) 4871.58 8437.83i 0.787454 1.36391i −0.140068 0.990142i \(-0.544732\pi\)
0.927522 0.373769i \(-0.121935\pi\)
\(338\) −1437.65 510.403i −0.231355 0.0821368i
\(339\) 0 0
\(340\) 544.158 + 442.104i 0.0867975 + 0.0705190i
\(341\) 8478.09i 1.34638i
\(342\) 0 0
\(343\) 1805.94i 0.284290i
\(344\) 5791.41 + 3162.62i 0.907709 + 0.495689i
\(345\) 0 0
\(346\) −2626.51 + 7398.09i −0.408098 + 1.14949i
\(347\) 3523.75 6103.31i 0.545143 0.944216i −0.453455 0.891279i \(-0.649809\pi\)
0.998598 0.0529363i \(-0.0168580\pi\)
\(348\) 0 0
\(349\) 603.773 + 1045.77i 0.0926052 + 0.160397i 0.908607 0.417653i \(-0.137147\pi\)
−0.816001 + 0.578050i \(0.803814\pi\)
\(350\) −881.886 + 162.713i −0.134682 + 0.0248497i
\(351\) 0 0
\(352\) 6912.94 + 5348.85i 1.04676 + 0.809928i
\(353\) −1316.47 + 760.063i −0.198494 + 0.114601i −0.595953 0.803019i \(-0.703226\pi\)
0.397459 + 0.917620i \(0.369892\pi\)
\(354\) 0 0
\(355\) −58.4957 33.7725i −0.00874544 0.00504918i
\(356\) 3293.01 + 527.000i 0.490250 + 0.0784576i
\(357\) 0 0
\(358\) −1027.94 + 876.517i −0.151756 + 0.129400i
\(359\) −6515.20 −0.957825 −0.478912 0.877863i \(-0.658969\pi\)
−0.478912 + 0.877863i \(0.658969\pi\)
\(360\) 0 0
\(361\) −8809.35 −1.28435
\(362\) 1576.19 1344.00i 0.228847 0.195135i
\(363\) 0 0
\(364\) −855.506 136.912i −0.123189 0.0197146i
\(365\) −259.787 149.988i −0.0372545 0.0215089i
\(366\) 0 0
\(367\) −3492.35 + 2016.31i −0.496729 + 0.286786i −0.727362 0.686254i \(-0.759254\pi\)
0.230633 + 0.973041i \(0.425920\pi\)
\(368\) 9258.94 8282.93i 1.31156 1.17331i
\(369\) 0 0
\(370\) 1336.12 246.522i 0.187734 0.0346380i
\(371\) 468.392 + 811.278i 0.0655463 + 0.113530i
\(372\) 0 0
\(373\) −1227.68 + 2126.40i −0.170420 + 0.295176i −0.938567 0.345098i \(-0.887846\pi\)
0.768147 + 0.640274i \(0.221179\pi\)
\(374\) −1661.97 + 4681.28i −0.229782 + 0.647228i
\(375\) 0 0
\(376\) 671.247 1229.19i 0.0920663 0.168592i
\(377\) 7220.81i 0.986448i
\(378\) 0 0
\(379\) 9518.27i 1.29003i 0.764171 + 0.645014i \(0.223149\pi\)
−0.764171 + 0.645014i \(0.776851\pi\)
\(380\) −1872.66 1521.45i −0.252804 0.205391i
\(381\) 0 0
\(382\) −8225.52 2920.27i −1.10171 0.391136i
\(383\) −4727.72 + 8188.65i −0.630744 + 1.09248i 0.356655 + 0.934236i \(0.383917\pi\)
−0.987400 + 0.158245i \(0.949416\pi\)
\(384\) 0 0
\(385\) 154.736 + 268.011i 0.0204833 + 0.0354781i
\(386\) 838.733 + 4545.83i 0.110597 + 0.599421i
\(387\) 0 0
\(388\) −11248.2 + 4297.01i −1.47176 + 0.562236i
\(389\) 2568.69 1483.04i 0.334802 0.193298i −0.323169 0.946341i \(-0.604748\pi\)
0.657971 + 0.753043i \(0.271415\pi\)
\(390\) 0 0
\(391\) 6114.50 + 3530.21i 0.790854 + 0.456600i
\(392\) −7598.96 + 180.614i −0.979095 + 0.0232714i
\(393\) 0 0
\(394\) −6149.10 7211.43i −0.786262 0.922097i
\(395\) 1804.02 0.229798
\(396\) 0 0
\(397\) 1296.85 0.163947 0.0819733 0.996635i \(-0.473878\pi\)
0.0819733 + 0.996635i \(0.473878\pi\)
\(398\) −1920.73 2252.55i −0.241903 0.283694i
\(399\) 0 0
\(400\) 1562.00 + 7466.82i 0.195250 + 0.933352i
\(401\) 1782.15 + 1028.93i 0.221936 + 0.128135i 0.606847 0.794819i \(-0.292434\pi\)
−0.384910 + 0.922954i \(0.625768\pi\)
\(402\) 0 0
\(403\) −6190.90 + 3574.32i −0.765238 + 0.441810i
\(404\) 1243.10 + 3254.03i 0.153085 + 0.400728i
\(405\) 0 0
\(406\) 242.108 + 1312.20i 0.0295951 + 0.160402i
\(407\) 4813.22 + 8336.74i 0.586198 + 1.01532i
\(408\) 0 0
\(409\) −2897.54 + 5018.69i −0.350304 + 0.606744i −0.986303 0.164946i \(-0.947255\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(410\) 1496.63 + 531.341i 0.180276 + 0.0640026i
\(411\) 0 0
\(412\) −8804.58 + 10837.0i −1.05284 + 1.29588i
\(413\) 376.608i 0.0448709i
\(414\) 0 0
\(415\) 840.635i 0.0994341i
\(416\) −991.398 + 7303.04i −0.116844 + 0.860723i
\(417\) 0 0
\(418\) 5719.48 16110.1i 0.669256 1.88509i
\(419\) −7052.61 + 12215.5i −0.822298 + 1.42426i 0.0816695 + 0.996659i \(0.473975\pi\)
−0.903967 + 0.427602i \(0.859359\pi\)
\(420\) 0 0
\(421\) −3210.43 5560.63i −0.371655 0.643726i 0.618165 0.786048i \(-0.287876\pi\)
−0.989820 + 0.142323i \(0.954543\pi\)
\(422\) −14680.3 + 2708.60i −1.69343 + 0.312447i
\(423\) 0 0
\(424\) 6804.57 4147.26i 0.779384 0.475021i
\(425\) −3754.61 + 2167.73i −0.428530 + 0.247412i
\(426\) 0 0
\(427\) 35.5457 + 20.5223i 0.00402852 + 0.00232587i
\(428\) 990.887 6191.65i 0.111907 0.699263i
\(429\) 0 0
\(430\) 1512.28 1289.51i 0.169602 0.144617i
\(431\) 1119.73 0.125140 0.0625700 0.998041i \(-0.480070\pi\)
0.0625700 + 0.998041i \(0.480070\pi\)
\(432\) 0 0
\(433\) −299.833 −0.0332773 −0.0166387 0.999862i \(-0.505296\pi\)
−0.0166387 + 0.999862i \(0.505296\pi\)
\(434\) 1005.19 857.116i 0.111177 0.0947993i
\(435\) 0 0
\(436\) 1999.83 12496.1i 0.219666 1.37260i
\(437\) −21042.4 12148.8i −2.30342 1.32988i
\(438\) 0 0
\(439\) −2090.02 + 1206.67i −0.227224 + 0.131188i −0.609291 0.792947i \(-0.708546\pi\)
0.382067 + 0.924135i \(0.375212\pi\)
\(440\) 2247.93 1370.07i 0.243559 0.148445i
\(441\) 0 0
\(442\) −4119.06 + 759.992i −0.443266 + 0.0817853i
\(443\) 2409.36 + 4173.14i 0.258402 + 0.447566i 0.965814 0.259236i \(-0.0834706\pi\)
−0.707412 + 0.706802i \(0.750137\pi\)
\(444\) 0 0
\(445\) 502.211 869.854i 0.0534990 0.0926630i
\(446\) 4504.08 12686.7i 0.478194 1.34693i
\(447\) 0 0
\(448\) −64.7043 1360.38i −0.00682364 0.143464i
\(449\) 8677.13i 0.912024i 0.889974 + 0.456012i \(0.150723\pi\)
−0.889974 + 0.456012i \(0.849277\pi\)
\(450\) 0 0
\(451\) 11252.3i 1.17484i
\(452\) 2238.93 2755.76i 0.232987 0.286770i
\(453\) 0 0
\(454\) −5945.12 2110.67i −0.614578 0.218191i
\(455\) −130.472 + 225.984i −0.0134431 + 0.0232841i
\(456\) 0 0
\(457\) 3460.04 + 5992.97i 0.354166 + 0.613434i 0.986975 0.160874i \(-0.0514313\pi\)
−0.632809 + 0.774308i \(0.718098\pi\)
\(458\) 2994.30 + 16228.8i 0.305491 + 1.65572i
\(459\) 0 0
\(460\) −1335.26 3495.29i −0.135341 0.354280i
\(461\) 13470.8 7777.39i 1.36095 0.785747i 0.371203 0.928552i \(-0.378945\pi\)
0.989751 + 0.142805i \(0.0456121\pi\)
\(462\) 0 0
\(463\) 9994.39 + 5770.27i 1.00319 + 0.579194i 0.909192 0.416378i \(-0.136701\pi\)
0.0940023 + 0.995572i \(0.470034\pi\)
\(464\) 11110.2 2324.16i 1.11159 0.232535i
\(465\) 0 0
\(466\) 5652.53 + 6629.06i 0.561906 + 0.658981i
\(467\) 7.01271 0.000694881 0.000347441 1.00000i \(-0.499889\pi\)
0.000347441 1.00000i \(0.499889\pi\)
\(468\) 0 0
\(469\) 404.383 0.0398138
\(470\) −273.690 320.973i −0.0268604 0.0315008i
\(471\) 0 0
\(472\) 3202.73 76.1234i 0.312326 0.00742344i
\(473\) 12194.7 + 7040.61i 1.18544 + 0.684414i
\(474\) 0 0
\(475\) 12921.1 7459.98i 1.24812 0.720605i
\(476\) 723.051 276.218i 0.0696239 0.0265975i
\(477\) 0 0
\(478\) −2715.57 14718.1i −0.259848 1.40834i
\(479\) 2830.70 + 4902.92i 0.270017 + 0.467683i 0.968866 0.247586i \(-0.0796373\pi\)
−0.698849 + 0.715269i \(0.746304\pi\)
\(480\) 0 0
\(481\) −4058.46 + 7029.46i −0.384719 + 0.666353i
\(482\) −13335.7 4734.52i −1.26022 0.447409i
\(483\) 0 0
\(484\) 6212.21 + 5047.14i 0.583415 + 0.473999i
\(485\) 3626.57i 0.339534i
\(486\) 0 0
\(487\) 9082.26i 0.845085i −0.906343 0.422542i \(-0.861138\pi\)
0.906343 0.422542i \(-0.138862\pi\)
\(488\) 167.340 306.435i 0.0155228 0.0284255i
\(489\) 0 0
\(490\) −765.932 + 2157.40i −0.0706149 + 0.198901i
\(491\) 5098.79 8831.36i 0.468646 0.811718i −0.530712 0.847552i \(-0.678075\pi\)
0.999358 + 0.0358342i \(0.0114088\pi\)
\(492\) 0 0
\(493\) 3225.45 + 5586.65i 0.294659 + 0.510365i
\(494\) 14175.3 2615.42i 1.29104 0.238205i
\(495\) 0 0
\(496\) −7492.24 8375.07i −0.678249 0.758169i
\(497\) −64.5778 + 37.2840i −0.00582839 + 0.00336502i
\(498\) 0 0
\(499\) 2353.15 + 1358.59i 0.211105 + 0.121881i 0.601825 0.798628i \(-0.294441\pi\)
−0.390720 + 0.920510i \(0.627774\pi\)
\(500\) 4647.89 + 743.831i 0.415720 + 0.0665302i
\(501\) 0 0
\(502\) −5547.77 + 4730.52i −0.493245 + 0.420585i
\(503\) −8294.45 −0.735251 −0.367626 0.929974i \(-0.619829\pi\)
−0.367626 + 0.929974i \(0.619829\pi\)
\(504\) 0 0
\(505\) 1049.14 0.0924479
\(506\) 20172.5 17200.9i 1.77229 1.51121i
\(507\) 0 0
\(508\) −3363.83 538.334i −0.293791 0.0470171i
\(509\) −2866.64 1655.05i −0.249629 0.144124i 0.369965 0.929046i \(-0.379370\pi\)
−0.619595 + 0.784922i \(0.712703\pi\)
\(510\) 0 0
\(511\) −286.798 + 165.583i −0.0248282 + 0.0143346i
\(512\) −11555.8 + 825.228i −0.997460 + 0.0712310i
\(513\) 0 0
\(514\) −2421.46 + 446.775i −0.207794 + 0.0383393i
\(515\) 2102.70 + 3641.98i 0.179914 + 0.311621i
\(516\) 0 0
\(517\) 1494.33 2588.25i 0.127119 0.220176i
\(518\) 501.828 1413.50i 0.0425657 0.119895i
\(519\) 0 0
\(520\) 1948.17 + 1063.88i 0.164294 + 0.0897193i
\(521\) 5030.71i 0.423031i −0.977375 0.211516i \(-0.932160\pi\)
0.977375 0.211516i \(-0.0678400\pi\)
\(522\) 0 0
\(523\) 9680.16i 0.809338i −0.914463 0.404669i \(-0.867387\pi\)
0.914463 0.404669i \(-0.132613\pi\)
\(524\) −10826.5 8796.08i −0.902595 0.733317i
\(525\) 0 0
\(526\) 11489.0 + 4078.90i 0.952369 + 0.338115i
\(527\) 3193.21 5530.81i 0.263944 0.457164i
\(528\) 0 0
\(529\) −12756.2 22094.4i −1.04843 1.81593i
\(530\) −435.479 2360.24i −0.0356905 0.193438i
\(531\) 0 0
\(532\) −2488.30 + 950.571i −0.202784 + 0.0774671i
\(533\) −8216.73 + 4743.93i −0.667742 + 0.385521i
\(534\) 0 0
\(535\) −1635.54 944.278i −0.132169 0.0763078i
\(536\) −81.7376 3438.94i −0.00658680 0.277126i
\(537\) 0 0
\(538\) 10283.5 + 12060.1i 0.824076 + 0.966443i
\(539\) −16220.3 −1.29621
\(540\) 0 0
\(541\) 18659.8 1.48290 0.741449 0.671009i \(-0.234139\pi\)
0.741449 + 0.671009i \(0.234139\pi\)
\(542\) 3944.21 + 4625.62i 0.312580 + 0.366582i
\(543\) 0 0
\(544\) −2495.15 6093.11i −0.196652 0.480220i
\(545\) −3300.88 1905.76i −0.259438 0.149787i
\(546\) 0 0
\(547\) −3928.78 + 2268.28i −0.307098 + 0.177303i −0.645627 0.763653i \(-0.723404\pi\)
0.338529 + 0.940956i \(0.390071\pi\)
\(548\) −4200.89 10996.6i −0.327469 0.857212i
\(549\) 0 0
\(550\) 2953.66 + 16008.5i 0.228990 + 1.24110i
\(551\) −11100.0 19225.8i −0.858216 1.48647i
\(552\) 0 0
\(553\) 995.797 1724.77i 0.0765743 0.132631i
\(554\) −8556.00 3037.59i −0.656154 0.232951i
\(555\) 0 0
\(556\) 6448.49 7937.04i 0.491865 0.605406i
\(557\) 17657.1i 1.34319i 0.740918 + 0.671596i \(0.234391\pi\)
−0.740918 + 0.671596i \(0.765609\pi\)
\(558\) 0 0
\(559\) 11873.1i 0.898355i
\(560\) −389.701 128.011i −0.0294069 0.00965974i
\(561\) 0 0
\(562\) −889.873 + 2506.51i −0.0667919 + 0.188133i
\(563\) −4972.47 + 8612.57i −0.372229 + 0.644719i −0.989908 0.141711i \(-0.954740\pi\)
0.617679 + 0.786430i \(0.288073\pi\)
\(564\) 0 0
\(565\) −534.697 926.122i −0.0398139 0.0689597i
\(566\) −5702.30 + 1052.11i −0.423473 + 0.0781334i
\(567\) 0 0
\(568\) 330.122 + 541.643i 0.0243866 + 0.0400121i
\(569\) 4084.02 2357.91i 0.300898 0.173724i −0.341948 0.939719i \(-0.611087\pi\)
0.642846 + 0.765995i \(0.277753\pi\)
\(570\) 0 0
\(571\) −7993.20 4614.88i −0.585823 0.338225i 0.177621 0.984099i \(-0.443160\pi\)
−0.763444 + 0.645874i \(0.776493\pi\)
\(572\) −2485.30 + 15529.6i −0.181671 + 1.13519i
\(573\) 0 0
\(574\) 1334.12 1137.59i 0.0970123 0.0827213i
\(575\) 23137.1 1.67806
\(576\) 0 0
\(577\) 4076.34 0.294108 0.147054 0.989128i \(-0.453021\pi\)
0.147054 + 0.989128i \(0.453021\pi\)
\(578\) −7726.53 + 6588.33i −0.556023 + 0.474115i
\(579\) 0 0
\(580\) 540.232 3375.69i 0.0386757 0.241669i
\(581\) 803.706 + 464.020i 0.0573896 + 0.0331339i
\(582\) 0 0
\(583\) 14726.8 8502.51i 1.04618 0.604010i
\(584\) 1466.12 + 2405.51i 0.103884 + 0.170447i
\(585\) 0 0
\(586\) −12340.6 + 2276.92i −0.869941 + 0.160509i
\(587\) −4317.74 7478.55i −0.303599 0.525848i 0.673350 0.739324i \(-0.264855\pi\)
−0.976948 + 0.213476i \(0.931522\pi\)
\(588\) 0 0
\(589\) −10989.1 + 19033.6i −0.768755 + 1.33152i
\(590\) 322.818 909.281i 0.0225258 0.0634483i
\(591\) 0 0
\(592\) −12122.1 3981.92i −0.841577 0.276446i
\(593\) 24260.9i 1.68006i −0.542537 0.840032i \(-0.682536\pi\)
0.542537 0.840032i \(-0.317464\pi\)
\(594\) 0 0
\(595\) 233.121i 0.0160622i
\(596\) −10841.1 + 13343.7i −0.745083 + 0.917076i
\(597\) 0 0
\(598\) 21065.1 + 7478.64i 1.44050 + 0.511412i
\(599\) 7549.02 13075.3i 0.514932 0.891889i −0.484917 0.874560i \(-0.661150\pi\)
0.999850 0.0173291i \(-0.00551631\pi\)
\(600\) 0 0
\(601\) −2964.13 5134.03i −0.201180 0.348455i 0.747729 0.664004i \(-0.231144\pi\)
−0.948909 + 0.315550i \(0.897811\pi\)
\(602\) −398.097 2157.64i −0.0269522 0.146078i
\(603\) 0 0
\(604\) −2731.62 7150.52i −0.184020 0.481706i
\(605\) 2087.73 1205.35i 0.140294 0.0809990i
\(606\) 0 0
\(607\) −16115.3 9304.20i −1.07760 0.622151i −0.147350 0.989084i \(-0.547074\pi\)
−0.930247 + 0.366933i \(0.880408\pi\)
\(608\) 8586.77 + 20968.7i 0.572762 + 1.39867i
\(609\) 0 0
\(610\) −68.2303 80.0179i −0.00452880 0.00531119i
\(611\) 2520.01 0.166855
\(612\) 0 0
\(613\) 7939.25 0.523105 0.261552 0.965189i \(-0.415766\pi\)
0.261552 + 0.965189i \(0.415766\pi\)
\(614\) 13567.1 + 15911.0i 0.891735 + 1.04579i
\(615\) 0 0
\(616\) −69.0572 2905.44i −0.00451687 0.190038i
\(617\) 25269.7 + 14589.5i 1.64882 + 0.951946i 0.977542 + 0.210740i \(0.0675873\pi\)
0.671277 + 0.741206i \(0.265746\pi\)
\(618\) 0 0
\(619\) −14117.6 + 8150.83i −0.916698 + 0.529256i −0.882580 0.470162i \(-0.844196\pi\)
−0.0341179 + 0.999418i \(0.510862\pi\)
\(620\) −3161.63 + 1207.80i −0.204797 + 0.0782359i
\(621\) 0 0
\(622\) 2512.88 + 13619.5i 0.161990 + 0.877963i
\(623\) −554.427 960.297i −0.0356544 0.0617552i
\(624\) 0 0
\(625\) −6740.81 + 11675.4i −0.431412 + 0.747227i
\(626\) 1817.08 + 645.110i 0.116015 + 0.0411882i
\(627\) 0 0
\(628\) 12996.8 + 10559.3i 0.825842 + 0.670959i
\(629\) 7251.46i 0.459674i
\(630\) 0 0
\(631\) 2517.83i 0.158848i 0.996841 + 0.0794242i \(0.0253082\pi\)
−0.996841 + 0.0794242i \(0.974692\pi\)
\(632\) −14869.0 8119.79i −0.935850 0.511057i
\(633\) 0 0
\(634\) 1468.72 4136.93i 0.0920034 0.259146i
\(635\) −513.012 + 888.562i −0.0320602 + 0.0555300i
\(636\) 0 0
\(637\) −6838.42 11844.5i −0.425350 0.736728i
\(638\) 23819.7 4394.88i 1.47811 0.272720i
\(639\) 0 0
\(640\) −1009.86 + 3339.96i −0.0623720 + 0.206287i
\(641\) −14572.0 + 8413.13i −0.897907 + 0.518407i −0.876520 0.481365i \(-0.840141\pi\)
−0.0213863 + 0.999771i \(0.506808\pi\)
\(642\) 0 0
\(643\) −17687.6 10211.9i −1.08481 0.626313i −0.152617 0.988285i \(-0.548770\pi\)
−0.932189 + 0.361973i \(0.882103\pi\)
\(644\) −4078.79 652.754i −0.249576 0.0399412i
\(645\) 0 0
\(646\) −9798.94 + 8355.44i −0.596802 + 0.508886i
\(647\) 21477.2 1.30503 0.652515 0.757776i \(-0.273714\pi\)
0.652515 + 0.757776i \(0.273714\pi\)
\(648\) 0 0
\(649\) 6836.40 0.413485
\(650\) −10444.5 + 8905.93i −0.630259 + 0.537415i
\(651\) 0 0
\(652\) 11601.2 + 1856.61i 0.696836 + 0.111519i
\(653\) −21836.5 12607.3i −1.30862 0.755533i −0.326756 0.945109i \(-0.605955\pi\)
−0.981866 + 0.189576i \(0.939289\pi\)
\(654\) 0 0
\(655\) −3638.46 + 2100.66i −0.217048 + 0.125313i
\(656\) −9943.90 11115.6i −0.591835 0.661573i
\(657\) 0 0
\(658\) −457.946 + 84.4938i −0.0271316 + 0.00500595i
\(659\) 6865.03 + 11890.6i 0.405802 + 0.702870i 0.994415 0.105545i \(-0.0336588\pi\)
−0.588612 + 0.808416i \(0.700325\pi\)
\(660\) 0 0
\(661\) −772.039 + 1337.21i −0.0454294 + 0.0786860i −0.887846 0.460141i \(-0.847799\pi\)
0.842417 + 0.538827i \(0.181132\pi\)
\(662\) −7004.37 + 19729.2i −0.411228 + 1.15831i
\(663\) 0 0
\(664\) 3783.65 6928.64i 0.221135 0.404945i
\(665\) 802.258i 0.0467823i
\(666\) 0 0
\(667\) 34426.6i 1.99851i
\(668\) 18927.6 + 15377.8i 1.09630 + 0.890696i
\(669\) 0 0
\(670\) −976.341 346.626i −0.0562975 0.0199870i
\(671\) 372.533 645.246i 0.0214329 0.0371229i
\(672\) 0 0
\(673\) 2684.11 + 4649.02i 0.153737 + 0.266280i 0.932598 0.360916i \(-0.117536\pi\)
−0.778861 + 0.627196i \(0.784202\pi\)
\(674\) 5000.19 + 27100.4i 0.285757 + 1.54877i
\(675\) 0 0
\(676\) 4030.84 1539.85i 0.229338 0.0876110i
\(677\) 16713.8 9649.71i 0.948838 0.547812i 0.0561181 0.998424i \(-0.482128\pi\)
0.892720 + 0.450612i \(0.148794\pi\)
\(678\) 0 0
\(679\) 3467.25 + 2001.82i 0.195966 + 0.113141i
\(680\) −1982.50 + 47.1205i −0.111802 + 0.00265734i
\(681\) 0 0
\(682\) −15558.9 18246.8i −0.873576 1.02450i
\(683\) −7466.11 −0.418276 −0.209138 0.977886i \(-0.567066\pi\)
−0.209138 + 0.977886i \(0.567066\pi\)
\(684\) 0 0
\(685\) −3545.45 −0.197759
\(686\) 3314.22 + 3886.79i 0.184457 + 0.216324i
\(687\) 0 0
\(688\) −18268.4 + 3821.61i −1.01232 + 0.211769i
\(689\) 12417.5 + 7169.23i 0.686600 + 0.396409i
\(690\) 0 0
\(691\) −20587.2 + 11886.0i −1.13339 + 0.654364i −0.944786 0.327689i \(-0.893730\pi\)
−0.188606 + 0.982053i \(0.560397\pi\)
\(692\) −7924.00 20742.5i −0.435297 1.13947i
\(693\) 0 0
\(694\) 3616.77 + 19602.5i 0.197825 + 1.07219i
\(695\) −1540.02 2667.39i −0.0840520 0.145582i
\(696\) 0 0
\(697\) 4238.12 7340.64i 0.230316 0.398919i
\(698\) −3218.63 1142.70i −0.174537 0.0619651i
\(699\) 0 0
\(700\) 1599.41 1968.62i 0.0863603 0.106296i
\(701\) 3501.89i 0.188680i 0.995540 + 0.0943399i \(0.0300740\pi\)
−0.995540 + 0.0943399i \(0.969926\pi\)
\(702\) 0 0
\(703\) 24955.1i 1.33883i
\(704\) −24694.4 + 1174.55i −1.32202 + 0.0628799i
\(705\) 0 0
\(706\) 1438.49 4051.79i 0.0766830 0.215993i
\(707\) 579.113 1003.05i 0.0308059 0.0533574i
\(708\) 0 0
\(709\) −2079.38 3601.59i −0.110145 0.190777i 0.805684 0.592346i \(-0.201798\pi\)
−0.915829 + 0.401569i \(0.868465\pi\)
\(710\) 187.875 34.6641i 0.00993074 0.00183228i
\(711\) 0 0
\(712\) −8054.45 + 4909.04i −0.423951 + 0.258391i
\(713\) −29516.3 + 17041.3i −1.55034 + 0.895091i
\(714\) 0 0
\(715\) 4102.18 + 2368.40i 0.214564 + 0.123878i
\(716\) 603.805 3772.93i 0.0315157 0.196929i
\(717\) 0 0
\(718\) 14022.2 11956.6i 0.728836 0.621470i
\(719\) −20077.1 −1.04137 −0.520687 0.853748i \(-0.674324\pi\)
−0.520687 + 0.853748i \(0.674324\pi\)
\(720\) 0 0
\(721\) 4642.64 0.239807
\(722\) 18959.8 16166.8i 0.977298 0.833331i
\(723\) 0 0
\(724\) −925.838 + 5785.19i −0.0475256 + 0.296968i
\(725\) 18307.5 + 10569.8i 0.937825 + 0.541454i
\(726\) 0 0
\(727\) 31220.9 18025.4i 1.59274 0.919566i 0.599900 0.800075i \(-0.295207\pi\)
0.992835 0.119491i \(-0.0381263\pi\)
\(728\) 2092.51 1275.35i 0.106529 0.0649278i
\(729\) 0 0
\(730\) 834.378 153.948i 0.0423037 0.00780530i
\(731\) −5303.59 9186.10i −0.268345 0.464788i
\(732\) 0 0
\(733\) 10850.9 18794.4i 0.546779 0.947049i −0.451714 0.892163i \(-0.649187\pi\)
0.998493 0.0548859i \(-0.0174795\pi\)
\(734\) 3816.05 10748.7i 0.191898 0.540519i
\(735\) 0 0
\(736\) −4726.68 + 34818.7i −0.236723 + 1.74379i
\(737\) 7340.58i 0.366884i
\(738\) 0 0
\(739\) 26112.0i 1.29979i 0.760024 + 0.649895i \(0.225187\pi\)
−0.760024 + 0.649895i \(0.774813\pi\)
\(740\) −2423.22 + 2982.60i −0.120378 + 0.148165i
\(741\) 0 0
\(742\) −2496.93 886.474i −0.123538 0.0438591i
\(743\) 2806.43 4860.88i 0.138570 0.240011i −0.788385 0.615182i \(-0.789083\pi\)
0.926956 + 0.375171i \(0.122416\pi\)
\(744\) 0 0
\(745\) 2589.06 + 4484.38i 0.127323 + 0.220530i
\(746\) −1260.09 6829.51i −0.0618432 0.335182i
\(747\) 0 0
\(748\) −5014.06 13125.2i −0.245096 0.641585i
\(749\) −1805.59 + 1042.46i −0.0880839 + 0.0508553i
\(750\) 0 0
\(751\) 24027.9 + 13872.5i 1.16750 + 0.674056i 0.953090 0.302688i \(-0.0978841\pi\)
0.214409 + 0.976744i \(0.431217\pi\)
\(752\) 811.113 + 3877.37i 0.0393328 + 0.188023i
\(753\) 0 0
\(754\) 13251.5 + 15540.9i 0.640042 + 0.750616i
\(755\) −2305.42 −0.111129
\(756\) 0 0
\(757\) −22792.6 −1.09433 −0.547167 0.837023i \(-0.684294\pi\)
−0.547167 + 0.837023i \(0.684294\pi\)
\(758\) −17467.8 20485.5i −0.837016 0.981620i
\(759\) 0 0
\(760\) 6822.54 162.160i 0.325631 0.00773968i
\(761\) −27979.1 16153.7i −1.33277 0.769477i −0.347049 0.937847i \(-0.612816\pi\)
−0.985724 + 0.168370i \(0.946150\pi\)
\(762\) 0 0
\(763\) −3644.08 + 2103.91i −0.172902 + 0.0998253i
\(764\) 23062.4 8810.24i 1.09211 0.417203i
\(765\) 0 0
\(766\) −4852.53 26300.1i −0.228889 1.24055i
\(767\) 2882.19 + 4992.10i 0.135684 + 0.235012i
\(768\) 0 0
\(769\) 1200.97 2080.14i 0.0563174 0.0975446i −0.836492 0.547979i \(-0.815397\pi\)
0.892810 + 0.450434i \(0.148731\pi\)
\(770\) −824.876 292.852i −0.0386058 0.0137060i
\(771\) 0 0
\(772\) −10147.6 8244.44i −0.473082 0.384358i
\(773\) 21135.4i 0.983424i 0.870758 + 0.491712i \(0.163629\pi\)
−0.870758 + 0.491712i \(0.836371\pi\)
\(774\) 0 0
\(775\) 20928.4i 0.970025i
\(776\) 16323.0 29890.7i 0.755103 1.38275i
\(777\) 0 0
\(778\) −2806.78 + 7905.87i −0.129342 + 0.364318i
\(779\) −14585.0 + 25262.0i −0.670811 + 1.16188i
\(780\) 0 0