Properties

Label 108.4.h.b.71.2
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 71.2
Character \(\chi\) \(=\) 108.71
Dual form 108.4.h.b.35.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.66543 + 0.946295i) q^{2} +(6.20905 - 5.04457i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +O(q^{10})\) \(q+(-2.66543 + 0.946295i) q^{2} +(6.20905 - 5.04457i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +(6.70190 + 1.23654i) q^{10} +(-24.1428 - 41.8166i) q^{11} +(-20.3570 + 35.2594i) q^{13} +(-4.88158 + 5.72493i) q^{14} +(13.1046 - 62.6440i) q^{16} -36.3729i q^{17} -125.173i q^{19} +(-19.0336 + 3.04606i) q^{20} +(103.922 + 88.6131i) q^{22} +(97.0560 - 168.106i) q^{23} +(-59.5972 - 103.225i) q^{25} +(20.8944 - 113.245i) q^{26} +(7.59405 - 19.8788i) q^{28} +(-153.593 + 88.6772i) q^{29} +(-152.058 - 87.7909i) q^{31} +(24.3503 + 179.374i) q^{32} +(34.4195 + 96.9496i) q^{34} -6.40918 q^{35} +199.364 q^{37} +(118.451 + 333.641i) q^{38} +(47.8502 - 26.1304i) q^{40} +(201.816 + 116.518i) q^{41} +(-252.553 + 145.812i) q^{43} +(-360.851 - 137.851i) q^{44} +(-99.6182 + 539.918i) q^{46} +(30.9476 + 53.6029i) q^{47} +(-167.962 + 290.919i) q^{49} +(256.534 + 218.744i) q^{50} +(51.4707 + 321.620i) q^{52} -352.175i q^{53} +116.343i q^{55} +(-1.43018 + 60.1718i) q^{56} +(325.478 - 381.708i) q^{58} +(-70.7911 + 122.614i) q^{59} +(-7.71518 - 13.3631i) q^{61} +(488.377 + 90.1086i) q^{62} +(-234.645 - 455.067i) q^{64} +(84.9565 - 49.0496i) q^{65} +(131.657 + 76.0120i) q^{67} +(-183.486 - 225.841i) q^{68} +(17.0832 - 6.06498i) q^{70} -28.0331 q^{71} +124.499 q^{73} +(-531.392 + 188.657i) q^{74} +(-631.445 - 777.207i) q^{76} +(-111.232 - 64.2199i) q^{77} +(648.411 - 374.360i) q^{79} +(-102.814 + 114.929i) q^{80} +(-648.187 - 119.595i) q^{82} +(174.444 + 302.146i) q^{83} +(-43.8198 + 75.8981i) q^{85} +(535.182 - 627.641i) q^{86} +(1092.27 + 25.9614i) q^{88} +416.864i q^{89} +108.299i q^{91} +(-245.397 - 1533.38i) q^{92} +(-133.213 - 113.589i) q^{94} +(-150.801 + 261.195i) q^{95} +(-752.565 - 1303.48i) q^{97} +(172.396 - 934.367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66543 + 0.946295i −0.942372 + 0.334566i
\(3\) 0 0
\(4\) 6.20905 5.04457i 0.776131 0.630571i
\(5\) −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 −0.436517 0.899696i \(-0.643788\pi\)
0.560901 + 0.827883i \(0.310455\pi\)
\(8\) −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 \(-0.936477\pi\)
0.318395 0.947958i \(1.60314\pi\)
\(12\) 0 0
\(13\) −20.3570 + 35.2594i −0.434309 + 0.752245i −0.997239 0.0742593i \(-0.976341\pi\)
0.562930 + 0.826505i \(0.309674\pi\)
\(14\) −4.88158 + 5.72493i −0.0931898 + 0.109289i
\(15\) 0 0
\(16\) 13.1046 62.6440i 0.204759 0.978812i
\(17\) 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 \(-0.727295\pi\)
0.654914 0.755703i \(-0.272705\pi\)
\(20\) −19.0336 + 3.04606i −0.212802 + 0.0340560i
\(21\) 0 0
\(22\) 103.922 + 88.6131i 1.00710 + 0.858745i
\(23\) 97.0560 168.106i 0.879894 1.52402i 0.0284384 0.999596i \(-0.490947\pi\)
0.851456 0.524426i \(-0.175720\pi\)
\(24\) 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 −0.0100006 0.999950i \(-0.503183\pi\)
−0.870982 + 0.491314i \(0.836517\pi\)
\(32\) 24.3503 + 179.374i 0.134518 + 0.990911i
\(33\) 0 0
\(34\) 34.4195 + 96.9496i 0.173615 + 0.489021i
\(35\) −6.40918 −0.0309529
\(36\) 0 0
\(37\) 199.364 0.885818 0.442909 0.896566i \(-0.353946\pi\)
0.442909 + 0.896566i \(0.353946\pi\)
\(38\) 118.451 + 333.641i 0.505665 + 1.42431i
\(39\) 0 0
\(40\) 47.8502 26.1304i 0.189145 0.103290i
\(41\) 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 −0.875794 0.482685i \(-0.839662\pi\)
−0.0198798 + 0.999802i \(0.506328\pi\)
\(44\) −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 0.910045 0.414510i \(-0.136047\pi\)
−0.813998 + 0.580867i \(0.802714\pi\)
\(48\) 0 0
\(49\) −167.962 + 290.919i −0.489686 + 0.848161i
\(50\) 256.534 + 218.744i 0.725588 + 0.618701i
\(51\) 0 0
\(52\) 51.4707 + 321.620i 0.137264 + 0.857704i
\(53\) 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
\(56\) −1.43018 + 60.1718i −0.00341278 + 0.143586i
\(57\) 0 0
\(58\) 325.478 381.708i 0.736851 0.864150i
\(59\) −70.7911 + 122.614i −0.156207 + 0.270559i −0.933498 0.358583i \(-0.883260\pi\)
0.777291 + 0.629141i \(0.216593\pi\)
\(60\) 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 0.615207 0.788366i \(-0.289072\pi\)
−0.375141 + 0.926968i \(0.622406\pi\)
\(68\) −183.486 225.841i −0.327220 0.402754i
\(69\) 0 0
\(70\) 17.0832 6.06498i 0.0291691 0.0103558i
\(71\) −28.0331 −0.0468580 −0.0234290 0.999726i \(-0.507458\pi\)
−0.0234290 + 0.999726i \(0.507458\pi\)
\(72\) 0 0
\(73\) 124.499 0.199609 0.0998047 0.995007i \(-0.468178\pi\)
0.0998047 + 0.995007i \(0.468178\pi\)
\(74\) −531.392 + 188.657i −0.834771 + 0.296365i
\(75\) 0 0
\(76\) −631.445 777.207i −0.953049 1.17305i
\(77\) −111.232 64.2199i −0.164624 0.0950459i
\(78\) 0 0
\(79\) 648.411 374.360i 0.923443 0.533150i 0.0387108 0.999250i \(-0.487675\pi\)
0.884732 + 0.466101i \(0.154342\pi\)
\(80\) −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 0.958013 0.286725i \(-0.0925667\pi\)
−0.727318 + 0.686301i \(0.759233\pi\)
\(84\) 0 0
\(85\) −43.8198 + 75.8981i −0.0559167 + 0.0968506i
\(86\) 535.182 627.641i 0.671048 0.786979i
\(87\) 0 0
\(88\) 1092.27 + 25.9614i 1.32314 + 0.0314488i
\(89\) 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
\(92\) −245.397 1533.38i −0.278091 1.73768i
\(93\) 0 0
\(94\) −133.213 113.589i −0.146169 0.124637i
\(95\) −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 0.998238 0.0593366i \(-0.0188985\pi\)
0.447732 + 0.894168i \(0.352232\pi\)
\(104\) −441.539 808.548i −0.416312 0.762353i
\(105\) 0 0
\(106\) 333.261 + 938.698i 0.305370 + 0.860136i
\(107\) −783.805 −0.708161 −0.354081 0.935215i \(-0.615206\pi\)
−0.354081 + 0.935215i \(0.615206\pi\)
\(108\) 0 0
\(109\) 1581.89 1.39007 0.695035 0.718976i \(-0.255389\pi\)
0.695035 + 0.718976i \(0.255389\pi\)
\(110\) −110.095 310.104i −0.0954285 0.268794i
\(111\) 0 0
\(112\) −53.1283 161.737i −0.0448228 0.136453i
\(113\) 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
\(122\) 33.2097 + 28.3175i 0.0246448 + 0.0210143i
\(123\) 0 0
\(124\) −1387.00 + 221.971i −1.00449 + 0.160755i
\(125\) 588.380i 0.421010i
\(126\) 0 0
\(127\) 425.829i 0.297529i 0.988873 + 0.148765i \(0.0475297\pi\)
−0.988873 + 0.148765i \(0.952470\pi\)
\(128\) 1056.06 + 990.906i 0.729244 + 0.684254i
\(129\) 0 0
\(130\) −180.030 + 211.132i −0.121459 + 0.142443i
\(131\) −871.836 + 1510.06i −0.581471 + 1.00714i 0.413835 + 0.910352i \(0.364189\pi\)
−0.995305 + 0.0967846i \(0.969144\pi\)
\(132\) 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 0.122641 0.992451i \(-0.460864\pi\)
−0.798167 + 0.602436i \(0.794197\pi\)
\(140\) −39.7949 + 32.3316i −0.0240235 + 0.0195180i
\(141\) 0 0
\(142\) 74.7204 26.5276i 0.0441577 0.0156771i
\(143\) 1965.90 1.14963
\(144\) 0 0
\(145\) 427.331 0.244744
\(146\) −331.843 + 117.813i −0.188106 + 0.0667825i
\(147\) 0 0
\(148\) 1237.86 1005.71i 0.687511 0.558572i
\(149\) −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 −0.706382 0.707831i \(-0.749674\pi\)
0.259808 + 0.965660i \(0.416341\pi\)
\(152\) 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 \(0.988098\pi\)
\(158\) −1374.04 + 1611.42i −0.691853 + 0.811378i
\(159\) 0 0
\(160\) 165.288 403.629i 0.0816696 0.199436i
\(161\) 516.337i 0.252752i
\(162\) 0 0
\(163\) 1468.60i 0.705703i −0.935679 0.352851i \(-0.885212\pi\)
0.935679 0.352851i \(-0.114788\pi\)
\(164\) 1840.87 294.606i 0.876511 0.140273i
\(165\) 0 0
\(166\) −750.887 640.273i −0.351085 0.299366i
\(167\) 1524.19 2639.98i 0.706261 1.22328i −0.259974 0.965616i \(-0.583714\pi\)
0.966235 0.257664i \(-0.0829527\pi\)
\(168\) 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
\(176\) −2935.94 + 964.414i −1.25742 + 0.413042i
\(177\) 0 0
\(178\) −394.476 1111.12i −0.166108 0.467877i
\(179\) −477.618 −0.199435 −0.0997174 0.995016i \(-0.531794\pi\)
−0.0997174 + 0.995016i \(0.531794\pi\)
\(180\) 0 0
\(181\) −732.350 −0.300747 −0.150373 0.988629i \(-0.548048\pi\)
−0.150373 + 0.988629i \(0.548048\pi\)
\(182\) −102.483 288.664i −0.0417392 0.117567i
\(183\) 0 0
\(184\) 2105.12 + 3854.91i 0.843433 + 1.54450i
\(185\) −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 \(-0.967941\pi\)
0.410391 0.911910i \(1.63461\pi\)
\(192\) 0 0
\(193\) 817.160 1415.36i 0.304769 0.527876i −0.672441 0.740151i \(-0.734754\pi\)
0.977210 + 0.212275i \(0.0680873\pi\)
\(194\) 3239.39 + 2762.19i 1.19884 + 1.02224i
\(195\) 0 0
\(196\) 424.676 + 2653.63i 0.154765 + 0.967066i
\(197\) 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 \(-0.940314\pi\)
0.982471 0.186413i \(-0.0596863\pi\)
\(200\) 2696.30 + 64.0864i 0.953286 + 0.0226580i
\(201\) 0 0
\(202\) 799.083 937.133i 0.278333 0.326418i
\(203\) −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 −0.491352 0.870961i \(-0.663497\pi\)
−0.999950 + 0.00995667i \(0.996831\pi\)
\(212\) −1776.57 2186.67i −0.575544 0.708402i
\(213\) 0 0
\(214\) 2089.18 741.711i 0.667352 0.236927i
\(215\) 702.658 0.222888
\(216\) 0 0
\(217\) −467.047 −0.146107
\(218\) −4216.42 + 1496.94i −1.30996 + 0.465070i
\(219\) 0 0
\(220\) 586.901 + 722.380i 0.179858 + 0.221377i
\(221\) 1282.49 + 740.444i 0.390359 + 0.225374i
\(222\) 0 0
\(223\) 4122.02 2379.85i 1.23781 0.714648i 0.269161 0.963095i \(-0.413254\pi\)
0.968645 + 0.248447i \(0.0799202\pi\)
\(224\) 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 0.655650 0.755065i \(-0.272395\pi\)
−0.981730 + 0.190277i \(0.939061\pi\)
\(228\) 0 0
\(229\) 2917.29 5052.89i 0.841833 1.45810i −0.0465095 0.998918i \(-0.514810\pi\)
0.888343 0.459181i \(-0.151857\pi\)
\(230\) 858.329 1006.61i 0.246072 0.288583i
\(231\) 0 0
\(232\) 95.3568 4011.94i 0.0269848 1.13533i
\(233\) 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
\(236\) 178.988 + 1118.43i 0.0493693 + 0.308489i
\(237\) 0 0
\(238\) 208.232 + 177.557i 0.0567130 + 0.0483586i
\(239\) 2645.73 4582.53i 0.716058 1.24025i −0.246492 0.969145i \(-0.579278\pi\)
0.962550 0.271104i \(-0.0873887\pi\)
\(240\) 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
\(248\) 3486.92 1904.16i 0.892820 0.487559i
\(249\) 0 0
\(250\) −556.781 1568.29i −0.140856 0.396748i
\(251\) −2577.68 −0.648215 −0.324107 0.946020i \(-0.605064\pi\)
−0.324107 + 0.946020i \(0.605064\pi\)
\(252\) 0 0
\(253\) −9372.83 −2.32911
\(254\) −402.960 1135.02i −0.0995432 0.280383i
\(255\) 0 0
\(256\) −3752.54 1641.85i −0.916147 0.400842i
\(257\) 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 \(0.00195289\pi\)
−0.494677 + 0.869077i \(0.664714\pi\)
\(264\) 0 0
\(265\) −424.278 + 734.871i −0.0983516 + 0.170350i
\(266\) 716.608 + 611.043i 0.165181 + 0.140848i
\(267\) 0 0
\(268\) 1200.91 192.189i 0.273721 0.0438052i
\(269\) 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 \(0.0774353\pi\)
−0.970555 + 0.240878i \(0.922565\pi\)
\(272\) −2278.55 476.653i −0.507931 0.106255i
\(273\) 0 0
\(274\) −2700.40 + 3166.93i −0.595392 + 0.698252i
\(275\) −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 0.301809 0.953369i \(-0.402410\pi\)
−0.674737 + 0.738058i \(0.735743\pi\)
\(284\) −174.059 + 141.415i −0.0363680 + 0.0295473i
\(285\) 0 0
\(286\) −5239.98 + 1860.33i −1.08338 + 0.384627i
\(287\) 619.877 0.127492
\(288\) 0 0
\(289\) 3590.01 0.730716
\(290\) −1139.02 + 404.381i −0.230640 + 0.0818830i
\(291\) 0 0
\(292\) 773.020 628.043i 0.154923 0.125868i
\(293\) 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
\(302\) 1755.93 2059.29i 0.334578 0.392380i
\(303\) 0 0
\(304\) −7841.35 1640.35i −1.47938 0.309475i
\(305\) 37.1790i 0.00697988i
\(306\) 0 0
\(307\) 7392.80i 1.37436i 0.726486 + 0.687181i \(0.241152\pi\)
−0.726486 + 0.687181i \(0.758848\pi\)
\(308\) −1014.61 + 162.374i −0.187703 + 0.0300393i
\(309\) 0 0
\(310\) −910.522 776.392i −0.166820 0.142245i
\(311\) −2448.25 + 4240.50i −0.446391 + 0.773172i −0.998148 0.0608332i \(-0.980624\pi\)
0.551757 + 0.834005i \(0.313958\pi\)
\(312\) 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
\(320\) −58.6103 + 1232.26i −0.0102388 + 0.215266i
\(321\) 0 0
\(322\) 488.607 + 1376.26i 0.0845621 + 0.238186i
\(323\) −4552.92 −0.784307
\(324\) 0 0
\(325\) 4852.88 0.828276
\(326\) 1389.73 + 3914.45i 0.236104 + 0.665035i
\(327\) 0 0
\(328\) −4627.93 + 2527.26i −0.779069 + 0.425441i
\(329\) 142.583 + 82.3206i 0.0238932 + 0.0137948i
\(330\) 0 0
\(331\) −6410.22 + 3700.94i −1.06446 + 0.614569i −0.926664 0.375891i \(-0.877337\pi\)
−0.137801 + 0.990460i \(0.544003\pi\)
\(332\) 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 \(-0.121935\pi\)
\(338\) −1160.85 989.842i −0.186810 0.159291i
\(339\) 0 0
\(340\) 110.794 + 692.307i 0.0176725 + 0.110428i
\(341\) 8478.09i 1.34638i
\(342\) 0 0
\(343\) 1805.94i 0.284290i
\(344\) 156.795 6596.82i 0.0245750 1.03394i
\(345\) 0 0
\(346\) −5093.68 + 5973.67i −0.791439 + 0.928169i
\(347\) −3523.75 + 6103.31i −0.545143 + 0.944216i 0.453455 + 0.891279i \(0.350191\pi\)
−0.998598 + 0.0529363i \(0.983142\pi\)
\(348\) 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
\(356\) 2102.90 + 2588.33i 0.313071 + 0.385340i
\(357\) 0 0
\(358\) 1273.06 451.968i 0.187942 0.0667241i
\(359\) 6515.20 0.957825 0.478912 0.877863i \(-0.341031\pi\)
0.478912 + 0.877863i \(0.341031\pi\)
\(360\) 0 0
\(361\) −8809.35 −1.28435
\(362\) 1952.03 693.020i 0.283415 0.100620i
\(363\) 0 0
\(364\) 546.322 + 672.434i 0.0786678 + 0.0968273i
\(365\) −259.787 149.988i −0.0372545 0.0215089i
\(366\) 0 0
\(367\) 3492.35 2016.31i 0.496729 0.286786i −0.230633 0.973041i \(-0.574080\pi\)
0.727362 + 0.686254i \(0.240746\pi\)
\(368\) −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 \(0.221179\pi\)
\(374\) 3223.12 3779.95i 0.445624 0.522611i
\(375\) 0 0
\(376\) −1400.14 33.2788i −0.192038 0.00456442i
\(377\) 7220.81i 0.986448i
\(378\) 0 0
\(379\) 9518.27i 1.29003i −0.764171 0.645014i \(-0.776851\pi\)
0.764171 0.645014i \(-0.223149\pi\)
\(380\) 381.285 + 2382.50i 0.0514724 + 0.321630i
\(381\) 0 0
\(382\) 6641.78 + 5663.37i 0.889589 + 0.758543i
\(383\) 4727.72 8188.65i 0.630744 1.09248i −0.356655 0.934236i \(-0.616083\pi\)
0.987400 0.158245i \(-0.0505837\pi\)
\(384\) 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
\(392\) −3643.06 6671.20i −0.469394 0.859557i
\(393\) 0 0
\(394\) −3170.73 8930.99i −0.405429 1.14197i
\(395\) −1804.02 −0.229798
\(396\) 0 0
\(397\) 1296.85 0.163947 0.0819733 0.996635i \(-0.473878\pi\)
0.0819733 + 0.996635i \(0.473878\pi\)
\(398\) 990.405 + 2789.68i 0.124735 + 0.351341i
\(399\) 0 0
\(400\) −7247.45 + 2380.68i −0.905931 + 0.297585i
\(401\) 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 \(0.280588\pi\)
\(410\) 1208.47 + 1030.45i 0.145566 + 0.124122i
\(411\) 0 0
\(412\) 13787.4 2206.48i 1.64868 0.263849i
\(413\) 376.608i 0.0448709i
\(414\) 0 0
\(415\) 840.635i 0.0994341i
\(416\) −6820.32 2792.94i −0.803830 0.329171i
\(417\) 0 0
\(418\) 11092.0 13008.3i 1.29791 1.52214i
\(419\) 7052.61 12215.5i 0.822298 1.42426i −0.0816695 0.996659i \(-0.526025\pi\)
0.903967 0.427602i \(-0.140641\pi\)
\(420\) 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
\(428\) −4866.68 + 3953.96i −0.549626 + 0.446546i
\(429\) 0 0
\(430\) −1872.89 + 664.922i −0.210043 + 0.0745707i
\(431\) −1119.73 −0.125140 −0.0625700 0.998041i \(-0.519930\pi\)
−0.0625700 + 0.998041i \(0.519930\pi\)
\(432\) 0 0
\(433\) −299.833 −0.0332773 −0.0166387 0.999862i \(-0.505296\pi\)
−0.0166387 + 0.999862i \(0.505296\pi\)
\(434\) 1244.88 441.964i 0.137687 0.0488824i
\(435\) 0 0
\(436\) 9822.04 7979.96i 1.07888 0.876539i
\(437\) −21042.4 12148.8i −2.30342 1.32988i
\(438\) 0 0
\(439\) 2090.02 1206.67i 0.227224 0.131188i −0.382067 0.924135i \(-0.624788\pi\)
0.609291 + 0.792947i \(0.291454\pi\)
\(440\) −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 0.707412 0.706802i \(-0.249863\pi\)
−0.965814 + 0.259236i \(0.916529\pi\)
\(444\) 0 0
\(445\) 502.211 869.854i 0.0534990 0.0926630i
\(446\) −8734.92 + 10244.0i −0.927378 + 1.08759i
\(447\) 0 0
\(448\) −1145.77 736.225i −0.120832 0.0776415i
\(449\) 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
\(452\) 3506.02 561.089i 0.364843 0.0583881i
\(453\) 0 0
\(454\) 4800.46 + 4093.29i 0.496248 + 0.423145i
\(455\) 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 −0.0940023 0.995572i \(-0.529966\pi\)
−0.909192 + 0.416378i \(0.863299\pi\)
\(464\) 3542.31 + 10783.8i 0.354413 + 1.07893i
\(465\) 0 0
\(466\) 2914.67 + 8209.76i 0.289742 + 0.816116i
\(467\) −7.01271 −0.000694881 −0.000347441 1.00000i \(-0.500111\pi\)
−0.000347441 1.00000i \(0.500111\pi\)
\(468\) 0 0
\(469\) 404.383 0.0398138
\(470\) 141.126 + 397.509i 0.0138503 + 0.0390122i
\(471\) 0 0
\(472\) −1535.44 2811.71i −0.149734 0.274194i
\(473\) 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 0.698849 0.715269i \(-0.253696\pi\)
−0.968866 + 0.247586i \(0.920363\pi\)
\(480\) 0 0
\(481\) −4058.46 + 7029.46i −0.384719 + 0.666353i
\(482\) −10768.1 9181.81i −1.01758 0.867677i
\(483\) 0 0
\(484\) 1264.84 + 7903.50i 0.118787 + 0.742252i
\(485\) 3626.57i 0.339534i
\(486\) 0 0
\(487\) 9082.26i 0.845085i 0.906343 + 0.422542i \(0.138862\pi\)
−0.906343 + 0.422542i \(0.861138\pi\)
\(488\) 349.051 + 8.29632i 0.0323786 + 0.000769584i
\(489\) 0 0
\(490\) −1485.40 + 1742.02i −0.136946 + 0.160605i
\(491\) −5098.79 + 8831.36i −0.468646 + 0.811718i −0.999358 0.0358342i \(-0.988591\pi\)
0.530712 + 0.847552i \(0.321925\pi\)
\(492\) 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 0.390720 0.920510i \(-0.372226\pi\)
−0.601825 + 0.798628i \(0.705559\pi\)
\(500\) 2968.12 + 3653.28i 0.265477 + 0.326759i
\(501\) 0 0
\(502\) 6870.64 2439.25i 0.610860 0.216871i
\(503\) 8294.45 0.735251 0.367626 0.929974i \(-0.380171\pi\)
0.367626 + 0.929974i \(0.380171\pi\)
\(504\) 0 0
\(505\) 1049.14 0.0924479
\(506\) 24982.6 8869.47i 2.19489 0.779241i
\(507\) 0 0
\(508\) 2148.13 + 2643.99i 0.187613 + 0.230922i
\(509\) −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
\(518\) −973.212 + 1141.35i −0.0825492 + 0.0968105i
\(519\) 0 0
\(520\) −52.7443 + 2219.11i −0.00444806 + 0.187143i
\(521\) 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 \(0.132613\pi\)
−0.914463 + 0.404669i \(0.867387\pi\)
\(524\) 2204.35 + 13774.1i 0.183774 + 1.14833i
\(525\) 0 0
\(526\) −9276.95 7910.35i −0.769000 0.655718i
\(527\) −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
\(536\) −3019.08 + 1648.68i −0.243291 + 0.132859i
\(537\) 0 0
\(538\) 5302.58 + 14935.8i 0.424927 + 1.19689i
\(539\) 16220.3 1.29621
\(540\) 0 0
\(541\) 18659.8 1.48290 0.741449 0.671009i \(-0.234139\pi\)
0.741449 + 0.671009i \(0.234139\pi\)
\(542\) −2033.80 5728.60i −0.161179 0.453993i
\(543\) 0 0
\(544\) 6524.36 885.691i 0.514209 0.0698046i
\(545\) −3300.88 1905.76i −0.259438 0.149787i
\(546\) 0 0
\(547\) 3928.78 2268.28i 0.307098 0.177303i −0.338529 0.940956i \(-0.609929\pi\)
0.645627 + 0.763653i \(0.276596\pi\)
\(548\) 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
\(554\) −6908.63 5890.91i −0.529819 0.451771i
\(555\) 0 0
\(556\) −10097.9 + 1616.03i −0.770229 + 0.123264i
\(557\) 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
\(560\) −83.9898 + 401.497i −0.00633789 + 0.0302970i
\(561\) 0 0
\(562\) −1725.76 + 2023.91i −0.129532 + 0.151910i
\(563\) 4972.47 8612.57i 0.372229 0.644719i −0.617679 0.786430i \(-0.711927\pi\)
0.989908 + 0.141711i \(0.0452604\pi\)
\(564\) 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 0.763444 0.645874i \(-0.223507\pi\)
−0.177621 + 0.984099i \(0.556840\pi\)
\(572\) 12206.4 9917.14i 0.892264 0.724924i
\(573\) 0 0
\(574\) −1652.24 + 586.587i −0.120145 + 0.0426545i
\(575\) −23137.1 −1.67806
\(576\) 0 0
\(577\) 4076.34 0.294108 0.147054 0.989128i \(-0.453021\pi\)
0.147054 + 0.989128i \(0.453021\pi\)
\(578\) −9568.92 + 3397.21i −0.688607 + 0.244473i
\(579\) 0 0
\(580\) 2653.32 2155.70i 0.189953 0.154329i
\(581\) 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 0.976948 0.213476i \(-0.0684785\pi\)
−0.673350 + 0.739324i \(0.735145\pi\)
\(588\) 0 0
\(589\) −10989.1 + 19033.6i −0.768755 + 1.33152i
\(590\) −626.052 + 734.209i −0.0436850 + 0.0512320i
\(591\) 0 0
\(592\) 2612.59 12489.0i 0.181380 0.867050i
\(593\) 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
\(596\) −16976.5 + 2716.85i −1.16675 + 0.186723i
\(597\) 0 0
\(598\) −17009.2 14503.6i −1.16314 0.991800i
\(599\) −7549.02 + 13075.3i −0.514932 + 0.891889i 0.484917 + 0.874560i \(0.338850\pi\)
−0.999850 + 0.0173291i \(0.994484\pi\)
\(600\) 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 0.930247 0.366933i \(-0.119592\pi\)
0.147350 + 0.989084i \(0.452926\pi\)
\(608\) 22452.8 3048.00i 1.49767 0.203311i
\(609\) 0 0
\(610\) −35.1823 99.0981i −0.00233523 0.00657765i
\(611\) −2520.01 −0.166855
\(612\) 0 0
\(613\) 7939.25 0.523105 0.261552 0.965189i \(-0.415766\pi\)
0.261552 + 0.965189i \(0.415766\pi\)
\(614\) −6995.77 19705.0i −0.459815 1.29516i
\(615\) 0 0
\(616\) 2550.71 1392.91i 0.166836 0.0911073i
\(617\) 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 0.0341179 0.999418i \(-0.489138\pi\)
0.882580 + 0.470162i \(0.155804\pi\)
\(620\) 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
\(626\) 1467.22 + 1251.08i 0.0936774 + 0.0798776i
\(627\) 0 0
\(628\) 2646.23 + 16535.2i 0.168147 + 1.05068i
\(629\) 7251.46i 0.459674i
\(630\) 0 0
\(631\) 2517.83i 0.158848i −0.996841 0.0794242i \(-0.974692\pi\)
0.996841 0.0794242i \(-0.0253082\pi\)
\(632\) −402.559 + 16936.8i −0.0253369 + 1.06600i
\(633\) 0 0
\(634\) 2848.33 3340.41i 0.178425 0.209250i
\(635\) 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 0.932189 0.361973i \(-0.117897\pi\)
0.152617 + 0.988285i \(0.451230\pi\)
\(644\) −2604.70 3205.96i −0.159378 0.196169i
\(645\) 0 0
\(646\) 12135.5 4308.41i 0.739109 0.262402i
\(647\) −21477.2 −1.30503 −0.652515 0.757776i \(-0.726286\pi\)
−0.652515 + 0.757776i \(0.726286\pi\)
\(648\) 0 0
\(649\) 6836.40 0.413485
\(650\) −12935.0 + 4592.26i −0.780544 + 0.277113i
\(651\) 0 0
\(652\) −7408.45 9118.60i −0.444996 0.547718i
\(653\) −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 0.588612 0.808416i \(-0.299675\pi\)
−0.994415 + 0.105545i \(0.966341\pi\)
\(660\) 0 0
\(661\) −772.039 + 1337.21i −0.0454294 + 0.0786860i −0.887846 0.460141i \(-0.847799\pi\)
0.842417 + 0.538827i \(0.181132\pi\)
\(662\) 13583.8 15930.6i 0.797508 0.935286i
\(663\) 0 0
\(664\) −7892.20 187.584i −0.461260 0.0109633i
\(665\) 802.258i 0.0467823i
\(666\) 0 0
\(667\) 34426.6i 1.99851i
\(668\) −3853.77 24080.7i −0.223214 1.39477i
\(669\) 0 0
\(670\) 788.357 + 672.223i 0.0454580 + 0.0387616i
\(671\) −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
\(680\) −950.441 1740.45i −0.0535996 0.0981520i
\(681\) 0 0
\(682\) −8022.78 22597.8i −0.450452 1.26879i
\(683\) 7466.11 0.418276 0.209138 0.977886i \(-0.432934\pi\)
0.209138 + 0.977886i \(0.432934\pi\)
\(684\) 0 0
\(685\) −3545.45 −0.197759
\(686\) −1708.95 4813.60i −0.0951136 0.267907i
\(687\) 0 0
\(688\) 5824.61 + 17731.7i 0.322763 + 0.982581i
\(689\) 12417.5 + 7169.23i 0.686600 + 0.396409i
\(690\) 0 0
\(691\) 20587.2 11886.0i 1.13339 0.654364i 0.188606 0.982053i \(-0.439603\pi\)
0.944786 + 0.327689i \(0.106270\pi\)
\(692\) 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
\(698\) −2598.92 2216.07i −0.140932 0.120171i
\(699\) 0 0
\(700\) −2504.58 + 400.823i −0.135235 + 0.0216424i
\(701\) 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
\(704\) −13364.4 + 20798.7i −0.715467 + 1.11346i
\(705\) 0 0
\(706\) 2789.71 3271.66i 0.148714 0.174406i
\(707\) −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
\(716\) −2965.55 + 2409.38i −0.154788 + 0.125758i
\(717\) 0 0
\(718\) −17365.8 + 6165.30i −0.902627 + 0.320455i
\(719\) 20077.1 1.04137 0.520687 0.853748i \(-0.325676\pi\)
0.520687 + 0.853748i \(0.325676\pi\)
\(720\) 0 0
\(721\) 4642.64 0.239807
\(722\) 23480.7 8336.24i 1.21033 0.429699i
\(723\) 0 0
\(724\) −4547.20 + 3694.39i −0.233419 + 0.189642i
\(725\) 18307.5 + 10569.8i 0.937825 + 0.541454i
\(726\) 0 0
\(727\) −31220.9 + 18025.4i −1.59274 + 0.919566i −0.599900 + 0.800075i \(0.704793\pi\)
−0.992835 + 0.119491i \(0.961874\pi\)
\(728\) −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 \(-0.0174795\pi\)
\(734\) −7400.60 + 8679.14i −0.372154 + 0.436448i
\(735\) 0 0
\(736\) 32517.2 + 13315.9i 1.62853 + 0.666889i
\(737\) 7340.58i 0.366884i
\(738\) 0 0
\(739\) 26112.0i 1.29979i −0.760024 0.649895i \(-0.774813\pi\)
0.760024 0.649895i \(-0.225187\pi\)
\(740\) −3794.61 + 607.275i −0.188504 + 0.0301674i
\(741\) 0 0
\(742\) 2016.18 + 1719.17i 0.0997522 + 0.0850576i
\(743\) −2806.43 + 4860.88i −0.138570 + 0.240011i −0.926956 0.375171i \(-0.877584\pi\)
0.788385 + 0.615182i \(0.210917\pi\)
\(744\) 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 −0.214409 0.976744i \(-0.568783\pi\)
−0.953090 + 0.302688i \(0.902116\pi\)
\(752\) 3763.46 1236.24i 0.182499 0.0599481i
\(753\) 0 0
\(754\) 6833.02 + 19246.6i 0.330032 + 0.929601i
\(755\) 2305.42 0.111129
\(756\) 0 0
\(757\) −22792.6 −1.09433 −0.547167 0.837023i \(-0.684294\pi\)
−0.547167 + 0.837023i \(0.684294\pi\)
\(758\) 9007.10 + 25370.3i 0.431600 + 1.21569i
\(759\) 0 0
\(760\) −3270.83 5989.57i −0.156113 0.285874i
\(761\) −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 \(0.148731\pi\)
\(770\) −666.055 567.938i −0.0311727 0.0265806i
\(771\) 0 0
\(772\) −2066.11 12910.3i −0.0963224 0.601880i
\(773\) 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
\(776\) 34047.6 + 809.252i 1.57505 + 0.0374362i
\(777\) 0 0
\(778\) −5443.29 + 6383.68i −0.250837 + 0.294172i
\(779\) 14585.0 25262.0i 0.670811 1.16188i
\(780\) 0 0