Properties

Label 108.5.f.a.91.9
Level 108
Weight 5
Character 108.91
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 91.9
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.29332 - 3.78514i) q^{2} +(-12.6546 + 9.79083i) q^{4} +(10.5756 - 18.3175i) q^{5} +(38.6407 - 22.3092i) q^{7} +(53.4262 + 35.2369i) q^{8} +O(q^{10})\) \(q+(-1.29332 - 3.78514i) q^{2} +(-12.6546 + 9.79083i) q^{4} +(10.5756 - 18.3175i) q^{5} +(38.6407 - 22.3092i) q^{7} +(53.4262 + 35.2369i) q^{8} +(-83.0119 - 16.3397i) q^{10} +(58.6904 - 33.8849i) q^{11} +(14.5519 - 25.2046i) q^{13} +(-134.419 - 117.408i) q^{14} +(64.2793 - 247.799i) q^{16} -402.841 q^{17} -644.741i q^{19} +(45.5130 + 335.344i) q^{20} +(-204.165 - 178.327i) q^{22} +(-335.527 - 193.717i) q^{23} +(88.8138 + 153.830i) q^{25} +(-114.223 - 22.4833i) q^{26} +(-270.558 + 660.639i) q^{28} +(362.210 + 627.366i) q^{29} +(-1090.90 - 629.833i) q^{31} +(-1021.09 + 77.1774i) q^{32} +(521.004 + 1524.81i) q^{34} -943.733i q^{35} -1402.04 q^{37} +(-2440.44 + 833.859i) q^{38} +(1210.46 - 605.982i) q^{40} +(774.166 - 1340.89i) q^{41} +(1620.98 - 935.875i) q^{43} +(-410.944 + 1003.43i) q^{44} +(-299.300 + 1520.56i) q^{46} +(3610.63 - 2084.60i) q^{47} +(-205.097 + 355.239i) q^{49} +(467.404 - 535.125i) q^{50} +(62.6253 + 461.430i) q^{52} -906.566 q^{53} -1433.41i q^{55} +(2850.53 + 169.681i) q^{56} +(1906.22 - 2182.40i) q^{58} +(3916.45 + 2261.16i) q^{59} +(-1314.22 - 2276.30i) q^{61} +(-973.119 + 4943.80i) q^{62} +(1612.72 + 3765.15i) q^{64} +(-307.789 - 533.107i) q^{65} +(-58.7165 - 33.9000i) q^{67} +(5097.81 - 3944.15i) q^{68} +(-3572.16 + 1220.55i) q^{70} +1315.04i q^{71} +9470.72 q^{73} +(1813.29 + 5306.91i) q^{74} +(6312.55 + 8158.96i) q^{76} +(1511.89 - 2618.67i) q^{77} +(-3783.95 + 2184.67i) q^{79} +(-3859.25 - 3798.05i) q^{80} +(-6076.73 - 1196.12i) q^{82} +(659.925 - 381.008i) q^{83} +(-4260.28 + 7379.03i) q^{85} +(-5638.88 - 4925.26i) q^{86} +(4329.61 + 257.724i) q^{88} -8083.40 q^{89} -1298.56i q^{91} +(6142.62 - 833.676i) q^{92} +(-12560.2 - 10970.7i) q^{94} +(-11810.0 - 6818.52i) q^{95} +(-3332.71 - 5772.42i) q^{97} +(1609.89 + 316.884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29332 3.78514i −0.323331 0.946286i
\(3\) 0 0
\(4\) −12.6546 + 9.79083i −0.790914 + 0.611927i
\(5\) 10.5756 18.3175i 0.423024 0.732698i −0.573210 0.819409i \(-0.694302\pi\)
0.996234 + 0.0867102i \(0.0276354\pi\)
\(6\) 0 0
\(7\) 38.6407 22.3092i 0.788586 0.455290i −0.0508787 0.998705i \(-0.516202\pi\)
0.839464 + 0.543415i \(0.182869\pi\)
\(8\) 53.4262 + 35.2369i 0.834785 + 0.550576i
\(9\) 0 0
\(10\) −83.0119 16.3397i −0.830119 0.163397i
\(11\) 58.6904 33.8849i 0.485045 0.280041i −0.237472 0.971394i \(-0.576319\pi\)
0.722516 + 0.691354i \(0.242985\pi\)
\(12\) 0 0
\(13\) 14.5519 25.2046i 0.0861058 0.149140i −0.819756 0.572713i \(-0.805891\pi\)
0.905862 + 0.423573i \(0.139224\pi\)
\(14\) −134.419 117.408i −0.685809 0.599018i
\(15\) 0 0
\(16\) 64.2793 247.799i 0.251091 0.967963i
\(17\) −402.841 −1.39391 −0.696957 0.717113i \(-0.745463\pi\)
−0.696957 + 0.717113i \(0.745463\pi\)
\(18\) 0 0
\(19\) 644.741i 1.78599i −0.450070 0.892993i \(-0.648601\pi\)
0.450070 0.892993i \(-0.351399\pi\)
\(20\) 45.5130 + 335.344i 0.113782 + 0.838361i
\(21\) 0 0
\(22\) −204.165 178.327i −0.421828 0.368445i
\(23\) −335.527 193.717i −0.634267 0.366194i 0.148136 0.988967i \(-0.452673\pi\)
−0.782403 + 0.622773i \(0.786006\pi\)
\(24\) 0 0
\(25\) 88.8138 + 153.830i 0.142102 + 0.246128i
\(26\) −114.223 22.4833i −0.168969 0.0332593i
\(27\) 0 0
\(28\) −270.558 + 660.639i −0.345099 + 0.842652i
\(29\) 362.210 + 627.366i 0.430690 + 0.745977i 0.996933 0.0782617i \(-0.0249370\pi\)
−0.566243 + 0.824238i \(0.691604\pi\)
\(30\) 0 0
\(31\) −1090.90 629.833i −1.13517 0.655393i −0.189944 0.981795i \(-0.560831\pi\)
−0.945231 + 0.326402i \(0.894164\pi\)
\(32\) −1021.09 + 77.1774i −0.997156 + 0.0753685i
\(33\) 0 0
\(34\) 521.004 + 1524.81i 0.450695 + 1.31904i
\(35\) 943.733i 0.770394i
\(36\) 0 0
\(37\) −1402.04 −1.02413 −0.512066 0.858946i \(-0.671120\pi\)
−0.512066 + 0.858946i \(0.671120\pi\)
\(38\) −2440.44 + 833.859i −1.69005 + 0.577464i
\(39\) 0 0
\(40\) 1210.46 605.982i 0.756540 0.378739i
\(41\) 774.166 1340.89i 0.460539 0.797677i −0.538449 0.842658i \(-0.680990\pi\)
0.998988 + 0.0449815i \(0.0143229\pi\)
\(42\) 0 0
\(43\) 1620.98 935.875i 0.876681 0.506152i 0.00711825 0.999975i \(-0.497734\pi\)
0.869563 + 0.493823i \(0.164401\pi\)
\(44\) −410.944 + 1003.43i −0.212264 + 0.518300i
\(45\) 0 0
\(46\) −299.300 + 1520.56i −0.141446 + 0.718599i
\(47\) 3610.63 2084.60i 1.63451 0.943683i 0.651828 0.758367i \(-0.274002\pi\)
0.982679 0.185316i \(-0.0593310\pi\)
\(48\) 0 0
\(49\) −205.097 + 355.239i −0.0854217 + 0.147955i
\(50\) 467.404 535.125i 0.186962 0.214050i
\(51\) 0 0
\(52\) 62.6253 + 461.430i 0.0231602 + 0.170647i
\(53\) −906.566 −0.322736 −0.161368 0.986894i \(-0.551591\pi\)
−0.161368 + 0.986894i \(0.551591\pi\)
\(54\) 0 0
\(55\) 1433.41i 0.473855i
\(56\) 2850.53 + 169.681i 0.908971 + 0.0541073i
\(57\) 0 0
\(58\) 1906.22 2182.40i 0.566652 0.648753i
\(59\) 3916.45 + 2261.16i 1.12509 + 0.649573i 0.942696 0.333652i \(-0.108281\pi\)
0.182397 + 0.983225i \(0.441614\pi\)
\(60\) 0 0
\(61\) −1314.22 2276.30i −0.353190 0.611743i 0.633617 0.773647i \(-0.281570\pi\)
−0.986806 + 0.161904i \(0.948236\pi\)
\(62\) −973.119 + 4943.80i −0.253153 + 1.28611i
\(63\) 0 0
\(64\) 1612.72 + 3765.15i 0.393731 + 0.919226i
\(65\) −307.789 533.107i −0.0728496 0.126179i
\(66\) 0 0
\(67\) −58.7165 33.9000i −0.0130801 0.00755179i 0.493446 0.869777i \(-0.335737\pi\)
−0.506526 + 0.862225i \(0.669070\pi\)
\(68\) 5097.81 3944.15i 1.10247 0.852974i
\(69\) 0 0
\(70\) −3572.16 + 1220.55i −0.729013 + 0.249092i
\(71\) 1315.04i 0.260869i 0.991457 + 0.130434i \(0.0416372\pi\)
−0.991457 + 0.130434i \(0.958363\pi\)
\(72\) 0 0
\(73\) 9470.72 1.77720 0.888602 0.458680i \(-0.151678\pi\)
0.888602 + 0.458680i \(0.151678\pi\)
\(74\) 1813.29 + 5306.91i 0.331133 + 0.969121i
\(75\) 0 0
\(76\) 6312.55 + 8158.96i 1.09289 + 1.41256i
\(77\) 1511.89 2618.67i 0.255000 0.441672i
\(78\) 0 0
\(79\) −3783.95 + 2184.67i −0.606305 + 0.350050i −0.771518 0.636207i \(-0.780502\pi\)
0.165213 + 0.986258i \(0.447169\pi\)
\(80\) −3859.25 3798.05i −0.603008 0.593445i
\(81\) 0 0
\(82\) −6076.73 1196.12i −0.903737 0.177888i
\(83\) 659.925 381.008i 0.0957940 0.0553067i −0.451338 0.892353i \(-0.649053\pi\)
0.547132 + 0.837047i \(0.315720\pi\)
\(84\) 0 0
\(85\) −4260.28 + 7379.03i −0.589659 + 1.02132i
\(86\) −5638.88 4925.26i −0.762422 0.665936i
\(87\) 0 0
\(88\) 4329.61 + 257.724i 0.559092 + 0.0332804i
\(89\) −8083.40 −1.02050 −0.510251 0.860025i \(-0.670448\pi\)
−0.510251 + 0.860025i \(0.670448\pi\)
\(90\) 0 0
\(91\) 1298.56i 0.156813i
\(92\) 6142.62 833.676i 0.725734 0.0984967i
\(93\) 0 0
\(94\) −12560.2 10970.7i −1.42148 1.24159i
\(95\) −11810.0 6818.52i −1.30859 0.755514i
\(96\) 0 0
\(97\) −3332.71 5772.42i −0.354204 0.613500i 0.632777 0.774334i \(-0.281915\pi\)
−0.986981 + 0.160834i \(0.948582\pi\)
\(98\) 1609.89 + 316.884i 0.167627 + 0.0329950i
\(99\) 0 0
\(100\) −2630.03 1077.10i −0.263003 0.107710i
\(101\) 4643.04 + 8041.97i 0.455155 + 0.788352i 0.998697 0.0510303i \(-0.0162505\pi\)
−0.543542 + 0.839382i \(0.682917\pi\)
\(102\) 0 0
\(103\) 9792.48 + 5653.69i 0.923035 + 0.532915i 0.884602 0.466346i \(-0.154430\pi\)
0.0384332 + 0.999261i \(0.487763\pi\)
\(104\) 1665.58 833.824i 0.153993 0.0770917i
\(105\) 0 0
\(106\) 1172.48 + 3431.48i 0.104351 + 0.305401i
\(107\) 6261.61i 0.546913i 0.961884 + 0.273456i \(0.0881669\pi\)
−0.961884 + 0.273456i \(0.911833\pi\)
\(108\) 0 0
\(109\) 3452.85 0.290620 0.145310 0.989386i \(-0.453582\pi\)
0.145310 + 0.989386i \(0.453582\pi\)
\(110\) −5425.67 + 1853.87i −0.448403 + 0.153212i
\(111\) 0 0
\(112\) −3044.40 11009.1i −0.242697 0.877641i
\(113\) −1272.55 + 2204.13i −0.0996597 + 0.172616i −0.911544 0.411203i \(-0.865109\pi\)
0.811884 + 0.583819i \(0.198442\pi\)
\(114\) 0 0
\(115\) −7096.79 + 4097.33i −0.536619 + 0.309817i
\(116\) −10726.1 4392.75i −0.797122 0.326453i
\(117\) 0 0
\(118\) 3493.59 17748.7i 0.250904 1.27469i
\(119\) −15566.1 + 8987.07i −1.09922 + 0.634636i
\(120\) 0 0
\(121\) −5024.12 + 8702.04i −0.343154 + 0.594361i
\(122\) −6916.39 + 7918.50i −0.464687 + 0.532014i
\(123\) 0 0
\(124\) 19971.6 2710.54i 1.29888 0.176284i
\(125\) 16976.5 1.08650
\(126\) 0 0
\(127\) 530.060i 0.0328638i 0.999865 + 0.0164319i \(0.00523067\pi\)
−0.999865 + 0.0164319i \(0.994769\pi\)
\(128\) 12165.9 10973.9i 0.742545 0.669796i
\(129\) 0 0
\(130\) −1619.82 + 1854.51i −0.0958471 + 0.109734i
\(131\) −802.198 463.149i −0.0467454 0.0269885i 0.476445 0.879204i \(-0.341925\pi\)
−0.523191 + 0.852216i \(0.675258\pi\)
\(132\) 0 0
\(133\) −14383.7 24913.2i −0.813142 1.40840i
\(134\) −52.3769 + 266.094i −0.00291696 + 0.0148192i
\(135\) 0 0
\(136\) −21522.3 14194.9i −1.16362 0.767456i
\(137\) 834.113 + 1444.73i 0.0444410 + 0.0769741i 0.887390 0.461019i \(-0.152516\pi\)
−0.842949 + 0.537993i \(0.819183\pi\)
\(138\) 0 0
\(139\) −717.766 414.402i −0.0371495 0.0214483i 0.481310 0.876550i \(-0.340161\pi\)
−0.518460 + 0.855102i \(0.673494\pi\)
\(140\) 9239.93 + 11942.6i 0.471425 + 0.609316i
\(141\) 0 0
\(142\) 4977.62 1700.77i 0.246857 0.0843470i
\(143\) 1972.36i 0.0964525i
\(144\) 0 0
\(145\) 15322.3 0.728768
\(146\) −12248.7 35848.0i −0.574625 1.68174i
\(147\) 0 0
\(148\) 17742.2 13727.1i 0.810000 0.626693i
\(149\) 1561.38 2704.39i 0.0703292 0.121814i −0.828716 0.559669i \(-0.810928\pi\)
0.899046 + 0.437855i \(0.144262\pi\)
\(150\) 0 0
\(151\) 7932.37 4579.76i 0.347896 0.200858i −0.315862 0.948805i \(-0.602294\pi\)
0.663758 + 0.747947i \(0.268960\pi\)
\(152\) 22718.7 34446.1i 0.983322 1.49091i
\(153\) 0 0
\(154\) −11867.4 2335.94i −0.500397 0.0984963i
\(155\) −23073.9 + 13321.7i −0.960411 + 0.554494i
\(156\) 0 0
\(157\) −10551.8 + 18276.3i −0.428084 + 0.741463i −0.996703 0.0811381i \(-0.974145\pi\)
0.568619 + 0.822601i \(0.307478\pi\)
\(158\) 13163.1 + 11497.3i 0.527285 + 0.460556i
\(159\) 0 0
\(160\) −9384.91 + 19519.9i −0.366598 + 0.762497i
\(161\) −17286.7 −0.666898
\(162\) 0 0
\(163\) 42771.0i 1.60981i 0.593405 + 0.804904i \(0.297783\pi\)
−0.593405 + 0.804904i \(0.702217\pi\)
\(164\) 3331.69 + 24548.2i 0.123873 + 0.912710i
\(165\) 0 0
\(166\) −2295.66 2005.14i −0.0833091 0.0727661i
\(167\) 9568.12 + 5524.16i 0.343079 + 0.198077i 0.661633 0.749828i \(-0.269864\pi\)
−0.318554 + 0.947905i \(0.603197\pi\)
\(168\) 0 0
\(169\) 13857.0 + 24001.0i 0.485172 + 0.840342i
\(170\) 33440.6 + 6582.32i 1.15711 + 0.227762i
\(171\) 0 0
\(172\) −11349.9 + 27713.9i −0.383651 + 0.936787i
\(173\) −10967.8 18996.8i −0.366461 0.634729i 0.622549 0.782581i \(-0.286097\pi\)
−0.989009 + 0.147852i \(0.952764\pi\)
\(174\) 0 0
\(175\) 6863.66 + 3962.73i 0.224119 + 0.129395i
\(176\) −4624.06 16721.5i −0.149279 0.539821i
\(177\) 0 0
\(178\) 10454.4 + 30596.8i 0.329960 + 0.965687i
\(179\) 11479.2i 0.358265i 0.983825 + 0.179133i \(0.0573291\pi\)
−0.983825 + 0.179133i \(0.942671\pi\)
\(180\) 0 0
\(181\) 45472.2 1.38800 0.693999 0.719976i \(-0.255847\pi\)
0.693999 + 0.719976i \(0.255847\pi\)
\(182\) −4915.25 + 1679.46i −0.148389 + 0.0507023i
\(183\) 0 0
\(184\) −11100.0 22172.5i −0.327858 0.654905i
\(185\) −14827.4 + 25681.7i −0.433232 + 0.750379i
\(186\) 0 0
\(187\) −23642.9 + 13650.2i −0.676111 + 0.390353i
\(188\) −25281.2 + 61730.8i −0.715290 + 1.74657i
\(189\) 0 0
\(190\) −10534.9 + 53521.2i −0.291825 + 1.48258i
\(191\) 60657.0 35020.3i 1.66270 0.959961i 0.691283 0.722584i \(-0.257046\pi\)
0.971418 0.237376i \(-0.0762875\pi\)
\(192\) 0 0
\(193\) 17426.4 30183.5i 0.467836 0.810316i −0.531488 0.847066i \(-0.678367\pi\)
0.999325 + 0.0367497i \(0.0117004\pi\)
\(194\) −17539.2 + 20080.4i −0.466021 + 0.533542i
\(195\) 0 0
\(196\) −882.655 6503.50i −0.0229762 0.169291i
\(197\) 30858.0 0.795124 0.397562 0.917575i \(-0.369856\pi\)
0.397562 + 0.917575i \(0.369856\pi\)
\(198\) 0 0
\(199\) 34262.5i 0.865192i −0.901588 0.432596i \(-0.857598\pi\)
0.901588 0.432596i \(-0.142402\pi\)
\(200\) −675.504 + 11348.1i −0.0168876 + 0.283702i
\(201\) 0 0
\(202\) 24435.1 27975.4i 0.598840 0.685605i
\(203\) 27992.1 + 16161.2i 0.679272 + 0.392178i
\(204\) 0 0
\(205\) −16374.5 28361.5i −0.389638 0.674872i
\(206\) 8735.19 44378.0i 0.205844 1.04576i
\(207\) 0 0
\(208\) −5310.28 5226.07i −0.122741 0.120795i
\(209\) −21847.0 37840.1i −0.500149 0.866283i
\(210\) 0 0
\(211\) −14989.6 8654.27i −0.336687 0.194386i 0.322119 0.946699i \(-0.395605\pi\)
−0.658806 + 0.752313i \(0.728938\pi\)
\(212\) 11472.3 8876.03i 0.255257 0.197491i
\(213\) 0 0
\(214\) 23701.1 8098.28i 0.517536 0.176834i
\(215\) 39589.7i 0.856457i
\(216\) 0 0
\(217\) −56204.3 −1.19358
\(218\) −4465.65 13069.5i −0.0939663 0.275009i
\(219\) 0 0
\(220\) 14034.3 + 18139.3i 0.289965 + 0.374779i
\(221\) −5862.10 + 10153.5i −0.120024 + 0.207888i
\(222\) 0 0
\(223\) 55484.8 32034.1i 1.11574 0.644174i 0.175432 0.984492i \(-0.443868\pi\)
0.940311 + 0.340317i \(0.110534\pi\)
\(224\) −37733.8 + 25761.9i −0.752028 + 0.513430i
\(225\) 0 0
\(226\) 9988.77 + 1966.15i 0.195567 + 0.0384946i
\(227\) −11857.8 + 6846.11i −0.230119 + 0.132859i −0.610627 0.791918i \(-0.709083\pi\)
0.380508 + 0.924778i \(0.375749\pi\)
\(228\) 0 0
\(229\) −32996.2 + 57151.0i −0.629205 + 1.08982i 0.358506 + 0.933527i \(0.383286\pi\)
−0.987711 + 0.156288i \(0.950047\pi\)
\(230\) 24687.4 + 21563.2i 0.466681 + 0.407622i
\(231\) 0 0
\(232\) −2754.91 + 46281.0i −0.0511838 + 0.859857i
\(233\) 63342.4 1.16676 0.583381 0.812198i \(-0.301729\pi\)
0.583381 + 0.812198i \(0.301729\pi\)
\(234\) 0 0
\(235\) 88183.3i 1.59680i
\(236\) −71699.9 + 9731.11i −1.28734 + 0.174718i
\(237\) 0 0
\(238\) 54149.3 + 47296.6i 0.955959 + 0.834980i
\(239\) −275.008 158.776i −0.00481448 0.00277964i 0.497591 0.867412i \(-0.334218\pi\)
−0.502405 + 0.864632i \(0.667551\pi\)
\(240\) 0 0
\(241\) −12752.6 22088.2i −0.219566 0.380300i 0.735109 0.677949i \(-0.237131\pi\)
−0.954675 + 0.297649i \(0.903798\pi\)
\(242\) 39436.3 + 7762.48i 0.673388 + 0.132547i
\(243\) 0 0
\(244\) 38917.8 + 15938.4i 0.653685 + 0.267710i
\(245\) 4338.05 + 7513.73i 0.0722708 + 0.125177i
\(246\) 0 0
\(247\) −16250.4 9382.19i −0.266361 0.153784i
\(248\) −36089.5 72089.6i −0.586783 1.17211i
\(249\) 0 0
\(250\) −21956.1 64258.6i −0.351298 1.02814i
\(251\) 40987.7i 0.650588i −0.945613 0.325294i \(-0.894537\pi\)
0.945613 0.325294i \(-0.105463\pi\)
\(252\) 0 0
\(253\) −26256.3 −0.410197
\(254\) 2006.35 685.539i 0.0310986 0.0106259i
\(255\) 0 0
\(256\) −57272.3 31856.6i −0.873907 0.486094i
\(257\) 15479.1 26810.5i 0.234357 0.405919i −0.724728 0.689035i \(-0.758035\pi\)
0.959086 + 0.283116i \(0.0913681\pi\)
\(258\) 0 0
\(259\) −54175.6 + 31278.3i −0.807615 + 0.466277i
\(260\) 9114.52 + 3732.76i 0.134830 + 0.0552183i
\(261\) 0 0
\(262\) −715.585 + 3635.44i −0.0104246 + 0.0529607i
\(263\) 13311.8 7685.54i 0.192453 0.111113i −0.400678 0.916219i \(-0.631225\pi\)
0.593130 + 0.805107i \(0.297892\pi\)
\(264\) 0 0
\(265\) −9587.47 + 16606.0i −0.136525 + 0.236468i
\(266\) −75697.5 + 86665.1i −1.06984 + 1.22485i
\(267\) 0 0
\(268\) 1074.94 145.891i 0.0149664 0.00203124i
\(269\) −76105.5 −1.05175 −0.525873 0.850563i \(-0.676261\pi\)
−0.525873 + 0.850563i \(0.676261\pi\)
\(270\) 0 0
\(271\) 78076.4i 1.06312i −0.847021 0.531559i \(-0.821606\pi\)
0.847021 0.531559i \(-0.178394\pi\)
\(272\) −25894.4 + 99823.5i −0.349999 + 1.34926i
\(273\) 0 0
\(274\) 4389.72 5025.74i 0.0584704 0.0669420i
\(275\) 10425.0 + 6018.90i 0.137852 + 0.0795887i
\(276\) 0 0
\(277\) −2369.97 4104.90i −0.0308875 0.0534987i 0.850168 0.526511i \(-0.176500\pi\)
−0.881056 + 0.473012i \(0.843167\pi\)
\(278\) −640.269 + 3252.80i −0.00828463 + 0.0420890i
\(279\) 0 0
\(280\) 33254.2 50420.1i 0.424161 0.643113i
\(281\) 21604.6 + 37420.3i 0.273612 + 0.473909i 0.969784 0.243966i \(-0.0784484\pi\)
−0.696172 + 0.717875i \(0.745115\pi\)
\(282\) 0 0
\(283\) −31277.1 18057.8i −0.390529 0.225472i 0.291860 0.956461i \(-0.405726\pi\)
−0.682389 + 0.730989i \(0.739059\pi\)
\(284\) −12875.3 16641.3i −0.159633 0.206325i
\(285\) 0 0
\(286\) −7465.66 + 2550.90i −0.0912717 + 0.0311861i
\(287\) 69084.1i 0.838715i
\(288\) 0 0
\(289\) 78760.1 0.942997
\(290\) −19816.7 57997.3i −0.235633 0.689623i
\(291\) 0 0
\(292\) −119848. + 92726.2i −1.40562 + 1.08752i
\(293\) −48046.7 + 83219.2i −0.559665 + 0.969368i 0.437859 + 0.899043i \(0.355737\pi\)
−0.997524 + 0.0703243i \(0.977597\pi\)
\(294\) 0 0
\(295\) 82837.5 47826.3i 0.951882 0.549569i
\(296\) −74905.5 49403.4i −0.854929 0.563862i
\(297\) 0 0
\(298\) −12255.9 2412.40i −0.138010 0.0271654i
\(299\) −9765.10 + 5637.88i −0.109228 + 0.0630628i
\(300\) 0 0
\(301\) 41757.3 72325.7i 0.460892 0.798288i
\(302\) −27594.2 24102.1i −0.302554 0.264265i
\(303\) 0 0
\(304\) −159766. 41443.5i −1.72877 0.448445i
\(305\) −55594.6 −0.597631
\(306\) 0 0
\(307\) 140641.i 1.49223i 0.665817 + 0.746115i \(0.268083\pi\)
−0.665817 + 0.746115i \(0.731917\pi\)
\(308\) 6506.56 + 47941.0i 0.0685883 + 0.505366i
\(309\) 0 0
\(310\) 80266.6 + 70108.7i 0.835240 + 0.729539i
\(311\) −141564. 81731.8i −1.46363 0.845027i −0.464453 0.885598i \(-0.653749\pi\)
−0.999177 + 0.0405712i \(0.987082\pi\)
\(312\) 0 0
\(313\) 25645.1 + 44418.7i 0.261768 + 0.453395i 0.966712 0.255868i \(-0.0823611\pi\)
−0.704944 + 0.709263i \(0.749028\pi\)
\(314\) 82825.4 + 16303.0i 0.840049 + 0.165352i
\(315\) 0 0
\(316\) 26494.8 64694.1i 0.265330 0.647874i
\(317\) −14025.0 24292.0i −0.139568 0.241738i 0.787765 0.615975i \(-0.211238\pi\)
−0.927333 + 0.374237i \(0.877905\pi\)
\(318\) 0 0
\(319\) 42516.5 + 24546.9i 0.417808 + 0.241221i
\(320\) 86023.4 + 10277.7i 0.840073 + 0.100368i
\(321\) 0 0
\(322\) 22357.2 + 65432.5i 0.215629 + 0.631076i
\(323\) 259728.i 2.48951i
\(324\) 0 0
\(325\) 5169.63 0.0489433
\(326\) 161894. 55316.7i 1.52334 0.520500i
\(327\) 0 0
\(328\) 88609.7 44359.7i 0.823633 0.412327i
\(329\) 93011.4 161101.i 0.859299 1.48835i
\(330\) 0 0
\(331\) −97678.0 + 56394.4i −0.891540 + 0.514731i −0.874446 0.485123i \(-0.838775\pi\)
−0.0170938 + 0.999854i \(0.505441\pi\)
\(332\) −4620.72 + 11282.7i −0.0419212 + 0.102362i
\(333\) 0 0
\(334\) 8535.06 43361.2i 0.0765092 0.388695i
\(335\) −1241.92 + 717.024i −0.0110664 + 0.00638917i
\(336\) 0 0
\(337\) 10409.8 18030.3i 0.0916606 0.158761i −0.816549 0.577276i \(-0.804116\pi\)
0.908210 + 0.418515i \(0.137449\pi\)
\(338\) 72925.7 83491.7i 0.638333 0.730819i
\(339\) 0 0
\(340\) −18334.5 135091.i −0.158603 1.16860i
\(341\) −85367.4 −0.734147
\(342\) 0 0
\(343\) 125431.i 1.06615i
\(344\) 119580. + 7118.12i 1.01052 + 0.0601518i
\(345\) 0 0
\(346\) −57720.7 + 66083.7i −0.482147 + 0.552004i
\(347\) 139615. + 80606.6i 1.15950 + 0.669440i 0.951185 0.308621i \(-0.0998676\pi\)
0.208318 + 0.978061i \(0.433201\pi\)
\(348\) 0 0
\(349\) 110742. + 191811.i 0.909205 + 1.57479i 0.815171 + 0.579220i \(0.196643\pi\)
0.0940341 + 0.995569i \(0.470024\pi\)
\(350\) 6122.59 31105.0i 0.0499803 0.253919i
\(351\) 0 0
\(352\) −57312.9 + 39129.0i −0.462559 + 0.315801i
\(353\) 109395. + 189477.i 0.877904 + 1.52057i 0.853637 + 0.520869i \(0.174392\pi\)
0.0242676 + 0.999705i \(0.492275\pi\)
\(354\) 0 0
\(355\) 24088.2 + 13907.3i 0.191138 + 0.110354i
\(356\) 102292. 79143.2i 0.807130 0.624473i
\(357\) 0 0
\(358\) 43450.3 14846.3i 0.339021 0.115838i
\(359\) 924.606i 0.00717411i 0.999994 + 0.00358705i \(0.00114180\pi\)
−0.999994 + 0.00358705i \(0.998858\pi\)
\(360\) 0 0
\(361\) −285370. −2.18975
\(362\) −58810.2 172119.i −0.448782 1.31344i
\(363\) 0 0
\(364\) 12714.0 + 16432.9i 0.0959578 + 0.124025i
\(365\) 100158. 173479.i 0.751799 1.30215i
\(366\) 0 0
\(367\) 35332.0 20398.9i 0.262323 0.151452i −0.363071 0.931762i \(-0.618272\pi\)
0.625394 + 0.780309i \(0.284938\pi\)
\(368\) −69570.1 + 70691.2i −0.513721 + 0.521999i
\(369\) 0 0
\(370\) 116386. + 22908.9i 0.850150 + 0.167340i
\(371\) −35030.3 + 20224.8i −0.254505 + 0.146939i
\(372\) 0 0
\(373\) 117265. 203109.i 0.842851 1.45986i −0.0446228 0.999004i \(-0.514209\pi\)
0.887474 0.460858i \(-0.152458\pi\)
\(374\) 82246.1 + 71837.7i 0.587993 + 0.513581i
\(375\) 0 0
\(376\) 266357. + 15855.1i 1.88403 + 0.112149i
\(377\) 21083.4 0.148340
\(378\) 0 0
\(379\) 185553.i 1.29178i 0.763428 + 0.645892i \(0.223515\pi\)
−0.763428 + 0.645892i \(0.776485\pi\)
\(380\) 216210. 29344.1i 1.49730 0.203214i
\(381\) 0 0
\(382\) −211006. 184303.i −1.44600 1.26301i
\(383\) −52190.3 30132.1i −0.355789 0.205415i 0.311443 0.950265i \(-0.399188\pi\)
−0.667232 + 0.744850i \(0.732521\pi\)
\(384\) 0 0
\(385\) −31978.3 55388.1i −0.215742 0.373675i
\(386\) −136787. 26924.6i −0.918056 0.180707i
\(387\) 0 0
\(388\) 98691.0 + 40417.8i 0.655562 + 0.268479i
\(389\) −6004.66 10400.4i −0.0396816 0.0687306i 0.845502 0.533971i \(-0.179301\pi\)
−0.885184 + 0.465241i \(0.845968\pi\)
\(390\) 0 0
\(391\) 135164. + 78037.0i 0.884113 + 0.510443i
\(392\) −23475.1 + 11752.1i −0.152769 + 0.0764792i
\(393\) 0 0
\(394\) −39909.3 116802.i −0.257088 0.752415i
\(395\) 92416.5i 0.592318i
\(396\) 0 0
\(397\) 32276.3 0.204787 0.102394 0.994744i \(-0.467350\pi\)
0.102394 + 0.994744i \(0.467350\pi\)
\(398\) −129688. + 44312.4i −0.818719 + 0.279743i
\(399\) 0 0
\(400\) 43827.8 12119.9i 0.273924 0.0757491i
\(401\) −93863.1 + 162576.i −0.583722 + 1.01104i 0.411311 + 0.911495i \(0.365071\pi\)
−0.995033 + 0.0995418i \(0.968262\pi\)
\(402\) 0 0
\(403\) −31749.4 + 18330.5i −0.195490 + 0.112866i
\(404\) −137494. 56309.0i −0.842402 0.344997i
\(405\) 0 0
\(406\) 24969.8 126856.i 0.151483 0.769588i
\(407\) −82286.0 + 47507.9i −0.496749 + 0.286798i
\(408\) 0 0
\(409\) 67272.0 116518.i 0.402149 0.696543i −0.591836 0.806059i \(-0.701597\pi\)
0.993985 + 0.109515i \(0.0349299\pi\)
\(410\) −86174.8 + 98660.5i −0.512640 + 0.586916i
\(411\) 0 0
\(412\) −179275. + 24331.1i −1.05615 + 0.143340i
\(413\) 201779. 1.18298
\(414\) 0 0
\(415\) 16117.5i 0.0935841i
\(416\) −12913.5 + 26859.2i −0.0746205 + 0.155205i
\(417\) 0 0
\(418\) −114975. + 131634.i −0.658038 + 0.753380i
\(419\) −73320.7 42331.7i −0.417637 0.241123i 0.276429 0.961034i \(-0.410849\pi\)
−0.694066 + 0.719912i \(0.744182\pi\)
\(420\) 0 0
\(421\) 57849.8 + 100199.i 0.326391 + 0.565325i 0.981793 0.189955i \(-0.0608341\pi\)
−0.655402 + 0.755280i \(0.727501\pi\)
\(422\) −13371.2 + 67930.7i −0.0750837 + 0.381453i
\(423\) 0 0
\(424\) −48434.4 31944.6i −0.269415 0.177691i
\(425\) −35777.9 61969.1i −0.198078 0.343081i
\(426\) 0 0
\(427\) −101565. 58638.4i −0.557041 0.321608i
\(428\) −61306.3 79238.3i −0.334671 0.432561i
\(429\) 0 0
\(430\) −149853. + 51202.3i −0.810453 + 0.276919i
\(431\) 294896.i 1.58750i −0.608241 0.793752i \(-0.708125\pi\)
0.608241 0.793752i \(-0.291875\pi\)
\(432\) 0 0
\(433\) −151284. −0.806895 −0.403447 0.915003i \(-0.632188\pi\)
−0.403447 + 0.915003i \(0.632188\pi\)
\(434\) 72690.4 + 212742.i 0.385920 + 1.12947i
\(435\) 0 0
\(436\) −43694.6 + 33806.3i −0.229855 + 0.177838i
\(437\) −124897. + 216328.i −0.654017 + 1.13279i
\(438\) 0 0
\(439\) −17332.7 + 10007.1i −0.0899369 + 0.0519251i −0.544294 0.838895i \(-0.683202\pi\)
0.454357 + 0.890820i \(0.349869\pi\)
\(440\) 50509.0 76581.8i 0.260893 0.395567i
\(441\) 0 0
\(442\) 46013.9 + 9057.19i 0.235529 + 0.0463606i
\(443\) −33466.7 + 19322.0i −0.170532 + 0.0984567i −0.582837 0.812589i \(-0.698057\pi\)
0.412305 + 0.911046i \(0.364724\pi\)
\(444\) 0 0
\(445\) −85486.7 + 148067.i −0.431696 + 0.747720i
\(446\) −193014. 168587.i −0.970327 0.847530i
\(447\) 0 0
\(448\) 146314. + 109509.i 0.729005 + 0.545626i
\(449\) −79457.9 −0.394135 −0.197067 0.980390i \(-0.563142\pi\)
−0.197067 + 0.980390i \(0.563142\pi\)
\(450\) 0 0
\(451\) 104930.i 0.515878i
\(452\) −5476.55 40351.8i −0.0268059 0.197509i
\(453\) 0 0
\(454\) 41249.5 + 36029.3i 0.200128 + 0.174801i
\(455\) −23786.4 13733.1i −0.114896 0.0663354i
\(456\) 0 0
\(457\) 131776. + 228243.i 0.630963 + 1.09286i 0.987355 + 0.158524i \(0.0506735\pi\)
−0.356392 + 0.934337i \(0.615993\pi\)
\(458\) 259000. + 50980.5i 1.23472 + 0.243037i
\(459\) 0 0
\(460\) 49691.0 121334.i 0.234834 0.573411i
\(461\) −100305. 173733.i −0.471976 0.817487i 0.527510 0.849549i \(-0.323126\pi\)
−0.999486 + 0.0320624i \(0.989792\pi\)
\(462\) 0 0
\(463\) −205297. 118528.i −0.957679 0.552916i −0.0622210 0.998062i \(-0.519818\pi\)
−0.895458 + 0.445146i \(0.853152\pi\)
\(464\) 178743. 49428.5i 0.830220 0.229584i
\(465\) 0 0
\(466\) −81922.2 239760.i −0.377250 1.10409i
\(467\) 230464.i 1.05674i 0.849014 + 0.528371i \(0.177197\pi\)
−0.849014 + 0.528371i \(0.822803\pi\)
\(468\) 0 0
\(469\) −3025.13 −0.0137530
\(470\) −333787. + 114050.i −1.51103 + 0.516295i
\(471\) 0 0
\(472\) 129565. + 258809.i 0.581571 + 1.16170i
\(473\) 63424.1 109854.i 0.283486 0.491013i
\(474\) 0 0
\(475\) 99180.5 57261.9i 0.439581 0.253792i
\(476\) 108992. 266133.i 0.481039 1.17459i
\(477\) 0 0
\(478\) −245.315 + 1246.29i −0.00107366 + 0.00545461i
\(479\) −2079.74 + 1200.74i −0.00906438 + 0.00523332i −0.504525 0.863397i \(-0.668332\pi\)
0.495461 + 0.868630i \(0.334999\pi\)
\(480\) 0 0
\(481\) −20402.3 + 35337.7i −0.0881836 + 0.152739i
\(482\) −67113.8 + 76837.7i −0.288880 + 0.330735i
\(483\) 0 0
\(484\) −21621.7 159311.i −0.0922997 0.680074i
\(485\) −140981. −0.599347
\(486\) 0 0
\(487\) 405227.i 1.70860i −0.519781 0.854300i \(-0.673986\pi\)
0.519781 0.854300i \(-0.326014\pi\)
\(488\) 9995.75 167923.i 0.0419736 0.705132i
\(489\) 0 0
\(490\) 22830.0 26137.8i 0.0950855 0.108862i
\(491\) −111325. 64273.4i −0.461773 0.266605i 0.251016 0.967983i \(-0.419235\pi\)
−0.712790 + 0.701378i \(0.752569\pi\)
\(492\) 0 0
\(493\) −145913. 252729.i −0.600345 1.03983i
\(494\) −14495.9 + 73644.5i −0.0594006 + 0.301777i
\(495\) 0 0
\(496\) −226194. + 229839.i −0.919429 + 0.934244i
\(497\) 29337.5 + 50814.1i 0.118771 + 0.205717i
\(498\) 0 0
\(499\) −111377. 64303.6i −0.447296 0.258246i 0.259392 0.965772i \(-0.416478\pi\)
−0.706687 + 0.707526i \(0.749811\pi\)
\(500\) −214832. + 166214.i −0.859326 + 0.664857i
\(501\) 0 0
\(502\) −155144. + 53010.3i −0.615642 + 0.210355i
\(503\) 368128.i 1.45500i −0.686109 0.727499i \(-0.740683\pi\)
0.686109 0.727499i \(-0.259317\pi\)
\(504\) 0 0
\(505\) 196411. 0.770165
\(506\) 33957.9 + 99383.8i 0.132629 + 0.388163i
\(507\) 0 0
\(508\) −5189.73 6707.72i −0.0201102 0.0259925i
\(509\) −40698.4 + 70491.6i −0.157087 + 0.272083i −0.933817 0.357751i \(-0.883544\pi\)
0.776730 + 0.629834i \(0.216877\pi\)
\(510\) 0 0
\(511\) 365955. 211284.i 1.40148 0.809143i
\(512\) −46510.3 + 257985.i −0.177423 + 0.984135i
\(513\) 0 0
\(514\) −121501. 23915.8i −0.459890 0.0905230i
\(515\) 207123. 119582.i 0.780931 0.450871i
\(516\) 0 0
\(517\) 141273. 244692.i 0.528539 0.915457i
\(518\) 188460. + 164610.i 0.702358 + 0.613473i
\(519\) 0 0
\(520\) 2341.00 39327.4i 0.00865754 0.145442i
\(521\) 17832.5 0.0656956 0.0328478 0.999460i \(-0.489542\pi\)
0.0328478 + 0.999460i \(0.489542\pi\)
\(522\) 0 0
\(523\) 51996.2i 0.190094i −0.995473 0.0950470i \(-0.969700\pi\)
0.995473 0.0950470i \(-0.0303001\pi\)
\(524\) 14686.1 1993.20i 0.0534866 0.00725920i
\(525\) 0 0
\(526\) −46307.3 40447.0i −0.167370 0.146189i
\(527\) 439461. + 253723.i 1.58234 + 0.913562i
\(528\) 0 0
\(529\) −64868.3 112355.i −0.231804 0.401496i
\(530\) 75255.7 + 14813.0i 0.267909 + 0.0527342i
\(531\) 0 0
\(532\) 425941. + 174440.i 1.50497 + 0.616343i
\(533\) −22531.1 39025.1i −0.0793101 0.137369i
\(534\) 0 0
\(535\) 114697. + 66220.2i 0.400722 + 0.231357i
\(536\) −1942.47 3880.13i −0.00676122 0.0135057i
\(537\) 0 0
\(538\) 98429.0 + 288070.i 0.340062 + 0.995253i
\(539\) 27798.8i 0.0956862i
\(540\) 0 0
\(541\) −329819. −1.12689 −0.563444 0.826154i \(-0.690524\pi\)
−0.563444 + 0.826154i \(0.690524\pi\)
\(542\) −295530. + 100978.i −1.00601 + 0.343739i
\(543\) 0 0
\(544\) 411336. 31090.2i 1.38995 0.105057i
\(545\) 36515.9 63247.5i 0.122939 0.212936i
\(546\) 0 0
\(547\) −306032. + 176688.i −1.02280 + 0.590517i −0.914915 0.403646i \(-0.867743\pi\)
−0.107890 + 0.994163i \(0.534409\pi\)
\(548\) −24700.5 10115.8i −0.0822516 0.0336853i
\(549\) 0 0
\(550\) 9299.45 47244.6i 0.0307420 0.156181i
\(551\) 404489. 233532.i 1.33230 0.769206i
\(552\) 0 0
\(553\) −97476.3 + 168834.i −0.318749 + 0.552090i
\(554\) −12472.5 + 14279.6i −0.0406382 + 0.0465262i
\(555\) 0 0
\(556\) 13140.4 1783.42i 0.0425069 0.00576903i
\(557\) 381405. 1.22935 0.614676 0.788780i \(-0.289287\pi\)
0.614676 + 0.788780i \(0.289287\pi\)
\(558\) 0 0
\(559\) 54475.0i 0.174330i
\(560\) −233856. 60662.5i −0.745713 0.193439i
\(561\) 0 0
\(562\) 113700. 130173.i 0.359987 0.412144i
\(563\) 203807. + 117668.i 0.642988 + 0.371229i 0.785765 0.618526i \(-0.212270\pi\)
−0.142776 + 0.989755i \(0.545603\pi\)
\(564\) 0 0
\(565\) 26916.0 + 46619.9i 0.0843168 + 0.146041i
\(566\) −27900.1 + 141743.i −0.0870909 + 0.442454i
\(567\) 0 0
\(568\) −46337.9 + 70257.6i −0.143628 + 0.217769i
\(569\) −110971. 192208.i −0.342757 0.593673i 0.642186 0.766549i \(-0.278028\pi\)
−0.984944 + 0.172875i \(0.944694\pi\)
\(570\) 0 0
\(571\) −34588.3 19969.5i −0.106086 0.0612486i 0.446018 0.895024i \(-0.352842\pi\)
−0.552104 + 0.833775i \(0.686175\pi\)
\(572\) 19311.0 + 24959.5i 0.0590219 + 0.0762857i
\(573\) 0 0
\(574\) −261493. + 89348.1i −0.793664 + 0.271182i
\(575\) 68818.8i 0.208148i
\(576\) 0 0
\(577\) 511135. 1.53527 0.767634 0.640889i \(-0.221434\pi\)
0.767634 + 0.640889i \(0.221434\pi\)
\(578\) −101862. 298118.i −0.304900 0.892345i
\(579\) 0 0
\(580\) −193899. + 150018.i −0.576393 + 0.445953i
\(581\) 17000.0 29444.8i 0.0503612 0.0872281i
\(582\) 0 0
\(583\) −53206.7 + 30718.9i −0.156541 + 0.0903793i
\(584\) 505985. + 333719.i 1.48358 + 0.978486i
\(585\) 0 0
\(586\) 377137. + 74234.1i 1.09826 + 0.216176i
\(587\) −60509.5 + 34935.2i −0.175609 + 0.101388i −0.585228 0.810869i \(-0.698995\pi\)
0.409619 + 0.912257i \(0.365662\pi\)
\(588\) 0 0
\(589\) −406079. + 703350.i −1.17052 + 2.02741i
\(590\) −288165. 251697.i −0.827823 0.723060i
\(591\) 0 0
\(592\) −90121.9 + 347423.i −0.257150 + 0.991322i
\(593\) −206980. −0.588599 −0.294299 0.955713i \(-0.595086\pi\)
−0.294299 + 0.955713i \(0.595086\pi\)
\(594\) 0 0
\(595\) 380174.i 1.07386i
\(596\) 6719.53 + 49510.2i 0.0189167 + 0.139381i
\(597\) 0 0
\(598\) 33969.6 + 29670.7i 0.0949923 + 0.0829708i
\(599\) −241159. 139233.i −0.672123 0.388051i 0.124757 0.992187i \(-0.460185\pi\)
−0.796881 + 0.604137i \(0.793518\pi\)
\(600\) 0 0
\(601\) −213736. 370201.i −0.591737 1.02492i −0.993999 0.109393i \(-0.965109\pi\)
0.402262 0.915525i \(-0.368224\pi\)
\(602\) −327769. 64516.8i −0.904430 0.178024i
\(603\) 0 0
\(604\) −55541.6 + 135620.i −0.152246 + 0.371748i
\(605\) 106266. + 184058.i 0.290325 + 0.502857i
\(606\) 0 0
\(607\) 361479. + 208700.i 0.981082 + 0.566428i 0.902597 0.430487i \(-0.141658\pi\)
0.0784853 + 0.996915i \(0.474992\pi\)
\(608\) 49759.4 + 658337.i 0.134607 + 1.78091i
\(609\) 0 0
\(610\) 71901.8 + 210434.i 0.193232 + 0.565530i
\(611\) 121339.i 0.325026i
\(612\) 0 0
\(613\) −23327.6 −0.0620796 −0.0310398 0.999518i \(-0.509882\pi\)
−0.0310398 + 0.999518i \(0.509882\pi\)
\(614\) 532347. 181895.i 1.41208 0.482484i
\(615\) 0 0
\(616\) 173049. 86631.5i 0.456044 0.228305i
\(617\) 39385.7 68218.0i 0.103459 0.179196i −0.809649 0.586915i \(-0.800342\pi\)
0.913108 + 0.407719i \(0.133676\pi\)
\(618\) 0 0
\(619\) −382655. + 220926.i −0.998679 + 0.576587i −0.907857 0.419280i \(-0.862283\pi\)
−0.0908215 + 0.995867i \(0.528949\pi\)
\(620\) 161561. 394494.i 0.420293 1.02626i
\(621\) 0 0
\(622\) −126279. + 641545.i −0.326401 + 1.65824i
\(623\) −312348. + 180334.i −0.804753 + 0.464625i
\(624\) 0 0
\(625\) 124028. 214823.i 0.317512 0.549947i
\(626\) 134964. 154518.i 0.344404 0.394304i
\(627\) 0 0
\(628\) −45410.7 334591.i −0.115143 0.848390i
\(629\) 564798. 1.42755
\(630\) 0 0
\(631\) 211599.i 0.531440i −0.964050 0.265720i \(-0.914390\pi\)
0.964050 0.265720i \(-0.0856097\pi\)
\(632\) −279143. 16616.2i −0.698864 0.0416005i
\(633\) 0 0
\(634\) −73809.9 + 84504.1i −0.183627 + 0.210232i
\(635\) 9709.36 + 5605.70i 0.0240793 + 0.0139022i
\(636\) 0 0
\(637\) 5969.11 + 10338.8i 0.0147106 + 0.0254795i
\(638\) 37926.0 192678.i 0.0931743 0.473360i
\(639\) 0 0
\(640\) −72353.7 338903.i −0.176645 0.827401i
\(641\) −2552.74 4421.47i −0.00621284 0.0107610i 0.862902 0.505371i \(-0.168644\pi\)
−0.869115 + 0.494610i \(0.835311\pi\)
\(642\) 0 0
\(643\) 69127.8 + 39911.0i 0.167198 + 0.0965318i 0.581264 0.813715i \(-0.302558\pi\)
−0.414066 + 0.910247i \(0.635892\pi\)
\(644\) 218756. 169251.i 0.527459 0.408093i
\(645\) 0 0
\(646\) 983109. 335913.i 2.35579 0.804936i
\(647\) 531516.i 1.26972i 0.772628 + 0.634859i \(0.218942\pi\)
−0.772628 + 0.634859i \(0.781058\pi\)
\(648\) 0 0
\(649\) 306477. 0.727627
\(650\) −6686.01 19567.8i −0.0158249 0.0463143i
\(651\) 0 0
\(652\) −418763. 541251.i −0.985085 1.27322i
\(653\) −235615. + 408097.i −0.552556 + 0.957055i 0.445533 + 0.895265i \(0.353014\pi\)
−0.998089 + 0.0617897i \(0.980319\pi\)
\(654\) 0 0
\(655\) −16967.4 + 9796.15i −0.0395488 + 0.0228335i
\(656\) −282509. 278029.i −0.656485 0.646074i
\(657\) 0 0
\(658\) −730082. 143707.i −1.68624 0.331913i
\(659\) −309469. + 178672.i −0.712601 + 0.411420i −0.812023 0.583625i \(-0.801634\pi\)
0.0994224 + 0.995045i \(0.468300\pi\)
\(660\) 0 0
\(661\) 282792. 489809.i 0.647237 1.12105i −0.336543 0.941668i \(-0.609258\pi\)
0.983780 0.179380i \(-0.0574090\pi\)
\(662\) 339790. + 296789.i 0.775345 + 0.677223i
\(663\) 0 0
\(664\) 48682.8 + 2897.89i 0.110418 + 0.00657272i
\(665\) −608463. −1.37591
\(666\) 0 0
\(667\) 280664.i 0.630864i
\(668\) −175167. + 23773.7i −0.392554 + 0.0532775i
\(669\) 0 0
\(670\) 4320.25 + 3773.51i 0.00962408 + 0.00840613i
\(671\) −154264. 89064.5i −0.342626 0.197815i
\(672\) 0 0
\(673\) 158119. + 273870.i 0.349103 + 0.604663i 0.986090 0.166211i \(-0.0531532\pi\)
−0.636988 + 0.770874i \(0.719820\pi\)
\(674\) −81710.5 16083.6i −0.179870 0.0354049i
\(675\) 0 0
\(676\) −410345. 168052.i −0.897957 0.367749i
\(677\) −300914. 521198.i −0.656545 1.13717i −0.981504 0.191441i \(-0.938684\pi\)
0.324959 0.945728i \(-0.394649\pi\)
\(678\) 0 0
\(679\) −257556. 148700.i −0.558641 0.322531i
\(680\) −487625. + 244115.i −1.05455 + 0.527929i
\(681\) 0 0
\(682\) 110408. + 323128.i 0.237372 + 0.694713i
\(683\) 385277.i 0.825909i −0.910752 0.412955i \(-0.864497\pi\)
0.910752 0.412955i \(-0.135503\pi\)
\(684\) 0 0
\(685\) 35285.0 0.0751984
\(686\) 474775. 162223.i 1.00888 0.344718i
\(687\) 0 0
\(688\) −127713. 461835.i −0.269810 0.975685i
\(689\) −13192.2 + 22849.6i −0.0277895 + 0.0481328i
\(690\) 0 0
\(691\) 397767. 229651.i 0.833053 0.480963i −0.0218438 0.999761i \(-0.506954\pi\)
0.854897 + 0.518798i \(0.173620\pi\)
\(692\) 324788. + 133014.i 0.678247 + 0.277769i
\(693\) 0 0
\(694\) 124541. 632712.i 0.258578 1.31367i
\(695\) −15181.6 + 8765.10i −0.0314303 + 0.0181463i
\(696\) 0 0
\(697\) −311866. + 540168.i −0.641952 + 1.11189i
\(698\) 582807. 667248.i 1.19623 1.36955i
\(699\) 0 0
\(700\) −125655. + 17054.0i −0.256440 + 0.0348040i
\(701\) 127011. 0.258467 0.129234 0.991614i \(-0.458748\pi\)
0.129234 + 0.991614i \(0.458748\pi\)
\(702\) 0 0
\(703\) 903950.i 1.82908i
\(704\) 222233. + 166331.i 0.448398 + 0.335605i
\(705\) 0 0
\(706\) 575716. 659130.i 1.15504 1.32240i
\(707\) 358820. + 207165.i 0.717857 + 0.414455i
\(708\) 0 0
\(709\) −247408. 428523.i −0.492177 0.852475i 0.507783 0.861485i \(-0.330465\pi\)
−0.999959 + 0.00901014i \(0.997132\pi\)
\(710\) 21487.4 109164.i 0.0426253 0.216552i
\(711\) 0 0
\(712\) −431865. 284834.i −0.851900 0.561864i
\(713\) 244018. + 422652.i 0.480002 + 0.831388i
\(714\) 0 0
\(715\) −36128.6 20858.8i −0.0706706 0.0408017i
\(716\) −112391. 145265.i −0.219232 0.283357i
\(717\) 0 0
\(718\) 3499.77 1195.82i 0.00678876 0.00231961i
\(719\) 614613.i 1.18890i 0.804134 + 0.594448i \(0.202629\pi\)
−0.804134 + 0.594448i \(0.797371\pi\)
\(720\) 0 0
\(721\) 504518. 0.970523
\(722\) 369076. + 1.08017e6i 0.708013 + 2.07213i
\(723\) 0 0
\(724\) −575434. + 445210.i −1.09779 + 0.849353i
\(725\) −64338.5 + 111438.i −0.122404 + 0.212010i
\(726\) 0 0
\(727\) 286999. 165699.i 0.543014 0.313509i −0.203286 0.979119i \(-0.565162\pi\)
0.746299 + 0.665610i \(0.231829\pi\)
\(728\) 45757.4 69377.4i 0.0863373 0.130905i
\(729\) 0 0
\(730\) −786182. 154749.i −1.47529 0.290390i
\(731\) −652999. + 377009.i −1.22202 + 0.705532i
\(732\) 0 0
\(733\) 25808.4 44701.5i 0.0480345 0.0831982i −0.841008 0.541022i \(-0.818038\pi\)
0.889043 + 0.457824i \(0.151371\pi\)
\(734\) −122909. 107354.i −0.228134 0.199263i
\(735\) 0 0
\(736\) 357553. + 171906.i 0.660062 + 0.317349i
\(737\) −4594.79 −0.00845923
\(738\) 0 0
\(739\) 228968.i 0.419263i 0.977780 + 0.209631i \(0.0672264\pi\)
−0.977780 + 0.209631i \(0.932774\pi\)
\(740\) −63810.8 470165.i −0.116528 0.858592i
\(741\) 0 0
\(742\) 121859. + 106438.i 0.221335 + 0.193325i
\(743\) −910009. 525394.i −1.64842 0.951716i −0.977700 0.210005i \(-0.932652\pi\)
−0.670720 0.741711i \(1.26599\pi\)
\(744\) 0 0
\(745\) −33025.0 57201.0i −0.0595018 0.103060i
\(746\) −920459. 181179.i −1.65397 0.325560i
\(747\) 0 0
\(748\) 165545. 404223.i 0.295878 0.722466i
\(749\) 139692. + 241953.i 0.249004 + 0.431288i
\(750\) 0 0
\(751\) 233295. + 134693.i 0.413643 + 0.238817i 0.692354 0.721558i \(-0.256574\pi\)
−0.278711 + 0.960375i \(0.589907\pi\)
\(752\) −284472. 1.02870e6i −0.503041 1.81909i
\(753\) 0 0
\(754\) −27267.6 79803.5i −0.0479627 0.140372i
\(755\) 193735.i 0.339870i
\(756\) 0 0
\(757\) −476176. −0.830952 −0.415476 0.909604i \(-0.636385\pi\)
−0.415476 + 0.909604i \(0.636385\pi\)
\(758\) 702346. 239980.i 1.22240 0.417674i
\(759\) 0 0
\(760\) −390701. 780436.i −0.676422 1.35117i
\(761\) 242197. 419498.i 0.418215 0.724370i −0.577545 0.816359i \(-0.695989\pi\)
0.995760 + 0.0919890i \(0.0293225\pi\)
\(762\) 0 0
\(763\) 133421. 77030.4i 0.229178 0.132316i
\(764\) −424714. + 1.03705e6i −0.727628 + 1.77670i
\(765\) 0 0
\(766\) −46555.3 + 236518.i −0.0793436 + 0.403095i
\(767\) 113983. 65808.4i 0.193754 0.111864i
\(768\) 0 0
\(769\) −251061. + 434851.i −0.424549 + 0.735340i −0.996378 0.0850327i \(-0.972901\pi\)
0.571830 + 0.820372i \(0.306234\pi\)
\(770\) −168293. + 192677.i −0.283848 + 0.324974i
\(771\) 0 0
\(772\) 74996.1 + 552580.i 0.125836 + 0.927172i
\(773\) −435529. −0.728884 −0.364442 0.931226i \(-0.618740\pi\)
−0.364442 + 0.931226i \(0.618740\pi\)
\(774\) 0 0
\(775\) 223752.i 0.372531i
\(776\) 25348.1 425833.i 0.0420941 0.707157i
\(777\) 0 0