Properties

Label 108.5.f.a.19.9
Level 108
Weight 5
Character 108.19
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 19.9
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.9

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.996234 0.0867102i \(-0.0276354\pi\)
−0.573210 + 0.819409i \(0.694302\pi\)
\(6\) 0 0
\(7\) 38.6407 + 22.3092i 0.788586 + 0.455290i 0.839464 0.543415i \(-0.182869\pi\)
−0.0508787 + 0.998705i \(0.516202\pi\)
\(8\) 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 0.722516 0.691354i \(-0.242985\pi\)
−0.237472 + 0.971394i \(0.576319\pi\)
\(12\) 0 0
\(13\) 14.5519 + 25.2046i 0.0861058 + 0.149140i 0.905862 0.423573i \(-0.139224\pi\)
−0.819756 + 0.572713i \(0.805891\pi\)
\(14\) −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 \(0.351399\pi\)
−0.450070 + 0.892993i \(0.648601\pi\)
\(20\) 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 −0.782403 0.622773i \(-0.786006\pi\)
0.148136 + 0.988967i \(0.452673\pi\)
\(24\) 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 −0.566243 0.824238i \(-0.691604\pi\)
0.996933 + 0.0782617i \(0.0249370\pi\)
\(30\) 0 0
\(31\) −1090.90 + 629.833i −1.13517 + 0.655393i −0.945231 0.326402i \(-0.894164\pi\)
−0.189944 + 0.981795i \(0.560831\pi\)
\(32\) −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 0.998988 0.0449815i \(-0.0143229\pi\)
−0.538449 + 0.842658i \(0.680990\pi\)
\(42\) 0 0
\(43\) 1620.98 + 935.875i 0.876681 + 0.506152i 0.869563 0.493823i \(-0.164401\pi\)
0.00711825 + 0.999975i \(0.497734\pi\)
\(44\) −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 0.982679 + 0.185316i \(0.0593310\pi\)
0.651828 + 0.758367i \(0.274002\pi\)
\(48\) 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 0.182397 0.983225i \(-0.441614\pi\)
0.942696 + 0.333652i \(0.108281\pi\)
\(60\) 0 0
\(61\) −1314.22 + 2276.30i −0.353190 + 0.611743i −0.986806 0.161904i \(-0.948236\pi\)
0.633617 + 0.773647i \(0.281570\pi\)
\(62\) −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 −0.506526 0.862225i \(-0.669070\pi\)
0.493446 + 0.869777i \(0.335737\pi\)
\(68\) 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 \(-0.958363\pi\)
0.991457 0.130434i \(-0.0416372\pi\)
\(72\) 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 0.165213 0.986258i \(-0.447169\pi\)
−0.771518 + 0.636207i \(0.780502\pi\)
\(80\) −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 0.547132 0.837047i \(-0.315720\pi\)
−0.451338 + 0.892353i \(0.649053\pi\)
\(84\) 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 −0.986981 0.160834i \(-0.948582\pi\)
0.632777 + 0.774334i \(0.281915\pi\)
\(98\) 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 −0.543542 0.839382i \(-0.682917\pi\)
0.998697 + 0.0510303i \(0.0162505\pi\)
\(102\) 0 0
\(103\) 9792.48 5653.69i 0.923035 0.532915i 0.0384332 0.999261i \(-0.487763\pi\)
0.884602 + 0.466346i \(0.154430\pi\)
\(104\) 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 \(-0.911833\pi\)
0.961884 0.273456i \(-0.0881669\pi\)
\(108\) 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 0.811884 0.583819i \(-0.198442\pi\)
−0.911544 + 0.411203i \(0.865109\pi\)
\(114\) 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 \(-0.994769\pi\)
0.999865 0.0164319i \(-0.00523067\pi\)
\(128\) 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 −0.523191 0.852216i \(-0.675258\pi\)
0.476445 + 0.879204i \(0.341925\pi\)
\(132\) 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 −0.842949 0.537993i \(-0.819183\pi\)
0.887390 + 0.461019i \(0.152516\pi\)
\(138\) 0 0
\(139\) −717.766 + 414.402i −0.0371495 + 0.0214483i −0.518460 0.855102i \(-0.673494\pi\)
0.481310 + 0.876550i \(0.340161\pi\)
\(140\) 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 0.899046 0.437855i \(-0.144262\pi\)
−0.828716 + 0.559669i \(0.810928\pi\)
\(150\) 0 0
\(151\) 7932.37 + 4579.76i 0.347896 + 0.200858i 0.663758 0.747947i \(-0.268960\pi\)
−0.315862 + 0.948805i \(0.602294\pi\)
\(152\) 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 0.568619 0.822601i \(-0.307478\pi\)
−0.996703 + 0.0811381i \(0.974145\pi\)
\(158\) 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 \(-0.702217\pi\)
0.593405 0.804904i \(-0.297783\pi\)
\(164\) 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 −0.318554 0.947905i \(-0.603197\pi\)
0.661633 + 0.749828i \(0.269864\pi\)
\(168\) 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 −0.989009 0.147852i \(-0.952764\pi\)
0.622549 + 0.782581i \(0.286097\pi\)
\(174\) 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 \(-0.942671\pi\)
0.983825 0.179133i \(-0.0573291\pi\)
\(180\) 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 0.971418 + 0.237376i \(0.0762875\pi\)
0.691283 + 0.722584i \(0.257046\pi\)
\(192\) 0 0
\(193\) 17426.4 + 30183.5i 0.467836 + 0.810316i 0.999325 0.0367497i \(-0.0117004\pi\)
−0.531488 + 0.847066i \(0.678367\pi\)
\(194\) −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 \(0.142402\pi\)
−0.901588 + 0.432596i \(0.857598\pi\)
\(200\) −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 −0.658806 0.752313i \(-0.728938\pi\)
0.322119 + 0.946699i \(0.395605\pi\)
\(212\) 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 0.940311 0.340317i \(-0.110534\pi\)
0.175432 + 0.984492i \(0.443868\pi\)
\(224\) −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 0.380508 0.924778i \(-0.375749\pi\)
−0.610627 + 0.791918i \(0.709083\pi\)
\(228\) 0 0
\(229\) −32996.2 57151.0i −0.629205 1.08982i −0.987711 0.156288i \(-0.950047\pi\)
0.358506 0.933527i \(-0.383286\pi\)
\(230\) 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 −0.502405 0.864632i \(-0.667551\pi\)
0.497591 + 0.867412i \(0.334218\pi\)
\(240\) 0 0
\(241\) −12752.6 + 22088.2i −0.219566 + 0.380300i −0.954675 0.297649i \(-0.903798\pi\)
0.735109 + 0.677949i \(0.237131\pi\)
\(242\) 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 \(0.105463\pi\)
−0.945613 + 0.325294i \(0.894537\pi\)
\(252\) 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 0.959086 0.283116i \(-0.0913681\pi\)
−0.724728 + 0.689035i \(0.758035\pi\)
\(258\) 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 0.593130 0.805107i \(-0.297892\pi\)
−0.400678 + 0.916219i \(0.631225\pi\)
\(264\) 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 \(0.178394\pi\)
−0.847021 + 0.531559i \(0.821606\pi\)
\(272\) −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 −0.881056 0.473012i \(-0.843167\pi\)
0.850168 + 0.526511i \(0.176500\pi\)
\(278\) −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 −0.696172 0.717875i \(-0.745115\pi\)
0.969784 + 0.243966i \(0.0784484\pi\)
\(282\) 0 0
\(283\) −31277.1 + 18057.8i −0.390529 + 0.225472i −0.682389 0.730989i \(-0.739059\pi\)
0.291860 + 0.956461i \(0.405726\pi\)
\(284\) −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 −0.997524 0.0703243i \(-0.977597\pi\)
0.437859 0.899043i \(-0.355737\pi\)
\(294\) 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 \(-0.731917\pi\)
0.665817 0.746115i \(-0.268083\pi\)
\(308\) 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 −0.999177 0.0405712i \(-0.987082\pi\)
−0.464453 + 0.885598i \(0.653749\pi\)
\(312\) 0 0
\(313\) 25645.1 44418.7i 0.261768 0.453395i −0.704944 0.709263i \(-0.749028\pi\)
0.966712 + 0.255868i \(0.0823611\pi\)
\(314\) 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 −0.927333 0.374237i \(-0.877905\pi\)
0.787765 + 0.615975i \(0.211238\pi\)
\(318\) 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 −0.0170938 0.999854i \(-0.505441\pi\)
−0.874446 + 0.485123i \(0.838775\pi\)
\(332\) −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 0.908210 0.418515i \(-0.137449\pi\)
−0.816549 + 0.577276i \(0.804116\pi\)
\(338\) 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 0.208318 0.978061i \(-0.433201\pi\)
0.951185 + 0.308621i \(0.0998676\pi\)
\(348\) 0 0
\(349\) 110742. 191811.i 0.909205 1.57479i 0.0940341 0.995569i \(-0.470024\pi\)
0.815171 0.579220i \(-0.196643\pi\)
\(350\) 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 0.0242676 0.999705i \(-0.492275\pi\)
0.853637 0.520869i \(-0.174392\pi\)
\(354\) 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 \(-0.998858\pi\)
0.999994 0.00358705i \(-0.00114180\pi\)
\(360\) 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 0.625394 0.780309i \(-0.284938\pi\)
−0.363071 + 0.931762i \(0.618272\pi\)
\(368\) −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 0.887474 + 0.460858i \(0.152458\pi\)
−0.0446228 + 0.999004i \(0.514209\pi\)
\(374\) 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 \(-0.776485\pi\)
0.763428 0.645892i \(-0.223515\pi\)
\(380\) 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 −0.667232 0.744850i \(-0.732521\pi\)
0.311443 + 0.950265i \(0.399188\pi\)
\(384\) 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 −0.885184 0.465241i \(-0.845968\pi\)
0.845502 + 0.533971i \(0.179301\pi\)
\(390\) 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 −0.995033 0.0995418i \(-0.968262\pi\)
0.411311 0.911495i \(-0.365071\pi\)
\(402\) 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 0.993985 0.109515i \(-0.0349299\pi\)
−0.591836 + 0.806059i \(0.701597\pi\)
\(410\) −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 −0.694066 0.719912i \(-0.744182\pi\)
0.276429 + 0.961034i \(0.410849\pi\)
\(420\) 0 0
\(421\) 57849.8 100199.i 0.326391 0.565325i −0.655402 0.755280i \(-0.727501\pi\)
0.981793 + 0.189955i \(0.0608341\pi\)
\(422\) −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 \(0.291875\pi\)
−0.608241 + 0.793752i \(0.708125\pi\)
\(432\) 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 0.454357 0.890820i \(-0.349869\pi\)
−0.544294 + 0.838895i \(0.683202\pi\)
\(440\) 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 0.412305 0.911046i \(-0.364724\pi\)
−0.582837 + 0.812589i \(0.698057\pi\)
\(444\) 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 −0.356392 0.934337i \(-0.615993\pi\)
0.987355 0.158524i \(-0.0506735\pi\)
\(458\) 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 −0.999486 0.0320624i \(-0.989792\pi\)
0.527510 + 0.849549i \(0.323126\pi\)
\(462\) 0 0
\(463\) −205297. + 118528.i −0.957679 + 0.552916i −0.895458 0.445146i \(-0.853152\pi\)
−0.0622210 + 0.998062i \(0.519818\pi\)
\(464\) 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 \(-0.822803\pi\)
0.849014 0.528371i \(-0.177197\pi\)
\(468\) 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 0.495461 0.868630i \(-0.334999\pi\)
−0.504525 + 0.863397i \(0.668332\pi\)
\(480\) 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 \(0.326014\pi\)
−0.519781 + 0.854300i \(0.673986\pi\)
\(488\) 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 −0.712790 0.701378i \(-0.752569\pi\)
0.251016 + 0.967983i \(0.419235\pi\)
\(492\) 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 −0.706687 0.707526i \(-0.749811\pi\)
0.259392 + 0.965772i \(0.416478\pi\)
\(500\) −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 \(0.259317\pi\)
−0.686109 + 0.727499i \(0.740683\pi\)
\(504\) 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 0.776730 0.629834i \(-0.216877\pi\)
−0.933817 + 0.357751i \(0.883544\pi\)
\(510\) 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 \(0.0303001\pi\)
−0.995473 + 0.0950470i \(0.969700\pi\)
\(524\) 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 −0.107890 0.994163i \(-0.534409\pi\)
−0.914915 + 0.403646i \(0.867743\pi\)
\(548\) −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 −0.142776 0.989755i \(-0.545603\pi\)
0.785765 + 0.618526i \(0.212270\pi\)
\(564\) 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 −0.984944 0.172875i \(-0.944694\pi\)
0.642186 + 0.766549i \(0.278028\pi\)
\(570\) 0 0
\(571\) −34588.3 + 19969.5i −0.106086 + 0.0612486i −0.552104 0.833775i \(-0.686175\pi\)
0.446018 + 0.895024i \(0.352842\pi\)
\(572\) 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 0.409619 0.912257i \(-0.365662\pi\)
−0.585228 + 0.810869i \(0.698995\pi\)
\(588\) 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 −0.796881 0.604137i \(-0.793518\pi\)
0.124757 + 0.992187i \(0.460185\pi\)
\(600\) 0 0
\(601\) −213736. + 370201.i −0.591737 + 1.02492i 0.402262 + 0.915525i \(0.368224\pi\)
−0.993999 + 0.109393i \(0.965109\pi\)
\(602\) −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 0.0784853 0.996915i \(-0.474992\pi\)
0.902597 + 0.430487i \(0.141658\pi\)
\(608\) 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 0.913108 0.407719i \(-0.133676\pi\)
−0.809649 + 0.586915i \(0.800342\pi\)
\(618\) 0 0
\(619\) −382655. 220926.i −0.998679 0.576587i −0.0908215 0.995867i \(-0.528949\pi\)
−0.907857 + 0.419280i \(0.862283\pi\)
\(620\) 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 \(0.0856097\pi\)
−0.964050 + 0.265720i \(0.914390\pi\)
\(632\) −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 −0.869115 0.494610i \(-0.835311\pi\)
0.862902 + 0.505371i \(0.168644\pi\)
\(642\) 0 0
\(643\) 69127.8 39911.0i 0.167198 0.0965318i −0.414066 0.910247i \(-0.635892\pi\)
0.581264 + 0.813715i \(0.302558\pi\)
\(644\) 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 \(-0.781058\pi\)
0.772628 0.634859i \(-0.218942\pi\)
\(648\) 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 −0.998089 0.0617897i \(-0.980319\pi\)
0.445533 0.895265i \(-0.353014\pi\)
\(654\) 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 0.0994224 0.995045i \(-0.468300\pi\)
−0.812023 + 0.583625i \(0.801634\pi\)
\(660\) 0 0
\(661\) 282792. + 489809.i 0.647237 + 1.12105i 0.983780 + 0.179380i \(0.0574090\pi\)
−0.336543 + 0.941668i \(0.609258\pi\)
\(662\) 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 −0.636988 0.770874i \(-0.719820\pi\)
0.986090 + 0.166211i \(0.0531532\pi\)
\(674\) −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 0.324959 + 0.945728i \(0.394649\pi\)
−0.981504 + 0.191441i \(0.938684\pi\)
\(678\) 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 \(0.135503\pi\)
−0.910752 + 0.412955i \(0.864497\pi\)
\(684\) 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 0.854897 0.518798i \(-0.173620\pi\)
−0.0218438 + 0.999761i \(0.506954\pi\)
\(692\) 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 −0.999959 0.00901014i \(-0.997132\pi\)
0.507783 + 0.861485i \(0.330465\pi\)
\(710\) 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 \(-0.797371\pi\)
0.804134 0.594448i \(-0.202629\pi\)
\(720\) 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 0.746299 0.665610i \(-0.231829\pi\)
−0.203286 + 0.979119i \(0.565162\pi\)
\(728\) 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 0.889043 0.457824i \(-0.151371\pi\)
−0.841008 + 0.541022i \(0.818038\pi\)
\(734\) −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 \(-0.932774\pi\)
0.977780 0.209631i \(-0.0672264\pi\)
\(740\) −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 −0.670720 + 0.741711i \(0.734015\pi\)
−0.977700 + 0.210005i \(0.932652\pi\)
\(744\) 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 −0.278711 0.960375i \(-0.589907\pi\)
0.692354 + 0.721558i \(0.256574\pi\)
\(752\) −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 0.995760 0.0919890i \(-0.0293225\pi\)
−0.577545 + 0.816359i \(0.695989\pi\)
\(762\) 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 0.571830 0.820372i \(-0.306234\pi\)
−0.996378 + 0.0850327i \(0.972901\pi\)
\(770\) −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