Properties

Label 108.5.f.a.19.6
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 19.6
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.63137 + 3.01262i) q^{2} +(-2.15179 - 15.8546i) q^{4} +(10.5756 + 18.3175i) q^{5} +(-38.6407 - 22.3092i) q^{7} +(53.4262 + 35.2369i) q^{8} +O(q^{10})\) \(q+(-2.63137 + 3.01262i) q^{2} +(-2.15179 - 15.8546i) q^{4} +(10.5756 + 18.3175i) q^{5} +(-38.6407 - 22.3092i) q^{7} +(53.4262 + 35.2369i) q^{8} +(-83.0119 - 16.3397i) q^{10} +(-58.6904 - 33.8849i) q^{11} +(14.5519 + 25.2046i) q^{13} +(168.887 - 57.7061i) q^{14} +(-246.740 + 68.2318i) q^{16} -402.841 q^{17} -644.741i q^{19} +(267.660 - 207.088i) q^{20} +(256.519 - 87.6483i) q^{22} +(335.527 - 193.717i) q^{23} +(88.8138 - 153.830i) q^{25} +(-114.223 - 22.4833i) q^{26} +(-270.558 + 660.639i) q^{28} +(362.210 - 627.366i) q^{29} +(1090.90 - 629.833i) q^{31} +(443.706 - 922.876i) q^{32} +(1060.02 - 1213.61i) q^{34} -943.733i q^{35} -1402.04 q^{37} +(1942.36 + 1696.55i) q^{38} +(-80.4363 + 1351.28i) q^{40} +(774.166 + 1340.89i) q^{41} +(-1620.98 - 935.875i) q^{43} +(-410.944 + 1003.43i) q^{44} +(-299.300 + 1520.56i) q^{46} +(-3610.63 - 2084.60i) q^{47} +(-205.097 - 355.239i) q^{49} +(229.730 + 672.346i) q^{50} +(368.297 - 284.950i) q^{52} -906.566 q^{53} -1433.41i q^{55} +(-1278.32 - 2553.48i) q^{56} +(936.910 + 2742.03i) q^{58} +(-3916.45 + 2261.16i) q^{59} +(-1314.22 + 2276.30i) q^{61} +(-973.119 + 4943.80i) q^{62} +(1612.72 + 3765.15i) q^{64} +(-307.789 + 533.107i) q^{65} +(58.7165 - 33.9000i) q^{67} +(866.831 + 6386.91i) q^{68} +(2843.11 + 2483.31i) q^{70} +1315.04i q^{71} +9470.72 q^{73} +(3689.27 - 4223.80i) q^{74} +(-10222.1 + 1387.35i) q^{76} +(1511.89 + 2618.67i) q^{77} +(3783.95 + 2184.67i) q^{79} +(-3859.25 - 3798.05i) q^{80} +(-6076.73 - 1196.12i) q^{82} +(-659.925 - 381.008i) q^{83} +(-4260.28 - 7379.03i) q^{85} +(7084.84 - 2420.78i) q^{86} +(-1941.61 - 3878.41i) q^{88} -8083.40 q^{89} -1298.56i q^{91} +(-3793.29 - 4902.82i) q^{92} +(15781.0 - 5392.11i) q^{94} +(11810.0 - 6818.52i) q^{95} +(-3332.71 + 5772.42i) q^{97} +(1609.89 + 316.884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63137 + 3.01262i −0.657842 + 0.753156i
\(3\) 0 0
\(4\) −2.15179 15.8546i −0.134487 0.990915i
\(5\) 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 0.0508787 0.998705i \(-0.483798\pi\)
−0.839464 + 0.543415i \(0.817131\pi\)
\(8\) 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 \(-0.423681\pi\)
−0.722516 + 0.691354i \(0.757015\pi\)
\(12\) 0 0
\(13\) 14.5519 + 25.2046i 0.0861058 + 0.149140i 0.905862 0.423573i \(-0.139224\pi\)
−0.819756 + 0.572713i \(0.805891\pi\)
\(14\) 168.887 57.7061i 0.861669 0.294419i
\(15\) 0 0
\(16\) −246.740 + 68.2318i −0.963826 + 0.266531i
\(17\) −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 \(-0.351399\pi\)
\(20\) 267.660 207.088i 0.669151 0.517719i
\(21\) 0 0
\(22\) 256.519 87.6483i 0.529997 0.181092i
\(23\) 335.527 193.717i 0.634267 0.366194i −0.148136 0.988967i \(-0.547327\pi\)
0.782403 + 0.622773i \(0.213994\pi\)
\(24\) 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 0.189944 0.981795i \(-0.439169\pi\)
0.945231 + 0.326402i \(0.105836\pi\)
\(32\) 443.706 922.876i 0.433307 0.901246i
\(33\) 0 0
\(34\) 1060.02 1213.61i 0.916976 1.04983i
\(35\) 943.733i 0.770394i
\(36\) 0 0
\(37\) −1402.04 −1.02413 −0.512066 0.858946i \(-0.671120\pi\)
−0.512066 + 0.858946i \(0.671120\pi\)
\(38\) 1942.36 + 1696.55i 1.34513 + 1.17490i
\(39\) 0 0
\(40\) −80.4363 + 1351.28i −0.0502727 + 0.844552i
\(41\) 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 −0.00711825 0.999975i \(-0.502266\pi\)
−0.869563 + 0.493823i \(0.835599\pi\)
\(44\) −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 \(-0.940669\pi\)
−0.651828 0.758367i \(1.27400\pi\)
\(48\) 0 0
\(49\) −205.097 355.239i −0.0854217 0.147955i
\(50\) 229.730 + 672.346i 0.0918920 + 0.268938i
\(51\) 0 0
\(52\) 368.297 284.950i 0.136205 0.105381i
\(53\) −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
\(56\) −1278.32 2553.48i −0.407627 0.814246i
\(57\) 0 0
\(58\) 936.910 + 2742.03i 0.278511 + 0.815111i
\(59\) −3916.45 + 2261.16i −1.12509 + 0.649573i −0.942696 0.333652i \(-0.891719\pi\)
−0.182397 + 0.983225i \(0.558386\pi\)
\(60\) 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 −0.493446 0.869777i \(-0.664263\pi\)
0.506526 + 0.862225i \(0.330930\pi\)
\(68\) 866.831 + 6386.91i 0.187463 + 1.38125i
\(69\) 0 0
\(70\) 2843.11 + 2483.31i 0.580227 + 0.506798i
\(71\) 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 \(0.151678\pi\)
\(74\) 3689.27 4223.80i 0.673717 0.771330i
\(75\) 0 0
\(76\) −10222.1 + 1387.35i −1.76976 + 0.240192i
\(77\) 1511.89 + 2618.67i 0.255000 + 0.441672i
\(78\) 0 0
\(79\) 3783.95 + 2184.67i 0.606305 + 0.350050i 0.771518 0.636207i \(-0.219498\pi\)
−0.165213 + 0.986258i \(0.552831\pi\)
\(80\) −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 \(-0.350947\pi\)
−0.547132 + 0.837047i \(0.684280\pi\)
\(84\) 0 0
\(85\) −4260.28 7379.03i −0.589659 1.02132i
\(86\) 7084.84 2420.78i 0.957929 0.327309i
\(87\) 0 0
\(88\) −1941.61 3878.41i −0.250724 0.500828i
\(89\) −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
\(92\) −3793.29 4902.82i −0.448168 0.579256i
\(93\) 0 0
\(94\) 15781.0 5392.11i 1.78599 0.610244i
\(95\) 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 −0.884602 0.466346i \(-0.845570\pi\)
−0.0384332 + 0.999261i \(0.512237\pi\)
\(104\) −110.679 + 1859.35i −0.0102329 + 0.171907i
\(105\) 0 0
\(106\) 2385.51 2731.14i 0.212310 0.243071i
\(107\) 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 \(0.453582\pi\)
\(110\) 4318.33 + 3771.84i 0.356887 + 0.311722i
\(111\) 0 0
\(112\) 11056.4 + 2868.04i 0.881409 + 0.228639i
\(113\) −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
\(122\) −3399.42 9949.02i −0.228394 0.668437i
\(123\) 0 0
\(124\) −12333.2 15940.6i −0.802106 1.03672i
\(125\) 16976.5 1.08650
\(126\) 0 0
\(127\) 530.060i 0.0328638i 0.999865 + 0.0164319i \(0.00523067\pi\)
−0.999865 + 0.0164319i \(0.994769\pi\)
\(128\) −15586.6 5048.97i −0.951333 0.308164i
\(129\) 0 0
\(130\) −796.142 2330.05i −0.0471090 0.137873i
\(131\) 802.198 463.149i 0.0467454 0.0269885i −0.476445 0.879204i \(-0.658075\pi\)
0.523191 + 0.852216i \(0.324742\pi\)
\(132\) 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 −0.481310 0.876550i \(-0.659839\pi\)
0.518460 + 0.855102i \(0.326506\pi\)
\(140\) −14962.5 + 2030.72i −0.763395 + 0.103608i
\(141\) 0 0
\(142\) −3961.72 3460.36i −0.196475 0.171611i
\(143\) 1972.36i 0.0964525i
\(144\) 0 0
\(145\) 15322.3 0.728768
\(146\) −24920.9 + 28531.7i −1.16912 + 1.33851i
\(147\) 0 0
\(148\) 3016.89 + 22228.8i 0.137732 + 1.01483i
\(149\) 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 0.315862 0.948805i \(-0.397706\pi\)
−0.663758 + 0.747947i \(0.731040\pi\)
\(152\) 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 \(0.974145\pi\)
\(158\) −16538.5 + 5650.96i −0.662496 + 0.226364i
\(159\) 0 0
\(160\) 21597.2 1632.39i 0.843641 0.0637653i
\(161\) −17286.7 −0.666898
\(162\) 0 0
\(163\) 42771.0i 1.60981i 0.593405 + 0.804904i \(0.297783\pi\)
−0.593405 + 0.804904i \(0.702217\pi\)
\(164\) 19593.6 15159.5i 0.728494 0.563632i
\(165\) 0 0
\(166\) 2884.34 985.532i 0.104672 0.0357647i
\(167\) −9568.12 + 5524.16i −0.343079 + 0.198077i −0.661633 0.749828i \(-0.730136\pi\)
0.318554 + 0.947905i \(0.396803\pi\)
\(168\) 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
\(176\) 16793.3 + 4356.20i 0.542138 + 0.140631i
\(177\) 0 0
\(178\) 21270.4 24352.2i 0.671329 0.768597i
\(179\) 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 \(0.255847\pi\)
\(182\) 3912.08 + 3417.00i 0.118104 + 0.103158i
\(183\) 0 0
\(184\) 24751.9 + 1473.38i 0.731094 + 0.0435190i
\(185\) −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 \(-0.923713\pi\)
−0.691283 0.722584i \(1.25705\pi\)
\(192\) 0 0
\(193\) 17426.4 + 30183.5i 0.467836 + 0.810316i 0.999325 0.0367497i \(-0.0117004\pi\)
−0.531488 + 0.847066i \(0.678367\pi\)
\(194\) −8620.54 25229.6i −0.229050 0.670357i
\(195\) 0 0
\(196\) −5190.87 + 4016.15i −0.135122 + 0.104544i
\(197\) 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 \(-0.142402\pi\)
\(200\) 10165.5 5089.04i 0.254137 0.127226i
\(201\) 0 0
\(202\) 12009.9 + 35149.1i 0.294331 + 0.861414i
\(203\) −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 \(-0.604395\pi\)
0.658806 + 0.752313i \(0.271062\pi\)
\(212\) 1950.74 + 14373.3i 0.0434038 + 0.319804i
\(213\) 0 0
\(214\) −18863.9 16476.6i −0.411911 0.359782i
\(215\) 39589.7i 0.856457i
\(216\) 0 0
\(217\) −56204.3 −1.19358
\(218\) −9085.73 + 10402.1i −0.191182 + 0.218882i
\(219\) 0 0
\(220\) −22726.2 + 3084.41i −0.469550 + 0.0637274i
\(221\) −5862.10 10153.5i −0.120024 0.207888i
\(222\) 0 0
\(223\) −55484.8 32034.1i −1.11574 0.644174i −0.175432 0.984492i \(-0.556132\pi\)
−0.940311 + 0.340317i \(0.889466\pi\)
\(224\) −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 \(-0.290917\pi\)
−0.380508 + 0.924778i \(0.624251\pi\)
\(228\) 0 0
\(229\) −32996.2 57151.0i −0.629205 1.08982i −0.987711 0.156288i \(-0.950047\pi\)
0.358506 0.933527i \(-0.383286\pi\)
\(230\) −31018.0 + 10598.4i −0.586352 + 0.200347i
\(231\) 0 0
\(232\) 41458.0 20754.7i 0.770250 0.385602i
\(233\) 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
\(236\) 44277.3 + 57228.4i 0.794982 + 1.02751i
\(237\) 0 0
\(238\) −68034.7 + 23246.4i −1.20109 + 0.410394i
\(239\) 275.008 158.776i 0.00481448 0.00277964i −0.497591 0.867412i \(-0.665782\pi\)
0.502405 + 0.864632i \(0.332449\pi\)
\(240\) 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
\(248\) 80476.2 + 4790.41i 1.30847 + 0.0778878i
\(249\) 0 0
\(250\) −44671.5 + 51143.9i −0.714744 + 0.818302i
\(251\) 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
\(254\) −1596.87 1394.78i −0.0247516 0.0216192i
\(255\) 0 0
\(256\) 56224.8 33671.0i 0.857923 0.513778i
\(257\) 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 0.400678 0.916219i \(-0.368775\pi\)
−0.593130 + 0.805107i \(0.702108\pi\)
\(264\) 0 0
\(265\) −9587.47 16606.0i −0.136525 0.236468i
\(266\) −37205.5 108889.i −0.525828 1.53893i
\(267\) 0 0
\(268\) −663.818 857.983i −0.00924228 0.0119456i
\(269\) −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 \(-0.178394\pi\)
\(272\) 99396.9 27486.6i 1.34349 0.371521i
\(273\) 0 0
\(274\) 2157.56 + 6314.48i 0.0287383 + 0.0841078i
\(275\) −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 −0.291860 0.956461i \(-0.594274\pi\)
0.682389 + 0.730989i \(0.260941\pi\)
\(284\) 20849.5 2829.69i 0.258499 0.0350835i
\(285\) 0 0
\(286\) 5941.97 + 5190.00i 0.0726438 + 0.0634505i
\(287\) 69084.1i 0.838715i
\(288\) 0 0
\(289\) 78760.1 0.942997
\(290\) −40318.7 + 46160.4i −0.479414 + 0.548876i
\(291\) 0 0
\(292\) −20379.0 150155.i −0.239011 1.76106i
\(293\) −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
\(302\) 34670.1 11846.2i 0.380138 0.129887i
\(303\) 0 0
\(304\) 43991.9 + 159083.i 0.476020 + 1.72138i
\(305\) −55594.6 −0.597631
\(306\) 0 0
\(307\) 140641.i 1.49223i 0.665817 + 0.746115i \(0.268083\pi\)
−0.665817 + 0.746115i \(0.731917\pi\)
\(308\) 38264.9 29605.4i 0.403366 0.312082i
\(309\) 0 0
\(310\) −100849. + 34458.6i −1.04942 + 0.358570i
\(311\) 141564. 81731.8i 1.46363 0.845027i 0.464453 0.885598i \(-0.346251\pi\)
0.999177 + 0.0405712i \(0.0129178\pi\)
\(312\) 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
\(320\) −51912.4 + 69359.7i −0.506957 + 0.677340i
\(321\) 0 0
\(322\) 45487.6 52078.2i 0.438714 0.502278i
\(323\) 259728.i 2.48951i
\(324\) 0 0
\(325\) 5169.63 0.0489433
\(326\) −128853. 112546.i −1.21244 1.05900i
\(327\) 0 0
\(328\) −5888.19 + 98918.1i −0.0547311 + 0.919450i
\(329\) 93011.4 + 161101.i 0.859299 + 1.48835i
\(330\) 0 0
\(331\) 97678.0 + 56394.4i 0.891540 + 0.514731i 0.874446 0.485123i \(-0.161225\pi\)
0.0170938 + 0.999854i \(0.494559\pi\)
\(332\) −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 \(0.804116\pi\)
\(338\) 35843.1 + 104901.i 0.313742 + 0.918222i
\(339\) 0 0
\(340\) −107825. + 83423.4i −0.932739 + 0.721656i
\(341\) −85367.4 −0.734147
\(342\) 0 0
\(343\) 125431.i 1.06615i
\(344\) −53625.7 107119.i −0.453165 0.905208i
\(345\) 0 0
\(346\) −28369.8 83029.5i −0.236976 0.693554i
\(347\) −139615. + 80606.6i −1.15950 + 0.669440i −0.951185 0.308621i \(-0.900132\pi\)
−0.208318 + 0.978061i \(0.566799\pi\)
\(348\) 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
\(356\) 17393.8 + 128159.i 0.137244 + 1.01123i
\(357\) 0 0
\(358\) −34582.4 30206.0i −0.269830 0.235682i
\(359\) 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
\(362\) −119654. + 136991.i −0.913084 + 1.04538i
\(363\) 0 0
\(364\) −20588.3 + 2794.24i −0.155388 + 0.0210893i
\(365\) 100158. + 173479.i 0.751799 + 1.30215i
\(366\) 0 0
\(367\) −35332.0 20398.9i −0.262323 0.151452i 0.363071 0.931762i \(-0.381728\pi\)
−0.625394 + 0.780309i \(0.715062\pi\)
\(368\) −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 \(0.514209\pi\)
\(374\) −103336. + 35308.4i −0.738771 + 0.252426i
\(375\) 0 0
\(376\) −119447. 238599.i −0.844892 1.68769i
\(377\) 21083.4 0.148340
\(378\) 0 0
\(379\) 185553.i 1.29178i 0.763428 + 0.645892i \(0.223515\pi\)
−0.763428 + 0.645892i \(0.776485\pi\)
\(380\) −133518. 172572.i −0.924639 1.19509i
\(381\) 0 0
\(382\) 265114. 90585.2i 1.81679 0.620770i
\(383\) 52190.3 30132.1i 0.355789 0.205415i −0.311443 0.950265i \(-0.600812\pi\)
0.667232 + 0.744850i \(0.267479\pi\)
\(384\) 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
\(392\) 1559.94 26206.1i 0.0101516 0.170542i
\(393\) 0 0
\(394\) −81198.7 + 92963.4i −0.523066 + 0.598852i
\(395\) 92416.5i 0.592318i
\(396\) 0 0
\(397\) 32276.3 0.204787 0.102394 0.994744i \(-0.467350\pi\)
0.102394 + 0.994744i \(0.467350\pi\)
\(398\) 103220. + 90157.2i 0.651624 + 0.569160i
\(399\) 0 0
\(400\) −11417.8 + 44015.9i −0.0713611 + 0.275099i
\(401\) −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 \(0.701597\pi\)
\(410\) −42355.1 123960.i −0.251964 0.737417i
\(411\) 0 0
\(412\) 110709. + 143091.i 0.652210 + 0.842980i
\(413\) 201779. 1.18298
\(414\) 0 0
\(415\) 16117.5i 0.0935841i
\(416\) 29717.5 2246.15i 0.171722 0.0129793i
\(417\) 0 0
\(418\) −56510.5 165388.i −0.323427 0.946568i
\(419\) 73320.7 42331.7i 0.417637 0.241123i −0.276429 0.961034i \(-0.589151\pi\)
0.694066 + 0.719912i \(0.255818\pi\)
\(420\) 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
\(428\) 99275.5 13473.7i 0.541944 0.0735527i
\(429\) 0 0
\(430\) 119269. + 104175.i 0.645045 + 0.563413i
\(431\) 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 \(0.632188\pi\)
\(434\) 147894. 169322.i 0.785185 0.898949i
\(435\) 0 0
\(436\) −7429.82 54743.7i −0.0390846 0.287979i
\(437\) −124897. 216328.i −0.654017 1.13279i
\(438\) 0 0
\(439\) 17332.7 + 10007.1i 0.0899369 + 0.0519251i 0.544294 0.838895i \(-0.316798\pi\)
−0.454357 + 0.890820i \(0.650131\pi\)
\(440\) 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 \(-0.301943\pi\)
−0.412305 + 0.911046i \(0.635276\pi\)
\(444\) 0 0
\(445\) −85486.7 148067.i −0.431696 0.747720i
\(446\) 242508. 82861.0i 1.21915 0.416563i
\(447\) 0 0
\(448\) 21680.7 181467.i 0.108023 0.904150i
\(449\) −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
\(452\) −32207.4 + 24918.7i −0.157645 + 0.121969i
\(453\) 0 0
\(454\) −51827.0 + 17708.5i −0.251446 + 0.0859151i
\(455\) 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 0.0622210 0.998062i \(-0.480182\pi\)
0.895458 + 0.445146i \(0.146848\pi\)
\(464\) −46565.2 + 179510.i −0.216285 + 0.833784i
\(465\) 0 0
\(466\) −166677. + 190827.i −0.767546 + 0.878754i
\(467\) 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
\(470\) 265663. + 232043.i 1.20264 + 1.05044i
\(471\) 0 0
\(472\) −288918. 17198.1i −1.29685 0.0771961i
\(473\) 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 \(-0.331668\pi\)
−0.495461 + 0.868630i \(0.665001\pi\)
\(480\) 0 0
\(481\) −20402.3 35337.7i −0.0881836 0.152739i
\(482\) −32986.6 96541.1i −0.141985 0.415545i
\(483\) 0 0
\(484\) −127157. + 98380.7i −0.542812 + 0.419971i
\(485\) −140981. −0.599347
\(486\) 0 0
\(487\) 405227.i 1.70860i −0.519781 0.854300i \(-0.673986\pi\)
0.519781 0.854300i \(-0.326014\pi\)
\(488\) −150423. + 75304.9i −0.631649 + 0.316216i
\(489\) 0 0
\(490\) 11221.0 + 32840.3i 0.0467347 + 0.136778i
\(491\) 111325. 64273.4i 0.461773 0.266605i −0.251016 0.967983i \(-0.580765\pi\)
0.712790 + 0.701378i \(0.247431\pi\)
\(492\) 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 \(-0.583522\pi\)
0.706687 + 0.707526i \(0.250189\pi\)
\(500\) −36530.0 269157.i −0.146120 1.07663i
\(501\) 0 0
\(502\) 123480. + 107854.i 0.489994 + 0.427984i
\(503\) 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
\(506\) 69090.0 79100.3i 0.269845 0.308942i
\(507\) 0 0
\(508\) 8403.92 1140.58i 0.0325653 0.00441976i
\(509\) −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
\(518\) −236786. + 80906.0i −0.882463 + 0.301523i
\(519\) 0 0
\(520\) −35229.1 + 17636.4i −0.130285 + 0.0652232i
\(521\) 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 \(-0.0303001\pi\)
\(524\) −9069.23 11722.0i −0.0330299 0.0426911i
\(525\) 0 0
\(526\) 58181.8 19879.8i 0.210289 0.0718522i
\(527\) −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
\(536\) 4331.53 + 257.838i 0.0150769 + 0.000897465i
\(537\) 0 0
\(538\) 200262. 229277.i 0.691884 0.792129i
\(539\) 27798.8i 0.0956862i
\(540\) 0 0
\(541\) −329819. −1.12689 −0.563444 0.826154i \(-0.690524\pi\)
−0.563444 + 0.826154i \(0.690524\pi\)
\(542\) 235215. + 205448.i 0.800693 + 0.699364i
\(543\) 0 0
\(544\) −178743. + 371773.i −0.603993 + 1.25626i
\(545\) 36515.9 + 63247.5i 0.122939 + 0.212936i
\(546\) 0 0
\(547\) 306032. + 176688.i 1.02280 + 0.590517i 0.914915 0.403646i \(-0.132257\pi\)
0.107890 + 0.994163i \(0.465591\pi\)
\(548\) −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
\(554\) −6130.27 17941.3i −0.0199738 0.0584568i
\(555\) 0 0
\(556\) −8114.69 10488.2i −0.0262496 0.0339275i
\(557\) 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
\(560\) 64392.6 + 232856.i 0.205334 + 0.742526i
\(561\) 0 0
\(562\) 55883.6 + 163553.i 0.176934 + 0.517830i
\(563\) −203807. + 117668.i −0.642988 + 0.371229i −0.785765 0.618526i \(-0.787730\pi\)
0.142776 + 0.989755i \(0.454397\pi\)
\(564\) 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 −0.446018 0.895024i \(-0.647158\pi\)
0.552104 + 0.833775i \(0.313825\pi\)
\(572\) −31271.0 + 4244.10i −0.0955763 + 0.0129716i
\(573\) 0 0
\(574\) 208124. + 181786.i 0.631683 + 0.551742i
\(575\) 68818.8i 0.208148i
\(576\) 0 0
\(577\) 511135. 1.53527 0.767634 0.640889i \(-0.221434\pi\)
0.767634 + 0.640889i \(0.221434\pi\)
\(578\) −207247. + 237274.i −0.620343 + 0.710224i
\(579\) 0 0
\(580\) −32970.5 242930.i −0.0980098 0.722147i
\(581\) 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 \(-0.301005\pi\)
−0.409619 + 0.912257i \(0.634338\pi\)
\(588\) 0 0
\(589\) −406079. 703350.i −1.17052 2.02741i
\(590\) 362059. 123710.i 1.04010 0.355385i
\(591\) 0 0
\(592\) 345938. 95663.4i 0.987085 0.272962i
\(593\) −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
\(596\) 39517.3 30574.4i 0.111249 0.0860726i
\(597\) 0 0
\(598\) −42680.4 + 14583.2i −0.119351 + 0.0407803i
\(599\) 241159. 139233.i 0.672123 0.388051i −0.124757 0.992187i \(-0.539815\pi\)
0.796881 + 0.604137i \(0.206482\pi\)
\(600\) 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 −0.902597 0.430487i \(-0.858342\pi\)
−0.0784853 + 0.996915i \(0.525008\pi\)
\(608\) −595016. 286076.i −1.60961 0.773880i
\(609\) 0 0
\(610\) 146290. 167486.i 0.393147 0.450109i
\(611\) 121339.i 0.325026i
\(612\) 0 0
\(613\) −23327.6 −0.0620796 −0.0310398 0.999518i \(-0.509882\pi\)
−0.0310398 + 0.999518i \(0.509882\pi\)
\(614\) −423699. 370079.i −1.12388 0.981652i
\(615\) 0 0
\(616\) −11499.2 + 193180.i −0.0303045 + 0.509098i
\(617\) 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 0.907857 0.419280i \(-0.137717\pi\)
0.0908215 + 0.995867i \(0.471051\pi\)
\(620\) 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
\(626\) 66334.9 + 194141.i 0.169275 + 0.495415i
\(627\) 0 0
\(628\) −267059. + 206623.i −0.677155 + 0.523912i
\(629\) 564798. 1.42755
\(630\) 0 0
\(631\) 211599.i 0.531440i −0.964050 0.265720i \(-0.914390\pi\)
0.964050 0.265720i \(-0.0856097\pi\)
\(632\) 125181. + 250053.i 0.313405 + 0.626034i
\(633\) 0 0
\(634\) −36277.7 106173.i −0.0902530 0.264142i
\(635\) −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 −0.581264 0.813715i \(-0.697442\pi\)
0.414066 + 0.910247i \(0.364108\pi\)
\(644\) 37197.3 + 274074.i 0.0896891 + 0.660839i
\(645\) 0 0
\(646\) −782463. 683441.i −1.87499 1.63771i
\(647\) 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
\(650\) −13603.2 + 15574.2i −0.0321969 + 0.0368619i
\(651\) 0 0
\(652\) 678119. 92034.3i 1.59518 0.216498i
\(653\) −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 0.812023 0.583625i \(-0.198366\pi\)
−0.0994224 + 0.995045i \(0.531700\pi\)
\(660\) 0 0
\(661\) 282792. + 489809.i 0.647237 + 1.12105i 0.983780 + 0.179380i \(0.0574090\pi\)
−0.336543 + 0.941668i \(0.609258\pi\)
\(662\) −426922. + 145872.i −0.974165 + 0.332857i
\(663\) 0 0
\(664\) −21831.8 43609.5i −0.0495168 0.0989111i
\(665\) −608463. −1.37591
\(666\) 0 0
\(667\) 280664.i 0.630864i
\(668\) 108172. + 139812.i 0.242417 + 0.313323i
\(669\) 0 0
\(670\) −5428.08 + 1854.69i −0.0120920 + 0.00413163i
\(671\) 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
\(680\) 32403.1 544353.i 0.0700758 1.17723i
\(681\) 0 0
\(682\) 224633. 257180.i 0.482953 0.552927i
\(683\) 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
\(686\) −377877. 330056.i −0.802975 0.701357i
\(687\) 0 0
\(688\) 463817. + 120315.i 0.979873 + 0.254180i
\(689\) −13192.2 22849.6i −0.0277895 0.0481328i
\(690\) 0 0
\(691\) −397767. 229651.i −0.833053 0.480963i 0.0218438 0.999761i \(-0.493046\pi\)
−0.854897 + 0.518798i \(0.826380\pi\)
\(692\) 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
\(698\) 286451. + 838349.i 0.587948 + 1.72074i
\(699\) 0 0
\(700\) 77596.9 + 100294.i 0.158361 + 0.204681i
\(701\) 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
\(704\) 32930.3 275625.i 0.0664432 0.556126i
\(705\) 0 0
\(706\) 282966. + 828150.i 0.567707 + 1.66150i
\(707\) −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
\(716\) 181998. 24700.8i 0.355011 0.0481820i
\(717\) 0 0
\(718\) −2785.49 2432.98i −0.00540322 0.00471943i
\(719\) 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
\(722\) 750914. 859712.i 1.44051 1.64922i
\(723\) 0 0
\(724\) −97846.7 720945.i −0.186668 1.37539i
\(725\) −64338.5 111438.i −0.122404 0.212010i
\(726\) 0 0
\(727\) −286999. 165699.i −0.543014 0.313509i 0.203286 0.979119i \(-0.434838\pi\)
−0.746299 + 0.665610i \(0.768171\pi\)
\(728\) 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 \(0.818038\pi\)
\(734\) 154426. 52764.9i 0.286634 0.0979383i
\(735\) 0 0
\(736\) −29901.1 395603.i −0.0551990 0.730305i
\(737\) −4594.79 −0.00845923
\(738\) 0 0
\(739\) 228968.i 0.419263i 0.977780 + 0.209631i \(0.0672264\pi\)
−0.977780 + 0.209631i \(0.932774\pi\)
\(740\) −375269. + 290344.i −0.685298 + 0.530212i
\(741\) 0 0
\(742\) −153107. + 52314.4i −0.278092 + 0.0950196i
\(743\) 910009. 525394.i 1.64842 0.951716i 0.670720 0.741711i \(-0.265985\pi\)
0.977700 0.210005i \(-0.0673480\pi\)
\(744\) 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 \(-0.743426\pi\)
0.278711 + 0.960375i \(0.410093\pi\)
\(752\) 1.03312e6 + 267993.i 1.82690 + 0.473901i
\(753\) 0 0
\(754\) −55478.1 + 63516.2i −0.0975840 + 0.111723i
\(755\) 193735.i 0.339870i
\(756\) 0 0
\(757\) −476176. −0.830952 −0.415476 0.909604i \(-0.636385\pi\)
−0.415476 + 0.909604i \(0.636385\pi\)
\(758\) −559002. 488259.i −0.972915 0.849791i
\(759\) 0 0
\(760\) 871228. + 51860.6i 1.50836 + 0.0897863i
\(761\) 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 \(0.972901\pi\)
\(770\) −82716.6 242085.i −0.139512 0.408307i
\(771\) 0 0
\(772\) 441050. 341238.i 0.740037 0.572563i
\(773\) −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
\(776\) −381456. + 190964.i −0.633463 + 0.317124i
\(777\) 0 0