Properties

Label 108.5.f.a.91.6
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 91.6
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.6

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 −0.573210 0.819409i \(-0.694302\pi\)
0.996234 + 0.0867102i \(0.0276354\pi\)
\(6\) 0 0
\(7\) −38.6407 + 22.3092i −0.788586 + 0.455290i −0.839464 0.543415i \(-0.817131\pi\)
0.0508787 + 0.998705i \(0.483798\pi\)
\(8\) 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 \(-0.757015\pi\)
0.237472 + 0.971394i \(0.423681\pi\)
\(12\) 0 0
\(13\) 14.5519 25.2046i 0.0861058 0.149140i −0.819756 0.572713i \(-0.805891\pi\)
0.905862 + 0.423573i \(0.139224\pi\)
\(14\) 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 \(0.351399\pi\)
−0.450070 + 0.892993i \(0.648601\pi\)
\(20\) 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 0.782403 0.622773i \(-0.213994\pi\)
−0.148136 + 0.988967i \(0.547327\pi\)
\(24\) 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 0.945231 0.326402i \(-0.105836\pi\)
0.189944 + 0.981795i \(0.439169\pi\)
\(32\) 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 −0.538449 0.842658i \(-0.680990\pi\)
0.998988 + 0.0449815i \(0.0143229\pi\)
\(42\) 0 0
\(43\) −1620.98 + 935.875i −0.876681 + 0.506152i −0.869563 0.493823i \(-0.835599\pi\)
−0.00711825 + 0.999975i \(0.502266\pi\)
\(44\) −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 \(0.725998\pi\)
−0.982679 + 0.185316i \(0.940669\pi\)
\(48\) 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 −0.182397 0.983225i \(-0.558386\pi\)
−0.942696 + 0.333652i \(0.891719\pi\)
\(60\) 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 0.506526 0.862225i \(-0.330930\pi\)
−0.493446 + 0.869777i \(0.664263\pi\)
\(68\) 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 \(-0.958363\pi\)
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 \(0.151678\pi\)
\(74\) 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 −0.165213 0.986258i \(-0.552831\pi\)
0.771518 + 0.636207i \(0.219498\pi\)
\(80\) −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 \(-0.684280\pi\)
0.451338 + 0.892353i \(0.350947\pi\)
\(84\) 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 0.632777 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 −0.0384332 0.999261i \(-0.512237\pi\)
−0.884602 + 0.466346i \(0.845570\pi\)
\(104\) −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 \(-0.911833\pi\)
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 \(0.453582\pi\)
\(110\) 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 −0.911544 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
\(122\) −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 \(-0.994769\pi\)
0.999865 0.0164319i \(-0.00523067\pi\)
\(128\) −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 0.523191 0.852216i \(-0.324742\pi\)
−0.476445 + 0.879204i \(0.658075\pi\)
\(132\) 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 0.518460 0.855102i \(-0.326506\pi\)
−0.481310 + 0.876550i \(0.659839\pi\)
\(140\) −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 −0.828716 0.559669i \(-0.810928\pi\)
0.899046 + 0.437855i \(0.144262\pi\)
\(150\) 0 0
\(151\) −7932.37 + 4579.76i −0.347896 + 0.200858i −0.663758 0.747947i \(-0.731040\pi\)
0.315862 + 0.948805i \(0.397706\pi\)
\(152\) 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 \(0.307478\pi\)
\(158\) −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 \(-0.702217\pi\)
0.593405 0.804904i \(-0.297783\pi\)
\(164\) 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 0.318554 0.947905i \(-0.396803\pi\)
−0.661633 + 0.749828i \(0.730136\pi\)
\(168\) 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
\(176\) 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 \(-0.942671\pi\)
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 \(0.255847\pi\)
\(182\) 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 −0.691283 + 0.722584i \(0.742954\pi\)
−0.971418 + 0.237376i \(0.923713\pi\)
\(192\) 0 0
\(193\) 17426.4 30183.5i 0.467836 0.810316i −0.531488 0.847066i \(-0.678367\pi\)
0.999325 + 0.0367497i \(0.0117004\pi\)
\(194\) −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 \(0.142402\pi\)
−0.901588 + 0.432596i \(0.857598\pi\)
\(200\) 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 0.658806 0.752313i \(-0.271062\pi\)
−0.322119 + 0.946699i \(0.604395\pi\)
\(212\) 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 −0.940311 0.340317i \(-0.889466\pi\)
−0.175432 + 0.984492i \(0.556132\pi\)
\(224\) −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 \(-0.624251\pi\)
0.610627 + 0.791918i \(0.290917\pi\)
\(228\) 0 0
\(229\) −32996.2 + 57151.0i −0.629205 + 1.08982i 0.358506 + 0.933527i \(0.383286\pi\)
−0.987711 + 0.156288i \(0.950047\pi\)
\(230\) −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 0.502405 0.864632i \(-0.332449\pi\)
−0.497591 + 0.867412i \(0.665782\pi\)
\(240\) 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
\(248\) 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 \(0.105463\pi\)
−0.945613 + 0.325294i \(0.894537\pi\)
\(252\) 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 −0.724728 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 −0.593130 0.805107i \(-0.702108\pi\)
0.400678 + 0.916219i \(0.368775\pi\)
\(264\) 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 \(0.178394\pi\)
−0.847021 + 0.531559i \(0.821606\pi\)
\(272\) 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 0.850168 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 0.682389 0.730989i \(-0.260941\pi\)
−0.291860 + 0.956461i \(0.594274\pi\)
\(284\) 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 0.437859 + 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
\(302\) 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 \(-0.731917\pi\)
0.665817 0.746115i \(-0.268083\pi\)
\(308\) 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 0.999177 0.0405712i \(-0.0129178\pi\)
0.464453 + 0.885598i \(0.346251\pi\)
\(312\) 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
\(320\) −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 0.0170938 0.999854i \(-0.494559\pi\)
0.874446 + 0.485123i \(0.161225\pi\)
\(332\) −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 \(0.137449\pi\)
\(338\) 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 −0.208318 0.978061i \(-0.566799\pi\)
−0.951185 + 0.308621i \(0.900132\pi\)
\(348\) 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
\(356\) 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 \(-0.998858\pi\)
0.999994 0.00358705i \(-0.00114180\pi\)
\(360\) 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 −0.625394 0.780309i \(-0.715062\pi\)
0.363071 + 0.931762i \(0.381728\pi\)
\(368\) −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 \(-0.152458\pi\)
\(374\) −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 \(-0.776485\pi\)
0.763428 0.645892i \(-0.223515\pi\)
\(380\) −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 0.667232 0.744850i \(-0.267479\pi\)
−0.311443 + 0.950265i \(0.600812\pi\)
\(384\) 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
\(392\) 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 0.411311 + 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 \(0.0349299\pi\)
\(410\) −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 0.694066 0.719912i \(-0.255818\pi\)
−0.276429 + 0.961034i \(0.589151\pi\)
\(420\) 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
\(428\) 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 \(0.291875\pi\)
−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 \(0.632188\pi\)
\(434\) 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 −0.454357 0.890820i \(-0.650131\pi\)
0.544294 + 0.838895i \(0.316798\pi\)
\(440\) 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 \(-0.635276\pi\)
0.582837 + 0.812589i \(0.301943\pi\)
\(444\) 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 0.987355 + 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 0.895458 0.445146i \(-0.146848\pi\)
0.0622210 + 0.998062i \(0.480182\pi\)
\(464\) −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 \(-0.822803\pi\)
0.849014 0.528371i \(-0.177197\pi\)
\(468\) 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 −0.495461 0.868630i \(-0.665001\pi\)
0.504525 + 0.863397i \(0.331668\pi\)
\(480\) 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 \(0.326014\pi\)
−0.519781 + 0.854300i \(0.673986\pi\)
\(488\) −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 0.712790 0.701378i \(-0.247431\pi\)
−0.251016 + 0.967983i \(0.580765\pi\)
\(492\) 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 \(-0.250189\pi\)
−0.259392 + 0.965772i \(0.583522\pi\)
\(500\) −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 \(0.259317\pi\)
−0.686109 + 0.727499i \(0.740683\pi\)
\(504\) 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 −0.933817 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
\(518\) −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 \(0.0303001\pi\)
−0.995473 + 0.0950470i \(0.969700\pi\)
\(524\) −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 0.107890 0.994163i \(-0.465591\pi\)
0.914915 + 0.403646i \(0.132257\pi\)
\(548\) −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 0.142776 0.989755i \(-0.454397\pi\)
−0.785765 + 0.618526i \(0.787730\pi\)
\(564\) 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 0.552104 0.833775i \(-0.313825\pi\)
−0.446018 + 0.895024i \(0.647158\pi\)
\(572\) −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 −0.409619 0.912257i \(-0.634338\pi\)
0.585228 + 0.810869i \(0.301005\pi\)
\(588\) 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 0.796881 0.604137i \(-0.206482\pi\)
−0.124757 + 0.992187i \(0.539815\pi\)
\(600\) 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 −0.0784853 0.996915i \(-0.525008\pi\)
−0.902597 + 0.430487i \(0.858342\pi\)
\(608\) −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 −0.809649 0.586915i \(-0.800342\pi\)
0.913108 + 0.407719i \(0.133676\pi\)
\(618\) 0 0
\(619\) 382655. 220926.i 0.998679 0.576587i 0.0908215 0.995867i \(-0.471051\pi\)
0.907857 + 0.419280i \(0.137717\pi\)
\(620\) 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 \(0.0856097\pi\)
−0.964050 + 0.265720i \(0.914390\pi\)
\(632\) 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 0.862902 0.505371i \(-0.168644\pi\)
−0.869115 + 0.494610i \(0.835311\pi\)
\(642\) 0 0
\(643\) −69127.8 39911.0i −0.167198 0.0965318i 0.414066 0.910247i \(-0.364108\pi\)
−0.581264 + 0.813715i \(0.697442\pi\)
\(644\) 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 \(-0.781058\pi\)
0.772628 0.634859i \(-0.218942\pi\)
\(648\) 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 0.445533 + 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 −0.0994224 0.995045i \(-0.531700\pi\)
0.812023 + 0.583625i \(0.198366\pi\)
\(660\) 0 0
\(661\) 282792. 489809.i 0.647237 1.12105i −0.336543 0.941668i \(-0.609258\pi\)
0.983780 0.179380i \(-0.0574090\pi\)
\(662\) −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 0.986090 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
\(680\) 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 \(0.135503\pi\)
−0.910752 + 0.412955i \(0.864497\pi\)
\(684\) 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 −0.854897 0.518798i \(-0.826380\pi\)
0.0218438 + 0.999761i \(0.493046\pi\)
\(692\) 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 0.507783 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
\(716\) 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 \(-0.797371\pi\)
0.804134 0.594448i \(-0.202629\pi\)
\(720\) 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 −0.746299 0.665610i \(-0.768171\pi\)
0.203286 + 0.979119i \(0.434838\pi\)
\(728\) 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 \(0.151371\pi\)
\(734\) 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 \(-0.932774\pi\)
0.977780 0.209631i \(-0.0672264\pi\)
\(740\) −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 0.977700 + 0.210005i \(0.0673480\pi\)
0.670720 + 0.741711i \(0.265985\pi\)
\(744\) 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 \(-0.410093\pi\)
−0.692354 + 0.721558i \(0.743426\pi\)
\(752\) 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 −0.577545 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 \(0.306234\pi\)
\(770\) −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
\(778\)