Properties

Label 108.5.f.a.91.8
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 91.8
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.52726 + 3.69695i) q^{2} +(-11.3349 - 11.2924i) q^{4} +(-11.0746 + 19.1817i) q^{5} +(82.7885 - 47.7980i) q^{7} +(59.0591 - 24.6582i) q^{8} +O(q^{10})\) \(q+(-1.52726 + 3.69695i) q^{2} +(-11.3349 - 11.2924i) q^{4} +(-11.0746 + 19.1817i) q^{5} +(82.7885 - 47.7980i) q^{7} +(59.0591 - 24.6582i) q^{8} +(-54.0000 - 70.2376i) q^{10} +(18.9394 - 10.9346i) q^{11} +(-63.1124 + 109.314i) q^{13} +(50.2669 + 379.065i) q^{14} +(0.961243 + 255.998i) q^{16} +283.865 q^{17} +323.729i q^{19} +(342.138 - 92.3643i) q^{20} +(11.4995 + 86.7180i) q^{22} +(-198.433 - 114.565i) q^{23} +(67.2085 + 116.409i) q^{25} +(-307.739 - 400.274i) q^{26} +(-1478.16 - 393.098i) q^{28} +(604.822 + 1047.58i) q^{29} +(718.565 + 414.863i) q^{31} +(-947.881 - 387.423i) q^{32} +(-433.537 + 1049.44i) q^{34} +2117.36i q^{35} -318.650 q^{37} +(-1196.81 - 494.420i) q^{38} +(-181.068 + 1405.93i) q^{40} +(164.418 - 284.781i) q^{41} +(-179.336 + 103.539i) q^{43} +(-338.155 - 89.9283i) q^{44} +(726.602 - 558.626i) q^{46} +(1062.42 - 613.390i) q^{47} +(3368.79 - 5834.92i) q^{49} +(-533.002 + 70.6801i) q^{50} +(1949.79 - 526.371i) q^{52} +2834.27 q^{53} +484.385i q^{55} +(3710.80 - 4864.32i) q^{56} +(-4796.58 + 636.063i) q^{58} +(-1278.13 - 737.929i) q^{59} +(936.180 + 1621.51i) q^{61} +(-2631.17 + 2022.89i) q^{62} +(2879.95 - 2912.58i) q^{64} +(-1397.88 - 2421.20i) q^{65} +(214.663 + 123.936i) q^{67} +(-3217.59 - 3205.53i) q^{68} +(-7827.80 - 3233.77i) q^{70} +4308.28i q^{71} +3010.75 q^{73} +(486.662 - 1178.03i) q^{74} +(3655.69 - 3669.45i) q^{76} +(1045.31 - 1810.52i) q^{77} +(6228.39 - 3595.96i) q^{79} +(-4921.12 - 2816.63i) q^{80} +(801.712 + 1042.78i) q^{82} +(-2877.35 + 1661.24i) q^{83} +(-3143.68 + 5445.01i) q^{85} +(-108.888 - 821.128i) q^{86} +(848.913 - 1112.80i) q^{88} +1549.85 q^{89} +12066.6i q^{91} +(955.500 + 3539.38i) q^{92} +(645.075 + 4864.54i) q^{94} +(-6209.67 - 3585.16i) q^{95} +(-2918.68 - 5055.31i) q^{97} +(16426.4 + 21365.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.52726 + 3.69695i −0.381816 + 0.924238i
\(3\) 0 0
\(4\) −11.3349 11.2924i −0.708433 0.705778i
\(5\) −11.0746 + 19.1817i −0.442982 + 0.767268i −0.997909 0.0646314i \(-0.979413\pi\)
0.554927 + 0.831899i \(0.312746\pi\)
\(6\) 0 0
\(7\) 82.7885 47.7980i 1.68956 0.975469i 0.734711 0.678380i \(-0.237318\pi\)
0.954850 0.297089i \(-0.0960158\pi\)
\(8\) 59.0591 24.6582i 0.922798 0.385284i
\(9\) 0 0
\(10\) −54.0000 70.2376i −0.540000 0.702376i
\(11\) 18.9394 10.9346i 0.156524 0.0903689i −0.419692 0.907666i \(-0.637862\pi\)
0.576216 + 0.817297i \(0.304529\pi\)
\(12\) 0 0
\(13\) −63.1124 + 109.314i −0.373446 + 0.646827i −0.990093 0.140412i \(-0.955157\pi\)
0.616647 + 0.787240i \(0.288491\pi\)
\(14\) 50.2669 + 379.065i 0.256464 + 1.93401i
\(15\) 0 0
\(16\) 0.961243 + 255.998i 0.00375485 + 0.999993i
\(17\) 283.865 0.982232 0.491116 0.871094i \(-0.336589\pi\)
0.491116 + 0.871094i \(0.336589\pi\)
\(18\) 0 0
\(19\) 323.729i 0.896756i 0.893844 + 0.448378i \(0.147998\pi\)
−0.893844 + 0.448378i \(0.852002\pi\)
\(20\) 342.138 92.3643i 0.855344 0.230911i
\(21\) 0 0
\(22\) 11.4995 + 86.7180i 0.0237592 + 0.179169i
\(23\) −198.433 114.565i −0.375109 0.216570i 0.300579 0.953757i \(-0.402820\pi\)
−0.675688 + 0.737187i \(0.736153\pi\)
\(24\) 0 0
\(25\) 67.2085 + 116.409i 0.107534 + 0.186254i
\(26\) −307.739 400.274i −0.455235 0.592122i
\(27\) 0 0
\(28\) −1478.16 393.098i −1.88541 0.501401i
\(29\) 604.822 + 1047.58i 0.719170 + 1.24564i 0.961329 + 0.275402i \(0.0888109\pi\)
−0.242160 + 0.970236i \(0.577856\pi\)
\(30\) 0 0
\(31\) 718.565 + 414.863i 0.747726 + 0.431700i 0.824872 0.565320i \(-0.191247\pi\)
−0.0771458 + 0.997020i \(0.524581\pi\)
\(32\) −947.881 387.423i −0.925666 0.378343i
\(33\) 0 0
\(34\) −433.537 + 1049.44i −0.375032 + 0.907816i
\(35\) 2117.36i 1.72846i
\(36\) 0 0
\(37\) −318.650 −0.232761 −0.116380 0.993205i \(-0.537129\pi\)
−0.116380 + 0.993205i \(0.537129\pi\)
\(38\) −1196.81 494.420i −0.828817 0.342396i
\(39\) 0 0
\(40\) −181.068 + 1405.93i −0.113167 + 0.878707i
\(41\) 164.418 284.781i 0.0978099 0.169412i −0.812968 0.582308i \(-0.802150\pi\)
0.910778 + 0.412897i \(0.135483\pi\)
\(42\) 0 0
\(43\) −179.336 + 103.539i −0.0969906 + 0.0559976i −0.547711 0.836668i \(-0.684501\pi\)
0.450720 + 0.892665i \(0.351167\pi\)
\(44\) −338.155 89.9283i −0.174667 0.0464506i
\(45\) 0 0
\(46\) 726.602 558.626i 0.343385 0.264001i
\(47\) 1062.42 613.390i 0.480952 0.277678i −0.239861 0.970807i \(-0.577102\pi\)
0.720813 + 0.693129i \(0.243769\pi\)
\(48\) 0 0
\(49\) 3368.79 5834.92i 1.40308 2.43020i
\(50\) −533.002 + 70.6801i −0.213201 + 0.0282720i
\(51\) 0 0
\(52\) 1949.79 526.371i 0.721078 0.194664i
\(53\) 2834.27 1.00900 0.504499 0.863412i \(-0.331677\pi\)
0.504499 + 0.863412i \(0.331677\pi\)
\(54\) 0 0
\(55\) 484.385i 0.160127i
\(56\) 3710.80 4864.32i 1.18329 1.55112i
\(57\) 0 0
\(58\) −4796.58 + 636.063i −1.42586 + 0.189079i
\(59\) −1278.13 737.929i −0.367173 0.211988i 0.305049 0.952337i \(-0.401327\pi\)
−0.672223 + 0.740349i \(0.734660\pi\)
\(60\) 0 0
\(61\) 936.180 + 1621.51i 0.251594 + 0.435773i 0.963965 0.266030i \(-0.0857120\pi\)
−0.712371 + 0.701803i \(0.752379\pi\)
\(62\) −2631.17 + 2022.89i −0.684487 + 0.526247i
\(63\) 0 0
\(64\) 2879.95 2912.58i 0.703113 0.711078i
\(65\) −1397.88 2421.20i −0.330860 0.573066i
\(66\) 0 0
\(67\) 214.663 + 123.936i 0.0478197 + 0.0276087i 0.523719 0.851891i \(-0.324544\pi\)
−0.475900 + 0.879500i \(0.657877\pi\)
\(68\) −3217.59 3205.53i −0.695846 0.693238i
\(69\) 0 0
\(70\) −7827.80 3233.77i −1.59751 0.659954i
\(71\) 4308.28i 0.854648i 0.904099 + 0.427324i \(0.140544\pi\)
−0.904099 + 0.427324i \(0.859456\pi\)
\(72\) 0 0
\(73\) 3010.75 0.564974 0.282487 0.959271i \(-0.408841\pi\)
0.282487 + 0.959271i \(0.408841\pi\)
\(74\) 486.662 1178.03i 0.0888718 0.215126i
\(75\) 0 0
\(76\) 3655.69 3669.45i 0.632911 0.635292i
\(77\) 1045.31 1810.52i 0.176304 0.305368i
\(78\) 0 0
\(79\) 6228.39 3595.96i 0.997980 0.576184i 0.0903300 0.995912i \(-0.471208\pi\)
0.907650 + 0.419728i \(0.137874\pi\)
\(80\) −4921.12 2816.63i −0.768926 0.440098i
\(81\) 0 0
\(82\) 801.712 + 1042.78i 0.119231 + 0.155084i
\(83\) −2877.35 + 1661.24i −0.417673 + 0.241144i −0.694081 0.719897i \(-0.744189\pi\)
0.276408 + 0.961040i \(0.410856\pi\)
\(84\) 0 0
\(85\) −3143.68 + 5445.01i −0.435111 + 0.753635i
\(86\) −108.888 821.128i −0.0147225 0.111023i
\(87\) 0 0
\(88\) 848.913 1112.80i 0.109622 0.143698i
\(89\) 1549.85 0.195664 0.0978318 0.995203i \(-0.468809\pi\)
0.0978318 + 0.995203i \(0.468809\pi\)
\(90\) 0 0
\(91\) 12066.6i 1.45714i
\(92\) 955.500 + 3539.38i 0.112890 + 0.418169i
\(93\) 0 0
\(94\) 645.075 + 4864.54i 0.0730053 + 0.550536i
\(95\) −6209.67 3585.16i −0.688052 0.397247i
\(96\) 0 0
\(97\) −2918.68 5055.31i −0.310201 0.537285i 0.668204 0.743978i \(-0.267063\pi\)
−0.978406 + 0.206693i \(0.933730\pi\)
\(98\) 16426.4 + 21365.7i 1.71037 + 2.22467i
\(99\) 0 0
\(100\) 552.734 2078.43i 0.0552734 0.207843i
\(101\) −2749.50 4762.27i −0.269532 0.466844i 0.699209 0.714918i \(-0.253536\pi\)
−0.968741 + 0.248074i \(0.920202\pi\)
\(102\) 0 0
\(103\) −15530.7 8966.63i −1.46391 0.845191i −0.464725 0.885455i \(-0.653847\pi\)
−0.999189 + 0.0402641i \(0.987180\pi\)
\(104\) −1031.88 + 8012.21i −0.0954032 + 0.740774i
\(105\) 0 0
\(106\) −4328.69 + 10478.2i −0.385251 + 0.932554i
\(107\) 8715.17i 0.761217i −0.924736 0.380608i \(-0.875715\pi\)
0.924736 0.380608i \(-0.124285\pi\)
\(108\) 0 0
\(109\) −12162.1 −1.02366 −0.511830 0.859087i \(-0.671032\pi\)
−0.511830 + 0.859087i \(0.671032\pi\)
\(110\) −1790.75 739.784i −0.147996 0.0611392i
\(111\) 0 0
\(112\) 12315.8 + 21147.8i 0.981806 + 1.68589i
\(113\) −10236.7 + 17730.5i −0.801684 + 1.38856i 0.116823 + 0.993153i \(0.462729\pi\)
−0.918507 + 0.395404i \(0.870604\pi\)
\(114\) 0 0
\(115\) 4395.11 2537.52i 0.332334 0.191873i
\(116\) 4974.15 18704.2i 0.369661 1.39003i
\(117\) 0 0
\(118\) 4680.13 3598.18i 0.336120 0.258415i
\(119\) 23500.8 13568.2i 1.65954 0.958136i
\(120\) 0 0
\(121\) −7081.37 + 12265.3i −0.483667 + 0.837736i
\(122\) −7424.45 + 984.538i −0.498821 + 0.0661474i
\(123\) 0 0
\(124\) −3460.05 12816.8i −0.225030 0.833559i
\(125\) −16820.4 −1.07651
\(126\) 0 0
\(127\) 8130.42i 0.504087i −0.967716 0.252044i \(-0.918897\pi\)
0.967716 0.252044i \(-0.0811026\pi\)
\(128\) 6369.21 + 15095.3i 0.388746 + 0.921345i
\(129\) 0 0
\(130\) 11086.0 1470.09i 0.655977 0.0869875i
\(131\) 14095.1 + 8137.79i 0.821343 + 0.474203i 0.850879 0.525361i \(-0.176070\pi\)
−0.0295362 + 0.999564i \(0.509403\pi\)
\(132\) 0 0
\(133\) 15473.6 + 26801.0i 0.874758 + 1.51512i
\(134\) −786.030 + 604.315i −0.0437754 + 0.0336554i
\(135\) 0 0
\(136\) 16764.8 6999.59i 0.906402 0.378438i
\(137\) 12331.4 + 21358.7i 0.657011 + 1.13798i 0.981386 + 0.192047i \(0.0615126\pi\)
−0.324375 + 0.945929i \(0.605154\pi\)
\(138\) 0 0
\(139\) −17078.1 9860.04i −0.883913 0.510328i −0.0119667 0.999928i \(-0.503809\pi\)
−0.871947 + 0.489601i \(0.837143\pi\)
\(140\) 23910.2 24000.2i 1.21991 1.22450i
\(141\) 0 0
\(142\) −15927.5 6579.88i −0.789898 0.326318i
\(143\) 2760.44i 0.134992i
\(144\) 0 0
\(145\) −26792.5 −1.27432
\(146\) −4598.21 + 11130.6i −0.215716 + 0.522171i
\(147\) 0 0
\(148\) 3611.87 + 3598.33i 0.164895 + 0.164277i
\(149\) 14942.7 25881.6i 0.673066 1.16578i −0.303965 0.952683i \(-0.598310\pi\)
0.977030 0.213101i \(-0.0683562\pi\)
\(150\) 0 0
\(151\) 5164.11 2981.50i 0.226486 0.130762i −0.382464 0.923970i \(-0.624924\pi\)
0.608950 + 0.793209i \(0.291591\pi\)
\(152\) 7982.56 + 19119.1i 0.345506 + 0.827525i
\(153\) 0 0
\(154\) 5096.97 + 6629.60i 0.214917 + 0.279541i
\(155\) −15915.6 + 9188.85i −0.662458 + 0.382471i
\(156\) 0 0
\(157\) 17493.5 30299.6i 0.709704 1.22924i −0.255262 0.966872i \(-0.582162\pi\)
0.964967 0.262372i \(-0.0845048\pi\)
\(158\) 3781.71 + 28518.1i 0.151487 + 1.14237i
\(159\) 0 0
\(160\) 17928.8 13891.4i 0.700344 0.542634i
\(161\) −21903.9 −0.845027
\(162\) 0 0
\(163\) 14509.8i 0.546118i 0.961997 + 0.273059i \(0.0880354\pi\)
−0.961997 + 0.273059i \(0.911965\pi\)
\(164\) −5079.55 + 1371.29i −0.188859 + 0.0509848i
\(165\) 0 0
\(166\) −1747.05 13174.6i −0.0634000 0.478102i
\(167\) −38640.1 22308.9i −1.38550 0.799917i −0.392693 0.919670i \(-0.628457\pi\)
−0.992804 + 0.119753i \(0.961790\pi\)
\(168\) 0 0
\(169\) 6314.16 + 10936.5i 0.221076 + 0.382916i
\(170\) −15328.7 19938.0i −0.530406 0.689896i
\(171\) 0 0
\(172\) 3201.97 + 851.526i 0.108233 + 0.0287833i
\(173\) −26443.3 45801.1i −0.883534 1.53033i −0.847385 0.530979i \(-0.821824\pi\)
−0.0361488 0.999346i \(-0.511509\pi\)
\(174\) 0 0
\(175\) 11128.2 + 6424.86i 0.363369 + 0.209791i
\(176\) 2817.45 + 4837.93i 0.0909560 + 0.156183i
\(177\) 0 0
\(178\) −2367.03 + 5729.73i −0.0747075 + 0.180840i
\(179\) 32840.8i 1.02496i −0.858698 0.512482i \(-0.828726\pi\)
0.858698 0.512482i \(-0.171274\pi\)
\(180\) 0 0
\(181\) −22758.6 −0.694685 −0.347343 0.937738i \(-0.612916\pi\)
−0.347343 + 0.937738i \(0.612916\pi\)
\(182\) −44609.5 18428.8i −1.34674 0.556359i
\(183\) 0 0
\(184\) −14544.2 1873.13i −0.429591 0.0553264i
\(185\) 3528.90 6112.24i 0.103109 0.178590i
\(186\) 0 0
\(187\) 5376.22 3103.96i 0.153742 0.0887632i
\(188\) −18969.2 5044.62i −0.536701 0.142729i
\(189\) 0 0
\(190\) 22738.0 17481.4i 0.629860 0.484249i
\(191\) −49799.3 + 28751.7i −1.36508 + 0.788127i −0.990294 0.138986i \(-0.955616\pi\)
−0.374782 + 0.927113i \(0.622282\pi\)
\(192\) 0 0
\(193\) 22470.8 38920.5i 0.603259 1.04488i −0.389065 0.921210i \(-0.627202\pi\)
0.992324 0.123665i \(-0.0394648\pi\)
\(194\) 23146.9 3069.45i 0.615019 0.0815562i
\(195\) 0 0
\(196\) −104076. + 28096.5i −2.70917 + 0.731374i
\(197\) 44514.7 1.14702 0.573510 0.819198i \(-0.305581\pi\)
0.573510 + 0.819198i \(0.305581\pi\)
\(198\) 0 0
\(199\) 19066.9i 0.481474i 0.970590 + 0.240737i \(0.0773892\pi\)
−0.970590 + 0.240737i \(0.922611\pi\)
\(200\) 6839.69 + 5217.74i 0.170992 + 0.130444i
\(201\) 0 0
\(202\) 21805.1 2891.52i 0.534387 0.0708637i
\(203\) 100145. + 57818.5i 2.43016 + 1.40305i
\(204\) 0 0
\(205\) 3641.72 + 6307.65i 0.0866561 + 0.150093i
\(206\) 56868.6 43721.7i 1.34010 1.03030i
\(207\) 0 0
\(208\) −28044.8 16051.6i −0.648225 0.371014i
\(209\) 3539.86 + 6131.22i 0.0810389 + 0.140364i
\(210\) 0 0
\(211\) −825.251 476.459i −0.0185362 0.0107019i 0.490703 0.871327i \(-0.336740\pi\)
−0.509239 + 0.860625i \(0.670073\pi\)
\(212\) −32126.3 32005.9i −0.714807 0.712128i
\(213\) 0 0
\(214\) 32219.6 + 13310.4i 0.703546 + 0.290645i
\(215\) 4586.61i 0.0992237i
\(216\) 0 0
\(217\) 79318.5 1.68444
\(218\) 18574.7 44962.7i 0.390850 0.946106i
\(219\) 0 0
\(220\) 5469.89 5490.47i 0.113014 0.113439i
\(221\) −17915.4 + 31030.4i −0.366810 + 0.635334i
\(222\) 0 0
\(223\) 37535.4 21671.1i 0.754800 0.435784i −0.0726258 0.997359i \(-0.523138\pi\)
0.827426 + 0.561575i \(0.189805\pi\)
\(224\) −96991.7 + 13232.6i −1.93303 + 0.263724i
\(225\) 0 0
\(226\) −49914.6 64923.7i −0.977262 1.27112i
\(227\) −5202.66 + 3003.76i −0.100966 + 0.0582925i −0.549633 0.835406i \(-0.685232\pi\)
0.448667 + 0.893699i \(0.351899\pi\)
\(228\) 0 0
\(229\) 2038.17 3530.22i 0.0388660 0.0673180i −0.845938 0.533281i \(-0.820959\pi\)
0.884804 + 0.465963i \(0.154292\pi\)
\(230\) 2668.59 + 20124.0i 0.0504460 + 0.380416i
\(231\) 0 0
\(232\) 61551.6 + 46955.4i 1.14357 + 0.872388i
\(233\) 37427.6 0.689414 0.344707 0.938710i \(-0.387978\pi\)
0.344707 + 0.938710i \(0.387978\pi\)
\(234\) 0 0
\(235\) 27172.1i 0.492025i
\(236\) 6154.50 + 22797.6i 0.110502 + 0.409322i
\(237\) 0 0
\(238\) 14269.0 + 107603.i 0.251907 + 1.89964i
\(239\) −22212.3 12824.3i −0.388865 0.224511i 0.292804 0.956173i \(-0.405412\pi\)
−0.681668 + 0.731662i \(0.738745\pi\)
\(240\) 0 0
\(241\) −38300.8 66339.0i −0.659438 1.14218i −0.980761 0.195211i \(-0.937461\pi\)
0.321323 0.946970i \(-0.395872\pi\)
\(242\) −34529.1 44911.8i −0.589596 0.766884i
\(243\) 0 0
\(244\) 7699.30 28951.5i 0.129322 0.486285i
\(245\) 74615.7 + 129238.i 1.24308 + 2.15307i
\(246\) 0 0
\(247\) −35388.1 20431.3i −0.580046 0.334890i
\(248\) 52667.5 + 6782.98i 0.856327 + 0.110285i
\(249\) 0 0
\(250\) 25689.2 62184.3i 0.411027 0.994948i
\(251\) 66642.6i 1.05780i 0.848683 + 0.528902i \(0.177396\pi\)
−0.848683 + 0.528902i \(0.822604\pi\)
\(252\) 0 0
\(253\) −5010.92 −0.0782846
\(254\) 30057.8 + 12417.3i 0.465897 + 0.192468i
\(255\) 0 0
\(256\) −65534.2 + 492.153i −0.999972 + 0.00750966i
\(257\) 29713.2 51464.8i 0.449866 0.779191i −0.548511 0.836143i \(-0.684805\pi\)
0.998377 + 0.0569526i \(0.0181384\pi\)
\(258\) 0 0
\(259\) −26380.5 + 15230.8i −0.393264 + 0.227051i
\(260\) −11496.4 + 43229.7i −0.170065 + 0.639492i
\(261\) 0 0
\(262\) −51611.9 + 39680.3i −0.751878 + 0.578059i
\(263\) 21772.1 12570.2i 0.314767 0.181731i −0.334290 0.942470i \(-0.608497\pi\)
0.649058 + 0.760739i \(0.275163\pi\)
\(264\) 0 0
\(265\) −31388.3 + 54366.2i −0.446968 + 0.774171i
\(266\) −122714. + 16272.9i −1.73433 + 0.229986i
\(267\) 0 0
\(268\) −1033.65 3828.87i −0.0143914 0.0533090i
\(269\) −2553.46 −0.0352877 −0.0176439 0.999844i \(-0.505617\pi\)
−0.0176439 + 0.999844i \(0.505617\pi\)
\(270\) 0 0
\(271\) 4623.11i 0.0629499i −0.999505 0.0314750i \(-0.989980\pi\)
0.999505 0.0314750i \(-0.0100204\pi\)
\(272\) 272.863 + 72668.9i 0.00368814 + 0.982225i
\(273\) 0 0
\(274\) −97795.3 + 12968.4i −1.30262 + 0.172737i
\(275\) 2545.77 + 1469.80i 0.0336631 + 0.0194354i
\(276\) 0 0
\(277\) 4927.19 + 8534.14i 0.0642154 + 0.111224i 0.896346 0.443356i \(-0.146212\pi\)
−0.832130 + 0.554580i \(0.812879\pi\)
\(278\) 62534.9 48078.0i 0.809157 0.622095i
\(279\) 0 0
\(280\) 52210.3 + 125050.i 0.665948 + 1.59502i
\(281\) −24208.6 41930.5i −0.306589 0.531028i 0.671025 0.741435i \(-0.265854\pi\)
−0.977614 + 0.210407i \(0.932521\pi\)
\(282\) 0 0
\(283\) 114515. + 66115.1i 1.42984 + 0.825520i 0.997108 0.0760012i \(-0.0242153\pi\)
0.432735 + 0.901521i \(0.357549\pi\)
\(284\) 48651.0 48834.0i 0.603192 0.605461i
\(285\) 0 0
\(286\) −10205.2 4215.93i −0.124764 0.0515420i
\(287\) 31435.5i 0.381642i
\(288\) 0 0
\(289\) −2941.65 −0.0352205
\(290\) 40919.2 99050.7i 0.486555 1.17777i
\(291\) 0 0
\(292\) −34126.6 33998.7i −0.400247 0.398747i
\(293\) −44759.6 + 77525.8i −0.521375 + 0.903049i 0.478315 + 0.878188i \(0.341248\pi\)
−0.999691 + 0.0248607i \(0.992086\pi\)
\(294\) 0 0
\(295\) 28309.5 16344.5i 0.325303 0.187814i
\(296\) −18819.1 + 7857.31i −0.214791 + 0.0896789i
\(297\) 0 0
\(298\) 72861.5 + 94770.6i 0.820475 + 1.06719i
\(299\) 25047.1 14461.0i 0.280166 0.161754i
\(300\) 0 0
\(301\) −9897.95 + 17143.8i −0.109248 + 0.189223i
\(302\) 3135.51 + 23645.0i 0.0343791 + 0.259254i
\(303\) 0 0
\(304\) −82874.1 + 311.182i −0.896750 + 0.00336719i
\(305\) −41471.1 −0.445806
\(306\) 0 0
\(307\) 62726.9i 0.665545i 0.943007 + 0.332772i \(0.107984\pi\)
−0.943007 + 0.332772i \(0.892016\pi\)
\(308\) −32293.7 + 8718.10i −0.340421 + 0.0919010i
\(309\) 0 0
\(310\) −9663.50 72872.9i −0.100557 0.758303i
\(311\) −106333. 61391.4i −1.09938 0.634726i −0.163321 0.986573i \(-0.552221\pi\)
−0.936058 + 0.351847i \(0.885554\pi\)
\(312\) 0 0
\(313\) 24294.6 + 42079.4i 0.247982 + 0.429518i 0.962966 0.269623i \(-0.0868992\pi\)
−0.714984 + 0.699141i \(0.753566\pi\)
\(314\) 85299.2 + 110948.i 0.865138 + 1.12528i
\(315\) 0 0
\(316\) −111206. 29573.8i −1.11366 0.296164i
\(317\) −55066.7 95378.4i −0.547988 0.949143i −0.998412 0.0563282i \(-0.982061\pi\)
0.450425 0.892815i \(-0.351273\pi\)
\(318\) 0 0
\(319\) 22909.9 + 13227.0i 0.225134 + 0.129981i
\(320\) 23974.0 + 87497.8i 0.234121 + 0.854471i
\(321\) 0 0
\(322\) 33453.1 80977.9i 0.322645 0.781006i
\(323\) 91895.4i 0.880823i
\(324\) 0 0
\(325\) −16966.7 −0.160632
\(326\) −53642.1 22160.3i −0.504743 0.208517i
\(327\) 0 0
\(328\) 2688.23 20873.2i 0.0249872 0.194017i
\(329\) 58637.6 101563.i 0.541732 0.938308i
\(330\) 0 0
\(331\) −159800. + 92260.3i −1.45854 + 0.842091i −0.998940 0.0460325i \(-0.985342\pi\)
−0.459605 + 0.888124i \(0.652009\pi\)
\(332\) 51374.0 + 13662.3i 0.466087 + 0.123950i
\(333\) 0 0
\(334\) 141489. 108779.i 1.26832 0.975108i
\(335\) −4754.59 + 2745.06i −0.0423665 + 0.0244603i
\(336\) 0 0
\(337\) −32813.1 + 56833.9i −0.288926 + 0.500435i −0.973554 0.228458i \(-0.926632\pi\)
0.684628 + 0.728893i \(0.259965\pi\)
\(338\) −50074.9 + 6640.32i −0.438316 + 0.0581240i
\(339\) 0 0
\(340\) 97120.9 26219.0i 0.840146 0.226808i
\(341\) 18145.5 0.156049
\(342\) 0 0
\(343\) 414560.i 3.52370i
\(344\) −8038.31 + 10537.0i −0.0679278 + 0.0890433i
\(345\) 0 0
\(346\) 209710. 27809.2i 1.75173 0.232293i
\(347\) −90819.3 52434.6i −0.754257 0.435470i 0.0729731 0.997334i \(-0.476751\pi\)
−0.827230 + 0.561864i \(0.810085\pi\)
\(348\) 0 0
\(349\) −43672.0 75642.1i −0.358552 0.621030i 0.629167 0.777270i \(-0.283396\pi\)
−0.987719 + 0.156240i \(0.950063\pi\)
\(350\) −40748.1 + 31327.9i −0.332637 + 0.255738i
\(351\) 0 0
\(352\) −22188.6 + 3027.20i −0.179079 + 0.0244318i
\(353\) −24354.3 42182.9i −0.195446 0.338522i 0.751601 0.659618i \(-0.229282\pi\)
−0.947047 + 0.321096i \(0.895949\pi\)
\(354\) 0 0
\(355\) −82640.1 47712.3i −0.655744 0.378594i
\(356\) −17567.5 17501.6i −0.138615 0.138095i
\(357\) 0 0
\(358\) 121411. + 50156.6i 0.947310 + 0.391347i
\(359\) 109409.i 0.848911i −0.905449 0.424456i \(-0.860465\pi\)
0.905449 0.424456i \(-0.139535\pi\)
\(360\) 0 0
\(361\) 25520.5 0.195828
\(362\) 34758.4 84137.4i 0.265242 0.642055i
\(363\) 0 0
\(364\) 136261. 136774.i 1.02842 1.03229i
\(365\) −33342.7 + 57751.3i −0.250274 + 0.433487i
\(366\) 0 0
\(367\) 1112.82 642.487i 0.00826215 0.00477015i −0.495863 0.868401i \(-0.665148\pi\)
0.504125 + 0.863630i \(0.331815\pi\)
\(368\) 29137.8 50908.6i 0.215160 0.375920i
\(369\) 0 0
\(370\) 17207.1 + 22381.2i 0.125691 + 0.163486i
\(371\) 234645. 135473.i 1.70476 0.984246i
\(372\) 0 0
\(373\) 36777.2 63699.9i 0.264339 0.457848i −0.703052 0.711139i \(-0.748180\pi\)
0.967390 + 0.253291i \(0.0815130\pi\)
\(374\) 3264.30 + 24616.2i 0.0233371 + 0.175986i
\(375\) 0 0
\(376\) 47620.7 62423.7i 0.336837 0.441544i
\(377\) −152687. −1.07428
\(378\) 0 0
\(379\) 139070.i 0.968176i 0.875019 + 0.484088i \(0.160848\pi\)
−0.875019 + 0.484088i \(0.839152\pi\)
\(380\) 29901.0 + 110760.i 0.207071 + 0.767035i
\(381\) 0 0
\(382\) −30236.8 228017.i −0.207209 1.56258i
\(383\) 90000.3 + 51961.7i 0.613545 + 0.354230i 0.774352 0.632756i \(-0.218076\pi\)
−0.160807 + 0.986986i \(0.551410\pi\)
\(384\) 0 0
\(385\) 23152.6 + 40101.5i 0.156199 + 0.270545i
\(386\) 109569. + 142515.i 0.735380 + 0.956505i
\(387\) 0 0
\(388\) −24003.7 + 90260.7i −0.159447 + 0.599563i
\(389\) −50040.9 86673.4i −0.330694 0.572778i 0.651954 0.758258i \(-0.273949\pi\)
−0.982648 + 0.185480i \(0.940616\pi\)
\(390\) 0 0
\(391\) −56328.2 32521.1i −0.368444 0.212721i
\(392\) 55079.4 427673.i 0.358441 2.78317i
\(393\) 0 0
\(394\) −67985.7 + 164569.i −0.437951 + 1.06012i
\(395\) 159295.i 1.02096i
\(396\) 0 0
\(397\) 164388. 1.04301 0.521507 0.853247i \(-0.325370\pi\)
0.521507 + 0.853247i \(0.325370\pi\)
\(398\) −70489.3 29120.1i −0.444997 0.183835i
\(399\) 0 0
\(400\) −29735.8 + 17317.2i −0.185849 + 0.108232i
\(401\) −78226.6 + 135492.i −0.486481 + 0.842609i −0.999879 0.0155412i \(-0.995053\pi\)
0.513399 + 0.858150i \(0.328386\pi\)
\(402\) 0 0
\(403\) −90700.6 + 52366.0i −0.558470 + 0.322433i
\(404\) −22612.3 + 85028.6i −0.138542 + 0.520958i
\(405\) 0 0
\(406\) −366699. + 281926.i −2.22463 + 1.71034i
\(407\) −6035.02 + 3484.32i −0.0364325 + 0.0210343i
\(408\) 0 0
\(409\) −135351. + 234435.i −0.809125 + 1.40145i 0.104346 + 0.994541i \(0.466725\pi\)
−0.913471 + 0.406904i \(0.866608\pi\)
\(410\) −28881.0 + 3829.83i −0.171808 + 0.0227831i
\(411\) 0 0
\(412\) 74783.7 + 277015.i 0.440568 + 1.63196i
\(413\) −141086. −0.827149
\(414\) 0 0
\(415\) 73589.9i 0.427290i
\(416\) 102174. 79165.3i 0.590408 0.457455i
\(417\) 0 0
\(418\) −28073.1 + 3722.71i −0.160671 + 0.0213062i
\(419\) 49366.2 + 28501.6i 0.281191 + 0.162346i 0.633963 0.773364i \(-0.281427\pi\)
−0.352771 + 0.935710i \(0.614761\pi\)
\(420\) 0 0
\(421\) −116812. 202325.i −0.659059 1.14152i −0.980860 0.194716i \(-0.937621\pi\)
0.321801 0.946807i \(-0.395712\pi\)
\(422\) 3021.82 2323.24i 0.0169685 0.0130457i
\(423\) 0 0
\(424\) 167390. 69888.0i 0.931101 0.388750i
\(425\) 19078.1 + 33044.3i 0.105623 + 0.182944i
\(426\) 0 0
\(427\) 155010. + 89495.0i 0.850166 + 0.490843i
\(428\) −98415.6 + 98785.8i −0.537250 + 0.539271i
\(429\) 0 0
\(430\) 16956.5 + 7004.97i 0.0917063 + 0.0378852i
\(431\) 333180.i 1.79360i −0.442439 0.896798i \(-0.645887\pi\)
0.442439 0.896798i \(-0.354113\pi\)
\(432\) 0 0
\(433\) −215343. −1.14856 −0.574282 0.818657i \(-0.694719\pi\)
−0.574282 + 0.818657i \(0.694719\pi\)
\(434\) −121140. + 293237.i −0.643145 + 1.55682i
\(435\) 0 0
\(436\) 137857. + 137340.i 0.725194 + 0.722477i
\(437\) 37088.1 64238.5i 0.194210 0.336382i
\(438\) 0 0
\(439\) −27053.2 + 15619.2i −0.140375 + 0.0810455i −0.568543 0.822654i \(-0.692493\pi\)
0.428168 + 0.903699i \(0.359159\pi\)
\(440\) 11944.0 + 28607.3i 0.0616944 + 0.147765i
\(441\) 0 0
\(442\) −87356.3 113624.i −0.447146 0.581601i
\(443\) −184829. + 106711.i −0.941809 + 0.543754i −0.890527 0.454930i \(-0.849664\pi\)
−0.0512822 + 0.998684i \(0.516331\pi\)
\(444\) 0 0
\(445\) −17163.9 + 29728.8i −0.0866755 + 0.150126i
\(446\) 22790.5 + 171864.i 0.114574 + 0.864004i
\(447\) 0 0
\(448\) 99211.6 378784.i 0.494318 1.88727i
\(449\) 393053. 1.94966 0.974828 0.222956i \(-0.0715707\pi\)
0.974828 + 0.222956i \(0.0715707\pi\)
\(450\) 0 0
\(451\) 7191.43i 0.0353559i
\(452\) 316253. 85376.4i 1.54795 0.417889i
\(453\) 0 0
\(454\) −3158.91 23821.5i −0.0153259 0.115573i
\(455\) −231457. 133632.i −1.11802 0.645487i
\(456\) 0 0
\(457\) 36178.7 + 62663.4i 0.173229 + 0.300042i 0.939547 0.342420i \(-0.111247\pi\)
−0.766318 + 0.642462i \(0.777913\pi\)
\(458\) 9938.23 + 12926.6i 0.0473782 + 0.0616246i
\(459\) 0 0
\(460\) −78473.1 20869.0i −0.370856 0.0986246i
\(461\) 29095.9 + 50395.5i 0.136908 + 0.237132i 0.926325 0.376726i \(-0.122950\pi\)
−0.789417 + 0.613858i \(0.789617\pi\)
\(462\) 0 0
\(463\) 64721.6 + 37367.0i 0.301917 + 0.174312i 0.643304 0.765611i \(-0.277563\pi\)
−0.341387 + 0.939923i \(0.610897\pi\)
\(464\) −267598. + 155840.i −1.24293 + 0.723842i
\(465\) 0 0
\(466\) −57161.8 + 138368.i −0.263229 + 0.637183i
\(467\) 264366.i 1.21219i 0.795392 + 0.606096i \(0.207265\pi\)
−0.795392 + 0.606096i \(0.792735\pi\)
\(468\) 0 0
\(469\) 23695.5 0.107726
\(470\) −100454. 41499.0i −0.454749 0.187863i
\(471\) 0 0
\(472\) −93681.2 12065.1i −0.420502 0.0541559i
\(473\) −2264.33 + 3921.94i −0.0101209 + 0.0175299i
\(474\) 0 0
\(475\) −37684.8 + 21757.3i −0.167024 + 0.0964314i
\(476\) −419597. 111587.i −1.85191 0.492492i
\(477\) 0 0
\(478\) 81334.9 62531.9i 0.355976 0.273682i
\(479\) −242211. + 139840.i −1.05566 + 0.609483i −0.924228 0.381842i \(-0.875290\pi\)
−0.131429 + 0.991326i \(0.541956\pi\)
\(480\) 0 0
\(481\) 20110.7 34832.8i 0.0869236 0.150556i
\(482\) 303748. 40279.2i 1.30743 0.173375i
\(483\) 0 0
\(484\) 218772. 59060.2i 0.933901 0.252118i
\(485\) 129293. 0.549655
\(486\) 0 0
\(487\) 62506.3i 0.263552i 0.991280 + 0.131776i \(0.0420679\pi\)
−0.991280 + 0.131776i \(0.957932\pi\)
\(488\) 95273.4 + 72680.5i 0.400066 + 0.305196i
\(489\) 0 0
\(490\) −591746. + 78470.0i −2.46458 + 0.326822i
\(491\) 291742. + 168437.i 1.21014 + 0.698674i 0.962790 0.270252i \(-0.0871070\pi\)
0.247350 + 0.968926i \(0.420440\pi\)
\(492\) 0 0
\(493\) 171688. + 297372.i 0.706391 + 1.22351i
\(494\) 129580. 99624.0i 0.530989 0.408235i
\(495\) 0 0
\(496\) −105514. + 184350.i −0.428889 + 0.749342i
\(497\) 205927. + 356676.i 0.833682 + 1.44398i
\(498\) 0 0
\(499\) 276635. + 159715.i 1.11098 + 0.641424i 0.939083 0.343691i \(-0.111677\pi\)
0.171896 + 0.985115i \(0.445011\pi\)
\(500\) 190658. + 189944.i 0.762633 + 0.759774i
\(501\) 0 0
\(502\) −246375. 101781.i −0.977662 0.403886i
\(503\) 28287.7i 0.111805i 0.998436 + 0.0559025i \(0.0178036\pi\)
−0.998436 + 0.0559025i \(0.982196\pi\)
\(504\) 0 0
\(505\) 121798. 0.477592
\(506\) 7653.00 18525.1i 0.0298903 0.0723536i
\(507\) 0 0
\(508\) −91812.3 + 92157.7i −0.355774 + 0.357112i
\(509\) 47278.6 81888.9i 0.182486 0.316074i −0.760241 0.649641i \(-0.774919\pi\)
0.942726 + 0.333567i \(0.108252\pi\)
\(510\) 0 0
\(511\) 249255. 143908.i 0.954559 0.551115i
\(512\) 98268.5 243028.i 0.374865 0.927080i
\(513\) 0 0
\(514\) 144883. + 188449.i 0.548392 + 0.713291i
\(515\) 343990. 198603.i 1.29698 0.748809i
\(516\) 0 0
\(517\) 13414.4 23234.4i 0.0501869 0.0869263i
\(518\) −16017.5 120789.i −0.0596948 0.450161i
\(519\) 0 0
\(520\) −142260. 108525.i −0.526110 0.401349i
\(521\) −369932. −1.36285 −0.681423 0.731890i \(-0.738638\pi\)
−0.681423 + 0.731890i \(0.738638\pi\)
\(522\) 0 0
\(523\) 65267.4i 0.238612i −0.992858 0.119306i \(-0.961933\pi\)
0.992858 0.119306i \(-0.0380670\pi\)
\(524\) −67871.0 251409.i −0.247185 0.915627i
\(525\) 0 0
\(526\) 13219.5 + 99688.5i 0.0477796 + 0.360308i
\(527\) 203975. + 117765.i 0.734440 + 0.424029i
\(528\) 0 0
\(529\) −113670. 196882.i −0.406195 0.703551i
\(530\) −153051. 199073.i −0.544859 0.708696i
\(531\) 0 0
\(532\) 127257. 478523.i 0.449634 1.69075i
\(533\) 20753.7 + 35946.4i 0.0730534 + 0.126532i
\(534\) 0 0
\(535\) 167172. + 96516.6i 0.584057 + 0.337205i
\(536\) 15733.8 + 2026.33i 0.0547651 + 0.00705312i
\(537\) 0 0
\(538\) 3899.80 9440.01i 0.0134734 0.0326143i
\(539\) 147346.i 0.507179i
\(540\) 0 0
\(541\) 176002. 0.601343 0.300671 0.953728i \(-0.402789\pi\)
0.300671 + 0.953728i \(0.402789\pi\)
\(542\) 17091.4 + 7060.70i 0.0581807 + 0.0240353i
\(543\) 0 0
\(544\) −269070. 109976.i −0.909218 0.371620i
\(545\) 134690. 233290.i 0.453463 0.785421i
\(546\) 0 0
\(547\) −236509. + 136549.i −0.790448 + 0.456365i −0.840120 0.542400i \(-0.817516\pi\)
0.0496725 + 0.998766i \(0.484182\pi\)
\(548\) 101416. 381351.i 0.337710 1.26988i
\(549\) 0 0
\(550\) −9321.85 + 7166.82i −0.0308160 + 0.0236920i
\(551\) −339133. + 195798.i −1.11703 + 0.644920i
\(552\) 0 0
\(553\) 343760. 595409.i 1.12410 1.94700i
\(554\) −39075.4 + 5181.70i −0.127316 + 0.0168831i
\(555\) 0 0
\(556\) 82235.0 + 304616.i 0.266016 + 0.985380i
\(557\) 454335. 1.46442 0.732211 0.681078i \(-0.238489\pi\)
0.732211 + 0.681078i \(0.238489\pi\)
\(558\) 0 0
\(559\) 26138.5i 0.0836482i
\(560\) −542042. + 2035.30i −1.72845 + 0.00649012i
\(561\) 0 0
\(562\) 191988. 25459.1i 0.607857 0.0806065i
\(563\) 27753.2 + 16023.3i 0.0875582 + 0.0505518i 0.543140 0.839642i \(-0.317235\pi\)
−0.455582 + 0.890194i \(0.650569\pi\)
\(564\) 0 0
\(565\) −226734. 392714.i −0.710263 1.23021i
\(566\) −419318. + 322380.i −1.30891 + 1.00632i
\(567\) 0 0
\(568\) 106234. + 254443.i 0.329282 + 0.788667i
\(569\) −138564. 240000.i −0.427982 0.741287i 0.568712 0.822537i \(-0.307442\pi\)
−0.996694 + 0.0812502i \(0.974109\pi\)
\(570\) 0 0
\(571\) −556449. 321266.i −1.70668 0.985355i −0.938600 0.345007i \(-0.887877\pi\)
−0.768085 0.640348i \(1.22121\pi\)
\(572\) 31172.2 31289.4i 0.0952741 0.0956325i
\(573\) 0 0
\(574\) 116215. + 48010.3i 0.352728 + 0.145717i
\(575\) 30799.0i 0.0931540i
\(576\) 0 0
\(577\) 451002. 1.35465 0.677324 0.735685i \(-0.263140\pi\)
0.677324 + 0.735685i \(0.263140\pi\)
\(578\) 4492.68 10875.1i 0.0134477 0.0325521i
\(579\) 0 0
\(580\) 303691. + 302553.i 0.902768 + 0.899385i
\(581\) −158808. + 275063.i −0.470456 + 0.814854i
\(582\) 0 0
\(583\) 53679.3 30991.8i 0.157932 0.0911820i
\(584\) 177812. 74239.5i 0.521357 0.217675i
\(585\) 0 0
\(586\) −218250. 283876.i −0.635563 0.826674i
\(587\) −327761. + 189233.i −0.951221 + 0.549188i −0.893460 0.449143i \(-0.851729\pi\)
−0.0577610 + 0.998330i \(0.518396\pi\)
\(588\) 0 0
\(589\) −134303. + 232620.i −0.387129 + 0.670528i
\(590\) 17188.7 + 129621.i 0.0493787 + 0.372367i
\(591\) 0 0
\(592\) −306.300 81573.7i −0.000873983 0.232759i
\(593\) −137966. −0.392339 −0.196170 0.980570i \(-0.562850\pi\)
−0.196170 + 0.980570i \(0.562850\pi\)
\(594\) 0 0
\(595\) 601046.i 1.69775i
\(596\) −461641. + 124626.i −1.29961 + 0.350845i
\(597\) 0 0
\(598\) 15207.9 + 114684.i 0.0425273 + 0.320701i
\(599\) −180870. 104426.i −0.504096 0.291040i 0.226307 0.974056i \(-0.427335\pi\)
−0.730404 + 0.683016i \(0.760668\pi\)
\(600\) 0 0
\(601\) −180004. 311775.i −0.498348 0.863163i 0.501651 0.865070i \(-0.332726\pi\)
−0.999998 + 0.00190701i \(0.999393\pi\)
\(602\) −48262.9 62775.3i −0.133174 0.173219i
\(603\) 0 0
\(604\) −92203.3 24520.4i −0.252739 0.0672130i
\(605\) −156846. 271665.i −0.428512 0.742204i
\(606\) 0 0
\(607\) −279709. 161490.i −0.759152 0.438297i 0.0698392 0.997558i \(-0.477751\pi\)
−0.828991 + 0.559262i \(0.811085\pi\)
\(608\) 125420. 306857.i 0.339281 0.830096i
\(609\) 0 0
\(610\) 63337.3 153317.i 0.170216 0.412031i
\(611\) 154850.i 0.414791i
\(612\) 0 0
\(613\) −392554. −1.04467 −0.522334 0.852741i \(-0.674939\pi\)
−0.522334 + 0.852741i \(0.674939\pi\)
\(614\) −231899. 95800.6i −0.615122 0.254116i
\(615\) 0 0
\(616\) 17090.7 132703.i 0.0450399 0.349720i
\(617\) 192102. 332730.i 0.504616 0.874020i −0.495370 0.868682i \(-0.664968\pi\)
0.999986 0.00533786i \(-0.00169910\pi\)
\(618\) 0 0
\(619\) 602573. 347896.i 1.57264 0.907962i 0.576792 0.816891i \(-0.304304\pi\)
0.995844 0.0910712i \(-0.0290291\pi\)
\(620\) 284166. + 75570.6i 0.739247 + 0.196594i
\(621\) 0 0
\(622\) 389360. 299347.i 1.00640 0.773739i
\(623\) 128310. 74079.7i 0.330586 0.190864i
\(624\) 0 0
\(625\) 144273. 249889.i 0.369339 0.639715i
\(626\) −192670. + 25549.5i −0.491660 + 0.0651979i
\(627\) 0 0
\(628\) −540445. + 145900.i −1.37035 + 0.369943i
\(629\) −90453.5 −0.228625
\(630\) 0 0
\(631\) 230753.i 0.579546i 0.957095 + 0.289773i \(0.0935798\pi\)
−0.957095 + 0.289773i \(0.906420\pi\)
\(632\) 279173. 365955.i 0.698940 0.916207i
\(633\) 0 0
\(634\) 436711. 57911.2i 1.08646 0.144073i
\(635\) 155955. + 90040.8i 0.386770 + 0.223302i
\(636\) 0 0
\(637\) 425225. + 736511.i 1.04795 + 1.81510i
\(638\) −83889.0 + 64495.5i −0.206093 + 0.158449i
\(639\) 0 0
\(640\) −360090. 45001.6i −0.879126 0.109867i
\(641\) 259471. + 449416.i 0.631498 + 1.09379i 0.987246 + 0.159205i \(0.0508931\pi\)
−0.355747 + 0.934582i \(0.615774\pi\)
\(642\) 0 0
\(643\) 195039. + 112606.i 0.471738 + 0.272358i 0.716967 0.697107i \(-0.245530\pi\)
−0.245229 + 0.969465i \(0.578863\pi\)
\(644\) 248280. + 247349.i 0.598645 + 0.596402i
\(645\) 0 0
\(646\) −339733. 140348.i −0.814090 0.336312i
\(647\) 153505.i 0.366703i 0.983047 + 0.183352i \(0.0586947\pi\)
−0.983047 + 0.183352i \(0.941305\pi\)
\(648\) 0 0
\(649\) −32276.0 −0.0766284
\(650\) 25912.7 62725.3i 0.0613318 0.148462i
\(651\) 0 0
\(652\) 163851. 164468.i 0.385438 0.386888i
\(653\) 36120.4 62562.3i 0.0847082 0.146719i −0.820559 0.571562i \(-0.806338\pi\)
0.905267 + 0.424843i \(0.139671\pi\)
\(654\) 0 0
\(655\) −312193. + 180245.i −0.727681 + 0.420127i
\(656\) 73061.5 + 41817.1i 0.169778 + 0.0971731i
\(657\) 0 0
\(658\) 285920. + 371895.i 0.660378 + 0.858950i
\(659\) 203157. 117293.i 0.467802 0.270086i −0.247517 0.968883i \(-0.579615\pi\)
0.715319 + 0.698798i \(0.246281\pi\)
\(660\) 0 0
\(661\) −298973. + 517837.i −0.684274 + 1.18520i 0.289391 + 0.957211i \(0.406547\pi\)
−0.973665 + 0.227986i \(0.926786\pi\)
\(662\) −97026.0 731678.i −0.221397 1.66957i
\(663\) 0 0
\(664\) −128971. + 169061.i −0.292519 + 0.383450i
\(665\) −685452. −1.55001
\(666\) 0 0
\(667\) 277166.i 0.623001i
\(668\) 186061. + 689211.i 0.416968 + 1.54454i
\(669\) 0 0
\(670\) −2886.86 21769.9i −0.00643096 0.0484961i
\(671\) 35461.3 + 20473.6i 0.0787607 + 0.0454725i
\(672\) 0 0
\(673\) 375852. + 650996.i 0.829826 + 1.43730i 0.898174 + 0.439640i \(0.144894\pi\)
−0.0683477 + 0.997662i \(0.521773\pi\)
\(674\) −159998. 208109.i −0.352204 0.458111i
\(675\) 0 0
\(676\) 51928.7 195266.i 0.113636 0.427301i
\(677\) −42323.8 73307.0i −0.0923437 0.159944i 0.816153 0.577836i \(-0.196103\pi\)
−0.908497 + 0.417892i \(0.862769\pi\)
\(678\) 0 0
\(679\) −483267. 279014.i −1.04821 0.605183i
\(680\) −51398.8 + 399095.i −0.111157 + 0.863094i
\(681\) 0 0
\(682\) −27713.0 + 67083.2i −0.0595820 + 0.144226i
\(683\) 635506.i 1.36232i −0.732136 0.681159i \(-0.761476\pi\)
0.732136 0.681159i \(-0.238524\pi\)
\(684\) 0 0
\(685\) −546260. −1.16418
\(686\) 1.53261e6 + 633142.i 3.25674 + 1.34540i
\(687\) 0 0
\(688\) −26678.3 45810.1i −0.0563614 0.0967797i
\(689\) −178878. + 309825.i −0.376806 + 0.652647i
\(690\) 0 0
\(691\) 384843. 222189.i 0.805986 0.465336i −0.0395741 0.999217i \(-0.512600\pi\)
0.845560 + 0.533881i \(0.179267\pi\)
\(692\) −217474. + 817762.i −0.454145 + 1.70771i
\(693\) 0 0
\(694\) 332553. 255673.i 0.690466 0.530844i
\(695\) 378265. 218391.i 0.783116 0.452132i
\(696\) 0 0
\(697\) 46672.6 80839.4i 0.0960720 0.166402i
\(698\) 346344. 45927.8i 0.710880 0.0942682i
\(699\) 0 0
\(700\) −53584.8 198490.i −0.109357 0.405081i
\(701\) 374624. 0.762359 0.381179 0.924501i \(-0.375518\pi\)
0.381179 + 0.924501i \(0.375518\pi\)
\(702\) 0 0
\(703\) 103156.i 0.208730i
\(704\) 22696.4 86653.5i 0.0457944 0.174840i
\(705\) 0 0
\(706\) 193144. 25612.3i 0.387499 0.0513854i
\(707\) −455254. 262841.i −0.910783 0.525841i
\(708\) 0 0
\(709\) −92815.5 160761.i −0.184641 0.319808i 0.758814 0.651307i \(-0.225779\pi\)
−0.943456 + 0.331499i \(0.892446\pi\)
\(710\) 302603. 232647.i 0.600284 0.461510i
\(711\) 0 0
\(712\) 91532.8 38216.5i 0.180558 0.0753860i
\(713\) −95057.9 164645.i −0.186986 0.323869i
\(714\) 0 0
\(715\) −52950.0 30570.7i −0.103575 0.0597989i
\(716\) −370854. + 372249.i −0.723396 + 0.726118i
\(717\) 0 0
\(718\) 404478. + 167096.i 0.784596 + 0.324128i
\(719\) 651163.i 1.25960i −0.776759 0.629799i \(-0.783137\pi\)
0.776759 0.629799i \(-0.216863\pi\)
\(720\) 0 0
\(721\) −1.71435e6 −3.29783
\(722\) −38976.5 + 94348.1i −0.0747702 + 0.180992i
\(723\) 0 0
\(724\) 257967. + 257000.i 0.492138 + 0.490294i
\(725\) −81298.3 + 140813.i −0.154670 + 0.267896i
\(726\) 0 0
\(727\) 207917. 120041.i 0.393389 0.227123i −0.290239 0.956954i \(-0.593735\pi\)
0.683627 + 0.729831i \(0.260401\pi\)
\(728\) 297539. + 712640.i 0.561412 + 1.34465i
\(729\) 0 0
\(730\) −162581. 211468.i −0.305086 0.396825i
\(731\) −50907.1 + 29391.2i −0.0952673 + 0.0550026i
\(732\) 0 0
\(733\) 27840.0 48220.4i 0.0518158 0.0897475i −0.838954 0.544202i \(-0.816832\pi\)
0.890770 + 0.454455i \(0.150166\pi\)
\(734\) 675.675 + 5095.29i 0.00125414 + 0.00945751i
\(735\) 0 0
\(736\) 143706. + 185472.i 0.265288 + 0.342391i
\(737\) 5420.76 0.00997988
\(738\) 0 0
\(739\) 327859.i 0.600341i −0.953886 0.300170i \(-0.902957\pi\)
0.953886 0.300170i \(-0.0970435\pi\)
\(740\) −109022. + 29431.8i −0.199091 + 0.0537470i
\(741\) 0 0
\(742\) 142470. + 1.07438e6i 0.258772 + 1.95141i
\(743\) 11150.8 + 6437.91i 0.0201989 + 0.0116618i 0.510065 0.860136i \(-0.329621\pi\)
−0.489867 + 0.871797i \(0.662955\pi\)
\(744\) 0 0
\(745\) 330968. + 573254.i 0.596312 + 1.03284i
\(746\) 179327. + 233250.i 0.322232 + 0.419126i
\(747\) 0 0
\(748\) −95990.4 25527.5i −0.171563 0.0456252i
\(749\) −416567. 721516.i −0.742543 1.28612i
\(750\) 0 0
\(751\) 460430. + 265829.i 0.816363 + 0.471328i 0.849161 0.528134i \(-0.177108\pi\)
−0.0327975 + 0.999462i \(0.510442\pi\)
\(752\) 158048. + 271389.i 0.279482 + 0.479906i
\(753\) 0 0
\(754\) 233193. 564476.i 0.410179 0.992894i
\(755\) 132075.i 0.231701i
\(756\) 0 0
\(757\) 614542. 1.07241 0.536204 0.844089i \(-0.319858\pi\)
0.536204 + 0.844089i \(0.319858\pi\)
\(758\) −514134. 212396.i −0.894825 0.369665i
\(759\) 0 0
\(760\) −455141. 58616.9i −0.787986 0.101484i
\(761\) −410349. + 710745.i −0.708571 + 1.22728i 0.256816 + 0.966460i \(0.417327\pi\)
−0.965387 + 0.260821i \(0.916007\pi\)
\(762\) 0 0
\(763\) −1.00688e6 + 581324.i −1.72954 + 0.998548i
\(764\) 889149. + 236458.i 1.52331 + 0.405105i
\(765\) 0 0
\(766\) −329554. + 253368.i −0.561654 + 0.431811i
\(767\) 161332. 93144.9i 0.274239 0.158332i
\(768\) 0 0
\(769\) 65721.6 113833.i 0.111136 0.192494i −0.805092 0.593149i \(-0.797884\pi\)
0.916229 + 0.400656i \(0.131218\pi\)
\(770\) −183614. + 24348.6i −0.309687 + 0.0410669i
\(771\) 0 0
\(772\) −694213. + 187411.i −1.16482 + 0.314457i
\(773\) 629.598 0.00105367 0.000526834 1.00000i \(-0.499832\pi\)
0.000526834 1.00000i \(0.499832\pi\)
\(774\) 0 0
\(775\) 111529.i 0.185689i
\(776\) −297029. 226593.i −0.493260 0.376290i
\(777\) 0 0
\(778\) 396853.