Properties

Label 108.5.k.a.5.8
Level 108
Weight 5
Character 108.5
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.8
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.8

$q$-expansion

\(f(q)\) \(=\) \(q+(4.78712 + 7.62125i) q^{3} +(-3.22217 - 8.85284i) q^{5} +(-16.2288 - 92.0381i) q^{7} +(-35.1670 + 72.9677i) q^{9} +O(q^{10})\) \(q+(4.78712 + 7.62125i) q^{3} +(-3.22217 - 8.85284i) q^{5} +(-16.2288 - 92.0381i) q^{7} +(-35.1670 + 72.9677i) q^{9} +(74.5484 - 204.820i) q^{11} +(-77.8115 - 65.2916i) q^{13} +(52.0448 - 66.9366i) q^{15} +(135.945 + 78.4880i) q^{17} +(237.980 + 412.193i) q^{19} +(623.756 - 564.281i) q^{21} +(50.4332 + 8.89274i) q^{23} +(410.787 - 344.691i) q^{25} +(-724.454 + 81.2889i) q^{27} +(-936.902 - 1116.56i) q^{29} +(62.7625 - 355.944i) q^{31} +(1917.86 - 412.346i) q^{33} +(-762.507 + 440.234i) q^{35} +(-499.310 + 864.830i) q^{37} +(125.111 - 905.580i) q^{39} +(1273.34 - 1517.51i) q^{41} +(739.364 + 269.107i) q^{43} +(759.286 + 76.2131i) q^{45} +(-280.621 + 49.4811i) q^{47} +(-5951.44 + 2166.15i) q^{49} +(52.6093 + 1411.80i) q^{51} -3261.43i q^{53} -2053.45 q^{55} +(-2002.19 + 3786.92i) q^{57} +(1215.30 + 3339.02i) q^{59} +(744.052 + 4219.73i) q^{61} +(7286.53 + 2052.52i) q^{63} +(-327.294 + 899.234i) q^{65} +(5409.04 + 4538.72i) q^{67} +(173.656 + 426.935i) q^{69} +(-6345.67 - 3663.67i) q^{71} +(851.462 + 1474.78i) q^{73} +(4593.47 + 1480.63i) q^{75} +(-20061.1 - 3537.31i) q^{77} +(-4665.20 + 3914.57i) q^{79} +(-4087.57 - 5132.10i) q^{81} +(1610.83 + 1919.72i) q^{83} +(256.803 - 1456.40i) q^{85} +(4024.49 - 12485.5i) q^{87} +(9812.53 - 5665.26i) q^{89} +(-4746.53 + 8221.23i) q^{91} +(3013.19 - 1225.62i) q^{93} +(2882.27 - 3434.95i) q^{95} +(-6396.61 - 2328.18i) q^{97} +(12323.6 + 12642.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.78712 + 7.62125i 0.531902 + 0.846806i
\(4\) 0 0
\(5\) −3.22217 8.85284i −0.128887 0.354114i 0.858418 0.512951i \(-0.171448\pi\)
−0.987305 + 0.158837i \(0.949226\pi\)
\(6\) 0 0
\(7\) −16.2288 92.0381i −0.331200 1.87833i −0.461939 0.886912i \(-0.652846\pi\)
0.130739 0.991417i \(-0.458265\pi\)
\(8\) 0 0
\(9\) −35.1670 + 72.9677i −0.434160 + 0.900836i
\(10\) 0 0
\(11\) 74.5484 204.820i 0.616102 1.69273i −0.100228 0.994965i \(-0.531957\pi\)
0.716330 0.697762i \(-0.245821\pi\)
\(12\) 0 0
\(13\) −77.8115 65.2916i −0.460423 0.386341i 0.382863 0.923805i \(-0.374938\pi\)
−0.843287 + 0.537464i \(0.819382\pi\)
\(14\) 0 0
\(15\) 52.0448 66.9366i 0.231310 0.297496i
\(16\) 0 0
\(17\) 135.945 + 78.4880i 0.470399 + 0.271585i 0.716407 0.697683i \(-0.245786\pi\)
−0.246008 + 0.969268i \(0.579119\pi\)
\(18\) 0 0
\(19\) 237.980 + 412.193i 0.659223 + 1.14181i 0.980817 + 0.194931i \(0.0624482\pi\)
−0.321594 + 0.946878i \(0.604219\pi\)
\(20\) 0 0
\(21\) 623.756 564.281i 1.41441 1.27955i
\(22\) 0 0
\(23\) 50.4332 + 8.89274i 0.0953369 + 0.0168105i 0.221113 0.975248i \(-0.429031\pi\)
−0.125776 + 0.992059i \(0.540142\pi\)
\(24\) 0 0
\(25\) 410.787 344.691i 0.657260 0.551506i
\(26\) 0 0
\(27\) −724.454 + 81.2889i −0.993764 + 0.111507i
\(28\) 0 0
\(29\) −936.902 1116.56i −1.11403 1.32765i −0.939323 0.343033i \(-0.888546\pi\)
−0.174710 0.984620i \(-0.555899\pi\)
\(30\) 0 0
\(31\) 62.7625 355.944i 0.0653095 0.370389i −0.934583 0.355745i \(-0.884227\pi\)
0.999893 0.0146442i \(-0.00466157\pi\)
\(32\) 0 0
\(33\) 1917.86 412.346i 1.76112 0.378646i
\(34\) 0 0
\(35\) −762.507 + 440.234i −0.622455 + 0.359374i
\(36\) 0 0
\(37\) −499.310 + 864.830i −0.364726 + 0.631724i −0.988732 0.149696i \(-0.952171\pi\)
0.624006 + 0.781419i \(0.285504\pi\)
\(38\) 0 0
\(39\) 125.111 905.580i 0.0822556 0.595385i
\(40\) 0 0
\(41\) 1273.34 1517.51i 0.757489 0.902740i −0.240198 0.970724i \(-0.577212\pi\)
0.997686 + 0.0679839i \(0.0216567\pi\)
\(42\) 0 0
\(43\) 739.364 + 269.107i 0.399872 + 0.145542i 0.534125 0.845405i \(-0.320641\pi\)
−0.134253 + 0.990947i \(0.542863\pi\)
\(44\) 0 0
\(45\) 759.286 + 76.2131i 0.374956 + 0.0376361i
\(46\) 0 0
\(47\) −280.621 + 49.4811i −0.127035 + 0.0223998i −0.236804 0.971557i \(-0.576100\pi\)
0.109769 + 0.993957i \(0.464989\pi\)
\(48\) 0 0
\(49\) −5951.44 + 2166.15i −2.47873 + 0.902185i
\(50\) 0 0
\(51\) 52.6093 + 1411.80i 0.0202265 + 0.542793i
\(52\) 0 0
\(53\) 3261.43i 1.16106i −0.814237 0.580532i \(-0.802845\pi\)
0.814237 0.580532i \(-0.197155\pi\)
\(54\) 0 0
\(55\) −2053.45 −0.678825
\(56\) 0 0
\(57\) −2002.19 + 3786.92i −0.616247 + 1.16556i
\(58\) 0 0
\(59\) 1215.30 + 3339.02i 0.349125 + 0.959213i 0.982647 + 0.185488i \(0.0593866\pi\)
−0.633522 + 0.773725i \(0.718391\pi\)
\(60\) 0 0
\(61\) 744.052 + 4219.73i 0.199960 + 1.13403i 0.905176 + 0.425038i \(0.139739\pi\)
−0.705215 + 0.708993i \(0.749150\pi\)
\(62\) 0 0
\(63\) 7286.53 + 2052.52i 1.83586 + 0.517138i
\(64\) 0 0
\(65\) −327.294 + 899.234i −0.0774661 + 0.212836i
\(66\) 0 0
\(67\) 5409.04 + 4538.72i 1.20495 + 1.01108i 0.999475 + 0.0324148i \(0.0103198\pi\)
0.205479 + 0.978661i \(0.434125\pi\)
\(68\) 0 0
\(69\) 173.656 + 426.935i 0.0364747 + 0.0896733i
\(70\) 0 0
\(71\) −6345.67 3663.67i −1.25881 0.726775i −0.285967 0.958239i \(-0.592315\pi\)
−0.972843 + 0.231465i \(0.925648\pi\)
\(72\) 0 0
\(73\) 851.462 + 1474.78i 0.159779 + 0.276745i 0.934789 0.355204i \(-0.115589\pi\)
−0.775010 + 0.631949i \(0.782255\pi\)
\(74\) 0 0
\(75\) 4593.47 + 1480.63i 0.816617 + 0.263224i
\(76\) 0 0
\(77\) −20061.1 3537.31i −3.38355 0.596611i
\(78\) 0 0
\(79\) −4665.20 + 3914.57i −0.747509 + 0.627234i −0.934843 0.355062i \(-0.884460\pi\)
0.187334 + 0.982296i \(0.440015\pi\)
\(80\) 0 0
\(81\) −4087.57 5132.10i −0.623010 0.782214i
\(82\) 0 0
\(83\) 1610.83 + 1919.72i 0.233827 + 0.278664i 0.870180 0.492734i \(-0.164002\pi\)
−0.636353 + 0.771398i \(0.719558\pi\)
\(84\) 0 0
\(85\) 256.803 1456.40i 0.0355437 0.201578i
\(86\) 0 0
\(87\) 4024.49 12485.5i 0.531708 1.64955i
\(88\) 0 0
\(89\) 9812.53 5665.26i 1.23880 0.715221i 0.269950 0.962874i \(-0.412993\pi\)
0.968849 + 0.247653i \(0.0796594\pi\)
\(90\) 0 0
\(91\) −4746.53 + 8221.23i −0.573183 + 0.992782i
\(92\) 0 0
\(93\) 3013.19 1225.62i 0.348386 0.141706i
\(94\) 0 0
\(95\) 2882.27 3434.95i 0.319365 0.380604i
\(96\) 0 0
\(97\) −6396.61 2328.18i −0.679840 0.247441i −0.0210609 0.999778i \(-0.506704\pi\)
−0.658779 + 0.752337i \(0.728927\pi\)
\(98\) 0 0
\(99\) 12323.6 + 12642.5i 1.25738 + 1.28992i
\(100\) 0 0
\(101\) 9985.15 1760.65i 0.978840 0.172596i 0.338734 0.940882i \(-0.390001\pi\)
0.640106 + 0.768286i \(0.278890\pi\)
\(102\) 0 0
\(103\) 6493.17 2363.32i 0.612044 0.222766i −0.0173536 0.999849i \(-0.505524\pi\)
0.629397 + 0.777084i \(0.283302\pi\)
\(104\) 0 0
\(105\) −7005.34 3703.81i −0.635405 0.335946i
\(106\) 0 0
\(107\) 6794.89i 0.593492i −0.954956 0.296746i \(-0.904099\pi\)
0.954956 0.296746i \(-0.0959015\pi\)
\(108\) 0 0
\(109\) 1303.17 0.109685 0.0548426 0.998495i \(-0.482534\pi\)
0.0548426 + 0.998495i \(0.482534\pi\)
\(110\) 0 0
\(111\) −8981.34 + 334.679i −0.728946 + 0.0271633i
\(112\) 0 0
\(113\) 2799.78 + 7692.32i 0.219264 + 0.602422i 0.999741 0.0227625i \(-0.00724614\pi\)
−0.780477 + 0.625184i \(0.785024\pi\)
\(114\) 0 0
\(115\) −83.7785 475.131i −0.00633486 0.0359267i
\(116\) 0 0
\(117\) 7500.57 3381.62i 0.547927 0.247032i
\(118\) 0 0
\(119\) 5017.66 13785.9i 0.354330 0.973512i
\(120\) 0 0
\(121\) −25178.1 21126.9i −1.71970 1.44300i
\(122\) 0 0
\(123\) 17660.9 + 2439.95i 1.16736 + 0.161276i
\(124\) 0 0
\(125\) −9474.39 5470.04i −0.606361 0.350083i
\(126\) 0 0
\(127\) 7118.80 + 12330.1i 0.441367 + 0.764469i 0.997791 0.0664288i \(-0.0211605\pi\)
−0.556425 + 0.830898i \(0.687827\pi\)
\(128\) 0 0
\(129\) 1488.50 + 6923.13i 0.0894475 + 0.416028i
\(130\) 0 0
\(131\) 2925.80 + 515.898i 0.170492 + 0.0300623i 0.258242 0.966080i \(-0.416857\pi\)
−0.0877506 + 0.996142i \(0.527968\pi\)
\(132\) 0 0
\(133\) 34075.3 28592.6i 1.92636 1.61640i
\(134\) 0 0
\(135\) 3053.95 + 6151.55i 0.167569 + 0.337534i
\(136\) 0 0
\(137\) 10598.0 + 12630.2i 0.564652 + 0.672926i 0.970524 0.241004i \(-0.0774766\pi\)
−0.405872 + 0.913930i \(0.633032\pi\)
\(138\) 0 0
\(139\) −669.020 + 3794.20i −0.0346266 + 0.196377i −0.997214 0.0745944i \(-0.976234\pi\)
0.962587 + 0.270971i \(0.0873449\pi\)
\(140\) 0 0
\(141\) −1720.47 1901.81i −0.0865386 0.0956598i
\(142\) 0 0
\(143\) −19173.7 + 11070.0i −0.937637 + 0.541345i
\(144\) 0 0
\(145\) −6865.84 + 11892.0i −0.326556 + 0.565612i
\(146\) 0 0
\(147\) −44999.0 34987.8i −2.08242 1.61913i
\(148\) 0 0
\(149\) 930.055 1108.40i 0.0418925 0.0499255i −0.744691 0.667409i \(-0.767403\pi\)
0.786584 + 0.617483i \(0.211848\pi\)
\(150\) 0 0
\(151\) 35146.0 + 12792.1i 1.54142 + 0.561033i 0.966386 0.257094i \(-0.0827649\pi\)
0.575038 + 0.818126i \(0.304987\pi\)
\(152\) 0 0
\(153\) −10507.9 + 7159.43i −0.448882 + 0.305841i
\(154\) 0 0
\(155\) −3353.34 + 591.285i −0.139577 + 0.0246112i
\(156\) 0 0
\(157\) −17397.8 + 6332.28i −0.705822 + 0.256898i −0.669895 0.742456i \(-0.733661\pi\)
−0.0359274 + 0.999354i \(0.511439\pi\)
\(158\) 0 0
\(159\) 24856.2 15612.9i 0.983196 0.617573i
\(160\) 0 0
\(161\) 4786.10i 0.184642i
\(162\) 0 0
\(163\) 7731.09 0.290982 0.145491 0.989360i \(-0.453524\pi\)
0.145491 + 0.989360i \(0.453524\pi\)
\(164\) 0 0
\(165\) −9830.09 15649.8i −0.361069 0.574833i
\(166\) 0 0
\(167\) 12185.8 + 33480.3i 0.436941 + 1.20048i 0.941472 + 0.337091i \(0.109443\pi\)
−0.504531 + 0.863393i \(0.668335\pi\)
\(168\) 0 0
\(169\) −3167.93 17966.2i −0.110918 0.629047i
\(170\) 0 0
\(171\) −38445.8 + 2869.26i −1.31479 + 0.0981245i
\(172\) 0 0
\(173\) −9745.05 + 26774.3i −0.325606 + 0.894594i 0.663604 + 0.748084i \(0.269026\pi\)
−0.989209 + 0.146510i \(0.953196\pi\)
\(174\) 0 0
\(175\) −38391.3 32214.2i −1.25359 1.05189i
\(176\) 0 0
\(177\) −19629.7 + 25246.4i −0.626567 + 0.805849i
\(178\) 0 0
\(179\) −970.180 560.134i −0.0302793 0.0174818i 0.484784 0.874634i \(-0.338898\pi\)
−0.515063 + 0.857152i \(0.672232\pi\)
\(180\) 0 0
\(181\) 14022.2 + 24287.1i 0.428014 + 0.741341i 0.996697 0.0812156i \(-0.0258802\pi\)
−0.568683 + 0.822557i \(0.692547\pi\)
\(182\) 0 0
\(183\) −28597.8 + 25871.0i −0.853945 + 0.772521i
\(184\) 0 0
\(185\) 9265.06 + 1633.68i 0.270710 + 0.0477336i
\(186\) 0 0
\(187\) 26210.4 21993.1i 0.749533 0.628933i
\(188\) 0 0
\(189\) 19238.7 + 65358.1i 0.538582 + 1.82968i
\(190\) 0 0
\(191\) 28168.4 + 33569.8i 0.772140 + 0.920201i 0.998550 0.0538315i \(-0.0171434\pi\)
−0.226410 + 0.974032i \(0.572699\pi\)
\(192\) 0 0
\(193\) 4122.59 23380.4i 0.110677 0.627678i −0.878124 0.478434i \(-0.841205\pi\)
0.988800 0.149245i \(-0.0476842\pi\)
\(194\) 0 0
\(195\) −8420.09 + 1810.35i −0.221436 + 0.0476094i
\(196\) 0 0
\(197\) 44291.2 25571.6i 1.14126 0.658908i 0.194519 0.980899i \(-0.437685\pi\)
0.946743 + 0.321991i \(0.104352\pi\)
\(198\) 0 0
\(199\) −4204.89 + 7283.09i −0.106181 + 0.183912i −0.914220 0.405218i \(-0.867196\pi\)
0.808039 + 0.589129i \(0.200529\pi\)
\(200\) 0 0
\(201\) −8697.03 + 62951.0i −0.215268 + 1.55816i
\(202\) 0 0
\(203\) −87560.9 + 104351.i −2.12480 + 2.53224i
\(204\) 0 0
\(205\) −17537.2 6383.00i −0.417303 0.151886i
\(206\) 0 0
\(207\) −2422.46 + 3367.26i −0.0565349 + 0.0785844i
\(208\) 0 0
\(209\) 102166. 18014.7i 2.33892 0.412414i
\(210\) 0 0
\(211\) 30234.2 11004.4i 0.679101 0.247172i 0.0206394 0.999787i \(-0.493430\pi\)
0.658461 + 0.752615i \(0.271208\pi\)
\(212\) 0 0
\(213\) −2455.70 65900.3i −0.0541273 1.45254i
\(214\) 0 0
\(215\) 7412.58i 0.160359i
\(216\) 0 0
\(217\) −33778.9 −0.717342
\(218\) 0 0
\(219\) −7163.58 + 13549.1i −0.149363 + 0.282503i
\(220\) 0 0
\(221\) −5453.50 14983.4i −0.111658 0.306778i
\(222\) 0 0
\(223\) −3467.79 19666.8i −0.0697337 0.395480i −0.999618 0.0276281i \(-0.991205\pi\)
0.929885 0.367852i \(-0.119907\pi\)
\(224\) 0 0
\(225\) 10705.2 + 42096.0i 0.211461 + 0.831525i
\(226\) 0 0
\(227\) 3080.37 8463.24i 0.0597793 0.164242i −0.906208 0.422833i \(-0.861036\pi\)
0.965987 + 0.258590i \(0.0832580\pi\)
\(228\) 0 0
\(229\) 1739.18 + 1459.35i 0.0331646 + 0.0278284i 0.659219 0.751951i \(-0.270887\pi\)
−0.626055 + 0.779779i \(0.715331\pi\)
\(230\) 0 0
\(231\) −69076.0 169824.i −1.29450 3.18255i
\(232\) 0 0
\(233\) −34404.1 19863.2i −0.633721 0.365879i 0.148471 0.988917i \(-0.452565\pi\)
−0.782192 + 0.623038i \(0.785898\pi\)
\(234\) 0 0
\(235\) 1342.26 + 2324.86i 0.0243052 + 0.0420979i
\(236\) 0 0
\(237\) −52166.8 16815.2i −0.928747 0.299367i
\(238\) 0 0
\(239\) −21056.6 3712.84i −0.368631 0.0649995i −0.0137356 0.999906i \(-0.504372\pi\)
−0.354895 + 0.934906i \(0.615483\pi\)
\(240\) 0 0
\(241\) 23758.0 19935.4i 0.409050 0.343234i −0.414929 0.909854i \(-0.636194\pi\)
0.823979 + 0.566620i \(0.191749\pi\)
\(242\) 0 0
\(243\) 19545.4 55720.4i 0.331002 0.943630i
\(244\) 0 0
\(245\) 38353.1 + 45707.4i 0.638952 + 0.761473i
\(246\) 0 0
\(247\) 8395.18 47611.4i 0.137606 0.780400i
\(248\) 0 0
\(249\) −6919.40 + 21466.5i −0.111601 + 0.346228i
\(250\) 0 0
\(251\) 82656.9 47722.0i 1.31199 0.757479i 0.329567 0.944132i \(-0.393097\pi\)
0.982426 + 0.186653i \(0.0597640\pi\)
\(252\) 0 0
\(253\) 5581.12 9666.79i 0.0871928 0.151022i
\(254\) 0 0
\(255\) 12329.0 5014.82i 0.189604 0.0771214i
\(256\) 0 0
\(257\) −53966.9 + 64315.2i −0.817073 + 0.973750i −0.999956 0.00938502i \(-0.997013\pi\)
0.182883 + 0.983135i \(0.441457\pi\)
\(258\) 0 0
\(259\) 87700.5 + 31920.4i 1.30738 + 0.475848i
\(260\) 0 0
\(261\) 114421. 29097.7i 1.67967 0.427147i
\(262\) 0 0
\(263\) −31439.9 + 5543.70i −0.454537 + 0.0801471i −0.396229 0.918152i \(-0.629681\pi\)
−0.0583075 + 0.998299i \(0.518570\pi\)
\(264\) 0 0
\(265\) −28872.9 + 10508.9i −0.411149 + 0.149646i
\(266\) 0 0
\(267\) 90150.1 + 47663.4i 1.26457 + 0.668594i
\(268\) 0 0
\(269\) 48870.4i 0.675370i −0.941259 0.337685i \(-0.890356\pi\)
0.941259 0.337685i \(-0.109644\pi\)
\(270\) 0 0
\(271\) 59047.3 0.804010 0.402005 0.915637i \(-0.368313\pi\)
0.402005 + 0.915637i \(0.368313\pi\)
\(272\) 0 0
\(273\) −85378.3 + 3181.52i −1.14557 + 0.0426884i
\(274\) 0 0
\(275\) −39976.2 109834.i −0.528610 1.45235i
\(276\) 0 0
\(277\) 6145.10 + 34850.6i 0.0800884 + 0.454204i 0.998309 + 0.0581339i \(0.0185150\pi\)
−0.918220 + 0.396070i \(0.870374\pi\)
\(278\) 0 0
\(279\) 23765.2 + 17097.1i 0.305305 + 0.219641i
\(280\) 0 0
\(281\) −9557.52 + 26259.1i −0.121041 + 0.332557i −0.985385 0.170344i \(-0.945512\pi\)
0.864344 + 0.502902i \(0.167734\pi\)
\(282\) 0 0
\(283\) 4019.76 + 3372.98i 0.0501912 + 0.0421154i 0.667538 0.744576i \(-0.267348\pi\)
−0.617347 + 0.786691i \(0.711793\pi\)
\(284\) 0 0
\(285\) 39976.4 + 5522.95i 0.492169 + 0.0679957i
\(286\) 0 0
\(287\) −160333. 92568.4i −1.94652 1.12383i
\(288\) 0 0
\(289\) −29439.8 50991.2i −0.352483 0.610519i
\(290\) 0 0
\(291\) −12877.7 59895.4i −0.152073 0.707307i
\(292\) 0 0
\(293\) 132502. + 23363.7i 1.54344 + 0.272149i 0.879594 0.475725i \(-0.157814\pi\)
0.663841 + 0.747874i \(0.268925\pi\)
\(294\) 0 0
\(295\) 25643.9 21517.8i 0.294673 0.247260i
\(296\) 0 0
\(297\) −37357.2 + 154442.i −0.423508 + 1.75087i
\(298\) 0 0
\(299\) −3343.66 3984.82i −0.0374007 0.0445725i
\(300\) 0 0
\(301\) 12769.1 72416.9i 0.140937 0.799295i
\(302\) 0 0
\(303\) 61218.5 + 67670.9i 0.666802 + 0.737083i
\(304\) 0 0
\(305\) 34959.2 20183.7i 0.375804 0.216970i
\(306\) 0 0
\(307\) −81998.8 + 142026.i −0.870023 + 1.50692i −0.00805046 + 0.999968i \(0.502563\pi\)
−0.861972 + 0.506956i \(0.830771\pi\)
\(308\) 0 0
\(309\) 49095.1 + 38172.6i 0.514187 + 0.399792i
\(310\) 0 0
\(311\) 19542.3 23289.6i 0.202048 0.240792i −0.655500 0.755195i \(-0.727542\pi\)
0.857548 + 0.514403i \(0.171987\pi\)
\(312\) 0 0
\(313\) 11927.4 + 4341.21i 0.121746 + 0.0443121i 0.402175 0.915563i \(-0.368254\pi\)
−0.280429 + 0.959875i \(0.590477\pi\)
\(314\) 0 0
\(315\) −5307.78 71120.1i −0.0534924 0.716755i
\(316\) 0 0
\(317\) 140231. 24726.4i 1.39548 0.246061i 0.575196 0.818016i \(-0.304926\pi\)
0.820285 + 0.571955i \(0.193815\pi\)
\(318\) 0 0
\(319\) −298537. + 108659.i −2.93371 + 1.06778i
\(320\) 0 0
\(321\) 51785.6 32527.9i 0.502572 0.315680i
\(322\) 0 0
\(323\) 74714.2i 0.716140i
\(324\) 0 0
\(325\) −54469.5 −0.515687
\(326\) 0 0
\(327\) 6238.43 + 9931.78i 0.0583418 + 0.0928820i
\(328\) 0 0
\(329\) 9108.29 + 25024.8i 0.0841482 + 0.231195i
\(330\) 0 0
\(331\) −23354.9 132452.i −0.213168 1.20893i −0.884058 0.467377i \(-0.845199\pi\)
0.670890 0.741557i \(-0.265912\pi\)
\(332\) 0 0
\(333\) −45545.4 66846.9i −0.410730 0.602827i
\(334\) 0 0
\(335\) 22751.7 62509.9i 0.202733 0.557005i
\(336\) 0 0
\(337\) −11763.7 9870.88i −0.103582 0.0869152i 0.589526 0.807749i \(-0.299315\pi\)
−0.693108 + 0.720834i \(0.743759\pi\)
\(338\) 0 0
\(339\) −45222.2 + 58161.9i −0.393507 + 0.506103i
\(340\) 0 0
\(341\) −68225.5 39390.0i −0.586730 0.338748i
\(342\) 0 0
\(343\) 183756. + 318275.i 1.56190 + 2.70530i
\(344\) 0 0
\(345\) 3220.04 2913.01i 0.0270535 0.0244739i
\(346\) 0 0
\(347\) −131462. 23180.4i −1.09180 0.192513i −0.401371 0.915916i \(-0.631466\pi\)
−0.690427 + 0.723402i \(0.742577\pi\)
\(348\) 0 0
\(349\) −81464.1 + 68356.5i −0.668830 + 0.561215i −0.912719 0.408588i \(-0.866021\pi\)
0.243889 + 0.969803i \(0.421577\pi\)
\(350\) 0 0
\(351\) 61678.3 + 40975.5i 0.500632 + 0.332591i
\(352\) 0 0
\(353\) −128967. 153697.i −1.03497 1.23343i −0.971893 0.235422i \(-0.924353\pi\)
−0.0630783 0.998009i \(-0.520092\pi\)
\(354\) 0 0
\(355\) −11987.1 + 67982.2i −0.0951168 + 0.539434i
\(356\) 0 0
\(357\) 129086. 27754.0i 1.01284 0.217765i
\(358\) 0 0
\(359\) −138211. + 79796.1i −1.07239 + 0.619145i −0.928834 0.370497i \(-0.879188\pi\)
−0.143557 + 0.989642i \(0.545854\pi\)
\(360\) 0 0
\(361\) −48108.1 + 83325.7i −0.369151 + 0.639388i
\(362\) 0 0
\(363\) 40483.1 293026.i 0.307228 2.22378i
\(364\) 0 0
\(365\) 10312.4 12289.8i 0.0774059 0.0922488i
\(366\) 0 0
\(367\) 19730.1 + 7181.15i 0.146486 + 0.0533165i 0.414223 0.910176i \(-0.364053\pi\)
−0.267737 + 0.963492i \(0.586276\pi\)
\(368\) 0 0
\(369\) 65949.5 + 146279.i 0.484349 + 1.07431i
\(370\) 0 0
\(371\) −300176. + 52929.1i −2.18086 + 0.384545i
\(372\) 0 0
\(373\) 126485. 46036.6i 0.909117 0.330892i 0.155217 0.987880i \(-0.450392\pi\)
0.753900 + 0.656989i \(0.228170\pi\)
\(374\) 0 0
\(375\) −3666.48 98392.5i −0.0260728 0.699680i
\(376\) 0 0
\(377\) 148053.i 1.04168i
\(378\) 0 0
\(379\) −14232.6 −0.0990847 −0.0495424 0.998772i \(-0.515776\pi\)
−0.0495424 + 0.998772i \(0.515776\pi\)
\(380\) 0 0
\(381\) −59892.4 + 113280.i −0.412593 + 0.780375i
\(382\) 0 0
\(383\) 29653.3 + 81471.7i 0.202151 + 0.555405i 0.998797 0.0490416i \(-0.0156167\pi\)
−0.796646 + 0.604446i \(0.793394\pi\)
\(384\) 0 0
\(385\) 33325.0 + 188995.i 0.224827 + 1.27506i
\(386\) 0 0
\(387\) −45637.3 + 44486.0i −0.304718 + 0.297031i
\(388\) 0 0
\(389\) 57297.2 157423.i 0.378647 1.04032i −0.593271 0.805003i \(-0.702164\pi\)
0.971918 0.235321i \(-0.0756140\pi\)
\(390\) 0 0
\(391\) 6158.18 + 5167.33i 0.0402809 + 0.0337997i
\(392\) 0 0
\(393\) 10074.4 + 24768.0i 0.0652279 + 0.160363i
\(394\) 0 0
\(395\) 49687.1 + 28686.9i 0.318456 + 0.183861i
\(396\) 0 0
\(397\) −70460.9 122042.i −0.447062 0.774333i 0.551132 0.834418i \(-0.314196\pi\)
−0.998193 + 0.0600849i \(0.980863\pi\)
\(398\) 0 0
\(399\) 381034. + 122820.i 2.39341 + 0.771480i
\(400\) 0 0
\(401\) −279401. 49266.0i −1.73756 0.306379i −0.787008 0.616943i \(-0.788371\pi\)
−0.950552 + 0.310564i \(0.899482\pi\)
\(402\) 0 0
\(403\) −28123.8 + 23598.7i −0.173166 + 0.145304i
\(404\) 0 0
\(405\) −32262.9 + 52723.1i −0.196695 + 0.321434i
\(406\) 0 0
\(407\) 139912. + 166740.i 0.844627 + 1.00659i
\(408\) 0 0
\(409\) −29298.1 + 166158.i −0.175143 + 0.993286i 0.762836 + 0.646593i \(0.223807\pi\)
−0.937979 + 0.346693i \(0.887305\pi\)
\(410\) 0 0
\(411\) −45523.9 + 141232.i −0.269498 + 0.836082i
\(412\) 0 0
\(413\) 287594. 166043.i 1.68609 0.973463i
\(414\) 0 0
\(415\) 11804.6 20446.1i 0.0685416 0.118718i
\(416\) 0 0
\(417\) −32119.2 + 13064.5i −0.184711 + 0.0751314i
\(418\) 0 0
\(419\) 209146. 249251.i 1.19130 1.41974i 0.307713 0.951479i \(-0.400436\pi\)
0.883590 0.468261i \(-0.155119\pi\)
\(420\) 0 0
\(421\) −186899. 68025.7i −1.05449 0.383804i −0.244136 0.969741i \(-0.578504\pi\)
−0.810356 + 0.585938i \(0.800726\pi\)
\(422\) 0 0
\(423\) 6258.07 22216.4i 0.0349752 0.124163i
\(424\) 0 0
\(425\) 82898.7 14617.3i 0.458955 0.0809261i
\(426\) 0 0
\(427\) 376301. 136962.i 2.06386 0.751182i
\(428\) 0 0
\(429\) −176154. 93134.7i −0.957146 0.506054i
\(430\) 0 0
\(431\) 42286.8i 0.227641i 0.993501 + 0.113820i \(0.0363088\pi\)
−0.993501 + 0.113820i \(0.963691\pi\)
\(432\) 0 0
\(433\) −133410. −0.711564 −0.355782 0.934569i \(-0.615785\pi\)
−0.355782 + 0.934569i \(0.615785\pi\)
\(434\) 0 0
\(435\) −123499. + 4602.06i −0.652659 + 0.0243206i
\(436\) 0 0
\(437\) 8336.55 + 22904.5i 0.0436540 + 0.119938i
\(438\) 0 0
\(439\) −1918.30 10879.2i −0.00995375 0.0564505i 0.979426 0.201802i \(-0.0646798\pi\)
−0.989380 + 0.145352i \(0.953569\pi\)
\(440\) 0 0
\(441\) 51235.2 510439.i 0.263446 2.62462i
\(442\) 0 0
\(443\) −14620.6 + 40169.8i −0.0745004 + 0.204688i −0.971353 0.237642i \(-0.923626\pi\)
0.896853 + 0.442330i \(0.145848\pi\)
\(444\) 0 0
\(445\) −81771.3 68614.3i −0.412934 0.346493i
\(446\) 0 0
\(447\) 12899.6 + 1782.16i 0.0645599 + 0.00891930i
\(448\) 0 0
\(449\) −217766. 125727.i −1.08018 0.623643i −0.149236 0.988802i \(-0.547681\pi\)
−0.930945 + 0.365159i \(0.881015\pi\)
\(450\) 0 0
\(451\) −215890. 373933.i −1.06140 1.83840i
\(452\) 0 0
\(453\) 70756.4 + 329094.i 0.344802 + 1.60370i
\(454\) 0 0
\(455\) 88075.4 + 15530.1i 0.425434 + 0.0750154i
\(456\) 0 0
\(457\) −210621. + 176732.i −1.00848 + 0.846218i −0.988137 0.153575i \(-0.950921\pi\)
−0.0203462 + 0.999793i \(0.506477\pi\)
\(458\) 0 0
\(459\) −104866. 45810.1i −0.497749 0.217438i
\(460\) 0 0
\(461\) −108791. 129652.i −0.511906 0.610066i 0.446741 0.894663i \(-0.352585\pi\)
−0.958647 + 0.284597i \(0.908140\pi\)
\(462\) 0 0
\(463\) −36940.9 + 209502.i −0.172324 + 0.977298i 0.768864 + 0.639413i \(0.220823\pi\)
−0.941187 + 0.337885i \(0.890289\pi\)
\(464\) 0 0
\(465\) −20559.2 22726.1i −0.0950824 0.105104i
\(466\) 0 0
\(467\) 291740. 168436.i 1.33771 0.772326i 0.351241 0.936285i \(-0.385760\pi\)
0.986467 + 0.163958i \(0.0524263\pi\)
\(468\) 0 0
\(469\) 329953. 571496.i 1.50005 2.59817i
\(470\) 0 0
\(471\) −131545. 102280.i −0.592971 0.461049i
\(472\) 0 0
\(473\) 110237. 131375.i 0.492724 0.587206i
\(474\) 0 0
\(475\) 239838. + 87294.0i 1.06300 + 0.386899i
\(476\) 0 0
\(477\) 237979. + 114695.i 1.04593 + 0.504088i
\(478\) 0 0
\(479\) 46210.0 8148.07i 0.201403 0.0355127i −0.0720366 0.997402i \(-0.522950\pi\)
0.273439 + 0.961889i \(0.411839\pi\)
\(480\) 0 0
\(481\) 95318.2 34693.0i 0.411989 0.149952i
\(482\) 0 0
\(483\) 36476.0 22911.6i 0.156356 0.0982113i
\(484\) 0 0
\(485\) 64130.0i 0.272632i
\(486\) 0 0
\(487\) 303643. 1.28028 0.640141 0.768257i \(-0.278876\pi\)
0.640141 + 0.768257i \(0.278876\pi\)
\(488\) 0 0
\(489\) 37009.7 + 58920.6i 0.154774 + 0.246405i
\(490\) 0 0
\(491\) 94072.6 + 258462.i 0.390212 + 1.07210i 0.966905 + 0.255137i \(0.0821206\pi\)
−0.576693 + 0.816961i \(0.695657\pi\)
\(492\) 0 0
\(493\) −39731.1 225326.i −0.163469 0.927081i
\(494\) 0 0
\(495\) 72213.5 149835.i 0.294719 0.611510i
\(496\) 0 0
\(497\) −234215. + 643500.i −0.948204 + 2.60517i
\(498\) 0 0
\(499\) 122094. + 102449.i 0.490336 + 0.411441i 0.854147 0.520032i \(-0.174080\pi\)
−0.363811 + 0.931473i \(0.618524\pi\)
\(500\) 0 0
\(501\) −196827. + 253146.i −0.784168 + 1.00854i
\(502\) 0 0
\(503\) −231464. 133636.i −0.914846 0.528187i −0.0328591 0.999460i \(-0.510461\pi\)
−0.881987 + 0.471273i \(0.843795\pi\)
\(504\) 0 0
\(505\) −47760.6 82723.8i −0.187278 0.324375i
\(506\) 0 0
\(507\) 121760. 110150.i 0.473683 0.428518i
\(508\) 0 0
\(509\) −49139.8 8664.68i −0.189670 0.0334439i 0.0780063 0.996953i \(-0.475145\pi\)
−0.267676 + 0.963509i \(0.586256\pi\)
\(510\) 0 0
\(511\) 121917. 102301.i 0.466900 0.391775i
\(512\) 0 0
\(513\) −205912. 279269.i −0.782432 1.06118i
\(514\) 0 0
\(515\) −41844.2 49868.0i −0.157769 0.188021i
\(516\) 0 0
\(517\) −10785.1 + 61165.5i −0.0403501 + 0.228837i
\(518\) 0 0
\(519\) −250704. + 53902.3i −0.930738 + 0.200112i
\(520\) 0 0
\(521\) 184784. 106685.i 0.680752 0.393032i −0.119386 0.992848i \(-0.538093\pi\)
0.800138 + 0.599816i \(0.204759\pi\)
\(522\) 0 0
\(523\) 30678.3 53136.3i 0.112157 0.194262i −0.804483 0.593976i \(-0.797557\pi\)
0.916640 + 0.399714i \(0.130891\pi\)
\(524\) 0 0
\(525\) 61728.2 446803.i 0.223957 1.62105i
\(526\) 0 0
\(527\) 36469.6 43462.7i 0.131314 0.156493i
\(528\) 0 0
\(529\) −260500. 94814.3i −0.930886 0.338815i
\(530\) 0 0
\(531\) −286379. 28745.3i −1.01567 0.101948i
\(532\) 0 0
\(533\) −198161. + 34941.1i −0.697531 + 0.122994i
\(534\) 0 0
\(535\) −60154.1 + 21894.3i −0.210164 + 0.0764933i
\(536\) 0 0
\(537\) −375.449 10075.4i −0.00130197 0.0349393i
\(538\) 0 0
\(539\) 1.38046e6i 4.75165i
\(540\) 0 0
\(541\) −68196.0 −0.233005 −0.116502 0.993190i \(-0.537168\pi\)
−0.116502 + 0.993190i \(0.537168\pi\)
\(542\) 0 0
\(543\) −117972. + 223132.i −0.400111 + 0.756765i
\(544\) 0 0
\(545\) −4199.03 11536.8i −0.0141370 0.0388410i
\(546\) 0 0
\(547\) 87643.7 + 497052.i 0.292918 + 1.66122i 0.675547 + 0.737317i \(0.263908\pi\)
−0.382629 + 0.923902i \(0.624981\pi\)
\(548\) 0 0
\(549\) −334070. 94103.3i −1.10839 0.312220i
\(550\) 0 0
\(551\) 237273. 651902.i 0.781529 2.14723i
\(552\) 0 0
\(553\) 436000. + 365848.i 1.42573 + 1.19633i
\(554\) 0 0
\(555\) 31902.3 + 78432.0i 0.103570 + 0.254629i
\(556\) 0 0
\(557\) 316880. + 182951.i 1.02137 + 0.589691i 0.914502 0.404582i \(-0.132583\pi\)
0.106873 + 0.994273i \(0.465916\pi\)
\(558\) 0 0
\(559\) −39960.6 69213.9i −0.127882 0.221498i
\(560\) 0 0
\(561\) 293088. + 94472.3i 0.931262 + 0.300178i
\(562\) 0 0
\(563\) 486748. + 85826.8i 1.53563 + 0.270773i 0.876555 0.481302i \(-0.159836\pi\)
0.659077 + 0.752075i \(0.270947\pi\)
\(564\) 0 0
\(565\) 59077.6 49572.0i 0.185066 0.155288i
\(566\) 0 0
\(567\) −406013. + 459500.i −1.26291 + 1.42929i
\(568\) 0 0
\(569\) 62776.8 + 74814.5i 0.193899 + 0.231079i 0.854230 0.519895i \(-0.174029\pi\)
−0.660332 + 0.750974i \(0.729584\pi\)
\(570\) 0 0
\(571\) 101941. 578137.i 0.312664 1.77320i −0.272367 0.962193i \(-0.587806\pi\)
0.585031 0.811011i \(-0.301082\pi\)
\(572\) 0 0
\(573\) −120998. + 375382.i −0.368528 + 1.14331i
\(574\) 0 0
\(575\) 23782.6 13730.9i 0.0719322 0.0415301i
\(576\) 0 0
\(577\) −118959. + 206042.i −0.357309 + 0.618878i −0.987510 0.157554i \(-0.949639\pi\)
0.630201 + 0.776432i \(0.282972\pi\)
\(578\) 0 0
\(579\) 197923. 80505.4i 0.590391 0.240142i
\(580\) 0 0
\(581\) 150545. 179413.i 0.445980 0.531498i
\(582\) 0 0
\(583\) −668006. 243134.i −1.96536 0.715334i
\(584\) 0 0
\(585\) −54105.1 55505.3i −0.158098 0.162189i
\(586\) 0 0
\(587\) −356147. + 62798.3i −1.03360 + 0.182252i −0.664617 0.747184i \(-0.731405\pi\)
−0.368984 + 0.929436i \(0.620294\pi\)
\(588\) 0 0
\(589\) 161654. 58837.1i 0.465967 0.169598i
\(590\) 0 0
\(591\) 406915. + 215141.i 1.16501 + 0.615952i
\(592\) 0 0
\(593\) 434745.i 1.23630i 0.786059 + 0.618151i \(0.212118\pi\)
−0.786059 + 0.618151i \(0.787882\pi\)
\(594\) 0 0
\(595\) −138212. −0.390403
\(596\) 0 0
\(597\) −75635.6 + 2818.47i −0.212216 + 0.00790797i
\(598\) 0 0
\(599\) −48494.3 133237.i −0.135157 0.371340i 0.853589 0.520947i \(-0.174421\pi\)
−0.988745 + 0.149608i \(0.952199\pi\)
\(600\) 0 0
\(601\) −92872.1 526704.i −0.257120 1.45820i −0.790571 0.612370i \(-0.790216\pi\)
0.533451 0.845831i \(-0.320895\pi\)
\(602\) 0 0
\(603\) −521399. + 235072.i −1.43396 + 0.646497i
\(604\) 0 0
\(605\) −105905. + 290972.i −0.289339 + 0.794952i
\(606\) 0 0
\(607\) −288297. 241910.i −0.782462 0.656564i 0.161405 0.986888i \(-0.448397\pi\)
−0.943867 + 0.330324i \(0.892842\pi\)
\(608\) 0 0
\(609\) −1.21445e6 167783.i −3.27450 0.452390i
\(610\) 0 0
\(611\) 25066.2 + 14472.0i 0.0671440 + 0.0387656i
\(612\) 0 0
\(613\) 62517.2 + 108283.i 0.166371 + 0.288164i 0.937141 0.348950i \(-0.113462\pi\)
−0.770770 + 0.637113i \(0.780128\pi\)
\(614\) 0 0
\(615\) −35306.0 164211.i −0.0933466 0.434163i
\(616\) 0 0
\(617\) 130509. + 23012.2i 0.342823 + 0.0604489i 0.342409 0.939551i \(-0.388757\pi\)
0.000413857 1.00000i \(0.499868\pi\)
\(618\) 0 0
\(619\) −69930.6 + 58678.7i −0.182510 + 0.153144i −0.729465 0.684018i \(-0.760231\pi\)
0.546956 + 0.837162i \(0.315787\pi\)
\(620\) 0 0
\(621\) −37259.4 2342.71i −0.0966168 0.00607486i
\(622\) 0 0
\(623\) −680666. 811186.i −1.75371 2.08999i
\(624\) 0 0
\(625\) 40301.4 228561.i 0.103172 0.585115i
\(626\) 0 0
\(627\) 626377. + 692397.i 1.59331 + 1.76125i
\(628\) 0 0
\(629\) −135758. + 78379.7i −0.343133 + 0.198108i
\(630\) 0 0
\(631\) 129807. 224832.i 0.326017 0.564677i −0.655701 0.755021i \(-0.727627\pi\)
0.981718 + 0.190343i \(0.0609601\pi\)
\(632\) 0 0
\(633\) 228602. + 177744.i 0.570522 + 0.443595i
\(634\) 0 0
\(635\) 86218.7 102751.i 0.213823 0.254824i
\(636\) 0 0
\(637\) 604521. + 220028.i 1.48982 + 0.542249i
\(638\) 0 0
\(639\) 490487. 334188.i 1.20123 0.818445i
\(640\) 0 0
\(641\) 61880.0 10911.1i 0.150603 0.0265554i −0.0978382 0.995202i \(-0.531193\pi\)
0.248441 + 0.968647i \(0.420082\pi\)
\(642\) 0 0
\(643\) −374496. + 136305.i −0.905786 + 0.329679i −0.752569 0.658514i \(-0.771186\pi\)
−0.153217 + 0.988193i \(0.548963\pi\)
\(644\) 0 0
\(645\) 56493.2 35484.9i 0.135793 0.0852952i
\(646\) 0 0
\(647\) 397193.i 0.948840i 0.880299 + 0.474420i \(0.157342\pi\)
−0.880299 + 0.474420i \(0.842658\pi\)
\(648\) 0 0
\(649\) 774497. 1.83878
\(650\) 0 0
\(651\) −161704. 257438.i −0.381556 0.607450i
\(652\) 0 0
\(653\) −58683.0 161230.i −0.137622 0.378112i 0.851667 0.524083i \(-0.175592\pi\)
−0.989289 + 0.145971i \(0.953369\pi\)
\(654\) 0 0
\(655\) −4860.28 27564.0i −0.0113287 0.0642480i
\(656\) 0 0
\(657\) −137554. + 10265.9i −0.318672 + 0.0237829i
\(658\) 0 0
\(659\) −31406.5 + 86288.6i −0.0723184 + 0.198693i −0.970585 0.240757i \(-0.922604\pi\)
0.898267 + 0.439450i \(0.144827\pi\)
\(660\) 0 0
\(661\) 601557. + 504767.i 1.37681 + 1.15528i 0.970376 + 0.241601i \(0.0776726\pi\)
0.406435 + 0.913680i \(0.366772\pi\)
\(662\) 0 0
\(663\) 88085.4 113290.i 0.200390 0.257729i
\(664\) 0 0
\(665\) −362922. 209533.i −0.820673 0.473816i
\(666\) 0 0
\(667\) −37321.7 64643.1i −0.0838900 0.145302i
\(668\) 0 0
\(669\) 133285. 120576.i 0.297803 0.269407i
\(670\) 0 0
\(671\) 919753. + 162177.i 2.04280 + 0.360201i
\(672\) 0 0
\(673\) −428014. + 359147.i −0.944992 + 0.792942i −0.978447 0.206498i \(-0.933793\pi\)
0.0334553 + 0.999440i \(0.489349\pi\)
\(674\) 0 0
\(675\) −269577. + 283105.i −0.591664 + 0.621356i
\(676\) 0 0
\(677\) 466782. + 556289.i 1.01844 + 1.21373i 0.976701 + 0.214604i \(0.0688460\pi\)
0.0417409 + 0.999128i \(0.486710\pi\)
\(678\) 0 0
\(679\) −110472. + 626515.i −0.239613 + 1.35891i
\(680\) 0 0
\(681\) 79246.5 17038.3i 0.170878 0.0367394i
\(682\) 0 0
\(683\) −38854.8 + 22432.8i −0.0832920 + 0.0480886i −0.541068 0.840979i \(-0.681980\pi\)
0.457776 + 0.889068i \(0.348646\pi\)
\(684\) 0 0
\(685\) 77664.3 134519.i 0.165516 0.286682i
\(686\) 0 0
\(687\) −2796.38 + 20240.8i −0.00592492 + 0.0428859i
\(688\) 0 0
\(689\) −212944. + 253777.i −0.448567 + 0.534581i
\(690\) 0 0
\(691\) −599696. 218272.i −1.25596 0.457131i −0.373547 0.927611i \(-0.621859\pi\)
−0.882411 + 0.470480i \(0.844081\pi\)
\(692\) 0 0
\(693\) 963596. 1.33941e6i 2.00645 2.78900i
\(694\) 0 0
\(695\) 35745.2 6302.84i 0.0740027 0.0130487i
\(696\) 0 0
\(697\) 292210. 106356.i 0.601492 0.218925i
\(698\) 0 0
\(699\) −13314.0 357289.i −0.0272492 0.731250i
\(700\) 0 0
\(701\) 260097.i 0.529296i −0.964345 0.264648i \(-0.914744\pi\)
0.964345 0.264648i \(-0.0852558\pi\)
\(702\) 0 0
\(703\) −475302. −0.961743
\(704\) 0 0
\(705\) −11292.8 + 21359.1i −0.0227207 + 0.0429738i
\(706\) 0 0
\(707\) −324094. 890441.i −0.648384 1.78142i
\(708\) 0 0
\(709\) 165213. + 936967.i 0.328663 + 1.86394i 0.482575 + 0.875855i \(0.339702\pi\)
−0.153912 + 0.988085i \(0.549187\pi\)
\(710\) 0 0
\(711\) −121576. 478073.i −0.240497 0.945703i
\(712\) 0 0
\(713\) 6330.62 17393.2i 0.0124528 0.0342138i
\(714\) 0 0
\(715\) 159782. + 134073.i 0.312547 + 0.262258i
\(716\) 0 0
\(717\) −72503.8 178251.i −0.141034 0.346732i
\(718\) 0 0
\(719\) −451724. 260803.i −0.873808 0.504493i −0.00519598 0.999987i \(-0.501654\pi\)
−0.868612 + 0.495493i \(0.834987\pi\)
\(720\) 0 0
\(721\) −322892. 559265.i −0.621136 1.07584i
\(722\) 0 0
\(723\) 265665. + 85633.0i 0.508227 + 0.163819i
\(724\) 0 0
\(725\) −769735. 135725.i −1.46442 0.258216i
\(726\) 0 0
\(727\) 497415. 417381.i 0.941131 0.789703i −0.0366508 0.999328i \(-0.511669\pi\)
0.977782 + 0.209626i \(0.0672245\pi\)
\(728\) 0 0
\(729\) 518225. 117780.i 0.975132 0.221624i
\(730\) 0 0
\(731\) 79391.4 + 94615.0i 0.148573 + 0.177062i
\(732\) 0 0
\(733\) −11853.3 + 67223.2i −0.0220612 + 0.125116i −0.993849 0.110740i \(-0.964678\pi\)
0.971788 + 0.235855i \(0.0757891\pi\)
\(734\) 0 0
\(735\) −164747. + 511106.i −0.304960 + 0.946098i
\(736\) 0 0
\(737\) 1.33286e6 769524.i 2.45385 1.41673i
\(738\) 0 0
\(739\) 287118. 497303.i 0.525741 0.910610i −0.473810 0.880627i \(-0.657122\pi\)
0.999550 0.0299825i \(-0.00954516\pi\)
\(740\) 0 0
\(741\) 403047. 163940.i 0.734040 0.298571i
\(742\) 0 0
\(743\) −61286.3 + 73038.2i −0.111016 + 0.132304i −0.818691 0.574235i \(-0.805300\pi\)
0.707675 + 0.706538i \(0.249744\pi\)
\(744\) 0 0
\(745\) −12809.3 4662.19i −0.0230787 0.00839996i
\(746\) 0 0
\(747\) −196726. + 50028.3i −0.352549 + 0.0896549i
\(748\) 0 0
\(749\) −625389. + 110273.i −1.11477 + 0.196565i
\(750\) 0 0
\(751\) −98404.2 + 35816.2i −0.174475 + 0.0635038i −0.427781 0.903883i \(-0.640704\pi\)
0.253306 + 0.967386i \(0.418482\pi\)
\(752\) 0 0
\(753\) 759389. + 401498.i 1.33929 + 0.708098i
\(754\) 0 0
\(755\) 352361.i 0.618150i
\(756\) 0 0
\(757\) −957516. −1.67091 −0.835457 0.549556i \(-0.814797\pi\)
−0.835457 + 0.549556i \(0.814797\pi\)
\(758\) 0 0
\(759\) 100391. 3740.94i 0.174265 0.00649377i
\(760\) 0 0
\(761\) −308545. 847721.i −0.532782 1.46381i −0.855747 0.517395i \(-0.826902\pi\)
0.322965 0.946411i \(-0.395320\pi\)
\(762\) 0 0
\(763\) −21148.9 119941.i −0.0363277 0.206025i
\(764\) 0 0
\(765\) 97239.5 + 69955.6i 0.166157 + 0.119536i
\(766\) 0 0
\(767\) 123445. 339163.i 0.209838 0.576525i
\(768\) 0 0
\(769\) 152004. + 127546.i 0.257040 + 0.215682i 0.762197 0.647345i \(-0.224121\pi\)
−0.505157 + 0.863028i \(0.668565\pi\)
\(770\) 0 0
\(771\) −748508. 103410.i −1.25918 0.173962i
\(772\) 0 0
\(773\) −811231. 468364.i −1.35764 0.783835i −0.368337 0.929692i \(-0.620073\pi\)
−0.989306 + 0.145857i \(0.953406\pi\)
\(774\) 0 0
\(775\) −96908.7 167851.i −0.161346 0.279460i
\(776\) 0 0
\(777\) 176560. + 821194.i 0.292448 + 1.36020i
\(778\) 0 0
\(779\) 928534. + 163726.i 1.53011 + 0.269800i
\(780\) 0 0