Properties

Label 108.5.k.a.5.7
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 5.7
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.126357 + 8.99911i) q^{3} +(-6.31102 - 17.3394i) q^{5} +(2.68521 + 15.2286i) q^{7} +(-80.9681 - 2.27420i) q^{9} +O(q^{10})\) \(q+(-0.126357 + 8.99911i) q^{3} +(-6.31102 - 17.3394i) q^{5} +(2.68521 + 15.2286i) q^{7} +(-80.9681 - 2.27420i) q^{9} +(-57.3804 + 157.651i) q^{11} +(-47.4796 - 39.8401i) q^{13} +(156.837 - 54.6026i) q^{15} +(-434.160 - 250.663i) q^{17} +(-226.022 - 391.482i) q^{19} +(-137.383 + 22.2403i) q^{21} +(-87.9439 - 15.5069i) q^{23} +(217.952 - 182.884i) q^{25} +(30.6966 - 728.353i) q^{27} +(-388.247 - 462.695i) q^{29} +(-253.555 + 1437.98i) q^{31} +(-1411.47 - 536.293i) q^{33} +(247.108 - 142.668i) q^{35} +(-743.956 + 1288.57i) q^{37} +(364.525 - 422.240i) q^{39} +(-1177.61 + 1403.43i) q^{41} +(1145.30 + 416.855i) q^{43} +(471.558 + 1418.29i) q^{45} +(-1675.90 + 295.507i) q^{47} +(2031.50 - 739.406i) q^{49} +(2310.60 - 3875.39i) q^{51} -448.959i q^{53} +3095.71 q^{55} +(3551.55 - 1984.53i) q^{57} +(519.236 + 1426.59i) q^{59} +(600.396 + 3405.01i) q^{61} +(-182.784 - 1239.14i) q^{63} +(-391.158 + 1074.70i) q^{65} +(130.770 + 109.729i) q^{67} +(150.660 - 789.458i) q^{69} +(-3379.60 - 1951.21i) q^{71} +(4207.66 + 7287.88i) q^{73} +(1618.25 + 1984.49i) q^{75} +(-2554.89 - 450.495i) q^{77} +(6492.89 - 5448.18i) q^{79} +(6550.66 + 368.274i) q^{81} +(-697.809 - 831.616i) q^{83} +(-1606.34 + 9110.01i) q^{85} +(4212.90 - 3435.42i) q^{87} +(-9947.94 + 5743.45i) q^{89} +(479.216 - 830.026i) q^{91} +(-12908.5 - 2463.47i) q^{93} +(-5361.62 + 6389.73i) q^{95} +(-1079.02 - 392.731i) q^{97} +(5004.51 - 12634.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

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
\(3\) −0.126357 + 8.99911i −0.0140396 + 0.999901i
\(4\) 0 0
\(5\) −6.31102 17.3394i −0.252441 0.693576i −0.999582 0.0289101i \(-0.990796\pi\)
0.747141 0.664665i \(-0.231426\pi\)
\(6\) 0 0
\(7\) 2.68521 + 15.2286i 0.0548002 + 0.310788i 0.999871 0.0160790i \(-0.00511834\pi\)
−0.945070 + 0.326867i \(0.894007\pi\)
\(8\) 0 0
\(9\) −80.9681 2.27420i −0.999606 0.0280765i
\(10\) 0 0
\(11\) −57.3804 + 157.651i −0.474218 + 1.30290i 0.440116 + 0.897941i \(0.354937\pi\)
−0.914334 + 0.404962i \(0.867285\pi\)
\(12\) 0 0
\(13\) −47.4796 39.8401i −0.280944 0.235740i 0.491416 0.870925i \(-0.336479\pi\)
−0.772360 + 0.635185i \(0.780924\pi\)
\(14\) 0 0
\(15\) 156.837 54.6026i 0.697051 0.242678i
\(16\) 0 0
\(17\) −434.160 250.663i −1.50229 0.867345i −0.999997 0.00264463i \(-0.999158\pi\)
−0.502289 0.864700i \(-0.667508\pi\)
\(18\) 0 0
\(19\) −226.022 391.482i −0.626100 1.08444i −0.988327 0.152347i \(-0.951317\pi\)
0.362228 0.932090i \(-0.382016\pi\)
\(20\) 0 0
\(21\) −137.383 + 22.2403i −0.311526 + 0.0504315i
\(22\) 0 0
\(23\) −87.9439 15.5069i −0.166246 0.0293136i 0.0899058 0.995950i \(-0.471343\pi\)
−0.256151 + 0.966637i \(0.582455\pi\)
\(24\) 0 0
\(25\) 217.952 182.884i 0.348724 0.292614i
\(26\) 0 0
\(27\) 30.6966 728.353i 0.0421078 0.999113i
\(28\) 0 0
\(29\) −388.247 462.695i −0.461650 0.550173i 0.484124 0.874999i \(-0.339138\pi\)
−0.945773 + 0.324827i \(0.894694\pi\)
\(30\) 0 0
\(31\) −253.555 + 1437.98i −0.263845 + 1.49634i 0.508460 + 0.861086i \(0.330215\pi\)
−0.772304 + 0.635253i \(0.780896\pi\)
\(32\) 0 0
\(33\) −1411.47 536.293i −1.29612 0.492464i
\(34\) 0 0
\(35\) 247.108 142.668i 0.201721 0.116464i
\(36\) 0 0
\(37\) −743.956 + 1288.57i −0.543430 + 0.941249i 0.455274 + 0.890351i \(0.349541\pi\)
−0.998704 + 0.0508971i \(0.983792\pi\)
\(38\) 0 0
\(39\) 364.525 422.240i 0.239661 0.277607i
\(40\) 0 0
\(41\) −1177.61 + 1403.43i −0.700544 + 0.834875i −0.992588 0.121529i \(-0.961220\pi\)
0.292044 + 0.956405i \(0.405665\pi\)
\(42\) 0 0
\(43\) 1145.30 + 416.855i 0.619416 + 0.225449i 0.632618 0.774464i \(-0.281980\pi\)
−0.0132024 + 0.999913i \(0.504203\pi\)
\(44\) 0 0
\(45\) 471.558 + 1418.29i 0.232868 + 0.700390i
\(46\) 0 0
\(47\) −1675.90 + 295.507i −0.758670 + 0.133774i −0.539584 0.841932i \(-0.681419\pi\)
−0.219086 + 0.975706i \(0.570307\pi\)
\(48\) 0 0
\(49\) 2031.50 739.406i 0.846107 0.307958i
\(50\) 0 0
\(51\) 2310.60 3875.39i 0.888351 1.48996i
\(52\) 0 0
\(53\) 448.959i 0.159829i −0.996802 0.0799144i \(-0.974535\pi\)
0.996802 0.0799144i \(-0.0254647\pi\)
\(54\) 0 0
\(55\) 3095.71 1.02337
\(56\) 0 0
\(57\) 3551.55 1984.53i 1.09312 0.610813i
\(58\) 0 0
\(59\) 519.236 + 1426.59i 0.149163 + 0.409821i 0.991660 0.128879i \(-0.0411378\pi\)
−0.842498 + 0.538700i \(0.818916\pi\)
\(60\) 0 0
\(61\) 600.396 + 3405.01i 0.161353 + 0.915080i 0.952745 + 0.303771i \(0.0982458\pi\)
−0.791392 + 0.611309i \(0.790643\pi\)
\(62\) 0 0
\(63\) −182.784 1239.14i −0.0460528 0.312204i
\(64\) 0 0
\(65\) −391.158 + 1074.70i −0.0925818 + 0.254366i
\(66\) 0 0
\(67\) 130.770 + 109.729i 0.0291311 + 0.0244439i 0.657237 0.753684i \(-0.271725\pi\)
−0.628106 + 0.778128i \(0.716170\pi\)
\(68\) 0 0
\(69\) 150.660 789.458i 0.0316447 0.165818i
\(70\) 0 0
\(71\) −3379.60 1951.21i −0.670423 0.387069i 0.125814 0.992054i \(-0.459846\pi\)
−0.796237 + 0.604985i \(0.793179\pi\)
\(72\) 0 0
\(73\) 4207.66 + 7287.88i 0.789578 + 1.36759i 0.926226 + 0.376969i \(0.123034\pi\)
−0.136648 + 0.990620i \(0.543633\pi\)
\(74\) 0 0
\(75\) 1618.25 + 1984.49i 0.287689 + 0.352798i
\(76\) 0 0
\(77\) −2554.89 450.495i −0.430913 0.0759816i
\(78\) 0 0
\(79\) 6492.89 5448.18i 1.04036 0.872966i 0.0483127 0.998832i \(-0.484616\pi\)
0.992047 + 0.125867i \(0.0401712\pi\)
\(80\) 0 0
\(81\) 6550.66 + 368.274i 0.998423 + 0.0561308i
\(82\) 0 0
\(83\) −697.809 831.616i −0.101293 0.120717i 0.713016 0.701148i \(-0.247329\pi\)
−0.814309 + 0.580431i \(0.802884\pi\)
\(84\) 0 0
\(85\) −1606.34 + 9110.01i −0.222331 + 1.26090i
\(86\) 0 0
\(87\) 4212.90 3435.42i 0.556600 0.453880i
\(88\) 0 0
\(89\) −9947.94 + 5743.45i −1.25589 + 0.725091i −0.972274 0.233846i \(-0.924869\pi\)
−0.283621 + 0.958937i \(0.591536\pi\)
\(90\) 0 0
\(91\) 479.216 830.026i 0.0578693 0.100233i
\(92\) 0 0
\(93\) −12908.5 2463.47i −1.49249 0.284827i
\(94\) 0 0
\(95\) −5361.62 + 6389.73i −0.594085 + 0.708003i
\(96\) 0 0
\(97\) −1079.02 392.731i −0.114680 0.0417399i 0.284043 0.958812i \(-0.408324\pi\)
−0.398723 + 0.917072i \(0.630546\pi\)
\(98\) 0 0
\(99\) 5004.51 12634.2i 0.510612 1.28908i
\(100\) 0 0
\(101\) 6324.41 1115.16i 0.619979 0.109319i 0.145169 0.989407i \(-0.453628\pi\)
0.474811 + 0.880088i \(0.342516\pi\)
\(102\) 0 0
\(103\) −6157.93 + 2241.30i −0.580444 + 0.211264i −0.615521 0.788120i \(-0.711054\pi\)
0.0350773 + 0.999385i \(0.488832\pi\)
\(104\) 0 0
\(105\) 1252.66 + 2241.78i 0.113620 + 0.203336i
\(106\) 0 0
\(107\) 4283.13i 0.374105i −0.982350 0.187052i \(-0.940107\pi\)
0.982350 0.187052i \(-0.0598934\pi\)
\(108\) 0 0
\(109\) −3812.13 −0.320859 −0.160430 0.987047i \(-0.551288\pi\)
−0.160430 + 0.987047i \(0.551288\pi\)
\(110\) 0 0
\(111\) −11502.0 6857.76i −0.933526 0.556591i
\(112\) 0 0
\(113\) −2239.98 6154.29i −0.175423 0.481971i 0.820555 0.571568i \(-0.193664\pi\)
−0.995978 + 0.0895965i \(0.971442\pi\)
\(114\) 0 0
\(115\) 286.136 + 1622.76i 0.0216360 + 0.122704i
\(116\) 0 0
\(117\) 3753.72 + 3333.75i 0.274215 + 0.243535i
\(118\) 0 0
\(119\) 2651.43 7284.73i 0.187234 0.514422i
\(120\) 0 0
\(121\) −10345.8 8681.13i −0.706630 0.592933i
\(122\) 0 0
\(123\) −12480.8 10774.8i −0.824958 0.712196i
\(124\) 0 0
\(125\) −14534.1 8391.29i −0.930185 0.537042i
\(126\) 0 0
\(127\) 11298.5 + 19569.6i 0.700511 + 1.21332i 0.968287 + 0.249839i \(0.0803778\pi\)
−0.267777 + 0.963481i \(0.586289\pi\)
\(128\) 0 0
\(129\) −3896.04 + 10254.0i −0.234123 + 0.616189i
\(130\) 0 0
\(131\) −2408.04 424.602i −0.140320 0.0247422i 0.103047 0.994677i \(-0.467141\pi\)
−0.243367 + 0.969934i \(0.578252\pi\)
\(132\) 0 0
\(133\) 5354.79 4493.21i 0.302719 0.254011i
\(134\) 0 0
\(135\) −12822.9 + 4064.39i −0.703590 + 0.223012i
\(136\) 0 0
\(137\) 8488.11 + 10115.7i 0.452241 + 0.538960i 0.943201 0.332222i \(-0.107798\pi\)
−0.490960 + 0.871182i \(0.663354\pi\)
\(138\) 0 0
\(139\) 6365.38 36099.8i 0.329454 1.86842i −0.146871 0.989156i \(-0.546920\pi\)
0.476325 0.879269i \(-0.341969\pi\)
\(140\) 0 0
\(141\) −2447.54 15119.0i −0.123109 0.760473i
\(142\) 0 0
\(143\) 9005.23 5199.17i 0.440375 0.254251i
\(144\) 0 0
\(145\) −5572.61 + 9652.05i −0.265047 + 0.459075i
\(146\) 0 0
\(147\) 6397.31 + 18375.1i 0.296048 + 0.850347i
\(148\) 0 0
\(149\) −13315.3 + 15868.5i −0.599760 + 0.714766i −0.977450 0.211166i \(-0.932274\pi\)
0.377691 + 0.925932i \(0.376718\pi\)
\(150\) 0 0
\(151\) −25658.1 9338.77i −1.12530 0.409577i −0.288719 0.957414i \(-0.593229\pi\)
−0.836585 + 0.547837i \(0.815451\pi\)
\(152\) 0 0
\(153\) 34583.1 + 21283.0i 1.47734 + 0.909182i
\(154\) 0 0
\(155\) 26533.9 4678.64i 1.10443 0.194741i
\(156\) 0 0
\(157\) −38577.4 + 14041.0i −1.56507 + 0.569639i −0.971891 0.235431i \(-0.924350\pi\)
−0.593180 + 0.805070i \(0.702128\pi\)
\(158\) 0 0
\(159\) 4040.23 + 56.7290i 0.159813 + 0.00224394i
\(160\) 0 0
\(161\) 1380.90i 0.0532734i
\(162\) 0 0
\(163\) 31743.5 1.19476 0.597378 0.801959i \(-0.296209\pi\)
0.597378 + 0.801959i \(0.296209\pi\)
\(164\) 0 0
\(165\) −391.163 + 27858.6i −0.0143678 + 1.02327i
\(166\) 0 0
\(167\) 18527.6 + 50904.2i 0.664334 + 1.82524i 0.556094 + 0.831119i \(0.312299\pi\)
0.108240 + 0.994125i \(0.465478\pi\)
\(168\) 0 0
\(169\) −4292.49 24343.9i −0.150292 0.852348i
\(170\) 0 0
\(171\) 17410.3 + 32211.5i 0.595406 + 1.10159i
\(172\) 0 0
\(173\) 16730.7 45967.2i 0.559012 1.53587i −0.262061 0.965051i \(-0.584402\pi\)
0.821074 0.570822i \(-0.193376\pi\)
\(174\) 0 0
\(175\) 3370.31 + 2828.03i 0.110051 + 0.0923437i
\(176\) 0 0
\(177\) −12903.6 + 4492.40i −0.411875 + 0.143394i
\(178\) 0 0
\(179\) −22709.4 13111.3i −0.708761 0.409203i 0.101841 0.994801i \(-0.467527\pi\)
−0.810602 + 0.585598i \(0.800860\pi\)
\(180\) 0 0
\(181\) −14057.5 24348.3i −0.429092 0.743209i 0.567701 0.823235i \(-0.307833\pi\)
−0.996793 + 0.0800256i \(0.974500\pi\)
\(182\) 0 0
\(183\) −30718.0 + 4972.78i −0.917256 + 0.148490i
\(184\) 0 0
\(185\) 27038.1 + 4767.55i 0.790011 + 0.139300i
\(186\) 0 0
\(187\) 64429.6 54062.8i 1.84248 1.54602i
\(188\) 0 0
\(189\) 11174.2 1488.32i 0.312819 0.0416650i
\(190\) 0 0
\(191\) 23218.0 + 27670.2i 0.636442 + 0.758482i 0.983804 0.179249i \(-0.0573668\pi\)
−0.347362 + 0.937731i \(0.612922\pi\)
\(192\) 0 0
\(193\) −3902.27 + 22130.9i −0.104762 + 0.594133i 0.886554 + 0.462626i \(0.153093\pi\)
−0.991315 + 0.131507i \(0.958018\pi\)
\(194\) 0 0
\(195\) −9621.90 3655.87i −0.253041 0.0961439i
\(196\) 0 0
\(197\) 56910.6 32857.3i 1.46643 0.846642i 0.467133 0.884187i \(-0.345287\pi\)
0.999295 + 0.0375447i \(0.0119536\pi\)
\(198\) 0 0
\(199\) −18862.4 + 32670.7i −0.476312 + 0.824997i −0.999632 0.0271397i \(-0.991360\pi\)
0.523319 + 0.852137i \(0.324693\pi\)
\(200\) 0 0
\(201\) −1003.98 + 1162.94i −0.0248505 + 0.0287851i
\(202\) 0 0
\(203\) 6003.67 7154.89i 0.145688 0.173625i
\(204\) 0 0
\(205\) 31766.5 + 11562.1i 0.755895 + 0.275123i
\(206\) 0 0
\(207\) 7085.38 + 1455.56i 0.165357 + 0.0339696i
\(208\) 0 0
\(209\) 74686.8 13169.3i 1.70982 0.301488i
\(210\) 0 0
\(211\) −46853.0 + 17053.1i −1.05238 + 0.383035i −0.809560 0.587036i \(-0.800295\pi\)
−0.242820 + 0.970071i \(0.578072\pi\)
\(212\) 0 0
\(213\) 17986.2 30166.9i 0.396443 0.664922i
\(214\) 0 0
\(215\) 22489.6i 0.486524i
\(216\) 0 0
\(217\) −22579.3 −0.479502
\(218\) 0 0
\(219\) −66116.1 + 36944.3i −1.37854 + 0.770299i
\(220\) 0 0
\(221\) 10627.3 + 29198.3i 0.217590 + 0.597824i
\(222\) 0 0
\(223\) −9188.10 52108.3i −0.184763 1.04784i −0.926259 0.376887i \(-0.876994\pi\)
0.741496 0.670958i \(-0.234117\pi\)
\(224\) 0 0
\(225\) −18063.1 + 14312.1i −0.356802 + 0.282708i
\(226\) 0 0
\(227\) −18336.8 + 50379.8i −0.355853 + 0.977698i 0.624600 + 0.780945i \(0.285262\pi\)
−0.980453 + 0.196753i \(0.936960\pi\)
\(228\) 0 0
\(229\) −72773.1 61063.9i −1.38771 1.16443i −0.966256 0.257582i \(-0.917074\pi\)
−0.421457 0.906848i \(-0.638481\pi\)
\(230\) 0 0
\(231\) 4376.88 22934.8i 0.0820240 0.429804i
\(232\) 0 0
\(233\) −59397.7 34293.3i −1.09410 0.631680i −0.159436 0.987208i \(-0.550968\pi\)
−0.934665 + 0.355528i \(0.884301\pi\)
\(234\) 0 0
\(235\) 15700.6 + 27194.2i 0.284302 + 0.492425i
\(236\) 0 0
\(237\) 48208.4 + 59118.6i 0.858273 + 1.05251i
\(238\) 0 0
\(239\) 25378.0 + 4474.83i 0.444285 + 0.0783395i 0.391315 0.920257i \(-0.372020\pi\)
0.0529698 + 0.998596i \(0.483131\pi\)
\(240\) 0 0
\(241\) −4966.35 + 4167.26i −0.0855073 + 0.0717492i −0.684539 0.728976i \(-0.739997\pi\)
0.599032 + 0.800725i \(0.295552\pi\)
\(242\) 0 0
\(243\) −4141.86 + 58903.6i −0.0701428 + 0.997537i
\(244\) 0 0
\(245\) −25641.7 30558.6i −0.427184 0.509098i
\(246\) 0 0
\(247\) −4865.23 + 27592.1i −0.0797461 + 0.452263i
\(248\) 0 0
\(249\) 7571.98 6174.58i 0.122127 0.0995884i
\(250\) 0 0
\(251\) −72828.7 + 42047.7i −1.15599 + 0.667413i −0.950341 0.311212i \(-0.899265\pi\)
−0.205653 + 0.978625i \(0.565932\pi\)
\(252\) 0 0
\(253\) 7490.93 12974.7i 0.117029 0.202701i
\(254\) 0 0
\(255\) −81779.1 15606.8i −1.25766 0.240012i
\(256\) 0 0
\(257\) −18558.1 + 22116.7i −0.280975 + 0.334853i −0.888012 0.459821i \(-0.847914\pi\)
0.607037 + 0.794674i \(0.292358\pi\)
\(258\) 0 0
\(259\) −21620.8 7869.32i −0.322308 0.117311i
\(260\) 0 0
\(261\) 30383.4 + 38346.5i 0.446021 + 0.562917i
\(262\) 0 0
\(263\) 2552.92 450.148i 0.0369084 0.00650795i −0.155163 0.987889i \(-0.549590\pi\)
0.192072 + 0.981381i \(0.438479\pi\)
\(264\) 0 0
\(265\) −7784.68 + 2833.39i −0.110853 + 0.0403473i
\(266\) 0 0
\(267\) −50428.9 90248.4i −0.707387 1.26595i
\(268\) 0 0
\(269\) 62120.1i 0.858475i −0.903192 0.429238i \(-0.858782\pi\)
0.903192 0.429238i \(-0.141218\pi\)
\(270\) 0 0
\(271\) 23727.3 0.323080 0.161540 0.986866i \(-0.448354\pi\)
0.161540 + 0.986866i \(0.448354\pi\)
\(272\) 0 0
\(273\) 7408.94 + 4417.39i 0.0994102 + 0.0592708i
\(274\) 0 0
\(275\) 16325.7 + 44854.4i 0.215877 + 0.593116i
\(276\) 0 0
\(277\) −12397.3 70308.5i −0.161572 0.916322i −0.952529 0.304449i \(-0.901528\pi\)
0.790956 0.611873i \(-0.209584\pi\)
\(278\) 0 0
\(279\) 23800.1 115854.i 0.305753 1.48834i
\(280\) 0 0
\(281\) 40372.1 110922.i 0.511292 1.40476i −0.368599 0.929589i \(-0.620162\pi\)
0.879891 0.475175i \(-0.157615\pi\)
\(282\) 0 0
\(283\) −67038.7 56252.2i −0.837053 0.702371i 0.119846 0.992792i \(-0.461760\pi\)
−0.956899 + 0.290422i \(0.906204\pi\)
\(284\) 0 0
\(285\) −56824.4 49057.2i −0.699593 0.603967i
\(286\) 0 0
\(287\) −24534.3 14164.9i −0.297859 0.171969i
\(288\) 0 0
\(289\) 83903.0 + 145324.i 1.00457 + 1.73997i
\(290\) 0 0
\(291\) 3670.57 9660.60i 0.0433459 0.114082i
\(292\) 0 0
\(293\) −147759. 26053.9i −1.72115 0.303485i −0.776149 0.630550i \(-0.782830\pi\)
−0.945002 + 0.327064i \(0.893941\pi\)
\(294\) 0 0
\(295\) 21459.3 18006.5i 0.246587 0.206911i
\(296\) 0 0
\(297\) 113064. + 46632.6i 1.28178 + 0.528660i
\(298\) 0 0
\(299\) 3557.74 + 4239.95i 0.0397953 + 0.0474262i
\(300\) 0 0
\(301\) −3272.74 + 18560.6i −0.0361226 + 0.204861i
\(302\) 0 0
\(303\) 9236.36 + 57055.0i 0.100604 + 0.621453i
\(304\) 0 0
\(305\) 55251.8 31899.6i 0.593945 0.342914i
\(306\) 0 0
\(307\) 2679.80 4641.56i 0.0284332 0.0492478i −0.851459 0.524422i \(-0.824282\pi\)
0.879892 + 0.475174i \(0.157615\pi\)
\(308\) 0 0
\(309\) −19391.6 55699.1i −0.203094 0.583353i
\(310\) 0 0
\(311\) −108484. + 129286.i −1.12161 + 1.33669i −0.186452 + 0.982464i \(0.559699\pi\)
−0.935161 + 0.354223i \(0.884746\pi\)
\(312\) 0 0
\(313\) 57251.6 + 20837.9i 0.584385 + 0.212699i 0.617258 0.786761i \(-0.288243\pi\)
−0.0328728 + 0.999460i \(0.510466\pi\)
\(314\) 0 0
\(315\) −20332.3 + 10989.6i −0.204911 + 0.110754i
\(316\) 0 0
\(317\) 4583.45 808.187i 0.0456115 0.00804254i −0.150796 0.988565i \(-0.548184\pi\)
0.196407 + 0.980522i \(0.437073\pi\)
\(318\) 0 0
\(319\) 95222.2 34658.1i 0.935744 0.340583i
\(320\) 0 0
\(321\) 38544.4 + 541.202i 0.374068 + 0.00525229i
\(322\) 0 0
\(323\) 226621.i 2.17218i
\(324\) 0 0
\(325\) −17634.4 −0.166953
\(326\) 0 0
\(327\) 481.688 34305.8i 0.00450474 0.320828i
\(328\) 0 0
\(329\) −9000.30 24728.1i −0.0831505 0.228454i
\(330\) 0 0
\(331\) 11428.8 + 64815.9i 0.104314 + 0.591596i 0.991492 + 0.130168i \(0.0415517\pi\)
−0.887178 + 0.461428i \(0.847337\pi\)
\(332\) 0 0
\(333\) 63167.1 102641.i 0.569643 0.925620i
\(334\) 0 0
\(335\) 1077.34 2959.96i 0.00959981 0.0263753i
\(336\) 0 0
\(337\) 97808.8 + 82071.3i 0.861228 + 0.722656i 0.962232 0.272230i \(-0.0877612\pi\)
−0.101004 + 0.994886i \(0.532206\pi\)
\(338\) 0 0
\(339\) 55666.2 19380.2i 0.484386 0.168639i
\(340\) 0 0
\(341\) −212151. 122485.i −1.82446 1.05335i
\(342\) 0 0
\(343\) 35279.1 + 61105.2i 0.299867 + 0.519385i
\(344\) 0 0
\(345\) −14639.5 + 2369.92i −0.122995 + 0.0199111i
\(346\) 0 0
\(347\) 54058.3 + 9531.94i 0.448956 + 0.0791630i 0.393555 0.919301i \(-0.371245\pi\)
0.0554011 + 0.998464i \(0.482356\pi\)
\(348\) 0 0
\(349\) −129327. + 108518.i −1.06179 + 0.890948i −0.994284 0.106771i \(-0.965949\pi\)
−0.0675069 + 0.997719i \(0.521504\pi\)
\(350\) 0 0
\(351\) −30475.1 + 33358.9i −0.247361 + 0.270768i
\(352\) 0 0
\(353\) 109221. + 130165.i 0.876512 + 1.04459i 0.998643 + 0.0520726i \(0.0165827\pi\)
−0.122131 + 0.992514i \(0.538973\pi\)
\(354\) 0 0
\(355\) −12504.1 + 70914.4i −0.0992193 + 0.562701i
\(356\) 0 0
\(357\) 65221.1 + 24781.0i 0.511743 + 0.194438i
\(358\) 0 0
\(359\) 96846.2 55914.2i 0.751439 0.433843i −0.0747748 0.997200i \(-0.523824\pi\)
0.826214 + 0.563357i \(0.190490\pi\)
\(360\) 0 0
\(361\) −37011.3 + 64105.5i −0.284001 + 0.491905i
\(362\) 0 0
\(363\) 79429.7 92005.8i 0.602795 0.698235i
\(364\) 0 0
\(365\) 99812.7 118952.i 0.749204 0.892867i
\(366\) 0 0
\(367\) 224386. + 81670.0i 1.66596 + 0.606360i 0.991283 0.131753i \(-0.0420605\pi\)
0.674677 + 0.738113i \(0.264283\pi\)
\(368\) 0 0
\(369\) 98540.8 110955.i 0.723708 0.814877i
\(370\) 0 0
\(371\) 6837.01 1205.55i 0.0496728 0.00875865i
\(372\) 0 0
\(373\) −59651.3 + 21711.3i −0.428748 + 0.156052i −0.547375 0.836887i \(-0.684373\pi\)
0.118627 + 0.992939i \(0.462151\pi\)
\(374\) 0 0
\(375\) 77350.6 129734.i 0.550049 0.922553i
\(376\) 0 0
\(377\) 37436.4i 0.263397i
\(378\) 0 0
\(379\) 259784. 1.80856 0.904281 0.426937i \(-0.140407\pi\)
0.904281 + 0.426937i \(0.140407\pi\)
\(380\) 0 0
\(381\) −177537. + 99204.1i −1.22304 + 0.683407i
\(382\) 0 0
\(383\) −24459.2 67201.2i −0.166742 0.458120i 0.827976 0.560763i \(-0.189492\pi\)
−0.994718 + 0.102643i \(0.967270\pi\)
\(384\) 0 0
\(385\) 8312.62 + 47143.2i 0.0560811 + 0.318052i
\(386\) 0 0
\(387\) −91784.7 36356.6i −0.612842 0.242751i
\(388\) 0 0
\(389\) −68567.8 + 188389.i −0.453128 + 1.24496i 0.477383 + 0.878696i \(0.341586\pi\)
−0.930511 + 0.366264i \(0.880637\pi\)
\(390\) 0 0
\(391\) 34294.8 + 28776.7i 0.224323 + 0.188230i
\(392\) 0 0
\(393\) 4125.31 21616.5i 0.0267099 0.139959i
\(394\) 0 0
\(395\) −135445. 78199.1i −0.868097 0.501196i
\(396\) 0 0
\(397\) −58749.4 101757.i −0.372754 0.645629i 0.617234 0.786779i \(-0.288253\pi\)
−0.989988 + 0.141151i \(0.954920\pi\)
\(398\) 0 0
\(399\) 39758.3 + 48756.1i 0.249736 + 0.306255i
\(400\) 0 0
\(401\) −18914.7 3335.17i −0.117628 0.0207410i 0.114524 0.993420i \(-0.463466\pi\)
−0.232152 + 0.972679i \(0.574577\pi\)
\(402\) 0 0
\(403\) 69328.0 58173.1i 0.426873 0.358189i
\(404\) 0 0
\(405\) −34955.7 115909.i −0.213112 0.706652i
\(406\) 0 0
\(407\) −160456. 191224.i −0.968651 1.15439i
\(408\) 0 0
\(409\) 20337.6 115340.i 0.121577 0.689499i −0.861705 0.507410i \(-0.830603\pi\)
0.983282 0.182089i \(-0.0582858\pi\)
\(410\) 0 0
\(411\) −92105.2 + 75107.3i −0.545256 + 0.444630i
\(412\) 0 0
\(413\) −20330.7 + 11737.9i −0.119193 + 0.0688162i
\(414\) 0 0
\(415\) −10015.8 + 17347.9i −0.0581555 + 0.100728i
\(416\) 0 0
\(417\) 324062. + 61844.2i 1.86362 + 0.355653i
\(418\) 0 0
\(419\) −6735.90 + 8027.53i −0.0383679 + 0.0457250i −0.784887 0.619639i \(-0.787279\pi\)
0.746519 + 0.665364i \(0.231724\pi\)
\(420\) 0 0
\(421\) −105571. 38424.7i −0.595635 0.216794i 0.0265709 0.999647i \(-0.491541\pi\)
−0.622206 + 0.782853i \(0.713763\pi\)
\(422\) 0 0
\(423\) 136367. 20115.3i 0.762127 0.112420i
\(424\) 0 0
\(425\) −140468. + 24768.4i −0.777680 + 0.137126i
\(426\) 0 0
\(427\) −50241.4 + 18286.4i −0.275553 + 0.100293i
\(428\) 0 0
\(429\) 45650.1 + 81696.1i 0.248043 + 0.443901i
\(430\) 0 0
\(431\) 288726.i 1.55428i 0.629325 + 0.777142i \(0.283332\pi\)
−0.629325 + 0.777142i \(0.716668\pi\)
\(432\) 0 0
\(433\) −212012. −1.13080 −0.565398 0.824818i \(-0.691277\pi\)
−0.565398 + 0.824818i \(0.691277\pi\)
\(434\) 0 0
\(435\) −86155.7 51368.2i −0.455308 0.271466i
\(436\) 0 0
\(437\) 13806.6 + 37933.3i 0.0722976 + 0.198636i
\(438\) 0 0
\(439\) −30463.9 172769.i −0.158072 0.896473i −0.955923 0.293618i \(-0.905141\pi\)
0.797851 0.602855i \(-0.205970\pi\)
\(440\) 0 0
\(441\) −166168. + 55248.3i −0.854420 + 0.284081i
\(442\) 0 0
\(443\) 25778.3 70825.2i 0.131355 0.360894i −0.856527 0.516102i \(-0.827382\pi\)
0.987882 + 0.155208i \(0.0496047\pi\)
\(444\) 0 0
\(445\) 162370. + 136244.i 0.819944 + 0.688015i
\(446\) 0 0
\(447\) −141120. 121831.i −0.706275 0.609736i
\(448\) 0 0
\(449\) 74850.4 + 43214.9i 0.371280 + 0.214359i 0.674017 0.738715i \(-0.264567\pi\)
−0.302738 + 0.953074i \(0.597901\pi\)
\(450\) 0 0
\(451\) −153680. 266181.i −0.755551 1.30865i
\(452\) 0 0
\(453\) 87282.7 229720.i 0.425336 1.11944i
\(454\) 0 0
\(455\) −17416.5 3070.99i −0.0841274 0.0148339i
\(456\) 0 0
\(457\) −98203.7 + 82402.7i −0.470214 + 0.394556i −0.846873 0.531796i \(-0.821517\pi\)
0.376659 + 0.926352i \(0.377073\pi\)
\(458\) 0 0
\(459\) −195898. + 308528.i −0.929833 + 1.46443i
\(460\) 0 0
\(461\) −65000.0 77464.0i −0.305852 0.364500i 0.591123 0.806582i \(-0.298685\pi\)
−0.896975 + 0.442081i \(0.854240\pi\)
\(462\) 0 0
\(463\) −551.115 + 3125.53i −0.00257087 + 0.0145801i −0.986066 0.166353i \(-0.946801\pi\)
0.983495 + 0.180933i \(0.0579119\pi\)
\(464\) 0 0
\(465\) 38750.9 + 239373.i 0.179216 + 1.10705i
\(466\) 0 0
\(467\) 350190. 202182.i 1.60572 0.927062i 0.615405 0.788211i \(-0.288992\pi\)
0.990313 0.138851i \(-0.0443410\pi\)
\(468\) 0 0
\(469\) −1319.87 + 2286.08i −0.00600047 + 0.0103931i
\(470\) 0 0
\(471\) −121482. 348937.i −0.547610 1.57291i
\(472\) 0 0
\(473\) −131435. + 156639.i −0.587476 + 0.700127i
\(474\) 0 0
\(475\) −120858. 43988.6i −0.535657 0.194963i
\(476\) 0 0
\(477\) −1021.02 + 36351.3i −0.00448743 + 0.159766i
\(478\) 0 0
\(479\) −323147. + 56979.5i −1.40841 + 0.248341i −0.825594 0.564264i \(-0.809160\pi\)
−0.582815 + 0.812605i \(0.698049\pi\)
\(480\) 0 0
\(481\) 86659.4 31541.4i 0.374564 0.136330i
\(482\) 0 0
\(483\) 12426.9 + 174.486i 0.0532682 + 0.000747939i
\(484\) 0 0
\(485\) 21188.1i 0.0900758i
\(486\) 0 0
\(487\) −115199. −0.485727 −0.242863 0.970061i \(-0.578087\pi\)
−0.242863 + 0.970061i \(0.578087\pi\)
\(488\) 0 0
\(489\) −4011.00 + 285663.i −0.0167739 + 1.19464i
\(490\) 0 0
\(491\) −101982. 280195.i −0.423022 1.16224i −0.949969 0.312344i \(-0.898886\pi\)
0.526947 0.849898i \(-0.323337\pi\)
\(492\) 0 0
\(493\) 52581.2 + 298203.i 0.216340 + 1.22693i
\(494\) 0 0
\(495\) −250653. 7040.24i −1.02297 0.0287327i
\(496\) 0 0
\(497\) 20639.3 56706.0i 0.0835568 0.229570i
\(498\) 0 0
\(499\) −26287.0 22057.4i −0.105570 0.0885835i 0.588475 0.808515i \(-0.299729\pi\)
−0.694045 + 0.719932i \(0.744173\pi\)
\(500\) 0 0
\(501\) −460434. + 160300.i −1.83439 + 0.638643i
\(502\) 0 0
\(503\) 138252. + 79820.0i 0.546432 + 0.315483i 0.747682 0.664057i \(-0.231167\pi\)
−0.201250 + 0.979540i \(0.564500\pi\)
\(504\) 0 0
\(505\) −59249.8 102624.i −0.232329 0.402406i
\(506\) 0 0
\(507\) 219616. 35552.6i 0.854374 0.138311i
\(508\) 0 0
\(509\) 212619. + 37490.4i 0.820665 + 0.144705i 0.568189 0.822898i \(-0.307644\pi\)
0.252475 + 0.967603i \(0.418755\pi\)
\(510\) 0 0
\(511\) −99685.7 + 83646.2i −0.381760 + 0.320335i
\(512\) 0 0
\(513\) −292075. + 152607.i −1.10984 + 0.579881i
\(514\) 0 0
\(515\) 77725.7 + 92629.8i 0.293056 + 0.349250i
\(516\) 0 0
\(517\) 49576.9 281164.i 0.185480 1.05191i
\(518\) 0 0
\(519\) 411550. + 156370.i 1.52787 + 0.580520i
\(520\) 0 0
\(521\) 456380. 263491.i 1.68132 0.970712i 0.720537 0.693416i \(-0.243895\pi\)
0.960785 0.277295i \(-0.0894380\pi\)
\(522\) 0 0
\(523\) 121475. 210401.i 0.444104 0.769210i −0.553885 0.832593i \(-0.686855\pi\)
0.997989 + 0.0633824i \(0.0201888\pi\)
\(524\) 0 0
\(525\) −25875.6 + 29972.5i −0.0938797 + 0.108744i
\(526\) 0 0
\(527\) 470532. 560758.i 1.69421 2.01908i
\(528\) 0 0
\(529\) −255471. 92983.8i −0.912914 0.332274i
\(530\) 0 0
\(531\) −38797.2 116689.i −0.137598 0.413848i
\(532\) 0 0
\(533\) 111825. 19717.8i 0.393627 0.0694071i
\(534\) 0 0
\(535\) −74266.8 + 27030.9i −0.259470 + 0.0944394i
\(536\) 0 0
\(537\) 120859. 202708.i 0.419113 0.702946i
\(538\) 0 0
\(539\) 362696.i 1.24843i
\(540\) 0 0
\(541\) −293805. −1.00384 −0.501921 0.864914i \(-0.667373\pi\)
−0.501921 + 0.864914i \(0.667373\pi\)
\(542\) 0 0
\(543\) 220889. 123428.i 0.749161 0.418616i
\(544\) 0 0
\(545\) 24058.4 + 66100.0i 0.0809980 + 0.222540i
\(546\) 0 0
\(547\) −23411.2 132772.i −0.0782437 0.443742i −0.998611 0.0526871i \(-0.983221\pi\)
0.920367 0.391055i \(-0.127890\pi\)
\(548\) 0 0
\(549\) −40869.2 277063.i −0.135598 0.919250i
\(550\) 0 0
\(551\) −93384.2 + 256571.i −0.307588 + 0.845092i
\(552\) 0 0
\(553\) 100403. + 84248.0i 0.328319 + 0.275492i
\(554\) 0 0
\(555\) −46320.2 + 242717.i −0.150378 + 0.787977i
\(556\) 0 0
\(557\) −184012. 106239.i −0.593111 0.342433i 0.173216 0.984884i \(-0.444584\pi\)
−0.766327 + 0.642451i \(0.777918\pi\)
\(558\) 0 0
\(559\) −37770.8 65420.9i −0.120874 0.209360i
\(560\) 0 0
\(561\) 478376. + 586640.i 1.52000 + 1.86400i
\(562\) 0 0
\(563\) 409414. + 72190.7i 1.29165 + 0.227753i 0.776921 0.629598i \(-0.216780\pi\)
0.514732 + 0.857351i \(0.327891\pi\)
\(564\) 0 0
\(565\) −92575.1 + 77679.7i −0.289999 + 0.243338i
\(566\) 0 0
\(567\) 11981.6 + 100746.i 0.0372691 + 0.313374i
\(568\) 0 0
\(569\) 57732.2 + 68802.6i 0.178317 + 0.212510i 0.847798 0.530319i \(-0.177928\pi\)
−0.669481 + 0.742829i \(0.733483\pi\)
\(570\) 0 0
\(571\) −18272.9 + 103631.i −0.0560449 + 0.317847i −0.999923 0.0124489i \(-0.996037\pi\)
0.943878 + 0.330295i \(0.107148\pi\)
\(572\) 0 0
\(573\) −251941. + 205446.i −0.767343 + 0.625731i
\(574\) 0 0
\(575\) −22003.5 + 12703.7i −0.0665513 + 0.0384234i
\(576\) 0 0
\(577\) 327443. 567148.i 0.983522 1.70351i 0.335192 0.942150i \(-0.391199\pi\)
0.648330 0.761360i \(-0.275468\pi\)
\(578\) 0 0
\(579\) −198665. 37913.3i −0.592604 0.113093i
\(580\) 0 0
\(581\) 10790.6 12859.7i 0.0319663 0.0380960i
\(582\) 0 0
\(583\) 70779.0 + 25761.4i 0.208241 + 0.0757937i
\(584\) 0 0
\(585\) 34115.4 86126.6i 0.0996870 0.251667i
\(586\) 0 0
\(587\) 281832. 49694.5i 0.817925 0.144222i 0.250995 0.967988i \(-0.419242\pi\)
0.566930 + 0.823766i \(0.308131\pi\)
\(588\) 0 0
\(589\) 620252. 225753.i 1.78788 0.650734i
\(590\) 0 0
\(591\) 288496. + 516297.i 0.825971 + 1.47817i
\(592\) 0 0
\(593\) 588614.i 1.67387i 0.547303 + 0.836935i \(0.315655\pi\)
−0.547303 + 0.836935i \(0.684345\pi\)
\(594\) 0 0
\(595\) −143046. −0.404056
\(596\) 0 0
\(597\) −291624. 173873.i −0.818228 0.487848i
\(598\) 0 0
\(599\) −87972.0 241701.i −0.245183 0.673635i −0.999846 0.0175230i \(-0.994422\pi\)
0.754663 0.656112i \(-0.227800\pi\)
\(600\) 0 0
\(601\) 92944.8 + 527116.i 0.257321 + 1.45934i 0.790043 + 0.613052i \(0.210058\pi\)
−0.532721 + 0.846291i \(0.678831\pi\)
\(602\) 0 0
\(603\) −10338.6 9181.91i −0.0284333 0.0252522i
\(604\) 0 0
\(605\) −85233.1 + 234176.i −0.232861 + 0.639781i
\(606\) 0 0
\(607\) 7438.44 + 6241.59i 0.0201885 + 0.0169402i 0.652826 0.757508i \(-0.273583\pi\)
−0.632638 + 0.774448i \(0.718028\pi\)
\(608\) 0 0
\(609\) 63629.1 + 54931.7i 0.171562 + 0.148112i
\(610\) 0 0
\(611\) 91344.1 + 52737.5i 0.244680 + 0.141266i
\(612\) 0 0
\(613\) −211500. 366328.i −0.562845 0.974876i −0.997247 0.0741567i \(-0.976373\pi\)
0.434402 0.900719i \(-0.356960\pi\)
\(614\) 0 0
\(615\) −108062. + 284409.i −0.285709 + 0.751958i
\(616\) 0 0
\(617\) −276732. 48795.3i −0.726923 0.128176i −0.202073 0.979371i \(-0.564768\pi\)
−0.524851 + 0.851194i \(0.675879\pi\)
\(618\) 0 0
\(619\) 10444.5 8763.96i 0.0272587 0.0228728i −0.629056 0.777360i \(-0.716559\pi\)
0.656315 + 0.754487i \(0.272114\pi\)
\(620\) 0 0
\(621\) −13994.1 + 63578.2i −0.0362878 + 0.164864i
\(622\) 0 0
\(623\) −114177. 136071.i −0.294173 0.350581i
\(624\) 0 0
\(625\) −22895.9 + 129849.i −0.0586136 + 0.332414i
\(626\) 0 0
\(627\) 109075. + 673779.i 0.277453 + 1.71389i
\(628\) 0 0
\(629\) 645992. 372964.i 1.63277 0.942682i
\(630\) 0 0
\(631\) −181931. + 315113.i −0.456927 + 0.791421i −0.998797 0.0490416i \(-0.984383\pi\)
0.541870 + 0.840463i \(0.317717\pi\)
\(632\) 0 0
\(633\) −147543. 423790.i −0.368222 1.05765i
\(634\) 0 0
\(635\) 268020. 319414.i 0.664692 0.792149i
\(636\) 0 0
\(637\) −125913. 45828.5i −0.310307 0.112942i
\(638\) 0 0
\(639\) 269202. + 165672.i 0.659291 + 0.405739i
\(640\) 0 0
\(641\) −182661. + 32208.0i −0.444559 + 0.0783877i −0.391447 0.920201i \(-0.628025\pi\)
−0.0531122 + 0.998589i \(0.516914\pi\)
\(642\) 0 0
\(643\) 151393. 55102.5i 0.366170 0.133275i −0.152380 0.988322i \(-0.548694\pi\)
0.518551 + 0.855047i \(0.326472\pi\)
\(644\) 0 0
\(645\) 202386. + 2841.71i 0.486476 + 0.00683062i
\(646\) 0 0
\(647\) 612652.i 1.46354i 0.681551 + 0.731771i \(0.261306\pi\)
−0.681551 + 0.731771i \(0.738694\pi\)
\(648\) 0 0
\(649\) −254697. −0.604693
\(650\) 0 0
\(651\) 2853.04 203193.i 0.00673203 0.479455i
\(652\) 0 0
\(653\) −96947.5 266361.i −0.227358 0.624661i 0.772589 0.634906i \(-0.218961\pi\)
−0.999948 + 0.0102448i \(0.996739\pi\)
\(654\) 0 0
\(655\) 7834.83 + 44433.5i 0.0182619 + 0.103569i
\(656\) 0 0
\(657\) −324112. 599655.i −0.750869 1.38922i
\(658\) 0 0
\(659\) 39534.0 108619.i 0.0910333 0.250112i −0.885817 0.464034i \(-0.846402\pi\)
0.976851 + 0.213922i \(0.0686238\pi\)
\(660\) 0 0
\(661\) −228769. 191960.i −0.523594 0.439348i 0.342289 0.939595i \(-0.388798\pi\)
−0.865883 + 0.500247i \(0.833242\pi\)
\(662\) 0 0
\(663\) −264102. + 91947.1i −0.600820 + 0.209176i
\(664\) 0 0
\(665\) −111704. 64492.1i −0.252595 0.145836i
\(666\) 0 0
\(667\) 26969.0 + 46711.7i 0.0606197 + 0.104996i
\(668\) 0 0
\(669\) 470089. 76100.5i 1.05034 0.170034i
\(670\) 0 0
\(671\) −571256. 100728.i −1.26878 0.223720i
\(672\) 0 0
\(673\) 51736.3 43412.0i 0.114226 0.0958471i −0.583886 0.811836i \(-0.698468\pi\)
0.698112 + 0.715989i \(0.254024\pi\)
\(674\) 0 0
\(675\) −126514. 164360.i −0.277670 0.360736i
\(676\) 0 0
\(677\) 32165.5 + 38333.3i 0.0701798 + 0.0836371i 0.799992 0.600011i \(-0.204837\pi\)
−0.729812 + 0.683648i \(0.760393\pi\)
\(678\) 0 0
\(679\) 3083.34 17486.5i 0.00668779 0.0379283i
\(680\) 0 0
\(681\) −451057. 171380.i −0.972606 0.369545i
\(682\) 0 0
\(683\) 356353. 205741.i 0.763905 0.441041i −0.0667911 0.997767i \(-0.521276\pi\)
0.830696 + 0.556726i \(0.187943\pi\)
\(684\) 0 0
\(685\) 121832. 211019.i 0.259645 0.449719i
\(686\) 0 0
\(687\) 558716. 647178.i 1.18380 1.37123i
\(688\) 0 0
\(689\) −17886.6 + 21316.4i −0.0376781 + 0.0449030i
\(690\) 0 0
\(691\) −869026. 316300.i −1.82002 0.662434i −0.995294 0.0969053i \(-0.969106\pi\)
−0.824729 0.565529i \(-0.808672\pi\)
\(692\) 0 0
\(693\) 205840. + 42286.0i 0.428610 + 0.0880502i
\(694\) 0 0
\(695\) −666121. + 117455.i −1.37906 + 0.243166i
\(696\) 0 0
\(697\) 863060. 314128.i 1.77654 0.646608i
\(698\) 0 0
\(699\) 316114. 530193.i 0.646978 1.08513i
\(700\) 0 0
\(701\) 503300.i 1.02421i 0.858922 + 0.512107i \(0.171135\pi\)
−0.858922 + 0.512107i \(0.828865\pi\)
\(702\) 0 0
\(703\) 672601. 1.36097
\(704\) 0 0
\(705\) −246707. + 137855.i −0.496368 + 0.277360i
\(706\) 0 0
\(707\) 33964.8 + 93317.4i 0.0679500 + 0.186691i
\(708\) 0 0
\(709\) 111417. + 631875.i 0.221645 + 1.25701i 0.868996 + 0.494819i \(0.164765\pi\)
−0.647352 + 0.762192i \(0.724123\pi\)
\(710\) 0 0
\(711\) −538107. + 426362.i −1.06446 + 0.843412i
\(712\) 0 0
\(713\) 44597.2 122530.i 0.0877261 0.241025i
\(714\) 0 0
\(715\) −146983. 123333.i −0.287511 0.241250i
\(716\) 0 0
\(717\) −43476.2 + 227814.i −0.0845693 + 0.443141i
\(718\) 0 0
\(719\) −818071. 472314.i −1.58246 0.913635i −0.994499 0.104748i \(-0.966597\pi\)
−0.587964 0.808887i \(-0.700070\pi\)
\(720\) 0 0
\(721\) −50667.2 87758.2i −0.0974668 0.168817i
\(722\) 0 0
\(723\) −36874.1 45219.3i −0.0705416 0.0865062i
\(724\) 0 0
\(725\) −169239. 29841.4i −0.321976 0.0567731i
\(726\) 0 0
\(727\) −670967. + 563008.i −1.26950 + 1.06524i −0.274896 + 0.961474i \(0.588643\pi\)
−0.994602 + 0.103762i \(0.966912\pi\)
\(728\) 0 0
\(729\) −529556. 44715.9i −0.996454 0.0841409i
\(730\) 0 0
\(731\) −392754. 468066.i −0.734997 0.875935i
\(732\) 0 0
\(733\) −33242.1 + 188525.i −0.0618701 + 0.350883i 0.938119 + 0.346312i \(0.112566\pi\)
−0.999990 + 0.00457085i \(0.998545\pi\)
\(734\) 0 0
\(735\) 278240. 226891.i 0.515045 0.419994i
\(736\) 0 0
\(737\) −24802.5 + 14319.7i −0.0456625 + 0.0263633i
\(738\) 0 0
\(739\) −463284. + 802431.i −0.848317 + 1.46933i 0.0343917 + 0.999408i \(0.489051\pi\)
−0.882709 + 0.469920i \(0.844283\pi\)
\(740\) 0 0
\(741\) −247690. 47269.2i −0.451099 0.0860879i
\(742\) 0 0
\(743\) −151441. + 180481.i −0.274326 + 0.326929i −0.885564 0.464518i \(-0.846228\pi\)
0.611238 + 0.791447i \(0.290672\pi\)
\(744\) 0 0
\(745\) 359183. + 130732.i 0.647148 + 0.235543i
\(746\) 0 0
\(747\) 54609.0 + 68921.3i 0.0978640 + 0.123513i
\(748\) 0 0
\(749\) 65226.0 11501.1i 0.116267 0.0205010i
\(750\) 0 0
\(751\) −975993. + 355232.i −1.73048 + 0.629843i −0.998665 0.0516592i \(-0.983549\pi\)
−0.731816 + 0.681503i \(0.761327\pi\)
\(752\) 0 0
\(753\) −369190. 660707.i −0.651118 1.16525i
\(754\) 0 0
\(755\) 503832.i 0.883877i
\(756\) 0 0
\(757\) 514913. 0.898550 0.449275 0.893394i \(-0.351682\pi\)
0.449275 + 0.893394i \(0.351682\pi\)
\(758\) 0 0
\(759\) 115814. + 69051.2i 0.201038 + 0.119864i
\(760\) 0 0
\(761\) 38646.1 + 106179.i 0.0667323 + 0.183346i 0.968576 0.248716i \(-0.0800086\pi\)
−0.901844 + 0.432061i \(0.857786\pi\)
\(762\) 0 0
\(763\) −10236.4 58053.3i −0.0175832 0.0997190i
\(764\) 0 0
\(765\) 150780. 733967.i 0.257645 1.25416i
\(766\) 0 0
\(767\) 32182.3 88420.2i 0.0547049 0.150301i
\(768\) 0 0
\(769\) 560141. + 470014.i 0.947206 + 0.794800i 0.978825 0.204700i \(-0.0656218\pi\)
−0.0316188 + 0.999500i \(0.510066\pi\)
\(770\) 0 0
\(771\) −196686. 169801.i −0.330875 0.285648i
\(772\) 0 0
\(773\) −692751. 399960.i −1.15936 0.669357i −0.208209 0.978084i \(-0.566763\pi\)
−0.951150 + 0.308728i \(0.900097\pi\)
\(774\) 0 0
\(775\) 207721. + 359783.i 0.345841 + 0.599014i
\(776\) 0 0
\(777\) 73548.8 193573.i 0.121824 0.320630i
\(778\) 0 0
\(779\) 815582. + 143809.i 1.34398 + 0.236980i
\(780\) 0 0