Properties

Label 108.5.f.a.91.20
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 91.20
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.20

$q$-expansion

\(f(q)\) \(=\) \(q+(3.86509 + 1.03009i) q^{2} +(13.8778 + 7.96277i) q^{4} +(5.89438 - 10.2094i) q^{5} +(50.5548 - 29.1878i) q^{7} +(45.4367 + 45.0722i) q^{8} +O(q^{10})\) \(q+(3.86509 + 1.03009i) q^{2} +(13.8778 + 7.96277i) q^{4} +(5.89438 - 10.2094i) q^{5} +(50.5548 - 29.1878i) q^{7} +(45.4367 + 45.0722i) q^{8} +(33.2988 - 33.3884i) q^{10} +(-86.9742 + 50.2146i) q^{11} +(85.3178 - 147.775i) q^{13} +(225.465 - 60.7377i) q^{14} +(129.189 + 221.012i) q^{16} +398.571 q^{17} +404.608i q^{19} +(163.096 - 94.7483i) q^{20} +(-387.889 + 104.493i) q^{22} +(-291.091 - 168.062i) q^{23} +(243.013 + 420.910i) q^{25} +(481.982 - 483.278i) q^{26} +(934.007 - 2.50777i) q^{28} +(-327.671 - 567.543i) q^{29} +(-550.166 - 317.638i) q^{31} +(271.664 + 987.307i) q^{32} +(1540.51 + 410.563i) q^{34} -688.176i q^{35} -1599.91 q^{37} +(-416.782 + 1563.85i) q^{38} +(727.980 - 198.207i) q^{40} +(1231.63 - 2133.25i) q^{41} +(-1933.38 + 1116.24i) q^{43} +(-1606.86 + 4.31435i) q^{44} +(-951.976 - 949.423i) q^{46} +(-2514.55 + 1451.78i) q^{47} +(503.358 - 871.842i) q^{49} +(505.691 + 1877.18i) q^{50} +(2360.72 - 1371.43i) q^{52} -1291.73 q^{53} +1183.94i q^{55} +(3612.60 + 952.417i) q^{56} +(-681.858 - 2531.13i) q^{58} +(1002.24 + 578.642i) q^{59} +(-2960.81 - 5128.28i) q^{61} +(-1799.24 - 1794.42i) q^{62} +(32.9923 + 4095.87i) q^{64} +(-1005.79 - 1742.08i) q^{65} +(3085.87 + 1781.63i) q^{67} +(5531.30 + 3173.73i) q^{68} +(708.882 - 2659.86i) q^{70} -5639.73i q^{71} -5496.39 q^{73} +(-6183.80 - 1648.05i) q^{74} +(-3221.80 + 5615.09i) q^{76} +(-2931.31 + 5077.18i) q^{77} +(-2788.94 + 1610.20i) q^{79} +(3017.88 - 16.2058i) q^{80} +(6957.81 - 6976.52i) q^{82} +(-7063.92 + 4078.36i) q^{83} +(2349.33 - 4069.15i) q^{85} +(-8622.53 + 2322.81i) q^{86} +(-6215.11 - 1638.53i) q^{88} -910.873 q^{89} -9960.97i q^{91} +(-2701.48 - 4650.22i) q^{92} +(-11214.4 + 3021.04i) q^{94} +(4130.79 + 2384.91i) q^{95} +(8804.44 + 15249.7i) q^{97} +(2843.60 - 2851.24i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.86509 + 1.03009i 0.966272 + 0.257522i
\(3\) 0 0
\(4\) 13.8778 + 7.96277i 0.867365 + 0.497673i
\(5\) 5.89438 10.2094i 0.235775 0.408374i −0.723723 0.690091i \(-0.757570\pi\)
0.959498 + 0.281717i \(0.0909038\pi\)
\(6\) 0 0
\(7\) 50.5548 29.1878i 1.03173 0.595670i 0.114251 0.993452i \(-0.463553\pi\)
0.917480 + 0.397782i \(0.130220\pi\)
\(8\) 45.4367 + 45.0722i 0.709949 + 0.704253i
\(9\) 0 0
\(10\) 33.2988 33.3884i 0.332988 0.333884i
\(11\) −86.9742 + 50.2146i −0.718795 + 0.414997i −0.814309 0.580431i \(-0.802884\pi\)
0.0955138 + 0.995428i \(0.469551\pi\)
\(12\) 0 0
\(13\) 85.3178 147.775i 0.504839 0.874407i −0.495145 0.868810i \(-0.664885\pi\)
0.999984 0.00559684i \(-0.00178154\pi\)
\(14\) 225.465 60.7377i 1.15033 0.309886i
\(15\) 0 0
\(16\) 129.189 + 221.012i 0.504643 + 0.863328i
\(17\) 398.571 1.37914 0.689569 0.724220i \(-0.257800\pi\)
0.689569 + 0.724220i \(0.257800\pi\)
\(18\) 0 0
\(19\) 404.608i 1.12080i 0.828223 + 0.560399i \(0.189352\pi\)
−0.828223 + 0.560399i \(0.810648\pi\)
\(20\) 163.096 94.7483i 0.407740 0.236871i
\(21\) 0 0
\(22\) −387.889 + 104.493i −0.801423 + 0.215894i
\(23\) −291.091 168.062i −0.550267 0.317697i 0.198963 0.980007i \(-0.436243\pi\)
−0.749230 + 0.662310i \(0.769576\pi\)
\(24\) 0 0
\(25\) 243.013 + 420.910i 0.388820 + 0.673456i
\(26\) 481.982 483.278i 0.712991 0.714908i
\(27\) 0 0
\(28\) 934.007 2.50777i 1.19134 0.00319868i
\(29\) −327.671 567.543i −0.389621 0.674843i 0.602778 0.797909i \(-0.294061\pi\)
−0.992398 + 0.123066i \(0.960727\pi\)
\(30\) 0 0
\(31\) −550.166 317.638i −0.572493 0.330529i 0.185651 0.982616i \(-0.440560\pi\)
−0.758144 + 0.652087i \(0.773894\pi\)
\(32\) 271.664 + 987.307i 0.265297 + 0.964167i
\(33\) 0 0
\(34\) 1540.51 + 410.563i 1.33262 + 0.355158i
\(35\) 688.176i 0.561776i
\(36\) 0 0
\(37\) −1599.91 −1.16867 −0.584336 0.811512i \(-0.698645\pi\)
−0.584336 + 0.811512i \(0.698645\pi\)
\(38\) −416.782 + 1563.85i −0.288630 + 1.08300i
\(39\) 0 0
\(40\) 727.980 198.207i 0.454987 0.123880i
\(41\) 1231.63 2133.25i 0.732679 1.26904i −0.223055 0.974806i \(-0.571603\pi\)
0.955734 0.294232i \(-0.0950637\pi\)
\(42\) 0 0
\(43\) −1933.38 + 1116.24i −1.04564 + 0.603699i −0.921425 0.388557i \(-0.872974\pi\)
−0.124212 + 0.992256i \(0.539640\pi\)
\(44\) −1606.86 + 4.31435i −0.829990 + 0.00222849i
\(45\) 0 0
\(46\) −951.976 949.423i −0.449894 0.448688i
\(47\) −2514.55 + 1451.78i −1.13832 + 0.657211i −0.946015 0.324124i \(-0.894931\pi\)
−0.192308 + 0.981335i \(0.561597\pi\)
\(48\) 0 0
\(49\) 503.358 871.842i 0.209645 0.363116i
\(50\) 505.691 + 1877.18i 0.202276 + 0.750872i
\(51\) 0 0
\(52\) 2360.72 1371.43i 0.873048 0.507185i
\(53\) −1291.73 −0.459852 −0.229926 0.973208i \(-0.573848\pi\)
−0.229926 + 0.973208i \(0.573848\pi\)
\(54\) 0 0
\(55\) 1183.94i 0.391384i
\(56\) 3612.60 + 952.417i 1.15198 + 0.303704i
\(57\) 0 0
\(58\) −681.858 2531.13i −0.202693 0.752418i
\(59\) 1002.24 + 578.642i 0.287917 + 0.166229i 0.637002 0.770862i \(-0.280174\pi\)
−0.349085 + 0.937091i \(0.613508\pi\)
\(60\) 0 0
\(61\) −2960.81 5128.28i −0.795703 1.37820i −0.922392 0.386256i \(-0.873768\pi\)
0.126688 0.991943i \(-0.459565\pi\)
\(62\) −1799.24 1794.42i −0.468066 0.466811i
\(63\) 0 0
\(64\) 32.9923 + 4095.87i 0.00805476 + 0.999968i
\(65\) −1005.79 1742.08i −0.238057 0.412327i
\(66\) 0 0
\(67\) 3085.87 + 1781.63i 0.687430 + 0.396888i 0.802648 0.596452i \(-0.203424\pi\)
−0.115219 + 0.993340i \(0.536757\pi\)
\(68\) 5531.30 + 3173.73i 1.19622 + 0.686360i
\(69\) 0 0
\(70\) 708.882 2659.86i 0.144670 0.542829i
\(71\) 5639.73i 1.11877i −0.828907 0.559386i \(-0.811037\pi\)
0.828907 0.559386i \(-0.188963\pi\)
\(72\) 0 0
\(73\) −5496.39 −1.03141 −0.515705 0.856766i \(-0.672470\pi\)
−0.515705 + 0.856766i \(0.672470\pi\)
\(74\) −6183.80 1648.05i −1.12926 0.300959i
\(75\) 0 0
\(76\) −3221.80 + 5615.09i −0.557791 + 0.972141i
\(77\) −2931.31 + 5077.18i −0.494402 + 0.856329i
\(78\) 0 0
\(79\) −2788.94 + 1610.20i −0.446874 + 0.258003i −0.706509 0.707704i \(-0.749731\pi\)
0.259635 + 0.965707i \(0.416398\pi\)
\(80\) 3017.88 16.2058i 0.471543 0.00253216i
\(81\) 0 0
\(82\) 6957.81 6976.52i 1.03477 1.03755i
\(83\) −7063.92 + 4078.36i −1.02539 + 0.592010i −0.915661 0.401951i \(-0.868332\pi\)
−0.109730 + 0.993961i \(0.534999\pi\)
\(84\) 0 0
\(85\) 2349.33 4069.15i 0.325166 0.563205i
\(86\) −8622.53 + 2322.81i −1.16584 + 0.314063i
\(87\) 0 0
\(88\) −6215.11 1638.53i −0.802571 0.211588i
\(89\) −910.873 −0.114995 −0.0574974 0.998346i \(-0.518312\pi\)
−0.0574974 + 0.998346i \(0.518312\pi\)
\(90\) 0 0
\(91\) 9960.97i 1.20287i
\(92\) −2701.48 4650.22i −0.319173 0.549412i
\(93\) 0 0
\(94\) −11214.4 + 3021.04i −1.26918 + 0.341902i
\(95\) 4130.79 + 2384.91i 0.457705 + 0.264256i
\(96\) 0 0
\(97\) 8804.44 + 15249.7i 0.935747 + 1.62076i 0.773297 + 0.634044i \(0.218606\pi\)
0.162450 + 0.986717i \(0.448060\pi\)
\(98\) 2843.60 2851.24i 0.296085 0.296881i
\(99\) 0 0
\(100\) 20.8792 + 7776.38i 0.00208792 + 0.777638i
\(101\) 3330.41 + 5768.44i 0.326479 + 0.565478i 0.981810 0.189863i \(-0.0608045\pi\)
−0.655332 + 0.755341i \(0.727471\pi\)
\(102\) 0 0
\(103\) 5848.70 + 3376.75i 0.551296 + 0.318291i 0.749645 0.661841i \(-0.230224\pi\)
−0.198348 + 0.980132i \(0.563558\pi\)
\(104\) 10537.1 2868.94i 0.974214 0.265250i
\(105\) 0 0
\(106\) −4992.64 1330.59i −0.444343 0.118422i
\(107\) 30.7569i 0.00268643i −0.999999 0.00134321i \(-0.999572\pi\)
0.999999 0.00134321i \(-0.000427558\pi\)
\(108\) 0 0
\(109\) 10691.4 0.899872 0.449936 0.893061i \(-0.351447\pi\)
0.449936 + 0.893061i \(0.351447\pi\)
\(110\) −1219.56 + 4576.02i −0.100790 + 0.378183i
\(111\) 0 0
\(112\) 12982.0 + 7402.48i 1.03491 + 0.590121i
\(113\) 5008.09 8674.27i 0.392207 0.679322i −0.600533 0.799600i \(-0.705045\pi\)
0.992740 + 0.120277i \(0.0383784\pi\)
\(114\) 0 0
\(115\) −3431.60 + 1981.24i −0.259479 + 0.149810i
\(116\) −28.1529 10485.4i −0.00209222 0.779238i
\(117\) 0 0
\(118\) 3277.69 + 3268.90i 0.235398 + 0.234767i
\(119\) 20149.7 11633.4i 1.42290 0.821511i
\(120\) 0 0
\(121\) −2277.49 + 3944.73i −0.155556 + 0.269430i
\(122\) −6161.23 22871.1i −0.413950 1.53663i
\(123\) 0 0
\(124\) −5105.83 8788.97i −0.332065 0.571603i
\(125\) 13097.6 0.838247
\(126\) 0 0
\(127\) 16087.8i 0.997444i −0.866762 0.498722i \(-0.833803\pi\)
0.866762 0.498722i \(-0.166197\pi\)
\(128\) −4091.59 + 15864.9i −0.249731 + 0.968315i
\(129\) 0 0
\(130\) −2092.97 7769.35i −0.123845 0.459725i
\(131\) 18105.5 + 10453.2i 1.05504 + 0.609127i 0.924056 0.382257i \(-0.124853\pi\)
0.130983 + 0.991385i \(0.458187\pi\)
\(132\) 0 0
\(133\) 11809.6 + 20454.9i 0.667626 + 1.15636i
\(134\) 10091.9 + 10064.9i 0.562037 + 0.560530i
\(135\) 0 0
\(136\) 18109.8 + 17964.5i 0.979117 + 0.971262i
\(137\) 2338.02 + 4049.57i 0.124568 + 0.215759i 0.921564 0.388226i \(-0.126912\pi\)
−0.796996 + 0.603985i \(0.793579\pi\)
\(138\) 0 0
\(139\) 8058.42 + 4652.53i 0.417081 + 0.240802i 0.693828 0.720141i \(-0.255923\pi\)
−0.276747 + 0.960943i \(0.589256\pi\)
\(140\) 5479.79 9550.40i 0.279581 0.487265i
\(141\) 0 0
\(142\) 5809.42 21798.0i 0.288108 1.08104i
\(143\) 17136.8i 0.838026i
\(144\) 0 0
\(145\) −7725.67 −0.367451
\(146\) −21244.0 5661.77i −0.996624 0.265611i
\(147\) 0 0
\(148\) −22203.3 12739.7i −1.01367 0.581617i
\(149\) −12385.8 + 21452.8i −0.557893 + 0.966299i 0.439779 + 0.898106i \(0.355057\pi\)
−0.997672 + 0.0681928i \(0.978277\pi\)
\(150\) 0 0
\(151\) 8841.72 5104.77i 0.387778 0.223884i −0.293419 0.955984i \(-0.594793\pi\)
0.681197 + 0.732100i \(0.261460\pi\)
\(152\) −18236.6 + 18384.1i −0.789326 + 0.795709i
\(153\) 0 0
\(154\) −16559.7 + 16604.2i −0.698251 + 0.700128i
\(155\) −6485.77 + 3744.56i −0.269959 + 0.155861i
\(156\) 0 0
\(157\) 14486.5 25091.4i 0.587712 1.01795i −0.406819 0.913509i \(-0.633362\pi\)
0.994531 0.104439i \(-0.0333046\pi\)
\(158\) −12438.2 + 3350.70i −0.498244 + 0.134221i
\(159\) 0 0
\(160\) 11681.1 + 3046.04i 0.456291 + 0.118986i
\(161\) −19621.4 −0.756970
\(162\) 0 0
\(163\) 17736.4i 0.667560i −0.942651 0.333780i \(-0.891676\pi\)
0.942651 0.333780i \(-0.108324\pi\)
\(164\) 34079.0 19797.7i 1.26707 0.736084i
\(165\) 0 0
\(166\) −31503.8 + 8486.75i −1.14326 + 0.307982i
\(167\) −35562.1 20531.8i −1.27513 0.736197i −0.299182 0.954196i \(-0.596714\pi\)
−0.975949 + 0.217999i \(0.930047\pi\)
\(168\) 0 0
\(169\) −277.761 481.096i −0.00972518 0.0168445i
\(170\) 13271.9 13307.6i 0.459237 0.460472i
\(171\) 0 0
\(172\) −35719.5 + 95.9053i −1.20739 + 0.00324180i
\(173\) 3477.87 + 6023.84i 0.116204 + 0.201271i 0.918260 0.395977i \(-0.129594\pi\)
−0.802056 + 0.597248i \(0.796261\pi\)
\(174\) 0 0
\(175\) 24570.9 + 14186.0i 0.802315 + 0.463217i
\(176\) −22334.1 12735.2i −0.721013 0.411131i
\(177\) 0 0
\(178\) −3520.61 938.280i −0.111116 0.0296137i
\(179\) 1754.50i 0.0547580i −0.999625 0.0273790i \(-0.991284\pi\)
0.999625 0.0273790i \(-0.00871609\pi\)
\(180\) 0 0
\(181\) −43787.9 −1.33659 −0.668293 0.743898i \(-0.732975\pi\)
−0.668293 + 0.743898i \(0.732975\pi\)
\(182\) 10260.7 38500.0i 0.309766 1.16230i
\(183\) 0 0
\(184\) −5651.33 20756.3i −0.166922 0.613076i
\(185\) −9430.49 + 16334.1i −0.275544 + 0.477256i
\(186\) 0 0
\(187\) −34665.4 + 20014.1i −0.991318 + 0.572338i
\(188\) −46456.8 + 124.734i −1.31442 + 0.00352915i
\(189\) 0 0
\(190\) 13509.2 + 13473.0i 0.374216 + 0.373213i
\(191\) 34403.1 19862.7i 0.943042 0.544466i 0.0521297 0.998640i \(-0.483399\pi\)
0.890913 + 0.454174i \(0.150066\pi\)
\(192\) 0 0
\(193\) 10547.2 18268.3i 0.283154 0.490437i −0.689006 0.724756i \(-0.741953\pi\)
0.972160 + 0.234319i \(0.0752859\pi\)
\(194\) 18321.4 + 68011.0i 0.486805 + 1.80707i
\(195\) 0 0
\(196\) 13927.8 8091.15i 0.362552 0.210619i
\(197\) −28256.1 −0.728080 −0.364040 0.931383i \(-0.618603\pi\)
−0.364040 + 0.931383i \(0.618603\pi\)
\(198\) 0 0
\(199\) 24063.5i 0.607650i 0.952728 + 0.303825i \(0.0982638\pi\)
−0.952728 + 0.303825i \(0.901736\pi\)
\(200\) −7929.65 + 30077.9i −0.198241 + 0.751947i
\(201\) 0 0
\(202\) 6930.33 + 25726.1i 0.169844 + 0.630481i
\(203\) −33130.7 19128.0i −0.803967 0.464171i
\(204\) 0 0
\(205\) −14519.4 25148.4i −0.345495 0.598415i
\(206\) 19127.4 + 19076.1i 0.450735 + 0.449527i
\(207\) 0 0
\(208\) 43682.1 234.571i 1.00966 0.00542184i
\(209\) −20317.2 35190.5i −0.465127 0.805624i
\(210\) 0 0
\(211\) −50298.6 29039.9i −1.12977 0.652274i −0.185895 0.982570i \(-0.559518\pi\)
−0.943878 + 0.330295i \(0.892852\pi\)
\(212\) −17926.4 10285.7i −0.398860 0.228856i
\(213\) 0 0
\(214\) 31.6823 118.878i 0.000691814 0.00259582i
\(215\) 26318.1i 0.569349i
\(216\) 0 0
\(217\) −37084.7 −0.787545
\(218\) 41323.1 + 11013.1i 0.869522 + 0.231737i
\(219\) 0 0
\(220\) −9427.40 + 16430.5i −0.194781 + 0.339472i
\(221\) 34005.2 58898.7i 0.696243 1.20593i
\(222\) 0 0
\(223\) 14429.6 8330.91i 0.290164 0.167526i −0.347852 0.937550i \(-0.613089\pi\)
0.638016 + 0.770023i \(0.279755\pi\)
\(224\) 42551.3 + 41983.8i 0.848040 + 0.836731i
\(225\) 0 0
\(226\) 28292.0 28368.0i 0.553919 0.555409i
\(227\) −48721.5 + 28129.4i −0.945515 + 0.545894i −0.891685 0.452657i \(-0.850476\pi\)
−0.0538304 + 0.998550i \(0.517143\pi\)
\(228\) 0 0
\(229\) −1223.91 + 2119.87i −0.0233388 + 0.0404239i −0.877459 0.479652i \(-0.840763\pi\)
0.854120 + 0.520076i \(0.174096\pi\)
\(230\) −15304.3 + 4122.81i −0.289306 + 0.0779358i
\(231\) 0 0
\(232\) 10692.1 40556.1i 0.198649 0.753495i
\(233\) 76971.2 1.41781 0.708903 0.705306i \(-0.249191\pi\)
0.708903 + 0.705306i \(0.249191\pi\)
\(234\) 0 0
\(235\) 34229.3i 0.619816i
\(236\) 9301.30 + 16010.9i 0.167001 + 0.287469i
\(237\) 0 0
\(238\) 89863.7 24208.3i 1.58646 0.427375i
\(239\) 22567.5 + 13029.4i 0.395083 + 0.228101i 0.684360 0.729144i \(-0.260082\pi\)
−0.289277 + 0.957245i \(0.593415\pi\)
\(240\) 0 0
\(241\) 13999.8 + 24248.4i 0.241039 + 0.417492i 0.961011 0.276512i \(-0.0891784\pi\)
−0.719971 + 0.694004i \(0.755845\pi\)
\(242\) −12866.1 + 12900.7i −0.219693 + 0.220284i
\(243\) 0 0
\(244\) −254.388 94745.6i −0.00427284 1.59140i
\(245\) −5933.96 10277.9i −0.0988582 0.171227i
\(246\) 0 0
\(247\) 59790.9 + 34520.3i 0.980034 + 0.565823i
\(248\) −10681.1 39229.6i −0.173665 0.637839i
\(249\) 0 0
\(250\) 50623.4 + 13491.7i 0.809975 + 0.215867i
\(251\) 19782.5i 0.314003i 0.987598 + 0.157001i \(0.0501827\pi\)
−0.987598 + 0.157001i \(0.949817\pi\)
\(252\) 0 0
\(253\) 33756.6 0.527373
\(254\) 16571.8 62180.7i 0.256864 0.963803i
\(255\) 0 0
\(256\) −32156.6 + 57104.5i −0.490670 + 0.871345i
\(257\) 38636.9 66921.1i 0.584974 1.01320i −0.409905 0.912128i \(-0.634438\pi\)
0.994879 0.101076i \(-0.0322285\pi\)
\(258\) 0 0
\(259\) −80883.2 + 46698.0i −1.20575 + 0.696143i
\(260\) −86.4158 32185.2i −0.00127834 0.476112i
\(261\) 0 0
\(262\) 59211.7 + 59053.0i 0.862592 + 0.860279i
\(263\) 18370.5 10606.2i 0.265588 0.153337i −0.361293 0.932452i \(-0.617665\pi\)
0.626881 + 0.779115i \(0.284331\pi\)
\(264\) 0 0
\(265\) −7613.92 + 13187.7i −0.108422 + 0.187792i
\(266\) 24574.9 + 91224.9i 0.347320 + 1.28929i
\(267\) 0 0
\(268\) 28638.5 + 49297.2i 0.398732 + 0.686361i
\(269\) −1106.24 −0.0152878 −0.00764389 0.999971i \(-0.502433\pi\)
−0.00764389 + 0.999971i \(0.502433\pi\)
\(270\) 0 0
\(271\) 33038.3i 0.449861i −0.974375 0.224931i \(-0.927784\pi\)
0.974375 0.224931i \(-0.0722155\pi\)
\(272\) 51490.8 + 88088.9i 0.695972 + 1.19065i
\(273\) 0 0
\(274\) 4865.25 + 18060.3i 0.0648043 + 0.240561i
\(275\) −42271.7 24405.6i −0.558964 0.322718i
\(276\) 0 0
\(277\) −14421.3 24978.4i −0.187951 0.325540i 0.756616 0.653859i \(-0.226851\pi\)
−0.944567 + 0.328319i \(0.893518\pi\)
\(278\) 26354.0 + 26283.3i 0.341002 + 0.340088i
\(279\) 0 0
\(280\) 31017.6 31268.5i 0.395633 0.398833i
\(281\) 16062.9 + 27821.8i 0.203428 + 0.352348i 0.949631 0.313371i \(-0.101458\pi\)
−0.746203 + 0.665719i \(0.768125\pi\)
\(282\) 0 0
\(283\) −61782.5 35670.2i −0.771424 0.445382i 0.0619586 0.998079i \(-0.480265\pi\)
−0.833382 + 0.552697i \(0.813599\pi\)
\(284\) 44907.8 78267.2i 0.556782 0.970383i
\(285\) 0 0
\(286\) −17652.4 + 66235.3i −0.215810 + 0.809762i
\(287\) 143795.i 1.74574i
\(288\) 0 0
\(289\) 75337.7 0.902021
\(290\) −29860.4 7958.12i −0.355058 0.0946268i
\(291\) 0 0
\(292\) −76278.0 43766.5i −0.894609 0.513305i
\(293\) −18320.8 + 31732.5i −0.213407 + 0.369631i −0.952779 0.303666i \(-0.901789\pi\)
0.739372 + 0.673297i \(0.235123\pi\)
\(294\) 0 0
\(295\) 11815.1 6821.47i 0.135767 0.0783852i
\(296\) −72694.8 72111.6i −0.829698 0.823041i
\(297\) 0 0
\(298\) −69970.4 + 70158.5i −0.787920 + 0.790038i
\(299\) −49670.5 + 28677.3i −0.555593 + 0.320772i
\(300\) 0 0
\(301\) −65161.2 + 112863.i −0.719211 + 1.24571i
\(302\) 39432.4 10622.6i 0.432354 0.116471i
\(303\) 0 0
\(304\) −89423.2 + 52270.8i −0.967616 + 0.565603i
\(305\) −69808.6 −0.750428
\(306\) 0 0
\(307\) 11668.1i 0.123801i −0.998082 0.0619005i \(-0.980284\pi\)
0.998082 0.0619005i \(-0.0197161\pi\)
\(308\) −81108.6 + 47118.9i −0.854999 + 0.496699i
\(309\) 0 0
\(310\) −28925.3 + 7792.15i −0.300992 + 0.0810837i
\(311\) 3755.11 + 2168.01i 0.0388242 + 0.0224151i 0.519286 0.854600i \(-0.326198\pi\)
−0.480462 + 0.877015i \(0.659531\pi\)
\(312\) 0 0
\(313\) −43249.3 74909.9i −0.441459 0.764629i 0.556339 0.830955i \(-0.312206\pi\)
−0.997798 + 0.0663262i \(0.978872\pi\)
\(314\) 81838.0 82058.1i 0.830034 0.832266i
\(315\) 0 0
\(316\) −51526.1 + 138.345i −0.516004 + 0.00138545i
\(317\) −12316.1 21332.1i −0.122562 0.212283i 0.798215 0.602372i \(-0.205778\pi\)
−0.920777 + 0.390089i \(0.872444\pi\)
\(318\) 0 0
\(319\) 56997.9 + 32907.7i 0.560115 + 0.323383i
\(320\) 42010.7 + 23805.8i 0.410260 + 0.232478i
\(321\) 0 0
\(322\) −75838.5 20211.8i −0.731439 0.194936i
\(323\) 161265.i 1.54573i
\(324\) 0 0
\(325\) 82933.2 0.785167
\(326\) 18270.0 68552.7i 0.171911 0.645044i
\(327\) 0 0
\(328\) 152112. 41415.5i 1.41389 0.384960i
\(329\) −84748.5 + 146789.i −0.782961 + 1.35613i
\(330\) 0 0
\(331\) 162176. 93632.3i 1.48023 0.854614i 0.480485 0.877003i \(-0.340461\pi\)
0.999749 + 0.0223896i \(0.00712742\pi\)
\(332\) −130507. + 350.405i −1.18402 + 0.00317903i
\(333\) 0 0
\(334\) −116301. 115989.i −1.04254 1.03974i
\(335\) 36378.6 21003.2i 0.324158 0.187152i
\(336\) 0 0
\(337\) 50479.6 87433.2i 0.444484 0.769868i −0.553532 0.832828i \(-0.686720\pi\)
0.998016 + 0.0629592i \(0.0200538\pi\)
\(338\) −577.999 2145.60i −0.00505934 0.0187808i
\(339\) 0 0
\(340\) 65005.3 37763.9i 0.562330 0.326677i
\(341\) 63800.3 0.548674
\(342\) 0 0
\(343\) 81392.2i 0.691823i
\(344\) −138158. 36423.6i −1.16751 0.307798i
\(345\) 0 0
\(346\) 7237.18 + 26865.2i 0.0604529 + 0.224408i
\(347\) 151470. + 87451.5i 1.25797 + 0.726287i 0.972679 0.232155i \(-0.0745777\pi\)
0.285287 + 0.958442i \(0.407911\pi\)
\(348\) 0 0
\(349\) −21948.5 38015.9i −0.180199 0.312114i 0.761749 0.647872i \(-0.224341\pi\)
−0.941948 + 0.335758i \(0.891008\pi\)
\(350\) 80355.9 + 80140.4i 0.655967 + 0.654208i
\(351\) 0 0
\(352\) −73205.0 72228.8i −0.590820 0.582941i
\(353\) 77789.6 + 134736.i 0.624270 + 1.08127i 0.988682 + 0.150029i \(0.0479367\pi\)
−0.364412 + 0.931238i \(0.618730\pi\)
\(354\) 0 0
\(355\) −57578.0 33242.7i −0.456878 0.263778i
\(356\) −12641.0 7253.07i −0.0997424 0.0572298i
\(357\) 0 0
\(358\) 1807.29 6781.30i 0.0141014 0.0529111i
\(359\) 184004.i 1.42771i −0.700295 0.713853i \(-0.746948\pi\)
0.700295 0.713853i \(-0.253052\pi\)
\(360\) 0 0
\(361\) −33386.7 −0.256188
\(362\) −169244. 45105.4i −1.29151 0.344200i
\(363\) 0 0
\(364\) 79316.9 138237.i 0.598636 1.04333i
\(365\) −32397.8 + 56114.6i −0.243181 + 0.421202i
\(366\) 0 0
\(367\) 143674. 82950.4i 1.06671 0.615866i 0.139430 0.990232i \(-0.455473\pi\)
0.927281 + 0.374366i \(0.122140\pi\)
\(368\) −462.064 86046.3i −0.00341198 0.635385i
\(369\) 0 0
\(370\) −53275.2 + 53418.5i −0.389154 + 0.390201i
\(371\) −65302.9 + 37702.7i −0.474444 + 0.273920i
\(372\) 0 0
\(373\) −65160.0 + 112861.i −0.468343 + 0.811193i −0.999345 0.0361768i \(-0.988482\pi\)
0.531003 + 0.847370i \(0.321815\pi\)
\(374\) −154601. + 41647.8i −1.10527 + 0.297748i
\(375\) 0 0
\(376\) −179688. 47372.4i −1.27099 0.335081i
\(377\) −111825. −0.786783
\(378\) 0 0
\(379\) 43645.6i 0.303852i −0.988392 0.151926i \(-0.951453\pi\)
0.988392 0.151926i \(-0.0485475\pi\)
\(380\) 38335.9 + 65990.0i 0.265484 + 0.456994i
\(381\) 0 0
\(382\) 153431. 41332.7i 1.05145 0.283248i
\(383\) 237186. + 136939.i 1.61693 + 0.933535i 0.987708 + 0.156310i \(0.0499599\pi\)
0.629223 + 0.777225i \(0.283373\pi\)
\(384\) 0 0
\(385\) 34556.5 + 59853.6i 0.233135 + 0.403802i
\(386\) 59583.9 59744.1i 0.399902 0.400978i
\(387\) 0 0
\(388\) 756.462 + 281741.i 0.00502486 + 1.87149i
\(389\) −122594. 212339.i −0.810159 1.40324i −0.912753 0.408513i \(-0.866048\pi\)
0.102594 0.994723i \(-0.467286\pi\)
\(390\) 0 0
\(391\) −116020. 66984.5i −0.758894 0.438148i
\(392\) 62166.8 16926.2i 0.404563 0.110151i
\(393\) 0 0
\(394\) −109212. 29106.2i −0.703524 0.187497i
\(395\) 37964.4i 0.243323i
\(396\) 0 0
\(397\) −4252.39 −0.0269806 −0.0134903 0.999909i \(-0.504294\pi\)
−0.0134903 + 0.999909i \(0.504294\pi\)
\(398\) −24787.6 + 93007.8i −0.156483 + 0.587155i
\(399\) 0 0
\(400\) −61631.7 + 108086.i −0.385198 + 0.675535i
\(401\) 3665.61 6349.02i 0.0227959 0.0394837i −0.854402 0.519612i \(-0.826077\pi\)
0.877198 + 0.480128i \(0.159410\pi\)
\(402\) 0 0
\(403\) −93877.9 + 54200.4i −0.578034 + 0.333728i
\(404\) 286.143 + 106573.i 0.00175315 + 0.652955i
\(405\) 0 0
\(406\) −108349. 108059.i −0.657317 0.655554i
\(407\) 139151. 80339.0i 0.840036 0.484995i
\(408\) 0 0
\(409\) 14207.0 24607.2i 0.0849289 0.147101i −0.820432 0.571744i \(-0.806267\pi\)
0.905361 + 0.424643i \(0.139600\pi\)
\(410\) −30213.8 112157.i −0.179737 0.667204i
\(411\) 0 0
\(412\) 54279.1 + 93433.8i 0.319770 + 0.550440i
\(413\) 67557.2 0.396070
\(414\) 0 0
\(415\) 96157.5i 0.558325i
\(416\) 169077. + 44089.8i 0.977007 + 0.254772i
\(417\) 0 0
\(418\) −42278.6 156943.i −0.241974 0.898233i
\(419\) −137256. 79245.0i −0.781816 0.451382i 0.0552577 0.998472i \(-0.482402\pi\)
−0.837073 + 0.547091i \(0.815735\pi\)
\(420\) 0 0
\(421\) 142796. + 247330.i 0.805659 + 1.39544i 0.915845 + 0.401532i \(0.131522\pi\)
−0.110186 + 0.993911i \(0.535145\pi\)
\(422\) −164495. 164054.i −0.923693 0.921216i
\(423\) 0 0
\(424\) −58691.8 58220.9i −0.326472 0.323853i
\(425\) 96857.7 + 167763.i 0.536237 + 0.928789i
\(426\) 0 0
\(427\) −299366. 172839.i −1.64190 0.947953i
\(428\) 244.910 426.839i 0.00133696 0.00233011i
\(429\) 0 0
\(430\) −27110.0 + 101722.i −0.146620 + 0.550146i
\(431\) 115124.i 0.619741i −0.950779 0.309870i \(-0.899714\pi\)
0.950779 0.309870i \(-0.100286\pi\)
\(432\) 0 0
\(433\) 95600.5 0.509899 0.254950 0.966954i \(-0.417941\pi\)
0.254950 + 0.966954i \(0.417941\pi\)
\(434\) −143336. 38200.5i −0.760983 0.202810i
\(435\) 0 0
\(436\) 148373. + 85133.0i 0.780517 + 0.447842i
\(437\) 67999.1 117778.i 0.356074 0.616738i
\(438\) 0 0
\(439\) 321749. 185762.i 1.66951 0.963890i 0.701603 0.712568i \(-0.252468\pi\)
0.967903 0.251322i \(-0.0808654\pi\)
\(440\) −53362.6 + 53794.1i −0.275633 + 0.277862i
\(441\) 0 0
\(442\) 192104. 192620.i 0.983313 0.985957i
\(443\) −119741. + 69132.2i −0.610146 + 0.352268i −0.773023 0.634379i \(-0.781256\pi\)
0.162877 + 0.986646i \(0.447923\pi\)
\(444\) 0 0
\(445\) −5369.03 + 9299.44i −0.0271129 + 0.0469609i
\(446\) 64353.2 17336.0i 0.323519 0.0871524i
\(447\) 0 0
\(448\) 121217. + 206103.i 0.603961 + 1.02690i
\(449\) −128427. −0.637035 −0.318518 0.947917i \(-0.603185\pi\)
−0.318518 + 0.947917i \(0.603185\pi\)
\(450\) 0 0
\(451\) 247384.i 1.21624i
\(452\) 138573. 80501.8i 0.678267 0.394030i
\(453\) 0 0
\(454\) −217289. + 58535.0i −1.05421 + 0.283991i
\(455\) −101695. 58713.7i −0.491221 0.283607i
\(456\) 0 0
\(457\) −146543. 253819.i −0.701668 1.21532i −0.967881 0.251410i \(-0.919106\pi\)
0.266213 0.963914i \(-0.414227\pi\)
\(458\) −6914.17 + 6932.76i −0.0329617 + 0.0330503i
\(459\) 0 0
\(460\) −63399.4 + 170.224i −0.299619 + 0.000804463i
\(461\) 148067. + 256460.i 0.696717 + 1.20675i 0.969598 + 0.244702i \(0.0786900\pi\)
−0.272881 + 0.962048i \(0.587977\pi\)
\(462\) 0 0
\(463\) 307165. + 177342.i 1.43288 + 0.827273i 0.997339 0.0728974i \(-0.0232246\pi\)
0.435539 + 0.900170i \(0.356558\pi\)
\(464\) 83102.4 145739.i 0.385991 0.676925i
\(465\) 0 0
\(466\) 297501. + 79287.2i 1.36999 + 0.365116i
\(467\) 116644.i 0.534848i 0.963579 + 0.267424i \(0.0861724\pi\)
−0.963579 + 0.267424i \(0.913828\pi\)
\(468\) 0 0
\(469\) 208007. 0.945656
\(470\) −35259.2 + 132299.i −0.159616 + 0.598911i
\(471\) 0 0
\(472\) 19457.7 + 71464.7i 0.0873389 + 0.320780i
\(473\) 112103. 194168.i 0.501066 0.867872i
\(474\) 0 0
\(475\) −170304. + 98324.9i −0.754809 + 0.435789i
\(476\) 372268. 999.522i 1.64302 0.00441142i
\(477\) 0 0
\(478\) 73804.1 + 73606.2i 0.323017 + 0.322151i
\(479\) −90134.6 + 52039.3i −0.392845 + 0.226809i −0.683392 0.730052i \(-0.739496\pi\)
0.290547 + 0.956861i \(0.406163\pi\)
\(480\) 0 0
\(481\) −136501. + 236427.i −0.589992 + 1.02190i
\(482\) 29132.5 + 108143.i 0.125396 + 0.465484i
\(483\) 0 0
\(484\) −63017.5 + 36609.1i −0.269011 + 0.156278i
\(485\) 207587. 0.882503
\(486\) 0 0
\(487\) 101284.i 0.427055i −0.976937 0.213527i \(-0.931505\pi\)
0.976937 0.213527i \(-0.0684953\pi\)
\(488\) 96613.2 366462.i 0.405692 1.53883i
\(489\) 0 0
\(490\) −12348.1 45837.6i −0.0514291 0.190911i
\(491\) −151749. 87612.6i −0.629454 0.363416i 0.151086 0.988521i \(-0.451723\pi\)
−0.780541 + 0.625105i \(0.785056\pi\)
\(492\) 0 0
\(493\) −130600. 226206.i −0.537341 0.930701i
\(494\) 195538. + 195014.i 0.801268 + 0.799119i
\(495\) 0 0
\(496\) −873.306 162628.i −0.00354979 0.661048i
\(497\) −164611. 285115.i −0.666418 1.15427i
\(498\) 0 0
\(499\) 83227.2 + 48051.2i 0.334244 + 0.192976i 0.657724 0.753259i \(-0.271519\pi\)
−0.323480 + 0.946235i \(0.604853\pi\)
\(500\) 181766. + 104293.i 0.727066 + 0.417173i
\(501\) 0 0
\(502\) −20377.7 + 76461.1i −0.0808627 + 0.303412i
\(503\) 164729.i 0.651080i 0.945528 + 0.325540i \(0.105546\pi\)
−0.945528 + 0.325540i \(0.894454\pi\)
\(504\) 0 0
\(505\) 78522.7 0.307902
\(506\) 130472. + 34772.3i 0.509586 + 0.135810i
\(507\) 0 0
\(508\) 128103. 223264.i 0.496401 0.865148i
\(509\) −42970.1 + 74426.4i −0.165856 + 0.287271i −0.936959 0.349440i \(-0.886372\pi\)
0.771103 + 0.636710i \(0.219705\pi\)
\(510\) 0 0
\(511\) −277869. + 160428.i −1.06414 + 0.614380i
\(512\) −183111. + 187590.i −0.698512 + 0.715598i
\(513\) 0 0
\(514\) 218270. 218857.i 0.826166 0.828388i
\(515\) 68948.9 39807.7i 0.259964 0.150090i
\(516\) 0 0
\(517\) 145801. 252535.i 0.545481 0.944800i
\(518\) −360724. + 97174.9i −1.34436 + 0.362155i
\(519\) 0 0
\(520\) 32819.6 124488.i 0.121374 0.460383i
\(521\) 173047. 0.637514 0.318757 0.947836i \(-0.396735\pi\)
0.318757 + 0.947836i \(0.396735\pi\)
\(522\) 0 0
\(523\) 252188.i 0.921978i −0.887406 0.460989i \(-0.847495\pi\)
0.887406 0.460989i \(-0.152505\pi\)
\(524\) 168029. + 289238.i 0.611958 + 1.05340i
\(525\) 0 0
\(526\) 81928.8 22070.7i 0.296118 0.0797709i
\(527\) −219280. 126601.i −0.789547 0.455845i
\(528\) 0 0
\(529\) −83431.1 144507.i −0.298137 0.516389i
\(530\) −43013.0 + 43128.6i −0.153126 + 0.153537i
\(531\) 0 0
\(532\) 1014.66 + 377907.i 0.00358508 + 1.33525i
\(533\) −210161. 364009.i −0.739770 1.28132i
\(534\) 0 0
\(535\) −314.008 181.293i −0.00109707 0.000633393i
\(536\) 59910.0 + 220038.i 0.208530 + 0.765894i
\(537\) 0 0
\(538\) −4275.71 1139.52i −0.0147722 0.00393694i
\(539\) 101104.i 0.348008i
\(540\) 0 0
\(541\) −472358. −1.61390 −0.806950 0.590620i \(-0.798883\pi\)
−0.806950 + 0.590620i \(0.798883\pi\)
\(542\) 34032.3 127696.i 0.115849 0.434688i
\(543\) 0 0
\(544\) 108277. + 393512.i 0.365881 + 1.32972i
\(545\) 63019.0 109152.i 0.212167 0.367485i
\(546\) 0 0
\(547\) −332881. + 192189.i −1.11254 + 0.642323i −0.939485 0.342590i \(-0.888696\pi\)
−0.173051 + 0.984913i \(0.555362\pi\)
\(548\) 200.879 + 74816.5i 0.000668918 + 0.249136i
\(549\) 0 0
\(550\) −138244. 137873.i −0.457005 0.455779i
\(551\) 229632. 132578.i 0.756362 0.436686i
\(552\) 0 0
\(553\) −93996.3 + 162806.i −0.307369 + 0.532379i
\(554\) −30009.5 111399.i −0.0977777 0.362962i
\(555\) 0 0
\(556\) 74786.4 + 128734.i 0.241921 + 0.416433i
\(557\) 19803.1 0.0638297 0.0319148 0.999491i \(-0.489839\pi\)
0.0319148 + 0.999491i \(0.489839\pi\)
\(558\) 0 0
\(559\) 380940.i 1.21908i
\(560\) 152095. 88904.6i 0.484997 0.283497i
\(561\) 0 0
\(562\) 33425.7 + 124080.i 0.105830 + 0.392851i
\(563\) −132566. 76536.8i −0.418229 0.241465i 0.276090 0.961132i \(-0.410961\pi\)
−0.694319 + 0.719667i \(0.744294\pi\)
\(564\) 0 0
\(565\) −59039.2 102259.i −0.184945 0.320335i
\(566\) −202052. 201510.i −0.630710 0.629019i
\(567\) 0 0
\(568\) 254195. 256251.i 0.787898 0.794271i
\(569\) −25955.5 44956.2i −0.0801687 0.138856i 0.823154 0.567819i \(-0.192213\pi\)
−0.903322 + 0.428963i \(0.858879\pi\)
\(570\) 0 0
\(571\) 92961.9 + 53671.6i 0.285123 + 0.164616i 0.635741 0.771903i \(-0.280695\pi\)
−0.350617 + 0.936519i \(0.614028\pi\)
\(572\) −136456. + 237822.i −0.417063 + 0.726874i
\(573\) 0 0
\(574\) 148121. 555780.i 0.449566 1.68686i
\(575\) 163364.i 0.494108i
\(576\) 0 0
\(577\) −114098. −0.342710 −0.171355 0.985209i \(-0.554814\pi\)
−0.171355 + 0.985209i \(0.554814\pi\)
\(578\) 291187. + 77604.5i 0.871598 + 0.232290i
\(579\) 0 0
\(580\) −107216. 61517.7i −0.318714 0.182871i
\(581\) −238077. + 412361.i −0.705285 + 1.22159i
\(582\) 0 0
\(583\) 112347. 64863.5i 0.330540 0.190837i
\(584\) −249738. 247734.i −0.732249 0.726374i
\(585\) 0 0
\(586\) −103499. + 103777.i −0.301397 + 0.302208i
\(587\) −45237.1 + 26117.7i −0.131286 + 0.0757980i −0.564205 0.825635i \(-0.690817\pi\)
0.432919 + 0.901433i \(0.357484\pi\)
\(588\) 0 0
\(589\) 128519. 222602.i 0.370456 0.641649i
\(590\) 52693.3 14195.0i 0.151374 0.0407784i
\(591\) 0 0
\(592\) −206691. 353600.i −0.589763 1.00895i
\(593\) −277354. −0.788724 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(594\) 0 0
\(595\) 274287.i 0.774767i
\(596\) −342711. + 199093.i −0.964797 + 0.560485i
\(597\) 0 0
\(598\) −221521. + 59675.3i −0.619460 + 0.166875i
\(599\) 16547.3 + 9553.58i 0.0461183 + 0.0266264i 0.522882 0.852405i \(-0.324857\pi\)
−0.476764 + 0.879032i \(0.658190\pi\)
\(600\) 0 0
\(601\) 209446. + 362771.i 0.579861 + 1.00435i 0.995495 + 0.0948161i \(0.0302263\pi\)
−0.415634 + 0.909532i \(0.636440\pi\)
\(602\) −368112. + 369102.i −1.01575 + 1.01848i
\(603\) 0 0
\(604\) 163352. 438.593i 0.447765 0.00120223i
\(605\) 26848.8 + 46503.4i 0.0733522 + 0.127050i
\(606\) 0 0
\(607\) −331153. 191191.i −0.898776 0.518909i −0.0219735 0.999759i \(-0.506995\pi\)
−0.876803 + 0.480850i \(0.840328\pi\)
\(608\) −399472. + 109917.i −1.08064 + 0.297344i
\(609\) 0 0
\(610\) −269816. 71909.0i −0.725118 0.193252i
\(611\) 495450.i 1.32714i
\(612\) 0 0
\(613\) −210852. −0.561121 −0.280560 0.959836i \(-0.590520\pi\)
−0.280560 + 0.959836i \(0.590520\pi\)
\(614\) 12019.2 45098.3i 0.0318815 0.119625i
\(615\) 0 0
\(616\) −362029. + 98569.7i −0.954073 + 0.259766i
\(617\) 313290. 542634.i 0.822955 1.42540i −0.0805170 0.996753i \(-0.525657\pi\)
0.903472 0.428647i \(-0.141010\pi\)
\(618\) 0 0
\(619\) −35684.5 + 20602.5i −0.0931319 + 0.0537697i −0.545843 0.837888i \(-0.683790\pi\)
0.452711 + 0.891657i \(0.350457\pi\)
\(620\) −119825. + 321.726i −0.311721 + 0.000836956i
\(621\) 0 0
\(622\) 12280.6 + 12247.7i 0.0317423 + 0.0316572i
\(623\) −46049.0 + 26586.4i −0.118644 + 0.0684989i
\(624\) 0 0
\(625\) −74680.7 + 129351.i −0.191183 + 0.331138i
\(626\) −89998.5 334084.i −0.229661 0.852525i
\(627\) 0 0
\(628\) 400838. 232861.i 1.01637 0.590443i
\(629\) −637678. −1.61176
\(630\) 0 0
\(631\) 150814.i 0.378777i −0.981902 0.189389i \(-0.939349\pi\)
0.981902 0.189389i \(-0.0606506\pi\)
\(632\) −199296. 52541.7i −0.498958 0.131544i
\(633\) 0 0
\(634\) −25628.9 95137.3i −0.0637605 0.236686i
\(635\) −164246. 94827.4i −0.407331 0.235172i
\(636\) 0 0
\(637\) −85890.8 148767.i −0.211674 0.366630i
\(638\) 186404. + 185904.i 0.457946 + 0.456718i
\(639\) 0 0
\(640\) 137853. + 135286.i 0.336555 + 0.330288i
\(641\) 214189. + 370987.i 0.521293 + 0.902906i 0.999693 + 0.0247640i \(0.00788343\pi\)
−0.478400 + 0.878142i \(0.658783\pi\)
\(642\) 0 0
\(643\) −74279.9 42885.5i −0.179659 0.103726i 0.407473 0.913217i \(-0.366410\pi\)
−0.587133 + 0.809491i \(0.699743\pi\)
\(644\) −272303. 156241.i −0.656569 0.376723i
\(645\) 0 0
\(646\) −166117. + 623304.i −0.398061 + 1.49360i
\(647\) 128368.i 0.306653i −0.988176 0.153327i \(-0.951001\pi\)
0.988176 0.153327i \(-0.0489986\pi\)
\(648\) 0 0
\(649\) −116225. −0.275937
\(650\) 320544. + 85428.6i 0.758685 + 0.202198i
\(651\) 0 0
\(652\) 141231. 246143.i 0.332226 0.579018i
\(653\) −232940. + 403463.i −0.546282 + 0.946189i 0.452243 + 0.891895i \(0.350624\pi\)
−0.998525 + 0.0542939i \(0.982709\pi\)
\(654\) 0 0
\(655\) 213442. 123231.i 0.497504 0.287234i
\(656\) 630587. 3386.22i 1.46534 0.00786878i
\(657\) 0 0
\(658\) −478766. + 480053.i −1.10579 + 1.10876i
\(659\) 303989. 175508.i 0.699983 0.404135i −0.107358 0.994220i \(-0.534239\pi\)
0.807341 + 0.590085i \(0.200906\pi\)
\(660\) 0 0
\(661\) 141131. 244446.i 0.323013 0.559475i −0.658095 0.752935i \(-0.728638\pi\)
0.981108 + 0.193460i \(0.0619709\pi\)
\(662\) 723274. 194842.i 1.65039 0.444597i
\(663\) 0 0
\(664\) −504782. 133079.i −1.14490 0.301838i
\(665\) 278442. 0.629638
\(666\) 0 0
\(667\) 220276.i 0.495125i
\(668\) −330035. 568110.i −0.739618 1.27315i
\(669\) 0 0
\(670\) 162242. 43706.0i 0.361420 0.0973625i
\(671\) 515029. + 297352.i 1.14390 + 0.660428i
\(672\) 0 0
\(673\) 398590. + 690378.i 0.880028 + 1.52425i 0.851309 + 0.524665i \(0.175809\pi\)
0.0287190 + 0.999588i \(0.490857\pi\)
\(674\) 285172. 285939.i 0.627751 0.629438i
\(675\) 0 0
\(676\) −23.8647 8888.32i −5.22231e−5 0.0194503i
\(677\) 140673. + 243653.i 0.306926 + 0.531612i 0.977688 0.210061i \(-0.0673662\pi\)
−0.670762 + 0.741673i \(0.734033\pi\)
\(678\) 0 0
\(679\) 890213. + 513965.i 1.93088 + 1.11479i
\(680\) 290151. 78999.7i 0.627490 0.170847i
\(681\) 0 0
\(682\) 246594. + 65720.0i 0.530168 + 0.141296i
\(683\) 687094.i 1.47291i −0.676489 0.736453i \(-0.736499\pi\)
0.676489 0.736453i \(-0.263501\pi\)
\(684\) 0 0
\(685\) 55124.8 0.117480
\(686\) −83841.2 + 314588.i −0.178160 + 0.668489i
\(687\) 0 0
\(688\) −496473. 283095.i −1.04886 0.598075i
\(689\) −110207. + 190884.i −0.232152 + 0.402098i
\(690\) 0 0
\(691\) 284957. 164520.i 0.596792 0.344558i −0.170986 0.985273i \(-0.554695\pi\)
0.767779 + 0.640715i \(0.221362\pi\)
\(692\) 298.812 + 111291.i 0.000624002 + 0.232407i
\(693\) 0 0
\(694\) 495364. + 494036.i 1.02850 + 1.02574i
\(695\) 94998.8 54847.6i 0.196675 0.113550i
\(696\) 0 0
\(697\) 490893. 850252.i 1.01047 1.75018i
\(698\) −45673.1 169544.i −0.0937453 0.347993i
\(699\) 0 0
\(700\) 228031. + 392524.i 0.465369 + 0.801069i
\(701\) 961471. 1.95659 0.978296 0.207214i \(-0.0664395\pi\)
0.978296 + 0.207214i \(0.0664395\pi\)
\(702\) 0 0
\(703\) 647338.i 1.30985i
\(704\) −208542. 354578.i −0.420773 0.715429i
\(705\) 0 0
\(706\) 161874. + 600895.i 0.324764 + 1.20556i
\(707\) 336736. + 194415.i 0.673676 + 0.388947i
\(708\) 0 0
\(709\) 299138. + 518122.i 0.595085 + 1.03072i 0.993535 + 0.113528i \(0.0362151\pi\)
−0.398450 + 0.917190i \(0.630452\pi\)
\(710\) −188301. 187796.i −0.373540 0.372538i
\(711\) 0 0
\(712\) −41387.1 41055.1i −0.0816404 0.0809854i
\(713\) 106766. + 184923.i 0.210016 + 0.363758i
\(714\) 0 0
\(715\) 174956. + 101011.i 0.342229 + 0.197586i
\(716\) 13970.7 24348.7i 0.0272516 0.0474951i
\(717\) 0 0
\(718\) 189541. 711193.i 0.367666 1.37955i
\(719\) 608601.i 1.17727i 0.808400 + 0.588633i \(0.200334\pi\)
−0.808400 + 0.588633i \(0.799666\pi\)
\(720\) 0 0
\(721\) 394240. 0.758385
\(722\) −129043. 34391.3i −0.247548 0.0659742i
\(723\) 0 0
\(724\) −607681. 348673.i −1.15931 0.665183i
\(725\) 159256. 275840.i 0.302985 0.524785i
\(726\) 0 0
\(727\) −396978. + 229195.i −0.751100 + 0.433648i −0.826091 0.563536i \(-0.809440\pi\)
0.0749911 + 0.997184i \(0.476107\pi\)
\(728\) 448963. 452594.i 0.847125 0.853976i
\(729\) 0 0
\(730\) −183023. + 183515.i −0.343448 + 0.344371i
\(731\) −770590. + 444900.i −1.44208 + 0.832584i
\(732\) 0 0
\(733\) −35347.8 + 61224.2i −0.0657892 + 0.113950i −0.897044 0.441942i \(-0.854290\pi\)
0.831255 + 0.555892i \(0.187623\pi\)
\(734\) 640760. 172614.i 1.18933 0.320393i
\(735\) 0 0
\(736\) 86849.4 333053.i 0.160329 0.614833i
\(737\) −357855. −0.658828
\(738\) 0 0
\(739\) 476430.i 0.872390i −0.899852 0.436195i \(-0.856326\pi\)
0.899852 0.436195i \(-0.143674\pi\)
\(740\) −260939. + 151589.i −0.476514 + 0.276824i
\(741\) 0 0
\(742\) −291239. + 78456.4i −0.528982 + 0.142502i
\(743\) −109137. 63010.2i −0.197694 0.114139i 0.397885 0.917435i \(-0.369744\pi\)
−0.595579 + 0.803296i \(0.703078\pi\)
\(744\) 0 0
\(745\) 146013. + 252902.i 0.263074 + 0.455658i
\(746\) −368106. + 369095.i −0.661447 + 0.663225i
\(747\) 0 0
\(748\) −640448. + 1719.57i −1.14467 + 0.00307339i
\(749\) −897.727 1554.91i −0.00160022 0.00277167i
\(750\) 0 0
\(751\) −176908. 102138.i −0.313667 0.181096i 0.334899 0.942254i \(-0.391298\pi\)
−0.648566 + 0.761158i \(0.724631\pi\)
\(752\) −645712. 368193.i −1.14184 0.651089i
\(753\) 0 0
\(754\) −432212. 115189.i −0.760247 0.202614i
\(755\) 120358.i 0.211145i
\(756\) 0 0
\(757\) 588244. 1.02652 0.513258 0.858235i \(-0.328438\pi\)
0.513258 + 0.858235i \(0.328438\pi\)
\(758\) 44958.8 168694.i 0.0782485 0.293603i
\(759\) 0 0
\(760\) 80196.3 + 294546.i 0.138844 + 0.509949i
\(761\) −25368.8 + 43940.0i −0.0438056 + 0.0758736i −0.887097 0.461583i \(-0.847282\pi\)
0.843291 + 0.537457i \(0.180615\pi\)
\(762\) 0 0
\(763\) 540501. 312058.i 0.928426 0.536027i
\(764\) 635603. 1706.56i 1.08893 0.00292372i
\(765\) 0 0
\(766\) 775685. + 773605.i 1.32199 + 1.31844i
\(767\) 171017. 98737.0i 0.290703 0.167838i
\(768\) 0 0
\(769\) −441340. + 764423.i −0.746312 + 1.29265i 0.203268 + 0.979123i \(0.434844\pi\)
−0.949579 + 0.313526i \(0.898490\pi\)
\(770\) 71909.4 + 266936.i 0.121284 + 0.450221i
\(771\) 0 0
\(772\) 291839. 169540.i 0.489675 0.284470i
\(773\) 100820. 0.168728 0.0843642 0.996435i \(-0.473114\pi\)
0.0843642 + 0.996435i \(0.473114\pi\)
\(774\) 0 0
\(775\) 308760.i 0.514065i
\(776\) −287294. + 1.08973e6i −0.477094 + 1.80966i
\(777\) 0 0
\(778\)