Properties

Label 108.5.f.a.19.20
Level 108
Weight 5
Character 108.19
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 19.20
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.20

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.959498 0.281717i \(-0.0909038\pi\)
−0.723723 + 0.690091i \(0.757570\pi\)
\(6\) 0 0
\(7\) 50.5548 + 29.1878i 1.03173 + 0.595670i 0.917480 0.397782i \(-0.130220\pi\)
0.114251 + 0.993452i \(0.463553\pi\)
\(8\) 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 0.0955138 0.995428i \(-0.469551\pi\)
−0.814309 + 0.580431i \(0.802884\pi\)
\(12\) 0 0
\(13\) 85.3178 + 147.775i 0.504839 + 0.874407i 0.999984 + 0.00559684i \(0.00178154\pi\)
−0.495145 + 0.868810i \(0.664885\pi\)
\(14\) 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 \(-0.810648\pi\)
0.828223 0.560399i \(-0.189352\pi\)
\(20\) 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 −0.749230 0.662310i \(-0.769576\pi\)
0.198963 + 0.980007i \(0.436243\pi\)
\(24\) 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 −0.992398 0.123066i \(-0.960727\pi\)
0.602778 + 0.797909i \(0.294061\pi\)
\(30\) 0 0
\(31\) −550.166 + 317.638i −0.572493 + 0.330529i −0.758144 0.652087i \(-0.773894\pi\)
0.185651 + 0.982616i \(0.440560\pi\)
\(32\) 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 0.955734 + 0.294232i \(0.0950637\pi\)
−0.223055 + 0.974806i \(0.571603\pi\)
\(42\) 0 0
\(43\) −1933.38 1116.24i −1.04564 0.603699i −0.124212 0.992256i \(-0.539640\pi\)
−0.921425 + 0.388557i \(0.872974\pi\)
\(44\) −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 −0.192308 0.981335i \(-0.561597\pi\)
−0.946015 + 0.324124i \(0.894931\pi\)
\(48\) 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 −0.349085 0.937091i \(-0.613508\pi\)
0.637002 + 0.770862i \(0.280174\pi\)
\(60\) 0 0
\(61\) −2960.81 + 5128.28i −0.795703 + 1.37820i 0.126688 + 0.991943i \(0.459565\pi\)
−0.922392 + 0.386256i \(0.873768\pi\)
\(62\) −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 −0.115219 0.993340i \(-0.536757\pi\)
0.802648 + 0.596452i \(0.203424\pi\)
\(68\) 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 \(0.188963\pi\)
−0.828907 + 0.559386i \(0.811037\pi\)
\(72\) 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 0.259635 0.965707i \(-0.416398\pi\)
−0.706509 + 0.707704i \(0.749731\pi\)
\(80\) 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 −0.109730 0.993961i \(-0.534999\pi\)
−0.915661 + 0.401951i \(0.868332\pi\)
\(84\) 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 0.162450 0.986717i \(-0.448060\pi\)
0.773297 0.634044i \(-0.218606\pi\)
\(98\) 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 −0.655332 0.755341i \(-0.727471\pi\)
0.981810 + 0.189863i \(0.0608045\pi\)
\(102\) 0 0
\(103\) 5848.70 3376.75i 0.551296 0.318291i −0.198348 0.980132i \(-0.563558\pi\)
0.749645 + 0.661841i \(0.230224\pi\)
\(104\) 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 \(0.000427558\pi\)
−0.999999 + 0.00134321i \(0.999572\pi\)
\(108\) 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 0.992740 0.120277i \(-0.0383784\pi\)
−0.600533 + 0.799600i \(0.705045\pi\)
\(114\) 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 \(0.166197\pi\)
−0.866762 + 0.498722i \(0.833803\pi\)
\(128\) −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 0.130983 0.991385i \(-0.458187\pi\)
0.924056 + 0.382257i \(0.124853\pi\)
\(132\) 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 −0.796996 0.603985i \(-0.793579\pi\)
0.921564 + 0.388226i \(0.126912\pi\)
\(138\) 0 0
\(139\) 8058.42 4652.53i 0.417081 0.240802i −0.276747 0.960943i \(-0.589256\pi\)
0.693828 + 0.720141i \(0.255923\pi\)
\(140\) 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 −0.997672 0.0681928i \(-0.978277\pi\)
0.439779 0.898106i \(-0.355057\pi\)
\(150\) 0 0
\(151\) 8841.72 + 5104.77i 0.387778 + 0.223884i 0.681197 0.732100i \(-0.261460\pi\)
−0.293419 + 0.955984i \(0.594793\pi\)
\(152\) −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 0.994531 + 0.104439i \(0.0333046\pi\)
−0.406819 + 0.913509i \(0.633362\pi\)
\(158\) −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 \(0.108324\pi\)
−0.942651 + 0.333780i \(0.891676\pi\)
\(164\) 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 −0.975949 0.217999i \(-0.930047\pi\)
−0.299182 + 0.954196i \(0.596714\pi\)
\(168\) 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 −0.802056 0.597248i \(-0.796261\pi\)
0.918260 + 0.395977i \(0.129594\pi\)
\(174\) 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 \(0.00871609\pi\)
−0.999625 + 0.0273790i \(0.991284\pi\)
\(180\) 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 0.890913 0.454174i \(-0.150066\pi\)
0.0521297 + 0.998640i \(0.483399\pi\)
\(192\) 0 0
\(193\) 10547.2 + 18268.3i 0.283154 + 0.490437i 0.972160 0.234319i \(-0.0752859\pi\)
−0.689006 + 0.724756i \(0.741953\pi\)
\(194\) 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 \(-0.901736\pi\)
0.952728 0.303825i \(-0.0982638\pi\)
\(200\) −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 −0.943878 0.330295i \(-0.892852\pi\)
−0.185895 + 0.982570i \(0.559518\pi\)
\(212\) −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 0.638016 0.770023i \(-0.279755\pi\)
−0.347852 + 0.937550i \(0.613089\pi\)
\(224\) 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 −0.0538304 0.998550i \(-0.517143\pi\)
−0.891685 + 0.452657i \(0.850476\pi\)
\(228\) 0 0
\(229\) −1223.91 2119.87i −0.0233388 0.0404239i 0.854120 0.520076i \(-0.174096\pi\)
−0.877459 + 0.479652i \(0.840763\pi\)
\(230\) −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 −0.289277 0.957245i \(-0.593415\pi\)
0.684360 + 0.729144i \(0.260082\pi\)
\(240\) 0 0
\(241\) 13999.8 24248.4i 0.241039 0.417492i −0.719971 0.694004i \(-0.755845\pi\)
0.961011 + 0.276512i \(0.0891784\pi\)
\(242\) −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 \(-0.949817\pi\)
0.987598 0.157001i \(-0.0501827\pi\)
\(252\) 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 0.994879 + 0.101076i \(0.0322285\pi\)
−0.409905 + 0.912128i \(0.634438\pi\)
\(258\) 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 0.626881 0.779115i \(-0.284331\pi\)
−0.361293 + 0.932452i \(0.617665\pi\)
\(264\) 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 \(0.0722155\pi\)
−0.974375 + 0.224931i \(0.927784\pi\)
\(272\) 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 −0.944567 0.328319i \(-0.893518\pi\)
0.756616 + 0.653859i \(0.226851\pi\)
\(278\) 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 −0.746203 0.665719i \(-0.768125\pi\)
0.949631 + 0.313371i \(0.101458\pi\)
\(282\) 0 0
\(283\) −61782.5 + 35670.2i −0.771424 + 0.445382i −0.833382 0.552697i \(-0.813599\pi\)
0.0619586 + 0.998079i \(0.480265\pi\)
\(284\) 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 0.739372 0.673297i \(-0.235123\pi\)
−0.952779 + 0.303666i \(0.901789\pi\)
\(294\) 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 \(0.0197161\pi\)
−0.998082 + 0.0619005i \(0.980284\pi\)
\(308\) −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 −0.480462 0.877015i \(-0.659531\pi\)
0.519286 + 0.854600i \(0.326198\pi\)
\(312\) 0 0
\(313\) −43249.3 + 74909.9i −0.441459 + 0.764629i −0.997798 0.0663262i \(-0.978872\pi\)
0.556339 + 0.830955i \(0.312206\pi\)
\(314\) 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 −0.920777 0.390089i \(-0.872444\pi\)
0.798215 + 0.602372i \(0.205778\pi\)
\(318\) 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 0.999749 0.0223896i \(-0.00712742\pi\)
0.480485 + 0.877003i \(0.340461\pi\)
\(332\) −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 0.998016 0.0629592i \(-0.0200538\pi\)
−0.553532 + 0.832828i \(0.686720\pi\)
\(338\) −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 0.285287 0.958442i \(-0.407911\pi\)
0.972679 + 0.232155i \(0.0745777\pi\)
\(348\) 0 0
\(349\) −21948.5 + 38015.9i −0.180199 + 0.312114i −0.941948 0.335758i \(-0.891008\pi\)
0.761749 + 0.647872i \(0.224341\pi\)
\(350\) 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 −0.364412 0.931238i \(-0.618730\pi\)
0.988682 0.150029i \(-0.0479367\pi\)
\(354\) 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 \(0.253052\pi\)
−0.700295 + 0.713853i \(0.746948\pi\)
\(360\) 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 0.927281 0.374366i \(-0.122140\pi\)
0.139430 + 0.990232i \(0.455473\pi\)
\(368\) −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 0.531003 0.847370i \(-0.321815\pi\)
−0.999345 + 0.0361768i \(0.988482\pi\)
\(374\) −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 \(0.0485475\pi\)
−0.988392 + 0.151926i \(0.951453\pi\)
\(380\) 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 0.629223 0.777225i \(-0.283373\pi\)
0.987708 0.156310i \(-0.0499599\pi\)
\(384\) 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 0.102594 + 0.994723i \(0.467286\pi\)
−0.912753 + 0.408513i \(0.866048\pi\)
\(390\) 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 0.877198 0.480128i \(-0.159410\pi\)
−0.854402 + 0.519612i \(0.826077\pi\)
\(402\) 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 0.905361 0.424643i \(-0.139600\pi\)
−0.820432 + 0.571744i \(0.806267\pi\)
\(410\) −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 −0.837073 0.547091i \(-0.815735\pi\)
0.0552577 + 0.998472i \(0.482402\pi\)
\(420\) 0 0
\(421\) 142796. 247330.i 0.805659 1.39544i −0.110186 0.993911i \(-0.535145\pi\)
0.915845 0.401532i \(-0.131522\pi\)
\(422\) −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 \(0.100286\pi\)
−0.950779 + 0.309870i \(0.899714\pi\)
\(432\) 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 0.967903 + 0.251322i \(0.0808654\pi\)
0.701603 + 0.712568i \(0.252468\pi\)
\(440\) −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 0.162877 0.986646i \(-0.447923\pi\)
−0.773023 + 0.634379i \(0.781256\pi\)
\(444\) 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 0.266213 + 0.963914i \(0.414227\pi\)
−0.967881 + 0.251410i \(0.919106\pi\)
\(458\) −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 −0.272881 0.962048i \(-0.587977\pi\)
0.969598 0.244702i \(-0.0786900\pi\)
\(462\) 0 0
\(463\) 307165. 177342.i 1.43288 0.827273i 0.435539 0.900170i \(-0.356558\pi\)
0.997339 + 0.0728974i \(0.0232246\pi\)
\(464\) 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 \(-0.913828\pi\)
0.963579 0.267424i \(-0.0861724\pi\)
\(468\) 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 0.290547 0.956861i \(-0.406163\pi\)
−0.683392 + 0.730052i \(0.739496\pi\)
\(480\) 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 \(0.0684953\pi\)
−0.976937 + 0.213527i \(0.931505\pi\)
\(488\) 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 −0.780541 0.625105i \(-0.785056\pi\)
0.151086 + 0.988521i \(0.451723\pi\)
\(492\) 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 −0.323480 0.946235i \(-0.604853\pi\)
0.657724 + 0.753259i \(0.271519\pi\)
\(500\) 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 \(-0.894454\pi\)
0.945528 0.325540i \(-0.105546\pi\)
\(504\) 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 0.771103 0.636710i \(-0.219705\pi\)
−0.936959 + 0.349440i \(0.886372\pi\)
\(510\) 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 \(0.152505\pi\)
−0.887406 + 0.460989i \(0.847495\pi\)
\(524\) 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 −0.173051 0.984913i \(-0.555362\pi\)
−0.939485 + 0.342590i \(0.888696\pi\)
\(548\) 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 −0.694319 0.719667i \(-0.744294\pi\)
0.276090 + 0.961132i \(0.410961\pi\)
\(564\) 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 −0.903322 0.428963i \(-0.858879\pi\)
0.823154 + 0.567819i \(0.192213\pi\)
\(570\) 0 0
\(571\) 92961.9 53671.6i 0.285123 0.164616i −0.350617 0.936519i \(-0.614028\pi\)
0.635741 + 0.771903i \(0.280695\pi\)
\(572\) −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 0.432919 0.901433i \(-0.357484\pi\)
−0.564205 + 0.825635i \(0.690817\pi\)
\(588\) 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 −0.476764 0.879032i \(-0.658190\pi\)
0.522882 + 0.852405i \(0.324857\pi\)
\(600\) 0 0
\(601\) 209446. 362771.i 0.579861 1.00435i −0.415634 0.909532i \(-0.636440\pi\)
0.995495 0.0948161i \(-0.0302263\pi\)
\(602\) −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 −0.876803 0.480850i \(-0.840328\pi\)
−0.0219735 + 0.999759i \(0.506995\pi\)
\(608\) −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 0.903472 + 0.428647i \(0.141010\pi\)
−0.0805170 + 0.996753i \(0.525657\pi\)
\(618\) 0 0
\(619\) −35684.5 20602.5i −0.0931319 0.0537697i 0.452711 0.891657i \(-0.350457\pi\)
−0.545843 + 0.837888i \(0.683790\pi\)
\(620\) −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 \(0.0606506\pi\)
−0.981902 + 0.189389i \(0.939349\pi\)
\(632\) −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 −0.478400 0.878142i \(-0.658783\pi\)
0.999693 0.0247640i \(-0.00788343\pi\)
\(642\) 0 0
\(643\) −74279.9 + 42885.5i −0.179659 + 0.103726i −0.587133 0.809491i \(-0.699743\pi\)
0.407473 + 0.913217i \(0.366410\pi\)
\(644\) −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 \(0.0489986\pi\)
−0.988176 + 0.153327i \(0.951001\pi\)
\(648\) 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 −0.998525 0.0542939i \(-0.982709\pi\)
0.452243 0.891895i \(-0.350624\pi\)
\(654\) 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 0.807341 0.590085i \(-0.200906\pi\)
−0.107358 + 0.994220i \(0.534239\pi\)
\(660\) 0 0
\(661\) 141131. + 244446.i 0.323013 + 0.559475i 0.981108 0.193460i \(-0.0619709\pi\)
−0.658095 + 0.752935i \(0.728638\pi\)
\(662\) 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 0.0287190 0.999588i \(-0.490857\pi\)
0.851309 0.524665i \(-0.175809\pi\)
\(674\) 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 −0.670762 0.741673i \(-0.734033\pi\)
0.977688 + 0.210061i \(0.0673662\pi\)
\(678\) 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 \(0.263501\pi\)
−0.676489 + 0.736453i \(0.736499\pi\)
\(684\) 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 0.767779 0.640715i \(-0.221362\pi\)
−0.170986 + 0.985273i \(0.554695\pi\)
\(692\) 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 −0.398450 0.917190i \(-0.630452\pi\)
0.993535 0.113528i \(-0.0362151\pi\)
\(710\) −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 \(-0.799666\pi\)
0.808400 0.588633i \(-0.200334\pi\)
\(720\) 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 0.0749911 0.997184i \(-0.476107\pi\)
−0.826091 + 0.563536i \(0.809440\pi\)
\(728\) 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 0.831255 0.555892i \(-0.187623\pi\)
−0.897044 + 0.441942i \(0.854290\pi\)
\(734\) 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 \(0.143674\pi\)
−0.899852 + 0.436195i \(0.856326\pi\)
\(740\) −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 −0.595579 0.803296i \(-0.703078\pi\)
0.397885 + 0.917435i \(0.369744\pi\)
\(744\) 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 −0.648566 0.761158i \(-0.724631\pi\)
0.334899 + 0.942254i \(0.391298\pi\)
\(752\) −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 0.843291 0.537457i \(-0.180615\pi\)
−0.887097 + 0.461583i \(0.847282\pi\)
\(762\) 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 −0.949579 0.313526i \(-0.898490\pi\)
0.203268 0.979123i \(-0.434844\pi\)
\(770\) 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