Properties

Label 108.5.f.a.19.10
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 19.10
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.04046 - 3.86231i) q^{2} +(-13.8349 + 8.03717i) q^{4} +(5.89438 + 10.2094i) q^{5} +(-50.5548 - 29.1878i) q^{7} +(45.4367 + 45.0722i) q^{8} +O(q^{10})\) \(q+(-1.04046 - 3.86231i) q^{2} +(-13.8349 + 8.03717i) q^{4} +(5.89438 + 10.2094i) q^{5} +(-50.5548 - 29.1878i) q^{7} +(45.4367 + 45.0722i) q^{8} +(33.2988 - 33.3884i) q^{10} +(86.9742 + 50.2146i) q^{11} +(85.3178 + 147.775i) q^{13} +(-60.1321 + 225.627i) q^{14} +(126.808 - 222.387i) q^{16} +398.571 q^{17} +404.608i q^{19} +(-163.602 - 93.8711i) q^{20} +(103.451 - 388.168i) q^{22} +(291.091 - 168.062i) q^{23} +(243.013 - 420.910i) q^{25} +(481.982 - 483.278i) q^{26} +(934.007 - 2.50777i) q^{28} +(-327.671 + 567.543i) q^{29} +(550.166 - 317.638i) q^{31} +(-990.865 - 258.386i) q^{32} +(-414.698 - 1539.40i) q^{34} -688.176i q^{35} -1599.91 q^{37} +(1562.72 - 420.979i) q^{38} +(-192.337 + 729.553i) q^{40} +(1231.63 + 2133.25i) q^{41} +(1933.38 + 1116.24i) q^{43} +(-1606.86 + 4.31435i) q^{44} +(-951.976 - 949.423i) q^{46} +(2514.55 + 1451.78i) q^{47} +(503.358 + 871.842i) q^{49} +(-1878.53 - 500.649i) q^{50} +(-2368.05 - 1358.73i) q^{52} -1291.73 q^{53} +1183.94i q^{55} +(-981.485 - 3604.82i) q^{56} +(2532.96 + 675.060i) q^{58} +(-1002.24 + 578.642i) q^{59} +(-2960.81 + 5128.28i) q^{61} +(-1799.24 - 1794.42i) q^{62} +(32.9923 + 4095.87i) q^{64} +(-1005.79 + 1742.08i) q^{65} +(-3085.87 + 1781.63i) q^{67} +(-5514.18 + 3203.38i) q^{68} +(-2657.95 + 716.021i) q^{70} -5639.73i q^{71} -5496.39 q^{73} +(1664.65 + 6179.36i) q^{74} +(-3251.91 - 5597.70i) q^{76} +(-2931.31 - 5077.18i) q^{77} +(2788.94 + 1610.20i) q^{79} +(3017.88 - 16.2058i) q^{80} +(6957.81 - 6976.52i) q^{82} +(7063.92 + 4078.36i) q^{83} +(2349.33 + 4069.15i) q^{85} +(2299.65 - 8628.73i) q^{86} +(1688.54 + 6201.71i) q^{88} -910.873 q^{89} -9960.97i q^{91} +(-2676.47 + 4664.66i) q^{92} +(2990.92 - 11222.5i) q^{94} +(-4130.79 + 2384.91i) q^{95} +(8804.44 - 15249.7i) q^{97} +(2843.60 - 2851.24i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04046 3.86231i −0.260116 0.965577i
\(3\) 0 0
\(4\) −13.8349 + 8.03717i −0.864680 + 0.502323i
\(5\) 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 −0.114251 0.993452i \(-0.536447\pi\)
−0.917480 + 0.397782i \(0.869780\pi\)
\(8\) 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 \(-0.197116\pi\)
−0.0955138 + 0.995428i \(0.530449\pi\)
\(12\) 0 0
\(13\) 85.3178 + 147.775i 0.504839 + 0.874407i 0.999984 + 0.00559684i \(0.00178154\pi\)
−0.495145 + 0.868810i \(0.664885\pi\)
\(14\) −60.1321 + 225.627i −0.306796 + 1.15116i
\(15\) 0 0
\(16\) 126.808 222.387i 0.495342 0.868698i
\(17\) 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 \(0.810648\pi\)
\(20\) −163.602 93.8711i −0.409006 0.234678i
\(21\) 0 0
\(22\) 103.451 388.168i 0.213742 0.802000i
\(23\) 291.091 168.062i 0.550267 0.317697i −0.198963 0.980007i \(-0.563757\pi\)
0.749230 + 0.662310i \(0.230424\pi\)
\(24\) 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 −0.185651 0.982616i \(-0.559440\pi\)
0.758144 + 0.652087i \(0.226106\pi\)
\(32\) −990.865 258.386i −0.967641 0.252330i
\(33\) 0 0
\(34\) −414.698 1539.40i −0.358735 1.33166i
\(35\) 688.176i 0.561776i
\(36\) 0 0
\(37\) −1599.91 −1.16867 −0.584336 0.811512i \(-0.698645\pi\)
−0.584336 + 0.811512i \(0.698645\pi\)
\(38\) 1562.72 420.979i 1.08222 0.291537i
\(39\) 0 0
\(40\) −192.337 + 729.553i −0.120211 + 0.455970i
\(41\) 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 0.921425 0.388557i \(-0.127026\pi\)
0.124212 + 0.992256i \(0.460360\pi\)
\(44\) −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 \(-0.105069\pi\)
0.192308 + 0.981335i \(0.438403\pi\)
\(48\) 0 0
\(49\) 503.358 + 871.842i 0.209645 + 0.363116i
\(50\) −1878.53 500.649i −0.751412 0.200260i
\(51\) 0 0
\(52\) −2368.05 1358.73i −0.875759 0.502490i
\(53\) −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
\(56\) −981.485 3604.82i −0.312973 1.14949i
\(57\) 0 0
\(58\) 2532.96 + 675.060i 0.752959 + 0.200672i
\(59\) −1002.24 + 578.642i −0.287917 + 0.166229i −0.637002 0.770862i \(-0.719826\pi\)
0.349085 + 0.937091i \(0.386492\pi\)
\(60\) 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 −0.802648 0.596452i \(-0.796576\pi\)
0.115219 + 0.993340i \(0.463243\pi\)
\(68\) −5514.18 + 3203.38i −1.19251 + 0.692773i
\(69\) 0 0
\(70\) −2657.95 + 716.021i −0.542439 + 0.146127i
\(71\) 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 \(0.672470\pi\)
\(74\) 1664.65 + 6179.36i 0.303990 + 1.12844i
\(75\) 0 0
\(76\) −3251.91 5597.70i −0.563003 0.969132i
\(77\) −2931.31 5077.18i −0.494402 0.856329i
\(78\) 0 0
\(79\) 2788.94 + 1610.20i 0.446874 + 0.258003i 0.706509 0.707704i \(-0.250269\pi\)
−0.259635 + 0.965707i \(0.583602\pi\)
\(80\) 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 \(-0.131668\pi\)
0.109730 + 0.993961i \(0.465001\pi\)
\(84\) 0 0
\(85\) 2349.33 + 4069.15i 0.325166 + 0.563205i
\(86\) 2299.65 8628.73i 0.310932 1.16668i
\(87\) 0 0
\(88\) 1688.54 + 6201.71i 0.218045 + 0.800840i
\(89\) −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
\(92\) −2676.47 + 4664.66i −0.316218 + 0.551118i
\(93\) 0 0
\(94\) 2990.92 11222.5i 0.338493 1.27009i
\(95\) −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 −0.749645 0.661841i \(-0.769776\pi\)
0.198348 + 0.980132i \(0.436442\pi\)
\(104\) −2783.97 + 10559.9i −0.257394 + 0.976319i
\(105\) 0 0
\(106\) 1343.99 + 4989.04i 0.119615 + 0.444023i
\(107\) 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 \(0.351447\pi\)
\(110\) 4572.72 1231.84i 0.377911 0.101805i
\(111\) 0 0
\(112\) −12901.7 + 7541.47i −1.02852 + 0.601202i
\(113\) 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
\(122\) 22887.6 + 6099.80i 1.53773 + 0.409822i
\(123\) 0 0
\(124\) −5058.56 + 8816.26i −0.328991 + 0.573378i
\(125\) 13097.6 0.838247
\(126\) 0 0
\(127\) 16087.8i 0.997444i −0.866762 0.498722i \(-0.833803\pi\)
0.866762 0.498722i \(-0.166197\pi\)
\(128\) 15785.2 4389.02i 0.963451 0.267885i
\(129\) 0 0
\(130\) 7774.94 + 2072.11i 0.460056 + 0.122610i
\(131\) −18105.5 + 10453.2i −1.05504 + 0.609127i −0.924056 0.382257i \(-0.875147\pi\)
−0.130983 + 0.991385i \(0.541813\pi\)
\(132\) 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 −0.693828 0.720141i \(-0.744077\pi\)
0.276747 + 0.960943i \(0.410744\pi\)
\(140\) 5530.99 + 9520.83i 0.282193 + 0.485757i
\(141\) 0 0
\(142\) −21782.4 + 5867.92i −1.08026 + 0.291010i
\(143\) 17136.8i 0.838026i
\(144\) 0 0
\(145\) −7725.67 −0.367451
\(146\) 5718.78 + 21228.8i 0.268286 + 0.995907i
\(147\) 0 0
\(148\) 22134.6 12858.8i 1.01053 0.587051i
\(149\) −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 0.293419 0.955984i \(-0.405207\pi\)
−0.681197 + 0.732100i \(0.738540\pi\)
\(152\) −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 \(0.633362\pi\)
\(158\) 3317.29 12447.1i 0.132883 0.498603i
\(159\) 0 0
\(160\) −3202.58 11639.1i −0.125101 0.454653i
\(161\) −19621.4 −0.756970
\(162\) 0 0
\(163\) 17736.4i 0.667560i −0.942651 0.333780i \(-0.891676\pi\)
0.942651 0.333780i \(-0.108324\pi\)
\(164\) −34184.8 19614.4i −1.27100 0.729269i
\(165\) 0 0
\(166\) 8402.14 31526.4i 0.304911 1.14409i
\(167\) 35562.1 20531.8i 1.27513 0.736197i 0.299182 0.954196i \(-0.403286\pi\)
0.975949 + 0.217999i \(0.0699530\pi\)
\(168\) 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
\(176\) 22196.1 12974.3i 0.716556 0.418851i
\(177\) 0 0
\(178\) 947.729 + 3518.08i 0.0299119 + 0.111036i
\(179\) 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 \(0.732975\pi\)
\(182\) −38472.3 + 10364.0i −1.16146 + 0.312885i
\(183\) 0 0
\(184\) 20801.1 + 5483.96i 0.614401 + 0.161979i
\(185\) −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 \(-0.516601\pi\)
−0.890913 + 0.454174i \(0.849934\pi\)
\(192\) 0 0
\(193\) 10547.2 + 18268.3i 0.283154 + 0.490437i 0.972160 0.234319i \(-0.0752859\pi\)
−0.689006 + 0.724756i \(0.741953\pi\)
\(194\) −68059.9 18138.7i −1.80837 0.481951i
\(195\) 0 0
\(196\) −13971.0 8016.25i −0.363678 0.208669i
\(197\) −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 \(0.901736\pi\)
\(200\) 30013.1 8171.67i 0.750326 0.204292i
\(201\) 0 0
\(202\) −25744.7 6861.23i −0.630935 0.168151i
\(203\) 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 \(-0.440482\pi\)
0.943878 + 0.330295i \(0.107148\pi\)
\(212\) 17870.9 10381.8i 0.397625 0.230995i
\(213\) 0 0
\(214\) −118.793 + 32.0014i −0.00259395 + 0.000698781i
\(215\) 26318.1i 0.569349i
\(216\) 0 0
\(217\) −37084.7 −0.787545
\(218\) −11124.0 41293.4i −0.234071 0.868896i
\(219\) 0 0
\(220\) −9515.49 16379.6i −0.196601 0.338421i
\(221\) 34005.2 + 58898.7i 0.696243 + 1.20593i
\(222\) 0 0
\(223\) −14429.6 8330.91i −0.290164 0.167526i 0.347852 0.937550i \(-0.386911\pi\)
−0.638016 + 0.770023i \(0.720245\pi\)
\(224\) 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 \(-0.149524\pi\)
0.0538304 + 0.998550i \(0.482857\pi\)
\(228\) 0 0
\(229\) −1223.91 2119.87i −0.0233388 0.0404239i 0.854120 0.520076i \(-0.174096\pi\)
−0.877459 + 0.479652i \(0.840763\pi\)
\(230\) 4081.70 15315.3i 0.0771588 0.289515i
\(231\) 0 0
\(232\) −40468.7 + 11018.4i −0.751871 + 0.204712i
\(233\) 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
\(236\) 9215.19 16060.6i 0.165455 0.288362i
\(237\) 0 0
\(238\) −23966.9 + 89928.4i −0.423114 + 1.58761i
\(239\) −22567.5 + 13029.4i −0.395083 + 0.228101i −0.684360 0.729144i \(-0.739918\pi\)
0.289277 + 0.957245i \(0.406585\pi\)
\(240\) 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
\(248\) 39314.4 + 10364.7i 0.639217 + 0.168521i
\(249\) 0 0
\(250\) −13627.6 50587.0i −0.218041 0.809392i
\(251\) 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
\(254\) −62136.0 + 16738.7i −0.963110 + 0.259451i
\(255\) 0 0
\(256\) −33375.6 56400.7i −0.509272 0.860606i
\(257\) 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 0.361293 0.932452i \(-0.382335\pi\)
−0.626881 + 0.779115i \(0.715669\pi\)
\(264\) 0 0
\(265\) −7613.92 13187.7i −0.108422 0.187792i
\(266\) −91290.6 24329.9i −1.29022 0.343857i
\(267\) 0 0
\(268\) 28373.4 49450.3i 0.395041 0.688493i
\(269\) −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 \(-0.0722155\pi\)
\(272\) 50541.8 88636.8i 0.683145 1.19805i
\(273\) 0 0
\(274\) −18073.3 4816.74i −0.240734 0.0641582i
\(275\) 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 −0.0619586 0.998079i \(-0.519735\pi\)
0.833382 + 0.552697i \(0.186401\pi\)
\(284\) 45327.5 + 78024.9i 0.561985 + 0.967379i
\(285\) 0 0
\(286\) 66187.6 17830.2i 0.809179 0.217984i
\(287\) 143795.i 1.74574i
\(288\) 0 0
\(289\) 75337.7 0.902021
\(290\) 8038.26 + 29838.9i 0.0955798 + 0.354803i
\(291\) 0 0
\(292\) 76041.9 44175.4i 0.891840 0.518102i
\(293\) −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
\(302\) −10516.7 + 39460.8i −0.115310 + 0.432665i
\(303\) 0 0
\(304\) 89979.4 + 51307.4i 0.973635 + 0.555179i
\(305\) −69808.6 −0.750428
\(306\) 0 0
\(307\) 11668.1i 0.123801i −0.998082 0.0619005i \(-0.980284\pi\)
0.998082 0.0619005i \(-0.0197161\pi\)
\(308\) 81360.5 + 46682.7i 0.857654 + 0.492101i
\(309\) 0 0
\(310\) 7714.46 28946.1i 0.0802753 0.301208i
\(311\) −3755.11 + 2168.01i −0.0388242 + 0.0224151i −0.519286 0.854600i \(-0.673802\pi\)
0.480462 + 0.877015i \(0.340469\pi\)
\(312\) 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
\(320\) −41621.7 + 24479.4i −0.406462 + 0.239057i
\(321\) 0 0
\(322\) 20415.3 + 75784.0i 0.196900 + 0.730913i
\(323\) 161265.i 1.54573i
\(324\) 0 0
\(325\) 82933.2 0.785167
\(326\) −68503.4 + 18454.0i −0.644580 + 0.173643i
\(327\) 0 0
\(328\) −40189.0 + 152440.i −0.373559 + 1.41694i
\(329\) −84748.5 146789.i −0.782961 1.35613i
\(330\) 0 0
\(331\) −162176. 93632.3i −1.48023 0.854614i −0.480485 0.877003i \(-0.659539\pi\)
−0.999749 + 0.0223896i \(0.992873\pi\)
\(332\) −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 \(0.686720\pi\)
\(338\) 2147.14 + 572.236i 0.0187943 + 0.00500890i
\(339\) 0 0
\(340\) −65207.1 37414.3i −0.564076 0.323653i
\(341\) 63800.3 0.548674
\(342\) 0 0
\(343\) 81392.2i 0.691823i
\(344\) 37535.2 + 137860.i 0.317192 + 1.16499i
\(345\) 0 0
\(346\) −26884.5 7165.02i −0.224569 0.0598501i
\(347\) −151470. + 87451.5i −1.25797 + 0.726287i −0.972679 0.232155i \(-0.925422\pi\)
−0.285287 + 0.958442i \(0.592089\pi\)
\(348\) 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
\(356\) 12601.8 7320.85i 0.0994336 0.0577646i
\(357\) 0 0
\(358\) −6776.42 + 1825.49i −0.0528731 + 0.0142434i
\(359\) 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
\(362\) 45559.7 + 169122.i 0.347667 + 1.29058i
\(363\) 0 0
\(364\) 80058.0 + 137809.i 0.604230 + 1.04010i
\(365\) −32397.8 56114.6i −0.243181 0.421202i
\(366\) 0 0
\(367\) −143674. 82950.4i −1.06671 0.615866i −0.139430 0.990232i \(-0.544527\pi\)
−0.927281 + 0.374366i \(0.877860\pi\)
\(368\) −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 \(0.988482\pi\)
\(374\) 41232.5 154712.i 0.294779 1.10607i
\(375\) 0 0
\(376\) 48818.3 + 179301.i 0.345308 + 1.26825i
\(377\) −111825. −0.786783
\(378\) 0 0
\(379\) 43645.6i 0.303852i −0.988392 0.151926i \(-0.951453\pi\)
0.988392 0.151926i \(-0.0485475\pi\)
\(380\) 37981.0 66194.9i 0.263026 0.458413i
\(381\) 0 0
\(382\) −40920.6 + 153542.i −0.280424 + 1.05220i
\(383\) −237186. + 136939.i −1.61693 + 0.933535i −0.629223 + 0.777225i \(0.716627\pi\)
−0.987708 + 0.156310i \(0.950040\pi\)
\(384\) 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
\(392\) −16424.9 + 62301.1i −0.106888 + 0.405437i
\(393\) 0 0
\(394\) 29399.4 + 109134.i 0.189385 + 0.703018i
\(395\) 37964.4i 0.243323i
\(396\) 0 0
\(397\) −4252.39 −0.0269806 −0.0134903 0.999909i \(-0.504294\pi\)
−0.0134903 + 0.999909i \(0.504294\pi\)
\(398\) 92940.9 25037.2i 0.586733 0.158059i
\(399\) 0 0
\(400\) −62789.0 107417.i −0.392431 0.671359i
\(401\) 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 \(0.806267\pi\)
\(410\) 112238. + 29912.6i 0.667685 + 0.177945i
\(411\) 0 0
\(412\) 53776.5 93723.9i 0.316810 0.552149i
\(413\) 67557.2 0.396070
\(414\) 0 0
\(415\) 96157.5i 0.558325i
\(416\) −46355.6 168470.i −0.267864 0.973498i
\(417\) 0 0
\(418\) 157056. + 41857.1i 0.898880 + 0.239561i
\(419\) 137256. 79245.0i 0.781816 0.451382i −0.0552577 0.998472i \(-0.517598\pi\)
0.837073 + 0.547091i \(0.184265\pi\)
\(420\) 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
\(428\) 247.199 + 425.518i 0.00134946 + 0.00232290i
\(429\) 0 0
\(430\) 101649. 27383.0i 0.549750 0.148096i
\(431\) 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 \(0.417941\pi\)
\(434\) 38585.2 + 143233.i 0.204853 + 0.760435i
\(435\) 0 0
\(436\) −147914. + 85928.5i −0.778101 + 0.452027i
\(437\) 67999.1 + 117778.i 0.356074 + 0.616738i
\(438\) 0 0
\(439\) −321749. 185762.i −1.66951 0.963890i −0.967903 0.251322i \(-0.919135\pi\)
−0.701603 0.712568i \(1.25247\pi\)
\(440\) −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 \(-0.218744\pi\)
−0.162877 + 0.986646i \(0.552077\pi\)
\(444\) 0 0
\(445\) −5369.03 9299.44i −0.0271129 0.0469609i
\(446\) −17163.2 + 64399.5i −0.0862834 + 0.323752i
\(447\) 0 0
\(448\) 117882. 208029.i 0.587340 1.03649i
\(449\) −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
\(452\) −139003. 79756.5i −0.680373 0.390382i
\(453\) 0 0
\(454\) 57951.4 217445.i 0.281159 1.05496i
\(455\) 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 −0.997339 0.0728974i \(-0.976775\pi\)
−0.435539 + 0.900170i \(0.643442\pi\)
\(464\) 84662.8 + 144838.i 0.393239 + 0.672741i
\(465\) 0 0
\(466\) −80085.7 297287.i −0.368793 1.36900i
\(467\) 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
\(470\) 132204. 35614.3i 0.598480 0.161224i
\(471\) 0 0
\(472\) −71619.1 18881.5i −0.321473 0.0847523i
\(473\) 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 \(-0.260504\pi\)
−0.290547 + 0.956861i \(0.593837\pi\)
\(480\) 0 0
\(481\) −136501. 236427.i −0.589992 1.02190i
\(482\) −108221. 28842.1i −0.465819 0.124146i
\(483\) 0 0
\(484\) 63213.2 + 36270.2i 0.269847 + 0.154832i
\(485\) 207587. 0.882503
\(486\) 0 0
\(487\) 101284.i 0.427055i −0.976937 0.213527i \(-0.931505\pi\)
0.976937 0.213527i \(-0.0684953\pi\)
\(488\) −365672. + 99561.8i −1.53551 + 0.418074i
\(489\) 0 0
\(490\) 45870.6 + 12225.0i 0.191048 + 0.0509163i
\(491\) 151749. 87612.6i 0.629454 0.363416i −0.151086 0.988521i \(-0.548277\pi\)
0.780541 + 0.625105i \(0.214944\pi\)
\(492\) 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 \(-0.728481\pi\)
0.323480 + 0.946235i \(0.395147\pi\)
\(500\) −181204. + 105268.i −0.724815 + 0.421071i
\(501\) 0 0
\(502\) 76406.1 20582.9i 0.303194 0.0816770i
\(503\) 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
\(506\) −35122.5 130378.i −0.137178 0.509219i
\(507\) 0 0
\(508\) 129300. + 222572.i 0.501040 + 0.862470i
\(509\) −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
\(518\) 96206.0 360984.i 0.358544 1.34533i
\(519\) 0 0
\(520\) −124219. + 33821.2i −0.459391 + 0.125079i
\(521\) 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 \(-0.152505\pi\)
\(524\) 166473. 290136.i 0.606292 1.05667i
\(525\) 0 0
\(526\) −21850.6 + 81987.8i −0.0789755 + 0.296331i
\(527\) 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
\(536\) −220514. 58135.7i −0.767549 0.202355i
\(537\) 0 0
\(538\) 1151.00 + 4272.64i 0.00397659 + 0.0147615i
\(539\) 101104.i 0.348008i
\(540\) 0 0
\(541\) −472358. −1.61390 −0.806950 0.590620i \(-0.798883\pi\)
−0.806950 + 0.590620i \(0.798883\pi\)
\(542\) −127604. + 34375.1i −0.434376 + 0.117016i
\(543\) 0 0
\(544\) −394930. 102985.i −1.33451 0.347997i
\(545\) 63019.0 + 109152.i 0.212167 + 0.367485i
\(546\) 0 0
\(547\) 332881. + 192189.i 1.11254 + 0.642323i 0.939485 0.342590i \(-0.111304\pi\)
0.173051 + 0.984913i \(0.444638\pi\)
\(548\) 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
\(554\) 111479. + 29710.3i 0.363223 + 0.0968028i
\(555\) 0 0
\(556\) 74094.1 129134.i 0.239681 0.417726i
\(557\) 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
\(560\) −153041. 87266.0i −0.488014 0.278272i
\(561\) 0 0
\(562\) −124169. 33092.4i −0.393134 0.104775i
\(563\) 132566. 76536.8i 0.418229 0.241465i −0.276090 0.961132i \(-0.589039\pi\)
0.694319 + 0.719667i \(0.255706\pi\)
\(564\) 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 −0.635741 0.771903i \(-0.719305\pi\)
0.350617 + 0.936519i \(0.385972\pi\)
\(572\) −137731. 237086.i −0.420960 0.724624i
\(573\) 0 0
\(574\) −555380. + 149613.i −1.68565 + 0.454094i
\(575\) 163364.i 0.494108i
\(576\) 0 0
\(577\) −114098. −0.342710 −0.171355 0.985209i \(-0.554814\pi\)
−0.171355 + 0.985209i \(0.554814\pi\)
\(578\) −78386.0 290977.i −0.234630 0.870971i
\(579\) 0 0
\(580\) 106884. 62092.5i 0.317728 0.184579i
\(581\) −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 \(-0.309183\pi\)
−0.432919 + 0.901433i \(0.642516\pi\)
\(588\) 0 0
\(589\) 128519. + 222602.i 0.370456 + 0.641649i
\(590\) −14053.4 + 52731.2i −0.0403718 + 0.151483i
\(591\) 0 0
\(592\) −202881. + 355799.i −0.578893 + 1.01522i
\(593\) −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
\(596\) 343776. + 197250.i 0.967793 + 0.555296i
\(597\) 0 0
\(598\) 59080.3 221681.i 0.165212 0.619906i
\(599\) −16547.3 + 9553.58i −0.0461183 + 0.0266264i −0.522882 0.852405i \(-0.675143\pi\)
0.476764 + 0.879032i \(0.341810\pi\)
\(600\) 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 0.0219735 0.999759i \(-0.493005\pi\)
0.876803 + 0.480850i \(0.159672\pi\)
\(608\) 104545. 400912.i 0.282811 1.08453i
\(609\) 0 0
\(610\) 72633.2 + 269622.i 0.195198 + 0.724597i
\(611\) 495450.i 1.32714i
\(612\) 0 0
\(613\) −210852. −0.561121 −0.280560 0.959836i \(-0.590520\pi\)
−0.280560 + 0.959836i \(0.590520\pi\)
\(614\) −45065.9 + 12140.2i −0.119539 + 0.0322026i
\(615\) 0 0
\(616\) 95650.5 362811.i 0.252073 0.956134i
\(617\) 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 0.545843 0.837888i \(-0.316210\pi\)
−0.452711 + 0.891657i \(0.649543\pi\)
\(620\) −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
\(626\) 334325. + 89101.2i 0.853139 + 0.227371i
\(627\) 0 0
\(628\) −402083. 230706.i −1.01952 0.584977i
\(629\) −637678. −1.61176
\(630\) 0 0
\(631\) 150814.i 0.378777i −0.981902 0.189389i \(-0.939349\pi\)
0.981902 0.189389i \(-0.0606506\pi\)
\(632\) 54145.3 + 198866.i 0.135558 + 0.497882i
\(633\) 0 0
\(634\) 95205.8 + 25373.4i 0.236856 + 0.0631248i
\(635\) 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 −0.407473 0.913217i \(-0.633590\pi\)
0.587133 + 0.809491i \(0.300257\pi\)
\(644\) 271460. 157701.i 0.654536 0.380244i
\(645\) 0 0
\(646\) 622855. 167790.i 1.49253 0.402070i
\(647\) 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
\(650\) −86288.9 320314.i −0.204234 0.758139i
\(651\) 0 0
\(652\) 142550. + 245381.i 0.335331 + 0.577225i
\(653\) −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 0.107358 0.994220i \(-0.465761\pi\)
−0.807341 + 0.590085i \(0.799094\pi\)
\(660\) 0 0
\(661\) 141131. + 244446.i 0.323013 + 0.559475i 0.981108 0.193460i \(-0.0619709\pi\)
−0.658095 + 0.752935i \(0.728638\pi\)
\(662\) −192899. + 723795.i −0.440164 + 1.65158i
\(663\) 0 0
\(664\) 137141. + 503694.i 0.311051 + 1.14243i
\(665\) 278442. 0.629638
\(666\) 0 0
\(667\) 220276.i 0.495125i
\(668\) −326980. + 569874.i −0.732771 + 1.27710i
\(669\) 0 0
\(670\) −43270.3 + 162358.i −0.0963918 + 0.361680i
\(671\) −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
\(680\) −76660.0 + 290778.i −0.165787 + 0.628846i
\(681\) 0 0
\(682\) −66381.8 246417.i −0.142719 0.529787i
\(683\) 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
\(686\) 314362. 84685.5i 0.668008 0.179954i
\(687\) 0 0
\(688\) 493405. 288411.i 1.04238 0.609305i
\(689\) −110207. 190884.i −0.232152 0.402098i
\(690\) 0 0
\(691\) −284957. 164520.i −0.596792 0.344558i 0.170986 0.985273i \(-0.445305\pi\)
−0.767779 + 0.640715i \(0.778638\pi\)
\(692\) 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
\(698\) 169666. + 45217.7i 0.348243 + 0.0928106i
\(699\) 0 0
\(700\) 225920. 393742.i 0.461061 0.803556i
\(701\) 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
\(704\) −202803. + 357892.i −0.409193 + 0.722115i
\(705\) 0 0
\(706\) −601328. 160260.i −1.20643 0.321526i
\(707\) −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
\(716\) 14101.2 + 24273.3i 0.0275062 + 0.0473481i
\(717\) 0 0
\(718\) −710682. + 191450.i −1.37856 + 0.371369i
\(719\) 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
\(722\) 34737.6 + 128950.i 0.0666386 + 0.247370i
\(723\) 0 0
\(724\) 605800. 351931.i 1.15572 0.671399i
\(725\) 159256. + 275840.i 0.302985 + 0.524785i
\(726\) 0 0
\(727\) 396978. + 229195.i 0.751100 + 0.433648i 0.826091 0.563536i \(-0.190560\pi\)
−0.0749911 + 0.997184i \(0.523893\pi\)
\(728\) 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 \(0.854290\pi\)
\(734\) −170892. + 641221.i −0.317198 + 1.19019i
\(735\) 0 0
\(736\) −331857. + 91312.6i −0.612626 + 0.168568i
\(737\) −357855. −0.658828
\(738\) 0 0
\(739\) 476430.i 0.872390i −0.899852 0.436195i \(-0.856326\pi\)
0.899852 0.436195i \(-0.143674\pi\)
\(740\) 261750. + 150186.i 0.477994 + 0.274261i
\(741\) 0 0
\(742\) 77674.1 291448.i 0.141081 0.529363i
\(743\) 109137. 63010.2i 0.197694 0.114139i −0.397885 0.917435i \(-0.630256\pi\)
0.595579 + 0.803296i \(0.296922\pi\)
\(744\) 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 \(-0.608702\pi\)
0.648566 + 0.761158i \(0.275369\pi\)
\(752\) 641721. 375107.i 1.13478 0.663314i
\(753\) 0 0
\(754\) 116349. + 431902.i 0.204655 + 0.759700i
\(755\) 120358.i 0.211145i
\(756\) 0 0
\(757\) 588244. 1.02652 0.513258 0.858235i \(-0.328438\pi\)
0.513258 + 0.858235i \(0.328438\pi\)
\(758\) −168573. + 45411.5i −0.293392 + 0.0790365i
\(759\) 0 0
\(760\) −295183. 77821.2i −0.511051 0.134732i
\(761\) −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 \(-0.434844\pi\)
\(770\) −267128. 71192.5i −0.450545 0.120075i
\(771\) 0 0
\(772\) −292745. 167970.i −0.491196 0.281836i
\(773\) 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
\(776\) 1.08738e6 296063.i 1.80576 0.491655i