Properties

Label 108.5.f.a.91.10
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 91.10
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.10

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 −0.723723 0.690091i \(-0.757570\pi\)
0.959498 + 0.281717i \(0.0909038\pi\)
\(6\) 0 0
\(7\) −50.5548 + 29.1878i −1.03173 + 0.595670i −0.917480 0.397782i \(-0.869780\pi\)
−0.114251 + 0.993452i \(0.536447\pi\)
\(8\) 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 \(-0.530449\pi\)
0.814309 + 0.580431i \(0.197116\pi\)
\(12\) 0 0
\(13\) 85.3178 147.775i 0.504839 0.874407i −0.495145 0.868810i \(-0.664885\pi\)
0.999984 0.00559684i \(-0.00178154\pi\)
\(14\) −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 \(-0.810648\pi\)
0.828223 0.560399i \(-0.189352\pi\)
\(20\) −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 0.749230 0.662310i \(-0.230424\pi\)
−0.198963 + 0.980007i \(0.563757\pi\)
\(24\) 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 0.758144 0.652087i \(-0.226106\pi\)
−0.185651 + 0.982616i \(0.559440\pi\)
\(32\) −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 −0.223055 0.974806i \(-0.571603\pi\)
0.955734 0.294232i \(-0.0950637\pi\)
\(42\) 0 0
\(43\) 1933.38 1116.24i 1.04564 0.603699i 0.124212 0.992256i \(-0.460360\pi\)
0.921425 + 0.388557i \(0.127026\pi\)
\(44\) −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 \(-0.438403\pi\)
0.946015 + 0.324124i \(0.105069\pi\)
\(48\) 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 0.349085 0.937091i \(-0.386492\pi\)
−0.637002 + 0.770862i \(0.719826\pi\)
\(60\) 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 0.115219 0.993340i \(-0.463243\pi\)
−0.802648 + 0.596452i \(0.796576\pi\)
\(68\) −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 \(0.188963\pi\)
−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 \(0.672470\pi\)
\(74\) 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 −0.259635 0.965707i \(-0.583602\pi\)
0.706509 + 0.707704i \(0.250269\pi\)
\(80\) 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 \(-0.465001\pi\)
0.915661 + 0.401951i \(0.131668\pi\)
\(84\) 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 0.773297 + 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 0.198348 0.980132i \(-0.436442\pi\)
−0.749645 + 0.661841i \(0.769776\pi\)
\(104\) −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 \(0.000427558\pi\)
−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 \(0.351447\pi\)
\(110\) 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 −0.600533 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
\(122\) 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 \(0.166197\pi\)
−0.866762 + 0.498722i \(0.833803\pi\)
\(128\) 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 −0.130983 0.991385i \(-0.541813\pi\)
−0.924056 + 0.382257i \(0.875147\pi\)
\(132\) 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 0.276747 0.960943i \(-0.410744\pi\)
−0.693828 + 0.720141i \(0.744077\pi\)
\(140\) 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 0.439779 + 0.898106i \(0.355057\pi\)
−0.997672 + 0.0681928i \(0.978277\pi\)
\(150\) 0 0
\(151\) −8841.72 + 5104.77i −0.387778 + 0.223884i −0.681197 0.732100i \(-0.738540\pi\)
0.293419 + 0.955984i \(0.405207\pi\)
\(152\) −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 \(-0.0333046\pi\)
\(158\) 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 \(0.108324\pi\)
−0.942651 + 0.333780i \(0.891676\pi\)
\(164\) −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 0.975949 0.217999i \(-0.0699530\pi\)
0.299182 + 0.954196i \(0.403286\pi\)
\(168\) 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
\(176\) 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 \(0.00871609\pi\)
−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 \(0.732975\pi\)
\(182\) −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 −0.890913 0.454174i \(-0.849934\pi\)
−0.0521297 + 0.998640i \(0.516601\pi\)
\(192\) 0 0
\(193\) 10547.2 18268.3i 0.283154 0.490437i −0.689006 0.724756i \(-0.741953\pi\)
0.972160 + 0.234319i \(0.0752859\pi\)
\(194\) −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 \(-0.901736\pi\)
0.952728 0.303825i \(-0.0982638\pi\)
\(200\) 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 0.943878 0.330295i \(-0.107148\pi\)
0.185895 + 0.982570i \(0.440482\pi\)
\(212\) 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 −0.638016 0.770023i \(-0.720245\pi\)
0.347852 + 0.937550i \(0.386911\pi\)
\(224\) 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 \(-0.482857\pi\)
0.891685 + 0.452657i \(0.149524\pi\)
\(228\) 0 0
\(229\) −1223.91 + 2119.87i −0.0233388 + 0.0404239i −0.877459 0.479652i \(-0.840763\pi\)
0.854120 + 0.520076i \(0.174096\pi\)
\(230\) 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 0.289277 0.957245i \(-0.406585\pi\)
−0.684360 + 0.729144i \(0.739918\pi\)
\(240\) 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
\(248\) 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 \(-0.949817\pi\)
0.987598 0.157001i \(-0.0501827\pi\)
\(252\) 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 −0.409905 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 −0.626881 0.779115i \(-0.715669\pi\)
0.361293 + 0.932452i \(0.382335\pi\)
\(264\) 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 \(0.0722155\pi\)
−0.974375 + 0.224931i \(0.927784\pi\)
\(272\) 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 0.756616 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 0.833382 0.552697i \(-0.186401\pi\)
−0.0619586 + 0.998079i \(0.519735\pi\)
\(284\) 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 −0.952779 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
\(302\) −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 \(0.0197161\pi\)
−0.998082 + 0.0619005i \(0.980284\pi\)
\(308\) 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 0.480462 0.877015i \(-0.340469\pi\)
−0.519286 + 0.854600i \(0.673802\pi\)
\(312\) 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
\(320\) −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 −0.999749 0.0223896i \(-0.992873\pi\)
−0.480485 + 0.877003i \(0.659539\pi\)
\(332\) −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 \(0.0200538\pi\)
\(338\) 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 −0.285287 0.958442i \(-0.592089\pi\)
−0.972679 + 0.232155i \(0.925422\pi\)
\(348\) 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
\(356\) 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 \(0.253052\pi\)
−0.700295 + 0.713853i \(0.746948\pi\)
\(360\) 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 −0.927281 0.374366i \(-0.877860\pi\)
−0.139430 + 0.990232i \(0.544527\pi\)
\(368\) −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 \(0.321815\pi\)
\(374\) 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 \(0.0485475\pi\)
−0.988392 + 0.151926i \(0.951453\pi\)
\(380\) 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 −0.987708 0.156310i \(-0.950040\pi\)
−0.629223 0.777225i \(1.28337\pi\)
\(384\) 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
\(392\) −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 −0.854402 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 \(0.139600\pi\)
\(410\) 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 0.837073 0.547091i \(-0.184265\pi\)
−0.0552577 + 0.998472i \(0.517598\pi\)
\(420\) 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
\(428\) 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 \(0.100286\pi\)
−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 \(0.417941\pi\)
\(434\) 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 −0.701603 + 0.712568i \(0.747532\pi\)
−0.967903 + 0.251322i \(0.919135\pi\)
\(440\) −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 \(-0.552077\pi\)
0.773023 + 0.634379i \(0.218744\pi\)
\(444\) 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 −0.967881 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 −0.435539 0.900170i \(-0.643442\pi\)
−0.997339 + 0.0728974i \(0.976775\pi\)
\(464\) 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 \(-0.913828\pi\)
0.963579 0.267424i \(-0.0861724\pi\)
\(468\) 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 −0.290547 0.956861i \(-0.593837\pi\)
0.683392 + 0.730052i \(0.260504\pi\)
\(480\) 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 \(0.0684953\pi\)
−0.976937 + 0.213527i \(0.931505\pi\)
\(488\) −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 0.780541 0.625105i \(-0.214944\pi\)
−0.151086 + 0.988521i \(0.548277\pi\)
\(492\) 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 \(-0.395147\pi\)
−0.657724 + 0.753259i \(0.728481\pi\)
\(500\) −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 \(-0.894454\pi\)
0.945528 0.325540i \(-0.105546\pi\)
\(504\) 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 −0.936959 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
\(518\) 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 \(0.152505\pi\)
−0.887406 + 0.460989i \(0.847495\pi\)
\(524\) 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 0.173051 0.984913i \(-0.444638\pi\)
0.939485 + 0.342590i \(0.111304\pi\)
\(548\) 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 0.694319 0.719667i \(-0.255706\pi\)
−0.276090 + 0.961132i \(0.589039\pi\)
\(564\) 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 0.350617 0.936519i \(-0.385972\pi\)
−0.635741 + 0.771903i \(0.719305\pi\)
\(572\) −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 −0.432919 0.901433i \(-0.642516\pi\)
0.564205 + 0.825635i \(0.309183\pi\)
\(588\) 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 0.476764 0.879032i \(-0.341810\pi\)
−0.522882 + 0.852405i \(0.675143\pi\)
\(600\) 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 0.876803 0.480850i \(-0.159672\pi\)
0.0219735 + 0.999759i \(0.493005\pi\)
\(608\) 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 −0.0805170 0.996753i \(-0.525657\pi\)
0.903472 0.428647i \(-0.141010\pi\)
\(618\) 0 0
\(619\) 35684.5 20602.5i 0.0931319 0.0537697i −0.452711 0.891657i \(-0.649543\pi\)
0.545843 + 0.837888i \(0.316210\pi\)
\(620\) −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 \(0.0606506\pi\)
−0.981902 + 0.189389i \(0.939349\pi\)
\(632\) 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 0.999693 + 0.0247640i \(0.00788343\pi\)
−0.478400 + 0.878142i \(0.658783\pi\)
\(642\) 0 0
\(643\) 74279.9 + 42885.5i 0.179659 + 0.103726i 0.587133 0.809491i \(-0.300257\pi\)
−0.407473 + 0.913217i \(0.633590\pi\)
\(644\) 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 \(0.0489986\pi\)
−0.988176 + 0.153327i \(0.951001\pi\)
\(648\) 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 0.452243 + 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 −0.807341 0.590085i \(-0.799094\pi\)
0.107358 + 0.994220i \(0.465761\pi\)
\(660\) 0 0
\(661\) 141131. 244446.i 0.323013 0.559475i −0.658095 0.752935i \(-0.728638\pi\)
0.981108 + 0.193460i \(0.0619709\pi\)
\(662\) −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 0.851309 + 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
\(680\) −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 \(0.263501\pi\)
−0.676489 + 0.736453i \(0.736499\pi\)
\(684\) 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 −0.767779 0.640715i \(-0.778638\pi\)
0.170986 + 0.985273i \(0.445305\pi\)
\(692\) 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 0.993535 + 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
\(716\) 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 \(-0.799666\pi\)
0.808400 0.588633i \(-0.200334\pi\)
\(720\) 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 −0.0749911 0.997184i \(-0.523893\pi\)
0.826091 + 0.563536i \(0.190560\pi\)
\(728\) 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 \(0.187623\pi\)
\(734\) −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 \(0.143674\pi\)
−0.899852 + 0.436195i \(0.856326\pi\)
\(740\) 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 0.595579 0.803296i \(-0.296922\pi\)
−0.397885 + 0.917435i \(0.630256\pi\)
\(744\) 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 \(-0.275369\pi\)
−0.334899 + 0.942254i \(0.608702\pi\)
\(752\) 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 −0.887097 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 \(0.898490\pi\)
\(770\) −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
\(777\) 0 0
\(778\) 947674.