Properties

Label 76.5.j.a.53.4
Level $76$
Weight $5$
Character 76.53
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 53.4
Character \(\chi\) \(=\) 76.53
Dual form 76.5.j.a.33.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.693233 - 0.122236i) q^{3} +(-24.2132 + 20.3173i) q^{5} +(32.5833 - 56.4359i) q^{7} +(-75.6495 + 27.5342i) q^{9} +O(q^{10})\) \(q+(0.693233 - 0.122236i) q^{3} +(-24.2132 + 20.3173i) q^{5} +(32.5833 - 56.4359i) q^{7} +(-75.6495 + 27.5342i) q^{9} +(-96.0822 - 166.419i) q^{11} +(-85.9617 - 15.1574i) q^{13} +(-14.3019 + 17.0443i) q^{15} +(-103.134 - 37.5377i) q^{17} +(-84.7252 + 350.917i) q^{19} +(15.6893 - 43.1061i) q^{21} +(-676.013 - 567.242i) q^{23} +(64.9565 - 368.387i) q^{25} +(-98.4562 + 56.8437i) q^{27} +(-495.669 - 1361.84i) q^{29} +(1387.38 + 801.005i) q^{31} +(-86.9497 - 103.623i) q^{33} +(357.679 + 2028.50i) q^{35} +2397.08i q^{37} -61.4442 q^{39} +(2312.10 - 407.686i) q^{41} +(175.985 - 147.669i) q^{43} +(1272.30 - 2203.68i) q^{45} +(344.708 - 125.464i) q^{47} +(-922.842 - 1598.41i) q^{49} +(-76.0843 - 13.4157i) q^{51} +(-2078.65 + 2477.24i) q^{53} +(5707.64 + 2077.41i) q^{55} +(-15.8397 + 253.624i) q^{57} +(-624.116 + 1714.75i) q^{59} +(-2111.67 - 1771.90i) q^{61} +(-910.993 + 5166.50i) q^{63} +(2389.36 - 1379.50i) q^{65} +(-2010.34 - 5523.36i) q^{67} +(-537.972 - 310.598i) q^{69} +(876.187 + 1044.20i) q^{71} +(-985.246 - 5587.61i) q^{73} -263.318i q^{75} -12522.7 q^{77} +(-4620.95 + 814.799i) q^{79} +(4933.97 - 4140.09i) q^{81} +(-375.320 + 650.073i) q^{83} +(3259.87 - 1186.49i) q^{85} +(-510.079 - 883.483i) q^{87} +(-7669.75 - 1352.38i) q^{89} +(-3656.33 + 4357.45i) q^{91} +(1059.69 + 385.695i) q^{93} +(-5078.21 - 10218.2i) q^{95} +(2188.55 - 6012.99i) q^{97} +(11850.8 + 9943.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.693233 0.122236i 0.0770259 0.0135817i −0.135002 0.990845i \(-0.543104\pi\)
0.212028 + 0.977264i \(0.431993\pi\)
\(4\) 0 0
\(5\) −24.2132 + 20.3173i −0.968527 + 0.812691i −0.982319 0.187214i \(-0.940054\pi\)
0.0137919 + 0.999905i \(0.495610\pi\)
\(6\) 0 0
\(7\) 32.5833 56.4359i 0.664965 1.15175i −0.314330 0.949314i \(-0.601780\pi\)
0.979295 0.202439i \(-0.0648869\pi\)
\(8\) 0 0
\(9\) −75.6495 + 27.5342i −0.933944 + 0.339928i
\(10\) 0 0
\(11\) −96.0822 166.419i −0.794068 1.37537i −0.923429 0.383768i \(-0.874626\pi\)
0.129362 0.991597i \(-0.458707\pi\)
\(12\) 0 0
\(13\) −85.9617 15.1574i −0.508649 0.0896885i −0.0865667 0.996246i \(-0.527590\pi\)
−0.422082 + 0.906558i \(0.638701\pi\)
\(14\) 0 0
\(15\) −14.3019 + 17.0443i −0.0635639 + 0.0757525i
\(16\) 0 0
\(17\) −103.134 37.5377i −0.356865 0.129888i 0.157365 0.987540i \(-0.449700\pi\)
−0.514230 + 0.857652i \(0.671922\pi\)
\(18\) 0 0
\(19\) −84.7252 + 350.917i −0.234696 + 0.972069i
\(20\) 0 0
\(21\) 15.6893 43.1061i 0.0355767 0.0977462i
\(22\) 0 0
\(23\) −676.013 567.242i −1.27791 1.07229i −0.993529 0.113580i \(-0.963768\pi\)
−0.284379 0.958712i \(-0.591787\pi\)
\(24\) 0 0
\(25\) 64.9565 368.387i 0.103930 0.589419i
\(26\) 0 0
\(27\) −98.4562 + 56.8437i −0.135056 + 0.0779749i
\(28\) 0 0
\(29\) −495.669 1361.84i −0.589380 1.61931i −0.771640 0.636059i \(-0.780564\pi\)
0.182260 0.983250i \(-0.441659\pi\)
\(30\) 0 0
\(31\) 1387.38 + 801.005i 1.44368 + 0.833512i 0.998093 0.0617246i \(-0.0196601\pi\)
0.445592 + 0.895236i \(0.352993\pi\)
\(32\) 0 0
\(33\) −86.9497 103.623i −0.0798436 0.0951539i
\(34\) 0 0
\(35\) 357.679 + 2028.50i 0.291983 + 1.65592i
\(36\) 0 0
\(37\) 2397.08i 1.75097i 0.483245 + 0.875485i \(0.339458\pi\)
−0.483245 + 0.875485i \(0.660542\pi\)
\(38\) 0 0
\(39\) −61.4442 −0.0403973
\(40\) 0 0
\(41\) 2312.10 407.686i 1.37543 0.242526i 0.563422 0.826169i \(-0.309485\pi\)
0.812010 + 0.583643i \(0.198373\pi\)
\(42\) 0 0
\(43\) 175.985 147.669i 0.0951785 0.0798642i −0.593957 0.804497i \(-0.702435\pi\)
0.689135 + 0.724633i \(0.257991\pi\)
\(44\) 0 0
\(45\) 1272.30 2203.68i 0.628294 1.08824i
\(46\) 0 0
\(47\) 344.708 125.464i 0.156047 0.0567966i −0.262816 0.964846i \(-0.584651\pi\)
0.418863 + 0.908050i \(0.362429\pi\)
\(48\) 0 0
\(49\) −922.842 1598.41i −0.384357 0.665726i
\(50\) 0 0
\(51\) −76.0843 13.4157i −0.0292519 0.00515791i
\(52\) 0 0
\(53\) −2078.65 + 2477.24i −0.739996 + 0.881892i −0.996409 0.0846749i \(-0.973015\pi\)
0.256413 + 0.966567i \(0.417459\pi\)
\(54\) 0 0
\(55\) 5707.64 + 2077.41i 1.88682 + 0.686748i
\(56\) 0 0
\(57\) −15.8397 + 253.624i −0.00487526 + 0.0780620i
\(58\) 0 0
\(59\) −624.116 + 1714.75i −0.179292 + 0.492602i −0.996486 0.0837619i \(-0.973306\pi\)
0.817194 + 0.576363i \(0.195529\pi\)
\(60\) 0 0
\(61\) −2111.67 1771.90i −0.567502 0.476191i 0.313314 0.949650i \(-0.398561\pi\)
−0.880816 + 0.473459i \(0.843005\pi\)
\(62\) 0 0
\(63\) −910.993 + 5166.50i −0.229527 + 1.30171i
\(64\) 0 0
\(65\) 2389.36 1379.50i 0.565529 0.326509i
\(66\) 0 0
\(67\) −2010.34 5523.36i −0.447837 1.23042i −0.934227 0.356680i \(-0.883909\pi\)
0.486390 0.873742i \(-0.338313\pi\)
\(68\) 0 0
\(69\) −537.972 310.598i −0.112996 0.0652380i
\(70\) 0 0
\(71\) 876.187 + 1044.20i 0.173812 + 0.207141i 0.845917 0.533315i \(-0.179054\pi\)
−0.672105 + 0.740456i \(0.734609\pi\)
\(72\) 0 0
\(73\) −985.246 5587.61i −0.184884 1.04853i −0.926105 0.377267i \(-0.876864\pi\)
0.741221 0.671261i \(-0.234247\pi\)
\(74\) 0 0
\(75\) 263.318i 0.0468121i
\(76\) 0 0
\(77\) −12522.7 −2.11211
\(78\) 0 0
\(79\) −4620.95 + 814.799i −0.740419 + 0.130556i −0.531121 0.847296i \(-0.678229\pi\)
−0.209298 + 0.977852i \(0.567118\pi\)
\(80\) 0 0
\(81\) 4933.97 4140.09i 0.752014 0.631015i
\(82\) 0 0
\(83\) −375.320 + 650.073i −0.0544810 + 0.0943639i −0.891980 0.452075i \(-0.850684\pi\)
0.837499 + 0.546439i \(0.184017\pi\)
\(84\) 0 0
\(85\) 3259.87 1186.49i 0.451192 0.164221i
\(86\) 0 0
\(87\) −510.079 883.483i −0.0673906 0.116724i
\(88\) 0 0
\(89\) −7669.75 1352.38i −0.968281 0.170734i −0.332925 0.942953i \(-0.608036\pi\)
−0.635356 + 0.772219i \(0.719147\pi\)
\(90\) 0 0
\(91\) −3656.33 + 4357.45i −0.441533 + 0.526198i
\(92\) 0 0
\(93\) 1059.69 + 385.695i 0.122522 + 0.0445942i
\(94\) 0 0
\(95\) −5078.21 10218.2i −0.562682 1.13221i
\(96\) 0 0
\(97\) 2188.55 6012.99i 0.232602 0.639068i −0.767396 0.641173i \(-0.778448\pi\)
0.999998 + 0.00210552i \(0.000670207\pi\)
\(98\) 0 0
\(99\) 11850.8 + 9943.99i 1.20914 + 1.01459i
\(100\) 0 0
\(101\) −683.910 + 3878.65i −0.0670435 + 0.380222i 0.932762 + 0.360493i \(0.117392\pi\)
−0.999805 + 0.0197293i \(0.993720\pi\)
\(102\) 0 0
\(103\) −10478.4 + 6049.68i −0.987685 + 0.570240i −0.904582 0.426301i \(-0.859817\pi\)
−0.0831035 + 0.996541i \(0.526483\pi\)
\(104\) 0 0
\(105\) 495.909 + 1362.50i 0.0449804 + 0.123583i
\(106\) 0 0
\(107\) −66.4411 38.3598i −0.00580322 0.00335049i 0.497096 0.867696i \(-0.334400\pi\)
−0.502899 + 0.864345i \(0.667733\pi\)
\(108\) 0 0
\(109\) 4428.59 + 5277.79i 0.372746 + 0.444221i 0.919511 0.393065i \(-0.128585\pi\)
−0.546765 + 0.837286i \(0.684141\pi\)
\(110\) 0 0
\(111\) 293.008 + 1661.73i 0.0237812 + 0.134870i
\(112\) 0 0
\(113\) 18412.6i 1.44197i −0.692948 0.720987i \(-0.743689\pi\)
0.692948 0.720987i \(-0.256311\pi\)
\(114\) 0 0
\(115\) 27893.2 2.10913
\(116\) 0 0
\(117\) 6920.30 1220.24i 0.505537 0.0891399i
\(118\) 0 0
\(119\) −5478.92 + 4597.36i −0.386902 + 0.324649i
\(120\) 0 0
\(121\) −11143.1 + 19300.4i −0.761087 + 1.31824i
\(122\) 0 0
\(123\) 1552.99 565.243i 0.102650 0.0373615i
\(124\) 0 0
\(125\) −3965.71 6868.81i −0.253805 0.439604i
\(126\) 0 0
\(127\) 9768.85 + 1722.51i 0.605670 + 0.106796i 0.468069 0.883692i \(-0.344950\pi\)
0.137601 + 0.990488i \(0.456061\pi\)
\(128\) 0 0
\(129\) 103.948 123.881i 0.00624651 0.00744430i
\(130\) 0 0
\(131\) −6000.91 2184.15i −0.349683 0.127274i 0.161206 0.986921i \(-0.448462\pi\)
−0.510889 + 0.859647i \(0.670684\pi\)
\(132\) 0 0
\(133\) 17043.7 + 16215.6i 0.963519 + 0.916703i
\(134\) 0 0
\(135\) 1229.03 3376.73i 0.0674364 0.185280i
\(136\) 0 0
\(137\) 3234.82 + 2714.34i 0.172349 + 0.144618i 0.724882 0.688873i \(-0.241894\pi\)
−0.552533 + 0.833491i \(0.686339\pi\)
\(138\) 0 0
\(139\) 2765.31 15682.9i 0.143125 0.811700i −0.825729 0.564067i \(-0.809236\pi\)
0.968854 0.247634i \(-0.0796529\pi\)
\(140\) 0 0
\(141\) 223.627 129.111i 0.0112483 0.00649420i
\(142\) 0 0
\(143\) 5736.91 + 15762.0i 0.280547 + 0.770797i
\(144\) 0 0
\(145\) 39670.6 + 22903.8i 1.88683 + 1.08936i
\(146\) 0 0
\(147\) −835.127 995.265i −0.0386472 0.0460579i
\(148\) 0 0
\(149\) 2527.38 + 14333.5i 0.113841 + 0.645622i 0.987318 + 0.158757i \(0.0507486\pi\)
−0.873477 + 0.486865i \(0.838140\pi\)
\(150\) 0 0
\(151\) 29961.2i 1.31403i −0.753878 0.657014i \(-0.771819\pi\)
0.753878 0.657014i \(-0.228181\pi\)
\(152\) 0 0
\(153\) 8835.60 0.377445
\(154\) 0 0
\(155\) −49867.1 + 8792.92i −2.07564 + 0.365991i
\(156\) 0 0
\(157\) 9032.84 7579.45i 0.366459 0.307495i −0.440900 0.897556i \(-0.645341\pi\)
0.807359 + 0.590061i \(0.200896\pi\)
\(158\) 0 0
\(159\) −1138.18 + 1971.39i −0.0450212 + 0.0779790i
\(160\) 0 0
\(161\) −54039.6 + 19668.8i −2.08478 + 0.758798i
\(162\) 0 0
\(163\) −2502.29 4334.09i −0.0941807 0.163126i 0.815086 0.579340i \(-0.196690\pi\)
−0.909266 + 0.416215i \(0.863356\pi\)
\(164\) 0 0
\(165\) 4210.66 + 742.453i 0.154661 + 0.0272710i
\(166\) 0 0
\(167\) 24384.0 29059.7i 0.874323 1.04198i −0.124439 0.992227i \(-0.539713\pi\)
0.998762 0.0497499i \(-0.0158424\pi\)
\(168\) 0 0
\(169\) −19678.9 7162.53i −0.689013 0.250780i
\(170\) 0 0
\(171\) −3252.79 28879.5i −0.111241 0.987638i
\(172\) 0 0
\(173\) 1148.94 3156.69i 0.0383889 0.105473i −0.919017 0.394217i \(-0.871016\pi\)
0.957406 + 0.288745i \(0.0932379\pi\)
\(174\) 0 0
\(175\) −18673.7 15669.1i −0.609755 0.511645i
\(176\) 0 0
\(177\) −223.055 + 1265.01i −0.00711976 + 0.0403782i
\(178\) 0 0
\(179\) 4338.08 2504.59i 0.135392 0.0781684i −0.430774 0.902460i \(-0.641759\pi\)
0.566166 + 0.824291i \(0.308426\pi\)
\(180\) 0 0
\(181\) 4371.44 + 12010.4i 0.133434 + 0.366608i 0.988358 0.152146i \(-0.0486184\pi\)
−0.854924 + 0.518754i \(0.826396\pi\)
\(182\) 0 0
\(183\) −1680.47 970.221i −0.0501798 0.0289713i
\(184\) 0 0
\(185\) −48702.1 58040.9i −1.42300 1.69586i
\(186\) 0 0
\(187\) 3662.34 + 20770.2i 0.104731 + 0.593960i
\(188\) 0 0
\(189\) 7408.62i 0.207402i
\(190\) 0 0
\(191\) 17413.4 0.477327 0.238664 0.971102i \(-0.423291\pi\)
0.238664 + 0.971102i \(0.423291\pi\)
\(192\) 0 0
\(193\) 30690.7 5411.60i 0.823933 0.145282i 0.254242 0.967141i \(-0.418174\pi\)
0.569691 + 0.821859i \(0.307063\pi\)
\(194\) 0 0
\(195\) 1487.76 1248.38i 0.0391258 0.0328305i
\(196\) 0 0
\(197\) −23799.8 + 41222.5i −0.613255 + 1.06219i 0.377433 + 0.926037i \(0.376807\pi\)
−0.990688 + 0.136152i \(0.956526\pi\)
\(198\) 0 0
\(199\) −49214.5 + 17912.6i −1.24276 + 0.452327i −0.877948 0.478755i \(-0.841088\pi\)
−0.364810 + 0.931082i \(0.618866\pi\)
\(200\) 0 0
\(201\) −2068.78 3583.24i −0.0512063 0.0886919i
\(202\) 0 0
\(203\) −93007.2 16399.7i −2.25696 0.397963i
\(204\) 0 0
\(205\) −47700.3 + 56847.0i −1.13505 + 1.35269i
\(206\) 0 0
\(207\) 66758.6 + 24298.1i 1.55800 + 0.567064i
\(208\) 0 0
\(209\) 66539.9 19617.0i 1.52331 0.449096i
\(210\) 0 0
\(211\) 15504.7 42598.8i 0.348255 0.956824i −0.634664 0.772788i \(-0.718862\pi\)
0.982920 0.184036i \(-0.0589163\pi\)
\(212\) 0 0
\(213\) 735.040 + 616.772i 0.0162014 + 0.0135946i
\(214\) 0 0
\(215\) −1260.93 + 7151.07i −0.0272780 + 0.154701i
\(216\) 0 0
\(217\) 90410.9 52198.7i 1.92000 1.10851i
\(218\) 0 0
\(219\) −1366.01 3753.08i −0.0284817 0.0782528i
\(220\) 0 0
\(221\) 8296.60 + 4790.04i 0.169870 + 0.0980742i
\(222\) 0 0
\(223\) −30355.7 36176.5i −0.610422 0.727473i 0.368970 0.929441i \(-0.379711\pi\)
−0.979392 + 0.201969i \(0.935266\pi\)
\(224\) 0 0
\(225\) 5229.29 + 29656.8i 0.103295 + 0.585813i
\(226\) 0 0
\(227\) 12826.9i 0.248926i −0.992224 0.124463i \(-0.960279\pi\)
0.992224 0.124463i \(-0.0397207\pi\)
\(228\) 0 0
\(229\) −70554.2 −1.34540 −0.672701 0.739915i \(-0.734866\pi\)
−0.672701 + 0.739915i \(0.734866\pi\)
\(230\) 0 0
\(231\) −8681.15 + 1530.72i −0.162687 + 0.0286861i
\(232\) 0 0
\(233\) 17559.4 14734.1i 0.323443 0.271401i −0.466579 0.884480i \(-0.654514\pi\)
0.790022 + 0.613079i \(0.210069\pi\)
\(234\) 0 0
\(235\) −5797.41 + 10041.4i −0.104978 + 0.181827i
\(236\) 0 0
\(237\) −3103.80 + 1129.69i −0.0552582 + 0.0201124i
\(238\) 0 0
\(239\) 21648.2 + 37495.7i 0.378988 + 0.656426i 0.990915 0.134488i \(-0.0429388\pi\)
−0.611927 + 0.790914i \(0.709606\pi\)
\(240\) 0 0
\(241\) 38715.2 + 6826.54i 0.666573 + 0.117535i 0.496688 0.867929i \(-0.334549\pi\)
0.169885 + 0.985464i \(0.445660\pi\)
\(242\) 0 0
\(243\) 8833.55 10527.4i 0.149597 0.178283i
\(244\) 0 0
\(245\) 54820.2 + 19952.9i 0.913290 + 0.332410i
\(246\) 0 0
\(247\) 12602.1 28881.2i 0.206561 0.473392i
\(248\) 0 0
\(249\) −180.722 + 496.529i −0.00291482 + 0.00800841i
\(250\) 0 0
\(251\) 48070.5 + 40336.0i 0.763012 + 0.640243i 0.938909 0.344165i \(-0.111838\pi\)
−0.175897 + 0.984409i \(0.556282\pi\)
\(252\) 0 0
\(253\) −29447.2 + 167003.i −0.460048 + 2.60906i
\(254\) 0 0
\(255\) 2114.81 1220.99i 0.0325231 0.0187772i
\(256\) 0 0
\(257\) −27288.3 74974.0i −0.413152 1.13513i −0.955505 0.294976i \(-0.904688\pi\)
0.542352 0.840151i \(-0.317534\pi\)
\(258\) 0 0
\(259\) 135281. + 78104.7i 2.01669 + 1.16433i
\(260\) 0 0
\(261\) 74994.2 + 89374.6i 1.10090 + 1.31200i
\(262\) 0 0
\(263\) 9564.63 + 54243.7i 0.138279 + 0.784220i 0.972520 + 0.232819i \(0.0747951\pi\)
−0.834241 + 0.551400i \(0.814094\pi\)
\(264\) 0 0
\(265\) 102214.i 1.45552i
\(266\) 0 0
\(267\) −5482.24 −0.0769016
\(268\) 0 0
\(269\) −31645.8 + 5580.00i −0.437332 + 0.0771134i −0.387979 0.921668i \(-0.626827\pi\)
−0.0493523 + 0.998781i \(0.515716\pi\)
\(270\) 0 0
\(271\) 40261.4 33783.3i 0.548214 0.460006i −0.326121 0.945328i \(-0.605742\pi\)
0.874336 + 0.485321i \(0.161297\pi\)
\(272\) 0 0
\(273\) −2002.06 + 3467.66i −0.0268628 + 0.0465277i
\(274\) 0 0
\(275\) −67547.8 + 24585.4i −0.893194 + 0.325096i
\(276\) 0 0
\(277\) −64329.5 111422.i −0.838399 1.45215i −0.891233 0.453546i \(-0.850159\pi\)
0.0528337 0.998603i \(-0.483175\pi\)
\(278\) 0 0
\(279\) −127010. 22395.2i −1.63165 0.287705i
\(280\) 0 0
\(281\) 18278.5 21783.4i 0.231487 0.275876i −0.637780 0.770219i \(-0.720147\pi\)
0.869267 + 0.494343i \(0.164591\pi\)
\(282\) 0 0
\(283\) 105516. + 38404.9i 1.31749 + 0.479527i 0.902653 0.430369i \(-0.141616\pi\)
0.414837 + 0.909896i \(0.363839\pi\)
\(284\) 0 0
\(285\) −4769.41 6462.85i −0.0587185 0.0795673i
\(286\) 0 0
\(287\) 52327.7 143769.i 0.635284 1.74543i
\(288\) 0 0
\(289\) −54753.3 45943.4i −0.655563 0.550082i
\(290\) 0 0
\(291\) 782.172 4435.92i 0.00923669 0.0523839i
\(292\) 0 0
\(293\) −115335. + 66588.6i −1.34346 + 0.775647i −0.987314 0.158782i \(-0.949243\pi\)
−0.356147 + 0.934430i \(0.615910\pi\)
\(294\) 0 0
\(295\) −19727.1 54199.8i −0.226683 0.622807i
\(296\) 0 0
\(297\) 18919.8 + 10923.3i 0.214488 + 0.123835i
\(298\) 0 0
\(299\) 49513.3 + 59007.7i 0.553834 + 0.660034i
\(300\) 0 0
\(301\) −2599.66 14743.4i −0.0286935 0.162729i
\(302\) 0 0
\(303\) 2772.41i 0.0301975i
\(304\) 0 0
\(305\) 87130.6 0.936637
\(306\) 0 0
\(307\) −5220.79 + 920.566i −0.0553936 + 0.00976738i −0.201276 0.979535i \(-0.564509\pi\)
0.145883 + 0.989302i \(0.453398\pi\)
\(308\) 0 0
\(309\) −6524.45 + 5474.66i −0.0683324 + 0.0573377i
\(310\) 0 0
\(311\) −74776.9 + 129517.i −0.773120 + 1.33908i 0.162725 + 0.986671i \(0.447972\pi\)
−0.935845 + 0.352411i \(0.885362\pi\)
\(312\) 0 0
\(313\) 30999.8 11283.0i 0.316424 0.115169i −0.178926 0.983863i \(-0.557262\pi\)
0.495350 + 0.868694i \(0.335040\pi\)
\(314\) 0 0
\(315\) −82911.1 143606.i −0.835587 1.44728i
\(316\) 0 0
\(317\) −407.501 71.8534i −0.00405518 0.000715038i 0.171620 0.985163i \(-0.445100\pi\)
−0.175675 + 0.984448i \(0.556211\pi\)
\(318\) 0 0
\(319\) −179011. + 213337.i −1.75913 + 2.09646i
\(320\) 0 0
\(321\) −50.7481 18.4708i −0.000492504 0.000179257i
\(322\) 0 0
\(323\) 21910.7 33011.1i 0.210015 0.316413i
\(324\) 0 0
\(325\) −11167.5 + 30682.6i −0.105728 + 0.290486i
\(326\) 0 0
\(327\) 3715.18 + 3117.41i 0.0347444 + 0.0291540i
\(328\) 0 0
\(329\) 4151.08 23541.9i 0.0383504 0.217496i
\(330\) 0 0
\(331\) −114465. + 66086.3i −1.04476 + 0.603191i −0.921177 0.389143i \(-0.872771\pi\)
−0.123581 + 0.992335i \(0.539438\pi\)
\(332\) 0 0
\(333\) −66001.5 181338.i −0.595204 1.63531i
\(334\) 0 0
\(335\) 160896. + 92893.5i 1.43369 + 0.827744i
\(336\) 0 0
\(337\) −111287. 132626.i −0.979905 1.16780i −0.985817 0.167822i \(-0.946326\pi\)
0.00591259 0.999983i \(-0.498118\pi\)
\(338\) 0 0
\(339\) −2250.67 12764.2i −0.0195845 0.111069i
\(340\) 0 0
\(341\) 307849.i 2.64746i
\(342\) 0 0
\(343\) 36188.1 0.307594
\(344\) 0 0
\(345\) 19336.5 3409.55i 0.162458 0.0286457i
\(346\) 0 0
\(347\) 30558.2 25641.4i 0.253787 0.212953i −0.507014 0.861938i \(-0.669251\pi\)
0.760801 + 0.648985i \(0.224806\pi\)
\(348\) 0 0
\(349\) −50857.7 + 88088.0i −0.417547 + 0.723213i −0.995692 0.0927212i \(-0.970443\pi\)
0.578145 + 0.815934i \(0.303777\pi\)
\(350\) 0 0
\(351\) 9325.06 3394.04i 0.0756898 0.0275488i
\(352\) 0 0
\(353\) −69157.7 119785.i −0.554998 0.961284i −0.997904 0.0647160i \(-0.979386\pi\)
0.442906 0.896568i \(-0.353947\pi\)
\(354\) 0 0
\(355\) −42430.5 7481.65i −0.336684 0.0593664i
\(356\) 0 0
\(357\) −3236.21 + 3856.76i −0.0253922 + 0.0302612i
\(358\) 0 0
\(359\) 44126.7 + 16060.8i 0.342384 + 0.124617i 0.507488 0.861659i \(-0.330574\pi\)
−0.165105 + 0.986276i \(0.552796\pi\)
\(360\) 0 0
\(361\) −115964. 59463.0i −0.889836 0.456281i
\(362\) 0 0
\(363\) −5365.55 + 14741.7i −0.0407194 + 0.111876i
\(364\) 0 0
\(365\) 137381. + 115276.i 1.03119 + 0.865275i
\(366\) 0 0
\(367\) 1580.16 8961.54i 0.0117319 0.0665351i −0.978380 0.206817i \(-0.933690\pi\)
0.990112 + 0.140282i \(0.0448008\pi\)
\(368\) 0 0
\(369\) −163684. + 94503.0i −1.20214 + 0.694053i
\(370\) 0 0
\(371\) 72075.9 + 198027.i 0.523651 + 1.43872i
\(372\) 0 0
\(373\) 190559. + 110019.i 1.36966 + 0.790771i 0.990884 0.134719i \(-0.0430133\pi\)
0.378771 + 0.925490i \(0.376347\pi\)
\(374\) 0 0
\(375\) −3588.77 4276.93i −0.0255202 0.0304138i
\(376\) 0 0
\(377\) 21966.6 + 124579.i 0.154554 + 0.876521i
\(378\) 0 0
\(379\) 2519.18i 0.0175380i −0.999962 0.00876900i \(-0.997209\pi\)
0.999962 0.00876900i \(-0.00279130\pi\)
\(380\) 0 0
\(381\) 6982.64 0.0481027
\(382\) 0 0
\(383\) −82852.9 + 14609.2i −0.564820 + 0.0995930i −0.448765 0.893650i \(-0.648136\pi\)
−0.116055 + 0.993243i \(0.537025\pi\)
\(384\) 0 0
\(385\) 303214. 254427.i 2.04564 1.71649i
\(386\) 0 0
\(387\) −9247.23 + 16016.7i −0.0617433 + 0.106943i
\(388\) 0 0
\(389\) −190672. + 69399.0i −1.26005 + 0.458621i −0.883786 0.467891i \(-0.845014\pi\)
−0.376265 + 0.926512i \(0.622792\pi\)
\(390\) 0 0
\(391\) 48427.0 + 83877.9i 0.316762 + 0.548649i
\(392\) 0 0
\(393\) −4427.01 780.601i −0.0286632 0.00505410i
\(394\) 0 0
\(395\) 95333.5 113614.i 0.611014 0.728179i
\(396\) 0 0
\(397\) 173205. + 63041.5i 1.09896 + 0.399987i 0.826931 0.562303i \(-0.190085\pi\)
0.272024 + 0.962290i \(0.412307\pi\)
\(398\) 0 0
\(399\) 13797.4 + 9157.82i 0.0866663 + 0.0575236i
\(400\) 0 0
\(401\) −19800.2 + 54400.7i −0.123135 + 0.338311i −0.985910 0.167278i \(-0.946502\pi\)
0.862775 + 0.505588i \(0.168725\pi\)
\(402\) 0 0
\(403\) −107120. 89884.8i −0.659572 0.553447i
\(404\) 0 0
\(405\) −35351.7 + 200489.i −0.215526 + 1.22231i
\(406\) 0 0
\(407\) 398920. 230317.i 2.40822 1.39039i
\(408\) 0 0
\(409\) 15173.5 + 41688.8i 0.0907065 + 0.249214i 0.976748 0.214393i \(-0.0687772\pi\)
−0.886041 + 0.463607i \(0.846555\pi\)
\(410\) 0 0
\(411\) 2574.28 + 1486.26i 0.0152395 + 0.00879854i
\(412\) 0 0
\(413\) 76437.5 + 91094.6i 0.448132 + 0.534063i
\(414\) 0 0
\(415\) −4120.02 23365.8i −0.0239223 0.135670i
\(416\) 0 0
\(417\) 11209.9i 0.0644658i
\(418\) 0 0
\(419\) 107796. 0.614006 0.307003 0.951709i \(-0.400674\pi\)
0.307003 + 0.951709i \(0.400674\pi\)
\(420\) 0 0
\(421\) −185201. + 32655.9i −1.04491 + 0.184246i −0.669652 0.742675i \(-0.733557\pi\)
−0.375257 + 0.926921i \(0.622446\pi\)
\(422\) 0 0
\(423\) −22622.5 + 18982.5i −0.126433 + 0.106090i
\(424\) 0 0
\(425\) −20527.6 + 35554.9i −0.113648 + 0.196844i
\(426\) 0 0
\(427\) −168804. + 61439.8i −0.925823 + 0.336972i
\(428\) 0 0
\(429\) 5903.70 + 10225.5i 0.0320782 + 0.0555610i
\(430\) 0 0
\(431\) 83201.5 + 14670.7i 0.447895 + 0.0789760i 0.393046 0.919519i \(-0.371421\pi\)
0.0548489 + 0.998495i \(0.482532\pi\)
\(432\) 0 0
\(433\) −197252. + 235076.i −1.05207 + 1.25381i −0.0857960 + 0.996313i \(0.527343\pi\)
−0.966278 + 0.257500i \(0.917101\pi\)
\(434\) 0 0
\(435\) 30300.6 + 11028.5i 0.160130 + 0.0582826i
\(436\) 0 0
\(437\) 256330. 189165.i 1.34226 0.990552i
\(438\) 0 0
\(439\) 11453.1 31467.2i 0.0594286 0.163279i −0.906425 0.422366i \(-0.861200\pi\)
0.965854 + 0.259088i \(0.0834218\pi\)
\(440\) 0 0
\(441\) 113823. + 95509.1i 0.585267 + 0.491097i
\(442\) 0 0
\(443\) −19837.3 + 112503.i −0.101082 + 0.573265i 0.891631 + 0.452763i \(0.149562\pi\)
−0.992713 + 0.120502i \(0.961549\pi\)
\(444\) 0 0
\(445\) 213186. 123083.i 1.07656 0.621553i
\(446\) 0 0
\(447\) 3504.12 + 9627.49i 0.0175373 + 0.0481835i
\(448\) 0 0
\(449\) −28145.4 16249.7i −0.139609 0.0806035i 0.428568 0.903509i \(-0.359018\pi\)
−0.568178 + 0.822906i \(0.692351\pi\)
\(450\) 0 0
\(451\) −289999. 345607.i −1.42575 1.69914i
\(452\) 0 0
\(453\) −3662.32 20770.1i −0.0178468 0.101214i
\(454\) 0 0
\(455\) 179794.i 0.868467i
\(456\) 0 0
\(457\) 180019. 0.861956 0.430978 0.902362i \(-0.358169\pi\)
0.430978 + 0.902362i \(0.358169\pi\)
\(458\) 0 0
\(459\) 12288.0 2166.70i 0.0583250 0.0102843i
\(460\) 0 0
\(461\) −227440. + 190845.i −1.07020 + 0.898005i −0.995071 0.0991692i \(-0.968381\pi\)
−0.0751296 + 0.997174i \(0.523937\pi\)
\(462\) 0 0
\(463\) −30464.3 + 52765.7i −0.142112 + 0.246144i −0.928292 0.371853i \(-0.878723\pi\)
0.786180 + 0.617998i \(0.212056\pi\)
\(464\) 0 0
\(465\) −33494.7 + 12191.1i −0.154907 + 0.0563815i
\(466\) 0 0
\(467\) 127334. + 220550.i 0.583864 + 1.01128i 0.995016 + 0.0997156i \(0.0317933\pi\)
−0.411152 + 0.911567i \(0.634873\pi\)
\(468\) 0 0
\(469\) −377219. 66514.0i −1.71494 0.302390i
\(470\) 0 0
\(471\) 5335.38 6358.46i 0.0240505 0.0286622i
\(472\) 0 0
\(473\) −41484.0 15098.9i −0.185421 0.0674876i
\(474\) 0 0
\(475\) 123770. + 54006.0i 0.548564 + 0.239362i
\(476\) 0 0
\(477\) 89040.0 244635.i 0.391335 1.07518i
\(478\) 0 0
\(479\) −44696.4 37504.7i −0.194806 0.163461i 0.540168 0.841558i \(-0.318361\pi\)
−0.734973 + 0.678096i \(0.762805\pi\)
\(480\) 0 0
\(481\) 36333.4 206057.i 0.157042 0.890629i
\(482\) 0 0
\(483\) −35057.8 + 20240.6i −0.150276 + 0.0867620i
\(484\) 0 0
\(485\) 69175.8 + 190059.i 0.294084 + 0.807988i
\(486\) 0 0
\(487\) −64126.5 37023.4i −0.270383 0.156106i 0.358679 0.933461i \(-0.383227\pi\)
−0.629062 + 0.777355i \(0.716561\pi\)
\(488\) 0 0
\(489\) −2264.45 2698.66i −0.00946988 0.0112858i
\(490\) 0 0
\(491\) 34828.9 + 197524.i 0.144470 + 0.819328i 0.967792 + 0.251753i \(0.0810071\pi\)
−0.823322 + 0.567575i \(0.807882\pi\)
\(492\) 0 0
\(493\) 159058.i 0.654428i
\(494\) 0 0
\(495\) −488980. −1.99563
\(496\) 0 0
\(497\) 87479.4 15425.0i 0.354155 0.0624470i
\(498\) 0 0
\(499\) −129561. + 108714.i −0.520322 + 0.436602i −0.864744 0.502213i \(-0.832519\pi\)
0.344422 + 0.938815i \(0.388075\pi\)
\(500\) 0 0
\(501\) 13351.6 23125.7i 0.0531936 0.0921340i
\(502\) 0 0
\(503\) −128080. + 46617.4i −0.506228 + 0.184252i −0.582493 0.812836i \(-0.697923\pi\)
0.0762650 + 0.997088i \(0.475700\pi\)
\(504\) 0 0
\(505\) −62243.9 107810.i −0.244070 0.422741i
\(506\) 0 0
\(507\) −14517.6 2559.84i −0.0564779 0.00995857i
\(508\) 0 0
\(509\) 301408. 359204.i 1.16337 1.38645i 0.255708 0.966754i \(-0.417691\pi\)
0.907663 0.419699i \(-0.137864\pi\)
\(510\) 0 0
\(511\) −347444. 126459.i −1.33059 0.484294i
\(512\) 0 0
\(513\) −11605.7 39366.0i −0.0440998 0.149585i
\(514\) 0 0
\(515\) 130801. 359373.i 0.493171 1.35498i
\(516\) 0 0
\(517\) −53999.9 45311.3i −0.202028 0.169522i
\(518\) 0 0
\(519\) 410.623 2328.76i 0.00152444 0.00864550i
\(520\) 0 0
\(521\) −72663.0 + 41952.0i −0.267694 + 0.154553i −0.627839 0.778343i \(-0.716060\pi\)
0.360145 + 0.932896i \(0.382727\pi\)
\(522\) 0 0
\(523\) −150695. 414032.i −0.550930 1.51367i −0.832443 0.554110i \(-0.813059\pi\)
0.281514 0.959557i \(-0.409164\pi\)
\(524\) 0 0
\(525\) −14860.6 8579.76i −0.0539160 0.0311284i
\(526\) 0 0
\(527\) −113018. 134690.i −0.406937 0.484969i
\(528\) 0 0
\(529\) 86636.0 + 491337.i 0.309590 + 1.75577i
\(530\) 0 0
\(531\) 146904.i 0.521009i
\(532\) 0 0
\(533\) −204932. −0.721364
\(534\) 0 0
\(535\) 2388.12 421.089i 0.00834349 0.00147118i
\(536\) 0 0
\(537\) 2701.15 2266.54i 0.00936700 0.00785985i
\(538\) 0 0
\(539\) −177337. + 307157.i −0.610411 + 1.05726i
\(540\) 0 0
\(541\) −234761. + 85446.1i −0.802106 + 0.291943i −0.710359 0.703840i \(-0.751467\pi\)
−0.0917472 + 0.995782i \(0.529245\pi\)
\(542\) 0 0
\(543\) 4498.53 + 7791.68i 0.0152571 + 0.0264260i
\(544\) 0 0
\(545\) −214461. 37815.2i −0.722029 0.127313i
\(546\) 0 0
\(547\) 284604. 339177.i 0.951187 1.13358i −0.0397445 0.999210i \(-0.512654\pi\)
0.990931 0.134370i \(-0.0429011\pi\)
\(548\) 0 0
\(549\) 208535. + 75900.5i 0.691885 + 0.251826i
\(550\) 0 0
\(551\) 519888. 58556.6i 1.71241 0.192873i
\(552\) 0 0
\(553\) −104582. + 287337.i −0.341985 + 0.939595i
\(554\) 0 0
\(555\) −40856.6 34282.7i −0.132640 0.111299i
\(556\) 0 0
\(557\) 18753.5 106357.i 0.0604467 0.342810i −0.939553 0.342403i \(-0.888759\pi\)
1.00000 0.000407388i \(-0.000129676\pi\)
\(558\) 0 0
\(559\) −17366.2 + 10026.4i −0.0555753 + 0.0320864i
\(560\) 0 0
\(561\) 5077.72 + 13950.9i 0.0161340 + 0.0443279i
\(562\) 0 0
\(563\) 17056.8 + 9847.76i 0.0538123 + 0.0310685i 0.526665 0.850073i \(-0.323442\pi\)
−0.472852 + 0.881142i \(0.656776\pi\)
\(564\) 0 0
\(565\) 374093. + 445827.i 1.17188 + 1.39659i
\(566\) 0 0
\(567\) −72884.9 413351.i −0.226710 1.28574i
\(568\) 0 0
\(569\) 558758.i 1.72584i 0.505344 + 0.862918i \(0.331365\pi\)
−0.505344 + 0.862918i \(0.668635\pi\)
\(570\) 0 0
\(571\) 538854. 1.65272 0.826359 0.563144i \(-0.190408\pi\)
0.826359 + 0.563144i \(0.190408\pi\)
\(572\) 0 0
\(573\) 12071.5 2128.53i 0.0367665 0.00648293i
\(574\) 0 0
\(575\) −252876. + 212188.i −0.764843 + 0.641779i
\(576\) 0 0
\(577\) 140861. 243978.i 0.423096 0.732824i −0.573145 0.819454i \(-0.694277\pi\)
0.996240 + 0.0866306i \(0.0276100\pi\)
\(578\) 0 0
\(579\) 20614.3 7502.99i 0.0614910 0.0223809i
\(580\) 0 0
\(581\) 24458.3 + 42363.0i 0.0724559 + 0.125497i
\(582\) 0 0
\(583\) 611981. + 107909.i 1.80053 + 0.317482i
\(584\) 0 0
\(585\) −142771. + 170147.i −0.417184 + 0.497180i
\(586\) 0 0
\(587\) −303711. 110542.i −0.881423 0.320812i −0.138639 0.990343i \(-0.544273\pi\)
−0.742784 + 0.669531i \(0.766495\pi\)
\(588\) 0 0
\(589\) −398632. + 418990.i −1.14906 + 1.20774i
\(590\) 0 0
\(591\) −11460.0 + 31486.0i −0.0328101 + 0.0901451i
\(592\) 0 0
\(593\) −65213.6 54720.7i −0.185451 0.155612i 0.545336 0.838218i \(-0.316402\pi\)
−0.730787 + 0.682606i \(0.760847\pi\)
\(594\) 0 0
\(595\) 39256.3 222633.i 0.110886 0.628863i
\(596\) 0 0
\(597\) −31927.5 + 18433.4i −0.0895811 + 0.0517197i
\(598\) 0 0
\(599\) 129481. + 355746.i 0.360871 + 0.991485i 0.978722 + 0.205190i \(0.0657813\pi\)
−0.617851 + 0.786295i \(0.711997\pi\)
\(600\) 0 0
\(601\) 334921. + 193367.i 0.927244 + 0.535345i 0.885939 0.463802i \(-0.153515\pi\)
0.0413051 + 0.999147i \(0.486848\pi\)
\(602\) 0 0
\(603\) 304162. + 362486.i 0.836509 + 0.996913i
\(604\) 0 0
\(605\) −122322. 693721.i −0.334189 1.89528i
\(606\) 0 0
\(607\) 243144.i 0.659912i −0.943996 0.329956i \(-0.892966\pi\)
0.943996 0.329956i \(-0.107034\pi\)
\(608\) 0 0
\(609\) −66480.3 −0.179250
\(610\) 0 0
\(611\) −31533.4 + 5560.19i −0.0844673 + 0.0148939i
\(612\) 0 0
\(613\) 177368. 148829.i 0.472012 0.396065i −0.375516 0.926816i \(-0.622534\pi\)
0.847528 + 0.530751i \(0.178090\pi\)
\(614\) 0 0
\(615\) −26118.7 + 45238.9i −0.0690559 + 0.119608i
\(616\) 0 0
\(617\) 512867. 186668.i 1.34721 0.490343i 0.435132 0.900366i \(-0.356702\pi\)
0.912075 + 0.410023i \(0.134479\pi\)
\(618\) 0 0
\(619\) −265793. 460367.i −0.693685 1.20150i −0.970622 0.240610i \(-0.922653\pi\)
0.276937 0.960888i \(-0.410681\pi\)
\(620\) 0 0
\(621\) 98801.8 + 17421.4i 0.256202 + 0.0451752i
\(622\) 0 0
\(623\) −326229. + 388784.i −0.840517 + 1.00169i
\(624\) 0 0
\(625\) 455272. + 165705.i 1.16550 + 0.424206i
\(626\) 0 0
\(627\) 43729.8 21732.7i 0.111235 0.0552813i
\(628\) 0 0
\(629\) 89980.8 247220.i 0.227430 0.624860i
\(630\) 0 0
\(631\) 208648. + 175076.i 0.524029 + 0.439712i 0.866033 0.499986i \(-0.166662\pi\)
−0.342005 + 0.939698i \(0.611106\pi\)
\(632\) 0 0
\(633\) 5541.27 31426.1i 0.0138293 0.0784301i
\(634\) 0 0
\(635\) −271532. + 156769.i −0.673400 + 0.388788i
\(636\) 0 0
\(637\) 55101.4 + 151390.i 0.135795 + 0.373093i
\(638\) 0 0
\(639\) −95034.2 54868.0i −0.232744 0.134375i
\(640\) 0 0
\(641\) −277020. 330140.i −0.674210 0.803492i 0.315140 0.949045i \(-0.397948\pi\)
−0.989351 + 0.145553i \(0.953504\pi\)
\(642\) 0 0
\(643\) 84349.0 + 478367.i 0.204013 + 1.15702i 0.898985 + 0.437979i \(0.144306\pi\)
−0.694972 + 0.719037i \(0.744583\pi\)
\(644\) 0 0
\(645\) 5111.49i 0.0122865i
\(646\) 0 0
\(647\) 95597.5 0.228369 0.114185 0.993460i \(-0.463574\pi\)
0.114185 + 0.993460i \(0.463574\pi\)
\(648\) 0 0
\(649\) 345333. 60891.6i 0.819877 0.144567i
\(650\) 0 0
\(651\) 56295.2 47237.3i 0.132834 0.111461i
\(652\) 0 0
\(653\) 251342. 435337.i 0.589438 1.02094i −0.404868 0.914375i \(-0.632683\pi\)
0.994306 0.106561i \(-0.0339841\pi\)
\(654\) 0 0
\(655\) 189677. 69036.8i 0.442112 0.160916i
\(656\) 0 0
\(657\) 228383. + 395572.i 0.529095 + 0.916419i
\(658\) 0 0
\(659\) 240961. + 42488.0i 0.554851 + 0.0978352i 0.444041 0.896006i \(-0.353544\pi\)
0.110810 + 0.993842i \(0.464656\pi\)
\(660\) 0 0
\(661\) 35563.9 42383.4i 0.0813967 0.0970048i −0.723809 0.690000i \(-0.757610\pi\)
0.805206 + 0.592996i \(0.202055\pi\)
\(662\) 0 0
\(663\) 6336.99 + 2306.48i 0.0144164 + 0.00524713i
\(664\) 0 0
\(665\) −742138. 46349.2i −1.67819 0.104809i
\(666\) 0 0
\(667\) −437414. + 1.20179e6i −0.983198 + 2.70132i
\(668\) 0 0
\(669\) −25465.6 21368.2i −0.0568987 0.0477436i
\(670\) 0 0
\(671\) −91984.8 + 521672.i −0.204301 + 1.15865i
\(672\) 0 0
\(673\) −371361. + 214405.i −0.819909 + 0.473375i −0.850385 0.526161i \(-0.823631\pi\)
0.0304761 + 0.999535i \(0.490298\pi\)
\(674\) 0 0
\(675\) 14545.1 + 39962.3i 0.0319234 + 0.0877088i
\(676\) 0 0
\(677\) −743727. 429391.i −1.62269 0.936862i −0.986196 0.165583i \(-0.947049\pi\)
−0.636497 0.771279i \(-0.719617\pi\)
\(678\) 0 0
\(679\) −268038. 319436.i −0.581376 0.692857i
\(680\) 0 0
\(681\) −1567.90 8892.02i −0.00338084 0.0191737i
\(682\) 0 0
\(683\) 231818.i 0.496942i −0.968639 0.248471i \(-0.920072\pi\)
0.968639 0.248471i \(-0.0799281\pi\)
\(684\) 0 0
\(685\) −133473. −0.284455
\(686\) 0 0
\(687\) −48910.5 + 8624.24i −0.103631 + 0.0182729i
\(688\) 0 0
\(689\) 216232. 181441.i 0.455494 0.382205i
\(690\) 0 0
\(691\) 300258. 520062.i 0.628837 1.08918i −0.358948 0.933358i \(-0.616864\pi\)
0.987785 0.155821i \(-0.0498022\pi\)
\(692\) 0 0
\(693\) 947335. 344802.i 1.97259 0.717965i
\(694\) 0 0
\(695\) 251676. + 435916.i 0.521041 + 0.902470i
\(696\) 0 0
\(697\) −253760. 44744.7i −0.522345 0.0921035i
\(698\) 0 0
\(699\) 10371.7 12360.5i 0.0212274 0.0252978i
\(700\) 0 0
\(701\) −256747. 93448.3i −0.522480 0.190167i 0.0672977 0.997733i \(-0.478562\pi\)
−0.589777 + 0.807566i \(0.700785\pi\)
\(702\) 0 0
\(703\) −841175. 203093.i −1.70206 0.410945i
\(704\) 0 0
\(705\) −2791.54 + 7669.68i −0.00561649 + 0.0154312i
\(706\) 0 0
\(707\) 196611. + 164976.i 0.393341 + 0.330052i
\(708\) 0 0
\(709\) 71493.5 405460.i 0.142224 0.806595i −0.827330 0.561717i \(-0.810141\pi\)
0.969554 0.244878i \(-0.0787478\pi\)
\(710\) 0 0
\(711\) 327138. 188873.i 0.647130 0.373621i
\(712\) 0 0
\(713\) −483524. 1.32847e6i −0.951128 2.61320i
\(714\) 0 0
\(715\) −459150. 265091.i −0.898137 0.518540i
\(716\) 0 0
\(717\) 19590.5 + 23347.1i 0.0381073 + 0.0454145i
\(718\) 0 0
\(719\) −123960. 703011.i −0.239786 1.35989i −0.832297 0.554330i \(-0.812975\pi\)
0.592511 0.805562i \(-0.298137\pi\)
\(720\) 0 0
\(721\) 788474.i 1.51676i
\(722\) 0 0
\(723\) 27673.1 0.0529397
\(724\) 0 0
\(725\) −533880. + 94137.5i −1.01571 + 0.179096i
\(726\) 0 0
\(727\) 767353. 643885.i 1.45186 1.21826i 0.520660 0.853764i \(-0.325686\pi\)
0.931205 0.364495i \(-0.118758\pi\)
\(728\) 0 0
\(729\) −256017. + 443434.i −0.481741 + 0.834400i
\(730\) 0 0
\(731\) −23693.2 + 8623.61i −0.0443393 + 0.0161382i
\(732\) 0 0
\(733\) −201153. 348407.i −0.374385 0.648454i 0.615850 0.787864i \(-0.288813\pi\)
−0.990235 + 0.139410i \(0.955480\pi\)
\(734\) 0 0
\(735\) 40442.2 + 7131.04i 0.0748617 + 0.0132001i
\(736\) 0 0
\(737\) −726036. + 865256.i −1.33667 + 1.59298i
\(738\) 0 0
\(739\) −840729. 306000.i −1.53946 0.560316i −0.573541 0.819177i \(-0.694431\pi\)
−0.965915 + 0.258860i \(0.916653\pi\)
\(740\) 0 0
\(741\) 5205.87 21561.8i 0.00948106 0.0392689i
\(742\) 0 0
\(743\) −188375. + 517555.i −0.341228 + 0.937516i 0.643811 + 0.765185i \(0.277352\pi\)
−0.985039 + 0.172332i \(0.944870\pi\)
\(744\) 0 0
\(745\) −352413. 295709.i −0.634949 0.532785i
\(746\) 0 0
\(747\) 10493.5 59511.8i 0.0188053 0.106650i
\(748\) 0 0
\(749\) −4329.74 + 2499.77i −0.00771788 + 0.00445592i
\(750\) 0 0
\(751\) 348702. + 958051.i 0.618265 + 1.69867i 0.711193 + 0.702997i \(0.248155\pi\)
−0.0929277 + 0.995673i \(0.529623\pi\)
\(752\) 0 0
\(753\) 38254.6 + 22086.3i 0.0674673 + 0.0389523i
\(754\) 0 0
\(755\) 608729. + 725455.i 1.06790 + 1.27267i
\(756\) 0 0
\(757\) −81811.7 463977.i −0.142766 0.809664i −0.969134 0.246534i \(-0.920708\pi\)
0.826368 0.563130i \(-0.190403\pi\)
\(758\) 0 0
\(759\) 119372.i 0.207214i
\(760\) 0 0
\(761\) −371141. −0.640869 −0.320434 0.947271i \(-0.603829\pi\)
−0.320434 + 0.947271i \(0.603829\pi\)
\(762\) 0 0
\(763\) 442155. 77963.9i 0.759496 0.133920i
\(764\) 0 0
\(765\) −213938. + 179515.i −0.365565 + 0.306746i
\(766\) 0 0
\(767\) 79641.1 137942.i 0.135378 0.234481i
\(768\) 0 0
\(769\) 443948. 161584.i 0.750723 0.273241i 0.0618129 0.998088i \(-0.480312\pi\)
0.688910 + 0.724847i \(0.258090\pi\)
\(770\) 0 0
\(771\) −28081.6 48638.8i −0.0472404 0.0818228i
\(772\) 0 0
\(773\) 891114. + 157127.i 1.49133 + 0.262962i 0.859096 0.511814i \(-0.171026\pi\)
0.632236 + 0.774776i \(0.282137\pi\)
\(774\) 0 0
\(775\) 385199. 459062.i 0.641330 0.764308i
\(776\) 0 0
\(777\) 103329. + 37608.6i 0.171151 + 0.0622938i
\(778\) 0 0
\(779\) −52829.3 + 845897.i −0.0870562 + 1.39393i
\(780\) 0 0
\(781\) 89588.8 246143.i 0.146876 0.403539i
\(782\) 0 0
\(783\) 126214. + 105906.i 0.205865 + 0.172741i
\(784\) 0 0
\(785\) −64720.0 + 367045.i −0.105027 + 0.595635i
\(786\) 0 0
\(787\) 27445.8 15845.8i 0.0443125 0.0255838i −0.477680 0.878534i \(-0.658522\pi\)
0.521993 + 0.852950i \(0.325189\pi\)
\(788\) 0 0
\(789\) 13261.0 + 36434.4i 0.0213021 + 0.0585271i
\(790\) 0 0
\(791\) −1.03913e6 599942.i −1.66080 0.958863i
\(792\)