Properties

Label 76.5.j.a.21.1
Level $76$
Weight $5$
Character 76.21
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 21.1
Character \(\chi\) \(=\) 76.21
Dual form 76.5.j.a.29.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.26669 + 9.85185i) q^{3} +(-19.2135 + 6.99315i) q^{5} +(1.56085 + 2.70347i) q^{7} +(-14.6554 - 83.1149i) q^{9} +O(q^{10})\) \(q+(-8.26669 + 9.85185i) q^{3} +(-19.2135 + 6.99315i) q^{5} +(1.56085 + 2.70347i) q^{7} +(-14.6554 - 83.1149i) q^{9} +(57.2296 - 99.1246i) q^{11} +(-73.1984 - 87.2344i) q^{13} +(89.9367 - 247.099i) q^{15} +(11.6409 - 66.0190i) q^{17} +(113.685 - 342.632i) q^{19} +(-39.5372 - 6.97148i) q^{21} +(-229.764 - 83.6274i) q^{23} +(-158.522 + 133.016i) q^{25} +(37.8358 + 21.8445i) q^{27} +(-1363.50 + 240.421i) q^{29} +(708.058 - 408.797i) q^{31} +(503.462 + 1383.25i) q^{33} +(-48.8952 - 41.0279i) q^{35} +1099.85i q^{37} +1464.53 q^{39} +(-51.0022 + 60.7821i) q^{41} +(-317.379 + 115.516i) q^{43} +(862.817 + 1494.44i) q^{45} +(-275.570 - 1562.84i) q^{47} +(1195.63 - 2070.89i) q^{49} +(554.178 + 660.443i) q^{51} +(-876.707 + 2408.73i) q^{53} +(-406.389 + 2304.75i) q^{55} +(2435.76 + 3952.44i) q^{57} +(-4803.44 - 846.977i) q^{59} +(-1504.98 - 547.766i) q^{61} +(201.824 - 169.350i) q^{63} +(2016.44 + 1164.19i) q^{65} +(-4753.54 + 838.177i) q^{67} +(2723.28 - 1572.28i) q^{69} +(183.202 + 503.344i) q^{71} +(-5428.81 - 4555.31i) q^{73} -2661.34i q^{75} +357.307 q^{77} +(7499.16 - 8937.15i) q^{79} +(5895.91 - 2145.94i) q^{81} +(-3230.90 - 5596.08i) q^{83} +(238.018 + 1349.86i) q^{85} +(8903.00 - 15420.5i) q^{87} +(-6885.48 - 8205.80i) q^{89} +(121.584 - 334.049i) q^{91} +(-1825.88 + 10355.1i) q^{93} +(211.792 + 7378.19i) q^{95} +(-4876.88 - 859.926i) q^{97} +(-9077.46 - 3303.92i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −8.26669 + 9.85185i −0.918521 + 1.09465i 0.0767054 + 0.997054i \(0.475560\pi\)
−0.995226 + 0.0975965i \(0.968885\pi\)
\(4\) 0 0
\(5\) −19.2135 + 6.99315i −0.768541 + 0.279726i −0.696386 0.717667i \(-0.745210\pi\)
−0.0721550 + 0.997393i \(0.522988\pi\)
\(6\) 0 0
\(7\) 1.56085 + 2.70347i 0.0318540 + 0.0551728i 0.881513 0.472160i \(-0.156525\pi\)
−0.849659 + 0.527333i \(0.823192\pi\)
\(8\) 0 0
\(9\) −14.6554 83.1149i −0.180931 1.02611i
\(10\) 0 0
\(11\) 57.2296 99.1246i 0.472972 0.819212i −0.526549 0.850145i \(-0.676514\pi\)
0.999521 + 0.0309329i \(0.00984782\pi\)
\(12\) 0 0
\(13\) −73.1984 87.2344i −0.433127 0.516180i 0.504695 0.863298i \(-0.331605\pi\)
−0.937822 + 0.347118i \(0.887160\pi\)
\(14\) 0 0
\(15\) 89.9367 247.099i 0.399719 1.09822i
\(16\) 0 0
\(17\) 11.6409 66.0190i 0.0402800 0.228439i −0.958022 0.286696i \(-0.907443\pi\)
0.998302 + 0.0582566i \(0.0185541\pi\)
\(18\) 0 0
\(19\) 113.685 342.632i 0.314916 0.949119i
\(20\) 0 0
\(21\) −39.5372 6.97148i −0.0896536 0.0158083i
\(22\) 0 0
\(23\) −229.764 83.6274i −0.434337 0.158086i 0.115593 0.993297i \(-0.463123\pi\)
−0.549930 + 0.835211i \(0.685346\pi\)
\(24\) 0 0
\(25\) −158.522 + 133.016i −0.253636 + 0.212826i
\(26\) 0 0
\(27\) 37.8358 + 21.8445i 0.0519010 + 0.0299651i
\(28\) 0 0
\(29\) −1363.50 + 240.421i −1.62128 + 0.285875i −0.909243 0.416266i \(-0.863338\pi\)
−0.712037 + 0.702142i \(0.752227\pi\)
\(30\) 0 0
\(31\) 708.058 408.797i 0.736793 0.425387i −0.0841094 0.996457i \(-0.526805\pi\)
0.820902 + 0.571069i \(0.193471\pi\)
\(32\) 0 0
\(33\) 503.462 + 1383.25i 0.462316 + 1.27020i
\(34\) 0 0
\(35\) −48.8952 41.0279i −0.0399144 0.0334922i
\(36\) 0 0
\(37\) 1099.85i 0.803397i 0.915772 + 0.401699i \(0.131580\pi\)
−0.915772 + 0.401699i \(0.868420\pi\)
\(38\) 0 0
\(39\) 1464.53 0.962872
\(40\) 0 0
\(41\) −51.0022 + 60.7821i −0.0303404 + 0.0361583i −0.781001 0.624529i \(-0.785291\pi\)
0.750661 + 0.660688i \(0.229735\pi\)
\(42\) 0 0
\(43\) −317.379 + 115.516i −0.171649 + 0.0624751i −0.426415 0.904528i \(-0.640224\pi\)
0.254766 + 0.967003i \(0.418001\pi\)
\(44\) 0 0
\(45\) 862.817 + 1494.44i 0.426083 + 0.737997i
\(46\) 0 0
\(47\) −275.570 1562.84i −0.124749 0.707486i −0.981457 0.191684i \(-0.938605\pi\)
0.856708 0.515802i \(-0.172506\pi\)
\(48\) 0 0
\(49\) 1195.63 2070.89i 0.497971 0.862510i
\(50\) 0 0
\(51\) 554.178 + 660.443i 0.213063 + 0.253919i
\(52\) 0 0
\(53\) −876.707 + 2408.73i −0.312106 + 0.857505i 0.680125 + 0.733097i \(0.261926\pi\)
−0.992231 + 0.124409i \(0.960297\pi\)
\(54\) 0 0
\(55\) −406.389 + 2304.75i −0.134344 + 0.761900i
\(56\) 0 0
\(57\) 2435.76 + 3952.44i 0.749697 + 1.21651i
\(58\) 0 0
\(59\) −4803.44 846.977i −1.37990 0.243314i −0.566044 0.824375i \(-0.691527\pi\)
−0.813860 + 0.581061i \(0.802638\pi\)
\(60\) 0 0
\(61\) −1504.98 547.766i −0.404455 0.147209i 0.131779 0.991279i \(-0.457931\pi\)
−0.536234 + 0.844070i \(0.680153\pi\)
\(62\) 0 0
\(63\) 201.824 169.350i 0.0508500 0.0426682i
\(64\) 0 0
\(65\) 2016.44 + 1164.19i 0.477264 + 0.275549i
\(66\) 0 0
\(67\) −4753.54 + 838.177i −1.05893 + 0.186718i −0.675881 0.737010i \(-0.736237\pi\)
−0.383048 + 0.923728i \(0.625126\pi\)
\(68\) 0 0
\(69\) 2723.28 1572.28i 0.571997 0.330242i
\(70\) 0 0
\(71\) 183.202 + 503.344i 0.0363425 + 0.0998501i 0.956537 0.291612i \(-0.0941916\pi\)
−0.920194 + 0.391462i \(0.871969\pi\)
\(72\) 0 0
\(73\) −5428.81 4555.31i −1.01873 0.854816i −0.0292626 0.999572i \(-0.509316\pi\)
−0.989467 + 0.144756i \(0.953760\pi\)
\(74\) 0 0
\(75\) 2661.34i 0.473127i
\(76\) 0 0
\(77\) 357.307 0.0602643
\(78\) 0 0
\(79\) 7499.16 8937.15i 1.20160 1.43201i 0.328469 0.944515i \(-0.393467\pi\)
0.873127 0.487492i \(-0.162088\pi\)
\(80\) 0 0
\(81\) 5895.91 2145.94i 0.898629 0.327074i
\(82\) 0 0
\(83\) −3230.90 5596.08i −0.468994 0.812321i 0.530378 0.847761i \(-0.322050\pi\)
−0.999372 + 0.0354403i \(0.988717\pi\)
\(84\) 0 0
\(85\) 238.018 + 1349.86i 0.0329436 + 0.186832i
\(86\) 0 0
\(87\) 8903.00 15420.5i 1.17625 2.03732i
\(88\) 0 0
\(89\) −6885.48 8205.80i −0.869269 1.03595i −0.999014 0.0444070i \(-0.985860\pi\)
0.129745 0.991547i \(-0.458584\pi\)
\(90\) 0 0
\(91\) 121.584 334.049i 0.0146823 0.0403392i
\(92\) 0 0
\(93\) −1825.88 + 10355.1i −0.211109 + 1.19726i
\(94\) 0 0
\(95\) 211.792 + 7378.19i 0.0234672 + 0.817528i
\(96\) 0 0
\(97\) −4876.88 859.926i −0.518321 0.0913940i −0.0916331 0.995793i \(-0.529209\pi\)
−0.426688 + 0.904399i \(0.640320\pi\)
\(98\) 0 0
\(99\) −9077.46 3303.92i −0.926177 0.337101i
\(100\) 0 0
\(101\) −10204.2 + 8562.37i −1.00032 + 0.839366i −0.987028 0.160546i \(-0.948675\pi\)
−0.0132891 + 0.999912i \(0.504230\pi\)
\(102\) 0 0
\(103\) 17592.0 + 10156.8i 1.65822 + 0.957372i 0.973537 + 0.228529i \(0.0733914\pi\)
0.684680 + 0.728844i \(0.259942\pi\)
\(104\) 0 0
\(105\) 808.402 142.543i 0.0733244 0.0129291i
\(106\) 0 0
\(107\) −446.474 + 257.772i −0.0389968 + 0.0225148i −0.519372 0.854548i \(-0.673834\pi\)
0.480375 + 0.877063i \(0.340501\pi\)
\(108\) 0 0
\(109\) 1442.56 + 3963.39i 0.121417 + 0.333591i 0.985480 0.169794i \(-0.0543101\pi\)
−0.864062 + 0.503385i \(0.832088\pi\)
\(110\) 0 0
\(111\) −10835.6 9092.12i −0.879439 0.737937i
\(112\) 0 0
\(113\) 21932.9i 1.71767i 0.512251 + 0.858836i \(0.328812\pi\)
−0.512251 + 0.858836i \(0.671188\pi\)
\(114\) 0 0
\(115\) 4999.40 0.378027
\(116\) 0 0
\(117\) −6177.73 + 7362.33i −0.451292 + 0.537828i
\(118\) 0 0
\(119\) 196.650 71.5748i 0.0138867 0.00505436i
\(120\) 0 0
\(121\) 770.041 + 1333.75i 0.0525949 + 0.0910970i
\(122\) 0 0
\(123\) −177.197 1004.93i −0.0117124 0.0664243i
\(124\) 0 0
\(125\) 8505.14 14731.3i 0.544329 0.942805i
\(126\) 0 0
\(127\) 8629.27 + 10284.0i 0.535016 + 0.637607i 0.964063 0.265675i \(-0.0855949\pi\)
−0.429047 + 0.903282i \(0.641151\pi\)
\(128\) 0 0
\(129\) 1485.62 4081.71i 0.0892747 0.245280i
\(130\) 0 0
\(131\) −3972.35 + 22528.3i −0.231476 + 1.31276i 0.618435 + 0.785836i \(0.287767\pi\)
−0.849910 + 0.526927i \(0.823344\pi\)
\(132\) 0 0
\(133\) 1103.74 227.453i 0.0623970 0.0128585i
\(134\) 0 0
\(135\) −879.722 155.119i −0.0482701 0.00851132i
\(136\) 0 0
\(137\) −3938.12 1433.36i −0.209820 0.0763684i 0.234972 0.972002i \(-0.424500\pi\)
−0.444792 + 0.895634i \(0.646722\pi\)
\(138\) 0 0
\(139\) 17460.2 14650.9i 0.903691 0.758287i −0.0672169 0.997738i \(-0.521412\pi\)
0.970908 + 0.239451i \(0.0769675\pi\)
\(140\) 0 0
\(141\) 17674.9 + 10204.6i 0.889034 + 0.513284i
\(142\) 0 0
\(143\) −12836.2 + 2263.37i −0.627717 + 0.110684i
\(144\) 0 0
\(145\) 24516.3 14154.5i 1.16605 0.673221i
\(146\) 0 0
\(147\) 10518.2 + 28898.5i 0.486751 + 1.33734i
\(148\) 0 0
\(149\) −24075.2 20201.5i −1.08442 0.909937i −0.0881403 0.996108i \(-0.528092\pi\)
−0.996280 + 0.0861711i \(0.972537\pi\)
\(150\) 0 0
\(151\) 24250.1i 1.06355i 0.846885 + 0.531776i \(0.178475\pi\)
−0.846885 + 0.531776i \(0.821525\pi\)
\(152\) 0 0
\(153\) −5657.77 −0.241692
\(154\) 0 0
\(155\) −10745.5 + 12806.0i −0.447263 + 0.533028i
\(156\) 0 0
\(157\) 4379.41 1593.98i 0.177671 0.0646669i −0.251653 0.967818i \(-0.580974\pi\)
0.429324 + 0.903151i \(0.358752\pi\)
\(158\) 0 0
\(159\) −16483.0 28549.4i −0.651992 1.12928i
\(160\) 0 0
\(161\) −132.543 751.691i −0.00511336 0.0289993i
\(162\) 0 0
\(163\) 1164.96 2017.78i 0.0438467 0.0759448i −0.843269 0.537492i \(-0.819372\pi\)
0.887116 + 0.461547i \(0.152705\pi\)
\(164\) 0 0
\(165\) −19346.6 23056.3i −0.710617 0.846880i
\(166\) 0 0
\(167\) −16240.9 + 44621.6i −0.582341 + 1.59997i 0.201826 + 0.979421i \(0.435312\pi\)
−0.784168 + 0.620549i \(0.786910\pi\)
\(168\) 0 0
\(169\) 2707.72 15356.3i 0.0948049 0.537665i
\(170\) 0 0
\(171\) −30143.9 4427.49i −1.03088 0.151414i
\(172\) 0 0
\(173\) 7189.27 + 1267.66i 0.240211 + 0.0423557i 0.292457 0.956279i \(-0.405527\pi\)
−0.0522465 + 0.998634i \(0.516638\pi\)
\(174\) 0 0
\(175\) −607.034 220.942i −0.0198215 0.00721445i
\(176\) 0 0
\(177\) 48052.9 40321.1i 1.53381 1.28702i
\(178\) 0 0
\(179\) −14758.6 8520.88i −0.460616 0.265937i 0.251687 0.967809i \(-0.419015\pi\)
−0.712303 + 0.701872i \(0.752348\pi\)
\(180\) 0 0
\(181\) 8504.11 1499.50i 0.259580 0.0457710i −0.0423434 0.999103i \(-0.513482\pi\)
0.301924 + 0.953332i \(0.402371\pi\)
\(182\) 0 0
\(183\) 17837.7 10298.6i 0.532643 0.307522i
\(184\) 0 0
\(185\) −7691.42 21132.0i −0.224731 0.617444i
\(186\) 0 0
\(187\) −5877.90 4932.15i −0.168089 0.141043i
\(188\) 0 0
\(189\) 136.384i 0.00381803i
\(190\) 0 0
\(191\) −12103.5 −0.331776 −0.165888 0.986145i \(-0.553049\pi\)
−0.165888 + 0.986145i \(0.553049\pi\)
\(192\) 0 0
\(193\) 1445.25 1722.38i 0.0387996 0.0462396i −0.746296 0.665615i \(-0.768169\pi\)
0.785095 + 0.619375i \(0.212614\pi\)
\(194\) 0 0
\(195\) −28138.8 + 10241.7i −0.740007 + 0.269340i
\(196\) 0 0
\(197\) 11434.8 + 19805.6i 0.294642 + 0.510335i 0.974902 0.222637i \(-0.0714663\pi\)
−0.680260 + 0.732971i \(0.738133\pi\)
\(198\) 0 0
\(199\) −8358.98 47406.2i −0.211080 1.19709i −0.887580 0.460653i \(-0.847615\pi\)
0.676500 0.736442i \(-0.263496\pi\)
\(200\) 0 0
\(201\) 31038.4 53760.1i 0.768258 1.33066i
\(202\) 0 0
\(203\) −2778.18 3310.91i −0.0674169 0.0803443i
\(204\) 0 0
\(205\) 554.874 1524.50i 0.0132034 0.0362761i
\(206\) 0 0
\(207\) −3583.40 + 20322.4i −0.0836285 + 0.474281i
\(208\) 0 0
\(209\) −27457.1 30877.7i −0.628583 0.706890i
\(210\) 0 0
\(211\) 48912.2 + 8624.53i 1.09863 + 0.193718i 0.693440 0.720514i \(-0.256094\pi\)
0.405191 + 0.914232i \(0.367205\pi\)
\(212\) 0 0
\(213\) −6473.35 2356.11i −0.142682 0.0519321i
\(214\) 0 0
\(215\) 5290.14 4438.96i 0.114443 0.0960293i
\(216\) 0 0
\(217\) 2210.34 + 1276.14i 0.0469397 + 0.0271006i
\(218\) 0 0
\(219\) 89756.6 15826.5i 1.87145 0.329987i
\(220\) 0 0
\(221\) −6611.23 + 3816.99i −0.135362 + 0.0781514i
\(222\) 0 0
\(223\) 22601.8 + 62097.9i 0.454499 + 1.24873i 0.929527 + 0.368755i \(0.120216\pi\)
−0.475027 + 0.879971i \(0.657562\pi\)
\(224\) 0 0
\(225\) 13378.8 + 11226.2i 0.264273 + 0.221752i
\(226\) 0 0
\(227\) 66333.9i 1.28731i −0.765315 0.643656i \(-0.777417\pi\)
0.765315 0.643656i \(-0.222583\pi\)
\(228\) 0 0
\(229\) −92938.4 −1.77225 −0.886124 0.463449i \(-0.846612\pi\)
−0.886124 + 0.463449i \(0.846612\pi\)
\(230\) 0 0
\(231\) −2953.75 + 3520.14i −0.0553540 + 0.0659683i
\(232\) 0 0
\(233\) −84238.9 + 30660.5i −1.55168 + 0.564764i −0.968810 0.247805i \(-0.920291\pi\)
−0.582866 + 0.812569i \(0.698069\pi\)
\(234\) 0 0
\(235\) 16223.8 + 28100.5i 0.293777 + 0.508836i
\(236\) 0 0
\(237\) 26054.3 + 147761.i 0.463856 + 2.63066i
\(238\) 0 0
\(239\) −24727.5 + 42829.3i −0.432897 + 0.749800i −0.997121 0.0758216i \(-0.975842\pi\)
0.564224 + 0.825622i \(0.309175\pi\)
\(240\) 0 0
\(241\) −58976.1 70284.9i −1.01541 1.21012i −0.977521 0.210837i \(-0.932381\pi\)
−0.0378895 0.999282i \(-0.512063\pi\)
\(242\) 0 0
\(243\) −28808.5 + 79150.8i −0.487875 + 1.34043i
\(244\) 0 0
\(245\) −8490.19 + 48150.3i −0.141444 + 0.802170i
\(246\) 0 0
\(247\) −38210.9 + 15162.9i −0.626315 + 0.248535i
\(248\) 0 0
\(249\) 81840.6 + 14430.7i 1.31999 + 0.232749i
\(250\) 0 0
\(251\) 42840.7 + 15592.7i 0.680000 + 0.247500i 0.658847 0.752277i \(-0.271044\pi\)
0.0211523 + 0.999776i \(0.493267\pi\)
\(252\) 0 0
\(253\) −21438.9 + 17989.3i −0.334935 + 0.281044i
\(254\) 0 0
\(255\) −15266.3 8813.99i −0.234776 0.135548i
\(256\) 0 0
\(257\) 101228. 17849.2i 1.53262 0.270242i 0.657240 0.753681i \(-0.271724\pi\)
0.875378 + 0.483439i \(0.160612\pi\)
\(258\) 0 0
\(259\) −2973.41 + 1716.70i −0.0443257 + 0.0255914i
\(260\) 0 0
\(261\) 39965.2 + 109803.i 0.586679 + 1.61189i
\(262\) 0 0
\(263\) −55109.3 46242.2i −0.796735 0.668540i 0.150668 0.988584i \(-0.451858\pi\)
−0.947402 + 0.320045i \(0.896302\pi\)
\(264\) 0 0
\(265\) 52411.2i 0.746332i
\(266\) 0 0
\(267\) 137762. 1.93245
\(268\) 0 0
\(269\) −3420.43 + 4076.32i −0.0472690 + 0.0563330i −0.789161 0.614186i \(-0.789484\pi\)
0.741892 + 0.670519i \(0.233929\pi\)
\(270\) 0 0
\(271\) −85921.4 + 31272.8i −1.16994 + 0.425822i −0.852638 0.522503i \(-0.824998\pi\)
−0.317300 + 0.948325i \(0.602776\pi\)
\(272\) 0 0
\(273\) 2285.91 + 3959.31i 0.0306714 + 0.0531244i
\(274\) 0 0
\(275\) 4112.99 + 23325.9i 0.0543867 + 0.308442i
\(276\) 0 0
\(277\) −4412.53 + 7642.73i −0.0575080 + 0.0996068i −0.893346 0.449369i \(-0.851649\pi\)
0.835838 + 0.548976i \(0.184982\pi\)
\(278\) 0 0
\(279\) −44354.0 52859.1i −0.569803 0.679065i
\(280\) 0 0
\(281\) 12846.7 35295.9i 0.162696 0.447005i −0.831378 0.555707i \(-0.812447\pi\)
0.994074 + 0.108703i \(0.0346697\pi\)
\(282\) 0 0
\(283\) 21836.2 123839.i 0.272649 1.54627i −0.473683 0.880696i \(-0.657076\pi\)
0.746332 0.665574i \(-0.231813\pi\)
\(284\) 0 0
\(285\) −74439.6 58906.6i −0.916462 0.725228i
\(286\) 0 0
\(287\) −243.929 43.0113i −0.00296142 0.000522178i
\(288\) 0 0
\(289\) 74261.1 + 27028.8i 0.889131 + 0.323617i
\(290\) 0 0
\(291\) 48787.5 40937.6i 0.576133 0.483433i
\(292\) 0 0
\(293\) −9067.24 5234.97i −0.105618 0.0609788i 0.446260 0.894903i \(-0.352756\pi\)
−0.551879 + 0.833924i \(0.686089\pi\)
\(294\) 0 0
\(295\) 98214.1 17317.8i 1.12857 0.198998i
\(296\) 0 0
\(297\) 4330.66 2500.31i 0.0490955 0.0283453i
\(298\) 0 0
\(299\) 9523.19 + 26164.8i 0.106522 + 0.292667i
\(300\) 0 0
\(301\) −807.675 677.720i −0.00891464 0.00748027i
\(302\) 0 0
\(303\) 171313.i 1.86597i
\(304\) 0 0
\(305\) 32746.5 0.352018
\(306\) 0 0
\(307\) −2931.65 + 3493.80i −0.0311053 + 0.0370699i −0.781373 0.624064i \(-0.785480\pi\)
0.750268 + 0.661134i \(0.229925\pi\)
\(308\) 0 0
\(309\) −245491. + 89351.3i −2.57109 + 0.935802i
\(310\) 0 0
\(311\) 10594.0 + 18349.3i 0.109531 + 0.189714i 0.915580 0.402135i \(-0.131732\pi\)
−0.806049 + 0.591848i \(0.798398\pi\)
\(312\) 0 0
\(313\) −4983.07 28260.4i −0.0508637 0.288463i 0.948757 0.316007i \(-0.102342\pi\)
−0.999621 + 0.0275445i \(0.991231\pi\)
\(314\) 0 0
\(315\) −2693.45 + 4665.20i −0.0271449 + 0.0470164i
\(316\) 0 0
\(317\) −8523.70 10158.2i −0.0848222 0.101087i 0.721964 0.691931i \(-0.243240\pi\)
−0.806786 + 0.590843i \(0.798795\pi\)
\(318\) 0 0
\(319\) −54200.7 + 148915.i −0.532628 + 1.46338i
\(320\) 0 0
\(321\) 1151.33 6529.52i 0.0111735 0.0633681i
\(322\) 0 0
\(323\) −21296.8 11493.9i −0.204131 0.110170i
\(324\) 0 0
\(325\) 23207.2 + 4092.05i 0.219713 + 0.0387413i
\(326\) 0 0
\(327\) −50971.9 18552.3i −0.476689 0.173501i
\(328\) 0 0
\(329\) 3794.95 3184.34i 0.0350602 0.0294190i
\(330\) 0 0
\(331\) −99006.8 57161.6i −0.903669 0.521733i −0.0252800 0.999680i \(-0.508048\pi\)
−0.878389 + 0.477947i \(0.841381\pi\)
\(332\) 0 0
\(333\) 91414.0 16118.8i 0.824374 0.145359i
\(334\) 0 0
\(335\) 85470.7 49346.5i 0.761601 0.439711i
\(336\) 0 0
\(337\) 49309.4 + 135477.i 0.434180 + 1.19290i 0.943223 + 0.332160i \(0.107777\pi\)
−0.509043 + 0.860741i \(0.670001\pi\)
\(338\) 0 0
\(339\) −216080. 181313.i −1.88025 1.57772i
\(340\) 0 0
\(341\) 93581.3i 0.804785i
\(342\) 0 0
\(343\) 14960.0 0.127158
\(344\) 0 0
\(345\) −41328.5 + 49253.4i −0.347225 + 0.413807i
\(346\) 0 0
\(347\) −44410.2 + 16164.0i −0.368828 + 0.134243i −0.519783 0.854298i \(-0.673987\pi\)
0.150955 + 0.988541i \(0.451765\pi\)
\(348\) 0 0
\(349\) 55218.0 + 95640.3i 0.453346 + 0.785218i 0.998591 0.0530586i \(-0.0168970\pi\)
−0.545246 + 0.838276i \(0.683564\pi\)
\(350\) 0 0
\(351\) −863.927 4899.57i −0.00701234 0.0397689i
\(352\) 0 0
\(353\) 102767. 177998.i 0.824717 1.42845i −0.0774187 0.996999i \(-0.524668\pi\)
0.902136 0.431453i \(-0.141999\pi\)
\(354\) 0 0
\(355\) −7039.93 8389.86i −0.0558613 0.0665730i
\(356\) 0 0
\(357\) −920.500 + 2529.05i −0.00722250 + 0.0198436i
\(358\) 0 0
\(359\) 22847.0 129572.i 0.177272 1.00536i −0.758216 0.652003i \(-0.773929\pi\)
0.935488 0.353357i \(-0.114960\pi\)
\(360\) 0 0
\(361\) −104473. 77904.2i −0.801655 0.597787i
\(362\) 0 0
\(363\) −19505.6 3439.36i −0.148029 0.0261015i
\(364\) 0 0
\(365\) 136163. + 49559.1i 1.02205 + 0.371996i
\(366\) 0 0
\(367\) 190217. 159611.i 1.41227 1.18504i 0.456940 0.889497i \(-0.348945\pi\)
0.955331 0.295539i \(-0.0954991\pi\)
\(368\) 0 0
\(369\) 5799.36 + 3348.26i 0.0425919 + 0.0245905i
\(370\) 0 0
\(371\) −7880.34 + 1389.52i −0.0572529 + 0.0100952i
\(372\) 0 0
\(373\) 65920.1 38059.0i 0.473805 0.273552i −0.244026 0.969769i \(-0.578468\pi\)
0.717831 + 0.696217i \(0.245135\pi\)
\(374\) 0 0
\(375\) 74821.6 + 205571.i 0.532065 + 1.46184i
\(376\) 0 0
\(377\) 120779. + 101345.i 0.849783 + 0.713052i
\(378\) 0 0
\(379\) 45055.4i 0.313667i 0.987625 + 0.156834i \(0.0501286\pi\)
−0.987625 + 0.156834i \(0.949871\pi\)
\(380\) 0 0
\(381\) −172651. −1.18938
\(382\) 0 0
\(383\) 34187.5 40743.1i 0.233061 0.277752i −0.636820 0.771012i \(-0.719751\pi\)
0.869882 + 0.493261i \(0.164195\pi\)
\(384\) 0 0
\(385\) −6865.13 + 2498.70i −0.0463156 + 0.0168575i
\(386\) 0 0
\(387\) 14252.5 + 24686.0i 0.0951629 + 0.164827i
\(388\) 0 0
\(389\) 19761.0 + 112070.i 0.130590 + 0.740611i 0.977830 + 0.209401i \(0.0671514\pi\)
−0.847240 + 0.531210i \(0.821738\pi\)
\(390\) 0 0
\(391\) −8195.67 + 14195.3i −0.0536082 + 0.0928521i
\(392\) 0 0
\(393\) −189108. 225370.i −1.22440 1.45919i
\(394\) 0 0
\(395\) −81586.5 + 224157.i −0.522906 + 1.43667i
\(396\) 0 0
\(397\) −39544.9 + 224270.i −0.250905 + 1.42295i 0.555464 + 0.831541i \(0.312541\pi\)
−0.806369 + 0.591413i \(0.798570\pi\)
\(398\) 0 0
\(399\) −6883.43 + 12754.2i −0.0432374 + 0.0801136i
\(400\) 0 0
\(401\) 302245. + 53294.0i 1.87962 + 0.331428i 0.991701 0.128565i \(-0.0410370\pi\)
0.887922 + 0.459993i \(0.152148\pi\)
\(402\) 0 0
\(403\) −87489.9 31843.7i −0.538701 0.196071i
\(404\) 0 0
\(405\) −98274.3 + 82462.0i −0.599142 + 0.502740i
\(406\) 0 0
\(407\) 109022. + 62944.0i 0.658152 + 0.379984i
\(408\) 0 0
\(409\) −262236. + 46239.3i −1.56764 + 0.276417i −0.888948 0.458008i \(-0.848563\pi\)
−0.678690 + 0.734425i \(0.737452\pi\)
\(410\) 0 0
\(411\) 46676.4 26948.6i 0.276321 0.159534i
\(412\) 0 0
\(413\) −5207.67 14308.0i −0.0305312 0.0838837i
\(414\) 0 0
\(415\) 101211. + 84926.2i 0.587668 + 0.493112i
\(416\) 0 0
\(417\) 293130.i 1.68573i
\(418\) 0 0
\(419\) 115258. 0.656514 0.328257 0.944588i \(-0.393539\pi\)
0.328257 + 0.944588i \(0.393539\pi\)
\(420\) 0 0
\(421\) −22344.9 + 26629.6i −0.126071 + 0.150245i −0.825387 0.564567i \(-0.809043\pi\)
0.699317 + 0.714812i \(0.253488\pi\)
\(422\) 0 0
\(423\) −125856. + 45808.0i −0.703387 + 0.256012i
\(424\) 0 0
\(425\) 6936.24 + 12013.9i 0.0384013 + 0.0665131i
\(426\) 0 0
\(427\) −868.170 4923.64i −0.00476156 0.0270041i
\(428\) 0 0
\(429\) 83814.4 145171.i 0.455412 0.788796i
\(430\) 0 0
\(431\) −9788.89 11665.9i −0.0526962 0.0628008i 0.739053 0.673648i \(-0.235274\pi\)
−0.791749 + 0.610847i \(0.790829\pi\)
\(432\) 0 0
\(433\) 1615.17 4437.64i 0.00861474 0.0236688i −0.935311 0.353827i \(-0.884880\pi\)
0.943925 + 0.330159i \(0.107102\pi\)
\(434\) 0 0
\(435\) −63220.5 + 358541.i −0.334102 + 1.89479i
\(436\) 0 0
\(437\) −54774.2 + 69217.5i −0.286822 + 0.362454i
\(438\) 0 0
\(439\) −256793. 45279.5i −1.33246 0.234949i −0.538349 0.842722i \(-0.680952\pi\)
−0.794111 + 0.607773i \(0.792063\pi\)
\(440\) 0 0
\(441\) −189644. 69024.8i −0.975129 0.354918i
\(442\) 0 0
\(443\) 128893. 108154.i 0.656783 0.551106i −0.252338 0.967639i \(-0.581199\pi\)
0.909121 + 0.416533i \(0.136755\pi\)
\(444\) 0 0
\(445\) 189679. + 109511.i 0.957852 + 0.553016i
\(446\) 0 0
\(447\) 398045. 70186.0i 1.99213 0.351265i
\(448\) 0 0
\(449\) 44967.9 25962.2i 0.223054 0.128780i −0.384310 0.923204i \(-0.625560\pi\)
0.607364 + 0.794424i \(0.292227\pi\)
\(450\) 0 0
\(451\) 3106.16 + 8534.11i 0.0152711 + 0.0419571i
\(452\) 0 0
\(453\) −238908. 200468.i −1.16422 0.976895i
\(454\) 0 0
\(455\) 7268.52i 0.0351094i
\(456\) 0 0
\(457\) −313833. −1.50268 −0.751341 0.659915i \(-0.770592\pi\)
−0.751341 + 0.659915i \(0.770592\pi\)
\(458\) 0 0
\(459\) 1882.60 2243.59i 0.00893578 0.0106492i
\(460\) 0 0
\(461\) 285937. 104073.i 1.34545 0.489705i 0.433928 0.900947i \(-0.357127\pi\)
0.911526 + 0.411242i \(0.134905\pi\)
\(462\) 0 0
\(463\) −38084.9 65964.9i −0.177660 0.307717i 0.763418 0.645904i \(-0.223520\pi\)
−0.941079 + 0.338188i \(0.890186\pi\)
\(464\) 0 0
\(465\) −37333.0 211726.i −0.172658 0.979194i
\(466\) 0 0
\(467\) 107590. 186351.i 0.493330 0.854473i −0.506640 0.862158i \(-0.669113\pi\)
0.999970 + 0.00768464i \(0.00244612\pi\)
\(468\) 0 0
\(469\) −9685.53 11542.8i −0.0440330 0.0524764i
\(470\) 0 0
\(471\) −20499.6 + 56322.2i −0.0924068 + 0.253886i
\(472\) 0 0
\(473\) −6712.95 + 38071.0i −0.0300048 + 0.170166i
\(474\) 0 0
\(475\) 27554.0 + 69436.8i 0.122123 + 0.307753i
\(476\) 0 0
\(477\) 213050. + 37566.5i 0.936365 + 0.165106i
\(478\) 0 0
\(479\) −115062. 41879.2i −0.501490 0.182527i 0.0788742 0.996885i \(-0.474867\pi\)
−0.580364 + 0.814357i \(0.697090\pi\)
\(480\) 0 0
\(481\) 95944.8 80507.3i 0.414698 0.347973i
\(482\) 0 0
\(483\) 8501.24 + 4908.19i 0.0364408 + 0.0210391i
\(484\) 0 0
\(485\) 99715.7 17582.6i 0.423916 0.0747479i
\(486\) 0 0
\(487\) 143586. 82899.5i 0.605417 0.349538i −0.165752 0.986167i \(-0.553005\pi\)
0.771170 + 0.636630i \(0.219672\pi\)
\(488\) 0 0
\(489\) 10248.4 + 28157.4i 0.0428588 + 0.117754i
\(490\) 0 0
\(491\) −341110. 286226.i −1.41492 1.18726i −0.953996 0.299819i \(-0.903074\pi\)
−0.460924 0.887440i \(-0.652482\pi\)
\(492\) 0 0
\(493\) 92815.4i 0.381879i
\(494\) 0 0
\(495\) 197515. 0.806101
\(496\) 0 0
\(497\) −1074.82 + 1280.93i −0.00435136 + 0.00518575i
\(498\) 0 0
\(499\) 30922.7 11254.9i 0.124187 0.0452003i −0.279179 0.960239i \(-0.590062\pi\)
0.403366 + 0.915039i \(0.367840\pi\)
\(500\) 0 0
\(501\) −305346. 528876.i −1.21651 2.10707i
\(502\) 0 0
\(503\) 9171.59 + 52014.6i 0.0362500 + 0.205584i 0.997553 0.0699076i \(-0.0222704\pi\)
−0.961303 + 0.275492i \(0.911159\pi\)
\(504\) 0 0
\(505\) 136181. 235873.i 0.533992 0.924902i
\(506\) 0 0
\(507\) 128904. + 153621.i 0.501475 + 0.597635i
\(508\) 0 0
\(509\) 97679.4 268372.i 0.377023 1.03586i −0.595561 0.803310i \(-0.703070\pi\)
0.972584 0.232552i \(-0.0747074\pi\)
\(510\) 0 0
\(511\) 3841.60 21786.8i 0.0147119 0.0834356i
\(512\) 0 0
\(513\) 11786.0 10480.4i 0.0447849 0.0398238i
\(514\) 0 0
\(515\) −409033. 72123.5i −1.54221 0.271933i
\(516\) 0 0
\(517\) −170686. 62124.7i −0.638583 0.232425i
\(518\) 0 0
\(519\) −71920.3 + 60348.3i −0.267003 + 0.224042i
\(520\) 0 0
\(521\) 319762. + 184615.i 1.17802 + 0.680128i 0.955555 0.294814i \(-0.0952577\pi\)
0.222461 + 0.974942i \(0.428591\pi\)
\(522\) 0 0
\(523\) −450051. + 79356.1i −1.64535 + 0.290119i −0.918128 0.396284i \(-0.870300\pi\)
−0.727221 + 0.686403i \(0.759188\pi\)
\(524\) 0 0
\(525\) 7194.85 4153.95i 0.0261038 0.0150710i
\(526\) 0 0
\(527\) −18745.9 51504.0i −0.0674972 0.185447i
\(528\) 0 0
\(529\) −168572. 141449.i −0.602387 0.505462i
\(530\) 0 0
\(531\) 411651.i 1.45996i
\(532\) 0 0
\(533\) 9035.57 0.0318054
\(534\) 0 0
\(535\) 6775.70 8074.97i 0.0236726 0.0282120i
\(536\) 0 0
\(537\) 205951. 74960.1i 0.714193 0.259945i
\(538\) 0 0
\(539\) −136851. 237032.i −0.471052 0.815887i
\(540\) 0 0
\(541\) 8700.04 + 49340.4i 0.0297253 + 0.168581i 0.996057 0.0887206i \(-0.0282778\pi\)
−0.966331 + 0.257301i \(0.917167\pi\)
\(542\) 0 0
\(543\) −55527.9 + 96177.1i −0.188327 + 0.326191i
\(544\) 0 0
\(545\) −55433.2 66062.7i −0.186628 0.222415i
\(546\) 0 0
\(547\) −66561.1 + 182875.i −0.222457 + 0.611195i −0.999841 0.0178308i \(-0.994324\pi\)
0.777384 + 0.629026i \(0.216546\pi\)
\(548\) 0 0
\(549\) −23471.5 + 133114.i −0.0778748 + 0.441650i
\(550\) 0 0
\(551\) −72632.9 + 494510.i −0.239238 + 1.62882i
\(552\) 0 0
\(553\) 35866.4 + 6324.21i 0.117284 + 0.0206803i
\(554\) 0 0
\(555\) 271772. + 98916.9i 0.882305 + 0.321133i
\(556\) 0 0
\(557\) −10023.2 + 8410.44i −0.0323069 + 0.0271087i −0.658798 0.752320i \(-0.728935\pi\)
0.626491 + 0.779428i \(0.284490\pi\)
\(558\) 0 0
\(559\) 33308.6 + 19230.7i 0.106594 + 0.0615421i
\(560\) 0 0
\(561\) 97181.5 17135.7i 0.308786 0.0544474i
\(562\) 0 0
\(563\) −133471. + 77059.4i −0.421085 + 0.243113i −0.695541 0.718486i \(-0.744835\pi\)
0.274456 + 0.961600i \(0.411502\pi\)
\(564\) 0 0
\(565\) −153380. 421409.i −0.480477 1.32010i
\(566\) 0 0
\(567\) 15004.1 + 12589.9i 0.0466706 + 0.0391613i
\(568\) 0 0
\(569\) 80777.1i 0.249496i 0.992188 + 0.124748i \(0.0398122\pi\)
−0.992188 + 0.124748i \(0.960188\pi\)
\(570\) 0 0
\(571\) 296393. 0.909065 0.454533 0.890730i \(-0.349806\pi\)
0.454533 + 0.890730i \(0.349806\pi\)
\(572\) 0 0
\(573\) 100056. 119242.i 0.304743 0.363179i
\(574\) 0 0
\(575\) 47546.6 17305.5i 0.143808 0.0523419i
\(576\) 0 0
\(577\) 185757. + 321741.i 0.557949 + 0.966396i 0.997668 + 0.0682605i \(0.0217449\pi\)
−0.439718 + 0.898136i \(0.644922\pi\)
\(578\) 0 0
\(579\) 5021.21 + 28476.7i 0.0149779 + 0.0849440i
\(580\) 0 0
\(581\) 10085.9 17469.3i 0.0298787 0.0517514i
\(582\) 0 0
\(583\) 188591. + 224754.i 0.554861 + 0.661257i
\(584\) 0 0
\(585\) 67210.1 184658.i 0.196392 0.539581i
\(586\) 0 0
\(587\) 4885.12 27704.9i 0.0141775 0.0804045i −0.976898 0.213706i \(-0.931447\pi\)
0.991076 + 0.133301i \(0.0425578\pi\)
\(588\) 0 0
\(589\) −59571.7 289077.i −0.171715 0.833266i
\(590\) 0 0
\(591\) −289649. 51073.0i −0.829273 0.146223i
\(592\) 0 0
\(593\) −16303.7 5934.06i −0.0463635 0.0168749i 0.318734 0.947844i \(-0.396742\pi\)
−0.365098 + 0.930969i \(0.618964\pi\)
\(594\) 0 0
\(595\) −3277.81 + 2750.41i −0.00925869 + 0.00776896i
\(596\) 0 0
\(597\) 536140. + 309540.i 1.50428 + 0.868498i
\(598\) 0 0
\(599\) −464365. + 81880.1i −1.29421 + 0.228205i −0.778005 0.628258i \(-0.783768\pi\)
−0.516209 + 0.856463i \(0.672657\pi\)
\(600\) 0 0
\(601\) 29997.0 17318.8i 0.0830478 0.0479477i −0.457901 0.889003i \(-0.651399\pi\)
0.540949 + 0.841055i \(0.318065\pi\)
\(602\) 0 0
\(603\) 139330. + 382806.i 0.383186 + 1.05280i
\(604\) 0 0
\(605\) −24122.3 20241.0i −0.0659035 0.0552996i
\(606\) 0 0
\(607\) 65.3741i 0.000177431i 1.00000 8.87153e-5i \(2.82389e-5\pi\)
−1.00000 8.87153e-5i \(0.999972\pi\)
\(608\) 0 0
\(609\) 55585.0 0.149873
\(610\) 0 0
\(611\) −116162. + 138436.i −0.311158 + 0.370824i
\(612\) 0 0
\(613\) 189683. 69038.8i 0.504785 0.183727i −0.0770598 0.997026i \(-0.524553\pi\)
0.581845 + 0.813300i \(0.302331\pi\)
\(614\) 0 0
\(615\) 10432.2 + 18069.1i 0.0275821 + 0.0477735i
\(616\) 0 0
\(617\) 13154.6 + 74603.7i 0.0345548 + 0.195970i 0.997198 0.0748014i \(-0.0238323\pi\)
−0.962644 + 0.270772i \(0.912721\pi\)
\(618\) 0 0
\(619\) 291209. 504389.i 0.760017 1.31639i −0.182824 0.983146i \(-0.558524\pi\)
0.942841 0.333243i \(-0.108143\pi\)
\(620\) 0 0
\(621\) −6866.53 8183.21i −0.0178055 0.0212198i
\(622\) 0 0
\(623\) 11436.9 31422.7i 0.0294668 0.0809594i
\(624\) 0 0
\(625\) −37936.4 + 215148.i −0.0971173 + 0.550779i
\(626\) 0 0
\(627\) 531182. 15247.6i 1.35116 0.0387853i
\(628\) 0 0
\(629\) 72611.0 + 12803.3i 0.183528 + 0.0323609i
\(630\) 0 0
\(631\) 322731. + 117464.i 0.810553 + 0.295017i 0.713852 0.700296i \(-0.246949\pi\)
0.0967008 + 0.995313i \(0.469171\pi\)
\(632\) 0 0
\(633\) −489309. + 410579.i −1.22117 + 1.02468i
\(634\) 0 0
\(635\) −237716. 137245.i −0.589537 0.340369i
\(636\) 0 0
\(637\) −268171. + 47285.7i −0.660895 + 0.116534i
\(638\) 0 0
\(639\) 39150.5 22603.6i 0.0958817 0.0553573i
\(640\) 0 0
\(641\) −22622.2 62153.9i −0.0550577 0.151270i 0.909115 0.416545i \(-0.136759\pi\)
−0.964173 + 0.265276i \(0.914537\pi\)
\(642\) 0 0
\(643\) 323935. + 271814.i 0.783496 + 0.657431i 0.944126 0.329584i \(-0.106908\pi\)
−0.160631 + 0.987015i \(0.551353\pi\)
\(644\) 0 0
\(645\) 88813.1i 0.213480i
\(646\) 0 0
\(647\) −748603. −1.78831 −0.894156 0.447757i \(-0.852223\pi\)
−0.894156 + 0.447757i \(0.852223\pi\)
\(648\) 0 0
\(649\) −358856. + 427667.i −0.851982 + 1.01535i
\(650\) 0 0
\(651\) −30844.6 + 11226.5i −0.0727807 + 0.0264900i
\(652\) 0 0
\(653\) 395000. + 684159.i 0.926340 + 1.60447i 0.789392 + 0.613889i \(0.210396\pi\)
0.136947 + 0.990578i \(0.456271\pi\)
\(654\) 0 0
\(655\) −81221.1 460628.i −0.189316 1.07366i
\(656\) 0 0
\(657\) −299053. + 517975.i −0.692816 + 1.19999i
\(658\) 0 0
\(659\) 75605.7 + 90103.4i 0.174094 + 0.207477i 0.846035 0.533128i \(-0.178983\pi\)
−0.671941 + 0.740605i \(0.734539\pi\)
\(660\) 0 0
\(661\) −107073. + 294181.i −0.245063 + 0.673304i 0.754787 + 0.655970i \(0.227740\pi\)
−0.999850 + 0.0173341i \(0.994482\pi\)
\(662\) 0 0
\(663\) 17048.5 96686.7i 0.0387845 0.219958i
\(664\) 0 0
\(665\) −19616.1 + 12088.8i −0.0443578 + 0.0273363i
\(666\) 0 0
\(667\) 333389. + 58785.5i 0.749375 + 0.132135i
\(668\) 0 0
\(669\) −798621. 290674.i −1.78439 0.649463i
\(670\) 0 0
\(671\) −140426. + 117832.i −0.311891 + 0.261708i
\(672\) 0 0
\(673\) −596200. 344216.i −1.31632 0.759978i −0.333186 0.942861i \(-0.608124\pi\)
−0.983135 + 0.182883i \(0.941457\pi\)
\(674\) 0 0
\(675\) −8903.50 + 1569.93i −0.0195413 + 0.00344566i
\(676\) 0 0
\(677\) −272892. + 157554.i −0.595406 + 0.343758i −0.767232 0.641369i \(-0.778367\pi\)
0.171826 + 0.985127i \(0.445033\pi\)
\(678\) 0 0
\(679\) −5287.29 14526.7i −0.0114682 0.0315085i
\(680\) 0 0
\(681\) 653512. + 548361.i 1.40916 + 1.18242i
\(682\) 0 0
\(683\) 732776.i 1.57083i −0.618968 0.785416i \(-0.712449\pi\)
0.618968 0.785416i \(-0.287551\pi\)
\(684\) 0 0
\(685\) 85688.8 0.182618
\(686\) 0 0
\(687\) 768293. 915616.i 1.62785 1.93999i
\(688\) 0 0
\(689\) 274298. 99836.3i 0.577809 0.210305i
\(690\) 0 0
\(691\) 10550.9 + 18274.7i 0.0220970 + 0.0382732i 0.876862 0.480741i \(-0.159632\pi\)
−0.854765 + 0.519014i \(0.826299\pi\)
\(692\) 0 0
\(693\) −5236.48 29697.5i −0.0109037 0.0618378i
\(694\) 0 0
\(695\) −233017. + 403597.i −0.482411 + 0.835561i
\(696\) 0 0
\(697\) 3419.06 + 4074.68i 0.00703787 + 0.00838740i
\(698\) 0 0
\(699\) 394314. 1.08337e6i 0.807027 2.21729i
\(700\) 0 0
\(701\) 93054.4 527738.i 0.189366 1.07395i −0.730851 0.682537i \(-0.760877\pi\)
0.920217 0.391409i \(-0.128012\pi\)
\(702\) 0 0
\(703\) 376844. + 125036.i 0.762520 + 0.253003i
\(704\) 0 0
\(705\) −410959. 72463.2i −0.826838 0.145794i
\(706\) 0 0
\(707\) −39075.4 14222.3i −0.0781744 0.0284531i
\(708\) 0 0
\(709\) 483631. 405815.i 0.962103 0.807300i −0.0191907 0.999816i \(-0.506109\pi\)
0.981294 + 0.192515i \(0.0616645\pi\)
\(710\) 0 0
\(711\) −852714. 492315.i −1.68680 0.973876i
\(712\) 0 0
\(713\) −196873. + 34714.0i −0.387264 + 0.0682851i
\(714\) 0 0
\(715\) 230800. 133253.i 0.451466 0.260654i
\(716\) 0 0
\(717\) −217534. 597669.i −0.423144 1.16258i
\(718\) 0 0
\(719\) 198461. + 166529.i 0.383899 + 0.322130i 0.814231 0.580541i \(-0.197159\pi\)
−0.430332 + 0.902671i \(0.641603\pi\)
\(720\) 0 0
\(721\) 63412.7i 0.121985i
\(722\) 0 0
\(723\) 1.17997e6 2.25733
\(724\) 0 0
\(725\) 184165. 219479.i 0.350373 0.417558i
\(726\) 0 0
\(727\) −182622. + 66469.1i −0.345529 + 0.125762i −0.508955 0.860793i \(-0.669968\pi\)
0.163425 + 0.986556i \(0.447746\pi\)
\(728\) 0 0
\(729\) −287522. 498003.i −0.541023 0.937080i
\(730\) 0 0
\(731\) 3931.69 + 22297.7i 0.00735775 + 0.0417279i
\(732\) 0 0
\(733\) −96413.3 + 166993.i −0.179444 + 0.310806i −0.941690 0.336481i \(-0.890763\pi\)
0.762246 + 0.647287i \(0.224097\pi\)
\(734\) 0 0
\(735\) −404183. 481687.i −0.748176 0.891642i
\(736\) 0 0
\(737\) −188959. + 519161.i −0.347883 + 0.955800i
\(738\) 0 0
\(739\) 139019. 788416.i 0.254557 1.44367i −0.542650 0.839959i \(-0.682579\pi\)
0.797207 0.603706i \(-0.206310\pi\)
\(740\) 0 0
\(741\) 166495. 501795.i 0.303224 0.913881i
\(742\) 0 0
\(743\) −329829. 58157.8i −0.597463 0.105349i −0.133265 0.991080i \(-0.542546\pi\)
−0.464198 + 0.885731i \(0.653657\pi\)
\(744\) 0 0
\(745\) 603842. + 219781.i 1.08795 + 0.395983i
\(746\) 0 0
\(747\) −417768. + 350549.i −0.748675 + 0.628213i
\(748\) 0 0
\(749\) −1393.76 804.686i −0.00248441 0.00143438i
\(750\) 0 0
\(751\) −16726.8 + 2949.38i −0.0296574 + 0.00522939i −0.188457 0.982081i \(-0.560349\pi\)
0.158800 + 0.987311i \(0.449238\pi\)
\(752\) 0 0
\(753\) −507768. + 293160.i −0.895519 + 0.517028i
\(754\) 0 0
\(755\) −169584. 465929.i −0.297503 0.817383i
\(756\) 0 0
\(757\) 483204. + 405457.i 0.843216 + 0.707543i 0.958285 0.285815i \(-0.0922643\pi\)
−0.115068 + 0.993358i \(0.536709\pi\)
\(758\) 0 0
\(759\) 359925.i 0.624782i
\(760\) 0 0
\(761\) −411928. −0.711299 −0.355650 0.934619i \(-0.615740\pi\)
−0.355650 + 0.934619i \(0.615740\pi\)
\(762\) 0 0
\(763\) −8463.30 + 10086.2i −0.0145375 + 0.0173251i
\(764\) 0 0
\(765\) 108706. 39565.6i 0.185750 0.0676075i
\(766\) 0 0
\(767\) 277719. + 481023.i 0.472079 + 0.817665i
\(768\) 0 0
\(769\) −14069.9 79794.5i −0.0237924 0.134934i 0.970598 0.240707i \(-0.0773793\pi\)
−0.994390 + 0.105773i \(0.966268\pi\)
\(770\) 0 0
\(771\) −660972. + 1.14484e6i −1.11192 + 1.92590i
\(772\) 0 0
\(773\) 533118. + 635345.i 0.892204 + 1.06329i 0.997626 + 0.0688597i \(0.0219361\pi\)
−0.105422 + 0.994428i \(0.533619\pi\)
\(774\) 0 0
\(775\) −57866.4 + 158987.i −0.0963436 + 0.264702i
\(776\) 0 0
\(777\) 7667.58 43485.0i 0.0127004 0.0720274i
\(778\) 0 0
\(779\) 15027.7 + 24385.0i 0.0247638 + 0.0401835i
\(780\) 0 0
\(781\) 60378.4 + 10646.3i 0.0989873 + 0.0174541i
\(782\) 0 0
\(783\) −56840.9 20688.4i −0.0927124 0.0337445i
\(784\) 0 0
\(785\) −72997.0 + 61251.8i −0.118458 + 0.0993984i
\(786\) 0 0
\(787\) −743260. 429121.i −1.20003 0.692836i −0.239466 0.970905i \(-0.576972\pi\)
−0.960561 + 0.278069i \(0.910306\pi\)
\(788\) 0 0
\(789\) 911143. 160659.i 1.46363 0.258078i
\(790\) 0 0
\(791\) −59295.0 + 34234.0i −0.0947688 + 0.0547148i
\(792\) 0