Properties

Label 76.5.j.a.29.1
Level $76$
Weight $5$
Character 76.29
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 29.1
Character \(\chi\) \(=\) 76.29
Dual form 76.5.j.a.21.1

$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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 −0.995226 0.0975965i \(-0.968885\pi\)
0.0767054 0.997054i \(-0.475560\pi\)
\(4\) 0 0
\(5\) −19.2135 6.99315i −0.768541 0.279726i −0.0721550 0.997393i \(-0.522988\pi\)
−0.696386 + 0.717667i \(0.745210\pi\)
\(6\) 0 0
\(7\) 1.56085 2.70347i 0.0318540 0.0551728i −0.849659 0.527333i \(-0.823192\pi\)
0.881513 + 0.472160i \(0.156525\pi\)
\(8\) 0 0
\(9\) −14.6554 + 83.1149i −0.180931 + 1.02611i
\(10\) 0 0
\(11\) 57.2296 + 99.1246i 0.472972 + 0.819212i 0.999521 0.0309329i \(-0.00984782\pi\)
−0.526549 + 0.850145i \(0.676514\pi\)
\(12\) 0 0
\(13\) −73.1984 + 87.2344i −0.433127 + 0.516180i −0.937822 0.347118i \(-0.887160\pi\)
0.504695 + 0.863298i \(0.331605\pi\)
\(14\) 0 0
\(15\) 89.9367 + 247.099i 0.399719 + 1.09822i
\(16\) 0 0
\(17\) 11.6409 + 66.0190i 0.0402800 + 0.228439i 0.998302 0.0582566i \(-0.0185541\pi\)
−0.958022 + 0.286696i \(0.907443\pi\)
\(18\) 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 −0.549930 0.835211i \(-0.685346\pi\)
0.115593 + 0.993297i \(0.463123\pi\)
\(24\) 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 −0.712037 0.702142i \(-0.752227\pi\)
−0.909243 + 0.416266i \(0.863338\pi\)
\(30\) 0 0
\(31\) 708.058 + 408.797i 0.736793 + 0.425387i 0.820902 0.571069i \(-0.193471\pi\)
−0.0841094 + 0.996457i \(0.526805\pi\)
\(32\) 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 \(-0.868420\pi\)
0.915772 0.401699i \(-0.131580\pi\)
\(38\) 0 0
\(39\) 1464.53 0.962872
\(40\) 0 0
\(41\) −51.0022 60.7821i −0.0303404 0.0361583i 0.750661 0.660688i \(-0.229735\pi\)
−0.781001 + 0.624529i \(0.785291\pi\)
\(42\) 0 0
\(43\) −317.379 115.516i −0.171649 0.0624751i 0.254766 0.967003i \(-0.418001\pi\)
−0.426415 + 0.904528i \(0.640224\pi\)
\(44\) 0 0
\(45\) 862.817 1494.44i 0.426083 0.737997i
\(46\) 0 0
\(47\) −275.570 + 1562.84i −0.124749 + 0.707486i 0.856708 + 0.515802i \(0.172506\pi\)
−0.981457 + 0.191684i \(0.938605\pi\)
\(48\) 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 −0.992231 0.124409i \(-0.960297\pi\)
0.680125 0.733097i \(-0.261926\pi\)
\(54\) 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 −0.813860 0.581061i \(-0.802638\pi\)
−0.566044 + 0.824375i \(0.691527\pi\)
\(60\) 0 0
\(61\) −1504.98 + 547.766i −0.404455 + 0.147209i −0.536234 0.844070i \(-0.680153\pi\)
0.131779 + 0.991279i \(0.457931\pi\)
\(62\) 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 −0.383048 0.923728i \(-0.625126\pi\)
−0.675881 + 0.737010i \(0.736237\pi\)
\(68\) 0 0
\(69\) 2723.28 + 1572.28i 0.571997 + 0.330242i
\(70\) 0 0
\(71\) 183.202 503.344i 0.0363425 0.0998501i −0.920194 0.391462i \(-0.871969\pi\)
0.956537 + 0.291612i \(0.0941916\pi\)
\(72\) 0 0
\(73\) −5428.81 + 4555.31i −1.01873 + 0.854816i −0.989467 0.144756i \(-0.953760\pi\)
−0.0292626 + 0.999572i \(0.509316\pi\)
\(74\) 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 0.873127 + 0.487492i \(0.162088\pi\)
0.328469 + 0.944515i \(0.393467\pi\)
\(80\) 0 0
\(81\) 5895.91 + 2145.94i 0.898629 + 0.327074i
\(82\) 0 0
\(83\) −3230.90 + 5596.08i −0.468994 + 0.812321i −0.999372 0.0354403i \(-0.988717\pi\)
0.530378 + 0.847761i \(0.322050\pi\)
\(84\) 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 0.129745 + 0.991547i \(0.458584\pi\)
−0.999014 + 0.0444070i \(0.985860\pi\)
\(90\) 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 −0.426688 0.904399i \(-0.640320\pi\)
−0.0916331 + 0.995793i \(0.529209\pi\)
\(98\) 0 0
\(99\) −9077.46 + 3303.92i −0.926177 + 0.337101i
\(100\) 0 0
\(101\) −10204.2 8562.37i −1.00032 0.839366i −0.0132891 0.999912i \(-0.504230\pi\)
−0.987028 + 0.160546i \(0.948675\pi\)
\(102\) 0 0
\(103\) 17592.0 10156.8i 1.65822 0.957372i 0.684680 0.728844i \(-0.259942\pi\)
0.973537 0.228529i \(-0.0733914\pi\)
\(104\) 0 0
\(105\) 808.402 + 142.543i 0.0733244 + 0.0129291i
\(106\) 0 0
\(107\) −446.474 257.772i −0.0389968 0.0225148i 0.480375 0.877063i \(-0.340501\pi\)
−0.519372 + 0.854548i \(0.673834\pi\)
\(108\) 0 0
\(109\) 1442.56 3963.39i 0.121417 0.333591i −0.864062 0.503385i \(-0.832088\pi\)
0.985480 + 0.169794i \(0.0543101\pi\)
\(110\) 0 0
\(111\) −10835.6 + 9092.12i −0.879439 + 0.737937i
\(112\) 0 0
\(113\) 21932.9i 1.71767i −0.512251 0.858836i \(-0.671188\pi\)
0.512251 0.858836i \(-0.328812\pi\)
\(114\) 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 −0.429047 0.903282i \(-0.641151\pi\)
0.964063 + 0.265675i \(0.0855949\pi\)
\(128\) 0 0
\(129\) 1485.62 + 4081.71i 0.0892747 + 0.245280i
\(130\) 0 0
\(131\) −3972.35 22528.3i −0.231476 1.31276i −0.849910 0.526927i \(-0.823344\pi\)
0.618435 0.785836i \(-0.287767\pi\)
\(132\) 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 −0.444792 0.895634i \(-0.646722\pi\)
0.234972 + 0.972002i \(0.424500\pi\)
\(138\) 0 0
\(139\) 17460.2 + 14650.9i 0.903691 + 0.758287i 0.970908 0.239451i \(-0.0769675\pi\)
−0.0672169 + 0.997738i \(0.521412\pi\)
\(140\) 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 −0.996280 0.0861711i \(-0.972537\pi\)
−0.0881403 + 0.996108i \(0.528092\pi\)
\(150\) 0 0
\(151\) 24250.1i 1.06355i −0.846885 0.531776i \(-0.821525\pi\)
0.846885 0.531776i \(-0.178475\pi\)
\(152\) 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 0.429324 0.903151i \(-0.358752\pi\)
−0.251653 + 0.967818i \(0.580974\pi\)
\(158\) 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 0.887116 0.461547i \(-0.152705\pi\)
−0.843269 + 0.537492i \(0.819372\pi\)
\(164\) 0 0
\(165\) −19346.6 + 23056.3i −0.710617 + 0.846880i
\(166\) 0 0
\(167\) −16240.9 44621.6i −0.582341 1.59997i −0.784168 0.620549i \(-0.786910\pi\)
0.201826 0.979421i \(-0.435312\pi\)
\(168\) 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 −0.0522465 0.998634i \(-0.516638\pi\)
0.292457 + 0.956279i \(0.405527\pi\)
\(174\) 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 −0.712303 0.701872i \(-0.752348\pi\)
0.251687 + 0.967809i \(0.419015\pi\)
\(180\) 0 0
\(181\) 8504.11 + 1499.50i 0.259580 + 0.0457710i 0.301924 0.953332i \(-0.402371\pi\)
−0.0423434 + 0.999103i \(0.513482\pi\)
\(182\) 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 0.785095 0.619375i \(-0.212614\pi\)
−0.746296 + 0.665615i \(0.768169\pi\)
\(194\) 0 0
\(195\) −28138.8 10241.7i −0.740007 0.269340i
\(196\) 0 0
\(197\) 11434.8 19805.6i 0.294642 0.510335i −0.680260 0.732971i \(-0.738133\pi\)
0.974902 + 0.222637i \(0.0714663\pi\)
\(198\) 0 0
\(199\) −8358.98 + 47406.2i −0.211080 + 1.19709i 0.676500 + 0.736442i \(0.263496\pi\)
−0.887580 + 0.460653i \(0.847615\pi\)
\(200\) 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 0.405191 0.914232i \(-0.367205\pi\)
0.693440 + 0.720514i \(0.256094\pi\)
\(212\) 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 −0.475027 0.879971i \(-0.657562\pi\)
0.929527 0.368755i \(-0.120216\pi\)
\(224\) 0 0
\(225\) 13378.8 11226.2i 0.264273 0.221752i
\(226\) 0 0
\(227\) 66333.9i 1.28731i 0.765315 + 0.643656i \(0.222583\pi\)
−0.765315 + 0.643656i \(0.777417\pi\)
\(228\) 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 −0.582866 0.812569i \(-0.698069\pi\)
−0.968810 + 0.247805i \(0.920291\pi\)
\(234\) 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 0.564224 0.825622i \(-0.309175\pi\)
−0.997121 + 0.0758216i \(0.975842\pi\)
\(240\) 0 0
\(241\) −58976.1 + 70284.9i −1.01541 + 1.21012i −0.0378895 + 0.999282i \(0.512063\pi\)
−0.977521 + 0.210837i \(0.932381\pi\)
\(242\) 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 0.0211523 0.999776i \(-0.493267\pi\)
0.658847 + 0.752277i \(0.271044\pi\)
\(252\) 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 0.875378 0.483439i \(-0.160612\pi\)
0.657240 + 0.753681i \(0.271724\pi\)
\(258\) 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 −0.947402 0.320045i \(-0.896302\pi\)
0.150668 + 0.988584i \(0.451858\pi\)
\(264\) 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 0.741892 0.670519i \(-0.233929\pi\)
−0.789161 + 0.614186i \(0.789484\pi\)
\(270\) 0 0
\(271\) −85921.4 31272.8i −1.16994 0.425822i −0.317300 0.948325i \(-0.602776\pi\)
−0.852638 + 0.522503i \(0.824998\pi\)
\(272\) 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 0.835838 0.548976i \(-0.184982\pi\)
−0.893346 + 0.449369i \(0.851649\pi\)
\(278\) 0 0
\(279\) −44354.0 + 52859.1i −0.569803 + 0.679065i
\(280\) 0 0
\(281\) 12846.7 + 35295.9i 0.162696 + 0.447005i 0.994074 0.108703i \(-0.0346697\pi\)
−0.831378 + 0.555707i \(0.812447\pi\)
\(282\) 0 0
\(283\) 21836.2 + 123839.i 0.272649 + 1.54627i 0.746332 + 0.665574i \(0.231813\pi\)
−0.473683 + 0.880696i \(0.657076\pi\)
\(284\) 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 −0.551879 0.833924i \(-0.686089\pi\)
0.446260 + 0.894903i \(0.352756\pi\)
\(294\) 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 0.750268 0.661134i \(-0.229925\pi\)
−0.781373 + 0.624064i \(0.785480\pi\)
\(308\) 0 0
\(309\) −245491. 89351.3i −2.57109 0.935802i
\(310\) 0 0
\(311\) 10594.0 18349.3i 0.109531 0.189714i −0.806049 0.591848i \(-0.798398\pi\)
0.915580 + 0.402135i \(0.131732\pi\)
\(312\) 0 0
\(313\) −4983.07 + 28260.4i −0.0508637 + 0.288463i −0.999621 0.0275445i \(-0.991231\pi\)
0.948757 + 0.316007i \(0.102342\pi\)
\(314\) 0 0
\(315\) −2693.45 4665.20i −0.0271449 0.0470164i
\(316\) 0 0
\(317\) −8523.70 + 10158.2i −0.0848222 + 0.101087i −0.806786 0.590843i \(-0.798795\pi\)
0.721964 + 0.691931i \(0.243240\pi\)
\(318\) 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 −0.878389 0.477947i \(-0.841381\pi\)
−0.0252800 + 0.999680i \(0.508048\pi\)
\(332\) 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 −0.509043 0.860741i \(-0.670001\pi\)
0.943223 0.332160i \(-0.107777\pi\)
\(338\) 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 0.150955 0.988541i \(-0.451765\pi\)
−0.519783 + 0.854298i \(0.673987\pi\)
\(348\) 0 0
\(349\) 55218.0 95640.3i 0.453346 0.785218i −0.545246 0.838276i \(-0.683564\pi\)
0.998591 + 0.0530586i \(0.0168970\pi\)
\(350\) 0 0
\(351\) −863.927 + 4899.57i −0.00701234 + 0.0397689i
\(352\) 0 0
\(353\) 102767. + 177998.i 0.824717 + 1.42845i 0.902136 + 0.431453i \(0.141999\pi\)
−0.0774187 + 0.996999i \(0.524668\pi\)
\(354\) 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 0.935488 + 0.353357i \(0.114960\pi\)
−0.758216 + 0.652003i \(0.773929\pi\)
\(360\) 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 0.955331 + 0.295539i \(0.0954991\pi\)
0.456940 + 0.889497i \(0.348945\pi\)
\(368\) 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 0.717831 0.696217i \(-0.245135\pi\)
−0.244026 + 0.969769i \(0.578468\pi\)
\(374\) 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 \(-0.949871\pi\)
0.987625 0.156834i \(-0.0501286\pi\)
\(380\) 0 0
\(381\) −172651. −1.18938
\(382\) 0 0
\(383\) 34187.5 + 40743.1i 0.233061 + 0.277752i 0.869882 0.493261i \(-0.164195\pi\)
−0.636820 + 0.771012i \(0.719751\pi\)
\(384\) 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 −0.847240 0.531210i \(-0.821738\pi\)
0.977830 0.209401i \(-0.0671514\pi\)
\(390\) 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 −0.806369 0.591413i \(-0.798570\pi\)
0.555464 0.831541i \(-0.312541\pi\)
\(398\) 0 0
\(399\) −6883.43 12754.2i −0.0432374 0.0801136i
\(400\) 0 0
\(401\) 302245. 53294.0i 1.87962 0.331428i 0.887922 0.459993i \(-0.152148\pi\)
0.991701 + 0.128565i \(0.0410370\pi\)
\(402\) 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 −0.678690 0.734425i \(-0.737452\pi\)
−0.888948 + 0.458008i \(0.848563\pi\)
\(410\) 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 0.699317 0.714812i \(-0.253488\pi\)
−0.825387 + 0.564567i \(0.809043\pi\)
\(422\) 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 −0.791749 0.610847i \(-0.790829\pi\)
0.739053 + 0.673648i \(0.235274\pi\)
\(432\) 0 0
\(433\) 1615.17 + 4437.64i 0.00861474 + 0.0236688i 0.943925 0.330159i \(-0.107102\pi\)
−0.935311 + 0.353827i \(0.884880\pi\)
\(434\) 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 −0.794111 0.607773i \(-0.792063\pi\)
−0.538349 + 0.842722i \(0.680952\pi\)
\(440\) 0 0
\(441\) −189644. + 69024.8i −0.975129 + 0.354918i
\(442\) 0 0
\(443\) 128893. + 108154.i 0.656783 + 0.551106i 0.909121 0.416533i \(-0.136755\pi\)
−0.252338 + 0.967639i \(0.581199\pi\)
\(444\) 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 0.607364 0.794424i \(-0.292227\pi\)
−0.384310 + 0.923204i \(0.625560\pi\)
\(450\) 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 0.911526 0.411242i \(-0.134905\pi\)
0.433928 + 0.900947i \(0.357127\pi\)
\(462\) 0 0
\(463\) −38084.9 + 65964.9i −0.177660 + 0.307717i −0.941079 0.338188i \(-0.890186\pi\)
0.763418 + 0.645904i \(0.223520\pi\)
\(464\) 0 0
\(465\) −37333.0 + 211726.i −0.172658 + 0.979194i
\(466\) 0 0
\(467\) 107590. + 186351.i 0.493330 + 0.854473i 0.999970 0.00768464i \(-0.00244612\pi\)
−0.506640 + 0.862158i \(0.669113\pi\)
\(468\) 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 −0.580364 0.814357i \(-0.697090\pi\)
0.0788742 + 0.996885i \(0.474867\pi\)
\(480\) 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 0.771170 0.636630i \(-0.219672\pi\)
−0.165752 + 0.986167i \(0.553005\pi\)
\(488\) 0 0
\(489\) 10248.4 28157.4i 0.0428588 0.117754i
\(490\) 0 0
\(491\) −341110. + 286226.i −1.41492 + 1.18726i −0.460924 + 0.887440i \(0.652482\pi\)
−0.953996 + 0.299819i \(0.903074\pi\)
\(492\) 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 0.403366 0.915039i \(-0.367840\pi\)
−0.279179 + 0.960239i \(0.590062\pi\)
\(500\) 0 0
\(501\) −305346. + 528876.i −1.21651 + 2.10707i
\(502\) 0 0
\(503\) 9171.59 52014.6i 0.0362500 0.205584i −0.961303 0.275492i \(-0.911159\pi\)
0.997553 + 0.0699076i \(0.0222704\pi\)
\(504\) 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 0.972584 + 0.232552i \(0.0747074\pi\)
−0.595561 + 0.803310i \(0.703070\pi\)
\(510\) 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 0.222461 0.974942i \(-0.428591\pi\)
0.955555 + 0.294814i \(0.0952577\pi\)
\(522\) 0 0
\(523\) −450051. 79356.1i −1.64535 0.290119i −0.727221 0.686403i \(-0.759188\pi\)
−0.918128 + 0.396284i \(0.870300\pi\)
\(524\) 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 −0.966331 0.257301i \(-0.917167\pi\)
0.996057 + 0.0887206i \(0.0282778\pi\)
\(542\) 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 0.777384 0.629026i \(-0.216546\pi\)
−0.999841 + 0.0178308i \(0.994324\pi\)
\(548\) 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 0.626491 0.779428i \(-0.284490\pi\)
−0.658798 + 0.752320i \(0.728935\pi\)
\(558\) 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 0.274456 0.961600i \(-0.411502\pi\)
−0.695541 + 0.718486i \(0.744835\pi\)
\(564\) 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 \(-0.960188\pi\)
0.992188 0.124748i \(-0.0398122\pi\)
\(570\) 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 −0.439718 0.898136i \(-0.644922\pi\)
0.997668 0.0682605i \(-0.0217449\pi\)
\(578\) 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 0.991076 0.133301i \(-0.0425578\pi\)
−0.976898 + 0.213706i \(0.931447\pi\)
\(588\) 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 −0.365098 0.930969i \(-0.618964\pi\)
0.318734 + 0.947844i \(0.396742\pi\)
\(594\) 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 −0.516209 0.856463i \(-0.672657\pi\)
−0.778005 + 0.628258i \(0.783768\pi\)
\(600\) 0 0
\(601\) 29997.0 + 17318.8i 0.0830478 + 0.0479477i 0.540949 0.841055i \(-0.318065\pi\)
−0.457901 + 0.889003i \(0.651399\pi\)
\(602\) 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 \(-0.999972\pi\)
1.00000 8.87153e-5i \(-2.82389e-5\pi\)
\(608\) 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 0.581845 0.813300i \(-0.302331\pi\)
−0.0770598 + 0.997026i \(0.524553\pi\)
\(614\) 0 0
\(615\) 10432.2 18069.1i 0.0275821 0.0477735i
\(616\) 0 0
\(617\) 13154.6 74603.7i 0.0345548 0.195970i −0.962644 0.270772i \(-0.912721\pi\)
0.997198 + 0.0748014i \(0.0238323\pi\)
\(618\) 0 0
\(619\) 291209. + 504389.i 0.760017 + 1.31639i 0.942841 + 0.333243i \(0.108143\pi\)
−0.182824 + 0.983146i \(0.558524\pi\)
\(620\) 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 0.0967008 0.995313i \(-0.469171\pi\)
0.713852 + 0.700296i \(0.246949\pi\)
\(632\) 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 −0.964173 0.265276i \(-0.914537\pi\)
0.909115 + 0.416545i \(0.136759\pi\)
\(642\) 0 0
\(643\) 323935. 271814.i 0.783496 0.657431i −0.160631 0.987015i \(-0.551353\pi\)
0.944126 + 0.329584i \(0.106908\pi\)
\(644\) 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 0.136947 0.990578i \(-0.456271\pi\)
0.789392 0.613889i \(-0.210396\pi\)
\(654\) 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 −0.671941 0.740605i \(-0.734539\pi\)
0.846035 + 0.533128i \(0.178983\pi\)
\(660\) 0 0
\(661\) −107073. 294181.i −0.245063 0.673304i −0.999850 0.0173341i \(-0.994482\pi\)
0.754787 0.655970i \(-0.227740\pi\)
\(662\) 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 −0.983135 0.182883i \(-0.941457\pi\)
−0.333186 + 0.942861i \(0.608124\pi\)
\(674\) 0 0
\(675\) −8903.50 1569.93i −0.0195413 0.00344566i
\(676\) 0 0
\(677\) −272892. 157554.i −0.595406 0.343758i 0.171826 0.985127i \(-0.445033\pi\)
−0.767232 + 0.641369i \(0.778367\pi\)
\(678\) 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 \(0.287551\pi\)
−0.618968 + 0.785416i \(0.712449\pi\)
\(684\) 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 −0.854765 0.519014i \(-0.826299\pi\)
0.876862 + 0.480741i \(0.159632\pi\)
\(692\) 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 0.920217 + 0.391409i \(0.128012\pi\)
−0.730851 + 0.682537i \(0.760877\pi\)
\(702\) 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 0.981294 0.192515i \(-0.0616645\pi\)
−0.0191907 + 0.999816i \(0.506109\pi\)
\(710\) 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 −0.430332 0.902671i \(-0.641603\pi\)
0.814231 + 0.580541i \(0.197159\pi\)
\(720\) 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 0.163425 0.986556i \(-0.447746\pi\)
−0.508955 + 0.860793i \(0.669968\pi\)
\(728\) 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 0.762246 0.647287i \(-0.224097\pi\)
−0.941690 + 0.336481i \(0.890763\pi\)
\(734\) 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 0.797207 + 0.603706i \(0.206310\pi\)
−0.542650 + 0.839959i \(0.682579\pi\)
\(740\) 0 0
\(741\) 166495. + 501795.i 0.303224 + 0.913881i
\(742\) 0 0
\(743\) −329829. + 58157.8i −0.597463 + 0.105349i −0.464198 0.885731i \(-0.653657\pi\)
−0.133265 + 0.991080i \(0.542546\pi\)
\(744\) 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 0.158800 0.987311i \(-0.449238\pi\)
−0.188457 + 0.982081i \(0.560349\pi\)
\(752\) 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 −0.115068 0.993358i \(-0.536709\pi\)
0.958285 + 0.285815i \(0.0922643\pi\)
\(758\) 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 −0.994390 0.105773i \(-0.966268\pi\)
0.970598 + 0.240707i \(0.0773793\pi\)
\(770\) 0 0
\(771\) −660972. 1.14484e6i −1.11192 1.92590i
\(772\) 0 0
\(773\) 533118. 635345.i 0.892204 1.06329i −0.105422 0.994428i \(-0.533619\pi\)
0.997626 0.0688597i \(-0.0219361\pi\)
\(774\) 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 −0.960561 0.278069i \(-0.910306\pi\)
−0.239466 + 0.970905i \(0.576972\pi\)
\(788\) 0 0
\(789\) 911143. + 160659.i 1.46363 + 0.258078i
\(790\) 0 0
\(791\) −59295.0 34234.0i −0.0947688 0.0547148i
\(792\)