Properties

Label 1050.3.q.b.199.5
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.22986704741655040229376.1
Defining polynomial: \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.5
Root \(-2.22431 + 0.596002i\) of defining polynomial
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.b.649.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.647280 - 1.12112i) q^{11} +(1.73205 + 3.00000i) q^{12} +3.22960 q^{13} +(-4.24500 + 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(15.1826 - 26.2970i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-28.9470 + 16.7125i) q^{19} +(-0.974040 - 12.0852i) q^{21} -1.83078i q^{22} +(30.9462 - 17.8668i) q^{23} +(4.24264 + 2.44949i) q^{24} +(3.95544 - 2.28367i) q^{26} +5.19615 q^{27} +(1.12472 + 13.9547i) q^{28} +32.8033 q^{29} +(39.5125 + 22.8125i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(1.12112 + 1.94184i) q^{33} -42.9428i q^{34} -6.00000 q^{36} +(34.6873 - 20.0267i) q^{37} +(-23.6351 + 40.9372i) q^{38} +(-2.79692 + 4.84440i) q^{39} +42.2993i q^{41} +(-9.73845 - 14.1125i) q^{42} +55.4597i q^{43} +(-1.29456 - 2.24224i) q^{44} +(25.2675 - 43.7646i) q^{46} +(-30.3745 - 52.6102i) q^{47} +6.92820 q^{48} +(17.3875 - 45.8113i) q^{49} +(26.2970 + 45.5477i) q^{51} +(3.22960 - 5.59383i) q^{52} +(47.3438 + 27.3340i) q^{53} +(6.36396 - 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} -57.8939i q^{57} +(40.1757 - 23.1954i) q^{58} +(-11.4277 - 6.59780i) q^{59} +(34.1684 - 19.7271i) q^{61} +64.5236 q^{62} +(18.9713 + 9.00500i) q^{63} -8.00000 q^{64} +(2.74618 + 1.58551i) q^{66} +(34.7163 + 20.0434i) q^{67} +(-30.3651 - 52.5940i) q^{68} +61.8924i q^{69} +46.4480 q^{71} +(-7.34847 + 4.24264i) q^{72} +(68.2001 - 118.126i) q^{73} +(28.3220 - 49.0552i) q^{74} +66.8501i q^{76} +(0.728012 + 9.03263i) q^{77} +7.91088i q^{78} +(-21.1511 - 36.6348i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(29.9101 + 51.8059i) q^{82} +1.53725 q^{83} +(-21.9062 - 10.3981i) q^{84} +(39.2160 + 67.9240i) q^{86} +(-28.4085 + 49.2050i) q^{87} +(-3.17101 - 1.83078i) q^{88} +(30.2844 - 17.4847i) q^{89} +(-18.6070 + 12.8400i) q^{91} -71.4672i q^{92} +(-68.4376 + 39.5125i) q^{93} +(-74.4020 - 42.9560i) q^{94} +(8.48528 - 4.89898i) q^{96} -150.516 q^{97} +(-11.0982 - 68.4020i) q^{98} -3.88368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.612372 0.353553i
\(3\) −0.866025 + 1.50000i −0.288675 + 0.500000i
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −5.76140 + 3.97571i −0.823057 + 0.567958i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.647280 1.12112i 0.0588436 0.101920i −0.835103 0.550094i \(-0.814592\pi\)
0.893947 + 0.448174i \(0.147925\pi\)
\(12\) 1.73205 + 3.00000i 0.144338 + 0.250000i
\(13\) 3.22960 0.248431 0.124215 0.992255i \(-0.460359\pi\)
0.124215 + 0.992255i \(0.460359\pi\)
\(14\) −4.24500 + 8.94315i −0.303214 + 0.638797i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 15.1826 26.2970i 0.893092 1.54688i 0.0569439 0.998377i \(-0.481864\pi\)
0.836148 0.548504i \(-0.184802\pi\)
\(18\) −3.67423 2.12132i −0.204124 0.117851i
\(19\) −28.9470 + 16.7125i −1.52352 + 0.879607i −0.523912 + 0.851773i \(0.675528\pi\)
−0.999613 + 0.0278345i \(0.991139\pi\)
\(20\) 0 0
\(21\) −0.974040 12.0852i −0.0463829 0.575484i
\(22\) 1.83078i 0.0832175i
\(23\) 30.9462 17.8668i 1.34549 0.776818i 0.357881 0.933767i \(-0.383499\pi\)
0.987607 + 0.156950i \(0.0501660\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) 3.95544 2.28367i 0.152132 0.0878336i
\(27\) 5.19615 0.192450
\(28\) 1.12472 + 13.9547i 0.0401687 + 0.498384i
\(29\) 32.8033 1.13115 0.565574 0.824697i \(-0.308655\pi\)
0.565574 + 0.824697i \(0.308655\pi\)
\(30\) 0 0
\(31\) 39.5125 + 22.8125i 1.27460 + 0.735888i 0.975849 0.218444i \(-0.0700981\pi\)
0.298747 + 0.954332i \(0.403431\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) 1.12112 + 1.94184i 0.0339734 + 0.0588436i
\(34\) 42.9428i 1.26302i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 34.6873 20.0267i 0.937494 0.541262i 0.0483201 0.998832i \(-0.484613\pi\)
0.889174 + 0.457570i \(0.151280\pi\)
\(38\) −23.6351 + 40.9372i −0.621976 + 1.07729i
\(39\) −2.79692 + 4.84440i −0.0717158 + 0.124215i
\(40\) 0 0
\(41\) 42.2993i 1.03169i 0.856682 + 0.515845i \(0.172522\pi\)
−0.856682 + 0.515845i \(0.827478\pi\)
\(42\) −9.73845 14.1125i −0.231868 0.336012i
\(43\) 55.4597i 1.28976i 0.764283 + 0.644881i \(0.223093\pi\)
−0.764283 + 0.644881i \(0.776907\pi\)
\(44\) −1.29456 2.24224i −0.0294218 0.0509601i
\(45\) 0 0
\(46\) 25.2675 43.7646i 0.549293 0.951403i
\(47\) −30.3745 52.6102i −0.646266 1.11937i −0.984008 0.178127i \(-0.942996\pi\)
0.337741 0.941239i \(-0.390337\pi\)
\(48\) 6.92820 0.144338
\(49\) 17.3875 45.8113i 0.354847 0.934924i
\(50\) 0 0
\(51\) 26.2970 + 45.5477i 0.515627 + 0.893092i
\(52\) 3.22960 5.59383i 0.0621077 0.107574i
\(53\) 47.3438 + 27.3340i 0.893280 + 0.515735i 0.875014 0.484098i \(-0.160852\pi\)
0.0182660 + 0.999833i \(0.494185\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 11.2450 + 16.2957i 0.200804 + 0.290995i
\(57\) 57.8939i 1.01568i
\(58\) 40.1757 23.1954i 0.692684 0.399921i
\(59\) −11.4277 6.59780i −0.193690 0.111827i 0.400019 0.916507i \(-0.369004\pi\)
−0.593709 + 0.804680i \(0.702337\pi\)
\(60\) 0 0
\(61\) 34.1684 19.7271i 0.560137 0.323395i −0.193064 0.981186i \(-0.561842\pi\)
0.753200 + 0.657791i \(0.228509\pi\)
\(62\) 64.5236 1.04070
\(63\) 18.9713 + 9.00500i 0.301132 + 0.142937i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 2.74618 + 1.58551i 0.0416087 + 0.0240228i
\(67\) 34.7163 + 20.0434i 0.518153 + 0.299156i 0.736179 0.676787i \(-0.236628\pi\)
−0.218026 + 0.975943i \(0.569962\pi\)
\(68\) −30.3651 52.5940i −0.446546 0.773440i
\(69\) 61.8924i 0.896992i
\(70\) 0 0
\(71\) 46.4480 0.654198 0.327099 0.944990i \(-0.393929\pi\)
0.327099 + 0.944990i \(0.393929\pi\)
\(72\) −7.34847 + 4.24264i −0.102062 + 0.0589256i
\(73\) 68.2001 118.126i 0.934247 1.61816i 0.158277 0.987395i \(-0.449406\pi\)
0.775970 0.630769i \(-0.217261\pi\)
\(74\) 28.3220 49.0552i 0.382730 0.662908i
\(75\) 0 0
\(76\) 66.8501i 0.879607i
\(77\) 0.728012 + 9.03263i 0.00945470 + 0.117307i
\(78\) 7.91088i 0.101422i
\(79\) −21.1511 36.6348i −0.267736 0.463732i 0.700541 0.713612i \(-0.252942\pi\)
−0.968277 + 0.249880i \(0.919609\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 29.9101 + 51.8059i 0.364758 + 0.631779i
\(83\) 1.53725 0.0185211 0.00926054 0.999957i \(-0.497052\pi\)
0.00926054 + 0.999957i \(0.497052\pi\)
\(84\) −21.9062 10.3981i −0.260788 0.123787i
\(85\) 0 0
\(86\) 39.2160 + 67.9240i 0.456000 + 0.789814i
\(87\) −28.4085 + 49.2050i −0.326534 + 0.565574i
\(88\) −3.17101 1.83078i −0.0360342 0.0208044i
\(89\) 30.2844 17.4847i 0.340274 0.196457i −0.320119 0.947377i \(-0.603723\pi\)
0.660393 + 0.750920i \(0.270390\pi\)
\(90\) 0 0
\(91\) −18.6070 + 12.8400i −0.204473 + 0.141098i
\(92\) 71.4672i 0.776818i
\(93\) −68.4376 + 39.5125i −0.735888 + 0.424865i
\(94\) −74.4020 42.9560i −0.791511 0.456979i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) −150.516 −1.55172 −0.775858 0.630907i \(-0.782683\pi\)
−0.775858 + 0.630907i \(0.782683\pi\)
\(98\) −11.0982 68.4020i −0.113247 0.697979i
\(99\) −3.88368 −0.0392291
\(100\) 0 0
\(101\) 103.806 + 59.9325i 1.02778 + 0.593391i 0.916349 0.400381i \(-0.131122\pi\)
0.111434 + 0.993772i \(0.464456\pi\)
\(102\) 64.4142 + 37.1895i 0.631511 + 0.364603i
\(103\) 49.8245 + 86.2986i 0.483733 + 0.837851i 0.999825 0.0186825i \(-0.00594715\pi\)
−0.516092 + 0.856533i \(0.672614\pi\)
\(104\) 9.13469i 0.0878336i
\(105\) 0 0
\(106\) 77.3122 0.729360
\(107\) 40.6950 23.4953i 0.380327 0.219582i −0.297634 0.954680i \(-0.596197\pi\)
0.677961 + 0.735098i \(0.262864\pi\)
\(108\) 5.19615 9.00000i 0.0481125 0.0833333i
\(109\) −29.0802 + 50.3683i −0.266791 + 0.462095i −0.968031 0.250830i \(-0.919297\pi\)
0.701241 + 0.712925i \(0.252630\pi\)
\(110\) 0 0
\(111\) 69.3746i 0.624996i
\(112\) 25.2951 + 12.0067i 0.225849 + 0.107202i
\(113\) 211.102i 1.86816i −0.357068 0.934078i \(-0.616224\pi\)
0.357068 0.934078i \(-0.383776\pi\)
\(114\) −40.9372 70.9053i −0.359098 0.621976i
\(115\) 0 0
\(116\) 32.8033 56.8170i 0.282787 0.489802i
\(117\) −4.84440 8.39075i −0.0414052 0.0717158i
\(118\) −18.6614 −0.158148
\(119\) 17.0762 + 211.869i 0.143498 + 1.78041i
\(120\) 0 0
\(121\) 59.6621 + 103.338i 0.493075 + 0.854031i
\(122\) 27.8983 48.3213i 0.228675 0.396077i
\(123\) −63.4490 36.6323i −0.515845 0.297823i
\(124\) 79.0250 45.6251i 0.637298 0.367944i
\(125\) 0 0
\(126\) 29.6025 2.38590i 0.234940 0.0189357i
\(127\) 90.2615i 0.710720i −0.934729 0.355360i \(-0.884358\pi\)
0.934729 0.355360i \(-0.115642\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) −83.1896 48.0296i −0.644881 0.372322i
\(130\) 0 0
\(131\) −174.806 + 100.924i −1.33440 + 0.770414i −0.985970 0.166923i \(-0.946617\pi\)
−0.348426 + 0.937336i \(0.613284\pi\)
\(132\) 4.48449 0.0339734
\(133\) 100.331 211.372i 0.754368 1.58927i
\(134\) 56.6914 0.423070
\(135\) 0 0
\(136\) −74.3791 42.9428i −0.546905 0.315756i
\(137\) −0.00352554 0.00203547i −2.57339e−5 1.48575e-5i 0.499987 0.866033i \(-0.333338\pi\)
−0.500013 + 0.866018i \(0.666671\pi\)
\(138\) 43.7646 + 75.8024i 0.317134 + 0.549293i
\(139\) 115.950i 0.834169i −0.908868 0.417085i \(-0.863052\pi\)
0.908868 0.417085i \(-0.136948\pi\)
\(140\) 0 0
\(141\) 105.220 0.746244
\(142\) 56.8870 32.8437i 0.400613 0.231294i
\(143\) 2.09046 3.62078i 0.0146186 0.0253201i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 192.899i 1.32123i
\(147\) 53.6589 + 65.7550i 0.365027 + 0.447313i
\(148\) 80.1068i 0.541262i
\(149\) −2.59675 4.49770i −0.0174278 0.0301859i 0.857180 0.515017i \(-0.172214\pi\)
−0.874608 + 0.484831i \(0.838881\pi\)
\(150\) 0 0
\(151\) 80.3710 139.207i 0.532258 0.921899i −0.467032 0.884240i \(-0.654677\pi\)
0.999291 0.0376583i \(-0.0119898\pi\)
\(152\) 47.2702 + 81.8744i 0.310988 + 0.538647i
\(153\) −91.0954 −0.595395
\(154\) 7.27866 + 10.5479i 0.0472640 + 0.0684928i
\(155\) 0 0
\(156\) 5.59383 + 9.68881i 0.0358579 + 0.0621077i
\(157\) −47.6157 + 82.4728i −0.303285 + 0.525305i −0.976878 0.213798i \(-0.931417\pi\)
0.673593 + 0.739102i \(0.264750\pi\)
\(158\) −51.8095 29.9122i −0.327908 0.189318i
\(159\) −82.0019 + 47.3438i −0.515735 + 0.297760i
\(160\) 0 0
\(161\) −107.260 + 225.971i −0.666214 + 1.40355i
\(162\) 12.7279i 0.0785674i
\(163\) 213.473 123.249i 1.30965 0.756128i 0.327615 0.944811i \(-0.393755\pi\)
0.982038 + 0.188683i \(0.0604218\pi\)
\(164\) 73.2645 + 42.2993i 0.446735 + 0.257923i
\(165\) 0 0
\(166\) 1.88274 1.08700i 0.0113418 0.00654819i
\(167\) −14.9445 −0.0894879 −0.0447439 0.998998i \(-0.514247\pi\)
−0.0447439 + 0.998998i \(0.514247\pi\)
\(168\) −34.1820 + 2.75500i −0.203464 + 0.0163988i
\(169\) −158.570 −0.938282
\(170\) 0 0
\(171\) 86.8409 + 50.1376i 0.507841 + 0.293202i
\(172\) 96.0591 + 55.4597i 0.558483 + 0.322440i
\(173\) 83.8331 + 145.203i 0.484584 + 0.839325i 0.999843 0.0177099i \(-0.00563752\pi\)
−0.515259 + 0.857035i \(0.672304\pi\)
\(174\) 80.3513i 0.461789i
\(175\) 0 0
\(176\) −5.17824 −0.0294218
\(177\) 19.7934 11.4277i 0.111827 0.0645635i
\(178\) 24.7271 42.8286i 0.138916 0.240610i
\(179\) 33.4724 57.9759i 0.186997 0.323888i −0.757251 0.653124i \(-0.773458\pi\)
0.944248 + 0.329236i \(0.106791\pi\)
\(180\) 0 0
\(181\) 24.9109i 0.137629i −0.997629 0.0688146i \(-0.978078\pi\)
0.997629 0.0688146i \(-0.0219217\pi\)
\(182\) −13.7097 + 28.8828i −0.0753278 + 0.158697i
\(183\) 68.3367i 0.373425i
\(184\) −50.5350 87.5291i −0.274647 0.475702i
\(185\) 0 0
\(186\) −55.8791 + 96.7854i −0.300425 + 0.520352i
\(187\) −19.6547 34.0430i −0.105106 0.182048i
\(188\) −121.498 −0.646266
\(189\) −29.9371 + 20.6584i −0.158397 + 0.109304i
\(190\) 0 0
\(191\) 6.80231 + 11.7819i 0.0356142 + 0.0616856i 0.883283 0.468840i \(-0.155328\pi\)
−0.847669 + 0.530526i \(0.821995\pi\)
\(192\) 6.92820 12.0000i 0.0360844 0.0625000i
\(193\) 157.978 + 91.2089i 0.818541 + 0.472585i 0.849913 0.526923i \(-0.176654\pi\)
−0.0313718 + 0.999508i \(0.509988\pi\)
\(194\) −184.344 + 106.431i −0.950228 + 0.548615i
\(195\) 0 0
\(196\) −61.9600 75.9273i −0.316122 0.387384i
\(197\) 286.679i 1.45522i −0.685989 0.727612i \(-0.740630\pi\)
0.685989 0.727612i \(-0.259370\pi\)
\(198\) −4.75652 + 2.74618i −0.0240228 + 0.0138696i
\(199\) 2.74117 + 1.58262i 0.0137747 + 0.00795285i 0.506872 0.862022i \(-0.330802\pi\)
−0.493097 + 0.869974i \(0.664135\pi\)
\(200\) 0 0
\(201\) −60.1303 + 34.7163i −0.299156 + 0.172718i
\(202\) 169.515 0.839181
\(203\) −188.993 + 130.416i −0.931000 + 0.642445i
\(204\) 105.188 0.515627
\(205\) 0 0
\(206\) 122.045 + 70.4625i 0.592450 + 0.342051i
\(207\) −92.8387 53.6004i −0.448496 0.258939i
\(208\) −6.45920 11.1877i −0.0310539 0.0537869i
\(209\) 43.2708i 0.207037i
\(210\) 0 0
\(211\) −179.324 −0.849878 −0.424939 0.905222i \(-0.639705\pi\)
−0.424939 + 0.905222i \(0.639705\pi\)
\(212\) 94.6877 54.6679i 0.446640 0.257868i
\(213\) −40.2252 + 69.6720i −0.188851 + 0.327099i
\(214\) 33.2273 57.5514i 0.155268 0.268932i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −318.343 + 25.6578i −1.46702 + 0.118239i
\(218\) 82.2512i 0.377299i
\(219\) 118.126 + 204.600i 0.539388 + 0.934247i
\(220\) 0 0
\(221\) 49.0336 84.9288i 0.221872 0.384293i
\(222\) 49.0552 + 84.9661i 0.220969 + 0.382730i
\(223\) −71.3345 −0.319886 −0.159943 0.987126i \(-0.551131\pi\)
−0.159943 + 0.987126i \(0.551131\pi\)
\(224\) 39.4700 3.18120i 0.176205 0.0142018i
\(225\) 0 0
\(226\) −149.271 258.546i −0.660493 1.14401i
\(227\) −71.2698 + 123.443i −0.313964 + 0.543802i −0.979217 0.202817i \(-0.934990\pi\)
0.665253 + 0.746618i \(0.268324\pi\)
\(228\) −100.275 57.8939i −0.439804 0.253921i
\(229\) −109.001 + 62.9320i −0.475989 + 0.274812i −0.718743 0.695276i \(-0.755282\pi\)
0.242755 + 0.970088i \(0.421949\pi\)
\(230\) 0 0
\(231\) −14.1794 6.73047i −0.0613828 0.0291362i
\(232\) 92.7817i 0.399921i
\(233\) 142.258 82.1326i 0.610549 0.352500i −0.162631 0.986687i \(-0.551998\pi\)
0.773180 + 0.634186i \(0.218665\pi\)
\(234\) −11.8663 6.85102i −0.0507108 0.0292779i
\(235\) 0 0
\(236\) −22.8555 + 13.1956i −0.0968452 + 0.0559136i
\(237\) 73.2697 0.309155
\(238\) 170.728 + 247.411i 0.717344 + 1.03954i
\(239\) 50.4246 0.210982 0.105491 0.994420i \(-0.466359\pi\)
0.105491 + 0.994420i \(0.466359\pi\)
\(240\) 0 0
\(241\) −169.006 97.5757i −0.701270 0.404879i 0.106550 0.994307i \(-0.466020\pi\)
−0.807820 + 0.589429i \(0.799353\pi\)
\(242\) 146.142 + 84.3749i 0.603891 + 0.348657i
\(243\) −7.79423 13.5000i −0.0320750 0.0555556i
\(244\) 78.9084i 0.323395i
\(245\) 0 0
\(246\) −103.612 −0.421186
\(247\) −93.4872 + 53.9748i −0.378491 + 0.218522i
\(248\) 64.5236 111.758i 0.260176 0.450638i
\(249\) −1.33130 + 2.30587i −0.00534657 + 0.00926054i
\(250\) 0 0
\(251\) 328.725i 1.30966i 0.755775 + 0.654832i \(0.227260\pi\)
−0.755775 + 0.654832i \(0.772740\pi\)
\(252\) 34.5684 23.8542i 0.137176 0.0946597i
\(253\) 46.2593i 0.182843i
\(254\) −63.8245 110.547i −0.251278 0.435225i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 201.596 + 349.175i 0.784420 + 1.35866i 0.929345 + 0.369213i \(0.120373\pi\)
−0.144924 + 0.989443i \(0.546294\pi\)
\(258\) −135.848 −0.526543
\(259\) −120.227 + 253.288i −0.464197 + 0.977947i
\(260\) 0 0
\(261\) −49.2050 85.2255i −0.188525 0.326534i
\(262\) −142.728 + 247.213i −0.544765 + 0.943560i
\(263\) −431.240 248.977i −1.63970 0.946679i −0.980937 0.194326i \(-0.937748\pi\)
−0.658759 0.752354i \(-0.728919\pi\)
\(264\) 5.49235 3.17101i 0.0208044 0.0120114i
\(265\) 0 0
\(266\) −26.5830 329.822i −0.0999360 1.23993i
\(267\) 60.5688i 0.226849i
\(268\) 69.4325 40.0869i 0.259077 0.149578i
\(269\) 155.357 + 89.6952i 0.577534 + 0.333439i 0.760153 0.649745i \(-0.225124\pi\)
−0.182619 + 0.983184i \(0.558457\pi\)
\(270\) 0 0
\(271\) −126.057 + 72.7792i −0.465156 + 0.268558i −0.714210 0.699932i \(-0.753214\pi\)
0.249054 + 0.968490i \(0.419880\pi\)
\(272\) −121.461 −0.446546
\(273\) −3.14576 39.0303i −0.0115229 0.142968i
\(274\) −0.00575719 −2.10116e−5
\(275\) 0 0
\(276\) 107.201 + 61.8924i 0.388409 + 0.224248i
\(277\) −185.057 106.843i −0.668076 0.385714i 0.127271 0.991868i \(-0.459378\pi\)
−0.795347 + 0.606154i \(0.792712\pi\)
\(278\) −81.9887 142.009i −0.294923 0.510822i
\(279\) 136.875i 0.490592i
\(280\) 0 0
\(281\) −349.479 −1.24370 −0.621849 0.783137i \(-0.713618\pi\)
−0.621849 + 0.783137i \(0.713618\pi\)
\(282\) 128.868 74.4020i 0.456979 0.263837i
\(283\) 47.1253 81.6234i 0.166521 0.288422i −0.770674 0.637230i \(-0.780080\pi\)
0.937194 + 0.348808i \(0.113413\pi\)
\(284\) 46.4480 80.4503i 0.163549 0.283276i
\(285\) 0 0
\(286\) 5.91271i 0.0206738i
\(287\) −168.170 243.703i −0.585957 0.849140i
\(288\) 16.9706i 0.0589256i
\(289\) −316.521 548.230i −1.09523 1.89699i
\(290\) 0 0
\(291\) 130.351 225.775i 0.447942 0.775858i
\(292\) −136.400 236.252i −0.467124 0.809082i
\(293\) −195.931 −0.668707 −0.334354 0.942448i \(-0.608518\pi\)
−0.334354 + 0.942448i \(0.608518\pi\)
\(294\) 112.214 + 42.5905i 0.381681 + 0.144866i
\(295\) 0 0
\(296\) −56.6441 98.1104i −0.191365 0.331454i
\(297\) 3.36337 5.82552i 0.0113245 0.0196145i
\(298\) −6.36070 3.67235i −0.0213446 0.0123233i
\(299\) 99.9440 57.7027i 0.334261 0.192986i
\(300\) 0 0
\(301\) −220.492 319.526i −0.732531 1.06155i
\(302\) 227.324i 0.752727i
\(303\) −179.797 + 103.806i −0.593391 + 0.342594i
\(304\) 115.788 + 66.8501i 0.380881 + 0.219902i
\(305\) 0 0
\(306\) −111.569 + 64.4142i −0.364603 + 0.210504i
\(307\) −452.419 −1.47368 −0.736839 0.676069i \(-0.763682\pi\)
−0.736839 + 0.676069i \(0.763682\pi\)
\(308\) 16.3730 + 7.77168i 0.0531590 + 0.0252327i
\(309\) −172.597 −0.558567
\(310\) 0 0
\(311\) −56.8889 32.8448i −0.182922 0.105610i 0.405743 0.913987i \(-0.367013\pi\)
−0.588665 + 0.808377i \(0.700346\pi\)
\(312\) 13.7020 + 7.91088i 0.0439168 + 0.0253554i
\(313\) 177.290 + 307.075i 0.566422 + 0.981071i 0.996916 + 0.0784776i \(0.0250059\pi\)
−0.430494 + 0.902593i \(0.641661\pi\)
\(314\) 134.678i 0.428909i
\(315\) 0 0
\(316\) −84.6045 −0.267736
\(317\) −116.792 + 67.4299i −0.368429 + 0.212713i −0.672772 0.739850i \(-0.734896\pi\)
0.304343 + 0.952563i \(0.401563\pi\)
\(318\) −66.9543 + 115.968i −0.210548 + 0.364680i
\(319\) 21.2329 36.7765i 0.0665609 0.115287i
\(320\) 0 0
\(321\) 81.3900i 0.253551i
\(322\) 28.4190 + 352.601i 0.0882576 + 1.09504i
\(323\) 1014.96i 3.14228i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 174.300 301.897i 0.534664 0.926064i
\(327\) −50.3683 87.2405i −0.154032 0.266791i
\(328\) 119.641 0.364758
\(329\) 384.162 + 182.348i 1.16767 + 0.554250i
\(330\) 0 0
\(331\) 90.2612 + 156.337i 0.272692 + 0.472317i 0.969550 0.244892i \(-0.0787525\pi\)
−0.696858 + 0.717209i \(0.745419\pi\)
\(332\) 1.53725 2.66259i 0.00463027 0.00801986i
\(333\) −104.062 60.0801i −0.312498 0.180421i
\(334\) −18.3032 + 10.5673i −0.0547999 + 0.0316387i
\(335\) 0 0
\(336\) −39.9162 + 27.5445i −0.118798 + 0.0819777i
\(337\) 5.84677i 0.0173495i 0.999962 + 0.00867473i \(0.00276129\pi\)
−0.999962 + 0.00867473i \(0.997239\pi\)
\(338\) −194.207 + 112.126i −0.574578 + 0.331733i
\(339\) 316.653 + 182.819i 0.934078 + 0.539290i
\(340\) 0 0
\(341\) 51.1513 29.5322i 0.150004 0.0866047i
\(342\) 141.811 0.414651
\(343\) 81.9559 + 333.065i 0.238938 + 0.971035i
\(344\) 156.864 0.456000
\(345\) 0 0
\(346\) 205.348 + 118.558i 0.593492 + 0.342653i
\(347\) 339.718 + 196.136i 0.979014 + 0.565234i 0.901972 0.431794i \(-0.142119\pi\)
0.0770414 + 0.997028i \(0.475453\pi\)
\(348\) 56.8170 + 98.4099i 0.163267 + 0.282787i
\(349\) 230.853i 0.661471i −0.943724 0.330735i \(-0.892703\pi\)
0.943724 0.330735i \(-0.107297\pi\)
\(350\) 0 0
\(351\) 16.7815 0.0478106
\(352\) −6.34202 + 3.66157i −0.0180171 + 0.0104022i
\(353\) 62.8188 108.805i 0.177957 0.308230i −0.763224 0.646134i \(-0.776385\pi\)
0.941181 + 0.337904i \(0.109718\pi\)
\(354\) 16.1613 27.9921i 0.0456533 0.0790738i
\(355\) 0 0
\(356\) 69.9388i 0.196457i
\(357\) −332.592 157.870i −0.931630 0.442212i
\(358\) 94.6743i 0.264453i
\(359\) 215.984 + 374.096i 0.601628 + 1.04205i 0.992575 + 0.121637i \(0.0388143\pi\)
−0.390947 + 0.920413i \(0.627852\pi\)
\(360\) 0 0
\(361\) 378.118 654.919i 1.04742 1.81418i
\(362\) −17.6147 30.5095i −0.0486593 0.0842803i
\(363\) −206.675 −0.569354
\(364\) 3.63241 + 45.0683i 0.00997916 + 0.123814i
\(365\) 0 0
\(366\) 48.3213 + 83.6950i 0.132026 + 0.228675i
\(367\) −236.049 + 408.849i −0.643185 + 1.11403i 0.341532 + 0.939870i \(0.389054\pi\)
−0.984717 + 0.174159i \(0.944279\pi\)
\(368\) −123.785 71.4672i −0.336372 0.194204i
\(369\) 109.897 63.4490i 0.297823 0.171948i
\(370\) 0 0
\(371\) −381.439 + 30.7432i −1.02814 + 0.0828658i
\(372\) 158.050i 0.424865i
\(373\) 75.7963 43.7610i 0.203207 0.117322i −0.394943 0.918705i \(-0.629236\pi\)
0.598151 + 0.801384i \(0.295902\pi\)
\(374\) −48.1441 27.7960i −0.128728 0.0743209i
\(375\) 0 0
\(376\) −148.804 + 85.9121i −0.395756 + 0.228490i
\(377\) 105.942 0.281012
\(378\) −22.0577 + 46.4700i −0.0583536 + 0.122936i
\(379\) 359.658 0.948965 0.474483 0.880265i \(-0.342635\pi\)
0.474483 + 0.880265i \(0.342635\pi\)
\(380\) 0 0
\(381\) 135.392 + 78.1687i 0.355360 + 0.205167i
\(382\) 16.6622 + 9.61992i 0.0436183 + 0.0251830i
\(383\) 242.085 + 419.304i 0.632077 + 1.09479i 0.987126 + 0.159942i \(0.0511306\pi\)
−0.355050 + 0.934847i \(0.615536\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 257.978 0.668336
\(387\) 144.089 83.1896i 0.372322 0.214960i
\(388\) −150.516 + 260.702i −0.387929 + 0.671913i
\(389\) −179.791 + 311.407i −0.462188 + 0.800533i −0.999070 0.0431246i \(-0.986269\pi\)
0.536882 + 0.843657i \(0.319602\pi\)
\(390\) 0 0
\(391\) 1085.06i 2.77508i
\(392\) −129.574 49.1793i −0.330546 0.125457i
\(393\) 349.612i 0.889597i
\(394\) −202.713 351.109i −0.514499 0.891139i
\(395\) 0 0
\(396\) −3.88368 + 6.72673i −0.00980727 + 0.0169867i
\(397\) −90.6969 157.092i −0.228456 0.395697i 0.728895 0.684626i \(-0.240034\pi\)
−0.957351 + 0.288929i \(0.906701\pi\)
\(398\) 4.47632 0.0112470
\(399\) 230.169 + 333.550i 0.576865 + 0.835965i
\(400\) 0 0
\(401\) 132.742 + 229.916i 0.331027 + 0.573355i 0.982713 0.185133i \(-0.0592716\pi\)
−0.651687 + 0.758488i \(0.725938\pi\)
\(402\) −49.0962 + 85.0371i −0.122130 + 0.211535i
\(403\) 127.610 + 73.6754i 0.316649 + 0.182817i
\(404\) 207.612 119.865i 0.513891 0.296695i
\(405\) 0 0
\(406\) −139.250 + 293.365i −0.342980 + 0.722574i
\(407\) 51.8516i 0.127399i
\(408\) 128.828 74.3791i 0.315756 0.182302i
\(409\) 492.567 + 284.384i 1.20432 + 0.695315i 0.961513 0.274759i \(-0.0885981\pi\)
0.242808 + 0.970074i \(0.421931\pi\)
\(410\) 0 0
\(411\) 0.00610642 0.00352554i 1.48575e−5 8.57797e-6i
\(412\) 199.298 0.483733
\(413\) 92.0707 7.42071i 0.222931 0.0179678i
\(414\) −151.605 −0.366195
\(415\) 0 0
\(416\) −15.8218 9.13469i −0.0380331 0.0219584i
\(417\) 173.924 + 100.415i 0.417085 + 0.240804i
\(418\) 30.5970 + 52.9956i 0.0731987 + 0.126784i
\(419\) 556.041i 1.32707i −0.748146 0.663534i \(-0.769056\pi\)
0.748146 0.663534i \(-0.230944\pi\)
\(420\) 0 0
\(421\) −476.267 −1.13128 −0.565638 0.824654i \(-0.691370\pi\)
−0.565638 + 0.824654i \(0.691370\pi\)
\(422\) −219.627 + 126.801i −0.520442 + 0.300477i
\(423\) −91.1235 + 157.831i −0.215422 + 0.373122i
\(424\) 77.3122 133.909i 0.182340 0.315822i
\(425\) 0 0
\(426\) 113.774i 0.267075i
\(427\) −118.428 + 249.499i −0.277350 + 0.584307i
\(428\) 93.9810i 0.219582i
\(429\) 3.62078 + 6.27137i 0.00844004 + 0.0146186i
\(430\) 0 0
\(431\) −229.808 + 398.039i −0.533196 + 0.923523i 0.466052 + 0.884757i \(0.345676\pi\)
−0.999248 + 0.0387660i \(0.987657\pi\)
\(432\) −10.3923 18.0000i −0.0240563 0.0416667i
\(433\) 65.9185 0.152237 0.0761183 0.997099i \(-0.475747\pi\)
0.0761183 + 0.997099i \(0.475747\pi\)
\(434\) −371.746 + 256.527i −0.856559 + 0.591076i
\(435\) 0 0
\(436\) 58.1604 + 100.737i 0.133395 + 0.231047i
\(437\) −597.199 + 1034.38i −1.36659 + 2.36700i
\(438\) 289.348 + 167.055i 0.660613 + 0.381405i
\(439\) 307.619 177.604i 0.700727 0.404565i −0.106891 0.994271i \(-0.534090\pi\)
0.807618 + 0.589706i \(0.200756\pi\)
\(440\) 0 0
\(441\) −145.102 + 23.5429i −0.329031 + 0.0533852i
\(442\) 138.688i 0.313774i
\(443\) −656.650 + 379.117i −1.48228 + 0.855795i −0.999798 0.0201113i \(-0.993598\pi\)
−0.482482 + 0.875906i \(0.660265\pi\)
\(444\) 120.160 + 69.3746i 0.270631 + 0.156249i
\(445\) 0 0
\(446\) −87.3666 + 50.4411i −0.195889 + 0.113097i
\(447\) 8.99539 0.0201239
\(448\) 46.0912 31.8057i 0.102882 0.0709948i
\(449\) −668.104 −1.48798 −0.743992 0.668189i \(-0.767070\pi\)
−0.743992 + 0.668189i \(0.767070\pi\)
\(450\) 0 0
\(451\) 47.4227 + 27.3795i 0.105150 + 0.0607084i
\(452\) −365.639 211.102i −0.808936 0.467039i
\(453\) 139.207 + 241.113i 0.307300 + 0.532258i
\(454\) 201.581i 0.444012i
\(455\) 0 0
\(456\) −163.749 −0.359098
\(457\) 645.475 372.665i 1.41242 0.815460i 0.416802 0.908997i \(-0.363151\pi\)
0.995616 + 0.0935379i \(0.0298176\pi\)
\(458\) −88.9993 + 154.151i −0.194322 + 0.336575i
\(459\) 78.8909 136.643i 0.171876 0.297697i
\(460\) 0 0
\(461\) 592.937i 1.28620i −0.765783 0.643099i \(-0.777648\pi\)
0.765783 0.643099i \(-0.222352\pi\)
\(462\) −22.1253 + 1.78326i −0.0478903 + 0.00385987i
\(463\) 529.829i 1.14434i −0.820136 0.572169i \(-0.806102\pi\)
0.820136 0.572169i \(-0.193898\pi\)
\(464\) −65.6066 113.634i −0.141394 0.244901i
\(465\) 0 0
\(466\) 116.153 201.183i 0.249255 0.431723i
\(467\) 83.6375 + 144.864i 0.179095 + 0.310202i 0.941571 0.336815i \(-0.109350\pi\)
−0.762476 + 0.647017i \(0.776016\pi\)
\(468\) −19.3776 −0.0414052
\(469\) −279.701 + 22.5434i −0.596378 + 0.0480669i
\(470\) 0 0
\(471\) −82.4728 142.847i −0.175102 0.303285i
\(472\) −18.6614 + 32.3225i −0.0395369 + 0.0684799i
\(473\) 62.1771 + 35.8980i 0.131453 + 0.0758943i
\(474\) 89.7367 51.8095i 0.189318 0.109303i
\(475\) 0 0
\(476\) 384.044 + 182.292i 0.806815 + 0.382966i
\(477\) 164.004i 0.343824i
\(478\) 61.7573 35.6556i 0.129199 0.0745933i
\(479\) −221.195 127.707i −0.461785 0.266612i 0.251009 0.967985i \(-0.419237\pi\)
−0.712795 + 0.701373i \(0.752571\pi\)
\(480\) 0 0
\(481\) 112.026 64.6783i 0.232902 0.134466i
\(482\) −275.986 −0.572585
\(483\) −246.066 356.587i −0.509454 0.738276i
\(484\) 238.648 0.493075
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) 525.531 + 303.415i 1.07912 + 0.623030i 0.930659 0.365889i \(-0.119235\pi\)
0.148460 + 0.988918i \(0.452568\pi\)
\(488\) −55.7967 96.6427i −0.114337 0.198038i
\(489\) 426.947i 0.873102i
\(490\) 0 0
\(491\) 707.855 1.44166 0.720830 0.693112i \(-0.243761\pi\)
0.720830 + 0.693112i \(0.243761\pi\)
\(492\) −126.898 + 73.2645i −0.257923 + 0.148912i
\(493\) 498.038 862.628i 1.01022 1.74975i
\(494\) −76.3319 + 132.211i −0.154518 + 0.267633i
\(495\) 0 0
\(496\) 182.500i 0.367944i
\(497\) −267.606 + 184.664i −0.538442 + 0.371557i
\(498\) 3.76548i 0.00756120i
\(499\) 330.115 + 571.776i 0.661553 + 1.14584i 0.980208 + 0.197972i \(0.0634357\pi\)
−0.318655 + 0.947871i \(0.603231\pi\)
\(500\) 0 0
\(501\) 12.9423 22.4167i 0.0258329 0.0447439i
\(502\) 232.444 + 402.605i 0.463036 + 0.802002i
\(503\) 254.083 0.505136 0.252568 0.967579i \(-0.418725\pi\)
0.252568 + 0.967579i \(0.418725\pi\)
\(504\) 25.4700 53.6589i 0.0505357 0.106466i
\(505\) 0 0
\(506\) −32.7103 56.6559i −0.0646448 0.111968i
\(507\) 137.325 237.855i 0.270859 0.469141i
\(508\) −156.337 90.2615i −0.307751 0.177680i
\(509\) −222.003 + 128.174i −0.436156 + 0.251815i −0.701966 0.712211i \(-0.747694\pi\)
0.265810 + 0.964026i \(0.414361\pi\)
\(510\) 0 0
\(511\) 76.7063 + 951.715i 0.150110 + 1.86246i
\(512\) 22.6274i 0.0441942i
\(513\) −150.413 + 86.8409i −0.293202 + 0.169280i
\(514\) 493.807 + 285.100i 0.960715 + 0.554669i
\(515\) 0 0
\(516\) −166.379 + 96.0591i −0.322440 + 0.186161i
\(517\) −78.6433 −0.152115
\(518\) 31.8545 + 395.227i 0.0614952 + 0.762986i
\(519\) −290.406 −0.559550
\(520\) 0 0
\(521\) 164.700 + 95.0898i 0.316124 + 0.182514i 0.649663 0.760222i \(-0.274910\pi\)
−0.333540 + 0.942736i \(0.608243\pi\)
\(522\) −120.527 69.5863i −0.230895 0.133307i
\(523\) −173.610 300.701i −0.331950 0.574954i 0.650944 0.759126i \(-0.274373\pi\)
−0.982894 + 0.184171i \(0.941040\pi\)
\(524\) 403.697i 0.770414i
\(525\) 0 0
\(526\) −704.212 −1.33881
\(527\) 1199.80 692.706i 2.27666 1.31443i
\(528\) 4.48449 7.76736i 0.00849335 0.0147109i
\(529\) 373.946 647.693i 0.706891 1.22437i
\(530\) 0 0
\(531\) 39.5868i 0.0745515i
\(532\) −265.777 385.151i −0.499580 0.723967i
\(533\) 136.610i 0.256304i
\(534\) 42.8286 + 74.1813i 0.0802033 + 0.138916i
\(535\) 0 0
\(536\) 56.6914 98.1924i 0.105768 0.183195i
\(537\) 57.9759 + 100.417i 0.107963 + 0.186997i
\(538\) 253.696 0.471554
\(539\) −40.1055 49.1462i −0.0744072 0.0911804i
\(540\) 0 0
\(541\) −216.672 375.287i −0.400503 0.693691i 0.593284 0.804993i \(-0.297831\pi\)
−0.993787 + 0.111302i \(0.964498\pi\)
\(542\) −102.925 + 178.272i −0.189899 + 0.328915i
\(543\) 37.3663 + 21.5735i 0.0688146 + 0.0397301i
\(544\) −148.758 + 85.8856i −0.273452 + 0.157878i
\(545\) 0 0
\(546\) −31.4513 45.5777i −0.0576032 0.0834757i
\(547\) 718.061i 1.31272i −0.754446 0.656362i \(-0.772094\pi\)
0.754446 0.656362i \(-0.227906\pi\)
\(548\) −0.00705109 + 0.00407095i −1.28670e−5 + 7.42874e-6i
\(549\) −102.505 59.1813i −0.186712 0.107798i
\(550\) 0 0
\(551\) −949.556 + 548.226i −1.72333 + 0.994966i
\(552\) 175.058 0.317134
\(553\) 267.510 + 126.977i 0.483742 + 0.229615i
\(554\) −302.197 −0.545482
\(555\) 0 0
\(556\) −200.830 115.950i −0.361206 0.208542i
\(557\) 858.396 + 495.595i 1.54111 + 0.889758i 0.998769 + 0.0495971i \(0.0157937\pi\)
0.542337 + 0.840161i \(0.317540\pi\)
\(558\) −96.7854 167.637i −0.173451 0.300425i
\(559\) 179.113i 0.320417i
\(560\) 0 0
\(561\) 68.0860 0.121365
\(562\) −428.023 + 247.119i −0.761606 + 0.439713i
\(563\) 290.108 502.481i 0.515289 0.892506i −0.484554 0.874762i \(-0.661018\pi\)
0.999843 0.0177449i \(-0.00564868\pi\)
\(564\) 105.220 182.247i 0.186561 0.323133i
\(565\) 0 0
\(566\) 133.291i 0.235496i
\(567\) −5.06126 62.7964i −0.00892639 0.110752i
\(568\) 131.375i 0.231294i
\(569\) −106.770 184.931i −0.187645 0.325010i 0.756820 0.653624i \(-0.226752\pi\)
−0.944465 + 0.328613i \(0.893419\pi\)
\(570\) 0 0
\(571\) 378.751 656.016i 0.663311 1.14889i −0.316429 0.948616i \(-0.602484\pi\)
0.979740 0.200273i \(-0.0641828\pi\)
\(572\) −4.18091 7.24156i −0.00730929 0.0126601i
\(573\) −23.5639 −0.0411237
\(574\) −378.289 179.560i −0.659040 0.312823i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −90.7836 + 157.242i −0.157337 + 0.272516i −0.933908 0.357514i \(-0.883624\pi\)
0.776570 + 0.630031i \(0.216958\pi\)
\(578\) −775.314 447.628i −1.34137 0.774442i
\(579\) −273.627 + 157.978i −0.472585 + 0.272847i
\(580\) 0 0
\(581\) −8.85671 + 6.11165i −0.0152439 + 0.0105192i
\(582\) 368.689i 0.633486i
\(583\) 61.2894 35.3855i 0.105128 0.0606955i
\(584\) −334.111 192.899i −0.572107 0.330306i
\(585\) 0 0
\(586\) −239.966 + 138.544i −0.409498 + 0.236424i
\(587\) 156.397 0.266434 0.133217 0.991087i \(-0.457469\pi\)
0.133217 + 0.991087i \(0.457469\pi\)
\(588\) 167.550 27.1850i 0.284949 0.0462329i
\(589\) −1525.02 −2.58917
\(590\) 0 0
\(591\) 430.019 + 248.271i 0.727612 + 0.420087i
\(592\) −138.749 80.1068i −0.234373 0.135316i
\(593\) −105.889 183.404i −0.178564 0.309282i 0.762825 0.646605i \(-0.223812\pi\)
−0.941389 + 0.337323i \(0.890479\pi\)
\(594\) 9.51303i 0.0160152i
\(595\) 0 0
\(596\) −10.3870 −0.0174278
\(597\) −4.74785 + 2.74117i −0.00795285 + 0.00459158i
\(598\) 81.6039 141.342i 0.136461 0.236358i
\(599\) 264.528 458.175i 0.441616 0.764901i −0.556194 0.831053i \(-0.687739\pi\)
0.997810 + 0.0661519i \(0.0210722\pi\)
\(600\) 0 0
\(601\) 899.473i 1.49663i 0.663345 + 0.748314i \(0.269136\pi\)
−0.663345 + 0.748314i \(0.730864\pi\)
\(602\) −495.985 235.427i −0.823895 0.391074i
\(603\) 120.261i 0.199437i
\(604\) −160.742 278.413i −0.266129 0.460949i
\(605\) 0 0
\(606\) −146.804 + 254.272i −0.242251 + 0.419591i
\(607\) −268.038 464.255i −0.441578 0.764835i 0.556229 0.831029i \(-0.312248\pi\)
−0.997807 + 0.0661939i \(0.978914\pi\)
\(608\) 189.081 0.310988
\(609\) −31.9517 396.433i −0.0524659 0.650958i
\(610\) 0 0
\(611\) −98.0976 169.910i −0.160552 0.278085i
\(612\) −91.0954 + 157.782i −0.148849 + 0.257813i
\(613\) −717.977 414.524i −1.17125 0.676222i −0.217276 0.976110i \(-0.569717\pi\)
−0.953974 + 0.299888i \(0.903051\pi\)
\(614\) −554.098 + 319.908i −0.902439 + 0.521024i
\(615\) 0 0
\(616\) 25.5481 2.05913i 0.0414742 0.00334274i
\(617\) 404.320i 0.655300i −0.944799 0.327650i \(-0.893743\pi\)
0.944799 0.327650i \(-0.106257\pi\)
\(618\) −211.388 + 122.045i −0.342051 + 0.197483i
\(619\) 346.662 + 200.145i 0.560036 + 0.323337i 0.753160 0.657838i \(-0.228529\pi\)
−0.193124 + 0.981174i \(0.561862\pi\)
\(620\) 0 0
\(621\) 160.801 92.8387i 0.258939 0.149499i
\(622\) −92.8991 −0.149355
\(623\) −104.966 + 221.138i −0.168485 + 0.354957i
\(624\) 22.3753 0.0358579
\(625\) 0 0
\(626\) 434.270 + 250.726i 0.693722 + 0.400521i
\(627\) −64.9061 37.4736i −0.103519 0.0597665i
\(628\) 95.2314 + 164.946i 0.151642 + 0.262652i
\(629\) 1216.23i 1.93359i
\(630\) 0 0
\(631\) 334.639 0.530331 0.265165 0.964203i \(-0.414573\pi\)
0.265165 + 0.964203i \(0.414573\pi\)
\(632\) −103.619 + 59.8244i −0.163954 + 0.0946589i
\(633\) 155.299 268.987i 0.245339 0.424939i
\(634\) −95.3603 + 165.169i −0.150411 + 0.260519i
\(635\) 0 0
\(636\) 189.375i 0.297760i
\(637\) 56.1547 147.952i 0.0881550 0.232264i
\(638\) 60.0558i 0.0941313i
\(639\) −69.6720 120.676i −0.109033 0.188851i
\(640\) 0 0
\(641\) 36.0084 62.3683i 0.0561753 0.0972984i −0.836570 0.547860i \(-0.815443\pi\)
0.892746 + 0.450561i \(0.148776\pi\)
\(642\) 57.5514 + 99.6819i 0.0896439 + 0.155268i
\(643\) −1254.20 −1.95054 −0.975269 0.221020i \(-0.929061\pi\)
−0.975269 + 0.221020i \(0.929061\pi\)
\(644\) 284.133 + 411.751i 0.441200 + 0.639366i
\(645\) 0 0
\(646\) 717.683 + 1243.06i 1.11096 + 1.92425i
\(647\) 73.1699 126.734i 0.113091 0.195879i −0.803924 0.594732i \(-0.797258\pi\)
0.917015 + 0.398853i \(0.130591\pi\)
\(648\) 22.0454 + 12.7279i 0.0340207 + 0.0196419i
\(649\) −14.7939 + 8.54125i −0.0227949 + 0.0131606i
\(650\) 0 0
\(651\) 237.207 499.735i 0.364373 0.767642i
\(652\) 492.996i 0.756128i
\(653\) 687.082 396.687i 1.05219 0.607484i 0.128930 0.991654i \(-0.458846\pi\)
0.923262 + 0.384170i \(0.125512\pi\)
\(654\) −123.377 71.2316i −0.188649 0.108917i
\(655\) 0 0
\(656\) 146.529 84.5986i 0.223368 0.128961i
\(657\) −409.200 −0.622832
\(658\) 599.441 48.3137i 0.911004 0.0734251i
\(659\) −35.5649 −0.0539680 −0.0269840 0.999636i \(-0.508590\pi\)
−0.0269840 + 0.999636i \(0.508590\pi\)
\(660\) 0 0
\(661\) 193.509 + 111.723i 0.292752 + 0.169021i 0.639182 0.769055i \(-0.279273\pi\)
−0.346430 + 0.938076i \(0.612606\pi\)
\(662\) 221.094 + 127.649i 0.333979 + 0.192823i
\(663\) 84.9288 + 147.101i 0.128098 + 0.221872i
\(664\) 4.34800i 0.00654819i
\(665\) 0 0
\(666\) −169.932 −0.255154
\(667\) 1015.14 586.090i 1.52195 0.878696i
\(668\) −14.9445 + 25.8846i −0.0223720 + 0.0387494i
\(669\) 61.7775 107.002i 0.0923431 0.159943i
\(670\) 0 0
\(671\) 51.0759i 0.0761190i
\(672\) −29.4102 + 61.9600i −0.0437652 + 0.0922024i
\(673\) 216.920i 0.322318i 0.986928 + 0.161159i \(0.0515232\pi\)
−0.986928 + 0.161159i \(0.948477\pi\)
\(674\) 4.13429 + 7.16080i 0.00613396 + 0.0106243i
\(675\) 0 0
\(676\) −158.570 + 274.651i −0.234571 + 0.406288i
\(677\) −23.4825 40.6729i −0.0346861 0.0600781i 0.848161 0.529738i \(-0.177710\pi\)
−0.882847 + 0.469660i \(0.844376\pi\)
\(678\) 517.091 0.762672
\(679\) 867.186 598.410i 1.27715 0.881310i
\(680\) 0 0
\(681\) −123.443 213.809i −0.181267 0.313964i
\(682\) 41.7648 72.3388i 0.0612388 0.106069i
\(683\) −51.1993 29.5599i −0.0749623 0.0432795i 0.462050 0.886854i \(-0.347114\pi\)
−0.537013 + 0.843574i \(0.680447\pi\)
\(684\) 173.682 100.275i 0.253921 0.146601i
\(685\) 0 0
\(686\) 335.888 + 349.968i 0.489632 + 0.510157i
\(687\) 218.003i 0.317326i
\(688\) 192.118 110.919i 0.279242 0.161220i
\(689\) 152.902 + 88.2779i 0.221918 + 0.128125i
\(690\) 0 0
\(691\) 916.389 529.078i 1.32618 0.765669i 0.341472 0.939892i \(-0.389075\pi\)
0.984706 + 0.174222i \(0.0557412\pi\)
\(692\) 335.332 0.484584
\(693\) 22.3754 15.4404i 0.0322878 0.0222805i
\(694\) 554.757 0.799361
\(695\) 0 0
\(696\) 139.173 + 80.3513i 0.199961 + 0.115447i
\(697\) 1112.34 + 642.212i 1.59590 + 0.921395i
\(698\) −163.238 282.736i −0.233865 0.405066i
\(699\) 284.516i 0.407032i
\(700\) 0 0
\(701\) −394.358 −0.562565 −0.281283 0.959625i \(-0.590760\pi\)
−0.281283 + 0.959625i \(0.590760\pi\)
\(702\) 20.5531 11.8663i 0.0292779 0.0169036i
\(703\) −669.394 + 1159.42i −0.952197 + 1.64925i
\(704\) −5.17824 + 8.96898i −0.00735546 + 0.0127400i
\(705\) 0 0
\(706\) 177.678i 0.251669i
\(707\) −836.342 + 67.4075i −1.18295 + 0.0953430i
\(708\) 45.7109i 0.0645635i
\(709\) −20.7217 35.8911i −0.0292267 0.0506221i 0.851042 0.525097i \(-0.175971\pi\)
−0.880269 + 0.474475i \(0.842638\pi\)
\(710\) 0 0
\(711\) −63.4534 + 109.905i −0.0892453 + 0.154577i
\(712\) −49.4542 85.6572i −0.0694581 0.120305i
\(713\) 1630.35 2.28660
\(714\) −518.971 + 41.8280i −0.726850 + 0.0585826i
\(715\) 0 0
\(716\) −66.9449 115.952i −0.0934984 0.161944i
\(717\) −43.6690 + 75.6369i −0.0609051 + 0.105491i
\(718\) 529.052 + 305.448i 0.736841 + 0.425415i
\(719\) −556.327 + 321.195i −0.773751 + 0.446725i −0.834211 0.551445i \(-0.814077\pi\)
0.0604602 + 0.998171i \(0.480743\pi\)
\(720\) 0 0
\(721\) −630.157 299.113i −0.874004 0.414859i
\(722\) 1069.48i 1.48127i
\(723\) 292.727 169.006i 0.404879 0.233757i
\(724\) −43.1469 24.9109i −0.0595952 0.0344073i
\(725\) 0 0
\(726\) −253.125 + 146.142i −0.348657 + 0.201297i
\(727\) 979.168 1.34686 0.673431 0.739250i \(-0.264820\pi\)
0.673431 + 0.739250i \(0.264820\pi\)
\(728\) 36.3169 + 52.6286i 0.0498858 + 0.0722921i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 1458.42 + 842.021i 1.99511 + 1.15188i
\(732\) 118.363 + 68.3367i 0.161698 + 0.0933562i
\(733\) −618.862 1071.90i −0.844286 1.46235i −0.886240 0.463227i \(-0.846692\pi\)
0.0419537 0.999120i \(-0.486642\pi\)
\(734\) 667.647i 0.909601i
\(735\) 0 0
\(736\) −202.140 −0.274647
\(737\) 44.9423 25.9474i 0.0609800 0.0352068i
\(738\) 89.7304 155.418i 0.121586 0.210593i
\(739\) −477.274 + 826.662i −0.645837 + 1.11862i 0.338271 + 0.941049i \(0.390158\pi\)
−0.984108 + 0.177574i \(0.943175\pi\)
\(740\) 0 0
\(741\) 186.974i 0.252327i
\(742\) −445.426 + 307.370i −0.600305 + 0.414246i
\(743\) 401.194i 0.539964i 0.962865 + 0.269982i \(0.0870178\pi\)
−0.962865 + 0.269982i \(0.912982\pi\)
\(744\) 111.758 + 193.571i 0.150213 + 0.260176i
\(745\) 0 0
\(746\) 61.8874 107.192i 0.0829590 0.143689i
\(747\) −2.30587 3.99389i −0.00308685 0.00534657i
\(748\) −78.6190 −0.105106
\(749\) −141.050 + 297.157i −0.188318 + 0.396738i
\(750\) 0 0
\(751\) 420.870 + 728.968i 0.560412 + 0.970662i 0.997460 + 0.0712243i \(0.0226906\pi\)
−0.437048 + 0.899438i \(0.643976\pi\)
\(752\) −121.498 + 210.441i −0.161567 + 0.279841i
\(753\) −493.088 284.685i −0.654832 0.378067i
\(754\) 129.751 74.9120i 0.172084 0.0993528i
\(755\) 0 0
\(756\) 5.84424 + 72.5110i 0.00773048 + 0.0959140i
\(757\) 1287.18i 1.70037i 0.526487 + 0.850183i \(0.323509\pi\)
−0.526487 + 0.850183i \(0.676491\pi\)
\(758\) 440.489 254.317i 0.581120 0.335510i
\(759\) 69.3890 + 40.0617i 0.0914216 + 0.0527823i
\(760\) 0 0
\(761\) −1237.18 + 714.288i −1.62573 + 0.938618i −0.640387 + 0.768052i \(0.721226\pi\)
−0.985346 + 0.170565i \(0.945441\pi\)
\(762\) 221.095 0.290150
\(763\) −32.7072 405.807i −0.0428666 0.531857i
\(764\) 27.2092 0.0356142
\(765\) 0 0
\(766\) 592.986 + 342.361i 0.774133 + 0.446946i
\(767\) −36.9070 21.3083i −0.0481187 0.0277813i
\(768\) −13.8564 24.0000i −0.0180422 0.0312500i
\(769\) 1030.04i 1.33945i −0.742608 0.669726i \(-0.766411\pi\)
0.742608 0.669726i \(-0.233589\pi\)
\(770\) 0 0
\(771\) −698.349 −0.905771
\(772\) 315.957 182.418i 0.409271 0.236293i
\(773\) 374.310 648.324i 0.484231 0.838712i −0.515605 0.856826i \(-0.672433\pi\)
0.999836 + 0.0181142i \(0.00576625\pi\)
\(774\) 117.648 203.772i 0.152000 0.263271i
\(775\) 0 0
\(776\) 425.725i 0.548615i
\(777\) −275.813 399.695i −0.354972 0.514408i
\(778\) 508.526i 0.653632i
\(779\) −706.929 1224.44i −0.907482 1.57181i
\(780\) 0 0
\(781\) 30.0649 52.0739i 0.0384954 0.0666759i