Properties

Label 1050.3.q.b.649.4
Level $1050$
Weight $3$
Character 1050.649
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 649.4
Root \(-0.337183 + 1.25838i\) of defining polynomial
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.b.199.4

$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.893947 0.448174i \(-0.147925\pi\)
−0.835103 + 0.550094i \(0.814592\pi\)
\(12\) −1.73205 + 3.00000i −0.144338 + 0.250000i
\(13\) −3.22960 −0.248431 −0.124215 0.992255i \(-0.539641\pi\)
−0.124215 + 0.992255i \(0.539641\pi\)
\(14\) −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 −0.836148 0.548504i \(-0.815198\pi\)
−0.0569439 0.998377i \(-0.518136\pi\)
\(18\) 3.67423 2.12132i 0.204124 0.117851i
\(19\) −28.9470 16.7125i −1.52352 0.879607i −0.999613 0.0278345i \(-0.991139\pi\)
−0.523912 0.851773i \(-0.675528\pi\)
\(20\) 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 \(-0.616501\pi\)
−0.987607 + 0.156950i \(0.949834\pi\)
\(24\) 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 0.298747 0.954332i \(-0.403431\pi\)
0.975849 + 0.218444i \(0.0700981\pi\)
\(32\) 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 \(-0.515387\pi\)
−0.889174 + 0.457570i \(0.848720\pi\)
\(38\) 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 \(-0.827478\pi\)
0.856682 0.515845i \(-0.172522\pi\)
\(42\) 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 −0.337741 0.941239i \(-0.609663\pi\)
0.984008 0.178127i \(-0.0570037\pi\)
\(48\) −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 \(-0.839148\pi\)
−0.0182660 + 0.999833i \(0.505815\pi\)
\(54\) 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 −0.593709 0.804680i \(-0.702337\pi\)
0.400019 + 0.916507i \(0.369004\pi\)
\(60\) 0 0
\(61\) 34.1684 + 19.7271i 0.560137 + 0.323395i 0.753200 0.657791i \(-0.228509\pi\)
−0.193064 + 0.981186i \(0.561842\pi\)
\(62\) −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 \(-0.763372\pi\)
0.218026 + 0.975943i \(0.430038\pi\)
\(68\) 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 −0.775970 0.630769i \(-0.782739\pi\)
−0.158277 0.987395i \(-0.550594\pi\)
\(74\) 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 −0.968277 0.249880i \(-0.919609\pi\)
0.700541 + 0.713612i \(0.252942\pi\)
\(80\) 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 \(-0.502948\pi\)
−0.00926054 + 0.999957i \(0.502948\pi\)
\(84\) −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 0.660393 0.750920i \(-0.270390\pi\)
−0.320119 + 0.947377i \(0.603723\pi\)
\(90\) 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 \(-0.217317\pi\)
0.775858 + 0.630907i \(0.217317\pi\)
\(98\) 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 0.111434 0.993772i \(-0.464456\pi\)
0.916349 + 0.400381i \(0.131122\pi\)
\(102\) −64.4142 + 37.1895i −0.631511 + 0.364603i
\(103\) −49.8245 + 86.2986i −0.483733 + 0.837851i −0.999825 0.0186825i \(-0.994053\pi\)
0.516092 + 0.856533i \(0.327386\pi\)
\(104\) 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 \(-0.403803\pi\)
−0.677961 + 0.735098i \(0.737136\pi\)
\(108\) −5.19615 9.00000i −0.0481125 0.0833333i
\(109\) −29.0802 50.3683i −0.266791 0.462095i 0.701241 0.712925i \(-0.252630\pi\)
−0.968031 + 0.250830i \(0.919297\pi\)
\(110\) 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 −0.348426 0.937336i \(-0.613284\pi\)
−0.985970 + 0.166923i \(0.946617\pi\)
\(132\) −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 \(-0.666662\pi\)
0.500013 + 0.866018i \(0.333329\pi\)
\(138\) −43.7646 + 75.8024i −0.317134 + 0.549293i
\(139\) 115.950i 0.834169i 0.908868 + 0.417085i \(0.136948\pi\)
−0.908868 + 0.417085i \(0.863052\pi\)
\(140\) 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 −0.874608 0.484831i \(-0.838881\pi\)
0.857180 + 0.515017i \(0.172214\pi\)
\(150\) 0 0
\(151\) 80.3710 + 139.207i 0.532258 + 0.921899i 0.999291 + 0.0376583i \(0.0119898\pi\)
−0.467032 + 0.884240i \(0.654677\pi\)
\(152\) −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 \(-0.0685833\pi\)
−0.673593 + 0.739102i \(0.735250\pi\)
\(158\) 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 \(-0.606245\pi\)
−0.982038 + 0.188683i \(0.939578\pi\)
\(164\) 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 \(-0.485753\pi\)
0.0447439 + 0.998998i \(0.485753\pi\)
\(168\) 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 \(-0.994362\pi\)
0.515259 + 0.857035i \(0.327696\pi\)
\(174\) 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 0.944248 0.329236i \(-0.106791\pi\)
−0.757251 + 0.653124i \(0.773458\pi\)
\(180\) 0 0
\(181\) 24.9109i 0.137629i 0.997629 + 0.0688146i \(0.0219217\pi\)
−0.997629 + 0.0688146i \(0.978078\pi\)
\(182\) 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 −0.847669 0.530526i \(-0.821995\pi\)
0.883283 + 0.468840i \(0.155328\pi\)
\(192\) −6.92820 12.0000i −0.0360844 0.0625000i
\(193\) −157.978 + 91.2089i −0.818541 + 0.472585i −0.849913 0.526923i \(-0.823346\pi\)
0.0313718 + 0.999508i \(0.490012\pi\)
\(194\) −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 −0.493097 0.869974i \(-0.664135\pi\)
0.506872 + 0.862022i \(0.330802\pi\)
\(200\) 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 \(-0.448869\pi\)
0.159943 + 0.987126i \(0.448869\pi\)
\(224\) 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 \(-0.0650096\pi\)
−0.665253 + 0.746618i \(0.731676\pi\)
\(228\) 100.275 57.8939i 0.439804 0.253921i
\(229\) −109.001 62.9320i −0.475989 0.274812i 0.242755 0.970088i \(-0.421949\pi\)
−0.718743 + 0.695276i \(0.755282\pi\)
\(230\) 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 \(-0.448002\pi\)
−0.773180 + 0.634186i \(0.781335\pi\)
\(234\) −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 −0.807820 0.589429i \(-0.799353\pi\)
0.106550 + 0.994307i \(0.466020\pi\)
\(242\) −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 \(-0.772740\pi\)
0.755775 0.654832i \(-0.227260\pi\)
\(252\) −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 0.144924 + 0.989443i \(0.453706\pi\)
−0.929345 + 0.369213i \(0.879627\pi\)
\(258\) 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 0.658759 0.752354i \(-0.271081\pi\)
0.980937 0.194326i \(-0.0622519\pi\)
\(264\) 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 −0.182619 0.983184i \(-0.558457\pi\)
0.760153 + 0.649745i \(0.225124\pi\)
\(270\) 0 0
\(271\) −126.057 72.7792i −0.465156 0.268558i 0.249054 0.968490i \(-0.419880\pi\)
−0.714210 + 0.699932i \(0.753214\pi\)
\(272\) 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 \(-0.540622\pi\)
0.795347 + 0.606154i \(0.207288\pi\)
\(278\) 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 \(-0.219920\pi\)
−0.937194 + 0.348808i \(0.886587\pi\)
\(284\) 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 \(-0.391482\pi\)
0.334354 + 0.942448i \(0.391482\pi\)
\(294\) 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 \(-0.236318\pi\)
0.736839 + 0.676069i \(0.236318\pi\)
\(308\) −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 −0.588665 0.808377i \(-0.700346\pi\)
0.405743 + 0.913987i \(0.367013\pi\)
\(312\) −13.7020 + 7.91088i −0.0439168 + 0.0253554i
\(313\) −177.290 + 307.075i −0.566422 + 0.981071i 0.430494 + 0.902593i \(0.358339\pi\)
−0.996916 + 0.0784776i \(0.974994\pi\)
\(314\) 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 \(-0.265104\pi\)
−0.304343 + 0.952563i \(0.598437\pi\)
\(318\) 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 −0.696858 0.717209i \(-0.745419\pi\)
0.969550 + 0.244892i \(0.0787525\pi\)
\(332\) −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 \(-0.857881\pi\)
−0.0770414 + 0.997028i \(0.524547\pi\)
\(348\) −56.8170 + 98.4099i −0.163267 + 0.282787i
\(349\) 230.853i 0.661471i 0.943724 + 0.330735i \(0.107297\pi\)
−0.943724 + 0.330735i \(0.892703\pi\)
\(350\) 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 \(-0.223615\pi\)
−0.941181 + 0.337904i \(0.890282\pi\)
\(354\) 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 −0.390947 0.920413i \(-0.627852\pi\)
0.992575 0.121637i \(-0.0388143\pi\)
\(360\) 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 0.984717 + 0.174159i \(0.0557208\pi\)
−0.341532 + 0.939870i \(0.610946\pi\)
\(368\) 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 \(-0.370764\pi\)
−0.598151 + 0.801384i \(0.704098\pi\)
\(374\) −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 0.355050 + 0.934847i \(0.384464\pi\)
−0.987126 + 0.159942i \(0.948869\pi\)
\(384\) 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 0.536882 0.843657i \(-0.319602\pi\)
−0.999070 + 0.0431246i \(0.986269\pi\)
\(390\) 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 \(-0.759966\pi\)
0.957351 + 0.288929i \(0.0932991\pi\)
\(398\) −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 −0.651687 0.758488i \(-0.725938\pi\)
0.982713 + 0.185133i \(0.0592716\pi\)
\(402\) 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 0.242808 0.970074i \(-0.421931\pi\)
0.961513 + 0.274759i \(0.0885981\pi\)
\(410\) 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 \(0.230944\pi\)
−0.748146 + 0.663534i \(0.769056\pi\)
\(420\) 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 −0.999248 0.0387660i \(-0.987657\pi\)
0.466052 0.884757i \(-0.345676\pi\)
\(432\) 10.3923 18.0000i 0.0240563 0.0416667i
\(433\) −65.9185 −0.152237 −0.0761183 0.997099i \(-0.524253\pi\)
−0.0761183 + 0.997099i \(0.524253\pi\)
\(434\) −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 0.807618 0.589706i \(-0.200756\pi\)
−0.106891 + 0.994271i \(0.534090\pi\)
\(440\) 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 \(-0.00640205\pi\)
0.482482 + 0.875906i \(0.339735\pi\)
\(444\) 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 \(-0.636849\pi\)
−0.995616 + 0.0935379i \(0.970182\pi\)
\(458\) 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 \(0.222352\pi\)
−0.765783 + 0.643099i \(0.777648\pi\)
\(462\) 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 \(-0.890650\pi\)
0.762476 + 0.647017i \(0.223984\pi\)
\(468\) 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 −0.712795 0.701373i \(-0.752571\pi\)
0.251009 + 0.967985i \(0.419237\pi\)
\(480\) 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 \(-0.880765\pi\)
−0.148460 + 0.988918i \(0.547432\pi\)
\(488\) 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 −0.318655 0.947871i \(-0.603231\pi\)
0.980208 0.197972i \(-0.0634357\pi\)
\(500\) 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 \(-0.581275\pi\)
−0.252568 + 0.967579i \(0.581275\pi\)
\(504\) 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 0.265810 0.964026i \(-0.414361\pi\)
−0.701966 + 0.712211i \(0.747694\pi\)
\(510\) 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 −0.333540 0.942736i \(-0.608243\pi\)
0.649663 + 0.760222i \(0.274910\pi\)
\(522\) 120.527 69.5863i 0.230895 0.133307i
\(523\) 173.610 300.701i 0.331950 0.574954i −0.650944 0.759126i \(-0.725627\pi\)
0.982894 + 0.184171i \(0.0589602\pi\)
\(524\) 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 −0.993787 0.111302i \(-0.964498\pi\)
0.593284 + 0.804993i \(0.297831\pi\)
\(542\) 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 −0.542337 + 0.840161i \(0.682460\pi\)
−0.998769 + 0.0495971i \(0.984206\pi\)
\(558\) 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 −0.999843 0.0177449i \(-0.994351\pi\)
0.484554 0.874762i \(-0.338982\pi\)
\(564\) 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 −0.944465 0.328613i \(-0.893419\pi\)
0.756820 + 0.653624i \(0.226752\pi\)
\(570\) 0 0
\(571\) 378.751 + 656.016i 0.663311 + 1.14889i 0.979740 + 0.200273i \(0.0641828\pi\)
−0.316429 + 0.948616i \(0.602484\pi\)
\(572\) 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 \(-0.116376\pi\)
−0.776570 + 0.630031i \(0.783042\pi\)
\(578\) 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 \(-0.542531\pi\)
−0.133217 + 0.991087i \(0.542531\pi\)
\(588\) −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 \(-0.776188\pi\)
0.941389 + 0.337323i \(0.109521\pi\)
\(594\) 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 0.997810 0.0661519i \(-0.0210722\pi\)
−0.556194 + 0.831053i \(0.687739\pi\)
\(600\) 0 0
\(601\) 899.473i 1.49663i −0.663345 0.748314i \(-0.730864\pi\)
0.663345 0.748314i \(-0.269136\pi\)
\(602\) 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 \(-0.687752\pi\)
0.997807 + 0.0661939i \(0.0210856\pi\)
\(608\) −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 \(-0.430283\pi\)
0.953974 + 0.299888i \(0.0969495\pi\)
\(614\) −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 −0.193124 0.981174i \(-0.561862\pi\)
0.753160 + 0.657838i \(0.228529\pi\)
\(620\) 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 0.892746 0.450561i \(-0.148776\pi\)
−0.836570 + 0.547860i \(0.815443\pi\)
\(642\) −57.5514 + 99.6819i −0.0896439 + 0.155268i
\(643\) 1254.20 1.95054 0.975269 0.221020i \(-0.0709386\pi\)
0.975269 + 0.221020i \(0.0709386\pi\)
\(644\) 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 \(-0.202742\pi\)
−0.917015 + 0.398853i \(0.869409\pi\)
\(648\) −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 \(-0.541154\pi\)
−0.923262 + 0.384170i \(0.874488\pi\)
\(654\) −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 −0.346430 0.938076i \(-0.612606\pi\)
0.639182 + 0.769055i \(0.279273\pi\)
\(662\) −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 \(-0.822290\pi\)
0.882847 + 0.469660i \(0.155624\pi\)
\(678\) −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 \(-0.652886\pi\)
0.537013 + 0.843574i \(0.319553\pi\)
\(684\) 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 0.984706 0.174222i \(-0.0557412\pi\)
0.341472 + 0.939892i \(0.389075\pi\)
\(692\) −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 −0.880269 0.474475i \(-0.842638\pi\)
0.851042 + 0.525097i \(0.175971\pi\)
\(710\) 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 0.0604602 0.998171i \(-0.480743\pi\)
−0.834211 + 0.551445i \(0.814077\pi\)
\(720\) 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 \(-0.735180\pi\)
−0.673431 + 0.739250i \(0.735180\pi\)
\(728\) −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 −0.0419537 0.999120i \(-0.513358\pi\)
0.886240 0.463227i \(-0.153308\pi\)
\(734\) 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 −0.984108 0.177574i \(-0.943175\pi\)
0.338271 0.941049i \(-0.390158\pi\)
\(740\) 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 −0.437048 0.899438i \(-0.643976\pi\)
0.997460 0.0712243i \(-0.0226906\pi\)
\(752\) 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 −0.985346 0.170565i \(-0.945441\pi\)
−0.640387 0.768052i \(-0.721226\pi\)
\(762\) −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 \(0.233589\pi\)
−0.742608 + 0.669726i \(0.766411\pi\)
\(770\) 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 \(-0.327567\pi\)
−0.999836 + 0.0181142i \(0.994234\pi\)
\(774\) 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