Properties

Label 1050.3.q.b.199.1
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 199.1
Root \(-1.25838 + 0.337183i\) of defining polynomial
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.b.649.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(2.76860 - 4.79536i) q^{11} +(1.73205 + 3.00000i) q^{12} +3.50434 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.06994 + 7.04933i) q^{17} +(3.67423 + 2.12132i) q^{18} +(15.3628 - 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} +7.83078i q^{22} +(10.3316 - 5.96495i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} +5.19615 q^{27} +(-6.22374 + 12.5405i) q^{28} +8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(4.89898 + 2.82843i) q^{32} +(4.79536 + 8.30580i) q^{33} -11.5115i q^{34} -6.00000 q^{36} +(-24.2950 + 14.0267i) q^{37} +(-12.5437 + 21.7263i) q^{38} +(-3.03484 + 5.25650i) q^{39} -3.14207i q^{41} +(1.07820 + 17.1125i) q^{42} +43.1943i q^{43} +(-5.53720 - 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(9.35524 + 16.2037i) q^{47} +6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(3.50434 - 6.06969i) q^{52} +(2.44037 + 1.40895i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +30.7257i q^{57} +(-10.4394 + 6.02720i) q^{58} +(26.1612 + 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} +10.9096 q^{62} +(11.6228 + 17.4903i) q^{63} -8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(-5.70032 - 3.29108i) q^{67} +(8.13987 + 14.0987i) q^{68} +20.6632i q^{69} -97.7751 q^{71} +(7.34847 - 4.24264i) q^{72} +(-30.5806 + 52.9672i) q^{73} +(19.8368 - 34.3583i) q^{74} -35.4790i q^{76} +(-17.2311 + 34.7197i) q^{77} -8.58383i q^{78} +(61.5670 + 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.22178 + 3.84823i) q^{82} +89.5815 q^{83} +(-13.4209 - 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(-7.38178 + 12.7856i) q^{87} +(13.5633 + 7.83078i) q^{88} +(102.290 - 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} -23.8598i q^{92} +(11.5713 - 6.68072i) q^{93} +(-22.9156 - 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} -65.1965 q^{97} +(-55.1890 + 41.9067i) q^{98} -16.6116 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
\(7\) −6.98615 + 0.440173i −0.998021 + 0.0628819i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.76860 4.79536i 0.251691 0.435942i −0.712301 0.701875i \(-0.752347\pi\)
0.963991 + 0.265933i \(0.0856800\pi\)
\(12\) 1.73205 + 3.00000i 0.144338 + 0.250000i
\(13\) 3.50434 0.269564 0.134782 0.990875i \(-0.456967\pi\)
0.134782 + 0.990875i \(0.456967\pi\)
\(14\) 8.24500 5.47905i 0.588928 0.391361i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −4.06994 + 7.04933i −0.239408 + 0.414667i −0.960545 0.278126i \(-0.910287\pi\)
0.721137 + 0.692793i \(0.243620\pi\)
\(18\) 3.67423 + 2.12132i 0.204124 + 0.117851i
\(19\) 15.3628 8.86974i 0.808571 0.466828i −0.0378887 0.999282i \(-0.512063\pi\)
0.846459 + 0.532454i \(0.178730\pi\)
\(20\) 0 0
\(21\) 5.38992 10.8604i 0.256663 0.517163i
\(22\) 7.83078i 0.355945i
\(23\) 10.3316 5.96495i 0.449200 0.259346i −0.258292 0.966067i \(-0.583160\pi\)
0.707492 + 0.706721i \(0.249826\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 0 0
\(26\) −4.29192 + 2.47794i −0.165074 + 0.0953054i
\(27\) 5.19615 0.192450
\(28\) −6.22374 + 12.5405i −0.222277 + 0.447876i
\(29\) 8.52374 0.293922 0.146961 0.989142i \(-0.453051\pi\)
0.146961 + 0.989142i \(0.453051\pi\)
\(30\) 0 0
\(31\) −6.68072 3.85711i −0.215507 0.124423i 0.388361 0.921507i \(-0.373041\pi\)
−0.603868 + 0.797084i \(0.706375\pi\)
\(32\) 4.89898 + 2.82843i 0.153093 + 0.0883883i
\(33\) 4.79536 + 8.30580i 0.145314 + 0.251691i
\(34\) 11.5115i 0.338574i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −24.2950 + 14.0267i −0.656621 + 0.379100i −0.790988 0.611831i \(-0.790433\pi\)
0.134367 + 0.990932i \(0.457100\pi\)
\(38\) −12.5437 + 21.7263i −0.330098 + 0.571746i
\(39\) −3.03484 + 5.25650i −0.0778165 + 0.134782i
\(40\) 0 0
\(41\) 3.14207i 0.0766358i −0.999266 0.0383179i \(-0.987800\pi\)
0.999266 0.0383179i \(-0.0121999\pi\)
\(42\) 1.07820 + 17.1125i 0.0256714 + 0.407440i
\(43\) 43.1943i 1.00452i 0.864717 + 0.502260i \(0.167498\pi\)
−0.864717 + 0.502260i \(0.832502\pi\)
\(44\) −5.53720 9.59071i −0.125845 0.217971i
\(45\) 0 0
\(46\) −8.43572 + 14.6111i −0.183385 + 0.317632i
\(47\) 9.35524 + 16.2037i 0.199048 + 0.344761i 0.948220 0.317615i \(-0.102882\pi\)
−0.749172 + 0.662375i \(0.769548\pi\)
\(48\) 6.92820 0.144338
\(49\) 48.6125 6.15023i 0.992092 0.125515i
\(50\) 0 0
\(51\) −7.04933 12.2098i −0.138222 0.239408i
\(52\) 3.50434 6.06969i 0.0673911 0.116725i
\(53\) 2.44037 + 1.40895i 0.0460448 + 0.0265840i 0.522846 0.852427i \(-0.324870\pi\)
−0.476801 + 0.879011i \(0.658204\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −1.24500 19.7598i −0.0222321 0.352854i
\(57\) 30.7257i 0.539047i
\(58\) −10.4394 + 6.02720i −0.179990 + 0.103917i
\(59\) 26.1612 + 15.1042i 0.443411 + 0.256003i 0.705043 0.709164i \(-0.250928\pi\)
−0.261633 + 0.965168i \(0.584261\pi\)
\(60\) 0 0
\(61\) −41.0095 + 23.6769i −0.672288 + 0.388145i −0.796943 0.604055i \(-0.793551\pi\)
0.124655 + 0.992200i \(0.460218\pi\)
\(62\) 10.9096 0.175961
\(63\) 11.6228 + 17.4903i 0.184489 + 0.277624i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −11.7462 6.78166i −0.177972 0.102752i
\(67\) −5.70032 3.29108i −0.0850794 0.0491206i 0.456857 0.889540i \(-0.348975\pi\)
−0.541936 + 0.840420i \(0.682309\pi\)
\(68\) 8.13987 + 14.0987i 0.119704 + 0.207333i
\(69\) 20.6632i 0.299467i
\(70\) 0 0
\(71\) −97.7751 −1.37711 −0.688557 0.725182i \(-0.741755\pi\)
−0.688557 + 0.725182i \(0.741755\pi\)
\(72\) 7.34847 4.24264i 0.102062 0.0589256i
\(73\) −30.5806 + 52.9672i −0.418913 + 0.725578i −0.995830 0.0912244i \(-0.970922\pi\)
0.576918 + 0.816802i \(0.304255\pi\)
\(74\) 19.8368 34.3583i 0.268064 0.464301i
\(75\) 0 0
\(76\) 35.4790i 0.466828i
\(77\) −17.2311 + 34.7197i −0.223780 + 0.450906i
\(78\) 8.58383i 0.110049i
\(79\) 61.5670 + 106.637i 0.779329 + 1.34984i 0.932329 + 0.361612i \(0.117773\pi\)
−0.152999 + 0.988226i \(0.548893\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 2.22178 + 3.84823i 0.0270948 + 0.0469296i
\(83\) 89.5815 1.07930 0.539648 0.841891i \(-0.318557\pi\)
0.539648 + 0.841891i \(0.318557\pi\)
\(84\) −13.4209 20.1960i −0.159772 0.240429i
\(85\) 0 0
\(86\) −30.5430 52.9020i −0.355151 0.615140i
\(87\) −7.38178 + 12.7856i −0.0848480 + 0.146961i
\(88\) 13.5633 + 7.83078i 0.154129 + 0.0889862i
\(89\) 102.290 59.0573i 1.14933 0.663566i 0.200606 0.979672i \(-0.435709\pi\)
0.948724 + 0.316107i \(0.102376\pi\)
\(90\) 0 0
\(91\) −24.4818 + 1.54251i −0.269031 + 0.0169507i
\(92\) 23.8598i 0.259346i
\(93\) 11.5713 6.68072i 0.124423 0.0718357i
\(94\) −22.9156 13.2303i −0.243783 0.140748i
\(95\) 0 0
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) −65.1965 −0.672128 −0.336064 0.941839i \(-0.609096\pi\)
−0.336064 + 0.941839i \(0.609096\pi\)
\(98\) −55.1890 + 41.9067i −0.563153 + 0.427619i
\(99\) −16.6116 −0.167794
\(100\) 0 0
\(101\) −120.895 69.7987i −1.19698 0.691076i −0.237099 0.971486i \(-0.576196\pi\)
−0.959881 + 0.280409i \(0.909530\pi\)
\(102\) 17.2673 + 9.96926i 0.169287 + 0.0977379i
\(103\) 87.2421 + 151.108i 0.847011 + 1.46707i 0.883863 + 0.467746i \(0.154934\pi\)
−0.0368520 + 0.999321i \(0.511733\pi\)
\(104\) 9.91176i 0.0953054i
\(105\) 0 0
\(106\) −3.98511 −0.0375954
\(107\) −52.3741 + 30.2382i −0.489477 + 0.282600i −0.724358 0.689424i \(-0.757864\pi\)
0.234880 + 0.972024i \(0.424530\pi\)
\(108\) 5.19615 9.00000i 0.0481125 0.0833333i
\(109\) −50.4057 + 87.3052i −0.462437 + 0.800965i −0.999082 0.0428435i \(-0.986358\pi\)
0.536644 + 0.843808i \(0.319692\pi\)
\(110\) 0 0
\(111\) 48.5899i 0.437747i
\(112\) 15.4971 + 23.3204i 0.138367 + 0.208218i
\(113\) 74.1876i 0.656527i −0.944586 0.328264i \(-0.893537\pi\)
0.944586 0.328264i \(-0.106463\pi\)
\(114\) −21.7263 37.6311i −0.190582 0.330098i
\(115\) 0 0
\(116\) 8.52374 14.7636i 0.0734805 0.127272i
\(117\) −5.25650 9.10453i −0.0449274 0.0778165i
\(118\) −42.7211 −0.362043
\(119\) 25.3302 51.0392i 0.212859 0.428901i
\(120\) 0 0
\(121\) 45.1697 + 78.2362i 0.373303 + 0.646580i
\(122\) 33.4842 57.9963i 0.274460 0.475379i
\(123\) 4.71310 + 2.72111i 0.0383179 + 0.0221228i
\(124\) −13.3614 + 7.71423i −0.107754 + 0.0622115i
\(125\) 0 0
\(126\) −26.6025 13.2026i −0.211131 0.104782i
\(127\) 151.093i 1.18971i 0.803833 + 0.594855i \(0.202791\pi\)
−0.803833 + 0.594855i \(0.797209\pi\)
\(128\) 9.79796 5.65685i 0.0765466 0.0441942i
\(129\) −64.7915 37.4074i −0.502260 0.289980i
\(130\) 0 0
\(131\) −186.820 + 107.861i −1.42611 + 0.823363i −0.996811 0.0798009i \(-0.974572\pi\)
−0.429296 + 0.903164i \(0.641238\pi\)
\(132\) 19.1814 0.145314
\(133\) −103.423 + 68.7276i −0.777615 + 0.516749i
\(134\) 9.30859 0.0694671
\(135\) 0 0
\(136\) −19.9385 11.5115i −0.146607 0.0846435i
\(137\) −115.736 66.8203i −0.844789 0.487739i 0.0141000 0.999901i \(-0.495512\pi\)
−0.858889 + 0.512161i \(0.828845\pi\)
\(138\) −14.6111 25.3072i −0.105877 0.183385i
\(139\) 193.762i 1.39397i 0.717085 + 0.696986i \(0.245476\pi\)
−0.717085 + 0.696986i \(0.754524\pi\)
\(140\) 0 0
\(141\) −32.4075 −0.229840
\(142\) 119.750 69.1374i 0.843306 0.486883i
\(143\) 9.70210 16.8045i 0.0678469 0.117514i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 86.4950i 0.592432i
\(147\) −32.8743 + 78.2450i −0.223635 + 0.532279i
\(148\) 56.1068i 0.379100i
\(149\) 33.0032 + 57.1632i 0.221498 + 0.383646i 0.955263 0.295758i \(-0.0955721\pi\)
−0.733765 + 0.679403i \(0.762239\pi\)
\(150\) 0 0
\(151\) −17.4410 + 30.2087i −0.115503 + 0.200057i −0.917981 0.396625i \(-0.870181\pi\)
0.802478 + 0.596682i \(0.203515\pi\)
\(152\) 25.0874 + 43.4527i 0.165049 + 0.285873i
\(153\) 24.4196 0.159605
\(154\) −3.44690 54.7070i −0.0223825 0.355240i
\(155\) 0 0
\(156\) 6.06969 + 10.5130i 0.0389082 + 0.0673911i
\(157\) 26.7503 46.3329i 0.170384 0.295114i −0.768170 0.640246i \(-0.778832\pi\)
0.938554 + 0.345132i \(0.112166\pi\)
\(158\) −150.808 87.0689i −0.954480 0.551069i
\(159\) −4.22685 + 2.44037i −0.0265840 + 0.0153483i
\(160\) 0 0
\(161\) −69.5525 + 46.2197i −0.432003 + 0.287079i
\(162\) 12.7279i 0.0785674i
\(163\) −178.387 + 102.992i −1.09440 + 0.631852i −0.934744 0.355321i \(-0.884372\pi\)
−0.159655 + 0.987173i \(0.551038\pi\)
\(164\) −5.44222 3.14207i −0.0331843 0.0191589i
\(165\) 0 0
\(166\) −109.714 + 63.3437i −0.660931 + 0.381589i
\(167\) −137.945 −0.826020 −0.413010 0.910727i \(-0.635523\pi\)
−0.413010 + 0.910727i \(0.635523\pi\)
\(168\) 30.7179 + 15.2450i 0.182845 + 0.0907440i
\(169\) −156.720 −0.927335
\(170\) 0 0
\(171\) −46.0885 26.6092i −0.269524 0.155609i
\(172\) 74.8148 + 43.1943i 0.434970 + 0.251130i
\(173\) −110.283 191.016i −0.637475 1.10414i −0.985985 0.166834i \(-0.946646\pi\)
0.348510 0.937305i \(-0.386688\pi\)
\(174\) 20.8788i 0.119993i
\(175\) 0 0
\(176\) −22.1488 −0.125845
\(177\) −45.3126 + 26.1612i −0.256003 + 0.147804i
\(178\) −83.5197 + 144.660i −0.469212 + 0.812699i
\(179\) −36.6501 + 63.4798i −0.204749 + 0.354636i −0.950053 0.312089i \(-0.898971\pi\)
0.745304 + 0.666725i \(0.232305\pi\)
\(180\) 0 0
\(181\) 61.4619i 0.339568i 0.985481 + 0.169784i \(0.0543071\pi\)
−0.985481 + 0.169784i \(0.945693\pi\)
\(182\) 28.8932 19.2004i 0.158754 0.105497i
\(183\) 82.0191i 0.448192i
\(184\) 16.8714 + 29.2222i 0.0916926 + 0.158816i
\(185\) 0 0
\(186\) −9.44796 + 16.3643i −0.0507955 + 0.0879804i
\(187\) 22.5360 + 39.0336i 0.120514 + 0.208736i
\(188\) 37.4210 0.199048
\(189\) −36.3011 + 2.28721i −0.192069 + 0.0121016i
\(190\) 0 0
\(191\) 179.931 + 311.650i 0.942048 + 1.63168i 0.761556 + 0.648099i \(0.224436\pi\)
0.180492 + 0.983577i \(0.442231\pi\)
\(192\) 6.92820 12.0000i 0.0360844 0.0625000i
\(193\) −121.023 69.8724i −0.627060 0.362033i 0.152552 0.988295i \(-0.451251\pi\)
−0.779613 + 0.626262i \(0.784584\pi\)
\(194\) 79.8490 46.1009i 0.411593 0.237633i
\(195\) 0 0
\(196\) 37.9600 90.3495i 0.193673 0.460967i
\(197\) 248.343i 1.26062i 0.776342 + 0.630311i \(0.217073\pi\)
−0.776342 + 0.630311i \(0.782927\pi\)
\(198\) 20.3450 11.7462i 0.102752 0.0593241i
\(199\) 106.170 + 61.2973i 0.533518 + 0.308026i 0.742448 0.669904i \(-0.233665\pi\)
−0.208930 + 0.977931i \(0.566998\pi\)
\(200\) 0 0
\(201\) 9.87325 5.70032i 0.0491206 0.0283598i
\(202\) 197.421 0.977329
\(203\) −59.5481 + 3.75192i −0.293341 + 0.0184824i
\(204\) −28.1973 −0.138222
\(205\) 0 0
\(206\) −213.699 123.379i −1.03737 0.598927i
\(207\) −30.9948 17.8949i −0.149733 0.0864486i
\(208\) −7.00867 12.1394i −0.0336955 0.0583624i
\(209\) 98.2271i 0.469986i
\(210\) 0 0
\(211\) 352.829 1.67218 0.836088 0.548596i \(-0.184837\pi\)
0.836088 + 0.548596i \(0.184837\pi\)
\(212\) 4.88074 2.81790i 0.0230224 0.0132920i
\(213\) 84.6757 146.663i 0.397538 0.688557i
\(214\) 42.7632 74.0681i 0.199828 0.346113i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 48.3703 + 24.0057i 0.222904 + 0.110625i
\(218\) 142.569i 0.653985i
\(219\) −52.9672 91.7418i −0.241859 0.418913i
\(220\) 0 0
\(221\) −14.2624 + 24.7032i −0.0645358 + 0.111779i
\(222\) 34.3583 + 59.5103i 0.154767 + 0.268064i
\(223\) −61.7420 −0.276870 −0.138435 0.990372i \(-0.544207\pi\)
−0.138435 + 0.990372i \(0.544207\pi\)
\(224\) −35.4700 17.6034i −0.158348 0.0785866i
\(225\) 0 0
\(226\) 52.4586 + 90.8609i 0.232118 + 0.402039i
\(227\) 104.762 181.452i 0.461505 0.799350i −0.537531 0.843244i \(-0.680643\pi\)
0.999036 + 0.0438940i \(0.0139764\pi\)
\(228\) 53.2184 + 30.7257i 0.233414 + 0.134762i
\(229\) 93.3568 53.8996i 0.407671 0.235369i −0.282117 0.959380i \(-0.591037\pi\)
0.689789 + 0.724011i \(0.257703\pi\)
\(230\) 0 0
\(231\) −37.1571 55.9148i −0.160853 0.242055i
\(232\) 24.1088i 0.103917i
\(233\) 283.057 163.423i 1.21484 0.701387i 0.251029 0.967980i \(-0.419231\pi\)
0.963809 + 0.266592i \(0.0858978\pi\)
\(234\) 12.8758 + 7.43382i 0.0550246 + 0.0317685i
\(235\) 0 0
\(236\) 52.3224 30.2084i 0.221705 0.128002i
\(237\) −213.274 −0.899892
\(238\) 5.06706 + 80.4211i 0.0212902 + 0.337904i
\(239\) 9.20117 0.0384986 0.0192493 0.999815i \(-0.493872\pi\)
0.0192493 + 0.999815i \(0.493872\pi\)
\(240\) 0 0
\(241\) 278.156 + 160.593i 1.15417 + 0.666362i 0.949900 0.312553i \(-0.101184\pi\)
0.204272 + 0.978914i \(0.434517\pi\)
\(242\) −110.643 63.8796i −0.457201 0.263965i
\(243\) −7.79423 13.5000i −0.0320750 0.0555556i
\(244\) 94.7075i 0.388145i
\(245\) 0 0
\(246\) −7.69646 −0.0312864
\(247\) 53.8365 31.0825i 0.217962 0.125840i
\(248\) 10.9096 18.8959i 0.0439902 0.0761932i
\(249\) −77.5799 + 134.372i −0.311566 + 0.539648i
\(250\) 0 0
\(251\) 19.2394i 0.0766511i −0.999265 0.0383255i \(-0.987798\pi\)
0.999265 0.0383255i \(-0.0122024\pi\)
\(252\) 41.9169 2.64104i 0.166337 0.0104803i
\(253\) 66.0583i 0.261100i
\(254\) −106.839 185.051i −0.420626 0.728546i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 64.7109 + 112.083i 0.251793 + 0.436119i 0.964020 0.265831i \(-0.0856464\pi\)
−0.712226 + 0.701950i \(0.752313\pi\)
\(258\) 105.804 0.410093
\(259\) 163.554 108.687i 0.631483 0.419640i
\(260\) 0 0
\(261\) −12.7856 22.1453i −0.0489870 0.0848480i
\(262\) 152.538 264.203i 0.582206 1.00841i
\(263\) 144.561 + 83.4625i 0.549663 + 0.317348i 0.748986 0.662586i \(-0.230541\pi\)
−0.199323 + 0.979934i \(0.563874\pi\)
\(264\) −23.4924 + 13.5633i −0.0889862 + 0.0513762i
\(265\) 0 0
\(266\) 78.0688 157.305i 0.293492 0.591371i
\(267\) 204.581i 0.766220i
\(268\) −11.4006 + 6.58217i −0.0425397 + 0.0245603i
\(269\) −181.081 104.547i −0.673162 0.388650i 0.124112 0.992268i \(-0.460392\pi\)
−0.797274 + 0.603618i \(0.793725\pi\)
\(270\) 0 0
\(271\) 123.029 71.0308i 0.453981 0.262106i −0.255529 0.966801i \(-0.582250\pi\)
0.709510 + 0.704695i \(0.248916\pi\)
\(272\) 32.5595 0.119704
\(273\) 18.8881 38.0586i 0.0691871 0.139409i
\(274\) 188.996 0.689768
\(275\) 0 0
\(276\) 35.7897 + 20.6632i 0.129673 + 0.0748667i
\(277\) −386.179 222.961i −1.39415 0.804912i −0.400377 0.916350i \(-0.631121\pi\)
−0.993771 + 0.111438i \(0.964454\pi\)
\(278\) −137.010 237.309i −0.492843 0.853630i
\(279\) 23.1427i 0.0829487i
\(280\) 0 0
\(281\) 482.012 1.71534 0.857672 0.514196i \(-0.171910\pi\)
0.857672 + 0.514196i \(0.171910\pi\)
\(282\) 39.6909 22.9156i 0.140748 0.0812609i
\(283\) −108.257 + 187.506i −0.382533 + 0.662566i −0.991424 0.130688i \(-0.958281\pi\)
0.608891 + 0.793254i \(0.291615\pi\)
\(284\) −97.7751 + 169.351i −0.344278 + 0.596308i
\(285\) 0 0
\(286\) 27.4417i 0.0959500i
\(287\) 1.38305 + 21.9509i 0.00481900 + 0.0764841i
\(288\) 16.9706i 0.0589256i
\(289\) 111.371 + 192.901i 0.385368 + 0.667476i
\(290\) 0 0
\(291\) 56.4618 97.7947i 0.194027 0.336064i
\(292\) 61.1612 + 105.934i 0.209456 + 0.362789i
\(293\) 383.704 1.30957 0.654786 0.755815i \(-0.272759\pi\)
0.654786 + 0.755815i \(0.272759\pi\)
\(294\) −15.0649 119.076i −0.0512412 0.405020i
\(295\) 0 0
\(296\) −39.6735 68.7166i −0.134032 0.232151i
\(297\) 14.3861 24.9174i 0.0484379 0.0838970i
\(298\) −80.8410 46.6736i −0.271278 0.156623i
\(299\) 36.2054 20.9032i 0.121088 0.0699104i
\(300\) 0 0
\(301\) −19.0130 301.762i −0.0631661 1.00253i
\(302\) 49.3305i 0.163346i
\(303\) 209.396 120.895i 0.691076 0.398993i
\(304\) −61.4514 35.4790i −0.202143 0.116707i
\(305\) 0 0
\(306\) −29.9078 + 17.2673i −0.0977379 + 0.0564290i
\(307\) −21.1264 −0.0688155 −0.0344078 0.999408i \(-0.510954\pi\)
−0.0344078 + 0.999408i \(0.510954\pi\)
\(308\) 42.9053 + 64.5648i 0.139303 + 0.209626i
\(309\) −302.216 −0.978044
\(310\) 0 0
\(311\) 75.0288 + 43.3179i 0.241250 + 0.139286i 0.615751 0.787941i \(-0.288853\pi\)
−0.374501 + 0.927226i \(0.622186\pi\)
\(312\) −14.8676 8.58383i −0.0476527 0.0275123i
\(313\) 1.41903 + 2.45782i 0.00453363 + 0.00785247i 0.868283 0.496069i \(-0.165224\pi\)
−0.863750 + 0.503921i \(0.831890\pi\)
\(314\) 75.6613i 0.240960i
\(315\) 0 0
\(316\) 246.268 0.779329
\(317\) 268.338 154.925i 0.846493 0.488723i −0.0129730 0.999916i \(-0.504130\pi\)
0.859466 + 0.511193i \(0.170796\pi\)
\(318\) 3.45121 5.97767i 0.0108529 0.0187977i
\(319\) 23.5988 40.8744i 0.0739776 0.128133i
\(320\) 0 0
\(321\) 104.748i 0.326318i
\(322\) 52.5018 105.788i 0.163049 0.328535i
\(323\) 144.397i 0.447050i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 145.652 252.278i 0.446787 0.773857i
\(327\) −87.3052 151.217i −0.266988 0.462437i
\(328\) 8.88711 0.0270948
\(329\) −72.4895 109.084i −0.220333 0.331562i
\(330\) 0 0
\(331\) 208.295 + 360.777i 0.629289 + 1.08996i 0.987695 + 0.156394i \(0.0499871\pi\)
−0.358406 + 0.933566i \(0.616680\pi\)
\(332\) 89.5815 155.160i 0.269824 0.467349i
\(333\) 72.8849 + 42.0801i 0.218874 + 0.126367i
\(334\) 168.948 97.5421i 0.505832 0.292042i
\(335\) 0 0
\(336\) −48.4014 + 3.04961i −0.144052 + 0.00907622i
\(337\) 155.491i 0.461399i −0.973025 0.230699i \(-0.925899\pi\)
0.973025 0.230699i \(-0.0741014\pi\)
\(338\) 191.942 110.818i 0.567874 0.327862i
\(339\) 111.281 + 64.2483i 0.328264 + 0.189523i
\(340\) 0 0
\(341\) −36.9925 + 21.3576i −0.108482 + 0.0626323i
\(342\) 75.2622 0.220065
\(343\) −336.907 + 64.3643i −0.982236 + 0.187651i
\(344\) −122.172 −0.355151
\(345\) 0 0
\(346\) 270.138 + 155.964i 0.780744 + 0.450763i
\(347\) −443.844 256.253i −1.27909 0.738482i −0.302408 0.953179i \(-0.597790\pi\)
−0.976681 + 0.214697i \(0.931124\pi\)
\(348\) 14.7636 + 25.5712i 0.0424240 + 0.0734805i
\(349\) 269.185i 0.771305i 0.922644 + 0.385652i \(0.126024\pi\)
−0.922644 + 0.385652i \(0.873976\pi\)
\(350\) 0 0
\(351\) 18.2091 0.0518777
\(352\) 27.1266 15.6616i 0.0770643 0.0444931i
\(353\) 293.231 507.890i 0.830682 1.43878i −0.0668166 0.997765i \(-0.521284\pi\)
0.897498 0.441018i \(-0.145382\pi\)
\(354\) 36.9976 64.0816i 0.104513 0.181022i
\(355\) 0 0
\(356\) 236.229i 0.663566i
\(357\) 54.6221 + 82.1966i 0.153003 + 0.230242i
\(358\) 103.662i 0.289559i
\(359\) 44.4221 + 76.9413i 0.123738 + 0.214321i 0.921239 0.388997i \(-0.127178\pi\)
−0.797501 + 0.603318i \(0.793845\pi\)
\(360\) 0 0
\(361\) −23.1554 + 40.1064i −0.0641424 + 0.111098i
\(362\) −43.4601 75.2751i −0.120056 0.207942i
\(363\) −156.472 −0.431054
\(364\) −21.8101 + 43.9462i −0.0599178 + 0.120731i
\(365\) 0 0
\(366\) 57.9963 + 100.452i 0.158460 + 0.274460i
\(367\) 353.019 611.446i 0.961904 1.66607i 0.244191 0.969727i \(-0.421478\pi\)
0.717713 0.696339i \(-0.245189\pi\)
\(368\) −41.3264 23.8598i −0.112300 0.0648365i
\(369\) −8.16333 + 4.71310i −0.0221228 + 0.0127726i
\(370\) 0 0
\(371\) −17.6690 8.76894i −0.0476253 0.0236360i
\(372\) 26.7229i 0.0718357i
\(373\) −44.3770 + 25.6211i −0.118973 + 0.0686892i −0.558306 0.829635i \(-0.688548\pi\)
0.439332 + 0.898325i \(0.355215\pi\)
\(374\) −55.2018 31.8708i −0.147598 0.0852160i
\(375\) 0 0
\(376\) −45.8311 + 26.4606i −0.121891 + 0.0703740i
\(377\) 29.8701 0.0792309
\(378\) 42.8423 28.4700i 0.113339 0.0753174i
\(379\) 194.724 0.513784 0.256892 0.966440i \(-0.417302\pi\)
0.256892 + 0.966440i \(0.417302\pi\)
\(380\) 0 0
\(381\) −226.640 130.851i −0.594855 0.343440i
\(382\) −440.740 254.461i −1.15377 0.666129i
\(383\) 262.540 + 454.732i 0.685482 + 1.18729i 0.973285 + 0.229600i \(0.0737418\pi\)
−0.287803 + 0.957690i \(0.592925\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 197.629 0.511993
\(387\) 112.222 64.7915i 0.289980 0.167420i
\(388\) −65.1965 + 112.924i −0.168032 + 0.291040i
\(389\) −201.765 + 349.467i −0.518675 + 0.898372i 0.481089 + 0.876672i \(0.340241\pi\)
−0.999765 + 0.0217005i \(0.993092\pi\)
\(390\) 0 0
\(391\) 97.1079i 0.248358i
\(392\) 17.3955 + 137.497i 0.0443762 + 0.350757i
\(393\) 373.640i 0.950738i
\(394\) −175.605 304.156i −0.445697 0.771971i
\(395\) 0 0
\(396\) −16.6116 + 28.7721i −0.0419485 + 0.0726569i
\(397\) 80.5960 + 139.596i 0.203013 + 0.351628i 0.949498 0.313774i \(-0.101593\pi\)
−0.746485 + 0.665402i \(0.768260\pi\)
\(398\) −173.375 −0.435615
\(399\) −13.5246 214.654i −0.0338963 0.537980i
\(400\) 0 0
\(401\) 212.506 + 368.071i 0.529940 + 0.917883i 0.999390 + 0.0349237i \(0.0111188\pi\)
−0.469450 + 0.882959i \(0.655548\pi\)
\(402\) −8.06147 + 13.9629i −0.0200534 + 0.0347335i
\(403\) −23.4115 13.5166i −0.0580930 0.0335400i
\(404\) −241.790 + 139.597i −0.598490 + 0.345538i
\(405\) 0 0
\(406\) 70.2782 46.7020i 0.173099 0.115030i
\(407\) 155.337i 0.381664i
\(408\) 34.5345 19.9385i 0.0846435 0.0488689i
\(409\) −373.605 215.701i −0.913460 0.527386i −0.0319171 0.999491i \(-0.510161\pi\)
−0.881543 + 0.472104i \(0.843495\pi\)
\(410\) 0 0
\(411\) 200.461 115.736i 0.487739 0.281596i
\(412\) 348.969 0.847011
\(413\) −189.415 94.0046i −0.458631 0.227614i
\(414\) 50.6143 0.122257
\(415\) 0 0
\(416\) 17.1677 + 9.91176i 0.0412684 + 0.0238263i
\(417\) −290.643 167.803i −0.696986 0.402405i
\(418\) 69.4570 + 120.303i 0.166165 + 0.287806i
\(419\) 585.412i 1.39716i −0.715530 0.698582i \(-0.753815\pi\)
0.715530 0.698582i \(-0.246185\pi\)
\(420\) 0 0
\(421\) 400.267 0.950754 0.475377 0.879782i \(-0.342312\pi\)
0.475377 + 0.879782i \(0.342312\pi\)
\(422\) −432.126 + 249.488i −1.02399 + 0.591203i
\(423\) 28.0657 48.6112i 0.0663492 0.114920i
\(424\) −3.98511 + 6.90241i −0.00939885 + 0.0162793i
\(425\) 0 0
\(426\) 239.499i 0.562204i
\(427\) 276.077 183.461i 0.646550 0.429652i
\(428\) 120.953i 0.282600i
\(429\) 16.8045 + 29.1063i 0.0391714 + 0.0678469i
\(430\) 0 0
\(431\) −197.631 + 342.307i −0.458541 + 0.794216i −0.998884 0.0472289i \(-0.984961\pi\)
0.540344 + 0.841445i \(0.318294\pi\)
\(432\) −10.3923 18.0000i −0.0240563 0.0416667i
\(433\) 2.39222 0.00552477 0.00276238 0.999996i \(-0.499121\pi\)
0.00276238 + 0.999996i \(0.499121\pi\)
\(434\) −76.2158 + 4.80210i −0.175613 + 0.0110647i
\(435\) 0 0
\(436\) 100.811 + 174.610i 0.231219 + 0.400482i
\(437\) 105.815 183.277i 0.242140 0.419399i
\(438\) 129.743 + 74.9069i 0.296216 + 0.171020i
\(439\) 350.264 202.225i 0.797867 0.460649i −0.0448578 0.998993i \(-0.514283\pi\)
0.842725 + 0.538345i \(0.180950\pi\)
\(440\) 0 0
\(441\) −88.8975 117.074i −0.201582 0.265473i
\(442\) 40.3402i 0.0912674i
\(443\) 252.889 146.005i 0.570855 0.329583i −0.186636 0.982429i \(-0.559758\pi\)
0.757491 + 0.652846i \(0.226425\pi\)
\(444\) −84.1603 48.5899i −0.189550 0.109437i
\(445\) 0 0
\(446\) 75.6182 43.6582i 0.169547 0.0978883i
\(447\) −114.326 −0.255764
\(448\) 55.8892 3.52139i 0.124753 0.00786024i
\(449\) −125.680 −0.279911 −0.139956 0.990158i \(-0.544696\pi\)
−0.139956 + 0.990158i \(0.544696\pi\)
\(450\) 0 0
\(451\) −15.0673 8.69913i −0.0334087 0.0192885i
\(452\) −128.497 74.1876i −0.284285 0.164132i
\(453\) −30.2087 52.3229i −0.0666858 0.115503i
\(454\) 296.310i 0.652666i
\(455\) 0 0
\(456\) −86.9054 −0.190582
\(457\) −74.4808 + 43.0015i −0.162978 + 0.0940952i −0.579270 0.815135i \(-0.696662\pi\)
0.416293 + 0.909231i \(0.363329\pi\)
\(458\) −76.2255 + 132.026i −0.166431 + 0.288267i
\(459\) −21.1480 + 36.6294i −0.0460741 + 0.0798027i
\(460\) 0 0
\(461\) 131.449i 0.285138i −0.989785 0.142569i \(-0.954464\pi\)
0.989785 0.142569i \(-0.0455362\pi\)
\(462\) 85.0456 + 42.2073i 0.184081 + 0.0913578i
\(463\) 73.9873i 0.159800i 0.996803 + 0.0798999i \(0.0254601\pi\)
−0.996803 + 0.0798999i \(0.974540\pi\)
\(464\) −17.0475 29.5271i −0.0367403 0.0636360i
\(465\) 0 0
\(466\) −231.115 + 400.303i −0.495956 + 0.859020i
\(467\) 223.453 + 387.032i 0.478486 + 0.828762i 0.999696 0.0246667i \(-0.00785244\pi\)
−0.521210 + 0.853429i \(0.674519\pi\)
\(468\) −21.0260 −0.0449274
\(469\) 41.2719 + 20.4829i 0.0879999 + 0.0436735i
\(470\) 0 0
\(471\) 46.3329 + 80.2509i 0.0983713 + 0.170384i
\(472\) −42.7211 + 73.9951i −0.0905108 + 0.156769i
\(473\) 207.132 + 119.588i 0.437912 + 0.252828i
\(474\) 261.207 150.808i 0.551069 0.318160i
\(475\) 0 0
\(476\) −63.0722 94.9124i −0.132505 0.199396i
\(477\) 8.45370i 0.0177226i
\(478\) −11.2691 + 6.50621i −0.0235755 + 0.0136113i
\(479\) −513.818 296.653i −1.07269 0.619318i −0.143775 0.989610i \(-0.545924\pi\)
−0.928915 + 0.370293i \(0.879257\pi\)
\(480\) 0 0
\(481\) −85.1377 + 49.1543i −0.177002 + 0.102192i
\(482\) −454.226 −0.942378
\(483\) −9.09539 144.356i −0.0188310 0.298874i
\(484\) 180.679 0.373303
\(485\) 0 0
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) −709.744 409.771i −1.45738 0.841418i −0.458498 0.888696i \(-0.651612\pi\)
−0.998882 + 0.0472773i \(0.984946\pi\)
\(488\) −66.9683 115.993i −0.137230 0.237690i
\(489\) 356.774i 0.729600i
\(490\) 0 0
\(491\) 554.724 1.12978 0.564892 0.825165i \(-0.308918\pi\)
0.564892 + 0.825165i \(0.308918\pi\)
\(492\) 9.42620 5.44222i 0.0191589 0.0110614i
\(493\) −34.6911 + 60.0867i −0.0703673 + 0.121880i
\(494\) −43.9574 + 76.1364i −0.0889825 + 0.154122i
\(495\) 0 0
\(496\) 30.8569i 0.0622115i
\(497\) 683.071 43.0380i 1.37439 0.0865955i
\(498\) 219.429i 0.440620i
\(499\) 317.394 + 549.742i 0.636060 + 1.10169i 0.986290 + 0.165024i \(0.0527701\pi\)
−0.350230 + 0.936664i \(0.613897\pi\)
\(500\) 0 0
\(501\) 119.464 206.918i 0.238451 0.413010i
\(502\) 13.6043 + 23.5634i 0.0271003 + 0.0469390i
\(503\) −120.116 −0.238800 −0.119400 0.992846i \(-0.538097\pi\)
−0.119400 + 0.992846i \(0.538097\pi\)
\(504\) −49.4700 + 32.8743i −0.0981547 + 0.0652268i
\(505\) 0 0
\(506\) 46.7103 + 80.9046i 0.0923128 + 0.159890i
\(507\) 135.723 235.079i 0.267699 0.463668i
\(508\) 261.701 + 151.093i 0.515160 + 0.297428i
\(509\) −51.1082 + 29.5073i −0.100409 + 0.0579712i −0.549364 0.835583i \(-0.685130\pi\)
0.448955 + 0.893555i \(0.351796\pi\)
\(510\) 0 0
\(511\) 190.326 383.497i 0.372458 0.750484i
\(512\) 22.6274i 0.0441942i
\(513\) 79.8277 46.0885i 0.155609 0.0898412i
\(514\) −158.509 91.5150i −0.308383 0.178045i
\(515\) 0 0
\(516\) −129.583 + 74.8148i −0.251130 + 0.144990i
\(517\) 103.604 0.200394
\(518\) −123.459 + 248.764i −0.238338 + 0.480239i
\(519\) 382.032 0.736093
\(520\) 0 0
\(521\) −841.241 485.691i −1.61467 0.932228i −0.988269 0.152725i \(-0.951195\pi\)
−0.626398 0.779504i \(-0.715471\pi\)
\(522\) 31.3182 + 18.0816i 0.0599966 + 0.0346391i
\(523\) 345.682 + 598.739i 0.660960 + 1.14482i 0.980364 + 0.197197i \(0.0631840\pi\)
−0.319404 + 0.947619i \(0.603483\pi\)
\(524\) 431.442i 0.823363i
\(525\) 0 0
\(526\) −236.068 −0.448798
\(527\) 54.3802 31.3964i 0.103188 0.0595757i
\(528\) 19.1814 33.2232i 0.0363285 0.0629227i
\(529\) −193.339 + 334.872i −0.365479 + 0.633029i
\(530\) 0 0
\(531\) 90.6251i 0.170669i
\(532\) 15.6169 + 247.861i 0.0293551 + 0.465905i
\(533\) 11.0109i 0.0206583i
\(534\) −144.660 250.559i −0.270900 0.469212i
\(535\) 0 0
\(536\) 9.30859 16.1229i 0.0173668 0.0300801i
\(537\) −63.4798 109.950i −0.118212 0.204749i
\(538\) 295.703 0.549635
\(539\) 105.096 250.142i 0.194983 0.464085i
\(540\) 0 0
\(541\) −270.888 469.192i −0.500717 0.867267i −1.00000 0.000828025i \(-0.999736\pi\)
0.499283 0.866439i \(-0.333597\pi\)
\(542\) −100.453 + 173.989i −0.185337 + 0.321013i
\(543\) −92.1928 53.2275i −0.169784 0.0980249i
\(544\) −39.8771 + 23.0230i −0.0733034 + 0.0423217i
\(545\) 0 0
\(546\) 3.77837 + 59.9679i 0.00692010 + 0.109831i
\(547\) 318.491i 0.582251i 0.956685 + 0.291126i \(0.0940297\pi\)
−0.956685 + 0.291126i \(0.905970\pi\)
\(548\) −231.472 + 133.641i −0.422395 + 0.243870i
\(549\) 123.029 + 71.0306i 0.224096 + 0.129382i
\(550\) 0 0
\(551\) 130.949 75.6034i 0.237657 0.137211i
\(552\) −58.4444 −0.105877
\(553\) −477.055 717.883i −0.862667 1.29816i
\(554\) 630.628 1.13832
\(555\) 0 0
\(556\) 335.606 + 193.762i 0.603607 + 0.348493i
\(557\) 499.660 + 288.479i 0.897055 + 0.517915i 0.876244 0.481869i \(-0.160042\pi\)
0.0208114 + 0.999783i \(0.493375\pi\)
\(558\) −16.3643 28.3439i −0.0293268 0.0507955i
\(559\) 151.367i 0.270783i
\(560\) 0 0
\(561\) −78.0672 −0.139157
\(562\) −590.342 + 340.834i −1.05043 + 0.606466i
\(563\) −177.985 + 308.279i −0.316137 + 0.547565i −0.979678 0.200574i \(-0.935719\pi\)
0.663542 + 0.748139i \(0.269053\pi\)
\(564\) −32.4075 + 56.1314i −0.0574601 + 0.0995238i
\(565\) 0 0
\(566\) 306.196i 0.540983i
\(567\) 28.0068 56.4324i 0.0493948 0.0995281i
\(568\) 276.550i 0.486883i
\(569\) −186.085 322.308i −0.327038 0.566447i 0.654885 0.755729i \(-0.272717\pi\)
−0.981923 + 0.189282i \(0.939384\pi\)
\(570\) 0 0
\(571\) 82.9355 143.649i 0.145246 0.251574i −0.784219 0.620485i \(-0.786936\pi\)
0.929465 + 0.368911i \(0.120269\pi\)
\(572\) −19.4042 33.6091i −0.0339234 0.0587571i
\(573\) −623.300 −1.08778
\(574\) −17.2155 25.9063i −0.0299922 0.0451330i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 8.06639 13.9714i 0.0139799 0.0242139i −0.858951 0.512058i \(-0.828883\pi\)
0.872931 + 0.487844i \(0.162217\pi\)
\(578\) −272.803 157.503i −0.471977 0.272496i
\(579\) 209.617 121.023i 0.362033 0.209020i
\(580\) 0 0
\(581\) −625.830 + 39.4314i −1.07716 + 0.0678681i
\(582\) 159.698i 0.274395i
\(583\) 13.5128 7.80164i 0.0231781 0.0133819i
\(584\) −149.814 86.4950i −0.256530 0.148108i
\(585\) 0 0
\(586\) −469.940 + 271.320i −0.801945 + 0.463003i
\(587\) 204.516 0.348409 0.174205 0.984709i \(-0.444265\pi\)
0.174205 + 0.984709i \(0.444265\pi\)
\(588\) 102.650 + 135.185i 0.174575 + 0.229906i
\(589\) −136.846 −0.232337
\(590\) 0 0
\(591\) −372.514 215.071i −0.630311 0.363910i
\(592\) 97.1799 + 56.1068i 0.164155 + 0.0947751i
\(593\) −345.011 597.577i −0.581806 1.00772i −0.995265 0.0971952i \(-0.969013\pi\)
0.413459 0.910523i \(-0.364320\pi\)
\(594\) 40.6899i 0.0685016i
\(595\) 0 0
\(596\) 132.013 0.221498
\(597\) −183.892 + 106.170i −0.308026 + 0.177839i
\(598\) −29.5616 + 51.2022i −0.0494341 + 0.0856224i
\(599\) −477.775 + 827.531i −0.797622 + 1.38152i 0.123539 + 0.992340i \(0.460575\pi\)
−0.921161 + 0.389182i \(0.872758\pi\)
\(600\) 0 0
\(601\) 587.954i 0.978293i 0.872202 + 0.489146i \(0.162692\pi\)
−0.872202 + 0.489146i \(0.837308\pi\)
\(602\) 236.664 + 356.137i 0.393130 + 0.591590i
\(603\) 19.7465i 0.0327471i
\(604\) 34.8820 + 60.4173i 0.0577516 + 0.100029i
\(605\) 0 0
\(606\) −170.971 + 296.131i −0.282131 + 0.488665i
\(607\) 259.483 + 449.438i 0.427485 + 0.740425i 0.996649 0.0817986i \(-0.0260664\pi\)
−0.569164 + 0.822224i \(0.692733\pi\)
\(608\) 100.350 0.165049
\(609\) 45.9423 92.5714i 0.0754389 0.152006i
\(610\) 0 0
\(611\) 32.7839 + 56.7834i 0.0536561 + 0.0929351i
\(612\) 24.4196 42.2960i 0.0399013 0.0691111i
\(613\) 110.465 + 63.7771i 0.180204 + 0.104041i 0.587389 0.809305i \(-0.300156\pi\)
−0.407184 + 0.913346i \(0.633489\pi\)
\(614\) 25.8744 14.9386i 0.0421407 0.0243300i
\(615\) 0 0
\(616\) −98.2022 48.7368i −0.159419 0.0791182i
\(617\) 486.581i 0.788624i 0.918977 + 0.394312i \(0.129017\pi\)
−0.918977 + 0.394312i \(0.870983\pi\)
\(618\) 370.137 213.699i 0.598927 0.345791i
\(619\) −370.662 214.002i −0.598808 0.345722i 0.169765 0.985485i \(-0.445699\pi\)
−0.768572 + 0.639763i \(0.779033\pi\)
\(620\) 0 0
\(621\) 53.6846 30.9948i 0.0864486 0.0499111i
\(622\) −122.522 −0.196980
\(623\) −688.620 + 457.609i −1.10533 + 0.734524i
\(624\) 24.2787 0.0389082
\(625\) 0 0
\(626\) −3.47589 2.00680i −0.00555254 0.00320576i
\(627\) 147.341 + 85.0671i 0.234993 + 0.135673i
\(628\) −53.5006 92.6658i −0.0851921 0.147557i
\(629\) 228.351i 0.363038i
\(630\) 0 0
\(631\) −64.4987 −0.102217 −0.0511083 0.998693i \(-0.516275\pi\)
−0.0511083 + 0.998693i \(0.516275\pi\)
\(632\) −301.616 + 174.138i −0.477240 + 0.275535i
\(633\) −305.559 + 529.244i −0.482716 + 0.836088i
\(634\) −219.097 + 379.488i −0.345579 + 0.598561i
\(635\) 0 0
\(636\) 9.76149i 0.0153483i
\(637\) 170.354 21.5525i 0.267432 0.0338343i
\(638\) 66.7476i 0.104620i
\(639\) 146.663 + 254.027i 0.229519 + 0.397538i
\(640\) 0 0
\(641\) −352.662 + 610.829i −0.550175 + 0.952932i 0.448086 + 0.893990i \(0.352106\pi\)
−0.998261 + 0.0589413i \(0.981228\pi\)
\(642\) 74.0681 + 128.290i 0.115371 + 0.199828i
\(643\) −1092.83 −1.69958 −0.849788 0.527124i \(-0.823270\pi\)
−0.849788 + 0.527124i \(0.823270\pi\)
\(644\) 10.5025 + 166.688i 0.0163082 + 0.258833i
\(645\) 0 0
\(646\) −102.104 176.850i −0.158056 0.273761i
\(647\) 257.546 446.083i 0.398062 0.689463i −0.595425 0.803411i \(-0.703016\pi\)
0.993487 + 0.113948i \(0.0363496\pi\)
\(648\) −22.0454 12.7279i −0.0340207 0.0196419i
\(649\) 144.860 83.6349i 0.223205 0.128867i
\(650\) 0 0
\(651\) −77.8984 + 51.7659i −0.119660 + 0.0795175i
\(652\) 411.967i 0.631852i
\(653\) 681.245 393.317i 1.04325 0.602323i 0.122501 0.992468i \(-0.460909\pi\)
0.920753 + 0.390145i \(0.127575\pi\)
\(654\) 213.853 + 123.468i 0.326993 + 0.188789i
\(655\) 0 0
\(656\) −10.8844 + 6.28413i −0.0165921 + 0.00957947i
\(657\) 183.484 0.279275
\(658\) 165.915 + 82.3420i 0.252151 + 0.125140i
\(659\) 819.425 1.24344 0.621719 0.783241i \(-0.286435\pi\)
0.621719 + 0.783241i \(0.286435\pi\)
\(660\) 0 0
\(661\) −889.453 513.526i −1.34562 0.776892i −0.357991 0.933725i \(-0.616538\pi\)
−0.987625 + 0.156833i \(0.949872\pi\)
\(662\) −510.216 294.573i −0.770718 0.444974i
\(663\) −24.7032 42.7873i −0.0372598 0.0645358i
\(664\) 253.375i 0.381589i
\(665\) 0 0
\(666\) −119.021 −0.178710
\(667\) 88.0639 50.8437i 0.132030 0.0762275i
\(668\) −137.945 + 238.928i −0.206505 + 0.357677i
\(669\) 53.4701 92.6130i 0.0799254 0.138435i
\(670\) 0 0
\(671\) 262.207i 0.390771i
\(672\) 57.1230 37.9600i 0.0850045 0.0564881i
\(673\) 669.779i 0.995213i −0.867403 0.497607i \(-0.834212\pi\)
0.867403 0.497607i \(-0.165788\pi\)
\(674\) 109.949 + 190.437i 0.163129 + 0.282548i
\(675\) 0 0
\(676\) −156.720 + 271.446i −0.231834 + 0.401548i
\(677\) 454.099 + 786.522i 0.670751 + 1.16178i 0.977691 + 0.210047i \(0.0673616\pi\)
−0.306940 + 0.951729i \(0.599305\pi\)
\(678\) −181.722 −0.268026
\(679\) 455.472 28.6977i 0.670798 0.0422647i
\(680\) 0 0
\(681\) 181.452 + 314.285i 0.266450 + 0.461505i
\(682\) 30.2042 52.3153i 0.0442877 0.0767086i
\(683\) 572.733 + 330.668i 0.838555 + 0.484140i 0.856773 0.515694i \(-0.172466\pi\)
−0.0182177 + 0.999834i \(0.505799\pi\)
\(684\) −92.1770 + 53.2184i −0.134762 + 0.0778047i
\(685\) 0 0
\(686\) 367.112 317.059i 0.535149 0.462185i
\(687\) 186.714i 0.271781i
\(688\) 149.630 86.3887i 0.217485 0.125565i
\(689\) 8.55188 + 4.93743i 0.0124120 + 0.00716608i
\(690\) 0 0
\(691\) −239.610 + 138.339i −0.346759 + 0.200201i −0.663257 0.748392i \(-0.730826\pi\)
0.316498 + 0.948593i \(0.397493\pi\)
\(692\) −441.133 −0.637475
\(693\) 116.051 7.31198i 0.167462 0.0105512i
\(694\) 724.794 1.04437
\(695\) 0 0
\(696\) −36.1632 20.8788i −0.0519586 0.0299983i
\(697\) 22.1495 + 12.7880i 0.0317783 + 0.0183472i
\(698\) −190.343 329.683i −0.272697 0.472326i
\(699\) 566.115i 0.809892i
\(700\) 0 0
\(701\) −415.967 −0.593391 −0.296696 0.954972i \(-0.595885\pi\)
−0.296696 + 0.954972i \(0.595885\pi\)
\(702\) −22.3015 + 12.8758i −0.0317685 + 0.0183415i
\(703\) −248.827 + 430.980i −0.353950 + 0.613059i
\(704\) −22.1488 + 38.3629i −0.0314614 + 0.0544927i
\(705\) 0 0
\(706\) 829.382i 1.17476i
\(707\) 875.313 + 434.409i 1.23807 + 0.614440i
\(708\) 104.645i 0.147804i
\(709\) 136.620 + 236.632i 0.192693 + 0.333755i 0.946142 0.323752i \(-0.104944\pi\)
−0.753449 + 0.657507i \(0.771611\pi\)
\(710\) 0 0
\(711\) 184.701 319.912i 0.259776 0.449946i
\(712\) 167.039 + 289.321i 0.234606 + 0.406349i
\(713\) −92.0300 −0.129074
\(714\) −125.020 62.0462i −0.175098 0.0868994i
\(715\) 0 0
\(716\) 73.3002 + 126.960i 0.102375 + 0.177318i
\(717\) −7.96845 + 13.8018i −0.0111136 + 0.0192493i
\(718\) −108.811 62.8223i −0.151548 0.0874962i
\(719\) −361.463 + 208.691i −0.502731 + 0.290252i −0.729840 0.683617i \(-0.760406\pi\)
0.227110 + 0.973869i \(0.427072\pi\)
\(720\) 0 0
\(721\) −676.000 1017.26i −0.937587 1.41090i
\(722\) 65.4934i 0.0907111i
\(723\) −481.779 + 278.156i −0.666362 + 0.384724i
\(724\) 106.455 + 61.4619i 0.147037 + 0.0848921i
\(725\) 0 0
\(726\) 191.639 110.643i 0.263965 0.152400i
\(727\) −357.267 −0.491426 −0.245713 0.969343i \(-0.579022\pi\)
−0.245713 + 0.969343i \(0.579022\pi\)
\(728\) −4.36289 69.2450i −0.00599298 0.0951167i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −304.491 175.798i −0.416541 0.240490i
\(732\) −142.061 82.0191i −0.194073 0.112048i
\(733\) 215.521 + 373.293i 0.294026 + 0.509267i 0.974758 0.223265i \(-0.0716716\pi\)
−0.680732 + 0.732532i \(0.738338\pi\)
\(734\) 998.488i 1.36034i
\(735\) 0 0
\(736\) 67.4858 0.0916926
\(737\) −31.5638 + 18.2234i −0.0428274 + 0.0247264i
\(738\) 6.66533 11.5447i 0.00903161 0.0156432i
\(739\) 159.512 276.282i 0.215848 0.373860i −0.737687 0.675143i \(-0.764082\pi\)
0.953535 + 0.301284i \(0.0974151\pi\)
\(740\) 0 0
\(741\) 107.673i 0.145308i
\(742\) 27.8406 1.75414i 0.0375210 0.00236407i
\(743\) 1303.33i 1.75414i 0.480360 + 0.877072i \(0.340506\pi\)
−0.480360 + 0.877072i \(0.659494\pi\)
\(744\) 18.8959 + 32.7287i 0.0253977 + 0.0439902i
\(745\) 0 0
\(746\) 36.2337 62.7585i 0.0485706 0.0841267i
\(747\) −134.372 232.740i −0.179883 0.311566i
\(748\) 90.1442 0.120514
\(749\) 352.583 234.302i 0.470738 0.312820i
\(750\) 0 0
\(751\) −614.473 1064.30i −0.818206 1.41717i −0.907003 0.421124i \(-0.861636\pi\)
0.0887971 0.996050i \(-0.471698\pi\)
\(752\) 37.4210 64.8150i 0.0497619 0.0861901i
\(753\) 28.8591 + 16.6618i 0.0383255 + 0.0221273i
\(754\) −36.5832 + 21.1213i −0.0485188 + 0.0280124i
\(755\) 0 0
\(756\) −32.3395 + 65.1625i −0.0427771 + 0.0861938i
\(757\) 1206.22i 1.59342i 0.604359 + 0.796712i \(0.293429\pi\)
−0.604359 + 0.796712i \(0.706571\pi\)
\(758\) −238.487 + 137.691i −0.314627 + 0.181650i
\(759\) 99.0874 + 57.2082i 0.130550 + 0.0753731i
\(760\) 0 0
\(761\) −204.456 + 118.043i −0.268667 + 0.155115i −0.628282 0.777986i \(-0.716242\pi\)
0.359614 + 0.933101i \(0.382908\pi\)
\(762\) 370.101 0.485697
\(763\) 313.712 632.114i 0.411156 0.828459i
\(764\) 719.725 0.942048
\(765\) 0 0
\(766\) −643.088 371.287i −0.839540 0.484709i
\(767\) 91.6777 + 52.9301i 0.119528 + 0.0690093i
\(768\) −13.8564 24.0000i −0.0180422 0.0312500i
\(769\) 1341.44i 1.74440i −0.489149 0.872200i \(-0.662693\pi\)
0.489149 0.872200i \(-0.337307\pi\)
\(770\) 0 0
\(771\) −224.165 −0.290746
\(772\) −242.045 + 139.745i −0.313530 + 0.181017i
\(773\) −90.0279 + 155.933i −0.116466 + 0.201724i −0.918365 0.395735i \(-0.870490\pi\)
0.801899 + 0.597460i \(0.203823\pi\)
\(774\) −91.6290 + 158.706i −0.118384 + 0.205047i
\(775\) 0 0
\(776\) 184.403i 0.237633i
\(777\) 21.3880 + 339.456i 0.0275264 + 0.436881i
\(778\) 570.677i 0.733518i
\(779\) −27.8693 48.2711i −0.0357758 0.0619654i
\(780\) 0 0
\(781\) −270.700 + 468.866i −0.346607 + 0.600341i