Properties

Label 1050.3.q.b.649.1
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 649.1
Root \(-1.25838 - 0.337183i\) of defining polynomial
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.b.199.1

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

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

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
\(7\) −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 0.963991 0.265933i \(-0.0856800\pi\)
−0.712301 + 0.701875i \(0.752347\pi\)
\(12\) 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 0.721137 0.692793i \(-0.243620\pi\)
−0.960545 + 0.278126i \(0.910287\pi\)
\(18\) 3.67423 2.12132i 0.204124 0.117851i
\(19\) 15.3628 + 8.86974i 0.808571 + 0.466828i 0.846459 0.532454i \(-0.178730\pi\)
−0.0378887 + 0.999282i \(0.512063\pi\)
\(20\) 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 0.707492 0.706721i \(-0.249826\pi\)
−0.258292 + 0.966067i \(0.583160\pi\)
\(24\) −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 −0.603868 0.797084i \(-0.706375\pi\)
0.388361 + 0.921507i \(0.373041\pi\)
\(32\) 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 0.134367 0.990932i \(-0.457100\pi\)
−0.790988 + 0.611831i \(0.790433\pi\)
\(38\) −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 \(0.0121999\pi\)
−0.999266 + 0.0383179i \(0.987800\pi\)
\(42\) 1.07820 17.1125i 0.0256714 0.407440i
\(43\) 43.1943i 1.00452i −0.864717 0.502260i \(-0.832502\pi\)
0.864717 0.502260i \(-0.167498\pi\)
\(44\) −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 −0.749172 0.662375i \(-0.769548\pi\)
0.948220 + 0.317615i \(0.102882\pi\)
\(48\) 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 −0.476801 0.879011i \(-0.658204\pi\)
0.522846 + 0.852427i \(0.324870\pi\)
\(54\) −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 −0.261633 0.965168i \(-0.584261\pi\)
0.705043 + 0.709164i \(0.250928\pi\)
\(60\) 0 0
\(61\) −41.0095 23.6769i −0.672288 0.388145i 0.124655 0.992200i \(-0.460218\pi\)
−0.796943 + 0.604055i \(0.793551\pi\)
\(62\) 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 −0.541936 0.840420i \(-0.682309\pi\)
0.456857 + 0.889540i \(0.348975\pi\)
\(68\) 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 0.576918 0.816802i \(-0.304255\pi\)
−0.995830 + 0.0912244i \(0.970922\pi\)
\(74\) 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 −0.152999 0.988226i \(-0.548893\pi\)
0.932329 0.361612i \(-0.117773\pi\)
\(80\) 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 0.948724 0.316107i \(-0.102376\pi\)
0.200606 + 0.979672i \(0.435709\pi\)
\(90\) 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 −0.959881 0.280409i \(-0.909530\pi\)
−0.237099 + 0.971486i \(0.576196\pi\)
\(102\) 17.2673 9.96926i 0.169287 0.0977379i
\(103\) 87.2421 151.108i 0.847011 1.46707i −0.0368520 0.999321i \(-0.511733\pi\)
0.883863 0.467746i \(-0.154934\pi\)
\(104\) 9.91176i 0.0953054i
\(105\) 0 0
\(106\) −3.98511 −0.0375954
\(107\) −52.3741 30.2382i −0.489477 0.282600i 0.234880 0.972024i \(-0.424530\pi\)
−0.724358 + 0.689424i \(0.757864\pi\)
\(108\) 5.19615 + 9.00000i 0.0481125 + 0.0833333i
\(109\) −50.4057 87.3052i −0.462437 0.800965i 0.536644 0.843808i \(-0.319692\pi\)
−0.999082 + 0.0428435i \(0.986358\pi\)
\(110\) 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 \(0.106463\pi\)
−0.944586 + 0.328264i \(0.893537\pi\)
\(114\) −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 \(-0.797209\pi\)
0.803833 0.594855i \(-0.202791\pi\)
\(128\) 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 −0.429296 0.903164i \(-0.641238\pi\)
−0.996811 + 0.0798009i \(0.974572\pi\)
\(132\) 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 −0.858889 0.512161i \(-0.828845\pi\)
0.0141000 + 0.999901i \(0.495512\pi\)
\(138\) −14.6111 + 25.3072i −0.105877 + 0.183385i
\(139\) 193.762i 1.39397i −0.717085 0.696986i \(-0.754524\pi\)
0.717085 0.696986i \(-0.245476\pi\)
\(140\) 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 −0.733765 0.679403i \(-0.762239\pi\)
0.955263 + 0.295758i \(0.0955721\pi\)
\(150\) 0 0
\(151\) −17.4410 30.2087i −0.115503 0.200057i 0.802478 0.596682i \(-0.203515\pi\)
−0.917981 + 0.396625i \(0.870181\pi\)
\(152\) 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 0.938554 0.345132i \(-0.112166\pi\)
−0.768170 + 0.640246i \(0.778832\pi\)
\(158\) −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 −0.159655 0.987173i \(-0.551038\pi\)
−0.934744 + 0.355321i \(0.884372\pi\)
\(164\) −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 0.348510 + 0.937305i \(0.386688\pi\)
−0.985985 + 0.166834i \(0.946646\pi\)
\(174\) 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 0.745304 0.666725i \(-0.232305\pi\)
−0.950053 + 0.312089i \(0.898971\pi\)
\(180\) 0 0
\(181\) 61.4619i 0.339568i −0.985481 0.169784i \(-0.945693\pi\)
0.985481 0.169784i \(-0.0543071\pi\)
\(182\) 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 0.180492 0.983577i \(-0.442231\pi\)
0.761556 0.648099i \(-0.224436\pi\)
\(192\) 6.92820 + 12.0000i 0.0360844 + 0.0625000i
\(193\) −121.023 + 69.8724i −0.627060 + 0.362033i −0.779613 0.626262i \(-0.784584\pi\)
0.152552 + 0.988295i \(0.451251\pi\)
\(194\) 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 \(-0.782927\pi\)
0.776342 0.630311i \(-0.217073\pi\)
\(198\) 20.3450 + 11.7462i 0.102752 + 0.0593241i
\(199\) 106.170 61.2973i 0.533518 0.308026i −0.208930 0.977931i \(-0.566998\pi\)
0.742448 + 0.669904i \(0.233665\pi\)
\(200\) 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 0.999036 0.0438940i \(-0.0139764\pi\)
−0.537531 + 0.843244i \(0.680643\pi\)
\(228\) 53.2184 30.7257i 0.233414 0.134762i
\(229\) 93.3568 + 53.8996i 0.407671 + 0.235369i 0.689789 0.724011i \(-0.257703\pi\)
−0.282117 + 0.959380i \(0.591037\pi\)
\(230\) 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 0.963809 0.266592i \(-0.0858978\pi\)
0.251029 + 0.967980i \(0.419231\pi\)
\(234\) 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 0.204272 0.978914i \(-0.434517\pi\)
0.949900 + 0.312553i \(0.101184\pi\)
\(242\) −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 \(0.0122024\pi\)
−0.999265 + 0.0383255i \(0.987798\pi\)
\(252\) 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 −0.712226 0.701950i \(-0.752313\pi\)
0.964020 + 0.265831i \(0.0856464\pi\)
\(258\) 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 −0.199323 0.979934i \(-0.563874\pi\)
0.748986 + 0.662586i \(0.230541\pi\)
\(264\) −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 −0.797274 0.603618i \(-0.793725\pi\)
0.124112 + 0.992268i \(0.460392\pi\)
\(270\) 0 0
\(271\) 123.029 + 71.0308i 0.453981 + 0.262106i 0.709510 0.704695i \(-0.248916\pi\)
−0.255529 + 0.966801i \(0.582250\pi\)
\(272\) 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 −0.993771 0.111438i \(-0.964454\pi\)
−0.400377 + 0.916350i \(0.631121\pi\)
\(278\) −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 0.608891 0.793254i \(-0.291615\pi\)
−0.991424 + 0.130688i \(0.958281\pi\)
\(284\) −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 −0.374501 0.927226i \(-0.622186\pi\)
0.615751 + 0.787941i \(0.288853\pi\)
\(312\) −14.8676 + 8.58383i −0.0476527 + 0.0275123i
\(313\) 1.41903 2.45782i 0.00453363 0.00785247i −0.863750 0.503921i \(-0.831890\pi\)
0.868283 + 0.496069i \(0.165224\pi\)
\(314\) 75.6613i 0.240960i
\(315\) 0 0
\(316\) 246.268 0.779329
\(317\) 268.338 + 154.925i 0.846493 + 0.488723i 0.859466 0.511193i \(-0.170796\pi\)
−0.0129730 + 0.999916i \(0.504130\pi\)
\(318\) 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 −0.358406 0.933566i \(-0.616680\pi\)
0.987695 0.156394i \(-0.0499871\pi\)
\(332\) 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 \(0.0741014\pi\)
−0.973025 + 0.230699i \(0.925899\pi\)
\(338\) 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 −0.976681 0.214697i \(-0.931124\pi\)
−0.302408 + 0.953179i \(0.597790\pi\)
\(348\) 14.7636 25.5712i 0.0424240 0.0734805i
\(349\) 269.185i 0.771305i −0.922644 0.385652i \(-0.873976\pi\)
0.922644 0.385652i \(-0.126024\pi\)
\(350\) 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 0.897498 + 0.441018i \(0.145382\pi\)
−0.0668166 + 0.997765i \(0.521284\pi\)
\(354\) 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 −0.797501 0.603318i \(-0.793845\pi\)
0.921239 + 0.388997i \(0.127178\pi\)
\(360\) 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 0.717713 + 0.696339i \(0.245189\pi\)
0.244191 + 0.969727i \(0.421478\pi\)
\(368\) −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 0.439332 0.898325i \(-0.355215\pi\)
−0.558306 + 0.829635i \(0.688548\pi\)
\(374\) −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 −0.287803 0.957690i \(-0.592925\pi\)
0.973285 0.229600i \(-0.0737418\pi\)
\(384\) 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 −0.999765 0.0217005i \(-0.993092\pi\)
0.481089 0.876672i \(-0.340241\pi\)
\(390\) 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 −0.746485 0.665402i \(-0.768260\pi\)
0.949498 + 0.313774i \(0.101593\pi\)
\(398\) −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 −0.469450 0.882959i \(-0.655548\pi\)
0.999390 0.0349237i \(-0.0111188\pi\)
\(402\) −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 −0.881543 0.472104i \(-0.843495\pi\)
−0.0319171 + 0.999491i \(0.510161\pi\)
\(410\) 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 \(0.246185\pi\)
−0.715530 + 0.698582i \(0.753815\pi\)
\(420\) 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 0.540344 0.841445i \(-0.318294\pi\)
−0.998884 + 0.0472289i \(0.984961\pi\)
\(432\) −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 0.842725 0.538345i \(-0.180950\pi\)
−0.0448578 + 0.998993i \(0.514283\pi\)
\(440\) 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 0.757491 0.652846i \(-0.226425\pi\)
−0.186636 + 0.982429i \(0.559758\pi\)
\(444\) −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 0.416293 0.909231i \(-0.363329\pi\)
−0.579270 + 0.815135i \(0.696662\pi\)
\(458\) −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 \(0.0455362\pi\)
−0.989785 + 0.142569i \(0.954464\pi\)
\(462\) 85.0456 42.2073i 0.184081 0.0913578i
\(463\) 73.9873i 0.159800i −0.996803 0.0798999i \(-0.974540\pi\)
0.996803 0.0798999i \(-0.0254601\pi\)
\(464\) −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 −0.521210 0.853429i \(-0.674519\pi\)
0.999696 + 0.0246667i \(0.00785244\pi\)
\(468\) −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 −0.928915 0.370293i \(-0.879257\pi\)
−0.143775 + 0.989610i \(0.545924\pi\)
\(480\) 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 −0.998882 0.0472773i \(-0.984946\pi\)
−0.458498 + 0.888696i \(0.651612\pi\)
\(488\) −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 −0.350230 0.936664i \(-0.613897\pi\)
0.986290 0.165024i \(-0.0527701\pi\)
\(500\) 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 0.448955 0.893555i \(-0.351796\pi\)
−0.549364 + 0.835583i \(0.685130\pi\)
\(510\) 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 −0.626398 + 0.779504i \(0.715471\pi\)
−0.988269 + 0.152725i \(0.951195\pi\)
\(522\) 31.3182 18.0816i 0.0599966 0.0346391i
\(523\) 345.682 598.739i 0.660960 1.14482i −0.319404 0.947619i \(-0.603483\pi\)
0.980364 0.197197i \(-0.0631840\pi\)
\(524\) 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 0.499283 + 0.866439i \(0.333597\pi\)
−1.00000 0.000828025i \(0.999736\pi\)
\(542\) −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 \(-0.905970\pi\)
0.956685 0.291126i \(-0.0940297\pi\)
\(548\) −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 0.0208114 0.999783i \(-0.493375\pi\)
0.876244 + 0.481869i \(0.160042\pi\)
\(558\) −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 0.663542 0.748139i \(-0.269053\pi\)
−0.979678 + 0.200574i \(0.935719\pi\)
\(564\) −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 −0.981923 0.189282i \(-0.939384\pi\)
0.654885 + 0.755729i \(0.272717\pi\)
\(570\) 0 0
\(571\) 82.9355 + 143.649i 0.145246 + 0.251574i 0.929465 0.368911i \(-0.120269\pi\)
−0.784219 + 0.620485i \(0.786936\pi\)
\(572\) −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 0.872931 0.487844i \(-0.162217\pi\)
−0.858951 + 0.512058i \(0.828883\pi\)
\(578\) −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 0.413459 + 0.910523i \(0.364320\pi\)
−0.995265 + 0.0971952i \(0.969013\pi\)
\(594\) 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 −0.921161 0.389182i \(-0.872758\pi\)
0.123539 0.992340i \(-0.460575\pi\)
\(600\) 0 0
\(601\) 587.954i 0.978293i −0.872202 0.489146i \(-0.837308\pi\)
0.872202 0.489146i \(-0.162692\pi\)
\(602\) 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 −0.569164 0.822224i \(-0.692733\pi\)
0.996649 + 0.0817986i \(0.0260664\pi\)
\(608\) 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 −0.407184 0.913346i \(-0.633489\pi\)
0.587389 + 0.809305i \(0.300156\pi\)
\(614\) 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 \(-0.870983\pi\)
0.918977 0.394312i \(-0.129017\pi\)
\(618\) 370.137 + 213.699i 0.598927 + 0.345791i
\(619\) −370.662 + 214.002i −0.598808 + 0.345722i −0.768572 0.639763i \(-0.779033\pi\)
0.169765 + 0.985485i \(0.445699\pi\)
\(620\) 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 −0.998261 0.0589413i \(-0.981228\pi\)
0.448086 0.893990i \(-0.352106\pi\)
\(642\) 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 0.993487 0.113948i \(-0.0363496\pi\)
−0.595425 + 0.803411i \(0.703016\pi\)
\(648\) −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 0.920753 0.390145i \(-0.127575\pi\)
0.122501 + 0.992468i \(0.460909\pi\)
\(654\) 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 −0.987625 0.156833i \(-0.949872\pi\)
−0.357991 + 0.933725i \(0.616538\pi\)
\(662\) −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 \(0.165788\pi\)
−0.867403 + 0.497607i \(0.834212\pi\)
\(674\) 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 −0.306940 0.951729i \(-0.599305\pi\)
0.977691 0.210047i \(-0.0673616\pi\)
\(678\) −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 −0.0182177 0.999834i \(-0.505799\pi\)
0.856773 + 0.515694i \(0.172466\pi\)
\(684\) −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 0.316498 0.948593i \(-0.397493\pi\)
−0.663257 + 0.748392i \(0.730826\pi\)
\(692\) −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 −0.753449 0.657507i \(-0.771611\pi\)
0.946142 + 0.323752i \(0.104944\pi\)
\(710\) 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 0.227110 0.973869i \(-0.427072\pi\)
−0.729840 + 0.683617i \(0.760406\pi\)
\(720\) 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 −0.680732 0.732532i \(-0.738338\pi\)
0.974758 + 0.223265i \(0.0716716\pi\)
\(734\) 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 0.953535 0.301284i \(-0.0974151\pi\)
−0.737687 + 0.675143i \(0.764082\pi\)
\(740\) 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 \(-0.659494\pi\)
0.480360 0.877072i \(-0.340506\pi\)
\(744\) 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 0.0887971 + 0.996050i \(0.471698\pi\)
−0.907003 + 0.421124i \(0.861636\pi\)
\(752\) 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 \(-0.706571\pi\)
0.604359 0.796712i \(-0.293429\pi\)
\(758\) −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 0.359614 0.933101i \(-0.382908\pi\)
−0.628282 + 0.777986i \(0.716242\pi\)
\(762\) 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 \(0.337307\pi\)
−0.489149 + 0.872200i \(0.662693\pi\)
\(770\) 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 0.801899 0.597460i \(-0.203823\pi\)
−0.918365 + 0.395735i \(0.870490\pi\)
\(774\) −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