Properties

Label 1050.3.p.c.451.4
Level $1050$
Weight $3$
Character 1050.451
Analytic conductor $28.610$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.151613669376.6
Defining polynomial: \( x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 451.4
Root \(-2.56149 + 0.662382i\) of defining polynomial
Character \(\chi\) \(=\) 1050.451
Dual form 1050.3.p.c.901.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(0.440173 + 6.98615i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(0.440173 + 6.98615i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.76860 - 4.79536i) q^{11} +(3.00000 - 1.73205i) q^{12} +3.50434i q^{13} +(-8.24500 + 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(7.04933 + 4.06994i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-15.3628 + 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} +7.83078 q^{22} +(5.96495 + 10.3316i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} -5.19615i q^{27} +(-12.5405 - 6.22374i) q^{28} -8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-8.30580 + 4.79536i) q^{33} +11.5115i q^{34} -6.00000 q^{36} +(14.0267 + 24.2950i) q^{37} +(-21.7263 - 12.5437i) q^{38} +(3.03484 - 5.25650i) q^{39} -3.14207i q^{41} +(17.1125 - 1.07820i) q^{42} -43.1943 q^{43} +(5.53720 + 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(16.2037 - 9.35524i) q^{47} +6.92820i q^{48} +(-48.6125 + 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(-6.06969 - 3.50434i) q^{52} +(-1.40895 + 2.44037i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +30.7257 q^{57} +(-6.02720 - 10.4394i) q^{58} +(-26.1612 - 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} -10.9096i q^{62} +(-17.4903 + 11.6228i) q^{63} +8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(-3.29108 + 5.70032i) q^{67} +(-14.0987 + 8.13987i) q^{68} -20.6632i q^{69} -97.7751 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-52.9672 - 30.5806i) q^{73} +(-19.8368 + 34.3583i) q^{74} -35.4790i q^{76} +(34.7197 + 17.2311i) q^{77} +8.58383 q^{78} +(-61.5670 - 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(3.84823 - 2.22178i) q^{82} +89.5815i q^{83} +(13.4209 + 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(12.7856 + 7.38178i) q^{87} +(-7.83078 + 13.5633i) q^{88} +(-102.290 + 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} -23.8598 q^{92} +(6.68072 + 11.5713i) q^{93} +(22.9156 + 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} +65.1965i q^{97} +(-41.9067 - 55.1890i) q^{98} +16.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 16 q^{14} - 16 q^{16} - 24 q^{17} + 72 q^{19} + 24 q^{22} + 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} + 12 q^{33} - 48 q^{36} - 24 q^{37} - 180 q^{38} - 12 q^{39} + 12 q^{42} - 112 q^{43} - 8 q^{44} + 32 q^{46} + 84 q^{47} - 264 q^{49} + 24 q^{51} + 24 q^{52} + 44 q^{53} + 40 q^{56} - 144 q^{57} + 104 q^{58} + 312 q^{59} - 204 q^{61} + 64 q^{64} - 36 q^{66} + 120 q^{67} + 48 q^{68} - 64 q^{71} + 84 q^{73} - 16 q^{74} + 228 q^{77} + 144 q^{78} - 144 q^{79} - 36 q^{81} - 60 q^{82} + 176 q^{86} + 36 q^{87} - 24 q^{88} - 336 q^{89} - 296 q^{91} - 240 q^{92} - 96 q^{93} + 36 q^{94} - 24 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.353553 + 0.612372i
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 0.440173 + 6.98615i 0.0628819 + 0.998021i
\(8\) −2.82843 −0.353553
\(9\) 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 \(0.0856800\pi\)
\(12\) 3.00000 1.73205i 0.250000 0.144338i
\(13\) 3.50434i 0.269564i 0.990875 + 0.134782i \(0.0430335\pi\)
−0.990875 + 0.134782i \(0.956967\pi\)
\(14\) −8.24500 + 5.47905i −0.588928 + 0.391361i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 7.04933 + 4.06994i 0.414667 + 0.239408i 0.692793 0.721137i \(-0.256380\pi\)
−0.278126 + 0.960545i \(0.589713\pi\)
\(18\) −2.12132 + 3.67423i −0.117851 + 0.204124i
\(19\) −15.3628 + 8.86974i −0.808571 + 0.466828i −0.846459 0.532454i \(-0.821270\pi\)
0.0378887 + 0.999282i \(0.487937\pi\)
\(20\) 0 0
\(21\) 5.38992 10.8604i 0.256663 0.517163i
\(22\) 7.83078 0.355945
\(23\) 5.96495 + 10.3316i 0.259346 + 0.449200i 0.966067 0.258292i \(-0.0831597\pi\)
−0.706721 + 0.707492i \(0.749826\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −4.29192 + 2.47794i −0.165074 + 0.0953054i
\(27\) 5.19615i 0.192450i
\(28\) −12.5405 6.22374i −0.447876 0.222277i
\(29\) −8.52374 −0.293922 −0.146961 0.989142i \(-0.546949\pi\)
−0.146961 + 0.989142i \(0.546949\pi\)
\(30\) 0 0
\(31\) −6.68072 3.85711i −0.215507 0.124423i 0.388361 0.921507i \(-0.373041\pi\)
−0.603868 + 0.797084i \(0.706375\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) −8.30580 + 4.79536i −0.251691 + 0.145314i
\(34\) 11.5115i 0.338574i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 14.0267 + 24.2950i 0.379100 + 0.656621i 0.990932 0.134367i \(-0.0429002\pi\)
−0.611831 + 0.790988i \(0.709567\pi\)
\(38\) −21.7263 12.5437i −0.571746 0.330098i
\(39\) 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 \(-0.0121999\pi\)
\(42\) 17.1125 1.07820i 0.407440 0.0256714i
\(43\) −43.1943 −1.00452 −0.502260 0.864717i \(-0.667498\pi\)
−0.502260 + 0.864717i \(0.667498\pi\)
\(44\) 5.53720 + 9.59071i 0.125845 + 0.217971i
\(45\) 0 0
\(46\) −8.43572 + 14.6111i −0.183385 + 0.317632i
\(47\) 16.2037 9.35524i 0.344761 0.199048i −0.317615 0.948220i \(-0.602882\pi\)
0.662375 + 0.749172i \(0.269548\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −48.6125 + 6.15023i −0.992092 + 0.125515i
\(50\) 0 0
\(51\) −7.04933 12.2098i −0.138222 0.239408i
\(52\) −6.06969 3.50434i −0.116725 0.0673911i
\(53\) −1.40895 + 2.44037i −0.0265840 + 0.0460448i −0.879011 0.476801i \(-0.841796\pi\)
0.852427 + 0.522846i \(0.175130\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −1.24500 19.7598i −0.0222321 0.352854i
\(57\) 30.7257 0.539047
\(58\) −6.02720 10.4394i −0.103917 0.179990i
\(59\) −26.1612 15.1042i −0.443411 0.256003i 0.261633 0.965168i \(-0.415739\pi\)
−0.705043 + 0.709164i \(0.749072\pi\)
\(60\) 0 0
\(61\) −41.0095 + 23.6769i −0.672288 + 0.388145i −0.796943 0.604055i \(-0.793551\pi\)
0.124655 + 0.992200i \(0.460218\pi\)
\(62\) 10.9096i 0.175961i
\(63\) −17.4903 + 11.6228i −0.277624 + 0.184489i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) −11.7462 6.78166i −0.177972 0.102752i
\(67\) −3.29108 + 5.70032i −0.0491206 + 0.0850794i −0.889540 0.456857i \(-0.848975\pi\)
0.840420 + 0.541936i \(0.182309\pi\)
\(68\) −14.0987 + 8.13987i −0.207333 + 0.119704i
\(69\) 20.6632i 0.299467i
\(70\) 0 0
\(71\) −97.7751 −1.37711 −0.688557 0.725182i \(-0.741755\pi\)
−0.688557 + 0.725182i \(0.741755\pi\)
\(72\) −4.24264 7.34847i −0.0589256 0.102062i
\(73\) −52.9672 30.5806i −0.725578 0.418913i 0.0912244 0.995830i \(-0.470922\pi\)
−0.816802 + 0.576918i \(0.804255\pi\)
\(74\) −19.8368 + 34.3583i −0.268064 + 0.464301i
\(75\) 0 0
\(76\) 35.4790i 0.466828i
\(77\) 34.7197 + 17.2311i 0.450906 + 0.223780i
\(78\) 8.58383 0.110049
\(79\) −61.5670 106.637i −0.779329 1.34984i −0.932329 0.361612i \(-0.882227\pi\)
0.152999 0.988226i \(-0.451107\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 3.84823 2.22178i 0.0469296 0.0270948i
\(83\) 89.5815i 1.07930i 0.841891 + 0.539648i \(0.181443\pi\)
−0.841891 + 0.539648i \(0.818557\pi\)
\(84\) 13.4209 + 20.1960i 0.159772 + 0.240429i
\(85\) 0 0
\(86\) −30.5430 52.9020i −0.355151 0.615140i
\(87\) 12.7856 + 7.38178i 0.146961 + 0.0848480i
\(88\) −7.83078 + 13.5633i −0.0889862 + 0.154129i
\(89\) −102.290 + 59.0573i −1.14933 + 0.663566i −0.948724 0.316107i \(-0.897624\pi\)
−0.200606 + 0.979672i \(0.564291\pi\)
\(90\) 0 0
\(91\) −24.4818 + 1.54251i −0.269031 + 0.0169507i
\(92\) −23.8598 −0.259346
\(93\) 6.68072 + 11.5713i 0.0718357 + 0.124423i
\(94\) 22.9156 + 13.2303i 0.243783 + 0.140748i
\(95\) 0 0
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) 65.1965i 0.672128i 0.941839 + 0.336064i \(0.109096\pi\)
−0.941839 + 0.336064i \(0.890904\pi\)
\(98\) −41.9067 55.1890i −0.427619 0.563153i
\(99\) 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 \(0.909530\pi\)
\(102\) 9.96926 17.2673i 0.0977379 0.169287i
\(103\) −151.108 + 87.2421i −1.46707 + 0.847011i −0.999321 0.0368520i \(-0.988267\pi\)
−0.467746 + 0.883863i \(0.654934\pi\)
\(104\) 9.91176i 0.0953054i
\(105\) 0 0
\(106\) −3.98511 −0.0375954
\(107\) 30.2382 + 52.3741i 0.282600 + 0.489477i 0.972024 0.234880i \(-0.0754698\pi\)
−0.689424 + 0.724358i \(0.742136\pi\)
\(108\) 9.00000 + 5.19615i 0.0833333 + 0.0481125i
\(109\) 50.4057 87.3052i 0.462437 0.800965i −0.536644 0.843808i \(-0.680308\pi\)
0.999082 + 0.0428435i \(0.0136417\pi\)
\(110\) 0 0
\(111\) 48.5899i 0.437747i
\(112\) 23.3204 15.4971i 0.208218 0.138367i
\(113\) 74.1876 0.656527 0.328264 0.944586i \(-0.393537\pi\)
0.328264 + 0.944586i \(0.393537\pi\)
\(114\) 21.7263 + 37.6311i 0.190582 + 0.330098i
\(115\) 0 0
\(116\) 8.52374 14.7636i 0.0734805 0.127272i
\(117\) −9.10453 + 5.25650i −0.0778165 + 0.0449274i
\(118\) 42.7211i 0.362043i
\(119\) −25.3302 + 51.0392i −0.212859 + 0.428901i
\(120\) 0 0
\(121\) 45.1697 + 78.2362i 0.373303 + 0.646580i
\(122\) −57.9963 33.4842i −0.475379 0.274460i
\(123\) −2.72111 + 4.71310i −0.0221228 + 0.0383179i
\(124\) 13.3614 7.71423i 0.107754 0.0622115i
\(125\) 0 0
\(126\) −26.6025 13.2026i −0.211131 0.104782i
\(127\) 151.093 1.18971 0.594855 0.803833i \(-0.297209\pi\)
0.594855 + 0.803833i \(0.297209\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) 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 \(0.641238\pi\)
\(132\) 19.1814i 0.145314i
\(133\) −68.7276 103.423i −0.516749 0.777615i
\(134\) −9.30859 −0.0694671
\(135\) 0 0
\(136\) −19.9385 11.5115i −0.146607 0.0846435i
\(137\) −66.8203 + 115.736i −0.487739 + 0.844789i −0.999901 0.0141000i \(-0.995512\pi\)
0.512161 + 0.858889i \(0.328845\pi\)
\(138\) 25.3072 14.6111i 0.183385 0.105877i
\(139\) 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
\(142\) −69.1374 119.750i −0.486883 0.843306i
\(143\) 16.8045 + 9.70210i 0.117514 + 0.0678469i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 86.4950i 0.592432i
\(147\) 78.2450 + 32.8743i 0.532279 + 0.223635i
\(148\) −56.1068 −0.379100
\(149\) −33.0032 57.1632i −0.221498 0.383646i 0.733765 0.679403i \(-0.237761\pi\)
−0.955263 + 0.295758i \(0.904428\pi\)
\(150\) 0 0
\(151\) −17.4410 + 30.2087i −0.115503 + 0.200057i −0.917981 0.396625i \(-0.870181\pi\)
0.802478 + 0.596682i \(0.203515\pi\)
\(152\) 43.4527 25.0874i 0.285873 0.165049i
\(153\) 24.4196i 0.159605i
\(154\) 3.44690 + 54.7070i 0.0223825 + 0.355240i
\(155\) 0 0
\(156\) 6.06969 + 10.5130i 0.0389082 + 0.0673911i
\(157\) −46.3329 26.7503i −0.295114 0.170384i 0.345132 0.938554i \(-0.387834\pi\)
−0.640246 + 0.768170i \(0.721168\pi\)
\(158\) 87.0689 150.808i 0.551069 0.954480i
\(159\) 4.22685 2.44037i 0.0265840 0.0153483i
\(160\) 0 0
\(161\) −69.5525 + 46.2197i −0.432003 + 0.287079i
\(162\) −12.7279 −0.0785674
\(163\) −102.992 178.387i −0.631852 1.09440i −0.987173 0.159655i \(-0.948962\pi\)
0.355321 0.934744i \(-0.384372\pi\)
\(164\) 5.44222 + 3.14207i 0.0331843 + 0.0191589i
\(165\) 0 0
\(166\) −109.714 + 63.3437i −0.660931 + 0.381589i
\(167\) 137.945i 0.826020i 0.910727 + 0.413010i \(0.135523\pi\)
−0.910727 + 0.413010i \(0.864477\pi\)
\(168\) −15.2450 + 30.7179i −0.0907440 + 0.182845i
\(169\) 156.720 0.927335
\(170\) 0 0
\(171\) −46.0885 26.6092i −0.269524 0.155609i
\(172\) 43.1943 74.8148i 0.251130 0.434970i
\(173\) 191.016 110.283i 1.10414 0.637475i 0.166834 0.985985i \(-0.446646\pi\)
0.937305 + 0.348510i \(0.113312\pi\)
\(174\) 20.8788i 0.119993i
\(175\) 0 0
\(176\) −22.1488 −0.125845
\(177\) 26.1612 + 45.3126i 0.147804 + 0.256003i
\(178\) −144.660 83.5197i −0.812699 0.469212i
\(179\) 36.6501 63.4798i 0.204749 0.354636i −0.745304 0.666725i \(-0.767695\pi\)
0.950053 + 0.312089i \(0.101029\pi\)
\(180\) 0 0
\(181\) 61.4619i 0.339568i 0.985481 + 0.169784i \(0.0543071\pi\)
−0.985481 + 0.169784i \(0.945693\pi\)
\(182\) −19.2004 28.8932i −0.105497 0.158754i
\(183\) 82.0191 0.448192
\(184\) −16.8714 29.2222i −0.0916926 0.158816i
\(185\) 0 0
\(186\) −9.44796 + 16.3643i −0.0507955 + 0.0879804i
\(187\) 39.0336 22.5360i 0.208736 0.120514i
\(188\) 37.4210i 0.199048i
\(189\) 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 \(0.442231\pi\)
\(192\) −12.0000 6.92820i −0.0625000 0.0360844i
\(193\) 69.8724 121.023i 0.362033 0.627060i −0.626262 0.779613i \(-0.715416\pi\)
0.988295 + 0.152552i \(0.0487493\pi\)
\(194\) −79.8490 + 46.1009i −0.411593 + 0.237633i
\(195\) 0 0
\(196\) 37.9600 90.3495i 0.193673 0.460967i
\(197\) 248.343 1.26062 0.630311 0.776342i \(-0.282927\pi\)
0.630311 + 0.776342i \(0.282927\pi\)
\(198\) 11.7462 + 20.3450i 0.0593241 + 0.102752i
\(199\) −106.170 61.2973i −0.533518 0.308026i 0.208930 0.977931i \(-0.433002\pi\)
−0.742448 + 0.669904i \(0.766335\pi\)
\(200\) 0 0
\(201\) 9.87325 5.70032i 0.0491206 0.0283598i
\(202\) 197.421i 0.977329i
\(203\) −3.75192 59.5481i −0.0184824 0.293341i
\(204\) 28.1973 0.138222
\(205\) 0 0
\(206\) −213.699 123.379i −1.03737 0.598927i
\(207\) −17.8949 + 30.9948i −0.0864486 + 0.149733i
\(208\) 12.1394 7.00867i 0.0583624 0.0336955i
\(209\) 98.2271i 0.469986i
\(210\) 0 0
\(211\) 352.829 1.67218 0.836088 0.548596i \(-0.184837\pi\)
0.836088 + 0.548596i \(0.184837\pi\)
\(212\) −2.81790 4.88074i −0.0132920 0.0230224i
\(213\) 146.663 + 84.6757i 0.688557 + 0.397538i
\(214\) −42.7632 + 74.0681i −0.199828 + 0.346113i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 24.0057 48.3703i 0.110625 0.222904i
\(218\) 142.569 0.653985
\(219\) 52.9672 + 91.7418i 0.241859 + 0.418913i
\(220\) 0 0
\(221\) −14.2624 + 24.7032i −0.0645358 + 0.111779i
\(222\) 59.5103 34.3583i 0.268064 0.154767i
\(223\) 61.7420i 0.276870i −0.990372 0.138435i \(-0.955793\pi\)
0.990372 0.138435i \(-0.0442072\pi\)
\(224\) 35.4700 + 17.6034i 0.158348 + 0.0785866i
\(225\) 0 0
\(226\) 52.4586 + 90.8609i 0.232118 + 0.402039i
\(227\) −181.452 104.762i −0.799350 0.461505i 0.0438940 0.999036i \(-0.486024\pi\)
−0.843244 + 0.537531i \(0.819357\pi\)
\(228\) −30.7257 + 53.2184i −0.134762 + 0.233414i
\(229\) −93.3568 + 53.8996i −0.407671 + 0.235369i −0.689789 0.724011i \(-0.742297\pi\)
0.282117 + 0.959380i \(0.408963\pi\)
\(230\) 0 0
\(231\) −37.1571 55.9148i −0.160853 0.242055i
\(232\) 24.1088 0.103917
\(233\) 163.423 + 283.057i 0.701387 + 1.21484i 0.967980 + 0.251029i \(0.0807689\pi\)
−0.266592 + 0.963809i \(0.585898\pi\)
\(234\) −12.8758 7.43382i −0.0550246 0.0317685i
\(235\) 0 0
\(236\) 52.3224 30.2084i 0.221705 0.128002i
\(237\) 213.274i 0.899892i
\(238\) −80.4211 + 5.06706i −0.337904 + 0.0212902i
\(239\) −9.20117 −0.0384986 −0.0192493 0.999815i \(-0.506128\pi\)
−0.0192493 + 0.999815i \(0.506128\pi\)
\(240\) 0 0
\(241\) 278.156 + 160.593i 1.15417 + 0.666362i 0.949900 0.312553i \(-0.101184\pi\)
0.204272 + 0.978914i \(0.434517\pi\)
\(242\) −63.8796 + 110.643i −0.263965 + 0.457201i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 94.7075i 0.388145i
\(245\) 0 0
\(246\) −7.69646 −0.0312864
\(247\) −31.0825 53.8365i −0.125840 0.217962i
\(248\) 18.8959 + 10.9096i 0.0761932 + 0.0439902i
\(249\) 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 \(-0.0122024\pi\)
\(252\) −2.64104 41.9169i −0.0104803 0.166337i
\(253\) 66.0583 0.261100
\(254\) 106.839 + 185.051i 0.420626 + 0.728546i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 112.083 64.7109i 0.436119 0.251793i −0.265831 0.964020i \(-0.585646\pi\)
0.701950 + 0.712226i \(0.252313\pi\)
\(258\) 105.804i 0.410093i
\(259\) −163.554 + 108.687i −0.631483 + 0.419640i
\(260\) 0 0
\(261\) −12.7856 22.1453i −0.0489870 0.0848480i
\(262\) −264.203 152.538i −1.00841 0.582206i
\(263\) −83.4625 + 144.561i −0.317348 + 0.549663i −0.979934 0.199323i \(-0.936126\pi\)
0.662586 + 0.748986i \(0.269459\pi\)
\(264\) 23.4924 13.5633i 0.0889862 0.0513762i
\(265\) 0 0
\(266\) 78.0688 157.305i 0.293492 0.591371i
\(267\) 204.581 0.766220
\(268\) −6.58217 11.4006i −0.0245603 0.0425397i
\(269\) 181.081 + 104.547i 0.673162 + 0.388650i 0.797274 0.603618i \(-0.206275\pi\)
−0.124112 + 0.992268i \(0.539608\pi\)
\(270\) 0 0
\(271\) 123.029 71.0308i 0.453981 0.262106i −0.255529 0.966801i \(-0.582250\pi\)
0.709510 + 0.704695i \(0.248916\pi\)
\(272\) 32.5595i 0.119704i
\(273\) 38.0586 + 18.8881i 0.139409 + 0.0691871i
\(274\) −188.996 −0.689768
\(275\) 0 0
\(276\) 35.7897 + 20.6632i 0.129673 + 0.0748667i
\(277\) −222.961 + 386.179i −0.804912 + 1.39415i 0.111438 + 0.993771i \(0.464454\pi\)
−0.916350 + 0.400377i \(0.868879\pi\)
\(278\) 237.309 137.010i 0.853630 0.492843i
\(279\) 23.1427i 0.0829487i
\(280\) 0 0
\(281\) 482.012 1.71534 0.857672 0.514196i \(-0.171910\pi\)
0.857672 + 0.514196i \(0.171910\pi\)
\(282\) −22.9156 39.6909i −0.0812609 0.140748i
\(283\) −187.506 108.257i −0.662566 0.382533i 0.130688 0.991424i \(-0.458281\pi\)
−0.793254 + 0.608891i \(0.791615\pi\)
\(284\) 97.7751 169.351i 0.344278 0.596308i
\(285\) 0 0
\(286\) 27.4417i 0.0959500i
\(287\) 21.9509 1.38305i 0.0764841 0.00481900i
\(288\) 16.9706 0.0589256
\(289\) −111.371 192.901i −0.385368 0.667476i
\(290\) 0 0
\(291\) 56.4618 97.7947i 0.194027 0.336064i
\(292\) 105.934 61.1612i 0.362789 0.209456i
\(293\) 383.704i 1.30957i 0.755815 + 0.654786i \(0.227241\pi\)
−0.755815 + 0.654786i \(0.772759\pi\)
\(294\) 15.0649 + 119.076i 0.0512412 + 0.405020i
\(295\) 0 0
\(296\) −39.6735 68.7166i −0.134032 0.232151i
\(297\) −24.9174 14.3861i −0.0838970 0.0484379i
\(298\) 46.6736 80.8410i 0.156623 0.271278i
\(299\) −36.2054 + 20.9032i −0.121088 + 0.0699104i
\(300\) 0 0
\(301\) −19.0130 301.762i −0.0631661 1.00253i
\(302\) −49.3305 −0.163346
\(303\) 120.895 + 209.396i 0.398993 + 0.691076i
\(304\) 61.4514 + 35.4790i 0.202143 + 0.116707i
\(305\) 0 0
\(306\) −29.9078 + 17.2673i −0.0977379 + 0.0564290i
\(307\) 21.1264i 0.0688155i 0.999408 + 0.0344078i \(0.0109545\pi\)
−0.999408 + 0.0344078i \(0.989046\pi\)
\(308\) −64.5648 + 42.9053i −0.209626 + 0.139303i
\(309\) 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 \(0.622186\pi\)
\(312\) −8.58383 + 14.8676i −0.0275123 + 0.0476527i
\(313\) −2.45782 + 1.41903i −0.00785247 + 0.00453363i −0.503921 0.863750i \(-0.668110\pi\)
0.496069 + 0.868283i \(0.334776\pi\)
\(314\) 75.6613i 0.240960i
\(315\) 0 0
\(316\) 246.268 0.779329
\(317\) −154.925 268.338i −0.488723 0.846493i 0.511193 0.859466i \(-0.329204\pi\)
−0.999916 + 0.0129730i \(0.995870\pi\)
\(318\) 5.97767 + 3.45121i 0.0187977 + 0.0108529i
\(319\) −23.5988 + 40.8744i −0.0739776 + 0.128133i
\(320\) 0 0
\(321\) 104.748i 0.326318i
\(322\) −105.788 52.5018i −0.328535 0.163049i
\(323\) −144.397 −0.447050
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) 145.652 252.278i 0.446787 0.773857i
\(327\) −151.217 + 87.3052i −0.462437 + 0.266988i
\(328\) 8.88711i 0.0270948i
\(329\) 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 \(0.616680\pi\)
\(332\) −155.160 89.5815i −0.467349 0.269824i
\(333\) −42.0801 + 72.8849i −0.126367 + 0.218874i
\(334\) −168.948 + 97.5421i −0.505832 + 0.292042i
\(335\) 0 0
\(336\) −48.4014 + 3.04961i −0.144052 + 0.00907622i
\(337\) −155.491 −0.461399 −0.230699 0.973025i \(-0.574101\pi\)
−0.230699 + 0.973025i \(0.574101\pi\)
\(338\) 110.818 + 191.942i 0.327862 + 0.567874i
\(339\) −111.281 64.2483i −0.328264 0.189523i
\(340\) 0 0
\(341\) −36.9925 + 21.3576i −0.108482 + 0.0626323i
\(342\) 75.2622i 0.220065i
\(343\) −64.3643 336.907i −0.187651 0.982236i
\(344\) 122.172 0.355151
\(345\) 0 0
\(346\) 270.138 + 155.964i 0.780744 + 0.450763i
\(347\) −256.253 + 443.844i −0.738482 + 1.27909i 0.214697 + 0.976681i \(0.431124\pi\)
−0.953179 + 0.302408i \(0.902210\pi\)
\(348\) −25.5712 + 14.7636i −0.0734805 + 0.0424240i
\(349\) 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
\(352\) −15.6616 27.1266i −0.0444931 0.0770643i
\(353\) 507.890 + 293.231i 1.43878 + 0.830682i 0.997765 0.0668166i \(-0.0212843\pi\)
0.441018 + 0.897498i \(0.354618\pi\)
\(354\) −36.9976 + 64.0816i −0.104513 + 0.181022i
\(355\) 0 0
\(356\) 236.229i 0.663566i
\(357\) 82.1966 54.6221i 0.230242 0.153003i
\(358\) 103.662 0.289559
\(359\) −44.4221 76.9413i −0.123738 0.214321i 0.797501 0.603318i \(-0.206155\pi\)
−0.921239 + 0.388997i \(0.872822\pi\)
\(360\) 0 0
\(361\) −23.1554 + 40.1064i −0.0641424 + 0.111098i
\(362\) −75.2751 + 43.4601i −0.207942 + 0.120056i
\(363\) 156.472i 0.431054i
\(364\) 21.8101 43.9462i 0.0599178 0.120731i
\(365\) 0 0
\(366\) 57.9963 + 100.452i 0.158460 + 0.274460i
\(367\) −611.446 353.019i −1.66607 0.961904i −0.969727 0.244191i \(-0.921478\pi\)
−0.696339 0.717713i \(-0.745189\pi\)
\(368\) 23.8598 41.3264i 0.0648365 0.112300i
\(369\) 8.16333 4.71310i 0.0221228 0.0127726i
\(370\) 0 0
\(371\) −17.6690 8.76894i −0.0476253 0.0236360i
\(372\) −26.7229 −0.0718357
\(373\) −25.6211 44.3770i −0.0686892 0.118973i 0.829635 0.558306i \(-0.188548\pi\)
−0.898325 + 0.439332i \(0.855215\pi\)
\(374\) 55.2018 + 31.8708i 0.147598 + 0.0852160i
\(375\) 0 0
\(376\) −45.8311 + 26.4606i −0.121891 + 0.0703740i
\(377\) 29.8701i 0.0792309i
\(378\) 28.4700 + 42.8423i 0.0753174 + 0.113339i
\(379\) −194.724 −0.513784 −0.256892 0.966440i \(-0.582698\pi\)
−0.256892 + 0.966440i \(0.582698\pi\)
\(380\) 0 0
\(381\) −226.640 130.851i −0.594855 0.343440i
\(382\) −254.461 + 440.740i −0.666129 + 1.15377i
\(383\) −454.732 + 262.540i −1.18729 + 0.685482i −0.957690 0.287803i \(-0.907075\pi\)
−0.229600 + 0.973285i \(0.573742\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 197.629 0.511993
\(387\) −64.7915 112.222i −0.167420 0.289980i
\(388\) −112.924 65.1965i −0.291040 0.168032i
\(389\) 201.765 349.467i 0.518675 0.898372i −0.481089 0.876672i \(-0.659759\pi\)
0.999765 0.0217005i \(-0.00690803\pi\)
\(390\) 0 0
\(391\) 97.1079i 0.248358i
\(392\) 137.497 17.3955i 0.350757 0.0443762i
\(393\) 373.640 0.950738
\(394\) 175.605 + 304.156i 0.445697 + 0.771971i
\(395\) 0 0
\(396\) −16.6116 + 28.7721i −0.0419485 + 0.0726569i
\(397\) 139.596 80.5960i 0.351628 0.203013i −0.313774 0.949498i \(-0.601593\pi\)
0.665402 + 0.746485i \(0.268260\pi\)
\(398\) 173.375i 0.435615i
\(399\) 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 \(0.655548\pi\)
\(402\) 13.9629 + 8.06147i 0.0347335 + 0.0200534i
\(403\) 13.5166 23.4115i 0.0335400 0.0580930i
\(404\) 241.790 139.597i 0.598490 0.345538i
\(405\) 0 0
\(406\) 70.2782 46.7020i 0.173099 0.115030i
\(407\) 155.337 0.381664
\(408\) 19.9385 + 34.5345i 0.0488689 + 0.0846435i
\(409\) 373.605 + 215.701i 0.913460 + 0.527386i 0.881543 0.472104i \(-0.156505\pi\)
0.0319171 + 0.999491i \(0.489839\pi\)
\(410\) 0 0
\(411\) 200.461 115.736i 0.487739 0.281596i
\(412\) 348.969i 0.847011i
\(413\) 94.0046 189.415i 0.227614 0.458631i
\(414\) −50.6143 −0.122257
\(415\) 0 0
\(416\) 17.1677 + 9.91176i 0.0412684 + 0.0238263i
\(417\) −167.803 + 290.643i −0.402405 + 0.696986i
\(418\) −120.303 + 69.4570i −0.287806 + 0.166165i
\(419\) 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 \(0.342312\pi\)
\(422\) 249.488 + 432.126i 0.591203 + 1.02399i
\(423\) 48.6112 + 28.0657i 0.114920 + 0.0663492i
\(424\) 3.98511 6.90241i 0.00939885 0.0162793i
\(425\) 0 0
\(426\) 239.499i 0.562204i
\(427\) −183.461 276.077i −0.429652 0.646550i
\(428\) −120.953 −0.282600
\(429\) −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 \(0.318294\pi\)
\(432\) −18.0000 + 10.3923i −0.0416667 + 0.0240563i
\(433\) 2.39222i 0.00552477i 0.999996 + 0.00276238i \(0.000879295\pi\)
−0.999996 + 0.00276238i \(0.999121\pi\)
\(434\) 76.2158 4.80210i 0.175613 0.0110647i
\(435\) 0 0
\(436\) 100.811 + 174.610i 0.231219 + 0.400482i
\(437\) −183.277 105.815i −0.419399 0.242140i
\(438\) −74.9069 + 129.743i −0.171020 + 0.296216i
\(439\) −350.264 + 202.225i −0.797867 + 0.460649i −0.842725 0.538345i \(-0.819050\pi\)
0.0448578 + 0.998993i \(0.485717\pi\)
\(440\) 0 0
\(441\) −88.8975 117.074i −0.201582 0.265473i
\(442\) −40.3402 −0.0912674
\(443\) 146.005 + 252.889i 0.329583 + 0.570855i 0.982429 0.186636i \(-0.0597584\pi\)
−0.652846 + 0.757491i \(0.726425\pi\)
\(444\) 84.1603 + 48.5899i 0.189550 + 0.109437i
\(445\) 0 0
\(446\) 75.6182 43.6582i 0.169547 0.0978883i
\(447\) 114.326i 0.255764i
\(448\) 3.52139 + 55.8892i 0.00786024 + 0.124753i
\(449\) 125.680 0.279911 0.139956 0.990158i \(-0.455304\pi\)
0.139956 + 0.990158i \(0.455304\pi\)
\(450\) 0 0
\(451\) −15.0673 8.69913i −0.0334087 0.0192885i
\(452\) −74.1876 + 128.497i −0.164132 + 0.284285i
\(453\) 52.3229 30.2087i 0.115503 0.0666858i
\(454\) 296.310i 0.652666i
\(455\) 0 0
\(456\) −86.9054 −0.190582
\(457\) 43.0015 + 74.4808i 0.0940952 + 0.162978i 0.909231 0.416293i \(-0.136671\pi\)
−0.815135 + 0.579270i \(0.803338\pi\)
\(458\) −132.026 76.2255i −0.288267 0.166431i
\(459\) 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 \(-0.0455362\pi\)
\(462\) 42.2073 85.0456i 0.0913578 0.184081i
\(463\) −73.9873 −0.159800 −0.0798999 0.996803i \(-0.525460\pi\)
−0.0798999 + 0.996803i \(0.525460\pi\)
\(464\) 17.0475 + 29.5271i 0.0367403 + 0.0636360i
\(465\) 0 0
\(466\) −231.115 + 400.303i −0.495956 + 0.859020i
\(467\) 387.032 223.453i 0.828762 0.478486i −0.0246667 0.999696i \(-0.507852\pi\)
0.853429 + 0.521210i \(0.174519\pi\)
\(468\) 21.0260i 0.0449274i
\(469\) −41.2719 20.4829i −0.0879999 0.0436735i
\(470\) 0 0
\(471\) 46.3329 + 80.2509i 0.0983713 + 0.170384i
\(472\) 73.9951 + 42.7211i 0.156769 + 0.0905108i
\(473\) −119.588 + 207.132i −0.252828 + 0.437912i
\(474\) −261.207 + 150.808i −0.551069 + 0.318160i
\(475\) 0 0
\(476\) −63.0722 94.9124i −0.132505 0.199396i
\(477\) −8.45370 −0.0177226
\(478\) −6.50621 11.2691i −0.0136113 0.0235755i
\(479\) 513.818 + 296.653i 1.07269 + 0.619318i 0.928915 0.370293i \(-0.120743\pi\)
0.143775 + 0.989610i \(0.454076\pi\)
\(480\) 0 0
\(481\) −85.1377 + 49.1543i −0.177002 + 0.102192i
\(482\) 454.226i 0.942378i
\(483\) 144.356 9.09539i 0.298874 0.0188310i
\(484\) −180.679 −0.373303
\(485\) 0 0
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) −409.771 + 709.744i −0.841418 + 1.45738i 0.0472773 + 0.998882i \(0.484946\pi\)
−0.888696 + 0.458498i \(0.848388\pi\)
\(488\) 115.993 66.9683i 0.237690 0.137230i
\(489\) 356.774i 0.729600i
\(490\) 0 0
\(491\) 554.724 1.12978 0.564892 0.825165i \(-0.308918\pi\)
0.564892 + 0.825165i \(0.308918\pi\)
\(492\) −5.44222 9.42620i −0.0110614 0.0191589i
\(493\) −60.0867 34.6911i −0.121880 0.0703673i
\(494\) 43.9574 76.1364i 0.0889825 0.154122i
\(495\) 0 0
\(496\) 30.8569i 0.0622115i
\(497\) −43.0380 683.071i −0.0865955 1.37439i
\(498\) 219.429 0.440620
\(499\) −317.394 549.742i −0.636060 1.10169i −0.986290 0.165024i \(-0.947230\pi\)
0.350230 0.936664i \(-0.386103\pi\)
\(500\) 0 0
\(501\) 119.464 206.918i 0.238451 0.413010i
\(502\) 23.5634 13.6043i 0.0469390 0.0271003i
\(503\) 120.116i 0.238800i −0.992846 0.119400i \(-0.961903\pi\)
0.992846 0.119400i \(-0.0380970\pi\)
\(504\) 49.4700 32.8743i 0.0981547 0.0652268i
\(505\) 0 0
\(506\) 46.7103 + 80.9046i 0.0923128 + 0.159890i
\(507\) −235.079 135.723i −0.463668 0.267699i
\(508\) −151.093 + 261.701i −0.297428 + 0.515160i
\(509\) 51.1082 29.5073i 0.100409 0.0579712i −0.448955 0.893555i \(-0.648204\pi\)
0.549364 + 0.835583i \(0.314870\pi\)
\(510\) 0 0
\(511\) 190.326 383.497i 0.372458 0.750484i
\(512\) −22.6274 −0.0441942
\(513\) 46.0885 + 79.8277i 0.0898412 + 0.155609i
\(514\) 158.509 + 91.5150i 0.308383 + 0.178045i
\(515\) 0 0
\(516\) −129.583 + 74.8148i −0.251130 + 0.144990i
\(517\) 103.604i 0.200394i
\(518\) −248.764 123.459i −0.480239 0.238338i
\(519\) −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 \(-0.715471\pi\)
\(522\) 18.0816 31.3182i 0.0346391 0.0599966i
\(523\) −598.739 + 345.682i −1.14482 + 0.660960i −0.947619 0.319404i \(-0.896517\pi\)
−0.197197 + 0.980364i \(0.563184\pi\)
\(524\) 431.442i 0.823363i
\(525\) 0 0
\(526\) −236.068 −0.448798
\(527\) −31.3964 54.3802i −0.0595757 0.103188i
\(528\) 33.2232 + 19.1814i 0.0629227 + 0.0363285i
\(529\) 193.339 334.872i 0.365479 0.633029i
\(530\) 0 0
\(531\) 90.6251i 0.170669i
\(532\) 247.861 15.6169i 0.465905 0.0293551i
\(533\) 11.0109 0.0206583
\(534\) 144.660 + 250.559i 0.270900 + 0.469212i
\(535\) 0 0
\(536\) 9.30859 16.1229i 0.0173668 0.0300801i
\(537\) −109.950 + 63.4798i −0.204749 + 0.118212i
\(538\) 295.703i 0.549635i
\(539\) −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 \(-0.333597\pi\)
\(542\) 173.989 + 100.453i 0.321013 + 0.185337i
\(543\) 53.2275 92.1928i 0.0980249 0.169784i
\(544\) 39.8771 23.0230i 0.0733034 0.0423217i
\(545\) 0 0
\(546\) 3.77837 + 59.9679i 0.00692010 + 0.109831i
\(547\) 318.491 0.582251 0.291126 0.956685i \(-0.405970\pi\)
0.291126 + 0.956685i \(0.405970\pi\)
\(548\) −133.641 231.472i −0.243870 0.422395i
\(549\) −123.029 71.0306i −0.224096 0.129382i
\(550\) 0 0
\(551\) 130.949 75.6034i 0.237657 0.137211i
\(552\) 58.4444i 0.105877i
\(553\) 717.883 477.055i 1.29816 0.862667i
\(554\) −630.628 −1.13832
\(555\) 0 0
\(556\) 335.606 + 193.762i 0.603607 + 0.348493i
\(557\) 288.479 499.660i 0.517915 0.897055i −0.481869 0.876244i \(-0.660042\pi\)
0.999783 0.0208114i \(-0.00662495\pi\)
\(558\) 28.3439 16.3643i 0.0507955 0.0293268i
\(559\) 151.367i 0.270783i
\(560\) 0 0
\(561\) −78.0672 −0.139157
\(562\) 340.834 + 590.342i 0.606466 + 1.05043i
\(563\) −308.279 177.985i −0.547565 0.316137i 0.200574 0.979678i \(-0.435719\pi\)
−0.748139 + 0.663542i \(0.769053\pi\)
\(564\) 32.4075 56.1314i 0.0574601 0.0995238i
\(565\) 0 0
\(566\) 306.196i 0.540983i
\(567\) −56.4324 28.0068i −0.0995281 0.0493948i
\(568\) 276.550 0.486883
\(569\) 186.085 + 322.308i 0.327038 + 0.566447i 0.981923 0.189282i \(-0.0606161\pi\)
−0.654885 + 0.755729i \(0.727283\pi\)
\(570\) 0 0
\(571\) 82.9355 143.649i 0.145246 0.251574i −0.784219 0.620485i \(-0.786936\pi\)
0.929465 + 0.368911i \(0.120269\pi\)
\(572\) −33.6091 + 19.4042i −0.0587571 + 0.0339234i
\(573\) 623.300i 1.08778i
\(574\) 17.2155 + 25.9063i 0.0299922 + 0.0451330i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −13.9714 8.06639i −0.0242139 0.0139799i 0.487844 0.872931i \(-0.337783\pi\)
−0.512058 + 0.858951i \(0.671117\pi\)
\(578\) 157.503 272.803i 0.272496 0.471977i
\(579\) −209.617 + 121.023i −0.362033 + 0.209020i
\(580\) 0 0
\(581\) −625.830 + 39.4314i −1.07716 + 0.0678681i
\(582\) 159.698 0.274395
\(583\) 7.80164 + 13.5128i 0.0133819 + 0.0231781i
\(584\) 149.814 + 86.4950i 0.256530 + 0.148108i
\(585\) 0 0
\(586\) −469.940 + 271.320i −0.801945 + 0.463003i
\(587\) 204.516i 0.348409i −0.984709 0.174205i \(-0.944265\pi\)
0.984709 0.174205i \(-0.0557354\pi\)
\(588\) −135.185 + 102.650i −0.229906 + 0.174575i
\(589\) 136.846 0.232337
\(590\) 0 0
\(591\) −372.514 215.071i −0.630311 0.363910i
\(592\) 56.1068 97.1799i 0.0947751 0.164155i
\(593\) 597.577 345.011i 1.00772 0.581806i 0.0971952 0.995265i \(-0.469013\pi\)
0.910523 + 0.413459i \(0.135680\pi\)
\(594\) 40.6899i 0.0685016i
\(595\) 0 0
\(596\) 132.013 0.221498
\(597\) 106.170 + 183.892i 0.177839 + 0.308026i
\(598\) −51.2022 29.5616i −0.0856224 0.0494341i
\(599\) 477.775 827.531i 0.797622 1.38152i −0.123539 0.992340i \(-0.539425\pi\)
0.921161 0.389182i \(-0.127242\pi\)
\(600\) 0 0
\(601\) 587.954i 0.978293i 0.872202 + 0.489146i \(0.162692\pi\)
−0.872202 + 0.489146i \(0.837308\pi\)
\(602\) 356.137 236.664i 0.591590 0.393130i
\(603\) −19.7465 −0.0327471
\(604\) −34.8820 60.4173i −0.0577516 0.100029i
\(605\) 0 0
\(606\) −170.971 + 296.131i −0.282131 + 0.488665i
\(607\) 449.438 259.483i 0.740425 0.427485i −0.0817986 0.996649i \(-0.526066\pi\)
0.822224 + 0.569164i \(0.192733\pi\)
\(608\) 100.350i 0.165049i
\(609\) −45.9423 + 92.5714i −0.0754389 + 0.152006i
\(610\) 0 0
\(611\) 32.7839 + 56.7834i 0.0536561 + 0.0929351i
\(612\) −42.2960 24.4196i −0.0691111 0.0399013i
\(613\) −63.7771 + 110.465i −0.104041 + 0.180204i −0.913346 0.407184i \(-0.866511\pi\)
0.809305 + 0.587389i \(0.199844\pi\)
\(614\) −25.8744 + 14.9386i −0.0421407 + 0.0243300i
\(615\) 0 0
\(616\) −98.2022 48.7368i −0.159419 0.0791182i
\(617\) 486.581 0.788624 0.394312 0.918977i \(-0.370983\pi\)
0.394312 + 0.918977i \(0.370983\pi\)
\(618\) 213.699 + 370.137i 0.345791 + 0.598927i
\(619\) 370.662 + 214.002i 0.598808 + 0.345722i 0.768572 0.639763i \(-0.220967\pi\)
−0.169765 + 0.985485i \(0.554301\pi\)
\(620\) 0 0
\(621\) 53.6846 30.9948i 0.0864486 0.0499111i
\(622\) 122.522i 0.196980i
\(623\) −457.609 688.620i −0.734524 1.10533i
\(624\) −24.2787 −0.0389082
\(625\) 0 0
\(626\) −3.47589 2.00680i −0.00555254 0.00320576i
\(627\) 85.0671 147.341i 0.135673 0.234993i
\(628\) 92.6658 53.5006i 0.147557 0.0851921i
\(629\) 228.351i 0.363038i
\(630\) 0 0
\(631\) −64.4987 −0.102217 −0.0511083 0.998693i \(-0.516275\pi\)
−0.0511083 + 0.998693i \(0.516275\pi\)
\(632\) 174.138 + 301.616i 0.275535 + 0.477240i
\(633\) −529.244 305.559i −0.836088 0.482716i
\(634\) 219.097 379.488i 0.345579 0.598561i
\(635\) 0 0
\(636\) 9.76149i 0.0153483i
\(637\) −21.5525 170.354i −0.0338343 0.267432i
\(638\) −66.7476 −0.104620
\(639\) −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 \(0.981228\pi\)
\(642\) 128.290 74.0681i 0.199828 0.115371i
\(643\) 1092.83i 1.69958i −0.527124 0.849788i \(-0.676730\pi\)
0.527124 0.849788i \(-0.323270\pi\)
\(644\) −10.5025 166.688i −0.0163082 0.258833i
\(645\) 0 0
\(646\) −102.104 176.850i −0.158056 0.273761i
\(647\) −446.083 257.546i −0.689463 0.398062i 0.113948 0.993487i \(-0.463650\pi\)
−0.803411 + 0.595425i \(0.796984\pi\)
\(648\) 12.7279 22.0454i 0.0196419 0.0340207i
\(649\) −144.860 + 83.6349i −0.223205 + 0.128867i
\(650\) 0 0
\(651\) −77.8984 + 51.7659i −0.119660 + 0.0795175i
\(652\) 411.967 0.631852
\(653\) 393.317 + 681.245i 0.602323 + 1.04325i 0.992468 + 0.122501i \(0.0390915\pi\)
−0.390145 + 0.920753i \(0.627575\pi\)
\(654\) −213.853 123.468i −0.326993 0.188789i
\(655\) 0 0
\(656\) −10.8844 + 6.28413i −0.0165921 + 0.00957947i
\(657\) 183.484i 0.279275i
\(658\) −82.3420 + 165.915i −0.125140 + 0.252151i
\(659\) −819.425 −1.24344 −0.621719 0.783241i \(-0.713565\pi\)
−0.621719 + 0.783241i \(0.713565\pi\)
\(660\) 0 0
\(661\) −889.453 513.526i −1.34562 0.776892i −0.357991 0.933725i \(-0.616538\pi\)
−0.987625 + 0.156833i \(0.949872\pi\)
\(662\) −294.573 + 510.216i −0.444974 + 0.770718i
\(663\) 42.7873 24.7032i 0.0645358 0.0372598i
\(664\) 253.375i 0.381589i
\(665\) 0 0
\(666\) −119.021 −0.178710
\(667\) −50.8437 88.0639i −0.0762275 0.132030i
\(668\) −238.928 137.945i −0.357677 0.206505i
\(669\) −53.4701 + 92.6130i −0.0799254 + 0.138435i
\(670\) 0 0
\(671\) 262.207i 0.390771i
\(672\) −37.9600 57.1230i −0.0564881 0.0850045i
\(673\) 669.779 0.995213 0.497607 0.867403i \(-0.334212\pi\)
0.497607 + 0.867403i \(0.334212\pi\)
\(674\) −109.949 190.437i −0.163129 0.282548i
\(675\) 0 0
\(676\) −156.720 + 271.446i −0.231834 + 0.401548i
\(677\) 786.522 454.099i 1.16178 0.670751i 0.210047 0.977691i \(-0.432638\pi\)
0.951729 + 0.306940i \(0.0993051\pi\)
\(678\) 181.722i 0.268026i
\(679\) −455.472 + 28.6977i −0.670798 + 0.0422647i
\(680\) 0 0
\(681\) 181.452 + 314.285i 0.266450 + 0.461505i
\(682\) −52.3153 30.2042i −0.0767086 0.0442877i
\(683\) −330.668 + 572.733i −0.484140 + 0.838555i −0.999834 0.0182177i \(-0.994201\pi\)
0.515694 + 0.856773i \(0.327534\pi\)
\(684\) 92.1770 53.2184i 0.134762 0.0778047i
\(685\) 0 0
\(686\) 367.112 317.059i 0.535149 0.462185i
\(687\) 186.714 0.271781
\(688\) 86.3887 + 149.630i 0.125565 + 0.217485i
\(689\) −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 \(0.397493\pi\)
\(692\) 441.133i 0.637475i
\(693\) 7.31198 + 116.051i 0.0105512 + 0.167462i
\(694\) −724.794 −1.04437
\(695\) 0 0
\(696\) −36.1632 20.8788i −0.0519586 0.0299983i
\(697\) 12.7880 22.1495i 0.0183472 0.0317783i
\(698\) 329.683 190.343i 0.472326 0.272697i
\(699\) 566.115i 0.809892i
\(700\) 0 0
\(701\) −415.967 −0.593391 −0.296696 0.954972i \(-0.595885\pi\)
−0.296696 + 0.954972i \(0.595885\pi\)
\(702\) 12.8758 + 22.3015i 0.0183415 + 0.0317685i
\(703\) −430.980 248.827i −0.613059 0.353950i
\(704\) 22.1488 38.3629i 0.0314614 0.0544927i
\(705\) 0 0
\(706\) 829.382i 1.17476i
\(707\) 434.409 875.313i 0.614440 1.23807i
\(708\) −104.645 −0.147804
\(709\) −136.620 236.632i −0.192693 0.333755i 0.753449 0.657507i \(-0.228389\pi\)
−0.946142 + 0.323752i \(0.895056\pi\)
\(710\) 0 0
\(711\) 184.701 319.912i 0.259776 0.449946i
\(712\) 289.321 167.039i 0.406349 0.234606i
\(713\) 92.0300i 0.129074i
\(714\) 125.020 + 62.0462i 0.175098 + 0.0868994i
\(715\) 0 0
\(716\) 73.3002 + 126.960i 0.102375 + 0.177318i
\(717\) 13.8018 + 7.96845i 0.0192493 + 0.0111136i
\(718\) 62.8223 108.811i 0.0874962 0.151548i
\(719\) 361.463 208.691i 0.502731 0.290252i −0.227110 0.973869i \(-0.572928\pi\)
0.729840 + 0.683617i \(0.239594\pi\)
\(720\) 0 0
\(721\) −676.000 1017.26i −0.937587 1.41090i
\(722\) −65.4934 −0.0907111
\(723\) −278.156 481.779i −0.384724 0.666362i
\(724\) −106.455 61.4619i −0.147037 0.0848921i
\(725\) 0 0
\(726\) 191.639 110.643i 0.263965 0.152400i
\(727\) 357.267i 0.491426i 0.969343 + 0.245713i \(0.0790221\pi\)
−0.969343 + 0.245713i \(0.920978\pi\)
\(728\) 69.2450 4.36289i 0.0951167 0.00599298i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −304.491 175.798i −0.416541 0.240490i
\(732\) −82.0191 + 142.061i −0.112048 + 0.194073i
\(733\) −373.293 + 215.521i −0.509267 + 0.294026i −0.732532 0.680732i \(-0.761662\pi\)
0.223265 + 0.974758i \(0.428328\pi\)
\(734\) 998.488i 1.36034i
\(735\) 0 0
\(736\) 67.4858 0.0916926
\(737\) 18.2234 + 31.5638i 0.0247264 + 0.0428274i
\(738\) 11.5447 + 6.66533i 0.0156432 + 0.00903161i
\(739\) −159.512 + 276.282i −0.215848 + 0.373860i −0.953535 0.301284i \(-0.902585\pi\)
0.737687 + 0.675143i \(0.235918\pi\)
\(740\) 0 0
\(741\) 107.673i 0.145308i
\(742\) −1.75414 27.8406i −0.00236407 0.0375210i
\(743\) −1303.33 −1.75414 −0.877072 0.480360i \(-0.840506\pi\)
−0.877072 + 0.480360i \(0.840506\pi\)
\(744\) −18.8959 32.7287i −0.0253977 0.0439902i
\(745\) 0 0
\(746\) 36.2337 62.7585i 0.0485706 0.0841267i
\(747\) −232.740 + 134.372i −0.311566 + 0.179883i
\(748\) 90.1442i 0.120514i
\(749\) −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 \(-0.471698\pi\)
\(752\) −64.8150 37.4210i −0.0861901 0.0497619i
\(753\) −16.6618 + 28.8591i −0.0221273 + 0.0383255i
\(754\) 36.5832 21.1213i 0.0485188 0.0280124i
\(755\) 0 0
\(756\) −32.3395 + 65.1625i −0.0427771 + 0.0861938i
\(757\) 1206.22 1.59342 0.796712 0.604359i \(-0.206571\pi\)
0.796712 + 0.604359i \(0.206571\pi\)
\(758\) −137.691 238.487i −0.181650 0.314627i
\(759\) −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 \(0.382908\pi\)
\(762\) 370.101i 0.485697i
\(763\) 632.114 + 313.712i 0.828459 + 0.411156i
\(764\) −719.725 −0.942048
\(765\) 0 0
\(766\) −643.088 371.287i −0.839540 0.484709i
\(767\) 52.9301 91.6777i 0.0690093 0.119528i
\(768\) 24.0000 13.8564i 0.0312500 0.0180422i
\(769\) 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
\(772\) 139.745 + 242.045i 0.181017 + 0.313530i
\(773\) −155.933 90.0279i −0.201724 0.116466i 0.395735 0.918365i \(-0.370490\pi\)
−0.597460 + 0.801899i \(0.703823\pi\)
\(774\) 91.6290 158.706i 0.118384 0.205047i
\(775\) 0 0
\(776\) 184.403i 0.237633i
\(777\) 339.456 21.3880i 0.436881 0.0275264i
\(778\) 570.677 0.733518
\(779\) 27.8693 + 48.2711i 0.0357758 + 0.0619654i