Properties

Label 1110.2.x.d.841.4
Level $1110$
Weight $2$
Character 1110.841
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 841.4
Root \(-1.68974i\) of defining polynomial
Character \(\chi\) \(=\) 1110.841
Dual form 1110.2.x.d.751.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.844871 + 1.46336i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.844871 + 1.46336i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -3.20374 q^{11} +(0.500000 - 0.866025i) q^{12} +(3.91698 - 2.26147i) q^{13} -1.68974i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.32938 - 1.34487i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.29583 + 1.32550i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.844871 - 1.46336i) q^{21} +(2.77452 + 1.60187i) q^{22} +6.25499i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -4.52294 q^{26} +1.00000 q^{27} +(-0.844871 + 1.46336i) q^{28} -6.29373i q^{29} +(-0.500000 - 0.866025i) q^{30} -2.13231i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.60187 + 2.77452i) q^{33} +(1.34487 + 2.32938i) q^{34} +(-1.46336 - 0.844871i) q^{35} -1.00000 q^{36} +(-6.07812 - 0.237625i) q^{37} +2.65100 q^{38} +(-3.91698 - 2.26147i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.65066 - 9.78723i) q^{41} +(-1.46336 + 0.844871i) q^{42} -4.12268i q^{43} +(-1.60187 - 2.77452i) q^{44} -1.00000i q^{45} +(3.12749 - 5.41698i) q^{46} -8.83821 q^{47} +1.00000 q^{48} +(2.07239 - 3.58948i) q^{49} +(-0.866025 + 0.500000i) q^{50} +2.68974i q^{51} +(3.91698 + 2.26147i) q^{52} +(-6.84663 + 11.8587i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(2.77452 - 1.60187i) q^{55} +(1.46336 - 0.844871i) q^{56} +(2.29583 + 1.32550i) q^{57} +(-3.14687 + 5.45053i) q^{58} +(0.611376 + 0.352978i) q^{59} +1.00000i q^{60} +(-8.81565 + 5.08972i) q^{61} +(-1.06615 + 1.84663i) q^{62} -1.68974 q^{63} -1.00000 q^{64} +(-2.26147 + 3.91698i) q^{65} -3.20374i q^{66} +(-0.212277 - 0.367674i) q^{67} -2.68974i q^{68} +(5.41698 - 3.12749i) q^{69} +(0.844871 + 1.46336i) q^{70} +(3.72548 + 6.45271i) q^{71} +(0.866025 + 0.500000i) q^{72} -11.3277 q^{73} +(5.14499 + 3.24485i) q^{74} -1.00000 q^{75} +(-2.29583 - 1.32550i) q^{76} +(-2.70674 - 4.68822i) q^{77} +(2.26147 + 3.91698i) q^{78} +(3.03296 - 1.75108i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +11.3013i q^{82} +(3.09959 - 5.36864i) q^{83} +1.68974 q^{84} +2.68974 q^{85} +(-2.06134 + 3.57035i) q^{86} +(-5.45053 + 3.14687i) q^{87} +3.20374i q^{88} +(1.23065 + 0.710515i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(6.61868 + 3.82130i) q^{91} +(-5.41698 + 3.12749i) q^{92} +(-1.84663 + 1.06615i) q^{93} +(7.65411 + 4.41910i) q^{94} +(1.32550 - 2.29583i) q^{95} +(-0.866025 - 0.500000i) q^{96} +12.9663i q^{97} +(-3.58948 + 2.07239i) q^{98} +(1.60187 - 2.77452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.866025 + 0.500000i −0.387298 + 0.223607i
\(6\) 1.00000i 0.408248i
\(7\) 0.844871 + 1.46336i 0.319331 + 0.553098i 0.980349 0.197273i \(-0.0632085\pi\)
−0.661018 + 0.750370i \(0.729875\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.00000 0.316228
\(11\) −3.20374 −0.965963 −0.482981 0.875631i \(-0.660446\pi\)
−0.482981 + 0.875631i \(0.660446\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 3.91698 2.26147i 1.08637 0.627219i 0.153766 0.988107i \(-0.450860\pi\)
0.932609 + 0.360889i \(0.117527\pi\)
\(14\) 1.68974i 0.451602i
\(15\) 0.866025 + 0.500000i 0.223607 + 0.129099i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.32938 1.34487i −0.564959 0.326179i 0.190175 0.981750i \(-0.439095\pi\)
−0.755133 + 0.655571i \(0.772428\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −2.29583 + 1.32550i −0.526700 + 0.304090i −0.739671 0.672968i \(-0.765019\pi\)
0.212972 + 0.977058i \(0.431686\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 0.844871 1.46336i 0.184366 0.319331i
\(22\) 2.77452 + 1.60187i 0.591529 + 0.341519i
\(23\) 6.25499i 1.30426i 0.758109 + 0.652128i \(0.226123\pi\)
−0.758109 + 0.652128i \(0.773877\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −4.52294 −0.887021
\(27\) 1.00000 0.192450
\(28\) −0.844871 + 1.46336i −0.159666 + 0.276549i
\(29\) 6.29373i 1.16872i −0.811496 0.584359i \(-0.801346\pi\)
0.811496 0.584359i \(-0.198654\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 2.13231i 0.382974i −0.981495 0.191487i \(-0.938669\pi\)
0.981495 0.191487i \(-0.0613309\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 1.60187 + 2.77452i 0.278849 + 0.482981i
\(34\) 1.34487 + 2.32938i 0.230643 + 0.399486i
\(35\) −1.46336 0.844871i −0.247353 0.142809i
\(36\) −1.00000 −0.166667
\(37\) −6.07812 0.237625i −0.999237 0.0390653i
\(38\) 2.65100 0.430048
\(39\) −3.91698 2.26147i −0.627219 0.362125i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −5.65066 9.78723i −0.882485 1.52851i −0.848569 0.529084i \(-0.822536\pi\)
−0.0339158 0.999425i \(-0.510798\pi\)
\(42\) −1.46336 + 0.844871i −0.225801 + 0.130366i
\(43\) 4.12268i 0.628703i −0.949307 0.314352i \(-0.898213\pi\)
0.949307 0.314352i \(-0.101787\pi\)
\(44\) −1.60187 2.77452i −0.241491 0.418274i
\(45\) 1.00000i 0.149071i
\(46\) 3.12749 5.41698i 0.461124 0.798690i
\(47\) −8.83821 −1.28919 −0.644593 0.764526i \(-0.722973\pi\)
−0.644593 + 0.764526i \(0.722973\pi\)
\(48\) 1.00000 0.144338
\(49\) 2.07239 3.58948i 0.296055 0.512783i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 2.68974i 0.376639i
\(52\) 3.91698 + 2.26147i 0.543187 + 0.313609i
\(53\) −6.84663 + 11.8587i −0.940456 + 1.62892i −0.175854 + 0.984416i \(0.556269\pi\)
−0.764603 + 0.644502i \(0.777065\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 2.77452 1.60187i 0.374116 0.215996i
\(56\) 1.46336 0.844871i 0.195550 0.112901i
\(57\) 2.29583 + 1.32550i 0.304090 + 0.175567i
\(58\) −3.14687 + 5.45053i −0.413204 + 0.715690i
\(59\) 0.611376 + 0.352978i 0.0795943 + 0.0459538i 0.539269 0.842134i \(-0.318701\pi\)
−0.459675 + 0.888087i \(0.652034\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −8.81565 + 5.08972i −1.12873 + 0.651672i −0.943615 0.331045i \(-0.892599\pi\)
−0.185114 + 0.982717i \(0.559265\pi\)
\(62\) −1.06615 + 1.84663i −0.135402 + 0.234523i
\(63\) −1.68974 −0.212887
\(64\) −1.00000 −0.125000
\(65\) −2.26147 + 3.91698i −0.280501 + 0.485842i
\(66\) 3.20374i 0.394353i
\(67\) −0.212277 0.367674i −0.0259337 0.0449185i 0.852767 0.522291i \(-0.174923\pi\)
−0.878701 + 0.477373i \(0.841589\pi\)
\(68\) 2.68974i 0.326179i
\(69\) 5.41698 3.12749i 0.652128 0.376506i
\(70\) 0.844871 + 1.46336i 0.100981 + 0.174905i
\(71\) 3.72548 + 6.45271i 0.442133 + 0.765796i 0.997848 0.0655766i \(-0.0208887\pi\)
−0.555715 + 0.831373i \(0.687555\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) −11.3277 −1.32581 −0.662906 0.748703i \(-0.730677\pi\)
−0.662906 + 0.748703i \(0.730677\pi\)
\(74\) 5.14499 + 3.24485i 0.598093 + 0.377206i
\(75\) −1.00000 −0.115470
\(76\) −2.29583 1.32550i −0.263350 0.152045i
\(77\) −2.70674 4.68822i −0.308462 0.534272i
\(78\) 2.26147 + 3.91698i 0.256061 + 0.443511i
\(79\) 3.03296 1.75108i 0.341235 0.197012i −0.319583 0.947558i \(-0.603543\pi\)
0.660818 + 0.750546i \(0.270209\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 11.3013i 1.24802i
\(83\) 3.09959 5.36864i 0.340224 0.589285i −0.644250 0.764815i \(-0.722830\pi\)
0.984474 + 0.175530i \(0.0561638\pi\)
\(84\) 1.68974 0.184366
\(85\) 2.68974 0.291743
\(86\) −2.06134 + 3.57035i −0.222280 + 0.385000i
\(87\) −5.45053 + 3.14687i −0.584359 + 0.337380i
\(88\) 3.20374i 0.341519i
\(89\) 1.23065 + 0.710515i 0.130448 + 0.0753144i 0.563804 0.825909i \(-0.309337\pi\)
−0.433356 + 0.901223i \(0.642671\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) 6.61868 + 3.82130i 0.693826 + 0.400581i
\(92\) −5.41698 + 3.12749i −0.564759 + 0.326064i
\(93\) −1.84663 + 1.06615i −0.191487 + 0.110555i
\(94\) 7.65411 + 4.41910i 0.789461 + 0.455796i
\(95\) 1.32550 2.29583i 0.135993 0.235547i
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) 12.9663i 1.31652i 0.752789 + 0.658262i \(0.228708\pi\)
−0.752789 + 0.658262i \(0.771292\pi\)
\(98\) −3.58948 + 2.07239i −0.362592 + 0.209343i
\(99\) 1.60187 2.77452i 0.160994 0.278849i
\(100\) 1.00000 0.100000
\(101\) −16.4457 −1.63641 −0.818205 0.574926i \(-0.805031\pi\)
−0.818205 + 0.574926i \(0.805031\pi\)
\(102\) 1.34487 2.32938i 0.133162 0.230643i
\(103\) 17.8336i 1.75720i 0.477557 + 0.878601i \(0.341522\pi\)
−0.477557 + 0.878601i \(0.658478\pi\)
\(104\) −2.26147 3.91698i −0.221755 0.384091i
\(105\) 1.68974i 0.164902i
\(106\) 11.8587 6.84663i 1.15182 0.665003i
\(107\) −1.97061 3.41320i −0.190506 0.329966i 0.754912 0.655826i \(-0.227680\pi\)
−0.945418 + 0.325860i \(0.894346\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −10.1898 5.88311i −0.976010 0.563500i −0.0749471 0.997188i \(-0.523879\pi\)
−0.901063 + 0.433688i \(0.857212\pi\)
\(110\) −3.20374 −0.305464
\(111\) 2.83327 + 5.38262i 0.268922 + 0.510896i
\(112\) −1.68974 −0.159666
\(113\) −11.1458 6.43505i −1.04851 0.605358i −0.126279 0.991995i \(-0.540303\pi\)
−0.922232 + 0.386636i \(0.873637\pi\)
\(114\) −1.32550 2.29583i −0.124144 0.215024i
\(115\) −3.12749 5.41698i −0.291640 0.505136i
\(116\) 5.45053 3.14687i 0.506069 0.292179i
\(117\) 4.52294i 0.418146i
\(118\) −0.352978 0.611376i −0.0324942 0.0562817i
\(119\) 4.54497i 0.416636i
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) −0.736075 −0.0669159
\(122\) 10.1794 0.921603
\(123\) −5.65066 + 9.78723i −0.509503 + 0.882485i
\(124\) 1.84663 1.06615i 0.165832 0.0957434i
\(125\) 1.00000i 0.0894427i
\(126\) 1.46336 + 0.844871i 0.130366 + 0.0752671i
\(127\) 1.49587 2.59092i 0.132737 0.229907i −0.791994 0.610529i \(-0.790957\pi\)
0.924731 + 0.380622i \(0.124290\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −3.57035 + 2.06134i −0.314352 + 0.181491i
\(130\) 3.91698 2.26147i 0.343542 0.198344i
\(131\) −11.4234 6.59528i −0.998063 0.576232i −0.0903884 0.995907i \(-0.528811\pi\)
−0.907675 + 0.419675i \(0.862144\pi\)
\(132\) −1.60187 + 2.77452i −0.139425 + 0.241491i
\(133\) −3.87936 2.23975i −0.336383 0.194211i
\(134\) 0.424553i 0.0366758i
\(135\) −0.866025 + 0.500000i −0.0745356 + 0.0430331i
\(136\) −1.34487 + 2.32938i −0.115322 + 0.199743i
\(137\) 21.7604 1.85912 0.929559 0.368674i \(-0.120188\pi\)
0.929559 + 0.368674i \(0.120188\pi\)
\(138\) −6.25499 −0.532460
\(139\) 8.83491 15.3025i 0.749367 1.29794i −0.198759 0.980048i \(-0.563691\pi\)
0.948126 0.317894i \(-0.102976\pi\)
\(140\) 1.68974i 0.142809i
\(141\) 4.41910 + 7.65411i 0.372156 + 0.644593i
\(142\) 7.45095i 0.625270i
\(143\) −12.5490 + 7.24515i −1.04940 + 0.605870i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 3.14687 + 5.45053i 0.261333 + 0.452642i
\(146\) 9.81011 + 5.66387i 0.811890 + 0.468745i
\(147\) −4.14477 −0.341855
\(148\) −2.83327 5.38262i −0.232893 0.442448i
\(149\) 2.80828 0.230064 0.115032 0.993362i \(-0.463303\pi\)
0.115032 + 0.993362i \(0.463303\pi\)
\(150\) 0.866025 + 0.500000i 0.0707107 + 0.0408248i
\(151\) 6.91805 + 11.9824i 0.562983 + 0.975114i 0.997234 + 0.0743228i \(0.0236795\pi\)
−0.434252 + 0.900792i \(0.642987\pi\)
\(152\) 1.32550 + 2.29583i 0.107512 + 0.186216i
\(153\) 2.32938 1.34487i 0.188320 0.108726i
\(154\) 5.41349i 0.436231i
\(155\) 1.06615 + 1.84663i 0.0856355 + 0.148325i
\(156\) 4.52294i 0.362125i
\(157\) −4.72532 + 8.18450i −0.377122 + 0.653194i −0.990642 0.136485i \(-0.956419\pi\)
0.613520 + 0.789679i \(0.289753\pi\)
\(158\) −3.50216 −0.278617
\(159\) 13.6933 1.08595
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) −9.15329 + 5.28466i −0.721381 + 0.416489i
\(162\) 1.00000i 0.0785674i
\(163\) 13.7430 + 7.93450i 1.07643 + 0.621478i 0.929932 0.367733i \(-0.119866\pi\)
0.146500 + 0.989211i \(0.453199\pi\)
\(164\) 5.65066 9.78723i 0.441243 0.764254i
\(165\) −2.77452 1.60187i −0.215996 0.124705i
\(166\) −5.36864 + 3.09959i −0.416688 + 0.240575i
\(167\) −20.2100 + 11.6682i −1.56390 + 0.902915i −0.567039 + 0.823691i \(0.691911\pi\)
−0.996857 + 0.0792243i \(0.974756\pi\)
\(168\) −1.46336 0.844871i −0.112901 0.0651832i
\(169\) 3.72849 6.45793i 0.286807 0.496764i
\(170\) −2.32938 1.34487i −0.178656 0.103147i
\(171\) 2.65100i 0.202727i
\(172\) 3.57035 2.06134i 0.272236 0.157176i
\(173\) 10.2250 17.7102i 0.777391 1.34648i −0.156049 0.987749i \(-0.549876\pi\)
0.933441 0.358732i \(-0.116791\pi\)
\(174\) 6.29373 0.477127
\(175\) 1.68974 0.127732
\(176\) 1.60187 2.77452i 0.120745 0.209137i
\(177\) 0.705956i 0.0530629i
\(178\) −0.710515 1.23065i −0.0532554 0.0922410i
\(179\) 22.0238i 1.64614i −0.567943 0.823068i \(-0.692261\pi\)
0.567943 0.823068i \(-0.307739\pi\)
\(180\) 0.866025 0.500000i 0.0645497 0.0372678i
\(181\) −7.63876 13.2307i −0.567785 0.983432i −0.996785 0.0801272i \(-0.974467\pi\)
0.429000 0.903304i \(-0.358866\pi\)
\(182\) −3.82130 6.61868i −0.283253 0.490609i
\(183\) 8.81565 + 5.08972i 0.651672 + 0.376243i
\(184\) 6.25499 0.461124
\(185\) 5.38262 2.83327i 0.395738 0.208306i
\(186\) 2.13231 0.156348
\(187\) 7.46273 + 4.30861i 0.545729 + 0.315077i
\(188\) −4.41910 7.65411i −0.322296 0.558234i
\(189\) 0.844871 + 1.46336i 0.0614553 + 0.106444i
\(190\) −2.29583 + 1.32550i −0.166557 + 0.0961618i
\(191\) 3.18103i 0.230171i 0.993356 + 0.115086i \(0.0367142\pi\)
−0.993356 + 0.115086i \(0.963286\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 7.53505i 0.542385i −0.962525 0.271192i \(-0.912582\pi\)
0.962525 0.271192i \(-0.0874180\pi\)
\(194\) 6.48313 11.2291i 0.465462 0.806204i
\(195\) 4.52294 0.323894
\(196\) 4.14477 0.296055
\(197\) −2.33537 + 4.04497i −0.166388 + 0.288192i −0.937147 0.348934i \(-0.886544\pi\)
0.770759 + 0.637126i \(0.219877\pi\)
\(198\) −2.77452 + 1.60187i −0.197176 + 0.113840i
\(199\) 10.3566i 0.734159i −0.930190 0.367079i \(-0.880358\pi\)
0.930190 0.367079i \(-0.119642\pi\)
\(200\) −0.866025 0.500000i −0.0612372 0.0353553i
\(201\) −0.212277 + 0.367674i −0.0149728 + 0.0259337i
\(202\) 14.2424 + 8.22286i 1.00209 + 0.578559i
\(203\) 9.20999 5.31739i 0.646415 0.373208i
\(204\) −2.32938 + 1.34487i −0.163090 + 0.0941598i
\(205\) 9.78723 + 5.65066i 0.683570 + 0.394659i
\(206\) 8.91682 15.4444i 0.621265 1.07606i
\(207\) −5.41698 3.12749i −0.376506 0.217376i
\(208\) 4.52294i 0.313609i
\(209\) 7.35524 4.24655i 0.508772 0.293740i
\(210\) 0.844871 1.46336i 0.0583016 0.100981i
\(211\) −24.5039 −1.68692 −0.843458 0.537195i \(-0.819484\pi\)
−0.843458 + 0.537195i \(0.819484\pi\)
\(212\) −13.6933 −0.940456
\(213\) 3.72548 6.45271i 0.255265 0.442133i
\(214\) 3.94122i 0.269416i
\(215\) 2.06134 + 3.57035i 0.140582 + 0.243496i
\(216\) 1.00000i 0.0680414i
\(217\) 3.12033 1.80152i 0.211822 0.122295i
\(218\) 5.88311 + 10.1898i 0.398455 + 0.690144i
\(219\) 5.66387 + 9.81011i 0.382729 + 0.662906i
\(220\) 2.77452 + 1.60187i 0.187058 + 0.107998i
\(221\) −12.1655 −0.818342
\(222\) 0.237625 6.07812i 0.0159483 0.407937i
\(223\) 11.9045 0.797182 0.398591 0.917129i \(-0.369499\pi\)
0.398591 + 0.917129i \(0.369499\pi\)
\(224\) 1.46336 + 0.844871i 0.0977748 + 0.0564503i
\(225\) 0.500000 + 0.866025i 0.0333333 + 0.0577350i
\(226\) 6.43505 + 11.1458i 0.428053 + 0.741409i
\(227\) 4.70710 2.71765i 0.312421 0.180377i −0.335588 0.942009i \(-0.608935\pi\)
0.648010 + 0.761632i \(0.275602\pi\)
\(228\) 2.65100i 0.175567i
\(229\) −8.22859 14.2523i −0.543761 0.941821i −0.998684 0.0512904i \(-0.983667\pi\)
0.454923 0.890531i \(-0.349667\pi\)
\(230\) 6.25499i 0.412442i
\(231\) −2.70674 + 4.68822i −0.178091 + 0.308462i
\(232\) −6.29373 −0.413204
\(233\) 1.39922 0.0916660 0.0458330 0.998949i \(-0.485406\pi\)
0.0458330 + 0.998949i \(0.485406\pi\)
\(234\) 2.26147 3.91698i 0.147837 0.256061i
\(235\) 7.65411 4.41910i 0.499299 0.288271i
\(236\) 0.705956i 0.0459538i
\(237\) −3.03296 1.75108i −0.197012 0.113745i
\(238\) −2.27248 + 3.93606i −0.147303 + 0.255137i
\(239\) 9.20151 + 5.31250i 0.595196 + 0.343637i 0.767150 0.641468i \(-0.221674\pi\)
−0.171953 + 0.985105i \(0.555008\pi\)
\(240\) −0.866025 + 0.500000i −0.0559017 + 0.0322749i
\(241\) −2.56645 + 1.48174i −0.165319 + 0.0954473i −0.580377 0.814348i \(-0.697095\pi\)
0.415058 + 0.909795i \(0.363761\pi\)
\(242\) 0.637460 + 0.368038i 0.0409775 + 0.0236584i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −8.81565 5.08972i −0.564364 0.325836i
\(245\) 4.14477i 0.264800i
\(246\) 9.78723 5.65066i 0.624011 0.360273i
\(247\) −5.99515 + 10.3839i −0.381462 + 0.660712i
\(248\) −2.13231 −0.135402
\(249\) −6.19918 −0.392857
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 5.17276i 0.326502i 0.986585 + 0.163251i \(0.0521980\pi\)
−0.986585 + 0.163251i \(0.947802\pi\)
\(252\) −0.844871 1.46336i −0.0532219 0.0921829i
\(253\) 20.0393i 1.25986i
\(254\) −2.59092 + 1.49587i −0.162569 + 0.0938591i
\(255\) −1.34487 2.32938i −0.0842191 0.145872i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.55097 + 2.62750i 0.283881 + 0.163899i 0.635179 0.772365i \(-0.280926\pi\)
−0.351298 + 0.936264i \(0.614260\pi\)
\(258\) 4.12268 0.256667
\(259\) −4.78749 9.09523i −0.297480 0.565150i
\(260\) −4.52294 −0.280501
\(261\) 5.45053 + 3.14687i 0.337380 + 0.194786i
\(262\) 6.59528 + 11.4234i 0.407458 + 0.705737i
\(263\) −6.35462 11.0065i −0.391843 0.678691i 0.600850 0.799362i \(-0.294829\pi\)
−0.992693 + 0.120670i \(0.961496\pi\)
\(264\) 2.77452 1.60187i 0.170760 0.0985882i
\(265\) 13.6933i 0.841170i
\(266\) 2.23975 + 3.87936i 0.137328 + 0.237859i
\(267\) 1.42103i 0.0869656i
\(268\) 0.212277 0.367674i 0.0129669 0.0224593i
\(269\) 16.9804 1.03531 0.517656 0.855589i \(-0.326805\pi\)
0.517656 + 0.855589i \(0.326805\pi\)
\(270\) 1.00000 0.0608581
\(271\) 2.29413 3.97356i 0.139359 0.241376i −0.787895 0.615809i \(-0.788829\pi\)
0.927254 + 0.374433i \(0.122163\pi\)
\(272\) 2.32938 1.34487i 0.141240 0.0815448i
\(273\) 7.64260i 0.462551i
\(274\) −18.8451 10.8802i −1.13847 0.657297i
\(275\) −1.60187 + 2.77452i −0.0965963 + 0.167310i
\(276\) 5.41698 + 3.12749i 0.326064 + 0.188253i
\(277\) 19.0145 10.9780i 1.14247 0.659604i 0.195428 0.980718i \(-0.437390\pi\)
0.947041 + 0.321114i \(0.104057\pi\)
\(278\) −15.3025 + 8.83491i −0.917784 + 0.529883i
\(279\) 1.84663 + 1.06615i 0.110555 + 0.0638289i
\(280\) −0.844871 + 1.46336i −0.0504907 + 0.0874524i
\(281\) −2.88933 1.66816i −0.172363 0.0995138i 0.411337 0.911484i \(-0.365062\pi\)
−0.583700 + 0.811970i \(0.698395\pi\)
\(282\) 8.83821i 0.526308i
\(283\) 3.97186 2.29315i 0.236102 0.136314i −0.377282 0.926099i \(-0.623141\pi\)
0.613384 + 0.789785i \(0.289808\pi\)
\(284\) −3.72548 + 6.45271i −0.221066 + 0.382898i
\(285\) −2.65100 −0.157031
\(286\) 14.4903 0.856829
\(287\) 9.54816 16.5379i 0.563610 0.976201i
\(288\) 1.00000i 0.0589256i
\(289\) −4.88265 8.45699i −0.287214 0.497470i
\(290\) 6.29373i 0.369581i
\(291\) 11.2291 6.48313i 0.658262 0.380048i
\(292\) −5.66387 9.81011i −0.331453 0.574093i
\(293\) 9.06792 + 15.7061i 0.529754 + 0.917560i 0.999398 + 0.0347042i \(0.0110489\pi\)
−0.469644 + 0.882856i \(0.655618\pi\)
\(294\) 3.58948 + 2.07239i 0.209343 + 0.120864i
\(295\) −0.705956 −0.0411023
\(296\) −0.237625 + 6.07812i −0.0138117 + 0.353284i
\(297\) −3.20374 −0.185900
\(298\) −2.43205 1.40414i −0.140885 0.0813398i
\(299\) 14.1455 + 24.5007i 0.818053 + 1.41691i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) 6.03296 3.48313i 0.347734 0.200764i
\(302\) 13.8361i 0.796178i
\(303\) 8.22286 + 14.2424i 0.472391 + 0.818205i
\(304\) 2.65100i 0.152045i
\(305\) 5.08972 8.81565i 0.291436 0.504783i
\(306\) −2.68974 −0.153762
\(307\) 9.93260 0.566883 0.283442 0.958990i \(-0.408524\pi\)
0.283442 + 0.958990i \(0.408524\pi\)
\(308\) 2.70674 4.68822i 0.154231 0.267136i
\(309\) 15.4444 8.91682i 0.878601 0.507260i
\(310\) 2.13231i 0.121107i
\(311\) 29.2291 + 16.8754i 1.65743 + 0.956918i 0.973895 + 0.227000i \(0.0728918\pi\)
0.683535 + 0.729917i \(0.260442\pi\)
\(312\) −2.26147 + 3.91698i −0.128030 + 0.221755i
\(313\) −4.94889 2.85724i −0.279728 0.161501i 0.353572 0.935407i \(-0.384967\pi\)
−0.633300 + 0.773906i \(0.718300\pi\)
\(314\) 8.18450 4.72532i 0.461878 0.266665i
\(315\) 1.46336 0.844871i 0.0824509 0.0476031i
\(316\) 3.03296 + 1.75108i 0.170618 + 0.0985061i
\(317\) 8.93237 15.4713i 0.501692 0.868956i −0.498306 0.867001i \(-0.666044\pi\)
0.999998 0.00195502i \(-0.000622302\pi\)
\(318\) −11.8587 6.84663i −0.665003 0.383940i
\(319\) 20.1635i 1.12894i
\(320\) 0.866025 0.500000i 0.0484123 0.0279508i
\(321\) −1.97061 + 3.41320i −0.109989 + 0.190506i
\(322\) 10.5693 0.589005
\(323\) 7.13050 0.396751
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 4.52294i 0.250887i
\(326\) −7.93450 13.7430i −0.439451 0.761152i
\(327\) 11.7662i 0.650674i
\(328\) −9.78723 + 5.65066i −0.540410 + 0.312006i
\(329\) −7.46714 12.9335i −0.411677 0.713045i
\(330\) 1.60187 + 2.77452i 0.0881799 + 0.152732i
\(331\) 19.5912 + 11.3110i 1.07683 + 0.621709i 0.930040 0.367459i \(-0.119772\pi\)
0.146791 + 0.989168i \(0.453105\pi\)
\(332\) 6.19918 0.340224
\(333\) 3.24485 5.14499i 0.177817 0.281944i
\(334\) 23.3365 1.27692
\(335\) 0.367674 + 0.212277i 0.0200882 + 0.0115979i
\(336\) 0.844871 + 1.46336i 0.0460915 + 0.0798328i
\(337\) 1.22150 + 2.11570i 0.0665395 + 0.115250i 0.897376 0.441267i \(-0.145471\pi\)
−0.830836 + 0.556517i \(0.812138\pi\)
\(338\) −6.45793 + 3.72849i −0.351265 + 0.202803i
\(339\) 12.8701i 0.699008i
\(340\) 1.34487 + 2.32938i 0.0729359 + 0.126329i
\(341\) 6.83135i 0.369938i
\(342\) −1.32550 + 2.29583i −0.0716747 + 0.124144i
\(343\) 18.8318 1.01682
\(344\) −4.12268 −0.222280
\(345\) −3.12749 + 5.41698i −0.168379 + 0.291640i
\(346\) −17.7102 + 10.2250i −0.952106 + 0.549699i
\(347\) 9.90993i 0.531993i 0.963974 + 0.265997i \(0.0857010\pi\)
−0.963974 + 0.265997i \(0.914299\pi\)
\(348\) −5.45053 3.14687i −0.292179 0.168690i
\(349\) 0.418227 0.724391i 0.0223872 0.0387758i −0.854615 0.519263i \(-0.826207\pi\)
0.877002 + 0.480487i \(0.159540\pi\)
\(350\) −1.46336 0.844871i −0.0782198 0.0451602i
\(351\) 3.91698 2.26147i 0.209073 0.120708i
\(352\) −2.77452 + 1.60187i −0.147882 + 0.0853799i
\(353\) −5.21645 3.01172i −0.277643 0.160298i 0.354713 0.934975i \(-0.384579\pi\)
−0.632356 + 0.774678i \(0.717912\pi\)
\(354\) −0.352978 + 0.611376i −0.0187606 + 0.0324942i
\(355\) −6.45271 3.72548i −0.342475 0.197728i
\(356\) 1.42103i 0.0753144i
\(357\) −3.93606 + 2.27248i −0.208318 + 0.120273i
\(358\) −11.0119 + 19.0732i −0.581997 + 1.00805i
\(359\) 9.58722 0.505994 0.252997 0.967467i \(-0.418584\pi\)
0.252997 + 0.967467i \(0.418584\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −5.98611 + 10.3682i −0.315058 + 0.545697i
\(362\) 15.2775i 0.802969i
\(363\) 0.368038 + 0.637460i 0.0193170 + 0.0334580i
\(364\) 7.64260i 0.400581i
\(365\) 9.81011 5.66387i 0.513484 0.296460i
\(366\) −5.08972 8.81565i −0.266044 0.460802i
\(367\) −14.0314 24.3030i −0.732431 1.26861i −0.955841 0.293883i \(-0.905052\pi\)
0.223410 0.974724i \(-0.428281\pi\)
\(368\) −5.41698 3.12749i −0.282380 0.163032i
\(369\) 11.3013 0.588323
\(370\) −6.07812 0.237625i −0.315986 0.0123535i
\(371\) −23.1381 −1.20127
\(372\) −1.84663 1.06615i −0.0957434 0.0552775i
\(373\) 2.84842 + 4.93361i 0.147486 + 0.255452i 0.930297 0.366806i \(-0.119549\pi\)
−0.782812 + 0.622258i \(0.786215\pi\)
\(374\) −4.30861 7.46273i −0.222793 0.385889i
\(375\) 0.866025 0.500000i 0.0447214 0.0258199i
\(376\) 8.83821i 0.455796i
\(377\) −14.2331 24.6524i −0.733041 1.26966i
\(378\) 1.68974i 0.0869109i
\(379\) −7.05060 + 12.2120i −0.362165 + 0.627288i −0.988317 0.152413i \(-0.951296\pi\)
0.626152 + 0.779701i \(0.284629\pi\)
\(380\) 2.65100 0.135993
\(381\) −2.99173 −0.153271
\(382\) 1.59051 2.75485i 0.0813778 0.140950i
\(383\) −23.7339 + 13.7028i −1.21275 + 0.700180i −0.963357 0.268223i \(-0.913564\pi\)
−0.249391 + 0.968403i \(0.580230\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 4.68822 + 2.70674i 0.238934 + 0.137948i
\(386\) −3.76753 + 6.52555i −0.191762 + 0.332141i
\(387\) 3.57035 + 2.06134i 0.181491 + 0.104784i
\(388\) −11.2291 + 6.48313i −0.570072 + 0.329131i
\(389\) 27.5718 15.9186i 1.39794 0.807103i 0.403767 0.914862i \(-0.367701\pi\)
0.994177 + 0.107759i \(0.0343674\pi\)
\(390\) −3.91698 2.26147i −0.198344 0.114514i
\(391\) 8.41215 14.5703i 0.425421 0.736850i
\(392\) −3.58948 2.07239i −0.181296 0.104671i
\(393\) 13.1906i 0.665375i
\(394\) 4.04497 2.33537i 0.203783 0.117654i
\(395\) −1.75108 + 3.03296i −0.0881065 + 0.152605i
\(396\) 3.20374 0.160994
\(397\) 13.9486 0.700058 0.350029 0.936739i \(-0.386172\pi\)
0.350029 + 0.936739i \(0.386172\pi\)
\(398\) −5.17829 + 8.96907i −0.259564 + 0.449579i
\(399\) 4.47950i 0.224255i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 13.2809i 0.663219i 0.943417 + 0.331609i \(0.107592\pi\)
−0.943417 + 0.331609i \(0.892408\pi\)
\(402\) 0.367674 0.212277i 0.0183379 0.0105874i
\(403\) −4.82215 8.35220i −0.240208 0.416053i
\(404\) −8.22286 14.2424i −0.409103 0.708587i
\(405\) 0.866025 + 0.500000i 0.0430331 + 0.0248452i
\(406\) −10.6348 −0.527795
\(407\) 19.4727 + 0.761288i 0.965225 + 0.0377356i
\(408\) 2.68974 0.133162
\(409\) −26.2478 15.1542i −1.29787 0.749325i −0.317833 0.948147i \(-0.602955\pi\)
−0.980036 + 0.198822i \(0.936289\pi\)
\(410\) −5.65066 9.78723i −0.279066 0.483357i
\(411\) −10.8802 18.8451i −0.536681 0.929559i
\(412\) −15.4444 + 8.91682i −0.760891 + 0.439300i
\(413\) 1.19288i 0.0586979i
\(414\) 3.12749 + 5.41698i 0.153708 + 0.266230i
\(415\) 6.19918i 0.304306i
\(416\) 2.26147 3.91698i 0.110878 0.192046i
\(417\) −17.6698 −0.865295
\(418\) −8.49309 −0.415411
\(419\) −5.06884 + 8.77949i −0.247629 + 0.428906i −0.962867 0.269974i \(-0.912985\pi\)
0.715238 + 0.698881i \(0.246318\pi\)
\(420\) −1.46336 + 0.844871i −0.0714046 + 0.0412255i
\(421\) 9.14846i 0.445869i 0.974833 + 0.222934i \(0.0715636\pi\)
−0.974833 + 0.222934i \(0.928436\pi\)
\(422\) 21.2210 + 12.2519i 1.03302 + 0.596415i
\(423\) 4.41910 7.65411i 0.214864 0.372156i
\(424\) 11.8587 + 6.84663i 0.575910 + 0.332502i
\(425\) −2.32938 + 1.34487i −0.112992 + 0.0652358i
\(426\) −6.45271 + 3.72548i −0.312635 + 0.180500i
\(427\) −14.8962 8.60031i −0.720876 0.416198i
\(428\) 1.97061 3.41320i 0.0952530 0.164983i
\(429\) 12.5490 + 7.24515i 0.605870 + 0.349799i
\(430\) 4.12268i 0.198813i
\(431\) −22.1050 + 12.7623i −1.06476 + 0.614739i −0.926745 0.375692i \(-0.877405\pi\)
−0.138014 + 0.990430i \(0.544072\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −28.5890 −1.37390 −0.686949 0.726705i \(-0.741051\pi\)
−0.686949 + 0.726705i \(0.741051\pi\)
\(434\) −3.60305 −0.172952
\(435\) 3.14687 5.45053i 0.150881 0.261333i
\(436\) 11.7662i 0.563500i
\(437\) −8.29098 14.3604i −0.396611 0.686951i
\(438\) 11.3277i 0.541260i
\(439\) −3.72066 + 2.14812i −0.177577 + 0.102524i −0.586154 0.810200i \(-0.699359\pi\)
0.408577 + 0.912724i \(0.366025\pi\)
\(440\) −1.60187 2.77452i −0.0763661 0.132270i
\(441\) 2.07239 + 3.58948i 0.0986851 + 0.170928i
\(442\) 10.5357 + 6.08277i 0.501130 + 0.289328i
\(443\) 34.1211 1.62114 0.810570 0.585642i \(-0.199157\pi\)
0.810570 + 0.585642i \(0.199157\pi\)
\(444\) −3.24485 + 5.14499i −0.153994 + 0.244171i
\(445\) −1.42103 −0.0673633
\(446\) −10.3096 5.95223i −0.488172 0.281846i
\(447\) −1.40414 2.43205i −0.0664137 0.115032i
\(448\) −0.844871 1.46336i −0.0399164 0.0691372i
\(449\) −17.4477 + 10.0734i −0.823406 + 0.475394i −0.851590 0.524209i \(-0.824361\pi\)
0.0281834 + 0.999603i \(0.491028\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 18.1032 + 31.3557i 0.852448 + 1.47648i
\(452\) 12.8701i 0.605358i
\(453\) 6.91805 11.9824i 0.325038 0.562983i
\(454\) −5.43530 −0.255091
\(455\) −7.64260 −0.358290
\(456\) 1.32550 2.29583i 0.0620721 0.107512i
\(457\) −20.6810 + 11.9402i −0.967416 + 0.558538i −0.898447 0.439081i \(-0.855304\pi\)
−0.0689682 + 0.997619i \(0.521971\pi\)
\(458\) 16.4572i 0.768994i
\(459\) −2.32938 1.34487i −0.108726 0.0627732i
\(460\) 3.12749 5.41698i 0.145820 0.252568i
\(461\) −20.1330 11.6238i −0.937688 0.541375i −0.0484534 0.998825i \(-0.515429\pi\)
−0.889235 + 0.457451i \(0.848763\pi\)
\(462\) 4.68822 2.70674i 0.218116 0.125929i
\(463\) −16.5274 + 9.54213i −0.768096 + 0.443460i −0.832195 0.554483i \(-0.812916\pi\)
0.0640992 + 0.997944i \(0.479583\pi\)
\(464\) 5.45053 + 3.14687i 0.253035 + 0.146090i
\(465\) 1.06615 1.84663i 0.0494417 0.0856355i
\(466\) −1.21176 0.699610i −0.0561337 0.0324088i
\(467\) 22.4662i 1.03961i 0.854284 + 0.519806i \(0.173996\pi\)
−0.854284 + 0.519806i \(0.826004\pi\)
\(468\) −3.91698 + 2.26147i −0.181062 + 0.104536i
\(469\) 0.358693 0.621274i 0.0165629 0.0286878i
\(470\) −8.83821 −0.407676
\(471\) 9.45064 0.435463
\(472\) 0.352978 0.611376i 0.0162471 0.0281408i
\(473\) 13.2080i 0.607304i
\(474\) 1.75108 + 3.03296i 0.0804299 + 0.139309i
\(475\) 2.65100i 0.121636i
\(476\) 3.93606 2.27248i 0.180409 0.104159i
\(477\) −6.84663 11.8587i −0.313485 0.542973i
\(478\) −5.31250 9.20151i −0.242988 0.420867i
\(479\) 19.9551 + 11.5211i 0.911772 + 0.526412i 0.881001 0.473115i \(-0.156870\pi\)
0.0307711 + 0.999526i \(0.490204\pi\)
\(480\) 1.00000 0.0456435
\(481\) −24.3453 + 12.8147i −1.11005 + 0.584300i
\(482\) 2.96348 0.134983
\(483\) 9.15329 + 5.28466i 0.416489 + 0.240460i
\(484\) −0.368038 0.637460i −0.0167290 0.0289755i
\(485\) −6.48313 11.2291i −0.294384 0.509888i
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 13.1644i 0.596537i 0.954482 + 0.298268i \(0.0964090\pi\)
−0.954482 + 0.298268i \(0.903591\pi\)
\(488\) 5.08972 + 8.81565i 0.230401 + 0.399066i
\(489\) 15.8690i 0.717621i
\(490\) 2.07239 3.58948i 0.0936209 0.162156i
\(491\) 3.21588 0.145131 0.0725653 0.997364i \(-0.476881\pi\)
0.0725653 + 0.997364i \(0.476881\pi\)
\(492\) −11.3013 −0.509503
\(493\) −8.46426 + 14.6605i −0.381211 + 0.660277i
\(494\) 10.3839 5.99515i 0.467194 0.269734i
\(495\) 3.20374i 0.143997i
\(496\) 1.84663 + 1.06615i 0.0829162 + 0.0478717i
\(497\) −6.29509 + 10.9034i −0.282373 + 0.489085i
\(498\) 5.36864 + 3.09959i 0.240575 + 0.138896i
\(499\) −16.1143 + 9.30362i −0.721377 + 0.416487i −0.815259 0.579096i \(-0.803406\pi\)
0.0938822 + 0.995583i \(0.470072\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) 20.2100 + 11.6682i 0.902915 + 0.521298i
\(502\) 2.58638 4.47974i 0.115436 0.199941i
\(503\) 19.1727 + 11.0694i 0.854869 + 0.493559i 0.862291 0.506414i \(-0.169029\pi\)
−0.00742159 + 0.999972i \(0.502362\pi\)
\(504\) 1.68974i 0.0752671i
\(505\) 14.2424 8.22286i 0.633779 0.365913i
\(506\) −10.0197 + 17.3546i −0.445429 + 0.771505i
\(507\) −7.45697 −0.331176
\(508\) 2.99173 0.132737
\(509\) 17.3019 29.9677i 0.766892 1.32830i −0.172349 0.985036i \(-0.555136\pi\)
0.939241 0.343259i \(-0.111531\pi\)
\(510\) 2.68974i 0.119104i
\(511\) −9.57047 16.5765i −0.423373 0.733303i
\(512\) 1.00000i 0.0441942i
\(513\) −2.29583 + 1.32550i −0.101363 + 0.0585222i
\(514\) −2.62750 4.55097i −0.115894 0.200734i
\(515\) −8.91682 15.4444i −0.392922 0.680561i
\(516\) −3.57035 2.06134i −0.157176 0.0907455i
\(517\) 28.3153 1.24530
\(518\) −0.401525 + 10.2704i −0.0176420 + 0.451258i
\(519\) −20.4500 −0.897654
\(520\) 3.91698 + 2.26147i 0.171771 + 0.0991720i
\(521\) 18.5319 + 32.0981i 0.811896 + 1.40625i 0.911535 + 0.411222i \(0.134898\pi\)
−0.0996392 + 0.995024i \(0.531769\pi\)
\(522\) −3.14687 5.45053i −0.137735 0.238563i
\(523\) −30.5973 + 17.6653i −1.33792 + 0.772451i −0.986499 0.163765i \(-0.947636\pi\)
−0.351425 + 0.936216i \(0.614303\pi\)
\(524\) 13.1906i 0.576232i
\(525\) −0.844871 1.46336i −0.0368732 0.0638662i
\(526\) 12.7092i 0.554149i
\(527\) −2.86768 + 4.96696i −0.124918 + 0.216364i
\(528\) −3.20374 −0.139425
\(529\) −16.1249 −0.701082
\(530\) −6.84663 + 11.8587i −0.297398 + 0.515109i
\(531\) −0.611376 + 0.352978i −0.0265314 + 0.0153179i
\(532\) 4.47950i 0.194211i
\(533\) −44.2671 25.5576i −1.91742 1.10702i
\(534\) −0.710515 + 1.23065i −0.0307470 + 0.0532554i
\(535\) 3.41320 + 1.97061i 0.147565 + 0.0851969i
\(536\) −0.367674 + 0.212277i −0.0158811 + 0.00916895i
\(537\) −19.0732 + 11.0119i −0.823068 + 0.475198i
\(538\) −14.7054 8.49019i −0.633996 0.366038i
\(539\) −6.63938 + 11.4997i −0.285978 + 0.495329i
\(540\) −0.866025 0.500000i −0.0372678 0.0215166i
\(541\) 27.4851i 1.18168i −0.806790 0.590838i \(-0.798797\pi\)
0.806790 0.590838i \(-0.201203\pi\)
\(542\) −3.97356 + 2.29413i −0.170679 + 0.0985415i
\(543\) −7.63876 + 13.2307i −0.327811 + 0.567785i
\(544\) −2.68974 −0.115322
\(545\) 11.7662 0.504010
\(546\) −3.82130 + 6.61868i −0.163536 + 0.283253i
\(547\) 30.7640i 1.31537i −0.753292 0.657686i \(-0.771535\pi\)
0.753292 0.657686i \(-0.228465\pi\)
\(548\) 10.8802 + 18.8451i 0.464779 + 0.805021i
\(549\) 10.1794i 0.434448i
\(550\) 2.77452 1.60187i 0.118306 0.0683039i
\(551\) 8.34233 + 14.4493i 0.355395 + 0.615563i
\(552\) −3.12749 5.41698i −0.133115 0.230562i
\(553\) 5.12492 + 2.95888i 0.217934 + 0.125824i
\(554\) −21.9560 −0.932822
\(555\) −5.14499 3.24485i −0.218393 0.137736i
\(556\) 17.6698 0.749367
\(557\) 14.7174 + 8.49710i 0.623597 + 0.360034i 0.778268 0.627932i \(-0.216099\pi\)
−0.154671 + 0.987966i \(0.549432\pi\)
\(558\) −1.06615 1.84663i −0.0451339 0.0781742i
\(559\) −9.32332 16.1485i −0.394334 0.683007i
\(560\) 1.46336 0.844871i 0.0618382 0.0357023i
\(561\) 8.61722i 0.363819i
\(562\) 1.66816 + 2.88933i 0.0703669 + 0.121879i
\(563\) 3.67732i 0.154980i 0.996993 + 0.0774902i \(0.0246907\pi\)
−0.996993 + 0.0774902i \(0.975309\pi\)
\(564\) −4.41910 + 7.65411i −0.186078 + 0.322296i
\(565\) 12.8701 0.541449
\(566\) −4.58630 −0.192777
\(567\) 0.844871 1.46336i 0.0354812 0.0614553i
\(568\) 6.45271 3.72548i 0.270750 0.156318i
\(569\) 8.07668i 0.338592i 0.985565 + 0.169296i \(0.0541494\pi\)
−0.985565 + 0.169296i \(0.945851\pi\)
\(570\) 2.29583 + 1.32550i 0.0961618 + 0.0555190i
\(571\) −5.54346 + 9.60155i −0.231986 + 0.401812i −0.958393 0.285453i \(-0.907856\pi\)
0.726406 + 0.687266i \(0.241189\pi\)
\(572\) −12.5490 7.24515i −0.524699 0.302935i
\(573\) 2.75485 1.59051i 0.115086 0.0664447i
\(574\) −16.5379 + 9.54816i −0.690278 + 0.398532i
\(575\) 5.41698 + 3.12749i 0.225904 + 0.130426i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 21.0142 + 12.1325i 0.874831 + 0.505084i 0.868951 0.494899i \(-0.164795\pi\)
0.00588031 + 0.999983i \(0.498128\pi\)
\(578\) 9.76529i 0.406183i
\(579\) −6.52555 + 3.76753i −0.271192 + 0.156573i
\(580\) −3.14687 + 5.45053i −0.130667 + 0.226321i
\(581\) 10.4750 0.434576
\(582\) −12.9663 −0.537469
\(583\) 21.9348 37.9922i 0.908446 1.57347i
\(584\) 11.3277i 0.468745i
\(585\) −2.26147 3.91698i −0.0935002 0.161947i
\(586\) 18.1358i 0.749185i
\(587\) −27.2504 + 15.7330i −1.12474 + 0.649370i −0.942607 0.333903i \(-0.891634\pi\)
−0.182135 + 0.983274i \(0.558301\pi\)
\(588\) −2.07239 3.58948i −0.0854638 0.148028i
\(589\) 2.82637 + 4.89542i 0.116459 + 0.201712i
\(590\) 0.611376 + 0.352978i 0.0251699 + 0.0145319i
\(591\) 4.67073 0.192128
\(592\) 3.24485 5.14499i 0.133362 0.211458i
\(593\) 27.4169 1.12588 0.562938 0.826499i \(-0.309671\pi\)
0.562938 + 0.826499i \(0.309671\pi\)
\(594\) 2.77452 + 1.60187i 0.113840 + 0.0657254i
\(595\) 2.27248 + 3.93606i 0.0931627 + 0.161363i
\(596\) 1.40414 + 2.43205i 0.0575159 + 0.0996205i
\(597\) −8.96907 + 5.17829i −0.367079 + 0.211933i
\(598\) 28.2909i 1.15690i
\(599\) 16.5443 + 28.6556i 0.675982 + 1.17084i 0.976181 + 0.216959i \(0.0696138\pi\)
−0.300198 + 0.953877i \(0.597053\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) 16.2965 28.2263i 0.664748 1.15138i −0.314606 0.949222i \(-0.601872\pi\)
0.979354 0.202154i \(-0.0647942\pi\)
\(602\) −6.96627 −0.283924
\(603\) 0.424553 0.0172891
\(604\) −6.91805 + 11.9824i −0.281491 + 0.487557i
\(605\) 0.637460 0.368038i 0.0259164 0.0149629i
\(606\) 16.4457i 0.668062i
\(607\) −14.5982 8.42827i −0.592522 0.342093i 0.173572 0.984821i \(-0.444469\pi\)
−0.766094 + 0.642728i \(0.777802\pi\)
\(608\) −1.32550 + 2.29583i −0.0537561 + 0.0931082i
\(609\) −9.20999 5.31739i −0.373208 0.215472i
\(610\) −8.81565 + 5.08972i −0.356935 + 0.206077i
\(611\) −34.6191 + 19.9873i −1.40054 + 0.808601i
\(612\) 2.32938 + 1.34487i 0.0941598 + 0.0543632i
\(613\) −8.50922 + 14.7384i −0.343684 + 0.595279i −0.985114 0.171903i \(-0.945008\pi\)
0.641430 + 0.767182i \(0.278342\pi\)
\(614\) −8.60188 4.96630i −0.347144 0.200423i
\(615\) 11.3013i 0.455713i
\(616\) −4.68822 + 2.70674i −0.188894 + 0.109058i
\(617\) −9.62460 + 16.6703i −0.387472 + 0.671121i −0.992109 0.125380i \(-0.959985\pi\)
0.604637 + 0.796501i \(0.293318\pi\)
\(618\) −17.8336 −0.717375
\(619\) −2.21721 −0.0891171 −0.0445585 0.999007i \(-0.514188\pi\)
−0.0445585 + 0.999007i \(0.514188\pi\)
\(620\) −1.06615 + 1.84663i −0.0428178 + 0.0741625i
\(621\) 6.25499i 0.251004i
\(622\) −16.8754 29.2291i −0.676643 1.17198i
\(623\) 2.40117i 0.0962010i
\(624\) 3.91698 2.26147i 0.156805 0.0905312i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 2.85724 + 4.94889i 0.114198 + 0.197798i
\(627\) −7.35524 4.24655i −0.293740 0.169591i
\(628\) −9.45064 −0.377122
\(629\) 13.8387 + 8.72780i 0.551785 + 0.348000i
\(630\) −1.68974 −0.0673209
\(631\) −33.8176 19.5246i −1.34626 0.777262i −0.358540 0.933514i \(-0.616725\pi\)
−0.987717 + 0.156252i \(0.950059\pi\)
\(632\) −1.75108 3.03296i −0.0696543 0.120645i
\(633\) 12.2519 + 21.2210i 0.486971 + 0.843458i
\(634\) −15.4713 + 8.93237i −0.614445 + 0.354750i
\(635\) 2.99173i 0.118723i
\(636\) 6.84663 + 11.8587i 0.271486 + 0.470228i
\(637\) 18.7466i 0.742766i
\(638\) 10.0817 17.4621i 0.399140 0.691330i
\(639\) −7.45095 −0.294755
\(640\) −1.00000 −0.0395285
\(641\) 12.0650 20.8972i 0.476539 0.825389i −0.523100 0.852271i \(-0.675225\pi\)
0.999639 + 0.0268821i \(0.00855785\pi\)
\(642\) 3.41320 1.97061i 0.134708 0.0777738i
\(643\) 23.7974i 0.938478i −0.883071 0.469239i \(-0.844528\pi\)
0.883071 0.469239i \(-0.155472\pi\)
\(644\) −9.15329 5.28466i −0.360690 0.208245i
\(645\) 2.06134 3.57035i 0.0811652 0.140582i
\(646\) −6.17519 3.56525i −0.242960 0.140273i
\(647\) 2.35379 1.35896i 0.0925371 0.0534263i −0.453017 0.891502i \(-0.649652\pi\)
0.545554 + 0.838075i \(0.316319\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −1.95869 1.13085i −0.0768851 0.0443897i
\(650\) −2.26147 + 3.91698i −0.0887021 + 0.153637i
\(651\) −3.12033 1.80152i −0.122295 0.0706073i
\(652\) 15.8690i 0.621478i
\(653\) 31.8316 18.3780i 1.24567 0.719186i 0.275424 0.961323i \(-0.411182\pi\)
0.970242 + 0.242137i \(0.0778483\pi\)
\(654\) 5.88311 10.1898i 0.230048 0.398455i
\(655\) 13.1906 0.515398
\(656\) 11.3013 0.441243
\(657\) 5.66387 9.81011i 0.220969 0.382729i
\(658\) 14.9343i 0.582199i
\(659\) −2.01447 3.48917i −0.0784727 0.135919i 0.824118 0.566418i \(-0.191671\pi\)
−0.902591 + 0.430499i \(0.858338\pi\)
\(660\) 3.20374i 0.124705i
\(661\) −34.3561 + 19.8355i −1.33630 + 0.771512i −0.986256 0.165222i \(-0.947166\pi\)
−0.350042 + 0.936734i \(0.613833\pi\)
\(662\) −11.3110 19.5912i −0.439614 0.761434i
\(663\) 6.08277 + 10.5357i 0.236235 + 0.409171i
\(664\) −5.36864 3.09959i −0.208344 0.120287i
\(665\) 4.47950 0.173708
\(666\) −5.38262 + 2.83327i −0.208572 + 0.109787i
\(667\) 39.3672 1.52431
\(668\) −20.2100 11.6682i −0.781948 0.451458i
\(669\) −5.95223 10.3096i −0.230127 0.398591i
\(670\) −0.212277 0.367674i −0.00820096 0.0142045i
\(671\) 28.2430 16.3061i 1.09031 0.629491i
\(672\) 1.68974i 0.0651832i
\(673\) 9.22709 + 15.9818i 0.355678 + 0.616053i 0.987234 0.159278i \(-0.0509166\pi\)
−0.631556 + 0.775331i \(0.717583\pi\)
\(674\) 2.44300i 0.0941010i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 7.45697 0.286807
\(677\) 3.66094 0.140701 0.0703506 0.997522i \(-0.477588\pi\)
0.0703506 + 0.997522i \(0.477588\pi\)
\(678\) 6.43505 11.1458i 0.247136 0.428053i
\(679\) −18.9743 + 10.9548i −0.728167 + 0.420407i
\(680\) 2.68974i 0.103147i
\(681\) −4.70710 2.71765i −0.180377 0.104140i
\(682\) 3.41567 5.91612i 0.130793 0.226540i
\(683\) −11.6297 6.71440i −0.444997 0.256919i 0.260718 0.965415i \(-0.416041\pi\)
−0.705715 + 0.708496i \(0.749374\pi\)
\(684\) 2.29583 1.32550i 0.0877833 0.0506817i
\(685\) −18.8451 + 10.8802i −0.720033 + 0.415711i
\(686\) −16.3088 9.41589i −0.622673 0.359500i
\(687\) −8.22859 + 14.2523i −0.313940 + 0.543761i
\(688\) 3.57035 + 2.06134i 0.136118 + 0.0785879i
\(689\) 61.9337i 2.35949i
\(690\) 5.41698 3.12749i 0.206221 0.119062i
\(691\) −0.0307256 + 0.0532183i −0.00116886 + 0.00202452i −0.866609 0.498987i \(-0.833705\pi\)
0.865440 + 0.501012i \(0.167039\pi\)
\(692\) 20.4500 0.777391
\(693\) 5.41349 0.205641
\(694\) 4.95497 8.58225i 0.188088 0.325778i
\(695\) 17.6698i 0.670255i
\(696\) 3.14687 + 5.45053i 0.119282 + 0.206602i
\(697\) 30.3976i 1.15139i
\(698\) −0.724391 + 0.418227i −0.0274186 + 0.0158301i
\(699\) −0.699610 1.21176i −0.0264617 0.0458330i
\(700\) 0.844871 + 1.46336i 0.0319331 + 0.0553098i
\(701\) −7.26675 4.19546i −0.274461 0.158460i 0.356452 0.934314i \(-0.383986\pi\)
−0.630913 + 0.775853i \(0.717320\pi\)
\(702\) −4.52294 −0.170707
\(703\) 14.2693 7.51099i 0.538177 0.283282i
\(704\) 3.20374 0.120745
\(705\) −7.65411 4.41910i −0.288271 0.166433i
\(706\) 3.01172 + 5.21645i 0.113347 + 0.196324i
\(707\) −13.8945 24.0660i −0.522557 0.905095i
\(708\) 0.611376 0.352978i 0.0229769 0.0132657i
\(709\) 17.1872i 0.645478i 0.946488 + 0.322739i \(0.104604\pi\)
−0.946488 + 0.322739i \(0.895396\pi\)
\(710\) 3.72548 + 6.45271i 0.139815 + 0.242166i
\(711\) 3.50216i 0.131341i
\(712\) 0.710515 1.23065i 0.0266277 0.0461205i
\(713\) 13.3376 0.499496
\(714\) 4.54497 0.170091
\(715\) 7.24515 12.5490i 0.270953 0.469305i
\(716\) 19.0732 11.0119i 0.712798 0.411534i
\(717\) 10.6250i 0.396798i
\(718\) −8.30278 4.79361i −0.309857 0.178896i
\(719\) −14.8025 + 25.6386i −0.552039 + 0.956160i 0.446088 + 0.894989i \(0.352817\pi\)
−0.998127 + 0.0611710i \(0.980516\pi\)
\(720\) 0.866025 + 0.500000i 0.0322749 + 0.0186339i
\(721\) −26.0970 + 15.0671i −0.971904 + 0.561129i
\(722\) 10.3682 5.98611i 0.385866 0.222780i
\(723\) 2.56645 + 1.48174i 0.0954473 + 0.0551065i
\(724\) 7.63876 13.2307i 0.283892 0.491716i
\(725\) −5.45053 3.14687i −0.202428 0.116872i
\(726\) 0.736075i 0.0273183i
\(727\) 26.0563 15.0436i 0.966373 0.557936i 0.0682444 0.997669i \(-0.478260\pi\)
0.898129 + 0.439733i \(0.144927\pi\)
\(728\) 3.82130 6.61868i 0.141627 0.245305i
\(729\) 1.00000 0.0370370
\(730\) −11.3277 −0.419258
\(731\) −5.54447 + 9.60331i −0.205070 + 0.355191i
\(732\) 10.1794i 0.376243i
\(733\) −22.3192 38.6579i −0.824377 1.42786i −0.902395 0.430910i \(-0.858192\pi\)
0.0780180 0.996952i \(-0.475141\pi\)
\(734\) 28.0627i 1.03581i
\(735\) 3.58948 2.07239i 0.132400 0.0764411i
\(736\) 3.12749 + 5.41698i 0.115281 + 0.199673i
\(737\) 0.680078 + 1.17793i 0.0250510 + 0.0433896i
\(738\) −9.78723 5.65066i −0.360273 0.208004i
\(739\) −5.42290 −0.199484 −0.0997422 0.995013i \(-0.531802\pi\)
−0.0997422 + 0.995013i \(0.531802\pi\)
\(740\) 5.14499 + 3.24485i 0.189134 + 0.119283i
\(741\) 11.9903 0.440474
\(742\) 20.0381 + 11.5690i 0.735623 + 0.424712i
\(743\) −10.3549 17.9352i −0.379884 0.657978i 0.611161 0.791506i \(-0.290703\pi\)
−0.991045 + 0.133528i \(0.957369\pi\)
\(744\) 1.06615 + 1.84663i 0.0390871 + 0.0677008i
\(745\) −2.43205 + 1.40414i −0.0891033 + 0.0514438i
\(746\) 5.69684i 0.208576i
\(747\) 3.09959 + 5.36864i 0.113408 + 0.196428i
\(748\) 8.61722i 0.315077i
\(749\) 3.32982 5.76742i 0.121669 0.210737i
\(750\) −1.00000 −0.0365148
\(751\) 2.54287 0.0927906 0.0463953 0.998923i \(-0.485227\pi\)
0.0463953 + 0.998923i \(0.485227\pi\)
\(752\) 4.41910 7.65411i 0.161148 0.279117i
\(753\) 4.47974 2.58638i 0.163251 0.0942530i
\(754\) 28.4662i 1.03668i
\(755\) −11.9824 6.91805i −0.436084 0.251773i
\(756\) −0.844871 + 1.46336i −0.0307276 + 0.0532219i
\(757\) 16.2988 + 9.41009i 0.592389 + 0.342016i 0.766041 0.642791i \(-0.222224\pi\)
−0.173653 + 0.984807i \(0.555557\pi\)
\(758\) 12.2120 7.05060i 0.443560 0.256089i
\(759\) −17.3546 + 10.0197i −0.629931 + 0.363691i
\(760\) −2.29583 1.32550i −0.0832785 0.0480809i
\(761\) 9.17785 15.8965i 0.332697 0.576248i −0.650343 0.759641i \(-0.725375\pi\)
0.983040 + 0.183393i \(0.0587081\pi\)
\(762\) 2.59092 + 1.49587i 0.0938591 + 0.0541896i
\(763\) 19.8819i 0.719772i
\(764\) −2.75485 + 1.59051i −0.0996670 + 0.0575428i
\(765\) −1.34487 + 2.32938i −0.0486239 + 0.0842191i
\(766\) 27.4056 0.990204
\(767\) 3.19299 0.115292
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 12.0032i 0.432846i −0.976300 0.216423i \(-0.930561\pi\)
0.976300 0.216423i \(-0.0694390\pi\)
\(770\) −2.70674 4.68822i −0.0975442 0.168952i
\(771\) 5.25500i 0.189254i
\(772\) 6.52555 3.76753i 0.234860 0.135596i
\(773\) 8.17897 + 14.1664i 0.294177 + 0.509530i 0.974793 0.223111i \(-0.0716211\pi\)
−0.680616 + 0.732640i \(0.738288\pi\)
\(774\) −2.06134 3.57035i −0.0740934 0.128333i
\(775\) −1.84663 1.06615i −0.0663330 0.0382974i
\(776\) 12.9663 0.465462