Properties

Label 1110.2.x.d.841.2
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 841.2
Root \(0.535537i\) of defining polynomial
Character \(\chi\) \(=\) 1110.841
Dual form 1110.2.x.d.751.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-0.267768 - 0.463788i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.267768 - 0.463788i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +5.44426 q^{11} +(0.500000 - 0.866025i) q^{12} +(0.556002 - 0.321008i) q^{13} +0.535537i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.402237 - 0.232232i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-7.12118 + 4.11142i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.267768 + 0.463788i) q^{21} +(-4.71487 - 2.72213i) q^{22} +2.37407i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -0.642016 q^{26} +1.00000 q^{27} +(0.267768 - 0.463788i) q^{28} +5.38430i q^{29} +(-0.500000 - 0.866025i) q^{30} -1.32755i q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.72213 - 4.71487i) q^{33} +(0.232232 + 0.402237i) q^{34} +(0.463788 + 0.267768i) q^{35} -1.00000 q^{36} +(6.01205 - 0.924822i) q^{37} +8.22283 q^{38} +(-0.556002 - 0.321008i) q^{39} +(0.500000 + 0.866025i) q^{40} +(4.86520 + 8.42677i) q^{41} +(0.463788 - 0.267768i) q^{42} -1.04652i q^{43} +(2.72213 + 4.71487i) q^{44} -1.00000i q^{45} +(1.18703 - 2.05600i) q^{46} +8.14127 q^{47} +1.00000 q^{48} +(3.35660 - 5.81380i) q^{49} +(-0.866025 + 0.500000i) q^{50} +0.464463i q^{51} +(0.556002 + 0.321008i) q^{52} +(2.89110 - 5.00753i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-4.71487 + 2.72213i) q^{55} +(-0.463788 + 0.267768i) q^{56} +(7.12118 + 4.11142i) q^{57} +(2.69215 - 4.66294i) q^{58} +(10.2224 + 5.90190i) q^{59} +1.00000i q^{60} +(2.55109 - 1.47287i) q^{61} +(-0.663773 + 1.14969i) q^{62} +0.535537 q^{63} -1.00000 q^{64} +(-0.321008 + 0.556002i) q^{65} +5.44426i q^{66} +(-2.04849 - 3.54808i) q^{67} -0.464463i q^{68} +(2.05600 - 1.18703i) q^{69} +(-0.267768 - 0.463788i) q^{70} +(2.17408 + 3.76562i) q^{71} +(0.866025 + 0.500000i) q^{72} -1.60237 q^{73} +(-5.66900 - 2.20510i) q^{74} -1.00000 q^{75} +(-7.12118 - 4.11142i) q^{76} +(-1.45780 - 2.52499i) q^{77} +(0.321008 + 0.556002i) q^{78} +(-3.48536 + 2.01228i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -9.73039i q^{82} +(3.61426 - 6.26008i) q^{83} -0.535537 q^{84} +0.464463 q^{85} +(-0.523261 + 0.906314i) q^{86} +(4.66294 - 2.69215i) q^{87} -5.44426i q^{88} +(3.69105 + 2.13103i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-0.297759 - 0.171911i) q^{91} +(-2.05600 + 1.18703i) q^{92} +(-1.14969 + 0.663773i) q^{93} +(-7.05055 - 4.07063i) q^{94} +(4.11142 - 7.12118i) q^{95} +(-0.866025 - 0.500000i) q^{96} +5.43955i q^{97} +(-5.81380 + 3.35660i) q^{98} +(-2.72213 + 4.71487i) 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
\(7\) −0.267768 0.463788i −0.101207 0.175295i 0.810975 0.585080i \(-0.198937\pi\)
−0.912182 + 0.409785i \(0.865604\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.00000 0.316228
\(11\) 5.44426 1.64151 0.820754 0.571282i \(-0.193554\pi\)
0.820754 + 0.571282i \(0.193554\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 0.556002 0.321008i 0.154207 0.0890316i −0.420911 0.907102i \(-0.638289\pi\)
0.575118 + 0.818070i \(0.304956\pi\)
\(14\) 0.535537i 0.143128i
\(15\) 0.866025 + 0.500000i 0.223607 + 0.129099i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.402237 0.232232i −0.0975568 0.0563245i 0.450428 0.892813i \(-0.351271\pi\)
−0.547985 + 0.836488i \(0.684605\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −7.12118 + 4.11142i −1.63371 + 0.943224i −0.650777 + 0.759269i \(0.725557\pi\)
−0.982935 + 0.183955i \(0.941110\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) −0.267768 + 0.463788i −0.0584318 + 0.101207i
\(22\) −4.71487 2.72213i −1.00521 0.580360i
\(23\) 2.37407i 0.495027i 0.968884 + 0.247514i \(0.0796135\pi\)
−0.968884 + 0.247514i \(0.920387\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −0.642016 −0.125910
\(27\) 1.00000 0.192450
\(28\) 0.267768 0.463788i 0.0506034 0.0876477i
\(29\) 5.38430i 0.999840i 0.866072 + 0.499920i \(0.166637\pi\)
−0.866072 + 0.499920i \(0.833363\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 1.32755i 0.238434i −0.992868 0.119217i \(-0.961962\pi\)
0.992868 0.119217i \(-0.0380385\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −2.72213 4.71487i −0.473862 0.820754i
\(34\) 0.232232 + 0.402237i 0.0398274 + 0.0689831i
\(35\) 0.463788 + 0.267768i 0.0783945 + 0.0452611i
\(36\) −1.00000 −0.166667
\(37\) 6.01205 0.924822i 0.988374 0.152040i
\(38\) 8.22283 1.33392
\(39\) −0.556002 0.321008i −0.0890316 0.0514024i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 4.86520 + 8.42677i 0.759816 + 1.31604i 0.942944 + 0.332951i \(0.108044\pi\)
−0.183128 + 0.983089i \(0.558622\pi\)
\(42\) 0.463788 0.267768i 0.0715641 0.0413175i
\(43\) 1.04652i 0.159593i −0.996811 0.0797965i \(-0.974573\pi\)
0.996811 0.0797965i \(-0.0254270\pi\)
\(44\) 2.72213 + 4.71487i 0.410377 + 0.710793i
\(45\) 1.00000i 0.149071i
\(46\) 1.18703 2.05600i 0.175019 0.303141i
\(47\) 8.14127 1.18753 0.593763 0.804640i \(-0.297642\pi\)
0.593763 + 0.804640i \(0.297642\pi\)
\(48\) 1.00000 0.144338
\(49\) 3.35660 5.81380i 0.479514 0.830543i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 0.464463i 0.0650379i
\(52\) 0.556002 + 0.321008i 0.0771036 + 0.0445158i
\(53\) 2.89110 5.00753i 0.397123 0.687837i −0.596247 0.802801i \(-0.703342\pi\)
0.993370 + 0.114964i \(0.0366753\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −4.71487 + 2.72213i −0.635753 + 0.367052i
\(56\) −0.463788 + 0.267768i −0.0619763 + 0.0357820i
\(57\) 7.12118 + 4.11142i 0.943224 + 0.544571i
\(58\) 2.69215 4.66294i 0.353497 0.612275i
\(59\) 10.2224 + 5.90190i 1.33084 + 0.768362i 0.985429 0.170088i \(-0.0544052\pi\)
0.345414 + 0.938450i \(0.387739\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 2.55109 1.47287i 0.326633 0.188582i −0.327712 0.944778i \(-0.606278\pi\)
0.654345 + 0.756196i \(0.272944\pi\)
\(62\) −0.663773 + 1.14969i −0.0842992 + 0.146011i
\(63\) 0.535537 0.0674713
\(64\) −1.00000 −0.125000
\(65\) −0.321008 + 0.556002i −0.0398161 + 0.0689636i
\(66\) 5.44426i 0.670142i
\(67\) −2.04849 3.54808i −0.250263 0.433468i 0.713335 0.700823i \(-0.247184\pi\)
−0.963598 + 0.267355i \(0.913850\pi\)
\(68\) 0.464463i 0.0563245i
\(69\) 2.05600 1.18703i 0.247514 0.142902i
\(70\) −0.267768 0.463788i −0.0320044 0.0554333i
\(71\) 2.17408 + 3.76562i 0.258016 + 0.446897i 0.965710 0.259622i \(-0.0835979\pi\)
−0.707694 + 0.706519i \(0.750265\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) −1.60237 −0.187543 −0.0937716 0.995594i \(-0.529892\pi\)
−0.0937716 + 0.995594i \(0.529892\pi\)
\(74\) −5.66900 2.20510i −0.659007 0.256338i
\(75\) −1.00000 −0.115470
\(76\) −7.12118 4.11142i −0.816856 0.471612i
\(77\) −1.45780 2.52499i −0.166132 0.287749i
\(78\) 0.321008 + 0.556002i 0.0363470 + 0.0629548i
\(79\) −3.48536 + 2.01228i −0.392134 + 0.226399i −0.683084 0.730339i \(-0.739362\pi\)
0.290950 + 0.956738i \(0.406029\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 9.73039i 1.07454i
\(83\) 3.61426 6.26008i 0.396716 0.687133i −0.596602 0.802537i \(-0.703483\pi\)
0.993319 + 0.115404i \(0.0368164\pi\)
\(84\) −0.535537 −0.0584318
\(85\) 0.464463 0.0503781
\(86\) −0.523261 + 0.906314i −0.0564246 + 0.0977303i
\(87\) 4.66294 2.69215i 0.499920 0.288629i
\(88\) 5.44426i 0.580360i
\(89\) 3.69105 + 2.13103i 0.391251 + 0.225889i 0.682702 0.730697i \(-0.260805\pi\)
−0.291451 + 0.956586i \(0.594138\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) −0.297759 0.171911i −0.0312137 0.0180212i
\(92\) −2.05600 + 1.18703i −0.214353 + 0.123757i
\(93\) −1.14969 + 0.663773i −0.119217 + 0.0688300i
\(94\) −7.05055 4.07063i −0.727208 0.419854i
\(95\) 4.11142 7.12118i 0.421823 0.730618i
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) 5.43955i 0.552303i 0.961114 + 0.276151i \(0.0890591\pi\)
−0.961114 + 0.276151i \(0.910941\pi\)
\(98\) −5.81380 + 3.35660i −0.587283 + 0.339068i
\(99\) −2.72213 + 4.71487i −0.273585 + 0.473862i
\(100\) 1.00000 0.100000
\(101\) 9.15512 0.910969 0.455484 0.890244i \(-0.349466\pi\)
0.455484 + 0.890244i \(0.349466\pi\)
\(102\) 0.232232 0.402237i 0.0229944 0.0398274i
\(103\) 10.5315i 1.03770i 0.854865 + 0.518850i \(0.173640\pi\)
−0.854865 + 0.518850i \(0.826360\pi\)
\(104\) −0.321008 0.556002i −0.0314774 0.0545205i
\(105\) 0.535537i 0.0522630i
\(106\) −5.00753 + 2.89110i −0.486374 + 0.280808i
\(107\) −7.54260 13.0642i −0.729170 1.26296i −0.957234 0.289314i \(-0.906573\pi\)
0.228064 0.973646i \(-0.426760\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 3.84093 + 2.21756i 0.367894 + 0.212404i 0.672538 0.740063i \(-0.265204\pi\)
−0.304644 + 0.952466i \(0.598537\pi\)
\(110\) 5.44426 0.519090
\(111\) −3.80694 4.74417i −0.361339 0.450297i
\(112\) 0.535537 0.0506034
\(113\) 7.78200 + 4.49294i 0.732069 + 0.422660i 0.819179 0.573539i \(-0.194430\pi\)
−0.0871097 + 0.996199i \(0.527763\pi\)
\(114\) −4.11142 7.12118i −0.385070 0.666960i
\(115\) −1.18703 2.05600i −0.110691 0.191723i
\(116\) −4.66294 + 2.69215i −0.432944 + 0.249960i
\(117\) 0.642016i 0.0593544i
\(118\) −5.90190 10.2224i −0.543314 0.941048i
\(119\) 0.248737i 0.0228017i
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) 18.6400 1.69455
\(122\) −2.94574 −0.266695
\(123\) 4.86520 8.42677i 0.438680 0.759816i
\(124\) 1.14969 0.663773i 0.103245 0.0596086i
\(125\) 1.00000i 0.0894427i
\(126\) −0.463788 0.267768i −0.0413175 0.0238547i
\(127\) 5.95507 10.3145i 0.528427 0.915262i −0.471024 0.882120i \(-0.656115\pi\)
0.999451 0.0331415i \(-0.0105512\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −0.906314 + 0.523261i −0.0797965 + 0.0460705i
\(130\) 0.556002 0.321008i 0.0487646 0.0281543i
\(131\) 7.32391 + 4.22846i 0.639893 + 0.369442i 0.784573 0.620036i \(-0.212882\pi\)
−0.144680 + 0.989478i \(0.546215\pi\)
\(132\) 2.72213 4.71487i 0.236931 0.410377i
\(133\) 3.81365 + 2.20181i 0.330686 + 0.190922i
\(134\) 4.09698i 0.353925i
\(135\) −0.866025 + 0.500000i −0.0745356 + 0.0430331i
\(136\) −0.232232 + 0.402237i −0.0199137 + 0.0344916i
\(137\) 19.7950 1.69120 0.845599 0.533818i \(-0.179243\pi\)
0.845599 + 0.533818i \(0.179243\pi\)
\(138\) −2.37407 −0.202094
\(139\) −3.66567 + 6.34913i −0.310918 + 0.538526i −0.978561 0.205955i \(-0.933970\pi\)
0.667643 + 0.744481i \(0.267303\pi\)
\(140\) 0.535537i 0.0452611i
\(141\) −4.07063 7.05055i −0.342809 0.593763i
\(142\) 4.34816i 0.364890i
\(143\) 3.02702 1.74765i 0.253132 0.146146i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −2.69215 4.66294i −0.223571 0.387236i
\(146\) 1.38769 + 0.801185i 0.114846 + 0.0663065i
\(147\) −6.71320 −0.553695
\(148\) 3.80694 + 4.74417i 0.312929 + 0.389969i
\(149\) −8.22737 −0.674012 −0.337006 0.941502i \(-0.609414\pi\)
−0.337006 + 0.941502i \(0.609414\pi\)
\(150\) 0.866025 + 0.500000i 0.0707107 + 0.0408248i
\(151\) −4.98628 8.63648i −0.405777 0.702827i 0.588634 0.808400i \(-0.299666\pi\)
−0.994412 + 0.105572i \(0.966333\pi\)
\(152\) 4.11142 + 7.12118i 0.333480 + 0.577604i
\(153\) 0.402237 0.232232i 0.0325189 0.0187748i
\(154\) 2.91560i 0.234946i
\(155\) 0.663773 + 1.14969i 0.0533155 + 0.0923452i
\(156\) 0.642016i 0.0514024i
\(157\) −2.88383 + 4.99495i −0.230155 + 0.398640i −0.957854 0.287257i \(-0.907257\pi\)
0.727699 + 0.685897i \(0.240590\pi\)
\(158\) 4.02455 0.320176
\(159\) −5.78220 −0.458558
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 1.10106 0.635700i 0.0867760 0.0501002i
\(162\) 1.00000i 0.0785674i
\(163\) 0.511813 + 0.295495i 0.0400883 + 0.0231450i 0.519910 0.854221i \(-0.325965\pi\)
−0.479822 + 0.877366i \(0.659299\pi\)
\(164\) −4.86520 + 8.42677i −0.379908 + 0.658020i
\(165\) 4.71487 + 2.72213i 0.367052 + 0.211918i
\(166\) −6.26008 + 3.61426i −0.485876 + 0.280521i
\(167\) −8.80330 + 5.08259i −0.681220 + 0.393302i −0.800314 0.599580i \(-0.795334\pi\)
0.119095 + 0.992883i \(0.462001\pi\)
\(168\) 0.463788 + 0.267768i 0.0357820 + 0.0206588i
\(169\) −6.29391 + 10.9014i −0.484147 + 0.838567i
\(170\) −0.402237 0.232232i −0.0308502 0.0178114i
\(171\) 8.22283i 0.628816i
\(172\) 0.906314 0.523261i 0.0691058 0.0398982i
\(173\) −7.70420 + 13.3441i −0.585739 + 1.01453i 0.409043 + 0.912515i \(0.365862\pi\)
−0.994783 + 0.102015i \(0.967471\pi\)
\(174\) −5.38430 −0.408183
\(175\) −0.535537 −0.0404828
\(176\) −2.72213 + 4.71487i −0.205188 + 0.355397i
\(177\) 11.8038i 0.887228i
\(178\) −2.13103 3.69105i −0.159728 0.276656i
\(179\) 7.91168i 0.591347i −0.955289 0.295673i \(-0.904456\pi\)
0.955289 0.295673i \(-0.0955440\pi\)
\(180\) 0.866025 0.500000i 0.0645497 0.0372678i
\(181\) 4.86182 + 8.42093i 0.361377 + 0.625922i 0.988188 0.153249i \(-0.0489736\pi\)
−0.626811 + 0.779171i \(0.715640\pi\)
\(182\) 0.171911 + 0.297759i 0.0127429 + 0.0220714i
\(183\) −2.55109 1.47287i −0.188582 0.108878i
\(184\) 2.37407 0.175019
\(185\) −4.74417 + 3.80694i −0.348799 + 0.279892i
\(186\) 1.32755 0.0973404
\(187\) −2.18988 1.26433i −0.160140 0.0924570i
\(188\) 4.07063 + 7.05055i 0.296882 + 0.514214i
\(189\) −0.267768 0.463788i −0.0194773 0.0337356i
\(190\) −7.12118 + 4.11142i −0.516625 + 0.298274i
\(191\) 16.0144i 1.15876i −0.815057 0.579380i \(-0.803295\pi\)
0.815057 0.579380i \(-0.196705\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 17.2656i 1.24281i −0.783490 0.621404i \(-0.786563\pi\)
0.783490 0.621404i \(-0.213437\pi\)
\(194\) 2.71977 4.71079i 0.195268 0.338215i
\(195\) 0.642016 0.0459757
\(196\) 6.71320 0.479514
\(197\) −12.1985 + 21.1285i −0.869110 + 1.50534i −0.00620326 + 0.999981i \(0.501975\pi\)
−0.862907 + 0.505363i \(0.831359\pi\)
\(198\) 4.71487 2.72213i 0.335071 0.193453i
\(199\) 0.826478i 0.0585875i 0.999571 + 0.0292937i \(0.00932582\pi\)
−0.999571 + 0.0292937i \(0.990674\pi\)
\(200\) −0.866025 0.500000i −0.0612372 0.0353553i
\(201\) −2.04849 + 3.54808i −0.144489 + 0.250263i
\(202\) −7.92857 4.57756i −0.557852 0.322076i
\(203\) 2.49718 1.44175i 0.175267 0.101191i
\(204\) −0.402237 + 0.232232i −0.0281622 + 0.0162595i
\(205\) −8.42677 4.86520i −0.588551 0.339800i
\(206\) 5.26575 9.12055i 0.366882 0.635459i
\(207\) −2.05600 1.18703i −0.142902 0.0825045i
\(208\) 0.642016i 0.0445158i
\(209\) −38.7696 + 22.3836i −2.68175 + 1.54831i
\(210\) −0.267768 + 0.463788i −0.0184778 + 0.0320044i
\(211\) 4.70749 0.324077 0.162039 0.986784i \(-0.448193\pi\)
0.162039 + 0.986784i \(0.448193\pi\)
\(212\) 5.78220 0.397123
\(213\) 2.17408 3.76562i 0.148966 0.258016i
\(214\) 15.0852i 1.03120i
\(215\) 0.523261 + 0.906314i 0.0356861 + 0.0618101i
\(216\) 1.00000i 0.0680414i
\(217\) −0.615700 + 0.355475i −0.0417964 + 0.0241312i
\(218\) −2.21756 3.84093i −0.150192 0.260140i
\(219\) 0.801185 + 1.38769i 0.0541391 + 0.0937716i
\(220\) −4.71487 2.72213i −0.317876 0.183526i
\(221\) −0.298193 −0.0200586
\(222\) 0.924822 + 6.01205i 0.0620700 + 0.403502i
\(223\) −8.14374 −0.545345 −0.272673 0.962107i \(-0.587908\pi\)
−0.272673 + 0.962107i \(0.587908\pi\)
\(224\) −0.463788 0.267768i −0.0309882 0.0178910i
\(225\) 0.500000 + 0.866025i 0.0333333 + 0.0577350i
\(226\) −4.49294 7.78200i −0.298866 0.517651i
\(227\) −3.39960 + 1.96276i −0.225639 + 0.130273i −0.608559 0.793509i \(-0.708252\pi\)
0.382919 + 0.923782i \(0.374919\pi\)
\(228\) 8.22283i 0.544571i
\(229\) 13.5993 + 23.5547i 0.898667 + 1.55654i 0.829200 + 0.558953i \(0.188797\pi\)
0.0694673 + 0.997584i \(0.477870\pi\)
\(230\) 2.37407i 0.156541i
\(231\) −1.45780 + 2.52499i −0.0959162 + 0.166132i
\(232\) 5.38430 0.353497
\(233\) 11.1032 0.727394 0.363697 0.931517i \(-0.381514\pi\)
0.363697 + 0.931517i \(0.381514\pi\)
\(234\) 0.321008 0.556002i 0.0209849 0.0363470i
\(235\) −7.05055 + 4.07063i −0.459927 + 0.265539i
\(236\) 11.8038i 0.768362i
\(237\) 3.48536 + 2.01228i 0.226399 + 0.130711i
\(238\) 0.124369 0.215413i 0.00806162 0.0139631i
\(239\) −8.61437 4.97351i −0.557217 0.321710i 0.194810 0.980841i \(-0.437591\pi\)
−0.752028 + 0.659131i \(0.770924\pi\)
\(240\) −0.866025 + 0.500000i −0.0559017 + 0.0322749i
\(241\) −18.7127 + 10.8038i −1.20539 + 0.695932i −0.961749 0.273933i \(-0.911675\pi\)
−0.243641 + 0.969865i \(0.578342\pi\)
\(242\) −16.1427 9.32000i −1.03769 0.599112i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 2.55109 + 1.47287i 0.163317 + 0.0942910i
\(245\) 6.71320i 0.428891i
\(246\) −8.42677 + 4.86520i −0.537271 + 0.310194i
\(247\) −2.63960 + 4.57191i −0.167953 + 0.290904i
\(248\) −1.32755 −0.0842992
\(249\) −7.22851 −0.458088
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 5.10425i 0.322178i −0.986940 0.161089i \(-0.948499\pi\)
0.986940 0.161089i \(-0.0515005\pi\)
\(252\) 0.267768 + 0.463788i 0.0168678 + 0.0292159i
\(253\) 12.9250i 0.812590i
\(254\) −10.3145 + 5.95507i −0.647188 + 0.373654i
\(255\) −0.232232 0.402237i −0.0145429 0.0251891i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 16.8491 + 9.72782i 1.05102 + 0.606805i 0.922934 0.384959i \(-0.125784\pi\)
0.128083 + 0.991763i \(0.459118\pi\)
\(258\) 1.04652 0.0651536
\(259\) −2.03876 2.54068i −0.126682 0.157870i
\(260\) −0.642016 −0.0398161
\(261\) −4.66294 2.69215i −0.288629 0.166640i
\(262\) −4.22846 7.32391i −0.261235 0.452473i
\(263\) −6.04317 10.4671i −0.372638 0.645428i 0.617332 0.786702i \(-0.288213\pi\)
−0.989970 + 0.141274i \(0.954880\pi\)
\(264\) −4.71487 + 2.72213i −0.290180 + 0.167536i
\(265\) 5.78220i 0.355198i
\(266\) −2.20181 3.81365i −0.135002 0.233830i
\(267\) 4.26206i 0.260834i
\(268\) 2.04849 3.54808i 0.125131 0.216734i
\(269\) −27.8139 −1.69584 −0.847921 0.530123i \(-0.822146\pi\)
−0.847921 + 0.530123i \(0.822146\pi\)
\(270\) 1.00000 0.0608581
\(271\) 2.68320 4.64744i 0.162993 0.282312i −0.772948 0.634470i \(-0.781219\pi\)
0.935941 + 0.352158i \(0.114552\pi\)
\(272\) 0.402237 0.232232i 0.0243892 0.0140811i
\(273\) 0.343823i 0.0208091i
\(274\) −17.1430 9.89749i −1.03564 0.597929i
\(275\) 2.72213 4.71487i 0.164151 0.284317i
\(276\) 2.05600 + 1.18703i 0.123757 + 0.0714510i
\(277\) −9.37602 + 5.41325i −0.563350 + 0.325250i −0.754489 0.656313i \(-0.772115\pi\)
0.191139 + 0.981563i \(0.438782\pi\)
\(278\) 6.34913 3.66567i 0.380795 0.219852i
\(279\) 1.14969 + 0.663773i 0.0688300 + 0.0397390i
\(280\) 0.267768 0.463788i 0.0160022 0.0277166i
\(281\) 12.7542 + 7.36363i 0.760851 + 0.439277i 0.829601 0.558356i \(-0.188568\pi\)
−0.0687503 + 0.997634i \(0.521901\pi\)
\(282\) 8.14127i 0.484806i
\(283\) 16.5272 9.54199i 0.982440 0.567212i 0.0794343 0.996840i \(-0.474689\pi\)
0.903006 + 0.429628i \(0.141355\pi\)
\(284\) −2.17408 + 3.76562i −0.129008 + 0.223448i
\(285\) −8.22283 −0.487079
\(286\) −3.49530 −0.206682
\(287\) 2.60549 4.51284i 0.153797 0.266385i
\(288\) 1.00000i 0.0589256i
\(289\) −8.39214 14.5356i −0.493655 0.855036i
\(290\) 5.38430i 0.316177i
\(291\) 4.71079 2.71977i 0.276151 0.159436i
\(292\) −0.801185 1.38769i −0.0468858 0.0812086i
\(293\) −1.27637 2.21073i −0.0745660 0.129152i 0.826331 0.563184i \(-0.190424\pi\)
−0.900897 + 0.434032i \(0.857090\pi\)
\(294\) 5.81380 + 3.35660i 0.339068 + 0.195761i
\(295\) −11.8038 −0.687244
\(296\) −0.924822 6.01205i −0.0537542 0.349443i
\(297\) 5.44426 0.315908
\(298\) 7.12511 + 4.11369i 0.412747 + 0.238299i
\(299\) 0.762094 + 1.31999i 0.0440731 + 0.0763368i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) −0.485364 + 0.280225i −0.0279759 + 0.0161519i
\(302\) 9.97255i 0.573856i
\(303\) −4.57756 7.92857i −0.262974 0.455484i
\(304\) 8.22283i 0.471612i
\(305\) −1.47287 + 2.55109i −0.0843364 + 0.146075i
\(306\) −0.464463 −0.0265516
\(307\) −1.60024 −0.0913305 −0.0456653 0.998957i \(-0.514541\pi\)
−0.0456653 + 0.998957i \(0.514541\pi\)
\(308\) 1.45780 2.52499i 0.0830659 0.143874i
\(309\) 9.12055 5.26575i 0.518850 0.299558i
\(310\) 1.32755i 0.0753995i
\(311\) −4.41158 2.54702i −0.250157 0.144428i 0.369679 0.929160i \(-0.379468\pi\)
−0.619836 + 0.784731i \(0.712801\pi\)
\(312\) −0.321008 + 0.556002i −0.0181735 + 0.0314774i
\(313\) −2.00909 1.15995i −0.113561 0.0655642i 0.442144 0.896944i \(-0.354218\pi\)
−0.555704 + 0.831380i \(0.687551\pi\)
\(314\) 4.99495 2.88383i 0.281881 0.162744i
\(315\) −0.463788 + 0.267768i −0.0261315 + 0.0150870i
\(316\) −3.48536 2.01228i −0.196067 0.113199i
\(317\) 6.42213 11.1235i 0.360703 0.624756i −0.627374 0.778718i \(-0.715870\pi\)
0.988077 + 0.153963i \(0.0492035\pi\)
\(318\) 5.00753 + 2.89110i 0.280808 + 0.162125i
\(319\) 29.3136i 1.64124i
\(320\) 0.866025 0.500000i 0.0484123 0.0279508i
\(321\) −7.54260 + 13.0642i −0.420987 + 0.729170i
\(322\) −1.27140 −0.0708523
\(323\) 3.81921 0.212506
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 0.642016i 0.0356126i
\(326\) −0.295495 0.511813i −0.0163660 0.0283467i
\(327\) 4.43512i 0.245263i
\(328\) 8.42677 4.86520i 0.465290 0.268636i
\(329\) −2.17997 3.77582i −0.120186 0.208168i
\(330\) −2.72213 4.71487i −0.149848 0.259545i
\(331\) −6.20441 3.58212i −0.341025 0.196891i 0.319700 0.947519i \(-0.396418\pi\)
−0.660725 + 0.750628i \(0.729751\pi\)
\(332\) 7.22851 0.396716
\(333\) −2.20510 + 5.66900i −0.120839 + 0.310659i
\(334\) 10.1652 0.556214
\(335\) 3.54808 + 2.04849i 0.193853 + 0.111921i
\(336\) −0.267768 0.463788i −0.0146080 0.0253017i
\(337\) −11.4507 19.8331i −0.623757 1.08038i −0.988780 0.149380i \(-0.952272\pi\)
0.365023 0.930999i \(-0.381061\pi\)
\(338\) 10.9014 6.29391i 0.592956 0.342343i
\(339\) 8.98588i 0.488046i
\(340\) 0.232232 + 0.402237i 0.0125945 + 0.0218144i
\(341\) 7.22751i 0.391391i
\(342\) −4.11142 + 7.12118i −0.222320 + 0.385070i
\(343\) −7.34392 −0.396534
\(344\) −1.04652 −0.0564246
\(345\) −1.18703 + 2.05600i −0.0639077 + 0.110691i
\(346\) 13.3441 7.70420i 0.717381 0.414180i
\(347\) 27.5385i 1.47835i 0.673516 + 0.739173i \(0.264783\pi\)
−0.673516 + 0.739173i \(0.735217\pi\)
\(348\) 4.66294 + 2.69215i 0.249960 + 0.144315i
\(349\) −11.8294 + 20.4892i −0.633216 + 1.09676i 0.353675 + 0.935369i \(0.384932\pi\)
−0.986890 + 0.161393i \(0.948401\pi\)
\(350\) 0.463788 + 0.267768i 0.0247905 + 0.0143128i
\(351\) 0.556002 0.321008i 0.0296772 0.0171341i
\(352\) 4.71487 2.72213i 0.251303 0.145090i
\(353\) −4.74750 2.74097i −0.252684 0.145887i 0.368309 0.929704i \(-0.379937\pi\)
−0.620992 + 0.783817i \(0.713270\pi\)
\(354\) −5.90190 + 10.2224i −0.313683 + 0.543314i
\(355\) −3.76562 2.17408i −0.199858 0.115388i
\(356\) 4.26206i 0.225889i
\(357\) 0.215413 0.124369i 0.0114008 0.00658228i
\(358\) −3.95584 + 6.85171i −0.209073 + 0.362124i
\(359\) −20.2538 −1.06895 −0.534477 0.845183i \(-0.679491\pi\)
−0.534477 + 0.845183i \(0.679491\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 24.3075 42.1018i 1.27934 2.21589i
\(362\) 9.72365i 0.511064i
\(363\) −9.32000 16.1427i −0.489173 0.847273i
\(364\) 0.343823i 0.0180212i
\(365\) 1.38769 0.801185i 0.0726352 0.0419359i
\(366\) 1.47287 + 2.55109i 0.0769882 + 0.133348i
\(367\) −14.5637 25.2250i −0.760217 1.31673i −0.942739 0.333532i \(-0.891759\pi\)
0.182522 0.983202i \(-0.441574\pi\)
\(368\) −2.05600 1.18703i −0.107177 0.0618784i
\(369\) −9.73039 −0.506544
\(370\) 6.01205 0.924822i 0.312551 0.0480792i
\(371\) −3.09658 −0.160766
\(372\) −1.14969 0.663773i −0.0596086 0.0344150i
\(373\) 18.0747 + 31.3063i 0.935871 + 1.62098i 0.773073 + 0.634317i \(0.218719\pi\)
0.162799 + 0.986659i \(0.447948\pi\)
\(374\) 1.26433 + 2.18988i 0.0653770 + 0.113236i
\(375\) 0.866025 0.500000i 0.0447214 0.0258199i
\(376\) 8.14127i 0.419854i
\(377\) 1.72840 + 2.99368i 0.0890174 + 0.154183i
\(378\) 0.535537i 0.0275450i
\(379\) 10.8574 18.8055i 0.557706 0.965976i −0.439981 0.898007i \(-0.645015\pi\)
0.997687 0.0679687i \(-0.0216518\pi\)
\(380\) 8.22283 0.421823
\(381\) −11.9101 −0.610175
\(382\) −8.00719 + 13.8689i −0.409684 + 0.709593i
\(383\) −27.9465 + 16.1349i −1.42800 + 0.824456i −0.996963 0.0778783i \(-0.975185\pi\)
−0.431037 + 0.902334i \(0.641852\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 2.52499 + 1.45780i 0.128685 + 0.0742964i
\(386\) −8.63282 + 14.9525i −0.439399 + 0.761061i
\(387\) 0.906314 + 0.523261i 0.0460705 + 0.0265988i
\(388\) −4.71079 + 2.71977i −0.239154 + 0.138076i
\(389\) −28.9212 + 16.6976i −1.46636 + 0.846604i −0.999292 0.0376165i \(-0.988023\pi\)
−0.467069 + 0.884221i \(0.654690\pi\)
\(390\) −0.556002 0.321008i −0.0281543 0.0162549i
\(391\) 0.551334 0.954938i 0.0278821 0.0482933i
\(392\) −5.81380 3.35660i −0.293641 0.169534i
\(393\) 8.45692i 0.426595i
\(394\) 21.1285 12.1985i 1.06444 0.614554i
\(395\) 2.01228 3.48536i 0.101249 0.175368i
\(396\) −5.44426 −0.273585
\(397\) −8.82763 −0.443046 −0.221523 0.975155i \(-0.571103\pi\)
−0.221523 + 0.975155i \(0.571103\pi\)
\(398\) 0.413239 0.715751i 0.0207138 0.0358774i
\(399\) 4.40363i 0.220457i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 35.0800i 1.75181i −0.482482 0.875906i \(-0.660264\pi\)
0.482482 0.875906i \(-0.339736\pi\)
\(402\) 3.54808 2.04849i 0.176962 0.102169i
\(403\) −0.426153 0.738118i −0.0212282 0.0367683i
\(404\) 4.57756 + 7.92857i 0.227742 + 0.394461i
\(405\) 0.866025 + 0.500000i 0.0430331 + 0.0248452i
\(406\) −2.88349 −0.143105
\(407\) 32.7312 5.03498i 1.62242 0.249575i
\(408\) 0.464463 0.0229944
\(409\) 31.4737 + 18.1714i 1.55627 + 0.898516i 0.997608 + 0.0691231i \(0.0220201\pi\)
0.558666 + 0.829392i \(0.311313\pi\)
\(410\) 4.86520 + 8.42677i 0.240275 + 0.416168i
\(411\) −9.89749 17.1430i −0.488207 0.845599i
\(412\) −9.12055 + 5.26575i −0.449337 + 0.259425i
\(413\) 6.32137i 0.311054i
\(414\) 1.18703 + 2.05600i 0.0583395 + 0.101047i
\(415\) 7.22851i 0.354834i
\(416\) 0.321008 0.556002i 0.0157387 0.0272602i
\(417\) 7.33134 0.359017
\(418\) 44.7673 2.18964
\(419\) −6.93685 + 12.0150i −0.338887 + 0.586970i −0.984224 0.176929i \(-0.943384\pi\)
0.645336 + 0.763898i \(0.276717\pi\)
\(420\) 0.463788 0.267768i 0.0226305 0.0130658i
\(421\) 3.08809i 0.150504i 0.997165 + 0.0752521i \(0.0239762\pi\)
−0.997165 + 0.0752521i \(0.976024\pi\)
\(422\) −4.07681 2.35375i −0.198456 0.114579i
\(423\) −4.07063 + 7.05055i −0.197921 + 0.342809i
\(424\) −5.00753 2.89110i −0.243187 0.140404i
\(425\) −0.402237 + 0.232232i −0.0195114 + 0.0112649i
\(426\) −3.76562 + 2.17408i −0.182445 + 0.105335i
\(427\) −1.36620 0.788777i −0.0661151 0.0381716i
\(428\) 7.54260 13.0642i 0.364585 0.631480i
\(429\) −3.02702 1.74765i −0.146146 0.0843774i
\(430\) 1.04652i 0.0504677i
\(431\) 34.4243 19.8749i 1.65816 0.957341i 0.684600 0.728919i \(-0.259977\pi\)
0.973562 0.228422i \(-0.0733565\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 2.97177 0.142814 0.0714070 0.997447i \(-0.477251\pi\)
0.0714070 + 0.997447i \(0.477251\pi\)
\(434\) 0.710949 0.0341267
\(435\) −2.69215 + 4.66294i −0.129079 + 0.223571i
\(436\) 4.43512i 0.212404i
\(437\) −9.76078 16.9062i −0.466921 0.808732i
\(438\) 1.60237i 0.0765642i
\(439\) 6.90136 3.98450i 0.329384 0.190170i −0.326184 0.945306i \(-0.605763\pi\)
0.655568 + 0.755137i \(0.272429\pi\)
\(440\) 2.72213 + 4.71487i 0.129773 + 0.224773i
\(441\) 3.35660 + 5.81380i 0.159838 + 0.276848i
\(442\) 0.258243 + 0.149096i 0.0122834 + 0.00709180i
\(443\) −34.0828 −1.61932 −0.809662 0.586897i \(-0.800349\pi\)
−0.809662 + 0.586897i \(0.800349\pi\)
\(444\) 2.20510 5.66900i 0.104650 0.269039i
\(445\) −4.26206 −0.202041
\(446\) 7.05269 + 4.07187i 0.333955 + 0.192809i
\(447\) 4.11369 + 7.12511i 0.194571 + 0.337006i
\(448\) 0.267768 + 0.463788i 0.0126509 + 0.0219119i
\(449\) 24.4617 14.1230i 1.15442 0.666505i 0.204460 0.978875i \(-0.434456\pi\)
0.949961 + 0.312370i \(0.101123\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 26.4874 + 45.8775i 1.24724 + 2.16029i
\(452\) 8.98588i 0.422660i
\(453\) −4.98628 + 8.63648i −0.234276 + 0.405777i
\(454\) 3.92552 0.184234
\(455\) 0.343823 0.0161187
\(456\) 4.11142 7.12118i 0.192535 0.333480i
\(457\) −26.8664 + 15.5113i −1.25676 + 0.725588i −0.972442 0.233143i \(-0.925099\pi\)
−0.284313 + 0.958731i \(0.591766\pi\)
\(458\) 27.1986i 1.27091i
\(459\) −0.402237 0.232232i −0.0187748 0.0108396i
\(460\) 1.18703 2.05600i 0.0553457 0.0958616i
\(461\) −3.95564 2.28379i −0.184233 0.106367i 0.405047 0.914296i \(-0.367255\pi\)
−0.589280 + 0.807929i \(0.700588\pi\)
\(462\) 2.52499 1.45780i 0.117473 0.0678230i
\(463\) −5.59102 + 3.22798i −0.259837 + 0.150017i −0.624260 0.781217i \(-0.714599\pi\)
0.364423 + 0.931233i \(0.381266\pi\)
\(464\) −4.66294 2.69215i −0.216472 0.124980i
\(465\) 0.663773 1.14969i 0.0307817 0.0533155i
\(466\) −9.61564 5.55159i −0.445436 0.257173i
\(467\) 22.5295i 1.04254i 0.853391 + 0.521271i \(0.174542\pi\)
−0.853391 + 0.521271i \(0.825458\pi\)
\(468\) −0.556002 + 0.321008i −0.0257012 + 0.0148386i
\(469\) −1.09704 + 1.90013i −0.0506566 + 0.0877398i
\(470\) 8.14127 0.375529
\(471\) 5.76767 0.265760
\(472\) 5.90190 10.2224i 0.271657 0.470524i
\(473\) 5.69754i 0.261973i
\(474\) −2.01228 3.48536i −0.0924269 0.160088i
\(475\) 8.22283i 0.377290i
\(476\) −0.215413 + 0.124369i −0.00987342 + 0.00570042i
\(477\) 2.89110 + 5.00753i 0.132374 + 0.229279i
\(478\) 4.97351 + 8.61437i 0.227483 + 0.394012i
\(479\) −7.02757 4.05737i −0.321098 0.185386i 0.330784 0.943706i \(-0.392687\pi\)
−0.651882 + 0.758321i \(0.726020\pi\)
\(480\) 1.00000 0.0456435
\(481\) 3.04583 2.44412i 0.138878 0.111442i
\(482\) 21.6075 0.984196
\(483\) −1.10106 0.635700i −0.0501002 0.0289253i
\(484\) 9.32000 + 16.1427i 0.423636 + 0.733760i
\(485\) −2.71977 4.71079i −0.123499 0.213906i
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 5.69618i 0.258118i 0.991637 + 0.129059i \(0.0411957\pi\)
−0.991637 + 0.129059i \(0.958804\pi\)
\(488\) −1.47287 2.55109i −0.0666738 0.115482i
\(489\) 0.590991i 0.0267255i
\(490\) 3.35660 5.81380i 0.151636 0.262641i
\(491\) 26.7699 1.20811 0.604054 0.796943i \(-0.293551\pi\)
0.604054 + 0.796943i \(0.293551\pi\)
\(492\) 9.73039 0.438680
\(493\) 1.25041 2.16577i 0.0563155 0.0975413i
\(494\) 4.57191 2.63960i 0.205700 0.118761i
\(495\) 5.44426i 0.244701i
\(496\) 1.14969 + 0.663773i 0.0516225 + 0.0298043i
\(497\) 1.16430 2.01663i 0.0522260 0.0904581i
\(498\) 6.26008 + 3.61426i 0.280521 + 0.161959i
\(499\) 37.4524 21.6232i 1.67660 0.967986i 0.712800 0.701368i \(-0.247427\pi\)
0.963802 0.266619i \(-0.0859064\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) 8.80330 + 5.08259i 0.393302 + 0.227073i
\(502\) −2.55213 + 4.42041i −0.113907 + 0.197293i
\(503\) −7.54680 4.35715i −0.336495 0.194276i 0.322226 0.946663i \(-0.395569\pi\)
−0.658721 + 0.752387i \(0.728902\pi\)
\(504\) 0.535537i 0.0238547i
\(505\) −7.92857 + 4.57756i −0.352817 + 0.203699i
\(506\) 6.46252 11.1934i 0.287294 0.497608i
\(507\) 12.5878 0.559045
\(508\) 11.9101 0.528427
\(509\) 21.0800 36.5117i 0.934356 1.61835i 0.158579 0.987346i \(-0.449309\pi\)
0.775778 0.631007i \(-0.217358\pi\)
\(510\) 0.464463i 0.0205668i
\(511\) 0.429064 + 0.743160i 0.0189807 + 0.0328755i
\(512\) 1.00000i 0.0441942i
\(513\) −7.12118 + 4.11142i −0.314408 + 0.181524i
\(514\) −9.72782 16.8491i −0.429076 0.743181i
\(515\) −5.26575 9.12055i −0.232037 0.401900i
\(516\) −0.906314 0.523261i −0.0398982 0.0230353i
\(517\) 44.3232 1.94933
\(518\) 0.495276 + 3.21967i 0.0217612 + 0.141464i
\(519\) 15.4084 0.676354
\(520\) 0.556002 + 0.321008i 0.0243823 + 0.0140771i
\(521\) 18.1567 + 31.4484i 0.795461 + 1.37778i 0.922546 + 0.385887i \(0.126104\pi\)
−0.127086 + 0.991892i \(0.540562\pi\)
\(522\) 2.69215 + 4.66294i 0.117832 + 0.204092i
\(523\) −11.5606 + 6.67449i −0.505508 + 0.291855i −0.730985 0.682393i \(-0.760939\pi\)
0.225477 + 0.974248i \(0.427606\pi\)
\(524\) 8.45692i 0.369442i
\(525\) 0.267768 + 0.463788i 0.0116864 + 0.0202414i
\(526\) 12.0863i 0.526990i
\(527\) −0.308298 + 0.533988i −0.0134297 + 0.0232609i
\(528\) 5.44426 0.236931
\(529\) 17.3638 0.754948
\(530\) 2.89110 5.00753i 0.125581 0.217513i
\(531\) −10.2224 + 5.90190i −0.443614 + 0.256121i
\(532\) 4.40363i 0.190922i
\(533\) 5.41012 + 3.12353i 0.234338 + 0.135295i
\(534\) −2.13103 + 3.69105i −0.0922187 + 0.159728i
\(535\) 13.0642 + 7.54260i 0.564813 + 0.326095i
\(536\) −3.54808 + 2.04849i −0.153254 + 0.0884812i
\(537\) −6.85171 + 3.95584i −0.295673 + 0.170707i
\(538\) 24.0875 + 13.9069i 1.03849 + 0.599570i
\(539\) 18.2742 31.6519i 0.787126 1.36334i
\(540\) −0.866025 0.500000i −0.0372678 0.0215166i
\(541\) 28.8021i 1.23830i −0.785273 0.619150i \(-0.787477\pi\)
0.785273 0.619150i \(-0.212523\pi\)
\(542\) −4.64744 + 2.68320i −0.199625 + 0.115253i
\(543\) 4.86182 8.42093i 0.208641 0.361377i
\(544\) −0.464463 −0.0199137
\(545\) −4.43512 −0.189980
\(546\) 0.171911 0.297759i 0.00735713 0.0127429i
\(547\) 11.5425i 0.493524i 0.969076 + 0.246762i \(0.0793665\pi\)
−0.969076 + 0.246762i \(0.920633\pi\)
\(548\) 9.89749 + 17.1430i 0.422800 + 0.732311i
\(549\) 2.94574i 0.125721i
\(550\) −4.71487 + 2.72213i −0.201043 + 0.116072i
\(551\) −22.1371 38.3426i −0.943073 1.63345i
\(552\) −1.18703 2.05600i −0.0505235 0.0875093i
\(553\) 1.86654 + 1.07765i 0.0793733 + 0.0458262i
\(554\) 10.8265 0.459974
\(555\) 5.66900 + 2.20510i 0.240635 + 0.0936014i
\(556\) −7.33134 −0.310918
\(557\) −19.0151 10.9784i −0.805694 0.465168i 0.0397643 0.999209i \(-0.487339\pi\)
−0.845458 + 0.534041i \(0.820673\pi\)
\(558\) −0.663773 1.14969i −0.0280997 0.0486702i
\(559\) −0.335942 0.581868i −0.0142088 0.0246104i
\(560\) −0.463788 + 0.267768i −0.0195986 + 0.0113153i
\(561\) 2.52866i 0.106760i
\(562\) −7.36363 12.7542i −0.310616 0.538003i
\(563\) 35.3758i 1.49091i −0.666555 0.745456i \(-0.732232\pi\)
0.666555 0.745456i \(-0.267768\pi\)
\(564\) 4.07063 7.05055i 0.171405 0.296882i
\(565\) −8.98588 −0.378039
\(566\) −19.0840 −0.802159
\(567\) −0.267768 + 0.463788i −0.0112452 + 0.0194773i
\(568\) 3.76562 2.17408i 0.158002 0.0912225i
\(569\) 0.0883529i 0.00370395i 0.999998 + 0.00185197i \(0.000589502\pi\)
−0.999998 + 0.00185197i \(0.999410\pi\)
\(570\) 7.12118 + 4.11142i 0.298274 + 0.172208i
\(571\) −21.1519 + 36.6361i −0.885177 + 1.53317i −0.0396672 + 0.999213i \(0.512630\pi\)
−0.845510 + 0.533959i \(0.820704\pi\)
\(572\) 3.02702 + 1.74765i 0.126566 + 0.0730730i
\(573\) −13.8689 + 8.00719i −0.579380 + 0.334505i
\(574\) −4.51284 + 2.60549i −0.188362 + 0.108751i
\(575\) 2.05600 + 1.18703i 0.0857412 + 0.0495027i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −21.4986 12.4122i −0.895000 0.516729i −0.0194254 0.999811i \(-0.506184\pi\)
−0.875575 + 0.483083i \(0.839517\pi\)
\(578\) 16.7843i 0.698134i
\(579\) −14.9525 + 8.63282i −0.621404 + 0.358768i
\(580\) 2.69215 4.66294i 0.111786 0.193618i
\(581\) −3.87113 −0.160602
\(582\) −5.43955 −0.225477
\(583\) 15.7399 27.2623i 0.651880 1.12909i
\(584\) 1.60237i 0.0663065i
\(585\) −0.321008 0.556002i −0.0132720 0.0229879i
\(586\) 2.55273i 0.105452i
\(587\) −27.7557 + 16.0248i −1.14560 + 0.661412i −0.947811 0.318832i \(-0.896709\pi\)
−0.197789 + 0.980245i \(0.563376\pi\)
\(588\) −3.35660 5.81380i −0.138424 0.239757i
\(589\) 5.45809 + 9.45370i 0.224897 + 0.389533i
\(590\) 10.2224 + 5.90190i 0.420849 + 0.242978i
\(591\) 24.3971 1.00356
\(592\) −2.20510 + 5.66900i −0.0906292 + 0.232994i
\(593\) 38.7563 1.59153 0.795765 0.605606i \(-0.207069\pi\)
0.795765 + 0.605606i \(0.207069\pi\)
\(594\) −4.71487 2.72213i −0.193453 0.111690i
\(595\) −0.124369 0.215413i −0.00509861 0.00883106i
\(596\) −4.11369 7.12511i −0.168503 0.291856i
\(597\) 0.715751 0.413239i 0.0292937 0.0169127i
\(598\) 1.52419i 0.0623287i
\(599\) −11.6301 20.1440i −0.475194 0.823060i 0.524402 0.851471i \(-0.324289\pi\)
−0.999596 + 0.0284104i \(0.990955\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) 7.34067 12.7144i 0.299432 0.518631i −0.676574 0.736375i \(-0.736536\pi\)
0.976006 + 0.217743i \(0.0698695\pi\)
\(602\) 0.560450 0.0228422
\(603\) 4.09698 0.166842
\(604\) 4.98628 8.63648i 0.202889 0.351414i
\(605\) −16.1427 + 9.32000i −0.656295 + 0.378912i
\(606\) 9.15512i 0.371902i
\(607\) 11.9650 + 6.90802i 0.485646 + 0.280388i 0.722766 0.691093i \(-0.242870\pi\)
−0.237121 + 0.971480i \(0.576204\pi\)
\(608\) −4.11142 + 7.12118i −0.166740 + 0.288802i
\(609\) −2.49718 1.44175i −0.101191 0.0584225i
\(610\) 2.55109 1.47287i 0.103291 0.0596348i
\(611\) 4.52656 2.61341i 0.183125 0.105727i
\(612\) 0.402237 + 0.232232i 0.0162595 + 0.00938741i
\(613\) −9.87091 + 17.0969i −0.398682 + 0.690538i −0.993564 0.113276i \(-0.963866\pi\)
0.594881 + 0.803814i \(0.297199\pi\)
\(614\) 1.38585 + 0.800120i 0.0559283 + 0.0322902i
\(615\) 9.73039i 0.392367i
\(616\) −2.52499 + 1.45780i −0.101735 + 0.0587365i
\(617\) 7.09744 12.2931i 0.285732 0.494903i −0.687054 0.726606i \(-0.741097\pi\)
0.972786 + 0.231703i \(0.0744299\pi\)
\(618\) −10.5315 −0.423639
\(619\) −16.2904 −0.654768 −0.327384 0.944891i \(-0.606167\pi\)
−0.327384 + 0.944891i \(0.606167\pi\)
\(620\) −0.663773 + 1.14969i −0.0266578 + 0.0461726i
\(621\) 2.37407i 0.0952680i
\(622\) 2.54702 + 4.41158i 0.102126 + 0.176888i
\(623\) 2.28249i 0.0914460i
\(624\) 0.556002 0.321008i 0.0222579 0.0128506i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 1.15995 + 2.00909i 0.0463609 + 0.0802994i
\(627\) 38.7696 + 22.3836i 1.54831 + 0.893916i
\(628\) −5.76767 −0.230155
\(629\) −2.63304 1.02419i −0.104986 0.0408371i
\(630\) 0.535537 0.0213363
\(631\) −24.7908 14.3130i −0.986907 0.569791i −0.0825589 0.996586i \(-0.526309\pi\)
−0.904348 + 0.426795i \(0.859643\pi\)
\(632\) 2.01228 + 3.48536i 0.0800440 + 0.138640i
\(633\) −2.35375 4.07681i −0.0935530 0.162039i
\(634\) −11.1235 + 6.42213i −0.441769 + 0.255055i
\(635\) 11.9101i 0.472639i
\(636\) −2.89110 5.00753i −0.114640 0.198562i
\(637\) 4.30998i 0.170768i
\(638\) 14.6568 25.3863i 0.580268 1.00505i
\(639\) −4.34816 −0.172011
\(640\) −1.00000 −0.0395285
\(641\) −19.3732 + 33.5553i −0.765194 + 1.32535i 0.174950 + 0.984577i \(0.444024\pi\)
−0.940144 + 0.340777i \(0.889310\pi\)
\(642\) 13.0642 7.54260i 0.515601 0.297683i
\(643\) 48.8691i 1.92721i −0.267331 0.963605i \(-0.586142\pi\)
0.267331 0.963605i \(-0.413858\pi\)
\(644\) 1.10106 + 0.635700i 0.0433880 + 0.0250501i
\(645\) 0.523261 0.906314i 0.0206034 0.0356861i
\(646\) −3.30753 1.90960i −0.130133 0.0751323i
\(647\) 34.6610 20.0115i 1.36266 0.786734i 0.372685 0.927958i \(-0.378437\pi\)
0.989978 + 0.141224i \(0.0451037\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 55.6534 + 32.1315i 2.18459 + 1.26127i
\(650\) −0.321008 + 0.556002i −0.0125910 + 0.0218082i
\(651\) 0.615700 + 0.355475i 0.0241312 + 0.0139321i
\(652\) 0.590991i 0.0231450i
\(653\) −27.2595 + 15.7383i −1.06675 + 0.615886i −0.927291 0.374342i \(-0.877869\pi\)
−0.139456 + 0.990228i \(0.544535\pi\)
\(654\) −2.21756 + 3.84093i −0.0867135 + 0.150192i
\(655\) −8.45692 −0.330439
\(656\) −9.73039 −0.379908
\(657\) 0.801185 1.38769i 0.0312572 0.0541391i
\(658\) 4.35995i 0.169968i
\(659\) −11.9225 20.6504i −0.464436 0.804426i 0.534740 0.845016i \(-0.320409\pi\)
−0.999176 + 0.0405905i \(0.987076\pi\)
\(660\) 5.44426i 0.211918i
\(661\) −1.01438 + 0.585655i −0.0394550 + 0.0227793i −0.519598 0.854411i \(-0.673918\pi\)
0.480143 + 0.877190i \(0.340585\pi\)
\(662\) 3.58212 + 6.20441i 0.139223 + 0.241141i
\(663\) 0.149096 + 0.258243i 0.00579043 + 0.0100293i
\(664\) −6.26008 3.61426i −0.242938 0.140260i
\(665\) −4.40363 −0.170765
\(666\) 4.74417 3.80694i 0.183833 0.147516i
\(667\) −12.7827 −0.494948
\(668\) −8.80330 5.08259i −0.340610 0.196651i
\(669\) 4.07187 + 7.05269i 0.157428 + 0.272673i
\(670\) −2.04849 3.54808i −0.0791400 0.137074i
\(671\) 13.8888 8.01870i 0.536171 0.309559i
\(672\) 0.535537i 0.0206588i
\(673\) 19.1006 + 33.0832i 0.736273 + 1.27526i 0.954163 + 0.299289i \(0.0967493\pi\)
−0.217890 + 0.975973i \(0.569917\pi\)
\(674\) 22.9013i 0.882126i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) −12.5878 −0.484147
\(677\) −27.9347 −1.07362 −0.536808 0.843704i \(-0.680370\pi\)
−0.536808 + 0.843704i \(0.680370\pi\)
\(678\) −4.49294 + 7.78200i −0.172550 + 0.298866i
\(679\) 2.52280 1.45654i 0.0968161 0.0558968i
\(680\) 0.464463i 0.0178114i
\(681\) 3.39960 + 1.96276i 0.130273 + 0.0752131i
\(682\) −3.61375 + 6.25920i −0.138378 + 0.239677i
\(683\) 17.2614 + 9.96585i 0.660487 + 0.381333i 0.792463 0.609920i \(-0.208799\pi\)
−0.131975 + 0.991253i \(0.542132\pi\)
\(684\) 7.12118 4.11142i 0.272285 0.157204i
\(685\) −17.1430 + 9.89749i −0.654999 + 0.378164i
\(686\) 6.36002 + 3.67196i 0.242827 + 0.140196i
\(687\) 13.5993 23.5547i 0.518846 0.898667i
\(688\) 0.906314 + 0.523261i 0.0345529 + 0.0199491i
\(689\) 3.71226i 0.141426i
\(690\) 2.05600 1.18703i 0.0782707 0.0451896i
\(691\) −6.02368 + 10.4333i −0.229152 + 0.396902i −0.957557 0.288244i \(-0.906929\pi\)
0.728405 + 0.685147i \(0.240262\pi\)
\(692\) −15.4084 −0.585739
\(693\) 2.91560 0.110755
\(694\) 13.7693 23.8491i 0.522674 0.905298i
\(695\) 7.33134i 0.278094i
\(696\) −2.69215 4.66294i −0.102046 0.176748i
\(697\) 4.51941i 0.171185i
\(698\) 20.4892 11.8294i 0.775528 0.447751i
\(699\) −5.55159 9.61564i −0.209980 0.363697i
\(700\) −0.267768 0.463788i −0.0101207 0.0175295i
\(701\) 34.1895 + 19.7393i 1.29132 + 0.745543i 0.978888 0.204398i \(-0.0655236\pi\)
0.312430 + 0.949941i \(0.398857\pi\)
\(702\) −0.642016 −0.0242313
\(703\) −39.0106 + 31.3039i −1.47131 + 1.18065i
\(704\) −5.44426 −0.205188
\(705\) 7.05055 + 4.07063i 0.265539 + 0.153309i
\(706\) 2.74097 + 4.74750i 0.103158 + 0.178674i
\(707\) −2.45145 4.24604i −0.0921963 0.159689i
\(708\) 10.2224 5.90190i 0.384181 0.221807i
\(709\) 14.5551i 0.546630i −0.961925 0.273315i \(-0.911880\pi\)
0.961925 0.273315i \(-0.0881202\pi\)
\(710\) 2.17408 + 3.76562i 0.0815918 + 0.141321i
\(711\) 4.02455i 0.150932i
\(712\) 2.13103 3.69105i 0.0798638 0.138328i
\(713\) 3.15168 0.118031
\(714\) −0.248737 −0.00930875
\(715\) −1.74765 + 3.02702i −0.0653585 + 0.113204i
\(716\) 6.85171 3.95584i 0.256061 0.147837i
\(717\) 9.94702i 0.371478i
\(718\) 17.5403 + 10.1269i 0.654597 + 0.377932i
\(719\) 3.55656 6.16015i 0.132637 0.229735i −0.792055 0.610450i \(-0.790989\pi\)
0.924692 + 0.380715i \(0.124322\pi\)
\(720\) 0.866025 + 0.500000i 0.0322749 + 0.0186339i
\(721\) 4.88439 2.82000i 0.181904 0.105022i
\(722\) −42.1018 + 24.3075i −1.56687 + 0.904632i
\(723\) 18.7127 + 10.8038i 0.695932 + 0.401797i
\(724\) −4.86182 + 8.42093i −0.180688 + 0.312961i
\(725\) 4.66294 + 2.69215i 0.173177 + 0.0999840i
\(726\) 18.6400i 0.691795i
\(727\) 23.4383 13.5321i 0.869277 0.501877i 0.00216883 0.999998i \(-0.499310\pi\)
0.867108 + 0.498121i \(0.165976\pi\)
\(728\) −0.171911 + 0.297759i −0.00637146 + 0.0110357i
\(729\) 1.00000 0.0370370
\(730\) −1.60237 −0.0593064
\(731\) −0.243035 + 0.420950i −0.00898899 + 0.0155694i
\(732\) 2.94574i 0.108878i
\(733\) −26.0354 45.0947i −0.961641 1.66561i −0.718382 0.695649i \(-0.755117\pi\)
−0.243259 0.969961i \(-0.578217\pi\)
\(734\) 29.1273i 1.07511i
\(735\) 5.81380 3.35660i 0.214445 0.123810i
\(736\) 1.18703 + 2.05600i 0.0437546 + 0.0757852i
\(737\) −11.1525 19.3167i −0.410808 0.711540i
\(738\) 8.42677 + 4.86520i 0.310194 + 0.179090i
\(739\) 24.0955 0.886369 0.443184 0.896430i \(-0.353849\pi\)
0.443184 + 0.896430i \(0.353849\pi\)
\(740\) −5.66900 2.20510i −0.208396 0.0810612i
\(741\) 5.27919 0.193936
\(742\) 2.68172 + 1.54829i 0.0984489 + 0.0568395i
\(743\) 5.81888 + 10.0786i 0.213474 + 0.369748i 0.952799 0.303601i \(-0.0981888\pi\)
−0.739325 + 0.673348i \(0.764856\pi\)
\(744\) 0.663773 + 1.14969i 0.0243351 + 0.0421496i
\(745\) 7.12511 4.11369i 0.261044 0.150714i
\(746\) 36.1494i 1.32352i
\(747\) 3.61426 + 6.26008i 0.132239 + 0.229044i
\(748\) 2.52866i 0.0924570i
\(749\) −4.03934 + 6.99633i −0.147594 + 0.255641i
\(750\) −1.00000 −0.0365148
\(751\) −31.7490 −1.15854 −0.579268 0.815137i \(-0.696662\pi\)
−0.579268 + 0.815137i \(0.696662\pi\)
\(752\) −4.07063 + 7.05055i −0.148441 + 0.257107i
\(753\) −4.42041 + 2.55213i −0.161089 + 0.0930046i
\(754\) 3.45681i 0.125890i
\(755\) 8.63648 + 4.98628i 0.314314 + 0.181469i
\(756\) 0.267768 0.463788i 0.00973864 0.0168678i
\(757\) 11.4286 + 6.59830i 0.415379 + 0.239819i 0.693098 0.720843i \(-0.256245\pi\)
−0.277719 + 0.960662i \(0.589578\pi\)
\(758\) −18.8055 + 10.8574i −0.683048 + 0.394358i
\(759\) 11.1934 6.46252i 0.406295 0.234575i
\(760\) −7.12118 4.11142i −0.258312 0.149137i
\(761\) 4.53306 7.85149i 0.164323 0.284616i −0.772091 0.635511i \(-0.780789\pi\)
0.936415 + 0.350895i \(0.114123\pi\)
\(762\) 10.3145 + 5.95507i 0.373654 + 0.215729i
\(763\) 2.37517i 0.0859869i
\(764\) 13.8689 8.00719i 0.501758 0.289690i
\(765\) −0.232232 + 0.402237i −0.00839636 + 0.0145429i
\(766\) 32.2698 1.16596
\(767\) 7.57823 0.273634
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 18.2259i 0.657241i 0.944462 + 0.328621i \(0.106584\pi\)
−0.944462 + 0.328621i \(0.893416\pi\)
\(770\) −1.45780 2.52499i −0.0525355 0.0909941i
\(771\) 19.4556i 0.700678i
\(772\) 14.9525 8.63282i 0.538152 0.310702i
\(773\) 7.27509 + 12.6008i 0.261667 + 0.453220i 0.966685 0.255969i \(-0.0823946\pi\)
−0.705018 + 0.709189i \(0.749061\pi\)
\(774\) −0.523261 0.906314i −0.0188082 0.0325768i
\(775\) −1.14969 0.663773i −0.0412980 0.0238434i
\(776\) 5.43955 0.195268