Properties

Label 24.3.b.a.19.1
Level 24
Weight 3
Character 24.19
Analytic conductor 0.654
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 24.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.653952634465\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.4752.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.1
Root \(0.866025 - 0.719687i\)
Character \(\chi\) = 24.19
Dual form 24.3.b.a.19.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-0.366025 - 1.96622i) q^{2}\) \(+1.73205 q^{3}\) \(+(-3.73205 + 1.43937i) q^{4}\) \(-2.87875i q^{5}\) \(+(-0.633975 - 3.40559i) q^{6}\) \(+10.7436i q^{7}\) \(+(4.19615 + 6.81119i) q^{8}\) \(+3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+(-0.366025 - 1.96622i) q^{2}\) \(+1.73205 q^{3}\) \(+(-3.73205 + 1.43937i) q^{4}\) \(-2.87875i q^{5}\) \(+(-0.633975 - 3.40559i) q^{6}\) \(+10.7436i q^{7}\) \(+(4.19615 + 6.81119i) q^{8}\) \(+3.00000 q^{9}\) \(+(-5.66025 + 1.05369i) q^{10}\) \(-8.00000 q^{11}\) \(+(-6.46410 + 2.49307i) q^{12}\) \(-15.7298i q^{13}\) \(+(21.1244 - 3.93244i) q^{14}\) \(-4.98614i q^{15}\) \(+(11.8564 - 10.7436i) q^{16}\) \(-15.8564 q^{17}\) \(+(-1.09808 - 5.89866i) q^{18}\) \(+1.07180 q^{19}\) \(+(4.14359 + 10.7436i) q^{20}\) \(+18.6085i q^{21}\) \(+(2.92820 + 15.7298i) q^{22}\) \(-21.4873i q^{23}\) \(+(7.26795 + 11.7973i) q^{24}\) \(+16.7128 q^{25}\) \(+(-30.9282 + 5.75749i) q^{26}\) \(+5.19615 q^{27}\) \(+(-15.4641 - 40.0958i) q^{28}\) \(+40.0958i q^{29}\) \(+(-9.80385 + 1.82505i) q^{30}\) \(+9.20092i q^{31}\) \(+(-25.4641 - 19.3799i) q^{32}\) \(-13.8564 q^{33}\) \(+(5.80385 + 31.1772i) q^{34}\) \(+30.9282 q^{35}\) \(+(-11.1962 + 4.31812i) q^{36}\) \(-9.97227i q^{37}\) \(+(-0.392305 - 2.10739i) q^{38}\) \(-27.2448i q^{39}\) \(+(19.6077 - 12.0797i) q^{40}\) \(+51.5692 q^{41}\) \(+(36.5885 - 6.81119i) q^{42}\) \(-12.7846 q^{43}\) \(+(29.8564 - 11.5150i) q^{44}\) \(-8.63624i q^{45}\) \(+(-42.2487 + 7.86488i) q^{46}\) \(+1.54272i q^{47}\) \(+(20.5359 - 18.6085i) q^{48}\) \(-66.4256 q^{49}\) \(+(-6.11731 - 32.8611i) q^{50}\) \(-27.4641 q^{51}\) \(+(22.6410 + 58.7043i) q^{52}\) \(-28.5808i q^{53}\) \(+(-1.90192 - 10.2168i) q^{54}\) \(+23.0300i q^{55}\) \(+(-73.1769 + 45.0819i) q^{56}\) \(+1.85641 q^{57}\) \(+(78.8372 - 14.6761i) q^{58}\) \(-11.2154 q^{59}\) \(+(7.17691 + 18.6085i) q^{60}\) \(-1.54272i q^{61}\) \(+(18.0910 - 3.36777i) q^{62}\) \(+32.2309i q^{63}\) \(+(-28.7846 + 57.1616i) q^{64}\) \(-45.2820 q^{65}\) \(+(5.07180 + 27.2448i) q^{66}\) \(-43.2154 q^{67}\) \(+(59.1769 - 22.8233i) q^{68}\) \(-37.2170i q^{69}\) \(+(-11.3205 - 60.8117i) q^{70}\) \(+84.4063i q^{71}\) \(+(12.5885 + 20.4336i) q^{72}\) \(+105.426 q^{73}\) \(+(-19.6077 + 3.65011i) q^{74}\) \(+28.9474 q^{75}\) \(+(-4.00000 + 1.54272i) q^{76}\) \(-85.9491i q^{77}\) \(+(-53.5692 + 9.97227i) q^{78}\) \(-73.6627i q^{79}\) \(+(-30.9282 - 34.1316i) q^{80}\) \(+9.00000 q^{81}\) \(+(-18.8756 - 101.396i) q^{82}\) \(+12.2872 q^{83}\) \(+(-26.7846 - 69.4479i) q^{84}\) \(+45.6466i q^{85}\) \(+(4.67949 + 25.1374i) q^{86}\) \(+69.4479i q^{87}\) \(+(-33.5692 - 54.4895i) q^{88}\) \(+33.1384 q^{89}\) \(+(-16.9808 + 3.16108i) q^{90}\) \(+168.995 q^{91}\) \(+(30.9282 + 80.1916i) q^{92}\) \(+15.9365i q^{93}\) \(+(3.03332 - 0.564673i) q^{94}\) \(-3.08543i q^{95}\) \(+(-44.1051 - 33.5669i) q^{96}\) \(-69.1384 q^{97}\) \(+(24.3135 + 130.607i) q^{98}\) \(-24.0000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 36q^{14} \) \(\mathstrut -\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 32q^{19} \) \(\mathstrut +\mathstrut 72q^{20} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut -\mathstrut 44q^{25} \) \(\mathstrut -\mathstrut 96q^{26} \) \(\mathstrut -\mathstrut 48q^{28} \) \(\mathstrut -\mathstrut 60q^{30} \) \(\mathstrut -\mathstrut 88q^{32} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 96q^{35} \) \(\mathstrut -\mathstrut 24q^{36} \) \(\mathstrut +\mathstrut 40q^{38} \) \(\mathstrut +\mathstrut 120q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 84q^{42} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 64q^{44} \) \(\mathstrut -\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 96q^{48} \) \(\mathstrut -\mathstrut 44q^{49} \) \(\mathstrut -\mathstrut 118q^{50} \) \(\mathstrut -\mathstrut 96q^{51} \) \(\mathstrut -\mathstrut 48q^{52} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 168q^{56} \) \(\mathstrut -\mathstrut 48q^{57} \) \(\mathstrut +\mathstrut 156q^{58} \) \(\mathstrut -\mathstrut 128q^{59} \) \(\mathstrut -\mathstrut 96q^{60} \) \(\mathstrut +\mathstrut 204q^{62} \) \(\mathstrut -\mathstrut 32q^{64} \) \(\mathstrut +\mathstrut 96q^{65} \) \(\mathstrut +\mathstrut 48q^{66} \) \(\mathstrut -\mathstrut 256q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut +\mathstrut 200q^{73} \) \(\mathstrut -\mathstrut 120q^{74} \) \(\mathstrut +\mathstrut 192q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 48q^{78} \) \(\mathstrut -\mathstrut 96q^{80} \) \(\mathstrut +\mathstrut 36q^{81} \) \(\mathstrut -\mathstrut 124q^{82} \) \(\mathstrut +\mathstrut 160q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut +\mathstrut 88q^{86} \) \(\mathstrut +\mathstrut 32q^{88} \) \(\mathstrut -\mathstrut 200q^{89} \) \(\mathstrut +\mathstrut 36q^{90} \) \(\mathstrut +\mathstrut 288q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut -\mathstrut 168q^{94} \) \(\mathstrut -\mathstrut 24q^{96} \) \(\mathstrut +\mathstrut 56q^{97} \) \(\mathstrut +\mathstrut 170q^{98} \) \(\mathstrut -\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 1.96622i −0.183013 0.983111i
\(3\) 1.73205 0.577350
\(4\) −3.73205 + 1.43937i −0.933013 + 0.359843i
\(5\) 2.87875i 0.575749i −0.957668 0.287875i \(-0.907051\pi\)
0.957668 0.287875i \(-0.0929487\pi\)
\(6\) −0.633975 3.40559i −0.105662 0.567599i
\(7\) 10.7436i 1.53480i 0.641166 + 0.767402i \(0.278451\pi\)
−0.641166 + 0.767402i \(0.721549\pi\)
\(8\) 4.19615 + 6.81119i 0.524519 + 0.851399i
\(9\) 3.00000 0.333333
\(10\) −5.66025 + 1.05369i −0.566025 + 0.105369i
\(11\) −8.00000 −0.727273 −0.363636 0.931541i \(-0.618465\pi\)
−0.363636 + 0.931541i \(0.618465\pi\)
\(12\) −6.46410 + 2.49307i −0.538675 + 0.207756i
\(13\) 15.7298i 1.20998i −0.796232 0.604991i \(-0.793177\pi\)
0.796232 0.604991i \(-0.206823\pi\)
\(14\) 21.1244 3.93244i 1.50888 0.280889i
\(15\) 4.98614i 0.332409i
\(16\) 11.8564 10.7436i 0.741025 0.671477i
\(17\) −15.8564 −0.932730 −0.466365 0.884592i \(-0.654437\pi\)
−0.466365 + 0.884592i \(0.654437\pi\)
\(18\) −1.09808 5.89866i −0.0610042 0.327704i
\(19\) 1.07180 0.0564104 0.0282052 0.999602i \(-0.491021\pi\)
0.0282052 + 0.999602i \(0.491021\pi\)
\(20\) 4.14359 + 10.7436i 0.207180 + 0.537182i
\(21\) 18.6085i 0.886120i
\(22\) 2.92820 + 15.7298i 0.133100 + 0.714989i
\(23\) 21.4873i 0.934229i −0.884197 0.467114i \(-0.845294\pi\)
0.884197 0.467114i \(-0.154706\pi\)
\(24\) 7.26795 + 11.7973i 0.302831 + 0.491555i
\(25\) 16.7128 0.668513
\(26\) −30.9282 + 5.75749i −1.18955 + 0.221442i
\(27\) 5.19615 0.192450
\(28\) −15.4641 40.0958i −0.552289 1.43199i
\(29\) 40.0958i 1.38261i 0.722562 + 0.691307i \(0.242965\pi\)
−0.722562 + 0.691307i \(0.757035\pi\)
\(30\) −9.80385 + 1.82505i −0.326795 + 0.0608351i
\(31\) 9.20092i 0.296804i 0.988927 + 0.148402i \(0.0474129\pi\)
−0.988927 + 0.148402i \(0.952587\pi\)
\(32\) −25.4641 19.3799i −0.795753 0.605621i
\(33\) −13.8564 −0.419891
\(34\) 5.80385 + 31.1772i 0.170701 + 0.916976i
\(35\) 30.9282 0.883663
\(36\) −11.1962 + 4.31812i −0.311004 + 0.119948i
\(37\) 9.97227i 0.269521i −0.990878 0.134760i \(-0.956974\pi\)
0.990878 0.134760i \(-0.0430265\pi\)
\(38\) −0.392305 2.10739i −0.0103238 0.0554576i
\(39\) 27.2448i 0.698584i
\(40\) 19.6077 12.0797i 0.490192 0.301992i
\(41\) 51.5692 1.25779 0.628893 0.777492i \(-0.283508\pi\)
0.628893 + 0.777492i \(0.283508\pi\)
\(42\) 36.5885 6.81119i 0.871154 0.162171i
\(43\) −12.7846 −0.297317 −0.148658 0.988889i \(-0.547495\pi\)
−0.148658 + 0.988889i \(0.547495\pi\)
\(44\) 29.8564 11.5150i 0.678555 0.261704i
\(45\) 8.63624i 0.191916i
\(46\) −42.2487 + 7.86488i −0.918450 + 0.170976i
\(47\) 1.54272i 0.0328237i 0.999865 + 0.0164119i \(0.00522430\pi\)
−0.999865 + 0.0164119i \(0.994776\pi\)
\(48\) 20.5359 18.6085i 0.427831 0.387677i
\(49\) −66.4256 −1.35563
\(50\) −6.11731 32.8611i −0.122346 0.657222i
\(51\) −27.4641 −0.538512
\(52\) 22.6410 + 58.7043i 0.435404 + 1.12893i
\(53\) 28.5808i 0.539260i −0.962964 0.269630i \(-0.913099\pi\)
0.962964 0.269630i \(-0.0869014\pi\)
\(54\) −1.90192 10.2168i −0.0352208 0.189200i
\(55\) 23.0300i 0.418727i
\(56\) −73.1769 + 45.0819i −1.30673 + 0.805034i
\(57\) 1.85641 0.0325685
\(58\) 78.8372 14.6761i 1.35926 0.253036i
\(59\) −11.2154 −0.190091 −0.0950457 0.995473i \(-0.530300\pi\)
−0.0950457 + 0.995473i \(0.530300\pi\)
\(60\) 7.17691 + 18.6085i 0.119615 + 0.310142i
\(61\) 1.54272i 0.0252904i −0.999920 0.0126452i \(-0.995975\pi\)
0.999920 0.0126452i \(-0.00402520\pi\)
\(62\) 18.0910 3.36777i 0.291791 0.0543189i
\(63\) 32.2309i 0.511602i
\(64\) −28.7846 + 57.1616i −0.449760 + 0.893150i
\(65\) −45.2820 −0.696647
\(66\) 5.07180 + 27.2448i 0.0768454 + 0.412799i
\(67\) −43.2154 −0.645006 −0.322503 0.946568i \(-0.604524\pi\)
−0.322503 + 0.946568i \(0.604524\pi\)
\(68\) 59.1769 22.8233i 0.870249 0.335637i
\(69\) 37.2170i 0.539377i
\(70\) −11.3205 60.8117i −0.161722 0.868738i
\(71\) 84.4063i 1.18882i 0.804162 + 0.594411i \(0.202615\pi\)
−0.804162 + 0.594411i \(0.797385\pi\)
\(72\) 12.5885 + 20.4336i 0.174840 + 0.283800i
\(73\) 105.426 1.44419 0.722093 0.691796i \(-0.243180\pi\)
0.722093 + 0.691796i \(0.243180\pi\)
\(74\) −19.6077 + 3.65011i −0.264969 + 0.0493258i
\(75\) 28.9474 0.385966
\(76\) −4.00000 + 1.54272i −0.0526316 + 0.0202989i
\(77\) 85.9491i 1.11622i
\(78\) −53.5692 + 9.97227i −0.686785 + 0.127850i
\(79\) 73.6627i 0.932439i −0.884669 0.466220i \(-0.845616\pi\)
0.884669 0.466220i \(-0.154384\pi\)
\(80\) −30.9282 34.1316i −0.386603 0.426645i
\(81\) 9.00000 0.111111
\(82\) −18.8756 101.396i −0.230191 1.23654i
\(83\) 12.2872 0.148038 0.0740192 0.997257i \(-0.476417\pi\)
0.0740192 + 0.997257i \(0.476417\pi\)
\(84\) −26.7846 69.4479i −0.318864 0.826761i
\(85\) 45.6466i 0.537019i
\(86\) 4.67949 + 25.1374i 0.0544127 + 0.292295i
\(87\) 69.4479i 0.798252i
\(88\) −33.5692 54.4895i −0.381468 0.619199i
\(89\) 33.1384 0.372342 0.186171 0.982517i \(-0.440392\pi\)
0.186171 + 0.982517i \(0.440392\pi\)
\(90\) −16.9808 + 3.16108i −0.188675 + 0.0351232i
\(91\) 168.995 1.85709
\(92\) 30.9282 + 80.1916i 0.336176 + 0.871647i
\(93\) 15.9365i 0.171360i
\(94\) 3.03332 0.564673i 0.0322694 0.00600716i
\(95\) 3.08543i 0.0324782i
\(96\) −44.1051 33.5669i −0.459428 0.349655i
\(97\) −69.1384 −0.712767 −0.356384 0.934340i \(-0.615990\pi\)
−0.356384 + 0.934340i \(0.615990\pi\)
\(98\) 24.3135 + 130.607i 0.248097 + 1.33273i
\(99\) −24.0000 −0.242424
\(100\) −62.3731 + 24.0560i −0.623731 + 0.240560i
\(101\) 97.2574i 0.962944i 0.876461 + 0.481472i \(0.159898\pi\)
−0.876461 + 0.481472i \(0.840102\pi\)
\(102\) 10.0526 + 54.0005i 0.0985545 + 0.529417i
\(103\) 139.667i 1.35599i −0.735065 0.677996i \(-0.762849\pi\)
0.735065 0.677996i \(-0.237151\pi\)
\(104\) 107.138 66.0045i 1.03018 0.634659i
\(105\) 53.5692 0.510183
\(106\) −56.1962 + 10.4613i −0.530152 + 0.0986915i
\(107\) −197.779 −1.84841 −0.924203 0.381901i \(-0.875269\pi\)
−0.924203 + 0.381901i \(0.875269\pi\)
\(108\) −19.3923 + 7.47921i −0.179558 + 0.0692519i
\(109\) 190.713i 1.74966i 0.484427 + 0.874832i \(0.339028\pi\)
−0.484427 + 0.874832i \(0.660972\pi\)
\(110\) 45.2820 8.42956i 0.411655 0.0766323i
\(111\) 17.2725i 0.155608i
\(112\) 115.426 + 127.381i 1.03059 + 1.13733i
\(113\) −113.713 −1.00631 −0.503154 0.864197i \(-0.667827\pi\)
−0.503154 + 0.864197i \(0.667827\pi\)
\(114\) −0.679492 3.65011i −0.00596046 0.0320185i
\(115\) −61.8564 −0.537882
\(116\) −57.7128 149.639i −0.497524 1.29000i
\(117\) 47.1893i 0.403327i
\(118\) 4.10512 + 22.0519i 0.0347891 + 0.186881i
\(119\) 170.355i 1.43156i
\(120\) 33.9615 20.9226i 0.283013 0.174355i
\(121\) −57.0000 −0.471074
\(122\) −3.03332 + 0.564673i −0.0248633 + 0.00462847i
\(123\) 89.3205 0.726183
\(124\) −13.2436 34.3383i −0.106803 0.276922i
\(125\) 120.081i 0.960645i
\(126\) 63.3731 11.7973i 0.502961 0.0936296i
\(127\) 36.8590i 0.290229i 0.989415 + 0.145114i \(0.0463550\pi\)
−0.989415 + 0.145114i \(0.953645\pi\)
\(128\) 122.928 + 35.6743i 0.960377 + 0.278706i
\(129\) −22.1436 −0.171656
\(130\) 16.5744 + 89.0345i 0.127495 + 0.684881i
\(131\) 194.641 1.48581 0.742905 0.669397i \(-0.233448\pi\)
0.742905 + 0.669397i \(0.233448\pi\)
\(132\) 51.7128 19.9445i 0.391764 0.151095i
\(133\) 11.5150i 0.0865789i
\(134\) 15.8179 + 84.9710i 0.118044 + 0.634112i
\(135\) 14.9584i 0.110803i
\(136\) −66.5359 108.001i −0.489235 0.794125i
\(137\) 16.4308 0.119933 0.0599664 0.998200i \(-0.480901\pi\)
0.0599664 + 0.998200i \(0.480901\pi\)
\(138\) −73.1769 + 13.6224i −0.530267 + 0.0987129i
\(139\) −113.492 −0.816491 −0.408246 0.912872i \(-0.633859\pi\)
−0.408246 + 0.912872i \(0.633859\pi\)
\(140\) −115.426 + 44.5172i −0.824469 + 0.317980i
\(141\) 2.67206i 0.0189508i
\(142\) 165.962 30.8949i 1.16874 0.217569i
\(143\) 125.838i 0.879987i
\(144\) 35.5692 32.2309i 0.247008 0.223826i
\(145\) 115.426 0.796039
\(146\) −38.5885 207.290i −0.264305 1.41980i
\(147\) −115.053 −0.782670
\(148\) 14.3538 + 37.2170i 0.0969853 + 0.251466i
\(149\) 31.6662i 0.212525i 0.994338 + 0.106262i \(0.0338884\pi\)
−0.994338 + 0.106262i \(0.966112\pi\)
\(150\) −10.5955 56.9171i −0.0706367 0.379447i
\(151\) 90.5218i 0.599482i 0.954021 + 0.299741i \(0.0969003\pi\)
−0.954021 + 0.299741i \(0.903100\pi\)
\(152\) 4.49742 + 7.30021i 0.0295883 + 0.0480277i
\(153\) −47.5692 −0.310910
\(154\) −168.995 + 31.4595i −1.09737 + 0.204283i
\(155\) 26.4871 0.170885
\(156\) 39.2154 + 101.679i 0.251381 + 0.651787i
\(157\) 231.016i 1.47144i −0.677287 0.735719i \(-0.736844\pi\)
0.677287 0.735719i \(-0.263156\pi\)
\(158\) −144.837 + 26.9624i −0.916691 + 0.170648i
\(159\) 49.5034i 0.311342i
\(160\) −55.7898 + 73.3047i −0.348686 + 0.458154i
\(161\) 230.851 1.43386
\(162\) −3.29423 17.6960i −0.0203347 0.109235i
\(163\) 22.3538 0.137140 0.0685700 0.997646i \(-0.478156\pi\)
0.0685700 + 0.997646i \(0.478156\pi\)
\(164\) −192.459 + 74.2274i −1.17353 + 0.452606i
\(165\) 39.8891i 0.241752i
\(166\) −4.49742 24.1593i −0.0270929 0.145538i
\(167\) 221.044i 1.32361i 0.749674 + 0.661807i \(0.230210\pi\)
−0.749674 + 0.661807i \(0.769790\pi\)
\(168\) −126.746 + 78.0842i −0.754441 + 0.464787i
\(169\) −78.4256 −0.464057
\(170\) 89.7513 16.7078i 0.527949 0.0982812i
\(171\) 3.21539 0.0188035
\(172\) 47.7128 18.4018i 0.277400 0.106987i
\(173\) 231.525i 1.33830i 0.743130 + 0.669148i \(0.233341\pi\)
−0.743130 + 0.669148i \(0.766659\pi\)
\(174\) 136.550 25.4197i 0.784770 0.146090i
\(175\) 179.556i 1.02604i
\(176\) −94.8513 + 85.9491i −0.538928 + 0.488347i
\(177\) −19.4256 −0.109749
\(178\) −12.1295 65.1575i −0.0681433 0.366053i
\(179\) 193.646 1.08182 0.540911 0.841080i \(-0.318080\pi\)
0.540911 + 0.841080i \(0.318080\pi\)
\(180\) 12.4308 + 32.2309i 0.0690599 + 0.179061i
\(181\) 270.492i 1.49443i −0.664583 0.747214i \(-0.731391\pi\)
0.664583 0.747214i \(-0.268609\pi\)
\(182\) −61.8564 332.281i −0.339870 1.82572i
\(183\) 2.67206i 0.0146014i
\(184\) 146.354 90.1638i 0.795401 0.490021i
\(185\) −28.7077 −0.155177
\(186\) 31.3346 5.83315i 0.168466 0.0313610i
\(187\) 126.851 0.678349
\(188\) −2.22055 5.75749i −0.0118114 0.0306250i
\(189\) 55.8255i 0.295373i
\(190\) −6.06664 + 1.12935i −0.0319297 + 0.00594393i
\(191\) 311.510i 1.63094i −0.578798 0.815471i \(-0.696478\pi\)
0.578798 0.815471i \(-0.303522\pi\)
\(192\) −49.8564 + 99.0068i −0.259669 + 0.515660i
\(193\) 48.2769 0.250139 0.125070 0.992148i \(-0.460085\pi\)
0.125070 + 0.992148i \(0.460085\pi\)
\(194\) 25.3064 + 135.941i 0.130445 + 0.700729i
\(195\) −78.4308 −0.402209
\(196\) 247.904 95.6113i 1.26482 0.487813i
\(197\) 251.883i 1.27859i −0.768960 0.639297i \(-0.779225\pi\)
0.768960 0.639297i \(-0.220775\pi\)
\(198\) 8.78461 + 47.1893i 0.0443667 + 0.238330i
\(199\) 72.1200i 0.362412i 0.983445 + 0.181206i \(0.0580001\pi\)
−0.983445 + 0.181206i \(0.942000\pi\)
\(200\) 70.1295 + 113.834i 0.350648 + 0.569171i
\(201\) −74.8513 −0.372394
\(202\) 191.229 35.5987i 0.946681 0.176231i
\(203\) −430.774 −2.12204
\(204\) 102.497 39.5311i 0.502438 0.193780i
\(205\) 148.455i 0.724170i
\(206\) −274.617 + 51.1217i −1.33309 + 0.248164i
\(207\) 64.4618i 0.311410i
\(208\) −168.995 186.499i −0.812475 0.896628i
\(209\) −8.57437 −0.0410257
\(210\) −19.6077 105.329i −0.0933700 0.501566i
\(211\) −264.918 −1.25554 −0.627768 0.778401i \(-0.716031\pi\)
−0.627768 + 0.778401i \(0.716031\pi\)
\(212\) 41.1384 + 106.665i 0.194049 + 0.503137i
\(213\) 146.196i 0.686367i
\(214\) 72.3923 + 388.878i 0.338282 + 1.81719i
\(215\) 36.8037i 0.171180i
\(216\) 21.8038 + 35.3920i 0.100944 + 0.163852i
\(217\) −98.8513 −0.455536
\(218\) 374.985 69.8059i 1.72011 0.320211i
\(219\) 182.603 0.833802
\(220\) −33.1487 85.9491i −0.150676 0.390678i
\(221\) 249.418i 1.12859i
\(222\) −33.9615 + 6.32217i −0.152980 + 0.0284782i
\(223\) 30.6882i 0.137615i 0.997630 + 0.0688076i \(0.0219195\pi\)
−0.997630 + 0.0688076i \(0.978081\pi\)
\(224\) 208.210 273.577i 0.929510 1.22133i
\(225\) 50.1384 0.222838
\(226\) 41.6218 + 223.585i 0.184167 + 0.989312i
\(227\) 295.846 1.30329 0.651643 0.758525i \(-0.274080\pi\)
0.651643 + 0.758525i \(0.274080\pi\)
\(228\) −6.92820 + 2.67206i −0.0303869 + 0.0117196i
\(229\) 256.718i 1.12104i 0.828141 + 0.560519i \(0.189398\pi\)
−0.828141 + 0.560519i \(0.810602\pi\)
\(230\) 22.6410 + 121.623i 0.0984392 + 0.528797i
\(231\) 148.868i 0.644451i
\(232\) −273.100 + 168.248i −1.17716 + 0.725207i
\(233\) −404.564 −1.73633 −0.868163 0.496279i \(-0.834699\pi\)
−0.868163 + 0.496279i \(0.834699\pi\)
\(234\) −92.7846 + 17.2725i −0.396515 + 0.0738140i
\(235\) 4.44109 0.0188983
\(236\) 41.8564 16.1431i 0.177358 0.0684031i
\(237\) 127.588i 0.538344i
\(238\) −334.956 + 62.3544i −1.40738 + 0.261993i
\(239\) 115.150i 0.481799i −0.970550 0.240899i \(-0.922558\pi\)
0.970550 0.240899i \(-0.0774424\pi\)
\(240\) −53.5692 59.1177i −0.223205 0.246324i
\(241\) 251.415 1.04322 0.521609 0.853185i \(-0.325332\pi\)
0.521609 + 0.853185i \(0.325332\pi\)
\(242\) 20.8634 + 112.075i 0.0862126 + 0.463118i
\(243\) 15.5885 0.0641500
\(244\) 2.22055 + 5.75749i 0.00910059 + 0.0235963i
\(245\) 191.223i 0.780500i
\(246\) −32.6936 175.624i −0.132901 0.713918i
\(247\) 16.8591i 0.0682555i
\(248\) −62.6692 + 38.6084i −0.252698 + 0.155679i
\(249\) 21.2820 0.0854700
\(250\) −236.105 + 43.9526i −0.944420 + 0.175810i
\(251\) 6.85125 0.0272958 0.0136479 0.999907i \(-0.495656\pi\)
0.0136479 + 0.999907i \(0.495656\pi\)
\(252\) −46.3923 120.287i −0.184096 0.477331i
\(253\) 171.898i 0.679439i
\(254\) 72.4730 13.4913i 0.285327 0.0531155i
\(255\) 79.0622i 0.310048i
\(256\) 25.1487 254.762i 0.0982373 0.995163i
\(257\) 248.277 0.966058 0.483029 0.875604i \(-0.339537\pi\)
0.483029 + 0.875604i \(0.339537\pi\)
\(258\) 8.10512 + 43.5392i 0.0314152 + 0.168757i
\(259\) 107.138 0.413662
\(260\) 168.995 65.1778i 0.649980 0.250684i
\(261\) 120.287i 0.460871i
\(262\) −71.2436 382.707i −0.271922 1.46071i
\(263\) 498.835i 1.89671i −0.317208 0.948356i \(-0.602745\pi\)
0.317208 0.948356i \(-0.397255\pi\)
\(264\) −58.1436 94.3786i −0.220241 0.357495i
\(265\) −82.2769 −0.310479
\(266\) 22.6410 4.21478i 0.0851166 0.0158450i
\(267\) 57.3975 0.214972
\(268\) 161.282 62.2031i 0.601799 0.232101i
\(269\) 234.611i 0.872158i −0.899908 0.436079i \(-0.856367\pi\)
0.899908 0.436079i \(-0.143633\pi\)
\(270\) −29.4115 + 5.47516i −0.108932 + 0.0202784i
\(271\) 101.321i 0.373878i −0.982372 0.186939i \(-0.940143\pi\)
0.982372 0.186939i \(-0.0598566\pi\)
\(272\) −188.000 + 170.355i −0.691176 + 0.626307i
\(273\) 292.708 1.07219
\(274\) −6.01408 32.3065i −0.0219492 0.117907i
\(275\) −133.703 −0.486191
\(276\) 53.5692 + 138.896i 0.194091 + 0.503246i
\(277\) 169.942i 0.613509i 0.951789 + 0.306755i \(0.0992431\pi\)
−0.951789 + 0.306755i \(0.900757\pi\)
\(278\) 41.5411 + 223.151i 0.149428 + 0.802701i
\(279\) 27.6027i 0.0989346i
\(280\) 129.779 + 210.658i 0.463498 + 0.752349i
\(281\) −111.128 −0.395474 −0.197737 0.980255i \(-0.563359\pi\)
−0.197737 + 0.980255i \(0.563359\pi\)
\(282\) 5.25387 0.978043i 0.0186307 0.00346824i
\(283\) 550.620 1.94566 0.972828 0.231531i \(-0.0743734\pi\)
0.972828 + 0.231531i \(0.0743734\pi\)
\(284\) −121.492 315.009i −0.427790 1.10919i
\(285\) 5.34413i 0.0187513i
\(286\) 247.426 46.0600i 0.865125 0.161049i
\(287\) 554.041i 1.93046i
\(288\) −76.3923 58.1396i −0.265251 0.201874i
\(289\) −37.5744 −0.130015
\(290\) −42.2487 226.952i −0.145685 0.782594i
\(291\) −119.751 −0.411516
\(292\) −393.454 + 151.747i −1.34744 + 0.519681i
\(293\) 223.509i 0.762829i −0.924404 0.381414i \(-0.875437\pi\)
0.924404 0.381414i \(-0.124563\pi\)
\(294\) 42.1122 + 226.219i 0.143239 + 0.769452i
\(295\) 32.2863i 0.109445i
\(296\) 67.9230 41.8452i 0.229470 0.141369i
\(297\) −41.5692 −0.139964
\(298\) 62.2628 11.5906i 0.208936 0.0388948i
\(299\) −337.990 −1.13040
\(300\) −108.033 + 41.6662i −0.360111 + 0.138887i
\(301\) 137.353i 0.456323i
\(302\) 177.986 33.1333i 0.589357 0.109713i
\(303\) 168.455i 0.555956i
\(304\) 12.7077 11.5150i 0.0418015 0.0378783i
\(305\) −4.44109 −0.0145610
\(306\) 17.4115 + 93.5316i 0.0569005 + 0.305659i
\(307\) −371.790 −1.21104 −0.605521 0.795829i \(-0.707035\pi\)
−0.605521 + 0.795829i \(0.707035\pi\)
\(308\) 123.713 + 320.766i 0.401665 + 1.04145i
\(309\) 241.911i 0.782883i
\(310\) −9.69496 52.0795i −0.0312741 0.167998i
\(311\) 330.023i 1.06117i 0.847633 + 0.530583i \(0.178027\pi\)
−0.847633 + 0.530583i \(0.821973\pi\)
\(312\) 185.569 114.323i 0.594773 0.366420i
\(313\) −80.2769 −0.256476 −0.128238 0.991743i \(-0.540932\pi\)
−0.128238 + 0.991743i \(0.540932\pi\)
\(314\) −454.228 + 84.5576i −1.44659 + 0.269292i
\(315\) 92.7846 0.294554
\(316\) 106.028 + 274.913i 0.335532 + 0.869978i
\(317\) 68.8833i 0.217297i −0.994080 0.108649i \(-0.965348\pi\)
0.994080 0.108649i \(-0.0346524\pi\)
\(318\) −97.3346 + 18.1195i −0.306084 + 0.0569795i
\(319\) 320.766i 1.00554i
\(320\) 164.554 + 82.8636i 0.514230 + 0.258949i
\(321\) −342.564 −1.06718
\(322\) −84.4974 453.905i −0.262414 1.40964i
\(323\) −16.9948 −0.0526156
\(324\) −33.5885 + 12.9544i −0.103668 + 0.0399826i
\(325\) 262.889i 0.808888i
\(326\) −8.18207 43.9526i −0.0250984 0.134824i
\(327\) 330.325i 1.01017i
\(328\) 216.392 + 351.248i 0.659733 + 1.07088i
\(329\) −16.5744 −0.0503780
\(330\) 78.4308 14.6004i 0.237669 0.0442437i
\(331\) −396.056 −1.19654 −0.598272 0.801293i \(-0.704146\pi\)
−0.598272 + 0.801293i \(0.704146\pi\)
\(332\) −45.8564 + 17.6859i −0.138122 + 0.0532706i
\(333\) 29.9168i 0.0898403i
\(334\) 434.620 80.9075i 1.30126 0.242238i
\(335\) 124.406i 0.371362i
\(336\) 199.923 + 220.630i 0.595009 + 0.656637i
\(337\) 231.723 0.687606 0.343803 0.939042i \(-0.388285\pi\)
0.343803 + 0.939042i \(0.388285\pi\)
\(338\) 28.7058 + 154.202i 0.0849283 + 0.456219i
\(339\) −196.956 −0.580992
\(340\) −65.7025 170.355i −0.193243 0.501045i
\(341\) 73.6073i 0.215857i
\(342\) −1.17691 6.32217i −0.00344127 0.0184859i
\(343\) 187.215i 0.545815i
\(344\) −53.6462 87.0784i −0.155948 0.253135i
\(345\) −107.138 −0.310546
\(346\) 455.229 84.7441i 1.31569 0.244925i
\(347\) 462.123 1.33177 0.665883 0.746056i \(-0.268055\pi\)
0.665883 + 0.746056i \(0.268055\pi\)
\(348\) −99.9615 259.183i −0.287246 0.744779i
\(349\) 266.993i 0.765022i 0.923951 + 0.382511i \(0.124941\pi\)
−0.923951 + 0.382511i \(0.875059\pi\)
\(350\) 353.047 65.7222i 1.00871 0.187778i
\(351\) 81.7343i 0.232861i
\(352\) 203.713 + 155.039i 0.578730 + 0.440452i
\(353\) 262.862 0.744650 0.372325 0.928102i \(-0.378561\pi\)
0.372325 + 0.928102i \(0.378561\pi\)
\(354\) 7.11027 + 38.1951i 0.0200855 + 0.107896i
\(355\) 242.985 0.684463
\(356\) −123.674 + 47.6986i −0.347400 + 0.133985i
\(357\) 295.064i 0.826510i
\(358\) −70.8794 380.751i −0.197987 1.06355i
\(359\) 164.185i 0.457339i 0.973504 + 0.228669i \(0.0734374\pi\)
−0.973504 + 0.228669i \(0.926563\pi\)
\(360\) 58.8231 36.2390i 0.163397 0.100664i
\(361\) −359.851 −0.996818
\(362\) −531.846 + 99.0068i −1.46919 + 0.273499i
\(363\) −98.7269 −0.271975
\(364\) −630.697 + 243.247i −1.73269 + 0.668260i
\(365\) 303.494i 0.831490i
\(366\) −5.25387 + 0.978043i −0.0143548 + 0.00267225i
\(367\) 242.475i 0.660696i −0.943859 0.330348i \(-0.892834\pi\)
0.943859 0.330348i \(-0.107166\pi\)
\(368\) −230.851 254.762i −0.627313 0.692287i
\(369\) 154.708 0.419262
\(370\) 10.5077 + 56.4456i 0.0283993 + 0.152556i
\(371\) 307.061 0.827659
\(372\) −22.9385 59.4757i −0.0616627 0.159881i
\(373\) 328.480i 0.880643i 0.897840 + 0.440321i \(0.145136\pi\)
−0.897840 + 0.440321i \(0.854864\pi\)
\(374\) −46.4308 249.418i −0.124146 0.666892i
\(375\) 207.986i 0.554629i
\(376\) −10.5077 + 6.47347i −0.0279461 + 0.0172167i
\(377\) 630.697 1.67294
\(378\) 109.765 20.4336i 0.290385 0.0540571i
\(379\) 36.2102 0.0955415 0.0477708 0.998858i \(-0.484788\pi\)
0.0477708 + 0.998858i \(0.484788\pi\)
\(380\) 4.44109 + 11.5150i 0.0116871 + 0.0303026i
\(381\) 63.8417i 0.167564i
\(382\) −612.497 + 114.021i −1.60340 + 0.298483i
\(383\) 164.295i 0.428969i −0.976727 0.214485i \(-0.931193\pi\)
0.976727 0.214485i \(-0.0688072\pi\)
\(384\) 212.918 + 61.7897i 0.554474 + 0.160911i
\(385\) −247.426 −0.642664
\(386\) −17.6706 94.9230i −0.0457787 0.245915i
\(387\) −38.3538 −0.0991055
\(388\) 258.028 99.5161i 0.665021 0.256485i
\(389\) 604.936i 1.55510i 0.628819 + 0.777552i \(0.283539\pi\)
−0.628819 + 0.777552i \(0.716461\pi\)
\(390\) 28.7077 + 154.212i 0.0736094 + 0.395416i
\(391\) 340.711i 0.871383i
\(392\) −278.732 452.438i −0.711051 1.15418i
\(393\) 337.128 0.857832
\(394\) −495.258 + 92.1956i −1.25700 + 0.233999i
\(395\) −212.056 −0.536851
\(396\) 89.5692 34.5450i 0.226185 0.0872348i
\(397\) 541.699i 1.36448i 0.731128 + 0.682241i \(0.238994\pi\)
−0.731128 + 0.682241i \(0.761006\pi\)
\(398\) 141.804 26.3977i 0.356291 0.0663260i
\(399\) 19.9445i 0.0499863i
\(400\) 198.154 179.556i 0.495385 0.448891i
\(401\) −379.569 −0.946557 −0.473278 0.880913i \(-0.656930\pi\)
−0.473278 + 0.880913i \(0.656930\pi\)
\(402\) 27.3975 + 147.174i 0.0681529 + 0.366105i
\(403\) 144.728 0.359127
\(404\) −139.990 362.969i −0.346509 0.898439i
\(405\) 25.9087i 0.0639722i
\(406\) 157.674 + 846.998i 0.388360 + 2.08620i
\(407\) 79.7782i 0.196015i
\(408\) −115.244 187.063i −0.282460 0.458488i
\(409\) 251.415 0.614707 0.307354 0.951595i \(-0.400557\pi\)
0.307354 + 0.951595i \(0.400557\pi\)
\(410\) −291.895 + 54.3382i −0.711939 + 0.132532i
\(411\) 28.4589 0.0692432
\(412\) 201.033 + 521.245i 0.487945 + 1.26516i
\(413\) 120.494i 0.291753i
\(414\) −126.746 + 23.5947i −0.306150 + 0.0569919i
\(415\) 35.3717i 0.0852330i
\(416\) −304.841 + 400.544i −0.732791 + 0.962847i
\(417\) −196.574 −0.471401
\(418\) 3.13844 + 16.8591i 0.00750823 + 0.0403328i
\(419\) 268.133 0.639936 0.319968 0.947428i \(-0.396328\pi\)
0.319968 + 0.947428i \(0.396328\pi\)
\(420\) −199.923 + 77.1061i −0.476007 + 0.183586i
\(421\) 218.261i 0.518434i −0.965819 0.259217i \(-0.916536\pi\)
0.965819 0.259217i \(-0.0834645\pi\)
\(422\) 96.9667 + 520.887i 0.229779 + 1.23433i
\(423\) 4.62815i 0.0109412i
\(424\) 194.669 119.929i 0.459125 0.282852i
\(425\) −265.005 −0.623542
\(426\) 287.454 53.5115i 0.674774 0.125614i
\(427\) 16.5744 0.0388159
\(428\) 738.123 284.679i 1.72459 0.665137i
\(429\) 217.958i 0.508061i
\(430\) 72.3641 13.4711i 0.168289 0.0313281i
\(431\) 550.955i 1.27832i −0.769074 0.639159i \(-0.779282\pi\)
0.769074 0.639159i \(-0.220718\pi\)
\(432\) 61.6077 55.8255i 0.142610 0.129226i
\(433\) −263.128 −0.607686 −0.303843 0.952722i \(-0.598270\pi\)
−0.303843 + 0.952722i \(0.598270\pi\)
\(434\) 36.1821 + 194.363i 0.0833688 + 0.447842i
\(435\) 199.923 0.459593
\(436\) −274.508 711.752i −0.629605 1.63246i
\(437\) 23.0300i 0.0527002i
\(438\) −66.8372 359.037i −0.152596 0.819719i
\(439\) 440.489i 1.00339i −0.865044 0.501696i \(-0.832710\pi\)
0.865044 0.501696i \(-0.167290\pi\)
\(440\) −156.862 + 96.6373i −0.356504 + 0.219630i
\(441\) −199.277 −0.451875
\(442\) 490.410 91.2932i 1.10953 0.206546i
\(443\) −228.708 −0.516270 −0.258135 0.966109i \(-0.583108\pi\)
−0.258135 + 0.966109i \(0.583108\pi\)
\(444\) 24.8616 + 64.4618i 0.0559945 + 0.145184i
\(445\) 95.3972i 0.214376i
\(446\) 60.3397 11.2327i 0.135291 0.0251853i
\(447\) 54.8475i 0.122701i
\(448\) −614.123 309.251i −1.37081 0.690293i
\(449\) −108.410 −0.241448 −0.120724 0.992686i \(-0.538522\pi\)
−0.120724 + 0.992686i \(0.538522\pi\)
\(450\) −18.3519 98.5833i −0.0407821 0.219074i
\(451\) −412.554 −0.914753
\(452\) 424.382 163.675i 0.938898 0.362113i
\(453\) 156.788i 0.346111i
\(454\) −108.287 581.699i −0.238518 1.28127i
\(455\) 486.493i 1.06922i
\(456\) 7.78976 + 12.6443i 0.0170828 + 0.0277288i
\(457\) 561.692 1.22909 0.614543 0.788883i \(-0.289340\pi\)
0.614543 + 0.788883i \(0.289340\pi\)
\(458\) 504.764 93.9652i 1.10210 0.205164i
\(459\) −82.3923 −0.179504
\(460\) 230.851 89.0345i 0.501851 0.193553i
\(461\) 335.160i 0.727028i 0.931589 + 0.363514i \(0.118423\pi\)
−0.931589 + 0.363514i \(0.881577\pi\)
\(462\) −292.708 + 54.4895i −0.633566 + 0.117943i
\(463\) 389.912i 0.842142i 0.907028 + 0.421071i \(0.138346\pi\)
−0.907028 + 0.421071i \(0.861654\pi\)
\(464\) 430.774 + 475.392i 0.928393 + 1.02455i
\(465\) 45.8770 0.0986603
\(466\) 148.081 + 795.462i 0.317770 + 1.70700i
\(467\) −546.410 −1.17004 −0.585022 0.811018i \(-0.698914\pi\)
−0.585022 + 0.811018i \(0.698914\pi\)
\(468\) 67.9230 + 176.113i 0.145135 + 0.376310i
\(469\) 464.290i 0.989958i
\(470\) −1.62555 8.73217i −0.00345862 0.0185791i
\(471\) 400.131i 0.849535i
\(472\) −47.0615 76.3902i −0.0997065 0.161844i
\(473\) 102.277 0.216230
\(474\) −250.865 + 46.7003i −0.529252 + 0.0985238i
\(475\) 17.9127 0.0377110
\(476\) 245.205 + 635.775i 0.515137 + 1.33566i
\(477\) 85.7424i 0.179753i
\(478\) −226.410 + 42.1478i −0.473661 + 0.0881753i
\(479\) 368.369i 0.769037i 0.923117 + 0.384519i \(0.125633\pi\)
−0.923117 + 0.384519i \(0.874367\pi\)
\(480\) −96.6307 + 126.967i −0.201314 + 0.264516i
\(481\) −156.862 −0.326116
\(482\) −92.0244 494.338i −0.190922 1.02560i
\(483\) 399.846 0.827839
\(484\) 212.727 82.0443i 0.439518 0.169513i
\(485\) 199.032i 0.410375i
\(486\) −5.70577 30.6504i −0.0117403 0.0630666i
\(487\) 90.6326i 0.186104i −0.995661 0.0930519i \(-0.970338\pi\)
0.995661 0.0930519i \(-0.0296623\pi\)
\(488\) 10.5077 6.47347i 0.0215322 0.0132653i
\(489\) 38.7180 0.0791778
\(490\) 375.986 69.9923i 0.767318 0.142841i
\(491\) −17.6462 −0.0359392 −0.0179696 0.999839i \(-0.505720\pi\)
−0.0179696 + 0.999839i \(0.505720\pi\)
\(492\) −333.349 + 128.566i −0.677538 + 0.261312i
\(493\) 635.775i 1.28960i
\(494\) −33.1487 + 6.17086i −0.0671027 + 0.0124916i
\(495\) 69.0899i 0.139576i
\(496\) 98.8513 + 109.090i 0.199297 + 0.219939i
\(497\) −906.831 −1.82461
\(498\) −7.78976 41.8452i −0.0156421 0.0840265i
\(499\) 548.631 1.09946 0.549730 0.835342i \(-0.314731\pi\)
0.549730 + 0.835342i \(0.314731\pi\)
\(500\) 172.841 + 448.147i 0.345682 + 0.896294i
\(501\) 382.859i 0.764189i
\(502\) −2.50773 13.4711i −0.00499548 0.0268348i
\(503\) 262.475i 0.521820i 0.965363 + 0.260910i \(0.0840225\pi\)
−0.965363 + 0.260910i \(0.915977\pi\)
\(504\) −219.531 + 135.246i −0.435577 + 0.268345i
\(505\) 279.979 0.554415
\(506\) 337.990 62.9191i 0.667964 0.124346i
\(507\) −135.837 −0.267923
\(508\) −53.0539 137.560i −0.104437 0.270787i
\(509\) 230.093i 0.452049i −0.974122 0.226025i \(-0.927427\pi\)
0.974122 0.226025i \(-0.0725730\pi\)
\(510\) 155.454 28.9388i 0.304811 0.0567427i
\(511\) 1132.65i 2.21654i
\(512\) −510.123 + 43.8013i −0.996334 + 0.0855493i
\(513\) 5.56922 0.0108562
\(514\) −90.8756 488.167i −0.176801 0.949742i
\(515\) −402.067 −0.780712
\(516\) 82.6410 31.8729i 0.160157 0.0617692i
\(517\) 12.3417i 0.0238718i
\(518\) −39.2154 210.658i −0.0757054 0.406675i
\(519\) 401.013i 0.772665i
\(520\) −190.010 308.425i −0.365404 0.593124i
\(521\) 164.144 0.315055 0.157527 0.987515i \(-0.449648\pi\)
0.157527 + 0.987515i \(0.449648\pi\)
\(522\) 236.512 44.0282i 0.453087 0.0843453i
\(523\) −185.492 −0.354670 −0.177335 0.984151i \(-0.556748\pi\)
−0.177335 + 0.984151i \(0.556748\pi\)
\(524\) −726.410 + 280.161i −1.38628 + 0.534659i
\(525\) 311.001i 0.592382i
\(526\) −980.820 + 182.586i −1.86468 + 0.347122i
\(527\) 145.893i 0.276838i
\(528\) −164.287 + 148.868i −0.311150 + 0.281947i
\(529\) 67.2975 0.127216
\(530\) 30.1154 + 161.775i 0.0568216 + 0.305235i
\(531\) −33.6462 −0.0633638
\(532\) −16.5744 42.9745i −0.0311548 0.0807792i
\(533\) 811.172i 1.52190i
\(534\) −21.0089 112.856i −0.0393426 0.211341i
\(535\) 569.357i 1.06422i
\(536\) −181.338 294.348i −0.338318 0.549157i
\(537\) 335.405 0.624590
\(538\) −461.296 + 85.8734i −0.857428 + 0.159616i
\(539\) 531.405 0.985909
\(540\) 21.5307 + 55.8255i 0.0398717 + 0.103381i
\(541\) 891.253i 1.64742i −0.567013 0.823709i \(-0.691901\pi\)
0.567013 0.823709i \(-0.308099\pi\)
\(542\) −199.219 + 37.0860i −0.367563 + 0.0684244i
\(543\) 468.505i 0.862809i
\(544\) 403.769 + 307.295i 0.742223 + 0.564881i
\(545\) 549.015 1.00737
\(546\) −107.138 575.528i −0.196224 1.05408i
\(547\) 524.631 0.959105 0.479553 0.877513i \(-0.340799\pi\)
0.479553 + 0.877513i \(0.340799\pi\)
\(548\) −61.3205 + 23.6500i −0.111899 + 0.0431570i
\(549\) 4.62815i 0.00843014i
\(550\) 48.9385 + 262.889i 0.0889791 + 0.477979i
\(551\) 42.9745i 0.0779937i
\(552\) 253.492 156.168i 0.459225 0.282914i
\(553\) 791.405 1.43111
\(554\) 334.144 62.2031i 0.603147 0.112280i
\(555\) −49.7231 −0.0895912
\(556\) 423.559 163.358i 0.761797 0.293809i
\(557\) 570.804i 1.02478i 0.858752 + 0.512391i \(0.171240\pi\)
−0.858752 + 0.512391i \(0.828760\pi\)
\(558\) 54.2731 10.1033i 0.0972636 0.0181063i
\(559\) 201.099i 0.359748i
\(560\) 366.697 332.281i 0.654817 0.593359i
\(561\) 219.713 0.391645
\(562\) 40.6757 + 218.502i 0.0723767 + 0.388794i
\(563\) −161.877 −0.287526 −0.143763 0.989612i \(-0.545920\pi\)
−0.143763 + 0.989612i \(0.545920\pi\)
\(564\) −3.84610 9.97227i −0.00681932 0.0176813i
\(565\) 327.350i 0.579381i
\(566\) −201.541 1082.64i −0.356080 1.91279i
\(567\) 96.6927i 0.170534i
\(568\) −574.908 + 354.182i −1.01216 + 0.623560i
\(569\) 624.123 1.09688 0.548438 0.836191i \(-0.315222\pi\)
0.548438 + 0.836191i \(0.315222\pi\)
\(570\) −10.5077 + 1.95609i −0.0184346 + 0.00343173i
\(571\) −593.031 −1.03858 −0.519291 0.854597i \(-0.673804\pi\)
−0.519291 + 0.854597i \(0.673804\pi\)
\(572\) −181.128 469.634i −0.316658 0.821039i
\(573\) 539.551i 0.941625i
\(574\) 1089.37 202.793i 1.89785 0.353298i
\(575\) 359.113i 0.624544i
\(576\) −86.3538 + 171.485i −0.149920 + 0.297717i
\(577\) −1003.68 −1.73948 −0.869742 0.493507i \(-0.835715\pi\)
−0.869742 + 0.493507i \(0.835715\pi\)
\(578\) 13.7532 + 73.8795i 0.0237944 + 0.127819i
\(579\) 83.6180 0.144418
\(580\) −430.774 + 166.141i −0.742714 + 0.286449i
\(581\) 132.009i 0.227210i
\(582\) 43.8320 + 235.458i 0.0753127 + 0.404566i
\(583\) 228.646i 0.392189i
\(584\) 442.382 + 718.074i 0.757503 + 1.22958i
\(585\) −135.846 −0.232216
\(586\) −439.468 + 81.8099i −0.749945 + 0.139607i
\(587\) 859.215 1.46374 0.731870 0.681444i \(-0.238648\pi\)
0.731870 + 0.681444i \(0.238648\pi\)
\(588\) 429.382 165.604i 0.730241 0.281639i
\(589\) 9.86151i 0.0167428i
\(590\) 63.4820 11.8176i 0.107597 0.0200298i
\(591\) 436.274i 0.738196i
\(592\) −107.138 118.235i −0.180977 0.199722i
\(593\) −1007.42 −1.69885 −0.849423 0.527713i \(-0.823050\pi\)
−0.849423 + 0.527713i \(0.823050\pi\)
\(594\) 15.2154 + 81.7343i 0.0256151 + 0.137600i
\(595\) −490.410 −0.824219
\(596\) −45.5795 118.180i −0.0764757 0.198289i
\(597\) 124.915i 0.209239i
\(598\) 123.713 + 664.562i 0.206878 + 1.11131i
\(599\) 86.0598i 0.143672i 0.997416 + 0.0718362i \(0.0228859\pi\)
−0.997416 + 0.0718362i \(0.977114\pi\)
\(600\) 121.468 + 197.167i 0.202446 + 0.328611i
\(601\) −406.000 −0.675541 −0.337770 0.941229i \(-0.609673\pi\)
−0.337770 + 0.941229i \(0.609673\pi\)
\(602\) −270.067 + 50.2747i −0.448616 + 0.0835129i
\(603\) −129.646 −0.215002
\(604\) −130.295 337.832i −0.215720 0.559325i
\(605\) 164.089i 0.271221i
\(606\) 331.219 61.6587i 0.546566 0.101747i
\(607\) 1187.80i 1.95684i −0.206617 0.978422i \(-0.566245\pi\)
0.206617 0.978422i \(-0.433755\pi\)
\(608\) −27.2923 20.7713i −0.0448887 0.0341633i
\(609\) −746.123 −1.22516
\(610\) 1.62555 + 8.73217i 0.00266484 + 0.0143150i
\(611\) 24.2666 0.0397162
\(612\) 177.531 68.4699i 0.290083 0.111879i
\(613\) 500.378i 0.816277i 0.912920 + 0.408139i \(0.133822\pi\)
−0.912920 + 0.408139i \(0.866178\pi\)
\(614\) 136.084 + 731.021i 0.221636 + 1.19059i
\(615\) 257.131i 0.418099i
\(616\) 585.415 360.655i 0.950350 0.585479i
\(617\) 88.8306 0.143972 0.0719859 0.997406i \(-0.477066\pi\)
0.0719859 + 0.997406i \(0.477066\pi\)
\(618\) −475.650 + 88.5455i −0.769660 + 0.143277i
\(619\) −424.231 −0.685349 −0.342674 0.939454i \(-0.611333\pi\)
−0.342674 + 0.939454i \(0.611333\pi\)
\(620\) −98.8513 + 38.1249i −0.159438 + 0.0614917i
\(621\) 111.651i 0.179792i
\(622\) 648.897 120.797i 1.04324 0.194207i
\(623\) 356.027i 0.571472i
\(624\) −292.708 323.025i −0.469083 0.517668i
\(625\) 72.1384 0.115422
\(626\) 29.3834 + 157.842i 0.0469383 + 0.252144i
\(627\) −14.8513 −0.0236862
\(628\) 332.518 + 862.163i 0.529487 + 1.37287i
\(629\) 158.124i 0.251390i
\(630\) −33.9615 182.435i −0.0539072 0.289579i
\(631\) 90.6326i 0.143633i −0.997418 0.0718166i \(-0.977120\pi\)
0.997418 0.0718166i \(-0.0228796\pi\)
\(632\) 501.731 309.100i 0.793878 0.489082i
\(633\) −458.851 −0.724883
\(634\) −135.440 + 25.2130i −0.213627 + 0.0397682i
\(635\) 106.108 0.167099
\(636\) 71.2539 + 184.749i 0.112034 + 0.290486i
\(637\) 1044.86i 1.64028i
\(638\) −630.697 + 117.409i −0.988554 + 0.184026i
\(639\) 253.219i 0.396274i
\(640\) 102.697 353.879i 0.160465 0.552936i
\(641\) 1090.40 1.70109 0.850546 0.525901i \(-0.176272\pi\)
0.850546 + 0.525901i \(0.176272\pi\)
\(642\) 125.387 + 673.557i 0.195307 + 1.04915i
\(643\) −454.200 −0.706376 −0.353188 0.935552i \(-0.614902\pi\)
−0.353188 + 0.935552i \(0.614902\pi\)
\(644\) −861.549 + 332.281i −1.33781 + 0.515965i
\(645\) 63.7458i 0.0988307i
\(646\) 6.22055 + 33.4156i 0.00962933 + 0.0517270i
\(647\) 610.789i 0.944032i −0.881590 0.472016i \(-0.843526\pi\)
0.881590 0.472016i \(-0.156474\pi\)
\(648\) 37.7654 + 61.3007i 0.0582799 + 0.0945999i
\(649\) 89.7231 0.138248
\(650\) −516.897 + 96.2239i −0.795227 + 0.148037i
\(651\) −171.215 −0.263004
\(652\) −83.4256 + 32.1755i −0.127953 + 0.0493489i
\(653\) 673.612i 1.03157i 0.856720 + 0.515783i \(0.172499\pi\)
−0.856720 + 0.515783i \(0.827501\pi\)
\(654\) 649.492 120.907i 0.993107 0.184874i
\(655\) 560.322i 0.855454i
\(656\) 611.426 554.041i 0.932051 0.844574i
\(657\) 316.277 0.481396
\(658\) 6.06664 + 32.5889i 0.00921982 + 0.0495272i
\(659\) −819.328 −1.24329 −0.621645 0.783299i \(-0.713535\pi\)
−0.621645 + 0.783299i \(0.713535\pi\)
\(660\) −57.4153 148.868i −0.0869929 0.225558i
\(661\) 370.628i 0.560707i −0.959897 0.280354i \(-0.909548\pi\)
0.959897 0.280354i \(-0.0904518\pi\)
\(662\) 144.967 + 778.734i 0.218983 + 1.17634i
\(663\) 432.004i 0.651590i
\(664\) 51.5589 + 83.6904i 0.0776490 + 0.126040i
\(665\) 33.1487 0.0498477
\(666\) −58.8231 + 10.9503i −0.0883230 + 0.0164419i
\(667\) 861.549 1.29168
\(668\) −318.164 824.946i −0.476294 1.23495i
\(669\) 53.1535i 0.0794521i
\(670\) 244.610 45.5358i 0.365090 0.0679639i
\(671\) 12.3417i 0.0183930i
\(672\) 360.631 473.849i 0.536653 0.705133i
\(673\) −255.703 −0.379944 −0.189972 0.981789i \(-0.560840\pi\)
−0.189972 + 0.981789i \(0.560840\pi\)
\(674\) −84.8165 455.619i −0.125841 0.675992i
\(675\) 86.8423 0.128655
\(676\) 292.688 112.884i 0.432971 0.166988i
\(677\) 934.323i 1.38009i −0.723765 0.690047i \(-0.757590\pi\)
0.723765 0.690047i \(-0.242410\pi\)
\(678\) 72.0910 + 387.260i 0.106329 + 0.571180i
\(679\) 742.798i 1.09396i
\(680\) −310.908 + 191.540i −0.457217 + 0.281677i
\(681\) 512.420 0.752453
\(682\) −144.728 + 26.9422i −0.212212 + 0.0395046i
\(683\) 1142.54 1.67283 0.836415 0.548096i \(-0.184647\pi\)
0.836415 + 0.548096i \(0.184647\pi\)
\(684\) −12.0000 + 4.62815i −0.0175439 + 0.00676630i
\(685\) 47.3001i 0.0690512i
\(686\) −368.105 + 68.5253i −0.536596 + 0.0998911i
\(687\) 444.648i 0.647232i
\(688\) −151.580 + 137.353i −0.220319 + 0.199641i
\(689\) −449.569 −0.652495
\(690\) 39.2154 + 210.658i 0.0568339 + 0.305301i
\(691\) 1316.90 1.90578 0.952892 0.303309i \(-0.0980913\pi\)
0.952892 + 0.303309i \(0.0980913\pi\)
\(692\) −333.251 864.063i −0.481577 1.24865i
\(693\) 257.847i 0.372074i
\(694\) −169.149 908.636i −0.243730 1.30927i
\(695\) 326.716i 0.470094i
\(696\) −473.023 + 291.414i −0.679631 + 0.418698i
\(697\) −817.703 −1.17317
\(698\) 524.967 97.7261i 0.752101 0.140009i
\(699\) −700.726 −1.00247
\(700\) −258.449 670.113i −0.369212 0.957305i
\(701\) 318.493i 0.454341i 0.973855 + 0.227170i \(0.0729474\pi\)
−0.973855 + 0.227170i \(0.927053\pi\)
\(702\) −160.708 + 29.9168i −0.228928 + 0.0426166i
\(703\) 10.6883i 0.0152038i
\(704\) 230.277 457.293i 0.327098 0.649563i
\(705\) 7.69219 0.0109109
\(706\) −96.2140 516.844i −0.136280 0.732074i
\(707\) −1044.90 −1.47793
\(708\) 72.4974 27.9607i 0.102397 0.0394926i
\(709\) 289.831i 0.408788i −0.978889 0.204394i \(-0.934478\pi\)
0.978889 0.204394i \(-0.0655224\pi\)
\(710\) −88.9385 477.761i −0.125266 0.672903i
\(711\) 220.988i 0.310813i
\(712\) 139.054 + 225.712i 0.195300 + 0.317012i
\(713\) 197.703 0.277283
\(714\) −580.161 + 108.001i −0.812551 + 0.151262i
\(715\) 362.256 0.506652
\(716\) −722.697 + 278.729i −1.00935 + 0.389287i
\(717\) 199.445i 0.278167i
\(718\) 322.823 60.0957i 0.449614 0.0836988i
\(719\) 491.122i 0.683062i 0.939870 + 0.341531i \(0.110945\pi\)
−0.939870 + 0.341531i \(0.889055\pi\)
\(720\) −92.7846 102.395i −0.128868 0.142215i
\(721\) 1500.53 2.08118
\(722\) 131.715 + 707.547i 0.182430 + 0.979982i
\(723\) 435.464 0.602302
\(724\) 389.338 + 1009.49i 0.537760 + 1.39432i
\(725\) 670.113i 0.924294i
\(726\) 36.1366 + 194.119i 0.0497749 + 0.267381i
\(727\) 774.918i 1.06591i −0.846143 0.532956i \(-0.821081\pi\)
0.846143 0.532956i \(-0.178919\pi\)
\(728\) 709.128 + 1151.06i 0.974077 + 1.58112i
\(729\) 27.0000 0.0370370
\(730\) −596.736 + 111.086i −0.817446 + 0.152173i
\(731\) 202.718 0.277316
\(732\) 3.84610 + 9.97227i 0.00525423 + 0.0136233i
\(733\) 858.966i 1.17185i 0.810365 + 0.585925i \(0.199269\pi\)
−0.810365 + 0.585925i \(0.800731\pi\)
\(734\) −476.760 + 88.7522i −0.649537 + 0.120916i
\(735\) 331.207i 0.450622i
\(736\) −416.420 + 547.154i −0.565789 + 0.743416i
\(737\) 345.723 0.469095
\(738\) −56.6269 304.189i −0.0767303 0.412181i
\(739\) 63.1948 0.0855139 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(740\) 107.138 41.3210i 0.144782 0.0558393i
\(741\) 29.2008i 0.0394073i
\(742\) −112.392 603.751i −0.151472 0.813680i
\(743\) 1105.00i 1.48721i 0.668620 + 0.743604i \(0.266885\pi\)
−0.668620 + 0.743604i \(0.733115\pi\)
\(744\) −108.546 + 66.8718i −0.145895 + 0.0898814i
\(745\) 91.1591 0.122361
\(746\) 645.864 120.232i 0.865769 0.161169i
\(747\) 36.8616 0.0493461
\(748\) −473.415 + 182.586i −0.632908 + 0.244099i
\(749\) 2124.87i 2.83694i
\(750\) −408.946 + 76.1281i −0.545261 + 0.101504i
\(751\) 804.119i 1.07073i 0.844621 + 0.535365i \(0.179826\pi\)
−0.844621 + 0.535365i \(0.820174\pi\)
\(752\) 16.5744 + 18.2911i 0.0220404 + 0.0243232i
\(753\) 11.8667 0.0157593
\(754\) −230.851 1240.09i −0.306169 1.64468i
\(755\) 260.589 0.345152
\(756\) −80.3538 208.344i −0.106288 0.275587i
\(757\) 1351.03i 1.78471i 0.451334 + 0.892355i \(0.350948\pi\)
−0.451334 + 0.892355i \(0.649052\pi\)
\(758\) −13.2539 71.1973i −0.0174853 0.0939279i
\(759\) 297.736i 0.392274i
\(760\) 21.0155 12.9469i 0.0276519 0.0170355i
\(761\) −709.805 −0.932726 −0.466363 0.884593i \(-0.654436\pi\)
−0.466363 + 0.884593i \(0.654436\pi\)
\(762\) 125.527 23.3677i 0.164734 0.0306663i
\(763\) −2048.95 −2.68539
\(764\) 448.379 + 1162.57i 0.586884 + 1.52169i
\(765\) 136.940i 0.179006i
\(766\) −323.041 + 60.1363i −0.421724 + 0.0785069i
\(767\) 176.415i 0.230007i
\(768\) 43.5589 441.260i 0.0567173 0.574558i
\(769\) −195.703 −0.254490 −0.127245 0.991871i \(-0.540613\pi\)
−0.127245 + 0.991871i \(0.540613\pi\)
\(770\) 90.5641 + 486.493i 0.117616 + 0.631810i
\(771\) 430.028 0.557754
\(772\) −180.172 + 69.4885i −0.233383 + 0.0900110i
\(773\) 12.5484i 0.0162334i −0.999967 0.00811670i \(-0.997416\pi\)
0.999967 0.00811670i \(-0.00258365\pi\)
\(774\) 14.0385 + 75.4121i 0.0181376 + 0.0974317i
\(775\) 153.773i 0.198417i
\(776\) −290.115 470.915i −0.373860 0.606849i
\(777\) 185.569 0.238828
\(778\) 1189.44 221.422i 1.52884 0.284604i
\(779\) 55.2717 0.0709521
\(780\) 292.708 112.891i 0.375266 0.144732i
\(781\) 675.251i 0.864598i
\(782\) 669.913 124.709i 0.856666 0.159474i
\(783\) 208.344i 0.266084i
\(784\) −787.569 + 713.652i −1.00455 + 0.910271i
\(785\) −665.036 −0.847180
\(786\) −123.397