Properties

Label 39.4.j.c.4.1
Level $39$
Weight $4$
Character 39.4
Analytic conductor $2.301$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.1
Root \(-5.36472i\) of defining polynomial
Character \(\chi\) \(=\) 39.4
Dual form 39.4.j.c.10.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.64599 - 2.68236i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(10.3901 + 17.9962i) q^{4} -2.69631i q^{5} +(13.9380 - 8.04709i) q^{6} +(13.1657 - 7.60123i) q^{7} -68.5626i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-4.64599 - 2.68236i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(10.3901 + 17.9962i) q^{4} -2.69631i q^{5} +(13.9380 - 8.04709i) q^{6} +(13.1657 - 7.60123i) q^{7} -68.5626i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-7.23249 + 12.5270i) q^{10} +(57.9240 + 33.4424i) q^{11} -62.3408 q^{12} +(46.8650 - 0.818689i) q^{13} -81.5570 q^{14} +(7.00522 + 4.04447i) q^{15} +(-100.789 + 174.571i) q^{16} +(2.08177 + 3.60573i) q^{17} +48.2825i q^{18} +(-22.5903 + 13.0425i) q^{19} +(48.5235 - 28.0150i) q^{20} +45.6074i q^{21} +(-179.409 - 310.746i) q^{22} +(23.6621 - 40.9839i) q^{23} +(178.131 + 102.844i) q^{24} +117.730 q^{25} +(-219.930 - 121.905i) q^{26} +27.0000 q^{27} +(273.587 + 157.956i) q^{28} +(-128.503 + 222.575i) q^{29} +(-21.6975 - 37.5811i) q^{30} -206.242i q^{31} +(461.511 - 266.453i) q^{32} +(-173.772 + 100.327i) q^{33} -22.3362i q^{34} +(-20.4953 - 35.4989i) q^{35} +(93.5112 - 161.966i) q^{36} +(-152.149 - 87.8430i) q^{37} +139.939 q^{38} +(-68.1705 + 122.987i) q^{39} -184.866 q^{40} +(135.501 + 78.2313i) q^{41} +(122.336 - 211.891i) q^{42} +(25.9922 + 45.0199i) q^{43} +1389.88i q^{44} +(-21.0157 + 12.1334i) q^{45} +(-219.868 + 126.941i) q^{46} -354.222i q^{47} +(-302.366 - 523.714i) q^{48} +(-55.9425 + 96.8953i) q^{49} +(-546.972 - 315.794i) q^{50} -12.4906 q^{51} +(501.667 + 834.888i) q^{52} -10.4723 q^{53} +(-125.442 - 72.4238i) q^{54} +(90.1712 - 156.181i) q^{55} +(-521.160 - 902.676i) q^{56} -78.2550i q^{57} +(1194.05 - 689.386i) q^{58} +(385.480 - 222.557i) q^{59} +168.090i q^{60} +(-59.8481 - 103.660i) q^{61} +(-553.216 + 958.199i) q^{62} +(-118.491 - 68.4111i) q^{63} -1246.28 q^{64} +(-2.20744 - 126.363i) q^{65} +1076.46 q^{66} +(-19.4057 - 11.2039i) q^{67} +(-43.2597 + 74.9281i) q^{68} +(70.9863 + 122.952i) q^{69} +219.903i q^{70} +(-246.997 + 142.604i) q^{71} +(-534.393 + 308.532i) q^{72} +740.989i q^{73} +(471.253 + 816.235i) q^{74} +(-176.595 + 305.871i) q^{75} +(-469.432 - 271.027i) q^{76} +1016.81 q^{77} +(646.615 - 388.538i) q^{78} -547.679 q^{79} +(470.698 + 271.758i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-419.689 - 726.923i) q^{82} -603.056i q^{83} +(-820.762 + 473.867i) q^{84} +(9.72218 - 5.61310i) q^{85} -278.882i q^{86} +(-385.510 - 667.724i) q^{87} +(2292.90 - 3971.42i) q^{88} +(-186.774 - 107.834i) q^{89} +130.185 q^{90} +(610.789 - 367.011i) q^{91} +983.409 q^{92} +(535.833 + 309.363i) q^{93} +(-950.153 + 1645.71i) q^{94} +(35.1666 + 60.9104i) q^{95} +1598.72i q^{96} +(-1253.58 + 723.752i) q^{97} +(519.817 - 300.116i) q^{98} -601.964i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25} - 30 q^{26} + 270 q^{27} + 150 q^{28} - 495 q^{29} + 120 q^{30} + 1440 q^{32} - 180 q^{33} + 60 q^{35} + 270 q^{36} - 405 q^{37} - 1380 q^{38} + 345 q^{39} + 2000 q^{40} + 1065 q^{41} + 90 q^{42} - 370 q^{43} - 135 q^{45} - 390 q^{46} - 750 q^{48} + 775 q^{49} - 4320 q^{50} - 630 q^{51} + 2940 q^{52} + 330 q^{53} - 260 q^{55} - 2670 q^{56} + 2040 q^{58} + 780 q^{59} - 1375 q^{61} - 780 q^{62} - 270 q^{63} - 3140 q^{64} + 1605 q^{65} + 1740 q^{66} + 1590 q^{67} - 600 q^{68} - 180 q^{69} + 1620 q^{71} + 2190 q^{74} + 1440 q^{75} - 5190 q^{76} - 4320 q^{77} + 2340 q^{78} + 1100 q^{79} + 8430 q^{80} - 405 q^{81} - 2390 q^{82} - 450 q^{84} + 525 q^{85} - 1485 q^{87} + 3170 q^{88} + 2040 q^{89} - 720 q^{90} + 4770 q^{91} - 1740 q^{92} - 990 q^{93} - 3230 q^{94} - 1380 q^{95} - 3750 q^{97} + 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.64599 2.68236i −1.64260 0.948358i −0.979903 0.199475i \(-0.936076\pi\)
−0.662702 0.748883i \(-0.730590\pi\)
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) 10.3901 + 17.9962i 1.29877 + 2.24953i
\(5\) 2.69631i 0.241165i −0.992703 0.120583i \(-0.961524\pi\)
0.992703 0.120583i \(-0.0384763\pi\)
\(6\) 13.9380 8.04709i 0.948358 0.547535i
\(7\) 13.1657 7.60123i 0.710882 0.410428i −0.100505 0.994937i \(-0.532046\pi\)
0.811388 + 0.584509i \(0.198713\pi\)
\(8\) 68.5626i 3.03007i
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −7.23249 + 12.5270i −0.228711 + 0.396140i
\(11\) 57.9240 + 33.4424i 1.58770 + 0.916661i 0.993685 + 0.112209i \(0.0357927\pi\)
0.594018 + 0.804451i \(0.297541\pi\)
\(12\) −62.3408 −1.49969
\(13\) 46.8650 0.818689i 0.999847 0.0174664i
\(14\) −81.5570 −1.55693
\(15\) 7.00522 + 4.04447i 0.120583 + 0.0696185i
\(16\) −100.789 + 174.571i −1.57482 + 2.72767i
\(17\) 2.08177 + 3.60573i 0.0297002 + 0.0514422i 0.880493 0.474058i \(-0.157211\pi\)
−0.850793 + 0.525501i \(0.823878\pi\)
\(18\) 48.2825i 0.632239i
\(19\) −22.5903 + 13.0425i −0.272766 + 0.157482i −0.630144 0.776478i \(-0.717004\pi\)
0.357378 + 0.933960i \(0.383671\pi\)
\(20\) 48.5235 28.0150i 0.542509 0.313218i
\(21\) 45.6074i 0.473921i
\(22\) −179.409 310.746i −1.73865 3.01142i
\(23\) 23.6621 40.9839i 0.214517 0.371554i −0.738606 0.674137i \(-0.764516\pi\)
0.953123 + 0.302583i \(0.0978490\pi\)
\(24\) 178.131 + 102.844i 1.51503 + 0.874705i
\(25\) 117.730 0.941839
\(26\) −219.930 121.905i −1.65892 0.919523i
\(27\) 27.0000 0.192450
\(28\) 273.587 + 157.956i 1.84654 + 1.06610i
\(29\) −128.503 + 222.575i −0.822845 + 1.42521i 0.0807106 + 0.996738i \(0.474281\pi\)
−0.903555 + 0.428471i \(0.859052\pi\)
\(30\) −21.6975 37.5811i −0.132047 0.228711i
\(31\) 206.242i 1.19491i −0.801903 0.597455i \(-0.796179\pi\)
0.801903 0.597455i \(-0.203821\pi\)
\(32\) 461.511 266.453i 2.54951 1.47196i
\(33\) −173.772 + 100.327i −0.916661 + 0.529234i
\(34\) 22.3362i 0.112666i
\(35\) −20.4953 35.4989i −0.0989811 0.171440i
\(36\) 93.5112 161.966i 0.432922 0.749843i
\(37\) −152.149 87.8430i −0.676029 0.390305i 0.122328 0.992490i \(-0.460964\pi\)
−0.798357 + 0.602184i \(0.794297\pi\)
\(38\) 139.939 0.597396
\(39\) −68.1705 + 122.987i −0.279898 + 0.504966i
\(40\) −184.866 −0.730748
\(41\) 135.501 + 78.2313i 0.516137 + 0.297992i 0.735353 0.677684i \(-0.237016\pi\)
−0.219216 + 0.975676i \(0.570350\pi\)
\(42\) 122.336 211.891i 0.449447 0.778466i
\(43\) 25.9922 + 45.0199i 0.0921809 + 0.159662i 0.908429 0.418040i \(-0.137283\pi\)
−0.816248 + 0.577702i \(0.803950\pi\)
\(44\) 1389.88i 4.76211i
\(45\) −21.0157 + 12.1334i −0.0696185 + 0.0401942i
\(46\) −219.868 + 126.941i −0.704733 + 0.406878i
\(47\) 354.222i 1.09933i −0.835384 0.549666i \(-0.814755\pi\)
0.835384 0.549666i \(-0.185245\pi\)
\(48\) −302.366 523.714i −0.909225 1.57482i
\(49\) −55.9425 + 96.8953i −0.163098 + 0.282494i
\(50\) −546.972 315.794i −1.54707 0.893201i
\(51\) −12.4906 −0.0342948
\(52\) 501.667 + 834.888i 1.33786 + 2.22650i
\(53\) −10.4723 −0.0271412 −0.0135706 0.999908i \(-0.504320\pi\)
−0.0135706 + 0.999908i \(0.504320\pi\)
\(54\) −125.442 72.4238i −0.316119 0.182512i
\(55\) 90.1712 156.181i 0.221067 0.382899i
\(56\) −521.160 902.676i −1.24362 2.15402i
\(57\) 78.2550i 0.181844i
\(58\) 1194.05 689.386i 2.70322 1.56070i
\(59\) 385.480 222.557i 0.850597 0.491092i −0.0102552 0.999947i \(-0.503264\pi\)
0.860852 + 0.508855i \(0.169931\pi\)
\(60\) 168.090i 0.361673i
\(61\) −59.8481 103.660i −0.125619 0.217579i 0.796356 0.604829i \(-0.206758\pi\)
−0.921975 + 0.387250i \(0.873425\pi\)
\(62\) −553.216 + 958.199i −1.13320 + 1.96276i
\(63\) −118.491 68.4111i −0.236961 0.136809i
\(64\) −1246.28 −2.43413
\(65\) −2.20744 126.363i −0.00421230 0.241129i
\(66\) 1076.46 2.00761
\(67\) −19.4057 11.2039i −0.0353848 0.0204294i 0.482203 0.876059i \(-0.339837\pi\)
−0.517588 + 0.855630i \(0.673170\pi\)
\(68\) −43.2597 + 74.9281i −0.0771473 + 0.133623i
\(69\) 70.9863 + 122.952i 0.123851 + 0.214517i
\(70\) 219.903i 0.375478i
\(71\) −246.997 + 142.604i −0.412861 + 0.238365i −0.692018 0.721880i \(-0.743278\pi\)
0.279157 + 0.960245i \(0.409945\pi\)
\(72\) −534.393 + 308.532i −0.874705 + 0.505011i
\(73\) 740.989i 1.18803i 0.804454 + 0.594015i \(0.202458\pi\)
−0.804454 + 0.594015i \(0.797542\pi\)
\(74\) 471.253 + 816.235i 0.740299 + 1.28223i
\(75\) −176.595 + 305.871i −0.271886 + 0.470920i
\(76\) −469.432 271.027i −0.708520 0.409064i
\(77\) 1016.81 1.50489
\(78\) 646.615 388.538i 0.938650 0.564016i
\(79\) −547.679 −0.779983 −0.389992 0.920818i \(-0.627522\pi\)
−0.389992 + 0.920818i \(0.627522\pi\)
\(80\) 470.698 + 271.758i 0.657821 + 0.379793i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −419.689 726.923i −0.565206 0.978966i
\(83\) 603.056i 0.797518i −0.917056 0.398759i \(-0.869441\pi\)
0.917056 0.398759i \(-0.130559\pi\)
\(84\) −820.762 + 473.867i −1.06610 + 0.615513i
\(85\) 9.72218 5.61310i 0.0124061 0.00716266i
\(86\) 278.882i 0.349682i
\(87\) −385.510 667.724i −0.475070 0.822845i
\(88\) 2292.90 3971.42i 2.77754 4.81085i
\(89\) −186.774 107.834i −0.222450 0.128431i 0.384634 0.923069i \(-0.374328\pi\)
−0.607084 + 0.794638i \(0.707661\pi\)
\(90\) 130.185 0.152474
\(91\) 610.789 367.011i 0.703605 0.422782i
\(92\) 983.409 1.11443
\(93\) 535.833 + 309.363i 0.597455 + 0.344941i
\(94\) −950.153 + 1645.71i −1.04256 + 1.80577i
\(95\) 35.1666 + 60.9104i 0.0379792 + 0.0657818i
\(96\) 1598.72i 1.69967i
\(97\) −1253.58 + 723.752i −1.31218 + 0.757586i −0.982457 0.186492i \(-0.940288\pi\)
−0.329722 + 0.944078i \(0.606955\pi\)
\(98\) 519.817 300.116i 0.535810 0.309350i
\(99\) 601.964i 0.611107i
\(100\) 1223.23 + 2118.70i 1.22323 + 2.11870i
\(101\) −441.725 + 765.090i −0.435181 + 0.753756i −0.997310 0.0732935i \(-0.976649\pi\)
0.562129 + 0.827049i \(0.309982\pi\)
\(102\) 58.0313 + 33.5044i 0.0563328 + 0.0325238i
\(103\) −1251.74 −1.19745 −0.598726 0.800954i \(-0.704326\pi\)
−0.598726 + 0.800954i \(0.704326\pi\)
\(104\) −56.1315 3213.19i −0.0529244 3.02961i
\(105\) 122.972 0.114293
\(106\) 48.6543 + 28.0906i 0.0445823 + 0.0257396i
\(107\) 170.807 295.846i 0.154323 0.267294i −0.778490 0.627658i \(-0.784014\pi\)
0.932812 + 0.360363i \(0.117347\pi\)
\(108\) 280.534 + 485.899i 0.249948 + 0.432922i
\(109\) 775.177i 0.681179i −0.940212 0.340589i \(-0.889373\pi\)
0.940212 0.340589i \(-0.110627\pi\)
\(110\) −837.869 + 483.744i −0.726251 + 0.419301i
\(111\) 456.446 263.529i 0.390305 0.225343i
\(112\) 3064.47i 2.58541i
\(113\) −639.524 1107.69i −0.532402 0.922147i −0.999284 0.0378273i \(-0.987956\pi\)
0.466883 0.884319i \(-0.345377\pi\)
\(114\) −209.908 + 363.572i −0.172454 + 0.298698i
\(115\) −110.505 63.8004i −0.0896060 0.0517340i
\(116\) −5340.67 −4.27473
\(117\) −217.274 361.593i −0.171683 0.285720i
\(118\) −2387.91 −1.86293
\(119\) 54.8160 + 31.6480i 0.0422267 + 0.0243796i
\(120\) 277.299 480.297i 0.210949 0.365374i
\(121\) 1571.29 + 2721.55i 1.18053 + 2.04474i
\(122\) 642.137i 0.476528i
\(123\) −406.502 + 234.694i −0.297992 + 0.172046i
\(124\) 3711.58 2142.88i 2.68798 1.55191i
\(125\) 654.476i 0.468305i
\(126\) 367.007 + 635.674i 0.259489 + 0.449447i
\(127\) −556.910 + 964.597i −0.389117 + 0.673970i −0.992331 0.123609i \(-0.960553\pi\)
0.603214 + 0.797579i \(0.293886\pi\)
\(128\) 2098.10 + 1211.34i 1.44881 + 0.836472i
\(129\) −155.953 −0.106441
\(130\) −328.695 + 593.001i −0.221757 + 0.400074i
\(131\) 2100.12 1.40068 0.700339 0.713811i \(-0.253032\pi\)
0.700339 + 0.713811i \(0.253032\pi\)
\(132\) −3611.03 2084.83i −2.38106 1.37470i
\(133\) −198.278 + 343.428i −0.129270 + 0.223902i
\(134\) 60.1057 + 104.106i 0.0387488 + 0.0671150i
\(135\) 72.8004i 0.0464123i
\(136\) 247.218 142.732i 0.155874 0.0899936i
\(137\) −1043.58 + 602.509i −0.650793 + 0.375736i −0.788760 0.614701i \(-0.789277\pi\)
0.137967 + 0.990437i \(0.455943\pi\)
\(138\) 761.643i 0.469822i
\(139\) −161.445 279.631i −0.0985149 0.170633i 0.812555 0.582884i \(-0.198076\pi\)
−0.911070 + 0.412251i \(0.864743\pi\)
\(140\) 425.898 737.677i 0.257107 0.445322i
\(141\) 920.297 + 531.334i 0.549666 + 0.317350i
\(142\) 1530.06 0.904223
\(143\) 2741.99 + 1519.86i 1.60347 + 0.888789i
\(144\) 1814.20 1.04988
\(145\) 600.131 + 346.486i 0.343711 + 0.198442i
\(146\) 1987.60 3442.63i 1.12668 1.95146i
\(147\) −167.828 290.686i −0.0941645 0.163098i
\(148\) 3650.80i 2.02766i
\(149\) −977.620 + 564.429i −0.537515 + 0.310335i −0.744071 0.668100i \(-0.767108\pi\)
0.206556 + 0.978435i \(0.433774\pi\)
\(150\) 1640.92 947.383i 0.893201 0.515690i
\(151\) 2940.44i 1.58470i −0.610066 0.792350i \(-0.708857\pi\)
0.610066 0.792350i \(-0.291143\pi\)
\(152\) 894.228 + 1548.85i 0.477181 + 0.826501i
\(153\) 18.7359 32.4516i 0.00990006 0.0171474i
\(154\) −4724.11 2727.46i −2.47194 1.42718i
\(155\) −556.093 −0.288171
\(156\) −2921.60 + 51.0377i −1.49946 + 0.0261942i
\(157\) 629.388 0.319940 0.159970 0.987122i \(-0.448860\pi\)
0.159970 + 0.987122i \(0.448860\pi\)
\(158\) 2544.51 + 1469.07i 1.28120 + 0.739703i
\(159\) 15.7085 27.2079i 0.00783500 0.0135706i
\(160\) −718.441 1244.38i −0.354986 0.614854i
\(161\) 719.444i 0.352175i
\(162\) 376.325 217.271i 0.182512 0.105373i
\(163\) −342.004 + 197.456i −0.164343 + 0.0948832i −0.579915 0.814677i \(-0.696914\pi\)
0.415573 + 0.909560i \(0.363581\pi\)
\(164\) 3251.33i 1.54809i
\(165\) 270.514 + 468.543i 0.127633 + 0.221067i
\(166\) −1617.61 + 2801.79i −0.756333 + 1.31001i
\(167\) 131.515 + 75.9299i 0.0609395 + 0.0351834i 0.530160 0.847898i \(-0.322132\pi\)
−0.469221 + 0.883081i \(0.655465\pi\)
\(168\) 3126.96 1.43601
\(169\) 2195.66 76.7357i 0.999390 0.0349275i
\(170\) −60.2255 −0.0271711
\(171\) 203.312 + 117.382i 0.0909221 + 0.0524939i
\(172\) −540.126 + 935.525i −0.239443 + 0.414728i
\(173\) 269.407 + 466.626i 0.118397 + 0.205069i 0.919132 0.393949i \(-0.128891\pi\)
−0.800736 + 0.599018i \(0.795558\pi\)
\(174\) 4136.31i 1.80214i
\(175\) 1550.00 894.892i 0.669537 0.386557i
\(176\) −11676.2 + 6741.24i −5.00070 + 2.88716i
\(177\) 1335.34i 0.567065i
\(178\) 578.500 + 1001.99i 0.243598 + 0.421924i
\(179\) −1110.40 + 1923.27i −0.463659 + 0.803081i −0.999140 0.0414660i \(-0.986797\pi\)
0.535481 + 0.844548i \(0.320130\pi\)
\(180\) −436.711 252.135i −0.180836 0.104406i
\(181\) 3822.78 1.56986 0.784932 0.619582i \(-0.212698\pi\)
0.784932 + 0.619582i \(0.212698\pi\)
\(182\) −3822.17 + 66.7698i −1.55669 + 0.0271940i
\(183\) 359.089 0.145052
\(184\) −2809.97 1622.33i −1.12583 0.650001i
\(185\) −236.852 + 410.240i −0.0941282 + 0.163035i
\(186\) −1659.65 2874.60i −0.654254 1.13320i
\(187\) 278.478i 0.108900i
\(188\) 6374.67 3680.42i 2.47298 1.42778i
\(189\) 355.474 205.233i 0.136809 0.0789869i
\(190\) 377.319i 0.144071i
\(191\) −1732.09 3000.08i −0.656178 1.13653i −0.981597 0.190964i \(-0.938839\pi\)
0.325419 0.945570i \(-0.394495\pi\)
\(192\) 1869.42 3237.92i 0.702674 1.21707i
\(193\) −4068.07 2348.70i −1.51723 0.875975i −0.999795 0.0202541i \(-0.993552\pi\)
−0.517438 0.855721i \(-0.673114\pi\)
\(194\) 7765.46 2.87385
\(195\) 331.611 + 183.809i 0.121780 + 0.0675017i
\(196\) −2325.00 −0.847304
\(197\) −2500.98 1443.94i −0.904506 0.522217i −0.0258469 0.999666i \(-0.508228\pi\)
−0.878660 + 0.477449i \(0.841562\pi\)
\(198\) −1614.68 + 2796.72i −0.579549 + 1.00381i
\(199\) 31.5046 + 54.5676i 0.0112226 + 0.0194382i 0.871582 0.490249i \(-0.163094\pi\)
−0.860360 + 0.509688i \(0.829761\pi\)
\(200\) 8071.87i 2.85384i
\(201\) 58.2171 33.6117i 0.0204294 0.0117949i
\(202\) 4104.50 2369.73i 1.42966 0.825415i
\(203\) 3907.14i 1.35087i
\(204\) −129.779 224.784i −0.0445410 0.0771473i
\(205\) 210.936 365.352i 0.0718654 0.124474i
\(206\) 5815.57 + 3357.62i 1.96694 + 1.13561i
\(207\) −425.918 −0.143011
\(208\) −4580.55 + 8263.80i −1.52694 + 2.75477i
\(209\) −1744.69 −0.577429
\(210\) −571.325 329.855i −0.187739 0.108391i
\(211\) 524.848 909.064i 0.171242 0.296600i −0.767612 0.640914i \(-0.778555\pi\)
0.938854 + 0.344315i \(0.111889\pi\)
\(212\) −108.809 188.463i −0.0352501 0.0610550i
\(213\) 855.622i 0.275241i
\(214\) −1587.13 + 916.331i −0.506982 + 0.292706i
\(215\) 121.388 70.0832i 0.0385050 0.0222309i
\(216\) 1851.19i 0.583137i
\(217\) −1567.69 2715.33i −0.490424 0.849440i
\(218\) −2079.30 + 3601.46i −0.646001 + 1.11891i
\(219\) −1925.15 1111.48i −0.594015 0.342955i
\(220\) 3747.56 1.14846
\(221\) 100.514 + 167.278i 0.0305942 + 0.0509156i
\(222\) −2827.52 −0.854823
\(223\) 2003.54 + 1156.75i 0.601647 + 0.347361i 0.769689 0.638419i \(-0.220411\pi\)
−0.168042 + 0.985780i \(0.553745\pi\)
\(224\) 4050.75 7016.10i 1.20827 2.09278i
\(225\) −529.785 917.614i −0.156973 0.271886i
\(226\) 6861.74i 2.01963i
\(227\) −3290.43 + 1899.73i −0.962085 + 0.555460i −0.896814 0.442407i \(-0.854125\pi\)
−0.0652711 + 0.997868i \(0.520791\pi\)
\(228\) 1408.30 813.080i 0.409064 0.236173i
\(229\) 4321.07i 1.24692i −0.781856 0.623459i \(-0.785727\pi\)
0.781856 0.623459i \(-0.214273\pi\)
\(230\) 342.271 + 592.832i 0.0981248 + 0.169957i
\(231\) −1525.22 + 2641.76i −0.434425 + 0.752446i
\(232\) 15260.3 + 8810.54i 4.31848 + 2.49328i
\(233\) −5279.77 −1.48450 −0.742251 0.670122i \(-0.766242\pi\)
−0.742251 + 0.670122i \(0.766242\pi\)
\(234\) 39.5284 + 2262.76i 0.0110429 + 0.632142i
\(235\) −955.094 −0.265121
\(236\) 8010.38 + 4624.79i 2.20945 + 1.27563i
\(237\) 821.518 1422.91i 0.225162 0.389992i
\(238\) −169.783 294.073i −0.0462412 0.0800920i
\(239\) 1547.92i 0.418939i −0.977815 0.209469i \(-0.932826\pi\)
0.977815 0.209469i \(-0.0671737\pi\)
\(240\) −1412.10 + 815.274i −0.379793 + 0.219274i
\(241\) −4259.12 + 2459.00i −1.13840 + 0.657255i −0.946033 0.324069i \(-0.894949\pi\)
−0.192365 + 0.981323i \(0.561616\pi\)
\(242\) 16859.1i 4.47828i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 1243.66 2154.08i 0.326300 0.565168i
\(245\) 261.260 + 150.839i 0.0681277 + 0.0393336i
\(246\) 2518.14 0.652644
\(247\) −1048.02 + 629.731i −0.269974 + 0.162222i
\(248\) −14140.5 −3.62066
\(249\) 1566.78 + 904.584i 0.398759 + 0.230224i
\(250\) −1755.54 + 3040.69i −0.444121 + 0.769239i
\(251\) 577.890 + 1000.94i 0.145323 + 0.251707i 0.929493 0.368839i \(-0.120244\pi\)
−0.784170 + 0.620546i \(0.786911\pi\)
\(252\) 2843.20i 0.710734i
\(253\) 2741.20 1582.63i 0.681178 0.393278i
\(254\) 5174.80 2987.67i 1.27833 0.738044i
\(255\) 33.6786i 0.00827073i
\(256\) −1513.40 2621.28i −0.369482 0.639962i
\(257\) 1175.98 2036.85i 0.285429 0.494378i −0.687284 0.726389i \(-0.741197\pi\)
0.972713 + 0.232011i \(0.0745304\pi\)
\(258\) 724.558 + 418.324i 0.174841 + 0.100945i
\(259\) −2670.86 −0.640769
\(260\) 2251.12 1352.65i 0.536956 0.322646i
\(261\) 2313.06 0.548563
\(262\) −9757.15 5633.29i −2.30076 1.32834i
\(263\) −2760.94 + 4782.09i −0.647326 + 1.12120i 0.336433 + 0.941707i \(0.390779\pi\)
−0.983759 + 0.179494i \(0.942554\pi\)
\(264\) 6878.70 + 11914.3i 1.60362 + 2.77754i
\(265\) 28.2367i 0.00654553i
\(266\) 1842.39 1063.71i 0.424678 0.245188i
\(267\) 560.322 323.502i 0.128431 0.0741499i
\(268\) 465.639i 0.106132i
\(269\) −1958.48 3392.18i −0.443905 0.768866i 0.554070 0.832470i \(-0.313074\pi\)
−0.997975 + 0.0636038i \(0.979741\pi\)
\(270\) −195.277 + 338.230i −0.0440155 + 0.0762371i
\(271\) 2405.41 + 1388.76i 0.539182 + 0.311297i 0.744747 0.667347i \(-0.232570\pi\)
−0.205566 + 0.978643i \(0.565903\pi\)
\(272\) −839.276 −0.187090
\(273\) 37.3383 + 2137.39i 0.00827771 + 0.473849i
\(274\) 6464.58 1.42533
\(275\) 6819.38 + 3937.17i 1.49536 + 0.863347i
\(276\) −1475.11 + 2554.97i −0.321708 + 0.557215i
\(277\) 3291.54 + 5701.12i 0.713969 + 1.23663i 0.963356 + 0.268227i \(0.0864378\pi\)
−0.249386 + 0.968404i \(0.580229\pi\)
\(278\) 1732.21i 0.373710i
\(279\) −1607.50 + 928.090i −0.344941 + 0.199152i
\(280\) −2433.90 + 1405.21i −0.519476 + 0.299919i
\(281\) 2871.66i 0.609640i 0.952410 + 0.304820i \(0.0985963\pi\)
−0.952410 + 0.304820i \(0.901404\pi\)
\(282\) −2850.46 4937.14i −0.601923 1.04256i
\(283\) 3759.02 6510.81i 0.789578 1.36759i −0.136648 0.990620i \(-0.543633\pi\)
0.926226 0.376969i \(-0.123034\pi\)
\(284\) −5132.66 2963.34i −1.07242 0.619162i
\(285\) −211.000 −0.0438546
\(286\) −8662.43 14416.2i −1.79098 2.98060i
\(287\) 2378.62 0.489217
\(288\) −4153.60 2398.08i −0.849837 0.490653i
\(289\) 2447.83 4239.77i 0.498236 0.862970i
\(290\) −1858.80 3219.54i −0.376388 0.651923i
\(291\) 4342.51i 0.874785i
\(292\) −13335.0 + 7698.97i −2.67251 + 1.54297i
\(293\) 3902.80 2253.28i 0.778171 0.449278i −0.0576104 0.998339i \(-0.518348\pi\)
0.835782 + 0.549062i \(0.185015\pi\)
\(294\) 1800.70i 0.357207i
\(295\) −600.083 1039.37i −0.118435 0.205135i
\(296\) −6022.75 + 10431.7i −1.18265 + 2.04841i
\(297\) 1563.95 + 902.945i 0.305554 + 0.176411i
\(298\) 6056.02 1.17723
\(299\) 1075.37 1940.08i 0.207994 0.375244i
\(300\) −7339.38 −1.41246
\(301\) 684.413 + 395.146i 0.131060 + 0.0756673i
\(302\) −7887.33 + 13661.3i −1.50286 + 2.60304i
\(303\) −1325.18 2295.27i −0.251252 0.435181i
\(304\) 5258.15i 0.992024i
\(305\) −279.500 + 161.369i −0.0524725 + 0.0302950i
\(306\) −174.094 + 100.513i −0.0325238 + 0.0187776i
\(307\) 9538.89i 1.77333i 0.462409 + 0.886667i \(0.346985\pi\)
−0.462409 + 0.886667i \(0.653015\pi\)
\(308\) 10564.8 + 18298.8i 1.95450 + 3.38530i
\(309\) 1877.61 3252.12i 0.345675 0.598726i
\(310\) 2583.60 + 1491.64i 0.473351 + 0.273289i
\(311\) 7466.28 1.36133 0.680666 0.732594i \(-0.261691\pi\)
0.680666 + 0.732594i \(0.261691\pi\)
\(312\) 8432.31 + 4673.95i 1.53008 + 0.848110i
\(313\) −1821.65 −0.328964 −0.164482 0.986380i \(-0.552595\pi\)
−0.164482 + 0.986380i \(0.552595\pi\)
\(314\) −2924.13 1688.25i −0.525536 0.303418i
\(315\) −184.458 + 319.490i −0.0329937 + 0.0571467i
\(316\) −5690.46 9856.16i −1.01302 1.75460i
\(317\) 3125.14i 0.553708i −0.960912 0.276854i \(-0.910708\pi\)
0.960912 0.276854i \(-0.0892918\pi\)
\(318\) −145.963 + 84.2717i −0.0257396 + 0.0148608i
\(319\) −14886.9 + 8594.93i −2.61287 + 1.50854i
\(320\) 3360.35i 0.587029i
\(321\) 512.420 + 887.538i 0.0890982 + 0.154323i
\(322\) −1929.81 + 3342.53i −0.333988 + 0.578484i
\(323\) −94.0554 54.3029i −0.0162024 0.00935448i
\(324\) −1683.20 −0.288615
\(325\) 5517.41 96.3842i 0.941696 0.0164506i
\(326\) 2118.60 0.359933
\(327\) 2013.97 + 1162.77i 0.340589 + 0.196639i
\(328\) 5363.74 9290.27i 0.902936 1.56393i
\(329\) −2692.53 4663.59i −0.451197 0.781496i
\(330\) 2902.46i 0.484167i
\(331\) 1345.52 776.836i 0.223433 0.128999i −0.384106 0.923289i \(-0.625490\pi\)
0.607539 + 0.794290i \(0.292157\pi\)
\(332\) 10852.7 6265.83i 1.79404 1.03579i
\(333\) 1581.17i 0.260204i
\(334\) −407.343 705.539i −0.0667330 0.115585i
\(335\) −30.2092 + 52.3238i −0.00492688 + 0.00853360i
\(336\) −7961.74 4596.71i −1.29270 0.746343i
\(337\) 3190.43 0.515709 0.257855 0.966184i \(-0.416984\pi\)
0.257855 + 0.966184i \(0.416984\pi\)
\(338\) −10406.8 5533.04i −1.67473 0.890408i
\(339\) 3837.15 0.614764
\(340\) 202.029 + 116.642i 0.0322252 + 0.0186053i
\(341\) 6897.24 11946.4i 1.09533 1.89716i
\(342\) −629.724 1090.71i −0.0995661 0.172454i
\(343\) 6915.37i 1.08862i
\(344\) 3086.68 1782.10i 0.483787 0.279315i
\(345\) 331.516 191.401i 0.0517340 0.0298687i
\(346\) 2890.59i 0.449130i
\(347\) 2859.34 + 4952.53i 0.442356 + 0.766183i 0.997864 0.0653283i \(-0.0208095\pi\)
−0.555508 + 0.831511i \(0.687476\pi\)
\(348\) 8011.01 13875.5i 1.23401 2.13737i
\(349\) 2882.53 + 1664.23i 0.442116 + 0.255256i 0.704495 0.709709i \(-0.251174\pi\)
−0.262379 + 0.964965i \(0.584507\pi\)
\(350\) −9601.70 −1.46638
\(351\) 1265.36 22.1046i 0.192421 0.00336141i
\(352\) 35643.4 5.39715
\(353\) −10657.7 6153.25i −1.60695 0.927774i −0.990047 0.140737i \(-0.955053\pi\)
−0.616905 0.787037i \(-0.711614\pi\)
\(354\) 3581.87 6203.98i 0.537781 0.931463i
\(355\) 384.504 + 665.981i 0.0574855 + 0.0995679i
\(356\) 4481.64i 0.667210i
\(357\) −164.448 + 94.9441i −0.0243796 + 0.0140756i
\(358\) 10317.8 5956.98i 1.52322 0.879430i
\(359\) 8539.97i 1.25549i 0.778418 + 0.627747i \(0.216023\pi\)
−0.778418 + 0.627747i \(0.783977\pi\)
\(360\) 831.898 + 1440.89i 0.121791 + 0.210949i
\(361\) −3089.29 + 5350.80i −0.450399 + 0.780114i
\(362\) −17760.6 10254.1i −2.57866 1.48879i
\(363\) −9427.74 −1.36316
\(364\) 12951.0 + 7178.61i 1.86488 + 1.03369i
\(365\) 1997.94 0.286512
\(366\) −1668.32 963.206i −0.238264 0.137562i
\(367\) −1248.33 + 2162.17i −0.177553 + 0.307532i −0.941042 0.338290i \(-0.890152\pi\)
0.763489 + 0.645821i \(0.223485\pi\)
\(368\) 4769.74 + 8261.44i 0.675652 + 1.17026i
\(369\) 1408.16i 0.198661i
\(370\) 2200.82 1270.65i 0.309231 0.178535i
\(371\) −137.876 + 79.6026i −0.0192942 + 0.0111395i
\(372\) 12857.3i 1.79199i
\(373\) 571.454 + 989.787i 0.0793264 + 0.137397i 0.902960 0.429726i \(-0.141390\pi\)
−0.823633 + 0.567123i \(0.808056\pi\)
\(374\) 746.978 1293.80i 0.103276 0.178880i
\(375\) 1700.38 + 981.713i 0.234152 + 0.135188i
\(376\) −24286.4 −3.33105
\(377\) −5840.10 + 10536.2i −0.797826 + 1.43936i
\(378\) −2202.04 −0.299632
\(379\) −10549.8 6090.91i −1.42983 0.825512i −0.432723 0.901527i \(-0.642447\pi\)
−0.997107 + 0.0760146i \(0.975780\pi\)
\(380\) −730.772 + 1265.73i −0.0986522 + 0.170871i
\(381\) −1670.73 2893.79i −0.224657 0.389117i
\(382\) 18584.4i 2.48917i
\(383\) 8816.66 5090.30i 1.17627 0.679118i 0.221119 0.975247i \(-0.429029\pi\)
0.955148 + 0.296129i \(0.0956957\pi\)
\(384\) −6294.31 + 3634.02i −0.836472 + 0.482937i
\(385\) 2741.65i 0.362928i
\(386\) 12600.1 + 21824.1i 1.66148 + 2.87776i
\(387\) 233.930 405.179i 0.0307270 0.0532207i
\(388\) −26049.6 15039.8i −3.40843 1.96786i
\(389\) −5845.83 −0.761941 −0.380971 0.924587i \(-0.624410\pi\)
−0.380971 + 0.924587i \(0.624410\pi\)
\(390\) −1047.62 1743.48i −0.136021 0.226370i
\(391\) 197.036 0.0254848
\(392\) 6643.40 + 3835.57i 0.855975 + 0.494197i
\(393\) −3150.19 + 5456.28i −0.404341 + 0.700339i
\(394\) 7746.36 + 13417.1i 0.990498 + 1.71559i
\(395\) 1476.71i 0.188105i
\(396\) 10833.1 6254.48i 1.37470 0.793686i
\(397\) −2165.86 + 1250.46i −0.273807 + 0.158083i −0.630617 0.776094i \(-0.717198\pi\)
0.356809 + 0.934177i \(0.383865\pi\)
\(398\) 338.027i 0.0425723i
\(399\) −594.834 1030.28i −0.0746340 0.129270i
\(400\) −11865.8 + 20552.2i −1.48323 + 2.56903i
\(401\) 7958.12 + 4594.62i 0.991046 + 0.572181i 0.905587 0.424161i \(-0.139431\pi\)
0.0854594 + 0.996342i \(0.472764\pi\)
\(402\) −360.634 −0.0447433
\(403\) −168.848 9665.54i −0.0208708 1.19473i
\(404\) −18358.3 −2.26080
\(405\) 189.141 + 109.201i 0.0232062 + 0.0133981i
\(406\) 10480.4 18152.5i 1.28111 2.21895i
\(407\) −5875.36 10176.4i −0.715555 1.23938i
\(408\) 856.390i 0.103916i
\(409\) −7979.89 + 4607.19i −0.964744 + 0.556995i −0.897630 0.440750i \(-0.854712\pi\)
−0.0671140 + 0.997745i \(0.521379\pi\)
\(410\) −1960.01 + 1131.61i −0.236093 + 0.136308i
\(411\) 3615.05i 0.433862i
\(412\) −13005.8 22526.6i −1.55521 2.69371i
\(413\) 3383.42 5860.25i 0.403116 0.698218i
\(414\) 1978.81 + 1142.47i 0.234911 + 0.135626i
\(415\) −1626.03 −0.192334
\(416\) 21410.6 12865.2i 2.52341 1.51627i
\(417\) 968.669 0.113755
\(418\) 8105.81 + 4679.89i 0.948488 + 0.547610i
\(419\) 3247.20 5624.32i 0.378607 0.655767i −0.612253 0.790662i \(-0.709737\pi\)
0.990860 + 0.134895i \(0.0430699\pi\)
\(420\) 1277.69 + 2213.03i 0.148441 + 0.257107i
\(421\) 3059.56i 0.354190i −0.984194 0.177095i \(-0.943330\pi\)
0.984194 0.177095i \(-0.0566699\pi\)
\(422\) −4876.88 + 2815.67i −0.562566 + 0.324797i
\(423\) −2760.89 + 1594.00i −0.317350 + 0.183222i
\(424\) 718.010i 0.0822398i
\(425\) 245.087 + 424.502i 0.0279728 + 0.0484503i
\(426\) −2295.09 + 3975.21i −0.261027 + 0.452112i
\(427\) −1575.89 909.839i −0.178601 0.103115i
\(428\) 7098.82 0.801716
\(429\) −8061.69 + 4844.10i −0.907277 + 0.545164i
\(430\) −751.954 −0.0843313
\(431\) 6873.69 + 3968.53i 0.768199 + 0.443520i 0.832232 0.554428i \(-0.187063\pi\)
−0.0640325 + 0.997948i \(0.520396\pi\)
\(432\) −2721.30 + 4713.42i −0.303075 + 0.524941i
\(433\) 3647.19 + 6317.11i 0.404786 + 0.701111i 0.994297 0.106650i \(-0.0340125\pi\)
−0.589510 + 0.807761i \(0.700679\pi\)
\(434\) 16820.5i 1.86039i
\(435\) −1800.39 + 1039.46i −0.198442 + 0.114570i
\(436\) 13950.3 8054.19i 1.53233 0.884692i
\(437\) 1234.45i 0.135130i
\(438\) 5962.80 + 10327.9i 0.650488 + 1.12668i
\(439\) 7607.35 13176.3i 0.827059 1.43251i −0.0732765 0.997312i \(-0.523346\pi\)
0.900335 0.435197i \(-0.143321\pi\)
\(440\) −10708.2 6182.37i −1.16021 0.669848i
\(441\) 1006.97 0.108732
\(442\) −18.2864 1046.79i −0.00196787 0.112649i
\(443\) 1517.05 0.162703 0.0813515 0.996685i \(-0.474076\pi\)
0.0813515 + 0.996685i \(0.474076\pi\)
\(444\) 9485.06 + 5476.20i 1.01383 + 0.585336i
\(445\) −290.754 + 503.601i −0.0309732 + 0.0536472i
\(446\) −6205.63 10748.5i −0.658845 1.14115i
\(447\) 3386.58i 0.358343i
\(448\) −16408.1 + 9473.24i −1.73038 + 0.999037i
\(449\) −610.761 + 352.623i −0.0641951 + 0.0370631i −0.531754 0.846899i \(-0.678467\pi\)
0.467559 + 0.883962i \(0.345134\pi\)
\(450\) 5684.30i 0.595467i
\(451\) 5232.48 + 9062.93i 0.546315 + 0.946245i
\(452\) 13289.5 23018.1i 1.38293 2.39531i
\(453\) 7639.49 + 4410.66i 0.792350 + 0.457464i
\(454\) 20383.1 2.10710
\(455\) −989.575 1646.88i −0.101960 0.169685i
\(456\) −5365.37 −0.551001
\(457\) −6302.69 3638.86i −0.645137 0.372470i 0.141454 0.989945i \(-0.454822\pi\)
−0.786591 + 0.617475i \(0.788156\pi\)
\(458\) −11590.7 + 20075.6i −1.18253 + 2.04820i
\(459\) 56.2078 + 97.3547i 0.00571580 + 0.00990006i
\(460\) 2651.58i 0.268762i
\(461\) −1699.04 + 980.941i −0.171653 + 0.0991041i −0.583365 0.812210i \(-0.698264\pi\)
0.411712 + 0.911314i \(0.364931\pi\)
\(462\) 14172.3 8182.39i 1.42718 0.823981i
\(463\) 10374.1i 1.04131i −0.853768 0.520653i \(-0.825689\pi\)
0.853768 0.520653i \(-0.174311\pi\)
\(464\) −25903.4 44866.0i −2.59167 4.48891i
\(465\) 834.140 1444.77i 0.0831878 0.144085i
\(466\) 24529.7 + 14162.2i 2.43845 + 1.40784i
\(467\) −8788.92 −0.870883 −0.435442 0.900217i \(-0.643408\pi\)
−0.435442 + 0.900217i \(0.643408\pi\)
\(468\) 4249.80 7667.10i 0.419759 0.757291i
\(469\) −340.653 −0.0335392
\(470\) 4437.36 + 2561.91i 0.435489 + 0.251430i
\(471\) −944.082 + 1635.20i −0.0923588 + 0.159970i
\(472\) −15259.1 26429.5i −1.48804 2.57737i
\(473\) 3476.97i 0.337995i
\(474\) −7633.53 + 4407.22i −0.739703 + 0.427068i
\(475\) −2659.55 + 1535.49i −0.256902 + 0.148322i
\(476\) 1315.31i 0.126654i
\(477\) 47.1255 + 81.6237i 0.00452354 + 0.00783500i
\(478\) −4152.07 + 7191.60i −0.397304 + 0.688151i
\(479\) 9648.96 + 5570.83i 0.920401 + 0.531394i 0.883763 0.467935i \(-0.155002\pi\)
0.0366382 + 0.999329i \(0.488335\pi\)
\(480\) 4310.65 0.409903
\(481\) −7202.36 3992.20i −0.682743 0.378438i
\(482\) 26383.8 2.49325
\(483\) 1869.17 + 1079.17i 0.176087 + 0.101664i
\(484\) −32651.8 + 56554.6i −3.06648 + 5.31129i
\(485\) 1951.46 + 3380.03i 0.182704 + 0.316452i
\(486\) 1303.63i 0.121674i
\(487\) 17009.1 9820.23i 1.58266 0.913752i 0.588195 0.808719i \(-0.299839\pi\)
0.994469 0.105033i \(-0.0334948\pi\)
\(488\) −7107.20 + 4103.34i −0.659278 + 0.380634i
\(489\) 1184.74i 0.109562i
\(490\) −809.207 1401.59i −0.0746046 0.129219i
\(491\) −1705.16 + 2953.42i −0.156726 + 0.271458i −0.933686 0.358092i \(-0.883427\pi\)
0.776960 + 0.629550i \(0.216761\pi\)
\(492\) −8447.21 4877.00i −0.774044 0.446895i
\(493\) −1070.06 −0.0977546
\(494\) 6558.23 114.566i 0.597305 0.0104344i
\(495\) −1623.08 −0.147378
\(496\) 36003.9 + 20786.9i 3.25932 + 1.88177i
\(497\) −2167.93 + 3754.96i −0.195664 + 0.338899i
\(498\) −4852.84 8405.37i −0.436669 0.756333i
\(499\) 5032.44i 0.451469i 0.974189 + 0.225735i \(0.0724782\pi\)
−0.974189 + 0.225735i \(0.927522\pi\)
\(500\) 11778.1 6800.09i 1.05347 0.608219i
\(501\) −394.544 + 227.790i −0.0351834 + 0.0203132i
\(502\) 6200.44i 0.551274i
\(503\) −8594.69 14886.4i −0.761866 1.31959i −0.941888 0.335927i \(-0.890950\pi\)
0.180022 0.983663i \(-0.442383\pi\)
\(504\) −4690.44 + 8124.09i −0.414542 + 0.718007i
\(505\) 2062.92 + 1191.03i 0.181780 + 0.104951i
\(506\) −16980.8 −1.49187
\(507\) −3094.12 + 5819.59i −0.271035 + 0.509778i
\(508\) −23145.5 −2.02149
\(509\) −805.889 465.280i −0.0701776 0.0405170i 0.464501 0.885573i \(-0.346234\pi\)
−0.534678 + 0.845056i \(0.679567\pi\)
\(510\) 90.3382 156.470i 0.00784361 0.0135855i
\(511\) 5632.43 + 9755.65i 0.487601 + 0.844549i
\(512\) 3143.50i 0.271337i
\(513\) −609.937 + 352.147i −0.0524939 + 0.0303074i
\(514\) −10927.1 + 6308.79i −0.937695 + 0.541379i
\(515\) 3375.08i 0.288784i
\(516\) −1620.38 2806.58i −0.138243 0.239443i
\(517\) 11846.1 20518.0i 1.00772 1.74541i
\(518\) 12408.8 + 7164.21i 1.05253 + 0.607679i
\(519\) −1616.44 −0.136713
\(520\) −8663.76 + 151.348i −0.730637 + 0.0127636i
\(521\) −9869.60 −0.829933 −0.414966 0.909837i \(-0.636207\pi\)
−0.414966 + 0.909837i \(0.636207\pi\)
\(522\) −10746.5 6204.47i −0.901072 0.520234i
\(523\) 10710.3 18550.8i 0.895466 1.55099i 0.0622398 0.998061i \(-0.480176\pi\)
0.833226 0.552932i \(-0.186491\pi\)
\(524\) 21820.6 + 37794.3i 1.81915 + 3.15087i
\(525\) 5369.35i 0.446358i
\(526\) 25654.6 14811.7i 2.12660 1.22779i
\(527\) 743.654 429.349i 0.0614688 0.0354890i
\(528\) 40447.4i 3.33380i
\(529\) 4963.71 + 8597.40i 0.407965 + 0.706616i
\(530\) 75.7410 131.187i 0.00620750 0.0107517i
\(531\) −3469.32 2003.01i −0.283532 0.163697i
\(532\) −8240.54 −0.671565
\(533\) 6414.28 + 3555.38i 0.521263 + 0.288931i
\(534\) −3471.00 −0.281283
\(535\) −797.693 460.548i −0.0644622 0.0372173i
\(536\) −768.168 + 1330.51i −0.0619026 + 0.107218i
\(537\) −3331.19 5769.80i −0.267694 0.463659i
\(538\) 21013.4i 1.68392i
\(539\) −6480.83 + 3741.71i −0.517902 + 0.299011i
\(540\) 1310.13 756.406i 0.104406 0.0602788i
\(541\) 7771.50i 0.617602i 0.951127 + 0.308801i \(0.0999277\pi\)
−0.951127 + 0.308801i \(0.900072\pi\)
\(542\) −7450.34 12904.4i −0.590442 1.02267i
\(543\) −5734.17 + 9931.88i −0.453180 + 0.784932i
\(544\) 1921.52 + 1109.39i 0.151442 + 0.0874350i
\(545\) −2090.12 −0.164277
\(546\) 5559.78 10030.4i 0.435782 0.786197i
\(547\) −15577.5 −1.21763 −0.608817 0.793310i \(-0.708356\pi\)
−0.608817 + 0.793310i \(0.708356\pi\)
\(548\) −21685.8 12520.3i −1.69046 0.975986i
\(549\) −538.633 + 932.940i −0.0418730 + 0.0725262i
\(550\) −21121.8 36584.1i −1.63752 2.83628i
\(551\) 6704.02i 0.518332i
\(552\) 8429.90 4867.00i 0.650001 0.375278i
\(553\) −7210.58 + 4163.03i −0.554476 + 0.320127i
\(554\) 35316.4i 2.70840i
\(555\) −710.556 1230.72i −0.0543449 0.0941282i
\(556\) 3354.87 5810.80i 0.255896 0.443225i
\(557\) 19749.3 + 11402.3i 1.50234 + 0.867377i 0.999996 + 0.00270962i \(0.000862500\pi\)
0.502345 + 0.864667i \(0.332471\pi\)
\(558\) 9957.89 0.755468
\(559\) 1254.98 + 2088.58i 0.0949556 + 0.158028i
\(560\) 8262.78 0.623511
\(561\) −723.506 417.716i −0.0544500 0.0314367i
\(562\) 7702.83 13341.7i 0.578157 1.00140i
\(563\) −1758.71 3046.17i −0.131653 0.228030i 0.792661 0.609663i \(-0.208695\pi\)
−0.924314 + 0.381633i \(0.875362\pi\)
\(564\) 22082.5i 1.64865i
\(565\) −2986.67 + 1724.36i −0.222390 + 0.128397i
\(566\) −34928.7 + 20166.1i −2.59393 + 1.49761i
\(567\) 1231.40i 0.0912062i
\(568\) 9777.29 + 16934.8i 0.722264 + 1.25100i
\(569\) −3046.72 + 5277.08i −0.224473 + 0.388799i −0.956161 0.292841i \(-0.905399\pi\)
0.731688 + 0.681640i \(0.238733\pi\)
\(570\) 980.303 + 565.978i 0.0720357 + 0.0415898i
\(571\) −10460.2 −0.766630 −0.383315 0.923618i \(-0.625218\pi\)
−0.383315 + 0.923618i \(0.625218\pi\)
\(572\) 1137.88 + 65137.0i 0.0831771 + 4.76139i
\(573\) 10392.6 0.757689
\(574\) −11051.0 6380.31i −0.803590 0.463953i
\(575\) 2785.74 4825.03i 0.202040 0.349944i
\(576\) 5608.25 + 9713.77i 0.405689 + 0.702674i
\(577\) 9648.19i 0.696117i 0.937473 + 0.348058i \(0.113159\pi\)
−0.937473 + 0.348058i \(0.886841\pi\)
\(578\) −22745.2 + 13131.9i −1.63681 + 0.945012i
\(579\) 12204.2 7046.10i 0.875975 0.505744i
\(580\) 14400.1i 1.03092i
\(581\) −4583.97 7939.66i −0.327324 0.566941i
\(582\) −11648.2 + 20175.3i −0.829610 + 1.43693i
\(583\) −606.599 350.220i −0.0430922 0.0248793i
\(584\) 50804.1 3.59981
\(585\) −974.966 + 585.838i −0.0689058 + 0.0414041i
\(586\) −24176.5 −1.70430
\(587\) 1879.91 + 1085.37i 0.132184 + 0.0763166i 0.564634 0.825341i \(-0.309017\pi\)
−0.432450 + 0.901658i \(0.642351\pi\)
\(588\) 3487.50 6040.53i 0.244596 0.423652i
\(589\) 2689.91 + 4659.06i 0.188176 + 0.325931i
\(590\) 6438.56i 0.449274i
\(591\) 7502.95 4331.83i 0.522217 0.301502i
\(592\) 30669.7 17707.2i 2.12925 1.22932i
\(593\) 22885.9i 1.58484i 0.609975 + 0.792421i \(0.291180\pi\)
−0.609975 + 0.792421i \(0.708820\pi\)
\(594\) −4844.05 8390.15i −0.334602 0.579549i
\(595\) 85.3330 147.801i 0.00587951 0.0101836i
\(596\) −20315.2 11729.0i −1.39621 0.806105i
\(597\) −189.028 −0.0129588
\(598\) −10200.2 + 6129.08i −0.697518 + 0.419125i
\(599\) −23978.7 −1.63563 −0.817815 0.575482i \(-0.804815\pi\)
−0.817815 + 0.575482i \(0.804815\pi\)
\(600\) 20971.3 + 12107.8i 1.42692 + 0.823832i
\(601\) −6436.62 + 11148.6i −0.436864 + 0.756671i −0.997446 0.0714284i \(-0.977244\pi\)
0.560582 + 0.828099i \(0.310578\pi\)
\(602\) −2119.85 3671.69i −0.143519 0.248583i
\(603\) 201.670i 0.0136196i
\(604\) 52916.9 30551.6i 3.56483 2.05816i
\(605\) 7338.16 4236.69i 0.493122 0.284704i
\(606\) 14218.4i 0.953107i
\(607\) 3558.57 + 6163.63i 0.237954 + 0.412148i 0.960127 0.279564i \(-0.0901899\pi\)
−0.722173 + 0.691712i \(0.756857\pi\)
\(608\) −6950.43 + 12038.5i −0.463614 + 0.803002i
\(609\) −10151.0 5860.71i −0.675437 0.389964i
\(610\) 1731.40 0.114922
\(611\) −289.998 16600.6i −0.0192014 1.09917i
\(612\) 778.675 0.0514315
\(613\) 150.079 + 86.6484i 0.00988850 + 0.00570913i 0.504936 0.863157i \(-0.331516\pi\)
−0.495048 + 0.868866i \(0.664849\pi\)
\(614\) 25586.8 44317.6i 1.68176 2.91289i
\(615\) 632.808 + 1096.06i 0.0414915 + 0.0718654i
\(616\) 69715.5i 4.55993i
\(617\) 5285.14 3051.38i 0.344849 0.199099i −0.317565 0.948236i \(-0.602865\pi\)
0.662414 + 0.749138i \(0.269532\pi\)
\(618\) −17446.7 + 10072.9i −1.13561 + 0.655647i
\(619\) 14867.8i 0.965409i −0.875783 0.482705i \(-0.839654\pi\)
0.875783 0.482705i \(-0.160346\pi\)
\(620\) −5777.88 10007.6i −0.374267 0.648249i
\(621\) 638.876 1106.57i 0.0412838 0.0715056i
\(622\) −34688.3 20027.3i −2.23613 1.29103i
\(623\) −3278.69 −0.210847
\(624\) −14599.2 24296.3i −0.936593 1.55870i
\(625\) 12951.6 0.828900
\(626\) 8463.35 + 4886.32i 0.540357 + 0.311975i
\(627\) 2617.03 4532.84i 0.166689 0.288715i
\(628\) 6539.43 + 11326.6i 0.415528 + 0.719716i
\(629\) 731.475i 0.0463686i
\(630\) 1713.98 989.565i 0.108391 0.0625797i
\(631\) −14904.8 + 8605.29i −0.940334 + 0.542902i −0.890065 0.455834i \(-0.849341\pi\)
−0.0502690 + 0.998736i \(0.516008\pi\)
\(632\) 37550.3i 2.36340i
\(633\) 1574.55 + 2727.19i 0.0988666 + 0.171242i
\(634\) −8382.76 + 14519.4i −0.525113 + 0.909523i
\(635\) 2600.86 + 1501.60i 0.162538 + 0.0938415i
\(636\) 652.853 0.0407033
\(637\) −2542.42 + 4586.80i −0.158139 + 0.285299i
\(638\) 92218.9 5.72254
\(639\) 2222.97 + 1283.43i 0.137620 + 0.0794552i
\(640\) 3266.15 5657.14i 0.201728 0.349403i
\(641\) −6318.01 10943.1i −0.389308 0.674301i 0.603049 0.797704i \(-0.293953\pi\)
−0.992357 + 0.123403i \(0.960619\pi\)
\(642\) 5497.99i 0.337988i
\(643\) 8302.04 4793.19i 0.509177 0.293973i −0.223318 0.974746i \(-0.571689\pi\)
0.732495 + 0.680772i \(0.238356\pi\)
\(644\) 12947.3 7475.12i 0.792228 0.457393i
\(645\) 420.499i 0.0256700i
\(646\) 291.320 + 504.581i 0.0177428 + 0.0307314i
\(647\) 2622.16 4541.72i 0.159332 0.275971i −0.775296 0.631598i \(-0.782399\pi\)
0.934628 + 0.355627i \(0.115733\pi\)
\(648\) 4809.54 + 2776.79i 0.291568 + 0.168337i
\(649\) 29771.4 1.80066
\(650\) −25892.4 14351.9i −1.56243 0.866043i
\(651\) 9406.17 0.566293
\(652\) −7106.94 4103.19i −0.426885 0.246462i
\(653\) −9434.51 + 16341.1i −0.565392 + 0.979288i 0.431621 + 0.902055i \(0.357942\pi\)
−0.997013 + 0.0772326i \(0.975392\pi\)
\(654\) −6237.91 10804.4i −0.372969 0.646001i
\(655\) 5662.59i 0.337795i
\(656\) −27313.8 + 15769.7i −1.62565 + 0.938570i
\(657\) 5775.44 3334.45i 0.342955 0.198005i
\(658\) 28889.3i 1.71159i
\(659\) 12149.9 + 21044.2i 0.718197 + 1.24395i 0.961713 + 0.274057i \(0.0883658\pi\)
−0.243516 + 0.969897i \(0.578301\pi\)
\(660\) −5621.35 + 9736.46i −0.331531 + 0.574229i
\(661\) −25907.2 14957.5i −1.52447 0.880151i −0.999580 0.0289779i \(-0.990775\pi\)
−0.524886 0.851173i \(-0.675892\pi\)
\(662\) −8335.03 −0.489350
\(663\) −585.373 + 10.2259i −0.0342896 + 0.000599008i
\(664\) −41347.1 −2.41653
\(665\) 925.988 + 534.620i 0.0539974 + 0.0311754i
\(666\) 4241.28 7346.11i 0.246766 0.427412i
\(667\) 6081.32 + 10533.2i 0.353028 + 0.611462i
\(668\) 3155.69i 0.182780i
\(669\) −6010.63 + 3470.24i −0.347361 + 0.200549i
\(670\) 280.703 162.064i 0.0161858 0.00934489i
\(671\) 8005.86i 0.460600i
\(672\) 12152.2 + 21048.3i 0.697593 + 1.20827i
\(673\) 7746.84 13417.9i 0.443713 0.768533i −0.554249 0.832351i \(-0.686994\pi\)
0.997962 + 0.0638177i \(0.0203276\pi\)
\(674\) −14822.7 8557.90i −0.847106 0.489077i
\(675\) 3178.71 0.181257
\(676\) 24194.2 + 38716.3i 1.37654 + 2.20279i
\(677\) 11729.7 0.665891 0.332945 0.942946i \(-0.391958\pi\)
0.332945 + 0.942946i \(0.391958\pi\)
\(678\) −17827.3 10292.6i −1.00981 0.583017i
\(679\) −11002.8 + 19057.4i −0.621869 + 1.07711i
\(680\) −384.849 666.578i −0.0217034 0.0375913i
\(681\) 11398.4i 0.641390i
\(682\) −64088.9 + 37001.8i −3.59838 + 2.07752i
\(683\) −1011.88 + 584.210i −0.0566889 + 0.0327294i −0.528077 0.849197i \(-0.677087\pi\)
0.471388 + 0.881926i \(0.343753\pi\)
\(684\) 4878.48i 0.272709i
\(685\) 1624.55 + 2813.81i 0.0906145 + 0.156949i
\(686\) 18549.5 32128.7i 1.03240 1.78816i
\(687\) 11226.5 + 6481.61i 0.623459 + 0.359955i
\(688\) −10478.9 −0.580675
\(689\) −490.786 + 8.57358i −0.0271371 + 0.000474060i
\(690\) −2053.63 −0.113305
\(691\) 28572.7 + 16496.4i 1.57302 + 0.908183i 0.995796 + 0.0915952i \(0.0291966\pi\)
0.577222 + 0.816587i \(0.304137\pi\)
\(692\) −5598.34 + 9696.62i −0.307539 + 0.532673i
\(693\) −4575.66 7925.28i −0.250815 0.434425i
\(694\) 30679.2i 1.67805i
\(695\) −753.972 + 435.306i −0.0411508 + 0.0237584i
\(696\) −45780.9 + 26431.6i −2.49328 + 1.43949i
\(697\) 651.438i 0.0354017i
\(698\) −8928.14 15464.0i −0.484147 0.838568i
\(699\) 7919.65 13717.2i 0.428539 0.742251i
\(700\) 32209.4 + 18596.1i 1.73914 + 1.00410i
\(701\) 14785.8 0.796651 0.398326 0.917244i \(-0.369591\pi\)
0.398326 + 0.917244i \(0.369591\pi\)
\(702\) −5938.12 3291.44i −0.319259 0.176962i
\(703\) 4582.77 0.245864
\(704\) −72189.3 41678.5i −3.86468 2.23128i
\(705\) 1432.64 2481.41i 0.0765339 0.132561i
\(706\) 33010.5 + 57175.8i 1.75973 + 3.04793i
\(707\) 13430.6i 0.714442i
\(708\) −24031.1 + 13874.4i −1.27563 + 0.736485i
\(709\) 10941.4 6317.00i 0.579565 0.334612i −0.181395 0.983410i \(-0.558061\pi\)
0.760961 + 0.648798i \(0.224728\pi\)
\(710\) 4125.52i 0.218067i
\(711\) 2464.55 + 4268.73i 0.129997 + 0.225162i
\(712\) −7393.39 + 12805.7i −0.389156 + 0.674038i
\(713\) −8452.62 4880.12i −0.443973 0.256328i
\(714\) 1018.70 0.0533947
\(715\) 4098.01 7393.25i 0.214345 0.386702i
\(716\) −46148.7 −2.40874
\(717\) 4021.60 + 2321.87i 0.209469 + 0.120937i
\(718\) 22907.3 39676.6i 1.19066 2.06228i
\(719\) −13648.3 23639.5i −0.707920 1.22615i −0.965627 0.259931i \(-0.916300\pi\)
0.257707 0.966223i \(-0.417033\pi\)
\(720\) 4891.64i 0.253195i
\(721\) −16480.1 + 9514.77i −0.851248 + 0.491468i
\(722\) 28705.6 16573.2i 1.47966 0.854279i
\(723\) 14754.0i 0.758932i
\(724\) 39719.2 + 68795.7i 2.03889 + 3.53145i
\(725\) −15128.7 + 26203.7i −0.774987 + 1.34232i
\(726\) 43801.2 + 25288.6i 2.23914 + 1.29277i
\(727\) −4658.21 −0.237639 −0.118819 0.992916i \(-0.537911\pi\)
−0.118819 + 0.992916i \(0.537911\pi\)
\(728\) −25163.2 41877.3i −1.28106 2.13197i
\(729\) 729.000 0.0370370
\(730\) −9282.39 5359.19i −0.470626 0.271716i
\(731\) −108.220 + 187.442i −0.00547558 + 0.00948399i
\(732\) 3730.98 + 6462.25i 0.188389 + 0.326300i
\(733\) 166.474i 0.00838864i 0.999991 + 0.00419432i \(0.00133510\pi\)
−0.999991 + 0.00419432i \(0.998665\pi\)
\(734\) 11599.4 6696.93i 0.583300 0.336769i
\(735\) −783.780 + 452.516i −0.0393336 + 0.0227092i
\(736\) 25219.4i 1.26304i
\(737\) −749.370 1297.95i −0.0374537 0.0648718i
\(738\) −3777.20 + 6542.31i −0.188402 + 0.326322i
\(739\) −11031.5 6369.03i −0.549120 0.317035i 0.199647 0.979868i \(-0.436020\pi\)
−0.748767 + 0.662833i \(0.769354\pi\)
\(740\) −9843.70 −0.489002
\(741\) −64.0665 3667.42i −0.00317617 0.181817i
\(742\) 854.092 0.0422570
\(743\) −26608.2 15362.2i −1.31381 0.758527i −0.331083 0.943602i \(-0.607414\pi\)
−0.982725 + 0.185074i \(0.940747\pi\)
\(744\) 21210.8 36738.1i 1.04519 1.81033i
\(745\) 1521.88 + 2635.97i 0.0748420 + 0.129630i
\(746\) 6131.38i 0.300919i
\(747\) −4700.35 + 2713.75i −0.230224 + 0.132920i
\(748\) −5011.55 + 2893.42i −0.244974 + 0.141436i
\(749\) 5193.37i 0.253353i
\(750\) −5266.62 9122.06i −0.256413 0.444121i
\(751\) −19769.3 + 34241.4i −0.960575 + 1.66376i −0.239514 + 0.970893i \(0.576988\pi\)
−0.721061 + 0.692872i \(0.756345\pi\)
\(752\) 61837.0 + 35701.6i 2.99862 + 1.73126i
\(753\) −3467.34 −0.167805
\(754\) 55394.8 33285.6i 2.67555 1.60768i
\(755\) −7928.35 −0.382175
\(756\) 7386.86 + 4264.80i 0.355367 + 0.205171i
\(757\) −11517.6 + 19949.0i −0.552990 + 0.957807i 0.445067 + 0.895497i \(0.353180\pi\)
−0.998057 + 0.0623093i \(0.980153\pi\)
\(758\) 32676.1 + 56596.6i 1.56576 + 2.71198i
\(759\) 9495.81i 0.454119i
\(760\) 4176.18 2411.12i 0.199323 0.115079i
\(761\) 28106.0 16227.0i 1.33882 0.772968i 0.352187 0.935930i \(-0.385438\pi\)
0.986632 + 0.162962i \(0.0521047\pi\)
\(762\) 17926.0i 0.852220i
\(763\) −5892.30 10205.8i −0.279575 0.484238i
\(764\) 35993.4 62342.4i 1.70444 2.95218i
\(765\) −87.4996 50.5179i −0.00413536 0.00238755i
\(766\) −54616.1 −2.57619
\(767\) 17883.3 10745.7i 0.841890 0.505874i
\(768\) 9080.40 0.426641
\(769\) −27900.1 16108.1i −1.30833 0.755362i −0.326509 0.945194i \(-0.605873\pi\)
−0.981817 + 0.189831i \(0.939206\pi\)
\(770\) −7354.10