Properties

Label 120.4.m.b.59.10
Level $120$
Weight $4$
Character 120.59
Analytic conductor $7.080$
Analytic rank $0$
Dimension $64$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [120,4,Mod(59,120)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(120, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("120.59");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.08022920069\)
Analytic rank: \(0\)
Dimension: \(64\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 59.10
Character \(\chi\) \(=\) 120.59
Dual form 120.4.m.b.59.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.22835 - 1.74197i) q^{2} +(4.99538 + 1.43044i) q^{3} +(1.93108 + 7.76344i) q^{4} +(10.2117 + 4.55196i) q^{5} +(-8.63968 - 11.8893i) q^{6} -3.90466 q^{7} +(9.22055 - 20.6635i) q^{8} +(22.9077 + 14.2912i) q^{9} +O(q^{10})\) \(q+(-2.22835 - 1.74197i) q^{2} +(4.99538 + 1.43044i) q^{3} +(1.93108 + 7.76344i) q^{4} +(10.2117 + 4.55196i) q^{5} +(-8.63968 - 11.8893i) q^{6} -3.90466 q^{7} +(9.22055 - 20.6635i) q^{8} +(22.9077 + 14.2912i) q^{9} +(-14.8260 - 27.9319i) q^{10} +59.1208i q^{11} +(-1.45861 + 41.5436i) q^{12} -63.6374 q^{13} +(8.70094 + 6.80180i) q^{14} +(44.5003 + 37.3460i) q^{15} +(-56.5419 + 29.9836i) q^{16} +69.6213 q^{17} +(-26.1516 - 71.7502i) q^{18} +33.0635 q^{19} +(-15.6191 + 88.0684i) q^{20} +(-19.5053 - 5.58537i) q^{21} +(102.987 - 131.742i) q^{22} -90.6431i q^{23} +(75.6180 - 90.0328i) q^{24} +(83.5594 + 92.9668i) q^{25} +(141.806 + 110.854i) q^{26} +(93.9902 + 104.158i) q^{27} +(-7.54021 - 30.3136i) q^{28} +172.259 q^{29} +(-34.1065 - 160.738i) q^{30} -61.7877i q^{31} +(178.226 + 31.6802i) q^{32} +(-84.5685 + 295.331i) q^{33} +(-155.141 - 121.278i) q^{34} +(-39.8734 - 17.7738i) q^{35} +(-66.7118 + 205.440i) q^{36} -10.7673 q^{37} +(-73.6770 - 57.5956i) q^{38} +(-317.893 - 91.0292i) q^{39} +(188.217 - 169.039i) q^{40} -475.596i q^{41} +(33.7350 + 46.4237i) q^{42} +59.3761i q^{43} +(-458.980 + 114.167i) q^{44} +(168.875 + 250.212i) q^{45} +(-157.898 + 201.985i) q^{46} +500.434i q^{47} +(-325.338 + 68.9003i) q^{48} -327.754 q^{49} +(-24.2541 - 352.720i) q^{50} +(347.785 + 99.5888i) q^{51} +(-122.889 - 494.045i) q^{52} -407.866i q^{53} +(-28.0032 - 395.828i) q^{54} +(-269.115 + 603.726i) q^{55} +(-36.0031 + 80.6840i) q^{56} +(165.165 + 47.2952i) q^{57} +(-383.853 - 300.070i) q^{58} +17.5094i q^{59} +(-204.000 + 417.593i) q^{60} -245.109i q^{61} +(-107.632 + 137.685i) q^{62} +(-89.4468 - 55.8021i) q^{63} +(-341.963 - 381.058i) q^{64} +(-649.849 - 289.675i) q^{65} +(702.906 - 510.785i) q^{66} +35.7817i q^{67} +(134.444 + 540.500i) q^{68} +(129.659 - 452.797i) q^{69} +(57.8903 + 109.065i) q^{70} -889.439 q^{71} +(506.527 - 341.582i) q^{72} -617.595i q^{73} +(23.9933 + 18.7563i) q^{74} +(284.428 + 583.931i) q^{75} +(63.8483 + 256.686i) q^{76} -230.847i q^{77} +(549.807 + 756.605i) q^{78} -108.663i q^{79} +(-713.875 + 48.8092i) q^{80} +(320.526 + 654.755i) q^{81} +(-828.473 + 1059.79i) q^{82} +628.531 q^{83} +(5.69538 - 162.214i) q^{84} +(710.955 + 316.913i) q^{85} +(103.431 - 132.311i) q^{86} +(860.499 + 246.405i) q^{87} +(1221.64 + 545.126i) q^{88} -763.668i q^{89} +(59.5504 - 851.736i) q^{90} +248.482 q^{91} +(703.702 - 175.039i) q^{92} +(88.3834 - 308.653i) q^{93} +(871.741 - 1115.14i) q^{94} +(337.636 + 150.504i) q^{95} +(844.989 + 413.195i) q^{96} -866.259i q^{97} +(730.350 + 570.937i) q^{98} +(-844.904 + 1354.32i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22835 1.74197i −0.787840 0.615879i
\(3\) 4.99538 + 1.43044i 0.961362 + 0.275288i
\(4\) 1.93108 + 7.76344i 0.241385 + 0.970429i
\(5\) 10.2117 + 4.55196i 0.913366 + 0.407139i
\(6\) −8.63968 11.8893i −0.587856 0.808966i
\(7\) −3.90466 −0.210832 −0.105416 0.994428i \(-0.533617\pi\)
−0.105416 + 0.994428i \(0.533617\pi\)
\(8\) 9.22055 20.6635i 0.407495 0.913208i
\(9\) 22.9077 + 14.2912i 0.848433 + 0.529302i
\(10\) −14.8260 27.9319i −0.468838 0.883284i
\(11\) 59.1208i 1.62051i 0.586079 + 0.810254i \(0.300671\pi\)
−0.586079 + 0.810254i \(0.699329\pi\)
\(12\) −1.45861 + 41.5436i −0.0350887 + 0.999384i
\(13\) −63.6374 −1.35768 −0.678840 0.734286i \(-0.737517\pi\)
−0.678840 + 0.734286i \(0.737517\pi\)
\(14\) 8.70094 + 6.80180i 0.166102 + 0.129847i
\(15\) 44.5003 + 37.3460i 0.765995 + 0.642847i
\(16\) −56.5419 + 29.9836i −0.883466 + 0.468494i
\(17\) 69.6213 0.993273 0.496636 0.867959i \(-0.334568\pi\)
0.496636 + 0.867959i \(0.334568\pi\)
\(18\) −26.1516 71.7502i −0.342444 0.939538i
\(19\) 33.0635 0.399226 0.199613 0.979875i \(-0.436032\pi\)
0.199613 + 0.979875i \(0.436032\pi\)
\(20\) −15.6191 + 88.0684i −0.174627 + 0.984635i
\(21\) −19.5053 5.58537i −0.202686 0.0580394i
\(22\) 102.987 131.742i 0.998038 1.27670i
\(23\) 90.6431i 0.821756i −0.911690 0.410878i \(-0.865222\pi\)
0.911690 0.410878i \(-0.134778\pi\)
\(24\) 75.6180 90.0328i 0.643144 0.765745i
\(25\) 83.5594 + 92.9668i 0.668475 + 0.743734i
\(26\) 141.806 + 110.854i 1.06964 + 0.836167i
\(27\) 93.9902 + 104.158i 0.669941 + 0.742414i
\(28\) −7.54021 30.3136i −0.0508917 0.204597i
\(29\) 172.259 1.10302 0.551511 0.834167i \(-0.314051\pi\)
0.551511 + 0.834167i \(0.314051\pi\)
\(30\) −34.1065 160.738i −0.207566 0.978221i
\(31\) 61.7877i 0.357981i −0.983851 0.178990i \(-0.942717\pi\)
0.983851 0.178990i \(-0.0572831\pi\)
\(32\) 178.226 + 31.6802i 0.984567 + 0.175010i
\(33\) −84.5685 + 295.331i −0.446106 + 1.55789i
\(34\) −155.141 121.278i −0.782541 0.611736i
\(35\) −39.8734 17.7738i −0.192567 0.0858379i
\(36\) −66.7118 + 205.440i −0.308851 + 0.951110i
\(37\) −10.7673 −0.0478414 −0.0239207 0.999714i \(-0.507615\pi\)
−0.0239207 + 0.999714i \(0.507615\pi\)
\(38\) −73.6770 57.5956i −0.314526 0.245875i
\(39\) −317.893 91.0292i −1.30522 0.373752i
\(40\) 188.217 169.039i 0.743994 0.668186i
\(41\) 475.596i 1.81160i −0.423707 0.905799i \(-0.639271\pi\)
0.423707 0.905799i \(-0.360729\pi\)
\(42\) 33.7350 + 46.4237i 0.123939 + 0.170556i
\(43\) 59.3761i 0.210576i 0.994442 + 0.105288i \(0.0335764\pi\)
−0.994442 + 0.105288i \(0.966424\pi\)
\(44\) −458.980 + 114.167i −1.57259 + 0.391166i
\(45\) 168.875 + 250.212i 0.559431 + 0.828877i
\(46\) −157.898 + 201.985i −0.506103 + 0.647413i
\(47\) 500.434i 1.55310i 0.630054 + 0.776551i \(0.283033\pi\)
−0.630054 + 0.776551i \(0.716967\pi\)
\(48\) −325.338 + 68.9003i −0.978302 + 0.207185i
\(49\) −327.754 −0.955550
\(50\) −24.2541 352.720i −0.0686011 0.997644i
\(51\) 347.785 + 99.5888i 0.954895 + 0.273436i
\(52\) −122.889 494.045i −0.327724 1.31753i
\(53\) 407.866i 1.05707i −0.848911 0.528535i \(-0.822741\pi\)
0.848911 0.528535i \(-0.177259\pi\)
\(54\) −28.0032 395.828i −0.0705694 0.997507i
\(55\) −269.115 + 603.726i −0.659772 + 1.48012i
\(56\) −36.0031 + 80.6840i −0.0859128 + 0.192533i
\(57\) 165.165 + 47.2952i 0.383800 + 0.109902i
\(58\) −383.853 300.070i −0.869006 0.679329i
\(59\) 17.5094i 0.0386360i 0.999813 + 0.0193180i \(0.00614950\pi\)
−0.999813 + 0.0193180i \(0.993851\pi\)
\(60\) −204.000 + 417.593i −0.438937 + 0.898518i
\(61\) 245.109i 0.514474i −0.966348 0.257237i \(-0.917188\pi\)
0.966348 0.257237i \(-0.0828122\pi\)
\(62\) −107.632 + 137.685i −0.220473 + 0.282032i
\(63\) −89.4468 55.8021i −0.178877 0.111594i
\(64\) −341.963 381.058i −0.667896 0.744254i
\(65\) −649.849 289.675i −1.24006 0.552765i
\(66\) 702.906 510.785i 1.31094 0.952625i
\(67\) 35.7817i 0.0652452i 0.999468 + 0.0326226i \(0.0103859\pi\)
−0.999468 + 0.0326226i \(0.989614\pi\)
\(68\) 134.444 + 540.500i 0.239761 + 0.963901i
\(69\) 129.659 452.797i 0.226219 0.790005i
\(70\) 57.8903 + 109.065i 0.0988460 + 0.186224i
\(71\) −889.439 −1.48672 −0.743359 0.668893i \(-0.766769\pi\)
−0.743359 + 0.668893i \(0.766769\pi\)
\(72\) 506.527 341.582i 0.829095 0.559108i
\(73\) 617.595i 0.990193i −0.868838 0.495096i \(-0.835133\pi\)
0.868838 0.495096i \(-0.164867\pi\)
\(74\) 23.9933 + 18.7563i 0.0376914 + 0.0294646i
\(75\) 284.428 + 583.931i 0.437906 + 0.899021i
\(76\) 63.8483 + 256.686i 0.0963671 + 0.387420i
\(77\) 230.847i 0.341655i
\(78\) 549.807 + 756.605i 0.798120 + 1.09832i
\(79\) 108.663i 0.154753i −0.997002 0.0773766i \(-0.975346\pi\)
0.997002 0.0773766i \(-0.0246544\pi\)
\(80\) −713.875 + 48.8092i −0.997671 + 0.0682130i
\(81\) 320.526 + 654.755i 0.439679 + 0.898155i
\(82\) −828.473 + 1059.79i −1.11573 + 1.42725i
\(83\) 628.531 0.831208 0.415604 0.909546i \(-0.363570\pi\)
0.415604 + 0.909546i \(0.363570\pi\)
\(84\) 5.69538 162.214i 0.00739782 0.210702i
\(85\) 710.955 + 316.913i 0.907222 + 0.404400i
\(86\) 103.431 132.311i 0.129689 0.165900i
\(87\) 860.499 + 246.405i 1.06040 + 0.303649i
\(88\) 1221.64 + 545.126i 1.47986 + 0.660348i
\(89\) 763.668i 0.909535i −0.890610 0.454768i \(-0.849722\pi\)
0.890610 0.454768i \(-0.150278\pi\)
\(90\) 59.5504 851.736i 0.0697462 0.997565i
\(91\) 248.482 0.286242
\(92\) 703.702 175.039i 0.797457 0.198360i
\(93\) 88.3834 308.653i 0.0985477 0.344149i
\(94\) 871.741 1115.14i 0.956524 1.22360i
\(95\) 337.636 + 150.504i 0.364639 + 0.162540i
\(96\) 844.989 + 413.195i 0.898347 + 0.439287i
\(97\) 866.259i 0.906755i −0.891319 0.453378i \(-0.850219\pi\)
0.891319 0.453378i \(-0.149781\pi\)
\(98\) 730.350 + 570.937i 0.752821 + 0.588504i
\(99\) −844.904 + 1354.32i −0.857738 + 1.37489i
\(100\) −560.382 + 828.234i −0.560382 + 0.828234i
\(101\) 1542.57 1.51972 0.759859 0.650088i \(-0.225268\pi\)
0.759859 + 0.650088i \(0.225268\pi\)
\(102\) −601.506 827.750i −0.583901 0.803524i
\(103\) −360.822 −0.345174 −0.172587 0.984994i \(-0.555213\pi\)
−0.172587 + 0.984994i \(0.555213\pi\)
\(104\) −586.772 + 1314.97i −0.553247 + 1.23984i
\(105\) −173.758 145.823i −0.161496 0.135532i
\(106\) −710.491 + 908.868i −0.651028 + 0.832803i
\(107\) −1347.63 −1.21757 −0.608785 0.793336i \(-0.708343\pi\)
−0.608785 + 0.793336i \(0.708343\pi\)
\(108\) −627.120 + 930.824i −0.558747 + 0.829338i
\(109\) 1187.79i 1.04376i −0.853019 0.521880i \(-0.825231\pi\)
0.853019 0.521880i \(-0.174769\pi\)
\(110\) 1651.36 876.522i 1.43137 0.759756i
\(111\) −53.7868 15.4019i −0.0459929 0.0131702i
\(112\) 220.777 117.076i 0.186263 0.0987735i
\(113\) −666.104 −0.554529 −0.277265 0.960794i \(-0.589428\pi\)
−0.277265 + 0.960794i \(0.589428\pi\)
\(114\) −285.658 393.102i −0.234687 0.322960i
\(115\) 412.603 925.624i 0.334569 0.750564i
\(116\) 332.646 + 1337.32i 0.266253 + 1.07041i
\(117\) −1457.79 909.452i −1.15190 0.718623i
\(118\) 30.5008 39.0170i 0.0237951 0.0304390i
\(119\) −271.847 −0.209413
\(120\) 1182.02 575.182i 0.899191 0.437556i
\(121\) −2164.27 −1.62605
\(122\) −426.972 + 546.187i −0.316854 + 0.405324i
\(123\) 680.309 2375.78i 0.498711 1.74160i
\(124\) 479.685 119.317i 0.347395 0.0864112i
\(125\) 430.106 + 1329.71i 0.307759 + 0.951464i
\(126\) 102.113 + 280.160i 0.0721981 + 0.198085i
\(127\) −259.670 −0.181433 −0.0907163 0.995877i \(-0.528916\pi\)
−0.0907163 + 0.995877i \(0.528916\pi\)
\(128\) 98.2209 + 1444.82i 0.0678249 + 0.997697i
\(129\) −84.9337 + 296.606i −0.0579689 + 0.202440i
\(130\) 943.485 + 1777.51i 0.636532 + 1.19922i
\(131\) 930.506i 0.620601i −0.950639 0.310300i \(-0.899570\pi\)
0.950639 0.310300i \(-0.100430\pi\)
\(132\) −2456.09 86.2343i −1.61951 0.0568616i
\(133\) −129.102 −0.0841694
\(134\) 62.3306 79.7340i 0.0401831 0.0514028i
\(135\) 485.682 + 1491.47i 0.309636 + 0.950855i
\(136\) 641.946 1438.62i 0.404753 0.907064i
\(137\) 360.083 0.224554 0.112277 0.993677i \(-0.464186\pi\)
0.112277 + 0.993677i \(0.464186\pi\)
\(138\) −1077.68 + 783.128i −0.664773 + 0.483074i
\(139\) −574.130 −0.350339 −0.175169 0.984538i \(-0.556047\pi\)
−0.175169 + 0.984538i \(0.556047\pi\)
\(140\) 60.9873 343.877i 0.0368169 0.207592i
\(141\) −715.839 + 2499.86i −0.427550 + 1.49309i
\(142\) 1981.98 + 1549.38i 1.17130 + 0.915639i
\(143\) 3762.29i 2.20013i
\(144\) −1723.74 121.192i −0.997538 0.0701343i
\(145\) 1759.06 + 784.115i 1.00746 + 0.449084i
\(146\) −1075.83 + 1376.22i −0.609839 + 0.780114i
\(147\) −1637.25 468.831i −0.918629 0.263051i
\(148\) −20.7925 83.5913i −0.0115482 0.0464267i
\(149\) −1402.68 −0.771223 −0.385611 0.922661i \(-0.626009\pi\)
−0.385611 + 0.922661i \(0.626009\pi\)
\(150\) 383.385 1796.67i 0.208689 0.977982i
\(151\) 713.088i 0.384306i −0.981365 0.192153i \(-0.938453\pi\)
0.981365 0.192153i \(-0.0615471\pi\)
\(152\) 304.864 683.208i 0.162682 0.364576i
\(153\) 1594.86 + 994.968i 0.842726 + 0.525741i
\(154\) −402.128 + 514.407i −0.210418 + 0.269169i
\(155\) 281.255 630.961i 0.145748 0.326968i
\(156\) 92.8222 2643.73i 0.0476393 1.35684i
\(157\) 1894.80 0.963192 0.481596 0.876393i \(-0.340057\pi\)
0.481596 + 0.876393i \(0.340057\pi\)
\(158\) −189.287 + 242.138i −0.0953093 + 0.121921i
\(159\) 583.427 2037.45i 0.290998 1.01623i
\(160\) 1675.79 + 1134.79i 0.828016 + 0.560704i
\(161\) 353.930i 0.173252i
\(162\) 426.320 2017.37i 0.206759 0.978392i
\(163\) 2482.58i 1.19295i 0.802633 + 0.596473i \(0.203432\pi\)
−0.802633 + 0.596473i \(0.796568\pi\)
\(164\) 3692.26 918.414i 1.75803 0.437293i
\(165\) −2207.93 + 2630.89i −1.04174 + 1.24130i
\(166\) −1400.59 1094.88i −0.654859 0.511924i
\(167\) 3112.29i 1.44213i 0.692865 + 0.721067i \(0.256348\pi\)
−0.692865 + 0.721067i \(0.743652\pi\)
\(168\) −295.263 + 351.548i −0.135595 + 0.161443i
\(169\) 1852.72 0.843294
\(170\) −1032.20 1944.65i −0.465684 0.877342i
\(171\) 757.409 + 472.515i 0.338716 + 0.211311i
\(172\) −460.962 + 114.660i −0.204349 + 0.0508299i
\(173\) 3100.30i 1.36250i −0.732053 0.681248i \(-0.761438\pi\)
0.732053 0.681248i \(-0.238562\pi\)
\(174\) −1488.26 2048.04i −0.648418 0.892308i
\(175\) −326.271 363.004i −0.140936 0.156803i
\(176\) −1772.66 3342.80i −0.759199 1.43166i
\(177\) −25.0460 + 87.4660i −0.0106360 + 0.0371432i
\(178\) −1330.29 + 1701.72i −0.560164 + 0.716569i
\(179\) 2018.40i 0.842805i −0.906874 0.421402i \(-0.861538\pi\)
0.906874 0.421402i \(-0.138462\pi\)
\(180\) −1616.40 + 1794.23i −0.669328 + 0.742967i
\(181\) 1943.41i 0.798079i 0.916934 + 0.399039i \(0.130656\pi\)
−0.916934 + 0.399039i \(0.869344\pi\)
\(182\) −553.705 432.849i −0.225513 0.176291i
\(183\) 350.612 1224.41i 0.141628 0.494596i
\(184\) −1873.01 835.779i −0.750434 0.334861i
\(185\) −109.953 49.0123i −0.0436968 0.0194781i
\(186\) −734.614 + 533.826i −0.289594 + 0.210441i
\(187\) 4116.06i 1.60961i
\(188\) −3885.09 + 966.379i −1.50718 + 0.374896i
\(189\) −367.000 406.701i −0.141245 0.156524i
\(190\) −490.198 923.526i −0.187172 0.352630i
\(191\) 3928.20 1.48814 0.744070 0.668101i \(-0.232893\pi\)
0.744070 + 0.668101i \(0.232893\pi\)
\(192\) −1163.16 2392.69i −0.437206 0.899361i
\(193\) 456.350i 0.170201i −0.996372 0.0851005i \(-0.972879\pi\)
0.996372 0.0851005i \(-0.0271211\pi\)
\(194\) −1509.00 + 1930.33i −0.558452 + 0.714379i
\(195\) −2831.88 2376.60i −1.03998 0.872780i
\(196\) −632.919 2544.49i −0.230656 0.927294i
\(197\) 4127.07i 1.49260i 0.665611 + 0.746299i \(0.268171\pi\)
−0.665611 + 0.746299i \(0.731829\pi\)
\(198\) 4241.93 1546.10i 1.52253 0.554933i
\(199\) 4395.85i 1.56590i 0.622087 + 0.782948i \(0.286285\pi\)
−0.622087 + 0.782948i \(0.713715\pi\)
\(200\) 2691.49 869.427i 0.951584 0.307389i
\(201\) −51.1834 + 178.743i −0.0179612 + 0.0627242i
\(202\) −3437.39 2687.11i −1.19730 0.935963i
\(203\) −672.612 −0.232552
\(204\) −101.550 + 2892.32i −0.0348527 + 0.992661i
\(205\) 2164.89 4856.66i 0.737573 1.65465i
\(206\) 804.038 + 628.542i 0.271942 + 0.212585i
\(207\) 1295.39 2076.43i 0.434957 0.697206i
\(208\) 3598.18 1908.08i 1.19946 0.636065i
\(209\) 1954.74i 0.646948i
\(210\) 133.174 + 627.628i 0.0437615 + 0.206240i
\(211\) 4297.34 1.40209 0.701045 0.713117i \(-0.252717\pi\)
0.701045 + 0.713117i \(0.252717\pi\)
\(212\) 3166.44 787.623i 1.02581 0.255161i
\(213\) −4443.09 1272.29i −1.42927 0.409275i
\(214\) 3002.98 + 2347.52i 0.959250 + 0.749876i
\(215\) −270.277 + 606.333i −0.0857337 + 0.192333i
\(216\) 3018.91 981.777i 0.950976 0.309266i
\(217\) 241.260i 0.0754737i
\(218\) −2069.10 + 2646.81i −0.642830 + 0.822316i
\(219\) 883.431 3085.13i 0.272588 0.951934i
\(220\) −5206.67 923.414i −1.59561 0.282984i
\(221\) −4430.52 −1.34855
\(222\) 93.0261 + 128.016i 0.0281239 + 0.0387021i
\(223\) −5589.89 −1.67859 −0.839297 0.543673i \(-0.817033\pi\)
−0.839297 + 0.543673i \(0.817033\pi\)
\(224\) −695.910 123.700i −0.207578 0.0368977i
\(225\) 585.551 + 3323.82i 0.173497 + 0.984834i
\(226\) 1484.31 + 1160.33i 0.436881 + 0.341523i
\(227\) 2119.31 0.619662 0.309831 0.950792i \(-0.399727\pi\)
0.309831 + 0.950792i \(0.399727\pi\)
\(228\) −48.2268 + 1373.58i −0.0140083 + 0.398980i
\(229\) 3484.25i 1.00544i 0.864449 + 0.502721i \(0.167668\pi\)
−0.864449 + 0.502721i \(0.832332\pi\)
\(230\) −2531.83 + 1343.87i −0.725844 + 0.385271i
\(231\) 330.211 1153.17i 0.0940533 0.328454i
\(232\) 1588.32 3559.48i 0.449476 1.00729i
\(233\) 635.469 0.178674 0.0893368 0.996001i \(-0.471525\pi\)
0.0893368 + 0.996001i \(0.471525\pi\)
\(234\) 1664.22 + 4566.00i 0.464929 + 1.27559i
\(235\) −2277.95 + 5110.31i −0.632329 + 1.41855i
\(236\) −135.933 + 33.8120i −0.0374935 + 0.00932616i
\(237\) 155.435 542.812i 0.0426016 0.148774i
\(238\) 605.771 + 473.550i 0.164984 + 0.128973i
\(239\) 3348.65 0.906302 0.453151 0.891434i \(-0.350300\pi\)
0.453151 + 0.891434i \(0.350300\pi\)
\(240\) −3635.90 777.332i −0.977901 0.209069i
\(241\) −4429.34 −1.18390 −0.591948 0.805976i \(-0.701641\pi\)
−0.591948 + 0.805976i \(0.701641\pi\)
\(242\) 4822.74 + 3770.09i 1.28106 + 1.00145i
\(243\) 664.564 + 3729.24i 0.175439 + 0.984490i
\(244\) 1902.88 473.324i 0.499261 0.124186i
\(245\) −3346.94 1491.92i −0.872767 0.389042i
\(246\) −5654.51 + 4108.99i −1.46552 + 1.06496i
\(247\) −2104.07 −0.542020
\(248\) −1276.75 569.717i −0.326911 0.145875i
\(249\) 3139.75 + 899.074i 0.799092 + 0.228821i
\(250\) 1357.89 3712.29i 0.343522 0.939145i
\(251\) 2194.08i 0.551750i −0.961194 0.275875i \(-0.911032\pi\)
0.961194 0.275875i \(-0.0889676\pi\)
\(252\) 260.487 802.173i 0.0651156 0.200524i
\(253\) 5358.89 1.33166
\(254\) 578.634 + 452.337i 0.142940 + 0.111741i
\(255\) 3098.17 + 2600.08i 0.760842 + 0.638522i
\(256\) 2297.96 3390.66i 0.561026 0.827798i
\(257\) 5497.40 1.33431 0.667156 0.744918i \(-0.267511\pi\)
0.667156 + 0.744918i \(0.267511\pi\)
\(258\) 705.941 512.990i 0.170349 0.123788i
\(259\) 42.0426 0.0100865
\(260\) 993.960 5604.44i 0.237088 1.33682i
\(261\) 3946.05 + 2461.78i 0.935842 + 0.583832i
\(262\) −1620.91 + 2073.49i −0.382215 + 0.488934i
\(263\) 3495.97i 0.819660i −0.912162 0.409830i \(-0.865588\pi\)
0.912162 0.409830i \(-0.134412\pi\)
\(264\) 5322.81 + 4470.60i 1.24090 + 1.04222i
\(265\) 1856.59 4165.02i 0.430375 0.965492i
\(266\) 287.684 + 224.891i 0.0663121 + 0.0518382i
\(267\) 1092.38 3814.81i 0.250384 0.874392i
\(268\) −277.789 + 69.0973i −0.0633158 + 0.0157492i
\(269\) 585.602 0.132732 0.0663658 0.997795i \(-0.478860\pi\)
0.0663658 + 0.997795i \(0.478860\pi\)
\(270\) 1515.83 4169.56i 0.341669 0.939821i
\(271\) 7517.66i 1.68511i −0.538609 0.842556i \(-0.681050\pi\)
0.538609 0.842556i \(-0.318950\pi\)
\(272\) −3936.52 + 2087.50i −0.877523 + 0.465343i
\(273\) 1241.26 + 355.438i 0.275182 + 0.0787989i
\(274\) −802.391 627.254i −0.176913 0.138298i
\(275\) −5496.27 + 4940.10i −1.20523 + 1.08327i
\(276\) 3765.64 + 132.213i 0.821250 + 0.0288344i
\(277\) −504.031 −0.109330 −0.0546648 0.998505i \(-0.517409\pi\)
−0.0546648 + 0.998505i \(0.517409\pi\)
\(278\) 1279.36 + 1000.12i 0.276011 + 0.215767i
\(279\) 883.018 1415.42i 0.189480 0.303723i
\(280\) −734.925 + 660.040i −0.156858 + 0.140875i
\(281\) 7892.83i 1.67561i 0.545969 + 0.837805i \(0.316161\pi\)
−0.545969 + 0.837805i \(0.683839\pi\)
\(282\) 5949.82 4323.59i 1.25641 0.913001i
\(283\) 5494.85i 1.15419i −0.816678 0.577094i \(-0.804187\pi\)
0.816678 0.577094i \(-0.195813\pi\)
\(284\) −1717.58 6905.10i −0.358872 1.44275i
\(285\) 1471.33 + 1234.79i 0.305805 + 0.256641i
\(286\) −6553.80 + 8383.70i −1.35502 + 1.73335i
\(287\) 1857.04i 0.381943i
\(288\) 3629.99 + 3272.77i 0.742706 + 0.669617i
\(289\) −65.8786 −0.0134090
\(290\) −2553.90 4811.52i −0.517139 0.974283i
\(291\) 1239.13 4327.30i 0.249619 0.871720i
\(292\) 4794.66 1192.63i 0.960912 0.239018i
\(293\) 688.366i 0.137252i 0.997642 + 0.0686259i \(0.0218615\pi\)
−0.997642 + 0.0686259i \(0.978139\pi\)
\(294\) 2831.69 + 3896.77i 0.561726 + 0.773007i
\(295\) −79.7019 + 178.801i −0.0157302 + 0.0352888i
\(296\) −99.2804 + 222.490i −0.0194951 + 0.0436892i
\(297\) −6157.89 + 5556.77i −1.20309 + 1.08565i
\(298\) 3125.67 + 2443.43i 0.607601 + 0.474980i
\(299\) 5768.29i 1.11568i
\(300\) −3984.06 + 3335.76i −0.766732 + 0.641967i
\(301\) 231.843i 0.0443961i
\(302\) −1242.18 + 1589.01i −0.236686 + 0.302772i
\(303\) 7705.73 + 2206.55i 1.46100 + 0.418360i
\(304\) −1869.47 + 991.364i −0.352702 + 0.187035i
\(305\) 1115.72 2502.99i 0.209463 0.469903i
\(306\) −1820.71 4995.34i −0.340140 0.933218i
\(307\) 5319.52i 0.988929i −0.869198 0.494464i \(-0.835364\pi\)
0.869198 0.494464i \(-0.164636\pi\)
\(308\) 1792.16 445.783i 0.331552 0.0824703i
\(309\) −1802.45 516.134i −0.331837 0.0950220i
\(310\) −1725.85 + 916.063i −0.316199 + 0.167835i
\(311\) −7832.47 −1.42810 −0.714049 0.700096i \(-0.753141\pi\)
−0.714049 + 0.700096i \(0.753141\pi\)
\(312\) −4812.13 + 5729.46i −0.873184 + 1.03964i
\(313\) 2374.67i 0.428831i −0.976743 0.214416i \(-0.931215\pi\)
0.976743 0.214416i \(-0.0687847\pi\)
\(314\) −4222.27 3300.68i −0.758842 0.593210i
\(315\) −659.399 976.994i −0.117946 0.174754i
\(316\) 843.595 209.836i 0.150177 0.0373551i
\(317\) 4106.84i 0.727643i 0.931469 + 0.363822i \(0.118528\pi\)
−0.931469 + 0.363822i \(0.881472\pi\)
\(318\) −4849.25 + 3523.83i −0.855134 + 0.621405i
\(319\) 10184.1i 1.78746i
\(320\) −1757.48 5447.87i −0.307019 0.951703i
\(321\) −6731.91 1927.69i −1.17052 0.335182i
\(322\) 616.536 788.681i 0.106703 0.136495i
\(323\) 2301.92 0.396540
\(324\) −4464.19 + 3752.77i −0.765464 + 0.643478i
\(325\) −5317.50 5916.17i −0.907575 1.00975i
\(326\) 4324.57 5532.05i 0.734711 0.939852i
\(327\) 1699.06 5933.47i 0.287334 1.00343i
\(328\) −9827.48 4385.25i −1.65437 0.738217i
\(329\) 1954.03i 0.327443i
\(330\) 9502.96 2016.41i 1.58522 0.336362i
\(331\) 4379.02 0.727168 0.363584 0.931562i \(-0.381553\pi\)
0.363584 + 0.931562i \(0.381553\pi\)
\(332\) 1213.74 + 4879.56i 0.200641 + 0.806629i
\(333\) −246.654 153.877i −0.0405903 0.0253226i
\(334\) 5421.52 6935.28i 0.888181 1.13617i
\(335\) −162.877 + 365.393i −0.0265639 + 0.0595927i
\(336\) 1270.33 269.032i 0.206257 0.0436812i
\(337\) 6774.53i 1.09505i −0.836789 0.547525i \(-0.815570\pi\)
0.836789 0.547525i \(-0.184430\pi\)
\(338\) −4128.50 3227.38i −0.664381 0.519368i
\(339\) −3327.45 952.820i −0.533104 0.152655i
\(340\) −1087.42 + 6131.43i −0.173452 + 0.978011i
\(341\) 3652.94 0.580111
\(342\) −864.663 2372.31i −0.136712 0.375088i
\(343\) 2619.06 0.412292
\(344\) 1226.92 + 547.480i 0.192300 + 0.0858085i
\(345\) 3385.16 4033.64i 0.528263 0.629461i
\(346\) −5400.63 + 6908.56i −0.839133 + 1.07343i
\(347\) 4789.77 0.741004 0.370502 0.928832i \(-0.379186\pi\)
0.370502 + 0.928832i \(0.379186\pi\)
\(348\) −251.259 + 7156.26i −0.0387037 + 1.10234i
\(349\) 3221.38i 0.494087i 0.969004 + 0.247043i \(0.0794590\pi\)
−0.969004 + 0.247043i \(0.920541\pi\)
\(350\) 94.7041 + 1377.25i 0.0144633 + 0.210335i
\(351\) −5981.29 6628.33i −0.909566 1.00796i
\(352\) −1872.96 + 10536.8i −0.283605 + 1.59550i
\(353\) −1778.82 −0.268207 −0.134104 0.990967i \(-0.542815\pi\)
−0.134104 + 0.990967i \(0.542815\pi\)
\(354\) 208.174 151.275i 0.0312552 0.0227124i
\(355\) −9082.72 4048.69i −1.35792 0.605301i
\(356\) 5928.69 1474.70i 0.882640 0.219548i
\(357\) −1357.98 388.860i −0.201322 0.0576489i
\(358\) −3515.99 + 4497.69i −0.519066 + 0.663996i
\(359\) −888.661 −0.130645 −0.0653227 0.997864i \(-0.520808\pi\)
−0.0653227 + 0.997864i \(0.520808\pi\)
\(360\) 6727.39 1182.46i 0.984902 0.173113i
\(361\) −5765.81 −0.840619
\(362\) 3385.36 4330.59i 0.491520 0.628759i
\(363\) −10811.3 3095.85i −1.56322 0.447630i
\(364\) 479.839 + 1929.08i 0.0690946 + 0.277778i
\(365\) 2811.27 6306.73i 0.403146 0.904409i
\(366\) −2914.17 + 2117.66i −0.416192 + 0.302437i
\(367\) −2399.81 −0.341333 −0.170666 0.985329i \(-0.554592\pi\)
−0.170666 + 0.985329i \(0.554592\pi\)
\(368\) 2717.81 + 5125.13i 0.384988 + 0.725994i
\(369\) 6796.81 10894.8i 0.958883 1.53702i
\(370\) 159.636 + 300.751i 0.0224299 + 0.0422576i
\(371\) 1592.58i 0.222864i
\(372\) 2566.89 + 90.1243i 0.357760 + 0.0125611i
\(373\) −7562.31 −1.04976 −0.524881 0.851175i \(-0.675890\pi\)
−0.524881 + 0.851175i \(0.675890\pi\)
\(374\) 7170.06 9172.03i 0.991324 1.26811i
\(375\) 246.478 + 7257.66i 0.0339415 + 0.999424i
\(376\) 10340.7 + 4614.28i 1.41831 + 0.632881i
\(377\) −10962.1 −1.49755
\(378\) 109.343 + 1545.57i 0.0148783 + 0.210306i
\(379\) −7024.75 −0.952077 −0.476038 0.879424i \(-0.657928\pi\)
−0.476038 + 0.879424i \(0.657928\pi\)
\(380\) −516.422 + 2911.85i −0.0697155 + 0.393091i
\(381\) −1297.15 371.441i −0.174422 0.0499462i
\(382\) −8753.41 6842.81i −1.17242 0.916515i
\(383\) 3306.11i 0.441081i 0.975378 + 0.220541i \(0.0707822\pi\)
−0.975378 + 0.220541i \(0.929218\pi\)
\(384\) −1576.07 + 7357.93i −0.209449 + 0.977819i
\(385\) 1050.80 2357.35i 0.139101 0.312056i
\(386\) −794.948 + 1016.91i −0.104823 + 0.134091i
\(387\) −848.553 + 1360.17i −0.111458 + 0.178660i
\(388\) 6725.15 1672.82i 0.879942 0.218877i
\(389\) 4431.14 0.577551 0.288776 0.957397i \(-0.406752\pi\)
0.288776 + 0.957397i \(0.406752\pi\)
\(390\) 2170.45 + 10229.0i 0.281808 + 1.32811i
\(391\) 6310.69i 0.816228i
\(392\) −3022.07 + 6772.55i −0.389381 + 0.872616i
\(393\) 1331.03 4648.23i 0.170844 0.596622i
\(394\) 7189.24 9196.56i 0.919261 1.17593i
\(395\) 494.628 1109.63i 0.0630061 0.141346i
\(396\) −12145.8 3944.06i −1.54128 0.500496i
\(397\) 10715.8 1.35469 0.677343 0.735668i \(-0.263131\pi\)
0.677343 + 0.735668i \(0.263131\pi\)
\(398\) 7657.44 9795.49i 0.964403 1.23368i
\(399\) −644.912 184.672i −0.0809173 0.0231708i
\(400\) −7512.09 2751.10i −0.939011 0.343888i
\(401\) 3245.09i 0.404120i −0.979373 0.202060i \(-0.935236\pi\)
0.979373 0.202060i \(-0.0647635\pi\)
\(402\) 425.420 309.142i 0.0527811 0.0383547i
\(403\) 3932.01i 0.486023i
\(404\) 2978.83 + 11975.6i 0.366837 + 1.47478i
\(405\) 292.711 + 8145.21i 0.0359134 + 0.999355i
\(406\) 1498.81 + 1171.67i 0.183214 + 0.143224i
\(407\) 636.571i 0.0775274i
\(408\) 5264.62 6268.20i 0.638818 0.760594i
\(409\) −3135.87 −0.379117 −0.189558 0.981869i \(-0.560706\pi\)
−0.189558 + 0.981869i \(0.560706\pi\)
\(410\) −13284.3 + 7051.16i −1.60016 + 0.849346i
\(411\) 1798.75 + 515.076i 0.215878 + 0.0618171i
\(412\) −696.777 2801.22i −0.0833198 0.334967i
\(413\) 68.3681i 0.00814570i
\(414\) −6503.66 + 2370.46i −0.772071 + 0.281406i
\(415\) 6418.40 + 2861.05i 0.759197 + 0.338418i
\(416\) −11341.8 2016.04i −1.33673 0.237608i
\(417\) −2868.00 821.257i −0.336803 0.0964440i
\(418\) 3405.10 4355.84i 0.398442 0.509692i
\(419\) 7364.44i 0.858655i 0.903149 + 0.429327i \(0.141249\pi\)
−0.903149 + 0.429327i \(0.858751\pi\)
\(420\) 796.549 1630.56i 0.0925420 0.189436i
\(421\) 4582.24i 0.530463i 0.964185 + 0.265231i \(0.0854483\pi\)
−0.964185 + 0.265231i \(0.914552\pi\)
\(422\) −9575.97 7485.83i −1.10462 0.863518i
\(423\) −7151.78 + 11463.8i −0.822060 + 1.31770i
\(424\) −8427.96 3760.75i −0.965325 0.430750i
\(425\) 5817.51 + 6472.47i 0.663978 + 0.738731i
\(426\) 7684.47 + 10574.8i 0.873976 + 1.20270i
\(427\) 957.065i 0.108468i
\(428\) −2602.37 10462.2i −0.293903 1.18157i
\(429\) 5381.72 18794.1i 0.605669 2.11512i
\(430\) 1658.49 880.307i 0.185998 0.0987260i
\(431\) −5956.76 −0.665724 −0.332862 0.942976i \(-0.608014\pi\)
−0.332862 + 0.942976i \(0.608014\pi\)
\(432\) −8437.41 3071.11i −0.939688 0.342034i
\(433\) 5990.82i 0.664897i 0.943121 + 0.332449i \(0.107875\pi\)
−0.943121 + 0.332449i \(0.892125\pi\)
\(434\) 420.268 537.612i 0.0464827 0.0594613i
\(435\) 7665.57 + 6433.18i 0.844910 + 0.709075i
\(436\) 9221.34 2293.72i 1.01289 0.251948i
\(437\) 2996.98i 0.328066i
\(438\) −7342.79 + 5335.83i −0.801032 + 0.582091i
\(439\) 3323.14i 0.361287i 0.983549 + 0.180644i \(0.0578180\pi\)
−0.983549 + 0.180644i \(0.942182\pi\)
\(440\) 9993.73 + 11127.6i 1.08280 + 1.20565i
\(441\) −7508.08 4683.98i −0.810721 0.505775i
\(442\) 9872.74 + 7717.83i 1.06244 + 0.830542i
\(443\) 10439.3 1.11961 0.559805 0.828624i \(-0.310876\pi\)
0.559805 + 0.828624i \(0.310876\pi\)
\(444\) 15.7053 447.313i 0.00167870 0.0478120i
\(445\) 3476.18 7798.38i 0.370307 0.830739i
\(446\) 12456.2 + 9737.41i 1.32246 + 1.03381i
\(447\) −7006.93 2006.45i −0.741424 0.212308i
\(448\) 1335.25 + 1487.90i 0.140814 + 0.156912i
\(449\) 1513.03i 0.159029i 0.996834 + 0.0795147i \(0.0253371\pi\)
−0.996834 + 0.0795147i \(0.974663\pi\)
\(450\) 4485.18 8426.64i 0.469852 0.882745i
\(451\) 28117.6 2.93571
\(452\) −1286.30 5171.26i −0.133855 0.538132i
\(453\) 1020.03 3562.15i 0.105795 0.369458i
\(454\) −4722.56 3691.77i −0.488195 0.381637i
\(455\) 2537.44 + 1131.08i 0.261444 + 0.116540i
\(456\) 2500.20 2976.80i 0.256760 0.305705i
\(457\) 14449.0i 1.47898i 0.673165 + 0.739492i \(0.264934\pi\)
−0.673165 + 0.739492i \(0.735066\pi\)
\(458\) 6069.47 7764.14i 0.619230 0.792127i
\(459\) 6543.72 + 7251.60i 0.665435 + 0.737420i
\(460\) 7982.79 + 1415.76i 0.809130 + 0.143501i
\(461\) 12494.6 1.26233 0.631164 0.775649i \(-0.282577\pi\)
0.631164 + 0.775649i \(0.282577\pi\)
\(462\) −2744.61 + 1994.44i −0.276387 + 0.200844i
\(463\) 1991.33 0.199881 0.0999406 0.994993i \(-0.468135\pi\)
0.0999406 + 0.994993i \(0.468135\pi\)
\(464\) −9739.83 + 5164.95i −0.974484 + 0.516760i
\(465\) 2307.53 2749.57i 0.230127 0.274212i
\(466\) −1416.05 1106.97i −0.140766 0.110041i
\(467\) 1976.98 0.195897 0.0979485 0.995191i \(-0.468772\pi\)
0.0979485 + 0.995191i \(0.468772\pi\)
\(468\) 4245.37 13073.7i 0.419321 1.29130i
\(469\) 139.715i 0.0137558i
\(470\) 13978.1 7419.42i 1.37183 0.728154i
\(471\) 9465.23 + 2710.39i 0.925976 + 0.265155i
\(472\) 361.805 + 161.446i 0.0352827 + 0.0157440i
\(473\) −3510.36 −0.341240
\(474\) −1291.92 + 938.811i −0.125190 + 0.0909726i
\(475\) 2762.77 + 3073.81i 0.266872 + 0.296918i
\(476\) −524.959 2110.47i −0.0505493 0.203221i
\(477\) 5828.88 9343.28i 0.559509 0.896854i
\(478\) −7461.97 5833.25i −0.714022 0.558173i
\(479\) −15429.2 −1.47177 −0.735884 0.677108i \(-0.763233\pi\)
−0.735884 + 0.677108i \(0.763233\pi\)
\(480\) 6747.96 + 8065.79i 0.641669 + 0.766982i
\(481\) 685.203 0.0649534
\(482\) 9870.12 + 7715.78i 0.932721 + 0.729137i
\(483\) −506.275 + 1768.02i −0.0476942 + 0.166558i
\(484\) −4179.38 16802.1i −0.392503 1.57796i
\(485\) 3943.17 8846.01i 0.369176 0.828200i
\(486\) 5015.35 9467.71i 0.468109 0.883671i
\(487\) 323.435 0.0300949 0.0150475 0.999887i \(-0.495210\pi\)
0.0150475 + 0.999887i \(0.495210\pi\)
\(488\) −5064.81 2260.04i −0.469822 0.209645i
\(489\) −3551.17 + 12401.4i −0.328403 + 1.14685i
\(490\) 4859.26 + 9154.78i 0.447998 + 0.844022i
\(491\) 10843.0i 0.996617i 0.867000 + 0.498308i \(0.166045\pi\)
−0.867000 + 0.498308i \(0.833955\pi\)
\(492\) 19758.0 + 693.709i 1.81048 + 0.0635667i
\(493\) 11992.9 1.09560
\(494\) 4688.61 + 3665.23i 0.427026 + 0.333819i
\(495\) −14792.8 + 9984.02i −1.34320 + 0.906562i
\(496\) 1852.62 + 3493.59i 0.167712 + 0.316264i
\(497\) 3472.96 0.313447
\(498\) −5430.31 7472.81i −0.488631 0.672419i
\(499\) −8534.00 −0.765599 −0.382800 0.923831i \(-0.625040\pi\)
−0.382800 + 0.923831i \(0.625040\pi\)
\(500\) −9492.56 + 5906.88i −0.849041 + 0.528328i
\(501\) −4451.94 + 15547.1i −0.397002 + 1.38641i
\(502\) −3822.02 + 4889.18i −0.339811 + 0.434691i
\(503\) 8197.47i 0.726654i 0.931662 + 0.363327i \(0.118359\pi\)
−0.931662 + 0.363327i \(0.881641\pi\)
\(504\) −1977.82 + 1333.76i −0.174800 + 0.117878i
\(505\) 15752.3 + 7021.71i 1.38806 + 0.618737i
\(506\) −11941.5 9335.03i −1.04914 0.820144i
\(507\) 9255.04 + 2650.20i 0.810711 + 0.232149i
\(508\) −501.443 2015.93i −0.0437951 0.176068i
\(509\) −9137.11 −0.795669 −0.397834 0.917457i \(-0.630238\pi\)
−0.397834 + 0.917457i \(0.630238\pi\)
\(510\) −2374.54 11190.8i −0.206170 0.971640i
\(511\) 2411.50i 0.208764i
\(512\) −11027.1 + 3552.60i −0.951823 + 0.306649i
\(513\) 3107.64 + 3443.82i 0.267458 + 0.296391i
\(514\) −12250.1 9576.30i −1.05123 0.821775i
\(515\) −3684.63 1642.45i −0.315270 0.140534i
\(516\) −2466.70 86.6066i −0.210446 0.00738884i
\(517\) −29586.1 −2.51682
\(518\) −93.6857 73.2370i −0.00794655 0.00621207i
\(519\) 4434.79 15487.2i 0.375078 1.30985i
\(520\) −11977.7 + 10757.2i −1.01011 + 0.907182i
\(521\) 9974.29i 0.838736i −0.907816 0.419368i \(-0.862252\pi\)
0.907816 0.419368i \(-0.137748\pi\)
\(522\) −4504.84 12359.6i −0.377724 1.03633i
\(523\) 13425.7i 1.12250i 0.827647 + 0.561248i \(0.189679\pi\)
−0.827647 + 0.561248i \(0.810321\pi\)
\(524\) 7223.92 1796.88i 0.602249 0.149804i
\(525\) −1110.59 2280.05i −0.0923244 0.189542i
\(526\) −6089.87 + 7790.23i −0.504812 + 0.645761i
\(527\) 4301.74i 0.355573i
\(528\) −4073.44 19234.2i −0.335745 1.58535i
\(529\) 3950.83 0.324717
\(530\) −11392.5 + 6047.01i −0.933694 + 0.495595i
\(531\) −250.229 + 401.099i −0.0204501 + 0.0327801i
\(532\) −249.306 1002.27i −0.0203172 0.0816805i
\(533\) 30265.7i 2.45957i
\(534\) −9079.49 + 6597.85i −0.735783 + 0.534676i
\(535\) −13761.6 6134.33i −1.11209 0.495720i
\(536\) 739.375 + 329.927i 0.0595824 + 0.0265870i
\(537\) 2887.19 10082.7i 0.232014 0.810241i
\(538\) −1304.93 1020.10i −0.104571 0.0817466i
\(539\) 19377.1i 1.54848i
\(540\) −10641.1 + 6650.71i −0.847996 + 0.530002i
\(541\) 8972.66i 0.713059i 0.934284 + 0.356530i \(0.116040\pi\)
−0.934284 + 0.356530i \(0.883960\pi\)
\(542\) −13095.5 + 16752.0i −1.03783 + 1.32760i
\(543\) −2779.92 + 9708.06i −0.219701 + 0.767243i
\(544\) 12408.3 + 2205.62i 0.977943 + 0.173833i
\(545\) 5406.77 12129.4i 0.424955 0.953334i
\(546\) −2146.81 2954.29i −0.168269 0.231560i
\(547\) 1210.47i 0.0946175i −0.998880 0.0473087i \(-0.984936\pi\)
0.998880 0.0473087i \(-0.0150645\pi\)
\(548\) 695.349 + 2795.48i 0.0542041 + 0.217914i
\(549\) 3502.88 5614.87i 0.272312 0.436497i
\(550\) 20853.1 1433.92i 1.61669 0.111169i
\(551\) 5695.48 0.440355
\(552\) −8160.86 6854.25i −0.629256 0.528508i
\(553\) 424.291i 0.0326269i
\(554\) 1123.16 + 878.008i 0.0861343 + 0.0673339i
\(555\) −479.148 402.116i −0.0366463 0.0307547i
\(556\) −1108.69 4457.22i −0.0845666 0.339979i
\(557\) 13253.5i 1.00820i −0.863644 0.504102i \(-0.831824\pi\)
0.863644 0.504102i \(-0.168176\pi\)
\(558\) −4433.28 + 1615.85i −0.336337 + 0.122588i
\(559\) 3778.54i 0.285895i
\(560\) 2787.44 190.583i 0.210341 0.0143815i
\(561\) −5887.77 + 20561.3i −0.443105 + 1.54741i
\(562\) 13749.1 17588.0i 1.03197 1.32011i
\(563\) −7028.69 −0.526152 −0.263076 0.964775i \(-0.584737\pi\)
−0.263076 + 0.964775i \(0.584737\pi\)
\(564\) −20789.8 729.939i −1.55215 0.0544964i
\(565\) −6802.09 3032.08i −0.506488 0.225771i
\(566\) −9571.87 + 12244.5i −0.710840 + 0.909316i
\(567\) −1251.54 2556.60i −0.0926983 0.189360i
\(568\) −8201.11 + 18378.9i −0.605829 + 1.35768i
\(569\) 15183.3i 1.11866i −0.828945 0.559330i \(-0.811058\pi\)
0.828945 0.559330i \(-0.188942\pi\)
\(570\) −1127.68 5314.56i −0.0828656 0.390531i
\(571\) −20286.3 −1.48679 −0.743395 0.668853i \(-0.766786\pi\)
−0.743395 + 0.668853i \(0.766786\pi\)
\(572\) 29208.3 7265.29i 2.13507 0.531079i
\(573\) 19622.9 + 5619.05i 1.43064 + 0.409667i
\(574\) 3234.91 4138.13i 0.235231 0.300910i
\(575\) 8426.80 7574.08i 0.611168 0.549324i
\(576\) −2387.82 13616.2i −0.172730 0.984969i
\(577\) 11832.9i 0.853744i 0.904312 + 0.426872i \(0.140385\pi\)
−0.904312 + 0.426872i \(0.859615\pi\)
\(578\) 146.801 + 114.759i 0.0105642 + 0.00825836i
\(579\) 652.780 2279.64i 0.0468542 0.163625i
\(580\) −2690.53 + 15170.6i −0.192618 + 1.08607i
\(581\) −2454.20 −0.175245
\(582\) −10299.2 + 7484.20i −0.733534 + 0.533041i
\(583\) 24113.4 1.71299
\(584\) −12761.7 5694.57i −0.904252 0.403498i
\(585\) −10746.8 15922.9i −0.759528 1.12535i
\(586\) 1199.11 1533.92i 0.0845306 0.108133i
\(587\) −18390.7 −1.29313 −0.646565 0.762859i \(-0.723795\pi\)
−0.646565 + 0.762859i \(0.723795\pi\)
\(588\) 478.065 13616.1i 0.0335290 0.954962i
\(589\) 2042.92i 0.142915i
\(590\) 489.070 259.593i 0.0341266 0.0181140i
\(591\) −5903.52 + 20616.3i −0.410894 + 1.43493i
\(592\) 608.803 322.843i 0.0422663 0.0224134i
\(593\) −26626.5 −1.84388 −0.921939 0.387335i \(-0.873396\pi\)
−0.921939 + 0.387335i \(0.873396\pi\)
\(594\) 23401.7 1655.57i 1.61647 0.114358i
\(595\) −2776.04 1237.44i −0.191271 0.0852605i
\(596\) −2708.69 10889.6i −0.186162 0.748417i
\(597\) −6287.98 + 21958.9i −0.431072 + 1.50539i
\(598\) 10048.2 12853.8i 0.687126 0.878979i
\(599\) 13589.0 0.926929 0.463465 0.886115i \(-0.346606\pi\)
0.463465 + 0.886115i \(0.346606\pi\)
\(600\) 14688.7 493.123i 0.999437 0.0335527i
\(601\) 271.371 0.0184184 0.00920920 0.999958i \(-0.497069\pi\)
0.00920920 + 0.999958i \(0.497069\pi\)
\(602\) −403.864 + 516.628i −0.0273426 + 0.0349770i
\(603\) −511.361 + 819.676i −0.0345344 + 0.0553562i
\(604\) 5536.01 1377.03i 0.372942 0.0927659i
\(605\) −22100.9 9851.65i −1.48518 0.662027i
\(606\) −13327.3 18340.1i −0.893375 1.22940i
\(607\) 21346.6 1.42740 0.713701 0.700451i \(-0.247018\pi\)
0.713701 + 0.700451i \(0.247018\pi\)
\(608\) 5892.76 + 1047.46i 0.393064 + 0.0698684i
\(609\) −3359.96 962.129i −0.223567 0.0640188i
\(610\) −6846.35 + 3633.97i −0.454427 + 0.241205i
\(611\) 31846.3i 2.10862i
\(612\) −4644.56 + 14303.0i −0.306773 + 0.944712i
\(613\) −25625.9 −1.68845 −0.844227 0.535986i \(-0.819940\pi\)
−0.844227 + 0.535986i \(0.819940\pi\)
\(614\) −9266.45 + 11853.8i −0.609061 + 0.779118i
\(615\) 17761.6 21164.1i 1.16458 1.38768i
\(616\) −4770.10 2128.53i −0.312002 0.139222i
\(617\) 25139.3 1.64031 0.820154 0.572142i \(-0.193888\pi\)
0.820154 + 0.572142i \(0.193888\pi\)
\(618\) 3117.39 + 4289.93i 0.202912 + 0.279234i
\(619\) 2383.46 0.154765 0.0773824 0.997001i \(-0.475344\pi\)
0.0773824 + 0.997001i \(0.475344\pi\)
\(620\) 5441.55 + 965.070i 0.352480 + 0.0625131i
\(621\) 9441.19 8519.56i 0.610083 0.550529i
\(622\) 17453.5 + 13643.9i 1.12511 + 0.879536i
\(623\) 2981.86i 0.191759i
\(624\) 20703.7 4384.63i 1.32822 0.281291i
\(625\) −1660.65 + 15536.5i −0.106282 + 0.994336i
\(626\) −4136.60 + 5291.59i −0.264108 + 0.337851i
\(627\) −2796.13 + 9764.67i −0.178097 + 0.621951i
\(628\) 3659.00 + 14710.1i 0.232500 + 0.934710i
\(629\) −749.633 −0.0475196
\(630\) −232.524 + 3325.74i −0.0147047 + 0.210318i
\(631\) 13751.7i 0.867585i −0.901013 0.433793i \(-0.857175\pi\)
0.901013 0.433793i \(-0.142825\pi\)
\(632\) −2245.35 1001.93i −0.141322 0.0630611i
\(633\) 21466.9 + 6147.07i 1.34792 + 0.385978i
\(634\) 7153.99 9151.47i 0.448140 0.573267i
\(635\) −2651.68 1182.00i −0.165714 0.0738684i
\(636\) 16944.2 + 594.918i 1.05642 + 0.0370913i
\(637\) 20857.4 1.29733
\(638\) 17740.4 22693.7i 1.10086 1.40823i
\(639\) −20375.0 12711.1i −1.26138 0.786923i
\(640\) −5573.75 + 15201.2i −0.344253 + 0.938877i
\(641\) 7866.10i 0.484699i 0.970189 + 0.242350i \(0.0779181\pi\)
−0.970189 + 0.242350i \(0.922082\pi\)
\(642\) 11643.1 + 16022.4i 0.715755 + 0.984972i
\(643\) 27498.6i 1.68653i −0.537498 0.843265i \(-0.680630\pi\)
0.537498 0.843265i \(-0.319370\pi\)
\(644\) −2747.72 + 683.468i −0.168129 + 0.0418205i
\(645\) −2217.46 + 2642.25i −0.135368 + 0.161300i
\(646\) −5129.49 4009.88i −0.312410 0.244221i
\(647\) 2282.05i 0.138666i −0.997594 0.0693328i \(-0.977913\pi\)
0.997594 0.0693328i \(-0.0220870\pi\)
\(648\) 16485.0 585.993i 0.999369 0.0355247i
\(649\) −1035.17 −0.0626100
\(650\) 1543.47 + 22446.2i 0.0931383 + 1.35448i
\(651\) −345.107 + 1205.19i −0.0207770 + 0.0725576i
\(652\) −19273.3 + 4794.05i −1.15767 + 0.287960i
\(653\) 12749.7i 0.764065i 0.924149 + 0.382032i \(0.124776\pi\)
−0.924149 + 0.382032i \(0.875224\pi\)
\(654\) −14122.0 + 10262.1i −0.844365 + 0.613580i
\(655\) 4235.62 9502.09i 0.252671 0.566836i
\(656\) 14260.1 + 26891.1i 0.848724 + 1.60049i
\(657\) 8826.15 14147.7i 0.524111 0.840113i
\(658\) −3403.85 + 4354.25i −0.201666 + 0.257973i
\(659\) 11221.7i 0.663329i 0.943397 + 0.331664i \(0.107610\pi\)
−0.943397 + 0.331664i \(0.892390\pi\)
\(660\) −24688.4 12060.6i −1.45605 0.711302i
\(661\) 16408.1i 0.965506i 0.875756 + 0.482753i \(0.160363\pi\)
−0.875756 + 0.482753i \(0.839637\pi\)
\(662\) −9757.98 7628.11i −0.572892 0.447848i
\(663\) −22132.1 6337.57i −1.29644 0.371238i
\(664\) 5795.40 12987.7i 0.338713 0.759066i
\(665\) −1318.35 587.665i −0.0768775 0.0342687i
\(666\) 281.582 + 772.556i 0.0163830 + 0.0449489i
\(667\) 15614.1i 0.906416i
\(668\) −24162.1 + 6010.09i −1.39949 + 0.348110i
\(669\) −27923.6 7995.98i −1.61374 0.462096i
\(670\) 999.450 530.497i 0.0576300 0.0305894i
\(671\) 14491.0 0.833710
\(672\) −3299.39 1613.39i −0.189400 0.0926156i
\(673\) 9153.75i 0.524296i −0.965028 0.262148i \(-0.915569\pi\)
0.965028 0.262148i \(-0.0844309\pi\)
\(674\) −11801.0 + 15096.0i −0.674419 + 0.862725i
\(675\) −1829.46 + 17441.3i −0.104320 + 0.994544i
\(676\) 3577.75 + 14383.5i 0.203559 + 0.818358i
\(677\) 17813.6i 1.01128i −0.862746 0.505638i \(-0.831257\pi\)
0.862746 0.505638i \(-0.168743\pi\)
\(678\) 5754.93 + 7919.53i 0.325983 + 0.448595i
\(679\) 3382.45i 0.191173i
\(680\) 13103.9 11768.7i 0.738989 0.663691i
\(681\) 10586.8 + 3031.53i 0.595720 + 0.170585i
\(682\) −8140.03 6363.31i −0.457035 0.357278i
\(683\) −1277.22 −0.0715540 −0.0357770 0.999360i \(-0.511391\pi\)
−0.0357770 + 0.999360i \(0.511391\pi\)
\(684\) −2205.73 + 6792.56i −0.123301 + 0.379708i
\(685\) 3677.07 + 1639.08i 0.205100 + 0.0914250i
\(686\) −5836.19 4562.33i −0.324820 0.253922i
\(687\) −4984.00 + 17405.2i −0.276785 + 0.966593i
\(688\) −1780.31 3357.23i −0.0986536 0.186037i
\(689\) 25955.5i 1.43516i
\(690\) −14569.8 + 3091.52i −0.803859 + 0.170569i
\(691\) −6041.97 −0.332630 −0.166315 0.986073i \(-0.553187\pi\)
−0.166315 + 0.986073i \(0.553187\pi\)
\(692\) 24069.0 5986.94i 1.32221 0.328886i
\(693\) 3299.06 5288.16i 0.180838 0.289871i
\(694\) −10673.3 8343.64i −0.583793 0.456369i
\(695\) −5862.87 2613.42i −0.319988 0.142637i
\(696\) 13025.9 15509.0i 0.709403 0.844634i
\(697\) 33111.6i 1.79941i
\(698\) 5611.54 7178.35i 0.304298 0.389262i
\(699\) 3174.41 + 908.998i 0.171770 + 0.0491866i
\(700\) 2188.10 3233.97i 0.118146 0.174618i
\(701\) −8649.55 −0.466033 −0.233016 0.972473i \(-0.574860\pi\)
−0.233016 + 0.972473i \(0.574860\pi\)
\(702\) 1782.05 + 25189.5i 0.0958106 + 1.35429i
\(703\) −356.005 −0.0190995
\(704\) 22528.5 20217.1i 1.20607 1.08233i
\(705\) −18689.2 + 22269.5i −0.998407 + 1.18967i
\(706\) 3963.83 + 3098.65i 0.211304 + 0.165183i
\(707\) −6023.21 −0.320405
\(708\) −727.402 25.5394i −0.0386122 0.00135569i
\(709\) 32669.4i 1.73050i 0.501339 + 0.865251i \(0.332841\pi\)
−0.501339 + 0.865251i \(0.667159\pi\)
\(710\) 13186.8 + 24843.7i 0.697030 + 1.31319i
\(711\) 1552.91 2489.21i 0.0819112 0.131298i
\(712\) −15780.1 7041.44i −0.830594 0.370631i
\(713\) −5600.63 −0.294173
\(714\) 2348.67 + 3232.08i 0.123105 + 0.169408i
\(715\) 17125.8 38419.6i 0.895760 2.00952i
\(716\) 15669.7 3897.69i 0.817883 0.203441i
\(717\) 16727.8 + 4790.03i 0.871285 + 0.249494i
\(718\) 1980.25 + 1548.02i 0.102928 + 0.0804618i
\(719\) 35829.6 1.85844 0.929221 0.369524i \(-0.120479\pi\)
0.929221 + 0.369524i \(0.120479\pi\)
\(720\) −17050.8 9083.99i −0.882563 0.470195i
\(721\) 1408.89 0.0727736
\(722\) 12848.2 + 10043.9i 0.662274 + 0.517720i
\(723\) −22126.3 6335.89i −1.13815 0.325912i
\(724\) −15087.5 + 3752.87i −0.774479 + 0.192644i
\(725\) 14393.8 + 16014.4i 0.737343 + 0.820356i
\(726\) 18698.6 + 25731.7i 0.955881 + 1.31542i
\(727\) −15633.8 −0.797561 −0.398781 0.917046i \(-0.630566\pi\)
−0.398781 + 0.917046i \(0.630566\pi\)
\(728\) 2291.14 5134.52i 0.116642 0.261398i
\(729\) −2014.70 + 19579.6i −0.102357 + 0.994748i
\(730\) −17250.6 + 9156.45i −0.874622 + 0.464240i
\(731\) 4133.84i 0.209159i
\(732\) 10182.7 + 357.518i 0.514158 + 0.0180523i
\(733\) 6139.39 0.309364 0.154682 0.987964i \(-0.450565\pi\)
0.154682 + 0.987964i \(0.450565\pi\)
\(734\) 5347.62 + 4180.40i 0.268916 + 0.210220i
\(735\) −14585.1 12240.3i −0.731946 0.614272i
\(736\) 2871.59 16154.9i 0.143816 0.809074i
\(737\) −2115.44 −0.105730
\(738\) −34124.1 + 12437.6i −1.70207 + 0.620371i
\(739\) −23289.0 −1.15927 −0.579634 0.814877i \(-0.696804\pi\)
−0.579634 + 0.814877i \(0.696804\pi\)
\(740\) 168.176 948.259i 0.00835441 0.0471063i
\(741\) −10510.7 3009.74i −0.521078 0.149211i
\(742\) 2774.22 3548.82i 0.137257 0.175581i
\(743\) 22930.0i 1.13219i −0.824339 0.566096i \(-0.808453\pi\)
0.824339 0.566096i \(-0.191547\pi\)
\(744\) −5562.93 4672.27i −0.274122 0.230233i
\(745\) −14323.8 6384.95i −0.704409 0.313995i
\(746\) 16851.5 + 13173.3i 0.827045 + 0.646527i
\(747\) 14398.2 + 8982.44i 0.705225 + 0.439960i
\(748\) −31954.8 + 7948.45i −1.56201 + 0.388535i
\(749\) 5262.02 0.256702
\(750\) 12093.4 16602.0i 0.588784 0.808290i
\(751\) 10373.1i 0.504023i −0.967724 0.252011i \(-0.918908\pi\)
0.967724 0.252011i \(-0.0810920\pi\)
\(752\) −15004.8 28295.5i −0.727620 1.37211i
\(753\) 3138.49 10960.3i 0.151890 0.530431i
\(754\) 24427.4 + 19095.7i 1.17983 + 0.922311i
\(755\) 3245.95 7281.87i 0.156466 0.351013i
\(756\) 2448.69 3634.55i 0.117802 0.174851i
\(757\) −19427.2 −0.932753 −0.466377 0.884586i \(-0.654441\pi\)
−0.466377 + 0.884586i \(0.654441\pi\)
\(758\) 15653.6 + 12236.9i 0.750085 + 0.586364i
\(759\) 26769.7 + 7665.55i 1.28021 + 0.366590i
\(760\) 6223.12 5589.02i 0.297022 0.266757i
\(761\) 17770.0i 0.846467i 0.906021 + 0.423233i \(0.139105\pi\)
−0.906021 + 0.423233i \(0.860895\pi\)
\(762\) 2243.46 + 3087.29i 0.106656 + 0.146773i
\(763\) 4637.92i 0.220058i
\(764\) 7585.68 + 30496.4i 0.359215 + 1.44414i
\(765\) 11757.3 + 17420.1i 0.555667 + 0.823301i
\(766\) 5759.14 7367.16i 0.271653 0.347502i
\(767\) 1114.25i 0.0524553i
\(768\) 16329.3 13650.6i 0.767232 0.641370i
\(769\) 6380.37 0.299196 0.149598 0.988747i \(-0.452202\pi\)
0.149598 + 0.988747i \(0.452202\pi\)
\(770\) −6447.98 + 3422.52i −0.301778 + 0.160181i