Properties

Label 120.4.m.b.59.3
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 59.3
Character \(\chi\) \(=\) 120.59
Dual form 120.4.m.b.59.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.80496 + 0.363625i) q^{2} +(3.73183 - 3.61572i) q^{3} +(7.73555 - 2.03990i) q^{4} +(-2.66357 + 10.8584i) q^{5} +(-9.15285 + 11.4989i) q^{6} -26.3409 q^{7} +(-20.9561 + 8.53468i) q^{8} +(0.853113 - 26.9865i) q^{9} +O(q^{10})\) \(q+(-2.80496 + 0.363625i) q^{2} +(3.73183 - 3.61572i) q^{3} +(7.73555 - 2.03990i) q^{4} +(-2.66357 + 10.8584i) q^{5} +(-9.15285 + 11.4989i) q^{6} -26.3409 q^{7} +(-20.9561 + 8.53468i) q^{8} +(0.853113 - 26.9865i) q^{9} +(3.52280 - 31.4259i) q^{10} +37.4262i q^{11} +(21.4921 - 35.5822i) q^{12} -30.8736 q^{13} +(73.8850 - 9.57820i) q^{14} +(29.3211 + 50.1525i) q^{15} +(55.6776 - 31.5596i) q^{16} -54.0168 q^{17} +(7.42002 + 76.0062i) q^{18} -4.70847 q^{19} +(1.54596 + 89.4294i) q^{20} +(-98.2997 + 95.2413i) q^{21} +(-13.6091 - 104.979i) q^{22} +129.048i q^{23} +(-47.3457 + 107.621i) q^{24} +(-110.811 - 57.8443i) q^{25} +(86.5990 - 11.2264i) q^{26} +(-94.3921 - 103.794i) q^{27} +(-203.761 + 53.7329i) q^{28} -230.566 q^{29} +(-100.481 - 130.014i) q^{30} +123.860i q^{31} +(-144.697 + 108.769i) q^{32} +(135.323 + 139.668i) q^{33} +(151.515 - 19.6419i) q^{34} +(70.1608 - 286.021i) q^{35} +(-48.4506 - 210.496i) q^{36} +349.557 q^{37} +(13.2070 - 1.71212i) q^{38} +(-115.215 + 111.630i) q^{39} +(-36.8551 - 250.283i) q^{40} +74.8414i q^{41} +(241.094 - 302.892i) q^{42} +364.853i q^{43} +(76.3458 + 289.512i) q^{44} +(290.759 + 81.1439i) q^{45} +(-46.9252 - 361.975i) q^{46} -45.7642i q^{47} +(93.6687 - 319.090i) q^{48} +350.842 q^{49} +(331.853 + 121.957i) q^{50} +(-201.582 + 195.310i) q^{51} +(-238.824 + 62.9791i) q^{52} -682.936i q^{53} +(302.508 + 256.814i) q^{54} +(-406.390 - 99.6872i) q^{55} +(552.003 - 224.811i) q^{56} +(-17.5712 + 17.0245i) q^{57} +(646.728 - 83.8397i) q^{58} +256.129i q^{59} +(329.121 + 328.145i) q^{60} -435.099i q^{61} +(-45.0386 - 347.422i) q^{62} +(-22.4718 + 710.849i) q^{63} +(366.318 - 357.708i) q^{64} +(82.2339 - 335.238i) q^{65} +(-430.361 - 342.556i) q^{66} -862.064i q^{67} +(-417.850 + 110.189i) q^{68} +(466.603 + 481.586i) q^{69} +(-92.7936 + 827.787i) q^{70} -366.537 q^{71} +(212.443 + 572.814i) q^{72} -215.240i q^{73} +(-980.492 + 127.108i) q^{74} +(-622.676 + 184.796i) q^{75} +(-36.4226 + 9.60482i) q^{76} -985.839i q^{77} +(282.581 - 355.013i) q^{78} +340.273i q^{79} +(194.386 + 688.632i) q^{80} +(-727.544 - 46.0451i) q^{81} +(-27.2142 - 209.927i) q^{82} +605.094 q^{83} +(-566.120 + 937.266i) q^{84} +(143.878 - 586.538i) q^{85} +(-132.670 - 1023.40i) q^{86} +(-860.434 + 833.664i) q^{87} +(-319.421 - 784.308i) q^{88} +517.431i q^{89} +(-845.071 - 121.878i) q^{90} +813.237 q^{91} +(263.246 + 998.260i) q^{92} +(447.843 + 462.225i) q^{93} +(16.6410 + 128.367i) q^{94} +(12.5413 - 51.1265i) q^{95} +(-146.708 + 929.093i) q^{96} +1441.60i q^{97} +(-984.097 + 127.575i) q^{98} +(1010.00 + 31.9288i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.80496 + 0.363625i −0.991702 + 0.128561i
\(3\) 3.73183 3.61572i 0.718191 0.695846i
\(4\) 7.73555 2.03990i 0.966944 0.254988i
\(5\) −2.66357 + 10.8584i −0.238237 + 0.971207i
\(6\) −9.15285 + 11.4989i −0.622773 + 0.782403i
\(7\) −26.3409 −1.42227 −0.711137 0.703053i \(-0.751819\pi\)
−0.711137 + 0.703053i \(0.751819\pi\)
\(8\) −20.9561 + 8.53468i −0.926139 + 0.377183i
\(9\) 0.853113 26.9865i 0.0315968 0.999501i
\(10\) 3.52280 31.4259i 0.111401 0.993776i
\(11\) 37.4262i 1.02586i 0.858431 + 0.512928i \(0.171439\pi\)
−0.858431 + 0.512928i \(0.828561\pi\)
\(12\) 21.4921 35.5822i 0.517018 0.855974i
\(13\) −30.8736 −0.658676 −0.329338 0.944212i \(-0.606826\pi\)
−0.329338 + 0.944212i \(0.606826\pi\)
\(14\) 73.8850 9.57820i 1.41047 0.182849i
\(15\) 29.3211 + 50.1525i 0.504711 + 0.863288i
\(16\) 55.6776 31.5596i 0.869962 0.493118i
\(17\) −54.0168 −0.770648 −0.385324 0.922781i \(-0.625910\pi\)
−0.385324 + 0.922781i \(0.625910\pi\)
\(18\) 7.42002 + 76.0062i 0.0971620 + 0.995269i
\(19\) −4.70847 −0.0568524 −0.0284262 0.999596i \(-0.509050\pi\)
−0.0284262 + 0.999596i \(0.509050\pi\)
\(20\) 1.54596 + 89.4294i 0.0172844 + 0.999851i
\(21\) −98.2997 + 95.2413i −1.02146 + 0.989684i
\(22\) −13.6091 104.979i −0.131885 1.01734i
\(23\) 129.048i 1.16993i 0.811058 + 0.584966i \(0.198892\pi\)
−0.811058 + 0.584966i \(0.801108\pi\)
\(24\) −47.3457 + 107.621i −0.402683 + 0.915339i
\(25\) −110.811 57.8443i −0.886486 0.462755i
\(26\) 86.5990 11.2264i 0.653210 0.0846799i
\(27\) −94.3921 103.794i −0.672806 0.739819i
\(28\) −203.761 + 53.7329i −1.37526 + 0.362663i
\(29\) −230.566 −1.47638 −0.738191 0.674591i \(-0.764320\pi\)
−0.738191 + 0.674591i \(0.764320\pi\)
\(30\) −100.481 130.014i −0.611508 0.791238i
\(31\) 123.860i 0.717610i 0.933413 + 0.358805i \(0.116816\pi\)
−0.933413 + 0.358805i \(0.883184\pi\)
\(32\) −144.697 + 108.769i −0.799347 + 0.600869i
\(33\) 135.323 + 139.668i 0.713838 + 0.736761i
\(34\) 151.515 19.6419i 0.764253 0.0990751i
\(35\) 70.1608 286.021i 0.338838 1.38132i
\(36\) −48.4506 210.496i −0.224308 0.974518i
\(37\) 349.557 1.55316 0.776579 0.630020i \(-0.216953\pi\)
0.776579 + 0.630020i \(0.216953\pi\)
\(38\) 13.2070 1.71212i 0.0563807 0.00730900i
\(39\) −115.215 + 111.630i −0.473055 + 0.458337i
\(40\) −36.8551 250.283i −0.145683 0.989331i
\(41\) 74.8414i 0.285080i 0.989789 + 0.142540i \(0.0455269\pi\)
−0.989789 + 0.142540i \(0.954473\pi\)
\(42\) 241.094 302.892i 0.885754 1.11279i
\(43\) 364.853i 1.29394i 0.762515 + 0.646971i \(0.223965\pi\)
−0.762515 + 0.646971i \(0.776035\pi\)
\(44\) 76.3458 + 289.512i 0.261581 + 0.991946i
\(45\) 290.759 + 81.1439i 0.963195 + 0.268805i
\(46\) −46.9252 361.975i −0.150407 1.16022i
\(47\) 45.7642i 0.142030i −0.997475 0.0710148i \(-0.977376\pi\)
0.997475 0.0710148i \(-0.0226238\pi\)
\(48\) 93.6687 319.090i 0.281665 0.959513i
\(49\) 350.842 1.02286
\(50\) 331.853 + 121.957i 0.938622 + 0.344947i
\(51\) −201.582 + 195.310i −0.553472 + 0.536252i
\(52\) −238.824 + 62.9791i −0.636903 + 0.167954i
\(53\) 682.936i 1.76997i −0.465619 0.884985i \(-0.654168\pi\)
0.465619 0.884985i \(-0.345832\pi\)
\(54\) 302.508 + 256.814i 0.762335 + 0.647183i
\(55\) −406.390 99.6872i −0.996319 0.244397i
\(56\) 552.003 224.811i 1.31722 0.536458i
\(57\) −17.5712 + 17.0245i −0.0408309 + 0.0395605i
\(58\) 646.728 83.8397i 1.46413 0.189805i
\(59\) 256.129i 0.565172i 0.959242 + 0.282586i \(0.0911923\pi\)
−0.959242 + 0.282586i \(0.908808\pi\)
\(60\) 329.121 + 328.145i 0.708156 + 0.706056i
\(61\) 435.099i 0.913259i −0.889657 0.456629i \(-0.849057\pi\)
0.889657 0.456629i \(-0.150943\pi\)
\(62\) −45.0386 347.422i −0.0922566 0.711655i
\(63\) −22.4718 + 710.849i −0.0449393 + 1.42156i
\(64\) 366.318 357.708i 0.715466 0.698648i
\(65\) 82.2339 335.238i 0.156921 0.639711i
\(66\) −430.361 342.556i −0.802633 0.638876i
\(67\) 862.064i 1.57191i −0.618285 0.785954i \(-0.712172\pi\)
0.618285 0.785954i \(-0.287828\pi\)
\(68\) −417.850 + 110.189i −0.745173 + 0.196506i
\(69\) 466.603 + 481.586i 0.814092 + 0.840235i
\(70\) −92.7936 + 827.787i −0.158442 + 1.41342i
\(71\) −366.537 −0.612675 −0.306338 0.951923i \(-0.599104\pi\)
−0.306338 + 0.951923i \(0.599104\pi\)
\(72\) 212.443 + 572.814i 0.347732 + 0.937594i
\(73\) 215.240i 0.345095i −0.985001 0.172547i \(-0.944800\pi\)
0.985001 0.172547i \(-0.0551998\pi\)
\(74\) −980.492 + 127.108i −1.54027 + 0.199675i
\(75\) −622.676 + 184.796i −0.958673 + 0.284512i
\(76\) −36.4226 + 9.60482i −0.0549731 + 0.0144967i
\(77\) 985.839i 1.45905i
\(78\) 282.581 355.013i 0.410205 0.515350i
\(79\) 340.273i 0.484604i 0.970201 + 0.242302i \(0.0779026\pi\)
−0.970201 + 0.242302i \(0.922097\pi\)
\(80\) 194.386 + 688.632i 0.271663 + 0.962392i
\(81\) −727.544 46.0451i −0.998003 0.0631620i
\(82\) −27.2142 209.927i −0.0366501 0.282714i
\(83\) 605.094 0.800214 0.400107 0.916469i \(-0.368973\pi\)
0.400107 + 0.916469i \(0.368973\pi\)
\(84\) −566.120 + 937.266i −0.735342 + 1.21743i
\(85\) 143.878 586.538i 0.183597 0.748458i
\(86\) −132.670 1023.40i −0.166350 1.28320i
\(87\) −860.434 + 833.664i −1.06032 + 1.02733i
\(88\) −319.421 784.308i −0.386936 0.950086i
\(89\) 517.431i 0.616265i 0.951343 + 0.308132i \(0.0997040\pi\)
−0.951343 + 0.308132i \(0.900296\pi\)
\(90\) −845.071 121.878i −0.989759 0.142745i
\(91\) 813.237 0.936818
\(92\) 263.246 + 998.260i 0.298319 + 1.13126i
\(93\) 447.843 + 462.225i 0.499346 + 0.515381i
\(94\) 16.6410 + 128.367i 0.0182595 + 0.140851i
\(95\) 12.5413 51.1265i 0.0135443 0.0552155i
\(96\) −146.708 + 929.093i −0.155972 + 0.987762i
\(97\) 1441.60i 1.50900i 0.656302 + 0.754498i \(0.272120\pi\)
−0.656302 + 0.754498i \(0.727880\pi\)
\(98\) −984.097 + 127.575i −1.01438 + 0.131500i
\(99\) 1010.00 + 31.9288i 1.02534 + 0.0324138i
\(100\) −975.180 221.414i −0.975180 0.221414i
\(101\) 422.189 0.415934 0.207967 0.978136i \(-0.433315\pi\)
0.207967 + 0.978136i \(0.433315\pi\)
\(102\) 494.408 621.136i 0.479938 0.602957i
\(103\) −1058.99 −1.01307 −0.506533 0.862221i \(-0.669073\pi\)
−0.506533 + 0.862221i \(0.669073\pi\)
\(104\) 646.990 263.496i 0.610025 0.248441i
\(105\) −772.343 1321.06i −0.717837 1.22783i
\(106\) 248.332 + 1915.60i 0.227549 + 1.75528i
\(107\) −819.034 −0.739991 −0.369995 0.929034i \(-0.620641\pi\)
−0.369995 + 0.929034i \(0.620641\pi\)
\(108\) −941.904 610.351i −0.839211 0.543806i
\(109\) 1139.42i 1.00125i −0.865663 0.500627i \(-0.833103\pi\)
0.865663 0.500627i \(-0.166897\pi\)
\(110\) 1176.15 + 131.845i 1.01947 + 0.114281i
\(111\) 1304.49 1263.90i 1.11546 1.08076i
\(112\) −1466.60 + 831.307i −1.23732 + 0.701349i
\(113\) 1448.12 1.20555 0.602776 0.797911i \(-0.294061\pi\)
0.602776 + 0.797911i \(0.294061\pi\)
\(114\) 43.0959 54.1423i 0.0354062 0.0444815i
\(115\) −1401.26 343.729i −1.13625 0.278721i
\(116\) −1783.56 + 470.333i −1.42758 + 0.376460i
\(117\) −26.3387 + 833.170i −0.0208120 + 0.658347i
\(118\) −93.1349 718.430i −0.0726590 0.560482i
\(119\) 1422.85 1.09607
\(120\) −1042.49 800.757i −0.793050 0.609156i
\(121\) −69.7203 −0.0523819
\(122\) 158.213 + 1220.43i 0.117409 + 0.905680i
\(123\) 270.606 + 279.295i 0.198372 + 0.204742i
\(124\) 252.662 + 958.126i 0.182982 + 0.693889i
\(125\) 923.250 1049.16i 0.660624 0.750717i
\(126\) −195.450 2002.07i −0.138191 1.41554i
\(127\) 1075.20 0.751245 0.375623 0.926773i \(-0.377429\pi\)
0.375623 + 0.926773i \(0.377429\pi\)
\(128\) −897.436 + 1136.56i −0.619710 + 0.784831i
\(129\) 1319.21 + 1361.57i 0.900384 + 0.929298i
\(130\) −108.761 + 970.231i −0.0733769 + 0.654576i
\(131\) 729.865i 0.486784i 0.969928 + 0.243392i \(0.0782601\pi\)
−0.969928 + 0.243392i \(0.921740\pi\)
\(132\) 1331.71 + 804.366i 0.878107 + 0.530387i
\(133\) 124.025 0.0808598
\(134\) 313.468 + 2418.05i 0.202086 + 1.55886i
\(135\) 1378.46 748.488i 0.878805 0.477182i
\(136\) 1131.98 461.016i 0.713727 0.290675i
\(137\) −505.557 −0.315275 −0.157637 0.987497i \(-0.550388\pi\)
−0.157637 + 0.987497i \(0.550388\pi\)
\(138\) −1483.92 1181.16i −0.915358 0.728602i
\(139\) −677.815 −0.413608 −0.206804 0.978382i \(-0.566306\pi\)
−0.206804 + 0.978382i \(0.566306\pi\)
\(140\) −40.7221 2355.65i −0.0245832 1.42206i
\(141\) −165.471 170.784i −0.0988308 0.102004i
\(142\) 1028.12 133.282i 0.607591 0.0787660i
\(143\) 1155.48i 0.675707i
\(144\) −804.184 1529.47i −0.465384 0.885109i
\(145\) 614.129 2503.59i 0.351729 1.43387i
\(146\) 78.2666 + 603.739i 0.0443657 + 0.342231i
\(147\) 1309.28 1268.55i 0.734612 0.711756i
\(148\) 2704.02 713.063i 1.50182 0.396037i
\(149\) −2640.39 −1.45174 −0.725869 0.687833i \(-0.758562\pi\)
−0.725869 + 0.687833i \(0.758562\pi\)
\(150\) 1679.38 744.765i 0.914140 0.405399i
\(151\) 2466.32i 1.32918i 0.747207 + 0.664591i \(0.231394\pi\)
−0.747207 + 0.664591i \(0.768606\pi\)
\(152\) 98.6712 40.1853i 0.0526532 0.0214438i
\(153\) −46.0825 + 1457.73i −0.0243500 + 0.770263i
\(154\) 358.476 + 2765.24i 0.187577 + 1.44694i
\(155\) −1344.92 329.910i −0.696948 0.170961i
\(156\) −663.536 + 1098.55i −0.340548 + 0.563810i
\(157\) −1553.13 −0.789512 −0.394756 0.918786i \(-0.629171\pi\)
−0.394756 + 0.918786i \(0.629171\pi\)
\(158\) −123.732 954.452i −0.0623011 0.480583i
\(159\) −2469.31 2548.60i −1.23163 1.27118i
\(160\) −795.648 1860.90i −0.393135 0.919481i
\(161\) 3399.25i 1.66396i
\(162\) 2057.47 135.399i 0.997842 0.0656662i
\(163\) 3936.58i 1.89164i 0.324694 + 0.945819i \(0.394739\pi\)
−0.324694 + 0.945819i \(0.605261\pi\)
\(164\) 152.669 + 578.940i 0.0726919 + 0.275656i
\(165\) −1877.02 + 1097.38i −0.885610 + 0.517761i
\(166\) −1697.26 + 220.027i −0.793573 + 0.102876i
\(167\) 1998.86i 0.926208i −0.886304 0.463104i \(-0.846736\pi\)
0.886304 0.463104i \(-0.153264\pi\)
\(168\) 1247.13 2834.85i 0.572726 1.30186i
\(169\) −1243.82 −0.566146
\(170\) −190.290 + 1697.53i −0.0858506 + 0.765851i
\(171\) −4.01686 + 127.065i −0.00179635 + 0.0568241i
\(172\) 744.264 + 2822.34i 0.329940 + 1.25117i
\(173\) 2816.75i 1.23788i 0.785438 + 0.618940i \(0.212438\pi\)
−0.785438 + 0.618940i \(0.787562\pi\)
\(174\) 2110.34 2651.27i 0.919451 1.15513i
\(175\) 2918.85 + 1523.67i 1.26083 + 0.658164i
\(176\) 1181.15 + 2083.80i 0.505869 + 0.892457i
\(177\) 926.091 + 955.830i 0.393273 + 0.405901i
\(178\) −188.151 1451.37i −0.0792275 0.611151i
\(179\) 905.857i 0.378251i −0.981953 0.189125i \(-0.939435\pi\)
0.981953 0.189125i \(-0.0605653\pi\)
\(180\) 2414.71 + 34.5732i 0.999898 + 0.0143163i
\(181\) 174.804i 0.0717851i 0.999356 + 0.0358925i \(0.0114274\pi\)
−0.999356 + 0.0358925i \(0.988573\pi\)
\(182\) −2281.09 + 295.713i −0.929044 + 0.120438i
\(183\) −1573.20 1623.72i −0.635487 0.655894i
\(184\) −1101.39 2704.35i −0.441279 1.08352i
\(185\) −931.069 + 3795.64i −0.370019 + 1.50844i
\(186\) −1424.26 1133.67i −0.561460 0.446908i
\(187\) 2021.65i 0.790574i
\(188\) −93.3546 354.011i −0.0362159 0.137335i
\(189\) 2486.37 + 2734.02i 0.956915 + 1.05223i
\(190\) −16.5870 + 147.968i −0.00633340 + 0.0564986i
\(191\) −1267.32 −0.480107 −0.240053 0.970760i \(-0.577165\pi\)
−0.240053 + 0.970760i \(0.577165\pi\)
\(192\) 73.6672 2659.41i 0.0276899 0.999617i
\(193\) 2265.21i 0.844838i 0.906401 + 0.422419i \(0.138819\pi\)
−0.906401 + 0.422419i \(0.861181\pi\)
\(194\) −524.203 4043.63i −0.193998 1.49647i
\(195\) −905.246 1548.39i −0.332441 0.568627i
\(196\) 2713.96 715.684i 0.989052 0.260818i
\(197\) 630.779i 0.228128i 0.993473 + 0.114064i \(0.0363868\pi\)
−0.993473 + 0.114064i \(0.963613\pi\)
\(198\) −2844.62 + 277.703i −1.02100 + 0.0996743i
\(199\) 3357.04i 1.19585i 0.801551 + 0.597926i \(0.204008\pi\)
−0.801551 + 0.597926i \(0.795992\pi\)
\(200\) 2815.85 + 266.458i 0.995553 + 0.0942072i
\(201\) −3116.98 3217.08i −1.09381 1.12893i
\(202\) −1184.22 + 153.518i −0.412482 + 0.0534728i
\(203\) 6073.32 2.09982
\(204\) −1160.93 + 1922.04i −0.398439 + 0.659655i
\(205\) −812.660 199.345i −0.276871 0.0679165i
\(206\) 2970.43 385.077i 1.00466 0.130241i
\(207\) 3482.56 + 110.093i 1.16935 + 0.0369661i
\(208\) −1718.97 + 974.356i −0.573023 + 0.324805i
\(209\) 176.220i 0.0583225i
\(210\) 2646.76 + 3424.68i 0.869732 + 1.12536i
\(211\) 3809.37 1.24288 0.621440 0.783462i \(-0.286548\pi\)
0.621440 + 0.783462i \(0.286548\pi\)
\(212\) −1393.12 5282.89i −0.451321 1.71146i
\(213\) −1367.85 + 1325.30i −0.440018 + 0.426327i
\(214\) 2297.35 297.821i 0.733850 0.0951338i
\(215\) −3961.73 971.810i −1.25669 0.308265i
\(216\) 2863.94 + 1369.51i 0.902159 + 0.431404i
\(217\) 3262.58i 1.02064i
\(218\) 414.322 + 3196.03i 0.128722 + 0.992946i
\(219\) −778.248 803.239i −0.240133 0.247844i
\(220\) −3347.00 + 57.8596i −1.02570 + 0.0177313i
\(221\) 1667.69 0.507607
\(222\) −3199.44 + 4019.53i −0.967264 + 1.21519i
\(223\) 4261.82 1.27979 0.639894 0.768463i \(-0.278978\pi\)
0.639894 + 0.768463i \(0.278978\pi\)
\(224\) 3811.46 2865.07i 1.13689 0.854601i
\(225\) −1655.55 + 2941.05i −0.490534 + 0.871422i
\(226\) −4061.90 + 526.571i −1.19555 + 0.154987i
\(227\) −4481.95 −1.31047 −0.655236 0.755424i \(-0.727431\pi\)
−0.655236 + 0.755424i \(0.727431\pi\)
\(228\) −101.195 + 167.538i −0.0293938 + 0.0486642i
\(229\) 1157.74i 0.334085i −0.985950 0.167042i \(-0.946578\pi\)
0.985950 0.167042i \(-0.0534216\pi\)
\(230\) 4055.47 + 454.611i 1.16265 + 0.130331i
\(231\) −3564.52 3678.98i −1.01527 1.04788i
\(232\) 4831.78 1967.81i 1.36733 0.556867i
\(233\) 2549.55 0.716852 0.358426 0.933558i \(-0.383314\pi\)
0.358426 + 0.933558i \(0.383314\pi\)
\(234\) −229.083 2346.58i −0.0639983 0.655559i
\(235\) 496.927 + 121.896i 0.137940 + 0.0338367i
\(236\) 522.478 + 1981.30i 0.144112 + 0.546490i
\(237\) 1230.33 + 1269.84i 0.337210 + 0.348039i
\(238\) −3991.04 + 517.384i −1.08698 + 0.140912i
\(239\) −714.592 −0.193402 −0.0967010 0.995313i \(-0.530829\pi\)
−0.0967010 + 0.995313i \(0.530829\pi\)
\(240\) 3215.32 + 1867.01i 0.864783 + 0.502146i
\(241\) −2330.00 −0.622774 −0.311387 0.950283i \(-0.600794\pi\)
−0.311387 + 0.950283i \(0.600794\pi\)
\(242\) 195.562 25.3520i 0.0519472 0.00673426i
\(243\) −2881.56 + 2458.77i −0.760708 + 0.649094i
\(244\) −887.561 3365.74i −0.232870 0.883070i
\(245\) −934.492 + 3809.60i −0.243684 + 0.993413i
\(246\) −860.596 685.012i −0.223047 0.177540i
\(247\) 145.367 0.0374473
\(248\) −1057.11 2595.63i −0.270670 0.664607i
\(249\) 2258.11 2187.85i 0.574706 0.556825i
\(250\) −2208.18 + 3278.56i −0.558629 + 0.829417i
\(251\) 3006.17i 0.755966i 0.925812 + 0.377983i \(0.123382\pi\)
−0.925812 + 0.377983i \(0.876618\pi\)
\(252\) 1276.23 + 5544.65i 0.319028 + 1.38603i
\(253\) −4829.79 −1.20018
\(254\) −3015.88 + 390.968i −0.745011 + 0.0965807i
\(255\) −1583.83 2709.08i −0.388954 0.665291i
\(256\) 2103.99 3514.32i 0.513669 0.857989i
\(257\) −7814.60 −1.89674 −0.948369 0.317170i \(-0.897267\pi\)
−0.948369 + 0.317170i \(0.897267\pi\)
\(258\) −4195.41 3339.44i −1.01238 0.805832i
\(259\) −9207.64 −2.20902
\(260\) −47.7294 2761.00i −0.0113848 0.658578i
\(261\) −196.699 + 6222.18i −0.0466490 + 1.47565i
\(262\) −265.397 2047.24i −0.0625813 0.482744i
\(263\) 4366.70i 1.02381i 0.859042 + 0.511905i \(0.171060\pi\)
−0.859042 + 0.511905i \(0.828940\pi\)
\(264\) −4027.86 1771.97i −0.939007 0.413095i
\(265\) 7415.61 + 1819.05i 1.71901 + 0.421672i
\(266\) −347.885 + 45.0987i −0.0801888 + 0.0103954i
\(267\) 1870.89 + 1930.96i 0.428825 + 0.442596i
\(268\) −1758.53 6668.54i −0.400818 1.51995i
\(269\) 4336.63 0.982933 0.491467 0.870896i \(-0.336461\pi\)
0.491467 + 0.870896i \(0.336461\pi\)
\(270\) −3594.34 + 2600.72i −0.810165 + 0.586202i
\(271\) 4429.78i 0.992952i 0.868050 + 0.496476i \(0.165373\pi\)
−0.868050 + 0.496476i \(0.834627\pi\)
\(272\) −3007.53 + 1704.75i −0.670434 + 0.380020i
\(273\) 3034.86 2940.44i 0.672814 0.651881i
\(274\) 1418.07 183.833i 0.312659 0.0405320i
\(275\) 2164.89 4147.23i 0.474720 0.909408i
\(276\) 4591.82 + 2773.51i 1.00143 + 0.604876i
\(277\) −3024.43 −0.656030 −0.328015 0.944673i \(-0.606380\pi\)
−0.328015 + 0.944673i \(0.606380\pi\)
\(278\) 1901.24 246.470i 0.410176 0.0531738i
\(279\) 3342.55 + 105.667i 0.717252 + 0.0226742i
\(280\) 970.796 + 6592.68i 0.207201 + 1.40710i
\(281\) 330.776i 0.0702223i −0.999383 0.0351112i \(-0.988821\pi\)
0.999383 0.0351112i \(-0.0111785\pi\)
\(282\) 526.239 + 418.873i 0.111124 + 0.0884522i
\(283\) 5051.97i 1.06116i −0.847635 0.530580i \(-0.821974\pi\)
0.847635 0.530580i \(-0.178026\pi\)
\(284\) −2835.37 + 747.700i −0.592423 + 0.156225i
\(285\) −138.057 236.141i −0.0286941 0.0490801i
\(286\) 420.161 + 3241.07i 0.0868695 + 0.670100i
\(287\) 1971.39i 0.405461i
\(288\) 2811.85 + 3997.67i 0.575312 + 0.817934i
\(289\) −1995.18 −0.406102
\(290\) −812.238 + 7245.76i −0.164470 + 1.46719i
\(291\) 5212.44 + 5379.82i 1.05003 + 1.08375i
\(292\) −439.069 1665.00i −0.0879950 0.333688i
\(293\) 1269.80i 0.253182i 0.991955 + 0.126591i \(0.0404036\pi\)
−0.991955 + 0.126591i \(0.959596\pi\)
\(294\) −3211.21 + 4034.31i −0.637012 + 0.800292i
\(295\) −2781.16 682.217i −0.548899 0.134645i
\(296\) −7325.36 + 2983.36i −1.43844 + 0.585825i
\(297\) 3884.60 3532.74i 0.758948 0.690203i
\(298\) 7406.17 960.111i 1.43969 0.186637i
\(299\) 3984.18i 0.770606i
\(300\) −4439.78 + 2699.70i −0.854436 + 0.519557i
\(301\) 9610.54i 1.84034i
\(302\) −896.817 6917.93i −0.170881 1.31815i
\(303\) 1575.54 1526.52i 0.298720 0.289426i
\(304\) −262.156 + 148.597i −0.0494595 + 0.0280350i
\(305\) 4724.50 + 1158.92i 0.886963 + 0.217572i
\(306\) −400.806 4105.62i −0.0748777 0.767001i
\(307\) 5056.64i 0.940057i 0.882651 + 0.470029i \(0.155756\pi\)
−0.882651 + 0.470029i \(0.844244\pi\)
\(308\) −2011.02 7626.01i −0.372040 1.41082i
\(309\) −3951.99 + 3829.03i −0.727575 + 0.704938i
\(310\) 3892.42 + 436.334i 0.713143 + 0.0799422i
\(311\) 2886.68 0.526329 0.263165 0.964751i \(-0.415234\pi\)
0.263165 + 0.964751i \(0.415234\pi\)
\(312\) 1461.73 3322.66i 0.265238 0.602912i
\(313\) 5771.03i 1.04217i 0.853506 + 0.521083i \(0.174472\pi\)
−0.853506 + 0.521083i \(0.825528\pi\)
\(314\) 4356.47 564.758i 0.782961 0.101500i
\(315\) −7658.84 2137.40i −1.36993 0.382314i
\(316\) 694.125 + 2632.20i 0.123568 + 0.468585i
\(317\) 1124.02i 0.199153i 0.995030 + 0.0995765i \(0.0317488\pi\)
−0.995030 + 0.0995765i \(0.968251\pi\)
\(318\) 7853.03 + 6250.81i 1.38483 + 1.10229i
\(319\) 8629.22i 1.51456i
\(320\) 2908.43 + 4930.42i 0.508081 + 0.861309i
\(321\) −3056.50 + 2961.40i −0.531455 + 0.514920i
\(322\) 1236.05 + 9534.74i 0.213921 + 1.65016i
\(323\) 254.337 0.0438132
\(324\) −5721.89 + 1127.94i −0.981119 + 0.193405i
\(325\) 3421.12 + 1785.86i 0.583907 + 0.304805i
\(326\) −1431.44 11041.9i −0.243191 1.87594i
\(327\) −4119.83 4252.13i −0.696719 0.719092i
\(328\) −638.747 1568.39i −0.107527 0.264023i
\(329\) 1205.47i 0.202005i
\(330\) 4865.92 3760.62i 0.811697 0.627319i
\(331\) 10427.1 1.73150 0.865752 0.500474i \(-0.166841\pi\)
0.865752 + 0.500474i \(0.166841\pi\)
\(332\) 4680.74 1234.33i 0.773762 0.204045i
\(333\) 298.212 9433.33i 0.0490748 1.55238i
\(334\) 726.836 + 5606.72i 0.119074 + 0.918522i
\(335\) 9360.65 + 2296.17i 1.52665 + 0.374486i
\(336\) −2467.32 + 8405.10i −0.400605 + 1.36469i
\(337\) 4932.89i 0.797364i −0.917089 0.398682i \(-0.869468\pi\)
0.917089 0.398682i \(-0.130532\pi\)
\(338\) 3488.87 452.285i 0.561448 0.0727842i
\(339\) 5404.12 5235.99i 0.865816 0.838878i
\(340\) −83.5081 4830.69i −0.0133202 0.770533i
\(341\) −4635.61 −0.736165
\(342\) −34.9369 357.873i −0.00552390 0.0565835i
\(343\) −206.574 −0.0325187
\(344\) −3113.90 7645.90i −0.488053 1.19837i
\(345\) −6472.10 + 3783.83i −1.00999 + 0.590478i
\(346\) −1024.24 7900.85i −0.159143 1.22761i
\(347\) −3247.36 −0.502385 −0.251192 0.967937i \(-0.580823\pi\)
−0.251192 + 0.967937i \(0.580823\pi\)
\(348\) −4955.34 + 8204.05i −0.763317 + 1.26375i
\(349\) 11995.6i 1.83986i −0.392086 0.919929i \(-0.628246\pi\)
0.392086 0.919929i \(-0.371754\pi\)
\(350\) −8741.30 3212.46i −1.33498 0.490609i
\(351\) 2914.22 + 3204.48i 0.443161 + 0.487301i
\(352\) −4070.81 5415.47i −0.616406 0.820016i
\(353\) −6654.12 −1.00330 −0.501648 0.865072i \(-0.667273\pi\)
−0.501648 + 0.865072i \(0.667273\pi\)
\(354\) −2945.21 2344.31i −0.442192 0.351974i
\(355\) 976.296 3980.01i 0.145962 0.595034i
\(356\) 1055.51 + 4002.61i 0.157140 + 0.595894i
\(357\) 5309.84 5144.64i 0.787189 0.762697i
\(358\) 329.392 + 2540.89i 0.0486283 + 0.375112i
\(359\) 5238.10 0.770073 0.385037 0.922901i \(-0.374189\pi\)
0.385037 + 0.922901i \(0.374189\pi\)
\(360\) −6785.72 + 781.071i −0.993441 + 0.114350i
\(361\) −6836.83 −0.996768
\(362\) −63.5632 490.318i −0.00922875 0.0711894i
\(363\) −260.184 + 252.089i −0.0376202 + 0.0364497i
\(364\) 6290.84 1658.93i 0.905851 0.238877i
\(365\) 2337.17 + 573.306i 0.335159 + 0.0822143i
\(366\) 5003.18 + 3982.40i 0.714536 + 0.568753i
\(367\) −3524.68 −0.501326 −0.250663 0.968074i \(-0.580649\pi\)
−0.250663 + 0.968074i \(0.580649\pi\)
\(368\) 4072.71 + 7185.10i 0.576915 + 1.01780i
\(369\) 2019.71 + 63.8482i 0.284937 + 0.00900760i
\(370\) 1231.42 10985.2i 0.173023 1.54349i
\(371\) 17989.1i 2.51738i
\(372\) 4407.21 + 2662.01i 0.614256 + 0.371018i
\(373\) 3078.40 0.427328 0.213664 0.976907i \(-0.431460\pi\)
0.213664 + 0.976907i \(0.431460\pi\)
\(374\) 735.121 + 5670.63i 0.101637 + 0.784014i
\(375\) −348.052 7253.50i −0.0479289 0.998851i
\(376\) 390.583 + 959.040i 0.0535712 + 0.131539i
\(377\) 7118.41 0.972458
\(378\) −7968.32 6764.70i −1.08425 0.920472i
\(379\) −3244.44 −0.439725 −0.219863 0.975531i \(-0.570561\pi\)
−0.219863 + 0.975531i \(0.570561\pi\)
\(380\) −7.27912 421.075i −0.000982661 0.0568440i
\(381\) 4012.45 3887.61i 0.539538 0.522751i
\(382\) 3554.79 460.831i 0.476123 0.0617229i
\(383\) 5023.39i 0.670191i 0.942184 + 0.335096i \(0.108769\pi\)
−0.942184 + 0.335096i \(0.891231\pi\)
\(384\) 760.395 + 7486.31i 0.101051 + 0.994881i
\(385\) 10704.7 + 2625.85i 1.41704 + 0.347599i
\(386\) −823.688 6353.83i −0.108613 0.837827i
\(387\) 9846.10 + 311.261i 1.29330 + 0.0408844i
\(388\) 2940.73 + 11151.6i 0.384776 + 1.45912i
\(389\) −289.283 −0.0377049 −0.0188525 0.999822i \(-0.506001\pi\)
−0.0188525 + 0.999822i \(0.506001\pi\)
\(390\) 3102.21 + 4013.99i 0.402785 + 0.521170i
\(391\) 6970.78i 0.901605i
\(392\) −7352.30 + 2994.33i −0.947314 + 0.385807i
\(393\) 2638.99 + 2723.73i 0.338726 + 0.349604i
\(394\) −229.367 1769.31i −0.0293283 0.226235i
\(395\) −3694.83 906.342i −0.470651 0.115451i
\(396\) 7878.06 1813.32i 0.999716 0.230108i
\(397\) 10915.5 1.37993 0.689964 0.723843i \(-0.257626\pi\)
0.689964 + 0.723843i \(0.257626\pi\)
\(398\) −1220.71 9416.36i −0.153740 1.18593i
\(399\) 462.841 448.441i 0.0580728 0.0562659i
\(400\) −7995.22 + 276.509i −0.999402 + 0.0345636i
\(401\) 9711.60i 1.20941i −0.796449 0.604706i \(-0.793291\pi\)
0.796449 0.604706i \(-0.206709\pi\)
\(402\) 9912.81 + 7890.34i 1.22987 + 0.978941i
\(403\) 3824.00i 0.472673i
\(404\) 3265.86 861.224i 0.402185 0.106058i
\(405\) 2437.84 7777.34i 0.299105 0.954220i
\(406\) −17035.4 + 2208.41i −2.08240 + 0.269955i
\(407\) 13082.6i 1.59332i
\(408\) 2557.46 5813.37i 0.310327 0.705404i
\(409\) 611.519 0.0739307 0.0369653 0.999317i \(-0.488231\pi\)
0.0369653 + 0.999317i \(0.488231\pi\)
\(410\) 2351.96 + 263.651i 0.283305 + 0.0317581i
\(411\) −1886.65 + 1827.95i −0.226428 + 0.219383i
\(412\) −8191.91 + 2160.25i −0.979578 + 0.258320i
\(413\) 6746.66i 0.803830i
\(414\) −9808.47 + 957.542i −1.16440 + 0.113673i
\(415\) −1611.71 + 6570.37i −0.190640 + 0.777173i
\(416\) 4467.32 3358.09i 0.526511 0.395778i
\(417\) −2529.49 + 2450.79i −0.297050 + 0.287807i
\(418\) 64.0780 + 494.289i 0.00749798 + 0.0578385i
\(419\) 5936.35i 0.692147i −0.938207 0.346073i \(-0.887515\pi\)
0.938207 0.346073i \(-0.112485\pi\)
\(420\) −8669.34 8643.64i −1.00719 1.00421i
\(421\) 7758.48i 0.898159i 0.893492 + 0.449080i \(0.148248\pi\)
−0.893492 + 0.449080i \(0.851752\pi\)
\(422\) −10685.1 + 1385.18i −1.23257 + 0.159786i
\(423\) −1235.02 39.0421i −0.141959 0.00448768i
\(424\) 5828.64 + 14311.7i 0.667603 + 1.63924i
\(425\) 5985.65 + 3124.57i 0.683169 + 0.356621i
\(426\) 3354.86 4214.78i 0.381557 0.479359i
\(427\) 11460.9i 1.29890i
\(428\) −6335.68 + 1670.75i −0.715530 + 0.188689i
\(429\) −4177.89 4312.06i −0.470188 0.485287i
\(430\) 11465.8 + 1285.30i 1.28589 + 0.144146i
\(431\) −3682.13 −0.411513 −0.205756 0.978603i \(-0.565965\pi\)
−0.205756 + 0.978603i \(0.565965\pi\)
\(432\) −8531.21 2800.01i −0.950134 0.311842i
\(433\) 9874.56i 1.09594i −0.836499 0.547969i \(-0.815401\pi\)
0.836499 0.547969i \(-0.184599\pi\)
\(434\) 1186.36 + 9151.40i 0.131214 + 1.01217i
\(435\) −6760.45 11563.5i −0.745146 1.27454i
\(436\) −2324.31 8814.06i −0.255308 0.968158i
\(437\) 607.620i 0.0665135i
\(438\) 2475.03 + 1970.06i 0.270003 + 0.214916i
\(439\) 12519.6i 1.36111i 0.732698 + 0.680554i \(0.238261\pi\)
−0.732698 + 0.680554i \(0.761739\pi\)
\(440\) 9367.15 1379.35i 1.01491 0.149449i
\(441\) 299.308 9468.01i 0.0323192 1.02235i
\(442\) −4677.80 + 606.415i −0.503395 + 0.0652584i
\(443\) −7308.73 −0.783856 −0.391928 0.919996i \(-0.628192\pi\)
−0.391928 + 0.919996i \(0.628192\pi\)
\(444\) 7512.70 12438.0i 0.803011 1.32946i
\(445\) −5618.48 1378.21i −0.598521 0.146817i
\(446\) −11954.2 + 1549.71i −1.26917 + 0.164531i
\(447\) −9853.48 + 9546.91i −1.04263 + 1.01019i
\(448\) −9649.15 + 9422.34i −1.01759 + 0.993669i
\(449\) 7884.95i 0.828761i 0.910104 + 0.414380i \(0.136002\pi\)
−0.910104 + 0.414380i \(0.863998\pi\)
\(450\) 3574.31 8851.52i 0.374432 0.927254i
\(451\) −2801.03 −0.292451
\(452\) 11202.0 2954.02i 1.16570 0.307401i
\(453\) 8917.54 + 9203.90i 0.924906 + 0.954607i
\(454\) 12571.7 1629.75i 1.29960 0.168475i
\(455\) −2166.11 + 8830.47i −0.223184 + 0.909844i
\(456\) 222.926 506.732i 0.0228935 0.0520393i
\(457\) 197.196i 0.0201847i 0.999949 + 0.0100924i \(0.00321256\pi\)
−0.999949 + 0.0100924i \(0.996787\pi\)
\(458\) 420.982 + 3247.40i 0.0429502 + 0.331312i
\(459\) 5098.76 + 5606.61i 0.518496 + 0.570140i
\(460\) −11540.7 + 199.504i −1.16976 + 0.0202216i
\(461\) 8936.49 0.902850 0.451425 0.892309i \(-0.350916\pi\)
0.451425 + 0.892309i \(0.350916\pi\)
\(462\) 11336.1 + 9023.24i 1.14156 + 0.908656i
\(463\) −18183.1 −1.82514 −0.912571 0.408919i \(-0.865906\pi\)
−0.912571 + 0.408919i \(0.865906\pi\)
\(464\) −12837.4 + 7276.57i −1.28440 + 0.728031i
\(465\) −6211.89 + 3631.71i −0.619505 + 0.362186i
\(466\) −7151.37 + 927.079i −0.710903 + 0.0921590i
\(467\) 81.4817 0.00807393 0.00403696 0.999992i \(-0.498715\pi\)
0.00403696 + 0.999992i \(0.498715\pi\)
\(468\) 1495.84 + 6498.76i 0.147746 + 0.641892i
\(469\) 22707.5i 2.23568i
\(470\) −1438.18 161.218i −0.141146 0.0158222i
\(471\) −5796.03 + 5615.69i −0.567021 + 0.549379i
\(472\) −2185.98 5367.47i −0.213173 0.523428i
\(473\) −13655.0 −1.32740
\(474\) −3912.78 3114.47i −0.379156 0.301798i
\(475\) 521.749 + 272.358i 0.0503989 + 0.0263087i
\(476\) 11006.5 2902.48i 1.05984 0.279485i
\(477\) −18430.1 582.622i −1.76909 0.0559254i
\(478\) 2004.40 259.843i 0.191797 0.0248639i
\(479\) −19196.4 −1.83112 −0.915559 0.402183i \(-0.868252\pi\)
−0.915559 + 0.402183i \(0.868252\pi\)
\(480\) −9697.72 4067.71i −0.922163 0.386802i
\(481\) −10792.1 −1.02303
\(482\) 6535.55 847.246i 0.617606 0.0800643i
\(483\) −12290.7 12685.4i −1.15786 1.19504i
\(484\) −539.325 + 142.223i −0.0506504 + 0.0133567i
\(485\) −15653.5 3839.81i −1.46555 0.359498i
\(486\) 7188.58 7944.53i 0.670947 0.741505i
\(487\) 2061.46 0.191814 0.0959072 0.995390i \(-0.469425\pi\)
0.0959072 + 0.995390i \(0.469425\pi\)
\(488\) 3713.43 + 9118.00i 0.344466 + 0.845804i
\(489\) 14233.6 + 14690.7i 1.31629 + 1.35856i
\(490\) 1235.95 11025.6i 0.113948 1.01650i
\(491\) 10688.0i 0.982371i −0.871055 0.491186i \(-0.836564\pi\)
0.871055 0.491186i \(-0.163436\pi\)
\(492\) 2663.02 + 1608.50i 0.244021 + 0.147391i
\(493\) 12454.5 1.13777
\(494\) −407.748 + 52.8591i −0.0371366 + 0.00481426i
\(495\) −3036.91 + 10882.0i −0.275755 + 0.988100i
\(496\) 3908.97 + 6896.23i 0.353867 + 0.624294i
\(497\) 9654.91 0.871392
\(498\) −5538.34 + 6957.93i −0.498351 + 0.626089i
\(499\) −5962.49 −0.534906 −0.267453 0.963571i \(-0.586182\pi\)
−0.267453 + 0.963571i \(0.586182\pi\)
\(500\) 5001.67 9999.16i 0.447363 0.894352i
\(501\) −7227.33 7459.42i −0.644498 0.665194i
\(502\) −1093.12 8432.16i −0.0971876 0.749693i
\(503\) 9237.66i 0.818861i −0.912341 0.409430i \(-0.865727\pi\)
0.912341 0.409430i \(-0.134273\pi\)
\(504\) −5595.95 15088.4i −0.494570 1.33352i
\(505\) −1124.53 + 4584.30i −0.0990908 + 0.403958i
\(506\) 13547.3 1756.23i 1.19022 0.154296i
\(507\) −4641.74 + 4497.32i −0.406601 + 0.393950i
\(508\) 8317.23 2193.29i 0.726412 0.191559i
\(509\) 9365.55 0.815561 0.407781 0.913080i \(-0.366303\pi\)
0.407781 + 0.913080i \(0.366303\pi\)
\(510\) 5427.67 + 7022.93i 0.471257 + 0.609766i
\(511\) 5669.61i 0.490820i
\(512\) −4623.70 + 10622.6i −0.399102 + 0.916906i
\(513\) 444.442 + 488.709i 0.0382507 + 0.0420605i
\(514\) 21919.6 2841.58i 1.88100 0.243846i
\(515\) 2820.70 11499.0i 0.241350 0.983897i
\(516\) 12982.3 + 7841.43i 1.10758 + 0.668992i
\(517\) 1712.78 0.145702
\(518\) 25827.0 3348.13i 2.19068 0.283993i
\(519\) 10184.6 + 10511.6i 0.861374 + 0.889035i
\(520\) 1137.85 + 7727.14i 0.0959576 + 0.651649i
\(521\) 10927.3i 0.918874i −0.888210 0.459437i \(-0.848051\pi\)
0.888210 0.459437i \(-0.151949\pi\)
\(522\) −1710.81 17524.5i −0.143448 1.46940i
\(523\) 5024.90i 0.420122i −0.977688 0.210061i \(-0.932634\pi\)
0.977688 0.210061i \(-0.0673662\pi\)
\(524\) 1488.86 + 5645.91i 0.124124 + 0.470693i
\(525\) 16401.8 4867.69i 1.36350 0.404654i
\(526\) −1587.84 12248.4i −0.131622 1.01531i
\(527\) 6690.53i 0.553025i
\(528\) 11942.3 + 3505.66i 0.984323 + 0.288948i
\(529\) −4486.47 −0.368741
\(530\) −21461.9 2405.84i −1.75895 0.197176i
\(531\) 6912.03 + 218.507i 0.564890 + 0.0178576i
\(532\) 959.404 252.999i 0.0781869 0.0206183i
\(533\) 2310.62i 0.187775i
\(534\) −5949.90 4735.97i −0.482167 0.383793i
\(535\) 2181.55 8893.42i 0.176293 0.718684i
\(536\) 7357.44 + 18065.5i 0.592897 + 1.45580i
\(537\) −3275.33 3380.50i −0.263204 0.271656i
\(538\) −12164.1 + 1576.91i −0.974776 + 0.126367i
\(539\) 13130.7i 1.04931i
\(540\) 9136.28 8601.88i 0.728079 0.685493i
\(541\) 4558.22i 0.362243i 0.983461 + 0.181121i \(0.0579727\pi\)
−0.983461 + 0.181121i \(0.942027\pi\)
\(542\) −1610.78 12425.3i −0.127655 0.984712i
\(543\) 632.044 + 652.340i 0.0499514 + 0.0515554i
\(544\) 7816.09 5875.36i 0.616015 0.463058i
\(545\) 12372.3 + 3034.93i 0.972426 + 0.238536i
\(546\) −7443.44 + 9351.35i −0.583425 + 0.732969i
\(547\) 6925.96i 0.541376i −0.962667 0.270688i \(-0.912749\pi\)
0.962667 0.270688i \(-0.0872512\pi\)
\(548\) −3910.76 + 1031.29i −0.304853 + 0.0803913i
\(549\) −11741.8 371.189i −0.912803 0.0288560i
\(550\) −4564.39 + 12420.0i −0.353866 + 0.962892i
\(551\) 1085.61 0.0839360
\(552\) −13888.4 6109.88i −1.07088 0.471112i
\(553\) 8963.10i 0.689240i
\(554\) 8483.38 1099.76i 0.650586 0.0843397i
\(555\) 10249.4 + 17531.2i 0.783896 + 1.34082i
\(556\) −5243.27 + 1382.68i −0.399936 + 0.105465i
\(557\) 13278.5i 1.01010i −0.863089 0.505052i \(-0.831473\pi\)
0.863089 0.505052i \(-0.168527\pi\)
\(558\) −9414.13 + 919.044i −0.714215 + 0.0697245i
\(559\) 11264.3i 0.852288i
\(560\) −5120.30 18139.2i −0.386379 1.36879i
\(561\) −7309.71 7544.44i −0.550118 0.567783i
\(562\) 120.279 + 927.813i 0.00902784 + 0.0696396i
\(563\) 14521.4 1.08704 0.543520 0.839396i \(-0.317091\pi\)
0.543520 + 0.839396i \(0.317091\pi\)
\(564\) −1628.39 983.566i −0.121574 0.0734319i
\(565\) −3857.16 + 15724.3i −0.287207 + 1.17084i
\(566\) 1837.02 + 14170.5i 0.136424 + 1.05235i
\(567\) 19164.2 + 1212.87i 1.41943 + 0.0898337i
\(568\) 7681.19 3128.28i 0.567422 0.231091i
\(569\) 1852.91i 0.136517i −0.997668 0.0682583i \(-0.978256\pi\)
0.997668 0.0682583i \(-0.0217442\pi\)
\(570\) 473.111 + 612.165i 0.0347657 + 0.0449838i
\(571\) 10888.0 0.797980 0.398990 0.916955i \(-0.369361\pi\)
0.398990 + 0.916955i \(0.369361\pi\)
\(572\) −2357.07 8938.28i −0.172297 0.653371i
\(573\) −4729.44 + 4582.29i −0.344808 + 0.334080i
\(574\) 716.846 + 5529.66i 0.0521265 + 0.402097i
\(575\) 7464.71 14299.9i 0.541391 1.03713i
\(576\) −9340.77 10190.8i −0.675692 0.737184i
\(577\) 23942.9i 1.72748i 0.503941 + 0.863738i \(0.331883\pi\)
−0.503941 + 0.863738i \(0.668117\pi\)
\(578\) 5596.39 725.497i 0.402732 0.0522088i
\(579\) 8190.38 + 8453.39i 0.587877 + 0.606755i
\(580\) −356.447 20619.4i −0.0255184 1.47616i
\(581\) −15938.7 −1.13812
\(582\) −16576.9 13194.8i −1.18064 0.939762i
\(583\) 25559.7 1.81574
\(584\) 1837.00 + 4510.60i 0.130164 + 0.319606i
\(585\) −8976.76 2505.20i −0.634433 0.177055i
\(586\) −461.730 3561.72i −0.0325493 0.251081i
\(587\) 10172.0 0.715239 0.357620 0.933867i \(-0.383588\pi\)
0.357620 + 0.933867i \(0.383588\pi\)
\(588\) 7540.32 12483.7i 0.528839 0.875545i
\(589\) 583.191i 0.0407979i
\(590\) 8049.09 + 902.290i 0.561654 + 0.0629605i
\(591\) 2280.72 + 2353.96i 0.158742 + 0.163839i
\(592\) 19462.5 11031.9i 1.35119 0.765890i
\(593\) −17454.1 −1.20869 −0.604346 0.796722i \(-0.706565\pi\)
−0.604346 + 0.796722i \(0.706565\pi\)
\(594\) −9611.55 + 11321.7i −0.663917 + 0.782046i
\(595\) −3789.86 + 15449.9i −0.261125 + 1.06451i
\(596\) −20424.9 + 5386.14i −1.40375 + 0.370176i
\(597\) 12138.1 + 12527.9i 0.832129 + 0.858850i
\(598\) 1448.75 + 11175.5i 0.0990697 + 0.764211i
\(599\) 239.830 0.0163592 0.00817961 0.999967i \(-0.497396\pi\)
0.00817961 + 0.999967i \(0.497396\pi\)
\(600\) 11471.7 9186.95i 0.780551 0.625093i
\(601\) 387.340 0.0262894 0.0131447 0.999914i \(-0.495816\pi\)
0.0131447 + 0.999914i \(0.495816\pi\)
\(602\) 3494.63 + 26957.1i 0.236596 + 1.82507i
\(603\) −23264.1 735.438i −1.57112 0.0496673i
\(604\) 5031.06 + 19078.4i 0.338926 + 1.28525i
\(605\) 185.705 757.053i 0.0124793 0.0508737i
\(606\) −3864.23 + 4854.72i −0.259032 + 0.325428i
\(607\) 3054.14 0.204223 0.102112 0.994773i \(-0.467440\pi\)
0.102112 + 0.994773i \(0.467440\pi\)
\(608\) 681.303 512.135i 0.0454448 0.0341609i
\(609\) 22664.6 21959.4i 1.50807 1.46115i
\(610\) −13673.4 1532.77i −0.907574 0.101738i
\(611\) 1412.90i 0.0935515i
\(612\) 2617.15 + 11370.3i 0.172863 + 0.751010i
\(613\) 1899.37 0.125146 0.0625732 0.998040i \(-0.480069\pi\)
0.0625732 + 0.998040i \(0.480069\pi\)
\(614\) −1838.72 14183.6i −0.120855 0.932256i
\(615\) −3753.49 + 2194.43i −0.246106 + 0.143883i
\(616\) 8413.82 + 20659.4i 0.550329 + 1.35128i
\(617\) −5098.97 −0.332701 −0.166351 0.986067i \(-0.553198\pi\)
−0.166351 + 0.986067i \(0.553198\pi\)
\(618\) 9692.82 12177.3i 0.630910 0.792626i
\(619\) −11519.4 −0.747988 −0.373994 0.927431i \(-0.622012\pi\)
−0.373994 + 0.927431i \(0.622012\pi\)
\(620\) −11076.7 + 191.483i −0.717503 + 0.0124035i
\(621\) 13394.4 12181.1i 0.865538 0.787137i
\(622\) −8097.00 + 1049.67i −0.521962 + 0.0676653i
\(623\) 13629.6i 0.876498i
\(624\) −2891.89 + 9851.43i −0.185526 + 0.632008i
\(625\) 8933.07 + 12819.6i 0.571716 + 0.820451i
\(626\) −2098.49 16187.5i −0.133982 1.03352i
\(627\) −637.163 657.623i −0.0405834 0.0418867i
\(628\) −12014.3 + 3168.24i −0.763414 + 0.201316i
\(629\) −18882.0 −1.19694
\(630\) 22259.9 + 3210.37i 1.40771 + 0.203023i
\(631\) 11392.7i 0.718757i −0.933192 0.359379i \(-0.882989\pi\)
0.933192 0.359379i \(-0.117011\pi\)
\(632\) −2904.12 7130.81i −0.182785 0.448811i
\(633\) 14215.9 13773.6i 0.892625 0.864853i
\(634\) −408.723 3152.84i −0.0256033 0.197500i
\(635\) −2863.86 + 11674.9i −0.178974 + 0.729615i
\(636\) −24300.3 14677.7i −1.51505 0.915107i
\(637\) −10831.8 −0.673736
\(638\) 3137.80 + 24204.6i 0.194713 + 1.50199i
\(639\) −312.698 + 9891.56i −0.0193586 + 0.612369i
\(640\) −9950.83 12772.0i −0.614596 0.788842i
\(641\) 2495.47i 0.153768i 0.997040 + 0.0768838i \(0.0244970\pi\)
−0.997040 + 0.0768838i \(0.975503\pi\)
\(642\) 7496.50 9418.01i 0.460846 0.578971i
\(643\) 1618.30i 0.0992527i −0.998768 0.0496263i \(-0.984197\pi\)
0.998768 0.0496263i \(-0.0158030\pi\)
\(644\) −6934.14 26295.1i −0.424291 1.60896i
\(645\) −18298.3 + 10697.9i −1.11705 + 0.653067i
\(646\) −713.403 + 92.4831i −0.0434496 + 0.00563266i
\(647\) 21039.5i 1.27844i −0.769025 0.639219i \(-0.779258\pi\)
0.769025 0.639219i \(-0.220742\pi\)
\(648\) 15639.5 5244.43i 0.948113 0.317933i
\(649\) −9585.93 −0.579785
\(650\) −10245.5 3765.25i −0.618248 0.227208i
\(651\) −11796.6 12175.4i −0.710207 0.733013i
\(652\) 8030.25 + 30451.7i 0.482345 + 1.82911i
\(653\) 3169.58i 0.189947i 0.995480 + 0.0949735i \(0.0302766\pi\)
−0.995480 + 0.0949735i \(0.969723\pi\)
\(654\) 13102.1 + 10429.0i 0.783385 + 0.623554i
\(655\) −7925.19 1944.05i −0.472768 0.115970i
\(656\) 2361.96 + 4166.99i 0.140578 + 0.248009i
\(657\) −5808.58 183.624i −0.344923 0.0109039i
\(658\) −438.339 3381.29i −0.0259699 0.200329i
\(659\) 3243.75i 0.191743i −0.995394 0.0958714i \(-0.969436\pi\)
0.995394 0.0958714i \(-0.0305638\pi\)
\(660\) −12281.2 + 12317.7i −0.724313 + 0.726466i
\(661\) 18084.9i 1.06418i 0.846689 + 0.532088i \(0.178592\pi\)
−0.846689 + 0.532088i \(0.821408\pi\)
\(662\) −29247.7 + 3791.57i −1.71713 + 0.222603i
\(663\) 6223.55 6029.91i 0.364559 0.353216i
\(664\) −12680.4 + 5164.29i −0.741109 + 0.301827i
\(665\) −330.350 + 1346.72i −0.0192638 + 0.0785316i
\(666\) 2593.72 + 26568.5i 0.150908 + 1.54581i
\(667\) 29754.2i 1.72727i
\(668\) −4077.49 15462.3i −0.236172 0.895591i
\(669\) 15904.4 15409.6i 0.919133 0.890536i
\(670\) −27091.2 3036.88i −1.56212 0.175112i
\(671\) 16284.1 0.936873
\(672\) 3864.41 24473.1i 0.221835 1.40487i
\(673\) 19706.8i 1.12874i −0.825523 0.564368i \(-0.809120\pi\)
0.825523 0.564368i \(-0.190880\pi\)
\(674\) 1793.72 + 13836.5i 0.102510 + 0.790747i
\(675\) 4455.78 + 16961.5i 0.254079 + 0.967184i
\(676\) −9621.66 + 2537.28i −0.547432 + 0.144360i
\(677\) 22320.7i 1.26714i 0.773686 + 0.633569i \(0.218411\pi\)
−0.773686 + 0.633569i \(0.781589\pi\)
\(678\) −13254.4 + 16651.8i −0.750785 + 0.943227i
\(679\) 37973.1i 2.14621i
\(680\) 1990.80 + 13519.5i 0.112270 + 0.762426i
\(681\) −16725.9 + 16205.5i −0.941170 + 0.911887i
\(682\) 13002.7 1685.62i 0.730056 0.0946420i
\(683\) 12949.2 0.725458 0.362729 0.931895i \(-0.381845\pi\)
0.362729 + 0.931895i \(0.381845\pi\)
\(684\) 228.128 + 991.113i 0.0127525 + 0.0554037i
\(685\) 1346.59 5489.55i 0.0751101 0.306197i
\(686\) 579.430 75.1153i 0.0322489 0.00418063i
\(687\) −4186.05 4320.48i −0.232471 0.239937i
\(688\) 11514.6 + 20314.1i 0.638066 + 1.12568i
\(689\) 21084.7i 1.16584i
\(690\) 16778.1 12966.9i 0.925695 0.715422i
\(691\) 14104.3 0.776489 0.388244 0.921556i \(-0.373082\pi\)
0.388244 + 0.921556i \(0.373082\pi\)
\(692\) 5745.89 + 21789.1i 0.315645 + 1.19696i
\(693\) −26604.4 841.033i −1.45832 0.0461013i
\(694\) 9108.70 1180.82i 0.498216 0.0645870i
\(695\) 1805.41 7360.00i 0.0985366 0.401699i
\(696\) 10916.3 24813.9i 0.594514 1.35139i
\(697\) 4042.70i 0.219696i
\(698\) 4361.90 + 33647.2i 0.236534 + 1.82459i
\(699\) 9514.48 9218.46i 0.514836 0.498818i
\(700\) 25687.1 + 5832.25i 1.38697 + 0.314912i
\(701\) 26508.0 1.42823 0.714117 0.700026i \(-0.246828\pi\)
0.714117 + 0.700026i \(0.246828\pi\)
\(702\) −9339.49 7928.75i −0.502131 0.426284i
\(703\) −1645.88 −0.0883008
\(704\) 13387.6 + 13709.9i 0.716712 + 0.733965i
\(705\) 2295.19 1341.85i 0.122613 0.0716839i
\(706\) 18664.5 2419.60i 0.994970 0.128984i
\(707\) −11120.8 −0.591572
\(708\) 9113.63 + 5504.74i 0.483773 + 0.292204i
\(709\) 5707.61i 0.302333i −0.988508 0.151166i \(-0.951697\pi\)
0.988508 0.151166i \(-0.0483029\pi\)
\(710\) −1291.24 + 11518.8i −0.0682524 + 0.608862i
\(711\) 9182.80 + 290.292i 0.484362 + 0.0153119i
\(712\) −4416.11 10843.3i −0.232445 0.570747i
\(713\) −15983.9 −0.839555
\(714\) −13023.2 + 16361.3i −0.682604 + 0.857570i
\(715\) 12546.7 + 3077.70i 0.656252 + 0.160978i
\(716\) −1847.86 7007.30i −0.0964494 0.365748i
\(717\) −2666.73 + 2583.76i −0.138900 + 0.134578i
\(718\) −14692.6 + 1904.70i −0.763683 + 0.0990012i
\(719\) 6320.76 0.327851 0.163925 0.986473i \(-0.447584\pi\)
0.163925 + 0.986473i \(0.447584\pi\)
\(720\) 18749.6 4658.32i 0.970496 0.241119i
\(721\) 27894.8 1.44086
\(722\) 19177.0 2486.04i 0.988496 0.128145i
\(723\) −8695.17 + 8424.63i −0.447271 + 0.433355i
\(724\) 356.584 + 1352.21i 0.0183043 + 0.0694122i
\(725\) 25549.2 + 13337.0i 1.30879 + 0.683203i
\(726\) 638.139 801.708i 0.0326220 0.0409837i
\(727\) −7788.82 −0.397347 −0.198674 0.980066i \(-0.563663\pi\)
−0.198674 + 0.980066i \(0.563663\pi\)
\(728\) −17042.3 + 6940.72i −0.867623 + 0.353352i
\(729\) −1863.28 + 19594.6i −0.0946642 + 0.995509i
\(730\) −6764.12 758.247i −0.342947 0.0384438i
\(731\) 19708.2i 0.997173i
\(732\) −15481.8 9351.18i −0.781726 0.472172i
\(733\) −37009.1 −1.86489 −0.932443 0.361317i \(-0.882327\pi\)
−0.932443 + 0.361317i \(0.882327\pi\)
\(734\) 9886.57 1281.66i 0.497166 0.0644509i
\(735\) 10287.1 + 17595.6i 0.516251 + 0.883027i
\(736\) −14036.4 18672.9i −0.702976 0.935182i
\(737\) 32263.8 1.61255
\(738\) −5688.41 + 555.325i −0.283731 + 0.0276989i
\(739\) 8679.66 0.432052 0.216026 0.976388i \(-0.430690\pi\)
0.216026 + 0.976388i \(0.430690\pi\)
\(740\) 540.403 + 31260.7i 0.0268454 + 1.55293i
\(741\) 542.486 525.607i 0.0268943 0.0260576i
\(742\) −6541.30 50458.7i −0.323637 2.49649i
\(743\) 18604.8i 0.918634i 0.888272 + 0.459317i \(0.151906\pi\)
−0.888272 + 0.459317i \(0.848094\pi\)
\(744\) −13330.0 5864.24i −0.656857 0.288970i
\(745\) 7032.85 28670.5i 0.345857 1.40994i
\(746\) −8634.77 + 1119.38i −0.423782 + 0.0549377i
\(747\) 516.214 16329.4i 0.0252842 0.799814i
\(748\) −4123.96 15638.5i −0.201587 0.764441i
\(749\) 21574.1 1.05247
\(750\) 3613.82 + 20219.2i 0.175944 + 0.984400i
\(751\) 23589.9i 1.14621i −0.819481 0.573107i \(-0.805738\pi\)
0.819481 0.573107i \(-0.194262\pi\)
\(752\) −1444.30 2548.04i −0.0700374 0.123560i
\(753\) 10869.5 + 11218.5i 0.526036 + 0.542928i
\(754\) −19966.8 + 2588.43i −0.964388 + 0.125020i
\(755\) −26780.4 6569.22i −1.29091 0.316660i
\(756\) 24810.6 + 16077.2i 1.19359 + 0.773442i
\(757\) −28338.1 −1.36059 −0.680294 0.732939i \(-0.738148\pi\)
−0.680294 + 0.732939i \(0.738148\pi\)
\(758\) 9100.52 1179.76i 0.436076 0.0565314i
\(759\) −18023.9 + 17463.2i −0.861960 + 0.835142i
\(760\) 173.531 + 1178.45i 0.00828241 + 0.0562459i
\(761\) 9122.56i 0.434550i 0.976110 + 0.217275i \(0.0697168\pi\)
−0.976110 + 0.217275i \(0.930283\pi\)
\(762\) −9841.10 + 12363.6i −0.467855 + 0.587777i
\(763\) 30013.4i 1.42406i
\(764\) −9803.46 + 2585.22i −0.464236 + 0.122421i
\(765\) −15705.9 4383.14i −0.742284 0.207154i
\(766\) −1826.63 14090.4i −0.0861603 0.664630i
\(767\) 7907.61i 0.372265i
\(768\) −4855.08 20722.3i −0.228116 0.973634i
\(769\) −28401.1 −1.33182 −0.665910 0.746032i \(-0.731956\pi\)
−0.665910 + 0.746032i \(0.731956\pi\)
\(770\) −30980.9 3472.91i −1.44997 0.162539i