Properties

Label 169.4.e.g.23.3
Level $169$
Weight $4$
Character 169.23
Analytic conductor $9.971$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,4,Mod(23,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.23");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), degree \(2\), not 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: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.3
Root \(1.35234 + 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 169.23
Dual form 169.4.e.g.147.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.379706 - 0.219224i) q^{2} +(1.84233 + 3.19101i) q^{3} +(-3.90388 + 6.76172i) q^{4} +17.8078i q^{5} +(1.39909 + 0.807764i) q^{6} +(-4.70983 - 2.71922i) q^{7} +6.93087i q^{8} +(6.71165 - 11.6249i) q^{9} +O(q^{10})\) \(q+(0.379706 - 0.219224i) q^{2} +(1.84233 + 3.19101i) q^{3} +(-3.90388 + 6.76172i) q^{4} +17.8078i q^{5} +(1.39909 + 0.807764i) q^{6} +(-4.70983 - 2.71922i) q^{7} +6.93087i q^{8} +(6.71165 - 11.6249i) q^{9} +(3.90388 + 6.76172i) q^{10} +(-19.4191 + 11.2116i) q^{11} -28.7689 q^{12} -2.38447 q^{14} +(-56.8247 + 32.8078i) q^{15} +(-29.7116 - 51.4621i) q^{16} +(33.9924 - 58.8766i) q^{17} -5.88540i q^{18} +(-69.9816 - 40.4039i) q^{19} +(-120.411 - 69.5194i) q^{20} -20.0388i q^{21} +(-4.91571 + 8.51427i) q^{22} +(70.2656 + 121.704i) q^{23} +(-22.1165 + 12.7689i) q^{24} -192.116 q^{25} +148.946 q^{27} +(36.7733 - 21.2311i) q^{28} +(53.3466 + 92.3990i) q^{29} +(-14.3845 + 24.9146i) q^{30} +276.155i q^{31} +(-70.5819 - 40.7505i) q^{32} +(-71.5529 - 41.3111i) q^{33} -29.8078i q^{34} +(48.4233 - 83.8716i) q^{35} +(52.4029 + 90.7646i) q^{36} +(-3.71670 + 2.14584i) q^{37} -35.4299 q^{38} -123.423 q^{40} +(-197.254 + 113.884i) q^{41} +(-4.39298 - 7.60887i) q^{42} +(13.7647 - 23.8411i) q^{43} -175.076i q^{44} +(207.014 + 119.519i) q^{45} +(53.3606 + 30.8078i) q^{46} +318.617i q^{47} +(109.477 - 189.620i) q^{48} +(-156.712 - 271.433i) q^{49} +(-72.9479 + 42.1165i) q^{50} +250.501 q^{51} -67.6562 q^{53} +(56.5558 - 32.6525i) q^{54} +(-199.654 - 345.811i) q^{55} +(18.8466 - 32.6432i) q^{56} -297.749i q^{57} +(40.5121 + 23.3897i) q^{58} +(252.113 + 145.557i) q^{59} -512.311i q^{60} +(-331.655 + 574.444i) q^{61} +(60.5398 + 104.858i) q^{62} +(-63.2215 + 36.5009i) q^{63} +439.652 q^{64} -36.2255 q^{66} +(368.149 - 212.551i) q^{67} +(265.405 + 459.695i) q^{68} +(-258.905 + 448.436i) q^{69} -42.4621i q^{70} +(-132.470 - 76.4815i) q^{71} +(80.5708 + 46.5175i) q^{72} +117.268i q^{73} +(-0.940837 + 1.62958i) q^{74} +(-353.942 - 613.045i) q^{75} +(546.400 - 315.464i) q^{76} +121.948 q^{77} +202.462 q^{79} +(916.425 - 529.098i) q^{80} +(93.1932 + 161.415i) q^{81} +(-49.9323 + 86.4853i) q^{82} -336.155i q^{83} +(135.497 + 78.2292i) q^{84} +(1048.46 + 605.329i) q^{85} -12.0702i q^{86} +(-196.564 + 340.459i) q^{87} +(-77.7065 - 134.592i) q^{88} +(621.974 - 359.097i) q^{89} +104.806 q^{90} -1097.23 q^{92} +(-881.214 + 508.769i) q^{93} +(69.8485 + 120.981i) q^{94} +(719.503 - 1246.22i) q^{95} -300.303i q^{96} +(657.632 + 379.684i) q^{97} +(-119.009 - 68.7098i) q^{98} +300.994i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9} - 10 q^{10} - 560 q^{12} - 184 q^{14} - 114 q^{16} + 140 q^{17} + 340 q^{22} + 290 q^{23} - 300 q^{25} + 1340 q^{27} - 68 q^{29} - 280 q^{30} + 140 q^{35} + 1450 q^{36} - 1240 q^{38} - 740 q^{40} + 740 q^{42} + 910 q^{43} + 480 q^{48} - 1130 q^{49} + 932 q^{51} + 2180 q^{53} - 1020 q^{55} - 344 q^{56} - 1004 q^{61} - 1000 q^{62} + 5084 q^{64} - 6392 q^{66} + 1010 q^{68} - 958 q^{69} - 1698 q^{74} - 3450 q^{75} - 1020 q^{77} + 960 q^{79} - 244 q^{81} - 3030 q^{82} - 3230 q^{87} - 2040 q^{88} + 2900 q^{90} - 4160 q^{92} - 2080 q^{94} + 2540 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.379706 0.219224i 0.134246 0.0775072i −0.431373 0.902174i \(-0.641971\pi\)
0.565619 + 0.824667i \(0.308637\pi\)
\(3\) 1.84233 + 3.19101i 0.354556 + 0.614110i 0.987042 0.160462i \(-0.0512985\pi\)
−0.632486 + 0.774572i \(0.717965\pi\)
\(4\) −3.90388 + 6.76172i −0.487985 + 0.845215i
\(5\) 17.8078i 1.59277i 0.604787 + 0.796387i \(0.293258\pi\)
−0.604787 + 0.796387i \(0.706742\pi\)
\(6\) 1.39909 + 0.807764i 0.0951959 + 0.0549614i
\(7\) −4.70983 2.71922i −0.254307 0.146824i 0.367428 0.930052i \(-0.380239\pi\)
−0.621735 + 0.783228i \(0.713572\pi\)
\(8\) 6.93087i 0.306304i
\(9\) 6.71165 11.6249i 0.248579 0.430552i
\(10\) 3.90388 + 6.76172i 0.123452 + 0.213824i
\(11\) −19.4191 + 11.2116i −0.532281 + 0.307313i −0.741945 0.670461i \(-0.766096\pi\)
0.209664 + 0.977774i \(0.432763\pi\)
\(12\) −28.7689 −0.692073
\(13\) 0 0
\(14\) −2.38447 −0.0455198
\(15\) −56.8247 + 32.8078i −0.978139 + 0.564729i
\(16\) −29.7116 51.4621i −0.464244 0.804095i
\(17\) 33.9924 58.8766i 0.484963 0.839981i −0.514888 0.857258i \(-0.672166\pi\)
0.999851 + 0.0172769i \(0.00549968\pi\)
\(18\) 5.88540i 0.0770668i
\(19\) −69.9816 40.4039i −0.844993 0.487857i 0.0139650 0.999902i \(-0.495555\pi\)
−0.858958 + 0.512045i \(0.828888\pi\)
\(20\) −120.411 69.5194i −1.34624 0.777251i
\(21\) 20.0388i 0.208230i
\(22\) −4.91571 + 8.51427i −0.0476379 + 0.0825113i
\(23\) 70.2656 + 121.704i 0.637017 + 1.10335i 0.986084 + 0.166248i \(0.0531653\pi\)
−0.349067 + 0.937098i \(0.613501\pi\)
\(24\) −22.1165 + 12.7689i −0.188104 + 0.108602i
\(25\) −192.116 −1.53693
\(26\) 0 0
\(27\) 148.946 1.06165
\(28\) 36.7733 21.2311i 0.248196 0.143296i
\(29\) 53.3466 + 92.3990i 0.341594 + 0.591657i 0.984729 0.174095i \(-0.0557001\pi\)
−0.643135 + 0.765753i \(0.722367\pi\)
\(30\) −14.3845 + 24.9146i −0.0875411 + 0.151626i
\(31\) 276.155i 1.59997i 0.600023 + 0.799983i \(0.295158\pi\)
−0.600023 + 0.799983i \(0.704842\pi\)
\(32\) −70.5819 40.7505i −0.389913 0.225117i
\(33\) −71.5529 41.3111i −0.377447 0.217919i
\(34\) 29.8078i 0.150353i
\(35\) 48.4233 83.8716i 0.233858 0.405054i
\(36\) 52.4029 + 90.7646i 0.242606 + 0.420206i
\(37\) −3.71670 + 2.14584i −0.0165141 + 0.00953442i −0.508234 0.861219i \(-0.669702\pi\)
0.491720 + 0.870753i \(0.336368\pi\)
\(38\) −35.4299 −0.151250
\(39\) 0 0
\(40\) −123.423 −0.487873
\(41\) −197.254 + 113.884i −0.751362 + 0.433799i −0.826186 0.563398i \(-0.809494\pi\)
0.0748237 + 0.997197i \(0.476161\pi\)
\(42\) −4.39298 7.60887i −0.0161393 0.0279541i
\(43\) 13.7647 23.8411i 0.0488162 0.0845521i −0.840585 0.541680i \(-0.817788\pi\)
0.889401 + 0.457128i \(0.151122\pi\)
\(44\) 175.076i 0.599856i
\(45\) 207.014 + 119.519i 0.685773 + 0.395931i
\(46\) 53.3606 + 30.8078i 0.171035 + 0.0987469i
\(47\) 318.617i 0.988832i 0.869225 + 0.494416i \(0.164618\pi\)
−0.869225 + 0.494416i \(0.835382\pi\)
\(48\) 109.477 189.620i 0.329202 0.570194i
\(49\) −156.712 271.433i −0.456885 0.791348i
\(50\) −72.9479 + 42.1165i −0.206328 + 0.119123i
\(51\) 250.501 0.687787
\(52\) 0 0
\(53\) −67.6562 −0.175345 −0.0876726 0.996149i \(-0.527943\pi\)
−0.0876726 + 0.996149i \(0.527943\pi\)
\(54\) 56.5558 32.6525i 0.142523 0.0822859i
\(55\) −199.654 345.811i −0.489480 0.847804i
\(56\) 18.8466 32.6432i 0.0449729 0.0778953i
\(57\) 297.749i 0.691892i
\(58\) 40.5121 + 23.3897i 0.0917155 + 0.0529519i
\(59\) 252.113 + 145.557i 0.556310 + 0.321186i 0.751663 0.659547i \(-0.229252\pi\)
−0.195353 + 0.980733i \(0.562585\pi\)
\(60\) 512.311i 1.10232i
\(61\) −331.655 + 574.444i −0.696133 + 1.20574i 0.273664 + 0.961825i \(0.411764\pi\)
−0.969797 + 0.243912i \(0.921569\pi\)
\(62\) 60.5398 + 104.858i 0.124009 + 0.214790i
\(63\) −63.2215 + 36.5009i −0.126431 + 0.0729950i
\(64\) 439.652 0.858696
\(65\) 0 0
\(66\) −36.2255 −0.0675613
\(67\) 368.149 212.551i 0.671291 0.387570i −0.125275 0.992122i \(-0.539981\pi\)
0.796566 + 0.604552i \(0.206648\pi\)
\(68\) 265.405 + 459.695i 0.473310 + 0.819796i
\(69\) −258.905 + 448.436i −0.451717 + 0.782397i
\(70\) 42.4621i 0.0725028i
\(71\) −132.470 76.4815i −0.221427 0.127841i 0.385184 0.922840i \(-0.374138\pi\)
−0.606611 + 0.794999i \(0.707471\pi\)
\(72\) 80.5708 + 46.5175i 0.131880 + 0.0761409i
\(73\) 117.268i 0.188016i 0.995571 + 0.0940081i \(0.0299680\pi\)
−0.995571 + 0.0940081i \(0.970032\pi\)
\(74\) −0.940837 + 1.62958i −0.00147797 + 0.00255993i
\(75\) −353.942 613.045i −0.544929 0.943845i
\(76\) 546.400 315.464i 0.824689 0.476134i
\(77\) 121.948 0.180484
\(78\) 0 0
\(79\) 202.462 0.288339 0.144169 0.989553i \(-0.453949\pi\)
0.144169 + 0.989553i \(0.453949\pi\)
\(80\) 916.425 529.098i 1.28074 0.739437i
\(81\) 93.1932 + 161.415i 0.127837 + 0.221420i
\(82\) −49.9323 + 86.4853i −0.0672452 + 0.116472i
\(83\) 336.155i 0.444552i −0.974984 0.222276i \(-0.928651\pi\)
0.974984 0.222276i \(-0.0713486\pi\)
\(84\) 135.497 + 78.2292i 0.175999 + 0.101613i
\(85\) 1048.46 + 605.329i 1.33790 + 0.772437i
\(86\) 12.0702i 0.0151344i
\(87\) −196.564 + 340.459i −0.242228 + 0.419552i
\(88\) −77.7065 134.592i −0.0941311 0.163040i
\(89\) 621.974 359.097i 0.740777 0.427688i −0.0815748 0.996667i \(-0.525995\pi\)
0.822352 + 0.568979i \(0.192662\pi\)
\(90\) 104.806 0.122750
\(91\) 0 0
\(92\) −1097.23 −1.24342
\(93\) −881.214 + 508.769i −0.982555 + 0.567278i
\(94\) 69.8485 + 120.981i 0.0766417 + 0.132747i
\(95\) 719.503 1246.22i 0.777047 1.34588i
\(96\) 300.303i 0.319266i
\(97\) 657.632 + 379.684i 0.688376 + 0.397434i 0.803003 0.595975i \(-0.203234\pi\)
−0.114628 + 0.993409i \(0.536567\pi\)
\(98\) −119.009 68.7098i −0.122670 0.0708238i
\(99\) 300.994i 0.305566i
\(100\) 750.000 1299.04i 0.750000 1.29904i
\(101\) −174.348 301.980i −0.171766 0.297507i 0.767272 0.641322i \(-0.221614\pi\)
−0.939037 + 0.343816i \(0.888280\pi\)
\(102\) 95.1168 54.9157i 0.0923330 0.0533085i
\(103\) 580.303 0.555136 0.277568 0.960706i \(-0.410472\pi\)
0.277568 + 0.960706i \(0.410472\pi\)
\(104\) 0 0
\(105\) 356.847 0.331663
\(106\) −25.6895 + 14.8318i −0.0235395 + 0.0135905i
\(107\) −285.747 494.928i −0.258170 0.447163i 0.707582 0.706631i \(-0.249786\pi\)
−0.965752 + 0.259468i \(0.916453\pi\)
\(108\) −581.468 + 1007.13i −0.518072 + 0.897327i
\(109\) 176.004i 0.154661i −0.997005 0.0773307i \(-0.975360\pi\)
0.997005 0.0773307i \(-0.0246397\pi\)
\(110\) −151.620 87.5379i −0.131422 0.0758765i
\(111\) −13.6948 7.90668i −0.0117104 0.00676098i
\(112\) 323.170i 0.272649i
\(113\) −632.441 + 1095.42i −0.526505 + 0.911933i 0.473018 + 0.881053i \(0.343165\pi\)
−0.999523 + 0.0308807i \(0.990169\pi\)
\(114\) −65.2736 113.057i −0.0536266 0.0928840i
\(115\) −2167.27 + 1251.27i −1.75738 + 1.01462i
\(116\) −833.035 −0.666770
\(117\) 0 0
\(118\) 127.638 0.0995768
\(119\) −320.197 + 184.866i −0.246659 + 0.142409i
\(120\) −227.386 393.845i −0.172979 0.299608i
\(121\) −414.098 + 717.239i −0.311118 + 0.538872i
\(122\) 290.827i 0.215821i
\(123\) −726.812 419.625i −0.532801 0.307613i
\(124\) −1867.29 1078.08i −1.35232 0.780760i
\(125\) 1195.19i 0.855211i
\(126\) −16.0037 + 27.7193i −0.0113153 + 0.0195986i
\(127\) 1302.05 + 2255.22i 0.909752 + 1.57574i 0.814408 + 0.580293i \(0.197062\pi\)
0.0953448 + 0.995444i \(0.469605\pi\)
\(128\) 731.594 422.386i 0.505190 0.291672i
\(129\) 101.436 0.0692323
\(130\) 0 0
\(131\) 2131.70 1.42174 0.710870 0.703324i \(-0.248302\pi\)
0.710870 + 0.703324i \(0.248302\pi\)
\(132\) 558.668 322.547i 0.368377 0.212683i
\(133\) 219.734 + 380.591i 0.143259 + 0.248131i
\(134\) 93.1922 161.414i 0.0600790 0.104060i
\(135\) 2652.40i 1.69098i
\(136\) 408.066 + 235.597i 0.257290 + 0.148546i
\(137\) −595.812 343.992i −0.371560 0.214520i 0.302580 0.953124i \(-0.402152\pi\)
−0.674140 + 0.738604i \(0.735485\pi\)
\(138\) 227.032i 0.140045i
\(139\) 339.790 588.534i 0.207343 0.359128i −0.743534 0.668698i \(-0.766852\pi\)
0.950877 + 0.309570i \(0.100185\pi\)
\(140\) 378.078 + 654.850i 0.228239 + 0.395321i
\(141\) −1016.71 + 586.998i −0.607252 + 0.350597i
\(142\) −67.0662 −0.0396343
\(143\) 0 0
\(144\) −797.656 −0.461607
\(145\) −1645.42 + 949.983i −0.942377 + 0.544082i
\(146\) 25.7079 + 44.5274i 0.0145726 + 0.0252405i
\(147\) 577.429 1000.14i 0.323983 0.561155i
\(148\) 33.5084i 0.0186106i
\(149\) −1710.80 987.731i −0.940632 0.543074i −0.0504739 0.998725i \(-0.516073\pi\)
−0.890159 + 0.455651i \(0.849407\pi\)
\(150\) −268.788 155.185i −0.146310 0.0844719i
\(151\) 1803.24i 0.971824i 0.874008 + 0.485912i \(0.161513\pi\)
−0.874008 + 0.485912i \(0.838487\pi\)
\(152\) 280.034 485.033i 0.149433 0.258825i
\(153\) −456.290 790.318i −0.241104 0.417604i
\(154\) 46.3044 26.7339i 0.0242293 0.0139888i
\(155\) −4917.71 −2.54839
\(156\) 0 0
\(157\) −397.168 −0.201894 −0.100947 0.994892i \(-0.532187\pi\)
−0.100947 + 0.994892i \(0.532187\pi\)
\(158\) 76.8762 44.3845i 0.0387085 0.0223483i
\(159\) −124.645 215.892i −0.0621698 0.107681i
\(160\) 725.675 1256.91i 0.358560 0.621044i
\(161\) 764.272i 0.374118i
\(162\) 70.7721 + 40.8603i 0.0343233 + 0.0198166i
\(163\) −815.270 470.696i −0.391760 0.226183i 0.291162 0.956674i \(-0.405958\pi\)
−0.682922 + 0.730491i \(0.739291\pi\)
\(164\) 1778.37i 0.846750i
\(165\) 735.658 1274.20i 0.347096 0.601189i
\(166\) −73.6932 127.640i −0.0344560 0.0596796i
\(167\) 3187.35 1840.22i 1.47691 0.852696i 0.477252 0.878766i \(-0.341633\pi\)
0.999660 + 0.0260704i \(0.00829942\pi\)
\(168\) 138.886 0.0637817
\(169\) 0 0
\(170\) 530.810 0.239478
\(171\) −939.383 + 542.353i −0.420096 + 0.242543i
\(172\) 107.471 + 186.146i 0.0476431 + 0.0825203i
\(173\) 711.387 1232.16i 0.312634 0.541499i −0.666297 0.745686i \(-0.732122\pi\)
0.978932 + 0.204187i \(0.0654552\pi\)
\(174\) 172.366i 0.0750978i
\(175\) 904.837 + 522.408i 0.390853 + 0.225659i
\(176\) 1153.95 + 666.233i 0.494217 + 0.285336i
\(177\) 1072.66i 0.455514i
\(178\) 157.445 272.703i 0.0662978 0.114831i
\(179\) 583.946 + 1011.42i 0.243833 + 0.422331i 0.961803 0.273743i \(-0.0882617\pi\)
−0.717970 + 0.696074i \(0.754928\pi\)
\(180\) −1616.31 + 933.179i −0.669294 + 0.386417i
\(181\) 1133.96 0.465673 0.232836 0.972516i \(-0.425199\pi\)
0.232836 + 0.972516i \(0.425199\pi\)
\(182\) 0 0
\(183\) −2444.07 −0.987274
\(184\) −843.512 + 487.002i −0.337959 + 0.195121i
\(185\) −38.2126 66.1861i −0.0151862 0.0263032i
\(186\) −223.068 + 386.366i −0.0879364 + 0.152310i
\(187\) 1524.44i 0.596141i
\(188\) −2154.40 1243.84i −0.835776 0.482536i
\(189\) −701.511 405.018i −0.269986 0.155877i
\(190\) 630.928i 0.240907i
\(191\) −1341.06 + 2322.78i −0.508040 + 0.879952i 0.491916 + 0.870642i \(0.336297\pi\)
−0.999957 + 0.00930919i \(0.997037\pi\)
\(192\) 809.985 + 1402.93i 0.304456 + 0.527334i
\(193\) −1706.65 + 985.333i −0.636514 + 0.367491i −0.783270 0.621681i \(-0.786450\pi\)
0.146757 + 0.989173i \(0.453117\pi\)
\(194\) 332.943 0.123216
\(195\) 0 0
\(196\) 2447.14 0.891813
\(197\) 3478.00 2008.02i 1.25785 0.726222i 0.285197 0.958469i \(-0.407941\pi\)
0.972657 + 0.232247i \(0.0746077\pi\)
\(198\) 65.9851 + 114.290i 0.0236836 + 0.0410212i
\(199\) −2113.03 + 3659.87i −0.752707 + 1.30373i 0.193800 + 0.981041i \(0.437919\pi\)
−0.946506 + 0.322685i \(0.895415\pi\)
\(200\) 1331.53i 0.470768i
\(201\) 1356.50 + 783.177i 0.476021 + 0.274831i
\(202\) −132.402 76.4426i −0.0461178 0.0266261i
\(203\) 580.245i 0.200617i
\(204\) −977.926 + 1693.82i −0.335630 + 0.581328i
\(205\) −2028.03 3512.65i −0.690944 1.19675i
\(206\) 220.345 127.216i 0.0745250 0.0430270i
\(207\) 1886.39 0.633398
\(208\) 0 0
\(209\) 1811.98 0.599699
\(210\) 135.497 78.2292i 0.0445247 0.0257063i
\(211\) −682.334 1181.84i −0.222625 0.385597i 0.732980 0.680251i \(-0.238129\pi\)
−0.955604 + 0.294654i \(0.904796\pi\)
\(212\) 264.122 457.473i 0.0855659 0.148204i
\(213\) 563.617i 0.181307i
\(214\) −217.000 125.285i −0.0693168 0.0400201i
\(215\) 424.557 + 245.118i 0.134672 + 0.0777532i
\(216\) 1032.33i 0.325189i
\(217\) 750.928 1300.65i 0.234914 0.406883i
\(218\) −38.5842 66.8297i −0.0119874 0.0207628i
\(219\) −374.203 + 216.046i −0.115463 + 0.0666624i
\(220\) 3117.71 0.955436
\(221\) 0 0
\(222\) −6.93332 −0.00209610
\(223\) 917.527 529.734i 0.275525 0.159075i −0.355871 0.934535i \(-0.615816\pi\)
0.631396 + 0.775461i \(0.282482\pi\)
\(224\) 221.619 + 383.856i 0.0661052 + 0.114498i
\(225\) −1289.42 + 2233.34i −0.382050 + 0.661729i
\(226\) 554.584i 0.163232i
\(227\) 3000.08 + 1732.10i 0.877190 + 0.506446i 0.869731 0.493526i \(-0.164292\pi\)
0.00745930 + 0.999972i \(0.497626\pi\)
\(228\) 2013.30 + 1162.38i 0.584797 + 0.337633i
\(229\) 2324.64i 0.670815i −0.942073 0.335407i \(-0.891126\pi\)
0.942073 0.335407i \(-0.108874\pi\)
\(230\) −548.617 + 950.233i −0.157282 + 0.272420i
\(231\) 224.668 + 389.137i 0.0639917 + 0.110837i
\(232\) −640.405 + 369.738i −0.181227 + 0.104631i
\(233\) 3731.01 1.04904 0.524521 0.851398i \(-0.324245\pi\)
0.524521 + 0.851398i \(0.324245\pi\)
\(234\) 0 0
\(235\) −5673.86 −1.57499
\(236\) −1968.44 + 1136.48i −0.542942 + 0.313468i
\(237\) 373.002 + 646.058i 0.102232 + 0.177072i
\(238\) −81.0540 + 140.390i −0.0220754 + 0.0382357i
\(239\) 6044.47i 1.63592i −0.575278 0.817958i \(-0.695106\pi\)
0.575278 0.817958i \(-0.304894\pi\)
\(240\) 3376.71 + 1949.55i 0.908191 + 0.524344i
\(241\) 4480.78 + 2586.98i 1.19765 + 0.691461i 0.960030 0.279898i \(-0.0903008\pi\)
0.237616 + 0.971359i \(0.423634\pi\)
\(242\) 363.120i 0.0964556i
\(243\) 1667.39 2888.00i 0.440176 0.762408i
\(244\) −2589.49 4485.12i −0.679405 1.17676i
\(245\) 4833.61 2790.68i 1.26044 0.727715i
\(246\) −367.967 −0.0953688
\(247\) 0 0
\(248\) −1914.00 −0.490076
\(249\) 1072.67 619.309i 0.273004 0.157619i
\(250\) −262.015 453.823i −0.0662851 0.114809i
\(251\) 2810.37 4867.70i 0.706728 1.22409i −0.259337 0.965787i \(-0.583504\pi\)
0.966064 0.258301i \(-0.0831628\pi\)
\(252\) 569.981i 0.142482i
\(253\) −2729.00 1575.59i −0.678144 0.391527i
\(254\) 988.796 + 570.882i 0.244262 + 0.141025i
\(255\) 4460.86i 1.09549i
\(256\) −1573.42 + 2725.24i −0.384135 + 0.665341i
\(257\) −837.070 1449.85i −0.203171 0.351903i 0.746377 0.665523i \(-0.231791\pi\)
−0.949549 + 0.313620i \(0.898458\pi\)
\(258\) 38.5160 22.2372i 0.00929420 0.00536601i
\(259\) 23.3401 0.00559954
\(260\) 0 0
\(261\) 1432.17 0.339653
\(262\) 809.422 467.320i 0.190864 0.110195i
\(263\) 3154.59 + 5463.91i 0.739622 + 1.28106i 0.952666 + 0.304020i \(0.0983289\pi\)
−0.213044 + 0.977043i \(0.568338\pi\)
\(264\) 286.322 495.924i 0.0667496 0.115614i
\(265\) 1204.81i 0.279285i
\(266\) 166.869 + 96.3419i 0.0384639 + 0.0222072i
\(267\) 2291.76 + 1323.15i 0.525294 + 0.303279i
\(268\) 3319.09i 0.756514i
\(269\) 1241.37 2150.11i 0.281366 0.487340i −0.690356 0.723470i \(-0.742546\pi\)
0.971721 + 0.236131i \(0.0758793\pi\)
\(270\) 581.468 + 1007.13i 0.131063 + 0.227008i
\(271\) 2455.81 1417.86i 0.550478 0.317819i −0.198837 0.980033i \(-0.563716\pi\)
0.749315 + 0.662214i \(0.230383\pi\)
\(272\) −4039.88 −0.900566
\(273\) 0 0
\(274\) −301.645 −0.0665075
\(275\) 3730.74 2153.94i 0.818080 0.472318i
\(276\) −2021.47 3501.28i −0.440863 0.763596i
\(277\) −1918.76 + 3323.38i −0.416198 + 0.720876i −0.995553 0.0941989i \(-0.969971\pi\)
0.579355 + 0.815075i \(0.303304\pi\)
\(278\) 297.960i 0.0642822i
\(279\) 3210.28 + 1853.46i 0.688869 + 0.397719i
\(280\) 581.303 + 335.616i 0.124070 + 0.0716317i
\(281\) 9122.13i 1.93659i −0.249819 0.968293i \(-0.580371\pi\)
0.249819 0.968293i \(-0.419629\pi\)
\(282\) −257.368 + 445.774i −0.0543476 + 0.0941328i
\(283\) 1063.92 + 1842.77i 0.223476 + 0.387072i 0.955861 0.293819i \(-0.0949262\pi\)
−0.732385 + 0.680891i \(0.761593\pi\)
\(284\) 1034.29 597.150i 0.216106 0.124769i
\(285\) 5302.24 1.10203
\(286\) 0 0
\(287\) 1238.71 0.254769
\(288\) −947.441 + 547.005i −0.193849 + 0.111919i
\(289\) 145.530 + 252.066i 0.0296215 + 0.0513059i
\(290\) −416.518 + 721.430i −0.0843405 + 0.146082i
\(291\) 2798.01i 0.563651i
\(292\) −792.934 457.800i −0.158914 0.0917491i
\(293\) −7166.16 4137.38i −1.42884 0.824944i −0.431815 0.901962i \(-0.642127\pi\)
−0.997030 + 0.0770183i \(0.975460\pi\)
\(294\) 506.344i 0.100444i
\(295\) −2592.05 + 4489.56i −0.511576 + 0.886076i
\(296\) −14.8725 25.7600i −0.00292043 0.00505834i
\(297\) −2892.40 + 1669.93i −0.565099 + 0.326260i
\(298\) −866.136 −0.168369
\(299\) 0 0
\(300\) 5526.99 1.06367
\(301\) −129.659 + 74.8585i −0.0248286 + 0.0143348i
\(302\) 395.312 + 684.701i 0.0753234 + 0.130464i
\(303\) 642.414 1112.69i 0.121801 0.210966i
\(304\) 4801.86i 0.905940i
\(305\) −10229.6 5906.04i −1.92047 1.10878i
\(306\) −346.513 200.059i −0.0647347 0.0373746i
\(307\) 3610.49i 0.671211i −0.942003 0.335605i \(-0.891059\pi\)
0.942003 0.335605i \(-0.108941\pi\)
\(308\) −476.070 + 824.578i −0.0880734 + 0.152548i
\(309\) 1069.11 + 1851.75i 0.196827 + 0.340914i
\(310\) −1867.29 + 1078.08i −0.342112 + 0.197518i
\(311\) −3331.06 −0.607354 −0.303677 0.952775i \(-0.598214\pi\)
−0.303677 + 0.952775i \(0.598214\pi\)
\(312\) 0 0
\(313\) −358.125 −0.0646724 −0.0323362 0.999477i \(-0.510295\pi\)
−0.0323362 + 0.999477i \(0.510295\pi\)
\(314\) −150.807 + 87.0685i −0.0271036 + 0.0156483i
\(315\) −650.000 1125.83i −0.116265 0.201376i
\(316\) −790.388 + 1368.99i −0.140705 + 0.243708i
\(317\) 3047.46i 0.539944i −0.962868 0.269972i \(-0.912986\pi\)
0.962868 0.269972i \(-0.0870144\pi\)
\(318\) −94.6570 54.6503i −0.0166921 0.00963721i
\(319\) −2071.89 1196.21i −0.363647 0.209952i
\(320\) 7829.23i 1.36771i
\(321\) 1052.88 1823.64i 0.183072 0.317089i
\(322\) −167.546 290.199i −0.0289969 0.0502241i
\(323\) −4757.69 + 2746.85i −0.819581 + 0.473185i
\(324\) −1455.26 −0.249530
\(325\) 0 0
\(326\) −412.751 −0.0701232
\(327\) 561.629 324.257i 0.0949791 0.0548362i
\(328\) −789.318 1367.14i −0.132874 0.230145i
\(329\) 866.392 1500.63i 0.145185 0.251467i
\(330\) 645.094i 0.107610i
\(331\) 6663.87 + 3847.39i 1.10658 + 0.638887i 0.937942 0.346791i \(-0.112729\pi\)
0.168641 + 0.985677i \(0.446062\pi\)
\(332\) 2272.99 + 1312.31i 0.375742 + 0.216935i
\(333\) 57.6084i 0.00948025i
\(334\) 806.838 1397.48i 0.132180 0.228943i
\(335\) 3785.05 + 6555.90i 0.617312 + 1.06922i
\(336\) −1031.24 + 595.386i −0.167437 + 0.0966696i
\(337\) −4712.21 −0.761693 −0.380846 0.924638i \(-0.624367\pi\)
−0.380846 + 0.924638i \(0.624367\pi\)
\(338\) 0 0
\(339\) −4660.66 −0.746703
\(340\) −8186.13 + 4726.27i −1.30575 + 0.753876i
\(341\) −3096.16 5362.70i −0.491690 0.851632i
\(342\) −237.793 + 411.870i −0.0375976 + 0.0651210i
\(343\) 3569.92i 0.561976i
\(344\) 165.240 + 95.4013i 0.0258986 + 0.0149526i
\(345\) −7985.65 4610.52i −1.24618 0.719484i
\(346\) 623.811i 0.0969257i
\(347\) 2630.99 4557.01i 0.407029 0.704995i −0.587526 0.809205i \(-0.699898\pi\)
0.994555 + 0.104210i \(0.0332315\pi\)
\(348\) −1534.72 2658.22i −0.236408 0.409470i
\(349\) 43.5909 25.1672i 0.00668587 0.00386009i −0.496653 0.867949i \(-0.665438\pi\)
0.503339 + 0.864089i \(0.332105\pi\)
\(350\) 458.096 0.0699608
\(351\) 0 0
\(352\) 1827.52 0.276725
\(353\) −7844.14 + 4528.82i −1.18272 + 0.682846i −0.956643 0.291263i \(-0.905925\pi\)
−0.226081 + 0.974109i \(0.572591\pi\)
\(354\) 235.152 + 407.295i 0.0353056 + 0.0611511i
\(355\) 1361.96 2358.99i 0.203621 0.352683i
\(356\) 5607.49i 0.834821i
\(357\) −1179.82 681.168i −0.174909 0.100984i
\(358\) 443.456 + 256.029i 0.0654675 + 0.0377977i
\(359\) 7177.86i 1.05525i 0.849479 + 0.527623i \(0.176917\pi\)
−0.849479 + 0.527623i \(0.823083\pi\)
\(360\) −828.373 + 1434.78i −0.121275 + 0.210055i
\(361\) −164.553 285.014i −0.0239908 0.0415532i
\(362\) 430.573 248.591i 0.0625150 0.0360930i
\(363\) −3051.62 −0.441235
\(364\) 0 0
\(365\) −2088.28 −0.299467
\(366\) −928.030 + 535.798i −0.132538 + 0.0765209i
\(367\) −2002.07 3467.69i −0.284761 0.493221i 0.687790 0.725910i \(-0.258581\pi\)
−0.972551 + 0.232689i \(0.925248\pi\)
\(368\) 4175.41 7232.03i 0.591463 1.02444i
\(369\) 3057.41i 0.431334i
\(370\) −29.0191 16.7542i −0.00407738 0.00235408i
\(371\) 318.649 + 183.972i 0.0445915 + 0.0257449i
\(372\) 7944.70i 1.10729i
\(373\) 5007.09 8672.53i 0.695060 1.20388i −0.275101 0.961415i \(-0.588711\pi\)
0.970161 0.242464i \(-0.0779555\pi\)
\(374\) 334.194 + 578.841i 0.0462053 + 0.0800299i
\(375\) 3813.87 2201.94i 0.525194 0.303221i
\(376\) −2208.30 −0.302883
\(377\) 0 0
\(378\) −355.158 −0.0483263
\(379\) 7074.66 4084.56i 0.958842 0.553587i 0.0630252 0.998012i \(-0.479925\pi\)
0.895816 + 0.444425i \(0.146592\pi\)
\(380\) 5617.71 + 9730.16i 0.758375 + 1.31354i
\(381\) −4797.62 + 8309.73i −0.645117 + 1.11738i
\(382\) 1175.97i 0.157507i
\(383\) −6330.86 3655.12i −0.844626 0.487645i 0.0142079 0.999899i \(-0.495477\pi\)
−0.858834 + 0.512254i \(0.828811\pi\)
\(384\) 2695.67 + 1556.35i 0.358237 + 0.206828i
\(385\) 2171.62i 0.287470i
\(386\) −432.017 + 748.275i −0.0569665 + 0.0986689i
\(387\) −184.767 320.027i −0.0242694 0.0420358i
\(388\) −5134.64 + 2964.48i −0.671834 + 0.387884i
\(389\) −8785.47 −1.14509 −0.572546 0.819872i \(-0.694044\pi\)
−0.572546 + 0.819872i \(0.694044\pi\)
\(390\) 0 0
\(391\) 9553.99 1.23572
\(392\) 1881.26 1086.15i 0.242393 0.139946i
\(393\) 3927.30 + 6802.29i 0.504087 + 0.873104i
\(394\) 880.412 1524.92i 0.112575 0.194986i
\(395\) 3605.40i 0.459259i
\(396\) −2035.24 1175.05i −0.258269 0.149112i
\(397\) −9757.33 5633.40i −1.23352 0.712171i −0.265756 0.964040i \(-0.585621\pi\)
−0.967761 + 0.251869i \(0.918955\pi\)
\(398\) 1852.90i 0.233361i
\(399\) −809.646 + 1402.35i −0.101586 + 0.175953i
\(400\) 5708.10 + 9886.71i 0.713512 + 1.23584i
\(401\) 1365.06 788.117i 0.169995 0.0981464i −0.412589 0.910917i \(-0.635375\pi\)
0.582583 + 0.812771i \(0.302042\pi\)
\(402\) 686.763 0.0852055
\(403\) 0 0
\(404\) 2722.54 0.335276
\(405\) −2874.45 + 1659.56i −0.352672 + 0.203616i
\(406\) −127.203 220.323i −0.0155493 0.0269321i
\(407\) 48.1168 83.3407i 0.00586010 0.0101500i
\(408\) 1736.19i 0.210672i
\(409\) 5850.68 + 3377.89i 0.707329 + 0.408377i 0.810071 0.586331i \(-0.199428\pi\)
−0.102742 + 0.994708i \(0.532762\pi\)
\(410\) −1540.11 889.183i −0.185514 0.107106i
\(411\) 2534.99i 0.304238i
\(412\) −2265.43 + 3923.85i −0.270898 + 0.469209i
\(413\) −791.606 1371.10i −0.0943157 0.163360i
\(414\) 716.275 413.542i 0.0850314 0.0490929i
\(415\) 5986.17 0.708072
\(416\) 0 0
\(417\) 2504.02 0.294059
\(418\) 688.019 397.228i 0.0805074 0.0464810i
\(419\) −5378.09 9315.13i −0.627057 1.08610i −0.988139 0.153561i \(-0.950926\pi\)
0.361082 0.932534i \(-0.382408\pi\)
\(420\) −1393.09 + 2412.90i −0.161847 + 0.280327i
\(421\) 7886.03i 0.912925i −0.889743 0.456463i \(-0.849116\pi\)
0.889743 0.456463i \(-0.150884\pi\)
\(422\) −518.173 299.167i −0.0597731 0.0345100i
\(423\) 3703.90 + 2138.45i 0.425744 + 0.245803i
\(424\) 468.916i 0.0537089i
\(425\) −6530.50 + 11311.2i −0.745355 + 1.29099i
\(426\) −123.558 214.009i −0.0140526 0.0243398i
\(427\) 3124.08 1803.69i 0.354063 0.204418i
\(428\) 4462.08 0.503932
\(429\) 0 0
\(430\) 214.943 0.0241057
\(431\) 12197.6 7042.31i 1.36320 0.787044i 0.373152 0.927770i \(-0.378277\pi\)
0.990049 + 0.140726i \(0.0449438\pi\)
\(432\) −4425.43 7665.07i −0.492867 0.853671i
\(433\) 932.072 1614.40i 0.103447 0.179175i −0.809656 0.586905i \(-0.800346\pi\)
0.913103 + 0.407730i \(0.133679\pi\)
\(434\) 658.485i 0.0728301i
\(435\) −6062.81 3500.36i −0.668252 0.385815i
\(436\) 1190.09 + 687.098i 0.130722 + 0.0754725i
\(437\) 11356.0i 1.24309i
\(438\) −94.7249 + 164.068i −0.0103336 + 0.0178984i
\(439\) 3077.24 + 5329.94i 0.334553 + 0.579463i 0.983399 0.181457i \(-0.0580813\pi\)
−0.648846 + 0.760920i \(0.724748\pi\)
\(440\) 2396.77 1383.78i 0.259686 0.149930i
\(441\) −4207.17 −0.454289
\(442\) 0 0
\(443\) −14539.3 −1.55933 −0.779663 0.626200i \(-0.784609\pi\)
−0.779663 + 0.626200i \(0.784609\pi\)
\(444\) 106.926 61.7335i 0.0114290 0.00659852i
\(445\) 6394.72 + 11076.0i 0.681210 + 1.17989i
\(446\) 232.261 402.287i 0.0246589 0.0427104i
\(447\) 7278.90i 0.770202i
\(448\) −2070.69 1195.51i −0.218373 0.126077i
\(449\) 6100.17 + 3521.93i 0.641169 + 0.370179i 0.785065 0.619414i \(-0.212630\pi\)
−0.143896 + 0.989593i \(0.545963\pi\)
\(450\) 1130.68i 0.118446i
\(451\) 2553.66 4423.08i 0.266624 0.461806i
\(452\) −4937.95 8552.78i −0.513853 0.890020i
\(453\) −5754.15 + 3322.16i −0.596807 + 0.344567i
\(454\) 1518.87 0.157013
\(455\) 0 0
\(456\) 2063.66 0.211929
\(457\) −12210.0 + 7049.43i −1.24980 + 0.721572i −0.971069 0.238798i \(-0.923247\pi\)
−0.278730 + 0.960370i \(0.589913\pi\)
\(458\) −509.616 882.681i −0.0519930 0.0900545i
\(459\) 5063.04 8769.44i 0.514863 0.891770i
\(460\) 19539.3i 1.98049i
\(461\) 12513.8 + 7224.85i 1.26426 + 0.729924i 0.973897 0.226991i \(-0.0728889\pi\)
0.290368 + 0.956915i \(0.406222\pi\)
\(462\) 170.616 + 98.5051i 0.0171813 + 0.00991964i
\(463\) 15806.5i 1.58659i 0.608840 + 0.793293i \(0.291635\pi\)
−0.608840 + 0.793293i \(0.708365\pi\)
\(464\) 3170.03 5490.65i 0.317166 0.549347i
\(465\) −9060.04 15692.4i −0.903547 1.56499i
\(466\) 1416.69 817.926i 0.140830 0.0813083i
\(467\) 15071.3 1.49340 0.746699 0.665162i \(-0.231638\pi\)
0.746699 + 0.665162i \(0.231638\pi\)
\(468\) 0 0
\(469\) −2311.89 −0.227619
\(470\) −2154.40 + 1243.84i −0.211437 + 0.122073i
\(471\) −731.713 1267.36i −0.0715830 0.123985i
\(472\) −1008.84 + 1747.36i −0.0983804 + 0.170400i
\(473\) 617.299i 0.0600073i
\(474\) 283.262 + 163.542i 0.0274487 + 0.0158475i
\(475\) 13444.6 + 7762.25i 1.29870 + 0.749803i
\(476\) 2886.78i 0.277973i
\(477\) −454.085 + 786.498i −0.0435872 + 0.0754953i
\(478\) −1325.09 2295.12i −0.126795 0.219616i
\(479\) −339.954 + 196.272i −0.0324277 + 0.0187222i −0.516126 0.856513i \(-0.672626\pi\)
0.483698 + 0.875235i \(0.339293\pi\)
\(480\) 5347.73 0.508519
\(481\) 0 0
\(482\) 2268.51 0.214373
\(483\) 2438.80 1408.04i 0.229750 0.132646i
\(484\) −3233.18 5600.03i −0.303642 0.525923i
\(485\) −6761.33 + 11711.0i −0.633023 + 1.09643i
\(486\) 1462.12i 0.136467i
\(487\) 8225.41 + 4748.94i 0.765357 + 0.441879i 0.831216 0.555950i \(-0.187645\pi\)
−0.0658588 + 0.997829i \(0.520979\pi\)
\(488\) −3981.40 2298.66i −0.369322 0.213228i
\(489\) 3468.71i 0.320778i
\(490\) 1223.57 2119.28i 0.112806 0.195386i
\(491\) −946.912 1640.10i −0.0870337 0.150747i 0.819222 0.573476i \(-0.194405\pi\)
−0.906256 + 0.422729i \(0.861072\pi\)
\(492\) 5674.78 3276.34i 0.519998 0.300221i
\(493\) 7253.52 0.662641
\(494\) 0 0
\(495\) −5360.04 −0.486699
\(496\) 14211.5 8205.03i 1.28652 0.742775i
\(497\) 415.941 + 720.430i 0.0375402 + 0.0650216i
\(498\) 271.534 470.311i 0.0244332 0.0423196i
\(499\) 13370.1i 1.19945i 0.800205 + 0.599727i \(0.204724\pi\)
−0.800205 + 0.599727i \(0.795276\pi\)
\(500\) 8081.57 + 4665.90i 0.722838 + 0.417330i
\(501\) 11744.3 + 6780.57i 1.04730 + 0.604658i
\(502\) 2464.39i 0.219106i
\(503\) −2777.36 + 4810.52i −0.246195 + 0.426423i −0.962467 0.271399i \(-0.912514\pi\)
0.716272 + 0.697822i \(0.245847\pi\)
\(504\) −252.983 438.180i −0.0223587 0.0387263i
\(505\) 5377.60 3104.76i 0.473861 0.273584i
\(506\) −1381.62 −0.121385
\(507\) 0 0
\(508\) −20332.3 −1.77578
\(509\) −1903.13 + 1098.78i −0.165727 + 0.0956824i −0.580569 0.814211i \(-0.697170\pi\)
0.414843 + 0.909893i \(0.363837\pi\)
\(510\) 977.926 + 1693.82i 0.0849084 + 0.147066i
\(511\) 318.878 552.313i 0.0276053 0.0478139i
\(512\) 8137.89i 0.702437i
\(513\) −10423.5 6018.00i −0.897091 0.517936i
\(514\) −635.682 367.011i −0.0545500 0.0314945i
\(515\) 10333.9i 0.884206i
\(516\) −395.996 + 685.884i −0.0337844 + 0.0585162i
\(517\) −3572.23 6187.28i −0.303881 0.526337i
\(518\) 8.86237 5.11669i 0.000751718 0.000434005i
\(519\) 5242.44 0.443386
\(520\) 0 0
\(521\) 17005.2 1.42997 0.714983 0.699142i \(-0.246435\pi\)
0.714983 + 0.699142i \(0.246435\pi\)
\(522\) 543.805 313.966i 0.0455972 0.0263255i
\(523\) 7243.11 + 12545.4i 0.605581 + 1.04890i 0.991959 + 0.126557i \(0.0403928\pi\)
−0.386378 + 0.922341i \(0.626274\pi\)
\(524\) −8321.92 + 14414.0i −0.693788 + 1.20168i
\(525\) 3849.79i 0.320035i
\(526\) 2395.64 + 1383.12i 0.198583 + 0.114652i
\(527\) 16259.1 + 9387.19i 1.34394 + 0.775925i
\(528\) 4909.68i 0.404671i
\(529\) −3791.02 + 6566.23i −0.311582 + 0.539675i
\(530\) −264.122 457.473i −0.0216466 0.0374931i
\(531\) 3384.18 1953.86i 0.276574 0.159680i
\(532\) −3431.27 −0.279632
\(533\) 0 0
\(534\) 1160.26 0.0940252
\(535\) 8813.56 5088.51i 0.712230 0.411206i
\(536\) 1473.16 + 2551.59i 0.118714 + 0.205619i
\(537\) −2151.64 + 3726.75i −0.172905 + 0.299481i
\(538\) 1088.55i 0.0872315i
\(539\) 6086.41 + 3513.99i 0.486383 + 0.280813i
\(540\) −17934.8 10354.6i −1.42924 0.825172i
\(541\) 15266.7i 1.21325i −0.794990 0.606623i \(-0.792524\pi\)
0.794990 0.606623i \(-0.207476\pi\)
\(542\) 621.657 1076.74i 0.0492665 0.0853321i
\(543\) 2089.13 + 3618.48i 0.165107 + 0.285974i
\(544\) −4798.50 + 2770.41i −0.378187 + 0.218347i
\(545\) 3134.23 0.246341
\(546\) 0 0
\(547\) 15260.5 1.19286 0.596430 0.802665i \(-0.296586\pi\)
0.596430 + 0.802665i \(0.296586\pi\)
\(548\) 4651.96 2685.81i 0.362631 0.209365i
\(549\) 4451.91 + 7710.93i 0.346089 + 0.599443i
\(550\) 944.390 1635.73i 0.0732162 0.126814i
\(551\) 8621.64i 0.666595i
\(552\) −3108.05 1794.44i −0.239651 0.138363i
\(553\) −953.563 550.540i −0.0733266 0.0423351i
\(554\) 1682.55i 0.129033i
\(555\) 140.800 243.873i 0.0107687 0.0186520i
\(556\) 2653.00 + 4595.13i 0.202360 + 0.350498i
\(557\) −9043.12 + 5221.05i −0.687916 + 0.397169i −0.802831 0.596207i \(-0.796674\pi\)
0.114915 + 0.993375i \(0.463341\pi\)
\(558\) 1625.29 0.123304
\(559\) 0 0
\(560\) −5754.94 −0.434269
\(561\) −4864.51 + 2808.53i −0.366096 + 0.211366i
\(562\) −1999.79 3463.73i −0.150099 0.259980i
\(563\) 3572.63 6187.98i 0.267440 0.463219i −0.700760 0.713397i \(-0.747156\pi\)
0.968200 + 0.250178i \(0.0804891\pi\)
\(564\) 9166.29i 0.684344i
\(565\) −19507.0 11262.4i −1.45250 0.838604i
\(566\) 807.958 + 466.475i 0.0600018 + 0.0346420i
\(567\) 1013.65i 0.0750783i
\(568\) 530.083 918.131i 0.0391581 0.0678238i
\(569\) 2219.43 + 3844.17i 0.163521 + 0.283226i 0.936129 0.351657i \(-0.114382\pi\)
−0.772608 + 0.634883i \(0.781048\pi\)
\(570\) 2013.30 1162.38i 0.147943 0.0854151i
\(571\) −10117.3 −0.741497 −0.370748 0.928733i \(-0.620899\pi\)
−0.370748 + 0.928733i \(0.620899\pi\)
\(572\) 0 0
\(573\) −9882.70 −0.720516
\(574\) 470.346 271.554i 0.0342018 0.0197464i
\(575\) −13499.2 23381.3i −0.979052 1.69577i
\(576\) 2950.79 5110.92i 0.213454 0.369714i
\(577\) 3105.60i 0.224069i −0.993704 0.112035i \(-0.964263\pi\)
0.993704 0.112035i \(-0.0357368\pi\)
\(578\) 110.518 + 63.8074i 0.00795316 + 0.00459176i
\(579\) −6288.41 3630.62i −0.451360 0.260593i
\(580\) 14834.5i 1.06202i
\(581\) −914.081 + 1583.24i −0.0652711 + 0.113053i
\(582\) 613.390 + 1062.42i 0.0436870 + 0.0756682i
\(583\) 1313.83 758.538i 0.0933329 0.0538858i
\(584\) −812.769 −0.0575901
\(585\) 0 0
\(586\) −3628.05 −0.255757
\(587\) −17028.1 + 9831.16i −1.19731 + 0.691270i −0.959956 0.280152i \(-0.909615\pi\)
−0.237359 + 0.971422i \(0.576282\pi\)
\(588\) 4508.43 + 7808.83i 0.316198 + 0.547671i
\(589\) 11157.7 19325.8i 0.780555 1.35196i
\(590\) 2272.95i 0.158603i
\(591\) 12815.2 + 7398.88i 0.891960 + 0.514974i
\(592\) 220.859 + 127.513i 0.0153332 + 0.00885261i
\(593\) 6395.51i 0.442888i 0.975173 + 0.221444i \(0.0710769\pi\)
−0.975173 + 0.221444i \(0.928923\pi\)
\(594\) −732.176 + 1268.17i −0.0505750 + 0.0875985i
\(595\) −3292.05 5702.00i −0.226825 0.392872i
\(596\) 13357.5 7711.97i 0.918029 0.530025i
\(597\) −15571.6 −1.06751
\(598\) 0 0
\(599\) 8878.48 0.605618 0.302809 0.953051i \(-0.402076\pi\)
0.302809 + 0.953051i \(0.402076\pi\)
\(600\) 4248.94 2453.12i 0.289103 0.166914i
\(601\) −9550.29 16541.6i −0.648194 1.12270i −0.983554 0.180615i \(-0.942191\pi\)
0.335360 0.942090i \(-0.391142\pi\)
\(602\) −32.8215 + 56.8485i −0.00222210 + 0.00384879i
\(603\) 5706.26i 0.385368i
\(604\) −12193.0 7039.63i −0.821401 0.474236i
\(605\) −12772.4 7374.16i −0.858302 0.495541i
\(606\) 563.330i 0.0377619i
\(607\) −8297.88 + 14372.4i −0.554861 + 0.961047i 0.443053 + 0.896495i \(0.353895\pi\)
−0.997914 + 0.0645522i \(0.979438\pi\)
\(608\) 3292.95 + 5703.56i 0.219650 + 0.380444i
\(609\) 1851.57 1069.00i 0.123201 0.0711300i
\(610\) −5178.97 −0.343755
\(611\) 0 0
\(612\) 7125.21 0.470620
\(613\) −14262.7 + 8234.58i −0.939748 + 0.542564i −0.889881 0.456192i \(-0.849213\pi\)
−0.0498668 + 0.998756i \(0.515880\pi\)
\(614\) −791.505 1370.93i −0.0520237 0.0901077i
\(615\) 7472.59 12942.9i 0.489958 0.848631i
\(616\) 845.205i 0.0552829i
\(617\) 8760.69 + 5057.99i 0.571624 + 0.330027i 0.757798 0.652489i \(-0.226275\pi\)
−0.186174 + 0.982517i \(0.559609\pi\)
\(618\) 811.895 + 468.748i 0.0528466 + 0.0305110i
\(619\) 18854.8i 1.22430i 0.790743 + 0.612148i \(0.209694\pi\)
−0.790743 + 0.612148i \(0.790306\pi\)
\(620\) 19198.2 33252.2i 1.24357 2.15393i
\(621\) 10465.8 + 18127.3i 0.676292 + 1.17137i
\(622\) −1264.83 + 730.247i −0.0815352 + 0.0470743i
\(623\) −3905.86 −0.251180
\(624\) 0 0
\(625\) −2730.82 −0.174773
\(626\) −135.983 + 78.5095i −0.00868204 + 0.00501258i
\(627\) 3338.26 + 5782.03i 0.212627 + 0.368281i
\(628\) 1550.50 2685.54i 0.0985215 0.170644i
\(629\) 291.769i 0.0184954i
\(630\) −493.618 284.991i −0.0312162 0.0180227i
\(631\) −16407.9 9473.12i −1.03517 0.597653i −0.116705 0.993167i \(-0.537233\pi\)
−0.918460 + 0.395514i \(0.870567\pi\)
\(632\) 1403.24i 0.0883194i
\(633\) 2514.17 4354.66i 0.157866 0.273432i
\(634\) −668.074 1157.14i −0.0418496 0.0724856i
\(635\) −40160.5 + 23186.7i −2.50979 + 1.44903i
\(636\) 1946.40 0.121352
\(637\) 0 0
\(638\) −1048.95 −0.0650912
\(639\) −1778.18 + 1026.63i −0.110084 + 0.0635571i
\(640\) 7521.75 + 13028.1i 0.464568 + 0.804655i
\(641\) −11793.5 + 20426.9i −0.726698 + 1.25868i 0.231573 + 0.972818i \(0.425613\pi\)
−0.958271 + 0.285861i \(0.907721\pi\)
\(642\) 923.263i 0.0567575i
\(643\) −23515.2 13576.5i −1.44222 0.832669i −0.444226 0.895915i \(-0.646521\pi\)
−0.997998 + 0.0632461i \(0.979855\pi\)
\(644\) 5167.79 + 2983.63i 0.316211 + 0.182564i
\(645\) 1806.35i 0.110272i
\(646\) −1204.35 + 2085.99i −0.0733506 + 0.127047i
\(647\) 3428.36 + 5938.09i 0.208319 + 0.360820i 0.951185 0.308620i \(-0.0998673\pi\)
−0.742866 + 0.669440i \(0.766534\pi\)
\(648\) −1118.75 + 645.910i −0.0678219 + 0.0391570i
\(649\) −6527.75 −0.394817
\(650\) 0 0
\(651\) 5533.83 0.333161
\(652\) 6365.44 3675.09i 0.382346 0.220748i
\(653\) 4036.95 + 6992.20i 0.241926 + 0.419029i 0.961263 0.275633i \(-0.0888874\pi\)
−0.719337 + 0.694662i \(0.755554\pi\)
\(654\) 142.169 246.245i 0.00850041 0.0147231i
\(655\) 37960.9i 2.26451i
\(656\) 11721.5 + 6767.39i 0.697632 + 0.402778i
\(657\) 1363.23 + 787.061i 0.0809508 + 0.0467370i
\(658\) 759.734i 0.0450114i
\(659\) −2652.86 + 4594.89i −0.156815 + 0.271611i −0.933718 0.358008i \(-0.883456\pi\)
0.776904 + 0.629620i \(0.216789\pi\)
\(660\) 5743.84 + 9948.63i 0.338756 + 0.586742i
\(661\) 22385.3 12924.2i 1.31723 0.760502i 0.333946 0.942592i \(-0.391620\pi\)
0.983282 + 0.182091i \(0.0582865\pi\)
\(662\) 3373.75 0.198073
\(663\) 0 0
\(664\) 2329.85 0.136168
\(665\) −6777.48 + 3912.98i −0.395217 + 0.228179i
\(666\) 12.6291 + 21.8743i 0.000734788 + 0.00127269i
\(667\) −7496.86 + 12984.9i −0.435202 + 0.753792i
\(668\) 28735.9i 1.66441i
\(669\) 3380.77 + 1951.89i 0.195379 + 0.112802i
\(670\) 2874.42 + 1659.55i 0.165744 + 0.0956923i
\(671\) 14873.6i 0.855722i
\(672\) −816.591 + 1414.38i −0.0468760 + 0.0811917i
\(673\) −7264.55 12582.6i −0.416089 0.720687i 0.579453 0.815005i \(-0.303266\pi\)
−0.995542 + 0.0943186i \(0.969933\pi\)
\(674\) −1789.26 + 1033.03i −0.102255 + 0.0590367i
\(675\) −28615.0 −1.63169
\(676\) 0 0
\(677\) 12058.1 0.684535 0.342267 0.939603i \(-0.388805\pi\)
0.342267 + 0.939603i \(0.388805\pi\)
\(678\) −1769.68 + 1021.73i −0.100242 + 0.0578749i
\(679\) −2064.89 3576.50i −0.116706 0.202140i
\(680\) −4195.46 + 7266.74i −0.236601 + 0.409804i
\(681\) 12764.4i 0.718255i
\(682\) −2351.26 1357.50i −0.132015 0.0762190i
\(683\) −26005.7 15014.4i −1.45693 0.841156i −0.458067 0.888918i \(-0.651458\pi\)
−0.998859 + 0.0477615i \(0.984791\pi\)
\(684\) 8469.13i 0.473429i
\(685\) 6125.74 10610.1i 0.341682 0.591811i
\(686\) 782.611 + 1355.52i 0.0435572 + 0.0754433i
\(687\) 7417.94 4282.75i 0.411954 0.237842i
\(688\) −1635.89 −0.0906505
\(689\) 0 0
\(690\) −4042.94 −0.223061
\(691\) −389.448 + 224.848i −0.0214404 + 0.0123786i −0.510682 0.859770i \(-0.670607\pi\)
0.489241 + 0.872148i \(0.337274\pi\)
\(692\) 5554.34 + 9620.40i 0.305122 + 0.528487i
\(693\) 818.471 1417.63i 0.0448646 0.0777077i
\(694\) 2307.10i 0.126191i
\(695\) 10480.5 + 6050.90i 0.572010 + 0.330250i
\(696\) −2359.68 1362.36i −0.128510 0.0741955i
\(697\) 15484.8i 0.841506i
\(698\) 11.0345 19.1123i 0.000598370 0.00103641i
\(699\) 6873.75 + 11905.7i 0.371944 + 0.644227i
\(700\) −7064.75 + 4078.84i −0.381461 + 0.220236i
\(701\) 26986.0 1.45399 0.726994 0.686644i \(-0.240917\pi\)
0.726994 + 0.686644i \(0.240917\pi\)
\(702\) 0 0
\(703\) 346.801 0.0186057
\(704\) −8537.67 + 4929.23i −0.457068 + 0.263888i
\(705\) −10453.1 18105.3i −0.558422 0.967215i
\(706\) −1985.65 + 3439.24i −0.105851 + 0.183339i
\(707\) 1896.37i 0.100877i
\(708\) −7253.01 4187.53i −0.385007 0.222284i
\(709\) 7879.85 + 4549.44i 0.417396 + 0.240984i 0.693963 0.720011i \(-0.255863\pi\)
−0.276566 + 0.960995i \(0.589197\pi\)
\(710\) 1194.30i 0.0631285i
\(711\) 1358.85 2353.60i 0.0716751 0.124145i
\(712\) 2488.85 + 4310.82i 0.131002 + 0.226903i
\(713\) −33609.1 + 19404.2i −1.76532 + 1.01921i
\(714\) −597.312 −0.0313079
\(715\) 0 0
\(716\) −9118.62 −0.475948
\(717\) 19287.9 11135.9i 1.00463 0.580025i
\(718\) 1573.56 + 2725.48i 0.0817892 + 0.141663i
\(719\) −3146.78 + 5450.38i −0.163220 + 0.282705i −0.936022 0.351942i \(-0.885521\pi\)
0.772802 + 0.634647i \(0.218855\pi\)
\(720\) 14204.5i 0.735235i
\(721\) −2733.13 1577.97i −0.141175 0.0815074i
\(722\) −124.963 72.1476i −0.00644135 0.00371892i
\(723\) 19064.3i 0.980648i
\(724\) −4426.86 + 7667.54i −0.227242 + 0.393594i
\(725\) −10248.8 17751.4i −0.525006 0.909337i
\(726\) −1158.72 + 668.987i −0.0592343 + 0.0341989i
\(727\) −18070.7 −0.921878 −0.460939 0.887432i \(-0.652487\pi\)
−0.460939 + 0.887432i \(0.652487\pi\)
\(728\) 0 0
\(729\) 17319.9 0.879944
\(730\) −792.934 + 457.800i −0.0402025 + 0.0232109i
\(731\) −935.790 1620.84i −0.0473481 0.0820093i
\(732\) 9541.37 16526.1i 0.481775 0.834459i
\(733\) 34771.5i 1.75214i −0.482188 0.876068i \(-0.660158\pi\)
0.482188 0.876068i \(-0.339842\pi\)
\(734\) −1520.40 877.803i −0.0764563 0.0441421i
\(735\) 17810.2 + 10282.7i 0.893794 + 0.516032i
\(736\) 11453.4i 0.573613i
\(737\) −4766.09 + 8255.10i −0.238210 + 0.412592i
\(738\) 670.256 + 1160.92i 0.0334315 + 0.0579051i
\(739\) 20465.4 11815.7i 1.01872 0.588158i 0.104986 0.994474i \(-0.466520\pi\)
0.913733 + 0.406316i \(0.133187\pi\)
\(740\) 596.710 0.0296425
\(741\) 0 0
\(742\) 161.324 0.00798167
\(743\) −28148.3 + 16251.4i −1.38985 + 0.802431i −0.993298 0.115581i \(-0.963127\pi\)
−0.396553 + 0.918012i \(0.629794\pi\)
\(744\) −3526.21 6107.58i −0.173760 0.300961i
\(745\) 17589.3 30465.5i 0.864995 1.49822i
\(746\) 4390.69i 0.215489i
\(747\) −3907.78 2256.16i −0.191403 0.110507i
\(748\) −10307.9 5951.25i −0.503868 0.290908i
\(749\) 3108.04i 0.151622i
\(750\) 965.435 1672.18i 0.0470036 0.0814126i
\(751\) 1010.43 + 1750.12i 0.0490960 + 0.0850368i 0.889529 0.456879i \(-0.151033\pi\)
−0.840433 + 0.541915i \(0.817699\pi\)
\(752\) 16396.7 9466.65i 0.795115 0.459060i
\(753\) 20710.5 1.00230
\(754\) 0 0
\(755\) −32111.6 −1.54790
\(756\) 5477.23 3162.28i 0.263499 0.152131i
\(757\) −6284.11 10884.4i −0.301717 0.522589i 0.674808 0.737993i \(-0.264226\pi\)
−0.976525 + 0.215404i \(0.930893\pi\)
\(758\) 1790.86 3101.87i 0.0858141 0.148634i
\(759\) 11611.0i 0.555273i
\(760\) 8637.36 + 4986.78i 0.412250 + 0.238013i
\(761\) 7538.59 + 4352.40i 0.359098 + 0.207325i 0.668685 0.743546i \(-0.266857\pi\)
−0.309587 + 0.950871i \(0.600191\pi\)
\(762\) 4207.01i 0.200005i
\(763\) −478.593 + 828.948i −0.0227081 + 0.0393315i
\(764\) −10470.7 18135.8i −0.495832 0.858807i
\(765\) 14073.8 8125.51i 0.665149 0.384024i
\(766\) −3205.16 −0.151184
\(767\) 0 0
\(768\) −11595.0 −0.544790
\(769\) 18979.7 10957.9i 0.890020 0.513853i 0.0160706 0.999871i \(-0.494884\pi\)
0.873949 + 0.486018i \(0.161551\pi\)
\(770\) 476.070 + 824.578i 0.0222810