Properties

Label 74.4.h.a.3.6
Level $74$
Weight $4$
Character 74.3
Analytic conductor $4.366$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,4,Mod(3,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([13]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.h (of order \(18\), degree \(6\), 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: \(4.36614134042\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 3.6
Character \(\chi\) \(=\) 74.3
Dual form 74.4.h.a.25.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.28558 - 1.53209i) q^{2} +(-6.88175 + 5.77448i) q^{3} +(-0.694593 - 3.93923i) q^{4} +(5.49624 - 15.1008i) q^{5} +17.9670i q^{6} +(27.7081 + 10.0849i) q^{7} +(-6.92820 - 4.00000i) q^{8} +(9.32545 - 52.8873i) q^{9} +O(q^{10})\) \(q+(1.28558 - 1.53209i) q^{2} +(-6.88175 + 5.77448i) q^{3} +(-0.694593 - 3.93923i) q^{4} +(5.49624 - 15.1008i) q^{5} +17.9670i q^{6} +(27.7081 + 10.0849i) q^{7} +(-6.92820 - 4.00000i) q^{8} +(9.32545 - 52.8873i) q^{9} +(-16.0699 - 27.8339i) q^{10} +(30.6869 - 53.1512i) q^{11} +(27.5270 + 23.0979i) q^{12} +(-31.6783 + 5.58574i) q^{13} +(51.0718 - 29.4863i) q^{14} +(49.3754 + 135.658i) q^{15} +(-15.0351 + 5.47232i) q^{16} +(56.5129 + 9.96475i) q^{17} +(-69.0394 - 82.2780i) q^{18} +(0.937113 + 1.11681i) q^{19} +(-63.3031 - 11.1621i) q^{20} +(-248.915 + 90.5978i) q^{21} +(-41.9821 - 115.345i) q^{22} +(-11.0732 + 6.39313i) q^{23} +(70.7761 - 12.4797i) q^{24} +(-102.070 - 85.6466i) q^{25} +(-32.1670 + 55.7148i) q^{26} +(119.944 + 207.749i) q^{27} +(20.4810 - 116.153i) q^{28} +(-126.928 - 73.2821i) q^{29} +(271.316 + 98.7508i) q^{30} +121.387i q^{31} +(-10.9446 + 30.0702i) q^{32} +(95.7410 + 542.974i) q^{33} +(87.9185 - 73.7723i) q^{34} +(304.580 - 362.985i) q^{35} -214.813 q^{36} +(135.208 + 179.922i) q^{37} +2.91578 q^{38} +(185.747 - 221.365i) q^{39} +(-98.4822 + 82.6364i) q^{40} +(-59.3952 - 336.847i) q^{41} +(-181.196 + 497.831i) q^{42} -157.053i q^{43} +(-230.690 - 83.9642i) q^{44} +(-747.385 - 431.503i) q^{45} +(-4.44062 + 25.1840i) q^{46} +(215.198 + 372.734i) q^{47} +(71.8679 - 124.479i) q^{48} +(403.279 + 338.391i) q^{49} +(-262.436 + 46.2746i) q^{50} +(-446.449 + 257.757i) q^{51} +(44.0070 + 120.908i) q^{52} +(-89.9779 + 32.7493i) q^{53} +(472.486 + 83.3120i) q^{54} +(-633.963 - 755.528i) q^{55} +(-151.628 - 180.703i) q^{56} +(-12.8980 - 2.27426i) q^{57} +(-275.451 + 100.256i) q^{58} +(76.4109 + 209.937i) q^{59} +(500.092 - 288.728i) q^{60} +(337.127 - 59.4445i) q^{61} +(185.976 + 156.052i) q^{62} +(791.754 - 1371.36i) q^{63} +(32.0000 + 55.4256i) q^{64} +(-89.7623 + 509.068i) q^{65} +(954.967 + 551.351i) q^{66} +(-163.376 - 59.4641i) q^{67} -229.539i q^{68} +(39.2863 - 107.938i) q^{69} +(-164.564 - 933.289i) q^{70} +(-352.073 + 295.425i) q^{71} +(-276.158 + 329.112i) q^{72} -923.821 q^{73} +(449.476 + 24.1532i) q^{74} +1196.98 q^{75} +(3.74845 - 4.46723i) q^{76} +(1386.30 - 1163.24i) q^{77} +(-100.359 - 569.163i) q^{78} +(-189.186 + 519.785i) q^{79} +257.119i q^{80} +(-662.523 - 241.139i) q^{81} +(-592.437 - 342.043i) q^{82} +(-237.350 + 1346.08i) q^{83} +(529.780 + 917.607i) q^{84} +(461.084 - 798.621i) q^{85} +(-240.619 - 201.903i) q^{86} +(1296.66 - 228.635i) q^{87} +(-425.210 + 245.495i) q^{88} +(564.652 + 1551.37i) q^{89} +(-1621.92 + 590.330i) q^{90} +(-934.076 - 164.703i) q^{91} +(32.8754 + 39.1794i) q^{92} +(-700.946 - 835.355i) q^{93} +(847.714 + 149.475i) q^{94} +(22.0153 - 8.01291i) q^{95} +(-98.3211 - 270.135i) q^{96} +(-617.193 + 356.337i) q^{97} +(1036.89 - 182.832i) q^{98} +(-2524.85 - 2118.60i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 12 q^{3} + 18 q^{5} + 150 q^{7} - 96 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 12 q^{3} + 18 q^{5} + 150 q^{7} - 96 q^{9} - 60 q^{10} + 66 q^{11} + 48 q^{12} + 204 q^{13} - 36 q^{14} - 198 q^{15} - 90 q^{17} + 18 q^{19} + 72 q^{20} - 18 q^{21} + 492 q^{25} - 192 q^{26} + 426 q^{27} + 192 q^{28} + 360 q^{29} + 144 q^{30} - 624 q^{33} - 24 q^{34} - 1494 q^{35} - 2592 q^{36} - 1482 q^{37} + 960 q^{38} - 2298 q^{39} - 672 q^{40} + 828 q^{41} - 96 q^{42} - 168 q^{44} + 3384 q^{45} + 1884 q^{46} + 444 q^{47} + 288 q^{48} - 126 q^{49} + 1512 q^{50} - 552 q^{52} + 834 q^{53} - 1080 q^{54} - 864 q^{55} + 3318 q^{57} - 1332 q^{58} - 2112 q^{59} + 2532 q^{61} + 2520 q^{62} + 2082 q^{63} + 1920 q^{64} - 540 q^{65} - 4002 q^{67} + 1596 q^{69} - 1512 q^{70} - 4302 q^{71} - 5460 q^{73} + 2328 q^{74} + 9144 q^{75} + 72 q^{76} - 4392 q^{77} + 732 q^{78} - 1854 q^{79} - 2856 q^{81} - 1320 q^{83} - 1008 q^{84} + 888 q^{85} + 1512 q^{86} + 3936 q^{87} + 2592 q^{88} + 3198 q^{89} - 8868 q^{90} - 2088 q^{91} + 2832 q^{92} + 15408 q^{93} + 5568 q^{94} + 2166 q^{95} - 540 q^{97} + 4056 q^{98} - 840 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28558 1.53209i 0.454519 0.541675i
\(3\) −6.88175 + 5.77448i −1.32439 + 1.11130i −0.339041 + 0.940771i \(0.610103\pi\)
−0.985353 + 0.170527i \(0.945453\pi\)
\(4\) −0.694593 3.93923i −0.0868241 0.492404i
\(5\) 5.49624 15.1008i 0.491598 1.35066i −0.407618 0.913152i \(-0.633641\pi\)
0.899217 0.437503i \(-0.144137\pi\)
\(6\) 17.9670i 1.22250i
\(7\) 27.7081 + 10.0849i 1.49610 + 0.544534i 0.955046 0.296456i \(-0.0958049\pi\)
0.541050 + 0.840991i \(0.318027\pi\)
\(8\) −6.92820 4.00000i −0.306186 0.176777i
\(9\) 9.32545 52.8873i 0.345387 1.95879i
\(10\) −16.0699 27.8339i −0.508176 0.880186i
\(11\) 30.6869 53.1512i 0.841131 1.45688i −0.0478080 0.998857i \(-0.515224\pi\)
0.888939 0.458025i \(-0.151443\pi\)
\(12\) 27.5270 + 23.0979i 0.662197 + 0.555649i
\(13\) −31.6783 + 5.58574i −0.675844 + 0.119170i −0.501027 0.865431i \(-0.667044\pi\)
−0.174817 + 0.984601i \(0.555933\pi\)
\(14\) 51.0718 29.4863i 0.974966 0.562897i
\(15\) 49.3754 + 135.658i 0.849912 + 2.33511i
\(16\) −15.0351 + 5.47232i −0.234923 + 0.0855050i
\(17\) 56.5129 + 9.96475i 0.806258 + 0.142165i 0.561562 0.827435i \(-0.310201\pi\)
0.244696 + 0.969600i \(0.421312\pi\)
\(18\) −69.0394 82.2780i −0.904042 1.07739i
\(19\) 0.937113 + 1.11681i 0.0113152 + 0.0134849i 0.771672 0.636020i \(-0.219421\pi\)
−0.760357 + 0.649505i \(0.774976\pi\)
\(20\) −63.3031 11.1621i −0.707751 0.124796i
\(21\) −248.915 + 90.5978i −2.58656 + 0.941431i
\(22\) −41.9821 115.345i −0.406846 1.11780i
\(23\) −11.0732 + 6.39313i −0.100388 + 0.0579592i −0.549354 0.835590i \(-0.685126\pi\)
0.448965 + 0.893549i \(0.351793\pi\)
\(24\) 70.7761 12.4797i 0.601963 0.106142i
\(25\) −102.070 85.6466i −0.816557 0.685173i
\(26\) −32.1670 + 55.7148i −0.242633 + 0.420253i
\(27\) 119.944 + 207.749i 0.854932 + 1.48079i
\(28\) 20.4810 116.153i 0.138234 0.783962i
\(29\) −126.928 73.2821i −0.812759 0.469247i 0.0351541 0.999382i \(-0.488808\pi\)
−0.847913 + 0.530135i \(0.822141\pi\)
\(30\) 271.316 + 98.7508i 1.65117 + 0.600978i
\(31\) 121.387i 0.703282i 0.936135 + 0.351641i \(0.114376\pi\)
−0.936135 + 0.351641i \(0.885624\pi\)
\(32\) −10.9446 + 30.0702i −0.0604612 + 0.166116i
\(33\) 95.7410 + 542.974i 0.505042 + 2.86423i
\(34\) 87.9185 73.7723i 0.443467 0.372113i
\(35\) 304.580 362.985i 1.47096 1.75302i
\(36\) −214.813 −0.994503
\(37\) 135.208 + 179.922i 0.600757 + 0.799432i
\(38\) 2.91578 0.0124474
\(39\) 185.747 221.365i 0.762651 0.908892i
\(40\) −98.4822 + 82.6364i −0.389285 + 0.326649i
\(41\) −59.3952 336.847i −0.226243 1.28309i −0.860294 0.509798i \(-0.829720\pi\)
0.634051 0.773291i \(-0.281391\pi\)
\(42\) −181.196 + 497.831i −0.665692 + 1.82897i
\(43\) 157.053i 0.556984i −0.960439 0.278492i \(-0.910165\pi\)
0.960439 0.278492i \(-0.0898346\pi\)
\(44\) −230.690 83.9642i −0.790405 0.287684i
\(45\) −747.385 431.503i −2.47586 1.42944i
\(46\) −4.44062 + 25.1840i −0.0142334 + 0.0807214i
\(47\) 215.198 + 372.734i 0.667869 + 1.15678i 0.978499 + 0.206252i \(0.0661267\pi\)
−0.310630 + 0.950531i \(0.600540\pi\)
\(48\) 71.8679 124.479i 0.216109 0.374312i
\(49\) 403.279 + 338.391i 1.17574 + 0.986564i
\(50\) −262.436 + 46.2746i −0.742282 + 0.130884i
\(51\) −446.449 + 257.757i −1.22579 + 0.707711i
\(52\) 44.0070 + 120.908i 0.117359 + 0.322441i
\(53\) −89.9779 + 32.7493i −0.233196 + 0.0848766i −0.455975 0.889992i \(-0.650709\pi\)
0.222779 + 0.974869i \(0.428487\pi\)
\(54\) 472.486 + 83.3120i 1.19069 + 0.209951i
\(55\) −633.963 755.528i −1.55425 1.85228i
\(56\) −151.628 180.703i −0.361823 0.431204i
\(57\) −12.8980 2.27426i −0.0299715 0.00528479i
\(58\) −275.451 + 100.256i −0.623594 + 0.226970i
\(59\) 76.4109 + 209.937i 0.168608 + 0.463246i 0.995003 0.0998444i \(-0.0318345\pi\)
−0.826395 + 0.563090i \(0.809612\pi\)
\(60\) 500.092 288.728i 1.07603 0.621244i
\(61\) 337.127 59.4445i 0.707617 0.124772i 0.191754 0.981443i \(-0.438582\pi\)
0.515863 + 0.856671i \(0.327471\pi\)
\(62\) 185.976 + 156.052i 0.380950 + 0.319655i
\(63\) 791.754 1371.36i 1.58336 2.74246i
\(64\) 32.0000 + 55.4256i 0.0625000 + 0.108253i
\(65\) −89.7623 + 509.068i −0.171287 + 0.971416i
\(66\) 954.967 + 551.351i 1.78104 + 1.02828i
\(67\) −163.376 59.4641i −0.297905 0.108428i 0.188744 0.982026i \(-0.439558\pi\)
−0.486648 + 0.873598i \(0.661781\pi\)
\(68\) 229.539i 0.409348i
\(69\) 39.2863 107.938i 0.0685436 0.188322i
\(70\) −164.564 933.289i −0.280988 1.59356i
\(71\) −352.073 + 295.425i −0.588499 + 0.493809i −0.887726 0.460373i \(-0.847716\pi\)
0.299227 + 0.954182i \(0.403271\pi\)
\(72\) −276.158 + 329.112i −0.452021 + 0.538697i
\(73\) −923.821 −1.48116 −0.740582 0.671965i \(-0.765450\pi\)
−0.740582 + 0.671965i \(0.765450\pi\)
\(74\) 449.476 + 24.1532i 0.706088 + 0.0379425i
\(75\) 1196.98 1.84288
\(76\) 3.74845 4.46723i 0.00565759 0.00674246i
\(77\) 1386.30 1163.24i 2.05174 1.72161i
\(78\) −100.359 569.163i −0.145685 0.826218i
\(79\) −189.186 + 519.785i −0.269432 + 0.740258i 0.729013 + 0.684500i \(0.239980\pi\)
−0.998444 + 0.0557574i \(0.982243\pi\)
\(80\) 257.119i 0.359334i
\(81\) −662.523 241.139i −0.908811 0.330780i
\(82\) −592.437 342.043i −0.797850 0.460639i
\(83\) −237.350 + 1346.08i −0.313887 + 1.78014i 0.264510 + 0.964383i \(0.414790\pi\)
−0.578396 + 0.815756i \(0.696321\pi\)
\(84\) 529.780 + 917.607i 0.688140 + 1.19189i
\(85\) 461.084 798.621i 0.588371 1.01909i
\(86\) −240.619 201.903i −0.301704 0.253160i
\(87\) 1296.66 228.635i 1.59789 0.281750i
\(88\) −425.210 + 245.495i −0.515086 + 0.297385i
\(89\) 564.652 + 1551.37i 0.672505 + 1.84769i 0.508095 + 0.861301i \(0.330350\pi\)
0.164411 + 0.986392i \(0.447428\pi\)
\(90\) −1621.92 + 590.330i −1.89961 + 0.691403i
\(91\) −934.076 164.703i −1.07602 0.189731i
\(92\) 32.8754 + 39.1794i 0.0372554 + 0.0443993i
\(93\) −700.946 835.355i −0.781556 0.931422i
\(94\) 847.714 + 149.475i 0.930160 + 0.164012i
\(95\) 22.0153 8.01291i 0.0237760 0.00865376i
\(96\) −98.3211 270.135i −0.104530 0.287193i
\(97\) −617.193 + 356.337i −0.646046 + 0.372995i −0.786940 0.617030i \(-0.788336\pi\)
0.140893 + 0.990025i \(0.455003\pi\)
\(98\) 1036.89 182.832i 1.06879 0.188457i
\(99\) −2524.85 2118.60i −2.56321 2.15079i
\(100\) −266.485 + 461.566i −0.266485 + 0.461566i
\(101\) −225.394 390.394i −0.222055 0.384611i 0.733377 0.679822i \(-0.237943\pi\)
−0.955432 + 0.295212i \(0.904610\pi\)
\(102\) −179.036 + 1015.37i −0.173797 + 0.985649i
\(103\) 605.775 + 349.744i 0.579502 + 0.334576i 0.760936 0.648827i \(-0.224740\pi\)
−0.181433 + 0.983403i \(0.558074\pi\)
\(104\) 241.816 + 88.0140i 0.228001 + 0.0829854i
\(105\) 4256.77i 3.95636i
\(106\) −65.4985 + 179.956i −0.0600168 + 0.164895i
\(107\) −168.414 955.124i −0.152161 0.862947i −0.961336 0.275379i \(-0.911197\pi\)
0.809175 0.587568i \(-0.199915\pi\)
\(108\) 735.058 616.787i 0.654916 0.549540i
\(109\) −281.806 + 335.843i −0.247634 + 0.295119i −0.875515 0.483190i \(-0.839478\pi\)
0.627881 + 0.778309i \(0.283922\pi\)
\(110\) −1972.54 −1.70977
\(111\) −1969.42 457.425i −1.68405 0.391143i
\(112\) −471.781 −0.398028
\(113\) 668.656 796.874i 0.556654 0.663394i −0.412181 0.911102i \(-0.635233\pi\)
0.968835 + 0.247708i \(0.0796773\pi\)
\(114\) −20.0657 + 16.8371i −0.0164853 + 0.0138328i
\(115\) 35.6803 + 202.353i 0.0289322 + 0.164083i
\(116\) −200.512 + 550.901i −0.160492 + 0.440948i
\(117\) 1727.47i 1.36499i
\(118\) 419.875 + 152.822i 0.327564 + 0.119224i
\(119\) 1465.37 + 846.032i 1.12883 + 0.651728i
\(120\) 200.548 1137.37i 0.152562 0.865224i
\(121\) −1217.87 2109.41i −0.915003 1.58483i
\(122\) 342.327 592.929i 0.254040 0.440010i
\(123\) 2353.86 + 1975.12i 1.72553 + 1.44789i
\(124\) 478.171 84.3145i 0.346299 0.0610618i
\(125\) −114.711 + 66.2282i −0.0820802 + 0.0473890i
\(126\) −1083.18 2976.02i −0.765854 2.10417i
\(127\) 1409.06 512.857i 0.984520 0.358336i 0.200924 0.979607i \(-0.435606\pi\)
0.783596 + 0.621271i \(0.213383\pi\)
\(128\) 126.055 + 22.2270i 0.0870455 + 0.0153485i
\(129\) 906.897 + 1080.80i 0.618976 + 0.737666i
\(130\) 664.541 + 791.969i 0.448339 + 0.534310i
\(131\) 1803.18 + 317.950i 1.20263 + 0.212056i 0.738836 0.673886i \(-0.235376\pi\)
0.463796 + 0.885942i \(0.346487\pi\)
\(132\) 2072.40 754.292i 1.36651 0.497369i
\(133\) 14.7027 + 40.3953i 0.00958560 + 0.0263362i
\(134\) −301.137 + 173.862i −0.194136 + 0.112085i
\(135\) 3796.41 669.409i 2.42032 0.426767i
\(136\) −351.674 295.089i −0.221734 0.186057i
\(137\) 108.382 187.722i 0.0675888 0.117067i −0.830251 0.557390i \(-0.811803\pi\)
0.897839 + 0.440323i \(0.145136\pi\)
\(138\) −114.865 198.953i −0.0708550 0.122724i
\(139\) 4.87395 27.6416i 0.00297413 0.0168671i −0.983285 0.182075i \(-0.941719\pi\)
0.986259 + 0.165208i \(0.0528296\pi\)
\(140\) −1641.44 947.686i −0.990907 0.572101i
\(141\) −3633.28 1322.41i −2.17005 0.789835i
\(142\) 919.198i 0.543221i
\(143\) −675.219 + 1855.15i −0.394858 + 1.08486i
\(144\) 149.207 + 846.196i 0.0863468 + 0.489697i
\(145\) −1804.25 + 1513.94i −1.03334 + 0.867077i
\(146\) −1187.64 + 1415.38i −0.673218 + 0.802310i
\(147\) −4729.30 −2.65351
\(148\) 614.840 657.586i 0.341483 0.365225i
\(149\) −2204.08 −1.21185 −0.605924 0.795523i \(-0.707196\pi\)
−0.605924 + 0.795523i \(0.707196\pi\)
\(150\) 1538.81 1833.88i 0.837623 0.998240i
\(151\) 217.489 182.495i 0.117212 0.0983525i −0.582298 0.812976i \(-0.697846\pi\)
0.699510 + 0.714623i \(0.253402\pi\)
\(152\) −2.02528 11.4859i −0.00108074 0.00612915i
\(153\) 1054.02 2895.89i 0.556942 1.53019i
\(154\) 3619.37i 1.89388i
\(155\) 1833.04 + 667.171i 0.949892 + 0.345732i
\(156\) −1001.03 577.943i −0.513759 0.296619i
\(157\) 325.307 1844.91i 0.165365 0.937834i −0.783322 0.621617i \(-0.786476\pi\)
0.948687 0.316217i \(-0.102413\pi\)
\(158\) 553.143 + 958.072i 0.278517 + 0.482406i
\(159\) 430.096 744.948i 0.214521 0.371561i
\(160\) 393.929 + 330.546i 0.194643 + 0.163325i
\(161\) −371.292 + 65.4689i −0.181751 + 0.0320476i
\(162\) −1221.17 + 705.042i −0.592247 + 0.341934i
\(163\) 57.5653 + 158.159i 0.0276617 + 0.0760000i 0.952755 0.303740i \(-0.0982355\pi\)
−0.925093 + 0.379740i \(0.876013\pi\)
\(164\) −1285.66 + 467.943i −0.612155 + 0.222806i
\(165\) 8725.56 + 1538.55i 4.11687 + 0.725916i
\(166\) 1757.18 + 2094.13i 0.821590 + 0.979132i
\(167\) 1422.05 + 1694.73i 0.658930 + 0.785283i 0.987232 0.159290i \(-0.0509206\pi\)
−0.328301 + 0.944573i \(0.606476\pi\)
\(168\) 2086.93 + 367.982i 0.958393 + 0.168990i
\(169\) −1092.19 + 397.525i −0.497129 + 0.180940i
\(170\) −630.800 1733.11i −0.284589 0.781902i
\(171\) 67.8039 39.1466i 0.0303222 0.0175065i
\(172\) −618.667 + 109.088i −0.274261 + 0.0483596i
\(173\) −1150.34 965.252i −0.505543 0.424201i 0.354014 0.935240i \(-0.384816\pi\)
−0.859558 + 0.511039i \(0.829261\pi\)
\(174\) 1316.66 2280.52i 0.573653 0.993597i
\(175\) −1964.42 3402.47i −0.848548 1.46973i
\(176\) −170.519 + 967.062i −0.0730304 + 0.414176i
\(177\) −1738.12 1003.50i −0.738108 0.426147i
\(178\) 3102.74 + 1129.30i 1.30652 + 0.475533i
\(179\) 1533.44i 0.640305i −0.947366 0.320152i \(-0.896266\pi\)
0.947366 0.320152i \(-0.103734\pi\)
\(180\) −1180.66 + 3243.84i −0.488896 + 1.34323i
\(181\) −515.613 2924.19i −0.211741 1.20085i −0.886472 0.462782i \(-0.846851\pi\)
0.674731 0.738064i \(-0.264260\pi\)
\(182\) −1453.16 + 1219.35i −0.591845 + 0.496617i
\(183\) −1976.76 + 2355.81i −0.798505 + 0.951622i
\(184\) 102.290 0.0409833
\(185\) 3460.10 1052.85i 1.37509 0.418416i
\(186\) −2180.96 −0.859761
\(187\) 2263.84 2697.94i 0.885287 1.05504i
\(188\) 1318.81 1106.61i 0.511617 0.429298i
\(189\) 1228.28 + 6965.94i 0.472722 + 2.68094i
\(190\) 16.0258 44.0306i 0.00611913 0.0168122i
\(191\) 2697.79i 1.02202i 0.859576 + 0.511008i \(0.170728\pi\)
−0.859576 + 0.511008i \(0.829272\pi\)
\(192\) −540.270 196.642i −0.203076 0.0739137i
\(193\) −1555.87 898.280i −0.580279 0.335024i 0.180966 0.983489i \(-0.442078\pi\)
−0.761244 + 0.648465i \(0.775411\pi\)
\(194\) −247.509 + 1403.69i −0.0915985 + 0.519481i
\(195\) −2321.88 4021.61i −0.852682 1.47689i
\(196\) 1052.89 1823.65i 0.383705 0.664597i
\(197\) 1841.95 + 1545.58i 0.666160 + 0.558974i 0.911926 0.410355i \(-0.134595\pi\)
−0.245766 + 0.969329i \(0.579040\pi\)
\(198\) −6491.78 + 1144.68i −2.33005 + 0.410851i
\(199\) −2773.99 + 1601.57i −0.988156 + 0.570512i −0.904723 0.426001i \(-0.859922\pi\)
−0.0834336 + 0.996513i \(0.526589\pi\)
\(200\) 364.573 + 1001.66i 0.128896 + 0.354139i
\(201\) 1467.69 534.196i 0.515039 0.187459i
\(202\) −887.880 156.557i −0.309262 0.0545313i
\(203\) −2777.90 3310.57i −0.960444 1.14461i
\(204\) 1325.47 + 1579.63i 0.454908 + 0.542138i
\(205\) −5413.11 954.477i −1.84423 0.325188i
\(206\) 1314.61 478.478i 0.444627 0.161831i
\(207\) 234.852 + 645.252i 0.0788569 + 0.216658i
\(208\) 445.719 257.336i 0.148582 0.0857838i
\(209\) 88.1168 15.5374i 0.0291635 0.00514231i
\(210\) 6521.74 + 5472.39i 2.14306 + 1.79824i
\(211\) −1547.35 + 2680.09i −0.504853 + 0.874431i 0.495131 + 0.868818i \(0.335120\pi\)
−0.999984 + 0.00561291i \(0.998213\pi\)
\(212\) 191.505 + 331.696i 0.0620406 + 0.107457i
\(213\) 716.959 4066.08i 0.230635 1.30800i
\(214\) −1679.84 969.859i −0.536597 0.309805i
\(215\) −2371.62 863.199i −0.752294 0.273812i
\(216\) 1919.10i 0.604529i
\(217\) −1224.18 + 3363.40i −0.382961 + 1.05218i
\(218\) 152.259 + 863.503i 0.0473040 + 0.268274i
\(219\) 6357.51 5334.58i 1.96165 1.64602i
\(220\) −2535.85 + 3022.11i −0.777124 + 0.926140i
\(221\) −1845.89 −0.561847
\(222\) −3232.65 + 2429.27i −0.977304 + 0.734424i
\(223\) 920.879 0.276532 0.138266 0.990395i \(-0.455847\pi\)
0.138266 + 0.990395i \(0.455847\pi\)
\(224\) −606.510 + 722.811i −0.180911 + 0.215602i
\(225\) −5481.46 + 4599.49i −1.62414 + 1.36281i
\(226\) −361.273 2048.88i −0.106334 0.603051i
\(227\) 582.500 1600.40i 0.170317 0.467941i −0.824941 0.565219i \(-0.808792\pi\)
0.995257 + 0.0972784i \(0.0310137\pi\)
\(228\) 52.3877i 0.0152169i
\(229\) 4786.97 + 1742.31i 1.38136 + 0.502775i 0.922591 0.385780i \(-0.126068\pi\)
0.458771 + 0.888555i \(0.348290\pi\)
\(230\) 355.892 + 205.474i 0.102030 + 0.0589069i
\(231\) −2823.05 + 16010.3i −0.804083 + 4.56018i
\(232\) 586.257 + 1015.43i 0.165904 + 0.287354i
\(233\) 1525.93 2642.99i 0.429043 0.743124i −0.567746 0.823204i \(-0.692184\pi\)
0.996788 + 0.0800801i \(0.0255176\pi\)
\(234\) 2646.63 + 2220.79i 0.739384 + 0.620417i
\(235\) 6811.35 1201.03i 1.89074 0.333388i
\(236\) 773.917 446.821i 0.213465 0.123244i
\(237\) −1699.55 4669.48i −0.465814 1.27981i
\(238\) 3180.04 1157.44i 0.866098 0.315234i
\(239\) −4598.06 810.762i −1.24445 0.219430i −0.487629 0.873051i \(-0.662138\pi\)
−0.756822 + 0.653621i \(0.773249\pi\)
\(240\) −1484.73 1769.43i −0.399328 0.475900i
\(241\) 3130.77 + 3731.10i 0.836806 + 0.997267i 0.999943 + 0.0106637i \(0.00339441\pi\)
−0.163137 + 0.986603i \(0.552161\pi\)
\(242\) −4797.47 845.923i −1.27435 0.224702i
\(243\) −134.583 + 48.9840i −0.0355287 + 0.0129314i
\(244\) −468.332 1286.73i −0.122876 0.337600i
\(245\) 7326.50 4229.95i 1.91050 1.10303i
\(246\) 6052.13 1067.15i 1.56858 0.276582i
\(247\) −35.9243 30.1441i −0.00925429 0.00776527i
\(248\) 485.548 840.993i 0.124324 0.215335i
\(249\) −6139.53 10634.0i −1.56256 2.70643i
\(250\) −46.0016 + 260.888i −0.0116376 + 0.0660000i
\(251\) −257.010 148.385i −0.0646307 0.0373145i 0.467336 0.884080i \(-0.345214\pi\)
−0.531967 + 0.846765i \(0.678547\pi\)
\(252\) −5952.04 2166.37i −1.48787 0.541541i
\(253\) 784.741i 0.195005i
\(254\) 1025.71 2818.12i 0.253382 0.696161i
\(255\) 1438.55 + 8158.43i 0.353277 + 2.00353i
\(256\) 196.107 164.554i 0.0478778 0.0401742i
\(257\) 3319.74 3956.31i 0.805758 0.960265i −0.194027 0.980996i \(-0.562155\pi\)
0.999785 + 0.0207315i \(0.00659952\pi\)
\(258\) 2821.76 0.680912
\(259\) 1931.85 + 6348.85i 0.463471 + 1.52316i
\(260\) 2067.68 0.493201
\(261\) −5059.36 + 6029.51i −1.19987 + 1.42995i
\(262\) 2805.25 2353.89i 0.661485 0.555052i
\(263\) −309.753 1756.70i −0.0726244 0.411873i −0.999347 0.0361275i \(-0.988498\pi\)
0.926723 0.375746i \(-0.122613\pi\)
\(264\) 1508.58 4144.80i 0.351693 0.966269i
\(265\) 1538.73i 0.356693i
\(266\) 80.7906 + 29.4054i 0.0186225 + 0.00677804i
\(267\) −12844.1 7415.57i −2.94400 1.69972i
\(268\) −120.763 + 684.881i −0.0275253 + 0.156104i
\(269\) −2275.15 3940.68i −0.515682 0.893188i −0.999834 0.0182041i \(-0.994205\pi\)
0.484152 0.874984i \(-0.339128\pi\)
\(270\) 3854.97 6677.01i 0.868912 1.50500i
\(271\) −1834.53 1539.35i −0.411216 0.345051i 0.413594 0.910461i \(-0.364273\pi\)
−0.824810 + 0.565410i \(0.808718\pi\)
\(272\) −904.206 + 159.436i −0.201565 + 0.0355413i
\(273\) 7379.16 4260.36i 1.63592 0.944500i
\(274\) −148.275 407.382i −0.0326920 0.0898205i
\(275\) −7684.42 + 2796.90i −1.68505 + 0.613307i
\(276\) −452.481 79.7846i −0.0986818 0.0174003i
\(277\) 4395.04 + 5237.80i 0.953329 + 1.13613i 0.990595 + 0.136828i \(0.0436907\pi\)
−0.0372658 + 0.999305i \(0.511865\pi\)
\(278\) −36.0835 43.0026i −0.00778469 0.00927744i
\(279\) 6419.82 + 1131.99i 1.37758 + 0.242904i
\(280\) −3562.13 + 1296.51i −0.760280 + 0.276719i
\(281\) 1855.31 + 5097.43i 0.393874 + 1.08216i 0.965217 + 0.261449i \(0.0842003\pi\)
−0.571343 + 0.820711i \(0.693577\pi\)
\(282\) −6696.90 + 3866.46i −1.41417 + 0.816469i
\(283\) 1434.75 252.986i 0.301368 0.0531393i −0.0209194 0.999781i \(-0.506659\pi\)
0.322287 + 0.946642i \(0.395548\pi\)
\(284\) 1408.29 + 1181.70i 0.294249 + 0.246905i
\(285\) −105.233 + 182.270i −0.0218719 + 0.0378832i
\(286\) 1974.21 + 3419.43i 0.408173 + 0.706976i
\(287\) 1751.35 9932.38i 0.360205 2.04282i
\(288\) 1488.26 + 859.250i 0.304503 + 0.175805i
\(289\) −1522.30 554.072i −0.309851 0.112777i
\(290\) 4710.55i 0.953839i
\(291\) 2189.72 6016.19i 0.441111 1.21194i
\(292\) 641.679 + 3639.14i 0.128601 + 0.729331i
\(293\) −3699.11 + 3103.92i −0.737557 + 0.618884i −0.932180 0.361994i \(-0.882096\pi\)
0.194623 + 0.980878i \(0.437652\pi\)
\(294\) −6079.87 + 7245.71i −1.20607 + 1.43734i
\(295\) 3590.19 0.708573
\(296\) −217.058 1787.37i −0.0426224 0.350975i
\(297\) 14722.8 2.87644
\(298\) −2833.51 + 3376.85i −0.550808 + 0.656428i
\(299\) 315.071 264.376i 0.0609398 0.0511346i
\(300\) −831.416 4715.19i −0.160006 0.907439i
\(301\) 1583.86 4351.63i 0.303297 0.833302i
\(302\) 567.823i 0.108194i
\(303\) 3805.43 + 1385.06i 0.721506 + 0.262607i
\(304\) −20.2011 11.6631i −0.00381123 0.00220041i
\(305\) 955.269 5417.60i 0.179340 1.01709i
\(306\) −3081.74 5337.73i −0.575723 0.997181i
\(307\) −3973.48 + 6882.27i −0.738692 + 1.27945i 0.214392 + 0.976748i \(0.431223\pi\)
−0.953084 + 0.302705i \(0.902110\pi\)
\(308\) −5545.20 4652.98i −1.02587 0.860805i
\(309\) −6188.38 + 1091.18i −1.13930 + 0.200890i
\(310\) 3378.67 1950.68i 0.619019 0.357391i
\(311\) 1270.32 + 3490.17i 0.231618 + 0.636365i 0.999993 0.00363418i \(-0.00115680\pi\)
−0.768375 + 0.639999i \(0.778935\pi\)
\(312\) −2172.36 + 790.673i −0.394184 + 0.143471i
\(313\) 4596.79 + 810.538i 0.830115 + 0.146372i 0.572530 0.819884i \(-0.305962\pi\)
0.257585 + 0.966256i \(0.417073\pi\)
\(314\) −2408.36 2870.17i −0.432839 0.515838i
\(315\) −16356.9 19493.4i −2.92574 3.48676i
\(316\) 2178.96 + 384.209i 0.387899 + 0.0683970i
\(317\) 1202.54 437.687i 0.213064 0.0775488i −0.233283 0.972409i \(-0.574947\pi\)
0.446347 + 0.894860i \(0.352725\pi\)
\(318\) −588.406 1616.63i −0.103761 0.285082i
\(319\) −7790.07 + 4497.60i −1.36727 + 0.789396i
\(320\) 1012.85 178.593i 0.176938 0.0311989i
\(321\) 6674.33 + 5600.43i 1.16051 + 0.973786i
\(322\) −377.020 + 653.018i −0.0652500 + 0.113016i
\(323\) 41.8303 + 72.4521i 0.00720588 + 0.0124809i
\(324\) −489.717 + 2777.32i −0.0839707 + 0.476221i
\(325\) 3711.79 + 2143.00i 0.633517 + 0.365761i
\(326\) 316.319 + 115.131i 0.0537401 + 0.0195598i
\(327\) 3938.47i 0.666049i
\(328\) −935.886 + 2571.33i −0.157548 + 0.432859i
\(329\) 2203.73 + 12498.0i 0.369288 + 2.09434i
\(330\) 13574.6 11390.4i 2.26441 1.90006i
\(331\) −4956.63 + 5907.09i −0.823085 + 0.980915i −0.999995 0.00331213i \(-0.998946\pi\)
0.176909 + 0.984227i \(0.443390\pi\)
\(332\) 5467.38 0.903800
\(333\) 10776.5 5472.91i 1.77341 0.900641i
\(334\) 4424.63 0.724865
\(335\) −1795.91 + 2140.28i −0.292899 + 0.349063i
\(336\) 3246.68 2724.29i 0.527146 0.442328i
\(337\) −201.972 1145.44i −0.0326472 0.185151i 0.964123 0.265455i \(-0.0855222\pi\)
−0.996770 + 0.0803035i \(0.974411\pi\)
\(338\) −795.051 + 2184.38i −0.127944 + 0.351523i
\(339\) 9345.03i 1.49720i
\(340\) −3466.22 1261.60i −0.552888 0.201235i
\(341\) 6451.86 + 3724.99i 1.02460 + 0.591552i
\(342\) 27.1909 154.208i 0.00429918 0.0243818i
\(343\) 2704.54 + 4684.40i 0.425747 + 0.737416i
\(344\) −628.211 + 1088.09i −0.0984618 + 0.170541i
\(345\) −1414.02 1186.51i −0.220662 0.185158i
\(346\) −2957.71 + 521.523i −0.459558 + 0.0810326i
\(347\) −8077.43 + 4663.50i −1.24962 + 0.721470i −0.971034 0.238941i \(-0.923200\pi\)
−0.278588 + 0.960411i \(0.589866\pi\)
\(348\) −1801.30 4949.02i −0.277470 0.762343i
\(349\) 5958.35 2168.66i 0.913877 0.332624i 0.158077 0.987427i \(-0.449471\pi\)
0.755800 + 0.654803i \(0.227248\pi\)
\(350\) −7738.29 1364.47i −1.18180 0.208383i
\(351\) −4960.04 5911.14i −0.754266 0.898899i
\(352\) 1262.41 + 1504.48i 0.191155 + 0.227810i
\(353\) 3001.25 + 529.201i 0.452522 + 0.0797919i 0.395264 0.918568i \(-0.370653\pi\)
0.0572581 + 0.998359i \(0.481764\pi\)
\(354\) −3771.94 + 1372.87i −0.566318 + 0.206123i
\(355\) 2526.07 + 6940.31i 0.377661 + 1.03762i
\(356\) 5718.99 3301.86i 0.851422 0.491569i
\(357\) −14969.7 + 2639.56i −2.21927 + 0.391318i
\(358\) −2349.36 1971.35i −0.346837 0.291031i
\(359\) 4549.78 7880.45i 0.668881 1.15854i −0.309336 0.950953i \(-0.600107\pi\)
0.978217 0.207583i \(-0.0665597\pi\)
\(360\) 3452.02 + 5979.08i 0.505382 + 0.875347i
\(361\) 1190.68 6752.70i 0.173594 0.984503i
\(362\) −5142.97 2969.30i −0.746709 0.431112i
\(363\) 20561.8 + 7483.89i 2.97305 + 1.08210i
\(364\) 3793.94i 0.546309i
\(365\) −5077.54 + 13950.4i −0.728138 + 2.00054i
\(366\) 1068.04 + 6057.15i 0.152534 + 0.865061i
\(367\) −10171.1 + 8534.54i −1.44666 + 1.21390i −0.511695 + 0.859167i \(0.670982\pi\)
−0.934970 + 0.354728i \(0.884573\pi\)
\(368\) 131.502 156.718i 0.0186277 0.0221996i
\(369\) −18368.8 −2.59144
\(370\) 2835.16 6654.69i 0.398359 0.935029i
\(371\) −2823.39 −0.395102
\(372\) −2803.78 + 3341.42i −0.390778 + 0.465711i
\(373\) 964.138 809.008i 0.133837 0.112303i −0.573412 0.819267i \(-0.694380\pi\)
0.707249 + 0.706965i \(0.249936\pi\)
\(374\) −1223.15 6936.82i −0.169111 0.959076i
\(375\) 406.977 1118.16i 0.0560432 0.153977i
\(376\) 3443.17i 0.472255i
\(377\) 4430.21 + 1612.46i 0.605218 + 0.220281i
\(378\) 12251.5 + 7073.40i 1.66706 + 0.962477i
\(379\) 1296.81 7354.55i 0.175758 0.996776i −0.761506 0.648157i \(-0.775540\pi\)
0.937265 0.348618i \(-0.113349\pi\)
\(380\) −46.8563 81.1576i −0.00632547 0.0109560i
\(381\) −6735.34 + 11665.9i −0.905674 + 1.56867i
\(382\) 4133.25 + 3468.21i 0.553601 + 0.464526i
\(383\) 3515.21 619.826i 0.468979 0.0826936i 0.0658354 0.997830i \(-0.479029\pi\)
0.403143 + 0.915137i \(0.367918\pi\)
\(384\) −995.831 + 574.944i −0.132339 + 0.0764062i
\(385\) −9946.47 27327.7i −1.31667 3.61753i
\(386\) −3376.43 + 1228.92i −0.445222 + 0.162048i
\(387\) −8306.09 1464.59i −1.09101 0.192375i
\(388\) 1832.39 + 2183.76i 0.239757 + 0.285731i
\(389\) −7324.74 8729.29i −0.954702 1.13777i −0.990376 0.138406i \(-0.955802\pi\)
0.0356733 0.999364i \(-0.488642\pi\)
\(390\) −9146.41 1612.76i −1.18755 0.209398i
\(391\) −689.486 + 250.953i −0.0891786 + 0.0324583i
\(392\) −1440.43 3957.56i −0.185594 0.509916i
\(393\) −14245.0 + 8224.38i −1.82842 + 1.05564i
\(394\) 4735.93 835.072i 0.605565 0.106777i
\(395\) 6809.35 + 5713.72i 0.867381 + 0.727819i
\(396\) −6591.93 + 11417.6i −0.836507 + 1.44887i
\(397\) 198.933 + 344.562i 0.0251490 + 0.0435594i 0.878326 0.478062i \(-0.158661\pi\)
−0.853177 + 0.521622i \(0.825327\pi\)
\(398\) −1112.44 + 6308.93i −0.140104 + 0.794569i
\(399\) −334.442 193.090i −0.0419625 0.0242271i
\(400\) 2003.31 + 729.146i 0.250414 + 0.0911432i
\(401\) 4643.24i 0.578235i −0.957294 0.289118i \(-0.906638\pi\)
0.957294 0.289118i \(-0.0933618\pi\)
\(402\) 1068.39 2935.38i 0.132554 0.364188i
\(403\) −678.035 3845.33i −0.0838098 0.475309i
\(404\) −1381.30 + 1159.04i −0.170104 + 0.142734i
\(405\) −7282.77 + 8679.26i −0.893540 + 1.06488i
\(406\) −8643.28 −1.05655
\(407\) 13712.2 1665.21i 1.66999 0.202804i
\(408\) 4124.12 0.500427
\(409\) 1702.58 2029.06i 0.205837 0.245307i −0.653243 0.757148i \(-0.726592\pi\)
0.859080 + 0.511841i \(0.171036\pi\)
\(410\) −8421.30 + 7066.31i −1.01439 + 0.851171i
\(411\) 338.143 + 1917.71i 0.0405824 + 0.230154i
\(412\) 956.956 2629.22i 0.114432 0.314398i
\(413\) 6587.56i 0.784873i
\(414\) 1290.50 + 469.705i 0.153200 + 0.0557602i
\(415\) 19022.3 + 10982.6i 2.25005 + 1.29907i
\(416\) 178.744 1013.70i 0.0210664 0.119473i
\(417\) 126.074 + 218.367i 0.0148055 + 0.0256438i
\(418\) 89.4761 154.977i 0.0104699 0.0181344i
\(419\) −11887.0 9974.40i −1.38597 1.16296i −0.966945 0.254986i \(-0.917929\pi\)
−0.419020 0.907977i \(-0.637626\pi\)
\(420\) 16768.4 2956.72i 1.94813 0.343507i
\(421\) −8970.12 + 5178.90i −1.03842 + 0.599535i −0.919387 0.393355i \(-0.871314\pi\)
−0.119038 + 0.992890i \(0.537981\pi\)
\(422\) 2116.90 + 5816.13i 0.244192 + 0.670912i
\(423\) 21719.7 7905.32i 2.49657 0.908676i
\(424\) 754.382 + 133.018i 0.0864057 + 0.0152357i
\(425\) −4914.81 5857.24i −0.560948 0.668512i
\(426\) −5307.89 6325.70i −0.603681 0.719439i
\(427\) 9940.63 + 1752.80i 1.12661 + 0.198651i
\(428\) −3645.48 + 1326.85i −0.411707 + 0.149849i
\(429\) −6065.82 16665.7i −0.682659 1.87559i
\(430\) −4371.39 + 2523.83i −0.490250 + 0.283046i
\(431\) 11385.1 2007.50i 1.27239 0.224357i 0.503645 0.863910i \(-0.331992\pi\)
0.768747 + 0.639553i \(0.220881\pi\)
\(432\) −2940.23 2467.15i −0.327458 0.274770i
\(433\) 1540.64 2668.47i 0.170990 0.296163i −0.767776 0.640718i \(-0.778637\pi\)
0.938766 + 0.344555i \(0.111970\pi\)
\(434\) 3579.25 + 6199.45i 0.395875 + 0.685675i
\(435\) 3674.15 20837.2i 0.404971 2.29670i
\(436\) 1518.70 + 876.824i 0.166818 + 0.0963125i
\(437\) −17.5168 6.37558i −0.00191748 0.000697907i
\(438\) 16598.3i 1.81072i
\(439\) 4966.56 13645.5i 0.539956 1.48352i −0.306924 0.951734i \(-0.599300\pi\)
0.846880 0.531784i \(-0.178478\pi\)
\(440\) 1370.11 + 7770.30i 0.148449 + 0.841897i
\(441\) 21657.4 18172.7i 2.33855 1.96228i
\(442\) −2373.03 + 2828.07i −0.255370 + 0.304338i
\(443\) −4198.05 −0.450237 −0.225119 0.974331i \(-0.572277\pi\)
−0.225119 + 0.974331i \(0.572277\pi\)
\(444\) −433.959 + 8075.73i −0.0463847 + 0.863192i
\(445\) 26530.3 2.82620
\(446\) 1183.86 1410.87i 0.125689 0.149790i
\(447\) 15167.9 12727.4i 1.60496 1.34672i
\(448\) 327.696 + 1858.46i 0.0345584 + 0.195991i
\(449\) 1053.22 2893.69i 0.110700 0.304146i −0.871956 0.489585i \(-0.837148\pi\)
0.982656 + 0.185439i \(0.0593706\pi\)
\(450\) 14311.1i 1.49918i
\(451\) −19726.5 7179.86i −2.05961 0.749637i
\(452\) −3603.51 2080.49i −0.374989 0.216500i
\(453\) −442.893 + 2511.77i −0.0459358 + 0.260515i
\(454\) −1703.12 2949.88i −0.176060 0.304945i
\(455\) −7621.05 + 13200.0i −0.785231 + 1.36006i
\(456\) 80.2627 + 67.3484i 0.00824264 + 0.00691640i
\(457\) −4641.33 + 818.392i −0.475081 + 0.0837697i −0.406062 0.913846i \(-0.633098\pi\)
−0.0690197 + 0.997615i \(0.521987\pi\)
\(458\) 8823.39 5094.19i 0.900196 0.519729i
\(459\) 4708.20 + 12935.7i 0.478780 + 1.31544i
\(460\) 772.331 281.106i 0.0782829 0.0284926i
\(461\) 2575.54 + 454.138i 0.260206 + 0.0458814i 0.302229 0.953235i \(-0.402269\pi\)
−0.0420231 + 0.999117i \(0.513380\pi\)
\(462\) 20900.0 + 24907.6i 2.10467 + 2.50824i
\(463\) 4109.48 + 4897.49i 0.412492 + 0.491589i 0.931787 0.363006i \(-0.118250\pi\)
−0.519295 + 0.854595i \(0.673805\pi\)
\(464\) 2309.40 + 407.210i 0.231059 + 0.0407419i
\(465\) −16467.1 + 5993.53i −1.64224 + 0.597727i
\(466\) −2087.59 5735.62i −0.207524 0.570166i
\(467\) −8209.20 + 4739.58i −0.813440 + 0.469640i −0.848149 0.529758i \(-0.822283\pi\)
0.0347092 + 0.999397i \(0.488949\pi\)
\(468\) 6804.89 1199.89i 0.672129 0.118514i
\(469\) −3927.16 3295.28i −0.386651 0.324439i
\(470\) 6916.43 11979.6i 0.678790 1.17570i
\(471\) 8414.71 + 14574.7i 0.823204 + 1.42583i
\(472\) 310.359 1760.13i 0.0302657 0.171645i
\(473\) −8347.54 4819.46i −0.811460 0.468497i
\(474\) −9338.97 3399.11i −0.904964 0.329380i
\(475\) 194.253i 0.0187641i
\(476\) 2314.88 6360.08i 0.222904 0.612424i
\(477\) 892.935 + 5064.09i 0.0857121 + 0.486098i
\(478\) −7153.31 + 6002.34i −0.684487 + 0.574353i
\(479\) 10520.8 12538.2i 1.00357 1.19600i 0.0230171 0.999735i \(-0.492673\pi\)
0.980550 0.196270i \(-0.0628828\pi\)
\(480\) −4619.65 −0.439286
\(481\) −5288.14 4944.38i −0.501286 0.468700i
\(482\) 9741.21 0.920540
\(483\) 2177.09 2594.56i 0.205096 0.244424i
\(484\) −7463.54 + 6262.65i −0.700933 + 0.588153i
\(485\) 1988.73 + 11278.6i 0.186192 + 1.05595i
\(486\) −97.9681 + 269.165i −0.00914387 + 0.0251226i
\(487\) 3726.47i 0.346740i 0.984857 + 0.173370i \(0.0554657\pi\)
−0.984857 + 0.173370i \(0.944534\pi\)
\(488\) −2573.46 936.663i −0.238719 0.0868868i
\(489\) −1309.44 756.005i −0.121094 0.0699135i
\(490\) 2938.10 16662.8i 0.270877 1.53622i
\(491\) −7105.93 12307.8i −0.653129 1.13125i −0.982359 0.187003i \(-0.940123\pi\)
0.329230 0.944250i \(-0.393211\pi\)
\(492\) 6145.49 10644.3i 0.563130 0.975370i
\(493\) −6442.85 5406.19i −0.588583 0.493880i
\(494\) −92.3668 + 16.2868i −0.00841251 + 0.00148335i
\(495\) −45869.8 + 26482.9i −4.16504 + 2.40469i
\(496\) −664.268 1825.06i −0.0601341 0.165217i
\(497\) −12734.6 + 4635.02i −1.14935 + 0.418328i
\(498\) −24185.0 4264.47i −2.17622 0.383726i
\(499\) 9762.78 + 11634.8i 0.875836 + 1.04378i 0.998680 + 0.0513549i \(0.0163540\pi\)
−0.122844 + 0.992426i \(0.539202\pi\)
\(500\) 340.565 + 405.870i 0.0304611 + 0.0363021i
\(501\) −19572.4 3451.14i −1.74537 0.307755i
\(502\) −557.743 + 203.002i −0.0495883 + 0.0180486i
\(503\) −4067.09 11174.2i −0.360522 0.990525i −0.978845 0.204602i \(-0.934410\pi\)
0.618324 0.785924i \(-0.287812\pi\)
\(504\) −10970.9 + 6334.03i −0.969606 + 0.559802i
\(505\) −7134.08 + 1257.93i −0.628639 + 0.110846i
\(506\) 1202.29 + 1008.84i 0.105629 + 0.0886336i
\(507\) 5220.69 9042.51i 0.457316 0.792094i
\(508\) −2998.98 5194.39i −0.261926 0.453669i
\(509\) −3245.43 + 18405.7i −0.282615 + 1.60279i 0.431067 + 0.902320i \(0.358137\pi\)
−0.713682 + 0.700470i \(0.752974\pi\)
\(510\) 14348.8 + 8284.29i 1.24583 + 0.719283i
\(511\) −25597.3 9316.66i −2.21596 0.806545i
\(512\) 512.000i 0.0441942i
\(513\) −119.614 + 328.638i −0.0102946 + 0.0282841i
\(514\) −1793.65 10172.3i −0.153919 0.872918i
\(515\) 8610.89 7225.40i 0.736779 0.618231i
\(516\) 3627.59 4323.19i 0.309488 0.368833i
\(517\) 26415.0 2.24706
\(518\) 12210.5 + 5202.17i 1.03571 + 0.441255i
\(519\) 13490.2 1.14095
\(520\) 2658.16 3167.87i 0.224169 0.267155i
\(521\) −979.426 + 821.836i −0.0823598 + 0.0691080i −0.683038 0.730383i \(-0.739342\pi\)
0.600678 + 0.799491i \(0.294897\pi\)
\(522\) 2733.56 + 15502.8i 0.229204 + 1.29988i
\(523\) −3900.58 + 10716.8i −0.326120 + 0.896006i 0.662964 + 0.748651i \(0.269298\pi\)
−0.989084 + 0.147355i \(0.952924\pi\)
\(524\) 7324.00i 0.610592i
\(525\) 33166.1 + 12071.5i 2.75712 + 1.00351i
\(526\) −3089.63 1783.80i −0.256111 0.147866i
\(527\) −1209.59 + 6859.93i −0.0999821 + 0.567027i
\(528\) −4410.81 7639.74i −0.363552 0.629691i
\(529\) −6001.76 + 10395.3i −0.493281 + 0.854389i
\(530\) 2357.48 + 1978.16i 0.193212 + 0.162124i
\(531\) 11815.6 2083.41i 0.965635 0.170268i
\(532\) 148.914 85.9756i 0.0121358 0.00700661i
\(533\) 3763.08 + 10339.0i 0.305810 + 0.840207i
\(534\) −27873.4 + 10145.1i −2.25880 + 0.822137i
\(535\) −15348.8 2706.40i −1.24035 0.218707i
\(536\) 894.048 + 1065.49i 0.0720467 + 0.0858619i
\(537\) 8854.81 + 10552.7i 0.711570 + 0.848016i
\(538\) −8962.36 1580.31i −0.718206 0.126639i
\(539\) 30361.3 11050.6i 2.42626 0.883086i
\(540\) −5273.91 14490.0i −0.420284 1.15472i
\(541\) 3747.88 2163.84i 0.297844 0.171960i −0.343630 0.939105i \(-0.611657\pi\)
0.641474 + 0.767145i \(0.278323\pi\)
\(542\) −4716.84 + 831.706i −0.373811 + 0.0659130i
\(543\) 20434.0 + 17146.1i 1.61493 + 1.35508i
\(544\) −918.155 + 1590.29i −0.0723632 + 0.125337i
\(545\) 3522.62 + 6101.36i 0.276867 + 0.479548i
\(546\) 2959.21 16782.5i 0.231946 1.31543i
\(547\) −8198.85 4733.61i −0.640873 0.370008i 0.144078 0.989566i \(-0.453978\pi\)
−0.784951 + 0.619558i \(0.787312\pi\)
\(548\) −814.763 296.550i −0.0635127 0.0231167i
\(549\) 18384.1i 1.42917i
\(550\) −5593.80 + 15368.8i −0.433674 + 1.19151i
\(551\) −37.1042 210.428i −0.00286877 0.0162696i
\(552\) −703.936 + 590.672i −0.0542781 + 0.0455447i
\(553\) −10484.0 + 12494.3i −0.806192 + 0.960782i
\(554\) 13674.9 1.04872
\(555\) −17731.9 + 27225.7i −1.35617 + 2.08228i
\(556\) −112.272 −0.00856365
\(557\) 7202.80 8583.97i 0.547922 0.652988i −0.419022 0.907976i \(-0.637627\pi\)
0.966944 + 0.254988i \(0.0820715\pi\)
\(558\) 9987.47 8380.48i 0.757712 0.635796i
\(559\) 877.255 + 4975.16i 0.0663755 + 0.376434i
\(560\) −2593.02 + 7124.27i −0.195670 + 0.537599i
\(561\) 31639.1i 2.38111i
\(562\) 10194.9 + 3710.62i 0.765203 + 0.278511i
\(563\) −16981.4 9804.24i −1.27119 0.733924i −0.295981 0.955194i \(-0.595647\pi\)
−0.975213 + 0.221270i \(0.928980\pi\)
\(564\) −2685.61 + 15230.9i −0.200505 + 1.13712i
\(565\) −8358.33 14477.0i −0.622367 1.07797i
\(566\) 1456.89 2523.40i 0.108193 0.187396i
\(567\) −15925.4 13363.0i −1.17955 0.989757i
\(568\) 3620.93 638.468i 0.267484 0.0471647i
\(569\) 18295.5 10562.9i 1.34795 0.778241i 0.359994 0.932955i \(-0.382779\pi\)
0.987959 + 0.154713i \(0.0494454\pi\)
\(570\) 143.968 + 395.548i 0.0105792 + 0.0290661i
\(571\) 12984.2 4725.86i 0.951614 0.346359i 0.180872 0.983507i \(-0.442108\pi\)
0.770742 + 0.637148i \(0.219886\pi\)
\(572\) 7776.86 + 1371.27i 0.568474 + 0.100237i
\(573\) −15578.3 18565.5i −1.13576 1.35355i
\(574\) −12965.8 15452.0i −0.942826 1.12362i
\(575\) 1677.79 + 295.840i 0.121685 + 0.0214563i
\(576\) 3229.72 1175.52i 0.233632 0.0850350i
\(577\) −6192.00 17012.4i −0.446753 1.22744i −0.934972 0.354722i \(-0.884576\pi\)
0.488219 0.872721i \(-0.337647\pi\)
\(578\) −2805.92 + 1620.00i −0.201922 + 0.116580i
\(579\) 15894.2 2802.58i 1.14083 0.201159i
\(580\) 7216.99 + 6055.77i 0.516671 + 0.433538i
\(581\) −20151.6 + 34903.7i −1.43895 + 2.49234i
\(582\) −6402.30 11089.1i −0.455986 0.789791i
\(583\) −1020.48 + 5787.41i −0.0724937 + 0.411132i
\(584\) 6400.42 + 3695.28i 0.453512 + 0.261835i
\(585\) 26086.1 + 9494.57i 1.84364 + 0.671029i
\(586\) 9657.68i 0.680811i
\(587\) −4394.05 + 12072.6i −0.308964 + 0.848872i 0.683895 + 0.729580i \(0.260285\pi\)
−0.992859 + 0.119292i \(0.961938\pi\)
\(588\) 3284.94 + 18629.8i 0.230389 + 1.30660i
\(589\) −135.566 + 113.753i −0.00948369 + 0.00795776i
\(590\) 4615.46 5500.49i 0.322060 0.383817i
\(591\) −21600.8 −1.50345
\(592\) −3017.45 1965.24i −0.209487 0.136437i
\(593\) −14582.2 −1.00981 −0.504905 0.863175i \(-0.668472\pi\)
−0.504905 + 0.863175i \(0.668472\pi\)
\(594\) 18927.3 22556.6i 1.30740 1.55810i
\(595\) 20829.8 17478.3i 1.43519 1.20427i
\(596\) 1530.94 + 8682.38i 0.105218 + 0.596718i
\(597\) 9841.73 27039.9i 0.674699 1.85372i
\(598\) 822.591i 0.0562512i
\(599\) −22668.4 8250.62i −1.54625 0.562790i −0.578719 0.815527i \(-0.696447\pi\)
−0.967535 + 0.252737i \(0.918669\pi\)
\(600\) −8292.94 4787.93i −0.564263 0.325777i
\(601\) −3901.91 + 22128.8i −0.264829 + 1.50192i 0.504694 + 0.863298i \(0.331605\pi\)
−0.769523 + 0.638620i \(0.779506\pi\)
\(602\) −4630.91 8020.97i −0.313524 0.543040i
\(603\) −4668.45 + 8086.00i −0.315281 + 0.546082i
\(604\) −869.956 729.980i −0.0586060 0.0491762i
\(605\) −38547.5 + 6796.96i −2.59038 + 0.456753i
\(606\) 7014.21 4049.65i 0.470186 0.271462i
\(607\) −6438.09 17688.5i −0.430501 1.18279i −0.945506 0.325604i \(-0.894432\pi\)
0.515005 0.857187i \(-0.327790\pi\)
\(608\) −43.8390 + 15.9561i −0.00292419 + 0.00106432i
\(609\) 38233.6 + 6741.62i 2.54401 + 0.448578i
\(610\) −7072.18 8428.29i −0.469416 0.559429i
\(611\) −8899.09 10605.5i −0.589229 0.702215i
\(612\) −12139.7 2140.55i −0.801826 0.141384i
\(613\) 9831.63 3578.42i 0.647791 0.235777i 0.00283460 0.999996i \(-0.499098\pi\)
0.644956 + 0.764219i \(0.276875\pi\)
\(614\) 5436.04 + 14935.4i 0.357298 + 0.981668i
\(615\) 42763.3 24689.4i 2.80387 1.61882i
\(616\) −14257.5 + 2513.99i −0.932554 + 0.164434i
\(617\) 3863.48 + 3241.84i 0.252087 + 0.211526i 0.760070 0.649841i \(-0.225164\pi\)
−0.507983 + 0.861367i \(0.669609\pi\)
\(618\) −6283.85 + 10883.9i −0.409018 + 0.708441i
\(619\) 3716.30 + 6436.81i 0.241309 + 0.417960i 0.961088 0.276244i \(-0.0890898\pi\)
−0.719778 + 0.694204i \(0.755756\pi\)
\(620\) 1354.93 7684.17i 0.0877664 0.497748i
\(621\) −2656.33 1533.63i −0.171650 0.0991023i
\(622\) 6980.35 + 2540.64i 0.449978 + 0.163779i
\(623\) 48679.9i 3.13053i
\(624\) −1581.35 + 4344.71i −0.101450 + 0.278730i
\(625\) −2522.54 14306.1i −0.161443 0.915588i
\(626\) 7151.34 6000.68i 0.456589 0.383124i
\(627\) −516.678 + 615.753i −0.0329093 + 0.0392198i
\(628\) −7493.48 −0.476151
\(629\) 5848.10 + 11515.2i 0.370714 + 0.729955i
\(630\) −50893.7 −3.21850
\(631\) 732.918 873.458i 0.0462393 0.0551059i −0.742429 0.669925i \(-0.766326\pi\)
0.788668 + 0.614819i \(0.210771\pi\)
\(632\) 3389.86 2844.43i 0.213357 0.179027i
\(633\) −4827.63 27378.9i −0.303130 1.71913i
\(634\) 875.375 2405.07i 0.0548353 0.150659i
\(635\) 24096.7i 1.50590i
\(636\) −3233.26 1176.81i −0.201584 0.0733704i
\(637\) −14665.4 8467.05i −0.912186 0.526651i
\(638\) −3124.00 + 17717.1i −0.193856 + 1.09941i
\(639\) 12341.0 + 21375.2i 0.764007 + 1.32330i
\(640\) 1028.48 1781.37i 0.0635220 0.110023i
\(641\) −4095.47 3436.51i −0.252358 0.211754i 0.507829 0.861458i \(-0.330448\pi\)
−0.760187 + 0.649704i \(0.774893\pi\)
\(642\) 17160.7 3025.90i 1.05495 0.186016i
\(643\) −10464.5 + 6041.70i −0.641805 + 0.370546i −0.785310 0.619103i \(-0.787496\pi\)
0.143504 + 0.989650i \(0.454163\pi\)
\(644\) 515.794 + 1417.13i 0.0315608 + 0.0867125i
\(645\) 21305.4 7754.54i 1.30062 0.473387i
\(646\) 164.779 + 29.0550i 0.0100358 + 0.00176959i
\(647\) 13522.3 + 16115.2i 0.821661 + 0.979218i 0.999989 0.00475337i \(-0.00151305\pi\)
−0.178327 + 0.983971i \(0.557069\pi\)
\(648\) 3625.54 + 4320.75i 0.219791 + 0.261937i
\(649\) 13503.2 + 2380.99i 0.816716 + 0.144009i
\(650\) 8055.06 2931.80i 0.486070 0.176915i
\(651\) −10997.4 30215.1i −0.662091 1.81908i
\(652\) 583.042 336.619i 0.0350210 0.0202194i
\(653\) 9816.44 1730.90i 0.588280 0.103730i 0.128418 0.991720i \(-0.459010\pi\)
0.459862 + 0.887990i \(0.347899\pi\)
\(654\) −6034.09 5063.20i −0.360782 0.302732i
\(655\) 14712.0 25481.9i 0.877627 1.52009i
\(656\) 2736.35 + 4739.49i 0.162860 + 0.282083i
\(657\) −8615.05 + 48858.4i −0.511575 + 2.90129i
\(658\) 21981.1 + 12690.8i 1.30230 + 0.751882i
\(659\) −12833.6 4671.05i −0.758614 0.276113i −0.0663883 0.997794i \(-0.521148\pi\)
−0.692226 + 0.721681i \(0.743370\pi\)
\(660\) 35440.7i 2.09019i
\(661\) −6308.37 + 17332.1i −0.371206 + 1.01988i 0.603690 + 0.797219i \(0.293697\pi\)
−0.974896 + 0.222661i \(0.928526\pi\)
\(662\) 2678.06 + 15188.0i 0.157229 + 0.891690i
\(663\) 12703.0 10659.1i 0.744106 0.624379i
\(664\) 7028.73 8376.52i 0.410795 0.489566i
\(665\) 690.811 0.0402834
\(666\) 5468.96 23546.3i 0.318195 1.36997i
\(667\) 1874.01 0.108789
\(668\) 5688.19 6778.92i 0.329465 0.392641i
\(669\) −6337.26 + 5317.59i −0.366237 + 0.307309i
\(670\) 970.326 + 5502.99i 0.0559507 + 0.317312i
\(671\) 7185.82 19742.9i 0.413421 1.13586i
\(672\) 8476.49i 0.486589i
\(673\) 15244.0 + 5548.35i 0.873124 + 0.317791i 0.739431 0.673232i \(-0.235094\pi\)
0.133692 + 0.991023i \(0.457317\pi\)
\(674\) −2014.56 1163.11i −0.115131 0.0664708i
\(675\) 5550.35 31477.6i 0.316494 1.79492i
\(676\) 2324.57 + 4026.28i 0.132258 + 0.229078i
\(677\) 1659.00 2873.47i 0.0941809 0.163126i −0.815086 0.579341i \(-0.803310\pi\)
0.909266 + 0.416215i \(0.136643\pi\)
\(678\) 14317.4 + 12013.7i 0.810999 + 0.680509i
\(679\) −20694.9 + 3649.07i −1.16966 + 0.206242i
\(680\) −6388.97 + 3688.67i −0.360302 + 0.208021i
\(681\) 5232.88 + 14377.2i 0.294456 + 0.809011i
\(682\) 14001.4 5096.08i 0.786129 0.286128i
\(683\) 17414.7 + 3070.69i 0.975631 + 0.172030i 0.638663 0.769486i \(-0.279488\pi\)
0.336968 + 0.941516i \(0.390599\pi\)
\(684\) −201.304 239.904i −0.0112530 0.0134108i
\(685\) −2239.07 2668.41i −0.124891 0.148839i
\(686\) 10653.8 + 1878.55i 0.592950 + 0.104553i
\(687\) −43003.7 + 15652.1i −2.38820 + 0.869234i
\(688\) 859.443 + 2361.30i 0.0476249 + 0.130848i
\(689\) 2667.42 1540.03i 0.147490 0.0851532i
\(690\) −3635.67 + 641.067i −0.200591 + 0.0353695i
\(691\) −3930.52 3298.10i −0.216388 0.181571i 0.528150 0.849151i \(-0.322886\pi\)
−0.744538 + 0.667580i \(0.767330\pi\)
\(692\) −3003.33 + 5201.92i −0.164985 + 0.285762i
\(693\) −48592.9 84165.4i −2.66363 4.61354i
\(694\) −3239.24 + 18370.6i −0.177175 + 1.00481i
\(695\) −390.621 225.525i −0.0213196 0.0123089i
\(696\) −9898.04 3602.59i −0.539058 0.196201i
\(697\) 19628.1i 1.06667i
\(698\) 4337.32 11916.7i 0.235201 0.646208i
\(699\) 4760.80 + 26999.8i 0.257611 + 1.46098i
\(700\) −12038.6 + 10101.6i −0.650025 + 0.545436i
\(701\) 18942.6 22575.0i 1.02062 1.21633i 0.0445181 0.999009i \(-0.485825\pi\)
0.976101 0.217318i \(-0.0697308\pi\)
\(702\) −15432.9 −0.829740
\(703\) −74.2334 + 319.608i −0.00398260 + 0.0171469i
\(704\) 3927.92 0.210283
\(705\) −39938.8 + 47597.2i −2.13359 + 2.54271i
\(706\) 4669.11 3917.85i 0.248901 0.208853i
\(707\) −2308.15 13090.2i −0.122782 0.696331i
\(708\) −2745.75 + 7543.88i −0.145751 + 0.400447i
\(709\) 3780.42i 0.200249i −0.994975 0.100125i \(-0.968076\pi\)
0.994975 0.100125i \(-0.0319241\pi\)
\(710\) 13880.6 + 5052.13i 0.733705 + 0.267047i
\(711\) 25725.7 + 14852.8i 1.35695 + 0.783435i
\(712\) 2293.45 13006.8i 0.120717 0.684621i
\(713\) −776.043 1344.15i −0.0407616 0.0706012i
\(714\) −15200.6 + 26328.3i −0.796736 + 1.37999i
\(715\) 24303.0 + 20392.7i 1.27116 + 1.06663i
\(716\) −6040.57 + 1065.12i −0.315289 + 0.0555939i
\(717\) 36324.5 20971.9i 1.89200 1.09234i
\(718\) −6224.47 17101.6i −0.323531 0.888893i
\(719\) −23579.4 + 8582.18i −1.22303 + 0.445148i −0.871206 0.490917i \(-0.836662\pi\)
−0.351828 + 0.936065i \(0.614440\pi\)
\(720\) 13598.3 + 2397.75i 0.703860 + 0.124109i
\(721\) 13257.7 + 15799.9i 0.684803 + 0.816116i
\(722\) −8815.03 10505.3i −0.454379 0.541507i
\(723\) −43090.3 7597.99i −2.21652 0.390833i
\(724\) −11160.9 + 4062.24i −0.572917 + 0.208525i
\(725\) 6679.17 + 18350.9i 0.342149 + 0.940047i
\(726\) 37899.8 21881.4i 1.93745 1.11859i
\(727\) −2996.93 + 528.440i −0.152889 + 0.0269584i −0.249569 0.968357i \(-0.580289\pi\)
0.0966799 + 0.995316i \(0.469178\pi\)
\(728\) 5812.66 + 4877.40i 0.295922 + 0.248308i
\(729\) 10161.4 17600.0i 0.516251 0.894174i
\(730\) 14845.7 + 25713.6i 0.752692 + 1.30370i
\(731\) 1564.99 8875.50i 0.0791837 0.449073i
\(732\) 10653.1 + 6150.59i 0.537912 + 0.310563i
\(733\) −1265.22 460.503i −0.0637544 0.0232047i 0.309946 0.950754i \(-0.399689\pi\)
−0.373701 + 0.927549i \(0.621911\pi\)
\(734\) 26554.8i 1.33536i
\(735\) −25993.4 + 71416.2i −1.30446 + 3.58398i
\(736\) −71.0500 402.945i −0.00355834 0.0201803i
\(737\) −8174.10 + 6858.89i −0.408544 + 0.342809i
\(738\) −23614.5 + 28142.6i −1.17786 + 1.40372i
\(739\) −5384.77 −0.268041 −0.134020 0.990979i \(-0.542789\pi\)
−0.134020 + 0.990979i \(0.542789\pi\)
\(740\) −6550.77 12898.8i −0.325420 0.640770i
\(741\) 421.289 0.0208859
\(742\) −3629.68 + 4325.68i −0.179582 + 0.214017i
\(743\) 12181.7 10221.7i 0.601485 0.504706i −0.290438 0.956894i \(-0.593801\pi\)
0.891923 + 0.452188i \(0.149356\pi\)
\(744\) 1514.88 + 8591.29i 0.0746480 + 0.423350i
\(745\) −12114.1 + 33283.3i −0.595742 + 1.63679i
\(746\) 2517.19i 0.123540i
\(747\) 68977.1 + 25105.6i 3.37850 + 1.22967i
\(748\) −12200.3 7043.83i −0.596372 0.344315i
\(749\) 4965.92 28163.1i 0.242257 1.37391i
\(750\) −1189.92 2061.00i −0.0579330 0.100343i
\(751\) 11944.4 20688.3i 0.580370 1.00523i −0.415066 0.909791i \(-0.636241\pi\)
0.995435 0.0954381i \(-0.0304252\pi\)
\(752\) −5275.24 4426.45i −0.255809 0.214649i
\(753\) 2625.52 462.950i 0.127064 0.0224048i
\(754\) 8165.80 4714.53i 0.394404 0.227710i
\(755\) −1560.45 4287.29i −0.0752191 0.206663i
\(756\) 26587.3 9676.98i 1.27906 0.465540i
\(757\) −15843.4 2793.63i −0.760687 0.134130i −0.220168 0.975462i \(-0.570661\pi\)
−0.540518 + 0.841332i \(0.681772\pi\)
\(758\) −9600.69 11441.7i −0.460043 0.548258i
\(759\) −4531.47 5400.40i −0.216709 0.258264i
\(760\) −184.578 32.5461i −0.00880967 0.00155338i
\(761\) −7928.37 + 2885.69i −0.377665 + 0.137459i −0.523876 0.851795i \(-0.675514\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(762\) 9214.49 + 25316.6i 0.438065 + 1.20357i
\(763\) −11195.2 + 6463.58i −0.531186 + 0.306681i
\(764\) 10627.2 1873.86i 0.503245 0.0887356i
\(765\) −37937.0 31833.0i −1.79296 1.50447i
\(766\) 3569.44 6182.45i 0.168367 0.291620i
\(767\) −3593.22 6223.64i −0.169157 0.292989i
\(768\) −399.352 + 2264.84i −0.0187635 + 0.106413i
\(769\) −33341.0 19249.4i −1.56347 0.902669i −0.996902 0.0786530i \(-0.974938\pi\)
−0.566566 0.824016i \(-0.691729\pi\)
\(770\) −54655.4 19892.9i −2.55798 0.931028i
\(771\) 46396.1i 2.16721i
\(772\) −2457.84 + 6752.86i −0.114585 + 0.314820i
\(773\) −5389.40 30564.8i −0.250768 1.42217i −0.806707 0.590951i \(-0.798753\pi\)
0.555940 0.831223i \(-0.312359\pi\)
\(774\) −12922.0 + 10842.8i −0.600092 + 0.503537i
\(775\) 10396.4 12389.9i 0.481870 0.574270i
\(776\) 5701.39 0.263747
\(777\) −49955.8 32535.8i −2.30650 1.50221i
\(778\) −22790.6 −1.05023
\(779\) 320.533 381.997i 0.0147424 0.0175693i
\(780\) −14229.3 + 11939.8i −0.653193 + 0.548094i
\(781\) 4898.15 + 27778.8i 0.224417 + 1.27273i
\(782\) −501.905 + 1378.97i −0.0229515 + 0.0630588i
\(783\) 35158.9i 1.60470i
\(784\) −7915.12 2880.87i −0.360565 0.131235i
\(785\) −26071.6 15052.5i −1.18540 0.684389i
\(786\) −5712.60 + 32397.7i −0.259239 + 1.47022i
\(787\) 12931.6 + 22398.2i 0.585720 + 1.01450i 0.994785 + 0.101992i \(0.0325216\pi\)
−0.409065 + 0.912505i \(0.634145\pi\)
\(788\) 4808.99 8329.41i 0.217402 0.376552i
\(789\) 12275.7 + 10300.5i 0.553897 + 0.464775i
\(790\) 17507.9 3087.11i 0.788483 0.139031i
\(791\) 26563.6 15336.5i 1.19405 0.689384i
\(792\) 9018.29 + 24777.5i 0.404610 + 1.11166i
\(793\) −10347.6 + 3766.20i −0.463370 + 0.168653i
\(794\) 783.643 + 138.177i 0.0350257 + 0.00617598i
\(795\) −8885.39 10589.2i −0.396393 0.472403i
\(796\) 8235.73 + 9814.96i 0.366718 + 0.437038i
\(797\) 20295.1 + 3578.57i 0.901992 + 0.159046i 0.605365 0.795948i \(-0.293027\pi\)
0.296627 + 0.954993i \(0.404138\pi\)
\(798\) −725.782 + 264.163i −0.0321960 + 0.0117184i
\(799\) 8447.26 + 23208.7i 0.374021 + 1.02761i
\(800\) 3692.52 2131.88i 0.163188 0.0942167i
\(801\) 87313.3 15395.7i 3.85151 0.679126i
\(802\) −7113.85 5969.23i −0.313216 0.262819i
\(803\) −28349.2 + 49102.2i −1.24585 + 2.15788i
\(804\) −3123.77 5410.52i −0.137023 0.237331i
\(805\) −1052.08 + 5966.64i −0.0460633 + 0.261238i
\(806\) −6763.05 3904.65i −0.295556 0.170639i
\(807\) 38412.4 + 13981.0i 1.67557 + 0.609856i
\(808\) 3606.31i 0.157017i
\(809\) 6052.41 16628.9i 0.263030 0.722669i −0.735929 0.677058i \(-0.763254\pi\)
0.998959 0.0456107i \(-0.0145234\pi\)
\(810\) 3934.86 + 22315.7i 0.170687 + 0.968017i
\(811\) −3492.91 + 2930.90i −0.151236 + 0.126902i −0.715266 0.698852i \(-0.753695\pi\)
0.564030 + 0.825754i \(0.309250\pi\)
\(812\) −11111.6 + 13242.3i −0.480222 + 0.572307i
\(813\) 21513.7 0.928067
\(814\) 15076.8 23149.0i 0.649190 0.996772i
\(815\) 2704.72 0.116248
\(816\) 5301.87 6318.52i 0.227454 0.271069i
\(817\) 175.398 147.176i 0.00751088 0.00630238i
\(818\) −919.901 5217.02i −0.0393198 0.222994i
\(819\) −17421.4 + 47864.8i −0.743287 + 2.04216i
\(820\) 21986.5i 0.936342i
\(821\) 9827.76 + 3577.01i 0.417773 + 0.152057i 0.542349 0.840153i \(-0.317535\pi\)
−0.124577 + 0.992210i \(0.539757\pi\)
\(822\) 3372.81 + 1947.29i 0.143114 + 0.0826272i
\(823\) −1388.43 + 7874.16i −0.0588062 + 0.333507i −0.999990 0.00438744i \(-0.998603\pi\)
0.941184 + 0.337894i \(0.109715\pi\)
\(824\) −2797.95 4846.20i −0.118290 0.204885i
\(825\) 36731.7 63621.1i 1.55010 2.68485i
\(826\) 10092.7 + 8468.80i 0.425146 + 0.356740i
\(827\) 15825.8 2790.52i 0.665439 0.117335i 0.169282 0.985568i \(-0.445855\pi\)
0.496157 + 0.868233i \(0.334744\pi\)
\(828\) 2378.67 1373.33i 0.0998363 0.0576405i
\(829\) −5872.11 16133.5i −0.246016 0.675922i −0.999823 0.0188265i \(-0.994007\pi\)
0.753807 0.657096i \(-0.228215\pi\)
\(830\) 41280.9 15025.0i 1.72636 0.628345i
\(831\) −60491.1 10666.2i −2.52517 0.445255i
\(832\) −1323.30 1577.04i −0.0551407 0.0657142i
\(833\) 19418.5 + 23142.0i 0.807696 + 0.962574i
\(834\) 496.636 + 87.5703i 0.0206200 + 0.00363586i
\(835\) 33407.7 12159.4i 1.38458 0.503944i
\(836\) −122.411 336.320i −0.00506418 0.0139137i
\(837\) −25218.0 + 14559.6i −1.04141 + 0.601258i
\(838\) −30563.3 + 5389.14i −1.25990 + 0.222154i
\(839\) −22104.2 18547.6i −0.909560 0.763211i 0.0624756 0.998046i \(-0.480100\pi\)
−0.972035 + 0.234835i \(0.924545\pi\)
\(840\) 17027.1 29491.7i 0.699392 1.21138i
\(841\) −1453.96 2518.33i −0.0596152 0.103257i
\(842\) −3597.23 + 20400.9i −0.147231 + 0.834989i
\(843\) −42202.8 24365.8i −1.72425 0.995495i
\(844\) 11632.3 + 4233.80i 0.474407 + 0.172670i
\(845\) 18677.9i 0.760400i
\(846\) 15810.6 43439.4i 0.642531 1.76534i
\(847\) −12471.6 70729.9i −0.505937 2.86931i
\(848\) 1173.61 984.776i 0.0475259 0.0398789i
\(849\) −8412.75 + 10025.9i −0.340076 + 0.405287i
\(850\) −15292.2 −0.617079
\(851\) −2647.45 1127.92i −0.106643 0.0454342i
\(852\) −16515.2 −0.664087
\(853\) −9219.49 + 10987.4i −0.370069 + 0.441031i −0.918654 0.395064i \(-0.870723\pi\)
0.548584 + 0.836095i \(0.315167\pi\)
\(854\) 15464.9 12976.6i 0.619669 0.519964i
\(855\) −218.478 1239.05i −0.00873895 0.0495610i
\(856\) −2653.69 + 7290.95i −0.105959 + 0.291121i
\(857\) 36965.7i 1.47342i 0.676206 + 0.736712i \(0.263623\pi\)
−0.676206 + 0.736712i \(0.736377\pi\)
\(858\) −33331.4 12131.6i −1.32624 0.482713i
\(859\) −37883.8 21872.2i −1.50475 0.868768i −0.999985 0.00551091i \(-0.998246\pi\)
−0.504765 0.863257i \(-0.668421\pi\)
\(860\) −1753.03 + 9941.93i −0.0695091 + 0.394206i
\(861\) 45302.0 + 78465.3i 1.79313 + 3.10580i
\(862\) 11560.7 20023.8i 0.456798 0.791198i
\(863\) −14080.0 11814.5i −0.555375 0.466015i 0.321381 0.946950i \(-0.395853\pi\)
−0.876756 + 0.480935i \(0.840297\pi\)
\(864\) −7559.78 + 1332.99i −0.297672 + 0.0524876i
\(865\) −20898.6 + 12065.8i −0.821474 + 0.474278i
\(866\) −2107.72 5790.92i −0.0827059 0.227233i
\(867\) 13675.6 4977.50i 0.535694 0.194977i
\(868\) 14099.5 + 2486.12i 0.551346 + 0.0972172i
\(869\) 21821.7 + 26006.1i 0.851841 + 1.01518i
\(870\) −27201.0 32416.9i −1.06000 1.26326i
\(871\) 5507.63 + 971.145i 0.214258 + 0.0377795i
\(872\) 3295.78 1199.57i 0.127992 0.0465853i
\(873\) 13090.1 + 35964.7i 0.507482 + 1.39430i
\(874\) −32.2871 + 18.6410i −0.00124957 + 0.000721442i
\(875\) −3846.31 + 678.209i −0.148605 + 0.0262030i
\(876\) −25430.0 21338.3i −0.980823 0.823008i
\(877\) 8167.24 14146.1i 0.314468 0.544674i −0.664857 0.746971i \(-0.731507\pi\)
0.979324 + 0.202297i \(0.0648407\pi\)
\(878\) −14521.2 25151.5i −0.558164 0.966769i
\(879\) 7532.83 42720.8i 0.289051 1.63929i
\(880\) 13666.2 + 7890.17i 0.523508 + 0.302247i
\(881\) 7499.44 + 2729.57i 0.286791 + 0.104383i 0.481410 0.876496i \(-0.340125\pi\)
−0.194619 + 0.980879i \(0.562347\pi\)
\(882\) 56543.3i 2.15863i
\(883\) 3891.18 10690.9i 0.148300 0.407450i −0.843193 0.537610i \(-0.819327\pi\)
0.991493 + 0.130161i \(0.0415494\pi\)
\(884\) 1282.14 + 7271.39i 0.0487818 + 0.276655i
\(885\) −24706.8 + 20731.5i −0.938430 + 0.787436i
\(886\) −5396.90 + 6431.78i −0.204642 + 0.243882i
\(887\) −44171.6 −1.67208 −0.836041 0.548667i \(-0.815135\pi\)
−0.836041 + 0.548667i \(0.815135\pi\)
\(888\) 11814.8 + 11046.8i 0.446487 + 0.417463i
\(889\) 44214.5 1.66806
\(890\) 34106.8 40646.8i 1.28456 1.53088i
\(891\) −33147.6 + 27814.1i −1.24634 + 1.04580i
\(892\) −639.636 3627.55i −0.0240096 0.136165i
\(893\) −214.607 + 589.628i −0.00804206 + 0.0220954i
\(894\) 39600.7i 1.48148i
\(895\) −23156.1 8428.14i −0.864832 0.314773i
\(896\) 3268.60 + 1887.12i 0.121871 + 0.0703621i
\(897\) −641.607 + 3638.74i −0.0238826 + 0.135445i
\(898\) −3079.40 5333.67i −0.114433 0.198204i
\(899\) 8895.49 15407.4i 0.330013 0.571599i
\(900\) 21925.8 + 18398.0i 0.812068 + 0.681406i
\(901\) −5411.25 + 954.149i −0.200083 + 0.0352800i
\(902\) −36360.1 + 20992.5i −1.34219 + 0.774915i
\(903\) 14228.6 + 39092.8i 0.524362 + 1.44067i
\(904\) −7820.08 + 2846.28i −0.287712 + 0.104719i
\(905\) −46991.4 8285.86i −1.72602 0.304344i
\(906\) 3278.88 + 3907.62i 0.120236 + 0.143291i
\(907\) 22751.4 + 27114.1i 0.832909 + 0.992623i 0.999978 + 0.00667734i \(0.00212548\pi\)
−0.167068 + 0.985945i \(0.553430\pi\)
\(908\) −6708.96 1182.97i −0.245204 0.0432360i
\(909\) −22748.8 + 8279.88i −0.830066 + 0.302119i
\(910\) 10426.2 + 28645.8i 0.379808 + 1.04351i
\(911\) 27438.5 15841.6i 0.997890 0.576132i 0.0902668 0.995918i \(-0.471228\pi\)
0.907623 + 0.419785i \(0.137895\pi\)
\(912\) 206.367 36.3881i 0.00749288 0.00132120i
\(913\) 64262.3 + 53922.5i 2.32943 + 1.95463i
\(914\) −4712.93 + 8163.03i −0.170558 + 0.295415i
\(915\) 24709.9 + 42798.8i 0.892769 + 1.54632i
\(916\) 3538.38 20067.2i 0.127633 0.723841i
\(917\) 46756.2 + 26994.7i 1.68378 + 0.972131i
\(918\) 25871.4 + 9416.41i 0.930155 + 0.338549i
\(919\) 28776.8i 1.03293i 0.856309 + 0.516464i \(0.172752\pi\)
−0.856309 + 0.516464i \(0.827248\pi\)
\(920\) 562.211 1544.66i 0.0201473 0.0553543i
\(921\) −12397.0 70306.9i −0.443534 2.51541i
\(922\) 4006.83 3362.13i 0.143122 0.120093i
\(923\) 9502.91 11325.1i 0.338886 0.403869i
\(924\) 65029.2 2.31526
\(925\) 1609.11 29944.6i 0.0571971 1.06440i
\(926\) 12786.4 0.453767
\(927\) 24146.1 28776.2i 0.855516 1.01956i
\(928\) 3592.79 3014.71i 0.127090 0.106641i
\(929\) −6435.50 36497.5i −0.227279 1.28896i −0.858281 0.513181i \(-0.828467\pi\)
0.631002 0.775781i \(-0.282644\pi\)
\(930\) −11987.1 + 32934.2i −0.422657 + 1.16124i
\(931\) 767.496i 0.0270179i
\(932\) −11471.2 4175.19i −0.403168 0.146741i
\(933\) −28896.0 16683.1i −1.01395 0.585402i
\(934\) −3292.08 + 18670.3i −0.115332 + 0.654080i
\(935\) −28298.5 49014.4i −0.989795 1.71438i
\(936\) 6909.87 11968.2i 0.241299 0.417943i
\(937\) −35787.4 30029.2i −1.24773 1.04697i −0.996879 0.0789441i \(-0.974845\pi\)
−0.250851 0.968026i \(-0.580710\pi\)
\(938\) −10097.3 + 1780.43i −0.351481 + 0.0619755i
\(939\) −36314.4 + 20966.1i −1.26206 + 0.728652i
\(940\) −9462.23 25997.3i −0.328323 0.902061i
\(941\) 27498.4 10008.6i 0.952627 0.346728i 0.181487 0.983393i \(-0.441909\pi\)
0.771140 + 0.636665i \(0.219687\pi\)
\(942\) 33147.5 + 5844.79i 1.14650 + 0.202159i
\(943\) 2811.21 + 3350.26i 0.0970790 + 0.115694i
\(944\) −2297.69 2738.28i −0.0792197 0.0944104i
\(945\) 111942. + 19738.4i 3.85341 + 0.679461i
\(946\) −18115.2 + 6593.41i −0.622597 + 0.226607i
\(947\) −3159.30 8680.11i −0.108409 0.297852i 0.873612 0.486624i \(-0.161772\pi\)
−0.982021 + 0.188772i \(0.939549\pi\)
\(948\) −17213.7 + 9938.32i −0.589741 + 0.340487i
\(949\) 29265.1 5160.22i 1.00104 0.176510i
\(950\) −297.613 249.727i −0.0101640 0.00852863i
\(951\) −5748.14 + 9956.07i −0.196000 + 0.339482i
\(952\) −6768.26 11723.0i −0.230421 0.399100i
\(953\) −6424.03 + 36432.5i −0.218357 + 1.23837i 0.656627 + 0.754215i \(0.271983\pi\)
−0.874984 + 0.484151i \(0.839129\pi\)
\(954\) 8906.56 + 5142.21i 0.302265 + 0.174513i
\(955\) 40738.7 + 14827.7i 1.38039 + 0.502421i
\(956\) 18676.0i 0.631824i
\(957\) 27638.1 75935.0i 0.933555 2.56492i
\(958\) −5684.37 32237.7i −0.191705 1.08721i
\(959\) 4896.21 4108.41i 0.164866 0.138339i
\(960\) −5938.91 + 7077.71i −0.199664 + 0.237950i
\(961\) 15056.2 0.505395
\(962\) −14373.5 + 1745.52i −0.481727 + 0.0585010i
\(963\) −52084.5 −1.74289
\(964\) 12523.1 14924.4i 0.418403 0.498634i
\(965\) −22116.2 + 18557.7i −0.737766 + 0.619059i
\(966\) −1176.28 6671.00i −0.0391782 0.222190i
\(967\) −10931.3 + 30033.5i −0.363523 + 0.998772i 0.614251 + 0.789111i \(0.289458\pi\)
−0.977774 + 0.209661i \(0.932764\pi\)
\(968\) 19485.9i 0.647005i
\(969\) −706.239 257.050i −0.0234135 0.00852181i
\(970\) 19836.5 + 11452.6i 0.656610 + 0.379094i
\(971\) 6030.31 34199.6i 0.199302 1.13030i −0.706857 0.707357i \(-0.749887\pi\)
0.906158 0.422939i \(-0.139001\pi\)
\(972\) 286.440 + 496.128i 0.00945221 + 0.0163717i
\(973\) 413.811 716.741i 0.0136343 0.0236153i
\(974\) 5709.28 + 4790.66i 0.187821 + 0.157600i
\(975\) −37918.4 + 6686.03i −1.24550 + 0.219615i
\(976\) −4743.43 + 2738.62i −0.155567 + 0.0898167i
\(977\) 444.760 + 1221.97i 0.0145641 + 0.0400145i 0.946762 0.321935i \(-0.104333\pi\)
−0.932198 + 0.361950i \(0.882111\pi\)
\(978\) −2841.65 + 1034.28i −0.0929099 + 0.0338164i
\(979\) 99784.5 + 17594.7i 3.25754 + 0.574391i
\(980\) −21751.7 25922.7i −0.709013 0.844968i
\(981\) 15133.9 + 18035.8i 0.492545 + 0.586992i
\(982\) −27991.9 4935.73i −0.909631 0.160393i
\(983\) −3930.60 + 1430.62i −0.127535 + 0.0464188i −0.404999 0.914317i \(-0.632728\pi\)
0.277464 + 0.960736i \(0.410506\pi\)
\(984\) −8407.53 23099.5i −0.272380 0.748359i
\(985\) 33463.3 19320.0i 1.08246 0.624961i
\(986\) −16565.5 + 2920.95i −0.535045 + 0.0943429i
\(987\) −87334.9 73282.7i −2.81652 2.36334i
\(988\) −93.7917 + 162.452i −0.00302015 + 0.00523106i
\(989\) 1004.06 + 1739.08i 0.0322823 + 0.0559146i
\(990\) −18394.9 + 104322.i −0.590532 + 3.34908i
\(991\) 16679.5 + 9629.92i 0.534654 + 0.308683i 0.742910 0.669392i \(-0.233445\pi\)
−0.208256 + 0.978074i \(0.566779\pi\)
\(992\) −3650.12 1328.54i −0.116826 0.0425213i
\(993\) 69273.1i 2.21381i
\(994\) −9270.04 + 25469.2i −0.295803 + 0.812711i
\(995\) 8938.38 + 50692.1i 0.284790 + 1.61512i
\(996\) −37625.2 + 31571.3i −1.19699 + 1.00439i
\(997\) −16213.4 + 19322.4i −0.515030 + 0.613789i −0.959398 0.282055i \(-0.908984\pi\)
0.444368 + 0.895844i \(0.353428\pi\)
\(998\) 30376.4 0.963475
\(999\) −21161.2 + 49669.7i −0.670182 + 1.57305i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 74.4.h.a.3.6 60
37.25 even 18 inner 74.4.h.a.25.6 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.4.h.a.3.6 60 1.1 even 1 trivial
74.4.h.a.25.6 yes 60 37.25 even 18 inner