Properties

Label 201.4.j.b.5.19
Level $201$
Weight $4$
Character 201.5
Analytic conductor $11.859$
Analytic rank $0$
Dimension $640$
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] = [201,4,Mod(5,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.j (of order \(22\), degree \(10\), 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: \(11.8593839112\)
Analytic rank: \(0\)
Dimension: \(640\)
Relative dimension: \(64\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.19
Character \(\chi\) \(=\) 201.5
Dual form 201.4.j.b.161.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.97915 + 2.28406i) q^{2} +(1.50596 + 4.97314i) q^{3} +(-0.161385 - 1.12245i) q^{4} +(9.47455 - 2.78198i) q^{5} +(-14.3395 - 6.40290i) q^{6} +(23.8049 + 20.6270i) q^{7} +(-17.4567 - 11.2187i) q^{8} +(-22.4642 + 14.9787i) q^{9} +O(q^{10})\) \(q+(-1.97915 + 2.28406i) q^{2} +(1.50596 + 4.97314i) q^{3} +(-0.161385 - 1.12245i) q^{4} +(9.47455 - 2.78198i) q^{5} +(-14.3395 - 6.40290i) q^{6} +(23.8049 + 20.6270i) q^{7} +(-17.4567 - 11.2187i) q^{8} +(-22.4642 + 14.9787i) q^{9} +(-12.3974 + 27.1465i) q^{10} +(9.36765 - 2.75059i) q^{11} +(5.33908 - 2.49296i) q^{12} +(16.2985 + 25.3609i) q^{13} +(-94.2270 + 13.5478i) q^{14} +(28.1034 + 42.9287i) q^{15} +(68.8782 - 20.2245i) q^{16} +(107.526 + 15.4599i) q^{17} +(10.2478 - 80.9547i) q^{18} +(47.9347 + 55.3196i) q^{19} +(-4.65169 - 10.1858i) q^{20} +(-66.7320 + 149.448i) q^{21} +(-12.2575 + 26.8402i) q^{22} +(-169.288 + 77.3113i) q^{23} +(29.5032 - 103.709i) q^{24} +(-23.1289 + 14.8641i) q^{25} +(-90.1831 - 12.9664i) q^{26} +(-108.321 - 89.1602i) q^{27} +(19.3112 - 30.0488i) q^{28} -201.497i q^{29} +(-153.673 - 20.7724i) q^{30} +(110.528 - 171.984i) q^{31} +(-21.1650 + 46.3450i) q^{32} +(27.7863 + 42.4443i) q^{33} +(-248.122 + 214.999i) q^{34} +(282.925 + 129.207i) q^{35} +(20.4383 + 22.7977i) q^{36} -126.122 q^{37} -221.224 q^{38} +(-101.578 + 119.247i) q^{39} +(-196.604 - 57.7282i) q^{40} +(68.6344 - 477.363i) q^{41} +(-209.277 - 448.201i) q^{42} +(-194.874 - 28.0187i) q^{43} +(-4.59921 - 10.0709i) q^{44} +(-171.168 + 204.411i) q^{45} +(158.463 - 539.676i) q^{46} +(-379.706 + 173.406i) q^{47} +(204.307 + 312.084i) q^{48} +(92.3833 + 642.540i) q^{49} +(11.8252 - 82.2463i) q^{50} +(85.0454 + 558.024i) q^{51} +(25.8362 - 22.3872i) q^{52} +(-20.2031 - 140.516i) q^{53} +(418.032 - 70.9505i) q^{54} +(81.1022 - 52.1212i) q^{55} +(-184.145 - 627.140i) q^{56} +(-202.924 + 321.695i) q^{57} +(460.231 + 398.792i) q^{58} +(30.0369 - 46.7383i) q^{59} +(43.6501 - 38.4729i) q^{60} +(195.873 - 667.082i) q^{61} +(174.072 + 592.835i) q^{62} +(-843.723 - 106.804i) q^{63} +(174.602 + 382.325i) q^{64} +(224.974 + 194.941i) q^{65} +(-151.939 - 20.5380i) q^{66} +(212.928 + 505.395i) q^{67} -123.188i q^{68} +(-639.420 - 725.466i) q^{69} +(-855.069 + 390.497i) q^{70} +(506.074 - 72.7625i) q^{71} +(560.191 - 9.45821i) q^{72} +(-64.7624 - 19.0159i) q^{73} +(249.615 - 288.071i) q^{74} +(-108.752 - 92.6388i) q^{75} +(54.3579 - 62.7323i) q^{76} +(279.732 + 127.749i) q^{77} +(-71.3284 - 468.020i) q^{78} +(402.077 + 625.644i) q^{79} +(596.326 - 383.235i) q^{80} +(280.279 - 672.967i) q^{81} +(954.489 + 1101.54i) q^{82} +(160.400 + 546.274i) q^{83} +(178.519 + 50.7850i) q^{84} +(1061.77 - 152.660i) q^{85} +(449.682 - 389.652i) q^{86} +(1002.07 - 303.445i) q^{87} +(-194.386 - 57.0769i) q^{88} +(-652.012 - 297.764i) q^{89} +(-128.121 - 795.519i) q^{90} +(-135.138 + 939.903i) q^{91} +(114.099 + 177.541i) q^{92} +(1021.75 + 290.668i) q^{93} +(355.426 - 1210.47i) q^{94} +(608.058 + 390.775i) q^{95} +(-262.353 - 35.4631i) q^{96} -863.513i q^{97} +(-1650.44 - 1060.68i) q^{98} +(-169.236 + 202.105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 640 q - 11 q^{3} - 290 q^{4} + 35 q^{6} - 22 q^{7} - 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 640 q - 11 q^{3} - 290 q^{4} + 35 q^{6} - 22 q^{7} - 33 q^{9} + 14 q^{10} - 143 q^{12} - 22 q^{13} - 31 q^{15} - 578 q^{16} - 11 q^{18} - 18 q^{19} - 1133 q^{21} - 382 q^{22} + 365 q^{24} - 2102 q^{25} - 11 q^{27} - 1870 q^{28} - 1210 q^{31} - 743 q^{33} - 22 q^{34} + 1563 q^{36} - 1048 q^{37} + 2475 q^{39} + 626 q^{40} - 11 q^{42} - 1738 q^{43} - 4521 q^{45} + 6578 q^{46} - 3531 q^{48} + 1198 q^{49} - 11 q^{51} + 10274 q^{52} + 1948 q^{54} + 3170 q^{55} - 8921 q^{57} + 418 q^{58} - 649 q^{60} - 2002 q^{61} - 5951 q^{63} - 14918 q^{64} + 2038 q^{67} - 11 q^{69} - 8734 q^{70} - 10681 q^{72} + 9870 q^{73} + 8426 q^{75} + 5230 q^{76} - 11 q^{78} + 10934 q^{79} + 2919 q^{81} + 7442 q^{82} - 4997 q^{84} - 22 q^{85} + 7480 q^{87} + 8630 q^{88} - 757 q^{90} + 13286 q^{91} - 6585 q^{93} + 7106 q^{94} + 16316 q^{96} + 2739 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97915 + 2.28406i −0.699736 + 0.807539i −0.988717 0.149796i \(-0.952138\pi\)
0.288981 + 0.957335i \(0.406684\pi\)
\(3\) 1.50596 + 4.97314i 0.289822 + 0.957081i
\(4\) −0.161385 1.12245i −0.0201731 0.140307i
\(5\) 9.47455 2.78198i 0.847430 0.248828i 0.170941 0.985281i \(-0.445319\pi\)
0.676488 + 0.736453i \(0.263501\pi\)
\(6\) −14.3395 6.40290i −0.975678 0.435662i
\(7\) 23.8049 + 20.6270i 1.28534 + 1.11376i 0.987243 + 0.159221i \(0.0508983\pi\)
0.298100 + 0.954535i \(0.403647\pi\)
\(8\) −17.4567 11.2187i −0.771483 0.495802i
\(9\) −22.4642 + 14.9787i −0.832007 + 0.554765i
\(10\) −12.3974 + 27.1465i −0.392039 + 0.858446i
\(11\) 9.36765 2.75059i 0.256768 0.0753940i −0.150815 0.988562i \(-0.548190\pi\)
0.407583 + 0.913168i \(0.366372\pi\)
\(12\) 5.33908 2.49296i 0.128438 0.0599712i
\(13\) 16.2985 + 25.3609i 0.347722 + 0.541066i 0.970428 0.241390i \(-0.0776033\pi\)
−0.622706 + 0.782456i \(0.713967\pi\)
\(14\) −94.2270 + 13.5478i −1.79880 + 0.258629i
\(15\) 28.1034 + 42.9287i 0.483752 + 0.738943i
\(16\) 68.8782 20.2245i 1.07622 0.316007i
\(17\) 107.526 + 15.4599i 1.53405 + 0.220564i 0.856979 0.515351i \(-0.172339\pi\)
0.677074 + 0.735915i \(0.263248\pi\)
\(18\) 10.2478 80.9547i 0.134191 1.06007i
\(19\) 47.9347 + 55.3196i 0.578789 + 0.667958i 0.967344 0.253468i \(-0.0815712\pi\)
−0.388555 + 0.921425i \(0.627026\pi\)
\(20\) −4.65169 10.1858i −0.0520075 0.113881i
\(21\) −66.7320 + 149.448i −0.693434 + 1.55297i
\(22\) −12.2575 + 26.8402i −0.118787 + 0.260106i
\(23\) −169.288 + 77.3113i −1.53474 + 0.700892i −0.990433 0.137994i \(-0.955935\pi\)
−0.544307 + 0.838886i \(0.683207\pi\)
\(24\) 29.5032 103.709i 0.250930 0.882066i
\(25\) −23.1289 + 14.8641i −0.185032 + 0.118913i
\(26\) −90.1831 12.9664i −0.680245 0.0978044i
\(27\) −108.321 89.1602i −0.772089 0.635515i
\(28\) 19.3112 30.0488i 0.130338 0.202810i
\(29\) 201.497i 1.29024i −0.764081 0.645120i \(-0.776807\pi\)
0.764081 0.645120i \(-0.223193\pi\)
\(30\) −153.673 20.7724i −0.935224 0.126417i
\(31\) 110.528 171.984i 0.640366 0.996429i −0.357674 0.933847i \(-0.616430\pi\)
0.998040 0.0625822i \(-0.0199335\pi\)
\(32\) −21.1650 + 46.3450i −0.116921 + 0.256022i
\(33\) 27.7863 + 42.4443i 0.146575 + 0.223897i
\(34\) −248.122 + 214.999i −1.25155 + 1.08447i
\(35\) 282.925 + 129.207i 1.36637 + 0.624001i
\(36\) 20.4383 + 22.7977i 0.0946215 + 0.105545i
\(37\) −126.122 −0.560388 −0.280194 0.959943i \(-0.590399\pi\)
−0.280194 + 0.959943i \(0.590399\pi\)
\(38\) −221.224 −0.944401
\(39\) −101.578 + 119.247i −0.417066 + 0.489610i
\(40\) −196.604 57.7282i −0.777147 0.228191i
\(41\) 68.6344 477.363i 0.261436 1.81833i −0.260646 0.965434i \(-0.583936\pi\)
0.522082 0.852895i \(-0.325155\pi\)
\(42\) −209.277 448.201i −0.768860 1.64664i
\(43\) −194.874 28.0187i −0.691117 0.0993676i −0.212198 0.977227i \(-0.568062\pi\)
−0.478919 + 0.877859i \(0.658971\pi\)
\(44\) −4.59921 10.0709i −0.0157581 0.0345054i
\(45\) −171.168 + 204.411i −0.567026 + 0.677151i
\(46\) 158.463 539.676i 0.507916 1.72980i
\(47\) −379.706 + 173.406i −1.17842 + 0.538167i −0.905697 0.423926i \(-0.860652\pi\)
−0.272723 + 0.962092i \(0.587924\pi\)
\(48\) 204.307 + 312.084i 0.614357 + 0.938445i
\(49\) 92.3833 + 642.540i 0.269339 + 1.87329i
\(50\) 11.8252 82.2463i 0.0334468 0.232628i
\(51\) 85.0454 + 558.024i 0.233505 + 1.53214i
\(52\) 25.8362 22.3872i 0.0689006 0.0597027i
\(53\) −20.2031 140.516i −0.0523606 0.364176i −0.999109 0.0422019i \(-0.986563\pi\)
0.946749 0.321974i \(-0.104346\pi\)
\(54\) 418.032 70.9505i 1.05346 0.178799i
\(55\) 81.1022 52.1212i 0.198833 0.127782i
\(56\) −184.145 627.140i −0.439418 1.49652i
\(57\) −202.924 + 321.695i −0.471544 + 0.747536i
\(58\) 460.231 + 398.792i 1.04192 + 0.902828i
\(59\) 30.0369 46.7383i 0.0662791 0.103132i −0.806532 0.591190i \(-0.798658\pi\)
0.872811 + 0.488058i \(0.162295\pi\)
\(60\) 43.6501 38.4729i 0.0939200 0.0827805i
\(61\) 195.873 667.082i 0.411130 1.40018i −0.450560 0.892746i \(-0.648776\pi\)
0.861690 0.507435i \(-0.169406\pi\)
\(62\) 174.072 + 592.835i 0.356568 + 1.21436i
\(63\) −843.723 106.804i −1.68729 0.213589i
\(64\) 174.602 + 382.325i 0.341019 + 0.746728i
\(65\) 224.974 + 194.941i 0.429302 + 0.371992i
\(66\) −151.939 20.5380i −0.283370 0.0383039i
\(67\) 212.928 + 505.395i 0.388259 + 0.921550i
\(68\) 123.188i 0.219688i
\(69\) −639.420 725.466i −1.11561 1.26574i
\(70\) −855.069 + 390.497i −1.46000 + 0.666762i
\(71\) 506.074 72.7625i 0.845915 0.121624i 0.294290 0.955716i \(-0.404917\pi\)
0.551625 + 0.834092i \(0.314008\pi\)
\(72\) 560.191 9.45821i 0.916933 0.0154814i
\(73\) −64.7624 19.0159i −0.103834 0.0304883i 0.229403 0.973332i \(-0.426323\pi\)
−0.333237 + 0.942843i \(0.608141\pi\)
\(74\) 249.615 288.071i 0.392124 0.452535i
\(75\) −108.752 92.6388i −0.167435 0.142627i
\(76\) 54.3579 62.7323i 0.0820431 0.0946828i
\(77\) 279.732 + 127.749i 0.414006 + 0.189070i
\(78\) −71.3284 468.020i −0.103543 0.679395i
\(79\) 402.077 + 625.644i 0.572623 + 0.891019i 0.999914 0.0130953i \(-0.00416850\pi\)
−0.427291 + 0.904114i \(0.640532\pi\)
\(80\) 596.326 383.235i 0.833391 0.535588i
\(81\) 280.279 672.967i 0.384471 0.923137i
\(82\) 954.489 + 1101.54i 1.28543 + 1.48347i
\(83\) 160.400 + 546.274i 0.212123 + 0.722426i 0.994967 + 0.100207i \(0.0319505\pi\)
−0.782843 + 0.622219i \(0.786231\pi\)
\(84\) 178.519 + 50.7850i 0.231881 + 0.0659654i
\(85\) 1061.77 152.660i 1.35488 0.194803i
\(86\) 449.682 389.652i 0.563843 0.488572i
\(87\) 1002.07 303.445i 1.23486 0.373940i
\(88\) −194.386 57.0769i −0.235473 0.0691411i
\(89\) −652.012 297.764i −0.776552 0.354639i −0.0126066 0.999921i \(-0.504013\pi\)
−0.763945 + 0.645281i \(0.776740\pi\)
\(90\) −128.121 795.519i −0.150057 0.931723i
\(91\) −135.138 + 939.903i −0.155673 + 1.08273i
\(92\) 114.099 + 177.541i 0.129300 + 0.201195i
\(93\) 1021.75 + 290.668i 1.13925 + 0.324095i
\(94\) 355.426 1210.47i 0.389993 1.32819i
\(95\) 608.058 + 390.775i 0.656689 + 0.422029i
\(96\) −262.353 35.4631i −0.278920 0.0377024i
\(97\) 863.513i 0.903881i −0.892048 0.451941i \(-0.850732\pi\)
0.892048 0.451941i \(-0.149268\pi\)
\(98\) −1650.44 1060.68i −1.70122 1.09331i
\(99\) −169.236 + 202.105i −0.171807 + 0.205175i
\(100\) 20.4169 + 23.5624i 0.0204169 + 0.0235624i
\(101\) 877.911 + 1013.16i 0.864905 + 0.998154i 0.999973 + 0.00731747i \(0.00232924\pi\)
−0.135068 + 0.990836i \(0.543125\pi\)
\(102\) −1442.88 910.165i −1.40065 0.883527i
\(103\) −450.478 289.504i −0.430941 0.276949i 0.307136 0.951666i \(-0.400629\pi\)
−0.738077 + 0.674717i \(0.764266\pi\)
\(104\) 625.565i 0.589824i
\(105\) −216.493 + 1601.60i −0.201215 + 1.48858i
\(106\) 360.932 + 231.957i 0.330725 + 0.212544i
\(107\) −8.42518 + 28.6935i −0.00761208 + 0.0259244i −0.963211 0.268745i \(-0.913391\pi\)
0.955599 + 0.294669i \(0.0952094\pi\)
\(108\) −82.5970 + 135.975i −0.0735917 + 0.121150i
\(109\) −382.533 595.234i −0.336147 0.523055i 0.631495 0.775380i \(-0.282441\pi\)
−0.967643 + 0.252324i \(0.918805\pi\)
\(110\) −41.4655 + 288.399i −0.0359416 + 0.249979i
\(111\) −189.935 627.223i −0.162413 0.536337i
\(112\) 2056.81 + 939.313i 1.73527 + 0.792471i
\(113\) 9.21659 + 2.70624i 0.00767278 + 0.00225293i 0.285567 0.958359i \(-0.407818\pi\)
−0.277894 + 0.960612i \(0.589636\pi\)
\(114\) −333.154 1100.18i −0.273708 0.903868i
\(115\) −1388.85 + 1203.45i −1.12618 + 0.975843i
\(116\) −226.171 + 32.5184i −0.181030 + 0.0260281i
\(117\) −746.004 325.583i −0.589471 0.257266i
\(118\) 47.3057 + 161.108i 0.0369054 + 0.125688i
\(119\) 2240.75 + 2585.97i 1.72613 + 1.99206i
\(120\) −8.98731 1064.68i −0.00683688 0.809927i
\(121\) −1039.52 + 668.060i −0.781008 + 0.501923i
\(122\) 1135.99 + 1767.64i 0.843018 + 1.31176i
\(123\) 2477.35 377.560i 1.81606 0.276776i
\(124\) −210.882 96.3066i −0.152724 0.0697467i
\(125\) −986.091 + 1138.01i −0.705589 + 0.814293i
\(126\) 1913.80 1715.74i 1.35314 1.21309i
\(127\) 1635.03 1886.92i 1.14240 1.31840i 0.201593 0.979469i \(-0.435388\pi\)
0.940810 0.338934i \(-0.110066\pi\)
\(128\) −1609.90 472.710i −1.11169 0.326422i
\(129\) −154.131 1011.33i −0.105198 0.690253i
\(130\) −890.517 + 128.037i −0.600796 + 0.0863815i
\(131\) 1485.88 678.576i 0.991004 0.452576i 0.147130 0.989117i \(-0.452997\pi\)
0.843874 + 0.536541i \(0.180269\pi\)
\(132\) 43.1576 38.0388i 0.0284575 0.0250822i
\(133\) 2305.63i 1.50318i
\(134\) −1575.77 513.912i −1.01587 0.331308i
\(135\) −1274.34 543.406i −0.812425 0.346437i
\(136\) −1703.61 1476.18i −1.07414 0.930747i
\(137\) 804.076 + 1760.68i 0.501437 + 1.09799i 0.976000 + 0.217772i \(0.0698789\pi\)
−0.474563 + 0.880222i \(0.657394\pi\)
\(138\) 2922.52 24.6700i 1.80276 0.0152178i
\(139\) −563.900 1920.47i −0.344096 1.17188i −0.931850 0.362844i \(-0.881806\pi\)
0.587754 0.809040i \(-0.300012\pi\)
\(140\) 99.3697 338.422i 0.0599877 0.204299i
\(141\) −1434.19 1627.19i −0.856601 0.971871i
\(142\) −835.404 + 1299.91i −0.493701 + 0.768214i
\(143\) 222.436 + 192.742i 0.130077 + 0.112712i
\(144\) −1244.36 + 1486.03i −0.720114 + 0.859971i
\(145\) −560.559 1909.09i −0.321048 1.09339i
\(146\) 171.608 110.286i 0.0972767 0.0625160i
\(147\) −3056.31 + 1427.07i −1.71483 + 0.800700i
\(148\) 20.3542 + 141.567i 0.0113048 + 0.0786263i
\(149\) 379.786 329.087i 0.208814 0.180938i −0.544174 0.838972i \(-0.683157\pi\)
0.752988 + 0.658034i \(0.228612\pi\)
\(150\) 426.830 65.0509i 0.232337 0.0354092i
\(151\) −475.985 + 3310.55i −0.256524 + 1.78416i 0.300617 + 0.953745i \(0.402807\pi\)
−0.557141 + 0.830418i \(0.688102\pi\)
\(152\) −216.165 1503.46i −0.115351 0.802282i
\(153\) −2647.05 + 1263.30i −1.39870 + 0.667529i
\(154\) −845.421 + 386.091i −0.442376 + 0.202027i
\(155\) 568.743 1936.96i 0.294726 1.00374i
\(156\) 150.243 + 94.7727i 0.0771092 + 0.0486403i
\(157\) −60.0915 131.582i −0.0305466 0.0668878i 0.893744 0.448578i \(-0.148069\pi\)
−0.924290 + 0.381690i \(0.875342\pi\)
\(158\) −2224.78 319.876i −1.12022 0.161063i
\(159\) 668.379 312.084i 0.333370 0.155659i
\(160\) −71.5985 + 497.978i −0.0353772 + 0.246054i
\(161\) −5624.59 1651.53i −2.75329 0.808439i
\(162\) 982.385 + 1972.08i 0.476441 + 0.956428i
\(163\) 2646.60 1.27176 0.635882 0.771786i \(-0.280637\pi\)
0.635882 + 0.771786i \(0.280637\pi\)
\(164\) −546.895 −0.260398
\(165\) 381.342 + 324.840i 0.179924 + 0.153265i
\(166\) −1565.18 714.795i −0.731817 0.334210i
\(167\) −2202.59 + 1908.55i −1.02061 + 0.884362i −0.993335 0.115266i \(-0.963228\pi\)
−0.0272731 + 0.999628i \(0.508682\pi\)
\(168\) 2841.54 1860.22i 1.30494 0.854282i
\(169\) 535.131 1171.77i 0.243573 0.533352i
\(170\) −1752.72 + 2727.29i −0.790751 + 1.23043i
\(171\) −1905.43 524.712i −0.852116 0.234653i
\(172\) 223.259i 0.0989730i
\(173\) −412.777 + 642.294i −0.181404 + 0.282270i −0.920032 0.391843i \(-0.871838\pi\)
0.738628 + 0.674113i \(0.235474\pi\)
\(174\) −1290.16 + 2889.36i −0.562108 + 1.25886i
\(175\) −857.184 123.244i −0.370269 0.0532366i
\(176\) 589.598 378.911i 0.252515 0.162281i
\(177\) 277.670 + 78.9916i 0.117915 + 0.0335445i
\(178\) 1970.54 899.917i 0.829766 0.378942i
\(179\) 1.10620 2.42224i 0.000461906 0.00101143i −0.909401 0.415921i \(-0.863459\pi\)
0.909863 + 0.414909i \(0.136187\pi\)
\(180\) 257.066 + 159.139i 0.106448 + 0.0658975i
\(181\) 686.952 + 1504.22i 0.282104 + 0.617721i 0.996643 0.0818747i \(-0.0260907\pi\)
−0.714539 + 0.699596i \(0.753363\pi\)
\(182\) −1879.34 2168.87i −0.765418 0.883339i
\(183\) 3612.46 30.4941i 1.45924 0.0123180i
\(184\) 3822.54 + 549.598i 1.53153 + 0.220201i
\(185\) −1194.95 + 350.870i −0.474890 + 0.139440i
\(186\) −2686.11 + 1758.47i −1.05890 + 0.693211i
\(187\) 1049.79 150.937i 0.410526 0.0590247i
\(188\) 255.919 + 398.217i 0.0992808 + 0.154484i
\(189\) −739.458 4356.79i −0.284591 1.67677i
\(190\) −2096.00 + 615.440i −0.800314 + 0.234993i
\(191\) −370.958 + 812.286i −0.140532 + 0.307722i −0.966791 0.255568i \(-0.917737\pi\)
0.826259 + 0.563290i \(0.190465\pi\)
\(192\) −1638.41 + 1444.08i −0.615844 + 0.542801i
\(193\) 2194.34 + 1410.21i 0.818403 + 0.525956i 0.881573 0.472047i \(-0.156485\pi\)
−0.0631701 + 0.998003i \(0.520121\pi\)
\(194\) 1972.32 + 1709.03i 0.729919 + 0.632479i
\(195\) −630.668 + 1412.40i −0.231606 + 0.518688i
\(196\) 706.313 207.392i 0.257403 0.0755802i
\(197\) −45.5652 316.913i −0.0164791 0.114615i 0.979922 0.199383i \(-0.0638939\pi\)
−0.996401 + 0.0847688i \(0.972985\pi\)
\(198\) −126.675 786.543i −0.0454668 0.282309i
\(199\) 545.540 629.587i 0.194333 0.224273i −0.650217 0.759748i \(-0.725322\pi\)
0.844551 + 0.535476i \(0.179868\pi\)
\(200\) 570.510 0.201706
\(201\) −2192.74 + 1820.03i −0.769472 + 0.638680i
\(202\) −4051.65 −1.41125
\(203\) 4156.28 4796.60i 1.43701 1.65840i
\(204\) 612.632 185.516i 0.210259 0.0636702i
\(205\) −677.733 4713.74i −0.230902 1.60596i
\(206\) 1552.81 455.946i 0.525192 0.154210i
\(207\) 2644.90 4272.45i 0.888083 1.43457i
\(208\) 1635.52 + 1417.19i 0.545206 + 0.472424i
\(209\) 601.198 + 386.366i 0.198975 + 0.127873i
\(210\) −3229.69 3664.30i −1.06129 1.20410i
\(211\) 734.174 1607.62i 0.239538 0.524516i −0.751237 0.660033i \(-0.770542\pi\)
0.990775 + 0.135517i \(0.0432695\pi\)
\(212\) −154.462 + 45.3542i −0.0500401 + 0.0146931i
\(213\) 1123.98 + 2407.20i 0.361569 + 0.774359i
\(214\) −48.8631 76.0325i −0.0156085 0.0242873i
\(215\) −1924.29 + 276.671i −0.610398 + 0.0877620i
\(216\) 890.661 + 2771.66i 0.280564 + 0.873092i
\(217\) 6178.62 1814.21i 1.93287 0.567541i
\(218\) 2116.64 + 304.327i 0.657602 + 0.0945489i
\(219\) −2.96046 350.709i −0.000913467 0.108213i
\(220\) −71.5924 82.6220i −0.0219398 0.0253199i
\(221\) 1360.43 + 2978.93i 0.414084 + 0.906718i
\(222\) 1808.53 + 807.548i 0.546759 + 0.244140i
\(223\) −300.811 + 658.684i −0.0903309 + 0.197797i −0.949405 0.314054i \(-0.898313\pi\)
0.859074 + 0.511851i \(0.171040\pi\)
\(224\) −1459.79 + 666.664i −0.435430 + 0.198854i
\(225\) 296.929 680.350i 0.0879790 0.201585i
\(226\) −24.4223 + 15.6952i −0.00718825 + 0.00461961i
\(227\) 3737.97 + 537.439i 1.09294 + 0.157141i 0.665131 0.746727i \(-0.268376\pi\)
0.427812 + 0.903868i \(0.359285\pi\)
\(228\) 393.837 + 175.857i 0.114397 + 0.0510807i
\(229\) 2109.59 3282.59i 0.608758 0.947246i −0.390882 0.920441i \(-0.627830\pi\)
0.999641 0.0268057i \(-0.00853355\pi\)
\(230\) 5554.03i 1.59227i
\(231\) −214.051 + 1583.53i −0.0609675 + 0.451034i
\(232\) −2260.53 + 3517.46i −0.639704 + 0.995398i
\(233\) −111.014 + 243.087i −0.0312136 + 0.0683482i −0.924597 0.380948i \(-0.875598\pi\)
0.893383 + 0.449296i \(0.148325\pi\)
\(234\) 2220.11 1059.54i 0.620227 0.296002i
\(235\) −3115.13 + 2699.28i −0.864718 + 0.749282i
\(236\) −57.3091 26.1722i −0.0158072 0.00721892i
\(237\) −2505.90 + 2941.78i −0.686818 + 0.806283i
\(238\) −10341.3 −2.81650
\(239\) −3049.43 −0.825319 −0.412660 0.910885i \(-0.635400\pi\)
−0.412660 + 0.910885i \(0.635400\pi\)
\(240\) 2803.92 + 2388.47i 0.754136 + 0.642397i
\(241\) 23.1500 + 6.79746i 0.00618765 + 0.00181686i 0.284825 0.958580i \(-0.408065\pi\)
−0.278637 + 0.960396i \(0.589883\pi\)
\(242\) 531.480 3696.53i 0.141177 0.981908i
\(243\) 3768.85 + 380.407i 0.994945 + 0.100424i
\(244\) −780.380 112.202i −0.204749 0.0294384i
\(245\) 2662.82 + 5830.77i 0.694374 + 1.52047i
\(246\) −4040.68 + 6405.68i −1.04725 + 1.66021i
\(247\) −621.694 + 2117.29i −0.160152 + 0.545426i
\(248\) −3858.89 + 1762.29i −0.988063 + 0.451233i
\(249\) −2475.14 + 1620.36i −0.629942 + 0.412394i
\(250\) −647.662 4504.59i −0.163847 1.13958i
\(251\) 375.453 2611.33i 0.0944159 0.656677i −0.886569 0.462595i \(-0.846918\pi\)
0.980985 0.194082i \(-0.0621727\pi\)
\(252\) 16.2808 + 964.278i 0.00406981 + 0.241047i
\(253\) −1373.18 + 1189.87i −0.341230 + 0.295677i
\(254\) 1073.88 + 7469.01i 0.265281 + 1.84507i
\(255\) 2358.18 + 5050.43i 0.579117 + 1.24028i
\(256\) 1437.26 923.672i 0.350894 0.225506i
\(257\) −882.904 3006.89i −0.214296 0.729825i −0.994541 0.104350i \(-0.966724\pi\)
0.780245 0.625474i \(-0.215095\pi\)
\(258\) 2614.99 + 1649.53i 0.631017 + 0.398044i
\(259\) −3002.33 2601.53i −0.720291 0.624136i
\(260\) 182.505 283.984i 0.0435327 0.0677382i
\(261\) 3018.15 + 4526.46i 0.715781 + 1.07349i
\(262\) −1390.86 + 4736.84i −0.327968 + 1.11696i
\(263\) −606.876 2066.83i −0.142287 0.484586i 0.857253 0.514895i \(-0.172169\pi\)
−0.999541 + 0.0303088i \(0.990351\pi\)
\(264\) −8.88590 1052.66i −0.00207155 0.245405i
\(265\) −582.327 1275.12i −0.134989 0.295585i
\(266\) −5266.21 4563.19i −1.21388 1.05183i
\(267\) 498.918 3690.96i 0.114357 0.846005i
\(268\) 532.920 320.566i 0.121467 0.0730659i
\(269\) 1000.66i 0.226807i −0.993549 0.113404i \(-0.963825\pi\)
0.993549 0.113404i \(-0.0361753\pi\)
\(270\) 3763.28 1835.18i 0.848244 0.413650i
\(271\) 6084.70 2778.79i 1.36391 0.622876i 0.407044 0.913409i \(-0.366560\pi\)
0.956865 + 0.290532i \(0.0938323\pi\)
\(272\) 7718.87 1109.81i 1.72068 0.247397i
\(273\) −4877.78 + 743.396i −1.08138 + 0.164807i
\(274\) −5612.90 1648.10i −1.23755 0.363376i
\(275\) −175.779 + 202.860i −0.0385450 + 0.0444833i
\(276\) −711.110 + 834.800i −0.155086 + 0.182062i
\(277\) 1380.01 1592.62i 0.299339 0.345456i −0.586077 0.810256i \(-0.699328\pi\)
0.885416 + 0.464800i \(0.153874\pi\)
\(278\) 5502.52 + 2512.91i 1.18712 + 0.542139i
\(279\) 93.1830 + 5519.04i 0.0199954 + 1.18429i
\(280\) −3489.38 5429.58i −0.744751 1.15886i
\(281\) −731.729 + 470.254i −0.155343 + 0.0998327i −0.616003 0.787744i \(-0.711249\pi\)
0.460660 + 0.887577i \(0.347613\pi\)
\(282\) 6555.08 55.3337i 1.38422 0.0116847i
\(283\) −4727.15 5455.42i −0.992932 1.14590i −0.989298 0.145911i \(-0.953389\pi\)
−0.00363381 0.999993i \(-0.501157\pi\)
\(284\) −163.345 556.303i −0.0341294 0.116234i
\(285\) −1027.67 + 3612.45i −0.213593 + 0.750818i
\(286\) −880.469 + 126.592i −0.182039 + 0.0261733i
\(287\) 11480.4 9947.83i 2.36121 2.04600i
\(288\) −218.730 1358.13i −0.0447528 0.277876i
\(289\) 6608.85 + 1940.53i 1.34518 + 0.394980i
\(290\) 5469.92 + 2498.03i 1.10760 + 0.505825i
\(291\) 4294.37 1300.41i 0.865087 0.261964i
\(292\) −10.8929 + 75.7617i −0.00218308 + 0.0151836i
\(293\) 1635.34 + 2544.63i 0.326066 + 0.507369i 0.965125 0.261789i \(-0.0843124\pi\)
−0.639059 + 0.769158i \(0.720676\pi\)
\(294\) 2789.39 9805.21i 0.553335 1.94507i
\(295\) 154.561 526.386i 0.0305047 0.103889i
\(296\) 2201.67 + 1414.93i 0.432330 + 0.277842i
\(297\) −1259.96 537.275i −0.246162 0.104969i
\(298\) 1518.77i 0.295235i
\(299\) −4719.82 3033.25i −0.912891 0.586679i
\(300\) −86.4319 + 137.020i −0.0166338 + 0.0263695i
\(301\) −4061.01 4686.66i −0.777650 0.897456i
\(302\) −6619.46 7639.26i −1.26128 1.45560i
\(303\) −3716.50 + 5891.75i −0.704645 + 1.11707i
\(304\) 4420.47 + 2840.86i 0.833984 + 0.535969i
\(305\) 6865.21i 1.28886i
\(306\) 2353.46 8546.31i 0.439668 1.59660i
\(307\) −6589.98 4235.12i −1.22511 0.787333i −0.241991 0.970278i \(-0.577801\pi\)
−0.983123 + 0.182945i \(0.941437\pi\)
\(308\) 98.2485 334.604i 0.0181761 0.0619020i
\(309\) 761.345 2676.27i 0.140166 0.492711i
\(310\) 3298.51 + 5132.58i 0.604332 + 0.940359i
\(311\) −530.568 + 3690.18i −0.0967388 + 0.672833i 0.882528 + 0.470259i \(0.155840\pi\)
−0.979267 + 0.202574i \(0.935069\pi\)
\(312\) 3111.02 942.074i 0.564509 0.170944i
\(313\) −847.966 387.253i −0.153131 0.0699324i 0.337376 0.941370i \(-0.390461\pi\)
−0.490506 + 0.871438i \(0.663188\pi\)
\(314\) 419.472 + 123.168i 0.0753891 + 0.0221362i
\(315\) −8291.02 + 1335.30i −1.48300 + 0.238843i
\(316\) 637.368 552.283i 0.113464 0.0983175i
\(317\) 5156.50 741.393i 0.913621 0.131359i 0.330558 0.943786i \(-0.392763\pi\)
0.583063 + 0.812427i \(0.301854\pi\)
\(318\) −610.005 + 2144.28i −0.107570 + 0.378130i
\(319\) −554.234 1887.55i −0.0972764 0.331293i
\(320\) 2717.90 + 3136.62i 0.474797 + 0.547945i
\(321\) −155.385 + 1.31166i −0.0270179 + 0.000228067i
\(322\) 14904.1 9578.29i 2.57942 1.65769i
\(323\) 4299.00 + 6689.37i 0.740565 + 1.15234i
\(324\) −800.608 205.994i −0.137278 0.0353214i
\(325\) −753.933 344.310i −0.128679 0.0587657i
\(326\) −5238.02 + 6045.00i −0.889899 + 1.02700i
\(327\) 2384.10 2798.79i 0.403183 0.473313i
\(328\) −6553.52 + 7563.17i −1.10322 + 1.27319i
\(329\) −12615.7 3704.30i −2.11406 0.620744i
\(330\) −1496.69 + 228.103i −0.249667 + 0.0380504i
\(331\) −9426.90 + 1355.38i −1.56541 + 0.225071i −0.869819 0.493371i \(-0.835765\pi\)
−0.695587 + 0.718442i \(0.744856\pi\)
\(332\) 587.282 268.203i 0.0970821 0.0443359i
\(333\) 2833.23 1889.14i 0.466247 0.310884i
\(334\) 8808.18i 1.44300i
\(335\) 3423.40 + 4196.03i 0.558330 + 0.684339i
\(336\) −1573.87 + 11643.4i −0.255540 + 1.89047i
\(337\) 6403.21 + 5548.41i 1.03503 + 0.896858i 0.994750 0.102330i \(-0.0326299\pi\)
0.0402791 + 0.999188i \(0.487175\pi\)
\(338\) 1617.30 + 3541.39i 0.260265 + 0.569900i
\(339\) 0.421315 + 49.9108i 6.75005e−5 + 0.00799642i
\(340\) −342.707 1167.15i −0.0546644 0.186170i
\(341\) 562.325 1915.10i 0.0893010 0.304131i
\(342\) 4969.61 3313.64i 0.785748 0.523921i
\(343\) −5213.48 + 8112.33i −0.820703 + 1.27704i
\(344\) 3087.52 + 2675.35i 0.483918 + 0.419317i
\(345\) −8076.45 5094.61i −1.26035 0.795027i
\(346\) −650.092 2214.01i −0.101009 0.344005i
\(347\) −2150.34 + 1381.94i −0.332669 + 0.213793i −0.696302 0.717749i \(-0.745173\pi\)
0.363633 + 0.931542i \(0.381536\pi\)
\(348\) −502.322 1075.81i −0.0773773 0.165716i
\(349\) −516.808 3594.48i −0.0792667 0.551312i −0.990296 0.138971i \(-0.955620\pi\)
0.911030 0.412341i \(-0.135289\pi\)
\(350\) 1978.00 1713.94i 0.302081 0.261755i
\(351\) 495.717 4200.30i 0.0753830 0.638733i
\(352\) −70.7906 + 492.360i −0.0107192 + 0.0745536i
\(353\) −891.815 6202.71i −0.134466 0.935232i −0.939633 0.342184i \(-0.888833\pi\)
0.805167 0.593048i \(-0.202076\pi\)
\(354\) −729.974 + 477.880i −0.109598 + 0.0717487i
\(355\) 4592.40 2097.28i 0.686590 0.313555i
\(356\) −229.002 + 779.908i −0.0340929 + 0.116110i
\(357\) −9485.89 + 15037.9i −1.40629 + 2.22939i
\(358\) 3.34321 + 7.32061i 0.000493559 + 0.00108074i
\(359\) −3419.59 491.662i −0.502726 0.0722812i −0.113714 0.993514i \(-0.536275\pi\)
−0.389013 + 0.921232i \(0.627184\pi\)
\(360\) 5281.25 1648.05i 0.773184 0.241278i
\(361\) 213.614 1485.72i 0.0311436 0.216609i
\(362\) −4795.31 1408.03i −0.696232 0.204432i
\(363\) −4887.83 4163.61i −0.706734 0.602019i
\(364\) 1076.81 0.155055
\(365\) −666.496 −0.0955781
\(366\) −7079.97 + 8311.45i −1.01114 + 1.18701i
\(367\) 6163.61 + 2814.83i 0.876670 + 0.400362i 0.802337 0.596872i \(-0.203590\pi\)
0.0743335 + 0.997233i \(0.476317\pi\)
\(368\) −10096.7 + 8748.82i −1.43023 + 1.23930i
\(369\) 5608.44 + 11751.6i 0.791229 + 1.65790i
\(370\) 1563.58 3423.77i 0.219694 0.481063i
\(371\) 2417.49 3761.69i 0.338302 0.526408i
\(372\) 161.367 1193.78i 0.0224905 0.166383i
\(373\) 8530.70i 1.18419i 0.805868 + 0.592095i \(0.201699\pi\)
−0.805868 + 0.592095i \(0.798301\pi\)
\(374\) −1732.95 + 2696.52i −0.239595 + 0.372817i
\(375\) −7144.49 3190.17i −0.983840 0.439306i
\(376\) 8573.78 + 1232.72i 1.17596 + 0.169077i
\(377\) 5110.14 3284.09i 0.698105 0.448645i
\(378\) 11414.7 + 6933.79i 1.55320 + 0.943481i
\(379\) 6260.21 2858.94i 0.848458 0.387478i 0.0567581 0.998388i \(-0.481924\pi\)
0.791700 + 0.610910i \(0.209196\pi\)
\(380\) 340.496 745.583i 0.0459661 0.100652i
\(381\) 11846.2 + 5289.59i 1.59291 + 0.711270i
\(382\) −1121.13 2454.93i −0.150162 0.328809i
\(383\) −2588.94 2987.80i −0.345402 0.398615i 0.556294 0.830985i \(-0.312223\pi\)
−0.901696 + 0.432370i \(0.857677\pi\)
\(384\) −73.5929 8718.14i −0.00978000 1.15858i
\(385\) 3005.74 + 432.159i 0.397887 + 0.0572075i
\(386\) −7563.95 + 2220.98i −0.997396 + 0.292862i
\(387\) 4797.37 2289.54i 0.630139 0.300733i
\(388\) −969.255 + 139.358i −0.126821 + 0.0182341i
\(389\) −5168.63 8042.55i −0.673676 1.04826i −0.994862 0.101244i \(-0.967718\pi\)
0.321185 0.947016i \(-0.395919\pi\)
\(390\) −1977.83 4235.84i −0.256798 0.549975i
\(391\) −19398.1 + 5695.80i −2.50896 + 0.736698i
\(392\) 5595.77 12253.0i 0.720993 1.57875i
\(393\) 5612.32 + 6367.55i 0.720366 + 0.817304i
\(394\) 814.029 + 523.145i 0.104087 + 0.0668925i
\(395\) 5550.03 + 4809.13i 0.706968 + 0.612591i
\(396\) 254.166 + 157.344i 0.0322533 + 0.0199667i
\(397\) −4316.15 + 1267.34i −0.545646 + 0.160216i −0.542926 0.839780i \(-0.682684\pi\)
−0.00271926 + 0.999996i \(0.500866\pi\)
\(398\) 358.310 + 2492.10i 0.0451267 + 0.313863i
\(399\) −11466.2 + 3472.18i −1.43867 + 0.435655i
\(400\) −1292.46 + 1491.58i −0.161558 + 0.186448i
\(401\) −5144.78 −0.640694 −0.320347 0.947300i \(-0.603799\pi\)
−0.320347 + 0.947300i \(0.603799\pi\)
\(402\) 182.709 8610.47i 0.0226683 1.06829i
\(403\) 6163.11 0.761802
\(404\) 995.549 1148.92i 0.122600 0.141488i
\(405\) 783.339 7155.79i 0.0961097 0.877961i
\(406\) 2729.83 + 18986.4i 0.333693 + 2.32089i
\(407\) −1181.47 + 346.911i −0.143890 + 0.0422499i
\(408\) 4775.70 10695.3i 0.579491 1.29779i
\(409\) −5074.60 4397.17i −0.613504 0.531604i 0.291740 0.956498i \(-0.405766\pi\)
−0.905243 + 0.424894i \(0.860311\pi\)
\(410\) 12107.8 + 7781.22i 1.45844 + 0.937286i
\(411\) −7545.20 + 6650.29i −0.905541 + 0.798138i
\(412\) −252.255 + 552.362i −0.0301644 + 0.0660508i
\(413\) 1679.10 493.027i 0.200056 0.0587416i
\(414\) 4523.88 + 14496.9i 0.537045 + 1.72098i
\(415\) 3039.45 + 4729.47i 0.359519 + 0.559423i
\(416\) −1520.31 + 218.587i −0.179181 + 0.0257623i
\(417\) 8701.54 5696.49i 1.02186 0.668965i
\(418\) −2072.35 + 608.496i −0.242492 + 0.0712022i
\(419\) 1691.19 + 243.156i 0.197183 + 0.0283507i 0.240199 0.970724i \(-0.422787\pi\)
−0.0430155 + 0.999074i \(0.513696\pi\)
\(420\) 1832.67 15.4702i 0.212917 0.00179730i
\(421\) 73.8427 + 85.2190i 0.00854839 + 0.00986537i 0.760008 0.649914i \(-0.225195\pi\)
−0.751459 + 0.659779i \(0.770650\pi\)
\(422\) 2218.86 + 4858.62i 0.255953 + 0.560459i
\(423\) 5932.39 9582.90i 0.681898 1.10151i
\(424\) −1223.73 + 2679.59i −0.140164 + 0.306916i
\(425\) −2716.76 + 1240.70i −0.310076 + 0.141607i
\(426\) −7722.73 2196.96i −0.878328 0.249867i
\(427\) 18422.7 11839.5i 2.08790 1.34181i
\(428\) 33.5669 + 4.82619i 0.00379093 + 0.000545053i
\(429\) −623.552 + 1396.46i −0.0701757 + 0.157161i
\(430\) 3176.53 4942.78i 0.356247 0.554330i
\(431\) 5352.65i 0.598209i 0.954220 + 0.299105i \(0.0966880\pi\)
−0.954220 + 0.299105i \(0.903312\pi\)
\(432\) −9264.18 3950.46i −1.03177 0.439969i
\(433\) −1792.53 + 2789.23i −0.198946 + 0.309565i −0.926364 0.376628i \(-0.877083\pi\)
0.727419 + 0.686194i \(0.240720\pi\)
\(434\) −8084.68 + 17703.0i −0.894186 + 1.95799i
\(435\) 8649.99 5662.75i 0.953414 0.624156i
\(436\) −606.388 + 525.438i −0.0666071 + 0.0577154i
\(437\) −12391.6 5659.06i −1.35646 0.619473i
\(438\) 806.902 + 687.346i 0.0880257 + 0.0749832i
\(439\) 10721.7 1.16565 0.582824 0.812598i \(-0.301948\pi\)
0.582824 + 0.812598i \(0.301948\pi\)
\(440\) −2000.51 −0.216751
\(441\) −11699.7 13050.4i −1.26333 1.40917i
\(442\) −9496.58 2788.45i −1.02196 0.300074i
\(443\) −1548.68 + 10771.3i −0.166095 + 1.15522i 0.720766 + 0.693178i \(0.243790\pi\)
−0.886861 + 0.462037i \(0.847119\pi\)
\(444\) −673.377 + 314.417i −0.0719754 + 0.0336072i
\(445\) −7005.89 1007.30i −0.746317 0.107304i
\(446\) −909.126 1990.71i −0.0965210 0.211352i
\(447\) 2208.53 + 1393.14i 0.233691 + 0.147412i
\(448\) −3729.86 + 12702.7i −0.393346 + 1.33961i
\(449\) −15346.9 + 7008.70i −1.61306 + 0.736661i −0.998631 0.0523080i \(-0.983342\pi\)
−0.614432 + 0.788969i \(0.710615\pi\)
\(450\) 966.295 + 2024.72i 0.101226 + 0.212103i
\(451\) −670.086 4660.55i −0.0699626 0.486600i
\(452\) 1.55021 10.7820i 0.000161318 0.00112199i
\(453\) −17180.6 + 2618.41i −1.78193 + 0.271575i
\(454\) −8625.57 + 7474.10i −0.891669 + 0.772636i
\(455\) 1334.42 + 9281.11i 0.137492 + 0.956275i
\(456\) 7151.39 3339.17i 0.734418 0.342919i
\(457\) −10777.4 + 6926.19i −1.10316 + 0.708958i −0.959792 0.280712i \(-0.909429\pi\)
−0.143368 + 0.989670i \(0.545793\pi\)
\(458\) 3322.44 + 11315.2i 0.338968 + 1.15442i
\(459\) −10268.9 11261.7i −1.04425 1.14521i
\(460\) 1574.95 + 1364.71i 0.159636 + 0.138325i
\(461\) −9361.05 + 14566.1i −0.945743 + 1.47160i −0.0650697 + 0.997881i \(0.520727\pi\)
−0.880673 + 0.473724i \(0.842909\pi\)
\(462\) −3193.25 3622.96i −0.321566 0.364838i
\(463\) 2053.56 6993.79i 0.206128 0.702006i −0.789922 0.613207i \(-0.789879\pi\)
0.996050 0.0887987i \(-0.0283028\pi\)
\(464\) −4075.16 13878.7i −0.407725 1.38858i
\(465\) 10489.3 88.5436i 1.04608 0.00883034i
\(466\) −335.512 734.668i −0.0333525 0.0730319i
\(467\) −4728.49 4097.26i −0.468541 0.405993i 0.388333 0.921519i \(-0.373051\pi\)
−0.856874 + 0.515526i \(0.827596\pi\)
\(468\) −245.058 + 889.901i −0.0242048 + 0.0878967i
\(469\) −5356.08 + 16423.0i −0.527336 + 1.61693i
\(470\) 12457.4i 1.22259i
\(471\) 563.880 497.000i 0.0551639 0.0486211i
\(472\) −1048.69 + 478.919i −0.102266 + 0.0467035i
\(473\) −1902.58 + 273.550i −0.184949 + 0.0265916i
\(474\) −1759.64 11545.9i −0.170513 1.11882i
\(475\) −1930.96 566.980i −0.186523 0.0547680i
\(476\) 2541.01 2932.48i 0.244678 0.282374i
\(477\) 2558.58 + 2853.96i 0.245596 + 0.273949i
\(478\) 6035.29 6965.10i 0.577506 0.666477i
\(479\) 152.924 + 69.8382i 0.0145872 + 0.00666177i 0.422695 0.906272i \(-0.361084\pi\)
−0.408108 + 0.912934i \(0.633811\pi\)
\(480\) −2584.34 + 393.865i −0.245747 + 0.0374529i
\(481\) −2055.60 3198.58i −0.194859 0.303207i
\(482\) −61.3433 + 39.4229i −0.00579691 + 0.00372545i
\(483\) −257.115 30459.0i −0.0242218 2.86942i
\(484\) 917.630 + 1059.00i 0.0861786 + 0.0994554i
\(485\) −2402.28 8181.40i −0.224911 0.765976i
\(486\) −8328.00 + 7855.40i −0.777295 + 0.733186i
\(487\) 11441.4 1645.02i 1.06460 0.153066i 0.412313 0.911042i \(-0.364721\pi\)
0.652282 + 0.757976i \(0.273812\pi\)
\(488\) −10903.1 + 9447.58i −1.01139 + 0.876377i
\(489\) 3985.66 + 13161.9i 0.368585 + 1.21718i
\(490\) −18588.0 5457.93i −1.71371 0.503192i
\(491\) 16420.9 + 7499.19i 1.50930 + 0.689275i 0.986587 0.163234i \(-0.0521925\pi\)
0.522713 + 0.852508i \(0.324920\pi\)
\(492\) −823.600 2719.78i −0.0754690 0.249222i
\(493\) 3115.12 21666.1i 0.284580 1.97930i
\(494\) −3605.61 5610.44i −0.328389 0.510983i
\(495\) −1041.19 + 2385.66i −0.0945413 + 0.216621i
\(496\) 4134.65 14081.3i 0.374297 1.27474i
\(497\) 13547.9 + 8706.71i 1.22275 + 0.785814i
\(498\) 1197.67 8860.31i 0.107769 0.797269i
\(499\) 11887.5i 1.06645i 0.845973 + 0.533226i \(0.179021\pi\)
−0.845973 + 0.533226i \(0.820979\pi\)
\(500\) 1436.50 + 923.186i 0.128485 + 0.0825722i
\(501\) −12808.5 8079.58i −1.14220 0.720497i
\(502\) 5221.38 + 6025.79i 0.464226 + 0.535745i
\(503\) −4505.70 5199.85i −0.399402 0.460934i 0.520051 0.854135i \(-0.325913\pi\)
−0.919452 + 0.393201i \(0.871368\pi\)
\(504\) 13530.4 + 11329.9i 1.19582 + 1.00134i
\(505\) 11136.4 + 7156.94i 0.981315 + 0.630653i
\(506\) 5491.36i 0.482452i
\(507\) 6633.27 + 896.639i 0.581053 + 0.0785427i
\(508\) −2381.85 1530.72i −0.208027 0.133691i
\(509\) −1256.92 + 4280.69i −0.109454 + 0.372767i −0.995943 0.0899826i \(-0.971319\pi\)
0.886489 + 0.462749i \(0.153137\pi\)
\(510\) −16202.7 4609.35i −1.40680 0.400206i
\(511\) −1149.42 1788.53i −0.0995054 0.154833i
\(512\) 1175.45 8175.42i 0.101461 0.705676i
\(513\) −260.030 10266.2i −0.0223793 0.883551i
\(514\) 8615.34 + 3934.50i 0.739312 + 0.337633i
\(515\) −5073.47 1489.71i −0.434104 0.127465i
\(516\) −1110.30 + 336.219i −0.0947251 + 0.0286845i
\(517\) −3079.98 + 2668.82i −0.262007 + 0.227030i
\(518\) 11884.1 1708.68i 1.00803 0.144933i
\(519\) −3815.84 1085.53i −0.322730 0.0918103i
\(520\) −1740.31 5926.95i −0.146765 0.499834i
\(521\) −6810.98 7860.29i −0.572734 0.660970i 0.393293 0.919413i \(-0.371336\pi\)
−0.966026 + 0.258443i \(0.916791\pi\)
\(522\) −16312.1 2064.90i −1.36774 0.173138i
\(523\) 13075.3 8403.00i 1.09320 0.702557i 0.135631 0.990759i \(-0.456694\pi\)
0.957570 + 0.288202i \(0.0930575\pi\)
\(524\) −1001.47 1558.32i −0.0834912 0.129915i
\(525\) −677.971 4448.49i −0.0563601 0.369806i
\(526\) 5921.87 + 2704.43i 0.490886 + 0.224180i
\(527\) 14543.5 16784.0i 1.20213 1.38733i
\(528\) 2772.29 + 2361.53i 0.228501 + 0.194644i
\(529\) 14713.7 16980.6i 1.20932 1.39563i
\(530\) 4064.97 + 1193.58i 0.333153 + 0.0978225i
\(531\) 25.3233 + 1499.85i 0.00206956 + 0.122576i
\(532\) 2587.97 372.093i 0.210907 0.0303239i
\(533\) 13225.0 6039.65i 1.07474 0.490818i
\(534\) 7442.96 + 8444.54i 0.603162 + 0.684328i
\(535\) 295.297i 0.0238632i
\(536\) 1952.87 11211.3i 0.157371 0.903460i
\(537\) 13.7120 + 1.85349i 0.00110189 + 0.000148946i
\(538\) 2285.57 + 1980.46i 0.183156 + 0.158705i
\(539\) 2632.78 + 5764.98i 0.210393 + 0.460696i
\(540\) −404.291 + 1518.08i −0.0322184 + 0.120977i
\(541\) −234.432 798.402i −0.0186303 0.0634491i 0.949653 0.313303i \(-0.101436\pi\)
−0.968284 + 0.249854i \(0.919617\pi\)
\(542\) −5695.62 + 19397.5i −0.451380 + 1.53726i
\(543\) −6446.15 + 5681.59i −0.509449 + 0.449025i
\(544\) −2992.28 + 4656.08i −0.235833 + 0.366963i
\(545\) −5280.26 4575.37i −0.415012 0.359610i
\(546\) 7955.90 12612.5i 0.623592 0.988577i
\(547\) 1815.72 + 6183.78i 0.141928 + 0.483362i 0.999520 0.0309676i \(-0.00985886\pi\)
−0.857592 + 0.514330i \(0.828041\pi\)
\(548\) 1846.52 1186.69i 0.143940 0.0925049i
\(549\) 5591.87 + 17919.4i 0.434709 + 1.39304i
\(550\) −115.451 802.981i −0.00895065 0.0622531i
\(551\) 11146.7 9658.68i 0.861826 0.746776i
\(552\) 3023.36 + 19837.7i 0.233121 + 1.52962i
\(553\) −3333.79 + 23187.0i −0.256360 + 1.78303i
\(554\) 906.390 + 6304.08i 0.0695105 + 0.483456i
\(555\) −3544.47 5414.27i −0.271089 0.414095i
\(556\) −2064.63 + 942.886i −0.157482 + 0.0719196i
\(557\) −1936.85 + 6596.32i −0.147338 + 0.501787i −0.999779 0.0210371i \(-0.993303\pi\)
0.852441 + 0.522824i \(0.175121\pi\)
\(558\) −12790.3 10710.2i −0.970350 0.812542i
\(559\) −2465.57 5398.85i −0.186552 0.408492i
\(560\) 22100.5 + 3177.57i 1.66771 + 0.239780i
\(561\) 2331.57 + 4993.45i 0.175471 + 0.375799i
\(562\) 374.114 2602.02i 0.0280802 0.195302i
\(563\) −12598.6 3699.30i −0.943108 0.276921i −0.226193 0.974082i \(-0.572628\pi\)
−0.716915 + 0.697161i \(0.754446\pi\)
\(564\) −1594.99 + 1872.42i −0.119080 + 0.139793i
\(565\) 94.8518 0.00706273
\(566\) 21816.3 1.62015
\(567\) 20553.3 10238.6i 1.52233 0.758341i
\(568\) −9650.67 4407.31i −0.712910 0.325575i
\(569\) 2964.85 2569.05i 0.218441 0.189280i −0.538766 0.842456i \(-0.681109\pi\)
0.757206 + 0.653176i \(0.226564\pi\)
\(570\) −6217.15 9496.85i −0.456856 0.697859i
\(571\) −7703.83 + 16869.0i −0.564615 + 1.23634i 0.385000 + 0.922917i \(0.374202\pi\)
−0.949615 + 0.313419i \(0.898526\pi\)
\(572\) 180.446 280.780i 0.0131903 0.0205245i
\(573\) −4598.26 621.559i −0.335244 0.0453159i
\(574\) 45910.3i 3.33843i
\(575\) 2766.30 4304.44i 0.200630 0.312187i
\(576\) −9649.01 5973.31i −0.697989 0.432097i
\(577\) 9172.90 + 1318.86i 0.661825 + 0.0951560i 0.465039 0.885290i \(-0.346040\pi\)
0.196786 + 0.980446i \(0.436950\pi\)
\(578\) −17512.2 + 11254.4i −1.26023 + 0.809901i
\(579\) −3708.61 + 13036.5i −0.266191 + 0.935711i
\(580\) −2052.40 + 937.300i −0.146933 + 0.0671022i
\(581\) −7449.70 + 16312.6i −0.531955 + 1.16482i
\(582\) −5528.99 + 12382.3i −0.393787 + 0.881898i
\(583\) −575.757 1260.73i −0.0409012 0.0895612i
\(584\) 917.200 + 1058.51i 0.0649898 + 0.0750022i
\(585\) −7973.82 1009.38i −0.563551 0.0713382i
\(586\) −9048.69 1301.00i −0.637880 0.0917133i
\(587\) 23993.6 7045.16i 1.68709 0.495375i 0.709292 0.704915i \(-0.249015\pi\)
0.977800 + 0.209540i \(0.0671967\pi\)
\(588\) 2095.07 + 3200.27i 0.146937 + 0.224450i
\(589\) 14812.2 2129.68i 1.03621 0.148984i
\(590\) 896.400 + 1394.83i 0.0625495 + 0.0973290i
\(591\) 1507.43 703.859i 0.104920 0.0489897i
\(592\) −8687.07 + 2550.75i −0.603102 + 0.177087i
\(593\) −495.692 + 1085.41i −0.0343265 + 0.0751646i −0.926019 0.377478i \(-0.876791\pi\)
0.891692 + 0.452643i \(0.149519\pi\)
\(594\) 3720.82 1814.47i 0.257015 0.125335i
\(595\) 28424.2 + 18267.1i 1.95845 + 1.25862i
\(596\) −430.676 373.183i −0.0295993 0.0256480i
\(597\) 3952.58 + 1764.92i 0.270969 + 0.120994i
\(598\) 16269.4 4777.12i 1.11255 0.326674i
\(599\) −2517.53 17509.8i −0.171725 1.19438i −0.875238 0.483692i \(-0.839295\pi\)
0.703513 0.710683i \(-0.251614\pi\)
\(600\) 859.164 + 2837.23i 0.0584587 + 0.193049i
\(601\) −1527.10 + 1762.36i −0.103647 + 0.119614i −0.805203 0.593000i \(-0.797944\pi\)
0.701556 + 0.712614i \(0.252489\pi\)
\(602\) 18742.0 1.26888
\(603\) −12353.4 8163.91i −0.834278 0.551343i
\(604\) 3792.76 0.255505
\(605\) −7990.47 + 9221.50i −0.536957 + 0.619681i
\(606\) −6101.61 20149.4i −0.409012 1.35068i
\(607\) −3187.63 22170.5i −0.213150 1.48249i −0.762549 0.646931i \(-0.776052\pi\)
0.549399 0.835560i \(-0.314857\pi\)
\(608\) −3578.33 + 1050.69i −0.238685 + 0.0700842i
\(609\) 30113.3 + 13446.3i 2.00370 + 0.894696i
\(610\) 15680.6 + 13587.3i 1.04080 + 0.901859i
\(611\) −10586.3 6803.43i −0.700946 0.450470i
\(612\) 1845.19 + 2767.32i 0.121875 + 0.182782i
\(613\) −5278.38 + 11558.0i −0.347784 + 0.761541i 0.652210 + 0.758039i \(0.273842\pi\)
−0.999994 + 0.00350269i \(0.998885\pi\)
\(614\) 22715.9 6669.99i 1.49306 0.438402i
\(615\) 22421.4 10469.1i 1.47011 0.686434i
\(616\) −3450.01 5368.32i −0.225657 0.351129i
\(617\) −12918.3 + 1857.37i −0.842905 + 0.121191i −0.550222 0.835018i \(-0.685457\pi\)
−0.292682 + 0.956210i \(0.594548\pi\)
\(618\) 4605.95 + 7035.71i 0.299803 + 0.457957i
\(619\) −14366.2 + 4218.29i −0.932836 + 0.273905i −0.712624 0.701547i \(-0.752493\pi\)
−0.220212 + 0.975452i \(0.570675\pi\)
\(620\) −2265.94 325.792i −0.146778 0.0211035i
\(621\) 25230.6 + 6719.33i 1.63038 + 0.434199i
\(622\) −7378.54 8515.29i −0.475647 0.548926i
\(623\) −9379.07 20537.3i −0.603154 1.32072i
\(624\) −4584.84 + 10267.9i −0.294135 + 0.658725i
\(625\) −4749.20 + 10399.3i −0.303949 + 0.665556i
\(626\) 2562.77 1170.38i 0.163624 0.0747246i
\(627\) −1016.07 + 3571.69i −0.0647179 + 0.227495i
\(628\) −137.997 + 88.6853i −0.00876860 + 0.00563524i
\(629\) −13561.4 1949.84i −0.859665 0.123601i
\(630\) 13359.3 21580.0i 0.844837 1.36471i
\(631\) 12805.9 19926.4i 0.807915 1.25714i −0.155155 0.987890i \(-0.549588\pi\)
0.963070 0.269250i \(-0.0867758\pi\)
\(632\) 15432.5i 0.971313i
\(633\) 9100.53 + 1230.15i 0.571428 + 0.0772415i
\(634\) −8512.11 + 13245.1i −0.533216 + 0.829701i
\(635\) 10241.8 22426.3i 0.640051 1.40152i
\(636\) −458.166 699.860i −0.0285652 0.0436340i
\(637\) −14789.7 + 12815.3i −0.919920 + 0.797115i
\(638\) 5408.20 + 2469.84i 0.335600 + 0.153263i
\(639\) −10278.7 + 9214.86i −0.636334 + 0.570476i
\(640\) −16568.2 −1.02330
\(641\) 21308.3 1.31299 0.656495 0.754331i \(-0.272038\pi\)
0.656495 + 0.754331i \(0.272038\pi\)
\(642\) 304.534 357.505i 0.0187212 0.0219776i
\(643\) −12534.5 3680.46i −0.768759 0.225728i −0.126242 0.991999i \(-0.540292\pi\)
−0.642517 + 0.766272i \(0.722110\pi\)
\(644\) −946.044 + 6579.88i −0.0578872 + 0.402614i
\(645\) −4273.83 9153.11i −0.260902 0.558765i
\(646\) −23787.3 3420.10i −1.44876 0.208300i
\(647\) 2669.23 + 5844.81i 0.162192 + 0.355151i 0.973227 0.229847i \(-0.0738225\pi\)
−0.811035 + 0.584998i \(0.801095\pi\)
\(648\) −12442.6 + 8603.39i −0.754306 + 0.521563i
\(649\) 152.817 520.447i 0.00924282 0.0314782i
\(650\) 2278.57 1040.59i 0.137497 0.0627928i
\(651\) 18327.0 + 27995.0i 1.10337 + 1.68542i
\(652\) −427.120 2970.69i −0.0256554 0.178437i
\(653\) 896.788 6237.30i 0.0537428 0.373789i −0.945146 0.326650i \(-0.894080\pi\)
0.998888 0.0471396i \(-0.0150106\pi\)
\(654\) 1674.11 + 10984.7i 0.100096 + 0.656780i
\(655\) 12190.2 10562.9i 0.727193 0.630116i
\(656\) −4926.99 34268.0i −0.293242 2.03954i
\(657\) 1739.67 542.876i 0.103304 0.0322369i
\(658\) 33429.3 21483.7i 1.98056 1.27283i
\(659\) 6273.86 + 21366.8i 0.370857 + 1.26302i 0.907799 + 0.419405i \(0.137761\pi\)
−0.536942 + 0.843619i \(0.680421\pi\)
\(660\) 303.076 480.464i 0.0178745 0.0283364i
\(661\) −24592.7 21309.7i −1.44712 1.25393i −0.912648 0.408747i \(-0.865966\pi\)
−0.534470 0.845187i \(-0.679489\pi\)
\(662\) 15561.5 24214.2i 0.913618 1.42162i
\(663\) −12765.9 + 11251.8i −0.747792 + 0.659098i
\(664\) 3328.44 11335.6i 0.194531 0.662510i
\(665\) 6414.21 + 21844.8i 0.374034 + 1.27384i
\(666\) −1292.48 + 10210.2i −0.0751990 + 0.594049i
\(667\) 15578.0 + 34111.0i 0.904319 + 1.98018i
\(668\) 2497.73 + 2164.30i 0.144671 + 0.125358i
\(669\) −3728.74 504.024i −0.215488 0.0291281i
\(670\) −16359.4 485.320i −0.943314 0.0279844i
\(671\) 6787.75i 0.390519i
\(672\) −5513.79 6255.77i −0.316517 0.359110i
\(673\) −21253.0 + 9705.92i −1.21730 + 0.555923i −0.917369 0.398038i \(-0.869691\pi\)
−0.299932 + 0.953961i \(0.596964\pi\)
\(674\) −25345.9 + 3644.18i −1.44850 + 0.208262i
\(675\) 3830.64 + 452.090i 0.218432 + 0.0257792i
\(676\) −1401.62 411.554i −0.0797465 0.0234157i
\(677\) −7879.12 + 9092.99i −0.447296 + 0.516207i −0.933958 0.357383i \(-0.883669\pi\)
0.486662 + 0.873590i \(0.338214\pi\)
\(678\) −114.833 97.8189i −0.00650465 0.00554087i
\(679\) 17811.7 20555.8i 1.00670 1.16180i
\(680\) −20247.6 9246.78i −1.14185 0.521467i
\(681\) 2956.47 + 19398.8i 0.166361 + 1.09158i
\(682\) 3261.29 + 5074.67i 0.183111 + 0.284926i
\(683\) 1827.51 1174.47i 0.102383 0.0657976i −0.488447 0.872593i \(-0.662437\pi\)
0.590830 + 0.806796i \(0.298800\pi\)
\(684\) −281.459 + 2223.44i −0.0157337 + 0.124291i
\(685\) 12516.4 + 14444.7i 0.698144 + 0.805701i
\(686\) −8210.81 27963.5i −0.456983 1.55634i
\(687\) 19501.7 + 5547.85i 1.08302 + 0.308098i
\(688\) −13989.2 + 2011.35i −0.775196 + 0.111456i
\(689\) 3234.33 2802.56i 0.178836 0.154962i
\(690\) 27621.0 8364.13i 1.52393 0.461474i
\(691\) 9940.69 + 2918.85i 0.547267 + 0.160692i 0.543666 0.839301i \(-0.317036\pi\)
0.00360079 + 0.999994i \(0.498854\pi\)
\(692\) 787.562 + 359.668i 0.0432639 + 0.0197580i
\(693\) −8197.48 + 1320.23i −0.449345 + 0.0723685i
\(694\) 1099.41 7646.57i 0.0601341 0.418242i
\(695\) −10685.4 16626.8i −0.583195 0.907469i
\(696\) −20897.1 5944.80i −1.13808 0.323760i
\(697\) 14760.0 50267.8i 0.802114 2.73175i
\(698\) 9232.86 + 5933.60i 0.500672 + 0.321762i
\(699\) −1376.08 186.009i −0.0744611 0.0100651i
\(700\) 982.040i 0.0530252i
\(701\) 11646.5 + 7484.74i 0.627506 + 0.403274i 0.815385 0.578919i \(-0.196525\pi\)
−0.187880 + 0.982192i \(0.560161\pi\)
\(702\) 8612.65 + 9445.28i 0.463053 + 0.507819i
\(703\) −6045.64 6977.04i −0.324346 0.374316i
\(704\) 2687.23 + 3101.23i 0.143862 + 0.166025i
\(705\) −18115.1 11427.0i −0.967737 0.610446i
\(706\) 15932.4 + 10239.1i 0.849327 + 0.545829i
\(707\) 42226.9i 2.24626i
\(708\) 43.8528 324.420i 0.00232781 0.0172210i
\(709\) −10524.4 6763.61i −0.557477 0.358269i 0.231363 0.972868i \(-0.425682\pi\)
−0.788840 + 0.614599i \(0.789318\pi\)
\(710\) −4298.74 + 14640.2i −0.227224 + 0.773854i
\(711\) −18403.6 8032.01i −0.970732 0.423662i
\(712\) 8041.42 + 12512.7i 0.423266 + 0.658614i
\(713\) −5414.68 + 37659.9i −0.284406 + 1.97809i
\(714\) −15573.6 51428.7i −0.816283 2.69562i
\(715\) 2643.68 + 1207.33i 0.138277 + 0.0631491i
\(716\) −2.89738 0.850747i −0.000151229 4.44049e-5i
\(717\) −4592.31 15165.2i −0.239195 0.789897i
\(718\) 7890.87 6837.48i 0.410146 0.355393i
\(719\) −31733.9 + 4562.64i −1.64600 + 0.236659i −0.902067 0.431597i \(-0.857950\pi\)
−0.743932 + 0.668255i \(0.767041\pi\)
\(720\) −7655.62 + 17541.2i −0.396261 + 0.907949i
\(721\) −4751.95 16183.6i −0.245453 0.835937i
\(722\) 2970.70 + 3428.38i 0.153128 + 0.176719i
\(723\) 1.05825 + 125.365i 5.44353e−5 + 0.00644865i
\(724\) 1577.55 1013.83i 0.0809796 0.0520424i
\(725\) 2995.06 + 4660.40i 0.153426 + 0.238735i
\(726\) 19183.7 2923.69i 0.980681 0.149460i
\(727\) 21676.2 + 9899.18i 1.10581 + 0.505007i 0.882772 0.469802i \(-0.155675\pi\)
0.223040 + 0.974809i \(0.428402\pi\)
\(728\) 12903.6 14891.5i 0.656920 0.758126i
\(729\) 3783.91 + 19315.9i 0.192242 + 0.981347i
\(730\) 1319.10 1522.32i 0.0668795 0.0771830i
\(731\) −20520.9 6025.47i −1.03829 0.304870i
\(732\) −617.225 4049.91i −0.0311657 0.204493i
\(733\) −22523.9 + 3238.45i −1.13498 + 0.163186i −0.684093 0.729395i \(-0.739802\pi\)
−0.450888 + 0.892581i \(0.648893\pi\)
\(734\) −18628.0 + 8507.12i −0.936746 + 0.427797i
\(735\) −24987.1 + 22023.5i −1.25396 + 1.10524i
\(736\) 9481.95i 0.474877i
\(737\) 3384.78 + 4148.69i 0.169172 + 0.207353i
\(738\) −37941.4 10448.2i −1.89247 0.521143i
\(739\) −16472.4 14273.4i −0.819957 0.710497i 0.140150 0.990130i \(-0.455242\pi\)
−0.960107 + 0.279634i \(0.909787\pi\)
\(740\) 586.682 + 1284.65i 0.0291444 + 0.0638174i
\(741\) −11465.8 + 96.7871i −0.568432 + 0.00479833i
\(742\) 3807.36 + 12966.7i 0.188373 + 0.641538i
\(743\) 1430.09 4870.45i 0.0706125 0.240484i −0.916623 0.399754i \(-0.869096\pi\)
0.987235 + 0.159270i \(0.0509139\pi\)
\(744\) −14575.4 16536.8i −0.718228 0.814879i
\(745\) 2682.79 4174.51i 0.131933 0.205291i
\(746\) −19484.7 16883.6i −0.956280 0.828621i
\(747\) −11785.7 9869.01i −0.577265 0.483385i
\(748\) −338.840 1153.98i −0.0165631 0.0564088i
\(749\) −792.423 + 509.259i −0.0386576 + 0.0248437i
\(750\) 21426.6 10004.6i 1.04318 0.487090i
\(751\) 137.273 + 954.752i 0.00666997 + 0.0463907i 0.992885 0.119080i \(-0.0379946\pi\)
−0.986215 + 0.165471i \(0.947086\pi\)
\(752\) −22646.4 + 19623.2i −1.09818 + 0.951576i
\(753\) 13551.9 2065.38i 0.655857 0.0999556i
\(754\) −2612.68 + 18171.6i −0.126191 + 0.877679i
\(755\) 4700.13 + 32690.1i 0.226563 + 1.57578i
\(756\) −4770.97 + 1533.13i −0.229522 + 0.0737557i
\(757\) −12259.3 + 5598.64i −0.588603 + 0.268806i −0.687373 0.726304i \(-0.741236\pi\)
0.0987706 + 0.995110i \(0.468509\pi\)
\(758\) −5859.91 + 19957.0i −0.280794 + 0.956295i
\(759\) −7985.33 5037.12i −0.381883 0.240891i
\(760\) −6230.67 13643.3i −0.297382 0.651176i
\(761\) 5171.41 + 743.537i 0.246338 + 0.0354181i 0.264378 0.964419i \(-0.414833\pi\)
−0.0180395 + 0.999837i \(0.505742\pi\)
\(762\) −35527.2 + 16588.6i −1.68900 + 0.788636i
\(763\) 3171.75 22060.0i 0.150491 1.04669i
\(764\) 971.621 + 285.294i 0.0460105 + 0.0135099i
\(765\) −21565.2 + 19333.3i −1.01920 + 0.913720i
\(766\) 11948.3 0.563587
\(767\) 1674.88 0.0788480
\(768\) 6758.00 + 5756.69i 0.317524 + 0.270477i
\(769\) −30652.1 13998.3i −1.43737 0.656427i −0.464040 0.885814i \(-0.653601\pi\)
−0.973335 + 0.229387i \(0.926328\pi\)
\(770\) −6935.89 + 6009.98i −0.324613 + 0.281279i
\(771\) 13624.1 8919.06i 0.636394 0.416617i
\(772\) 1228.77 2690.63i 0.0572855 0.125438i
\(773\) 4419.37 6876.67i 0.205632 0.319970i −0.723085 0.690759i \(-0.757276\pi\)
0.928717 + 0.370789i \(0.120913\pi\)
\(774\) −4265.28 + 15488.8i −0.198078 + 0.719296i
\(775\) 5620.71i 0.260518i
\(776\) −9687.51 + 15074.1i −0.448146 + 0.697329i
\(777\) 8416.39 18848.8i 0.388592 0.870265i
\(778\) 28599.2 + 4111.95i 1.31791 + 0.189486i
\(779\) 29697.5 19085.4i 1.36588 0.877800i
\(780\) 1687.14 + 479.957i 0.0774477 + 0.0220323i
\(781\) 4540.59 2073.62i 0.208034 0.0950062i
\(782\) 25382.3 55579.4i 1.16070 2.54158i
\(783\) −17965.5 + 21826.3i −0.819967 + 0.996180i
\(784\) 19358.2 + 42388.6i 0.881843 + 1.93097i
\(785\) −935.398 1079.51i −0.0425297 0.0490819i
\(786\) −25651.5 + 216.534i −1.16407 + 0.00982633i
\(787\) 28227.7 + 4058.53i 1.27854 + 0.183826i 0.747922 0.663787i \(-0.231052\pi\)
0.530615 + 0.847613i \(0.321961\pi\)
\(788\) −348.367 + 102.290i −0.0157488 + 0.00462426i
\(789\) 9364.70 6130.64i 0.422550 0.276624i
\(790\) −21968.7 + 3158.63i −0.989382 + 0.142252i
\(791\) 163.578 + 254.533i 0.00735293 + 0.0114414i
\(792\) 5221.66 1629.46i 0.234272 0.0731064i
\(793\) 20110.2 5904.89i 0.900549 0.264425i
\(794\) 5647.64 12366.6i 0.252427 0.552739i
\(795\) 5464.38 4816.27i 0.243776 0.214862i
\(796\) −794.725 510.739i −0.0353873 0.0227420i
\(797\) −30256.6 26217.5i −1.34472 1.16521i −0.971385 0.237510i \(-0.923669\pi\)
−0.373335 0.927696i \(-0.621786\pi\)
\(798\) 14762.7 33061.5i 0.654880 1.46662i
\(799\) −43509.1 + 12775.4i −1.92646 + 0.565659i
\(800\) −199.350 1386.51i −0.00881010 0.0612756i
\(801\) 19107.0 3077.25i 0.842838 0.135742i
\(802\) 10182.3 11751.0i 0.448317 0.517385i
\(803\) −658.976 −0.0289599
\(804\) 2396.77 + 2167.53i 0.105134 + 0.0950781i
\(805\) −57885.0 −2.53438
\(806\) −12197.7 + 14076.9i −0.533061 + 0.615185i
\(807\) 4976.41 1506.95i 0.217073 0.0657337i
\(808\) −3959.01 27535.5i −0.172373 1.19888i
\(809\) 4216.33 1238.03i 0.183236 0.0538030i −0.188827 0.982010i \(-0.560469\pi\)
0.372063 + 0.928207i \(0.378650\pi\)
\(810\) 14793.9 + 15951.6i 0.641736 + 0.691953i
\(811\) 21500.7 + 18630.5i 0.930941 + 0.806665i 0.981383 0.192062i \(-0.0615175\pi\)
−0.0504419 + 0.998727i \(0.516063\pi\)
\(812\) −6054.73 3891.14i −0.261674 0.168168i
\(813\) 22982.6 + 26075.3i 0.991433 + 1.12485i
\(814\) 1545.94 3385.14i 0.0665666 0.145761i
\(815\) 25075.3 7362.78i 1.07773 0.316450i
\(816\) 17143.5 + 36715.7i 0.735469 + 1.57513i
\(817\) −7791.25 12123.4i −0.333637 0.519149i
\(818\) 20086.8 2888.05i 0.858581 0.123445i
\(819\) −11042.7 23138.3i −0.471141 0.987202i
\(820\) −5181.58 + 1521.45i −0.220669 + 0.0647943i
\(821\) −15285.1 2197.67i −0.649762 0.0934217i −0.190450 0.981697i \(-0.560995\pi\)
−0.459312 + 0.888275i \(0.651904\pi\)
\(822\) −256.580 30395.7i −0.0108872 1.28975i
\(823\) −7887.57 9102.74i −0.334074 0.385542i 0.563714 0.825970i \(-0.309372\pi\)
−0.897788 + 0.440428i \(0.854827\pi\)
\(824\) 4615.97 + 10107.6i 0.195152 + 0.427322i
\(825\) −1273.56 568.675i −0.0537452 0.0239984i
\(826\) −2197.08 + 4810.94i −0.0925500 + 0.202656i
\(827\) −38915.2 + 17772.0i −1.63629 + 0.747270i −0.999713 0.0239408i \(-0.992379\pi\)
−0.636580 + 0.771211i \(0.719651\pi\)
\(828\) −5222.47 2279.27i −0.219195 0.0956645i
\(829\) 2111.31 1356.86i 0.0884547 0.0568464i −0.495666 0.868513i \(-0.665076\pi\)
0.584120 + 0.811667i \(0.301440\pi\)
\(830\) −16817.9 2418.06i −0.703325 0.101123i
\(831\) 9998.56 + 4464.58i 0.417384 + 0.186371i
\(832\) −6850.36 + 10659.4i −0.285449 + 0.444167i
\(833\) 70518.0i 2.93314i
\(834\) −4210.51 + 31149.1i −0.174818 + 1.29329i
\(835\) −15559.0 + 24210.3i −0.644840 + 1.00339i
\(836\) 336.655 737.171i 0.0139276 0.0304971i
\(837\) −27306.6 + 8774.85i −1.12766 + 0.362370i
\(838\) −3902.50 + 3381.53i −0.160871 + 0.139395i
\(839\) 39699.2 + 18130.0i 1.63357 + 0.746027i 0.999626 0.0273496i \(-0.00870672\pi\)
0.633946 + 0.773377i \(0.281434\pi\)
\(840\) 21747.2 25529.9i 0.893273 1.04865i
\(841\) −16211.9 −0.664720
\(842\) −340.792 −0.0139483
\(843\) −3440.59 2930.81i −0.140570 0.119742i
\(844\) −1922.96 564.632i −0.0784254 0.0230278i
\(845\) 1810.28 12590.8i 0.0736987 0.512586i
\(846\) 10146.9 + 32516.0i 0.412359 + 1.32142i
\(847\) −38525.8 5539.17i −1.56288 0.224709i
\(848\) −4233.41 9269.87i −0.171434 0.375388i
\(849\) 20011.7 31724.4i 0.808950 1.28242i
\(850\) 2543.04 8660.80i 0.102618 0.349486i
\(851\) 21351.0 9750.68i 0.860051 0.392772i
\(852\) 2520.58 1650.11i 0.101354 0.0663518i
\(853\) 2894.94 + 20134.7i 0.116202 + 0.808206i 0.961676 + 0.274189i \(0.0884093\pi\)
−0.845473 + 0.534017i \(0.820682\pi\)
\(854\) −9419.02 + 65510.7i −0.377415 + 2.62498i
\(855\) −19512.8 + 329.453i −0.780497 + 0.0131778i
\(856\) 468.980 406.374i 0.0187259 0.0162261i
\(857\) −5921.38 41184.1i −0.236022 1.64157i −0.671239 0.741241i \(-0.734237\pi\)
0.435217 0.900326i \(-0.356672\pi\)
\(858\) −1955.51 4188.05i −0.0778089 0.166641i
\(859\) 12913.2 8298.80i 0.512913 0.329629i −0.258450 0.966025i \(-0.583212\pi\)
0.771363 + 0.636395i \(0.219575\pi\)
\(860\) 621.102 + 2115.28i 0.0246272 + 0.0838726i
\(861\) 66761.0 + 42112.7i 2.64252 + 1.66689i
\(862\) −12225.8 10593.7i −0.483077 0.418589i
\(863\) −5460.46 + 8496.64i −0.215384 + 0.335144i −0.932087 0.362235i \(-0.882014\pi\)
0.716703 + 0.697378i \(0.245650\pi\)
\(864\) 6424.75 3133.06i 0.252979 0.123367i
\(865\) −2124.03 + 7233.79i −0.0834905 + 0.284342i
\(866\) −2823.09 9614.56i −0.110777 0.377270i
\(867\) 302.108 + 35789.1i 0.0118341 + 1.40192i
\(868\) −3033.50 6642.44i −0.118622 0.259746i
\(869\) 5487.41 + 4754.87i 0.214209 + 0.185613i
\(870\) −4185.57 + 30964.6i −0.163108 + 1.20666i
\(871\) −9346.88 + 13637.2i −0.363613 + 0.530517i
\(872\) 14682.3i 0.570191i
\(873\) 12934.3 + 19398.1i 0.501442 + 0.752035i
\(874\) 37450.6 17103.1i 1.44941 0.661923i
\(875\) −46947.6 + 6750.04i −1.81385 + 0.260792i
\(876\) −393.178 + 59.9221i −0.0151647 + 0.00231116i
\(877\) 6654.19 + 1953.85i 0.256210 + 0.0752300i 0.407315 0.913288i \(-0.366465\pi\)
−0.151105 + 0.988518i \(0.548283\pi\)
\(878\) −21219.9 + 24489.1i −0.815646 + 0.941306i
\(879\) −10192.1 + 11964.9i −0.391092 + 0.459118i
\(880\) 4532.05 5230.26i 0.173608 0.200355i
\(881\) 6281.01 + 2868.44i 0.240196 + 0.109694i 0.531876 0.846822i \(-0.321487\pi\)
−0.291680 + 0.956516i \(0.594214\pi\)
\(882\) 52963.4 894.228i 2.02196 0.0341386i
\(883\) 8584.64 + 13358.0i 0.327176 + 0.509096i 0.965406 0.260750i \(-0.0839697\pi\)
−0.638231 + 0.769845i \(0.720333\pi\)
\(884\) 3124.16 2007.78i 0.118865 0.0763901i
\(885\) 2850.55 24.0625i 0.108272 0.000913958i
\(886\) −21537.3 24855.4i −0.816658 0.942474i
\(887\) −7279.18 24790.6i −0.275548 0.938430i −0.974711 0.223468i \(-0.928262\pi\)
0.699163 0.714962i \(-0.253556\pi\)
\(888\) −3721.01 + 13080.1i −0.140618 + 0.494299i
\(889\) 77843.2 11192.2i 2.93676 0.422242i
\(890\) 16166.5 14008.3i 0.608878 0.527595i
\(891\) 774.501 7075.05i 0.0291209 0.266019i
\(892\) 787.890 + 231.345i 0.0295745 + 0.00868387i
\(893\) −27793.8 12693.0i −1.04153 0.475650i
\(894\) −7553.04 + 2287.20i −0.282563 + 0.0855654i
\(895\) 3.74212 26.0271i 0.000139760 0.000972054i
\(896\) −28572.9 44460.3i −1.06535 1.65772i
\(897\) 7976.90 28040.3i 0.296924 1.04374i
\(898\) 14365.6 48924.6i 0.533836 1.81808i
\(899\) −34654.2 22270.9i −1.28563 0.826226i
\(900\) −811.582 223.491i −0.0300586 0.00827746i
\(901\) 15421.4i 0.570214i
\(902\) 11971.2 + 7693.42i 0.441904 + 0.283994i
\(903\) 17191.7 27253.9i 0.633558 1.00438i
\(904\) −130.530 150.640i −0.00480241 0.00554228i
\(905\) 10693.3 + 12340.7i 0.392769 + 0.453280i
\(906\) 28022.5 44423.9i 1.02758 1.62901i
\(907\) 17192.3 + 11048.8i 0.629394 + 0.404487i 0.816085 0.577931i \(-0.196140\pi\)
−0.186691 + 0.982419i \(0.559776\pi\)
\(908\) 4282.44i 0.156517i
\(909\) −34897.4 9609.95i −1.27335 0.350651i
\(910\) −23839.7 15320.8i −0.868437 0.558111i
\(911\) −8199.98 + 27926.6i −0.298219 + 1.01564i 0.664982 + 0.746859i \(0.268439\pi\)
−0.963201 + 0.268781i \(0.913379\pi\)
\(912\) −7470.96 + 26261.8i −0.271259 + 0.953526i
\(913\) 3005.15 + 4676.11i 0.108933 + 0.169503i
\(914\) 5510.19 38324.2i 0.199410 1.38693i
\(915\) 34141.6 10338.7i 1.23354 0.373538i
\(916\) −4025.01 1838.16i −0.145186 0.0663041i
\(917\) 49368.1 + 14495.8i 1.77784 + 0.522021i
\(918\) 46046.2 1166.30i 1.65550 0.0419320i
\(919\) −12320.1 + 10675.4i −0.442223 + 0.383188i −0.847318 0.531086i \(-0.821784\pi\)
0.405095 + 0.914275i \(0.367238\pi\)
\(920\) 37745.8 5427.03i 1.35266 0.194483i
\(921\) 11137.6 39150.8i 0.398477 1.40072i
\(922\) −14742.9 50209.7i −0.526607 1.79346i
\(923\) 10093.6 + 11648.6i 0.359950 + 0.415404i
\(924\) 1811.99 15.2956i 0.0645130 0.000544577i
\(925\) 2917.08 1874.69i 0.103690 0.0666372i
\(926\) 11909.9 + 18532.2i 0.422662 + 0.657675i
\(927\) 14456.0 244.074i 0.512187 0.00864772i
\(928\) 9338.35 + 4264.68i 0.330330 + 0.150857i
\(929\) 18540.5 21396.8i 0.654782 0.755659i −0.327133 0.944978i \(-0.606083\pi\)
0.981916 + 0.189319i \(0.0606280\pi\)
\(930\) −20557.6 + 24133.4i −0.724851 + 0.850931i
\(931\) −31116.7 + 35910.6i −1.09539 + 1.26415i
\(932\) 290.770 + 85.3777i 0.0102194 + 0.00300069i
\(933\) −19150.8 + 2918.67i −0.671993 + 0.102415i
\(934\) 18716.8 2691.07i 0.655710 0.0942768i
\(935\) 9526.39 4350.56i 0.333205 0.152169i
\(936\) 9370.13 + 14052.8i 0.327214 + 0.490738i
\(937\) 29155.9i 1.01652i 0.861203 + 0.508261i \(0.169712\pi\)
−0.861203 + 0.508261i \(0.830288\pi\)
\(938\) −26910.6 44737.2i −0.936740 1.55727i
\(939\) 648.862 4800.24i 0.0225504 0.166826i
\(940\) 3532.55 + 3060.97i 0.122573 + 0.106211i
\(941\) −2938.46 6434.34i −0.101797 0.222905i 0.851880 0.523738i \(-0.175463\pi\)
−0.953677 + 0.300833i \(0.902735\pi\)
\(942\) 19.1752 + 2271.58i 0.000663228 + 0.0785690i
\(943\) 25286.5 + 86118.0i 0.873216 + 2.97390i
\(944\) 1123.63 3826.73i 0.0387405 0.131938i
\(945\) −19126.5 39221.5i −0.658398 1.35013i
\(946\) 3140.69 4887.01i 0.107942 0.167960i
\(947\) 14441.2 + 12513.3i 0.495538 + 0.429386i 0.866437 0.499287i \(-0.166405\pi\)
−0.370898 + 0.928673i \(0.620950\pi\)
\(948\) 3706.43 + 2338.01i 0.126982 + 0.0801001i
\(949\) −573.266 1952.36i −0.0196091 0.0667823i
\(950\) 5116.67 3288.29i 0.174744 0.112301i
\(951\) 11452.5 + 24527.5i 0.390508 + 0.836338i
\(952\) −10104.8 70280.7i −0.344012 2.39266i
\(953\) −12281.2 + 10641.8i −0.417448 + 0.361721i −0.838114 0.545494i \(-0.816342\pi\)
0.420666 + 0.907216i \(0.361796\pi\)
\(954\) −11582.4 + 195.557i −0.393077 + 0.00663668i
\(955\) −1254.90 + 8728.04i −0.0425212 + 0.295741i
\(956\) 492.131 + 3422.85i 0.0166492 + 0.115798i
\(957\) 8552.39 5598.85i 0.288881 0.189117i
\(958\) −462.176 + 211.069i −0.0155869 + 0.00711828i
\(959\) −17176.7 + 58498.5i −0.578378 + 1.96978i
\(960\) −11505.8 + 18240.1i −0.386821 + 0.613225i
\(961\) −4986.62 10919.2i −0.167387 0.366526i
\(962\) 11374.1 + 1635.35i 0.381201 + 0.0548085i
\(963\) −240.526 770.775i −0.00804864 0.0257922i
\(964\) 3.89378 27.0819i 0.000130094 0.000904822i
\(965\) 24713.6 + 7256.55i 0.824412 + 0.242069i
\(966\) 70079.1 + 59695.7i 2.33412 + 1.98828i
\(967\) −35738.5 −1.18849 −0.594246 0.804283i \(-0.702549\pi\)
−0.594246 + 0.804283i \(0.702549\pi\)
\(968\) 25641.4 0.851389
\(969\) −26793.0 + 31453.4i −0.888252 + 1.04275i
\(970\) 23441.3 + 10705.3i 0.775934 + 0.354357i
\(971\) 16276.5 14103.7i 0.537938 0.466126i −0.343015 0.939330i \(-0.611448\pi\)
0.880953 + 0.473204i \(0.156903\pi\)
\(972\) −181.244 4291.75i −0.00598087 0.141623i
\(973\) 26190.0 57348.1i 0.862911 1.88951i
\(974\) −18886.9 + 29388.6i −0.621329 + 0.966808i
\(975\) 576.908 4267.93i 0.0189496 0.140188i
\(976\) 49908.8i 1.63683i
\(977\) 12034.0 18725.3i 0.394067 0.613180i −0.586363 0.810048i \(-0.699441\pi\)
0.980430 + 0.196869i \(0.0630772\pi\)
\(978\) −37950.8 16945.9i −1.24083 0.554059i
\(979\) −6926.84 995.930i −0.226132 0.0325128i
\(980\) 6115.04 3929.90i 0.199324 0.128098i
\(981\) 17509.1 + 7641.60i 0.569850 + 0.248703i
\(982\) −49628.2 + 22664.4i −1.61273 + 0.736508i
\(983\) 5610.25 12284.7i 0.182034 0.398599i −0.796513 0.604621i \(-0.793325\pi\)
0.978547 + 0.206022i \(0.0660519\pi\)
\(984\) −47482.0 21201.8i −1.53828 0.686877i
\(985\) −1313.35 2875.84i −0.0424842 0.0930274i
\(986\) 43321.5 + 49995.7i 1.39923 + 1.61480i
\(987\) −576.697 68318.1i −0.0185982 2.20323i
\(988\) 2476.90 + 356.124i 0.0797578 + 0.0114674i
\(989\) 35156.0 10322.7i 1.13033 0.331895i
\(990\) −3388.34 7099.74i −0.108776 0.227924i
\(991\) −52860.0 + 7600.13i −1.69440 + 0.243618i −0.920796 0.390046i \(-0.872459\pi\)
−0.773608 + 0.633664i \(0.781550\pi\)
\(992\) 5631.28 + 8762.45i 0.180235 + 0.280452i
\(993\) −20937.0 44840.1i −0.669100 1.43299i
\(994\) −46700.1 + 13712.4i −1.49018 + 0.437556i
\(995\) 3417.25 7482.74i 0.108879 0.238411i
\(996\) 2218.23 + 2516.73i 0.0705696 + 0.0800659i
\(997\) 7489.93 + 4813.49i 0.237922 + 0.152903i 0.654169 0.756348i \(-0.273018\pi\)
−0.416247 + 0.909252i \(0.636655\pi\)
\(998\) −27151.9 23527.3i −0.861202 0.746235i
\(999\) 13661.7 + 11245.1i 0.432670 + 0.356135i
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 201.4.j.b.5.19 640
3.2 odd 2 inner 201.4.j.b.5.46 yes 640
67.27 odd 22 inner 201.4.j.b.161.46 yes 640
201.161 even 22 inner 201.4.j.b.161.19 yes 640
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.4.j.b.5.19 640 1.1 even 1 trivial
201.4.j.b.5.46 yes 640 3.2 odd 2 inner
201.4.j.b.161.19 yes 640 201.161 even 22 inner
201.4.j.b.161.46 yes 640 67.27 odd 22 inner