Properties

Label 143.4.w.a.2.13
Level $143$
Weight $4$
Character 143.2
Analytic conductor $8.437$
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] = [143,4,Mod(2,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([6, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.w (of order \(60\), degree \(16\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(640\)
Relative dimension: \(40\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 2.13
Character \(\chi\) \(=\) 143.2
Dual form 143.4.w.a.72.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.03945 - 1.32443i) q^{2} +(-3.45137 - 1.53665i) q^{3} +(-0.848666 - 1.90614i) q^{4} +(7.68362 + 3.91500i) q^{5} +(5.00371 + 7.70503i) q^{6} +(11.4289 - 29.7734i) q^{7} +(-3.83703 + 24.2261i) q^{8} +(-8.51585 - 9.45781i) q^{9} +O(q^{10})\) \(q+(-2.03945 - 1.32443i) q^{2} +(-3.45137 - 1.53665i) q^{3} +(-0.848666 - 1.90614i) q^{4} +(7.68362 + 3.91500i) q^{5} +(5.00371 + 7.70503i) q^{6} +(11.4289 - 29.7734i) q^{7} +(-3.83703 + 24.2261i) q^{8} +(-8.51585 - 9.45781i) q^{9} +(-10.4852 - 18.1609i) q^{10} +(36.0102 - 5.85390i) q^{11} +7.88289i q^{12} +(39.3067 - 25.5340i) q^{13} +(-62.7416 + 45.5844i) q^{14} +(-20.5031 - 25.3192i) q^{15} +(28.7420 - 31.9212i) q^{16} +(-83.6083 - 17.7715i) q^{17} +(4.84140 + 30.5674i) q^{18} +(0.390050 - 0.481672i) q^{19} +(0.941692 - 17.9685i) q^{20} +(-85.1967 + 85.1967i) q^{21} +(-81.1940 - 35.7543i) q^{22} +(-170.458 + 98.4140i) q^{23} +(50.4700 - 77.7170i) q^{24} +(-29.7624 - 40.9644i) q^{25} +(-113.982 + 0.0160933i) q^{26} +(46.3796 + 142.742i) q^{27} +(-66.4514 + 3.48257i) q^{28} +(-146.434 - 15.3908i) q^{29} +(8.28138 + 78.7921i) q^{30} +(-26.9879 - 52.9668i) q^{31} +(88.6429 - 23.7518i) q^{32} +(-133.280 - 35.1310i) q^{33} +(146.978 + 146.978i) q^{34} +(204.378 - 184.023i) q^{35} +(-10.8007 + 24.2589i) q^{36} +(187.964 - 152.210i) q^{37} +(-1.43343 + 0.465750i) q^{38} +(-174.899 + 27.7266i) q^{39} +(-124.327 + 171.122i) q^{40} +(39.2072 + 102.138i) q^{41} +(286.592 - 60.9170i) q^{42} +(-17.2372 + 29.8557i) q^{43} +(-41.7189 - 63.6722i) q^{44} +(-28.4052 - 106.010i) q^{45} +(477.983 + 25.0500i) q^{46} +(-277.591 - 43.9661i) q^{47} +(-148.251 + 66.0056i) q^{48} +(-500.934 - 451.043i) q^{49} +(6.44422 + 122.963i) q^{50} +(261.255 + 189.813i) q^{51} +(-82.0294 - 53.2541i) q^{52} +(67.1400 - 206.636i) q^{53} +(94.4631 - 352.541i) q^{54} +(299.606 + 96.0007i) q^{55} +(677.438 + 391.119i) q^{56} +(-2.08637 + 1.06306i) q^{57} +(278.260 + 225.330i) q^{58} +(628.324 + 241.191i) q^{59} +(-30.8615 + 60.5691i) q^{60} +(11.7160 - 55.1193i) q^{61} +(-15.1105 + 143.767i) q^{62} +(-378.918 + 145.453i) q^{63} +(-539.055 - 175.150i) q^{64} +(401.983 - 42.3075i) q^{65} +(225.289 + 248.168i) q^{66} +(-261.297 - 70.0143i) q^{67} +(37.0807 + 174.451i) q^{68} +(739.542 - 77.7290i) q^{69} +(-660.545 + 104.620i) q^{70} +(606.780 - 394.048i) q^{71} +(261.801 - 170.016i) q^{72} +(90.8153 - 14.3837i) q^{73} +(-584.936 + 61.4792i) q^{74} +(39.7731 + 187.118i) q^{75} +(-1.24915 - 0.334710i) q^{76} +(237.267 - 1139.05i) q^{77} +(393.419 + 175.095i) q^{78} +(-493.751 - 160.429i) q^{79} +(345.814 - 132.746i) q^{80} +(23.3525 - 222.185i) q^{81} +(55.3142 - 260.233i) q^{82} +(-179.347 + 351.989i) q^{83} +(234.700 + 90.0929i) q^{84} +(-572.839 - 463.876i) q^{85} +(74.6962 - 38.0596i) q^{86} +(481.747 + 278.137i) q^{87} +(3.64471 + 894.846i) q^{88} +(34.9404 - 130.399i) q^{89} +(-82.4718 + 253.822i) q^{90} +(-310.999 - 1462.12i) q^{91} +(332.252 + 241.395i) q^{92} +(11.7540 + 224.279i) q^{93} +(507.902 + 457.317i) q^{94} +(4.88274 - 2.17394i) q^{95} +(-342.438 - 54.2368i) q^{96} +(-685.789 - 35.9407i) q^{97} +(424.253 + 1583.33i) q^{98} +(-362.022 - 290.726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 640 q - 20 q^{2} - 6 q^{3} - 18 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 642 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 640 q - 20 q^{2} - 6 q^{3} - 18 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 642 q^{9} - 140 q^{11} - 60 q^{13} + 24 q^{14} - 144 q^{15} - 1310 q^{16} - 30 q^{17} - 20 q^{18} - 20 q^{19} + 942 q^{20} - 38 q^{22} - 960 q^{23} - 760 q^{24} - 516 q^{26} - 864 q^{27} - 20 q^{28} - 710 q^{29} - 30 q^{30} + 260 q^{31} - 1354 q^{33} + 1508 q^{34} - 1310 q^{35} + 3540 q^{36} - 348 q^{37} - 1860 q^{39} + 1240 q^{40} + 2200 q^{41} - 1174 q^{42} - 124 q^{44} - 936 q^{45} + 1340 q^{46} - 2564 q^{47} - 490 q^{48} - 18 q^{49} + 1230 q^{50} + 1430 q^{52} - 3912 q^{53} - 692 q^{55} + 1296 q^{56} - 20 q^{57} - 2556 q^{58} - 668 q^{59} + 6556 q^{60} + 470 q^{61} - 30 q^{62} - 5010 q^{63} + 24980 q^{66} - 5384 q^{67} - 250 q^{68} - 18 q^{69} + 1262 q^{70} + 1296 q^{71} + 11020 q^{72} - 1940 q^{73} - 10 q^{74} - 8862 q^{75} + 10476 q^{78} - 9400 q^{79} + 12112 q^{80} + 4294 q^{81} - 9414 q^{82} - 4500 q^{83} + 920 q^{84} + 140 q^{85} - 4708 q^{86} - 10182 q^{88} - 2208 q^{89} + 9988 q^{91} - 9440 q^{92} + 13400 q^{93} - 3210 q^{94} - 9330 q^{95} - 6270 q^{96} + 4872 q^{97} + 6876 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.03945 1.32443i −0.721054 0.468258i 0.131220 0.991353i \(-0.458111\pi\)
−0.852274 + 0.523095i \(0.824777\pi\)
\(3\) −3.45137 1.53665i −0.664217 0.295728i 0.0467990 0.998904i \(-0.485098\pi\)
−0.711016 + 0.703176i \(0.751765\pi\)
\(4\) −0.848666 1.90614i −0.106083 0.238267i
\(5\) 7.68362 + 3.91500i 0.687244 + 0.350168i 0.762493 0.646996i \(-0.223975\pi\)
−0.0752490 + 0.997165i \(0.523975\pi\)
\(6\) 5.00371 + 7.70503i 0.340459 + 0.524261i
\(7\) 11.4289 29.7734i 0.617104 1.60761i −0.166284 0.986078i \(-0.553177\pi\)
0.783388 0.621533i \(-0.213490\pi\)
\(8\) −3.83703 + 24.2261i −0.169574 + 1.07065i
\(9\) −8.51585 9.45781i −0.315402 0.350289i
\(10\) −10.4852 18.1609i −0.331571 0.574298i
\(11\) 36.0102 5.85390i 0.987043 0.160456i
\(12\) 7.88289i 0.189633i
\(13\) 39.3067 25.5340i 0.838594 0.544757i
\(14\) −62.7416 + 45.5844i −1.19774 + 0.870210i
\(15\) −20.5031 25.3192i −0.352924 0.435825i
\(16\) 28.7420 31.9212i 0.449093 0.498769i
\(17\) −83.6083 17.7715i −1.19282 0.253542i −0.431620 0.902056i \(-0.642058\pi\)
−0.761204 + 0.648513i \(0.775391\pi\)
\(18\) 4.84140 + 30.5674i 0.0633960 + 0.400267i
\(19\) 0.390050 0.481672i 0.00470967 0.00581595i −0.774786 0.632224i \(-0.782142\pi\)
0.779495 + 0.626408i \(0.215476\pi\)
\(20\) 0.941692 17.9685i 0.0105284 0.200894i
\(21\) −85.1967 + 85.1967i −0.885307 + 0.885307i
\(22\) −81.1940 35.7543i −0.786846 0.346493i
\(23\) −170.458 + 98.4140i −1.54535 + 0.892206i −0.546858 + 0.837225i \(0.684176\pi\)
−0.998487 + 0.0549806i \(0.982490\pi\)
\(24\) 50.4700 77.7170i 0.429256 0.660997i
\(25\) −29.7624 40.9644i −0.238099 0.327715i
\(26\) −113.982 + 0.0160933i −0.859758 + 0.000121390i
\(27\) 46.3796 + 142.742i 0.330584 + 1.01743i
\(28\) −66.4514 + 3.48257i −0.448505 + 0.0235051i
\(29\) −146.434 15.3908i −0.937657 0.0985517i −0.376643 0.926358i \(-0.622922\pi\)
−0.561014 + 0.827807i \(0.689588\pi\)
\(30\) 8.28138 + 78.7921i 0.0503989 + 0.479513i
\(31\) −26.9879 52.9668i −0.156360 0.306874i 0.799515 0.600646i \(-0.205090\pi\)
−0.955876 + 0.293771i \(0.905090\pi\)
\(32\) 88.6429 23.7518i 0.489687 0.131211i
\(33\) −133.280 35.1310i −0.703062 0.185319i
\(34\) 146.978 + 146.978i 0.741367 + 0.741367i
\(35\) 204.378 184.023i 0.987035 0.888731i
\(36\) −10.8007 + 24.2589i −0.0500035 + 0.112310i
\(37\) 187.964 152.210i 0.835165 0.676303i −0.113169 0.993576i \(-0.536100\pi\)
0.948334 + 0.317272i \(0.102767\pi\)
\(38\) −1.43343 + 0.465750i −0.00611929 + 0.00198828i
\(39\) −174.899 + 27.7266i −0.718108 + 0.113841i
\(40\) −124.327 + 171.122i −0.491447 + 0.676419i
\(41\) 39.2072 + 102.138i 0.149345 + 0.389056i 0.987761 0.155974i \(-0.0498516\pi\)
−0.838417 + 0.545030i \(0.816518\pi\)
\(42\) 286.592 60.9170i 1.05291 0.223802i
\(43\) −17.2372 + 29.8557i −0.0611313 + 0.105883i −0.894971 0.446124i \(-0.852804\pi\)
0.833840 + 0.552006i \(0.186138\pi\)
\(44\) −41.7189 63.6722i −0.142940 0.218158i
\(45\) −28.4052 106.010i −0.0940978 0.351178i
\(46\) 477.983 + 25.0500i 1.53206 + 0.0802919i
\(47\) −277.591 43.9661i −0.861506 0.136449i −0.289980 0.957033i \(-0.593649\pi\)
−0.571527 + 0.820584i \(0.693649\pi\)
\(48\) −148.251 + 66.0056i −0.445796 + 0.198481i
\(49\) −500.934 451.043i −1.46045 1.31500i
\(50\) 6.44422 + 122.963i 0.0182270 + 0.347792i
\(51\) 261.255 + 189.813i 0.717314 + 0.521159i
\(52\) −82.0294 53.2541i −0.218758 0.142019i
\(53\) 67.1400 206.636i 0.174007 0.535540i −0.825579 0.564286i \(-0.809152\pi\)
0.999587 + 0.0287464i \(0.00915154\pi\)
\(54\) 94.4631 352.541i 0.238052 0.888422i
\(55\) 299.606 + 96.0007i 0.734526 + 0.235359i
\(56\) 677.438 + 391.119i 1.61654 + 0.933313i
\(57\) −2.08637 + 1.06306i −0.00484818 + 0.00247027i
\(58\) 278.260 + 225.330i 0.629954 + 0.510127i
\(59\) 628.324 + 241.191i 1.38645 + 0.532210i 0.933260 0.359202i \(-0.116951\pi\)
0.453194 + 0.891412i \(0.350284\pi\)
\(60\) −30.8615 + 60.5691i −0.0664034 + 0.130324i
\(61\) 11.7160 55.1193i 0.0245914 0.115693i −0.964140 0.265394i \(-0.914498\pi\)
0.988731 + 0.149701i \(0.0478311\pi\)
\(62\) −15.1105 + 143.767i −0.0309522 + 0.294490i
\(63\) −378.918 + 145.453i −0.757764 + 0.290878i
\(64\) −539.055 175.150i −1.05284 0.342089i
\(65\) 401.983 42.3075i 0.767075 0.0807324i
\(66\) 225.289 + 248.168i 0.420169 + 0.462840i
\(67\) −261.297 70.0143i −0.476455 0.127666i 0.0125963 0.999921i \(-0.495990\pi\)
−0.489052 + 0.872255i \(0.662657\pi\)
\(68\) 37.0807 + 174.451i 0.0661278 + 0.311107i
\(69\) 739.542 77.7290i 1.29030 0.135616i
\(70\) −660.545 + 104.620i −1.12786 + 0.178636i
\(71\) 606.780 394.048i 1.01425 0.658660i 0.0733338 0.997307i \(-0.476636\pi\)
0.940913 + 0.338648i \(0.109969\pi\)
\(72\) 261.801 170.016i 0.428521 0.278285i
\(73\) 90.8153 14.3837i 0.145604 0.0230615i −0.0832067 0.996532i \(-0.526516\pi\)
0.228811 + 0.973471i \(0.426516\pi\)
\(74\) −584.936 + 61.4792i −0.918884 + 0.0965786i
\(75\) 39.7731 + 187.118i 0.0612347 + 0.288086i
\(76\) −1.24915 0.334710i −0.00188537 0.000505182i
\(77\) 237.267 1139.05i 0.351157 1.68580i
\(78\) 393.419 + 175.095i 0.571102 + 0.254174i
\(79\) −493.751 160.429i −0.703182 0.228478i −0.0644654 0.997920i \(-0.520534\pi\)
−0.638716 + 0.769442i \(0.720534\pi\)
\(80\) 345.814 132.746i 0.483290 0.185518i
\(81\) 23.3525 222.185i 0.0320337 0.304780i
\(82\) 55.3142 260.233i 0.0744931 0.350462i
\(83\) −179.347 + 351.989i −0.237180 + 0.465492i −0.978661 0.205482i \(-0.934124\pi\)
0.741481 + 0.670974i \(0.234124\pi\)
\(84\) 234.700 + 90.0929i 0.304856 + 0.117023i
\(85\) −572.839 463.876i −0.730978 0.591935i
\(86\) 74.6962 38.0596i 0.0936593 0.0477218i
\(87\) 481.747 + 278.137i 0.593663 + 0.342752i
\(88\) 3.64471 + 894.846i 0.00441508 + 1.08399i
\(89\) 34.9404 130.399i 0.0416143 0.155307i −0.941992 0.335635i \(-0.891049\pi\)
0.983607 + 0.180328i \(0.0577159\pi\)
\(90\) −82.4718 + 253.822i −0.0965922 + 0.297280i
\(91\) −310.999 1462.12i −0.358258 1.68430i
\(92\) 332.252 + 241.395i 0.376518 + 0.273557i
\(93\) 11.7540 + 224.279i 0.0131057 + 0.250071i
\(94\) 507.902 + 457.317i 0.557299 + 0.501795i
\(95\) 4.88274 2.17394i 0.00527325 0.00234780i
\(96\) −342.438 54.2368i −0.364062 0.0576617i
\(97\) −685.789 35.9407i −0.717848 0.0376208i −0.310085 0.950709i \(-0.600358\pi\)
−0.407763 + 0.913088i \(0.633691\pi\)
\(98\) 424.253 + 1583.33i 0.437307 + 1.63205i
\(99\) −362.022 290.726i −0.367521 0.295142i
\(100\) −52.8253 + 91.4961i −0.0528253 + 0.0914961i
\(101\) 409.715 87.0876i 0.403645 0.0857974i −0.00161525 0.999999i \(-0.500514\pi\)
0.405261 + 0.914201i \(0.367181\pi\)
\(102\) −281.422 733.128i −0.273185 0.711672i
\(103\) −754.527 + 1038.52i −0.721803 + 0.993477i 0.277659 + 0.960680i \(0.410442\pi\)
−0.999462 + 0.0327971i \(0.989558\pi\)
\(104\) 467.766 + 1050.22i 0.441041 + 0.990218i
\(105\) −988.165 + 321.074i −0.918428 + 0.298416i
\(106\) −410.604 + 332.500i −0.376239 + 0.304673i
\(107\) −348.232 + 782.142i −0.314625 + 0.706659i −0.999763 0.0217537i \(-0.993075\pi\)
0.685138 + 0.728413i \(0.259742\pi\)
\(108\) 232.724 209.546i 0.207351 0.186700i
\(109\) 1074.81 + 1074.81i 0.944477 + 0.944477i 0.998538 0.0540610i \(-0.0172166\pi\)
−0.0540610 + 0.998538i \(0.517217\pi\)
\(110\) −483.885 592.597i −0.419424 0.513654i
\(111\) −882.628 + 236.500i −0.754733 + 0.202230i
\(112\) −621.912 1220.57i −0.524689 1.02976i
\(113\) −217.398 2068.40i −0.180983 1.72194i −0.588295 0.808647i \(-0.700200\pi\)
0.407312 0.913289i \(-0.366466\pi\)
\(114\) 5.66299 + 0.595205i 0.00465253 + 0.000489000i
\(115\) −1695.03 + 88.8325i −1.37445 + 0.0720320i
\(116\) 94.9364 + 292.184i 0.0759881 + 0.233867i
\(117\) −576.225 154.312i −0.455316 0.121933i
\(118\) −961.993 1324.07i −0.750497 1.03297i
\(119\) −1484.67 + 2286.19i −1.14369 + 1.76113i
\(120\) 692.055 399.558i 0.526464 0.303954i
\(121\) 1262.46 421.599i 0.948508 0.316754i
\(122\) −96.8959 + 96.8959i −0.0719061 + 0.0719061i
\(123\) 21.6321 412.765i 0.0158577 0.302583i
\(124\) −78.0581 + 96.3937i −0.0565308 + 0.0698097i
\(125\) −236.934 1495.94i −0.169536 1.07041i
\(126\) 965.426 + 205.208i 0.682595 + 0.145090i
\(127\) 122.139 135.649i 0.0853394 0.0947790i −0.698963 0.715158i \(-0.746355\pi\)
0.784302 + 0.620379i \(0.213021\pi\)
\(128\) 405.380 + 500.603i 0.279929 + 0.345684i
\(129\) 105.370 76.5555i 0.0719169 0.0522507i
\(130\) −875.858 446.116i −0.590906 0.300977i
\(131\) 988.948i 0.659579i −0.944055 0.329789i \(-0.893022\pi\)
0.944055 0.329789i \(-0.106978\pi\)
\(132\) 46.1456 + 283.864i 0.0304277 + 0.187176i
\(133\) −9.88314 17.1181i −0.00644344 0.0111604i
\(134\) 440.172 + 488.861i 0.283769 + 0.315158i
\(135\) −202.471 + 1278.35i −0.129081 + 0.814984i
\(136\) 751.341 1957.31i 0.473728 1.23410i
\(137\) −544.567 838.560i −0.339602 0.522942i 0.627068 0.778964i \(-0.284255\pi\)
−0.966671 + 0.256022i \(0.917588\pi\)
\(138\) −1611.20 820.950i −0.993876 0.506405i
\(139\) 97.3558 + 218.665i 0.0594073 + 0.133431i 0.940810 0.338935i \(-0.110067\pi\)
−0.881402 + 0.472366i \(0.843400\pi\)
\(140\) −524.222 233.399i −0.316463 0.140898i
\(141\) 890.509 + 578.304i 0.531875 + 0.345404i
\(142\) −1759.39 −1.03975
\(143\) 1265.97 1149.58i 0.740318 0.672256i
\(144\) −546.667 −0.316358
\(145\) −1064.89 691.545i −0.609889 0.396067i
\(146\) −204.263 90.9439i −0.115787 0.0515519i
\(147\) 1035.82 + 2326.48i 0.581174 + 1.30534i
\(148\) −449.652 229.109i −0.249738 0.127248i
\(149\) 1308.26 + 2014.55i 0.719310 + 1.10764i 0.989458 + 0.144822i \(0.0462609\pi\)
−0.270147 + 0.962819i \(0.587072\pi\)
\(150\) 166.710 434.294i 0.0907453 0.236399i
\(151\) −128.902 + 813.858i −0.0694697 + 0.438615i 0.928298 + 0.371837i \(0.121272\pi\)
−0.997768 + 0.0667779i \(0.978728\pi\)
\(152\) 10.1724 + 11.2976i 0.00542822 + 0.00602865i
\(153\) 543.916 + 942.091i 0.287405 + 0.497801i
\(154\) −1992.49 + 2008.78i −1.04259 + 1.05112i
\(155\) 512.634i 0.265650i
\(156\) 201.281 + 309.850i 0.103304 + 0.159025i
\(157\) 2736.28 1988.03i 1.39095 1.01058i 0.395189 0.918600i \(-0.370679\pi\)
0.995760 0.0919846i \(-0.0293211\pi\)
\(158\) 794.502 + 981.128i 0.400046 + 0.494015i
\(159\) −549.252 + 610.006i −0.273953 + 0.304256i
\(160\) 774.087 + 164.537i 0.382481 + 0.0812988i
\(161\) 981.964 + 6199.87i 0.480681 + 3.03490i
\(162\) −341.895 + 422.205i −0.165814 + 0.204763i
\(163\) 169.611 3236.36i 0.0815026 1.55516i −0.585849 0.810420i \(-0.699239\pi\)
0.667352 0.744743i \(-0.267428\pi\)
\(164\) 161.415 161.415i 0.0768562 0.0768562i
\(165\) −886.534 791.724i −0.418282 0.373549i
\(166\) 831.956 480.330i 0.388990 0.224583i
\(167\) 1344.90 2070.96i 0.623182 0.959616i −0.376270 0.926510i \(-0.622794\pi\)
0.999452 0.0331058i \(-0.0105398\pi\)
\(168\) −1737.08 2390.88i −0.797729 1.09798i
\(169\) 893.034 2007.31i 0.406479 0.913660i
\(170\) 553.903 + 1704.74i 0.249897 + 0.769103i
\(171\) −7.87717 + 0.412825i −0.00352270 + 0.000184617i
\(172\) 71.5376 + 7.51890i 0.0317133 + 0.00333320i
\(173\) 190.675 + 1814.15i 0.0837964 + 0.797269i 0.953032 + 0.302871i \(0.0979450\pi\)
−0.869235 + 0.494399i \(0.835388\pi\)
\(174\) −614.125 1205.29i −0.267567 0.525130i
\(175\) −1559.80 + 417.947i −0.673770 + 0.180536i
\(176\) 848.140 1317.74i 0.363244 0.564366i
\(177\) −1797.95 1797.95i −0.763517 0.763517i
\(178\) −243.964 + 219.666i −0.102730 + 0.0924983i
\(179\) 1444.57 3244.55i 0.603196 1.35480i −0.311341 0.950298i \(-0.600778\pi\)
0.914537 0.404502i \(-0.132555\pi\)
\(180\) −177.962 + 144.111i −0.0736918 + 0.0596745i
\(181\) 4129.03 1341.60i 1.69563 0.550943i 0.707789 0.706424i \(-0.249693\pi\)
0.987839 + 0.155482i \(0.0496929\pi\)
\(182\) −1302.21 + 3393.81i −0.530365 + 1.38223i
\(183\) −125.135 + 172.234i −0.0505479 + 0.0695731i
\(184\) −1730.13 4507.14i −0.693190 1.80582i
\(185\) 2040.15 433.647i 0.810782 0.172337i
\(186\) 273.071 472.973i 0.107648 0.186452i
\(187\) −3114.78 150.520i −1.21805 0.0588616i
\(188\) 151.777 + 566.438i 0.0588801 + 0.219743i
\(189\) 4779.97 + 250.508i 1.83964 + 0.0964114i
\(190\) −12.8373 2.03324i −0.00490168 0.000776349i
\(191\) −1709.82 + 761.259i −0.647738 + 0.288391i −0.704188 0.710014i \(-0.748689\pi\)
0.0564497 + 0.998405i \(0.482022\pi\)
\(192\) 1591.34 + 1432.85i 0.598150 + 0.538577i
\(193\) −69.7792 1331.47i −0.0260250 0.496586i −0.980283 0.197600i \(-0.936685\pi\)
0.954258 0.298985i \(-0.0966482\pi\)
\(194\) 1351.03 + 981.581i 0.499991 + 0.363265i
\(195\) −1452.41 471.689i −0.533379 0.173222i
\(196\) −434.624 + 1337.63i −0.158391 + 0.487476i
\(197\) −660.237 + 2464.04i −0.238781 + 0.891144i 0.737626 + 0.675209i \(0.235947\pi\)
−0.976408 + 0.215935i \(0.930720\pi\)
\(198\) 353.278 + 1072.40i 0.126800 + 0.384908i
\(199\) 3531.30 + 2038.80i 1.25793 + 0.726264i 0.972671 0.232188i \(-0.0745884\pi\)
0.285255 + 0.958452i \(0.407922\pi\)
\(200\) 1106.60 563.843i 0.391244 0.199349i
\(201\) 794.246 + 643.167i 0.278715 + 0.225699i
\(202\) −950.935 365.030i −0.331225 0.127146i
\(203\) −2131.82 + 4183.92i −0.737065 + 1.44657i
\(204\) 140.091 659.075i 0.0480800 0.226198i
\(205\) −98.6179 + 938.287i −0.0335989 + 0.319672i
\(206\) 2914.27 1118.68i 0.985662 0.378360i
\(207\) 2382.37 + 774.080i 0.799935 + 0.259915i
\(208\) 314.678 1988.61i 0.104899 0.662911i
\(209\) 11.2261 19.6284i 0.00371544 0.00649629i
\(210\) 2440.55 + 653.944i 0.801972 + 0.214888i
\(211\) 1089.26 + 5124.56i 0.355392 + 1.67199i 0.685522 + 0.728052i \(0.259574\pi\)
−0.330130 + 0.943935i \(0.607093\pi\)
\(212\) −450.855 + 47.3868i −0.146061 + 0.0153516i
\(213\) −2699.74 + 427.596i −0.868465 + 0.137551i
\(214\) 1746.10 1133.93i 0.557760 0.362214i
\(215\) −249.329 + 161.916i −0.0790888 + 0.0513609i
\(216\) −3636.03 + 575.891i −1.14537 + 0.181409i
\(217\) −1885.44 + 198.168i −0.589825 + 0.0619931i
\(218\) −768.504 3615.53i −0.238760 1.12328i
\(219\) −335.540 89.9077i −0.103533 0.0277416i
\(220\) −71.2755 652.563i −0.0218427 0.199981i
\(221\) −3740.15 + 1436.31i −1.13841 + 0.437180i
\(222\) 2113.30 + 686.654i 0.638899 + 0.207591i
\(223\) −168.262 + 64.5897i −0.0505276 + 0.0193957i −0.383501 0.923541i \(-0.625282\pi\)
0.332973 + 0.942936i \(0.391948\pi\)
\(224\) 305.922 2910.65i 0.0912513 0.868198i
\(225\) −133.981 + 630.333i −0.0396982 + 0.186765i
\(226\) −2296.09 + 4506.33i −0.675812 + 1.32636i
\(227\) −609.995 234.155i −0.178356 0.0684644i 0.267551 0.963544i \(-0.413786\pi\)
−0.445907 + 0.895079i \(0.647119\pi\)
\(228\) 3.79696 + 3.07472i 0.00110290 + 0.000893107i
\(229\) 1502.45 765.536i 0.433557 0.220908i −0.223570 0.974688i \(-0.571771\pi\)
0.657128 + 0.753779i \(0.271771\pi\)
\(230\) 3574.57 + 2063.78i 1.02478 + 0.591659i
\(231\) −2569.22 + 3566.68i −0.731783 + 1.01589i
\(232\) 934.729 3488.46i 0.264517 0.987192i
\(233\) 1511.90 4653.16i 0.425099 1.30832i −0.477800 0.878469i \(-0.658566\pi\)
0.902899 0.429852i \(-0.141434\pi\)
\(234\) 970.806 + 1077.88i 0.271212 + 0.301126i
\(235\) −1960.78 1424.59i −0.544285 0.395446i
\(236\) −73.4946 1402.36i −0.0202716 0.386805i
\(237\) 1457.60 + 1312.42i 0.399498 + 0.359710i
\(238\) 6055.82 2696.23i 1.64933 0.734329i
\(239\) −2067.87 327.519i −0.559663 0.0886419i −0.129807 0.991539i \(-0.541436\pi\)
−0.429856 + 0.902897i \(0.641436\pi\)
\(240\) −1397.52 73.2407i −0.375872 0.0196986i
\(241\) 569.882 + 2126.83i 0.152321 + 0.568469i 0.999320 + 0.0368747i \(0.0117402\pi\)
−0.846999 + 0.531594i \(0.821593\pi\)
\(242\) −3133.11 812.219i −0.832248 0.215750i
\(243\) 1604.16 2778.49i 0.423486 0.733499i
\(244\) −115.008 + 24.4456i −0.0301746 + 0.00641382i
\(245\) −2083.16 5426.80i −0.543216 1.41513i
\(246\) −590.797 + 813.162i −0.153121 + 0.210753i
\(247\) 3.03260 28.8925i 0.000781212 0.00744285i
\(248\) 1386.73 450.576i 0.355070 0.115369i
\(249\) 1159.88 939.251i 0.295198 0.239047i
\(250\) −1498.06 + 3364.71i −0.378983 + 0.851211i
\(251\) 3125.92 2814.59i 0.786081 0.707791i −0.174845 0.984596i \(-0.555942\pi\)
0.960926 + 0.276805i \(0.0892758\pi\)
\(252\) 598.827 + 598.827i 0.149693 + 0.149693i
\(253\) −5562.12 + 4541.75i −1.38216 + 1.12861i
\(254\) −428.755 + 114.885i −0.105915 + 0.0283799i
\(255\) 1264.27 + 2481.26i 0.310476 + 0.609344i
\(256\) 310.234 + 2951.68i 0.0757407 + 0.720624i
\(257\) −4874.62 512.343i −1.18315 0.124354i −0.507551 0.861621i \(-0.669449\pi\)
−0.675601 + 0.737267i \(0.736116\pi\)
\(258\) −316.289 + 16.5760i −0.0763228 + 0.00399991i
\(259\) −2383.59 7335.93i −0.571849 1.75997i
\(260\) −421.793 730.329i −0.100610 0.174204i
\(261\) 1101.44 + 1516.01i 0.261217 + 0.359534i
\(262\) −1309.80 + 2016.91i −0.308853 + 0.475592i
\(263\) 4699.95 2713.52i 1.10195 0.636208i 0.165214 0.986258i \(-0.447169\pi\)
0.936731 + 0.350049i \(0.113835\pi\)
\(264\) 1362.49 3094.05i 0.317633 0.721309i
\(265\) 1324.86 1324.86i 0.307114 0.307114i
\(266\) −2.51563 + 48.0011i −0.000579861 + 0.0110644i
\(267\) −320.970 + 396.365i −0.0735695 + 0.0908508i
\(268\) 88.2971 + 557.486i 0.0201254 + 0.127067i
\(269\) −3221.72 684.798i −0.730230 0.155215i −0.172231 0.985057i \(-0.555098\pi\)
−0.557999 + 0.829841i \(0.688431\pi\)
\(270\) 2106.02 2338.97i 0.474697 0.527204i
\(271\) 3086.13 + 3811.06i 0.691769 + 0.854263i 0.995126 0.0986138i \(-0.0314408\pi\)
−0.303357 + 0.952877i \(0.598108\pi\)
\(272\) −2970.36 + 2158.09i −0.662148 + 0.481079i
\(273\) −1173.39 + 5524.21i −0.260135 + 1.22469i
\(274\) 2431.44i 0.536091i
\(275\) −1311.55 1300.91i −0.287598 0.285264i
\(276\) −775.786 1343.70i −0.169191 0.293048i
\(277\) −5361.52 5954.57i −1.16297 1.29161i −0.949182 0.314729i \(-0.898086\pi\)
−0.213788 0.976880i \(-0.568580\pi\)
\(278\) 91.0547 574.897i 0.0196442 0.124029i
\(279\) −271.124 + 706.303i −0.0581785 + 0.151560i
\(280\) 3673.95 + 5657.38i 0.784144 + 1.20748i
\(281\) 1341.75 + 683.654i 0.284847 + 0.145137i 0.590576 0.806982i \(-0.298900\pi\)
−0.305730 + 0.952118i \(0.598900\pi\)
\(282\) −1050.22 2358.84i −0.221773 0.498110i
\(283\) 1702.67 + 758.075i 0.357643 + 0.159233i 0.577690 0.816256i \(-0.303954\pi\)
−0.220047 + 0.975489i \(0.570621\pi\)
\(284\) −1266.06 822.190i −0.264531 0.171789i
\(285\) −20.1927 −0.00419690
\(286\) −4104.42 + 667.818i −0.848599 + 0.138073i
\(287\) 3489.09 0.717612
\(288\) −979.509 636.101i −0.200410 0.130148i
\(289\) 2186.28 + 973.394i 0.444999 + 0.198126i
\(290\) 1255.88 + 2820.74i 0.254302 + 0.571171i
\(291\) 2311.68 + 1177.86i 0.465682 + 0.237277i
\(292\) −104.489 160.899i −0.0209410 0.0322463i
\(293\) 2187.44 5698.47i 0.436148 1.13621i −0.522758 0.852481i \(-0.675097\pi\)
0.958906 0.283724i \(-0.0915700\pi\)
\(294\) 968.775 6116.61i 0.192177 1.21336i
\(295\) 3883.54 + 4313.11i 0.766469 + 0.851250i
\(296\) 2966.23 + 5137.67i 0.582462 + 1.00885i
\(297\) 2505.73 + 4868.65i 0.489553 + 0.951205i
\(298\) 5841.28i 1.13549i
\(299\) −4187.24 + 8220.80i −0.809881 + 1.59004i
\(300\) 322.917 234.613i 0.0621455 0.0451513i
\(301\) 691.902 + 854.427i 0.132493 + 0.163616i
\(302\) 1340.79 1489.10i 0.255476 0.283735i
\(303\) −1547.90 329.017i −0.293481 0.0623813i
\(304\) −4.16473 26.2951i −0.000785736 0.00496094i
\(305\) 305.813 377.647i 0.0574124 0.0708985i
\(306\) 138.447 2641.73i 0.0258643 0.493521i
\(307\) −1201.88 + 1201.88i −0.223436 + 0.223436i −0.809943 0.586508i \(-0.800502\pi\)
0.586508 + 0.809943i \(0.300502\pi\)
\(308\) −2372.54 + 514.408i −0.438922 + 0.0951659i
\(309\) 4199.99 2424.87i 0.773233 0.446426i
\(310\) −678.950 + 1045.49i −0.124393 + 0.191548i
\(311\) −1949.28 2682.96i −0.355414 0.489185i 0.593450 0.804871i \(-0.297765\pi\)
−0.948864 + 0.315686i \(0.897765\pi\)
\(312\) −0.613265 4343.50i −0.000111280 0.788148i
\(313\) −1862.72 5732.87i −0.336381 1.03528i −0.966038 0.258402i \(-0.916804\pi\)
0.629656 0.776874i \(-0.283196\pi\)
\(314\) −8213.52 + 430.452i −1.47616 + 0.0773625i
\(315\) −3480.91 365.858i −0.622625 0.0654405i
\(316\) 113.230 + 1077.31i 0.0201572 + 0.191783i
\(317\) −842.852 1654.19i −0.149335 0.293087i 0.804205 0.594352i \(-0.202591\pi\)
−0.953541 + 0.301265i \(0.902591\pi\)
\(318\) 1928.08 516.628i 0.340005 0.0911040i
\(319\) −5363.20 + 302.982i −0.941321 + 0.0531779i
\(320\) −3456.19 3456.19i −0.603771 0.603771i
\(321\) 2403.76 2164.35i 0.417958 0.376331i
\(322\) 6208.66 13944.9i 1.07452 2.41341i
\(323\) −41.1715 + 33.3400i −0.00709239 + 0.00574331i
\(324\) −443.332 + 144.047i −0.0760172 + 0.0246995i
\(325\) −2215.84 850.223i −0.378193 0.145114i
\(326\) −4632.26 + 6375.76i −0.786985 + 1.08319i
\(327\) −2057.96 5361.17i −0.348029 0.906646i
\(328\) −2624.85 + 557.928i −0.441868 + 0.0939220i
\(329\) −4481.59 + 7762.33i −0.750996 + 1.30076i
\(330\) 759.454 + 2788.84i 0.126687 + 0.465213i
\(331\) −2322.82 8668.89i −0.385721 1.43953i −0.837027 0.547162i \(-0.815708\pi\)
0.451305 0.892370i \(-0.350959\pi\)
\(332\) 823.144 + 43.1392i 0.136072 + 0.00713123i
\(333\) −3040.25 481.528i −0.500314 0.0792420i
\(334\) −5485.70 + 2442.39i −0.898695 + 0.400125i
\(335\) −1733.60 1560.94i −0.282736 0.254577i
\(336\) 270.859 + 5168.30i 0.0439779 + 0.839149i
\(337\) −7149.54 5194.45i −1.15567 0.839643i −0.166445 0.986051i \(-0.553229\pi\)
−0.989224 + 0.146408i \(0.953229\pi\)
\(338\) −4479.85 + 2911.05i −0.720922 + 0.468462i
\(339\) −2428.09 + 7472.88i −0.389014 + 1.19726i
\(340\) −398.061 + 1485.59i −0.0634939 + 0.236962i
\(341\) −1281.90 1749.36i −0.203574 0.277809i
\(342\) 16.6118 + 9.59085i 0.00262651 + 0.00151641i
\(343\) −9407.67 + 4793.45i −1.48095 + 0.754582i
\(344\) −657.146 532.146i −0.102997 0.0834052i
\(345\) 5986.67 + 2298.07i 0.934236 + 0.358620i
\(346\) 2013.85 3952.41i 0.312906 0.614112i
\(347\) −2581.95 + 12147.1i −0.399443 + 1.87923i 0.0721186 + 0.997396i \(0.477024\pi\)
−0.471561 + 0.881833i \(0.656309\pi\)
\(348\) 121.324 1154.32i 0.0186886 0.177811i
\(349\) 6970.74 2675.82i 1.06916 0.410410i 0.240777 0.970580i \(-0.422598\pi\)
0.828378 + 0.560170i \(0.189264\pi\)
\(350\) 3734.67 + 1213.47i 0.570362 + 0.185322i
\(351\) 5467.79 + 4426.45i 0.831479 + 0.673124i
\(352\) 3053.00 1374.21i 0.462289 0.208084i
\(353\) 11943.8 + 3200.32i 1.80086 + 0.482538i 0.994111 0.108364i \(-0.0345611\pi\)
0.806744 + 0.590901i \(0.201228\pi\)
\(354\) 1285.56 + 6048.10i 0.193014 + 0.908059i
\(355\) 6204.96 652.168i 0.927677 0.0975028i
\(356\) −278.211 + 44.0643i −0.0414190 + 0.00656013i
\(357\) 8637.23 5609.08i 1.28048 0.831552i
\(358\) −7243.31 + 4703.86i −1.06933 + 0.694433i
\(359\) 2831.38 448.446i 0.416252 0.0659278i 0.0552041 0.998475i \(-0.482419\pi\)
0.361048 + 0.932547i \(0.382419\pi\)
\(360\) 2677.19 281.384i 0.391945 0.0411951i
\(361\) 1425.99 + 6708.74i 0.207900 + 0.978093i
\(362\) −10197.8 2732.50i −1.48062 0.396732i
\(363\) −5005.08 484.868i −0.723688 0.0701074i
\(364\) −2523.06 + 1833.66i −0.363309 + 0.264038i
\(365\) 754.102 + 245.023i 0.108141 + 0.0351372i
\(366\) 483.319 185.529i 0.0690259 0.0264966i
\(367\) −1287.05 + 12245.4i −0.183061 + 1.74171i 0.388768 + 0.921336i \(0.372901\pi\)
−0.571829 + 0.820373i \(0.693766\pi\)
\(368\) −1757.81 + 8269.84i −0.249000 + 1.17145i
\(369\) 632.121 1240.61i 0.0891786 0.175023i
\(370\) −4735.11 1817.64i −0.665316 0.255391i
\(371\) −5384.90 4360.61i −0.753559 0.610220i
\(372\) 417.531 212.743i 0.0581935 0.0296510i
\(373\) 3.15048 + 1.81893i 0.000437334 + 0.000252495i 0.500219 0.865899i \(-0.333253\pi\)
−0.499781 + 0.866152i \(0.666586\pi\)
\(374\) 6153.09 + 4432.30i 0.850718 + 0.612804i
\(375\) −1480.99 + 5527.15i −0.203942 + 0.761122i
\(376\) 2130.25 6556.24i 0.292179 0.899234i
\(377\) −6148.81 + 3134.07i −0.840000 + 0.428151i
\(378\) −9416.72 6841.65i −1.28133 0.930943i
\(379\) 163.453 + 3118.87i 0.0221531 + 0.422706i 0.987084 + 0.160203i \(0.0512148\pi\)
−0.964931 + 0.262504i \(0.915452\pi\)
\(380\) −8.28764 7.46222i −0.00111881 0.00100738i
\(381\) −629.994 + 280.491i −0.0847128 + 0.0377166i
\(382\) 4495.32 + 711.989i 0.602096 + 0.0953626i
\(383\) −5275.02 276.452i −0.703762 0.0368826i −0.302902 0.953022i \(-0.597955\pi\)
−0.400860 + 0.916139i \(0.631289\pi\)
\(384\) −629.867 2350.70i −0.0837051 0.312392i
\(385\) 6282.44 7823.11i 0.831644 1.03559i
\(386\) −1621.13 + 2807.88i −0.213765 + 0.370252i
\(387\) 429.158 91.2204i 0.0563704 0.0119819i
\(388\) 513.498 + 1337.71i 0.0671879 + 0.175030i
\(389\) −3300.74 + 4543.09i −0.430217 + 0.592143i −0.968003 0.250939i \(-0.919261\pi\)
0.537786 + 0.843081i \(0.319261\pi\)
\(390\) 2337.39 + 2885.60i 0.303483 + 0.374662i
\(391\) 16000.7 5198.93i 2.06954 0.672433i
\(392\) 12849.1 10405.0i 1.65556 1.34064i
\(393\) −1519.67 + 3413.23i −0.195056 + 0.438103i
\(394\) 4609.97 4150.84i 0.589459 0.530752i
\(395\) −3165.72 3165.72i −0.403252 0.403252i
\(396\) −246.928 + 936.792i −0.0313348 + 0.118878i
\(397\) 2844.30 762.128i 0.359575 0.0963479i −0.0745086 0.997220i \(-0.523739\pi\)
0.434084 + 0.900872i \(0.357072\pi\)
\(398\) −4501.65 8835.00i −0.566954 1.11271i
\(399\) 7.80587 + 74.2679i 0.000979404 + 0.00931841i
\(400\) −2163.06 227.347i −0.270383 0.0284184i
\(401\) 12240.3 641.486i 1.52432 0.0798860i 0.728340 0.685216i \(-0.240292\pi\)
0.795975 + 0.605330i \(0.206959\pi\)
\(402\) −767.991 2363.63i −0.0952833 0.293252i
\(403\) −2413.26 1392.84i −0.298295 0.172165i
\(404\) −513.712 707.064i −0.0632627 0.0870736i
\(405\) 1049.28 1615.76i 0.128739 0.198241i
\(406\) 9889.06 5709.45i 1.20883 0.697919i
\(407\) 5877.60 6581.44i 0.715827 0.801548i
\(408\) −5600.86 + 5600.86i −0.679618 + 0.679618i
\(409\) 465.907 8890.03i 0.0563267 1.07478i −0.813546 0.581501i \(-0.802466\pi\)
0.869873 0.493276i \(-0.164201\pi\)
\(410\) 1443.83 1782.98i 0.173916 0.214768i
\(411\) 590.931 + 3730.99i 0.0709209 + 0.447777i
\(412\) 2619.89 + 556.876i 0.313284 + 0.0665905i
\(413\) 14362.1 15950.8i 1.71117 1.90045i
\(414\) −3833.51 4733.99i −0.455089 0.561988i
\(415\) −2756.07 + 2002.40i −0.326001 + 0.236853i
\(416\) 2877.78 3197.01i 0.339170 0.376794i
\(417\) 904.296i 0.106196i
\(418\) −48.8916 + 25.1629i −0.00572097 + 0.00294439i
\(419\) 3431.90 + 5944.22i 0.400141 + 0.693065i 0.993743 0.111694i \(-0.0356278\pi\)
−0.593601 + 0.804759i \(0.702294\pi\)
\(420\) 1450.63 + 1611.09i 0.168532 + 0.187174i
\(421\) −945.320 + 5968.52i −0.109435 + 0.690945i 0.870581 + 0.492025i \(0.163743\pi\)
−0.980016 + 0.198919i \(0.936257\pi\)
\(422\) 4565.65 11893.9i 0.526665 1.37201i
\(423\) 1948.10 + 2999.81i 0.223924 + 0.344813i
\(424\) 4748.35 + 2419.41i 0.543869 + 0.277115i
\(425\) 1760.38 + 3953.88i 0.200920 + 0.451274i
\(426\) 6072.30 + 2703.56i 0.690619 + 0.307484i
\(427\) −1507.19 978.777i −0.170815 0.110928i
\(428\) 1786.40 0.201750
\(429\) −6135.83 + 2022.28i −0.690537 + 0.227591i
\(430\) 722.941 0.0810774
\(431\) 13353.5 + 8671.86i 1.49238 + 0.969162i 0.994811 + 0.101737i \(0.0324401\pi\)
0.497568 + 0.867425i \(0.334227\pi\)
\(432\) 5889.53 + 2622.19i 0.655926 + 0.292037i
\(433\) 2876.71 + 6461.19i 0.319274 + 0.717101i 0.999879 0.0155494i \(-0.00494971\pi\)
−0.680605 + 0.732650i \(0.738283\pi\)
\(434\) 4107.72 + 2092.99i 0.454325 + 0.231490i
\(435\) 2612.66 + 4023.14i 0.287971 + 0.443436i
\(436\) 1136.58 2960.88i 0.124844 0.325231i
\(437\) −19.0839 + 120.491i −0.00208904 + 0.0131896i
\(438\) 565.240 + 627.763i 0.0616626 + 0.0684833i
\(439\) −5181.15 8974.02i −0.563287 0.975641i −0.997207 0.0746898i \(-0.976203\pi\)
0.433920 0.900951i \(-0.357130\pi\)
\(440\) −3475.32 + 6889.93i −0.376544 + 0.746510i
\(441\) 8578.76i 0.926332i
\(442\) 9530.14 + 2024.29i 1.02557 + 0.217840i
\(443\) −8523.75 + 6192.87i −0.914166 + 0.664181i −0.942065 0.335430i \(-0.891118\pi\)
0.0278987 + 0.999611i \(0.491118\pi\)
\(444\) 1199.86 + 1481.70i 0.128249 + 0.158375i
\(445\) 778.982 865.147i 0.0829826 0.0921615i
\(446\) 428.706 + 91.1244i 0.0455153 + 0.00967458i
\(447\) −1419.65 8963.31i −0.150217 0.948434i
\(448\) −11375.6 + 14047.7i −1.19966 + 1.48146i
\(449\) 681.972 13012.8i 0.0716799 1.36773i −0.691887 0.722005i \(-0.743221\pi\)
0.763567 0.645728i \(-0.223446\pi\)
\(450\) 1108.08 1108.08i 0.116079 0.116079i
\(451\) 2009.76 + 3448.50i 0.209836 + 0.360052i
\(452\) −3758.15 + 2169.77i −0.391081 + 0.225791i
\(453\) 1695.51 2610.85i 0.175854 0.270791i
\(454\) 933.931 + 1285.45i 0.0965452 + 0.132883i
\(455\) 3334.60 12451.9i 0.343579 1.28298i
\(456\) −17.7483 54.6235i −0.00182267 0.00560961i
\(457\) −1210.83 + 63.4569i −0.123939 + 0.00649538i −0.114205 0.993457i \(-0.536432\pi\)
−0.00973452 + 0.999953i \(0.503099\pi\)
\(458\) −4078.07 428.622i −0.416060 0.0437297i
\(459\) −1340.99 12758.6i −0.136366 1.29743i
\(460\) 1607.84 + 3155.56i 0.162969 + 0.319845i
\(461\) 1937.33 519.107i 0.195728 0.0524452i −0.159623 0.987178i \(-0.551028\pi\)
0.355351 + 0.934733i \(0.384361\pi\)
\(462\) 9963.61 3871.31i 1.00335 0.389847i
\(463\) 813.945 + 813.945i 0.0817003 + 0.0817003i 0.746776 0.665076i \(-0.231601\pi\)
−0.665076 + 0.746776i \(0.731601\pi\)
\(464\) −4700.09 + 4231.98i −0.470250 + 0.423415i
\(465\) −787.739 + 1769.29i −0.0785603 + 0.176449i
\(466\) −9246.25 + 7487.47i −0.919151 + 0.744314i
\(467\) −5824.54 + 1892.51i −0.577147 + 0.187526i −0.583022 0.812456i \(-0.698130\pi\)
0.00587502 + 0.999983i \(0.498130\pi\)
\(468\) 194.883 + 1229.32i 0.0192489 + 0.121422i
\(469\) −5070.91 + 6979.50i −0.499259 + 0.687172i
\(470\) 2112.13 + 5502.29i 0.207288 + 0.540004i
\(471\) −12498.8 + 2656.71i −1.22275 + 0.259904i
\(472\) −8254.00 + 14296.4i −0.804918 + 1.39416i
\(473\) −445.942 + 1176.01i −0.0433497 + 0.114319i
\(474\) −1234.47 4607.11i −0.119623 0.446438i
\(475\) −31.3402 1.64247i −0.00302734 0.000158656i
\(476\) 5617.78 + 889.769i 0.540947 + 0.0856775i
\(477\) −2526.07 + 1124.68i −0.242476 + 0.107957i
\(478\) 3783.54 + 3406.71i 0.362040 + 0.325982i
\(479\) −916.161 17481.4i −0.0873914 1.66753i −0.593332 0.804958i \(-0.702188\pi\)
0.505941 0.862568i \(-0.331146\pi\)
\(480\) −2418.83 1757.38i −0.230008 0.167110i
\(481\) 3501.72 10782.4i 0.331943 1.02211i
\(482\) 1654.60 5092.33i 0.156359 0.481222i
\(483\) 6137.92 22907.0i 0.578229 2.15798i
\(484\) −1875.04 2048.63i −0.176093 0.192396i
\(485\) −5128.63 2961.02i −0.480163 0.277222i
\(486\) −6951.54 + 3541.98i −0.648823 + 0.330592i
\(487\) 8329.33 + 6744.96i 0.775027 + 0.627604i 0.933015 0.359837i \(-0.117168\pi\)
−0.157989 + 0.987441i \(0.550501\pi\)
\(488\) 1290.37 + 495.326i 0.119697 + 0.0459474i
\(489\) −5558.55 + 10909.3i −0.514041 + 1.00886i
\(490\) −2938.95 + 13826.7i −0.270956 + 1.27475i
\(491\) −2118.77 + 20158.8i −0.194743 + 1.85286i 0.264296 + 0.964442i \(0.414861\pi\)
−0.459039 + 0.888416i \(0.651806\pi\)
\(492\) −805.144 + 309.066i −0.0737778 + 0.0283206i
\(493\) 11969.6 + 3889.15i 1.09347 + 0.355291i
\(494\) −44.4510 + 54.9082i −0.00404847 + 0.00500089i
\(495\) −1643.45 3651.15i −0.149227 0.331529i
\(496\) −2466.45 660.883i −0.223280 0.0598277i
\(497\) −4797.28 22569.4i −0.432973 2.03698i
\(498\) −3609.49 + 379.372i −0.324789 + 0.0341367i
\(499\) 6597.48 1044.94i 0.591871 0.0937431i 0.146688 0.989183i \(-0.453139\pi\)
0.445183 + 0.895440i \(0.353139\pi\)
\(500\) −2650.39 + 1721.19i −0.237058 + 0.153948i
\(501\) −7824.09 + 5081.02i −0.697714 + 0.453101i
\(502\) −10102.9 + 1600.14i −0.898235 + 0.142267i
\(503\) −2061.10 + 216.631i −0.182704 + 0.0192029i −0.195438 0.980716i \(-0.562613\pi\)
0.0127347 + 0.999919i \(0.495946\pi\)
\(504\) −2069.83 9737.79i −0.182932 0.860626i
\(505\) 3489.04 + 934.886i 0.307446 + 0.0823800i
\(506\) 17358.9 1896.01i 1.52509 0.166577i
\(507\) −6166.73 + 5555.70i −0.540185 + 0.486661i
\(508\) −362.222 117.693i −0.0316358 0.0102791i
\(509\) −10777.4 + 4137.05i −0.938504 + 0.360258i −0.779060 0.626949i \(-0.784303\pi\)
−0.159444 + 0.987207i \(0.550970\pi\)
\(510\) 707.861 6734.85i 0.0614600 0.584753i
\(511\) 609.669 2868.27i 0.0527792 0.248307i
\(512\) 5616.12 11022.3i 0.484765 0.951405i
\(513\) 86.8450 + 33.3367i 0.00747427 + 0.00286910i
\(514\) 9262.97 + 7501.00i 0.794887 + 0.643687i
\(515\) −9863.29 + 5025.60i −0.843939 + 0.430008i
\(516\) −235.349 135.879i −0.0200788 0.0115925i
\(517\) −10253.5 + 41.7624i −0.872238 + 0.00355262i
\(518\) −4854.74 + 18118.1i −0.411786 + 1.53681i
\(519\) 2129.63 6554.32i 0.180116 0.554341i
\(520\) −517.478 + 9900.81i −0.0436402 + 0.834960i
\(521\) −7821.70 5682.79i −0.657725 0.477865i 0.208169 0.978093i \(-0.433250\pi\)
−0.865894 + 0.500228i \(0.833250\pi\)
\(522\) −238.487 4550.61i −0.0199968 0.381561i
\(523\) −14752.7 13283.4i −1.23344 1.11059i −0.990057 0.140664i \(-0.955076\pi\)
−0.243383 0.969930i \(-0.578257\pi\)
\(524\) −1885.07 + 839.287i −0.157156 + 0.0699703i
\(525\) 6025.69 + 954.375i 0.500919 + 0.0793378i
\(526\) −13179.2 690.692i −1.09247 0.0572540i
\(527\) 1315.12 + 4908.08i 0.108705 + 0.405691i
\(528\) −4952.15 + 3244.72i −0.408172 + 0.267440i
\(529\) 13287.1 23014.0i 1.09206 1.89151i
\(530\) −4456.66 + 947.293i −0.365255 + 0.0776373i
\(531\) −3069.57 7996.51i −0.250863 0.653519i
\(532\) −24.2419 + 33.3662i −0.00197560 + 0.00271918i
\(533\) 4149.10 + 3013.60i 0.337181 + 0.244903i
\(534\) 1179.56 383.263i 0.0955892 0.0310588i
\(535\) −5737.77 + 4646.35i −0.463674 + 0.375476i
\(536\) 2698.78 6061.55i 0.217480 0.488468i
\(537\) −9971.48 + 8978.36i −0.801306 + 0.721499i
\(538\) 5663.57 + 5663.57i 0.453855 + 0.453855i
\(539\) −20679.1 13309.7i −1.65253 1.06362i
\(540\) 2608.54 698.955i 0.207877 0.0557005i
\(541\) 3167.38 + 6216.34i 0.251712 + 0.494013i 0.981940 0.189190i \(-0.0605862\pi\)
−0.730228 + 0.683203i \(0.760586\pi\)
\(542\) −1246.52 11859.8i −0.0987871 0.939896i
\(543\) −16312.4 1714.50i −1.28919 0.135500i
\(544\) −7833.39 + 410.531i −0.617378 + 0.0323554i
\(545\) 4050.54 + 12466.3i 0.318360 + 0.979812i
\(546\) 9709.53 9712.27i 0.761043 0.761258i
\(547\) 13666.5 + 18810.3i 1.06826 + 1.47033i 0.871828 + 0.489812i \(0.162935\pi\)
0.196429 + 0.980518i \(0.437065\pi\)
\(548\) −1136.25 + 1749.68i −0.0885736 + 0.136391i
\(549\) −621.079 + 358.580i −0.0482823 + 0.0278758i
\(550\) 951.870 + 4390.19i 0.0737961 + 0.340361i
\(551\) −64.5298 + 64.5298i −0.00498922 + 0.00498922i
\(552\) −954.578 + 18214.4i −0.0736043 + 1.40445i
\(553\) −10419.6 + 12867.1i −0.801239 + 0.989448i
\(554\) 3048.11 + 19245.0i 0.233758 + 1.47589i
\(555\) −7707.68 1638.32i −0.589500 0.125302i
\(556\) 334.182 371.147i 0.0254901 0.0283096i
\(557\) 2620.27 + 3235.77i 0.199326 + 0.246147i 0.867002 0.498305i \(-0.166044\pi\)
−0.667676 + 0.744452i \(0.732711\pi\)
\(558\) 1488.40 1081.38i 0.112919 0.0820405i
\(559\) 84.7969 + 1613.66i 0.00641597 + 0.122094i
\(560\) 11813.2i 0.891425i
\(561\) 10519.0 + 5305.83i 0.791643 + 0.399309i
\(562\) −1830.97 3171.33i −0.137428 0.238033i
\(563\) 1557.08 + 1729.31i 0.116560 + 0.129452i 0.798600 0.601862i \(-0.205574\pi\)
−0.682041 + 0.731314i \(0.738907\pi\)
\(564\) 346.580 2188.22i 0.0258752 0.163370i
\(565\) 6427.39 16743.9i 0.478588 1.24676i
\(566\) −2468.48 3801.12i −0.183318 0.282285i
\(567\) −6348.29 3234.62i −0.470200 0.239579i
\(568\) 7217.99 + 16211.9i 0.533204 + 1.19760i
\(569\) −3593.11 1599.76i −0.264730 0.117865i 0.270080 0.962838i \(-0.412950\pi\)
−0.534809 + 0.844973i \(0.679617\pi\)
\(570\) 41.1821 + 26.7440i 0.00302619 + 0.00196523i
\(571\) −4990.70 −0.365769 −0.182885 0.983134i \(-0.558543\pi\)
−0.182885 + 0.983134i \(0.558543\pi\)
\(572\) −3265.64 1437.50i −0.238712 0.105078i
\(573\) 7071.00 0.515524
\(574\) −7115.83 4621.07i −0.517437 0.336028i
\(575\) 9104.70 + 4053.67i 0.660334 + 0.294000i
\(576\) 2933.98 + 6589.83i 0.212238 + 0.476695i
\(577\) −16937.4 8630.04i −1.22203 0.622657i −0.280590 0.959828i \(-0.590530\pi\)
−0.941444 + 0.337171i \(0.890530\pi\)
\(578\) −3169.61 4880.77i −0.228094 0.351234i
\(579\) −1805.16 + 4702.61i −0.129568 + 0.337537i
\(580\) −414.446 + 2616.71i −0.0296706 + 0.187333i
\(581\) 8430.15 + 9362.63i 0.601965 + 0.668549i
\(582\) −3154.56 5463.86i −0.224675 0.389148i
\(583\) 1208.10 7834.02i 0.0858222 0.556521i
\(584\) 2255.29i 0.159802i
\(585\) −3823.36 3441.60i −0.270216 0.243235i
\(586\) −12008.4 + 8724.62i −0.846524 + 0.615036i
\(587\) 13437.7 + 16594.2i 0.944863 + 1.16681i 0.985847 + 0.167649i \(0.0536174\pi\)
−0.0409839 + 0.999160i \(0.513049\pi\)
\(588\) 3555.52 3948.81i 0.249366 0.276949i
\(589\) −36.0392 7.66038i −0.00252117 0.000535892i
\(590\) −2207.85 13939.8i −0.154061 0.972702i
\(591\) 6065.09 7489.76i 0.422139 0.521298i
\(592\) 543.724 10374.9i 0.0377482 0.720278i
\(593\) 7335.84 7335.84i 0.508005 0.508005i −0.405909 0.913914i \(-0.633045\pi\)
0.913914 + 0.405909i \(0.133045\pi\)
\(594\) 1337.89 13248.0i 0.0924148 0.915107i
\(595\) −20358.1 + 11753.8i −1.40269 + 0.809843i
\(596\) 2729.73 4203.41i 0.187607 0.288890i
\(597\) −9054.92 12463.0i −0.620759 0.854401i
\(598\) 19427.6 11220.2i 1.32852 0.767269i
\(599\) −5779.16 17786.4i −0.394207 1.21324i −0.929577 0.368627i \(-0.879828\pi\)
0.535370 0.844617i \(-0.320172\pi\)
\(600\) −4685.73 + 245.569i −0.318824 + 0.0167088i
\(601\) 5585.81 + 587.092i 0.379118 + 0.0398469i 0.292171 0.956366i \(-0.405622\pi\)
0.0869468 + 0.996213i \(0.472289\pi\)
\(602\) −279.466 2658.94i −0.0189205 0.180017i
\(603\) 1562.98 + 3067.53i 0.105555 + 0.207163i
\(604\) 1660.72 444.988i 0.111877 0.0299773i
\(605\) 11350.9 + 1703.14i 0.762773 + 0.114450i
\(606\) 2721.11 + 2721.11i 0.182405 + 0.182405i
\(607\) −6207.33 + 5589.11i −0.415071 + 0.373731i −0.850044 0.526712i \(-0.823425\pi\)
0.434973 + 0.900443i \(0.356758\pi\)
\(608\) 23.1346 51.9612i 0.00154314 0.00346596i
\(609\) 13786.9 11164.4i 0.917363 0.742866i
\(610\) −1123.86 + 365.164i −0.0745962 + 0.0242378i
\(611\) −12033.8 + 5359.84i −0.796786 + 0.354887i
\(612\) 1334.15 1836.30i 0.0881206 0.121288i
\(613\) −1469.78 3828.90i −0.0968414 0.252280i 0.876599 0.481222i \(-0.159807\pi\)
−0.973440 + 0.228942i \(0.926474\pi\)
\(614\) 4042.97 859.360i 0.265735 0.0564836i
\(615\) 1782.19 3086.84i 0.116853 0.202396i
\(616\) 26684.2 + 10118.6i 1.74535 + 0.661835i
\(617\) 878.801 + 3279.73i 0.0573407 + 0.213998i 0.988652 0.150227i \(-0.0480004\pi\)
−0.931311 + 0.364225i \(0.881334\pi\)
\(618\) −11777.2 617.219i −0.766586 0.0401751i
\(619\) 27400.2 + 4339.76i 1.77917 + 0.281793i 0.957555 0.288249i \(-0.0930732\pi\)
0.821615 + 0.570042i \(0.193073\pi\)
\(620\) −977.150 + 435.055i −0.0632956 + 0.0281810i
\(621\) −21953.6 19767.1i −1.41862 1.27734i
\(622\) 422.063 + 8053.45i 0.0272077 + 0.519154i
\(623\) −3483.09 2530.62i −0.223992 0.162740i
\(624\) −4141.87 + 6379.90i −0.265717 + 0.409295i
\(625\) 2080.23 6402.30i 0.133135 0.409747i
\(626\) −3793.88 + 14159.0i −0.242227 + 0.904003i
\(627\) −68.9075 + 50.4943i −0.00438900 + 0.00321619i
\(628\) −6111.64 3528.55i −0.388345 0.224211i
\(629\) −18420.4 + 9385.65i −1.16768 + 0.594961i
\(630\) 6614.58 + 5356.38i 0.418303 + 0.338735i
\(631\) 19891.7 + 7635.72i 1.25496 + 0.481732i 0.892829 0.450396i \(-0.148717\pi\)
0.362127 + 0.932129i \(0.382051\pi\)
\(632\) 5781.11 11346.1i 0.363861 0.714118i
\(633\) 4115.22 19360.6i 0.258397 1.21566i
\(634\) −471.911 + 4489.94i −0.0295615 + 0.281259i
\(635\) 1469.54 564.103i 0.0918376 0.0352532i
\(636\) 1628.89 + 529.257i 0.101556 + 0.0329975i
\(637\) −31207.0 4938.19i −1.94108 0.307156i
\(638\) 11339.2 + 6485.28i 0.703644 + 0.402437i
\(639\) −8894.07 2383.16i −0.550617 0.147537i
\(640\) 1154.93 + 5433.51i 0.0713321 + 0.335591i
\(641\) −8680.07 + 912.312i −0.534855 + 0.0562155i −0.368106 0.929784i \(-0.619994\pi\)
−0.166749 + 0.985999i \(0.553327\pi\)
\(642\) −7768.88 + 1230.47i −0.477591 + 0.0756430i
\(643\) −4122.36 + 2677.09i −0.252830 + 0.164190i −0.664831 0.746993i \(-0.731497\pi\)
0.412001 + 0.911183i \(0.364830\pi\)
\(644\) 10984.4 7133.38i 0.672124 0.436482i
\(645\) 1109.34 175.701i 0.0677210 0.0107260i
\(646\) 128.124 13.4663i 0.00780335 0.000820165i
\(647\) 968.904 + 4558.34i 0.0588741 + 0.276981i 0.997731 0.0673267i \(-0.0214470\pi\)
−0.938857 + 0.344308i \(0.888114\pi\)
\(648\) 5293.05 + 1418.27i 0.320881 + 0.0859798i
\(649\) 24037.9 + 5007.18i 1.45389 + 0.302849i
\(650\) 3393.03 + 4668.72i 0.204747 + 0.281727i
\(651\) 6811.88 + 2213.31i 0.410105 + 0.133251i
\(652\) −6312.89 + 2423.29i −0.379190 + 0.145557i
\(653\) −692.126 + 6585.14i −0.0414778 + 0.394635i 0.954012 + 0.299768i \(0.0969092\pi\)
−0.995490 + 0.0948668i \(0.969757\pi\)
\(654\) −2903.41 + 13659.5i −0.173597 + 0.816708i
\(655\) 3871.73 7598.70i 0.230964 0.453291i
\(656\) 4387.27 + 1684.11i 0.261119 + 0.100234i
\(657\) −909.407 736.424i −0.0540021 0.0437300i
\(658\) 19420.7 9895.32i 1.15060 0.586261i
\(659\) 6713.45 + 3876.01i 0.396842 + 0.229117i 0.685121 0.728430i \(-0.259750\pi\)
−0.288278 + 0.957547i \(0.593083\pi\)
\(660\) −756.763 + 2361.76i −0.0446317 + 0.139290i
\(661\) 587.862 2193.93i 0.0345918 0.129098i −0.946471 0.322790i \(-0.895379\pi\)
0.981063 + 0.193691i \(0.0620460\pi\)
\(662\) −6744.09 + 20756.2i −0.395946 + 1.21860i
\(663\) 15115.7 + 790.043i 0.885440 + 0.0462786i
\(664\) −7839.14 5695.47i −0.458159 0.332872i
\(665\) −8.92093 170.221i −0.000520209 0.00992618i
\(666\) 5562.68 + 5008.66i 0.323648 + 0.291414i
\(667\) 26475.5 11787.6i 1.53693 0.684287i
\(668\) −5088.90 806.003i −0.294754 0.0466844i
\(669\) 679.987 + 35.6366i 0.0392972 + 0.00205948i
\(670\) 1468.23 + 5479.50i 0.0846605 + 0.315957i
\(671\) 99.2313 2053.44i 0.00570906 0.118140i
\(672\) −5528.51 + 9575.66i −0.317361 + 0.549686i
\(673\) 26490.1 5630.64i 1.51726 0.322504i 0.627387 0.778708i \(-0.284125\pi\)
0.889875 + 0.456204i \(0.150791\pi\)
\(674\) 7701.43 + 20062.9i 0.440130 + 1.14658i
\(675\) 4466.96 6148.24i 0.254716 0.350586i
\(676\) −4584.09 + 1.29447i −0.260816 + 7.36498e-5i
\(677\) 2975.77 966.887i 0.168934 0.0548900i −0.223329 0.974743i \(-0.571692\pi\)
0.392263 + 0.919853i \(0.371692\pi\)
\(678\) 14849.3 12024.7i 0.841127 0.681131i
\(679\) −8907.90 + 20007.5i −0.503467 + 1.13080i
\(680\) 13435.9 12097.7i 0.757710 0.682246i
\(681\) 1745.51 + 1745.51i 0.0982201 + 0.0982201i
\(682\) 297.464 + 5265.52i 0.0167016 + 0.295641i
\(683\) −6903.44 + 1849.77i −0.386754 + 0.103630i −0.446956 0.894556i \(-0.647492\pi\)
0.0602024 + 0.998186i \(0.480825\pi\)
\(684\) 7.47198 + 14.6646i 0.000417688 + 0.000819759i
\(685\) −901.286 8575.16i −0.0502721 0.478307i
\(686\) 25535.1 + 2683.84i 1.42118 + 0.149373i
\(687\) −6361.87 + 333.412i −0.353305 + 0.0185159i
\(688\) 457.598 + 1408.34i 0.0253572 + 0.0780415i
\(689\) −2637.18 9836.52i −0.145818 0.543892i
\(690\) −9165.87 12615.7i −0.505708 0.696048i
\(691\) −12512.4 + 19267.4i −0.688847 + 1.06073i 0.305253 + 0.952271i \(0.401259\pi\)
−0.994101 + 0.108461i \(0.965408\pi\)
\(692\) 3296.20 1903.06i 0.181073 0.104543i
\(693\) −12793.4 + 7455.93i −0.701273 + 0.408697i
\(694\) 21353.8 21353.8i 1.16798 1.16798i
\(695\) −108.027 + 2061.29i −0.00589599 + 0.112502i
\(696\) −8586.64 + 10603.6i −0.467637 + 0.577484i
\(697\) −1462.90 9236.37i −0.0794996 0.501941i
\(698\) −17760.4 3775.09i −0.963096 0.204712i
\(699\) −12368.4 + 13736.5i −0.669266 + 0.743295i
\(700\) 2120.41 + 2618.49i 0.114491 + 0.141385i
\(701\) −6815.26 + 4951.58i −0.367202 + 0.266788i −0.756050 0.654514i \(-0.772873\pi\)
0.388848 + 0.921302i \(0.372873\pi\)
\(702\) −5288.74 16269.2i −0.284345 0.874705i
\(703\) 149.907i 0.00804244i
\(704\) −20436.8 3151.60i −1.09409 0.168722i
\(705\) 4578.28 + 7929.81i 0.244579 + 0.423623i
\(706\) −20120.1 22345.6i −1.07256 1.19120i
\(707\) 2089.71 13193.9i 0.111162 0.701850i
\(708\) −1901.28 + 4953.00i −0.100924 + 0.262917i
\(709\) −12460.4 19187.4i −0.660029 1.01636i −0.997190 0.0749092i \(-0.976133\pi\)
0.337161 0.941447i \(-0.390533\pi\)
\(710\) −13518.5 6888.00i −0.714562 0.364087i
\(711\) 2687.40 + 6036.00i 0.141752 + 0.318379i
\(712\) 3024.99 + 1346.81i 0.159222 + 0.0708904i
\(713\) 9812.97 + 6372.62i 0.515426 + 0.334722i
\(714\) −25044.0 −1.31267
\(715\) 14227.8 3876.67i 0.744182 0.202768i
\(716\) −7410.51 −0.386793
\(717\) 6633.71 + 4307.98i 0.345524 + 0.224386i
\(718\) −6368.39 2835.39i −0.331011 0.147376i
\(719\) −3922.33 8809.70i −0.203447 0.456949i 0.782790 0.622285i \(-0.213796\pi\)
−0.986237 + 0.165336i \(0.947129\pi\)
\(720\) −4200.38 2140.20i −0.217415 0.110779i
\(721\) 22296.7 + 34333.9i 1.15170 + 1.77346i
\(722\) 5977.05 15570.8i 0.308093 0.802609i
\(723\) 1301.32 8216.19i 0.0669384 0.422632i
\(724\) −6061.45 6731.92i −0.311149 0.345566i
\(725\) 3727.74 + 6456.63i 0.190958 + 0.330749i
\(726\) 9565.44 + 7617.76i 0.488990 + 0.389424i
\(727\) 4279.62i 0.218325i 0.994024 + 0.109163i \(0.0348169\pi\)
−0.994024 + 0.109163i \(0.965183\pi\)
\(728\) 36614.7 1924.08i 1.86405 0.0979548i
\(729\) −14686.1 + 10670.1i −0.746134 + 0.542098i
\(730\) −1213.44 1498.47i −0.0615224 0.0759738i
\(731\) 1971.75 2189.85i 0.0997646 0.110800i
\(732\) 434.499 + 92.3556i 0.0219393 + 0.00466333i
\(733\) −595.159 3757.69i −0.0299900 0.189350i 0.968145 0.250389i \(-0.0805585\pi\)
−0.998135 + 0.0610393i \(0.980558\pi\)
\(734\) 18843.1 23269.3i 0.947565 1.17015i
\(735\) −1149.36 + 21931.0i −0.0576797 + 1.10060i
\(736\) −12772.4 + 12772.4i −0.639669 + 0.639669i
\(737\) −9819.20 991.622i −0.490767 0.0495615i
\(738\) −2932.28 + 1692.95i −0.146258 + 0.0844423i
\(739\) 360.226 554.700i 0.0179312 0.0276116i −0.829591 0.558371i \(-0.811427\pi\)
0.847523 + 0.530759i \(0.178093\pi\)
\(740\) −2557.99 3520.78i −0.127073 0.174900i
\(741\) −54.8642 + 95.0586i −0.00271996 + 0.00471264i
\(742\) 5206.90 + 16025.2i 0.257616 + 0.792861i
\(743\) 8352.14 437.717i 0.412396 0.0216128i 0.154990 0.987916i \(-0.450465\pi\)
0.257406 + 0.966303i \(0.417132\pi\)
\(744\) −5478.50 575.813i −0.269962 0.0283741i
\(745\) 2165.24 + 20600.9i 0.106481 + 1.01310i
\(746\) −4.01619 7.88221i −0.000197109 0.000386848i
\(747\) 4856.34 1301.25i 0.237864 0.0637353i
\(748\) 2356.50 + 6064.94i 0.115190 + 0.296465i
\(749\) 19307.1 + 19307.1i 0.941877 + 0.941877i
\(750\) 10340.7 9310.85i 0.503454 0.453312i
\(751\) −4784.67 + 10746.6i −0.232484 + 0.522167i −0.991685 0.128689i \(-0.958923\pi\)
0.759201 + 0.650856i \(0.225590\pi\)
\(752\) −9381.96 + 7597.37i −0.454954 + 0.368414i
\(753\) −15113.8 + 4910.76i −0.731442 + 0.237660i
\(754\) 16691.1 + 1751.92i 0.806170 + 0.0846169i
\(755\) −4176.69 + 5748.72i −0.201332 + 0.277109i
\(756\) −3579.10 9323.87i −0.172183 0.448553i
\(757\) −20634.5 + 4386.01i −0.990720 + 0.210584i −0.674639 0.738148i \(-0.735701\pi\)
−0.316082 + 0.948732i \(0.602367\pi\)
\(758\) 3797.38 6577.26i 0.181962 0.315167i
\(759\) 26176.0 7128.23i 1.25182 0.340894i
\(760\) 33.9307 + 126.631i 0.00161947 + 0.00604394i
\(761\) −38880.3 2037.63i −1.85205 0.0970618i −0.906433 0.422349i \(-0.861206\pi\)
−0.945615 + 0.325287i \(0.894539\pi\)
\(762\) 1656.33 + 262.337i 0.0787436 + 0.0124718i
\(763\) 44284.6 19716.8i 2.10119 0.935510i
\(764\) 2902.13 + 2613.09i 0.137428 + 0.123741i
\(765\) 490.961 + 9368.10i 0.0232036 + 0.442751i
\(766\) 10392.0 + 7550.22i 0.490180 + 0.356136i
\(767\) 30855.9 6563.17i 1.45260 0.308973i
\(768\) 3464.96 10664.1i 0.162801 0.501050i
\(769\) 5324.57 19871.6i 0.249687 0.931843i −0.721283 0.692641i \(-0.756447\pi\)
0.970970 0.239203i \(-0.0768861\pi\)
\(770\) −23173.9 + 7634.15i −1.08458 + 0.357293i
\(771\) 16036.8 + 9258.87i 0.749095 + 0.432490i
\(772\) −2478.74 + 1262.98i −0.115559 + 0.0588803i
\(773\) 10471.9 + 8479.98i 0.487255 + 0.394571i 0.841225 0.540686i \(-0.181835\pi\)
−0.353970 + 0.935257i \(0.615168\pi\)
\(774\) −996.062 382.352i −0.0462567 0.0177563i
\(775\) −1366.53 + 2681.96i −0.0633381 + 0.124308i
\(776\) 3502.09 16476.1i 0.162008 0.762186i
\(777\) −3046.10 + 28981.8i −0.140641 + 1.33811i
\(778\) 12748.7 4893.77i 0.587485 0.225514i
\(779\) 64.4899 + 20.9540i 0.00296610 + 0.000963743i
\(780\) 333.505 + 3168.79i 0.0153095 + 0.145463i
\(781\) 19543.5 17741.7i 0.895420 0.812867i
\(782\) −39518.2 10588.9i −1.80712 0.484216i
\(783\) −4594.63 21616.0i −0.209704 0.986582i
\(784\) −28795.7 + 3026.55i −1.31176 + 0.137871i
\(785\) 28807.7 4562.69i 1.30980 0.207451i
\(786\) 7619.88 4948.41i 0.345791 0.224560i
\(787\) 6628.98 4304.91i 0.300251 0.194985i −0.385717 0.922617i \(-0.626046\pi\)
0.685968 + 0.727632i \(0.259379\pi\)
\(788\) 5257.11 832.644i 0.237661 0.0376418i
\(789\) −20391.0 + 2143.18i −0.920076 + 0.0967038i
\(790\) 2263.53 + 10649.1i 0.101940 + 0.479592i
\(791\) −64067.9 17166.9i −2.87989 0.771664i
\(792\) 8432.24 7654.84i 0.378317 0.343438i
\(793\) −946.897 2465.71i −0.0424027 0.110416i
\(794\) −6810.19 2212.77i −0.304389 0.0989019i
\(795\) −6608.42 + 2536.73i −0.294813 + 0.113168i
\(796\) 889.328 8461.39i 0.0395998 0.376767i
\(797\) 5929.12 27894.3i 0.263514 1.23973i −0.624905 0.780700i \(-0.714862\pi\)
0.888419 0.459033i \(-0.151804\pi\)
\(798\) 82.4432 161.804i 0.00365721 0.00717769i
\(799\) 22427.6 + 8609.14i 0.993030 + 0.381188i
\(800\) −3611.20 2924.29i −0.159594 0.129237i
\(801\) −1530.84 + 780.001i −0.0675274 + 0.0344070i
\(802\) −25813.0 14903.2i −1.13652 0.656171i
\(803\) 3186.07 1049.58i 0.140017 0.0461258i
\(804\) 551.915 2059.77i 0.0242096 0.0903515i
\(805\) −16727.5 + 51481.9i −0.732380 + 2.25403i
\(806\) 3076.99 + 6036.82i 0.134469 + 0.263819i
\(807\) 10067.1 + 7314.16i 0.439130 + 0.319046i
\(808\) 537.701 + 10259.9i 0.0234112 + 0.446712i
\(809\) 14579.1 + 13127.1i 0.633591 + 0.570488i 0.922082 0.386995i \(-0.126487\pi\)
−0.288491 + 0.957483i \(0.593154\pi\)
\(810\) −4279.93 + 1905.55i −0.185656 + 0.0826593i
\(811\) 14465.6 + 2291.13i 0.626333 + 0.0992014i 0.461529 0.887125i \(-0.347301\pi\)
0.164804 + 0.986326i \(0.447301\pi\)
\(812\) 9784.33 + 512.775i 0.422860 + 0.0221612i
\(813\) −4795.14 17895.7i −0.206855 0.771992i
\(814\) −20703.7 + 5638.03i −0.891481 + 0.242768i
\(815\) 13973.6 24203.0i 0.600581 1.04024i
\(816\) 13568.0 2883.98i 0.582079 0.123725i
\(817\) 7.65727 + 19.9479i 0.000327900 + 0.000854208i
\(818\) −12724.5 + 17513.7i −0.543888 + 0.748597i
\(819\) −11180.0 + 15392.5i −0.476998 + 0.656726i
\(820\) 1872.20 608.313i 0.0797316 0.0259064i
\(821\) −21974.1 + 17794.3i −0.934107 + 0.756425i −0.970044 0.242929i \(-0.921892\pi\)
0.0359370 + 0.999354i \(0.488558\pi\)
\(822\) 3736.28 8391.82i 0.158537 0.356081i
\(823\) 13388.8 12055.3i 0.567076 0.510597i −0.334975 0.942227i \(-0.608728\pi\)
0.902051 + 0.431630i \(0.142061\pi\)
\(824\) −22264.0 22264.0i −0.941268 0.941268i
\(825\) 2527.60 + 6505.31i 0.106666 + 0.274528i
\(826\) −50416.5 + 13509.1i −2.12375 + 0.569057i
\(827\) 8708.28 + 17091.0i 0.366163 + 0.718635i 0.998424 0.0561205i \(-0.0178731\pi\)
−0.632261 + 0.774755i \(0.717873\pi\)
\(828\) −546.339 5198.06i −0.0229306 0.218171i
\(829\) −17712.0 1861.61i −0.742056 0.0779932i −0.274046 0.961717i \(-0.588362\pi\)
−0.468010 + 0.883723i \(0.655029\pi\)
\(830\) 8272.92 433.565i 0.345973 0.0181317i
\(831\) 9354.51 + 28790.2i 0.390499 + 1.20183i
\(832\) −25660.8 + 6879.66i −1.06926 + 0.286670i
\(833\) 33866.6 + 46613.3i 1.40865 + 1.93884i
\(834\) −1197.68 + 1844.26i −0.0497269 + 0.0765727i
\(835\) 18441.5 10647.2i 0.764305 0.441272i
\(836\) −46.9416 4.74054i −0.00194200 0.000196118i
\(837\) 6308.88 6308.88i 0.260534 0.260534i
\(838\) 873.546 16668.3i 0.0360097 0.687106i
\(839\) −18363.8 + 22677.5i −0.755650 + 0.933150i −0.999326 0.0367065i \(-0.988313\pi\)
0.243676 + 0.969857i \(0.421647\pi\)
\(840\) −3986.74 25171.3i −0.163757 1.03392i
\(841\) −2650.09 563.294i −0.108659 0.0230962i
\(842\) 9832.83 10920.5i 0.402449 0.446965i
\(843\) −3580.33 4421.34i −0.146279 0.180639i
\(844\) 8843.69 6425.32i 0.360678 0.262048i
\(845\) 14720.4 11927.2i 0.599285 0.485572i
\(846\) 8698.09i 0.353483i
\(847\) 1876.17 42406.2i 0.0761109 1.72030i
\(848\) −4666.32 8082.31i −0.188965 0.327297i
\(849\) −4711.64 5232.80i −0.190463 0.211530i
\(850\) 1646.45 10395.3i 0.0664384 0.419476i
\(851\) −17060.4 + 44443.8i −0.687217 + 1.79026i
\(852\) 3106.23 + 4783.18i 0.124903 + 0.192334i
\(853\) −40087.9 20425.8i −1.60913 0.819891i −0.999633 0.0271006i \(-0.991373\pi\)
−0.609494 0.792791i \(-0.708627\pi\)
\(854\) 1777.50 + 3992.33i 0.0712235 + 0.159971i
\(855\) −62.1414 27.6671i −0.00248560 0.00110666i
\(856\) −17612.0 11437.4i −0.703233 0.456685i
\(857\) 15308.6 0.610190 0.305095 0.952322i \(-0.401312\pi\)
0.305095 + 0.952322i \(0.401312\pi\)
\(858\) 15192.1 + 4002.16i 0.604486 + 0.159244i
\(859\) −24289.3 −0.964774 −0.482387 0.875958i \(-0.660230\pi\)
−0.482387 + 0.875958i \(0.660230\pi\)
\(860\) 520.231 + 337.842i 0.0206276 + 0.0133957i
\(861\) −12042.2 5361.52i −0.476650 0.212218i
\(862\) −15748.5 35371.6i −0.622268 1.39764i
\(863\) −12772.7 6508.00i −0.503808 0.256703i 0.183565 0.983008i \(-0.441236\pi\)
−0.687373 + 0.726304i \(0.741236\pi\)
\(864\) 7501.59 + 11551.4i 0.295381 + 0.454847i
\(865\) −5637.34 + 14685.8i −0.221590 + 0.577261i
\(866\) 2690.52 16987.3i 0.105575 0.666571i
\(867\) −6049.90 6719.09i −0.236984 0.263198i
\(868\) 1977.84 + 3425.73i 0.0773415 + 0.133959i
\(869\) −18719.2 2886.72i −0.730731 0.112687i
\(870\) 11665.3i 0.454586i
\(871\) −12058.5 + 3919.91i −0.469099 + 0.152493i
\(872\) −30162.4 + 21914.3i −1.17136 + 0.851046i
\(873\) 5500.15 + 6792.12i 0.213232 + 0.263320i
\(874\) 198.503 220.460i 0.00768247 0.00853224i
\(875\) −47247.2 10042.7i −1.82543 0.388006i
\(876\) 113.385 + 715.886i 0.00437321 + 0.0276114i
\(877\) −20090.1 + 24809.3i −0.773542 + 0.955244i −0.999823 0.0188177i \(-0.994010\pi\)
0.226281 + 0.974062i \(0.427343\pi\)
\(878\) −1318.80 + 25164.1i −0.0506916 + 0.967253i
\(879\) −16306.2 + 16306.2i −0.625705 + 0.625705i
\(880\) 11675.7 6804.55i 0.447260 0.260661i
\(881\) 14371.8 8297.58i 0.549602 0.317313i −0.199360 0.979926i \(-0.563886\pi\)
0.748961 + 0.662614i \(0.230553\pi\)
\(882\) 11362.0 17495.9i 0.433762 0.667935i
\(883\) 23890.9 + 32883.0i 0.910523 + 1.25323i 0.966988 + 0.254823i \(0.0820173\pi\)
−0.0564642 + 0.998405i \(0.517983\pi\)
\(884\) 5911.94 + 5910.27i 0.224932 + 0.224869i
\(885\) −6775.80 20853.8i −0.257363 0.792081i
\(886\) 25585.8 1340.89i 0.970171 0.0508445i
\(887\) 8207.96 + 862.692i 0.310706 + 0.0326565i 0.258598 0.965985i \(-0.416739\pi\)
0.0521078 + 0.998641i \(0.483406\pi\)
\(888\) −2342.78 22290.1i −0.0885344 0.842349i
\(889\) −2642.82 5186.82i −0.0997045 0.195681i
\(890\) −2734.52 + 732.713i −0.102990 + 0.0275962i
\(891\) −459.717 8137.61i −0.0172852 0.305971i
\(892\) 265.915 + 265.915i 0.00998149 + 0.00998149i
\(893\) −129.452 + 116.559i −0.00485099 + 0.00436785i
\(894\) −8976.01 + 20160.4i −0.335797 + 0.754213i
\(895\) 23801.9 19274.4i 0.888951 0.719858i
\(896\) 19537.7 6348.19i 0.728470 0.236694i
\(897\) 27084.2 21938.7i 1.00816 0.816624i
\(898\) −18625.4 + 25635.7i −0.692137 + 0.952645i
\(899\) 3136.74 + 8171.48i 0.116369 + 0.303153i
\(900\) 1315.21 279.555i 0.0487113 0.0103539i
\(901\) −9285.69 + 16083.3i −0.343342 + 0.594686i
\(902\) 468.498 9694.83i 0.0172941 0.357874i
\(903\) −1075.05 4012.16i −0.0396186 0.147859i
\(904\) 50943.4 + 2669.83i 1.87428 + 0.0982270i
\(905\) 36978.3 + 5856.79i 1.35823 + 0.215123i
\(906\) −6915.79 + 3079.11i −0.253600 + 0.112910i
\(907\) 10288.0 + 9263.34i 0.376634 + 0.339123i 0.835607 0.549327i \(-0.185116\pi\)
−0.458973 + 0.888450i \(0.651783\pi\)
\(908\) 71.3507 + 1361.45i 0.00260777 + 0.0497592i
\(909\) −4312.73 3133.38i −0.157364 0.114332i
\(910\) −23292.5 + 20978.6i −0.848504 + 0.764213i
\(911\) 5803.92 17862.6i 0.211078 0.649633i −0.788330 0.615252i \(-0.789054\pi\)
0.999409 0.0343805i \(-0.0109458\pi\)
\(912\) −26.0323 + 97.1538i −0.000945192 + 0.00352751i
\(913\) −4397.82 + 13725.1i −0.159416 + 0.497517i
\(914\) 2553.47 + 1474.25i 0.0924084 + 0.0533520i
\(915\) −1635.79 + 833.475i −0.0591010 + 0.0301135i
\(916\) −2734.29 2214.19i −0.0986284 0.0798677i
\(917\) −29444.3 11302.6i −1.06035 0.407029i
\(918\) −14163.1 + 27796.6i −0.509206 + 0.999374i
\(919\) 3992.36 18782.6i 0.143303 0.674189i −0.846575 0.532270i \(-0.821339\pi\)
0.989878 0.141920i \(-0.0453274\pi\)
\(920\) 4351.80 41404.6i 0.155951 1.48377i
\(921\) 5994.99 2301.26i 0.214486 0.0823334i
\(922\) −4638.62 1507.18i −0.165688 0.0538354i
\(923\) 13788.9 30982.2i 0.491731 1.10487i
\(924\) 8978.98 + 1870.35i 0.319683 + 0.0665909i
\(925\) −11829.5 3169.69i −0.420487 0.112669i
\(926\) −581.983 2738.02i −0.0206535 0.0971672i
\(927\) 16247.5 1707.68i 0.575662 0.0605045i
\(928\) −13345.9 + 2113.78i −0.472090 + 0.0747717i
\(929\) 10872.8 7060.86i 0.383987 0.249364i −0.338182 0.941081i \(-0.609812\pi\)
0.722169 + 0.691717i \(0.243145\pi\)
\(930\) 3949.86 2565.07i 0.139270 0.0904430i
\(931\) −412.645 + 65.3565i −0.0145262 + 0.00230072i
\(932\) −10152.7 + 1067.09i −0.356825 + 0.0375039i
\(933\) 2604.93 + 12255.3i 0.0914059 + 0.430031i
\(934\) 14385.4 + 3854.55i 0.503965 + 0.135037i
\(935\) −23343.5 13350.9i −0.816486 0.466975i
\(936\) 5949.36 13367.6i 0.207757 0.466808i
\(937\) 23123.1 + 7513.16i 0.806190 + 0.261947i 0.682983 0.730434i \(-0.260682\pi\)
0.123207 + 0.992381i \(0.460682\pi\)
\(938\) 19585.7 7518.26i 0.681767 0.261706i
\(939\) −2380.47 + 22648.6i −0.0827302 + 0.787125i
\(940\) −1051.41 + 4946.50i −0.0364822 + 0.171635i
\(941\) −11889.2 + 23333.8i −0.411877 + 0.808353i −1.00000 0.000417914i \(-0.999867\pi\)
0.588123 + 0.808771i \(0.299867\pi\)
\(942\) 29009.4 + 11135.6i 1.00337 + 0.385158i
\(943\) −16735.0 13551.7i −0.577907 0.467980i
\(944\) 25758.4 13124.5i 0.888097 0.452508i
\(945\) 35746.7 + 20638.4i 1.23052 + 0.710441i
\(946\) 2467.03 1807.80i 0.0847885 0.0621317i
\(947\) 1950.25 7278.45i 0.0669216 0.249755i −0.924359 0.381524i \(-0.875399\pi\)
0.991280 + 0.131770i \(0.0420659\pi\)
\(948\) 1264.65 3892.18i 0.0433268 0.133346i
\(949\) 3202.38 2884.25i 0.109540 0.0986583i
\(950\) 61.7414 + 44.8577i 0.00210858 + 0.00153198i
\(951\) 367.085 + 7004.39i 0.0125169 + 0.238836i
\(952\) −49688.7 44739.9i −1.69162 1.52314i
\(953\) −38268.8 + 17038.4i −1.30078 + 0.579146i −0.936018 0.351953i \(-0.885518\pi\)
−0.364766 + 0.931099i \(0.618851\pi\)
\(954\) 6641.36 + 1051.89i 0.225390 + 0.0356983i
\(955\) −16117.9 844.704i −0.546139 0.0286220i
\(956\) 1130.64 + 4219.59i 0.0382504 + 0.142753i
\(957\) 18976.0 + 7195.65i 0.640968 + 0.243054i
\(958\) −21284.5 + 36865.8i −0.717819 + 1.24330i
\(959\) −31190.6 + 6629.76i −1.05026 + 0.223239i
\(960\) 6617.64 + 17239.5i 0.222483 + 0.579587i
\(961\) 15433.6 21242.5i 0.518062 0.713051i
\(962\) −21422.1 + 17352.3i −0.717958 + 0.581559i
\(963\) 10362.8 3367.09i 0.346768 0.112672i
\(964\) 3570.38 2891.24i 0.119289 0.0965981i
\(965\) 4676.54 10503.7i 0.156003 0.350389i
\(966\) −42856.8 + 38588.4i −1.42743 + 1.28526i
\(967\) 11128.1 + 11128.1i 0.370068 + 0.370068i 0.867502 0.497434i \(-0.165724\pi\)
−0.497434 + 0.867502i \(0.665724\pi\)
\(968\) 5369.58 + 32202.2i 0.178290 + 1.06923i
\(969\) 193.330 51.8026i 0.00640935 0.00171738i
\(970\) 6537.91 + 12831.4i 0.216412 + 0.424733i
\(971\) −3805.46 36206.5i −0.125770 1.19663i −0.857301 0.514816i \(-0.827860\pi\)
0.731530 0.681809i \(-0.238806\pi\)
\(972\) −6657.58 699.740i −0.219693 0.0230907i
\(973\) 7623.06 399.508i 0.251166 0.0131630i
\(974\) −8053.99 24787.6i −0.264955 0.815449i
\(975\) 6341.20 + 6339.41i 0.208288 + 0.208229i
\(976\) −1422.73 1958.22i −0.0466604 0.0642226i
\(977\) −21765.4 + 33515.8i −0.712731 + 1.09751i 0.277856 + 0.960623i \(0.410376\pi\)
−0.990587 + 0.136887i \(0.956290\pi\)
\(978\) 25785.0 14887.0i 0.843060 0.486741i
\(979\) 494.865 4900.24i 0.0161552 0.159972i
\(980\) −8576.32 + 8576.32i −0.279552 + 0.279552i
\(981\) 1012.43 19318.2i 0.0329503 0.628729i
\(982\) 31020.1 38306.6i 1.00804 1.24482i
\(983\) −701.995 4432.23i −0.0227774 0.143811i 0.973679 0.227925i \(-0.0731940\pi\)
−0.996456 + 0.0841140i \(0.973194\pi\)
\(984\) 9916.66 + 2107.85i 0.321272 + 0.0682885i
\(985\) −14719.7 + 16347.9i −0.476151 + 0.528820i
\(986\) −19260.4 23784.6i −0.622085 0.768211i
\(987\) 27395.6 19904.1i 0.883497 0.641898i
\(988\) −57.6466 + 18.7395i −0.00185626 + 0.000603424i
\(989\) 6785.52i 0.218167i
\(990\) −1483.98 + 9622.96i −0.0476403 + 0.308927i
\(991\) −8173.46 14156.8i −0.261996 0.453791i 0.704776 0.709430i \(-0.251048\pi\)
−0.966772 + 0.255639i \(0.917714\pi\)
\(992\) −3650.34 4054.11i −0.116833 0.129756i
\(993\) −5304.12 + 33488.9i −0.169508 + 1.07023i
\(994\) −20107.9 + 52382.9i −0.641634 + 1.67151i
\(995\) 19151.3 + 29490.4i 0.610187 + 0.939606i
\(996\) −2774.69 1413.77i −0.0882725 0.0449771i
\(997\) −19954.8 44819.2i −0.633877 1.42371i −0.889501 0.456934i \(-0.848948\pi\)
0.255624 0.966776i \(-0.417719\pi\)
\(998\) −14839.2 6606.82i −0.470667 0.209554i
\(999\) 30444.5 + 19770.9i 0.964184 + 0.626149i
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 143.4.w.a.2.13 640
11.6 odd 10 inner 143.4.w.a.28.13 yes 640
13.7 odd 12 inner 143.4.w.a.46.13 yes 640
143.72 even 60 inner 143.4.w.a.72.13 yes 640
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.w.a.2.13 640 1.1 even 1 trivial
143.4.w.a.28.13 yes 640 11.6 odd 10 inner
143.4.w.a.46.13 yes 640 13.7 odd 12 inner
143.4.w.a.72.13 yes 640 143.72 even 60 inner