Properties

Label 128.5.l.a.3.3
Level $128$
Weight $5$
Character 128.3
Analytic conductor $13.231$
Analytic rank $0$
Dimension $1008$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [128,5,Mod(3,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([16, 3]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.3");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 128.l (of order \(32\), 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: \(13.2313552747\)
Analytic rank: \(0\)
Dimension: \(1008\)
Relative dimension: \(63\) over \(\Q(\zeta_{32})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 3.3
Character \(\chi\) \(=\) 128.3
Dual form 128.5.l.a.43.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.93898 + 0.696008i) q^{2} +(6.46187 - 5.30312i) q^{3} +(15.0311 - 5.48312i) q^{4} +(-28.0844 - 8.51932i) q^{5} +(-21.7622 + 25.3864i) q^{6} +(0.922571 + 4.63808i) q^{7} +(-55.3911 + 32.0597i) q^{8} +(-2.16964 + 10.9075i) q^{9} +O(q^{10})\) \(q+(-3.93898 + 0.696008i) q^{2} +(6.46187 - 5.30312i) q^{3} +(15.0311 - 5.48312i) q^{4} +(-28.0844 - 8.51932i) q^{5} +(-21.7622 + 25.3864i) q^{6} +(0.922571 + 4.63808i) q^{7} +(-55.3911 + 32.0597i) q^{8} +(-2.16964 + 10.9075i) q^{9} +(116.554 + 14.0104i) q^{10} +(9.26117 + 94.0302i) q^{11} +(68.0516 - 115.143i) q^{12} +(63.0563 + 207.869i) q^{13} +(-6.86213 - 17.6272i) q^{14} +(-226.657 + 93.8843i) q^{15} +(195.871 - 164.835i) q^{16} +(-47.6951 + 115.146i) q^{17} +(0.954454 - 44.4746i) q^{18} +(321.819 - 602.081i) q^{19} +(-468.854 + 25.9353i) q^{20} +(30.5578 + 25.0781i) q^{21} +(-101.925 - 363.937i) q^{22} +(507.473 - 339.083i) q^{23} +(-187.913 + 500.911i) q^{24} +(196.488 + 131.289i) q^{25} +(-393.056 - 774.904i) q^{26} +(363.010 + 679.144i) q^{27} +(39.2985 + 64.6571i) q^{28} +(-118.546 + 1203.62i) q^{29} +(827.453 - 527.563i) q^{30} +(1052.39 + 1052.39i) q^{31} +(-656.804 + 785.611i) q^{32} +(558.498 + 558.498i) q^{33} +(107.728 - 486.755i) q^{34} +(13.6034 - 138.117i) q^{35} +(27.1951 + 175.849i) q^{36} +(-5.20680 - 9.74124i) q^{37} +(-848.586 + 2595.58i) q^{38} +(1509.81 + 1008.83i) q^{39} +(1828.75 - 428.485i) q^{40} +(612.421 - 409.207i) q^{41} +(-137.821 - 77.5139i) q^{42} +(-93.4742 - 76.7123i) q^{43} +(654.785 + 1362.60i) q^{44} +(153.858 - 287.848i) q^{45} +(-1762.92 + 1688.84i) q^{46} +(-716.417 + 1729.58i) q^{47} +(391.550 - 2103.87i) q^{48} +(2197.57 - 910.265i) q^{49} +(-865.340 - 380.388i) q^{50} +(302.434 + 996.992i) q^{51} +(2087.58 + 2778.76i) q^{52} +(200.197 + 2032.64i) q^{53} +(-1902.58 - 2422.48i) q^{54} +(540.979 - 2719.68i) q^{55} +(-199.798 - 227.331i) q^{56} +(-1113.36 - 5597.22i) q^{57} +(-370.778 - 4823.55i) q^{58} +(-1105.97 - 335.493i) q^{59} +(-2892.13 + 2653.98i) q^{60} +(-4909.36 + 4029.01i) q^{61} +(-4877.80 - 3412.86i) q^{62} -52.5916 q^{63} +(2040.35 - 3551.65i) q^{64} -6375.08i q^{65} +(-2588.63 - 1811.19i) q^{66} +(2217.87 + 2702.48i) q^{67} +(-85.5513 + 1992.30i) q^{68} +(1481.03 - 4882.29i) q^{69} +(42.5474 + 553.510i) q^{70} +(-9758.56 + 1941.10i) q^{71} +(-229.513 - 673.738i) q^{72} +(3559.65 + 708.058i) q^{73} +(27.2895 + 34.7466i) q^{74} +(1965.92 - 193.626i) q^{75} +(1536.02 - 10814.5i) q^{76} +(-427.575 + 129.704i) q^{77} +(-6649.28 - 2922.90i) q^{78} +(969.545 + 2340.69i) q^{79} +(-6905.20 + 2960.62i) q^{80} +(5115.06 + 2118.73i) q^{81} +(-2127.50 + 2038.11i) q^{82} +(1603.10 + 856.873i) q^{83} +(596.825 + 209.401i) q^{84} +(2320.46 - 2827.49i) q^{85} +(421.586 + 237.110i) q^{86} +(5616.92 + 8406.31i) q^{87} +(-3527.57 - 4911.53i) q^{88} +(4631.84 - 6932.04i) q^{89} +(-405.699 + 1240.91i) q^{90} +(-905.938 + 484.234i) q^{91} +(5768.67 - 7879.34i) q^{92} +(12381.3 + 1219.45i) q^{93} +(1618.15 - 7311.43i) q^{94} +(-14167.4 + 14167.4i) q^{95} +(-77.9968 + 8559.62i) q^{96} +(-6240.39 + 6240.39i) q^{97} +(-8022.65 + 5115.05i) q^{98} +(-1045.73 - 102.995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 43072 q^{50} - 16 q^{51} - 17968 q^{52} - 16 q^{53} + 31088 q^{54} - 16 q^{55} + 49376 q^{56} - 16 q^{57} + 65504 q^{58} - 16 q^{59} + 63920 q^{60} - 16 q^{61} + 11792 q^{62} - 32 q^{63} - 24400 q^{64} - 70864 q^{66} - 16 q^{67} - 53296 q^{68} - 16 q^{69} - 122320 q^{70} - 16 q^{71} - 81664 q^{72} - 16 q^{73} - 33280 q^{74} - 16 q^{75} + 28272 q^{76} - 16 q^{77} + 99344 q^{78} - 16 q^{79} + 105248 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{32}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.93898 + 0.696008i −0.984745 + 0.174002i
\(3\) 6.46187 5.30312i 0.717985 0.589235i −0.202839 0.979212i \(-0.565017\pi\)
0.920825 + 0.389977i \(0.127517\pi\)
\(4\) 15.0311 5.48312i 0.939447 0.342695i
\(5\) −28.0844 8.51932i −1.12338 0.340773i −0.326670 0.945138i \(-0.605927\pi\)
−0.796707 + 0.604366i \(0.793427\pi\)
\(6\) −21.7622 + 25.3864i −0.604504 + 0.705178i
\(7\) 0.922571 + 4.63808i 0.0188280 + 0.0946547i 0.989057 0.147536i \(-0.0471341\pi\)
−0.970229 + 0.242190i \(0.922134\pi\)
\(8\) −55.3911 + 32.0597i −0.865486 + 0.500933i
\(9\) −2.16964 + 10.9075i −0.0267857 + 0.134661i
\(10\) 116.554 + 14.0104i 1.16554 + 0.140104i
\(11\) 9.26117 + 94.0302i 0.0765386 + 0.777109i 0.954467 + 0.298317i \(0.0964253\pi\)
−0.877928 + 0.478792i \(0.841075\pi\)
\(12\) 68.0516 115.143i 0.472581 0.799605i
\(13\) 63.0563 + 207.869i 0.373114 + 1.22999i 0.919711 + 0.392597i \(0.128423\pi\)
−0.546596 + 0.837396i \(0.684077\pi\)
\(14\) −6.86213 17.6272i −0.0350109 0.0899346i
\(15\) −226.657 + 93.8843i −1.00736 + 0.417264i
\(16\) 195.871 164.835i 0.765120 0.643888i
\(17\) −47.6951 + 115.146i −0.165035 + 0.398430i −0.984663 0.174466i \(-0.944180\pi\)
0.819628 + 0.572896i \(0.194180\pi\)
\(18\) 0.954454 44.4746i 0.00294585 0.137267i
\(19\) 321.819 602.081i 0.891466 1.66782i 0.158709 0.987325i \(-0.449267\pi\)
0.732757 0.680490i \(-0.238233\pi\)
\(20\) −468.854 + 25.9353i −1.17213 + 0.0648382i
\(21\) 30.5578 + 25.0781i 0.0692921 + 0.0568665i
\(22\) −101.925 363.937i −0.210590 0.751937i
\(23\) 507.473 339.083i 0.959306 0.640988i 0.0258447 0.999666i \(-0.491772\pi\)
0.933461 + 0.358678i \(0.116772\pi\)
\(24\) −187.913 + 500.911i −0.326239 + 0.869637i
\(25\) 196.488 + 131.289i 0.314381 + 0.210062i
\(26\) −393.056 774.904i −0.581444 1.14631i
\(27\) 363.010 + 679.144i 0.497956 + 0.931611i
\(28\) 39.2985 + 64.6571i 0.0501256 + 0.0824707i
\(29\) −118.546 + 1203.62i −0.140959 + 1.43118i 0.621130 + 0.783707i \(0.286674\pi\)
−0.762089 + 0.647472i \(0.775826\pi\)
\(30\) 827.453 527.563i 0.919392 0.586182i
\(31\) 1052.39 + 1052.39i 1.09509 + 1.09509i 0.994975 + 0.100119i \(0.0319223\pi\)
0.100119 + 0.994975i \(0.468078\pi\)
\(32\) −656.804 + 785.611i −0.641410 + 0.767198i
\(33\) 558.498 + 558.498i 0.512854 + 0.512854i
\(34\) 107.728 486.755i 0.0931899 0.421068i
\(35\) 13.6034 138.117i 0.0111048 0.112749i
\(36\) 27.1951 + 175.849i 0.0209839 + 0.135686i
\(37\) −5.20680 9.74124i −0.00380336 0.00711559i 0.880012 0.474951i \(-0.157534\pi\)
−0.883816 + 0.467835i \(0.845034\pi\)
\(38\) −848.586 + 2595.58i −0.587664 + 1.79749i
\(39\) 1509.81 + 1008.83i 0.992646 + 0.663265i
\(40\) 1828.75 428.485i 1.14297 0.267803i
\(41\) 612.421 409.207i 0.364319 0.243430i −0.359914 0.932986i \(-0.617194\pi\)
0.724233 + 0.689555i \(0.242194\pi\)
\(42\) −137.821 77.5139i −0.0781299 0.0439421i
\(43\) −93.4742 76.7123i −0.0505539 0.0414886i 0.608777 0.793341i \(-0.291660\pi\)
−0.659331 + 0.751853i \(0.729160\pi\)
\(44\) 654.785 + 1362.60i 0.338216 + 0.703823i
\(45\) 153.858 287.848i 0.0759792 0.142147i
\(46\) −1762.92 + 1688.84i −0.833139 + 0.798131i
\(47\) −716.417 + 1729.58i −0.324318 + 0.782972i 0.674676 + 0.738114i \(0.264283\pi\)
−0.998993 + 0.0448576i \(0.985717\pi\)
\(48\) 391.550 2103.87i 0.169943 0.913138i
\(49\) 2197.57 910.265i 0.915275 0.379119i
\(50\) −865.340 380.388i −0.346136 0.152155i
\(51\) 302.434 + 996.992i 0.116276 + 0.383311i
\(52\) 2087.58 + 2778.76i 0.772034 + 1.02765i
\(53\) 200.197 + 2032.64i 0.0712700 + 0.723616i 0.962720 + 0.270498i \(0.0871884\pi\)
−0.891450 + 0.453118i \(0.850312\pi\)
\(54\) −1902.58 2422.48i −0.652462 0.830754i
\(55\) 540.979 2719.68i 0.178836 0.899069i
\(56\) −199.798 227.331i −0.0637110 0.0724907i
\(57\) −1113.36 5597.22i −0.342676 1.72275i
\(58\) −370.778 4823.55i −0.110219 1.43387i
\(59\) −1105.97 335.493i −0.317717 0.0963784i 0.127398 0.991852i \(-0.459337\pi\)
−0.445115 + 0.895473i \(0.646837\pi\)
\(60\) −2892.13 + 2653.98i −0.803370 + 0.737216i
\(61\) −4909.36 + 4029.01i −1.31937 + 1.08278i −0.328997 + 0.944331i \(0.606711\pi\)
−0.990370 + 0.138446i \(0.955789\pi\)
\(62\) −4877.80 3412.86i −1.26894 0.887840i
\(63\) −52.5916 −0.0132506
\(64\) 2040.35 3551.65i 0.498132 0.867101i
\(65\) 6375.08i 1.50889i
\(66\) −2588.63 1811.19i −0.594268 0.415793i
\(67\) 2217.87 + 2702.48i 0.494067 + 0.602022i 0.959029 0.283309i \(-0.0914321\pi\)
−0.464962 + 0.885331i \(0.653932\pi\)
\(68\) −85.5513 + 1992.30i −0.0185016 + 0.430860i
\(69\) 1481.03 4882.29i 0.311075 1.02548i
\(70\) 42.5474 + 553.510i 0.00868314 + 0.112961i
\(71\) −9758.56 + 1941.10i −1.93584 + 0.385062i −0.936423 + 0.350874i \(0.885884\pi\)
−0.999415 + 0.0341880i \(0.989116\pi\)
\(72\) −229.513 673.738i −0.0442734 0.129965i
\(73\) 3559.65 + 708.058i 0.667976 + 0.132869i 0.517419 0.855732i \(-0.326893\pi\)
0.150558 + 0.988601i \(0.451893\pi\)
\(74\) 27.2895 + 34.7466i 0.00498347 + 0.00634525i
\(75\) 1965.92 193.626i 0.349497 0.0344224i
\(76\) 1536.02 10814.5i 0.265932 1.87232i
\(77\) −427.575 + 129.704i −0.0721159 + 0.0218761i
\(78\) −6649.28 2922.90i −1.09291 0.480425i
\(79\) 969.545 + 2340.69i 0.155351 + 0.375050i 0.982323 0.187192i \(-0.0599388\pi\)
−0.826972 + 0.562242i \(0.809939\pi\)
\(80\) −6905.20 + 2960.62i −1.07894 + 0.462597i
\(81\) 5115.06 + 2118.73i 0.779616 + 0.322927i
\(82\) −2127.50 + 2038.11i −0.316404 + 0.303109i
\(83\) 1603.10 + 856.873i 0.232704 + 0.124383i 0.583628 0.812021i \(-0.301633\pi\)
−0.350924 + 0.936404i \(0.614133\pi\)
\(84\) 596.825 + 209.401i 0.0845841 + 0.0296770i
\(85\) 2320.46 2827.49i 0.321171 0.391347i
\(86\) 421.586 + 237.110i 0.0570019 + 0.0320592i
\(87\) 5616.92 + 8406.31i 0.742095 + 1.11062i
\(88\) −3527.57 4911.53i −0.455523 0.634236i
\(89\) 4631.84 6932.04i 0.584755 0.875148i −0.414638 0.909986i \(-0.636092\pi\)
0.999393 + 0.0348389i \(0.0110918\pi\)
\(90\) −405.699 + 1240.91i −0.0500863 + 0.153199i
\(91\) −905.938 + 484.234i −0.109400 + 0.0584753i
\(92\) 5768.67 7879.34i 0.681553 0.930923i
\(93\) 12381.3 + 1219.45i 1.43153 + 0.140993i
\(94\) 1618.15 7311.43i 0.183132 0.827460i
\(95\) −14167.4 + 14167.4i −1.56980 + 1.56980i
\(96\) −77.9968 + 8559.62i −0.00846320 + 0.928778i
\(97\) −6240.39 + 6240.39i −0.663236 + 0.663236i −0.956141 0.292905i \(-0.905378\pi\)
0.292905 + 0.956141i \(0.405378\pi\)
\(98\) −8022.65 + 5115.05i −0.835345 + 0.532595i
\(99\) −1045.73 102.995i −0.106696 0.0105087i
\(100\) 3673.31 + 896.057i 0.367331 + 0.0896057i
\(101\) 3976.54 2125.50i 0.389818 0.208362i −0.264831 0.964295i \(-0.585316\pi\)
0.654649 + 0.755933i \(0.272816\pi\)
\(102\) −1885.20 3716.64i −0.181199 0.357232i
\(103\) 5635.02 8433.40i 0.531154 0.794929i −0.464740 0.885447i \(-0.653852\pi\)
0.995895 + 0.0905182i \(0.0288523\pi\)
\(104\) −10157.0 9492.52i −0.939070 0.877637i
\(105\) −644.550 964.637i −0.0584626 0.0874954i
\(106\) −2203.31 7867.19i −0.196093 0.700177i
\(107\) 291.792 355.550i 0.0254862 0.0310551i −0.760111 0.649793i \(-0.774856\pi\)
0.785598 + 0.618738i \(0.212356\pi\)
\(108\) 9180.29 + 8217.89i 0.787062 + 0.704552i
\(109\) −13506.0 7219.13i −1.13678 0.607620i −0.207952 0.978139i \(-0.566680\pi\)
−0.928825 + 0.370519i \(0.879180\pi\)
\(110\) −237.984 + 11089.3i −0.0196681 + 0.916472i
\(111\) −85.3046 35.3343i −0.00692351 0.00286781i
\(112\) 945.224 + 756.391i 0.0753526 + 0.0602991i
\(113\) 2181.12 + 5265.69i 0.170814 + 0.412381i 0.985984 0.166841i \(-0.0533565\pi\)
−0.815170 + 0.579222i \(0.803357\pi\)
\(114\) 8281.19 + 21272.4i 0.637211 + 1.63684i
\(115\) −17140.8 + 5199.62i −1.29609 + 0.393166i
\(116\) 4817.72 + 18741.8i 0.358035 + 1.39282i
\(117\) −2404.15 + 236.788i −0.175626 + 0.0172977i
\(118\) 4589.91 + 551.736i 0.329640 + 0.0396248i
\(119\) −578.059 114.983i −0.0408205 0.00811970i
\(120\) 9544.86 12466.9i 0.662838 0.865758i
\(121\) 5603.76 1114.66i 0.382745 0.0761326i
\(122\) 16533.7 19287.2i 1.11084 1.29583i
\(123\) 1787.31 5891.98i 0.118138 0.389449i
\(124\) 21588.9 + 10048.2i 1.40407 + 0.653499i
\(125\) 7236.66 + 8817.90i 0.463146 + 0.564345i
\(126\) 207.157 36.6042i 0.0130485 0.00230563i
\(127\) 8413.39i 0.521631i 0.965389 + 0.260816i \(0.0839915\pi\)
−0.965389 + 0.260816i \(0.916009\pi\)
\(128\) −5564.92 + 15410.0i −0.339656 + 0.940550i
\(129\) −1010.83 −0.0607435
\(130\) 4437.10 + 25111.3i 0.262550 + 1.48588i
\(131\) −7058.52 + 5792.78i −0.411312 + 0.337555i −0.817186 0.576374i \(-0.804467\pi\)
0.405874 + 0.913929i \(0.366967\pi\)
\(132\) 11457.2 + 5332.55i 0.657551 + 0.306046i
\(133\) 3089.40 + 937.160i 0.174651 + 0.0529798i
\(134\) −10617.1 9101.35i −0.591283 0.506870i
\(135\) −4409.09 22166.0i −0.241925 1.21624i
\(136\) −1049.67 7907.17i −0.0567512 0.427507i
\(137\) 5574.39 28024.4i 0.297000 1.49312i −0.487572 0.873083i \(-0.662117\pi\)
0.784572 0.620037i \(-0.212883\pi\)
\(138\) −2435.63 + 20262.1i −0.127895 + 1.06396i
\(139\) 2943.55 + 29886.3i 0.152350 + 1.54683i 0.702450 + 0.711733i \(0.252089\pi\)
−0.550101 + 0.835098i \(0.685411\pi\)
\(140\) −552.841 2150.65i −0.0282062 0.109727i
\(141\) 4542.80 + 14975.6i 0.228499 + 0.753261i
\(142\) 37087.8 14438.0i 1.83931 0.716028i
\(143\) −18962.0 + 7854.31i −0.927282 + 0.384093i
\(144\) 1372.98 + 2494.10i 0.0662122 + 0.120279i
\(145\) 13583.3 32793.1i 0.646057 1.55972i
\(146\) −14514.2 311.484i −0.680906 0.0146127i
\(147\) 9373.19 17536.0i 0.433763 0.811514i
\(148\) −131.677 117.872i −0.00601153 0.00538132i
\(149\) −32901.1 27001.2i −1.48196 1.21622i −0.921701 0.387901i \(-0.873200\pi\)
−0.560262 0.828315i \(-0.689300\pi\)
\(150\) −7608.95 + 2130.99i −0.338176 + 0.0947105i
\(151\) −2431.43 + 1624.63i −0.106637 + 0.0712526i −0.607745 0.794132i \(-0.707926\pi\)
0.501108 + 0.865385i \(0.332926\pi\)
\(152\) 1476.64 + 43667.4i 0.0639128 + 1.89004i
\(153\) −1152.48 770.062i −0.0492323 0.0328960i
\(154\) 1593.94 808.496i 0.0672093 0.0340907i
\(155\) −20590.0 38521.3i −0.857026 1.60338i
\(156\) 28225.8 + 6885.31i 1.15984 + 0.282927i
\(157\) 2016.44 20473.2i 0.0818060 0.830590i −0.863488 0.504370i \(-0.831725\pi\)
0.945294 0.326220i \(-0.105775\pi\)
\(158\) −5448.16 8545.11i −0.218240 0.342297i
\(159\) 12073.0 + 12073.0i 0.477551 + 0.477551i
\(160\) 25138.8 16467.9i 0.981986 0.643277i
\(161\) 2040.87 + 2040.87i 0.0787343 + 0.0787343i
\(162\) −21622.8 4785.50i −0.823913 0.182347i
\(163\) −1799.24 + 18268.0i −0.0677196 + 0.687569i 0.900059 + 0.435767i \(0.143523\pi\)
−0.967779 + 0.251801i \(0.918977\pi\)
\(164\) 6961.66 9508.82i 0.258836 0.353540i
\(165\) −10927.1 20443.1i −0.401362 0.750895i
\(166\) −6910.96 2259.44i −0.250797 0.0819944i
\(167\) 25815.1 + 17249.1i 0.925639 + 0.618492i 0.924366 0.381507i \(-0.124595\pi\)
0.00127283 + 0.999999i \(0.499595\pi\)
\(168\) −2496.63 409.431i −0.0884577 0.0145065i
\(169\) −15485.8 + 10347.3i −0.542200 + 0.362286i
\(170\) −7172.29 + 12752.5i −0.248176 + 0.441262i
\(171\) 5868.99 + 4816.55i 0.200711 + 0.164719i
\(172\) −1825.65 640.543i −0.0617107 0.0216517i
\(173\) −18952.5 + 35457.6i −0.633248 + 1.18472i 0.336747 + 0.941595i \(0.390673\pi\)
−0.969994 + 0.243128i \(0.921827\pi\)
\(174\) −27975.8 29202.9i −0.924025 0.964555i
\(175\) −427.655 + 1032.45i −0.0139642 + 0.0337126i
\(176\) 17313.5 + 16891.2i 0.558932 + 0.545300i
\(177\) −8925.81 + 3697.19i −0.284906 + 0.118012i
\(178\) −13420.0 + 30529.0i −0.423557 + 0.963546i
\(179\) −5815.43 19170.9i −0.181500 0.598324i −0.999726 0.0234275i \(-0.992542\pi\)
0.818226 0.574897i \(-0.194958\pi\)
\(180\) 734.355 5170.30i 0.0226653 0.159577i
\(181\) −2361.50 23976.8i −0.0720828 0.731869i −0.961506 0.274784i \(-0.911394\pi\)
0.889423 0.457085i \(-0.151106\pi\)
\(182\) 3231.44 2537.93i 0.0975559 0.0766190i
\(183\) −10357.3 + 52069.9i −0.309276 + 1.55484i
\(184\) −17238.6 + 35051.6i −0.509174 + 1.03531i
\(185\) 63.2413 + 317.936i 0.00184781 + 0.00928957i
\(186\) −49618.5 + 3814.09i −1.43423 + 0.110246i
\(187\) −11268.9 3418.39i −0.322255 0.0977550i
\(188\) −1285.05 + 29925.8i −0.0363583 + 0.846702i
\(189\) −2815.02 + 2310.23i −0.0788058 + 0.0646743i
\(190\) 45944.6 65665.9i 1.27270 1.81900i
\(191\) 39092.8 1.07159 0.535797 0.844347i \(-0.320011\pi\)
0.535797 + 0.844347i \(0.320011\pi\)
\(192\) −5650.34 33770.5i −0.153275 0.916083i
\(193\) 191.973i 0.00515378i −0.999997 0.00257689i \(-0.999180\pi\)
0.999997 0.00257689i \(-0.000820251\pi\)
\(194\) 20237.4 28924.1i 0.537714 0.768523i
\(195\) −33807.8 41194.9i −0.889093 1.08336i
\(196\) 28041.0 25731.9i 0.729929 0.669822i
\(197\) 4501.42 14839.2i 0.115989 0.382365i −0.879654 0.475615i \(-0.842226\pi\)
0.995643 + 0.0932502i \(0.0297256\pi\)
\(198\) 4190.80 322.140i 0.106897 0.00821701i
\(199\) 42110.6 8376.33i 1.06337 0.211518i 0.367750 0.929925i \(-0.380128\pi\)
0.695623 + 0.718407i \(0.255128\pi\)
\(200\) −15092.8 972.896i −0.377319 0.0243224i
\(201\) 28663.1 + 5701.44i 0.709465 + 0.141121i
\(202\) −14184.1 + 11140.0i −0.347616 + 0.273013i
\(203\) −5691.86 + 560.599i −0.138122 + 0.0136038i
\(204\) 10012.6 + 13327.7i 0.240594 + 0.320253i
\(205\) −20685.7 + 6274.92i −0.492223 + 0.149314i
\(206\) −16326.5 + 37141.0i −0.384733 + 0.875224i
\(207\) 2597.52 + 6270.96i 0.0606203 + 0.146350i
\(208\) 46615.0 + 30321.5i 1.07745 + 0.700849i
\(209\) 59594.3 + 24684.8i 1.36431 + 0.565114i
\(210\) 3210.26 + 3351.08i 0.0727951 + 0.0759881i
\(211\) −29704.0 15877.1i −0.667190 0.356621i 0.102777 0.994704i \(-0.467227\pi\)
−0.769967 + 0.638084i \(0.779727\pi\)
\(212\) 14154.4 + 29455.2i 0.314934 + 0.655375i
\(213\) −52764.6 + 64293.9i −1.16301 + 1.41713i
\(214\) −901.898 + 1603.59i −0.0196938 + 0.0350160i
\(215\) 1971.63 + 2950.76i 0.0426530 + 0.0638347i
\(216\) −41880.7 25980.6i −0.897649 0.556853i
\(217\) −3910.15 + 5851.95i −0.0830374 + 0.124274i
\(218\) 58224.6 + 19035.7i 1.22516 + 0.400549i
\(219\) 26756.9 14301.8i 0.557888 0.298197i
\(220\) −6780.83 43846.2i −0.140100 0.905914i
\(221\) −26942.8 2653.63i −0.551643 0.0543321i
\(222\) 360.606 + 79.8086i 0.00731690 + 0.00161936i
\(223\) −21968.9 + 21968.9i −0.441773 + 0.441773i −0.892608 0.450834i \(-0.851127\pi\)
0.450834 + 0.892608i \(0.351127\pi\)
\(224\) −4249.67 2321.53i −0.0846953 0.0462677i
\(225\) −1858.35 + 1858.35i −0.0367081 + 0.0367081i
\(226\) −12256.4 19223.4i −0.239963 0.376368i
\(227\) −82132.8 8089.38i −1.59391 0.156987i −0.738254 0.674523i \(-0.764349\pi\)
−0.855661 + 0.517536i \(0.826849\pi\)
\(228\) −47425.2 78027.9i −0.912304 1.50100i
\(229\) 9176.95 4905.18i 0.174996 0.0935372i −0.381573 0.924339i \(-0.624618\pi\)
0.556569 + 0.830801i \(0.312118\pi\)
\(230\) 63898.5 32411.4i 1.20791 0.612691i
\(231\) −2075.10 + 3105.61i −0.0388880 + 0.0582000i
\(232\) −32021.4 70470.5i −0.594927 1.30928i
\(233\) 38093.2 + 57010.5i 0.701674 + 1.05013i 0.995545 + 0.0942849i \(0.0300565\pi\)
−0.293871 + 0.955845i \(0.594944\pi\)
\(234\) 9305.08 2606.01i 0.169937 0.0475931i
\(235\) 34855.1 42471.0i 0.631146 0.769054i
\(236\) −18463.6 + 1021.34i −0.331507 + 0.0183378i
\(237\) 18678.0 + 9983.60i 0.332532 + 0.177742i
\(238\) 2356.99 + 50.5826i 0.0416106 + 0.000892991i
\(239\) −23928.1 9911.36i −0.418903 0.173515i 0.163268 0.986582i \(-0.447796\pi\)
−0.582171 + 0.813067i \(0.697796\pi\)
\(240\) −28920.0 + 55750.2i −0.502083 + 0.967886i
\(241\) −37137.1 89656.8i −0.639401 1.54365i −0.827479 0.561497i \(-0.810226\pi\)
0.188078 0.982154i \(-0.439774\pi\)
\(242\) −21297.3 + 8290.88i −0.363659 + 0.141570i
\(243\) −15401.4 + 4671.96i −0.260824 + 0.0791201i
\(244\) −51701.8 + 87479.3i −0.868413 + 1.46935i
\(245\) −69472.5 + 6842.44i −1.15739 + 0.113993i
\(246\) −2939.33 + 24452.4i −0.0485710 + 0.404065i
\(247\) 145447. + 28931.2i 2.38402 + 0.474211i
\(248\) −92032.0 24553.6i −1.49636 0.399220i
\(249\) 14903.1 2964.41i 0.240369 0.0478123i
\(250\) −34642.4 29696.8i −0.554278 0.475148i
\(251\) 22268.2 73408.4i 0.353458 1.16519i −0.582425 0.812884i \(-0.697896\pi\)
0.935883 0.352311i \(-0.114604\pi\)
\(252\) −790.512 + 288.366i −0.0124482 + 0.00454092i
\(253\) 36583.8 + 44577.5i 0.571541 + 0.696425i
\(254\) −5855.79 33140.2i −0.0907649 0.513674i
\(255\) 30576.5i 0.470227i
\(256\) 11194.7 64572.8i 0.170817 0.985303i
\(257\) −34925.5 −0.528781 −0.264391 0.964416i \(-0.585171\pi\)
−0.264391 + 0.964416i \(0.585171\pi\)
\(258\) 3981.65 703.548i 0.0598169 0.0105695i
\(259\) 40.3770 33.1365i 0.000601914 0.000493978i
\(260\) −34955.3 95824.7i −0.517091 1.41752i
\(261\) −12871.3 3904.48i −0.188948 0.0573168i
\(262\) 23771.6 27730.4i 0.346302 0.403975i
\(263\) 10187.7 + 51217.2i 0.147287 + 0.740464i 0.981866 + 0.189575i \(0.0607112\pi\)
−0.834579 + 0.550889i \(0.814289\pi\)
\(264\) −48841.1 13030.5i −0.700773 0.186962i
\(265\) 11694.3 58791.0i 0.166526 0.837181i
\(266\) −12821.4 1541.21i −0.181205 0.0217820i
\(267\) −6831.08 69357.2i −0.0958224 0.972901i
\(268\) 48155.1 + 28460.5i 0.670459 + 0.396253i
\(269\) 4297.73 + 14167.7i 0.0593930 + 0.195792i 0.981616 0.190866i \(-0.0611294\pi\)
−0.922223 + 0.386658i \(0.873629\pi\)
\(270\) 32795.0 + 84242.6i 0.449863 + 1.15559i
\(271\) 89298.4 36988.6i 1.21592 0.503651i 0.319810 0.947482i \(-0.396381\pi\)
0.896111 + 0.443831i \(0.146381\pi\)
\(272\) 9638.08 + 30415.6i 0.130273 + 0.411111i
\(273\) −3286.10 + 7933.35i −0.0440916 + 0.106447i
\(274\) −2452.25 + 114267.i −0.0326635 + 1.52202i
\(275\) −10525.4 + 19691.7i −0.139179 + 0.260386i
\(276\) −4508.68 81507.1i −0.0591877 1.06998i
\(277\) 24865.1 + 20406.2i 0.324064 + 0.265952i 0.782332 0.622862i \(-0.214030\pi\)
−0.458268 + 0.888814i \(0.651530\pi\)
\(278\) −32395.7 115673.i −0.419177 1.49673i
\(279\) −13762.2 + 9195.63i −0.176799 + 0.118133i
\(280\) 3674.50 + 8086.60i 0.0468686 + 0.103145i
\(281\) 56475.1 + 37735.4i 0.715227 + 0.477900i 0.859173 0.511686i \(-0.170979\pi\)
−0.143945 + 0.989586i \(0.545979\pi\)
\(282\) −28317.1 55826.7i −0.356083 0.702011i
\(283\) −34141.9 63875.0i −0.426300 0.797550i 0.573465 0.819230i \(-0.305599\pi\)
−0.999765 + 0.0216794i \(0.993099\pi\)
\(284\) −136039. + 82684.3i −1.68666 + 1.02515i
\(285\) −16416.5 + 166680.i −0.202112 + 2.05207i
\(286\) 69224.2 44135.7i 0.846303 0.539582i
\(287\) 2462.93 + 2462.93i 0.0299012 + 0.0299012i
\(288\) −7144.04 8868.61i −0.0861309 0.106923i
\(289\) 48074.4 + 48074.4i 0.575597 + 0.575597i
\(290\) −30680.3 + 138625.i −0.364807 + 1.64834i
\(291\) −7231.05 + 73418.1i −0.0853916 + 0.866996i
\(292\) 57387.9 8875.06i 0.673062 0.104089i
\(293\) 23192.6 + 43390.2i 0.270155 + 0.505425i 0.980016 0.198917i \(-0.0637423\pi\)
−0.709861 + 0.704342i \(0.751242\pi\)
\(294\) −24715.6 + 75597.8i −0.285941 + 0.874610i
\(295\) 28202.5 + 18844.3i 0.324073 + 0.216539i
\(296\) 600.712 + 372.650i 0.00685619 + 0.00425321i
\(297\) −60498.2 + 40423.6i −0.685851 + 0.458271i
\(298\) 148390. + 83457.9i 1.67098 + 0.939798i
\(299\) 102484. + 84106.5i 1.14634 + 0.940778i
\(300\) 28488.3 13689.8i 0.316537 0.152109i
\(301\) 269.561 504.313i 0.00297526 0.00556631i
\(302\) 8446.60 8091.68i 0.0926122 0.0887207i
\(303\) 14424.1 34822.8i 0.157109 0.379296i
\(304\) −36209.3 170977.i −0.391808 1.85008i
\(305\) 172201. 71328.0i 1.85113 0.766762i
\(306\) 5075.56 + 2231.12i 0.0542053 + 0.0238276i
\(307\) −23217.2 76536.8i −0.246339 0.812070i −0.989697 0.143177i \(-0.954268\pi\)
0.743358 0.668893i \(-0.233232\pi\)
\(308\) −5715.77 + 4294.04i −0.0602522 + 0.0452653i
\(309\) −8310.57 84378.7i −0.0870390 0.883722i
\(310\) 107915. + 137404.i 1.12294 + 1.42980i
\(311\) −4593.45 + 23092.8i −0.0474918 + 0.238757i −0.997239 0.0742612i \(-0.976340\pi\)
0.949747 + 0.313018i \(0.101340\pi\)
\(312\) −115973. 7475.74i −1.19137 0.0767972i
\(313\) 15961.4 + 80243.6i 0.162923 + 0.819071i 0.972652 + 0.232267i \(0.0746142\pi\)
−0.809729 + 0.586804i \(0.800386\pi\)
\(314\) 6306.82 + 82047.1i 0.0639663 + 0.832154i
\(315\) 1477.01 + 448.045i 0.0148854 + 0.00451544i
\(316\) 27407.6 + 29867.1i 0.274472 + 0.299102i
\(317\) 131137. 107621.i 1.30499 1.07097i 0.312334 0.949972i \(-0.398889\pi\)
0.992652 0.121003i \(-0.0386109\pi\)
\(318\) −55958.1 39152.3i −0.553361 0.387171i
\(319\) −114275. −1.12297
\(320\) −87559.6 + 82363.6i −0.855075 + 0.804332i
\(321\) 3844.92i 0.0373145i
\(322\) −9459.42 6618.49i −0.0912331 0.0638333i
\(323\) 53978.2 + 65772.6i 0.517384 + 0.630435i
\(324\) 88502.4 + 3800.39i 0.843073 + 0.0362024i
\(325\) −14901.1 + 49122.3i −0.141075 + 0.465063i
\(326\) −5627.50 73209.6i −0.0529518 0.688863i
\(327\) −125558. + 24975.1i −1.17422 + 0.233567i
\(328\) −20803.6 + 42300.4i −0.193371 + 0.393185i
\(329\) −8682.89 1727.14i −0.0802182 0.0159564i
\(330\) 57270.1 + 72919.7i 0.525896 + 0.669602i
\(331\) −71052.7 + 6998.08i −0.648522 + 0.0638738i −0.416929 0.908939i \(-0.636894\pi\)
−0.231593 + 0.972813i \(0.574394\pi\)
\(332\) 28794.7 + 4089.81i 0.261238 + 0.0371045i
\(333\) 117.550 35.6583i 0.00106007 0.000321568i
\(334\) −113691. 49976.4i −1.01914 0.447994i
\(335\) −39264.2 94792.2i −0.349871 0.844662i
\(336\) 10119.1 124.931i 0.0896324 0.00110661i
\(337\) 161479. + 66886.9i 1.42186 + 0.588954i 0.955327 0.295549i \(-0.0955027\pi\)
0.466534 + 0.884503i \(0.345503\pi\)
\(338\) 53796.4 51535.9i 0.470890 0.451103i
\(339\) 42018.7 + 22459.5i 0.365631 + 0.195434i
\(340\) 19375.7 55223.7i 0.167610 0.477714i
\(341\) −89209.7 + 108702.i −0.767191 + 0.934825i
\(342\) −26470.2 14887.5i −0.226311 0.127282i
\(343\) 12557.4 + 18793.4i 0.106736 + 0.159741i
\(344\) 7637.02 + 1252.42i 0.0645367 + 0.0105836i
\(345\) −83187.6 + 124499.i −0.698909 + 1.04599i
\(346\) 49974.7 152858.i 0.417443 1.27684i
\(347\) 96550.0 51607.1i 0.801850 0.428598i −0.0189448 0.999821i \(-0.506031\pi\)
0.820795 + 0.571223i \(0.193531\pi\)
\(348\) 130522. + 95558.2i 1.07776 + 0.789059i
\(349\) −142677. 14052.5i −1.17139 0.115372i −0.506453 0.862268i \(-0.669043\pi\)
−0.664941 + 0.746896i \(0.731543\pi\)
\(350\) 965.930 4364.45i 0.00788515 0.0356282i
\(351\) −118283. + 118283.i −0.960081 + 0.960081i
\(352\) −79953.9 54483.8i −0.645289 0.439726i
\(353\) 29173.2 29173.2i 0.234118 0.234118i −0.580291 0.814409i \(-0.697061\pi\)
0.814409 + 0.580291i \(0.197061\pi\)
\(354\) 32585.3 20775.6i 0.260025 0.165786i
\(355\) 290600. + 28621.6i 2.30589 + 0.227111i
\(356\) 31612.7 129594.i 0.249437 1.02255i
\(357\) −4345.11 + 2322.51i −0.0340929 + 0.0182231i
\(358\) 36250.0 + 71466.3i 0.282841 + 0.557616i
\(359\) 39844.8 59631.9i 0.309159 0.462690i −0.644057 0.764977i \(-0.722750\pi\)
0.953217 + 0.302287i \(0.0977502\pi\)
\(360\) 705.964 + 20876.9i 0.00544725 + 0.161087i
\(361\) −186532. 279165.i −1.43133 2.14213i
\(362\) 25989.9 + 92800.4i 0.198330 + 0.708162i
\(363\) 30299.6 36920.2i 0.229945 0.280189i
\(364\) −10962.2 + 12246.0i −0.0827359 + 0.0924252i
\(365\) −93938.5 50211.2i −0.705111 0.376890i
\(366\) 4556.33 212311.i 0.0340136 1.58493i
\(367\) 39735.7 + 16459.1i 0.295018 + 0.122201i 0.525283 0.850927i \(-0.323959\pi\)
−0.230265 + 0.973128i \(0.573959\pi\)
\(368\) 43506.3 150066.i 0.321260 1.10812i
\(369\) 3134.70 + 7567.83i 0.0230220 + 0.0555800i
\(370\) −470.392 1208.33i −0.00343603 0.00882634i
\(371\) −9242.84 + 2803.78i −0.0671518 + 0.0203703i
\(372\) 192792. 49558.5i 1.39316 0.358123i
\(373\) −10490.0 + 1033.18i −0.0753979 + 0.00742604i −0.135646 0.990757i \(-0.543311\pi\)
0.0602479 + 0.998183i \(0.480811\pi\)
\(374\) 46767.4 + 5621.72i 0.334349 + 0.0401908i
\(375\) 93524.7 + 18603.2i 0.665064 + 0.132290i
\(376\) −15766.8 118772.i −0.111524 0.840112i
\(377\) −257671. + 51253.9i −1.81293 + 0.360615i
\(378\) 9480.38 11059.2i 0.0663502 0.0774000i
\(379\) −5450.86 + 17969.1i −0.0379478 + 0.125097i −0.973868 0.227115i \(-0.927071\pi\)
0.935920 + 0.352212i \(0.114571\pi\)
\(380\) −135271. + 290635.i −0.936779 + 2.01270i
\(381\) 44617.2 + 54366.2i 0.307364 + 0.374524i
\(382\) −153986. + 27208.9i −1.05525 + 0.186460i
\(383\) 190563.i 1.29909i −0.760322 0.649547i \(-0.774959\pi\)
0.760322 0.649547i \(-0.225041\pi\)
\(384\) 45761.1 + 129089.i 0.310337 + 0.875438i
\(385\) 13113.2 0.0884682
\(386\) 133.615 + 756.179i 0.000896768 + 0.00507516i
\(387\) 1039.55 853.135i 0.00694101 0.00569634i
\(388\) −59583.4 + 128017.i −0.395787 + 0.850363i
\(389\) 216277. + 65607.0i 1.42926 + 0.433562i 0.907688 0.419645i \(-0.137846\pi\)
0.521573 + 0.853207i \(0.325346\pi\)
\(390\) 161840. + 138735.i 1.06404 + 0.912133i
\(391\) 14840.1 + 74606.2i 0.0970695 + 0.488001i
\(392\) −92543.2 + 120874.i −0.602244 + 0.786614i
\(393\) −14891.4 + 74864.3i −0.0964166 + 0.484719i
\(394\) −7402.81 + 61584.3i −0.0476875 + 0.396714i
\(395\) −7288.04 73996.7i −0.0467107 0.474262i
\(396\) −16283.3 + 4185.73i −0.103837 + 0.0266920i
\(397\) 61407.0 + 202432.i 0.389616 + 1.28439i 0.904258 + 0.426987i \(0.140425\pi\)
−0.514641 + 0.857406i \(0.672075\pi\)
\(398\) −160043. + 62303.5i −1.01035 + 0.393320i
\(399\) 24933.2 10327.7i 0.156614 0.0648718i
\(400\) 60127.3 6672.47i 0.375795 0.0417029i
\(401\) 25259.7 60982.3i 0.157087 0.379241i −0.825668 0.564157i \(-0.809201\pi\)
0.982754 + 0.184916i \(0.0592014\pi\)
\(402\) −116872. 2508.14i −0.723198 0.0155203i
\(403\) −152399. + 285118.i −0.938363 + 1.75555i
\(404\) 48117.5 53752.6i 0.294809 0.329334i
\(405\) −125603. 103080.i −0.765758 0.628441i
\(406\) 22029.9 6169.77i 0.133648 0.0374297i
\(407\) 867.750 579.812i 0.00523849 0.00350025i
\(408\) −48715.5 45528.5i −0.292649 0.273504i
\(409\) −129227. 86346.6i −0.772513 0.516177i 0.105728 0.994395i \(-0.466283\pi\)
−0.878241 + 0.478218i \(0.841283\pi\)
\(410\) 77113.0 39114.2i 0.458733 0.232684i
\(411\) −112596. 210651.i −0.666557 1.24704i
\(412\) 38459.4 157661.i 0.226573 0.928817i
\(413\) 535.705 5439.11i 0.00314070 0.0318880i
\(414\) −14596.2 22893.3i −0.0851608 0.133570i
\(415\) −37722.1 37722.1i −0.219028 0.219028i
\(416\) −204720. 86991.4i −1.18297 0.502678i
\(417\) 177511. + 177511.i 1.02083 + 1.02083i
\(418\) −251921. 55754.7i −1.44183 0.319102i
\(419\) 5982.72 60743.6i 0.0340777 0.345997i −0.962994 0.269523i \(-0.913134\pi\)
0.997072 0.0764738i \(-0.0243662\pi\)
\(420\) −14977.5 10965.5i −0.0849067 0.0621624i
\(421\) −62622.8 117159.i −0.353320 0.661015i 0.640989 0.767550i \(-0.278524\pi\)
−0.994309 + 0.106535i \(0.966024\pi\)
\(422\) 128054. + 41865.4i 0.719065 + 0.235088i
\(423\) −17311.1 11566.9i −0.0967486 0.0646453i
\(424\) −76255.0 106172.i −0.424167 0.590578i
\(425\) −24488.9 + 16363.0i −0.135579 + 0.0905909i
\(426\) 163090. 289977.i 0.898686 1.59788i
\(427\) −23216.1 19053.0i −0.127331 0.104498i
\(428\) 2436.45 6944.25i 0.0133005 0.0379086i
\(429\) −80877.5 + 151311.i −0.439454 + 0.822160i
\(430\) −9819.98 10250.7i −0.0531097 0.0554392i
\(431\) 81416.0 196556.i 0.438284 1.05811i −0.538257 0.842780i \(-0.680917\pi\)
0.976541 0.215330i \(-0.0690828\pi\)
\(432\) 183050. + 73187.6i 0.980849 + 0.392166i
\(433\) −61206.9 + 25352.7i −0.326456 + 0.135222i −0.539891 0.841735i \(-0.681535\pi\)
0.213436 + 0.976957i \(0.431535\pi\)
\(434\) 11329.0 25772.2i 0.0601467 0.136827i
\(435\) −86131.9 283939.i −0.455182 1.50053i
\(436\) −242595. 34456.5i −1.27617 0.181258i
\(437\) −40840.8 414663.i −0.213861 2.17136i
\(438\) −95440.6 + 74957.7i −0.497491 + 0.390722i
\(439\) 39463.7 198397.i 0.204771 1.02945i −0.732477 0.680792i \(-0.761636\pi\)
0.937248 0.348662i \(-0.113364\pi\)
\(440\) 57226.9 + 167990.i 0.295593 + 0.867717i
\(441\) 5160.79 + 25945.1i 0.0265362 + 0.133407i
\(442\) 107974. 8299.78i 0.552682 0.0424837i
\(443\) −271875. 82472.5i −1.38536 0.420244i −0.492395 0.870372i \(-0.663878\pi\)
−0.892964 + 0.450128i \(0.851378\pi\)
\(444\) −1475.97 63.3796i −0.00748706 0.000321502i
\(445\) −189139. + 155222.i −0.955127 + 0.783852i
\(446\) 71244.7 101826.i 0.358165 0.511904i
\(447\) −355793. −1.78067
\(448\) 18355.2 + 6186.65i 0.0914540 + 0.0308247i
\(449\) 375259.i 1.86140i −0.365789 0.930698i \(-0.619201\pi\)
0.365789 0.930698i \(-0.380799\pi\)
\(450\) 6026.57 8613.42i 0.0297608 0.0425354i
\(451\) 44149.5 + 53796.3i 0.217057 + 0.264484i
\(452\) 61657.2 + 67190.1i 0.301792 + 0.328873i
\(453\) −7095.98 + 23392.3i −0.0345793 + 0.113993i
\(454\) 329150. 25301.2i 1.59692 0.122752i
\(455\) 29568.1 5881.46i 0.142824 0.0284094i
\(456\) 241115. + 274342.i 1.15956 + 1.31936i
\(457\) −75197.9 14957.8i −0.360059 0.0716201i 0.0117462 0.999931i \(-0.496261\pi\)
−0.371805 + 0.928311i \(0.621261\pi\)
\(458\) −32733.8 + 25708.7i −0.156051 + 0.122560i
\(459\) −95514.7 + 9407.38i −0.453362 + 0.0446522i
\(460\) −229136. + 172142.i −1.08287 + 0.813523i
\(461\) 87576.2 26566.0i 0.412083 0.125004i −0.0774348 0.996997i \(-0.524673\pi\)
0.489517 + 0.871994i \(0.337173\pi\)
\(462\) 6012.26 13677.2i 0.0281679 0.0640788i
\(463\) 20914.0 + 50490.9i 0.0975609 + 0.235533i 0.965123 0.261795i \(-0.0843145\pi\)
−0.867563 + 0.497328i \(0.834315\pi\)
\(464\) 175180. + 255295.i 0.813668 + 1.18579i
\(465\) −337333. 139728.i −1.56010 0.646215i
\(466\) −189728. 198050.i −0.873695 0.912018i
\(467\) 325987. + 174243.i 1.49474 + 0.798956i 0.997635 0.0687342i \(-0.0218961\pi\)
0.497106 + 0.867690i \(0.334396\pi\)
\(468\) −34838.7 + 16741.4i −0.159063 + 0.0764365i
\(469\) −10488.2 + 12779.9i −0.0476819 + 0.0581006i
\(470\) −107733. + 191552.i −0.487701 + 0.867143i
\(471\) −95541.9 142989.i −0.430678 0.644555i
\(472\) 72016.9 16873.8i 0.323259 0.0757408i
\(473\) 6347.60 9499.85i 0.0283718 0.0424614i
\(474\) −80521.0 26325.2i −0.358387 0.117170i
\(475\) 142280. 76050.4i 0.630605 0.337065i
\(476\) −9319.36 + 1441.24i −0.0411313 + 0.00636097i
\(477\) −22605.4 2226.44i −0.0993518 0.00978530i
\(478\) 101151. + 22386.5i 0.442704 + 0.0979783i
\(479\) −150096. + 150096.i −0.654179 + 0.654179i −0.953997 0.299817i \(-0.903074\pi\)
0.299817 + 0.953997i \(0.403074\pi\)
\(480\) 75112.6 239728.i 0.326010 1.04048i
\(481\) 1696.58 1696.58i 0.00733304 0.00733304i
\(482\) 208684. + 327309.i 0.898246 + 1.40885i
\(483\) 24010.8 + 2364.86i 0.102923 + 0.0101370i
\(484\) 78119.2 47480.7i 0.333478 0.202687i
\(485\) 228422. 122094.i 0.971077 0.519052i
\(486\) 57414.1 29122.3i 0.243078 0.123297i
\(487\) −26433.9 + 39561.2i −0.111456 + 0.166806i −0.883004 0.469365i \(-0.844483\pi\)
0.771548 + 0.636171i \(0.219483\pi\)
\(488\) 142766. 380564.i 0.599495 1.59804i
\(489\) 85251.0 + 127587.i 0.356518 + 0.533567i
\(490\) 268888. 75305.6i 1.11990 0.313643i
\(491\) 254362. 309941.i 1.05509 1.28563i 0.0982030 0.995166i \(-0.468691\pi\)
0.956886 0.290463i \(-0.0938095\pi\)
\(492\) −5441.10 98363.2i −0.0224779 0.406352i
\(493\) −132938. 71057.0i −0.546961 0.292357i
\(494\) −593048. 12727.2i −2.43017 0.0521529i
\(495\) 28491.3 + 11801.5i 0.116279 + 0.0481644i
\(496\) 379602. + 32661.2i 1.54300 + 0.132761i
\(497\) −18005.9 43470.2i −0.0728958 0.175986i
\(498\) −56639.8 + 22049.4i −0.228382 + 0.0889076i
\(499\) −335090. + 101649.i −1.34574 + 0.408225i −0.879275 0.476315i \(-0.841972\pi\)
−0.466464 + 0.884540i \(0.654472\pi\)
\(500\) 157125. + 92863.6i 0.628500 + 0.371454i
\(501\) 258288. 25439.2i 1.02903 0.101351i
\(502\) −36621.2 + 304653.i −0.145320 + 1.20892i
\(503\) 89097.0 + 17722.5i 0.352149 + 0.0700469i 0.367995 0.929828i \(-0.380044\pi\)
−0.0158461 + 0.999874i \(0.505044\pi\)
\(504\) 2913.11 1686.07i 0.0114682 0.00663766i
\(505\) −129787. + 25816.2i −0.508917 + 0.101230i
\(506\) −175129. 150127.i −0.684002 0.586352i
\(507\) −45194.2 + 148985.i −0.175819 + 0.579599i
\(508\) 46131.7 + 126463.i 0.178761 + 0.490045i
\(509\) 55422.4 + 67532.4i 0.213919 + 0.260662i 0.868904 0.494981i \(-0.164825\pi\)
−0.654985 + 0.755642i \(0.727325\pi\)
\(510\) 21281.5 + 120440.i 0.0818204 + 0.463054i
\(511\) 17163.1i 0.0657287i
\(512\) 847.637 + 262143.i 0.00323348 + 0.999995i
\(513\) 525724. 1.99767
\(514\) 137571. 24308.4i 0.520715 0.0920090i
\(515\) −230103. + 188841.i −0.867577 + 0.712002i
\(516\) −15194.0 + 5542.52i −0.0570653 + 0.0208165i
\(517\) −169268. 51346.9i −0.633277 0.192103i
\(518\) −135.981 + 158.627i −0.000506779 + 0.000591177i
\(519\) 65567.3 + 329629.i 0.243418 + 1.22375i
\(520\) 204383. + 353122.i 0.755855 + 1.30593i
\(521\) 53124.2 267073.i 0.195712 0.983909i −0.750626 0.660728i \(-0.770248\pi\)
0.946337 0.323181i \(-0.104752\pi\)
\(522\) 53417.5 + 6421.11i 0.196039 + 0.0235651i
\(523\) 49430.2 + 501874.i 0.180713 + 1.83481i 0.476052 + 0.879417i \(0.342067\pi\)
−0.295339 + 0.955392i \(0.595433\pi\)
\(524\) −74335.1 + 125775.i −0.270727 + 0.458069i
\(525\) 2711.75 + 8939.45i 0.00983856 + 0.0324334i
\(526\) −75776.8 194653.i −0.273883 0.703540i
\(527\) −171372. + 70984.5i −0.617047 + 0.255589i
\(528\) 201453. + 17333.2i 0.722615 + 0.0621743i
\(529\) 35461.2 85611.0i 0.126719 0.305927i
\(530\) −5144.46 + 239716.i −0.0183142 + 0.853386i
\(531\) 6058.97 11335.5i 0.0214887 0.0402025i
\(532\) 51575.8 2852.99i 0.182231 0.0100804i
\(533\) 123678. + 101500.i 0.435351 + 0.357283i
\(534\) 75180.6 + 268442.i 0.263647 + 0.941387i
\(535\) −11223.9 + 7499.54i −0.0392134 + 0.0262015i
\(536\) −209491. 78589.0i −0.729180 0.273547i
\(537\) −139244. 93040.0i −0.482868 0.322642i
\(538\) −26789.5 52815.2i −0.0925552 0.182471i
\(539\) 105945. + 198208.i 0.364671 + 0.682251i
\(540\) −187812. 309005.i −0.644076 1.05969i
\(541\) 10917.1 110844.i 0.0373005 0.378718i −0.958353 0.285585i \(-0.907812\pi\)
0.995654 0.0931326i \(-0.0296880\pi\)
\(542\) −326000. + 207850.i −1.10974 + 0.707540i
\(543\) −142411. 142411.i −0.482997 0.482997i
\(544\) −59133.7 113098.i −0.199819 0.382172i
\(545\) 317808. + 317808.i 1.06997 + 1.06997i
\(546\) 7422.22 33536.5i 0.0248971 0.112495i
\(547\) −53299.7 + 541161.i −0.178136 + 1.80864i 0.326381 + 0.945238i \(0.394171\pi\)
−0.504517 + 0.863402i \(0.668329\pi\)
\(548\) −69871.6 451803.i −0.232669 1.50449i
\(549\) −33295.0 62290.6i −0.110467 0.206670i
\(550\) 27753.9 84891.0i 0.0917484 0.280631i
\(551\) 686528. + 458723.i 2.26128 + 1.51094i
\(552\) 74489.2 + 317917.i 0.244464 + 1.04336i
\(553\) −9961.82 + 6656.27i −0.0325753 + 0.0217661i
\(554\) −112146. 63073.5i −0.365396 0.205507i
\(555\) 2094.71 + 1719.08i 0.00680045 + 0.00558098i
\(556\) 208115. + 433086.i 0.673216 + 1.40096i
\(557\) 195173. 365143.i 0.629085 1.17693i −0.342338 0.939577i \(-0.611219\pi\)
0.971422 0.237358i \(-0.0762813\pi\)
\(558\) 47808.9 45800.0i 0.153547 0.147095i
\(559\) 10052.0 24267.6i 0.0321682 0.0776610i
\(560\) −20102.1 29295.5i −0.0641012 0.0934167i
\(561\) −90946.5 + 37671.3i −0.288975 + 0.119697i
\(562\) −248718. 109332.i −0.787472 0.346159i
\(563\) 142748. + 470577.i 0.450353 + 1.48461i 0.829093 + 0.559111i \(0.188858\pi\)
−0.378740 + 0.925503i \(0.623642\pi\)
\(564\) 150396. + 200192.i 0.472802 + 0.629343i
\(565\) −16395.4 166466.i −0.0513601 0.521468i
\(566\) 178942. + 227839.i 0.558572 + 0.711207i
\(567\) −5107.81 + 25678.7i −0.0158880 + 0.0798743i
\(568\) 478306. 420376.i 1.48255 1.30299i
\(569\) 106138. + 533590.i 0.327827 + 1.64810i 0.695781 + 0.718254i \(0.255059\pi\)
−0.367953 + 0.929844i \(0.619941\pi\)
\(570\) −51346.0 667974.i −0.158036 2.05594i
\(571\) −272419. 82637.3i −0.835535 0.253457i −0.156607 0.987661i \(-0.550055\pi\)
−0.678929 + 0.734204i \(0.737555\pi\)
\(572\) −241954. + 222030.i −0.739505 + 0.678610i
\(573\) 252613. 207314.i 0.769389 0.631421i
\(574\) −11415.7 7987.23i −0.0346480 0.0242422i
\(575\) 144230. 0.436235
\(576\) 34312.9 + 29961.0i 0.103422 + 0.0903048i
\(577\) 387934.i 1.16522i 0.812753 + 0.582608i \(0.197968\pi\)
−0.812753 + 0.582608i \(0.802032\pi\)
\(578\) −222825. 155904.i −0.666972 0.466661i
\(579\) −1018.06 1240.51i −0.00303679 0.00370034i
\(580\) 24364.6 567397.i 0.0724275 1.68667i
\(581\) −2495.27 + 8225.81i −0.00739207 + 0.0243684i
\(582\) −22616.6 294225.i −0.0667700 0.868628i
\(583\) −189275. + 37649.2i −0.556874 + 0.110769i
\(584\) −219873. + 74901.2i −0.644683 + 0.219615i
\(585\) 69536.3 + 13831.6i 0.203189 + 0.0404168i
\(586\) −121555. 154771.i −0.353979 0.450707i
\(587\) −141553. + 13941.7i −0.410812 + 0.0404614i −0.301312 0.953525i \(-0.597425\pi\)
−0.109499 + 0.993987i \(0.534925\pi\)
\(588\) 44737.7 314981.i 0.129395 0.911023i
\(589\) 972300. 294944.i 2.80265 0.850176i
\(590\) −124205. 54598.1i −0.356808 0.156846i
\(591\) −49606.4 119760.i −0.142024 0.342877i
\(592\) −2625.56 1049.76i −0.00749167 0.00299534i
\(593\) 222944. + 92346.6i 0.633997 + 0.262610i 0.676450 0.736488i \(-0.263517\pi\)
−0.0424533 + 0.999098i \(0.513517\pi\)
\(594\) 210166. 201335.i 0.595648 0.570619i
\(595\) 15254.9 + 8153.91i 0.0430899 + 0.0230320i
\(596\) −642592. 225458.i −1.80902 0.634708i
\(597\) 227693. 277444.i 0.638852 0.778444i
\(598\) −462222. 259964.i −1.29255 0.726961i
\(599\) −52062.1 77916.5i −0.145100 0.217158i 0.751800 0.659392i \(-0.229186\pi\)
−0.896900 + 0.442234i \(0.854186\pi\)
\(600\) −102687. + 73752.0i −0.285241 + 0.204867i
\(601\) −155152. + 232201.i −0.429545 + 0.642859i −0.981600 0.190948i \(-0.938844\pi\)
0.552055 + 0.833807i \(0.313844\pi\)
\(602\) −710.790 + 2174.10i −0.00196132 + 0.00599910i
\(603\) −34289.3 + 18328.0i −0.0943027 + 0.0504058i
\(604\) −27639.1 + 37751.9i −0.0757618 + 0.103482i
\(605\) −166875. 16435.7i −0.455910 0.0449033i
\(606\) −32579.2 + 147205.i −0.0887145 + 0.400847i
\(607\) −83137.3 + 83137.3i −0.225641 + 0.225641i −0.810869 0.585228i \(-0.801005\pi\)
0.585228 + 0.810869i \(0.301005\pi\)
\(608\) 261629. + 648274.i 0.707749 + 1.75369i
\(609\) −33807.1 + 33807.1i −0.0911535 + 0.0911535i
\(610\) −628652. + 400813.i −1.68947 + 1.07717i
\(611\) −404701. 39859.6i −1.08406 0.106770i
\(612\) −21545.4 5255.73i −0.0575244 0.0140323i
\(613\) 185536. 99171.3i 0.493751 0.263916i −0.205675 0.978620i \(-0.565939\pi\)
0.699426 + 0.714705i \(0.253439\pi\)
\(614\) 144722. + 285318.i 0.383883 + 0.756819i
\(615\) −100391. + 150246.i −0.265427 + 0.397240i
\(616\) 19525.6 20892.4i 0.0514569 0.0550588i
\(617\) −324454. 485579.i −0.852280 1.27553i −0.959619 0.281304i \(-0.909233\pi\)
0.107339 0.994222i \(-0.465767\pi\)
\(618\) 91463.4 + 326582.i 0.239481 + 0.855096i
\(619\) 232468. 283263.i 0.606711 0.739280i −0.375549 0.926803i \(-0.622546\pi\)
0.982260 + 0.187523i \(0.0600458\pi\)
\(620\) −520709. 466121.i −1.35460 1.21259i
\(621\) 414504. + 221557.i 1.07484 + 0.574516i
\(622\) 2020.72 94159.3i 0.00522306 0.243379i
\(623\) 36424.6 + 15087.5i 0.0938465 + 0.0388725i
\(624\) 462019. 51271.3i 1.18656 0.131676i
\(625\) −184636. 445751.i −0.472668 1.14112i
\(626\) −118722. 304969.i −0.302958 0.778228i
\(627\) 515996. 156526.i 1.31254 0.398154i
\(628\) −81947.9 318792.i −0.207787 0.808330i
\(629\) 1370.01 134.934i 0.00346275 0.000341051i
\(630\) −6129.74 736.832i −0.0154440 0.00185647i
\(631\) −34099.6 6782.84i −0.0856428 0.0170354i 0.152083 0.988368i \(-0.451402\pi\)
−0.237726 + 0.971332i \(0.576402\pi\)
\(632\) −128746. 98569.9i −0.322329 0.246780i
\(633\) −276141. + 54927.9i −0.689166 + 0.137084i
\(634\) −441640. + 515190.i −1.09873 + 1.28171i
\(635\) 71676.4 236285.i 0.177758 0.585989i
\(636\) 247668. + 115273.i 0.612288 + 0.284979i
\(637\) 327787. + 399409.i 0.807816 + 0.984327i
\(638\) 450126. 79536.1i 1.10584 0.195399i
\(639\) 110653.i 0.270996i
\(640\) 287570. 385371.i 0.702075 0.940847i
\(641\) −339527. −0.826338 −0.413169 0.910654i \(-0.635578\pi\)
−0.413169 + 0.910654i \(0.635578\pi\)
\(642\) 2676.10 + 15145.1i 0.00649279 + 0.0367453i
\(643\) −553998. + 454655.i −1.33994 + 1.09966i −0.353522 + 0.935426i \(0.615016\pi\)
−0.986421 + 0.164237i \(0.947484\pi\)
\(644\) 41867.0 + 19486.3i 0.100949 + 0.0469848i
\(645\) 28388.7 + 8611.61i 0.0682379 + 0.0206997i
\(646\) −258397. 221508.i −0.619189 0.530792i
\(647\) −58924.4 296233.i −0.140762 0.707660i −0.985118 0.171878i \(-0.945017\pi\)
0.844356 0.535783i \(-0.179983\pi\)
\(648\) −351255. + 46628.7i −0.836512 + 0.111046i
\(649\) 21303.9 107102.i 0.0505790 0.254278i
\(650\) 24505.6 203863.i 0.0580014 0.482516i
\(651\) 5766.72 + 58550.5i 0.0136071 + 0.138156i
\(652\) 73121.1 + 284455.i 0.172008 + 0.669141i
\(653\) −179879. 592980.i −0.421845 1.39064i −0.868393 0.495877i \(-0.834847\pi\)
0.446548 0.894760i \(-0.352653\pi\)
\(654\) 477188. 185766.i 1.11567 0.434321i
\(655\) 247585. 102553.i 0.577088 0.239038i
\(656\) 52503.6 181100.i 0.122006 0.420834i
\(657\) −15446.3 + 37290.7i −0.0357844 + 0.0863913i
\(658\) 35403.9 + 759.789i 0.0817709 + 0.00175486i
\(659\) 188024. 351769.i 0.432956 0.810003i −0.566950 0.823752i \(-0.691877\pi\)
0.999905 + 0.0137490i \(0.00437659\pi\)
\(660\) −276339. 247369.i −0.634386 0.567881i
\(661\) −638317. 523853.i −1.46094 1.19897i −0.938018 0.346587i \(-0.887340\pi\)
−0.522926 0.852378i \(-0.675160\pi\)
\(662\) 275004. 77018.5i 0.627514 0.175743i
\(663\) −188173. + 125733.i −0.428086 + 0.286038i
\(664\) −116268. + 3931.69i −0.263709 + 0.00891750i
\(665\) −78780.1 52639.2i −0.178145 0.119033i
\(666\) −438.208 + 222.273i −0.000987943 + 0.000501116i
\(667\) 347968. + 651002.i 0.782146 + 1.46329i
\(668\) 482610. + 117726.i 1.08154 + 0.263828i
\(669\) −25456.5 + 258464.i −0.0568783 + 0.577495i
\(670\) 220637. + 346057.i 0.491506 + 0.770899i
\(671\) −424315. 424315.i −0.942418 0.942418i
\(672\) −39772.2 + 7535.10i −0.0880725 + 0.0166859i
\(673\) 199887. + 199887.i 0.441320 + 0.441320i 0.892455 0.451136i \(-0.148981\pi\)
−0.451136 + 0.892455i \(0.648981\pi\)
\(674\) −682618. 151075.i −1.50265 0.332563i
\(675\) −17837.1 + 181103.i −0.0391486 + 0.397482i
\(676\) −176033. + 240441.i −0.385214 + 0.526158i
\(677\) 88194.2 + 165000.i 0.192426 + 0.360003i 0.959569 0.281472i \(-0.0908227\pi\)
−0.767144 + 0.641475i \(0.778323\pi\)
\(678\) −181143. 59222.1i −0.394060 0.128832i
\(679\) −34700.6 23186.2i −0.0752658 0.0502910i
\(680\) −37884.3 + 231011.i −0.0819297 + 0.499591i
\(681\) −573630. + 383288.i −1.23691 + 0.826477i
\(682\) 275738. 490267.i 0.592826 1.05406i
\(683\) 448132. + 367772.i 0.960648 + 0.788384i 0.977383 0.211476i \(-0.0678271\pi\)
−0.0167348 + 0.999860i \(0.505327\pi\)
\(684\) 114627. + 40217.9i 0.245006 + 0.0859622i
\(685\) −395302. + 739558.i −0.842458 + 1.57613i
\(686\) −62543.5 65286.8i −0.132903 0.138732i
\(687\) 33287.5 80363.1i 0.0705290 0.170272i
\(688\) −30953.8 + 382.156i −0.0653938 + 0.000807354i
\(689\) −409899. + 169786.i −0.863451 + 0.357653i
\(690\) 241022. 548299.i 0.506243 1.15165i
\(691\) −25936.3 85500.6i −0.0543191 0.179066i 0.925583 0.378544i \(-0.123575\pi\)
−0.979902 + 0.199478i \(0.936075\pi\)
\(692\) −90459.0 + 636887.i −0.188903 + 1.32999i
\(693\) −487.060 4945.20i −0.00101418 0.0102972i
\(694\) −344390. + 270479.i −0.715042 + 0.561583i
\(695\) 171943. 864417.i 0.355972 1.78959i
\(696\) −580631. 285558.i −1.19862 0.589489i
\(697\) 17909.1 + 90035.1i 0.0368645 + 0.185330i
\(698\) 571782. 43951.9i 1.17360 0.0902126i
\(699\) 548487. + 166382.i 1.12257 + 0.340527i
\(700\) −767.090 + 17863.8i −0.00156549 + 0.0364567i
\(701\) −237230. + 194689.i −0.482762 + 0.396192i −0.844052 0.536261i \(-0.819836\pi\)
0.361291 + 0.932453i \(0.382336\pi\)
\(702\) 383588. 548240.i 0.778379 1.11249i
\(703\) −7540.67 −0.0152581
\(704\) 352858. + 158962.i 0.711959 + 0.320736i
\(705\) 459282.i 0.924063i
\(706\) −94607.8 + 135217.i −0.189809 + 0.271283i
\(707\) 13526.9 + 16482.6i 0.0270619 + 0.0329751i
\(708\) −113893. + 104514.i −0.227212 + 0.208502i
\(709\) 175572. 578785.i 0.349272 1.15140i −0.589764 0.807576i \(-0.700779\pi\)
0.939036 0.343820i \(-0.111721\pi\)
\(710\) −1.16459e6 + 89520.1i −2.31024 + 0.177584i
\(711\) −27634.7 + 5496.88i −0.0546657 + 0.0108737i
\(712\) −34323.5 + 532469.i −0.0677068 + 1.05035i
\(713\) 890903. + 177212.i 1.75247 + 0.348588i
\(714\) 15498.8 12172.6i 0.0304020 0.0238773i
\(715\) 599450. 59040.6i 1.17258 0.115489i
\(716\) −192529. 256274.i −0.375552 0.499895i
\(717\) −207182. + 62847.8i −0.403007 + 0.122251i
\(718\) −115444. + 262621.i −0.223934 + 0.509426i
\(719\) −109573. 264534.i −0.211957 0.511709i 0.781767 0.623571i \(-0.214319\pi\)
−0.993724 + 0.111862i \(0.964319\pi\)
\(720\) −17311.2 81742.2i −0.0333936 0.157682i
\(721\) 44313.5 + 18355.2i 0.0852443 + 0.0353093i
\(722\) 929047. + 969797.i 1.78223 + 1.86040i
\(723\) −715435. 382408.i −1.36865 0.731561i
\(724\) −166964. 347450.i −0.318526 0.662849i
\(725\) −181315. + 220933.i −0.344952 + 0.420325i
\(726\) −93652.9 + 166517.i −0.177684 + 0.315925i
\(727\) −473468. 708595.i −0.895822 1.34069i −0.939823 0.341661i \(-0.889010\pi\)
0.0440007 0.999031i \(-0.485990\pi\)
\(728\) 34656.5 55866.4i 0.0653916 0.105411i
\(729\) −323895. + 484743.i −0.609465 + 0.912129i
\(730\) 404969. + 132399.i 0.759935 + 0.248450i
\(731\) 13291.4 7104.40i 0.0248734 0.0132951i
\(732\) 129823. + 839460.i 0.242286 + 1.56667i
\(733\) 808021. + 79583.2i 1.50389 + 0.148120i 0.816150 0.577841i \(-0.196104\pi\)
0.687736 + 0.725960i \(0.258604\pi\)
\(734\) −167974. 37175.6i −0.311781 0.0690027i
\(735\) −412636. + 412636.i −0.763822 + 0.763822i
\(736\) −66923.5 + 621387.i −0.123544 + 1.14711i
\(737\) −233574. + 233574.i −0.430022 + 0.430022i
\(738\) −17614.8 27627.8i −0.0323418 0.0507263i
\(739\) 551375. + 54305.7i 1.00962 + 0.0994389i 0.589281 0.807928i \(-0.299411\pi\)
0.420339 + 0.907367i \(0.361911\pi\)
\(740\) 2693.87 + 4432.18i 0.00491941 + 0.00809382i
\(741\) 1.09328e6 584372.i 1.99111 1.06427i
\(742\) 34455.9 17477.1i 0.0625829 0.0317441i
\(743\) 91494.2 136931.i 0.165736 0.248041i −0.739300 0.673376i \(-0.764844\pi\)
0.905036 + 0.425335i \(0.139844\pi\)
\(744\) −724909. + 329394.i −1.30960 + 0.595073i
\(745\) 693976. + 1.03861e6i 1.25035 + 1.87128i
\(746\) 40600.9 11370.8i 0.0729555 0.0204321i
\(747\) −12824.5 + 15626.7i −0.0229826 + 0.0280044i
\(748\) −188128. + 10406.6i −0.336242 + 0.0185997i
\(749\) 1918.27 + 1025.33i 0.00341936 + 0.00182769i
\(750\) −381340. 8183.80i −0.677938 0.0145490i
\(751\) 559531. + 231765.i 0.992075 + 0.410931i 0.818885 0.573958i \(-0.194593\pi\)
0.173190 + 0.984888i \(0.444593\pi\)
\(752\) 144771. + 456866.i 0.256004 + 0.807891i
\(753\) −245399. 592447.i −0.432796 1.04486i
\(754\) 979286. 381229.i 1.72253 0.670568i
\(755\) 82126.1 24912.7i 0.144074 0.0437045i
\(756\) −29645.7 + 50160.5i −0.0518703 + 0.0877644i
\(757\) −1.01320e6 + 99791.4i −1.76809 + 0.174141i −0.929054 0.369943i \(-0.879377\pi\)
−0.839031 + 0.544084i \(0.816877\pi\)
\(758\) 8964.21 74573.7i 0.0156018 0.129792i
\(759\) 472799. + 94045.6i 0.820717 + 0.163251i
\(760\) 330546. 1.23895e6i 0.572275 2.14500i
\(761\) 512172. 101877.i 0.884395 0.175917i 0.268061 0.963402i \(-0.413617\pi\)
0.616334 + 0.787485i \(0.288617\pi\)
\(762\) −213586. 183094.i −0.367843 0.315328i
\(763\) 21022.6 69302.3i 0.0361108 0.119041i
\(764\) 587610. 214351.i 1.00671 0.367230i
\(765\) 25806.3 + 31445.1i 0.0440964 + 0.0537316i
\(766\) 132633. + 750623.i 0.226045 + 1.27928i
\(767\) 251052.i 0.426750i
\(768\) −270099. 476627.i −0.457931 0.808084i
\(769\) −1.07892e6 −1.82447 −0.912236 0.409665i \(-0.865646\pi\)
−0.912236 + 0.409665i \(0.865646\pi\)
\(770\) −51652.6 + 9126.89i −0.0871186 + 0.0153936i
\(771\) −225684. + 185214.i −0.379657 + 0.311576i
\(772\) −1052.61 2885.58i −0.00176618 0.00484170i
\(773\) −426847. 129483.i −0.714353 0.216697i −0.0878704 0.996132i \(-0.528006\pi\)
−0.626483 + 0.779435i \(0.715506\pi\)
\(774\) −3500.97 + 4084.01i −0.00584395 + 0.00681719i
\(775\) 68614.4 + 344948.i 0.114238 + 0.574315i
\(776\) 145597. 545727.i 0.241785 0.906259i
\(777\) 85.1838 428.248i 0.000141096 0.000709338i
\(778\) −897575. 107894.i −1.48290 0.178253i
\(779\) −49286.8 500418.i −0.0812187 0.824627i
\(780\) −734046. 433834.i −1.20652 0.713074i
\(781\) −272898. 899623.i −0.447402 1.47489i
\(782\) −110381. 283543.i −0.180502 0.463667i
\(783\) −860467. + 356417.i −1.40349 + 0.581346i
\(784\) 280397. 540532.i 0.456185 0.879406i
\(785\) −231048. + 557800.i −0.374942 + 0.905189i
\(786\) 6550.94 305254.i 0.0106037 0.494101i
\(787\) 113881. 213056.i 0.183865 0.343988i −0.773055 0.634339i \(-0.781272\pi\)
0.956920 + 0.290351i \(0.0937722\pi\)
\(788\) −13703.6 247732.i −0.0220690 0.398960i
\(789\) 337442. + 276932.i 0.542058 + 0.444855i
\(790\) 80209.8 + 286399.i 0.128521 + 0.458900i
\(791\) −22410.5 + 14974.2i −0.0358177 + 0.0239326i
\(792\) 61226.2 27820.8i 0.0976083 0.0443526i
\(793\) −1.14707e6 766449.i −1.82408 1.21881i
\(794\) −382775. 754636.i −0.607160 1.19701i
\(795\) −236209. 441916.i −0.373734 0.699206i
\(796\) 587043. 356804.i 0.926496 0.563123i
\(797\) −111915. + 1.13629e6i −0.176186 + 1.78885i 0.348252 + 0.937401i \(0.386775\pi\)
−0.524439 + 0.851448i \(0.675725\pi\)
\(798\) −91023.2 + 58034.1i −0.142937 + 0.0911334i
\(799\) −164985. 164985.i −0.258435 0.258435i
\(800\) −232196. + 68131.8i −0.362806 + 0.106456i
\(801\) 65562.0 + 65562.0i 0.102185 + 0.102185i
\(802\) −57053.3 + 257789.i −0.0887017 + 0.400789i
\(803\) −33612.3 + 341272.i −0.0521276 + 0.529260i
\(804\) 462101. 71464.1i 0.714866 0.110554i
\(805\) −39929.9 74703.5i −0.0616178 0.115279i
\(806\) 401851. 1.22914e6i 0.618579 1.89205i
\(807\) 102905. + 68758.6i 0.158011 + 0.105580i
\(808\) −152122. + 245221.i −0.233007 + 0.375607i
\(809\) 972997. 650136.i 1.48667 0.993361i 0.494404 0.869232i \(-0.335386\pi\)
0.992266 0.124129i \(-0.0396136\pi\)
\(810\) 566494. + 318609.i 0.863426 + 0.485611i
\(811\) 443397. + 363887.i 0.674142 + 0.553254i 0.907976 0.419022i \(-0.137627\pi\)
−0.233834 + 0.972277i \(0.575127\pi\)
\(812\) −82481.3 + 39635.6i −0.125096 + 0.0601137i
\(813\) 380880. 712576.i 0.576244 1.07808i
\(814\) −3014.50 + 2887.83i −0.00454953 + 0.00435836i
\(815\) 206162. 497718.i 0.310379 0.749322i
\(816\) 223578. + 145430.i 0.335775 + 0.218410i
\(817\) −76268.9 + 31591.6i −0.114262 + 0.0473290i
\(818\) 569120. + 250175.i 0.850545 + 0.373884i
\(819\) −3316.23 10932.2i −0.00494399 0.0162981i
\(820\) −276523. + 207741.i −0.411248 + 0.308955i
\(821\) 49369.1 + 501253.i 0.0732434 + 0.743653i 0.959735 + 0.280908i \(0.0906355\pi\)
−0.886491 + 0.462745i \(0.846865\pi\)
\(822\) 590127. + 751385.i 0.873377 + 1.11204i
\(823\) −17561.1 + 88285.7i −0.0259270 + 0.130344i −0.991581 0.129487i \(-0.958667\pi\)
0.965654 + 0.259831i \(0.0836669\pi\)
\(824\) −41757.4 + 647792.i −0.0615006 + 0.954073i
\(825\) 36413.4 + 183063.i 0.0535000 + 0.268963i
\(826\) 1675.53 + 21797.4i 0.00245579 + 0.0319481i
\(827\) −566269. 171776.i −0.827965 0.251160i −0.152267 0.988339i \(-0.548657\pi\)
−0.675698 + 0.737179i \(0.736157\pi\)
\(828\) 73428.1 + 80017.2i 0.107103 + 0.116714i
\(829\) −865330. + 710158.i −1.25914 + 1.03335i −0.261460 + 0.965214i \(0.584204\pi\)
−0.997676 + 0.0681318i \(0.978296\pi\)
\(830\) 174841. + 122332.i 0.253798 + 0.177575i
\(831\) 268892. 0.389381
\(832\) 866934. + 200171.i 1.25239 + 0.289171i
\(833\) 296458.i 0.427241i
\(834\) −822764. 575665.i −1.18289 0.827633i
\(835\) −578053. 704359.i −0.829076 1.01023i
\(836\) 1.03112e6 + 44277.4i 1.47536 + 0.0633533i
\(837\) −332695. + 1.09675e6i −0.474893 + 1.56551i
\(838\) 18712.2 + 243432.i 0.0266463 + 0.346649i
\(839\) 645897. 128477.i 0.917571 0.182516i 0.286355 0.958124i \(-0.407556\pi\)
0.631216 + 0.775607i \(0.282556\pi\)
\(840\) 66628.3 + 32768.2i 0.0944279 + 0.0464402i
\(841\) −740961. 147386.i −1.04762 0.208384i
\(842\) 328213. + 417901.i 0.462948 + 0.589453i
\(843\) 565050. 55652.6i 0.795118 0.0783123i
\(844\) −533541. 75780.5i −0.749002 0.106383i
\(845\) 523060. 158669.i 0.732552 0.222217i
\(846\) 76238.9 + 33513.2i 0.106521 + 0.0468247i
\(847\) 10339.7 + 24962.3i 0.0144126 + 0.0347951i
\(848\) 374263. + 365135.i 0.520458 + 0.507763i
\(849\) −559357. 231693.i −0.776022 0.321439i
\(850\) 85072.7 81498.0i 0.117748 0.112800i
\(851\) −5945.40 3177.88i −0.00820959 0.00438812i
\(852\) −440582. + 1.25573e6i −0.606942 + 1.72988i
\(853\) −614103. + 748286.i −0.844001 + 1.02842i 0.155177 + 0.987887i \(0.450405\pi\)
−0.999178 + 0.0405317i \(0.987095\pi\)
\(854\) 104709. + 58890.7i 0.143571 + 0.0807478i
\(855\) −123793. 185270.i −0.169342 0.253439i
\(856\) −4763.86 + 29049.0i −0.00650147 + 0.0396446i
\(857\) 763297. 1.14236e6i 1.03928 1.55539i 0.225477 0.974248i \(-0.427606\pi\)
0.813802 0.581142i \(-0.197394\pi\)
\(858\) 213261. 652303.i 0.289692 0.886084i
\(859\) −359189. + 191990.i −0.486784 + 0.260191i −0.696481 0.717575i \(-0.745252\pi\)
0.209697 + 0.977766i \(0.432752\pi\)
\(860\) 45815.3 + 33542.6i 0.0619460 + 0.0453523i
\(861\) 28976.4 + 2853.92i 0.0390875 + 0.00384978i
\(862\) −183892. + 830896.i −0.247485 + 1.11823i
\(863\) 162994. 162994.i 0.218851 0.218851i −0.589163 0.808014i \(-0.700542\pi\)
0.808014 + 0.589163i \(0.200542\pi\)
\(864\) −771970. 160880.i −1.03412 0.215514i
\(865\) 834344. 834344.i 1.11510 1.11510i
\(866\) 223447. 142464.i 0.297947 0.189964i
\(867\) 565595. + 55706.3i 0.752432 + 0.0741081i
\(868\) −26687.0 + 109401.i −0.0354210 + 0.145205i
\(869\) −211116. + 112844.i −0.279565 + 0.149430i
\(870\) 536895. + 1.05848e6i 0.709335 + 1.39844i
\(871\) −421910. + 631433.i −0.556140 + 0.832322i
\(872\) 979558. 33124.4i 1.28824 0.0435627i
\(873\) −54527.8 81606.6i −0.0715467 0.107077i
\(874\) 449480. + 1.60493e6i 0.588420 + 2.10103i
\(875\) −34221.8 + 41699.3i −0.0446978 + 0.0544644i
\(876\) 323768. 361684.i 0.421915 0.471326i
\(877\) −1.22520e6 654883.i −1.59297 0.851461i −0.998892 0.0470535i \(-0.985017\pi\)
−0.594078 0.804407i \(-0.702483\pi\)
\(878\) −17360.6 + 808951.i −0.0225204 + 1.04938i
\(879\) 379971. + 157389.i 0.491782 + 0.203703i
\(880\) −342338. 621879.i −0.442069 0.803046i
\(881\) −153704. 371075.i −0.198031 0.478090i 0.793403 0.608697i \(-0.208307\pi\)
−0.991434 + 0.130607i \(0.958307\pi\)
\(882\) −38386.2 98605.1i −0.0493444 0.126754i
\(883\) 941719. 285667.i 1.20781 0.366386i 0.378728 0.925508i \(-0.376362\pi\)
0.829086 + 0.559122i \(0.188862\pi\)
\(884\) −419531. + 107844.i −0.536858 + 0.138003i
\(885\) 282174. 27791.7i 0.360272 0.0354837i
\(886\) 1.12831e6 + 135630.i 1.43735 + 0.172778i
\(887\) −853435. 169759.i −1.08473 0.215767i −0.379820 0.925060i \(-0.624014\pi\)
−0.704913 + 0.709293i \(0.749014\pi\)
\(888\) 5857.93 777.635i 0.00742879 0.000986165i
\(889\) −39022.0 + 7761.95i −0.0493748 + 0.00982126i
\(890\) 636979. 743060.i 0.804165 0.938089i
\(891\) −151853. + 500592.i −0.191279 + 0.630563i
\(892\) −209760. + 450677.i −0.263629 + 0.566416i
\(893\) 810794. + 987955.i 1.01673 + 1.23889i
\(894\) 1.40146e6 247635.i 1.75350 0.309839i
\(895\) 587948.i 0.733994i
\(896\) −76606.7 11593.7i −0.0954225 0.0144413i
\(897\) 1.10827e6 1.37740
\(898\) 261183. + 1.47814e6i 0.323887 + 1.83300i
\(899\) −1.39143e6 + 1.14192e6i −1.72164 + 1.41291i
\(900\) −17743.5 + 38122.6i −0.0219056 + 0.0470650i
\(901\) −243599. 73895.0i −0.300072 0.0910260i
\(902\) −211347. 181174.i −0.259766 0.222681i
\(903\) −932.565 4688.32i −0.00114368 0.00574966i
\(904\) −289631. 221746.i −0.354412 0.271344i
\(905\) −137944. + 693492.i −0.168425 + 0.846729i
\(906\) 11669.7 97080.7i 0.0142168 0.118270i
\(907\) 27093.0 + 275079.i 0.0329338 + 0.334383i 0.997507 + 0.0705673i \(0.0224809\pi\)
−0.964573 + 0.263815i \(0.915019\pi\)
\(908\) −1.27891e6 + 328752.i −1.55120 + 0.398746i
\(909\) 14556.3 + 47985.8i 0.0176167 + 0.0580744i
\(910\) −112375. + 43746.6i −0.135702 + 0.0528277i
\(911\) −1.00048e6 + 414410.i −1.20551 + 0.499337i −0.892774 0.450504i \(-0.851244\pi\)
−0.312732 + 0.949841i \(0.601244\pi\)
\(912\) −1.14069e6 912810.i −1.37145 1.09747i
\(913\) −65725.4 + 158675.i −0.0788482 + 0.190356i
\(914\) 306614. + 6580.13i 0.367028 + 0.00787666i
\(915\) 734480. 1.37412e6i 0.877279 1.64127i
\(916\) 111044. 124049.i 0.132344 0.147843i
\(917\) −33379.3 27393.7i −0.0396953 0.0325771i
\(918\) 369683. 103534.i 0.438676 0.122857i
\(919\) −392368. + 262172.i −0.464582 + 0.310424i −0.765740 0.643150i \(-0.777627\pi\)
0.301158 + 0.953574i \(0.402627\pi\)
\(920\) 782752. 837543.i 0.924801 0.989536i
\(921\) −555910. 371447.i −0.655368 0.437903i
\(922\) −326471. + 165597.i −0.384045 + 0.194800i
\(923\) −1.01883e6 1.90610e6i −1.19591 2.23740i
\(924\) −14162.7 + 58058.9i −0.0165883 + 0.0680025i
\(925\) 255.844 2597.63i 0.000299015 0.00303595i
\(926\) −117522. 184327.i −0.137056 0.214964i
\(927\) 79761.6 + 79761.6i 0.0928184 + 0.0928184i
\(928\) −867716. 883675.i −1.00759 1.02612i
\(929\) 816420. + 816420.i 0.945980 + 0.945980i 0.998614 0.0526338i \(-0.0167616\pi\)
−0.0526338 + 0.998614i \(0.516762\pi\)
\(930\) 1.42600e6 + 315599.i 1.64874 + 0.364897i
\(931\) 159168. 1.61606e6i 0.183635 1.86448i
\(932\) 885180. + 648064.i 1.01906 + 0.746081i
\(933\) 92781.7 + 173582.i 0.106586 + 0.199408i
\(934\) −1.40533e6 459452.i −1.61096 0.526680i
\(935\) 287359. + 192007.i 0.328702 + 0.219631i
\(936\) 125577. 90192.2i 0.143337 0.102948i
\(937\) 914141. 610809.i 1.04120 0.695707i 0.0874069 0.996173i \(-0.472142\pi\)
0.953793 + 0.300465i \(0.0971420\pi\)
\(938\) 32417.8 57639.5i 0.0368449 0.0655110i
\(939\) 528682. + 433878.i 0.599602 + 0.492081i
\(940\) 291038. 829503.i 0.329377 0.938776i
\(941\) −54974.7 + 102850.i −0.0620845 + 0.116152i −0.911049 0.412298i \(-0.864726\pi\)
0.848965 + 0.528450i \(0.177226\pi\)
\(942\) 475859. + 496732.i 0.536262 + 0.559783i
\(943\) 172032. 415322.i 0.193458 0.467049i
\(944\) −271929. + 116590.i −0.305149 + 0.130833i
\(945\) 98739.9 40899.4i 0.110568 0.0457987i
\(946\) −18391.1 + 41837.7i −0.0205506 + 0.0467504i
\(947\) −122158. 402701.i −0.136214 0.449037i 0.862122 0.506701i \(-0.169135\pi\)
−0.998336 + 0.0576633i \(0.981635\pi\)
\(948\) 335493. + 47651.2i 0.373308 + 0.0530221i
\(949\) 77275.1 + 784587.i 0.0858039 + 0.871182i
\(950\) −507508. + 398589.i −0.562335 + 0.441650i
\(951\) 276661. 1.39087e6i 0.305905 1.53789i
\(952\) 35705.7 12163.4i 0.0393970 0.0134209i
\(953\) −54020.4 271579.i −0.0594801 0.299027i 0.939582 0.342324i \(-0.111214\pi\)
−0.999062 + 0.0432968i \(0.986214\pi\)
\(954\) 90591.9 6963.65i 0.0995389 0.00765139i
\(955\) −1.09790e6 333044.i −1.20380 0.365170i
\(956\) −414013. 17778.1i −0.452999 0.0194523i
\(957\) −738428. + 606012.i −0.806277 + 0.661694i
\(958\) 486756. 695691.i 0.530372 0.758029i
\(959\) 135122. 0.146923
\(960\) −129015. + 996562.i −0.139990 + 1.08134i
\(961\) 1.29151e6i 1.39846i
\(962\) −5501.96 + 7863.63i −0.00594521 + 0.00849714i
\(963\) 3245.08 + 3954.14i 0.00349924 + 0.00426383i
\(964\) −1.04981e6 1.14402e6i −1.12969 1.23106i
\(965\) −1635.48 + 5391.46i −0.00175627 + 0.00578964i
\(966\) −96224.1 + 7396.58i −0.103117 + 0.00792642i
\(967\) 939268. 186832.i 1.00447 0.199801i 0.334663 0.942338i \(-0.391377\pi\)
0.669806 + 0.742536i \(0.266377\pi\)
\(968\) −274663. + 241397.i −0.293123 + 0.257621i
\(969\) 697600. + 138761.i 0.742948 + 0.147782i
\(970\) −814770. + 639909.i −0.865948 + 0.680103i
\(971\) −209886. + 20671.9i −0.222610 + 0.0219251i −0.208707 0.977978i \(-0.566926\pi\)
−0.0139027 + 0.999903i \(0.504426\pi\)
\(972\) −205884. + 154673.i −0.217916 + 0.163712i
\(973\) −135899. + 41224.6i −0.143546 + 0.0435443i
\(974\) 76587.9 174229.i 0.0807313 0.183655i
\(975\) 164213. + 396444.i 0.172742 + 0.417035i
\(976\) −297477. + 1.59840e6i −0.312287 + 1.67798i
\(977\) −927710. 384270.i −0.971904 0.402576i −0.160483 0.987039i \(-0.551305\pi\)
−0.811420 + 0.584463i \(0.801305\pi\)
\(978\) −424604. 443228.i −0.443921 0.463393i
\(979\) 694718. + 371334.i 0.724842 + 0.387436i
\(980\) −1.00673e6 + 483776.i −1.04824 + 0.503723i
\(981\) 108046. 131655.i 0.112272 0.136804i
\(982\) −786206. + 1.39789e6i −0.815292 + 1.44961i
\(983\) −217342. 325276.i −0.224925 0.336624i 0.701794 0.712380i \(-0.252383\pi\)
−0.926718 + 0.375757i \(0.877383\pi\)
\(984\) 89894.0 + 383664.i 0.0928411 + 0.396242i
\(985\) −252840. + 378401.i −0.260599 + 0.390014i
\(986\) 573098. + 187366.i 0.589488 + 0.192725i
\(987\) −65266.9 + 34885.9i −0.0669975 + 0.0358109i
\(988\) 2.34486e6 362634.i 2.40217 0.371497i
\(989\) −73447.5 7233.94i −0.0750904 0.00739575i
\(990\) −120441. 26655.6i −0.122886 0.0271969i
\(991\) 716947. 716947.i 0.730028 0.730028i −0.240597 0.970625i \(-0.577343\pi\)
0.970625 + 0.240597i \(0.0773433\pi\)
\(992\) −1.51798e6 + 135554.i −1.54256 + 0.137749i
\(993\) −422021. + 422021.i −0.427992 + 0.427992i
\(994\) 101181. + 158696.i 0.102406 + 0.160618i
\(995\) −1.25401e6 123510.i −1.26665 0.124754i
\(996\) 207756. 126274.i 0.209428 0.127290i
\(997\) 676822. 361769.i 0.680901 0.363949i −0.0944058 0.995534i \(-0.530095\pi\)
0.775307 + 0.631585i \(0.217595\pi\)
\(998\) 1.24917e6 633617.i 1.25418 0.636159i
\(999\) 4725.59 7072.34i 0.00473505 0.00708651i
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 128.5.l.a.3.3 1008
128.43 odd 32 inner 128.5.l.a.43.3 yes 1008
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.5.l.a.3.3 1008 1.1 even 1 trivial
128.5.l.a.43.3 yes 1008 128.43 odd 32 inner