Properties

Label 128.5.l.a.3.9
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 3.9
Character \(\chi\) \(=\) 128.3
Dual form 128.5.l.a.43.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.81656 - 1.19746i) q^{2} +(-9.21046 + 7.55883i) q^{3} +(13.1322 + 9.14031i) q^{4} +(-23.7963 - 7.21854i) q^{5} +(44.2036 - 17.8196i) q^{6} +(16.4786 + 82.8433i) q^{7} +(-39.1746 - 50.6098i) q^{8} +(11.8943 - 59.7969i) q^{9} +O(q^{10})\) \(q+(-3.81656 - 1.19746i) q^{2} +(-9.21046 + 7.55883i) q^{3} +(13.1322 + 9.14031i) q^{4} +(-23.7963 - 7.21854i) q^{5} +(44.2036 - 17.8196i) q^{6} +(16.4786 + 82.8433i) q^{7} +(-39.1746 - 50.6098i) q^{8} +(11.8943 - 59.7969i) q^{9} +(82.1761 + 56.0450i) q^{10} +(20.8775 + 211.972i) q^{11} +(-190.044 + 15.0775i) q^{12} +(64.7754 + 213.536i) q^{13} +(36.3099 - 335.908i) q^{14} +(273.739 - 113.386i) q^{15} +(88.9093 + 240.065i) q^{16} +(135.129 - 326.230i) q^{17} +(-117.000 + 213.975i) q^{18} +(-152.189 + 284.726i) q^{19} +(-246.518 - 312.301i) q^{20} +(-777.973 - 638.466i) q^{21} +(174.148 - 834.004i) q^{22} +(-266.539 + 178.096i) q^{23} +(743.367 + 170.025i) q^{24} +(-5.51054 - 3.68203i) q^{25} +(8.48085 - 892.538i) q^{26} +(-112.512 - 210.495i) q^{27} +(-540.814 + 1238.53i) q^{28} +(-65.0999 + 660.970i) q^{29} +(-1180.51 + 104.955i) q^{30} +(131.950 + 131.950i) q^{31} +(-51.8602 - 1022.69i) q^{32} +(-1794.55 - 1794.55i) q^{33} +(-906.374 + 1083.27i) q^{34} +(205.878 - 2090.32i) q^{35} +(702.761 - 676.546i) q^{36} +(39.8945 + 74.6374i) q^{37} +(921.785 - 904.432i) q^{38} +(-2210.69 - 1477.14i) q^{39} +(566.884 + 1487.11i) q^{40} +(-891.856 + 595.919i) q^{41} +(2204.64 + 3368.33i) q^{42} +(-105.156 - 86.2993i) q^{43} +(-1663.33 + 2974.49i) q^{44} +(-714.688 + 1337.09i) q^{45} +(1230.52 - 360.543i) q^{46} +(903.327 - 2180.82i) q^{47} +(-2633.50 - 1539.06i) q^{48} +(-4373.23 + 1811.45i) q^{49} +(16.6222 + 20.6513i) q^{50} +(1221.32 + 4026.15i) q^{51} +(-1101.14 + 3396.26i) q^{52} +(-56.3753 - 572.388i) q^{53} +(177.350 + 938.094i) q^{54} +(1033.32 - 5194.87i) q^{55} +(3547.14 - 4079.33i) q^{56} +(-750.462 - 3772.83i) q^{57} +(1039.94 - 2444.68i) q^{58} +(5517.65 + 1673.76i) q^{59} +(4631.18 + 1013.05i) q^{60} +(1205.52 - 989.346i) q^{61} +(-345.590 - 661.597i) q^{62} +5149.77 q^{63} +(-1026.69 + 3965.24i) q^{64} -5548.95i q^{65} +(4700.12 + 8997.91i) q^{66} +(590.365 + 719.362i) q^{67} +(4756.39 - 3049.00i) q^{68} +(1108.75 - 3655.07i) q^{69} +(-3288.81 + 7731.28i) q^{70} +(1946.01 - 387.085i) q^{71} +(-3492.26 + 1740.55i) q^{72} +(8342.29 + 1659.39i) q^{73} +(-62.8847 - 332.630i) q^{74} +(78.5864 - 7.74008i) q^{75} +(-4601.06 + 2348.02i) q^{76} +(-17216.5 + 5222.56i) q^{77} +(6668.42 + 8284.78i) q^{78} +(-638.154 - 1540.64i) q^{79} +(-382.798 - 6354.46i) q^{80} +(7189.90 + 2978.16i) q^{81} +(4117.41 - 1206.40i) q^{82} +(-4543.68 - 2428.65i) q^{83} +(-4380.72 - 15495.4i) q^{84} +(-5570.48 + 6787.65i) q^{85} +(297.994 + 455.286i) q^{86} +(-4396.56 - 6579.92i) q^{87} +(9910.00 - 9360.55i) q^{88} +(-8281.33 + 12393.9i) q^{89} +(4328.75 - 4247.26i) q^{90} +(-16622.6 + 8884.97i) q^{91} +(-5128.09 - 97.4627i) q^{92} +(-2212.70 - 217.932i) q^{93} +(-6059.04 + 7241.54i) q^{94} +(5676.85 - 5676.85i) q^{95} +(8207.96 + 9027.40i) q^{96} +(8113.61 - 8113.61i) q^{97} +(18859.8 - 1676.76i) q^{98} +(12923.6 + 1272.86i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.81656 1.19746i −0.954139 0.299364i
\(3\) −9.21046 + 7.55883i −1.02338 + 0.839870i −0.987202 0.159476i \(-0.949020\pi\)
−0.0361822 + 0.999345i \(0.511520\pi\)
\(4\) 13.1322 + 9.14031i 0.820762 + 0.571270i
\(5\) −23.7963 7.21854i −0.951853 0.288741i −0.224089 0.974569i \(-0.571941\pi\)
−0.727764 + 0.685827i \(0.759441\pi\)
\(6\) 44.2036 17.8196i 1.22788 0.494988i
\(7\) 16.4786 + 82.8433i 0.336297 + 1.69068i 0.665482 + 0.746414i \(0.268226\pi\)
−0.329185 + 0.944265i \(0.606774\pi\)
\(8\) −39.1746 50.6098i −0.612104 0.790777i
\(9\) 11.8943 59.7969i 0.146844 0.738233i
\(10\) 82.1761 + 56.0450i 0.821761 + 0.560450i
\(11\) 20.8775 + 211.972i 0.172541 + 1.75184i 0.558667 + 0.829392i \(0.311313\pi\)
−0.386126 + 0.922446i \(0.626187\pi\)
\(12\) −190.044 + 15.0775i −1.31975 + 0.104705i
\(13\) 64.7754 + 213.536i 0.383286 + 1.26353i 0.910399 + 0.413731i \(0.135775\pi\)
−0.527113 + 0.849795i \(0.676725\pi\)
\(14\) 36.3099 335.908i 0.185254 1.71382i
\(15\) 273.739 113.386i 1.21662 0.503939i
\(16\) 88.9093 + 240.065i 0.347302 + 0.937753i
\(17\) 135.129 326.230i 0.467575 1.12883i −0.497644 0.867381i \(-0.665801\pi\)
0.965219 0.261444i \(-0.0841986\pi\)
\(18\) −117.000 + 213.975i −0.361110 + 0.660417i
\(19\) −152.189 + 284.726i −0.421576 + 0.788714i −0.999628 0.0272864i \(-0.991313\pi\)
0.578051 + 0.816000i \(0.303813\pi\)
\(20\) −246.518 312.301i −0.616296 0.780753i
\(21\) −777.973 638.466i −1.76411 1.44777i
\(22\) 174.148 834.004i 0.359809 1.72315i
\(23\) −266.539 + 178.096i −0.503855 + 0.336665i −0.781382 0.624053i \(-0.785485\pi\)
0.277528 + 0.960718i \(0.410485\pi\)
\(24\) 743.367 + 170.025i 1.29057 + 0.295182i
\(25\) −5.51054 3.68203i −0.00881687 0.00589124i
\(26\) 8.48085 892.538i 0.0125456 1.32032i
\(27\) −112.512 210.495i −0.154337 0.288745i
\(28\) −540.814 + 1238.53i −0.689814 + 1.57976i
\(29\) −65.0999 + 660.970i −0.0774077 + 0.785934i 0.875610 + 0.483019i \(0.160460\pi\)
−0.953018 + 0.302915i \(0.902040\pi\)
\(30\) −1180.51 + 104.955i −1.31168 + 0.116617i
\(31\) 131.950 + 131.950i 0.137305 + 0.137305i 0.772419 0.635114i \(-0.219047\pi\)
−0.635114 + 0.772419i \(0.719047\pi\)
\(32\) −51.8602 1022.69i −0.0506447 0.998717i
\(33\) −1794.55 1794.55i −1.64789 1.64789i
\(34\) −906.374 + 1083.27i −0.784061 + 0.937081i
\(35\) 205.878 2090.32i 0.168064 1.70638i
\(36\) 702.761 676.546i 0.542254 0.522027i
\(37\) 39.8945 + 74.6374i 0.0291414 + 0.0545197i 0.896071 0.443912i \(-0.146410\pi\)
−0.866929 + 0.498431i \(0.833910\pi\)
\(38\) 921.785 904.432i 0.638355 0.626338i
\(39\) −2210.69 1477.14i −1.45345 0.971162i
\(40\) 566.884 + 1487.11i 0.354303 + 0.929444i
\(41\) −891.856 + 595.919i −0.530551 + 0.354503i −0.791812 0.610765i \(-0.790862\pi\)
0.261260 + 0.965268i \(0.415862\pi\)
\(42\) 2204.64 + 3368.33i 1.24980 + 1.90948i
\(43\) −105.156 86.2993i −0.0568718 0.0466735i 0.605528 0.795824i \(-0.292962\pi\)
−0.662400 + 0.749151i \(0.730462\pi\)
\(44\) −1663.33 + 2974.49i −0.859157 + 1.53641i
\(45\) −714.688 + 1337.09i −0.352932 + 0.660290i
\(46\) 1230.52 360.543i 0.581533 0.170389i
\(47\) 903.327 2180.82i 0.408930 0.987245i −0.576490 0.817104i \(-0.695578\pi\)
0.985420 0.170140i \(-0.0544221\pi\)
\(48\) −2633.50 1539.06i −1.14301 0.667994i
\(49\) −4373.23 + 1811.45i −1.82142 + 0.754457i
\(50\) 16.6222 + 20.6513i 0.00664889 + 0.00826051i
\(51\) 1221.32 + 4026.15i 0.469557 + 1.54792i
\(52\) −1101.14 + 3396.26i −0.407227 + 1.25601i
\(53\) −56.3753 572.388i −0.0200695 0.203769i −0.999990 0.00438257i \(-0.998605\pi\)
0.979921 0.199387i \(-0.0638950\pi\)
\(54\) 177.350 + 938.094i 0.0608195 + 0.321706i
\(55\) 1033.32 5194.87i 0.341595 1.71731i
\(56\) 3547.14 4079.33i 1.13110 1.30081i
\(57\) −750.462 3772.83i −0.230982 1.16123i
\(58\) 1039.94 2444.68i 0.309138 0.726717i
\(59\) 5517.65 + 1673.76i 1.58508 + 0.480827i 0.955223 0.295887i \(-0.0956152\pi\)
0.629853 + 0.776715i \(0.283115\pi\)
\(60\) 4631.18 + 1013.05i 1.28644 + 0.281402i
\(61\) 1205.52 989.346i 0.323978 0.265882i −0.458319 0.888788i \(-0.651548\pi\)
0.782297 + 0.622906i \(0.214048\pi\)
\(62\) −345.590 661.597i −0.0899036 0.172112i
\(63\) 5149.77 1.29750
\(64\) −1026.69 + 3965.24i −0.250658 + 0.968076i
\(65\) 5548.95i 1.31336i
\(66\) 4700.12 + 8997.91i 1.07900 + 2.06564i
\(67\) 590.365 + 719.362i 0.131514 + 0.160250i 0.834604 0.550851i \(-0.185697\pi\)
−0.703090 + 0.711101i \(0.748197\pi\)
\(68\) 4756.39 3049.00i 1.02863 0.659386i
\(69\) 1108.75 3655.07i 0.232882 0.767710i
\(70\) −3288.81 + 7731.28i −0.671185 + 1.57781i
\(71\) 1946.01 387.085i 0.386036 0.0767874i 0.00174297 0.999998i \(-0.499445\pi\)
0.384293 + 0.923211i \(0.374445\pi\)
\(72\) −3492.26 + 1740.55i −0.673662 + 0.335755i
\(73\) 8342.29 + 1659.39i 1.56545 + 0.311388i 0.900283 0.435305i \(-0.143360\pi\)
0.665169 + 0.746693i \(0.268360\pi\)
\(74\) −62.8847 332.630i −0.0114837 0.0607432i
\(75\) 78.5864 7.74008i 0.0139709 0.00137601i
\(76\) −4601.06 + 2348.02i −0.796583 + 0.406513i
\(77\) −17216.5 + 5222.56i −2.90377 + 0.880849i
\(78\) 6668.42 + 8284.78i 1.09606 + 1.36173i
\(79\) −638.154 1540.64i −0.102252 0.246858i 0.864472 0.502682i \(-0.167653\pi\)
−0.966723 + 0.255824i \(0.917653\pi\)
\(80\) −382.798 6354.46i −0.0598121 0.992884i
\(81\) 7189.90 + 2978.16i 1.09585 + 0.453918i
\(82\) 4117.41 1206.40i 0.612345 0.179417i
\(83\) −4543.68 2428.65i −0.659556 0.352540i 0.107422 0.994214i \(-0.465741\pi\)
−0.766978 + 0.641673i \(0.778241\pi\)
\(84\) −4380.72 15495.4i −0.620850 2.19606i
\(85\) −5570.48 + 6787.65i −0.771001 + 0.939468i
\(86\) 297.994 + 455.286i 0.0402913 + 0.0615584i
\(87\) −4396.56 6579.92i −0.580864 0.869324i
\(88\) 9910.00 9360.55i 1.27970 1.20875i
\(89\) −8281.33 + 12393.9i −1.04549 + 1.56469i −0.241176 + 0.970481i \(0.577533\pi\)
−0.804314 + 0.594205i \(0.797467\pi\)
\(90\) 4328.75 4247.26i 0.534413 0.524353i
\(91\) −16622.6 + 8884.97i −2.00732 + 1.07293i
\(92\) −5128.09 97.4627i −0.605871 0.0115150i
\(93\) −2212.70 217.932i −0.255833 0.0251974i
\(94\) −6059.04 + 7241.54i −0.685722 + 0.819550i
\(95\) 5676.85 5676.85i 0.629013 0.629013i
\(96\) 8207.96 + 9027.40i 0.890621 + 0.979536i
\(97\) 8113.61 8113.61i 0.862325 0.862325i −0.129283 0.991608i \(-0.541268\pi\)
0.991608 + 0.129283i \(0.0412676\pi\)
\(98\) 18859.8 1676.76i 1.96375 0.174589i
\(99\) 12923.6 + 1272.86i 1.31860 + 0.129871i
\(100\) −38.7106 98.7212i −0.00387106 0.00987212i
\(101\) 9787.84 5231.71i 0.959498 0.512862i 0.0842012 0.996449i \(-0.473166\pi\)
0.875297 + 0.483587i \(0.160666\pi\)
\(102\) 159.904 16828.5i 0.0153694 1.61750i
\(103\) −2194.99 + 3285.04i −0.206899 + 0.309646i −0.920378 0.391031i \(-0.872119\pi\)
0.713479 + 0.700677i \(0.247119\pi\)
\(104\) 8269.45 11643.5i 0.764557 1.07650i
\(105\) 13904.1 + 20809.0i 1.26114 + 1.88744i
\(106\) −470.250 + 2252.06i −0.0418521 + 0.200432i
\(107\) −11537.7 + 14058.7i −1.00775 + 1.22794i −0.0342082 + 0.999415i \(0.510891\pi\)
−0.973538 + 0.228527i \(0.926609\pi\)
\(108\) 446.462 3792.66i 0.0382769 0.325159i
\(109\) −5776.64 3087.68i −0.486209 0.259884i 0.210029 0.977695i \(-0.432644\pi\)
−0.696238 + 0.717811i \(0.745144\pi\)
\(110\) −10164.4 + 18589.2i −0.840030 + 1.53629i
\(111\) −931.618 385.889i −0.0756122 0.0313196i
\(112\) −18422.7 + 11321.5i −1.46864 + 0.902540i
\(113\) −4456.33 10758.5i −0.348996 0.842551i −0.996739 0.0806921i \(-0.974287\pi\)
0.647743 0.761859i \(-0.275713\pi\)
\(114\) −1653.61 + 15297.8i −0.127240 + 1.17712i
\(115\) 7628.24 2314.00i 0.576805 0.174972i
\(116\) −6896.38 + 8084.96i −0.512513 + 0.600844i
\(117\) 13539.2 1333.50i 0.989060 0.0974139i
\(118\) −19054.2 12995.1i −1.36844 0.933291i
\(119\) 29252.7 + 5818.73i 2.06573 + 0.410898i
\(120\) −16462.1 9411.98i −1.14320 0.653610i
\(121\) −30136.8 + 5994.57i −2.05838 + 0.409438i
\(122\) −5785.64 + 2332.33i −0.388715 + 0.156701i
\(123\) 3709.95 12230.1i 0.245221 0.808386i
\(124\) 526.728 + 2938.85i 0.0342565 + 0.191132i
\(125\) 9964.25 + 12141.5i 0.637712 + 0.777054i
\(126\) −19654.4 6166.62i −1.23799 0.388424i
\(127\) 30744.4i 1.90616i −0.302721 0.953079i \(-0.597895\pi\)
0.302721 0.953079i \(-0.402105\pi\)
\(128\) 8666.63 13904.1i 0.528969 0.848641i
\(129\) 1620.86 0.0974014
\(130\) −6644.63 + 21177.9i −0.393173 + 1.25313i
\(131\) −5181.96 + 4252.73i −0.301962 + 0.247814i −0.773156 0.634216i \(-0.781323\pi\)
0.471194 + 0.882029i \(0.343823\pi\)
\(132\) −7163.65 39969.2i −0.411137 2.29392i
\(133\) −26095.5 7915.98i −1.47524 0.447508i
\(134\) −1391.76 3452.42i −0.0775093 0.192271i
\(135\) 1157.91 + 5821.18i 0.0635339 + 0.319406i
\(136\) −21804.1 + 5941.11i −1.17885 + 0.321211i
\(137\) 3385.98 17022.5i 0.180403 0.906946i −0.779455 0.626458i \(-0.784504\pi\)
0.959858 0.280487i \(-0.0904961\pi\)
\(138\) −8608.39 + 12622.1i −0.452027 + 0.662785i
\(139\) 439.943 + 4466.81i 0.0227702 + 0.231189i 0.999834 + 0.0182410i \(0.00580663\pi\)
−0.977063 + 0.212948i \(0.931693\pi\)
\(140\) 21809.8 25568.7i 1.11274 1.30452i
\(141\) 8164.42 + 26914.5i 0.410664 + 1.35378i
\(142\) −7890.57 852.927i −0.391319 0.0422995i
\(143\) −43911.4 + 18188.7i −2.14736 + 0.889466i
\(144\) 15412.6 2461.09i 0.743280 0.118687i
\(145\) 6320.38 15258.7i 0.300612 0.725743i
\(146\) −29851.8 16322.7i −1.40044 0.765747i
\(147\) 26587.0 49740.8i 1.23037 2.30186i
\(148\) −158.307 + 1344.80i −0.00722729 + 0.0613953i
\(149\) −4457.58 3658.24i −0.200783 0.164778i 0.528629 0.848853i \(-0.322706\pi\)
−0.729412 + 0.684075i \(0.760206\pi\)
\(150\) −309.198 64.5633i −0.0137421 0.00286948i
\(151\) 19993.8 13359.4i 0.876884 0.585915i −0.0336114 0.999435i \(-0.510701\pi\)
0.910495 + 0.413520i \(0.135701\pi\)
\(152\) 20371.9 3451.78i 0.881746 0.149402i
\(153\) −17900.3 11960.6i −0.764676 0.510940i
\(154\) 71961.4 + 683.774i 3.03430 + 0.0288318i
\(155\) −2187.44 4092.40i −0.0910483 0.170339i
\(156\) −15529.7 39604.5i −0.638139 1.62740i
\(157\) −1590.16 + 16145.2i −0.0645122 + 0.655004i 0.907497 + 0.420059i \(0.137991\pi\)
−0.972009 + 0.234944i \(0.924509\pi\)
\(158\) 590.702 + 6644.10i 0.0236621 + 0.266147i
\(159\) 4845.83 + 4845.83i 0.191679 + 0.191679i
\(160\) −6148.21 + 24710.5i −0.240165 + 0.965255i
\(161\) −19146.2 19146.2i −0.738637 0.738637i
\(162\) −23874.5 19975.9i −0.909711 0.761160i
\(163\) −3443.94 + 34967.0i −0.129623 + 1.31608i 0.681765 + 0.731572i \(0.261213\pi\)
−0.811387 + 0.584509i \(0.801287\pi\)
\(164\) −17158.9 326.116i −0.637973 0.0121251i
\(165\) 29749.7 + 55657.8i 1.09274 + 2.04437i
\(166\) 14433.0 + 14709.9i 0.523771 + 0.533820i
\(167\) 38941.0 + 26019.5i 1.39628 + 0.932967i 0.999889 + 0.0148867i \(0.00473876\pi\)
0.396395 + 0.918080i \(0.370261\pi\)
\(168\) −1835.78 + 64384.7i −0.0650434 + 2.28120i
\(169\) −17654.1 + 11796.1i −0.618120 + 0.413015i
\(170\) 29388.0 19235.0i 1.01688 0.665573i
\(171\) 15215.5 + 12487.1i 0.520349 + 0.427039i
\(172\) −592.127 2094.46i −0.0200151 0.0707970i
\(173\) 13126.8 24558.6i 0.438600 0.820562i −0.561376 0.827561i \(-0.689728\pi\)
0.999976 + 0.00699877i \(0.00222779\pi\)
\(174\) 8900.56 + 30377.3i 0.293981 + 1.00335i
\(175\) 214.225 517.186i 0.00699511 0.0168877i
\(176\) −49030.9 + 23858.3i −1.58287 + 0.770218i
\(177\) −63471.7 + 26290.9i −2.02597 + 0.839186i
\(178\) 46447.3 37385.4i 1.46595 1.17995i
\(179\) −16352.3 53906.4i −0.510356 1.68242i −0.711360 0.702828i \(-0.751920\pi\)
0.201004 0.979590i \(-0.435580\pi\)
\(180\) −21606.8 + 11026.4i −0.666877 + 0.340321i
\(181\) 2985.45 + 30311.8i 0.0911281 + 0.925239i 0.926686 + 0.375837i \(0.122645\pi\)
−0.835558 + 0.549402i \(0.814855\pi\)
\(182\) 74080.5 14005.1i 2.23646 0.422810i
\(183\) −3625.11 + 18224.6i −0.108248 + 0.544198i
\(184\) 19455.0 + 6512.64i 0.574638 + 0.192363i
\(185\) −410.570 2064.08i −0.0119962 0.0603090i
\(186\) 8183.94 + 3481.36i 0.236557 + 0.100629i
\(187\) 71973.0 + 21832.8i 2.05819 + 0.624347i
\(188\) 31796.1 20382.3i 0.899618 0.576684i
\(189\) 15584.1 12789.5i 0.436272 0.358039i
\(190\) −28463.8 + 14868.2i −0.788470 + 0.411862i
\(191\) 39753.1 1.08969 0.544847 0.838535i \(-0.316588\pi\)
0.544847 + 0.838535i \(0.316588\pi\)
\(192\) −20516.2 44282.3i −0.556538 1.20123i
\(193\) 21565.7i 0.578960i −0.957184 0.289480i \(-0.906518\pi\)
0.957184 0.289480i \(-0.0934823\pi\)
\(194\) −40681.7 + 21250.4i −1.08093 + 0.564629i
\(195\) 41943.6 + 51108.4i 1.10305 + 1.34407i
\(196\) −73987.4 16184.4i −1.92595 0.421292i
\(197\) 14217.0 46867.3i 0.366334 1.20764i −0.559219 0.829020i \(-0.688899\pi\)
0.925552 0.378620i \(-0.123601\pi\)
\(198\) −47799.5 20333.4i −1.21925 0.518657i
\(199\) 31385.5 6242.96i 0.792543 0.157647i 0.217814 0.975990i \(-0.430107\pi\)
0.574729 + 0.818344i \(0.305107\pi\)
\(200\) 29.5271 + 423.129i 0.000738177 + 0.0105782i
\(201\) −10875.1 2163.18i −0.269178 0.0535429i
\(202\) −43620.6 + 8246.60i −1.06903 + 0.202103i
\(203\) −55829.7 + 5498.74i −1.35479 + 0.133436i
\(204\) −20761.7 + 64035.4i −0.498887 + 1.53872i
\(205\) 25524.6 7742.80i 0.607366 0.184243i
\(206\) 12311.0 9909.13i 0.290107 0.233508i
\(207\) 7479.26 + 18056.5i 0.174549 + 0.421399i
\(208\) −45503.3 + 34535.6i −1.05176 + 0.798253i
\(209\) −63531.3 26315.5i −1.45444 0.602448i
\(210\) −28148.0 96068.2i −0.638276 2.17842i
\(211\) 24377.5 + 13030.1i 0.547551 + 0.292672i 0.721884 0.692015i \(-0.243277\pi\)
−0.174332 + 0.984687i \(0.555777\pi\)
\(212\) 4491.48 8032.00i 0.0999349 0.178711i
\(213\) −14997.7 + 18274.8i −0.330572 + 0.402803i
\(214\) 60868.9 39840.0i 1.32913 0.869944i
\(215\) 1879.37 + 2812.68i 0.0406570 + 0.0608476i
\(216\) −6245.49 + 13940.3i −0.133862 + 0.298788i
\(217\) −8756.81 + 13105.5i −0.185963 + 0.278313i
\(218\) 18349.5 + 18701.6i 0.386111 + 0.393519i
\(219\) −89379.3 + 47774.3i −1.86358 + 0.996106i
\(220\) 61052.6 58775.2i 1.26142 1.21436i
\(221\) 78415.0 + 7723.20i 1.60552 + 0.158129i
\(222\) 3093.49 + 2588.34i 0.0627686 + 0.0525188i
\(223\) −58724.8 + 58724.8i −1.18090 + 1.18090i −0.201385 + 0.979512i \(0.564544\pi\)
−0.979512 + 0.201385i \(0.935456\pi\)
\(224\) 83868.1 21148.7i 1.67148 0.421489i
\(225\) −285.718 + 285.718i −0.00564381 + 0.00564381i
\(226\) 4124.97 + 46396.8i 0.0807613 + 0.908388i
\(227\) −96152.1 9470.16i −1.86598 0.183783i −0.898883 0.438188i \(-0.855620\pi\)
−0.967098 + 0.254405i \(0.918120\pi\)
\(228\) 24629.6 56404.9i 0.473792 1.08504i
\(229\) −40094.7 + 21431.0i −0.764567 + 0.408670i −0.807092 0.590426i \(-0.798960\pi\)
0.0425247 + 0.999095i \(0.486460\pi\)
\(230\) −31884.5 302.965i −0.602732 0.00572714i
\(231\) 119095. 178238.i 2.23187 3.34024i
\(232\) 36001.8 22598.6i 0.668880 0.419861i
\(233\) 14939.4 + 22358.5i 0.275184 + 0.411842i 0.943159 0.332342i \(-0.107839\pi\)
−0.667975 + 0.744183i \(0.732839\pi\)
\(234\) −53270.1 11123.3i −0.972863 0.203143i
\(235\) −37238.2 + 45374.9i −0.674300 + 0.821637i
\(236\) 57160.2 + 72413.2i 1.02629 + 1.30015i
\(237\) 17523.1 + 9366.30i 0.311971 + 0.166752i
\(238\) −104677. 57236.4i −1.84798 1.01046i
\(239\) 13762.3 + 5700.54i 0.240933 + 0.0997976i 0.499883 0.866093i \(-0.333376\pi\)
−0.258950 + 0.965891i \(0.583376\pi\)
\(240\) 51558.0 + 55634.0i 0.895104 + 0.965867i
\(241\) 33883.7 + 81802.4i 0.583387 + 1.40842i 0.889725 + 0.456497i \(0.150896\pi\)
−0.306338 + 0.951923i \(0.599104\pi\)
\(242\) 122197. + 13208.8i 2.08655 + 0.225545i
\(243\) −70233.2 + 21305.0i −1.18941 + 0.360802i
\(244\) 24874.1 1973.44i 0.417799 0.0331470i
\(245\) 117143. 11537.6i 1.95157 0.192213i
\(246\) −28804.2 + 42234.3i −0.475977 + 0.697903i
\(247\) −70657.3 14054.6i −1.15815 0.230369i
\(248\) 1508.86 11847.0i 0.0245327 0.192622i
\(249\) 60207.1 11975.9i 0.971067 0.193157i
\(250\) −23490.2 58270.4i −0.375844 0.932326i
\(251\) −11596.9 + 38230.0i −0.184076 + 0.606816i 0.815530 + 0.578715i \(0.196446\pi\)
−0.999605 + 0.0281004i \(0.991054\pi\)
\(252\) 67627.8 + 47070.5i 1.06494 + 0.741221i
\(253\) −43316.0 52780.7i −0.676718 0.824583i
\(254\) −36815.1 + 117338.i −0.570635 + 1.81874i
\(255\) 104624.i 1.60898i
\(256\) −49726.3 + 42688.0i −0.758763 + 0.651367i
\(257\) −44547.6 −0.674463 −0.337231 0.941422i \(-0.609490\pi\)
−0.337231 + 0.941422i \(0.609490\pi\)
\(258\) −6186.09 1940.90i −0.0929344 0.0291585i
\(259\) −5525.80 + 4534.91i −0.0823751 + 0.0676035i
\(260\) 50719.2 72870.0i 0.750284 1.07796i
\(261\) 38749.6 + 11754.6i 0.568835 + 0.172554i
\(262\) 24869.7 10025.6i 0.362300 0.146052i
\(263\) 12116.3 + 60913.0i 0.175170 + 0.880640i 0.963974 + 0.265995i \(0.0857005\pi\)
−0.788804 + 0.614644i \(0.789299\pi\)
\(264\) −20520.9 + 161123.i −0.294435 + 2.31180i
\(265\) −2790.28 + 14027.7i −0.0397334 + 0.199753i
\(266\) 90115.8 + 61459.9i 1.27361 + 0.868618i
\(267\) −17408.4 176750.i −0.244195 2.47935i
\(268\) 1177.60 + 14842.9i 0.0163956 + 0.206657i
\(269\) −16308.3 53761.1i −0.225374 0.742957i −0.994582 0.103959i \(-0.966849\pi\)
0.769208 0.638998i \(-0.220651\pi\)
\(270\) 2551.40 23603.4i 0.0349986 0.323778i
\(271\) 36127.1 14964.3i 0.491920 0.203760i −0.122913 0.992418i \(-0.539223\pi\)
0.614833 + 0.788657i \(0.289223\pi\)
\(272\) 90330.7 + 3434.82i 1.22095 + 0.0464266i
\(273\) 85941.9 207482.i 1.15313 2.78391i
\(274\) −33306.4 + 60912.6i −0.443636 + 0.811346i
\(275\) 665.442 1244.95i 0.00879923 0.0164622i
\(276\) 47968.8 37864.7i 0.629710 0.497069i
\(277\) 38983.5 + 31992.9i 0.508067 + 0.416960i 0.853192 0.521597i \(-0.174663\pi\)
−0.345125 + 0.938557i \(0.612163\pi\)
\(278\) 3669.74 17574.6i 0.0474839 0.227403i
\(279\) 9459.64 6320.73i 0.121525 0.0812005i
\(280\) −113856. + 71468.0i −1.45224 + 0.911581i
\(281\) −54423.0 36364.3i −0.689239 0.460535i 0.160984 0.986957i \(-0.448533\pi\)
−0.850223 + 0.526422i \(0.823533\pi\)
\(282\) 1068.94 112497.i 0.0134418 1.41463i
\(283\) −35394.6 66218.6i −0.441941 0.826813i 0.558055 0.829804i \(-0.311548\pi\)
−0.999996 + 0.00299126i \(0.999048\pi\)
\(284\) 29093.4 + 12703.8i 0.360710 + 0.157507i
\(285\) −9376.05 + 95196.6i −0.115433 + 1.17201i
\(286\) 189370. 16836.2i 2.31515 0.205832i
\(287\) −64064.4 64064.4i −0.777774 0.777774i
\(288\) −61770.3 9063.09i −0.744723 0.109268i
\(289\) −29108.2 29108.2i −0.348513 0.348513i
\(290\) −42393.7 + 50667.5i −0.504087 + 0.602467i
\(291\) −13400.7 + 136059.i −0.158249 + 1.60673i
\(292\) 94385.4 + 98042.6i 1.10698 + 1.14987i
\(293\) −13001.9 24324.9i −0.151451 0.283345i 0.794742 0.606947i \(-0.207606\pi\)
−0.946193 + 0.323602i \(0.895106\pi\)
\(294\) −161033. + 158002.i −1.86303 + 1.82796i
\(295\) −119218. 79658.7i −1.36992 0.915354i
\(296\) 2214.53 4942.95i 0.0252754 0.0564160i
\(297\) 42270.2 28244.0i 0.479205 0.320194i
\(298\) 12632.0 + 19299.6i 0.142246 + 0.217329i
\(299\) −55295.0 45379.4i −0.618506 0.507594i
\(300\) 1102.76 + 616.660i 0.0122529 + 0.00685178i
\(301\) 5416.50 10133.6i 0.0597841 0.111848i
\(302\) −92304.9 + 27045.4i −1.01207 + 0.296537i
\(303\) −50604.9 + 122171.i −0.551197 + 1.33071i
\(304\) −81883.7 11220.5i −0.886034 0.121413i
\(305\) −35828.6 + 14840.7i −0.385150 + 0.159534i
\(306\) 53995.2 + 67083.1i 0.576650 + 0.716424i
\(307\) 25566.2 + 84280.6i 0.271263 + 0.894234i 0.981694 + 0.190467i \(0.0610001\pi\)
−0.710431 + 0.703767i \(0.751500\pi\)
\(308\) −273826. 88780.2i −2.88651 0.935868i
\(309\) −4614.15 46848.3i −0.0483253 0.490655i
\(310\) 3448.00 + 18238.2i 0.0358793 + 0.189784i
\(311\) −25583.8 + 128618.i −0.264511 + 1.32979i 0.588755 + 0.808312i \(0.299618\pi\)
−0.853266 + 0.521476i \(0.825382\pi\)
\(312\) 11845.5 + 169749.i 0.121687 + 1.74380i
\(313\) −7049.77 35441.6i −0.0719592 0.361763i 0.927982 0.372626i \(-0.121542\pi\)
−0.999941 + 0.0108622i \(0.996542\pi\)
\(314\) 25402.1 59714.9i 0.257638 0.605652i
\(315\) −122546. 37173.8i −1.23503 0.374642i
\(316\) 5701.57 26064.9i 0.0570979 0.261025i
\(317\) 77107.2 63280.2i 0.767320 0.629723i −0.167082 0.985943i \(-0.553435\pi\)
0.934402 + 0.356220i \(0.115935\pi\)
\(318\) −12691.7 24297.0i −0.125506 0.240270i
\(319\) −141467. −1.39018
\(320\) 53054.8 86946.9i 0.518113 0.849091i
\(321\) 216698.i 2.10303i
\(322\) 50145.8 + 95999.3i 0.483641 + 0.925884i
\(323\) 72321.0 + 88123.4i 0.693202 + 0.844669i
\(324\) 67198.0 + 104828.i 0.640127 + 0.998587i
\(325\) 429.297 1415.20i 0.00406435 0.0133984i
\(326\) 55015.4 129329.i 0.517665 1.21692i
\(327\) 76544.8 15225.7i 0.715847 0.142391i
\(328\) 65097.5 + 21791.7i 0.605085 + 0.202555i
\(329\) 195552. + 38897.7i 1.80664 + 0.359362i
\(330\) −46893.7 248045.i −0.430613 2.27773i
\(331\) −82582.3 + 8133.65i −0.753757 + 0.0742386i −0.467595 0.883943i \(-0.654879\pi\)
−0.286162 + 0.958181i \(0.592379\pi\)
\(332\) −37469.9 73424.2i −0.339944 0.666136i
\(333\) 4937.60 1497.81i 0.0445274 0.0135073i
\(334\) −117463. 145935.i −1.05295 1.30818i
\(335\) −8855.78 21379.7i −0.0789109 0.190508i
\(336\) 84104.2 243530.i 0.744971 2.15711i
\(337\) −47070.7 19497.3i −0.414468 0.171678i 0.165698 0.986177i \(-0.447012\pi\)
−0.580166 + 0.814498i \(0.697012\pi\)
\(338\) 81503.3 23880.5i 0.713414 0.209031i
\(339\) 122367. + 65406.4i 1.06479 + 0.569142i
\(340\) −135194. + 38220.8i −1.16950 + 0.330630i
\(341\) −25214.9 + 30724.5i −0.216845 + 0.264226i
\(342\) −43118.2 65877.5i −0.368645 0.563229i
\(343\) −109460. 163818.i −0.930391 1.39243i
\(344\) −248.137 + 8702.66i −0.00209688 + 0.0735420i
\(345\) −52768.5 + 78973.6i −0.443339 + 0.663504i
\(346\) −79507.2 + 78010.5i −0.664132 + 0.651629i
\(347\) −56437.0 + 30166.2i −0.468711 + 0.250531i −0.688804 0.724948i \(-0.741864\pi\)
0.220093 + 0.975479i \(0.429364\pi\)
\(348\) 2406.01 126595.i 0.0198673 1.04534i
\(349\) 187807. + 18497.4i 1.54192 + 0.151866i 0.832939 0.553365i \(-0.186657\pi\)
0.708978 + 0.705231i \(0.249157\pi\)
\(350\) −1436.91 + 1717.34i −0.0117299 + 0.0140191i
\(351\) 37660.3 37660.3i 0.305681 0.305681i
\(352\) 215699. 32344.0i 1.74085 0.261041i
\(353\) −97689.8 + 97689.8i −0.783971 + 0.783971i −0.980498 0.196528i \(-0.937033\pi\)
0.196528 + 0.980498i \(0.437033\pi\)
\(354\) 273726. 24335.9i 2.18428 0.194196i
\(355\) −49102.0 4836.13i −0.389621 0.0383744i
\(356\) −222036. + 87065.0i −1.75196 + 0.686979i
\(357\) −313414. + 167523.i −2.45913 + 1.31443i
\(358\) −2140.96 + 225318.i −0.0167049 + 1.75804i
\(359\) 13575.9 20317.8i 0.105337 0.157648i −0.775056 0.631892i \(-0.782279\pi\)
0.880393 + 0.474244i \(0.157279\pi\)
\(360\) 95667.2 16209.7i 0.738173 0.125075i
\(361\) 14495.2 + 21693.6i 0.111227 + 0.166463i
\(362\) 24902.9 119261.i 0.190034 0.910087i
\(363\) 232261. 283011.i 1.76264 2.14778i
\(364\) −299503. 35256.7i −2.26047 0.266096i
\(365\) −186538. 99706.4i −1.40017 0.748406i
\(366\) 35658.6 65214.5i 0.266197 0.486835i
\(367\) 121468. + 50313.8i 0.901843 + 0.373556i 0.784928 0.619586i \(-0.212700\pi\)
0.116914 + 0.993142i \(0.462700\pi\)
\(368\) −66452.3 48152.3i −0.490698 0.355567i
\(369\) 25026.1 + 60418.3i 0.183798 + 0.443727i
\(370\) −904.676 + 8369.30i −0.00660830 + 0.0611344i
\(371\) 46489.5 14102.4i 0.337759 0.102458i
\(372\) −27065.7 23086.7i −0.195584 0.166831i
\(373\) −8566.66 + 843.742i −0.0615735 + 0.00606446i −0.128757 0.991676i \(-0.541099\pi\)
0.0671835 + 0.997741i \(0.478599\pi\)
\(374\) −248545. 169511.i −1.77690 1.21186i
\(375\) −183551. 36510.5i −1.30525 0.259630i
\(376\) −145758. + 39715.9i −1.03100 + 0.280924i
\(377\) −145358. + 28913.5i −1.02272 + 0.203431i
\(378\) −74792.3 + 30150.7i −0.523448 + 0.211015i
\(379\) −27595.6 + 90970.6i −0.192115 + 0.633319i 0.806971 + 0.590591i \(0.201105\pi\)
−0.999087 + 0.0427288i \(0.986395\pi\)
\(380\) 126438. 22661.3i 0.875607 0.156934i
\(381\) 232392. + 283170.i 1.60092 + 1.95073i
\(382\) −151720. 47602.6i −1.03972 0.326215i
\(383\) 227395.i 1.55018i 0.631849 + 0.775092i \(0.282296\pi\)
−0.631849 + 0.775092i \(0.717704\pi\)
\(384\) 25275.3 + 193573.i 0.171409 + 1.31275i
\(385\) 447388. 3.01830
\(386\) −25823.9 + 82306.6i −0.173320 + 0.552408i
\(387\) −6411.19 + 5261.53i −0.0428072 + 0.0351309i
\(388\) 180711. 32388.6i 1.20038 0.215144i
\(389\) −78869.3 23924.8i −0.521206 0.158106i 0.0187103 0.999825i \(-0.494044\pi\)
−0.539916 + 0.841719i \(0.681544\pi\)
\(390\) −98880.0 245284.i −0.650098 1.61265i
\(391\) 22083.1 + 111019.i 0.144446 + 0.726180i
\(392\) 262997. + 150365.i 1.71151 + 0.978532i
\(393\) 15582.6 78339.1i 0.100892 0.507217i
\(394\) −110382. + 161847.i −0.711057 + 1.04259i
\(395\) 4064.55 + 41268.1i 0.0260507 + 0.264497i
\(396\) 158081. + 134841.i 1.00807 + 0.859870i
\(397\) −807.694 2662.61i −0.00512467 0.0168938i 0.954341 0.298720i \(-0.0965597\pi\)
−0.959465 + 0.281826i \(0.909060\pi\)
\(398\) −127260. 13756.1i −0.803390 0.0868420i
\(399\) 300187. 124341.i 1.88558 0.781034i
\(400\) 393.987 1650.25i 0.00246242 0.0103141i
\(401\) −49962.1 + 120619.i −0.310707 + 0.750114i 0.688972 + 0.724788i \(0.258062\pi\)
−0.999679 + 0.0253260i \(0.991938\pi\)
\(402\) 38915.0 + 21278.3i 0.240805 + 0.131670i
\(403\) −19628.9 + 36723.1i −0.120861 + 0.226115i
\(404\) 176355. + 20760.1i 1.08050 + 0.127194i
\(405\) −149595. 122770.i −0.912028 0.748482i
\(406\) 219662. + 45867.3i 1.33261 + 0.278260i
\(407\) −14988.2 + 10014.8i −0.0904815 + 0.0604578i
\(408\) 155918. 219534.i 0.936645 1.31881i
\(409\) 180482. + 120594.i 1.07892 + 0.720909i 0.962224 0.272259i \(-0.0877709\pi\)
0.116692 + 0.993168i \(0.462771\pi\)
\(410\) −106688. 1013.74i −0.634668 0.00603059i
\(411\) 97483.4 + 182379.i 0.577095 + 1.07967i
\(412\) −58851.4 + 23076.9i −0.346707 + 0.135951i
\(413\) −47736.9 + 484681.i −0.279869 + 2.84156i
\(414\) −6923.12 77869.9i −0.0403925 0.454327i
\(415\) 90591.7 + 90591.7i 0.526008 + 0.526008i
\(416\) 215021. 77318.9i 1.24249 0.446786i
\(417\) −37815.9 37815.9i −0.217472 0.217472i
\(418\) 210959. + 176511.i 1.20739 + 1.01023i
\(419\) −11760.5 + 119407.i −0.0669883 + 0.680144i 0.901783 + 0.432189i \(0.142259\pi\)
−0.968772 + 0.247955i \(0.920241\pi\)
\(420\) −7609.01 + 400356.i −0.0431350 + 2.26959i
\(421\) −131308. 245661.i −0.740846 1.38603i −0.915876 0.401462i \(-0.868502\pi\)
0.175029 0.984563i \(-0.443998\pi\)
\(422\) −77435.3 78921.0i −0.434825 0.443167i
\(423\) −119662. 79955.6i −0.668768 0.446856i
\(424\) −26759.9 + 25276.2i −0.148852 + 0.140599i
\(425\) −1945.82 + 1300.16i −0.0107727 + 0.00719810i
\(426\) 79122.8 51787.6i 0.435996 0.285369i
\(427\) 101826. + 83566.3i 0.558473 + 0.458327i
\(428\) −280016. + 79163.7i −1.52861 + 0.432154i
\(429\) 266959. 499445.i 1.45054 2.71377i
\(430\) −3804.67 12985.2i −0.0205769 0.0702283i
\(431\) −82969.4 + 200306.i −0.446646 + 1.07830i 0.526924 + 0.849912i \(0.323345\pi\)
−0.973570 + 0.228387i \(0.926655\pi\)
\(432\) 40529.1 45725.1i 0.217170 0.245012i
\(433\) 101468. 42029.3i 0.541193 0.224169i −0.0953047 0.995448i \(-0.530383\pi\)
0.636498 + 0.771279i \(0.280383\pi\)
\(434\) 49114.1 39531.9i 0.260751 0.209879i
\(435\) 57124.6 + 188315.i 0.301887 + 0.995189i
\(436\) −47637.7 93348.4i −0.250598 0.491059i
\(437\) −10144.1 102995.i −0.0531191 0.539327i
\(438\) 398329. 75305.3i 2.07632 0.392534i
\(439\) 67275.8 338218.i 0.349084 1.75496i −0.263596 0.964633i \(-0.584909\pi\)
0.612680 0.790331i \(-0.290091\pi\)
\(440\) −303391. + 151211.i −1.56710 + 0.781048i
\(441\) 56302.5 + 283052.i 0.289501 + 1.45542i
\(442\) −290027. 123374.i −1.48455 0.631511i
\(443\) 211199. + 64066.5i 1.07618 + 0.326455i 0.778135 0.628097i \(-0.216166\pi\)
0.298044 + 0.954552i \(0.403666\pi\)
\(444\) −8707.05 13582.9i −0.0441677 0.0689009i
\(445\) 286531. 235150.i 1.44694 1.18748i
\(446\) 294447. 153806.i 1.48026 0.773222i
\(447\) 68708.4 0.343870
\(448\) −345412. 19713.3i −1.72100 0.0982208i
\(449\) 197158.i 0.977960i −0.872295 0.488980i \(-0.837369\pi\)
0.872295 0.488980i \(-0.162631\pi\)
\(450\) 1432.59 748.324i 0.00707453 0.00369543i
\(451\) −144938. 176608.i −0.712574 0.868273i
\(452\) 39815.0 182015.i 0.194881 0.890905i
\(453\) −83170.5 + 274176.i −0.405297 + 1.33608i
\(454\) 355630. + 151281.i 1.72539 + 0.733962i
\(455\) 459694. 91438.7i 2.22047 0.441680i
\(456\) −161543. + 185780.i −0.776887 + 0.893447i
\(457\) −250236. 49775.1i −1.19817 0.238330i −0.444617 0.895721i \(-0.646660\pi\)
−0.753550 + 0.657390i \(0.771660\pi\)
\(458\) 178686. 33781.2i 0.851844 0.161044i
\(459\) −83873.5 + 8260.82i −0.398107 + 0.0392101i
\(460\) 121326. + 39336.6i 0.573376 + 0.185901i
\(461\) 23289.7 7064.84i 0.109588 0.0332430i −0.235015 0.971992i \(-0.575514\pi\)
0.344602 + 0.938749i \(0.388014\pi\)
\(462\) −667966. + 537646.i −3.12947 + 2.51891i
\(463\) 2339.85 + 5648.90i 0.0109151 + 0.0263513i 0.929243 0.369469i \(-0.120460\pi\)
−0.918328 + 0.395820i \(0.870460\pi\)
\(464\) −164464. + 43138.2i −0.763896 + 0.200367i
\(465\) 51081.0 + 21158.5i 0.236240 + 0.0978539i
\(466\) −30244.0 103222.i −0.139273 0.475334i
\(467\) 18259.8 + 9760.08i 0.0837265 + 0.0447527i 0.512729 0.858551i \(-0.328635\pi\)
−0.429002 + 0.903303i \(0.641135\pi\)
\(468\) 189989. + 106241.i 0.867433 + 0.485066i
\(469\) −49865.9 + 60761.8i −0.226704 + 0.276239i
\(470\) 196456. 128585.i 0.889344 0.582095i
\(471\) −107393. 160724.i −0.484097 0.724502i
\(472\) −131443. 344816.i −0.590004 1.54776i
\(473\) 16097.7 24091.9i 0.0719517 0.107683i
\(474\) −55662.2 56730.2i −0.247744 0.252498i
\(475\) 1887.01 1008.63i 0.00836349 0.00447038i
\(476\) 330968. + 343792.i 1.46074 + 1.51734i
\(477\) −34897.6 3437.11i −0.153376 0.0151063i
\(478\) −45698.5 38236.2i −0.200007 0.167347i
\(479\) −170673. + 170673.i −0.743862 + 0.743862i −0.973319 0.229456i \(-0.926305\pi\)
0.229456 + 0.973319i \(0.426305\pi\)
\(480\) −130155. 274069.i −0.564908 1.18953i
\(481\) −13353.6 + 13353.6i −0.0577175 + 0.0577175i
\(482\) −31364.1 352778.i −0.135002 1.51847i
\(483\) 321068. + 31622.5i 1.37627 + 0.135551i
\(484\) −450554. 196738.i −1.92334 0.839840i
\(485\) −251643. + 134506.i −1.06980 + 0.571817i
\(486\) 293561. + 2789.40i 1.24287 + 0.0118097i
\(487\) 87449.0 130877.i 0.368720 0.551829i −0.599995 0.800004i \(-0.704831\pi\)
0.968715 + 0.248175i \(0.0798307\pi\)
\(488\) −97296.4 22253.9i −0.408561 0.0934471i
\(489\) −232589. 348094.i −0.972683 1.45572i
\(490\) −460898. 96239.7i −1.91961 0.400832i
\(491\) −270755. + 329916.i −1.12309 + 1.36849i −0.201881 + 0.979410i \(0.564705\pi\)
−0.921206 + 0.389075i \(0.872795\pi\)
\(492\) 160507. 126698.i 0.663075 0.523406i
\(493\) 206832. + 110554.i 0.850988 + 0.454862i
\(494\) 252838. + 138249.i 1.03607 + 0.566511i
\(495\) −298346. 123579.i −1.21762 0.504353i
\(496\) −19944.9 + 43408.0i −0.0810717 + 0.176444i
\(497\) 64134.8 + 154835.i 0.259646 + 0.626840i
\(498\) −244125. 26388.5i −0.984357 0.106404i
\(499\) 71669.4 21740.7i 0.287828 0.0873115i −0.143069 0.989713i \(-0.545697\pi\)
0.430897 + 0.902401i \(0.358197\pi\)
\(500\) 19875.6 + 250521.i 0.0795025 + 1.00208i
\(501\) −555341. + 54696.3i −2.21251 + 0.217913i
\(502\) 90039.1 132020.i 0.357292 0.523881i
\(503\) 102961. + 20480.2i 0.406945 + 0.0809465i 0.394319 0.918974i \(-0.370981\pi\)
0.0126268 + 0.999920i \(0.495981\pi\)
\(504\) −201740. 260629.i −0.794204 1.02603i
\(505\) −270680. + 53841.6i −1.06139 + 0.211123i
\(506\) 102115. + 253310.i 0.398832 + 0.989352i
\(507\) 73437.9 242092.i 0.285696 0.941813i
\(508\) 281014. 403742.i 1.08893 1.56450i
\(509\) −196584. 239538.i −0.758772 0.924567i 0.240161 0.970733i \(-0.422800\pi\)
−0.998934 + 0.0461661i \(0.985300\pi\)
\(510\) −125282. + 399302.i −0.481670 + 1.53519i
\(511\) 718447.i 2.75140i
\(512\) 240900. 103376.i 0.918961 0.394349i
\(513\) 77056.5 0.292802
\(514\) 170018. + 53343.8i 0.643531 + 0.201910i
\(515\) 75945.9 62327.2i 0.286345 0.234997i
\(516\) 21285.4 + 14815.1i 0.0799434 + 0.0556424i
\(517\) 481134. + 145950.i 1.80005 + 0.546039i
\(518\) 26519.9 10690.8i 0.0988353 0.0398430i
\(519\) 64730.0 + 325420.i 0.240309 + 1.20812i
\(520\) −280831. + 217378.i −1.03858 + 0.803914i
\(521\) −16777.5 + 84346.3i −0.0618091 + 0.310735i −0.999306 0.0372593i \(-0.988137\pi\)
0.937497 + 0.347995i \(0.113137\pi\)
\(522\) −133815. 91263.0i −0.491091 0.334930i
\(523\) −39398.3 400017.i −0.144037 1.46243i −0.747086 0.664727i \(-0.768548\pi\)
0.603049 0.797704i \(-0.293952\pi\)
\(524\) −106922. + 8482.89i −0.389407 + 0.0308945i
\(525\) 1936.20 + 6382.81i 0.00702478 + 0.0231576i
\(526\) 26697.9 246987.i 0.0964951 0.892692i
\(527\) 60876.3 25215.8i 0.219193 0.0907927i
\(528\) 271257. 590362.i 0.973000 2.11763i
\(529\) −67765.5 + 163600.i −0.242157 + 0.584619i
\(530\) 27446.8 50196.2i 0.0977102 0.178698i
\(531\) 165714. 310030.i 0.587721 1.09955i
\(532\) −270336. 342475.i −0.955171 1.21006i
\(533\) −185021. 151842.i −0.651277 0.534489i
\(534\) −145211. + 695424.i −0.509232 + 2.43875i
\(535\) 376038. 251260.i 1.31378 0.877842i
\(536\) 13279.4 58059.0i 0.0462220 0.202088i
\(537\) 558081. + 372898.i 1.93530 + 1.29313i
\(538\) −2135.19 + 224711.i −0.00737687 + 0.776353i
\(539\) −475280. 889186.i −1.63596 3.06066i
\(540\) −38001.6 + 87028.5i −0.130321 + 0.298452i
\(541\) 20445.2 207584.i 0.0698551 0.709250i −0.894929 0.446208i \(-0.852774\pi\)
0.964784 0.263042i \(-0.0847259\pi\)
\(542\) −155800. + 13851.6i −0.530359 + 0.0471522i
\(543\) −256619. 256619.i −0.870339 0.870339i
\(544\) −340639. 121276.i −1.15106 0.409806i
\(545\) 115174. + 115174.i 0.387760 + 0.387760i
\(546\) −576453. + 688955.i −1.93365 + 2.31103i
\(547\) −2963.42 + 30088.1i −0.00990419 + 0.100559i −0.998866 0.0476125i \(-0.984839\pi\)
0.988962 + 0.148171i \(0.0473387\pi\)
\(548\) 200056. 192593.i 0.666178 0.641328i
\(549\) −44820.9 83854.0i −0.148709 0.278214i
\(550\) −4030.47 + 3954.60i −0.0133239 + 0.0130731i
\(551\) −178288. 119128.i −0.587244 0.392384i
\(552\) −228417. + 87072.2i −0.749635 + 0.285760i
\(553\) 117116. 78254.3i 0.382970 0.255893i
\(554\) −110473. 168784.i −0.359944 0.549935i
\(555\) 19383.5 + 15907.7i 0.0629284 + 0.0516440i
\(556\) −35050.7 + 62680.3i −0.113383 + 0.202760i
\(557\) −41599.8 + 77827.7i −0.134085 + 0.250856i −0.939999 0.341177i \(-0.889174\pi\)
0.805914 + 0.592033i \(0.201674\pi\)
\(558\) −43672.0 + 12795.9i −0.140260 + 0.0410963i
\(559\) 11616.5 28044.7i 0.0371750 0.0897483i
\(560\) 520116. 136424.i 1.65853 0.435027i
\(561\) −827934. + 342942.i −2.63069 + 1.08967i
\(562\) 164164. + 203956.i 0.519762 + 0.645748i
\(563\) −47584.9 156866.i −0.150125 0.494895i 0.849332 0.527860i \(-0.177005\pi\)
−0.999457 + 0.0329642i \(0.989505\pi\)
\(564\) −138790. + 428072.i −0.436315 + 1.34573i
\(565\) 28383.4 + 288182.i 0.0889135 + 0.902754i
\(566\) 55791.5 + 295110.i 0.174155 + 0.921195i
\(567\) −128241. + 644711.i −0.398897 + 2.00539i
\(568\) −95824.5 83323.1i −0.297016 0.258267i
\(569\) −44234.1 222380.i −0.136626 0.686865i −0.987004 0.160693i \(-0.948627\pi\)
0.850379 0.526171i \(-0.176373\pi\)
\(570\) 149778. 352096.i 0.460997 1.08371i
\(571\) 230350. + 69876.0i 0.706507 + 0.214317i 0.623036 0.782193i \(-0.285899\pi\)
0.0834718 + 0.996510i \(0.473399\pi\)
\(572\) −742903. 162506.i −2.27060 0.496682i
\(573\) −366145. + 300487.i −1.11518 + 0.915201i
\(574\) 167791. + 321220.i 0.509267 + 0.974941i
\(575\) 2124.53 0.00642579
\(576\) 224897. + 108557.i 0.677858 + 0.327200i
\(577\) 168719.i 0.506770i 0.967365 + 0.253385i \(0.0815440\pi\)
−0.967365 + 0.253385i \(0.918456\pi\)
\(578\) 76237.2 + 145949.i 0.228198 + 0.436862i
\(579\) 163011. + 198630.i 0.486251 + 0.592498i
\(580\) 222470. 142611.i 0.661326 0.423931i
\(581\) 126324. 416434.i 0.374226 1.23366i
\(582\) 214070. 503232.i 0.631988 1.48567i
\(583\) 120154. 23900.0i 0.353508 0.0703171i
\(584\) −242825. 487207.i −0.711981 1.42853i
\(585\) −331810. 66001.1i −0.969567 0.192859i
\(586\) 20494.6 + 108407.i 0.0596821 + 0.315690i
\(587\) −280861. + 27662.4i −0.815108 + 0.0802812i −0.496975 0.867765i \(-0.665556\pi\)
−0.318133 + 0.948046i \(0.603056\pi\)
\(588\) 803793. 410192.i 2.32482 1.18641i
\(589\) −57650.8 + 17488.2i −0.166178 + 0.0504097i
\(590\) 359613. + 446780.i 1.03307 + 1.28348i
\(591\) 223316. + 539133.i 0.639360 + 1.54355i
\(592\) −14370.8 + 16213.2i −0.0410051 + 0.0462622i
\(593\) −316314. 131021.i −0.899515 0.372591i −0.115482 0.993310i \(-0.536841\pi\)
−0.784034 + 0.620718i \(0.786841\pi\)
\(594\) −195148. + 57178.3i −0.553083 + 0.162053i
\(595\) −654105. 349626.i −1.84762 0.987575i
\(596\) −25100.4 88784.5i −0.0706623 0.249945i
\(597\) −241885. + 294738.i −0.678673 + 0.826966i
\(598\) 156697. + 239407.i 0.438185 + 0.669474i
\(599\) −215133. 321970.i −0.599589 0.897349i 0.400229 0.916415i \(-0.368931\pi\)
−0.999818 + 0.0190666i \(0.993931\pi\)
\(600\) −3470.32 3674.02i −0.00963977 0.0102056i
\(601\) −190057. + 284440.i −0.526181 + 0.787485i −0.995421 0.0955855i \(-0.969528\pi\)
0.469241 + 0.883070i \(0.344528\pi\)
\(602\) −32806.8 + 32189.3i −0.0905256 + 0.0888215i
\(603\) 50037.6 26745.7i 0.137614 0.0735561i
\(604\) 384672. + 7310.94i 1.05443 + 0.0200401i
\(605\) 760416. + 74894.5i 2.07750 + 0.204616i
\(606\) 339431. 405675.i 0.924285 1.10467i
\(607\) 169711. 169711.i 0.460611 0.460611i −0.438245 0.898856i \(-0.644400\pi\)
0.898856 + 0.438245i \(0.144400\pi\)
\(608\) 299078. + 140876.i 0.809053 + 0.381091i
\(609\) 472653. 472653.i 1.27441 1.27441i
\(610\) 154513. 13737.2i 0.415246 0.0369179i
\(611\) 524198. + 51629.0i 1.40415 + 0.138296i
\(612\) −125747. 320683.i −0.335733 0.856196i
\(613\) 358503. 191624.i 0.954051 0.509951i 0.0805381 0.996752i \(-0.474336\pi\)
0.873513 + 0.486801i \(0.161836\pi\)
\(614\) 3347.31 352276.i 0.00887891 0.934429i
\(615\) −176567. + 264251.i −0.466829 + 0.698660i
\(616\) 938761. + 666729.i 2.47397 + 1.75707i
\(617\) 208965. + 312739.i 0.548914 + 0.821508i 0.997384 0.0722903i \(-0.0230308\pi\)
−0.448470 + 0.893798i \(0.648031\pi\)
\(618\) −38488.6 + 184324.i −0.100775 + 0.482620i
\(619\) 387801. 472536.i 1.01211 1.23326i 0.0398850 0.999204i \(-0.487301\pi\)
0.972224 0.234054i \(-0.0751992\pi\)
\(620\) 8680.02 73736.1i 0.0225807 0.191821i
\(621\) 67477.1 + 36067.3i 0.174974 + 0.0935255i
\(622\) 251657. 460244.i 0.650471 1.18962i
\(623\) −1.16321e6 481819.i −2.99698 1.24139i
\(624\) 158058. 662041.i 0.405926 1.70026i
\(625\) −147884. 357023.i −0.378582 0.913979i
\(626\) −15533.9 + 143707.i −0.0396398 + 0.366714i
\(627\) 784067. 237844.i 1.99443 0.605003i
\(628\) −168454. + 197487.i −0.427133 + 0.500749i
\(629\) 29739.9 2929.13i 0.0751689 0.00740349i
\(630\) 423188. + 288619.i 1.06623 + 0.727183i
\(631\) −65411.3 13011.1i −0.164283 0.0326780i 0.112263 0.993679i \(-0.464190\pi\)
−0.276547 + 0.961000i \(0.589190\pi\)
\(632\) −52971.9 + 92650.8i −0.132621 + 0.231961i
\(633\) −323020. + 64252.7i −0.806162 + 0.160356i
\(634\) −370059. + 149180.i −0.920646 + 0.371135i
\(635\) −221930. + 731605.i −0.550387 + 1.81438i
\(636\) 19344.0 + 107929.i 0.0478224 + 0.266823i
\(637\) −670088. 816505.i −1.65140 2.01224i
\(638\) 539915. + 169400.i 1.32643 + 0.416171i
\(639\) 120969.i 0.296260i
\(640\) −306602. + 268307.i −0.748539 + 0.655046i
\(641\) −104497. −0.254324 −0.127162 0.991882i \(-0.540587\pi\)
−0.127162 + 0.991882i \(0.540587\pi\)
\(642\) −259487. + 827042.i −0.629572 + 2.00658i
\(643\) 389988. 320055.i 0.943255 0.774109i −0.0310092 0.999519i \(-0.509872\pi\)
0.974264 + 0.225410i \(0.0723721\pi\)
\(644\) −76429.5 426434.i −0.184285 1.02821i
\(645\) −38570.4 11700.2i −0.0927118 0.0281238i
\(646\) −170493. 422929.i −0.408547 1.01345i
\(647\) −21957.1 110386.i −0.0524525 0.263696i 0.945656 0.325168i \(-0.105421\pi\)
−0.998109 + 0.0614713i \(0.980421\pi\)
\(648\) −130938. 480547.i −0.311829 1.14442i
\(649\) −239597. + 1.20453e6i −0.568841 + 2.85976i
\(650\) −3333.08 + 4887.14i −0.00788895 + 0.0115672i
\(651\) −18407.9 186899.i −0.0434353 0.441006i
\(652\) −364835. + 427714.i −0.858226 + 1.00614i
\(653\) 23198.3 + 76474.6i 0.0544039 + 0.179346i 0.979932 0.199335i \(-0.0638780\pi\)
−0.925528 + 0.378680i \(0.876378\pi\)
\(654\) −310370. 33549.2i −0.725644 0.0784381i
\(655\) 154010. 63793.1i 0.358977 0.148693i
\(656\) −222354. 161121.i −0.516698 0.374407i
\(657\) 198452. 479106.i 0.459753 1.10994i
\(658\) −699757. 382620.i −1.61620 0.883723i
\(659\) 217204. 406361.i 0.500147 0.935709i −0.497521 0.867452i \(-0.665756\pi\)
0.997668 0.0682571i \(-0.0217438\pi\)
\(660\) −118051. + 1.00283e6i −0.271007 + 2.30219i
\(661\) −269594. 221250.i −0.617032 0.506385i 0.273161 0.961968i \(-0.411931\pi\)
−0.890193 + 0.455583i \(0.849431\pi\)
\(662\) 324920. + 67846.2i 0.741413 + 0.154814i
\(663\) −780616. + 521591.i −1.77587 + 1.18660i
\(664\) 55083.9 + 325096.i 0.124936 + 0.737353i
\(665\) 563835. + 376742.i 1.27500 + 0.851924i
\(666\) −20638.2 196.103i −0.0465289 0.000442116i
\(667\) −100364. 187768.i −0.225594 0.422057i
\(668\) 273554. + 697626.i 0.613041 + 1.56340i
\(669\) 96991.7 984773.i 0.216712 2.20031i
\(670\) 8197.28 + 92201.4i 0.0182608 + 0.205394i
\(671\) 234882. + 234882.i 0.521681 + 0.521681i
\(672\) −612604. + 828733.i −1.35657 + 1.83517i
\(673\) 42017.9 + 42017.9i 0.0927694 + 0.0927694i 0.751968 0.659199i \(-0.229105\pi\)
−0.659199 + 0.751968i \(0.729105\pi\)
\(674\) 156301. + 130778.i 0.344066 + 0.287882i
\(675\) −155.047 + 1574.21i −0.000340294 + 0.00345506i
\(676\) −339658. 6455.41i −0.743273 0.0141264i
\(677\) −274145. 512890.i −0.598141 1.11904i −0.980775 0.195143i \(-0.937483\pi\)
0.382634 0.923900i \(-0.375017\pi\)
\(678\) −388698. 396156.i −0.845577 0.861800i
\(679\) 805859. + 538458.i 1.74791 + 1.16792i
\(680\) 561743. + 16016.8i 1.21484 + 0.0346385i
\(681\) 957188. 639573.i 2.06397 1.37910i
\(682\) 133025. 87067.9i 0.286000 0.187193i
\(683\) −90852.1 74560.4i −0.194757 0.159833i 0.531961 0.846769i \(-0.321455\pi\)
−0.726718 + 0.686936i \(0.758955\pi\)
\(684\) 85677.6 + 303057.i 0.183128 + 0.647757i
\(685\) −203451. + 380630.i −0.433590 + 0.811189i
\(686\) 221594. + 756293.i 0.470879 + 1.60710i
\(687\) 207297. 500458.i 0.439217 1.06036i
\(688\) 11368.1 32917.1i 0.0240165 0.0695415i
\(689\) 118574. 49114.8i 0.249776 0.103460i
\(690\) 295961. 238219.i 0.621636 0.500355i
\(691\) 59348.9 + 195647.i 0.124296 + 0.409748i 0.996900 0.0786799i \(-0.0250705\pi\)
−0.872604 + 0.488428i \(0.837570\pi\)
\(692\) 396858. 202525.i 0.828748 0.422928i
\(693\) 107514. + 1.09161e6i 0.223872 + 2.27301i
\(694\) 251518. 47550.2i 0.522215 0.0987264i
\(695\) 21774.8 109469.i 0.0450801 0.226633i
\(696\) −160774. + 480275.i −0.331893 + 0.991451i
\(697\) 73891.3 + 371477.i 0.152100 + 0.764656i
\(698\) −694626. 295487.i −1.42574 0.606495i
\(699\) −306603. 93007.0i −0.627512 0.190354i
\(700\) 7540.49 4833.70i 0.0153888 0.00986469i
\(701\) −737890. + 605571.i −1.50161 + 1.23234i −0.599832 + 0.800126i \(0.704766\pi\)
−0.901773 + 0.432209i \(0.857734\pi\)
\(702\) −188829. + 98636.0i −0.383173 + 0.200153i
\(703\) −27322.7 −0.0552857
\(704\) −861956. 134847.i −1.73916 0.272079i
\(705\) 699401.i 1.40717i
\(706\) 489818. 255859.i 0.982709 0.513324i
\(707\) 594701. + 724645.i 1.18976 + 1.44973i
\(708\) −1.07383e6 234895.i −2.14224 0.468605i
\(709\) 242538. 799542.i 0.482490 1.59056i −0.290985 0.956728i \(-0.593983\pi\)
0.773475 0.633827i \(-0.218517\pi\)
\(710\) 181610. + 77254.9i 0.360265 + 0.153253i
\(711\) −99715.9 + 19834.7i −0.197254 + 0.0392362i
\(712\) 951669. 66410.0i 1.87727 0.131001i
\(713\) −58669.4 11670.1i −0.115407 0.0229559i
\(714\) 1.39676e6 264062.i 2.73985 0.517976i
\(715\) 1.17623e6 115848.i 2.30080 0.226609i
\(716\) 277979. 857374.i 0.542233 1.67242i
\(717\) −169847. + 51522.4i −0.330384 + 0.100221i
\(718\) −76143.0 + 61287.5i −0.147700 + 0.118884i
\(719\) 126615. + 305676.i 0.244922 + 0.591295i 0.997759 0.0669129i \(-0.0213150\pi\)
−0.752837 + 0.658207i \(0.771315\pi\)
\(720\) −384530. 52692.0i −0.741763 0.101643i
\(721\) −308314. 127708.i −0.593092 0.245667i
\(722\) −29344.7 100152.i −0.0562931 0.192126i
\(723\) −930414. 497317.i −1.77992 0.951386i
\(724\) −237854. + 425348.i −0.453767 + 0.811460i
\(725\) 2792.44 3402.60i 0.00531262 0.00647344i
\(726\) −1.22533e6 + 802006.i −2.32477 + 1.52161i
\(727\) 23784.3 + 35595.8i 0.0450010 + 0.0673488i 0.853288 0.521440i \(-0.174605\pi\)
−0.808287 + 0.588789i \(0.799605\pi\)
\(728\) 1.10085e6 + 493201.i 2.07714 + 0.930595i
\(729\) 135627. 202980.i 0.255205 0.381942i
\(730\) 592537. + 603906.i 1.11191 + 1.13324i
\(731\) −42363.1 + 22643.5i −0.0792780 + 0.0423750i
\(732\) −214185. + 206195.i −0.399730 + 0.384819i
\(733\) 128757. + 12681.5i 0.239642 + 0.0236027i 0.217125 0.976144i \(-0.430332\pi\)
0.0225171 + 0.999746i \(0.492832\pi\)
\(734\) −403342. 337478.i −0.748654 0.626403i
\(735\) −991729. + 991729.i −1.83577 + 1.83577i
\(736\) 195959. + 263350.i 0.361750 + 0.486158i
\(737\) −140160. + 140160.i −0.258040 + 0.258040i
\(738\) −23165.2 260557.i −0.0425327 0.478400i
\(739\) −440041. 43340.3i −0.805758 0.0793602i −0.313253 0.949670i \(-0.601419\pi\)
−0.492505 + 0.870310i \(0.663919\pi\)
\(740\) 13474.6 30858.6i 0.0246067 0.0563525i
\(741\) 757022. 404637.i 1.37871 0.736935i
\(742\) −194317. 1846.39i −0.352942 0.00335364i
\(743\) −90810.6 + 135908.i −0.164497 + 0.246188i −0.904556 0.426354i \(-0.859798\pi\)
0.740059 + 0.672542i \(0.234798\pi\)
\(744\) 75652.3 + 120522.i 0.136671 + 0.217731i
\(745\) 79666.9 + 119230.i 0.143538 + 0.214819i
\(746\) 33705.5 + 7038.00i 0.0605651 + 0.0126465i
\(747\) −199270. + 242811.i −0.357109 + 0.435138i
\(748\) 745605. + 944568.i 1.33262 + 1.68822i
\(749\) −1.35479e6 724152.i −2.41496 1.29082i
\(750\) 656811. + 359138.i 1.16766 + 0.638468i
\(751\) 172199. + 71327.0i 0.305316 + 0.126466i 0.530081 0.847947i \(-0.322161\pi\)
−0.224765 + 0.974413i \(0.572161\pi\)
\(752\) 603853. + 22961.5i 1.06781 + 0.0406036i
\(753\) −182161. 439775.i −0.321266 0.775605i
\(754\) 589389. + 63709.7i 1.03671 + 0.112063i
\(755\) −572215. + 173580.i −1.00384 + 0.304512i
\(756\) 321553. 25511.2i 0.562612 0.0446361i
\(757\) −736203. + 72509.7i −1.28471 + 0.126533i −0.717221 0.696846i \(-0.754586\pi\)
−0.567492 + 0.823379i \(0.692086\pi\)
\(758\) 214254. 314150.i 0.372898 0.546762i
\(759\) 797921. + 158716.i 1.38508 + 0.275510i
\(760\) −509692. 64915.3i −0.882431 0.112388i
\(761\) 117810. 23433.8i 0.203429 0.0404645i −0.0923241 0.995729i \(-0.529430\pi\)
0.295753 + 0.955265i \(0.404430\pi\)
\(762\) −547852. 1.35901e6i −0.943526 2.34053i
\(763\) 160603. 529437.i 0.275870 0.909421i
\(764\) 522046. + 363356.i 0.894380 + 0.622509i
\(765\) 339623. + 413832.i 0.580329 + 0.707133i
\(766\) 272295. 867865.i 0.464069 1.47909i
\(767\) 1.28663e6i 2.18708i
\(768\) 135331. 769048.i 0.229442 1.30386i
\(769\) −47696.7 −0.0806558 −0.0403279 0.999187i \(-0.512840\pi\)
−0.0403279 + 0.999187i \(0.512840\pi\)
\(770\) −1.70748e6 535727.i −2.87988 0.903571i
\(771\) 410304. 336727.i 0.690234 0.566461i
\(772\) 197117. 283205.i 0.330742 0.475188i
\(773\) 663102. + 201150.i 1.10974 + 0.336636i 0.791374 0.611332i \(-0.209366\pi\)
0.318365 + 0.947968i \(0.396866\pi\)
\(774\) 30769.1 12403.8i 0.0513609 0.0207049i
\(775\) −241.272 1212.96i −0.000401702 0.00201949i
\(776\) −728476. 92780.0i −1.20974 0.154075i
\(777\) 16616.6 83537.2i 0.0275232 0.138369i
\(778\) 272360. + 185753.i 0.449971 + 0.306885i
\(779\) −33942.8 344627.i −0.0559336 0.567903i
\(780\) 83664.6 + 1.05454e6i 0.137516 + 1.73331i
\(781\) 122679. + 404419.i 0.201126 + 0.663024i
\(782\) 48659.2 450154.i 0.0795704 0.736118i
\(783\) 146455. 60663.8i 0.238881 0.0989479i
\(784\) −823687. 888804.i −1.34008 1.44602i
\(785\) 154385. 372718.i 0.250533 0.604840i
\(786\) −153280. + 280326.i −0.248107 + 0.453752i
\(787\) −202405. + 378672.i −0.326792 + 0.611384i −0.990643 0.136481i \(-0.956421\pi\)
0.663851 + 0.747865i \(0.268921\pi\)
\(788\) 615083. 485523.i 0.990561 0.781910i
\(789\) −572028. 469451.i −0.918889 0.754112i
\(790\) 33904.1 162369.i 0.0543248 0.260165i
\(791\) 817838. 546462.i 1.30712 0.873388i
\(792\) −441859. 703925.i −0.704422 1.12221i
\(793\) 289349. + 193337.i 0.460125 + 0.307446i
\(794\) −105.749 + 11129.2i −0.000167739 + 0.0176531i
\(795\) −80333.1 150293.i −0.127104 0.237795i
\(796\) 469223. + 204889.i 0.740548 + 0.323365i
\(797\) −20938.2 + 212589.i −0.0329626 + 0.334675i 0.964534 + 0.263959i \(0.0850284\pi\)
−0.997496 + 0.0707161i \(0.977472\pi\)
\(798\) −1.29457e6 + 115096.i −2.03292 + 0.180739i
\(799\) −589385. 589385.i −0.923221 0.923221i
\(800\) −3479.78 + 5826.50i −0.00543715 + 0.00910391i
\(801\) 642614. + 642614.i 1.00158 + 1.00158i
\(802\) 335119. 400522.i 0.521015 0.622699i
\(803\) −177578. + 1.80298e6i −0.275396 + 2.79615i
\(804\) −123041. 127809.i −0.190344 0.197719i
\(805\) 317402. + 593817.i 0.489799 + 0.916349i
\(806\) 118889. 116651.i 0.183009 0.179564i
\(807\) 556577. + 371893.i 0.854631 + 0.571046i
\(808\) −648210. 290410.i −0.992872 0.444824i
\(809\) 209898. 140249.i 0.320709 0.214291i −0.384786 0.923006i \(-0.625725\pi\)
0.705495 + 0.708715i \(0.250725\pi\)
\(810\) 423928. + 647692.i 0.646133 + 0.987184i
\(811\) 612707. + 502835.i 0.931560 + 0.764512i 0.972076 0.234667i \(-0.0754000\pi\)
−0.0405155 + 0.999179i \(0.512900\pi\)
\(812\) −783427. 438090.i −1.18819 0.664434i
\(813\) −219634. + 410907.i −0.332292 + 0.621674i
\(814\) 69195.5 20274.3i 0.104431 0.0305983i
\(815\) 334363. 807225.i 0.503389 1.21529i
\(816\) −857950. + 651158.i −1.28849 + 0.977926i
\(817\) 40575.2 16806.8i 0.0607879 0.0251792i
\(818\) −544414. 676374.i −0.813622 1.01084i
\(819\) 333579. + 1.09966e6i 0.497314 + 1.63942i
\(820\) 405965. + 131623.i 0.603756 + 0.195751i
\(821\) −21863.1 221980.i −0.0324359 0.329327i −0.997685 0.0679975i \(-0.978339\pi\)
0.965250 0.261330i \(-0.0841610\pi\)
\(822\) −153661. 812791.i −0.227415 1.20292i
\(823\) 243025. 1.22177e6i 0.358799 1.80380i −0.205975 0.978557i \(-0.566037\pi\)
0.564774 0.825246i \(-0.308963\pi\)
\(824\) 252243. 17602.2i 0.371505 0.0259246i
\(825\) 3281.37 + 16496.6i 0.00482111 + 0.0242374i
\(826\) 762575. 1.79265e6i 1.11769 2.62746i
\(827\) −555599. 168539.i −0.812364 0.246428i −0.143344 0.989673i \(-0.545786\pi\)
−0.669019 + 0.743245i \(0.733286\pi\)
\(828\) −66823.3 + 305485.i −0.0974691 + 0.445583i
\(829\) −645600. + 529830.i −0.939409 + 0.770953i −0.973552 0.228464i \(-0.926630\pi\)
0.0341436 + 0.999417i \(0.489130\pi\)
\(830\) −237269. 454228.i −0.344417 0.659352i
\(831\) −600885. −0.870140
\(832\) −913225. + 37613.9i −1.31926 + 0.0543378i
\(833\) 1.67146e6i 2.40883i
\(834\) 99043.7 + 189609.i 0.142395 + 0.272601i
\(835\) −738829. 900266.i −1.05967 1.29121i
\(836\) −593774. 926277.i −0.849588 1.32534i
\(837\) 12928.8 42620.7i 0.0184548 0.0608372i
\(838\) 187869. 441640.i 0.267527 0.628898i
\(839\) −67125.4 + 13352.1i −0.0953593 + 0.0189681i −0.242539 0.970142i \(-0.577980\pi\)
0.147180 + 0.989110i \(0.452980\pi\)
\(840\) 508448. 1.51887e6i 0.720590 2.15259i
\(841\) 261047. + 51925.5i 0.369086 + 0.0734157i
\(842\) 206978. + 1.09481e6i 0.291944 + 1.54424i
\(843\) 776132. 76442.3i 1.09215 0.107567i
\(844\) 201032. + 393932.i 0.282215 + 0.553014i
\(845\) 505254. 153267.i 0.707614 0.214652i
\(846\) 360953. + 448445.i 0.504325 + 0.626568i
\(847\) −993220. 2.39785e6i −1.38446 3.34237i
\(848\) 132398. 64424.4i 0.184115 0.0895898i
\(849\) 826535. + 342362.i 1.14669 + 0.474975i
\(850\) 8983.22 2632.09i 0.0124335 0.00364303i
\(851\) −23926.1 12788.7i −0.0330379 0.0176591i
\(852\) −363990. + 102904.i −0.501430 + 0.141760i
\(853\) −189696. + 231145.i −0.260712 + 0.317678i −0.886871 0.462017i \(-0.847126\pi\)
0.626159 + 0.779695i \(0.284626\pi\)
\(854\) −288557. 440868.i −0.395655 0.604495i
\(855\) −271935. 406980.i −0.371992 0.556725i
\(856\) 1.16349e6 + 33174.4i 1.58787 + 0.0452746i
\(857\) −644920. + 965191.i −0.878100 + 1.31417i 0.0704405 + 0.997516i \(0.477559\pi\)
−0.948541 + 0.316654i \(0.897441\pi\)
\(858\) −1.61693e6 + 1.58649e6i −2.19642 + 2.15507i
\(859\) −1.26840e6 + 677974.i −1.71898 + 0.918811i −0.753841 + 0.657057i \(0.771801\pi\)
−0.965135 + 0.261754i \(0.915699\pi\)
\(860\) −1028.48 + 54114.7i −0.00139060 + 0.0731675i
\(861\) 1.07431e6 + 105811.i 1.44919 + 0.142733i
\(862\) 556515. 665126.i 0.748966 0.895137i
\(863\) 890699. 890699.i 1.19594 1.19594i 0.220568 0.975372i \(-0.429209\pi\)
0.975372 0.220568i \(-0.0707910\pi\)
\(864\) −209435. + 125981.i −0.280558 + 0.168763i
\(865\) −489648. + 489648.i −0.654413 + 0.654413i
\(866\) −437585. + 38904.1i −0.583481 + 0.0518751i
\(867\) 488123. + 48075.9i 0.649369 + 0.0639572i
\(868\) −234784. + 92063.9i −0.311623 + 0.122194i
\(869\) 313250. 167436.i 0.414812 0.221722i
\(870\) 7479.16 787117.i 0.00988130 1.03992i
\(871\) −115368. + 172661.i −0.152073 + 0.227593i
\(872\) 70031.3 + 413313.i 0.0920998 + 0.543559i
\(873\) −388663. 581675.i −0.509970 0.763223i
\(874\) −84616.2 + 405232.i −0.110772 + 0.530495i
\(875\) −841643. + 1.02555e6i −1.09929 + 1.33949i
\(876\) −1.61042e6 189574.i −2.09860 0.247042i
\(877\) −32002.7 17105.8i −0.0416090 0.0222405i 0.450461 0.892796i \(-0.351260\pi\)
−0.492070 + 0.870556i \(0.663760\pi\)
\(878\) −661764. + 1.21027e6i −0.858448 + 1.56998i
\(879\) 303621. + 125764.i 0.392966 + 0.162772i
\(880\) 1.33898e6 213807.i 1.72905 0.276094i
\(881\) 38989.9 + 94129.9i 0.0502343 + 0.121276i 0.947005 0.321220i \(-0.104093\pi\)
−0.896770 + 0.442496i \(0.854093\pi\)
\(882\) 124060. 1.14770e6i 0.159476 1.47534i
\(883\) 179517. 54455.8i 0.230241 0.0698430i −0.173056 0.984912i \(-0.555364\pi\)
0.403297 + 0.915069i \(0.367864\pi\)
\(884\) 959168. + 818160.i 1.22741 + 1.04697i
\(885\) 1.70018e6 167453.i 2.17074 0.213799i
\(886\) −729336. 497415.i −0.929095 0.633653i
\(887\) −1.21497e6 241673.i −1.54426 0.307172i −0.651831 0.758364i \(-0.725999\pi\)
−0.892427 + 0.451192i \(0.850999\pi\)
\(888\) 16966.1 + 62266.0i 0.0215157 + 0.0789633i
\(889\) 2.54697e6 506624.i 3.22270 0.641035i
\(890\) −1.37514e6 + 554354.i −1.73607 + 0.699854i
\(891\) −481180. + 1.58624e6i −0.606111 + 1.99808i
\(892\) −1.30795e6 + 234423.i −1.64385 + 0.294625i
\(893\) 483460. + 589098.i 0.606259 + 0.738728i
\(894\) −262229. 82275.3i −0.328100 0.102942i
\(895\) 1.40081e6i 1.74878i
\(896\) 1.29468e6 + 488852.i 1.61267 + 0.608922i
\(897\) 852308. 1.05928
\(898\) −236088. + 752464.i −0.292766 + 0.933110i
\(899\) −95804.7 + 78624.9i −0.118541 + 0.0972839i
\(900\) −6363.66 + 1140.55i −0.00785636 + 0.00140809i
\(901\) −194348. 58954.9i −0.239404 0.0726224i
\(902\) 341685. + 847590.i 0.419964 + 1.04177i
\(903\) 26709.4 + 134277.i 0.0327558 + 0.164674i
\(904\) −369912. + 646996.i −0.452648 + 0.791707i
\(905\) 147764. 742859.i 0.180414 0.907004i
\(906\) 645739. 946817.i 0.786685 1.15348i
\(907\) 115520. + 1.17290e6i 0.140425 + 1.42576i 0.764616 + 0.644486i \(0.222929\pi\)
−0.624191 + 0.781272i \(0.714571\pi\)
\(908\) −1.17613e6 1.00322e6i −1.42654 1.21682i
\(909\) −196420. 647510.i −0.237716 0.783644i
\(910\) −1.86394e6 201482.i −2.25086 0.243306i
\(911\) −828607. + 343220.i −0.998416 + 0.413558i −0.821216 0.570617i \(-0.806704\pi\)
−0.177200 + 0.984175i \(0.556704\pi\)
\(912\) 839000. 515599.i 1.00872 0.619901i
\(913\) 419946. 1.01384e6i 0.503793 1.21626i
\(914\) 895437. + 489616.i 1.07187 + 0.586089i
\(915\) 217820. 407512.i 0.260169 0.486741i
\(916\) −722418. 85041.1i −0.860989 0.101353i
\(917\) −437701. 359212.i −0.520522 0.427181i
\(918\) 330000. + 68907.0i 0.391587 + 0.0817670i
\(919\) −552506. + 369173.i −0.654193 + 0.437118i −0.837871 0.545868i \(-0.816200\pi\)
0.183677 + 0.982987i \(0.441200\pi\)
\(920\) −415945. 295413.i −0.491428 0.349023i
\(921\) −872539. 583012.i −1.02865 0.687319i
\(922\) −97346.1 924.979i −0.114513 0.00108810i
\(923\) 208710. + 390469.i 0.244985 + 0.458335i
\(924\) 3.19313e6 1.25210e6i 3.74001 1.46654i
\(925\) 54.9764 558.185i 6.42530e−5 0.000652371i
\(926\) −2165.86 24361.2i −0.00252586 0.0284104i
\(927\) 170327. + 170327.i 0.198209 + 0.198209i
\(928\) 679341. + 32298.7i 0.788845 + 0.0375050i
\(929\) −624259. 624259.i −0.723325 0.723325i 0.245956 0.969281i \(-0.420898\pi\)
−0.969281 + 0.245956i \(0.920898\pi\)
\(930\) −169617. 141920.i −0.196112 0.164088i
\(931\) 149791. 1.52086e6i 0.172817 1.75464i
\(932\) −8175.60 + 430167.i −0.00941212 + 0.495228i
\(933\) −736566. 1.37802e6i −0.846152 1.58304i
\(934\) −58002.4 59115.2i −0.0664893 0.0677650i
\(935\) −1.55509e6 1.03908e6i −1.77882 1.18857i
\(936\) −597883. 632978.i −0.682440 0.722499i
\(937\) 383722. 256395.i 0.437056 0.292032i −0.317511 0.948255i \(-0.602847\pi\)
0.754567 + 0.656223i \(0.227847\pi\)
\(938\) 263076. 172189.i 0.299003 0.195704i
\(939\) 332828. + 273145.i 0.377476 + 0.309786i
\(940\) −903761. + 255503.i −1.02282 + 0.289162i
\(941\) 380168. 711244.i 0.429335 0.803229i −0.570502 0.821296i \(-0.693251\pi\)
0.999837 + 0.0180673i \(0.00575131\pi\)
\(942\) 217409. + 742011.i 0.245006 + 0.836197i
\(943\) 131584. 317672.i 0.147972 0.357236i
\(944\) 88759.2 + 1.47341e6i 0.0996023 + 1.65340i
\(945\) −463165. + 191849.i −0.518648 + 0.214831i
\(946\) −90286.6 + 72671.7i −0.100888 + 0.0812051i
\(947\) −71490.8 235674.i −0.0797169 0.262791i 0.908018 0.418931i \(-0.137595\pi\)
−0.987735 + 0.156140i \(0.950095\pi\)
\(948\) 144506. + 283167.i 0.160794 + 0.315084i
\(949\) 186037. + 1.88887e6i 0.206570 + 2.09734i
\(950\) −8409.67 + 1589.87i −0.00931820 + 0.00176163i
\(951\) −231868. + 1.16568e6i −0.256378 + 1.28890i
\(952\) −851481. 1.70842e6i −0.939509 1.88504i
\(953\) 37225.0 + 187143.i 0.0409872 + 0.206057i 0.995852 0.0909826i \(-0.0290008\pi\)
−0.954865 + 0.297039i \(0.904001\pi\)
\(954\) 129073. + 54906.2i 0.141820 + 0.0603288i
\(955\) −945979. 286960.i −1.03723 0.314640i
\(956\) 128625. + 200652.i 0.140737 + 0.219548i
\(957\) 1.30297e6 1.06932e6i 1.42269 1.16757i
\(958\) 855754. 447008.i 0.932434 0.487063i
\(959\) 1.46599e6 1.59402
\(960\) 168558. + 1.20185e6i 0.182897 + 1.30409i
\(961\) 888700.i 0.962295i
\(962\) 66955.0 34974.4i 0.0723491 0.0377920i
\(963\) 703434. + 857136.i 0.758526 + 0.924267i
\(964\) −302733. + 1.38395e6i −0.325766 + 1.48925i
\(965\) −155673. + 513184.i −0.167170 + 0.551085i
\(966\) −1.18751e6 505154.i −1.27257 0.541339i
\(967\) −244629. + 48659.7i −0.261610 + 0.0520375i −0.324153 0.946005i \(-0.605079\pi\)
0.0625424 + 0.998042i \(0.480079\pi\)
\(968\) 1.48398e6 + 1.29038e6i 1.58372 + 1.37710i
\(969\) −1.33222e6 264995.i −1.41882 0.282221i
\(970\) 1.12147e6 212018.i 1.19191 0.225335i
\(971\) 1.40334e6 138217.i 1.48842 0.146596i 0.679133 0.734015i \(-0.262356\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(972\) −1.11705e6 362172.i −1.18233 0.383338i
\(973\) −362796. + 110053.i −0.383210 + 0.116245i
\(974\) −490473. + 394782.i −0.517008 + 0.416140i
\(975\) 6743.25 + 16279.7i 0.00709349 + 0.0171252i
\(976\) 344689. + 201441.i 0.361850 + 0.211470i
\(977\) −259881. 107646.i −0.272261 0.112774i 0.242376 0.970182i \(-0.422073\pi\)
−0.514637 + 0.857408i \(0.672073\pi\)
\(978\) 470861. + 1.60703e6i 0.492284 + 1.68015i
\(979\) −2.80005e6 1.49666e6i −2.92147 1.56156i
\(980\) 1.64380e6 + 919209.i 1.71158 + 0.957111i
\(981\) −253343. + 308699.i −0.263252 + 0.320773i
\(982\) 1.42841e6 934925.i 1.48126 0.969514i
\(983\) 655966. + 981723.i 0.678851 + 1.01597i 0.997675 + 0.0681582i \(0.0217123\pi\)
−0.318824 + 0.947814i \(0.603288\pi\)
\(984\) −764297. + 291349.i −0.789355 + 0.300901i
\(985\) −676627. + 1.01264e6i −0.697392 + 1.04372i
\(986\) −657001. 669607.i −0.675791 0.688757i
\(987\) −2.09515e6 + 1.11988e6i −2.15070 + 1.14957i
\(988\) −799422. 830398.i −0.818959 0.850692i
\(989\) 43397.7 + 4274.30i 0.0443684 + 0.00436991i
\(990\) 990675. + 828903.i 1.01079 + 0.845733i
\(991\) −208999. + 208999.i −0.212813 + 0.212813i −0.805461 0.592649i \(-0.798082\pi\)
0.592649 + 0.805461i \(0.298082\pi\)
\(992\) 128100. 141786.i 0.130175 0.144082i
\(993\) 699140. 699140.i 0.709032 0.709032i
\(994\) −59365.8 667735.i −0.0600847 0.675821i
\(995\) −791924. 77997.8i −0.799903 0.0787836i
\(996\) 900116. + 393042.i 0.907360 + 0.396205i
\(997\) −406715. + 217394.i −0.409166 + 0.218704i −0.663121 0.748512i \(-0.730769\pi\)
0.253955 + 0.967216i \(0.418269\pi\)
\(998\) −299564. 2846.44i −0.300765 0.00285786i
\(999\) 11222.2 16795.2i 0.0112447 0.0168288i
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.3.9 1008
128.43 odd 32 inner 128.5.l.a.43.9 yes 1008
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.5.l.a.3.9 1008 1.1 even 1 trivial
128.5.l.a.43.9 yes 1008 128.43 odd 32 inner