Properties

Label 161.4.e.a.93.5
Level $161$
Weight $4$
Character 161.93
Analytic conductor $9.499$
Analytic rank $0$
Dimension $44$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [161,4,Mod(93,161)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(161, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("161.93");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 161.e (of order \(3\), degree \(2\), 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: \(9.49930751092\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 93.5
Character \(\chi\) \(=\) 161.93
Dual form 161.4.e.a.116.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.86723 + 3.23414i) q^{2} +(1.89237 + 3.27768i) q^{3} +(-2.97311 - 5.14958i) q^{4} +(5.27939 - 9.14417i) q^{5} -14.1340 q^{6} +(18.0686 - 4.06535i) q^{7} -7.66976 q^{8} +(6.33786 - 10.9775i) q^{9} +(19.7157 + 34.1486i) q^{10} +(32.8419 + 56.8838i) q^{11} +(11.2525 - 19.4898i) q^{12} +32.1382 q^{13} +(-20.5903 + 66.0272i) q^{14} +39.9623 q^{15} +(38.1061 - 66.0017i) q^{16} +(3.45319 + 5.98111i) q^{17} +(23.6685 + 40.9951i) q^{18} +(-14.7296 + 25.5125i) q^{19} -62.7849 q^{20} +(47.5174 + 51.5299i) q^{21} -245.294 q^{22} +(11.5000 - 19.9186i) q^{23} +(-14.5140 - 25.1390i) q^{24} +(6.75608 + 11.7019i) q^{25} +(-60.0094 + 103.939i) q^{26} +150.162 q^{27} +(-74.6547 - 80.9588i) q^{28} -89.9938 q^{29} +(-74.6188 + 129.244i) q^{30} +(-104.152 - 180.396i) q^{31} +(111.627 + 193.343i) q^{32} +(-124.298 + 215.291i) q^{33} -25.7917 q^{34} +(58.2168 - 186.685i) q^{35} -75.3726 q^{36} +(-166.574 + 288.515i) q^{37} +(-55.0073 - 95.2754i) q^{38} +(60.8174 + 105.339i) q^{39} +(-40.4916 + 70.1336i) q^{40} -309.362 q^{41} +(-255.381 + 57.4596i) q^{42} +251.681 q^{43} +(195.285 - 338.244i) q^{44} +(-66.9201 - 115.909i) q^{45} +(42.9463 + 74.3852i) q^{46} +(-26.9415 + 46.6640i) q^{47} +288.444 q^{48} +(309.946 - 146.910i) q^{49} -50.4607 q^{50} +(-13.0694 + 22.6370i) q^{51} +(-95.5504 - 165.498i) q^{52} +(165.232 + 286.190i) q^{53} +(-280.388 + 485.646i) q^{54} +693.540 q^{55} +(-138.581 + 31.1802i) q^{56} -111.496 q^{57} +(168.039 - 291.053i) q^{58} +(106.027 + 183.645i) q^{59} +(-118.812 - 205.789i) q^{60} +(181.518 - 314.398i) q^{61} +777.901 q^{62} +(69.8887 - 224.113i) q^{63} -224.035 q^{64} +(169.670 - 293.877i) q^{65} +(-464.187 - 803.995i) q^{66} +(-109.534 - 189.718i) q^{67} +(20.5335 - 35.5650i) q^{68} +87.0491 q^{69} +(495.060 + 536.865i) q^{70} +591.325 q^{71} +(-48.6098 + 84.1947i) q^{72} +(-509.826 - 883.044i) q^{73} +(-622.066 - 1077.45i) q^{74} +(-25.5700 + 44.2886i) q^{75} +175.171 q^{76} +(824.658 + 894.295i) q^{77} -454.241 q^{78} +(-168.304 + 291.510i) q^{79} +(-402.354 - 696.898i) q^{80} +(113.041 + 195.793i) q^{81} +(577.650 - 1000.52i) q^{82} -415.472 q^{83} +(124.083 - 397.899i) q^{84} +72.9230 q^{85} +(-469.948 + 813.973i) q^{86} +(-170.302 - 294.971i) q^{87} +(-251.889 - 436.285i) q^{88} +(-300.116 + 519.817i) q^{89} +499.821 q^{90} +(580.690 - 130.653i) q^{91} -136.763 q^{92} +(394.187 - 682.752i) q^{93} +(-100.612 - 174.265i) q^{94} +(155.527 + 269.381i) q^{95} +(-422.479 + 731.755i) q^{96} +612.267 q^{97} +(-103.613 + 1276.72i) q^{98} +832.588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/161\mathbb{Z}\right)^\times\).

\(n\) \(24\) \(120\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86723 + 3.23414i −0.660166 + 1.14344i 0.320405 + 0.947280i \(0.396181\pi\)
−0.980572 + 0.196161i \(0.937152\pi\)
\(3\) 1.89237 + 3.27768i 0.364187 + 0.630791i 0.988645 0.150268i \(-0.0480135\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(4\) −2.97311 5.14958i −0.371639 0.643698i
\(5\) 5.27939 9.14417i 0.472203 0.817880i −0.527291 0.849685i \(-0.676792\pi\)
0.999494 + 0.0318051i \(0.0101256\pi\)
\(6\) −14.1340 −0.961696
\(7\) 18.0686 4.06535i 0.975611 0.219508i
\(8\) −7.66976 −0.338959
\(9\) 6.33786 10.9775i 0.234735 0.406574i
\(10\) 19.7157 + 34.1486i 0.623465 + 1.07987i
\(11\) 32.8419 + 56.8838i 0.900200 + 1.55919i 0.827234 + 0.561857i \(0.189913\pi\)
0.0729654 + 0.997334i \(0.476754\pi\)
\(12\) 11.2525 19.4898i 0.270692 0.468853i
\(13\) 32.1382 0.685656 0.342828 0.939398i \(-0.388615\pi\)
0.342828 + 0.939398i \(0.388615\pi\)
\(14\) −20.5903 + 66.0272i −0.393071 + 1.26047i
\(15\) 39.9623 0.687881
\(16\) 38.1061 66.0017i 0.595408 1.03128i
\(17\) 3.45319 + 5.98111i 0.0492660 + 0.0853312i 0.889607 0.456727i \(-0.150978\pi\)
−0.840341 + 0.542058i \(0.817645\pi\)
\(18\) 23.6685 + 40.9951i 0.309929 + 0.536813i
\(19\) −14.7296 + 25.5125i −0.177853 + 0.308051i −0.941145 0.338003i \(-0.890249\pi\)
0.763292 + 0.646054i \(0.223582\pi\)
\(20\) −62.7849 −0.701956
\(21\) 47.5174 + 51.5299i 0.493768 + 0.535464i
\(22\) −245.294 −2.37713
\(23\) 11.5000 19.9186i 0.104257 0.180579i
\(24\) −14.5140 25.1390i −0.123444 0.213812i
\(25\) 6.75608 + 11.7019i 0.0540486 + 0.0936150i
\(26\) −60.0094 + 103.939i −0.452647 + 0.784007i
\(27\) 150.162 1.07032
\(28\) −74.6547 80.9588i −0.503872 0.546420i
\(29\) −89.9938 −0.576256 −0.288128 0.957592i \(-0.593033\pi\)
−0.288128 + 0.957592i \(0.593033\pi\)
\(30\) −74.6188 + 129.244i −0.454116 + 0.786552i
\(31\) −104.152 180.396i −0.603425 1.04516i −0.992298 0.123872i \(-0.960469\pi\)
0.388873 0.921291i \(-0.372864\pi\)
\(32\) 111.627 + 193.343i 0.616657 + 1.06808i
\(33\) −124.298 + 215.291i −0.655682 + 1.13567i
\(34\) −25.7917 −0.130095
\(35\) 58.2168 186.685i 0.281155 0.901584i
\(36\) −75.3726 −0.348947
\(37\) −166.574 + 288.515i −0.740126 + 1.28194i 0.212312 + 0.977202i \(0.431901\pi\)
−0.952438 + 0.304733i \(0.901433\pi\)
\(38\) −55.0073 95.2754i −0.234825 0.406729i
\(39\) 60.8174 + 105.339i 0.249707 + 0.432505i
\(40\) −40.4916 + 70.1336i −0.160057 + 0.277227i
\(41\) −309.362 −1.17839 −0.589197 0.807989i \(-0.700556\pi\)
−0.589197 + 0.807989i \(0.700556\pi\)
\(42\) −255.381 + 57.4596i −0.938241 + 0.211100i
\(43\) 251.681 0.892583 0.446291 0.894888i \(-0.352745\pi\)
0.446291 + 0.894888i \(0.352745\pi\)
\(44\) 195.285 338.244i 0.669099 1.15891i
\(45\) −66.9201 115.909i −0.221686 0.383971i
\(46\) 42.9463 + 74.3852i 0.137654 + 0.238424i
\(47\) −26.9415 + 46.6640i −0.0836131 + 0.144822i −0.904799 0.425838i \(-0.859979\pi\)
0.821186 + 0.570660i \(0.193313\pi\)
\(48\) 288.444 0.867360
\(49\) 309.946 146.910i 0.903632 0.428309i
\(50\) −50.4607 −0.142724
\(51\) −13.0694 + 22.6370i −0.0358841 + 0.0621531i
\(52\) −95.5504 165.498i −0.254816 0.441355i
\(53\) 165.232 + 286.190i 0.428232 + 0.741720i 0.996716 0.0809742i \(-0.0258031\pi\)
−0.568484 + 0.822694i \(0.692470\pi\)
\(54\) −280.388 + 485.646i −0.706592 + 1.22385i
\(55\) 693.540 1.70031
\(56\) −138.581 + 31.1802i −0.330692 + 0.0744042i
\(57\) −111.496 −0.259087
\(58\) 168.039 291.053i 0.380425 0.658915i
\(59\) 106.027 + 183.645i 0.233959 + 0.405229i 0.958970 0.283509i \(-0.0914985\pi\)
−0.725011 + 0.688738i \(0.758165\pi\)
\(60\) −118.812 205.789i −0.255643 0.442787i
\(61\) 181.518 314.398i 0.380999 0.659910i −0.610206 0.792243i \(-0.708913\pi\)
0.991205 + 0.132332i \(0.0422466\pi\)
\(62\) 777.901 1.59344
\(63\) 69.8887 224.113i 0.139764 0.448184i
\(64\) −224.035 −0.437569
\(65\) 169.670 293.877i 0.323769 0.560784i
\(66\) −464.187 803.995i −0.865719 1.49947i
\(67\) −109.534 189.718i −0.199726 0.345936i 0.748713 0.662894i \(-0.230672\pi\)
−0.948440 + 0.316958i \(0.897339\pi\)
\(68\) 20.5335 35.5650i 0.0366183 0.0634248i
\(69\) 87.0491 0.151877
\(70\) 495.060 + 536.865i 0.845300 + 0.916680i
\(71\) 591.325 0.988413 0.494207 0.869344i \(-0.335459\pi\)
0.494207 + 0.869344i \(0.335459\pi\)
\(72\) −48.6098 + 84.1947i −0.0795656 + 0.137812i
\(73\) −509.826 883.044i −0.817405 1.41579i −0.907588 0.419862i \(-0.862078\pi\)
0.0901826 0.995925i \(-0.471255\pi\)
\(74\) −622.066 1077.45i −0.977212 1.69258i
\(75\) −25.5700 + 44.2886i −0.0393676 + 0.0681867i
\(76\) 175.171 0.264389
\(77\) 824.658 + 894.295i 1.22050 + 1.32356i
\(78\) −454.241 −0.659392
\(79\) −168.304 + 291.510i −0.239692 + 0.415158i −0.960626 0.277846i \(-0.910380\pi\)
0.720934 + 0.693004i \(0.243713\pi\)
\(80\) −402.354 696.898i −0.562307 0.973944i
\(81\) 113.041 + 195.793i 0.155063 + 0.268577i
\(82\) 577.650 1000.52i 0.777936 1.34743i
\(83\) −415.472 −0.549446 −0.274723 0.961523i \(-0.588586\pi\)
−0.274723 + 0.961523i \(0.588586\pi\)
\(84\) 124.083 397.899i 0.161173 0.516837i
\(85\) 72.9230 0.0930542
\(86\) −469.948 + 813.973i −0.589253 + 1.02062i
\(87\) −170.302 294.971i −0.209865 0.363497i
\(88\) −251.889 436.285i −0.305130 0.528501i
\(89\) −300.116 + 519.817i −0.357441 + 0.619107i −0.987533 0.157414i \(-0.949684\pi\)
0.630091 + 0.776521i \(0.283017\pi\)
\(90\) 499.821 0.585397
\(91\) 580.690 130.653i 0.668933 0.150507i
\(92\) −136.763 −0.154984
\(93\) 394.187 682.752i 0.439519 0.761270i
\(94\) −100.612 174.265i −0.110397 0.191213i
\(95\) 155.527 + 269.381i 0.167966 + 0.290925i
\(96\) −422.479 + 731.755i −0.449157 + 0.777963i
\(97\) 612.267 0.640889 0.320445 0.947267i \(-0.396168\pi\)
0.320445 + 0.947267i \(0.396168\pi\)
\(98\) −103.613 + 1276.72i −0.106801 + 1.31601i
\(99\) 832.588 0.845235
\(100\) 40.1732 69.5819i 0.0401732 0.0695819i
\(101\) 436.405 + 755.876i 0.429940 + 0.744678i 0.996867 0.0790898i \(-0.0252014\pi\)
−0.566928 + 0.823768i \(0.691868\pi\)
\(102\) −48.8074 84.5369i −0.0473789 0.0820627i
\(103\) 961.229 1664.90i 0.919541 1.59269i 0.119427 0.992843i \(-0.461894\pi\)
0.800114 0.599848i \(-0.204772\pi\)
\(104\) −246.492 −0.232409
\(105\) 722.061 162.461i 0.671104 0.150995i
\(106\) −1234.10 −1.13082
\(107\) −123.633 + 214.138i −0.111701 + 0.193472i −0.916456 0.400135i \(-0.868963\pi\)
0.804755 + 0.593607i \(0.202297\pi\)
\(108\) −446.450 773.273i −0.397774 0.688965i
\(109\) 50.7507 + 87.9028i 0.0445967 + 0.0772437i 0.887462 0.460881i \(-0.152466\pi\)
−0.842865 + 0.538124i \(0.819133\pi\)
\(110\) −1295.00 + 2243.01i −1.12249 + 1.94420i
\(111\) −1260.88 −1.07818
\(112\) 420.203 1347.47i 0.354513 1.13682i
\(113\) −1652.92 −1.37605 −0.688026 0.725686i \(-0.741522\pi\)
−0.688026 + 0.725686i \(0.741522\pi\)
\(114\) 208.188 360.593i 0.171041 0.296251i
\(115\) −121.426 210.316i −0.0984611 0.170540i
\(116\) 267.562 + 463.430i 0.214159 + 0.370935i
\(117\) 203.687 352.796i 0.160948 0.278770i
\(118\) −791.910 −0.617807
\(119\) 86.7095 + 94.0315i 0.0667954 + 0.0724358i
\(120\) −306.501 −0.233163
\(121\) −1491.68 + 2583.66i −1.12072 + 1.94114i
\(122\) 677.872 + 1174.11i 0.503046 + 0.871301i
\(123\) −585.427 1013.99i −0.429156 0.743320i
\(124\) −619.309 + 1072.67i −0.448512 + 0.776846i
\(125\) 1462.52 1.04649
\(126\) 594.315 + 644.501i 0.420205 + 0.455688i
\(127\) −1617.35 −1.13005 −0.565026 0.825073i \(-0.691134\pi\)
−0.565026 + 0.825073i \(0.691134\pi\)
\(128\) −474.689 + 822.185i −0.327789 + 0.567747i
\(129\) 476.275 + 824.932i 0.325067 + 0.563033i
\(130\) 633.626 + 1097.47i 0.427482 + 0.740421i
\(131\) −1097.18 + 1900.37i −0.731765 + 1.26745i 0.224363 + 0.974506i \(0.427970\pi\)
−0.956128 + 0.292949i \(0.905364\pi\)
\(132\) 1478.21 0.974708
\(133\) −162.426 + 520.855i −0.105896 + 0.339578i
\(134\) 818.098 0.527410
\(135\) 792.766 1373.11i 0.505411 0.875397i
\(136\) −26.4851 45.8736i −0.0166991 0.0289238i
\(137\) −1087.44 1883.50i −0.678149 1.17459i −0.975538 0.219831i \(-0.929449\pi\)
0.297389 0.954756i \(-0.403884\pi\)
\(138\) −162.541 + 281.529i −0.100264 + 0.173662i
\(139\) −342.050 −0.208722 −0.104361 0.994540i \(-0.533280\pi\)
−0.104361 + 0.994540i \(0.533280\pi\)
\(140\) −1134.43 + 255.242i −0.684836 + 0.154085i
\(141\) −203.933 −0.121803
\(142\) −1104.14 + 1912.43i −0.652517 + 1.13019i
\(143\) 1055.48 + 1828.14i 0.617227 + 1.06907i
\(144\) −483.022 836.619i −0.279527 0.484155i
\(145\) −475.112 + 822.919i −0.272110 + 0.471308i
\(146\) 3807.85 2.15849
\(147\) 1068.06 + 737.896i 0.599265 + 0.414018i
\(148\) 1980.98 1.10024
\(149\) 379.214 656.817i 0.208499 0.361131i −0.742743 0.669577i \(-0.766475\pi\)
0.951242 + 0.308446i \(0.0998088\pi\)
\(150\) −95.4904 165.394i −0.0519784 0.0900292i
\(151\) −1512.38 2619.52i −0.815071 1.41174i −0.909277 0.416191i \(-0.863365\pi\)
0.0942065 0.995553i \(-0.469969\pi\)
\(152\) 112.973 195.674i 0.0602848 0.104416i
\(153\) 87.5434 0.0462579
\(154\) −4432.10 + 997.204i −2.31915 + 0.521798i
\(155\) −2199.43 −1.13976
\(156\) 361.634 626.368i 0.185602 0.321472i
\(157\) −1684.65 2917.91i −0.856370 1.48328i −0.875368 0.483457i \(-0.839381\pi\)
0.0189983 0.999820i \(-0.493952\pi\)
\(158\) −628.524 1088.63i −0.316473 0.548146i
\(159\) −625.360 + 1083.15i −0.311913 + 0.540250i
\(160\) 2357.29 1.16475
\(161\) 126.813 406.652i 0.0620759 0.199060i
\(162\) −844.295 −0.409469
\(163\) 2047.38 3546.16i 0.983821 1.70403i 0.336760 0.941590i \(-0.390669\pi\)
0.647061 0.762438i \(-0.275998\pi\)
\(164\) 919.767 + 1593.08i 0.437937 + 0.758530i
\(165\) 1312.44 + 2273.21i 0.619230 + 1.07254i
\(166\) 775.783 1343.70i 0.362725 0.628259i
\(167\) 487.681 0.225975 0.112988 0.993596i \(-0.463958\pi\)
0.112988 + 0.993596i \(0.463958\pi\)
\(168\) −364.447 395.222i −0.167367 0.181500i
\(169\) −1164.14 −0.529876
\(170\) −136.164 + 235.843i −0.0614313 + 0.106402i
\(171\) 186.709 + 323.389i 0.0834969 + 0.144621i
\(172\) −748.277 1296.05i −0.331718 0.574553i
\(173\) 1323.85 2292.98i 0.581795 1.00770i −0.413471 0.910517i \(-0.635684\pi\)
0.995267 0.0971820i \(-0.0309829\pi\)
\(174\) 1271.97 0.554183
\(175\) 169.645 + 183.970i 0.0732797 + 0.0794677i
\(176\) 5005.90 2.14394
\(177\) −401.286 + 695.048i −0.170410 + 0.295158i
\(178\) −1120.77 1941.24i −0.471942 0.817427i
\(179\) −135.500 234.693i −0.0565796 0.0979988i 0.836348 0.548198i \(-0.184686\pi\)
−0.892928 + 0.450200i \(0.851353\pi\)
\(180\) −397.922 + 689.220i −0.164774 + 0.285397i
\(181\) 4414.00 1.81265 0.906327 0.422577i \(-0.138874\pi\)
0.906327 + 0.422577i \(0.138874\pi\)
\(182\) −661.734 + 2121.99i −0.269511 + 0.864245i
\(183\) 1374.00 0.555020
\(184\) −88.2022 + 152.771i −0.0353389 + 0.0612087i
\(185\) 1758.82 + 3046.37i 0.698979 + 1.21067i
\(186\) 1472.08 + 2549.71i 0.580312 + 1.00513i
\(187\) −226.819 + 392.861i −0.0886985 + 0.153630i
\(188\) 320.400 0.124296
\(189\) 2713.22 610.462i 1.04422 0.234945i
\(190\) −1161.62 −0.443541
\(191\) 591.727 1024.90i 0.224167 0.388268i −0.731902 0.681409i \(-0.761367\pi\)
0.956069 + 0.293141i \(0.0947007\pi\)
\(192\) −423.958 734.317i −0.159357 0.276014i
\(193\) −555.607 962.340i −0.207220 0.358916i 0.743618 0.668605i \(-0.233108\pi\)
−0.950838 + 0.309689i \(0.899775\pi\)
\(194\) −1143.24 + 1980.16i −0.423093 + 0.732819i
\(195\) 1284.31 0.471650
\(196\) −1678.03 1159.31i −0.611526 0.422490i
\(197\) −4927.09 −1.78193 −0.890967 0.454068i \(-0.849972\pi\)
−0.890967 + 0.454068i \(0.849972\pi\)
\(198\) −1554.64 + 2692.71i −0.557996 + 0.966477i
\(199\) −1240.22 2148.12i −0.441793 0.765207i 0.556030 0.831162i \(-0.312324\pi\)
−0.997823 + 0.0659549i \(0.978991\pi\)
\(200\) −51.8175 89.7505i −0.0183202 0.0317316i
\(201\) 414.556 718.033i 0.145475 0.251971i
\(202\) −3259.48 −1.13533
\(203\) −1626.06 + 365.856i −0.562202 + 0.126493i
\(204\) 155.428 0.0533437
\(205\) −1633.24 + 2828.86i −0.556442 + 0.963785i
\(206\) 3589.67 + 6217.50i 1.21410 + 2.10288i
\(207\) −145.771 252.482i −0.0489457 0.0847765i
\(208\) 1224.66 2121.17i 0.408245 0.707101i
\(209\) −1934.99 −0.640413
\(210\) −822.835 + 2638.60i −0.270386 + 0.867050i
\(211\) −2729.88 −0.890676 −0.445338 0.895362i \(-0.646917\pi\)
−0.445338 + 0.895362i \(0.646917\pi\)
\(212\) 982.504 1701.75i 0.318296 0.551304i
\(213\) 1119.01 + 1938.18i 0.359967 + 0.623482i
\(214\) −461.702 799.691i −0.147483 0.255448i
\(215\) 1328.72 2301.42i 0.421480 0.730025i
\(216\) −1151.71 −0.362796
\(217\) −2615.24 2836.08i −0.818130 0.887215i
\(218\) −379.053 −0.117765
\(219\) 1929.56 3342.09i 0.595377 1.03122i
\(220\) −2061.97 3571.44i −0.631901 1.09448i
\(221\) 110.979 + 192.222i 0.0337795 + 0.0585079i
\(222\) 2354.36 4077.87i 0.711776 1.23283i
\(223\) 4010.07 1.20419 0.602094 0.798425i \(-0.294333\pi\)
0.602094 + 0.798425i \(0.294333\pi\)
\(224\) 2802.95 + 3039.64i 0.836070 + 0.906670i
\(225\) 171.276 0.0507485
\(226\) 3086.39 5345.78i 0.908423 1.57343i
\(227\) −2416.92 4186.23i −0.706681 1.22401i −0.966081 0.258238i \(-0.916858\pi\)
0.259400 0.965770i \(-0.416475\pi\)
\(228\) 331.489 + 574.156i 0.0962869 + 0.166774i
\(229\) −2718.97 + 4709.39i −0.784605 + 1.35898i 0.144630 + 0.989486i \(0.453801\pi\)
−0.929235 + 0.369490i \(0.879532\pi\)
\(230\) 906.922 0.260003
\(231\) −1370.66 + 4395.31i −0.390401 + 1.25190i
\(232\) 690.231 0.195327
\(233\) 2059.93 3567.90i 0.579186 1.00318i −0.416387 0.909187i \(-0.636704\pi\)
0.995573 0.0939917i \(-0.0299627\pi\)
\(234\) 760.662 + 1317.51i 0.212505 + 0.368069i
\(235\) 284.469 + 492.715i 0.0789647 + 0.136771i
\(236\) 630.462 1091.99i 0.173896 0.301198i
\(237\) −1273.97 −0.349170
\(238\) −466.018 + 104.852i −0.126922 + 0.0285569i
\(239\) −599.850 −0.162348 −0.0811738 0.996700i \(-0.525867\pi\)
−0.0811738 + 0.996700i \(0.525867\pi\)
\(240\) 1522.81 2637.58i 0.409570 0.709396i
\(241\) 1191.55 + 2063.83i 0.318484 + 0.551631i 0.980172 0.198148i \(-0.0634928\pi\)
−0.661688 + 0.749780i \(0.730159\pi\)
\(242\) −5570.61 9648.59i −1.47972 2.56295i
\(243\) 1599.36 2770.18i 0.422218 0.731304i
\(244\) −2158.69 −0.566377
\(245\) 292.955 3609.79i 0.0763928 0.941311i
\(246\) 4372.52 1.13326
\(247\) −473.383 + 819.924i −0.121946 + 0.211217i
\(248\) 798.817 + 1383.59i 0.204536 + 0.354267i
\(249\) −786.228 1361.79i −0.200101 0.346585i
\(250\) −2730.86 + 4729.99i −0.690860 + 1.19660i
\(251\) −3857.12 −0.969956 −0.484978 0.874526i \(-0.661172\pi\)
−0.484978 + 0.874526i \(0.661172\pi\)
\(252\) −1361.88 + 306.416i −0.340437 + 0.0765968i
\(253\) 1510.73 0.375409
\(254\) 3019.97 5230.74i 0.746022 1.29215i
\(255\) 137.997 + 239.019i 0.0338892 + 0.0586977i
\(256\) −2668.85 4622.58i −0.651575 1.12856i
\(257\) −2417.01 + 4186.39i −0.586650 + 1.01611i 0.408018 + 0.912974i \(0.366220\pi\)
−0.994668 + 0.103133i \(0.967113\pi\)
\(258\) −3557.26 −0.858393
\(259\) −1836.84 + 5890.24i −0.440679 + 1.41313i
\(260\) −2017.79 −0.481300
\(261\) −570.368 + 987.906i −0.135268 + 0.234291i
\(262\) −4097.39 7096.88i −0.966173 1.67346i
\(263\) −263.698 456.738i −0.0618262 0.107086i 0.833456 0.552587i \(-0.186359\pi\)
−0.895282 + 0.445500i \(0.853026\pi\)
\(264\) 953.336 1651.23i 0.222249 0.384947i
\(265\) 3489.29 0.808850
\(266\) −1381.23 1497.87i −0.318378 0.345263i
\(267\) −2271.73 −0.520702
\(268\) −651.311 + 1128.10i −0.148452 + 0.257126i
\(269\) 130.674 + 226.334i 0.0296184 + 0.0513005i 0.880455 0.474130i \(-0.157237\pi\)
−0.850836 + 0.525431i \(0.823904\pi\)
\(270\) 2960.56 + 5127.83i 0.667310 + 1.15581i
\(271\) −1368.85 + 2370.92i −0.306833 + 0.531450i −0.977668 0.210157i \(-0.932603\pi\)
0.670835 + 0.741607i \(0.265936\pi\)
\(272\) 526.351 0.117334
\(273\) 1527.12 + 1656.08i 0.338555 + 0.367144i
\(274\) 8122.02 1.79076
\(275\) −443.765 + 768.623i −0.0973091 + 0.168544i
\(276\) −258.807 448.266i −0.0564432 0.0977625i
\(277\) 2049.83 + 3550.41i 0.444629 + 0.770120i 0.998026 0.0627972i \(-0.0200021\pi\)
−0.553397 + 0.832918i \(0.686669\pi\)
\(278\) 638.687 1106.24i 0.137791 0.238661i
\(279\) −2640.39 −0.566581
\(280\) −446.508 + 1431.83i −0.0952999 + 0.305600i
\(281\) 1600.73 0.339828 0.169914 0.985459i \(-0.445651\pi\)
0.169914 + 0.985459i \(0.445651\pi\)
\(282\) 380.790 659.548i 0.0804104 0.139275i
\(283\) 2903.21 + 5028.51i 0.609816 + 1.05623i 0.991270 + 0.131845i \(0.0420901\pi\)
−0.381454 + 0.924388i \(0.624577\pi\)
\(284\) −1758.07 3045.07i −0.367333 0.636239i
\(285\) −588.630 + 1019.54i −0.122342 + 0.211902i
\(286\) −7883.29 −1.62989
\(287\) −5589.72 + 1257.66i −1.14965 + 0.258667i
\(288\) 2829.90 0.579005
\(289\) 2432.65 4213.47i 0.495146 0.857618i
\(290\) −1774.29 3073.16i −0.359276 0.622284i
\(291\) 1158.64 + 2006.82i 0.233404 + 0.404267i
\(292\) −3031.54 + 5250.78i −0.607559 + 1.05232i
\(293\) 727.432 0.145041 0.0725205 0.997367i \(-0.476896\pi\)
0.0725205 + 0.997367i \(0.476896\pi\)
\(294\) −4380.77 + 2076.42i −0.869020 + 0.411903i
\(295\) 2239.04 0.441904
\(296\) 1277.58 2212.84i 0.250872 0.434523i
\(297\) 4931.61 + 8541.81i 0.963506 + 1.66884i
\(298\) 1416.16 + 2452.86i 0.275288 + 0.476813i
\(299\) 369.589 640.147i 0.0714845 0.123815i
\(300\) 304.090 0.0585222
\(301\) 4547.52 1023.17i 0.870813 0.195929i
\(302\) 11295.9 2.15233
\(303\) −1651.68 + 2860.80i −0.313157 + 0.542404i
\(304\) 1122.58 + 1944.36i 0.211790 + 0.366832i
\(305\) −1916.61 3319.66i −0.359818 0.623223i
\(306\) −163.464 + 283.128i −0.0305379 + 0.0528932i
\(307\) −6262.33 −1.16420 −0.582101 0.813117i \(-0.697769\pi\)
−0.582101 + 0.813117i \(0.697769\pi\)
\(308\) 2153.44 6905.48i 0.398389 1.27752i
\(309\) 7276.01 1.33954
\(310\) 4106.84 7113.26i 0.752429 1.30324i
\(311\) 2839.84 + 4918.75i 0.517790 + 0.896839i 0.999786 + 0.0206654i \(0.00657847\pi\)
−0.481996 + 0.876173i \(0.660088\pi\)
\(312\) −466.454 807.923i −0.0846403 0.146601i
\(313\) 581.100 1006.49i 0.104938 0.181758i −0.808775 0.588119i \(-0.799869\pi\)
0.913713 + 0.406360i \(0.133202\pi\)
\(314\) 12582.6 2.26139
\(315\) −1680.36 1822.25i −0.300564 0.325944i
\(316\) 2001.54 0.356315
\(317\) −3871.48 + 6705.61i −0.685944 + 1.18809i 0.287195 + 0.957872i \(0.407277\pi\)
−0.973139 + 0.230218i \(0.926056\pi\)
\(318\) −2335.38 4045.00i −0.411829 0.713310i
\(319\) −2955.56 5119.19i −0.518746 0.898494i
\(320\) −1182.77 + 2048.62i −0.206621 + 0.357879i
\(321\) −935.836 −0.162721
\(322\) 1078.38 + 1169.44i 0.186633 + 0.202393i
\(323\) −203.457 −0.0350485
\(324\) 672.167 1164.23i 0.115255 0.199627i
\(325\) 217.128 + 376.077i 0.0370588 + 0.0641876i
\(326\) 7645.85 + 13243.0i 1.29897 + 2.24988i
\(327\) −192.078 + 332.690i −0.0324831 + 0.0562623i
\(328\) 2372.73 0.399427
\(329\) −297.088 + 952.677i −0.0497842 + 0.159644i
\(330\) −9802.49 −1.63518
\(331\) −3301.74 + 5718.78i −0.548278 + 0.949645i 0.450115 + 0.892971i \(0.351383\pi\)
−0.998393 + 0.0566743i \(0.981950\pi\)
\(332\) 1235.24 + 2139.51i 0.204195 + 0.353677i
\(333\) 2111.45 + 3657.14i 0.347468 + 0.601831i
\(334\) −910.614 + 1577.23i −0.149181 + 0.258390i
\(335\) −2313.08 −0.377245
\(336\) 5211.76 1172.62i 0.846205 0.190392i
\(337\) −5975.53 −0.965898 −0.482949 0.875648i \(-0.660434\pi\)
−0.482949 + 0.875648i \(0.660434\pi\)
\(338\) 2173.72 3764.99i 0.349806 0.605883i
\(339\) −3127.94 5417.76i −0.501140 0.868000i
\(340\) −216.808 375.523i −0.0345826 0.0598988i
\(341\) 6841.07 11849.1i 1.08641 1.88171i
\(342\) −1394.51 −0.220487
\(343\) 5003.04 3914.49i 0.787576 0.616217i
\(344\) −1930.34 −0.302549
\(345\) 459.566 795.992i 0.0717166 0.124217i
\(346\) 4943.88 + 8563.05i 0.768163 + 1.33050i
\(347\) −1867.29 3234.23i −0.288879 0.500354i 0.684663 0.728860i \(-0.259949\pi\)
−0.973543 + 0.228506i \(0.926616\pi\)
\(348\) −1012.65 + 1753.96i −0.155988 + 0.270179i
\(349\) 4115.40 0.631210 0.315605 0.948891i \(-0.397792\pi\)
0.315605 + 0.948891i \(0.397792\pi\)
\(350\) −911.752 + 205.140i −0.139243 + 0.0313292i
\(351\) 4825.94 0.733874
\(352\) −7332.07 + 12699.5i −1.11023 + 1.92297i
\(353\) −2374.92 4113.48i −0.358085 0.620222i 0.629556 0.776955i \(-0.283237\pi\)
−0.987641 + 0.156734i \(0.949904\pi\)
\(354\) −1498.59 2595.63i −0.224997 0.389707i
\(355\) 3121.83 5407.18i 0.466732 0.808403i
\(356\) 3569.12 0.531357
\(357\) −144.119 + 462.149i −0.0213658 + 0.0685141i
\(358\) 1012.04 0.149408
\(359\) −854.496 + 1480.03i −0.125623 + 0.217585i −0.921976 0.387247i \(-0.873426\pi\)
0.796353 + 0.604832i \(0.206760\pi\)
\(360\) 513.261 + 888.993i 0.0751422 + 0.130150i
\(361\) 2995.58 + 5188.49i 0.436737 + 0.756450i
\(362\) −8241.97 + 14275.5i −1.19665 + 2.07266i
\(363\) −11291.2 −1.63261
\(364\) −2399.26 2601.87i −0.345483 0.374656i
\(365\) −10766.3 −1.54392
\(366\) −2565.57 + 4443.70i −0.366406 + 0.634633i
\(367\) −755.329 1308.27i −0.107433 0.186079i 0.807297 0.590146i \(-0.200930\pi\)
−0.914730 + 0.404067i \(0.867596\pi\)
\(368\) −876.440 1518.04i −0.124151 0.215036i
\(369\) −1960.69 + 3396.02i −0.276611 + 0.479104i
\(370\) −13136.5 −1.84577
\(371\) 4148.96 + 4499.31i 0.580602 + 0.629630i
\(372\) −4687.85 −0.653370
\(373\) −6328.35 + 10961.0i −0.878471 + 1.52156i −0.0254526 + 0.999676i \(0.508103\pi\)
−0.853019 + 0.521881i \(0.825231\pi\)
\(374\) −847.046 1467.13i −0.117112 0.202843i
\(375\) 2767.63 + 4793.68i 0.381120 + 0.660118i
\(376\) 206.634 357.901i 0.0283414 0.0490887i
\(377\) −2892.24 −0.395113
\(378\) −3091.89 + 9914.81i −0.420713 + 1.34911i
\(379\) −9215.14 −1.24894 −0.624472 0.781047i \(-0.714686\pi\)
−0.624472 + 0.781047i \(0.714686\pi\)
\(380\) 924.798 1601.80i 0.124845 0.216238i
\(381\) −3060.63 5301.16i −0.411550 0.712826i
\(382\) 2209.78 + 3827.45i 0.295975 + 0.512643i
\(383\) 306.679 531.183i 0.0409153 0.0708674i −0.844843 0.535015i \(-0.820306\pi\)
0.885758 + 0.464148i \(0.153639\pi\)
\(384\) −3593.15 −0.477506
\(385\) 12531.3 2819.48i 1.65884 0.373231i
\(386\) 4149.79 0.547199
\(387\) 1595.12 2762.83i 0.209521 0.362901i
\(388\) −1820.34 3152.92i −0.238179 0.412539i
\(389\) −584.829 1012.95i −0.0762263 0.132028i 0.825393 0.564559i \(-0.190954\pi\)
−0.901619 + 0.432531i \(0.857620\pi\)
\(390\) −2398.11 + 4153.65i −0.311367 + 0.539304i
\(391\) 158.847 0.0205453
\(392\) −2377.21 + 1126.76i −0.306294 + 0.145179i
\(393\) −8305.10 −1.06600
\(394\) 9200.03 15934.9i 1.17637 2.03754i
\(395\) 1777.08 + 3077.99i 0.226366 + 0.392078i
\(396\) −2475.38 4287.48i −0.314122 0.544076i
\(397\) 3233.76 5601.04i 0.408811 0.708081i −0.585946 0.810350i \(-0.699277\pi\)
0.994757 + 0.102269i \(0.0326103\pi\)
\(398\) 9263.10 1.16663
\(399\) −2014.57 + 453.269i −0.252768 + 0.0568718i
\(400\) 1029.79 0.128724
\(401\) −84.7378 + 146.770i −0.0105526 + 0.0182777i −0.871253 0.490833i \(-0.836692\pi\)
0.860701 + 0.509111i \(0.170026\pi\)
\(402\) 1548.15 + 2681.47i 0.192076 + 0.332685i
\(403\) −3347.24 5797.59i −0.413742 0.716622i
\(404\) 2594.96 4494.61i 0.319565 0.553503i
\(405\) 2387.15 0.292885
\(406\) 1853.00 5942.04i 0.226509 0.726351i
\(407\) −21882.4 −2.66504
\(408\) 100.239 173.620i 0.0121632 0.0210673i
\(409\) 3294.12 + 5705.59i 0.398249 + 0.689788i 0.993510 0.113745i \(-0.0362846\pi\)
−0.595261 + 0.803533i \(0.702951\pi\)
\(410\) −6099.28 10564.3i −0.734688 1.27252i
\(411\) 4115.69 7128.58i 0.493946 0.855539i
\(412\) −11431.4 −1.36695
\(413\) 2662.34 + 2887.16i 0.317204 + 0.343990i
\(414\) 1088.75 0.129249
\(415\) −2193.44 + 3799.15i −0.259450 + 0.449380i
\(416\) 3587.48 + 6213.70i 0.422814 + 0.732336i
\(417\) −647.286 1121.13i −0.0760137 0.131660i
\(418\) 3613.08 6258.05i 0.422779 0.732275i
\(419\) 4312.62 0.502829 0.251414 0.967880i \(-0.419104\pi\)
0.251414 + 0.967880i \(0.419104\pi\)
\(420\) −2983.37 3235.30i −0.346604 0.375872i
\(421\) 7210.67 0.834742 0.417371 0.908736i \(-0.362952\pi\)
0.417371 + 0.908736i \(0.362952\pi\)
\(422\) 5097.32 8828.82i 0.587995 1.01844i
\(423\) 341.502 + 591.499i 0.0392539 + 0.0679898i
\(424\) −1267.29 2195.01i −0.145153 0.251412i
\(425\) −46.6601 + 80.8176i −0.00532552 + 0.00922407i
\(426\) −8357.78 −0.950553
\(427\) 2001.63 6418.65i 0.226851 0.727448i
\(428\) 1470.30 0.166050
\(429\) −3994.71 + 6919.04i −0.449572 + 0.778682i
\(430\) 4962.07 + 8594.56i 0.556494 + 0.963876i
\(431\) 4952.65 + 8578.24i 0.553505 + 0.958700i 0.998018 + 0.0629270i \(0.0200435\pi\)
−0.444513 + 0.895773i \(0.646623\pi\)
\(432\) 5722.11 9910.98i 0.637280 1.10380i
\(433\) −3132.44 −0.347657 −0.173829 0.984776i \(-0.555614\pi\)
−0.173829 + 0.984776i \(0.555614\pi\)
\(434\) 14055.5 3162.44i 1.55458 0.349774i
\(435\) −3596.36 −0.396396
\(436\) 301.775 522.690i 0.0331477 0.0574135i
\(437\) 338.782 + 586.787i 0.0370849 + 0.0642330i
\(438\) 7205.87 + 12480.9i 0.786095 + 1.36156i
\(439\) 2151.11 3725.83i 0.233865 0.405066i −0.725077 0.688668i \(-0.758196\pi\)
0.958942 + 0.283601i \(0.0915293\pi\)
\(440\) −5319.28 −0.576334
\(441\) 351.690 4333.52i 0.0379754 0.467933i
\(442\) −828.896 −0.0892004
\(443\) −2474.22 + 4285.47i −0.265358 + 0.459613i −0.967657 0.252268i \(-0.918823\pi\)
0.702299 + 0.711882i \(0.252157\pi\)
\(444\) 3748.74 + 6493.01i 0.400693 + 0.694020i
\(445\) 3168.86 + 5488.63i 0.337570 + 0.584688i
\(446\) −7487.72 + 12969.1i −0.794964 + 1.37692i
\(447\) 2870.45 0.303731
\(448\) −4048.00 + 910.782i −0.426897 + 0.0960500i
\(449\) 7606.44 0.799488 0.399744 0.916627i \(-0.369099\pi\)
0.399744 + 0.916627i \(0.369099\pi\)
\(450\) −319.813 + 553.932i −0.0335025 + 0.0580280i
\(451\) −10160.0 17597.7i −1.06079 1.83734i
\(452\) 4914.32 + 8511.86i 0.511394 + 0.885761i
\(453\) 5723.97 9914.20i 0.593676 1.02828i
\(454\) 18051.8 1.86611
\(455\) 1870.98 5999.70i 0.192776 0.618177i
\(456\) 855.145 0.0878198
\(457\) −1603.02 + 2776.52i −0.164084 + 0.284202i −0.936330 0.351122i \(-0.885800\pi\)
0.772246 + 0.635324i \(0.219133\pi\)
\(458\) −10153.9 17587.1i −1.03594 1.79430i
\(459\) 518.540 + 898.137i 0.0527306 + 0.0913321i
\(460\) −722.026 + 1250.59i −0.0731840 + 0.126758i
\(461\) 11181.4 1.12965 0.564825 0.825211i \(-0.308944\pi\)
0.564825 + 0.825211i \(0.308944\pi\)
\(462\) −11655.7 12640.0i −1.17375 1.27287i
\(463\) −2334.72 −0.234349 −0.117174 0.993111i \(-0.537384\pi\)
−0.117174 + 0.993111i \(0.537384\pi\)
\(464\) −3429.31 + 5939.75i −0.343108 + 0.594280i
\(465\) −4162.13 7209.03i −0.415085 0.718948i
\(466\) 7692.72 + 13324.2i 0.764718 + 1.32453i
\(467\) 7306.43 12655.1i 0.723986 1.25398i −0.235404 0.971898i \(-0.575641\pi\)
0.959390 0.282083i \(-0.0910253\pi\)
\(468\) −2422.34 −0.239258
\(469\) −2750.38 2982.63i −0.270791 0.293657i
\(470\) −2124.68 −0.208519
\(471\) 6375.99 11043.5i 0.623758 1.08038i
\(472\) −813.203 1408.51i −0.0793024 0.137356i
\(473\) 8265.69 + 14316.6i 0.803503 + 1.39171i
\(474\) 2378.80 4120.20i 0.230510 0.399256i
\(475\) −398.058 −0.0384509
\(476\) 226.426 726.084i 0.0218030 0.0699160i
\(477\) 4188.86 0.402085
\(478\) 1120.06 1940.00i 0.107176 0.185635i
\(479\) −6026.15 10437.6i −0.574827 0.995629i −0.996060 0.0886769i \(-0.971736\pi\)
0.421234 0.906952i \(-0.361597\pi\)
\(480\) 4460.86 + 7726.44i 0.424187 + 0.734713i
\(481\) −5353.39 + 9272.35i −0.507471 + 0.878966i
\(482\) −8899.63 −0.841011
\(483\) 1572.85 353.885i 0.148172 0.0333381i
\(484\) 17739.7 1.66601
\(485\) 3232.39 5598.67i 0.302630 0.524170i
\(486\) 5972.76 + 10345.1i 0.557469 + 0.965564i
\(487\) −9112.51 15783.3i −0.847900 1.46861i −0.883079 0.469225i \(-0.844533\pi\)
0.0351786 0.999381i \(-0.488800\pi\)
\(488\) −1392.20 + 2411.36i −0.129143 + 0.223682i
\(489\) 15497.6 1.43318
\(490\) 11127.6 + 7687.78i 1.02590 + 0.708773i
\(491\) −3903.86 −0.358816 −0.179408 0.983775i \(-0.557418\pi\)
−0.179408 + 0.983775i \(0.557418\pi\)
\(492\) −3481.08 + 6029.41i −0.318982 + 0.552494i
\(493\) −310.766 538.262i −0.0283898 0.0491727i
\(494\) −1767.83 3061.98i −0.161009 0.278876i
\(495\) 4395.56 7613.33i 0.399123 0.691301i
\(496\) −15875.2 −1.43714
\(497\) 10684.4 2403.94i 0.964306 0.216965i
\(498\) 5872.28 0.528400
\(499\) −9922.49 + 17186.3i −0.890163 + 1.54181i −0.0504848 + 0.998725i \(0.516077\pi\)
−0.839679 + 0.543084i \(0.817257\pi\)
\(500\) −4348.23 7531.36i −0.388918 0.673625i
\(501\) 922.874 + 1598.46i 0.0822973 + 0.142543i
\(502\) 7202.13 12474.5i 0.640332 1.10909i
\(503\) 9819.27 0.870417 0.435208 0.900330i \(-0.356675\pi\)
0.435208 + 0.900330i \(0.356675\pi\)
\(504\) −536.029 + 1718.89i −0.0473743 + 0.151916i
\(505\) 9215.81 0.812076
\(506\) −2820.88 + 4885.90i −0.247832 + 0.429258i
\(507\) −2202.98 3815.68i −0.192974 0.334241i
\(508\) 4808.56 + 8328.67i 0.419971 + 0.727411i
\(509\) −8586.30 + 14871.9i −0.747704 + 1.29506i 0.201217 + 0.979547i \(0.435510\pi\)
−0.948921 + 0.315514i \(0.897823\pi\)
\(510\) −1030.69 −0.0894899
\(511\) −12801.7 13882.7i −1.10825 1.20183i
\(512\) 12338.4 1.06501
\(513\) −2211.84 + 3831.01i −0.190361 + 0.329714i
\(514\) −9026.24 15633.9i −0.774573 1.34160i
\(515\) −10149.4 17579.3i −0.868420 1.50415i
\(516\) 2832.04 4905.23i 0.241615 0.418490i
\(517\) −3539.23 −0.301074
\(518\) −15620.0 16939.1i −1.32491 1.43679i
\(519\) 10020.9 0.847530
\(520\) −1301.33 + 2253.96i −0.109744 + 0.190082i
\(521\) −4924.97 8530.31i −0.414140 0.717312i 0.581198 0.813762i \(-0.302584\pi\)
−0.995338 + 0.0964507i \(0.969251\pi\)
\(522\) −2130.02 3689.30i −0.178598 0.309342i
\(523\) 5103.26 8839.10i 0.426673 0.739019i −0.569902 0.821712i \(-0.693019\pi\)
0.996575 + 0.0826937i \(0.0263523\pi\)
\(524\) 13048.2 1.08781
\(525\) −281.965 + 904.182i −0.0234399 + 0.0751652i
\(526\) 1969.54 0.163262
\(527\) 719.311 1245.88i 0.0594567 0.102982i
\(528\) 9473.03 + 16407.8i 0.780797 + 1.35238i
\(529\) −264.500 458.127i −0.0217391 0.0376533i
\(530\) −6515.31 + 11284.9i −0.533976 + 0.924873i
\(531\) 2687.94 0.219674
\(532\) 3165.09 712.132i 0.257940 0.0580354i
\(533\) −9942.32 −0.807973
\(534\) 4241.84 7347.09i 0.343750 0.595393i
\(535\) 1305.41 + 2261.04i 0.105491 + 0.182716i
\(536\) 840.096 + 1455.09i 0.0676989 + 0.117258i
\(537\) 512.833 888.253i 0.0412112 0.0713798i
\(538\) −975.995 −0.0782122
\(539\) 18536.0 + 12806.1i 1.48127 + 1.02337i
\(540\) −9427.93 −0.751321
\(541\) −4695.10 + 8132.14i −0.373120 + 0.646263i −0.990044 0.140760i \(-0.955045\pi\)
0.616924 + 0.787023i \(0.288379\pi\)
\(542\) −5111.92 8854.10i −0.405121 0.701691i
\(543\) 8352.94 + 14467.7i 0.660145 + 1.14341i
\(544\) −770.938 + 1335.30i −0.0607605 + 0.105240i
\(545\) 1071.73 0.0842347
\(546\) −8207.47 + 1846.65i −0.643310 + 0.144742i
\(547\) 18781.7 1.46809 0.734047 0.679099i \(-0.237629\pi\)
0.734047 + 0.679099i \(0.237629\pi\)
\(548\) −6466.17 + 11199.7i −0.504053 + 0.873045i
\(549\) −2300.87 3985.22i −0.178868 0.309809i
\(550\) −1657.22 2870.39i −0.128480 0.222535i
\(551\) 1325.58 2295.96i 0.102489 0.177516i
\(552\) −667.645 −0.0514798
\(553\) −1855.91 + 5951.39i −0.142715 + 0.457647i
\(554\) −15310.0 −1.17412
\(555\) −6656.69 + 11529.7i −0.509118 + 0.881819i
\(556\) 1016.95 + 1761.41i 0.0775691 + 0.134354i
\(557\) −10532.7 18243.2i −0.801229 1.38777i −0.918807 0.394706i \(-0.870846\pi\)
0.117578 0.993064i \(-0.462487\pi\)
\(558\) 4930.22 8539.40i 0.374038 0.647852i
\(559\) 8088.58 0.612004
\(560\) −10103.1 10956.2i −0.762381 0.826759i
\(561\) −1716.90 −0.129211
\(562\) −2988.94 + 5177.00i −0.224343 + 0.388574i
\(563\) −980.682 1698.59i −0.0734117 0.127153i 0.826983 0.562227i \(-0.190055\pi\)
−0.900394 + 0.435074i \(0.856722\pi\)
\(564\) 606.316 + 1050.17i 0.0452668 + 0.0784044i
\(565\) −8726.42 + 15114.6i −0.649776 + 1.12544i
\(566\) −21683.9 −1.61032
\(567\) 2838.45 + 3078.14i 0.210236 + 0.227989i
\(568\) −4535.32 −0.335031
\(569\) −9982.48 + 17290.2i −0.735478 + 1.27389i 0.219035 + 0.975717i \(0.429709\pi\)
−0.954513 + 0.298169i \(0.903624\pi\)
\(570\) −2198.22 3807.42i −0.161532 0.279781i
\(571\) 5325.77 + 9224.51i 0.390327 + 0.676066i 0.992493 0.122305i \(-0.0390287\pi\)
−0.602166 + 0.798371i \(0.705695\pi\)
\(572\) 6276.10 10870.5i 0.458771 0.794615i
\(573\) 4479.07 0.326555
\(574\) 6369.85 20426.3i 0.463192 1.48533i
\(575\) 310.780 0.0225398
\(576\) −1419.90 + 2459.35i −0.102713 + 0.177904i
\(577\) 7918.21 + 13714.7i 0.571299 + 0.989519i 0.996433 + 0.0843885i \(0.0268937\pi\)
−0.425134 + 0.905130i \(0.639773\pi\)
\(578\) 9084.65 + 15735.1i 0.653757 + 1.13234i
\(579\) 2102.83 3642.21i 0.150934 0.261425i
\(580\) 5650.25 0.404507
\(581\) −7506.98 + 1689.04i −0.536045 + 0.120608i
\(582\) −8653.77 −0.616341
\(583\) −10853.0 + 18798.0i −0.770989 + 1.33539i
\(584\) 3910.24 + 6772.73i 0.277067 + 0.479893i
\(585\) −2150.69 3725.10i −0.152000 0.263272i
\(586\) −1358.28 + 2352.62i −0.0957512 + 0.165846i
\(587\) 12834.5 0.902444 0.451222 0.892412i \(-0.350988\pi\)
0.451222 + 0.892412i \(0.350988\pi\)
\(588\) 624.404 7693.90i 0.0437925 0.539610i
\(589\) 6136.46 0.429284
\(590\) −4180.80 + 7241.36i −0.291730 + 0.505292i
\(591\) −9323.90 16149.5i −0.648957 1.12403i
\(592\) 12695.0 + 21988.4i 0.881353 + 1.52655i
\(593\) 6525.01 11301.6i 0.451855 0.782636i −0.546646 0.837364i \(-0.684096\pi\)
0.998501 + 0.0547278i \(0.0174291\pi\)
\(594\) −36833.9 −2.54430
\(595\) 1317.61 296.457i 0.0907847 0.0204262i
\(596\) −4509.78 −0.309946
\(597\) 4693.91 8130.09i 0.321790 0.557357i
\(598\) 1380.22 + 2390.61i 0.0943834 + 0.163477i
\(599\) −136.649 236.683i −0.00932109 0.0161446i 0.861327 0.508051i \(-0.169634\pi\)
−0.870648 + 0.491906i \(0.836300\pi\)
\(600\) 196.116 339.683i 0.0133440 0.0231125i
\(601\) 4002.62 0.271665 0.135832 0.990732i \(-0.456629\pi\)
0.135832 + 0.990732i \(0.456629\pi\)
\(602\) −5182.19 + 16617.8i −0.350848 + 1.12507i
\(603\) −2776.83 −0.187531
\(604\) −8992.94 + 15576.2i −0.605824 + 1.04932i
\(605\) 15750.3 + 27280.3i 1.05841 + 1.83323i
\(606\) −6168.15 10683.5i −0.413472 0.716154i
\(607\) −7427.06 + 12864.1i −0.496631 + 0.860191i −0.999992 0.00388537i \(-0.998763\pi\)
0.503361 + 0.864076i \(0.332097\pi\)
\(608\) −6576.89 −0.438698
\(609\) −4276.27 4637.37i −0.284537 0.308564i
\(610\) 14315.0 0.950159
\(611\) −865.849 + 1499.69i −0.0573298 + 0.0992981i
\(612\) −260.276 450.812i −0.0171912 0.0297761i
\(613\) 14931.8 + 25862.7i 0.983834 + 1.70405i 0.647005 + 0.762485i \(0.276021\pi\)
0.336829 + 0.941566i \(0.390646\pi\)
\(614\) 11693.2 20253.2i 0.768566 1.33120i
\(615\) −12362.8 −0.810595
\(616\) −6324.92 6859.02i −0.413699 0.448633i
\(617\) −16055.1 −1.04758 −0.523789 0.851848i \(-0.675482\pi\)
−0.523789 + 0.851848i \(0.675482\pi\)
\(618\) −13586.0 + 23531.6i −0.884319 + 1.53168i
\(619\) −9893.35 17135.8i −0.642403 1.11267i −0.984895 0.173154i \(-0.944604\pi\)
0.342492 0.939521i \(-0.388729\pi\)
\(620\) 6539.14 + 11326.1i 0.423578 + 0.733658i
\(621\) 1726.87 2991.02i 0.111589 0.193278i
\(622\) −21210.6 −1.36731
\(623\) −3309.44 + 10612.4i −0.212825 + 0.682468i
\(624\) 9270.05 0.594710
\(625\) 6876.70 11910.8i 0.440109 0.762291i
\(626\) 2170.10 + 3758.72i 0.138553 + 0.239982i
\(627\) −3661.73 6342.30i −0.233230 0.403967i
\(628\) −10017.3 + 17350.5i −0.636521 + 1.10249i
\(629\) −2300.85 −0.145852
\(630\) 9031.05 2031.95i 0.571120 0.128499i
\(631\) −1044.43 −0.0658927 −0.0329463 0.999457i \(-0.510489\pi\)
−0.0329463 + 0.999457i \(0.510489\pi\)
\(632\) 1290.85 2235.81i 0.0812455 0.140721i
\(633\) −5165.95 8947.69i −0.324373 0.561830i
\(634\) −14457.9 25041.9i −0.905674 1.56867i
\(635\) −8538.62 + 14789.3i −0.533614 + 0.924246i
\(636\) 7437.05 0.463677
\(637\) 9961.09 4721.42i 0.619581 0.293672i
\(638\) 22074.9 1.36983
\(639\) 3747.73 6491.26i 0.232016 0.401863i
\(640\) 5012.14 + 8681.27i 0.309566 + 0.536184i
\(641\) −7026.86 12170.9i −0.432987 0.749955i 0.564142 0.825678i \(-0.309207\pi\)
−0.997129 + 0.0757228i \(0.975874\pi\)
\(642\) 1747.42 3026.63i 0.107423 0.186061i
\(643\) −14339.0 −0.879431 −0.439715 0.898137i \(-0.644921\pi\)
−0.439715 + 0.898137i \(0.644921\pi\)
\(644\) −2471.11 + 555.990i −0.151204 + 0.0340203i
\(645\) 10057.8 0.613991
\(646\) 379.902 658.009i 0.0231378 0.0400759i
\(647\) 8368.35 + 14494.4i 0.508491 + 0.880732i 0.999952 + 0.00983244i \(0.00312981\pi\)
−0.491461 + 0.870900i \(0.663537\pi\)
\(648\) −866.996 1501.68i −0.0525599 0.0910365i
\(649\) −6964.27 + 12062.5i −0.421219 + 0.729574i
\(650\) −1621.71 −0.0978598
\(651\) 4346.77 13938.9i 0.261695 0.839181i
\(652\) −24348.3 −1.46251
\(653\) 15313.9 26524.5i 0.917733 1.58956i 0.114883 0.993379i \(-0.463351\pi\)
0.802850 0.596181i \(-0.203316\pi\)
\(654\) −717.310 1242.42i −0.0428884 0.0742850i
\(655\) 11584.9 + 20065.6i 0.691083 + 1.19699i
\(656\) −11788.6 + 20418.4i −0.701626 + 1.21525i
\(657\) −12924.8 −0.767496
\(658\) −2526.36 2739.69i −0.149677 0.162317i
\(659\) −9716.61 −0.574363 −0.287182 0.957876i \(-0.592718\pi\)
−0.287182 + 0.957876i \(0.592718\pi\)
\(660\) 7804.04 13517.0i 0.460260 0.797194i
\(661\) −2548.38 4413.93i −0.149955 0.259730i 0.781255 0.624212i \(-0.214580\pi\)
−0.931211 + 0.364481i \(0.881246\pi\)
\(662\) −12330.2 21356.6i −0.723909 1.25385i
\(663\) −420.028 + 727.510i −0.0246041 + 0.0426156i
\(664\) 3186.57 0.186239
\(665\) 3905.27 + 4235.05i 0.227729 + 0.246960i
\(666\) −15770.3 −0.917545
\(667\) −1034.93 + 1792.55i −0.0600789 + 0.104060i
\(668\) −1449.93 2511.35i −0.0839812 0.145460i
\(669\) 7588.54 + 13143.7i 0.438550 + 0.759590i
\(670\) 4319.06 7480.83i 0.249044 0.431358i
\(671\) 23845.5 1.37190
\(672\) −4658.75 + 14939.3i −0.267433 + 0.857583i
\(673\) 18211.9 1.04311 0.521557 0.853216i \(-0.325351\pi\)
0.521557 + 0.853216i \(0.325351\pi\)
\(674\) 11157.7 19325.7i 0.637654 1.10445i
\(675\) 1014.51 + 1757.18i 0.0578496 + 0.100198i
\(676\) 3461.11 + 5994.82i 0.196923 + 0.341080i
\(677\) −12346.0 + 21383.9i −0.700879 + 1.21396i 0.267280 + 0.963619i \(0.413875\pi\)
−0.968158 + 0.250339i \(0.919458\pi\)
\(678\) 23362.4 1.32334
\(679\) 11062.8 2489.08i 0.625258 0.140680i
\(680\) −559.302 −0.0315415
\(681\) 9147.42 15843.8i 0.514728 0.891536i
\(682\) 25547.7 + 44249.9i 1.43442 + 2.48448i
\(683\) −8687.76 15047.6i −0.486717 0.843019i 0.513166 0.858289i \(-0.328473\pi\)
−0.999883 + 0.0152701i \(0.995139\pi\)
\(684\) 1110.21 1922.94i 0.0620614 0.107493i
\(685\) −22964.1 −1.28090
\(686\) 3318.18 + 23489.8i 0.184677 + 1.30735i
\(687\) −20581.2 −1.14297
\(688\) 9590.60 16611.4i 0.531451 0.920500i
\(689\) 5310.24 + 9197.61i 0.293620 + 0.508565i
\(690\) 1716.23 + 2972.60i 0.0946897 + 0.164007i
\(691\) 5712.94 9895.10i 0.314516 0.544757i −0.664819 0.747005i \(-0.731491\pi\)
0.979334 + 0.202247i \(0.0648245\pi\)
\(692\) −15743.8 −0.864871
\(693\) 15043.7 3384.76i 0.824621 0.185536i
\(694\) 13946.6 0.762834
\(695\) −1805.82 + 3127.76i −0.0985590 + 0.170709i
\(696\) 1306.17 + 2262.36i 0.0711356 + 0.123210i
\(697\) −1068.29 1850.33i −0.0580548 0.100554i
\(698\) −7684.41 + 13309.8i −0.416704 + 0.721752i
\(699\) 15592.6 0.843728
\(700\) 442.996 1420.56i 0.0239196 0.0767032i
\(701\) 19974.7 1.07623 0.538114 0.842872i \(-0.319137\pi\)
0.538114 + 0.842872i \(0.319137\pi\)
\(702\) −9011.16 + 15607.8i −0.484479 + 0.839142i
\(703\) −4907.16 8499.44i −0.263267 0.455992i
\(704\) −7357.74 12744.0i −0.393900 0.682254i
\(705\) −1076.64 + 1864.80i −0.0575159 + 0.0996204i
\(706\) 17738.1 0.945583
\(707\) 10958.1 + 11883.5i 0.582917 + 0.632140i
\(708\) 4772.27 0.253323
\(709\) 8646.62 14976.4i 0.458012 0.793301i −0.540843 0.841123i \(-0.681895\pi\)
0.998856 + 0.0478226i \(0.0152282\pi\)
\(710\) 11658.4 + 20192.9i 0.616241 + 1.06736i
\(711\) 2133.37 + 3695.10i 0.112528 + 0.194905i
\(712\) 2301.82 3986.87i 0.121158 0.209852i
\(713\) −4790.97 −0.251646
\(714\) −1225.55 1329.04i −0.0642368 0.0696612i
\(715\) 22289.1 1.16583
\(716\) −805.714 + 1395.54i −0.0420544 + 0.0728404i
\(717\) −1135.14 1966.12i −0.0591249 0.102407i
\(718\) −3191.08 5527.12i −0.165864 0.287285i
\(719\) −13617.6 + 23586.4i −0.706332 + 1.22340i 0.259877 + 0.965642i \(0.416318\pi\)
−0.966209 + 0.257760i \(0.917015\pi\)
\(720\) −10200.3 −0.527973
\(721\) 10599.6 33990.0i 0.547505 1.75569i
\(722\) −22373.7 −1.15327
\(723\) −4509.73 + 7811.08i −0.231976 + 0.401794i
\(724\) −13123.3 22730.3i −0.673653 1.16680i
\(725\) −608.005 1053.10i −0.0311459 0.0539462i
\(726\) 21083.3 36517.4i 1.07779 1.86679i
\(727\) 33672.5 1.71780 0.858901 0.512141i \(-0.171148\pi\)
0.858901 + 0.512141i \(0.171148\pi\)
\(728\) −4453.75 + 1002.08i −0.226741 + 0.0510156i
\(729\) 18210.6 0.925192
\(730\) 20103.1 34819.6i 1.01925 1.76539i
\(731\) 869.104 + 1505.33i 0.0439740 + 0.0761652i
\(732\) −4085.04 7075.50i −0.206267 0.357265i
\(733\) −13840.0 + 23971.5i −0.697396 + 1.20793i 0.271970 + 0.962306i \(0.412325\pi\)
−0.969366 + 0.245620i \(0.921009\pi\)
\(734\) 5641.50 0.283694
\(735\) 12386.1 5870.86i 0.621592 0.294626i
\(736\) 5134.84 0.257164
\(737\) 7194.57 12461.4i 0.359587 0.622823i
\(738\) −7322.13 12682.3i −0.365219 0.632577i
\(739\) 10075.5 + 17451.3i 0.501535 + 0.868684i 0.999998 + 0.00177310i \(0.000564397\pi\)
−0.498464 + 0.866911i \(0.666102\pi\)
\(740\) 10458.3 18114.4i 0.519536 0.899862i
\(741\) −3583.27 −0.177645
\(742\) −22298.5 + 5017.06i −1.10324 + 0.248224i
\(743\) 13758.0 0.679315 0.339658 0.940549i \(-0.389689\pi\)
0.339658 + 0.940549i \(0.389689\pi\)
\(744\) −3023.32 + 5236.54i −0.148979 + 0.258039i
\(745\) −4004.03 6935.19i −0.196908 0.341055i
\(746\) −23633.0 40933.6i −1.15987 2.00896i
\(747\) −2633.20 + 4560.84i −0.128974 + 0.223390i
\(748\) 2697.43 0.131855
\(749\) −1363.32 + 4371.78i −0.0665082 + 0.213273i
\(750\) −20671.2 −1.00641
\(751\) −15544.2 + 26923.3i −0.755279 + 1.30818i 0.189957 + 0.981792i \(0.439165\pi\)
−0.945236 + 0.326389i \(0.894168\pi\)
\(752\) 2053.27 + 3556.36i 0.0995678 + 0.172456i
\(753\) −7299.10 12642.4i −0.353246 0.611839i
\(754\) 5400.48 9353.90i 0.260840 0.451789i
\(755\) −31937.8 −1.53952
\(756\) −11210.3 12157.0i −0.539306 0.584847i
\(757\) 16596.6 0.796847 0.398423 0.917202i \(-0.369557\pi\)
0.398423 + 0.917202i \(0.369557\pi\)
\(758\) 17206.8 29803.0i 0.824511 1.42809i
\(759\) 2858.86 + 4951.68i 0.136719 + 0.236805i
\(760\) −1192.85 2066.08i −0.0569334 0.0986115i
\(761\) 8613.00 14918.1i 0.410277 0.710621i −0.584643 0.811291i \(-0.698765\pi\)
0.994920 + 0.100670i \(0.0320987\pi\)
\(762\) 22859.6 1.08677
\(763\) 1274.35 + 1381.96i 0.0604646 + 0.0655705i
\(764\) −7037.08 −0.333236
\(765\) 462.176 800.512i 0.0218431 0.0378334i
\(766\) 1145.28 + 1983.68i 0.0540218 + 0.0935685i
\(767\) 3407.52 + 5902.00i 0.160415 + 0.277847i
\(768\) 10100.9 17495.3i 0.474590 0.822014i
\(769\) −7949.04 −0.372757 −0.186378 0.982478i \(-0.559675\pi\)
−0.186378 + 0.982478i \(0.559675\pi\)
\(770\) −14280.2 + 45792.5i −0.668341 + 2.14318i
\(771\) −18295.5 −0.854601
\(772\) −3303.76 + 5722.29i −0.154022 + 0.266774i
\(773\) −11989.8 20767.0i −0.557884 0.966284i −0.997673 0.0681828i \(-0.978280\pi\)
0.439788 0.898101i \(-0.355053\pi\)
\(774\) 5956.92 + 10317.7i 0.276637 + 0.479150i
\(775\) 1407.31 2437.54i 0.0652286 0.112979i
\(776\) −4695.94 −0.217235
\(777\) −22782.3 + 5125.92i −1.05188 + 0.236669i
\(778\) 4368.05 0.201288
\(779\) 4556.78 7892.58i 0.209581 0.363005i
\(780\) −3818.41 6613.68i −0.175283 0.303600i
\(781\) 19420.2 + 33636.8i 0.889769 + 1.54113i
\(782\) −296.604 + 513.733i −0.0135633 + 0.0234924i
\(783\) −13513.7 −0.616781
\(784\) 2114.52 26055.1i 0.0963248 1.18691i
\(785\) −35575.8 −1.61752
\(786\) 15507.6 26859.9i 0.703736 1.21891i
\(787\) 3448.66 + 5973.26i 0.156203 + 0.270551i 0.933496 0.358587i \(-0.116741\pi\)
−0.777294 + 0.629138i \(0.783408\pi\)
\(788\) 14648.8 + 25372.5i 0.662236 + 1.14703i
\(789\) 998.028 1728.64i 0.0450326 0.0779988i
\(790\) −13272.9 −0.597757
\(791\) −29865.9 + 6719.70i −1.34249 + 0.302055i
\(792\) −6385.75 −0.286500
\(793\) 5833.65 10104.2i 0.261234 0.452471i
\(794\) 12076.4 + 20916.9i 0.539766 + 0.934903i
\(795\) 6603.03 + 11436.8i 0.294573 + 0.510215i
\(796\) −7374.61 + 12773.2i −0.328375 + 0.568762i
\(797\) −23415.9 −1.04070 −0.520348 0.853954i \(-0.674198\pi\)
−0.520348 + 0.853954i \(0.674198\pi\)
\(798\) 2295.73 7361.76i 0.101840 0.326571i
\(799\) −372.136 −0.0164771
\(800\) −1508.32 + 2612.49i −0.0666590 + 0.115457i
\(801\) 3804.19 + 6589.05i 0.167808 + 0.290653i
\(802\) −316.450 548.108i −0.0139330 0.0241326i
\(803\) 33487.3 58001.6i 1.47166 2.54898i
\(804\) −4930.09 −0.216257
\(805\) −3049.00 3306.47i −0.133495 0.144767i
\(806\) 25000.3 1.09255
\(807\) −494.568 + 856.617i −0.0215733 + 0.0373660i
\(808\) −3347.12 5797.38i −0.145732 0.252415i
\(809\) −16714.7 28950.7i −0.726399 1.25816i −0.958396 0.285443i \(-0.907859\pi\)
0.231997 0.972716i \(-0.425474\pi\)
\(810\) −4457.36 + 7720.38i −0.193353 + 0.334897i
\(811\) −8822.63 −0.382003 −0.191001 0.981590i \(-0.561174\pi\)
−0.191001 + 0.981590i \(0.561174\pi\)
\(812\) 6718.46 + 7285.79i 0.290359 + 0.314878i
\(813\) −10361.5 −0.446978
\(814\) 40859.6 70770.9i 1.75937 3.04732i
\(815\) −21617.8 37443.1i −0.929127 1.60929i
\(816\) 996.052 + 1725.21i 0.0427314 + 0.0740129i
\(817\) −3707.17 + 6421.01i −0.158749 + 0.274961i
\(818\) −24603.6 −1.05164
\(819\) 2246.09 7202.58i 0.0958301 0.307300i
\(820\) 19423.2 0.827181
\(821\) −13854.7 + 23997.1i −0.588956 + 1.02010i 0.405413 + 0.914134i \(0.367128\pi\)
−0.994369 + 0.105969i \(0.966206\pi\)
\(822\) 15369.9 + 26621.4i 0.652173 + 1.12960i
\(823\) −6054.26 10486.3i −0.256425 0.444142i 0.708856 0.705353i \(-0.249211\pi\)
−0.965282 + 0.261211i \(0.915878\pi\)
\(824\) −7372.39 + 12769.4i −0.311686 + 0.539856i
\(825\) −3359.07 −0.141755
\(826\) −14308.7 + 3219.39i −0.602739 + 0.135614i
\(827\) 16709.2 0.702583 0.351292 0.936266i \(-0.385743\pi\)
0.351292 + 0.936266i \(0.385743\pi\)
\(828\) −866.785 + 1501.32i −0.0363803 + 0.0630125i
\(829\) 18843.8 + 32638.5i 0.789474 + 1.36741i 0.926290 + 0.376812i \(0.122980\pi\)
−0.136816 + 0.990597i \(0.543687\pi\)
\(830\) −8191.32 14187.8i −0.342560 0.593331i
\(831\) −7758.08 + 13437.4i −0.323856 + 0.560936i
\(832\) −7200.09 −0.300022
\(833\) 1948.99 + 1346.51i 0.0810665 + 0.0560070i
\(834\) 4834.53 0.200727
\(835\) 2574.66 4459.44i 0.106706 0.184821i
\(836\) 5752.95 + 9964.41i 0.238003 + 0.412232i
\(837\) −15639.7 27088.7i −0.645861 1.11866i
\(838\) −8052.66 + 13947.6i −0.331950 + 0.574955i
\(839\) 4982.49 0.205023 0.102512 0.994732i \(-0.467312\pi\)
0.102512 + 0.994732i \(0.467312\pi\)
\(840\) −5538.03 + 1246.03i −0.227476 + 0.0511812i
\(841\) −16290.1 −0.667929
\(842\) −13464.0 + 23320.3i −0.551068 + 0.954479i
\(843\) 3029.18 + 5246.70i 0.123761 + 0.214360i
\(844\) 8116.24 + 14057.7i 0.331010 + 0.573326i
\(845\) −6145.94 + 10645.1i −0.250209 + 0.433375i
\(846\) −2550.66 −0.103656
\(847\) −16449.0 + 52747.2i −0.667289 + 2.13981i
\(848\) 25185.3 1.01989
\(849\) −10987.9 + 19031.6i −0.444175 + 0.769333i
\(850\) −174.250 301.811i −0.00703146 0.0121788i
\(851\) 3831.21 + 6635.85i 0.154327 + 0.267302i
\(852\) 6653.86 11524.8i 0.267556 0.463420i
\(853\) 20816.1 0.835557 0.417778 0.908549i \(-0.362809\pi\)
0.417778 + 0.908549i \(0.362809\pi\)
\(854\) 17021.3 + 18458.7i 0.682035 + 0.739628i
\(855\) 3942.83 0.157710
\(856\) 948.233 1642.39i 0.0378621 0.0655790i
\(857\) −8612.45 14917.2i −0.343286 0.594588i 0.641755 0.766910i \(-0.278207\pi\)
−0.985041 + 0.172321i \(0.944873\pi\)
\(858\) −14918.1 25838.9i −0.593585 1.02812i
\(859\) 22307.1 38637.0i 0.886039 1.53466i 0.0415208 0.999138i \(-0.486780\pi\)
0.844518 0.535527i \(-0.179887\pi\)
\(860\) −15801.8 −0.626554
\(861\) −14700.1 15941.4i −0.581854 0.630988i
\(862\) −36991.0 −1.46162
\(863\) −5735.38 + 9933.97i −0.226228 + 0.391838i −0.956687 0.291118i \(-0.905973\pi\)
0.730459 + 0.682956i \(0.239306\pi\)
\(864\) 16762.2 + 29032.9i 0.660023 + 1.14319i
\(865\) −13978.3 24211.1i −0.549451 0.951677i
\(866\) 5849.00 10130.8i 0.229512 0.397526i
\(867\) 18413.9 0.721303
\(868\) −6829.22 + 21899.4i −0.267049 + 0.856352i
\(869\) −22109.6 −0.863081
\(870\) 6715.23 11631.1i 0.261687 0.453255i
\(871\) −3520.21 6097.18i −0.136943 0.237193i
\(872\) −389.246 674.193i −0.0151164 0.0261824i
\(873\) 3880.46 6721.15i 0.150439 0.260569i
\(874\) −2530.34 −0.0979289
\(875\) 26425.6 5945.65i 1.02097 0.229714i
\(876\) −22947.2 −0.885061
\(877\) 5950.84 10307.2i 0.229129 0.396862i −0.728422 0.685129i \(-0.759746\pi\)
0.957550 + 0.288267i \(0.0930790\pi\)
\(878\) 8033.23 + 13914.0i 0.308780 + 0.534822i
\(879\) 1376.57 + 2384.29i 0.0528221 + 0.0914905i
\(880\) 26428.1 45774.8i 1.01238 1.75349i
\(881\) 3538.35 0.135312 0.0676561 0.997709i \(-0.478448\pi\)
0.0676561 + 0.997709i \(0.478448\pi\)
\(882\) 13358.5 + 9229.11i 0.509983 + 0.352336i
\(883\) −7915.33 −0.301667 −0.150834 0.988559i \(-0.548196\pi\)
−0.150834 + 0.988559i \(0.548196\pi\)
\(884\) 659.908 1142.99i 0.0251076 0.0434876i
\(885\) 4237.09 + 7338.86i 0.160936 + 0.278749i
\(886\) −9239.87 16003.9i −0.350361 0.606843i
\(887\) −13364.5 + 23148.0i −0.505903 + 0.876251i 0.494073 + 0.869420i \(0.335507\pi\)
−0.999977 + 0.00683020i \(0.997826\pi\)
\(888\) 9670.66 0.365457
\(889\) −29223.2 + 6575.09i −1.10249 + 0.248055i
\(890\) −23668.0 −0.891409
\(891\) −7424.95 + 12860.4i −0.279175 + 0.483546i
\(892\) −11922.4 20650.2i −0.447523 0.775133i
\(893\) −793.675 1374.69i −0.0297417 0.0515141i
\(894\) −5359.80 + 9283.45i −0.200513 + 0.347299i
\(895\) −2861.43 −0.106868
\(896\) −5234.48 + 16785.5i −0.195169 + 0.625852i
\(897\) 2797.60 0.104135
\(898\) −14203.0 + 24600.3i −0.527795 + 0.914168i
\(899\) 9373.00 + 16234.5i 0.347727 + 0.602282i
\(900\) −509.224 882.001i −0.0188601 0.0326667i
\(901\) −1141.15 + 1976.54i −0.0421946 + 0.0730832i
\(902\) 75884.5 2.80119
\(903\) 11959.2 + 12969.1i 0.440729 + 0.477946i
\(904\) 12677.5 0.466425
\(905\) 23303.3 40362.4i 0.855941 1.48253i
\(906\) 21376.0 + 37024.2i 0.783850 + 1.35767i
\(907\) 18971.8 + 32860.1i 0.694541 + 1.20298i 0.970335 + 0.241764i \(0.0777259\pi\)
−0.275794 + 0.961217i \(0.588941\pi\)
\(908\) −14371.5 + 24892.2i −0.525260 + 0.909778i
\(909\) 11063.5 0.403689
\(910\) 15910.3 + 17253.8i 0.579585 + 0.628527i
\(911\) 28622.9 1.04097 0.520483 0.853872i \(-0.325752\pi\)
0.520483 + 0.853872i \(0.325752\pi\)
\(912\) −4248.67 + 7358.91i −0.154263 + 0.267191i
\(913\) −13644.9 23633.6i −0.494611 0.856691i
\(914\) −5986.44 10368.8i −0.216645 0.375241i
\(915\) 7253.86 12564.1i 0.262082 0.453940i
\(916\) 32335.2 1.16636
\(917\) −12098.8 + 38797.5i −0.435701 + 1.39717i
\(918\) −3872.94 −0.139244
\(919\) 3113.01 5391.90i 0.111740 0.193539i −0.804732 0.593638i \(-0.797691\pi\)
0.916472 + 0.400099i \(0.131024\pi\)
\(920\) 931.308 + 1613.07i 0.0333742 + 0.0578059i
\(921\) −11850.6 20525.9i −0.423987 0.734367i
\(922\) −20878.2 + 36162.1i −0.745756 + 1.29169i
\(923\) 19004.1 0.677711
\(924\) 26709.1 6009.43i 0.950936 0.213956i
\(925\) −4501.56 −0.160011
\(926\) 4359.46 7550.81i 0.154709 0.267964i
\(927\) −12184.3 21103.8i −0.431698 0.747722i
\(928\) −10045.7 17399.7i −0.355353 0.615489i
\(929\) −15455.2 + 26769.2i −0.545822 + 0.945391i 0.452733 + 0.891646i \(0.350449\pi\)
−0.998555 + 0.0537450i \(0.982884\pi\)
\(930\) 31086.7 1.09610
\(931\) −817.353 + 10071.4i −0.0287730 + 0.354541i
\(932\) −24497.6 −0.860992
\(933\) −10748.1 + 18616.2i −0.377145 + 0.653234i
\(934\) 27285.6 + 47260.1i 0.955902 + 1.65567i
\(935\) 2394.93 + 4148.14i 0.0837674 + 0.145089i
\(936\) −1562.23 + 2705.86i −0.0545546 + 0.0944914i
\(937\) −24419.6 −0.851390 −0.425695 0.904867i \(-0.639970\pi\)
−0.425695 + 0.904867i \(0.639970\pi\)
\(938\) 14781.9 3325.85i 0.514547 0.115771i
\(939\) 4398.63 0.152869
\(940\) 1691.52 2929.79i 0.0586927 0.101659i
\(941\) −27851.7 48240.5i −0.964865 1.67120i −0.709977 0.704225i \(-0.751295\pi\)
−0.254888 0.966970i \(-0.582039\pi\)
\(942\) 23810.9 + 41241.7i 0.823568 + 1.42646i
\(943\) −3557.66 + 6162.05i −0.122856 + 0.212793i
\(944\) 16161.1 0.557204
\(945\) 8741.97 28033.0i 0.300927 0.964988i
\(946\) −61735.8 −2.12178
\(947\) 14811.5 25654.2i 0.508245 0.880306i −0.491710 0.870759i \(-0.663628\pi\)
0.999954 0.00954673i \(-0.00303887\pi\)
\(948\) 3787.66 + 6560.42i 0.129765 + 0.224760i
\(949\) −16384.9 28379.4i −0.560459 0.970743i
\(950\) 743.267 1287.38i 0.0253840 0.0439663i
\(951\) −29305.2 −0.999248
\(952\) −665.041 721.199i −0.0226409 0.0245527i
\(953\) 21996.3 0.747671 0.373835 0.927495i \(-0.378043\pi\)
0.373835 + 0.927495i \(0.378043\pi\)
\(954\) −7821.57 + 13547.4i −0.265443 + 0.459761i
\(955\) −6247.91 10821.7i −0.211704 0.366683i
\(956\) 1783.42 + 3088.98i 0.0603347 + 0.104503i
\(957\) 11186.1 19374.8i 0.377841 0.654440i
\(958\) 45008.9 1.51792
\(959\) −27305.6 29611.4i −0.919441 0.997081i
\(960\) −8952.96 −0.300995
\(961\) −6799.60 + 11777.3i −0.228244 + 0.395329i
\(962\) −19992.1 34627.3i −0.670031 1.16053i
\(963\) 1567.13 + 2714.35i 0.0524405 + 0.0908295i
\(964\) 7085.25 12272.0i 0.236722 0.410015i
\(965\) −11733.1 −0.391400
\(966\) −1792.37 + 5747.61i −0.0596982 + 0.191435i
\(967\) −25243.2 −0.839470 −0.419735 0.907647i \(-0.637877\pi\)
−0.419735 + 0.907647i \(0.637877\pi\)
\(968\) 11440.8 19816.0i 0.379877 0.657967i
\(969\) −385.016 666.868i −0.0127642 0.0221082i
\(970\) 12071.3 + 20908.0i 0.399572 + 0.692079i
\(971\) 25647.0 44421.8i 0.847632 1.46814i −0.0356846 0.999363i \(-0.511361\pi\)
0.883316 0.468778i \(-0.155305\pi\)
\(972\) −19020.3 −0.627651
\(973\) −6180.35 + 1390.55i −0.203631 + 0.0458161i
\(974\) 68060.7 2.23902
\(975\) −821.774 + 1423.35i −0.0269926 + 0.0467526i
\(976\) −13833.9 23961.0i −0.453700 0.785832i
\(977\) −4815.82 8341.24i −0.157699 0.273142i 0.776340 0.630315i \(-0.217074\pi\)
−0.934038 + 0.357173i \(0.883741\pi\)
\(978\) −28937.6 + 50121.4i −0.946137 + 1.63876i
\(979\) −39425.5 −1.28707
\(980\) −19459.9 + 9223.72i −0.634310 + 0.300654i
\(981\) 1286.60 0.0418737
\(982\) 7289.41 12625.6i 0.236878 0.410285i
\(983\) −17510.9 30329.8i −0.568170 0.984099i −0.996747 0.0805940i \(-0.974318\pi\)
0.428577 0.903505i \(-0.359015\pi\)
\(984\) 4490.09 + 7777.06i 0.145466 + 0.251955i
\(985\) −26012.1 + 45054.2i −0.841435 + 1.45741i
\(986\) 2321.09 0.0749681
\(987\) −3684.78 + 829.058i −0.118833 + 0.0267368i
\(988\) 5629.69 0.181280
\(989\) 2894.34 5013.14i 0.0930582 0.161181i
\(990\) 16415.1 + 28431.7i 0.526975 + 0.912747i
\(991\) 24574.2 + 42563.8i 0.787714 + 1.36436i 0.927364 + 0.374160i \(0.122069\pi\)
−0.139650 + 0.990201i \(0.544598\pi\)
\(992\) 23252.2 40274.0i 0.744213 1.28901i
\(993\) −24992.5 −0.798703
\(994\) −12175.6 + 39043.5i −0.388516 + 1.24586i
\(995\) −26190.4 −0.834463
\(996\) −4675.08 + 8097.48i −0.148731 + 0.257609i
\(997\) 9314.55 + 16133.3i 0.295883 + 0.512484i 0.975190 0.221370i \(-0.0710530\pi\)
−0.679307 + 0.733854i \(0.737720\pi\)
\(998\) −37055.2 64181.4i −1.17531 2.03570i
\(999\) −25013.2 + 43324.1i −0.792175 + 1.37209i
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 161.4.e.a.93.5 44
7.2 even 3 1127.4.a.l.1.18 22
7.4 even 3 inner 161.4.e.a.116.5 yes 44
7.5 odd 6 1127.4.a.k.1.18 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.4.e.a.93.5 44 1.1 even 1 trivial
161.4.e.a.116.5 yes 44 7.4 even 3 inner
1127.4.a.k.1.18 22 7.5 odd 6
1127.4.a.l.1.18 22 7.2 even 3