Properties

Label 114.4.e.d.7.3
Level $114$
Weight $4$
Character 114.7
Analytic conductor $6.726$
Analytic rank $0$
Dimension $6$
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] = [114,4,Mod(7,114)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(114, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("114.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 114.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: \(6.72621774065\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.627014547.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 26x^{4} + 169x^{2} + 147 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 7.3
Root \(1.01248i\) of defining polynomial
Character \(\chi\) \(=\) 114.7
Dual form 114.4.e.d.49.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(4.22121 + 7.31135i) q^{5} +(3.00000 - 5.19615i) q^{6} -9.44242 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(4.22121 + 7.31135i) q^{5} +(3.00000 - 5.19615i) q^{6} -9.44242 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(8.44242 - 14.6227i) q^{10} -47.4865 q^{11} -12.0000 q^{12} +(-33.8272 + 58.5905i) q^{13} +(9.44242 + 16.3547i) q^{14} +(-12.6636 + 21.9340i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(38.8052 + 67.2126i) q^{17} +18.0000 q^{18} +(53.6901 - 63.0585i) q^{19} -33.7697 q^{20} +(-14.1636 - 24.5321i) q^{21} +(47.4865 + 82.2490i) q^{22} +(-85.4773 + 148.051i) q^{23} +(12.0000 + 20.7846i) q^{24} +(26.8628 - 46.5277i) q^{25} +135.309 q^{26} -27.0000 q^{27} +(18.8848 - 32.7095i) q^{28} +(-120.061 + 207.952i) q^{29} +50.6545 q^{30} +279.104 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-71.2297 - 123.373i) q^{33} +(77.6104 - 134.425i) q^{34} +(-39.8584 - 69.0368i) q^{35} +(-18.0000 - 31.1769i) q^{36} -20.0617 q^{37} +(-162.911 - 29.9354i) q^{38} -202.963 q^{39} +(33.7697 + 58.4908i) q^{40} +(-35.9106 - 62.1990i) q^{41} +(-28.3272 + 49.0642i) q^{42} +(-73.6589 - 127.581i) q^{43} +(94.9729 - 164.498i) q^{44} -75.9817 q^{45} +341.909 q^{46} +(103.671 - 179.564i) q^{47} +(24.0000 - 41.5692i) q^{48} -253.841 q^{49} -107.451 q^{50} +(-116.416 + 201.638i) q^{51} +(-135.309 - 234.362i) q^{52} +(130.761 - 226.486i) q^{53} +(27.0000 + 46.7654i) q^{54} +(-200.450 - 347.190i) q^{55} -75.5393 q^{56} +(244.366 + 44.9031i) q^{57} +480.245 q^{58} +(10.9909 + 19.0367i) q^{59} +(-50.6545 - 87.7362i) q^{60} +(326.552 - 565.604i) q^{61} +(-279.104 - 483.423i) q^{62} +(42.4909 - 73.5963i) q^{63} +64.0000 q^{64} -571.167 q^{65} +(-142.459 + 246.747i) q^{66} +(206.898 - 358.357i) q^{67} -310.442 q^{68} -512.864 q^{69} +(-79.7168 + 138.074i) q^{70} +(78.9726 + 136.785i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(551.073 + 954.486i) q^{73} +(20.0617 + 34.7478i) q^{74} +161.177 q^{75} +(111.061 + 312.105i) q^{76} +448.387 q^{77} +(202.963 + 351.543i) q^{78} +(208.907 + 361.837i) q^{79} +(67.5393 - 116.982i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-71.8213 + 124.398i) q^{82} +1431.80 q^{83} +113.309 q^{84} +(-327.610 + 567.437i) q^{85} +(-147.318 + 255.162i) q^{86} -720.368 q^{87} -379.892 q^{88} +(-644.697 + 1116.65i) q^{89} +(75.9817 + 131.604i) q^{90} +(319.411 - 553.236i) q^{91} +(-341.909 - 592.204i) q^{92} +(418.657 + 725.135i) q^{93} -414.686 q^{94} +(687.680 + 126.363i) q^{95} -96.0000 q^{96} +(-69.3811 - 120.172i) q^{97} +(253.841 + 439.665i) q^{98} +(213.689 - 370.120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9} - 20 q^{10} - 88 q^{11} - 72 q^{12} + 9 q^{13} - 14 q^{14} + 30 q^{15} - 48 q^{16} + 84 q^{17} + 108 q^{18} + 32 q^{19} + 80 q^{20} + 21 q^{21} + 88 q^{22} + 2 q^{23} + 72 q^{24} + 83 q^{25} - 36 q^{26} - 162 q^{27} - 28 q^{28} - 92 q^{29} - 120 q^{30} - 218 q^{31} - 96 q^{32} - 132 q^{33} + 168 q^{34} - 282 q^{35} - 108 q^{36} + 490 q^{37} - 74 q^{38} + 54 q^{39} - 80 q^{40} + 688 q^{41} + 42 q^{42} + 103 q^{43} + 176 q^{44} + 180 q^{45} - 8 q^{46} - 322 q^{47} + 144 q^{48} - 1508 q^{49} - 332 q^{50} - 252 q^{51} + 36 q^{52} + 1322 q^{53} + 162 q^{54} + 248 q^{55} + 112 q^{56} + 111 q^{57} + 368 q^{58} - 252 q^{59} + 120 q^{60} + 435 q^{61} + 218 q^{62} - 63 q^{63} + 384 q^{64} - 3164 q^{65} - 264 q^{66} + 719 q^{67} - 672 q^{68} + 12 q^{69} - 564 q^{70} + 62 q^{71} - 216 q^{72} + 581 q^{73} - 490 q^{74} + 498 q^{75} + 20 q^{76} - 408 q^{77} - 54 q^{78} + 489 q^{79} - 160 q^{80} - 243 q^{81} + 1376 q^{82} + 4992 q^{83} - 168 q^{84} - 1632 q^{85} + 206 q^{86} - 552 q^{87} - 704 q^{88} - 1584 q^{89} - 180 q^{90} + 1573 q^{91} + 8 q^{92} - 327 q^{93} + 1288 q^{94} + 2362 q^{95} - 576 q^{96} - 974 q^{97} + 1508 q^{98} + 396 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 4.22121 + 7.31135i 0.377556 + 0.653947i 0.990706 0.136020i \(-0.0434311\pi\)
−0.613150 + 0.789967i \(0.710098\pi\)
\(6\) 3.00000 5.19615i 0.204124 0.353553i
\(7\) −9.44242 −0.509843 −0.254921 0.966962i \(-0.582050\pi\)
−0.254921 + 0.966962i \(0.582050\pi\)
\(8\) 8.00000 0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 8.44242 14.6227i 0.266973 0.462410i
\(11\) −47.4865 −1.30161 −0.650805 0.759245i \(-0.725568\pi\)
−0.650805 + 0.759245i \(0.725568\pi\)
\(12\) −12.0000 −0.288675
\(13\) −33.8272 + 58.5905i −0.721692 + 1.25001i 0.238630 + 0.971111i \(0.423302\pi\)
−0.960321 + 0.278896i \(0.910032\pi\)
\(14\) 9.44242 + 16.3547i 0.180257 + 0.312214i
\(15\) −12.6636 + 21.9340i −0.217982 + 0.377556i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 38.8052 + 67.2126i 0.553626 + 0.958909i 0.998009 + 0.0630719i \(0.0200898\pi\)
−0.444383 + 0.895837i \(0.646577\pi\)
\(18\) 18.0000 0.235702
\(19\) 53.6901 63.0585i 0.648281 0.761401i
\(20\) −33.7697 −0.377556
\(21\) −14.1636 24.5321i −0.147179 0.254921i
\(22\) 47.4865 + 82.2490i 0.460189 + 0.797070i
\(23\) −85.4773 + 148.051i −0.774924 + 1.34221i 0.159913 + 0.987131i \(0.448879\pi\)
−0.934837 + 0.355077i \(0.884455\pi\)
\(24\) 12.0000 + 20.7846i 0.102062 + 0.176777i
\(25\) 26.8628 46.5277i 0.214902 0.372222i
\(26\) 135.309 1.02063
\(27\) −27.0000 −0.192450
\(28\) 18.8848 32.7095i 0.127461 0.220768i
\(29\) −120.061 + 207.952i −0.768787 + 1.33158i 0.169433 + 0.985542i \(0.445806\pi\)
−0.938221 + 0.346037i \(0.887527\pi\)
\(30\) 50.6545 0.308273
\(31\) 279.104 1.61705 0.808526 0.588460i \(-0.200265\pi\)
0.808526 + 0.588460i \(0.200265\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) −71.2297 123.373i −0.375742 0.650805i
\(34\) 77.6104 134.425i 0.391473 0.678051i
\(35\) −39.8584 69.0368i −0.192494 0.333410i
\(36\) −18.0000 31.1769i −0.0833333 0.144338i
\(37\) −20.0617 −0.0891383 −0.0445692 0.999006i \(-0.514192\pi\)
−0.0445692 + 0.999006i \(0.514192\pi\)
\(38\) −162.911 29.9354i −0.695463 0.127794i
\(39\) −202.963 −0.833338
\(40\) 33.7697 + 58.4908i 0.133486 + 0.231205i
\(41\) −35.9106 62.1990i −0.136788 0.236923i 0.789491 0.613762i \(-0.210345\pi\)
−0.926279 + 0.376839i \(0.877011\pi\)
\(42\) −28.3272 + 49.0642i −0.104071 + 0.180257i
\(43\) −73.6589 127.581i −0.261230 0.452463i 0.705339 0.708870i \(-0.250795\pi\)
−0.966569 + 0.256407i \(0.917461\pi\)
\(44\) 94.9729 164.498i 0.325402 0.563614i
\(45\) −75.9817 −0.251704
\(46\) 341.909 1.09591
\(47\) 103.671 179.564i 0.321746 0.557280i −0.659103 0.752053i \(-0.729064\pi\)
0.980848 + 0.194773i \(0.0623971\pi\)
\(48\) 24.0000 41.5692i 0.0721688 0.125000i
\(49\) −253.841 −0.740061
\(50\) −107.451 −0.303918
\(51\) −116.416 + 201.638i −0.319636 + 0.553626i
\(52\) −135.309 234.362i −0.360846 0.625003i
\(53\) 130.761 226.486i 0.338896 0.586985i −0.645330 0.763904i \(-0.723280\pi\)
0.984225 + 0.176920i \(0.0566133\pi\)
\(54\) 27.0000 + 46.7654i 0.0680414 + 0.117851i
\(55\) −200.450 347.190i −0.491431 0.851184i
\(56\) −75.5393 −0.180257
\(57\) 244.366 + 44.9031i 0.567843 + 0.104343i
\(58\) 480.245 1.08723
\(59\) 10.9909 + 19.0367i 0.0242524 + 0.0420063i 0.877897 0.478850i \(-0.158946\pi\)
−0.853644 + 0.520856i \(0.825613\pi\)
\(60\) −50.6545 87.7362i −0.108991 0.188778i
\(61\) 326.552 565.604i 0.685420 1.18718i −0.287884 0.957665i \(-0.592952\pi\)
0.973304 0.229518i \(-0.0737149\pi\)
\(62\) −279.104 483.423i −0.571715 0.990239i
\(63\) 42.4909 73.5963i 0.0849738 0.147179i
\(64\) 64.0000 0.125000
\(65\) −571.167 −1.08992
\(66\) −142.459 + 246.747i −0.265690 + 0.460189i
\(67\) 206.898 358.357i 0.377262 0.653438i −0.613400 0.789772i \(-0.710199\pi\)
0.990663 + 0.136334i \(0.0435322\pi\)
\(68\) −310.442 −0.553626
\(69\) −512.864 −0.894805
\(70\) −79.7168 + 138.074i −0.136114 + 0.235756i
\(71\) 78.9726 + 136.785i 0.132005 + 0.228639i 0.924449 0.381305i \(-0.124525\pi\)
−0.792445 + 0.609944i \(0.791192\pi\)
\(72\) −36.0000 + 62.3538i −0.0589256 + 0.102062i
\(73\) 551.073 + 954.486i 0.883537 + 1.53033i 0.847382 + 0.530984i \(0.178178\pi\)
0.0361550 + 0.999346i \(0.488489\pi\)
\(74\) 20.0617 + 34.7478i 0.0315151 + 0.0545858i
\(75\) 161.177 0.248148
\(76\) 111.061 + 312.105i 0.167626 + 0.471064i
\(77\) 448.387 0.663616
\(78\) 202.963 + 351.543i 0.294629 + 0.510313i
\(79\) 208.907 + 361.837i 0.297517 + 0.515314i 0.975567 0.219701i \(-0.0705083\pi\)
−0.678050 + 0.735015i \(0.737175\pi\)
\(80\) 67.5393 116.982i 0.0943891 0.163487i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −71.8213 + 124.398i −0.0967236 + 0.167530i
\(83\) 1431.80 1.89350 0.946751 0.321967i \(-0.104344\pi\)
0.946751 + 0.321967i \(0.104344\pi\)
\(84\) 113.309 0.147179
\(85\) −327.610 + 567.437i −0.418050 + 0.724084i
\(86\) −147.318 + 255.162i −0.184717 + 0.319940i
\(87\) −720.368 −0.887719
\(88\) −379.892 −0.460189
\(89\) −644.697 + 1116.65i −0.767839 + 1.32994i 0.170893 + 0.985290i \(0.445335\pi\)
−0.938732 + 0.344647i \(0.887999\pi\)
\(90\) 75.9817 + 131.604i 0.0889909 + 0.154137i
\(91\) 319.411 553.236i 0.367949 0.637306i
\(92\) −341.909 592.204i −0.387462 0.671104i
\(93\) 418.657 + 725.135i 0.466803 + 0.808526i
\(94\) −414.686 −0.455017
\(95\) 687.680 + 126.363i 0.742678 + 0.136470i
\(96\) −96.0000 −0.102062
\(97\) −69.3811 120.172i −0.0726245 0.125789i 0.827426 0.561574i \(-0.189804\pi\)
−0.900051 + 0.435785i \(0.856471\pi\)
\(98\) 253.841 + 439.665i 0.261651 + 0.453193i
\(99\) 213.689 370.120i 0.216935 0.375742i
\(100\) 107.451 + 186.111i 0.107451 + 0.186111i
\(101\) 34.8153 60.3018i 0.0342995 0.0594085i −0.848366 0.529410i \(-0.822413\pi\)
0.882666 + 0.470002i \(0.155747\pi\)
\(102\) 465.663 0.452034
\(103\) −644.346 −0.616401 −0.308201 0.951321i \(-0.599727\pi\)
−0.308201 + 0.951321i \(0.599727\pi\)
\(104\) −270.618 + 468.724i −0.255157 + 0.441944i
\(105\) 119.575 207.110i 0.111137 0.192494i
\(106\) −523.046 −0.479271
\(107\) −189.454 −0.171171 −0.0855853 0.996331i \(-0.527276\pi\)
−0.0855853 + 0.996331i \(0.527276\pi\)
\(108\) 54.0000 93.5307i 0.0481125 0.0833333i
\(109\) 119.576 + 207.112i 0.105076 + 0.181998i 0.913769 0.406233i \(-0.133158\pi\)
−0.808693 + 0.588231i \(0.799825\pi\)
\(110\) −400.901 + 694.380i −0.347494 + 0.601878i
\(111\) −30.0925 52.1217i −0.0257320 0.0445692i
\(112\) 75.5393 + 130.838i 0.0637303 + 0.110384i
\(113\) 162.743 0.135483 0.0677413 0.997703i \(-0.478421\pi\)
0.0677413 + 0.997703i \(0.478421\pi\)
\(114\) −166.592 468.157i −0.136866 0.384622i
\(115\) −1443.27 −1.17031
\(116\) −480.245 831.809i −0.384394 0.665789i
\(117\) −304.445 527.315i −0.240564 0.416669i
\(118\) 21.9817 38.0735i 0.0171490 0.0297030i
\(119\) −366.415 634.649i −0.282262 0.488893i
\(120\) −101.309 + 175.472i −0.0770684 + 0.133486i
\(121\) 923.965 0.694188
\(122\) −1306.21 −0.969331
\(123\) 107.732 186.597i 0.0789745 0.136788i
\(124\) −558.209 + 966.846i −0.404263 + 0.700204i
\(125\) 1508.88 1.07966
\(126\) −169.963 −0.120171
\(127\) 48.6891 84.3320i 0.0340194 0.0589233i −0.848514 0.529172i \(-0.822503\pi\)
0.882534 + 0.470249i \(0.155836\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 220.977 382.743i 0.150821 0.261230i
\(130\) 571.167 + 989.291i 0.385344 + 0.667435i
\(131\) −189.699 328.568i −0.126520 0.219138i 0.795806 0.605551i \(-0.207047\pi\)
−0.922326 + 0.386413i \(0.873714\pi\)
\(132\) 569.838 0.375742
\(133\) −506.964 + 595.425i −0.330521 + 0.388195i
\(134\) −827.591 −0.533530
\(135\) −113.973 197.406i −0.0726607 0.125852i
\(136\) 310.442 + 537.701i 0.195736 + 0.339026i
\(137\) −1206.84 + 2090.31i −0.752609 + 1.30356i 0.193945 + 0.981012i \(0.437872\pi\)
−0.946554 + 0.322545i \(0.895462\pi\)
\(138\) 512.864 + 888.307i 0.316362 + 0.547954i
\(139\) 1554.52 2692.51i 0.948582 1.64299i 0.200166 0.979762i \(-0.435852\pi\)
0.748416 0.663230i \(-0.230815\pi\)
\(140\) 318.867 0.192494
\(141\) 622.029 0.371520
\(142\) 157.945 273.569i 0.0933414 0.161672i
\(143\) 1606.34 2782.26i 0.939361 1.62702i
\(144\) 144.000 0.0833333
\(145\) −2027.22 −1.16104
\(146\) 1102.15 1908.97i 0.624755 1.08211i
\(147\) −380.761 659.498i −0.213637 0.370030i
\(148\) 40.1233 69.4956i 0.0222846 0.0385980i
\(149\) 1459.55 + 2528.02i 0.802491 + 1.38995i 0.917972 + 0.396645i \(0.129826\pi\)
−0.115481 + 0.993310i \(0.536841\pi\)
\(150\) −161.177 279.166i −0.0877336 0.151959i
\(151\) −1915.72 −1.03244 −0.516221 0.856455i \(-0.672662\pi\)
−0.516221 + 0.856455i \(0.672662\pi\)
\(152\) 429.520 504.468i 0.229202 0.269196i
\(153\) −698.494 −0.369084
\(154\) −448.387 776.629i −0.234624 0.406380i
\(155\) 1178.16 + 2040.63i 0.610529 + 1.05747i
\(156\) 405.927 703.086i 0.208334 0.360846i
\(157\) 1268.34 + 2196.84i 0.644744 + 1.11673i 0.984361 + 0.176166i \(0.0563694\pi\)
−0.339616 + 0.940564i \(0.610297\pi\)
\(158\) 417.813 723.673i 0.210376 0.364382i
\(159\) 784.569 0.391323
\(160\) −270.157 −0.133486
\(161\) 807.113 1397.96i 0.395089 0.684315i
\(162\) −81.0000 + 140.296i −0.0392837 + 0.0680414i
\(163\) −1731.52 −0.832044 −0.416022 0.909355i \(-0.636576\pi\)
−0.416022 + 0.909355i \(0.636576\pi\)
\(164\) 287.285 0.136788
\(165\) 601.351 1041.57i 0.283728 0.491431i
\(166\) −1431.80 2479.95i −0.669454 1.15953i
\(167\) 715.062 1238.52i 0.331336 0.573891i −0.651438 0.758702i \(-0.725834\pi\)
0.982774 + 0.184811i \(0.0591672\pi\)
\(168\) −113.309 196.257i −0.0520356 0.0901283i
\(169\) −1190.07 2061.25i −0.541677 0.938213i
\(170\) 1310.44 0.591212
\(171\) 249.887 + 702.236i 0.111751 + 0.314043i
\(172\) 589.271 0.261230
\(173\) −146.662 254.027i −0.0644539 0.111638i 0.831998 0.554779i \(-0.187197\pi\)
−0.896452 + 0.443142i \(0.853864\pi\)
\(174\) 720.368 + 1247.71i 0.313856 + 0.543615i
\(175\) −253.650 + 439.334i −0.109566 + 0.189775i
\(176\) 379.892 + 657.992i 0.162701 + 0.281807i
\(177\) −32.9726 + 57.1102i −0.0140021 + 0.0242524i
\(178\) 2578.79 1.08589
\(179\) −3843.52 −1.60490 −0.802452 0.596716i \(-0.796472\pi\)
−0.802452 + 0.596716i \(0.796472\pi\)
\(180\) 151.963 263.208i 0.0629261 0.108991i
\(181\) −884.639 + 1532.24i −0.363286 + 0.629229i −0.988499 0.151224i \(-0.951678\pi\)
0.625214 + 0.780454i \(0.285012\pi\)
\(182\) −1277.64 −0.520359
\(183\) 1959.31 0.791455
\(184\) −683.819 + 1184.41i −0.273977 + 0.474542i
\(185\) −84.6845 146.678i −0.0336547 0.0582917i
\(186\) 837.313 1450.27i 0.330080 0.571715i
\(187\) −1842.72 3191.69i −0.720606 1.24813i
\(188\) 414.686 + 718.257i 0.160873 + 0.278640i
\(189\) 254.945 0.0981192
\(190\) −468.812 1317.46i −0.179006 0.503045i
\(191\) −504.006 −0.190935 −0.0954676 0.995433i \(-0.530435\pi\)
−0.0954676 + 0.995433i \(0.530435\pi\)
\(192\) 96.0000 + 166.277i 0.0360844 + 0.0625000i
\(193\) 1083.79 + 1877.19i 0.404213 + 0.700118i 0.994230 0.107273i \(-0.0342120\pi\)
−0.590016 + 0.807391i \(0.700879\pi\)
\(194\) −138.762 + 240.343i −0.0513533 + 0.0889465i
\(195\) −856.751 1483.94i −0.314632 0.544958i
\(196\) 507.682 879.330i 0.185015 0.320456i
\(197\) 2111.10 0.763501 0.381750 0.924265i \(-0.375321\pi\)
0.381750 + 0.924265i \(0.375321\pi\)
\(198\) −854.756 −0.306792
\(199\) −1069.30 + 1852.08i −0.380907 + 0.659750i −0.991192 0.132432i \(-0.957722\pi\)
0.610285 + 0.792182i \(0.291055\pi\)
\(200\) 214.902 372.222i 0.0759795 0.131600i
\(201\) 1241.39 0.435625
\(202\) −139.261 −0.0485068
\(203\) 1133.67 1963.57i 0.391961 0.678896i
\(204\) −465.663 806.551i −0.159818 0.276813i
\(205\) 303.172 525.110i 0.103290 0.178904i
\(206\) 644.346 + 1116.04i 0.217931 + 0.377467i
\(207\) −769.296 1332.46i −0.258308 0.447403i
\(208\) 1082.47 0.360846
\(209\) −2549.55 + 2994.43i −0.843809 + 0.991047i
\(210\) −478.301 −0.157171
\(211\) 487.977 + 845.200i 0.159212 + 0.275763i 0.934585 0.355741i \(-0.115771\pi\)
−0.775373 + 0.631504i \(0.782438\pi\)
\(212\) 523.046 + 905.942i 0.169448 + 0.293492i
\(213\) −236.918 + 410.354i −0.0762129 + 0.132005i
\(214\) 189.454 + 328.145i 0.0605179 + 0.104820i
\(215\) 621.859 1077.09i 0.197258 0.341661i
\(216\) −216.000 −0.0680414
\(217\) −2635.42 −0.824442
\(218\) 239.152 414.224i 0.0743002 0.128692i
\(219\) −1653.22 + 2863.46i −0.510110 + 0.883537i
\(220\) 1603.60 0.491431
\(221\) −5250.70 −1.59819
\(222\) −60.1850 + 104.243i −0.0181953 + 0.0315151i
\(223\) 1787.73 + 3096.43i 0.536839 + 0.929832i 0.999072 + 0.0430737i \(0.0137150\pi\)
−0.462233 + 0.886758i \(0.652952\pi\)
\(224\) 151.079 261.676i 0.0450641 0.0780534i
\(225\) 241.765 + 418.750i 0.0716341 + 0.124074i
\(226\) −162.743 281.878i −0.0479003 0.0829658i
\(227\) −86.5237 −0.0252986 −0.0126493 0.999920i \(-0.504027\pi\)
−0.0126493 + 0.999920i \(0.504027\pi\)
\(228\) −644.281 + 756.702i −0.187143 + 0.219798i
\(229\) −3928.05 −1.13351 −0.566753 0.823888i \(-0.691801\pi\)
−0.566753 + 0.823888i \(0.691801\pi\)
\(230\) 1443.27 + 2499.82i 0.413767 + 0.716666i
\(231\) 672.581 + 1164.94i 0.191569 + 0.331808i
\(232\) −960.491 + 1663.62i −0.271807 + 0.470784i
\(233\) −510.013 883.368i −0.143399 0.248375i 0.785375 0.619020i \(-0.212470\pi\)
−0.928775 + 0.370645i \(0.879137\pi\)
\(234\) −608.890 + 1054.63i −0.170104 + 0.294629i
\(235\) 1750.48 0.485908
\(236\) −87.9270 −0.0242524
\(237\) −626.720 + 1085.51i −0.171771 + 0.297517i
\(238\) −732.830 + 1269.30i −0.199590 + 0.345699i
\(239\) 264.681 0.0716351 0.0358175 0.999358i \(-0.488596\pi\)
0.0358175 + 0.999358i \(0.488596\pi\)
\(240\) 405.236 0.108991
\(241\) 86.1935 149.292i 0.0230382 0.0399034i −0.854276 0.519819i \(-0.825999\pi\)
0.877315 + 0.479916i \(0.159333\pi\)
\(242\) −923.965 1600.35i −0.245433 0.425102i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 1306.21 + 2262.42i 0.342710 + 0.593592i
\(245\) −1071.51 1855.92i −0.279415 0.483960i
\(246\) −430.928 −0.111687
\(247\) 1878.44 + 5278.82i 0.483897 + 1.35985i
\(248\) 2232.84 0.571715
\(249\) 2147.70 + 3719.93i 0.546607 + 0.946751i
\(250\) −1508.88 2613.45i −0.381719 0.661156i
\(251\) 2442.43 4230.42i 0.614203 1.06383i −0.376321 0.926490i \(-0.622811\pi\)
0.990524 0.137342i \(-0.0438558\pi\)
\(252\) 169.963 + 294.385i 0.0424869 + 0.0735894i
\(253\) 4059.02 7030.42i 1.00865 1.74703i
\(254\) −194.757 −0.0481107
\(255\) −1965.66 −0.482723
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2011.32 + 3483.71i −0.488181 + 0.845555i −0.999908 0.0135936i \(-0.995673\pi\)
0.511726 + 0.859149i \(0.329006\pi\)
\(258\) −883.907 −0.213293
\(259\) 189.431 0.0454465
\(260\) 1142.33 1978.58i 0.272479 0.471948i
\(261\) −1080.55 1871.57i −0.256262 0.443860i
\(262\) −379.398 + 657.136i −0.0894629 + 0.154954i
\(263\) 3571.06 + 6185.26i 0.837266 + 1.45019i 0.892172 + 0.451695i \(0.149181\pi\)
−0.0549063 + 0.998492i \(0.517486\pi\)
\(264\) −569.838 986.988i −0.132845 0.230094i
\(265\) 2207.89 0.511809
\(266\) 1538.27 + 282.662i 0.354577 + 0.0651546i
\(267\) −3868.18 −0.886625
\(268\) 827.591 + 1433.43i 0.188631 + 0.326719i
\(269\) −2540.63 4400.50i −0.575855 0.997410i −0.995948 0.0899291i \(-0.971336\pi\)
0.420093 0.907481i \(-0.361997\pi\)
\(270\) −227.945 + 394.813i −0.0513789 + 0.0889909i
\(271\) 1486.90 + 2575.39i 0.333295 + 0.577284i 0.983156 0.182770i \(-0.0585062\pi\)
−0.649861 + 0.760053i \(0.725173\pi\)
\(272\) 620.884 1075.40i 0.138407 0.239727i
\(273\) 1916.47 0.424871
\(274\) 4827.37 1.06435
\(275\) −1275.62 + 2209.44i −0.279719 + 0.484488i
\(276\) 1025.73 1776.61i 0.223701 0.387462i
\(277\) 7778.48 1.68723 0.843617 0.536946i \(-0.180422\pi\)
0.843617 + 0.536946i \(0.180422\pi\)
\(278\) −6218.09 −1.34150
\(279\) −1255.97 + 2175.40i −0.269509 + 0.466803i
\(280\) −318.867 552.294i −0.0680570 0.117878i
\(281\) −1110.34 + 1923.16i −0.235720 + 0.408279i −0.959482 0.281771i \(-0.909078\pi\)
0.723762 + 0.690050i \(0.242411\pi\)
\(282\) −622.029 1077.39i −0.131352 0.227508i
\(283\) 3808.17 + 6595.95i 0.799902 + 1.38547i 0.919679 + 0.392671i \(0.128449\pi\)
−0.119777 + 0.992801i \(0.538218\pi\)
\(284\) −631.781 −0.132005
\(285\) 703.218 + 1976.19i 0.146158 + 0.410735i
\(286\) −6425.35 −1.32846
\(287\) 339.083 + 587.309i 0.0697402 + 0.120794i
\(288\) −144.000 249.415i −0.0294628 0.0510310i
\(289\) −555.190 + 961.618i −0.113004 + 0.195729i
\(290\) 2027.22 + 3511.24i 0.410490 + 0.710990i
\(291\) 208.143 360.515i 0.0419298 0.0726245i
\(292\) −4408.58 −0.883537
\(293\) −9036.61 −1.80179 −0.900894 0.434038i \(-0.857088\pi\)
−0.900894 + 0.434038i \(0.857088\pi\)
\(294\) −761.522 + 1319.00i −0.151064 + 0.261651i
\(295\) −92.7895 + 160.716i −0.0183133 + 0.0317195i
\(296\) −160.493 −0.0315151
\(297\) 1282.13 0.250495
\(298\) 2919.10 5056.03i 0.567447 0.982846i
\(299\) −5782.93 10016.3i −1.11851 1.93732i
\(300\) −322.354 + 558.333i −0.0620370 + 0.107451i
\(301\) 695.518 + 1204.67i 0.133186 + 0.230685i
\(302\) 1915.72 + 3318.12i 0.365023 + 0.632239i
\(303\) 208.892 0.0396057
\(304\) −1303.29 239.483i −0.245883 0.0451819i
\(305\) 5513.77 1.03514
\(306\) 698.494 + 1209.83i 0.130491 + 0.226017i
\(307\) −3898.58 6752.55i −0.724769 1.25534i −0.959069 0.283172i \(-0.908613\pi\)
0.234300 0.972164i \(-0.424720\pi\)
\(308\) −896.774 + 1553.26i −0.165904 + 0.287354i
\(309\) −966.519 1674.06i −0.177940 0.308201i
\(310\) 2356.32 4081.26i 0.431709 0.747742i
\(311\) 2737.49 0.499128 0.249564 0.968358i \(-0.419713\pi\)
0.249564 + 0.968358i \(0.419713\pi\)
\(312\) −1623.71 −0.294629
\(313\) 3823.08 6621.76i 0.690393 1.19580i −0.281316 0.959615i \(-0.590771\pi\)
0.971709 0.236181i \(-0.0758957\pi\)
\(314\) 2536.69 4393.67i 0.455903 0.789647i
\(315\) 717.451 0.128330
\(316\) −1671.25 −0.297517
\(317\) 3210.19 5560.22i 0.568777 0.985152i −0.427910 0.903821i \(-0.640750\pi\)
0.996687 0.0813300i \(-0.0259168\pi\)
\(318\) −784.569 1358.91i −0.138354 0.239635i
\(319\) 5701.29 9874.92i 1.00066 1.73320i
\(320\) 270.157 + 467.926i 0.0471945 + 0.0817433i
\(321\) −284.182 492.217i −0.0494127 0.0855853i
\(322\) −3228.45 −0.558741
\(323\) 6321.78 + 1161.65i 1.08902 + 0.200111i
\(324\) 324.000 0.0555556
\(325\) 1817.39 + 3147.81i 0.310187 + 0.537259i
\(326\) 1731.52 + 2999.08i 0.294172 + 0.509521i
\(327\) −358.728 + 621.336i −0.0606658 + 0.105076i
\(328\) −287.285 497.592i −0.0483618 0.0837651i
\(329\) −978.909 + 1695.52i −0.164040 + 0.284125i
\(330\) −2405.40 −0.401252
\(331\) −4594.77 −0.762996 −0.381498 0.924370i \(-0.624592\pi\)
−0.381498 + 0.924370i \(0.624592\pi\)
\(332\) −2863.60 + 4959.91i −0.473375 + 0.819910i
\(333\) 90.2775 156.365i 0.0148564 0.0257320i
\(334\) −2860.25 −0.468580
\(335\) 3493.43 0.569751
\(336\) −226.618 + 392.514i −0.0367947 + 0.0637303i
\(337\) −3305.63 5725.53i −0.534331 0.925488i −0.999195 0.0401060i \(-0.987230\pi\)
0.464865 0.885382i \(-0.346103\pi\)
\(338\) −2380.13 + 4122.51i −0.383024 + 0.663417i
\(339\) 244.114 + 422.818i 0.0391105 + 0.0677413i
\(340\) −1310.44 2269.75i −0.209025 0.362042i
\(341\) −13253.7 −2.10477
\(342\) 966.421 1135.05i 0.152801 0.179464i
\(343\) 5635.62 0.887157
\(344\) −589.271 1020.65i −0.0923586 0.159970i
\(345\) −2164.91 3749.73i −0.337839 0.585155i
\(346\) −293.325 + 508.053i −0.0455758 + 0.0789396i
\(347\) 1249.31 + 2163.88i 0.193276 + 0.334764i 0.946334 0.323190i \(-0.104755\pi\)
−0.753058 + 0.657954i \(0.771422\pi\)
\(348\) 1440.74 2495.43i 0.221930 0.384394i
\(349\) 10330.5 1.58447 0.792235 0.610216i \(-0.208917\pi\)
0.792235 + 0.610216i \(0.208917\pi\)
\(350\) 1014.60 0.154950
\(351\) 913.336 1581.94i 0.138890 0.240564i
\(352\) 759.784 1315.98i 0.115047 0.199268i
\(353\) 2608.83 0.393354 0.196677 0.980468i \(-0.436985\pi\)
0.196677 + 0.980468i \(0.436985\pi\)
\(354\) 131.890 0.0198020
\(355\) −666.720 + 1154.79i −0.0996783 + 0.172648i
\(356\) −2578.79 4466.59i −0.383920 0.664968i
\(357\) 1099.25 1903.95i 0.162964 0.282262i
\(358\) 3843.52 + 6657.16i 0.567419 + 0.982799i
\(359\) −2075.16 3594.29i −0.305078 0.528410i 0.672201 0.740369i \(-0.265349\pi\)
−0.977279 + 0.211958i \(0.932016\pi\)
\(360\) −607.854 −0.0889909
\(361\) −1093.76 6771.23i −0.159463 0.987204i
\(362\) 3538.56 0.513764
\(363\) 1385.95 + 2400.53i 0.200395 + 0.347094i
\(364\) 1277.64 + 2212.94i 0.183975 + 0.318653i
\(365\) −4652.38 + 8058.17i −0.667170 + 1.15557i
\(366\) −1959.31 3393.62i −0.279822 0.484665i
\(367\) 3685.24 6383.02i 0.524163 0.907878i −0.475441 0.879748i \(-0.657711\pi\)
0.999604 0.0281300i \(-0.00895523\pi\)
\(368\) 2735.27 0.387462
\(369\) 646.391 0.0911918
\(370\) −169.369 + 293.356i −0.0237975 + 0.0412185i
\(371\) −1234.70 + 2138.57i −0.172783 + 0.299270i
\(372\) −3349.25 −0.466803
\(373\) 13166.5 1.82772 0.913858 0.406035i \(-0.133089\pi\)
0.913858 + 0.406035i \(0.133089\pi\)
\(374\) −3685.45 + 6383.38i −0.509545 + 0.882558i
\(375\) 2263.31 + 3920.17i 0.311672 + 0.539832i
\(376\) 829.372 1436.51i 0.113754 0.197028i
\(377\) −8122.69 14068.9i −1.10965 1.92198i
\(378\) −254.945 441.578i −0.0346904 0.0600855i
\(379\) −14284.2 −1.93596 −0.967978 0.251034i \(-0.919230\pi\)
−0.967978 + 0.251034i \(0.919230\pi\)
\(380\) −1813.10 + 2129.47i −0.244763 + 0.287472i
\(381\) 292.135 0.0392822
\(382\) 504.006 + 872.965i 0.0675058 + 0.116923i
\(383\) 4729.31 + 8191.40i 0.630957 + 1.09285i 0.987357 + 0.158515i \(0.0506708\pi\)
−0.356400 + 0.934334i \(0.615996\pi\)
\(384\) 192.000 332.554i 0.0255155 0.0441942i
\(385\) 1892.73 + 3278.31i 0.250552 + 0.433970i
\(386\) 2167.59 3754.37i 0.285822 0.495058i
\(387\) 1325.86 0.174153
\(388\) 555.048 0.0726245
\(389\) 3550.48 6149.61i 0.462767 0.801536i −0.536330 0.844008i \(-0.680190\pi\)
0.999098 + 0.0424717i \(0.0135232\pi\)
\(390\) −1713.50 + 2967.87i −0.222478 + 0.385344i
\(391\) −13267.9 −1.71607
\(392\) −2030.73 −0.261651
\(393\) 569.097 985.704i 0.0730461 0.126520i
\(394\) −2111.10 3656.53i −0.269938 0.467547i
\(395\) −1763.68 + 3054.78i −0.224659 + 0.389120i
\(396\) 854.756 + 1480.48i 0.108467 + 0.187871i
\(397\) −958.081 1659.44i −0.121120 0.209786i 0.799090 0.601212i \(-0.205315\pi\)
−0.920210 + 0.391426i \(0.871982\pi\)
\(398\) 4277.19 0.538684
\(399\) −2307.40 423.993i −0.289511 0.0531985i
\(400\) −859.610 −0.107451
\(401\) 2784.34 + 4822.63i 0.346742 + 0.600575i 0.985669 0.168693i \(-0.0539546\pi\)
−0.638927 + 0.769268i \(0.720621\pi\)
\(402\) −1241.39 2150.14i −0.154017 0.266765i
\(403\) −9441.34 + 16352.9i −1.16701 + 2.02133i
\(404\) 139.261 + 241.207i 0.0171498 + 0.0297042i
\(405\) 341.918 592.219i 0.0419507 0.0726607i
\(406\) −4534.68 −0.554316
\(407\) 952.658 0.116023
\(408\) −931.325 + 1613.10i −0.113009 + 0.195736i
\(409\) −36.3567 + 62.9716i −0.00439541 + 0.00761307i −0.868215 0.496189i \(-0.834732\pi\)
0.863819 + 0.503802i \(0.168066\pi\)
\(410\) −1212.69 −0.146074
\(411\) −7241.05 −0.869038
\(412\) 1288.69 2232.08i 0.154100 0.266910i
\(413\) −103.780 179.753i −0.0123649 0.0214166i
\(414\) −1538.59 + 2664.92i −0.182651 + 0.316362i
\(415\) 6043.93 + 10468.4i 0.714904 + 1.23825i
\(416\) −1082.47 1874.90i −0.127578 0.220972i
\(417\) 9327.13 1.09533
\(418\) 7736.05 + 1421.53i 0.905222 + 0.166337i
\(419\) 340.170 0.0396620 0.0198310 0.999803i \(-0.493687\pi\)
0.0198310 + 0.999803i \(0.493687\pi\)
\(420\) 478.301 + 828.441i 0.0555683 + 0.0962471i
\(421\) −738.497 1279.11i −0.0854920 0.148077i 0.820109 0.572208i \(-0.193913\pi\)
−0.905601 + 0.424131i \(0.860580\pi\)
\(422\) 975.953 1690.40i 0.112580 0.194994i
\(423\) 933.043 + 1616.08i 0.107249 + 0.185760i
\(424\) 1046.09 1811.88i 0.119818 0.207530i
\(425\) 4169.67 0.475903
\(426\) 947.672 0.107781
\(427\) −3083.44 + 5340.67i −0.349457 + 0.605276i
\(428\) 378.909 656.289i 0.0427926 0.0741190i
\(429\) 9638.02 1.08468
\(430\) −2487.44 −0.278965
\(431\) 6139.52 10634.0i 0.686149 1.18844i −0.286925 0.957953i \(-0.592633\pi\)
0.973074 0.230492i \(-0.0740335\pi\)
\(432\) 216.000 + 374.123i 0.0240563 + 0.0416667i
\(433\) −3105.77 + 5379.35i −0.344697 + 0.597032i −0.985299 0.170841i \(-0.945352\pi\)
0.640602 + 0.767873i \(0.278685\pi\)
\(434\) 2635.42 + 4564.68i 0.291484 + 0.504866i
\(435\) −3040.82 5266.86i −0.335164 0.580521i
\(436\) −956.609 −0.105076
\(437\) 4746.60 + 13338.9i 0.519590 + 1.46016i
\(438\) 6612.87 0.721405
\(439\) 6734.49 + 11664.5i 0.732164 + 1.26814i 0.955957 + 0.293508i \(0.0948228\pi\)
−0.223793 + 0.974637i \(0.571844\pi\)
\(440\) −1603.60 2777.52i −0.173747 0.300939i
\(441\) 1142.28 1978.49i 0.123343 0.213637i
\(442\) 5250.70 + 9094.47i 0.565046 + 0.978688i
\(443\) −3705.54 + 6418.19i −0.397417 + 0.688346i −0.993406 0.114646i \(-0.963427\pi\)
0.595989 + 0.802992i \(0.296760\pi\)
\(444\) 240.740 0.0257320
\(445\) −10885.6 −1.15961
\(446\) 3575.45 6192.87i 0.379602 0.657491i
\(447\) −4378.65 + 7584.05i −0.463318 + 0.802491i
\(448\) −604.315 −0.0637303
\(449\) −3345.93 −0.351680 −0.175840 0.984419i \(-0.556264\pi\)
−0.175840 + 0.984419i \(0.556264\pi\)
\(450\) 483.530 837.499i 0.0506530 0.0877336i
\(451\) 1705.27 + 2953.61i 0.178044 + 0.308382i
\(452\) −325.485 + 563.757i −0.0338706 + 0.0586657i
\(453\) −2873.57 4977.17i −0.298040 0.516221i
\(454\) 86.5237 + 149.864i 0.00894441 + 0.0154922i
\(455\) 5393.20 0.555686
\(456\) 1954.93 + 359.224i 0.200763 + 0.0368908i
\(457\) −542.238 −0.0555029 −0.0277515 0.999615i \(-0.508835\pi\)
−0.0277515 + 0.999615i \(0.508835\pi\)
\(458\) 3928.05 + 6803.59i 0.400755 + 0.694128i
\(459\) −1047.74 1814.74i −0.106545 0.184542i
\(460\) 2886.54 4999.64i 0.292578 0.506759i
\(461\) −1911.72 3311.19i −0.193140 0.334528i 0.753149 0.657850i \(-0.228534\pi\)
−0.946289 + 0.323322i \(0.895200\pi\)
\(462\) 1345.16 2329.89i 0.135460 0.234624i
\(463\) −3750.37 −0.376445 −0.188223 0.982126i \(-0.560273\pi\)
−0.188223 + 0.982126i \(0.560273\pi\)
\(464\) 3841.96 0.384394
\(465\) −3534.47 + 6121.89i −0.352489 + 0.610529i
\(466\) −1020.03 + 1766.74i −0.101399 + 0.175628i
\(467\) −2981.61 −0.295444 −0.147722 0.989029i \(-0.547194\pi\)
−0.147722 + 0.989029i \(0.547194\pi\)
\(468\) 2435.56 0.240564
\(469\) −1953.61 + 3383.76i −0.192344 + 0.333150i
\(470\) −1750.48 3031.91i −0.171795 0.297557i
\(471\) −3805.03 + 6590.51i −0.372243 + 0.644744i
\(472\) 87.9270 + 152.294i 0.00857451 + 0.0148515i
\(473\) 3497.80 + 6058.37i 0.340019 + 0.588930i
\(474\) 2506.88 0.242921
\(475\) −1491.71 4192.01i −0.144093 0.404931i
\(476\) 2931.32 0.282262
\(477\) 1176.85 + 2038.37i 0.112965 + 0.195662i
\(478\) −264.681 458.441i −0.0253268 0.0438674i
\(479\) −7677.92 + 13298.6i −0.732387 + 1.26853i 0.223474 + 0.974710i \(0.428260\pi\)
−0.955860 + 0.293821i \(0.905073\pi\)
\(480\) −405.236 701.889i −0.0385342 0.0667432i
\(481\) 678.631 1175.42i 0.0643304 0.111423i
\(482\) −344.774 −0.0325810
\(483\) 4842.68 0.456210
\(484\) −1847.93 + 3200.71i −0.173547 + 0.300592i
\(485\) 585.744 1014.54i 0.0548397 0.0949851i
\(486\) −486.000 −0.0453609
\(487\) 439.463 0.0408911 0.0204455 0.999791i \(-0.493492\pi\)
0.0204455 + 0.999791i \(0.493492\pi\)
\(488\) 2612.41 4524.83i 0.242333 0.419733i
\(489\) −2597.28 4498.62i −0.240190 0.416022i
\(490\) −2143.03 + 3711.84i −0.197576 + 0.342212i
\(491\) −9882.91 17117.7i −0.908370 1.57334i −0.816329 0.577587i \(-0.803994\pi\)
−0.0920410 0.995755i \(-0.529339\pi\)
\(492\) 430.928 + 746.388i 0.0394872 + 0.0683939i
\(493\) −18636.0 −1.70248
\(494\) 7264.75 8532.39i 0.661653 0.777106i
\(495\) 3608.10 0.327621
\(496\) −2232.84 3867.38i −0.202132 0.350102i
\(497\) −745.692 1291.58i −0.0673016 0.116570i
\(498\) 4295.41 7439.86i 0.386509 0.669454i
\(499\) −4079.86 7066.53i −0.366011 0.633950i 0.622926 0.782280i \(-0.285944\pi\)
−0.988938 + 0.148330i \(0.952610\pi\)
\(500\) −3017.75 + 5226.90i −0.269916 + 0.467508i
\(501\) 4290.37 0.382594
\(502\) −9769.73 −0.868614
\(503\) 9837.15 17038.4i 0.872002 1.51035i 0.0120790 0.999927i \(-0.496155\pi\)
0.859923 0.510424i \(-0.170512\pi\)
\(504\) 339.927 588.771i 0.0300428 0.0520356i
\(505\) 587.850 0.0518000
\(506\) −16236.1 −1.42645
\(507\) 3570.20 6183.76i 0.312738 0.541677i
\(508\) 194.757 + 337.328i 0.0170097 + 0.0294616i
\(509\) 3427.87 5937.25i 0.298502 0.517021i −0.677291 0.735715i \(-0.736846\pi\)
0.975794 + 0.218694i \(0.0701796\pi\)
\(510\) 1965.66 + 3404.62i 0.170668 + 0.295606i
\(511\) −5203.46 9012.65i −0.450465 0.780228i
\(512\) 512.000 0.0441942
\(513\) −1449.63 + 1702.58i −0.124762 + 0.146532i
\(514\) 8045.28 0.690393
\(515\) −2719.92 4711.04i −0.232726 0.403093i
\(516\) 883.907 + 1530.97i 0.0754105 + 0.130615i
\(517\) −4922.99 + 8526.87i −0.418787 + 0.725361i
\(518\) −189.431 328.103i −0.0160678 0.0278302i
\(519\) 439.987 762.080i 0.0372125 0.0644539i
\(520\) −4569.34 −0.385344
\(521\) −12666.6 −1.06513 −0.532567 0.846388i \(-0.678773\pi\)
−0.532567 + 0.846388i \(0.678773\pi\)
\(522\) −2161.10 + 3743.14i −0.181205 + 0.313856i
\(523\) −2358.62 + 4085.24i −0.197199 + 0.341559i −0.947619 0.319402i \(-0.896518\pi\)
0.750420 + 0.660961i \(0.229851\pi\)
\(524\) 1517.59 0.126520
\(525\) −1521.90 −0.126516
\(526\) 7142.12 12370.5i 0.592036 1.02544i
\(527\) 10830.7 + 18759.3i 0.895243 + 1.55061i
\(528\) −1139.68 + 1973.98i −0.0939356 + 0.162701i
\(529\) −8529.25 14773.1i −0.701015 1.21419i
\(530\) −2207.89 3824.17i −0.180952 0.313418i
\(531\) −197.836 −0.0161682
\(532\) −1048.68 2947.02i −0.0854629 0.240169i
\(533\) 4859.03 0.394874
\(534\) 3868.18 + 6699.88i 0.313469 + 0.542944i
\(535\) −799.726 1385.17i −0.0646265 0.111936i
\(536\) 1655.18 2866.86i 0.133382 0.231025i
\(537\) −5765.27 9985.75i −0.463296 0.802452i
\(538\) −5081.26 + 8801.00i −0.407191 + 0.705275i
\(539\) 12054.0 0.963270
\(540\) 911.781 0.0726607
\(541\) −5870.58 + 10168.1i −0.466536 + 0.808064i −0.999269 0.0382192i \(-0.987831\pi\)
0.532733 + 0.846283i \(0.321165\pi\)
\(542\) 2973.80 5150.78i 0.235675 0.408201i
\(543\) −5307.83 −0.419486
\(544\) −2483.53 −0.195736
\(545\) −1009.51 + 1748.53i −0.0793445 + 0.137429i
\(546\) −1916.47 3319.42i −0.150215 0.260179i
\(547\) 11131.1 19279.6i 0.870073 1.50701i 0.00815327 0.999967i \(-0.497405\pi\)
0.861920 0.507044i \(-0.169262\pi\)
\(548\) −4827.37 8361.24i −0.376305 0.651779i
\(549\) 2938.96 + 5090.44i 0.228473 + 0.395728i
\(550\) 5102.48 0.395583
\(551\) 6667.07 + 18735.9i 0.515475 + 1.44859i
\(552\) −4102.91 −0.316362
\(553\) −1972.58 3416.61i −0.151687 0.262729i
\(554\) −7778.48 13472.7i −0.596527 1.03322i
\(555\) 254.053 440.033i 0.0194306 0.0336547i
\(556\) 6218.09 + 10770.0i 0.474291 + 0.821496i
\(557\) 9813.87 16998.1i 0.746548 1.29306i −0.202920 0.979195i \(-0.565043\pi\)
0.949468 0.313864i \(-0.101623\pi\)
\(558\) 5023.88 0.381143
\(559\) 9966.71 0.754109
\(560\) −637.734 + 1104.59i −0.0481236 + 0.0833525i
\(561\) 5528.17 9575.07i 0.416042 0.720606i
\(562\) 4441.36 0.333358
\(563\) 9810.37 0.734384 0.367192 0.930145i \(-0.380319\pi\)
0.367192 + 0.930145i \(0.380319\pi\)
\(564\) −1244.06 + 2154.77i −0.0928799 + 0.160873i
\(565\) 686.970 + 1189.87i 0.0511523 + 0.0885984i
\(566\) 7616.34 13191.9i 0.565616 0.979676i
\(567\) 382.418 + 662.367i 0.0283246 + 0.0490596i
\(568\) 631.781 + 1094.28i 0.0466707 + 0.0808360i
\(569\) 2528.37 0.186282 0.0931412 0.995653i \(-0.470309\pi\)
0.0931412 + 0.995653i \(0.470309\pi\)
\(570\) 2719.64 3194.20i 0.199848 0.234720i
\(571\) −21892.0 −1.60447 −0.802233 0.597011i \(-0.796355\pi\)
−0.802233 + 0.597011i \(0.796355\pi\)
\(572\) 6425.35 + 11129.0i 0.469680 + 0.813510i
\(573\) −756.009 1309.45i −0.0551182 0.0954676i
\(574\) 678.166 1174.62i 0.0493138 0.0854140i
\(575\) 4592.32 + 7954.14i 0.333066 + 0.576888i
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) −4002.61 −0.288788 −0.144394 0.989520i \(-0.546123\pi\)
−0.144394 + 0.989520i \(0.546123\pi\)
\(578\) 2220.76 0.159812
\(579\) −3251.38 + 5631.56i −0.233373 + 0.404213i
\(580\) 4054.43 7022.48i 0.290261 0.502746i
\(581\) −13519.7 −0.965388
\(582\) −832.573 −0.0592977
\(583\) −6209.40 + 10755.0i −0.441110 + 0.764025i
\(584\) 4408.58 + 7635.89i 0.312377 + 0.541054i
\(585\) 2570.25 4451.81i 0.181653 0.314632i
\(586\) 9036.61 + 15651.9i 0.637029 + 1.10337i
\(587\) −12259.2 21233.6i −0.861998 1.49302i −0.869997 0.493056i \(-0.835880\pi\)
0.00799928 0.999968i \(-0.497454\pi\)
\(588\) 3046.09 0.213637
\(589\) 14985.1 17599.9i 1.04831 1.23123i
\(590\) 371.158 0.0258989
\(591\) 3166.65 + 5484.80i 0.220404 + 0.381750i
\(592\) 160.493 + 277.983i 0.0111423 + 0.0192990i
\(593\) 8849.35 15327.5i 0.612815 1.06143i −0.377948 0.925827i \(-0.623370\pi\)
0.990764 0.135600i \(-0.0432963\pi\)
\(594\) −1282.13 2220.72i −0.0885633 0.153396i
\(595\) 3093.43 5357.97i 0.213140 0.369169i
\(596\) −11676.4 −0.802491
\(597\) −6415.78 −0.439833
\(598\) −11565.9 + 20032.6i −0.790908 + 1.36989i
\(599\) −1804.00 + 3124.63i −0.123054 + 0.213137i −0.920971 0.389632i \(-0.872602\pi\)
0.797916 + 0.602768i \(0.205936\pi\)
\(600\) 1289.41 0.0877336
\(601\) 23195.0 1.57429 0.787143 0.616771i \(-0.211559\pi\)
0.787143 + 0.616771i \(0.211559\pi\)
\(602\) 1391.04 2409.34i 0.0941767 0.163119i
\(603\) 1862.08 + 3225.22i 0.125754 + 0.217813i
\(604\) 3831.43 6636.23i 0.258110 0.447060i
\(605\) 3900.25 + 6755.43i 0.262095 + 0.453962i
\(606\) −208.892 361.811i −0.0140027 0.0242534i
\(607\) −3485.49 −0.233067 −0.116534 0.993187i \(-0.537178\pi\)
−0.116534 + 0.993187i \(0.537178\pi\)
\(608\) 888.488 + 2496.84i 0.0592647 + 0.166546i
\(609\) 6802.02 0.452597
\(610\) −5513.77 9550.13i −0.365977 0.633891i
\(611\) 7013.84 + 12148.3i 0.464402 + 0.804368i
\(612\) 1396.99 2419.65i 0.0922711 0.159818i
\(613\) 5476.62 + 9485.79i 0.360846 + 0.625004i 0.988100 0.153811i \(-0.0491546\pi\)
−0.627254 + 0.778815i \(0.715821\pi\)
\(614\) −7797.17 + 13505.1i −0.512489 + 0.887657i
\(615\) 1819.03 0.119269
\(616\) 3587.10 0.234624
\(617\) −3504.76 + 6070.42i −0.228681 + 0.396088i −0.957418 0.288707i \(-0.906775\pi\)
0.728736 + 0.684794i \(0.240108\pi\)
\(618\) −1933.04 + 3348.12i −0.125822 + 0.217931i
\(619\) 24225.1 1.57301 0.786503 0.617587i \(-0.211890\pi\)
0.786503 + 0.617587i \(0.211890\pi\)
\(620\) −9425.26 −0.610529
\(621\) 2307.89 3997.38i 0.149134 0.258308i
\(622\) −2737.49 4741.47i −0.176468 0.305652i
\(623\) 6087.49 10543.8i 0.391477 0.678058i
\(624\) 1623.71 + 2812.34i 0.104167 + 0.180423i
\(625\) 3011.43 + 5215.95i 0.192731 + 0.333821i
\(626\) −15292.3 −0.976363
\(627\) −11604.1 2132.29i −0.739110 0.135814i
\(628\) −10146.7 −0.644744
\(629\) −778.497 1348.40i −0.0493493 0.0854755i
\(630\) −717.451 1242.66i −0.0453713 0.0785855i
\(631\) −7452.24 + 12907.7i −0.470157 + 0.814336i −0.999418 0.0341235i \(-0.989136\pi\)
0.529261 + 0.848459i \(0.322469\pi\)
\(632\) 1671.25 + 2894.69i 0.105188 + 0.182191i
\(633\) −1463.93 + 2535.60i −0.0919210 + 0.159212i
\(634\) −12840.8 −0.804373
\(635\) 822.108 0.0513769
\(636\) −1569.14 + 2717.83i −0.0978308 + 0.169448i
\(637\) 8586.74 14872.7i 0.534095 0.925081i
\(638\) −22805.2 −1.41515
\(639\) −1421.51 −0.0880031
\(640\) 540.315 935.852i 0.0333716 0.0578013i
\(641\) 8374.53 + 14505.1i 0.516028 + 0.893787i 0.999827 + 0.0186079i \(0.00592342\pi\)
−0.483799 + 0.875179i \(0.660743\pi\)
\(642\) −568.363 + 984.434i −0.0349400 + 0.0605179i
\(643\) 3554.81 + 6157.10i 0.218022 + 0.377624i 0.954203 0.299160i \(-0.0967064\pi\)
−0.736181 + 0.676784i \(0.763373\pi\)
\(644\) 3228.45 + 5591.84i 0.197545 + 0.342157i
\(645\) 3731.15 0.227774
\(646\) −4309.75 12111.3i −0.262484 0.737636i
\(647\) 6637.82 0.403338 0.201669 0.979454i \(-0.435363\pi\)
0.201669 + 0.979454i \(0.435363\pi\)
\(648\) −324.000 561.184i −0.0196419 0.0340207i
\(649\) −521.918 903.988i −0.0315671 0.0546759i
\(650\) 3634.78 6295.62i 0.219335 0.379899i
\(651\) −3953.13 6847.02i −0.237996 0.412221i
\(652\) 3463.04 5998.16i 0.208011 0.360285i
\(653\) −18762.0 −1.12437 −0.562184 0.827012i \(-0.690039\pi\)
−0.562184 + 0.827012i \(0.690039\pi\)
\(654\) 1434.91 0.0857944
\(655\) 1601.52 2773.91i 0.0955365 0.165474i
\(656\) −574.570 + 995.185i −0.0341969 + 0.0592308i
\(657\) −9919.31 −0.589024
\(658\) 3915.64 0.231987
\(659\) −3078.28 + 5331.74i −0.181962 + 0.315167i −0.942549 0.334069i \(-0.891578\pi\)
0.760587 + 0.649236i \(0.224911\pi\)
\(660\) 2405.40 + 4166.28i 0.141864 + 0.245716i
\(661\) −13082.6 + 22659.7i −0.769824 + 1.33337i 0.167835 + 0.985815i \(0.446322\pi\)
−0.937658 + 0.347558i \(0.887011\pi\)
\(662\) 4594.77 + 7958.38i 0.269760 + 0.467238i
\(663\) −7876.04 13641.7i −0.461358 0.799095i
\(664\) 11454.4 0.669454
\(665\) −6493.36 1193.18i −0.378649 0.0695780i
\(666\) −361.110 −0.0210101
\(667\) −20525.1 35550.4i −1.19150 2.06375i
\(668\) 2860.25 + 4954.09i 0.165668 + 0.286946i
\(669\) −5363.18 + 9289.30i −0.309944 + 0.536839i
\(670\) −3493.43 6050.80i −0.201437 0.348900i
\(671\) −15506.8 + 26858.5i −0.892150 + 1.54525i
\(672\) 906.472 0.0520356
\(673\) 31028.8 1.77723 0.888613 0.458657i \(-0.151669\pi\)
0.888613 + 0.458657i \(0.151669\pi\)
\(674\) −6611.27 + 11451.1i −0.377829 + 0.654419i
\(675\) −725.296 + 1256.25i −0.0413580 + 0.0716341i
\(676\) 9520.52 0.541677
\(677\) −4341.55 −0.246469 −0.123234 0.992378i \(-0.539327\pi\)
−0.123234 + 0.992378i \(0.539327\pi\)
\(678\) 488.228 845.635i 0.0276553 0.0479003i
\(679\) 655.125 + 1134.71i 0.0370271 + 0.0641328i
\(680\) −2620.88 + 4539.49i −0.147803 + 0.256002i
\(681\) −129.786 224.795i −0.00730308 0.0126493i
\(682\) 13253.7 + 22956.1i 0.744149 + 1.28890i
\(683\) 16457.2 0.921986 0.460993 0.887404i \(-0.347493\pi\)
0.460993 + 0.887404i \(0.347493\pi\)
\(684\) −2932.39 538.837i −0.163922 0.0301213i
\(685\) −20377.3 −1.13661
\(686\) −5635.62 9761.18i −0.313657 0.543270i
\(687\) −5892.08 10205.4i −0.327215 0.566753i
\(688\) −1178.54 + 2041.30i −0.0653074 + 0.113116i
\(689\) 8846.60 + 15322.8i 0.489156 + 0.847244i
\(690\) −4329.81 + 7499.45i −0.238889 + 0.413767i
\(691\) 2522.21 0.138856 0.0694280 0.997587i \(-0.477883\pi\)
0.0694280 + 0.997587i \(0.477883\pi\)
\(692\) 1173.30 0.0644539
\(693\) −2017.74 + 3494.83i −0.110603 + 0.191569i
\(694\) 2498.63 4327.75i 0.136667 0.236714i
\(695\) 26247.8 1.43257
\(696\) −5762.95 −0.313856
\(697\) 2787.04 4827.29i 0.151459 0.262334i
\(698\) −10330.5 17893.0i −0.560195 0.970286i
\(699\) 1530.04 2650.10i 0.0827917 0.143399i
\(700\) −1014.60 1757.34i −0.0547832 0.0948873i
\(701\) −2009.91 3481.27i −0.108293 0.187569i 0.806786 0.590844i \(-0.201205\pi\)
−0.915079 + 0.403275i \(0.867872\pi\)
\(702\) −3653.34 −0.196420
\(703\) −1077.11 + 1265.06i −0.0577867 + 0.0678700i
\(704\) −3039.13 −0.162701
\(705\) 2625.71 + 4547.87i 0.140270 + 0.242954i
\(706\) −2608.83 4518.62i −0.139072 0.240879i
\(707\) −328.740 + 569.395i −0.0174874 + 0.0302890i
\(708\) −131.890 228.441i −0.00700106 0.0121262i
\(709\) 5026.45 8706.07i 0.266252 0.461161i −0.701639 0.712533i \(-0.747548\pi\)
0.967891 + 0.251371i \(0.0808814\pi\)
\(710\) 2666.88 0.140966
\(711\) −3760.32 −0.198344
\(712\) −5157.57 + 8933.18i −0.271472 + 0.470204i
\(713\) −23857.1 + 41321.7i −1.25309 + 2.17042i
\(714\) −4396.98 −0.230466
\(715\) 27122.7 1.41865
\(716\) 7687.03 13314.3i 0.401226 0.694944i
\(717\) 397.021 + 687.661i 0.0206793 + 0.0358175i
\(718\) −4150.33 + 7188.58i −0.215723 + 0.373643i
\(719\) −5215.18 9032.95i −0.270505 0.468529i 0.698486 0.715624i \(-0.253857\pi\)
−0.968991 + 0.247095i \(0.920524\pi\)
\(720\) 607.854 + 1052.83i 0.0314630 + 0.0544956i
\(721\) 6084.18 0.314268
\(722\) −10634.4 + 8665.67i −0.548158 + 0.446680i
\(723\) 517.161 0.0266022
\(724\) −3538.56 6128.96i −0.181643 0.314615i
\(725\) 6450.37 + 11172.4i 0.330429 + 0.572319i
\(726\) 2771.89 4801.06i 0.141701 0.245433i
\(727\) 10846.7 + 18787.1i 0.553346 + 0.958424i 0.998030 + 0.0627365i \(0.0199828\pi\)
−0.444684 + 0.895688i \(0.646684\pi\)
\(728\) 2555.29 4425.89i 0.130090 0.225322i
\(729\) 729.000 0.0370370
\(730\) 18609.5 0.943520
\(731\) 5716.70 9901.61i 0.289247 0.500991i
\(732\) −3918.62 + 6787.25i −0.197864 + 0.342710i
\(733\) −3382.86 −0.170462 −0.0852310 0.996361i \(-0.527163\pi\)
−0.0852310 + 0.996361i \(0.527163\pi\)
\(734\) −14741.0 −0.741279
\(735\) 3214.54 5567.75i 0.161320 0.279415i
\(736\) −2735.27 4737.64i −0.136989 0.237271i
\(737\) −9824.84 + 17017.1i −0.491048 + 0.850521i
\(738\) −646.391 1119.58i −0.0322412 0.0558434i
\(739\) −4008.94 6943.69i −0.199555 0.345640i 0.748829 0.662763i \(-0.230616\pi\)
−0.948384 + 0.317123i \(0.897283\pi\)
\(740\) 677.476 0.0336547
\(741\) −10897.1 + 12798.6i −0.540237 + 0.634504i
\(742\) 4938.82 0.244353
\(743\) −4678.96 8104.19i −0.231029 0.400153i 0.727082 0.686550i \(-0.240876\pi\)
−0.958111 + 0.286397i \(0.907542\pi\)
\(744\) 3349.25 + 5801.08i 0.165040 + 0.285857i
\(745\) −12322.1 + 21342.6i −0.605971 + 1.04957i
\(746\) −13166.5 22805.1i −0.646195 1.11924i
\(747\) −6443.11 + 11159.8i −0.315584 + 0.546607i
\(748\) 14741.8 0.720606
\(749\) 1788.91 0.0872700
\(750\) 4526.63 7840.35i 0.220385 0.381719i
\(751\) 6483.64 11230.0i 0.315035 0.545657i −0.664410 0.747368i \(-0.731317\pi\)
0.979445 + 0.201712i \(0.0646504\pi\)
\(752\) −3317.49 −0.160873
\(753\) 14654.6 0.709221
\(754\) −16245.4 + 28137.8i −0.784644 + 1.35904i
\(755\) −8086.63 14006.5i −0.389805 0.675162i
\(756\) −509.890 + 883.156i −0.0245298 + 0.0424869i
\(757\) −13890.7 24059.4i −0.666931 1.15516i −0.978758 0.205019i \(-0.934274\pi\)
0.311827 0.950139i \(-0.399059\pi\)
\(758\) 14284.2 + 24740.9i 0.684464 + 1.18553i
\(759\) 24354.1 1.16469
\(760\) 5501.44 + 1010.91i 0.262576 + 0.0482493i
\(761\) 26066.1 1.24165 0.620825 0.783949i \(-0.286798\pi\)
0.620825 + 0.783949i \(0.286798\pi\)
\(762\) −292.135 505.992i −0.0138884 0.0240553i
\(763\) −1129.09 1955.64i −0.0535724 0.0927901i
\(764\) 1008.01 1745.93i 0.0477338 0.0826774i
\(765\) −2948.49 5106.93i −0.139350 0.241361i
\(766\) 9458.62 16382.8i 0.446154 0.772761i
\(767\) −1487.16 −0.0700109
\(768\) −768.000 −0.0360844
\(769\) 18417.7 31900.4i 0.863665 1.49591i −0.00470099 0.999989i \(-0.501496\pi\)
0.868366 0.495923i \(-0.165170\pi\)
\(770\) 3785.47 6556.63i 0.177167 0.306863i
\(771\) −12067.9 −0.563703
\(772\) −8670.35 −0.404213
\(773\) −5604.20 + 9706.76i −0.260762 + 0.451653i −0.966445 0.256875i \(-0.917307\pi\)
0.705683 + 0.708528i \(0.250640\pi\)
\(774\) −1325.86 2296.46i −0.0615724 0.106647i
\(775\) 7497.53 12986.1i 0.347509 0.601903i
\(776\) −555.048 961.372i −0.0256766 0.0444733i
\(777\) 284.146 + 492.155i 0.0131193 + 0.0227233i
\(778\) −14201.9 −0.654452
\(779\) −5850.22 1075.00i −0.269071 0.0494426i
\(780\) 6854.01 0.314632
\(781\) −3750.13 6495.42i −0.171819 0.297598i
\(782\) 13267.9 + 22980.6i 0.606724 + 1.05088i
\(783\) 3241.66 5614.71i 0.147953 0.256262i
\(784\) 2030.73 + 3517.32i 0.0925076 + 0.160228i
\(785\) −10707.9 + 18546.6i −0.486854 + 0.843257i
\(786\) −2276.39 −0.103303
\(787\) −25466.9 −1.15349 −0.576745 0.816924i \(-0.695677\pi\)
−0.576745 + 0.816924i \(0.695677\pi\)
\(788\) −4222.20 + 7313.07i −0.190875 + 0.330606i
\(789\) −10713.2 + 18555.8i −0.483396 + 0.837266i
\(790\) 7054.70 0.317715
\(791\) −1536.68 −0.0690748
\(792\) 1709.51 2960.96i 0.0766981 0.132845i
\(793\) 22092.7 + 38265.7i 0.989324 + 1.71356i
\(794\) −1916.16 + 3318.89i −0.0856449 + 0.148341i
\(795\) 3311.83 + 5736.26i 0.147746 + 0.255904i
\(796\) −4277.19 7408.31i −0.190453 0.329875i
\(797\) 31745.4 1.41089 0.705446 0.708764i \(-0.250747\pi\)
0.705446 + 0.708764i \(0.250747\pi\)
\(798\) 1573.03 + 4420.54i 0.0697801 + 0.196097i
\(799\) 16092.0 0.712507
\(800\) 859.610 + 1488.89i 0.0379897 + 0.0658002i
\(801\) −5802.27 10049.8i −0.255946 0.443312i
\(802\) 5568.69 9645.25i 0.245184 0.424670i
\(803\) −26168.5 45325.2i −1.15002 1.99189i
\(804\) −2482.77 + 4300.29i −0.108906 + 0.188631i
\(805\) 13628.0 0.596674
\(806\) 37765.3 1.65041
\(807\) 7621.89 13201.5i 0.332470 0.575855i
\(808\) 278.522 482.415i 0.0121267 0.0210041i
\(809\) −14106.2 −0.613040 −0.306520 0.951864i \(-0.599165\pi\)
−0.306520 + 0.951864i \(0.599165\pi\)
\(810\) −1367.67 −0.0593273
\(811\) −21337.7 + 36958.0i −0.923882 + 1.60021i −0.130532 + 0.991444i \(0.541669\pi\)
−0.793350 + 0.608766i \(0.791665\pi\)
\(812\) 4534.68 + 7854.29i 0.195980 + 0.339448i
\(813\) −4460.71 + 7726.17i −0.192428 + 0.333295i
\(814\) −952.658 1650.05i −0.0410204 0.0710495i
\(815\) −7309.11 12659.7i −0.314143 0.544112i
\(816\) 3725.30 0.159818
\(817\) −11999.8 2205.01i −0.513856 0.0944228i
\(818\) 145.427 0.00621604
\(819\) 2874.70 + 4979.12i 0.122650 + 0.212435i
\(820\) 1212.69 + 2100.44i 0.0516451 + 0.0894519i
\(821\) 9719.65 16834.9i 0.413177 0.715643i −0.582058 0.813147i \(-0.697752\pi\)
0.995235 + 0.0975038i \(0.0310858\pi\)
\(822\) 7241.05 + 12541.9i 0.307251 + 0.532175i
\(823\) 12511.7 21670.9i 0.529928 0.917863i −0.469462 0.882953i \(-0.655552\pi\)
0.999390 0.0349103i \(-0.0111145\pi\)
\(824\) −5154.77 −0.217931
\(825\) −7653.72 −0.322992
\(826\) −207.561 + 359.506i −0.00874330 + 0.0151438i
\(827\) 16772.9 29051.5i 0.705260 1.22155i −0.261338 0.965247i \(-0.584164\pi\)
0.966598 0.256298i \(-0.0825029\pi\)
\(828\) 6154.37 0.258308
\(829\) 5555.52 0.232752 0.116376 0.993205i \(-0.462872\pi\)
0.116376 + 0.993205i \(0.462872\pi\)
\(830\) 12087.9 20936.8i 0.505513 0.875575i
\(831\) 11667.7 + 20209.1i 0.487062 + 0.843617i
\(832\) −2164.94 + 3749.79i −0.0902114 + 0.156251i
\(833\) −9850.35 17061.3i −0.409717 0.709651i
\(834\) −9327.13 16155.1i −0.387257 0.670749i
\(835\) 12073.7 0.500392
\(836\) −5273.90 14820.8i −0.218184 0.613142i
\(837\) −7535.82 −0.311202
\(838\) −340.170 589.192i −0.0140227 0.0242879i
\(839\) −20491.2 35491.8i −0.843188 1.46044i −0.887185 0.461413i \(-0.847343\pi\)
0.0439970 0.999032i \(-0.485991\pi\)
\(840\) 956.602 1656.88i 0.0392927 0.0680570i
\(841\) −16635.0 28812.6i −0.682068 1.18138i
\(842\) −1476.99 + 2558.23i −0.0604520 + 0.104706i
\(843\) −6662.04 −0.272186
\(844\) −3903.81 −0.159212
\(845\) 10047.0 17402.0i 0.409028 0.708456i
\(846\) 1866.09 3232.16i 0.0758362 0.131352i
\(847\) −8724.46 −0.353927
\(848\) −4184.37 −0.169448
\(849\) −11424.5 + 19787.8i −0.461824 + 0.799902i
\(850\) −4169.67 7222.08i −0.168257 0.291430i
\(851\) 1714.82 2970.15i 0.0690754 0.119642i
\(852\) −947.672 1641.42i −0.0381064 0.0660023i
\(853\) 15804.6 + 27374.4i 0.634397 + 1.09881i 0.986643 + 0.162900i \(0.0520849\pi\)
−0.352245 + 0.935908i \(0.614582\pi\)
\(854\) 12333.7 0.494206
\(855\) −4079.46 + 4791.30i −0.163175 + 0.191648i
\(856\) −1515.63 −0.0605179
\(857\) −10481.8 18155.1i −0.417798 0.723647i 0.577920 0.816094i \(-0.303865\pi\)
−0.995718 + 0.0924465i \(0.970531\pi\)
\(858\) −9638.02 16693.5i −0.383492 0.664228i
\(859\) −1948.32 + 3374.59i −0.0773875 + 0.134039i −0.902122 0.431481i \(-0.857991\pi\)
0.824735 + 0.565520i \(0.191325\pi\)
\(860\) 2487.44 + 4308.37i 0.0986289 + 0.170830i
\(861\) −1017.25 + 1761.93i −0.0402645 + 0.0697402i
\(862\) −24558.1 −0.970361
\(863\) 2630.83 0.103771 0.0518856 0.998653i \(-0.483477\pi\)
0.0518856 + 0.998653i \(0.483477\pi\)
\(864\) 432.000 748.246i 0.0170103 0.0294628i
\(865\) 1238.18 2144.60i 0.0486700 0.0842989i
\(866\) 12423.1 0.487475
\(867\) −3331.14 −0.130486
\(868\) 5270.84 9129.36i 0.206111 0.356994i
\(869\) −9920.23 17182.3i −0.387251 0.670738i
\(870\) −6081.65 + 10533.7i −0.236997 + 0.410490i
\(871\) 13997.6 + 24244.5i 0.544534 + 0.943161i
\(872\) 956.609 + 1656.90i 0.0371501 + 0.0643458i
\(873\) 1248.86 0.0484164
\(874\) 18357.1 21560.3i 0.710457 0.834426i
\(875\) −14247.4 −0.550459
\(876\) −6612.87 11453.8i −0.255055 0.441768i
\(877\) 18288.7 + 31676.9i 0.704178 + 1.21967i 0.966987 + 0.254825i \(0.0820178\pi\)
−0.262809 + 0.964848i \(0.584649\pi\)
\(878\) 13469.0 23329.0i 0.517718 0.896714i
\(879\) −13554.9 23477.8i −0.520132 0.900894i
\(880\) −3207.20 + 5555.04i −0.122858 + 0.212796i
\(881\) 6389.06 0.244328 0.122164 0.992510i \(-0.461017\pi\)
0.122164 + 0.992510i \(0.461017\pi\)
\(882\) −4569.13 −0.174434
\(883\) 8868.92 15361.4i 0.338010 0.585451i −0.646048 0.763297i \(-0.723580\pi\)
0.984058 + 0.177846i \(0.0569129\pi\)
\(884\) 10501.4 18188.9i 0.399548 0.692037i
\(885\) −556.737 −0.0211463
\(886\) 14822.2 0.562033
\(887\) −14810.5 + 25652.6i −0.560641 + 0.971058i 0.436800 + 0.899559i \(0.356112\pi\)
−0.997441 + 0.0714994i \(0.977222\pi\)
\(888\) −240.740 416.974i −0.00909764 0.0157576i
\(889\) −459.743 + 796.298i −0.0173445 + 0.0300416i
\(890\) 10885.6 + 18854.4i 0.409984 + 0.710114i
\(891\) 1923.20 + 3331.08i 0.0723117 + 0.125247i
\(892\) −14301.8 −0.536839
\(893\) −5756.93 16178.2i −0.215732 0.606251i
\(894\) 17514.6 0.655231
\(895\) −16224.3 28101.3i −0.605942 1.04952i
\(896\) 604.315 + 1046.70i 0.0225321 + 0.0390267i
\(897\) 17348.8 30049.0i 0.645774 1.11851i
\(898\) 3345.93 + 5795.33i 0.124338 + 0.215359i
\(899\) −33509.7 + 58040.4i −1.24317 + 2.15323i
\(900\) −1934.12 −0.0716341
\(901\) 20296.9 0.750486
\(902\) 3410.54 5907.23i 0.125896 0.218059i
\(903\) −2086.55 + 3614.02i −0.0768950 + 0.133186i
\(904\) 1301.94 0.0479003
\(905\) −14937.0 −0.548643
\(906\) −5747.15 + 9954.35i −0.210746 + 0.365023i
\(907\) −7176.13 12429.4i −0.262712 0.455030i 0.704250 0.709952i \(-0.251283\pi\)
−0.966962 + 0.254922i \(0.917950\pi\)
\(908\) 173.047 299.727i 0.00632465 0.0109546i
\(909\) 313.338 + 542.717i 0.0114332 + 0.0198028i
\(910\) −5393.20 9341.30i −0.196465 0.340287i
\(911\) 50.5532 0.00183853 0.000919266 1.00000i \(-0.499707\pi\)
0.000919266 1.00000i \(0.499707\pi\)
\(912\) −1332.73 3745.26i −0.0483895 0.135985i
\(913\) −67991.2 −2.46460
\(914\) 542.238 + 939.184i 0.0196232 + 0.0339885i
\(915\) 8270.65 + 14325.2i 0.298819 + 0.517570i
\(916\) 7856.10 13607.2i 0.283377 0.490823i
\(917\) 1791.22 + 3102.48i 0.0645051 + 0.111726i
\(918\) −2095.48 + 3629.48i −0.0753390 + 0.130491i
\(919\) −38362.9 −1.37701 −0.688507 0.725230i \(-0.741734\pi\)
−0.688507 + 0.725230i \(0.741734\pi\)
\(920\) −11546.2 −0.413767
\(921\) 11695.8 20257.6i 0.418445 0.724769i
\(922\) −3823.43 + 6622.38i −0.136571 + 0.236547i
\(923\) −10685.7 −0.381066
\(924\) −5380.64 −0.191569
\(925\) −538.913 + 933.424i −0.0191560 + 0.0331792i
\(926\) 3750.37 + 6495.82i 0.133094 + 0.230525i
\(927\) 2899.56 5022.18i 0.102734 0.177940i
\(928\) −3841.96 6654.48i −0.135904 0.235392i
\(929\) 19043.5 + 32984.3i 0.672548 + 1.16489i 0.977179 + 0.212417i \(0.0681335\pi\)
−0.304631 + 0.952470i \(0.598533\pi\)
\(930\) 14137.9 0.498494
\(931\) −13628.7 + 16006.8i −0.479767 + 0.563483i
\(932\) 4080.10 0.143399
\(933\) 4106.24 + 7112.21i 0.144086 + 0.249564i
\(934\) 2981.61 + 5164.30i 0.104455 + 0.180922i
\(935\) 15557.0 26945.6i 0.544138 0.942475i
\(936\) −2435.56 4218.52i −0.0850522 0.147315i
\(937\) −22120.0 + 38313.0i −0.771217 + 1.33579i 0.165680 + 0.986180i \(0.447018\pi\)
−0.936897 + 0.349607i \(0.886315\pi\)
\(938\) 7814.46 0.272016
\(939\) 22938.5 0.797197
\(940\) −3500.95 + 6063.83i −0.121477 + 0.210404i
\(941\) −12104.5 + 20965.7i −0.419338 + 0.726314i −0.995873 0.0907581i \(-0.971071\pi\)
0.576535 + 0.817072i \(0.304404\pi\)
\(942\) 15220.1 0.526431
\(943\) 12278.2 0.424001
\(944\) 175.854 304.588i 0.00606309 0.0105016i
\(945\) 1076.18 + 1863.99i 0.0370455 + 0.0641648i
\(946\) 6995.60 12116.7i 0.240430 0.416437i
\(947\) 10262.4 + 17774.9i 0.352146 + 0.609935i 0.986625 0.163005i \(-0.0521187\pi\)
−0.634479 + 0.772940i \(0.718785\pi\)
\(948\) −2506.88 4342.04i −0.0858857 0.148758i
\(949\) −74565.1 −2.55056
\(950\) −5769.06 + 6775.72i −0.197024 + 0.231403i
\(951\) 19261.2 0.656768
\(952\) −2931.32 5077.20i −0.0997948 0.172850i
\(953\) 2455.68 + 4253.36i 0.0834703 + 0.144575i 0.904738 0.425968i \(-0.140066\pi\)
−0.821268 + 0.570543i \(0.806733\pi\)
\(954\) 2353.71 4076.74i 0.0798785 0.138354i
\(955\) −2127.52 3684.96i −0.0720888 0.124861i
\(956\) −529.362 + 916.882i −0.0179088 + 0.0310189i
\(957\) 34207.7 1.15546
\(958\) 30711.7 1.03575
\(959\) 11395.5 19737.6i 0.383712 0.664609i
\(960\) −810.472 + 1403.78i −0.0272478 + 0.0471945i
\(961\) 48108.3 1.61486
\(962\) −2714.52 −0.0909769
\(963\) 852.545 1476.65i 0.0285284 0.0494127i
\(964\) 344.774 + 597.166i 0.0115191 + 0.0199517i
\(965\) −9149.84 + 15848.0i −0.305227 + 0.528668i
\(966\) −4842.68 8387.76i −0.161295 0.279370i
\(967\) 20197.3 + 34982.8i 0.671668 + 1.16336i 0.977431 + 0.211255i \(0.0677551\pi\)
−0.305763 + 0.952108i \(0.598912\pi\)
\(968\) 7391.72 0.245433
\(969\) 6464.62 + 18166.9i 0.214317 + 0.602277i
\(970\) −2342.98 −0.0775550
\(971\) 13395.9 + 23202.4i 0.442735 + 0.766840i 0.997891 0.0649061i \(-0.0206748\pi\)
−0.555156 + 0.831746i \(0.687341\pi\)
\(972\) 486.000 + 841.777i 0.0160375 + 0.0277778i
\(973\) −14678.4 + 25423.8i −0.483627 + 0.837667i
\(974\) −439.463 761.172i −0.0144572 0.0250406i
\(975\) −5452.17 + 9443.43i −0.179086 + 0.310187i
\(976\) −10449.7 −0.342710
\(977\) −8122.31 −0.265973 −0.132987 0.991118i \(-0.542457\pi\)
−0.132987 + 0.991118i \(0.542457\pi\)
\(978\) −5194.56 + 8997.24i −0.169840 + 0.294172i
\(979\) 30614.4 53025.6i 0.999427 1.73106i
\(980\) 8572.12 0.279415
\(981\) −2152.37 −0.0700509
\(982\) −19765.8 + 34235.4i −0.642314 + 1.11252i
\(983\) 16459.0 + 28507.9i 0.534041 + 0.924986i 0.999209 + 0.0397634i \(0.0126604\pi\)
−0.465168 + 0.885222i \(0.654006\pi\)
\(984\) 861.855 1492.78i 0.0279217 0.0483618i
\(985\) 8911.39 + 15435.0i 0.288265 + 0.499289i
\(986\) 18636.0 + 32278.6i 0.601919 + 1.04255i
\(987\) −5873.46 −0.189417
\(988\) −22043.3 4050.52i −0.709808 0.130430i
\(989\) 25184.7 0.809733
\(990\) −3608.10 6249.42i −0.115831 0.200626i
\(991\) 15885.1 + 27513.7i 0.509189 + 0.881941i 0.999943 + 0.0106428i \(0.00338777\pi\)
−0.490755 + 0.871298i \(0.663279\pi\)
\(992\) −4465.67 + 7734.77i −0.142929 + 0.247560i
\(993\) −6892.16 11937.6i −0.220258 0.381498i
\(994\) −1491.38 + 2583.15i −0.0475894 + 0.0824272i
\(995\) −18054.9 −0.575255
\(996\) −17181.6 −0.546607
\(997\) −7753.26 + 13429.0i −0.246287 + 0.426582i −0.962493 0.271308i \(-0.912544\pi\)
0.716206 + 0.697889i \(0.245877\pi\)
\(998\) −8159.72 + 14133.1i −0.258809 + 0.448271i
\(999\) 541.665 0.0171547
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 114.4.e.d.7.3 6
3.2 odd 2 342.4.g.h.235.1 6
19.7 even 3 2166.4.a.u.1.1 3
19.11 even 3 inner 114.4.e.d.49.3 yes 6
19.12 odd 6 2166.4.a.t.1.1 3
57.11 odd 6 342.4.g.h.163.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.4.e.d.7.3 6 1.1 even 1 trivial
114.4.e.d.49.3 yes 6 19.11 even 3 inner
342.4.g.h.163.1 6 57.11 odd 6
342.4.g.h.235.1 6 3.2 odd 2
2166.4.a.t.1.1 3 19.12 odd 6
2166.4.a.u.1.1 3 19.7 even 3