Properties

Label 342.4.g.h.235.1
Level $342$
Weight $4$
Character 342.235
Analytic conductor $20.179$
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] = [342,4,Mod(163,342)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(342, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("342.163");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 342.g (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: \(20.1786532220\)
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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.1
Root \(1.01248i\) of defining polynomial
Character \(\chi\) \(=\) 342.235
Dual form 342.4.g.h.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.22121 - 7.31135i) q^{5} -9.44242 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.22121 - 7.31135i) q^{5} -9.44242 q^{7} -8.00000 q^{8} +(8.44242 - 14.6227i) q^{10} +47.4865 q^{11} +(-33.8272 + 58.5905i) q^{13} +(-9.44242 - 16.3547i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-38.8052 - 67.2126i) q^{17} +(53.6901 - 63.0585i) q^{19} +33.7697 q^{20} +(47.4865 + 82.2490i) q^{22} +(85.4773 - 148.051i) q^{23} +(26.8628 - 46.5277i) q^{25} -135.309 q^{26} +(18.8848 - 32.7095i) q^{28} +(120.061 - 207.952i) q^{29} +279.104 q^{31} +(16.0000 - 27.7128i) q^{32} +(77.6104 - 134.425i) q^{34} +(39.8584 + 69.0368i) q^{35} -20.0617 q^{37} +(162.911 + 29.9354i) q^{38} +(33.7697 + 58.4908i) q^{40} +(35.9106 + 62.1990i) q^{41} +(-73.6589 - 127.581i) q^{43} +(-94.9729 + 164.498i) q^{44} +341.909 q^{46} +(-103.671 + 179.564i) q^{47} -253.841 q^{49} +107.451 q^{50} +(-135.309 - 234.362i) q^{52} +(-130.761 + 226.486i) q^{53} +(-200.450 - 347.190i) q^{55} +75.5393 q^{56} +480.245 q^{58} +(-10.9909 - 19.0367i) q^{59} +(326.552 - 565.604i) q^{61} +(279.104 + 483.423i) q^{62} +64.0000 q^{64} +571.167 q^{65} +(206.898 - 358.357i) q^{67} +310.442 q^{68} +(-79.7168 + 138.074i) q^{70} +(-78.9726 - 136.785i) q^{71} +(551.073 + 954.486i) q^{73} +(-20.0617 - 34.7478i) q^{74} +(111.061 + 312.105i) q^{76} -448.387 q^{77} +(208.907 + 361.837i) q^{79} +(-67.5393 + 116.982i) q^{80} +(-71.8213 + 124.398i) q^{82} -1431.80 q^{83} +(-327.610 + 567.437i) q^{85} +(147.318 - 255.162i) q^{86} -379.892 q^{88} +(644.697 - 1116.65i) q^{89} +(319.411 - 553.236i) q^{91} +(341.909 + 592.204i) q^{92} -414.686 q^{94} +(-687.680 - 126.363i) q^{95} +(-69.3811 - 120.172i) q^{97} +(-253.841 - 439.665i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8} - 20 q^{10} + 88 q^{11} + 9 q^{13} + 14 q^{14} - 48 q^{16} - 84 q^{17} + 32 q^{19} - 80 q^{20} + 88 q^{22} - 2 q^{23} + 83 q^{25} + 36 q^{26} - 28 q^{28} + 92 q^{29} - 218 q^{31} + 96 q^{32} + 168 q^{34} + 282 q^{35} + 490 q^{37} + 74 q^{38} - 80 q^{40} - 688 q^{41} + 103 q^{43} - 176 q^{44} - 8 q^{46} + 322 q^{47} - 1508 q^{49} + 332 q^{50} + 36 q^{52} - 1322 q^{53} + 248 q^{55} - 112 q^{56} + 368 q^{58} + 252 q^{59} + 435 q^{61} - 218 q^{62} + 384 q^{64} + 3164 q^{65} + 719 q^{67} + 672 q^{68} - 564 q^{70} - 62 q^{71} + 581 q^{73} + 490 q^{74} + 20 q^{76} + 408 q^{77} + 489 q^{79} + 160 q^{80} + 1376 q^{82} - 4992 q^{83} - 1632 q^{85} - 206 q^{86} - 704 q^{88} + 1584 q^{89} + 1573 q^{91} - 8 q^{92} + 1288 q^{94} - 2362 q^{95} - 974 q^{97} - 1508 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −4.22121 7.31135i −0.377556 0.653947i 0.613150 0.789967i \(-0.289902\pi\)
−0.990706 + 0.136020i \(0.956569\pi\)
\(6\) 0 0
\(7\) −9.44242 −0.509843 −0.254921 0.966962i \(-0.582050\pi\)
−0.254921 + 0.966962i \(0.582050\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 8.44242 14.6227i 0.266973 0.462410i
\(11\) 47.4865 1.30161 0.650805 0.759245i \(-0.274432\pi\)
0.650805 + 0.759245i \(0.274432\pi\)
\(12\) 0 0
\(13\) −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
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −38.8052 67.2126i −0.553626 0.958909i −0.998009 0.0630719i \(-0.979910\pi\)
0.444383 0.895837i \(-0.353423\pi\)
\(18\) 0 0
\(19\) 53.6901 63.0585i 0.648281 0.761401i
\(20\) 33.7697 0.377556
\(21\) 0 0
\(22\) 47.4865 + 82.2490i 0.460189 + 0.797070i
\(23\) 85.4773 148.051i 0.774924 1.34221i −0.159913 0.987131i \(-0.551121\pi\)
0.934837 0.355077i \(-0.115545\pi\)
\(24\) 0 0
\(25\) 26.8628 46.5277i 0.214902 0.372222i
\(26\) −135.309 −1.02063
\(27\) 0 0
\(28\) 18.8848 32.7095i 0.127461 0.220768i
\(29\) 120.061 207.952i 0.768787 1.33158i −0.169433 0.985542i \(-0.554194\pi\)
0.938221 0.346037i \(-0.112473\pi\)
\(30\) 0 0
\(31\) 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
\(33\) 0 0
\(34\) 77.6104 134.425i 0.391473 0.678051i
\(35\) 39.8584 + 69.0368i 0.192494 + 0.333410i
\(36\) 0 0
\(37\) −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
\(39\) 0 0
\(40\) 33.7697 + 58.4908i 0.133486 + 0.231205i
\(41\) 35.9106 + 62.1990i 0.136788 + 0.236923i 0.926279 0.376839i \(-0.122989\pi\)
−0.789491 + 0.613762i \(0.789655\pi\)
\(42\) 0 0
\(43\) −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
\(45\) 0 0
\(46\) 341.909 1.09591
\(47\) −103.671 + 179.564i −0.321746 + 0.557280i −0.980848 0.194773i \(-0.937603\pi\)
0.659103 + 0.752053i \(0.270936\pi\)
\(48\) 0 0
\(49\) −253.841 −0.740061
\(50\) 107.451 0.303918
\(51\) 0 0
\(52\) −135.309 234.362i −0.360846 0.625003i
\(53\) −130.761 + 226.486i −0.338896 + 0.586985i −0.984225 0.176920i \(-0.943387\pi\)
0.645330 + 0.763904i \(0.276720\pi\)
\(54\) 0 0
\(55\) −200.450 347.190i −0.491431 0.851184i
\(56\) 75.5393 0.180257
\(57\) 0 0
\(58\) 480.245 1.08723
\(59\) −10.9909 19.0367i −0.0242524 0.0420063i 0.853644 0.520856i \(-0.174387\pi\)
−0.877897 + 0.478850i \(0.841054\pi\)
\(60\) 0 0
\(61\) 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
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 571.167 1.08992
\(66\) 0 0
\(67\) 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
\(69\) 0 0
\(70\) −79.7168 + 138.074i −0.136114 + 0.235756i
\(71\) −78.9726 136.785i −0.132005 0.228639i 0.792445 0.609944i \(-0.208808\pi\)
−0.924449 + 0.381305i \(0.875475\pi\)
\(72\) 0 0
\(73\) 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
\(75\) 0 0
\(76\) 111.061 + 312.105i 0.167626 + 0.471064i
\(77\) −448.387 −0.663616
\(78\) 0 0
\(79\) 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
\(81\) 0 0
\(82\) −71.8213 + 124.398i −0.0967236 + 0.167530i
\(83\) −1431.80 −1.89350 −0.946751 0.321967i \(-0.895656\pi\)
−0.946751 + 0.321967i \(0.895656\pi\)
\(84\) 0 0
\(85\) −327.610 + 567.437i −0.418050 + 0.724084i
\(86\) 147.318 255.162i 0.184717 0.319940i
\(87\) 0 0
\(88\) −379.892 −0.460189
\(89\) 644.697 1116.65i 0.767839 1.32994i −0.170893 0.985290i \(-0.554665\pi\)
0.938732 0.344647i \(-0.112001\pi\)
\(90\) 0 0
\(91\) 319.411 553.236i 0.367949 0.637306i
\(92\) 341.909 + 592.204i 0.387462 + 0.671104i
\(93\) 0 0
\(94\) −414.686 −0.455017
\(95\) −687.680 126.363i −0.742678 0.136470i
\(96\) 0 0
\(97\) −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
\(99\) 0 0
\(100\) 107.451 + 186.111i 0.107451 + 0.186111i
\(101\) −34.8153 + 60.3018i −0.0342995 + 0.0594085i −0.882666 0.470002i \(-0.844253\pi\)
0.848366 + 0.529410i \(0.177587\pi\)
\(102\) 0 0
\(103\) −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
\(105\) 0 0
\(106\) −523.046 −0.479271
\(107\) 189.454 0.171171 0.0855853 0.996331i \(-0.472724\pi\)
0.0855853 + 0.996331i \(0.472724\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) 75.5393 + 130.838i 0.0637303 + 0.110384i
\(113\) −162.743 −0.135483 −0.0677413 0.997703i \(-0.521579\pi\)
−0.0677413 + 0.997703i \(0.521579\pi\)
\(114\) 0 0
\(115\) −1443.27 −1.17031
\(116\) 480.245 + 831.809i 0.384394 + 0.665789i
\(117\) 0 0
\(118\) 21.9817 38.0735i 0.0171490 0.0297030i
\(119\) 366.415 + 634.649i 0.282262 + 0.488893i
\(120\) 0 0
\(121\) 923.965 0.694188
\(122\) 1306.21 0.969331
\(123\) 0 0
\(124\) −558.209 + 966.846i −0.404263 + 0.700204i
\(125\) −1508.88 −1.07966
\(126\) 0 0
\(127\) 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
\(129\) 0 0
\(130\) 571.167 + 989.291i 0.385344 + 0.667435i
\(131\) 189.699 + 328.568i 0.126520 + 0.219138i 0.922326 0.386413i \(-0.126286\pi\)
−0.795806 + 0.605551i \(0.792953\pi\)
\(132\) 0 0
\(133\) −506.964 + 595.425i −0.330521 + 0.388195i
\(134\) 827.591 0.533530
\(135\) 0 0
\(136\) 310.442 + 537.701i 0.195736 + 0.339026i
\(137\) 1206.84 2090.31i 0.752609 1.30356i −0.193945 0.981012i \(-0.562128\pi\)
0.946554 0.322545i \(-0.104538\pi\)
\(138\) 0 0
\(139\) 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
\(141\) 0 0
\(142\) 157.945 273.569i 0.0933414 0.161672i
\(143\) −1606.34 + 2782.26i −0.939361 + 1.62702i
\(144\) 0 0
\(145\) −2027.22 −1.16104
\(146\) −1102.15 + 1908.97i −0.624755 + 1.08211i
\(147\) 0 0
\(148\) 40.1233 69.4956i 0.0222846 0.0385980i
\(149\) −1459.55 2528.02i −0.802491 1.38995i −0.917972 0.396645i \(-0.870174\pi\)
0.115481 0.993310i \(-0.463159\pi\)
\(150\) 0 0
\(151\) −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
\(153\) 0 0
\(154\) −448.387 776.629i −0.234624 0.406380i
\(155\) −1178.16 2040.63i −0.610529 1.05747i
\(156\) 0 0
\(157\) 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
\(159\) 0 0
\(160\) −270.157 −0.133486
\(161\) −807.113 + 1397.96i −0.395089 + 0.684315i
\(162\) 0 0
\(163\) −1731.52 −0.832044 −0.416022 0.909355i \(-0.636576\pi\)
−0.416022 + 0.909355i \(0.636576\pi\)
\(164\) −287.285 −0.136788
\(165\) 0 0
\(166\) −1431.80 2479.95i −0.669454 1.15953i
\(167\) −715.062 + 1238.52i −0.331336 + 0.573891i −0.982774 0.184811i \(-0.940833\pi\)
0.651438 + 0.758702i \(0.274166\pi\)
\(168\) 0 0
\(169\) −1190.07 2061.25i −0.541677 0.938213i
\(170\) −1310.44 −0.591212
\(171\) 0 0
\(172\) 589.271 0.261230
\(173\) 146.662 + 254.027i 0.0644539 + 0.111638i 0.896452 0.443142i \(-0.146136\pi\)
−0.831998 + 0.554779i \(0.812803\pi\)
\(174\) 0 0
\(175\) −253.650 + 439.334i −0.109566 + 0.189775i
\(176\) −379.892 657.992i −0.162701 0.281807i
\(177\) 0 0
\(178\) 2578.79 1.08589
\(179\) 3843.52 1.60490 0.802452 0.596716i \(-0.203528\pi\)
0.802452 + 0.596716i \(0.203528\pi\)
\(180\) 0 0
\(181\) −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
\(183\) 0 0
\(184\) −683.819 + 1184.41i −0.273977 + 0.474542i
\(185\) 84.6845 + 146.678i 0.0336547 + 0.0582917i
\(186\) 0 0
\(187\) −1842.72 3191.69i −0.720606 1.24813i
\(188\) −414.686 718.257i −0.160873 0.278640i
\(189\) 0 0
\(190\) −468.812 1317.46i −0.179006 0.503045i
\(191\) 504.006 0.190935 0.0954676 0.995433i \(-0.469565\pi\)
0.0954676 + 0.995433i \(0.469565\pi\)
\(192\) 0 0
\(193\) 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
\(195\) 0 0
\(196\) 507.682 879.330i 0.185015 0.320456i
\(197\) −2111.10 −0.763501 −0.381750 0.924265i \(-0.624679\pi\)
−0.381750 + 0.924265i \(0.624679\pi\)
\(198\) 0 0
\(199\) −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
\(201\) 0 0
\(202\) −139.261 −0.0485068
\(203\) −1133.67 + 1963.57i −0.391961 + 0.678896i
\(204\) 0 0
\(205\) 303.172 525.110i 0.103290 0.178904i
\(206\) −644.346 1116.04i −0.217931 0.377467i
\(207\) 0 0
\(208\) 1082.47 0.360846
\(209\) 2549.55 2994.43i 0.843809 0.991047i
\(210\) 0 0
\(211\) 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
\(213\) 0 0
\(214\) 189.454 + 328.145i 0.0605179 + 0.104820i
\(215\) −621.859 + 1077.09i −0.197258 + 0.341661i
\(216\) 0 0
\(217\) −2635.42 −0.824442
\(218\) −239.152 + 414.224i −0.0743002 + 0.128692i
\(219\) 0 0
\(220\) 1603.60 0.491431
\(221\) 5250.70 1.59819
\(222\) 0 0
\(223\) 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
\(225\) 0 0
\(226\) −162.743 281.878i −0.0479003 0.0829658i
\(227\) 86.5237 0.0252986 0.0126493 0.999920i \(-0.495973\pi\)
0.0126493 + 0.999920i \(0.495973\pi\)
\(228\) 0 0
\(229\) −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
\(231\) 0 0
\(232\) −960.491 + 1663.62i −0.271807 + 0.470784i
\(233\) 510.013 + 883.368i 0.143399 + 0.248375i 0.928775 0.370645i \(-0.120863\pi\)
−0.785375 + 0.619020i \(0.787530\pi\)
\(234\) 0 0
\(235\) 1750.48 0.485908
\(236\) 87.9270 0.0242524
\(237\) 0 0
\(238\) −732.830 + 1269.30i −0.199590 + 0.345699i
\(239\) −264.681 −0.0716351 −0.0358175 0.999358i \(-0.511404\pi\)
−0.0358175 + 0.999358i \(0.511404\pi\)
\(240\) 0 0
\(241\) 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
\(243\) 0 0
\(244\) 1306.21 + 2262.42i 0.342710 + 0.593592i
\(245\) 1071.51 + 1855.92i 0.279415 + 0.483960i
\(246\) 0 0
\(247\) 1878.44 + 5278.82i 0.483897 + 1.35985i
\(248\) −2232.84 −0.571715
\(249\) 0 0
\(250\) −1508.88 2613.45i −0.381719 0.661156i
\(251\) −2442.43 + 4230.42i −0.614203 + 1.06383i 0.376321 + 0.926490i \(0.377189\pi\)
−0.990524 + 0.137342i \(0.956144\pi\)
\(252\) 0 0
\(253\) 4059.02 7030.42i 1.00865 1.74703i
\(254\) 194.757 0.0481107
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 2011.32 3483.71i 0.488181 0.845555i −0.511726 0.859149i \(-0.670994\pi\)
0.999908 + 0.0135936i \(0.00432710\pi\)
\(258\) 0 0
\(259\) 189.431 0.0454465
\(260\) −1142.33 + 1978.58i −0.272479 + 0.471948i
\(261\) 0 0
\(262\) −379.398 + 657.136i −0.0894629 + 0.154954i
\(263\) −3571.06 6185.26i −0.837266 1.45019i −0.892172 0.451695i \(-0.850819\pi\)
0.0549063 0.998492i \(-0.482514\pi\)
\(264\) 0 0
\(265\) 2207.89 0.511809
\(266\) −1538.27 282.662i −0.354577 0.0651546i
\(267\) 0 0
\(268\) 827.591 + 1433.43i 0.188631 + 0.326719i
\(269\) 2540.63 + 4400.50i 0.575855 + 0.997410i 0.995948 + 0.0899291i \(0.0286640\pi\)
−0.420093 + 0.907481i \(0.638003\pi\)
\(270\) 0 0
\(271\) 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
\(273\) 0 0
\(274\) 4827.37 1.06435
\(275\) 1275.62 2209.44i 0.279719 0.484488i
\(276\) 0 0
\(277\) 7778.48 1.68723 0.843617 0.536946i \(-0.180422\pi\)
0.843617 + 0.536946i \(0.180422\pi\)
\(278\) 6218.09 1.34150
\(279\) 0 0
\(280\) −318.867 552.294i −0.0680570 0.117878i
\(281\) 1110.34 1923.16i 0.235720 0.408279i −0.723762 0.690050i \(-0.757589\pi\)
0.959482 + 0.281771i \(0.0909219\pi\)
\(282\) 0 0
\(283\) 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
\(285\) 0 0
\(286\) −6425.35 −1.32846
\(287\) −339.083 587.309i −0.0697402 0.120794i
\(288\) 0 0
\(289\) −555.190 + 961.618i −0.113004 + 0.195729i
\(290\) −2027.22 3511.24i −0.410490 0.710990i
\(291\) 0 0
\(292\) −4408.58 −0.883537
\(293\) 9036.61 1.80179 0.900894 0.434038i \(-0.142912\pi\)
0.900894 + 0.434038i \(0.142912\pi\)
\(294\) 0 0
\(295\) −92.7895 + 160.716i −0.0183133 + 0.0317195i
\(296\) 160.493 0.0315151
\(297\) 0 0
\(298\) 2919.10 5056.03i 0.567447 0.982846i
\(299\) 5782.93 + 10016.3i 1.11851 + 1.93732i
\(300\) 0 0
\(301\) 695.518 + 1204.67i 0.133186 + 0.230685i
\(302\) −1915.72 3318.12i −0.365023 0.632239i
\(303\) 0 0
\(304\) −1303.29 239.483i −0.245883 0.0451819i
\(305\) −5513.77 −1.03514
\(306\) 0 0
\(307\) −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
\(309\) 0 0
\(310\) 2356.32 4081.26i 0.431709 0.747742i
\(311\) −2737.49 −0.499128 −0.249564 0.968358i \(-0.580287\pi\)
−0.249564 + 0.968358i \(0.580287\pi\)
\(312\) 0 0
\(313\) 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
\(315\) 0 0
\(316\) −1671.25 −0.297517
\(317\) −3210.19 + 5560.22i −0.568777 + 0.985152i 0.427910 + 0.903821i \(0.359250\pi\)
−0.996687 + 0.0813300i \(0.974083\pi\)
\(318\) 0 0
\(319\) 5701.29 9874.92i 1.00066 1.73320i
\(320\) −270.157 467.926i −0.0471945 0.0817433i
\(321\) 0 0
\(322\) −3228.45 −0.558741
\(323\) −6321.78 1161.65i −1.08902 0.200111i
\(324\) 0 0
\(325\) 1817.39 + 3147.81i 0.310187 + 0.537259i
\(326\) −1731.52 2999.08i −0.294172 0.509521i
\(327\) 0 0
\(328\) −287.285 497.592i −0.0483618 0.0837651i
\(329\) 978.909 1695.52i 0.164040 0.284125i
\(330\) 0 0
\(331\) −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
\(333\) 0 0
\(334\) −2860.25 −0.468580
\(335\) −3493.43 −0.569751
\(336\) 0 0
\(337\) −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
\(339\) 0 0
\(340\) −1310.44 2269.75i −0.209025 0.362042i
\(341\) 13253.7 2.10477
\(342\) 0 0
\(343\) 5635.62 0.887157
\(344\) 589.271 + 1020.65i 0.0923586 + 0.159970i
\(345\) 0 0
\(346\) −293.325 + 508.053i −0.0455758 + 0.0789396i
\(347\) −1249.31 2163.88i −0.193276 0.334764i 0.753058 0.657954i \(-0.228578\pi\)
−0.946334 + 0.323190i \(0.895245\pi\)
\(348\) 0 0
\(349\) 10330.5 1.58447 0.792235 0.610216i \(-0.208917\pi\)
0.792235 + 0.610216i \(0.208917\pi\)
\(350\) −1014.60 −0.154950
\(351\) 0 0
\(352\) 759.784 1315.98i 0.115047 0.199268i
\(353\) −2608.83 −0.393354 −0.196677 0.980468i \(-0.563015\pi\)
−0.196677 + 0.980468i \(0.563015\pi\)
\(354\) 0 0
\(355\) −666.720 + 1154.79i −0.0996783 + 0.172648i
\(356\) 2578.79 + 4466.59i 0.383920 + 0.664968i
\(357\) 0 0
\(358\) 3843.52 + 6657.16i 0.567419 + 0.982799i
\(359\) 2075.16 + 3594.29i 0.305078 + 0.528410i 0.977279 0.211958i \(-0.0679842\pi\)
−0.672201 + 0.740369i \(0.734651\pi\)
\(360\) 0 0
\(361\) −1093.76 6771.23i −0.159463 0.987204i
\(362\) −3538.56 −0.513764
\(363\) 0 0
\(364\) 1277.64 + 2212.94i 0.183975 + 0.318653i
\(365\) 4652.38 8058.17i 0.667170 1.15557i
\(366\) 0 0
\(367\) 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
\(369\) 0 0
\(370\) −169.369 + 293.356i −0.0237975 + 0.0412185i
\(371\) 1234.70 2138.57i 0.172783 0.299270i
\(372\) 0 0
\(373\) 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
\(375\) 0 0
\(376\) 829.372 1436.51i 0.113754 0.197028i
\(377\) 8122.69 + 14068.9i 1.10965 + 1.92198i
\(378\) 0 0
\(379\) −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
\(381\) 0 0
\(382\) 504.006 + 872.965i 0.0675058 + 0.116923i
\(383\) −4729.31 8191.40i −0.630957 1.09285i −0.987357 0.158515i \(-0.949329\pi\)
0.356400 0.934334i \(-0.384004\pi\)
\(384\) 0 0
\(385\) 1892.73 + 3278.31i 0.250552 + 0.433970i
\(386\) −2167.59 + 3754.37i −0.285822 + 0.495058i
\(387\) 0 0
\(388\) 555.048 0.0726245
\(389\) −3550.48 + 6149.61i −0.462767 + 0.801536i −0.999098 0.0424717i \(-0.986477\pi\)
0.536330 + 0.844008i \(0.319810\pi\)
\(390\) 0 0
\(391\) −13267.9 −1.71607
\(392\) 2030.73 0.261651
\(393\) 0 0
\(394\) −2111.10 3656.53i −0.269938 0.467547i
\(395\) 1763.68 3054.78i 0.224659 0.389120i
\(396\) 0 0
\(397\) −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
\(399\) 0 0
\(400\) −859.610 −0.107451
\(401\) −2784.34 4822.63i −0.346742 0.600575i 0.638927 0.769268i \(-0.279379\pi\)
−0.985669 + 0.168693i \(0.946045\pi\)
\(402\) 0 0
\(403\) −9441.34 + 16352.9i −1.16701 + 2.02133i
\(404\) −139.261 241.207i −0.0171498 0.0297042i
\(405\) 0 0
\(406\) −4534.68 −0.554316
\(407\) −952.658 −0.116023
\(408\) 0 0
\(409\) −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
\(411\) 0 0
\(412\) 1288.69 2232.08i 0.154100 0.266910i
\(413\) 103.780 + 179.753i 0.0123649 + 0.0214166i
\(414\) 0 0
\(415\) 6043.93 + 10468.4i 0.714904 + 1.23825i
\(416\) 1082.47 + 1874.90i 0.127578 + 0.220972i
\(417\) 0 0
\(418\) 7736.05 + 1421.53i 0.905222 + 0.166337i
\(419\) −340.170 −0.0396620 −0.0198310 0.999803i \(-0.506313\pi\)
−0.0198310 + 0.999803i \(0.506313\pi\)
\(420\) 0 0
\(421\) −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
\(423\) 0 0
\(424\) 1046.09 1811.88i 0.119818 0.207530i
\(425\) −4169.67 −0.475903
\(426\) 0 0
\(427\) −3083.44 + 5340.67i −0.349457 + 0.605276i
\(428\) −378.909 + 656.289i −0.0427926 + 0.0741190i
\(429\) 0 0
\(430\) −2487.44 −0.278965
\(431\) −6139.52 + 10634.0i −0.686149 + 1.18844i 0.286925 + 0.957953i \(0.407367\pi\)
−0.973074 + 0.230492i \(0.925966\pi\)
\(432\) 0 0
\(433\) −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
\(435\) 0 0
\(436\) −956.609 −0.105076
\(437\) −4746.60 13338.9i −0.519590 1.46016i
\(438\) 0 0
\(439\) 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
\(441\) 0 0
\(442\) 5250.70 + 9094.47i 0.565046 + 0.978688i
\(443\) 3705.54 6418.19i 0.397417 0.688346i −0.595989 0.802992i \(-0.703240\pi\)
0.993406 + 0.114646i \(0.0365733\pi\)
\(444\) 0 0
\(445\) −10885.6 −1.15961
\(446\) −3575.45 + 6192.87i −0.379602 + 0.657491i
\(447\) 0 0
\(448\) −604.315 −0.0637303
\(449\) 3345.93 0.351680 0.175840 0.984419i \(-0.443736\pi\)
0.175840 + 0.984419i \(0.443736\pi\)
\(450\) 0 0
\(451\) 1705.27 + 2953.61i 0.178044 + 0.308382i
\(452\) 325.485 563.757i 0.0338706 0.0586657i
\(453\) 0 0
\(454\) 86.5237 + 149.864i 0.00894441 + 0.0154922i
\(455\) −5393.20 −0.555686
\(456\) 0 0
\(457\) −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
\(459\) 0 0
\(460\) 2886.54 4999.64i 0.292578 0.506759i
\(461\) 1911.72 + 3311.19i 0.193140 + 0.334528i 0.946289 0.323322i \(-0.104800\pi\)
−0.753149 + 0.657850i \(0.771466\pi\)
\(462\) 0 0
\(463\) −3750.37 −0.376445 −0.188223 0.982126i \(-0.560273\pi\)
−0.188223 + 0.982126i \(0.560273\pi\)
\(464\) −3841.96 −0.384394
\(465\) 0 0
\(466\) −1020.03 + 1766.74i −0.101399 + 0.175628i
\(467\) 2981.61 0.295444 0.147722 0.989029i \(-0.452806\pi\)
0.147722 + 0.989029i \(0.452806\pi\)
\(468\) 0 0
\(469\) −1953.61 + 3383.76i −0.192344 + 0.333150i
\(470\) 1750.48 + 3031.91i 0.171795 + 0.297557i
\(471\) 0 0
\(472\) 87.9270 + 152.294i 0.00857451 + 0.0148515i
\(473\) −3497.80 6058.37i −0.340019 0.588930i
\(474\) 0 0
\(475\) −1491.71 4192.01i −0.144093 0.404931i
\(476\) −2931.32 −0.282262
\(477\) 0 0
\(478\) −264.681 458.441i −0.0253268 0.0438674i
\(479\) 7677.92 13298.6i 0.732387 1.26853i −0.223474 0.974710i \(-0.571740\pi\)
0.955860 0.293821i \(-0.0949270\pi\)
\(480\) 0 0
\(481\) 678.631 1175.42i 0.0643304 0.111423i
\(482\) 344.774 0.0325810
\(483\) 0 0
\(484\) −1847.93 + 3200.71i −0.173547 + 0.300592i
\(485\) −585.744 + 1014.54i −0.0548397 + 0.0949851i
\(486\) 0 0
\(487\) 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
\(489\) 0 0
\(490\) −2143.03 + 3711.84i −0.197576 + 0.342212i
\(491\) 9882.91 + 17117.7i 0.908370 + 1.57334i 0.816329 + 0.577587i \(0.196006\pi\)
0.0920410 + 0.995755i \(0.470661\pi\)
\(492\) 0 0
\(493\) −18636.0 −1.70248
\(494\) −7264.75 + 8532.39i −0.661653 + 0.777106i
\(495\) 0 0
\(496\) −2232.84 3867.38i −0.202132 0.350102i
\(497\) 745.692 + 1291.58i 0.0673016 + 0.116570i
\(498\) 0 0
\(499\) −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
\(501\) 0 0
\(502\) −9769.73 −0.868614
\(503\) −9837.15 + 17038.4i −0.872002 + 1.51035i −0.0120790 + 0.999927i \(0.503845\pi\)
−0.859923 + 0.510424i \(0.829488\pi\)
\(504\) 0 0
\(505\) 587.850 0.0518000
\(506\) 16236.1 1.42645
\(507\) 0 0
\(508\) 194.757 + 337.328i 0.0170097 + 0.0294616i
\(509\) −3427.87 + 5937.25i −0.298502 + 0.517021i −0.975794 0.218694i \(-0.929820\pi\)
0.677291 + 0.735715i \(0.263154\pi\)
\(510\) 0 0
\(511\) −5203.46 9012.65i −0.450465 0.780228i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 8045.28 0.690393
\(515\) 2719.92 + 4711.04i 0.232726 + 0.403093i
\(516\) 0 0
\(517\) −4922.99 + 8526.87i −0.418787 + 0.725361i
\(518\) 189.431 + 328.103i 0.0160678 + 0.0278302i
\(519\) 0 0
\(520\) −4569.34 −0.385344
\(521\) 12666.6 1.06513 0.532567 0.846388i \(-0.321227\pi\)
0.532567 + 0.846388i \(0.321227\pi\)
\(522\) 0 0
\(523\) −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
\(525\) 0 0
\(526\) 7142.12 12370.5i 0.592036 1.02544i
\(527\) −10830.7 18759.3i −0.895243 1.55061i
\(528\) 0 0
\(529\) −8529.25 14773.1i −0.701015 1.21419i
\(530\) 2207.89 + 3824.17i 0.180952 + 0.313418i
\(531\) 0 0
\(532\) −1048.68 2947.02i −0.0854629 0.240169i
\(533\) −4859.03 −0.394874
\(534\) 0 0
\(535\) −799.726 1385.17i −0.0646265 0.111936i
\(536\) −1655.18 + 2866.86i −0.133382 + 0.231025i
\(537\) 0 0
\(538\) −5081.26 + 8801.00i −0.407191 + 0.705275i
\(539\) −12054.0 −0.963270
\(540\) 0 0
\(541\) −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
\(543\) 0 0
\(544\) −2483.53 −0.195736
\(545\) 1009.51 1748.53i 0.0793445 0.137429i
\(546\) 0 0
\(547\) 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
\(549\) 0 0
\(550\) 5102.48 0.395583
\(551\) −6667.07 18735.9i −0.515475 1.44859i
\(552\) 0 0
\(553\) −1972.58 3416.61i −0.151687 0.262729i
\(554\) 7778.48 + 13472.7i 0.596527 + 1.03322i
\(555\) 0 0
\(556\) 6218.09 + 10770.0i 0.474291 + 0.821496i
\(557\) −9813.87 + 16998.1i −0.746548 + 1.29306i 0.202920 + 0.979195i \(0.434957\pi\)
−0.949468 + 0.313864i \(0.898377\pi\)
\(558\) 0 0
\(559\) 9966.71 0.754109
\(560\) 637.734 1104.59i 0.0481236 0.0833525i
\(561\) 0 0
\(562\) 4441.36 0.333358
\(563\) −9810.37 −0.734384 −0.367192 0.930145i \(-0.619681\pi\)
−0.367192 + 0.930145i \(0.619681\pi\)
\(564\) 0 0
\(565\) 686.970 + 1189.87i 0.0511523 + 0.0885984i
\(566\) −7616.34 + 13191.9i −0.565616 + 0.979676i
\(567\) 0 0
\(568\) 631.781 + 1094.28i 0.0466707 + 0.0808360i
\(569\) −2528.37 −0.186282 −0.0931412 0.995653i \(-0.529691\pi\)
−0.0931412 + 0.995653i \(0.529691\pi\)
\(570\) 0 0
\(571\) −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
\(573\) 0 0
\(574\) 678.166 1174.62i 0.0493138 0.0854140i
\(575\) −4592.32 7954.14i −0.333066 0.576888i
\(576\) 0 0
\(577\) −4002.61 −0.288788 −0.144394 0.989520i \(-0.546123\pi\)
−0.144394 + 0.989520i \(0.546123\pi\)
\(578\) −2220.76 −0.159812
\(579\) 0 0
\(580\) 4054.43 7022.48i 0.290261 0.502746i
\(581\) 13519.7 0.965388
\(582\) 0 0
\(583\) −6209.40 + 10755.0i −0.441110 + 0.764025i
\(584\) −4408.58 7635.89i −0.312377 0.541054i
\(585\) 0 0
\(586\) 9036.61 + 15651.9i 0.637029 + 1.10337i
\(587\) 12259.2 + 21233.6i 0.861998 + 1.49302i 0.869997 + 0.493056i \(0.164120\pi\)
−0.00799928 + 0.999968i \(0.502546\pi\)
\(588\) 0 0
\(589\) 14985.1 17599.9i 1.04831 1.23123i
\(590\) −371.158 −0.0258989
\(591\) 0 0
\(592\) 160.493 + 277.983i 0.0111423 + 0.0192990i
\(593\) −8849.35 + 15327.5i −0.612815 + 1.06143i 0.377948 + 0.925827i \(0.376630\pi\)
−0.990764 + 0.135600i \(0.956704\pi\)
\(594\) 0 0
\(595\) 3093.43 5357.97i 0.213140 0.369169i
\(596\) 11676.4 0.802491
\(597\) 0 0
\(598\) −11565.9 + 20032.6i −0.790908 + 1.36989i
\(599\) 1804.00 3124.63i 0.123054 0.213137i −0.797916 0.602768i \(-0.794064\pi\)
0.920971 + 0.389632i \(0.127398\pi\)
\(600\) 0 0
\(601\) 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
\(603\) 0 0
\(604\) 3831.43 6636.23i 0.258110 0.447060i
\(605\) −3900.25 6755.43i −0.262095 0.453962i
\(606\) 0 0
\(607\) −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
\(609\) 0 0
\(610\) −5513.77 9550.13i −0.365977 0.633891i
\(611\) −7013.84 12148.3i −0.464402 0.804368i
\(612\) 0 0
\(613\) 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
\(615\) 0 0
\(616\) 3587.10 0.234624
\(617\) 3504.76 6070.42i 0.228681 0.396088i −0.728736 0.684794i \(-0.759892\pi\)
0.957418 + 0.288707i \(0.0932253\pi\)
\(618\) 0 0
\(619\) 24225.1 1.57301 0.786503 0.617587i \(-0.211890\pi\)
0.786503 + 0.617587i \(0.211890\pi\)
\(620\) 9425.26 0.610529
\(621\) 0 0
\(622\) −2737.49 4741.47i −0.176468 0.305652i
\(623\) −6087.49 + 10543.8i −0.391477 + 0.678058i
\(624\) 0 0
\(625\) 3011.43 + 5215.95i 0.192731 + 0.333821i
\(626\) 15292.3 0.976363
\(627\) 0 0
\(628\) −10146.7 −0.644744
\(629\) 778.497 + 1348.40i 0.0493493 + 0.0854755i
\(630\) 0 0
\(631\) −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
\(633\) 0 0
\(634\) −12840.8 −0.804373
\(635\) −822.108 −0.0513769
\(636\) 0 0
\(637\) 8586.74 14872.7i 0.534095 0.925081i
\(638\) 22805.2 1.41515
\(639\) 0 0
\(640\) 540.315 935.852i 0.0333716 0.0578013i
\(641\) −8374.53 14505.1i −0.516028 0.893787i −0.999827 0.0186079i \(-0.994077\pi\)
0.483799 0.875179i \(-0.339257\pi\)
\(642\) 0 0
\(643\) 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
\(645\) 0 0
\(646\) −4309.75 12111.3i −0.262484 0.737636i
\(647\) −6637.82 −0.403338 −0.201669 0.979454i \(-0.564637\pi\)
−0.201669 + 0.979454i \(0.564637\pi\)
\(648\) 0 0
\(649\) −521.918 903.988i −0.0315671 0.0546759i
\(650\) −3634.78 + 6295.62i −0.219335 + 0.379899i
\(651\) 0 0
\(652\) 3463.04 5998.16i 0.208011 0.360285i
\(653\) 18762.0 1.12437 0.562184 0.827012i \(-0.309961\pi\)
0.562184 + 0.827012i \(0.309961\pi\)
\(654\) 0 0
\(655\) 1601.52 2773.91i 0.0955365 0.165474i
\(656\) 574.570 995.185i 0.0341969 0.0592308i
\(657\) 0 0
\(658\) 3915.64 0.231987
\(659\) 3078.28 5331.74i 0.181962 0.315167i −0.760587 0.649236i \(-0.775089\pi\)
0.942549 + 0.334069i \(0.108422\pi\)
\(660\) 0 0
\(661\) −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
\(663\) 0 0
\(664\) 11454.4 0.669454
\(665\) 6493.36 + 1193.18i 0.378649 + 0.0695780i
\(666\) 0 0
\(667\) −20525.1 35550.4i −1.19150 2.06375i
\(668\) −2860.25 4954.09i −0.165668 0.286946i
\(669\) 0 0
\(670\) −3493.43 6050.80i −0.201437 0.348900i
\(671\) 15506.8 26858.5i 0.892150 1.54525i
\(672\) 0 0
\(673\) 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
\(675\) 0 0
\(676\) 9520.52 0.541677
\(677\) 4341.55 0.246469 0.123234 0.992378i \(-0.460673\pi\)
0.123234 + 0.992378i \(0.460673\pi\)
\(678\) 0 0
\(679\) 655.125 + 1134.71i 0.0370271 + 0.0641328i
\(680\) 2620.88 4539.49i 0.147803 0.256002i
\(681\) 0 0
\(682\) 13253.7 + 22956.1i 0.744149 + 1.28890i
\(683\) −16457.2 −0.921986 −0.460993 0.887404i \(-0.652507\pi\)
−0.460993 + 0.887404i \(0.652507\pi\)
\(684\) 0 0
\(685\) −20377.3 −1.13661
\(686\) 5635.62 + 9761.18i 0.313657 + 0.543270i
\(687\) 0 0
\(688\) −1178.54 + 2041.30i −0.0653074 + 0.113116i
\(689\) −8846.60 15322.8i −0.489156 0.847244i
\(690\) 0 0
\(691\) 2522.21 0.138856 0.0694280 0.997587i \(-0.477883\pi\)
0.0694280 + 0.997587i \(0.477883\pi\)
\(692\) −1173.30 −0.0644539
\(693\) 0 0
\(694\) 2498.63 4327.75i 0.136667 0.236714i
\(695\) −26247.8 −1.43257
\(696\) 0 0
\(697\) 2787.04 4827.29i 0.151459 0.262334i
\(698\) 10330.5 + 17893.0i 0.560195 + 0.970286i
\(699\) 0 0
\(700\) −1014.60 1757.34i −0.0547832 0.0948873i
\(701\) 2009.91 + 3481.27i 0.108293 + 0.187569i 0.915079 0.403275i \(-0.132128\pi\)
−0.806786 + 0.590844i \(0.798795\pi\)
\(702\) 0 0
\(703\) −1077.11 + 1265.06i −0.0577867 + 0.0678700i
\(704\) 3039.13 0.162701
\(705\) 0 0
\(706\) −2608.83 4518.62i −0.139072 0.240879i
\(707\) 328.740 569.395i 0.0174874 0.0302890i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) −5157.57 + 8933.18i −0.271472 + 0.470204i
\(713\) 23857.1 41321.7i 1.25309 2.17042i
\(714\) 0 0
\(715\) 27122.7 1.41865
\(716\) −7687.03 + 13314.3i −0.401226 + 0.694944i
\(717\) 0 0
\(718\) −4150.33 + 7188.58i −0.215723 + 0.373643i
\(719\) 5215.18 + 9032.95i 0.270505 + 0.468529i 0.968991 0.247095i \(-0.0794759\pi\)
−0.698486 + 0.715624i \(0.746143\pi\)
\(720\) 0 0
\(721\) 6084.18 0.314268
\(722\) 10634.4 8665.67i 0.548158 0.446680i
\(723\) 0 0
\(724\) −3538.56 6128.96i −0.181643 0.314615i
\(725\) −6450.37 11172.4i −0.330429 0.572319i
\(726\) 0 0
\(727\) 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
\(729\) 0 0
\(730\) 18609.5 0.943520
\(731\) −5716.70 + 9901.61i −0.289247 + 0.500991i
\(732\) 0 0
\(733\) −3382.86 −0.170462 −0.0852310 0.996361i \(-0.527163\pi\)
−0.0852310 + 0.996361i \(0.527163\pi\)
\(734\) 14741.0 0.741279
\(735\) 0 0
\(736\) −2735.27 4737.64i −0.136989 0.237271i
\(737\) 9824.84 17017.1i 0.491048 0.850521i
\(738\) 0 0
\(739\) −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
\(741\) 0 0
\(742\) 4938.82 0.244353
\(743\) 4678.96 + 8104.19i 0.231029 + 0.400153i 0.958111 0.286397i \(-0.0924576\pi\)
−0.727082 + 0.686550i \(0.759124\pi\)
\(744\) 0 0
\(745\) −12322.1 + 21342.6i −0.605971 + 1.04957i
\(746\) 13166.5 + 22805.1i 0.646195 + 1.11924i
\(747\) 0 0
\(748\) 14741.8 0.720606
\(749\) −1788.91 −0.0872700
\(750\) 0 0
\(751\) 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
\(753\) 0 0
\(754\) −16245.4 + 28137.8i −0.784644 + 1.35904i
\(755\) 8086.63 + 14006.5i 0.389805 + 0.675162i
\(756\) 0 0
\(757\) −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
\(759\) 0 0
\(760\) 5501.44 + 1010.91i 0.262576 + 0.0482493i
\(761\) −26066.1 −1.24165 −0.620825 0.783949i \(-0.713202\pi\)
−0.620825 + 0.783949i \(0.713202\pi\)
\(762\) 0 0
\(763\) −1129.09 1955.64i −0.0535724 0.0927901i
\(764\) −1008.01 + 1745.93i −0.0477338 + 0.0826774i
\(765\) 0 0
\(766\) 9458.62 16382.8i 0.446154 0.772761i
\(767\) 1487.16 0.0700109
\(768\) 0 0
\(769\) 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
\(771\) 0 0
\(772\) −8670.35 −0.404213
\(773\) 5604.20 9706.76i 0.260762 0.451653i −0.705683 0.708528i \(-0.749360\pi\)
0.966445 + 0.256875i \(0.0826929\pi\)
\(774\) 0 0
\(775\) 7497.53 12986.1i 0.347509 0.601903i
\(776\) 555.048 + 961.372i 0.0256766 + 0.0444733i
\(777\) 0 0
\(778\) −14201.9 −0.654452
\(779\) 5850.22 + 1075.00i 0.269071 + 0.0494426i
\(780\) 0 0
\(781\) −3750.13 6495.42i −0.171819 0.297598i
\(782\) −13267.9 22980.6i −0.606724 1.05088i
\(783\) 0 0
\(784\) 2030.73 + 3517.32i 0.0925076 + 0.160228i
\(785\) 10707.9 18546.6i 0.486854 0.843257i
\(786\) 0 0
\(787\) −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
\(789\) 0 0
\(790\) 7054.70 0.317715
\(791\) 1536.68 0.0690748
\(792\) 0 0
\(793\) 22092.7 + 38265.7i 0.989324 + 1.71356i
\(794\) 1916.16 3318.89i 0.0856449 0.148341i
\(795\) 0 0
\(796\) −4277.19 7408.31i −0.190453 0.329875i
\(797\) −31745.4 −1.41089 −0.705446 0.708764i \(-0.749253\pi\)
−0.705446 + 0.708764i \(0.749253\pi\)
\(798\) 0 0
\(799\) 16092.0 0.712507
\(800\) −859.610 1488.89i −0.0379897 0.0658002i
\(801\) 0 0
\(802\) 5568.69 9645.25i 0.245184 0.424670i
\(803\) 26168.5 + 45325.2i 1.15002 + 1.99189i
\(804\) 0 0
\(805\) 13628.0 0.596674
\(806\) −37765.3 −1.65041
\(807\) 0 0
\(808\) 278.522 482.415i 0.0121267 0.0210041i
\(809\) 14106.2 0.613040 0.306520 0.951864i \(-0.400835\pi\)
0.306520 + 0.951864i \(0.400835\pi\)
\(810\) 0 0
\(811\) −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
\(813\) 0 0
\(814\) −952.658 1650.05i −0.0410204 0.0710495i
\(815\) 7309.11 + 12659.7i 0.314143 + 0.544112i
\(816\) 0 0
\(817\) −11999.8 2205.01i −0.513856 0.0944228i
\(818\) −145.427 −0.00621604
\(819\) 0 0
\(820\) 1212.69 + 2100.44i 0.0516451 + 0.0894519i
\(821\) −9719.65 + 16834.9i −0.413177 + 0.715643i −0.995235 0.0975038i \(-0.968914\pi\)
0.582058 + 0.813147i \(0.302248\pi\)
\(822\) 0 0
\(823\) 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
\(825\) 0 0
\(826\) −207.561 + 359.506i −0.00874330 + 0.0151438i
\(827\) −16772.9 + 29051.5i −0.705260 + 1.22155i 0.261338 + 0.965247i \(0.415836\pi\)
−0.966598 + 0.256298i \(0.917497\pi\)
\(828\) 0 0
\(829\) 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
\(831\) 0 0
\(832\) −2164.94 + 3749.79i −0.0902114 + 0.156251i
\(833\) 9850.35 + 17061.3i 0.409717 + 0.709651i
\(834\) 0 0
\(835\) 12073.7 0.500392
\(836\) 5273.90 + 14820.8i 0.218184 + 0.613142i
\(837\) 0 0
\(838\) −340.170 589.192i −0.0140227 0.0242879i
\(839\) 20491.2 + 35491.8i 0.843188 + 1.46044i 0.887185 + 0.461413i \(0.152657\pi\)
−0.0439970 + 0.999032i \(0.514009\pi\)
\(840\) 0 0
\(841\) −16635.0 28812.6i −0.682068 1.18138i
\(842\) 1476.99 2558.23i 0.0604520 0.104706i
\(843\) 0 0
\(844\) −3903.81 −0.159212
\(845\) −10047.0 + 17402.0i −0.409028 + 0.708456i
\(846\) 0 0
\(847\) −8724.46 −0.353927
\(848\) 4184.37 0.169448
\(849\) 0 0
\(850\) −4169.67 7222.08i −0.168257 0.291430i
\(851\) −1714.82 + 2970.15i −0.0690754 + 0.119642i
\(852\) 0 0
\(853\) 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
\(855\) 0 0
\(856\) −1515.63 −0.0605179
\(857\) 10481.8 + 18155.1i 0.417798 + 0.723647i 0.995718 0.0924465i \(-0.0294687\pi\)
−0.577920 + 0.816094i \(0.696135\pi\)
\(858\) 0 0
\(859\) −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
\(861\) 0 0
\(862\) −24558.1 −0.970361
\(863\) −2630.83 −0.103771 −0.0518856 0.998653i \(-0.516523\pi\)
−0.0518856 + 0.998653i \(0.516523\pi\)
\(864\) 0 0
\(865\) 1238.18 2144.60i 0.0486700 0.0842989i
\(866\) −12423.1 −0.487475
\(867\) 0 0
\(868\) 5270.84 9129.36i 0.206111 0.356994i
\(869\) 9920.23 + 17182.3i 0.387251 + 0.670738i
\(870\) 0 0
\(871\) 13997.6 + 24244.5i 0.544534 + 0.943161i
\(872\) −956.609 1656.90i −0.0371501 0.0643458i
\(873\) 0 0
\(874\) 18357.1 21560.3i 0.710457 0.834426i
\(875\) 14247.4 0.550459
\(876\) 0 0
\(877\) 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
\(879\) 0 0
\(880\) −3207.20 + 5555.04i −0.122858 + 0.212796i
\(881\) −6389.06 −0.244328 −0.122164 0.992510i \(-0.538983\pi\)
−0.122164 + 0.992510i \(0.538983\pi\)
\(882\) 0 0
\(883\) 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
\(885\) 0 0
\(886\) 14822.2 0.562033
\(887\) 14810.5 25652.6i 0.560641 0.971058i −0.436800 0.899559i \(-0.643888\pi\)
0.997441 0.0714994i \(-0.0227784\pi\)
\(888\) 0 0
\(889\) −459.743 + 796.298i −0.0173445 + 0.0300416i
\(890\) −10885.6 18854.4i −0.409984 0.710114i
\(891\) 0 0
\(892\) −14301.8 −0.536839
\(893\) 5756.93 + 16178.2i 0.215732 + 0.606251i
\(894\) 0 0
\(895\) −16224.3 28101.3i −0.605942 1.04952i
\(896\) −604.315 1046.70i −0.0225321 0.0390267i
\(897\) 0 0
\(898\) 3345.93 + 5795.33i 0.124338 + 0.215359i
\(899\) 33509.7 58040.4i 1.24317 2.15323i
\(900\) 0 0
\(901\) 20296.9 0.750486
\(902\) −3410.54 + 5907.23i −0.125896 + 0.218059i
\(903\) 0 0
\(904\) 1301.94 0.0479003
\(905\) 14937.0 0.548643
\(906\) 0 0
\(907\) −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
\(909\) 0 0
\(910\) −5393.20 9341.30i −0.196465 0.340287i
\(911\) −50.5532 −0.00183853 −0.000919266 1.00000i \(-0.500293\pi\)
−0.000919266 1.00000i \(0.500293\pi\)
\(912\) 0 0
\(913\) −67991.2 −2.46460
\(914\) −542.238 939.184i −0.0196232 0.0339885i
\(915\) 0 0
\(916\) 7856.10 13607.2i 0.283377 0.490823i
\(917\) −1791.22 3102.48i −0.0645051 0.111726i
\(918\) 0 0
\(919\) −38362.9 −1.37701 −0.688507 0.725230i \(-0.741734\pi\)
−0.688507 + 0.725230i \(0.741734\pi\)
\(920\) 11546.2 0.413767
\(921\) 0 0
\(922\) −3823.43 + 6622.38i −0.136571 + 0.236547i
\(923\) 10685.7 0.381066
\(924\) 0 0
\(925\) −538.913 + 933.424i −0.0191560 + 0.0331792i
\(926\) −3750.37 6495.82i −0.133094 0.230525i
\(927\) 0 0
\(928\) −3841.96 6654.48i −0.135904 0.235392i
\(929\) −19043.5 32984.3i −0.672548 1.16489i −0.977179 0.212417i \(-0.931867\pi\)
0.304631 0.952470i \(-0.401467\pi\)
\(930\) 0 0
\(931\) −13628.7 + 16006.8i −0.479767 + 0.563483i
\(932\) −4080.10 −0.143399
\(933\) 0 0
\(934\) 2981.61 + 5164.30i 0.104455 + 0.180922i
\(935\) −15557.0 + 26945.6i −0.544138 + 0.942475i
\(936\) 0 0
\(937\) −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
\(939\) 0 0
\(940\) −3500.95 + 6063.83i −0.121477 + 0.210404i
\(941\) 12104.5 20965.7i 0.419338 0.726314i −0.576535 0.817072i \(-0.695596\pi\)
0.995873 + 0.0907581i \(0.0289290\pi\)
\(942\) 0 0
\(943\) 12278.2 0.424001
\(944\) −175.854 + 304.588i −0.00606309 + 0.0105016i
\(945\) 0 0
\(946\) 6995.60 12116.7i 0.240430 0.416437i
\(947\) −10262.4 17774.9i −0.352146 0.609935i 0.634479 0.772940i \(-0.281215\pi\)
−0.986625 + 0.163005i \(0.947881\pi\)
\(948\) 0 0
\(949\) −74565.1 −2.55056
\(950\) 5769.06 6775.72i 0.197024 0.231403i
\(951\) 0 0
\(952\) −2931.32 5077.20i −0.0997948 0.172850i
\(953\) −2455.68 4253.36i −0.0834703 0.144575i 0.821268 0.570543i \(-0.193267\pi\)
−0.904738 + 0.425968i \(0.859934\pi\)
\(954\) 0 0
\(955\) −2127.52 3684.96i −0.0720888 0.124861i
\(956\) 529.362 916.882i 0.0179088 0.0310189i
\(957\) 0 0
\(958\) 30711.7 1.03575
\(959\) −11395.5 + 19737.6i −0.383712 + 0.664609i
\(960\) 0 0
\(961\) 48108.3 1.61486
\(962\) 2714.52 0.0909769
\(963\) 0 0
\(964\) 344.774 + 597.166i 0.0115191 + 0.0199517i
\(965\) 9149.84 15848.0i 0.305227 0.528668i
\(966\) 0 0
\(967\) 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
\(969\) 0 0
\(970\) −2342.98 −0.0775550
\(971\) −13395.9 23202.4i −0.442735 0.766840i 0.555156 0.831746i \(-0.312659\pi\)
−0.997891 + 0.0649061i \(0.979325\pi\)
\(972\) 0 0
\(973\) −14678.4 + 25423.8i −0.483627 + 0.837667i
\(974\) 439.463 + 761.172i 0.0144572 + 0.0250406i
\(975\) 0 0
\(976\) −10449.7 −0.342710
\(977\) 8122.31 0.265973 0.132987 0.991118i \(-0.457543\pi\)
0.132987 + 0.991118i \(0.457543\pi\)
\(978\) 0 0
\(979\) 30614.4 53025.6i 0.999427 1.73106i
\(980\) −8572.12 −0.279415
\(981\) 0 0
\(982\) −19765.8 + 34235.4i −0.642314 + 1.11252i
\(983\) −16459.0 28507.9i −0.534041 0.924986i −0.999209 0.0397634i \(-0.987340\pi\)
0.465168 0.885222i \(-0.345994\pi\)
\(984\) 0 0
\(985\) 8911.39 + 15435.0i 0.288265 + 0.499289i
\(986\) −18636.0 32278.6i −0.601919 1.04255i
\(987\) 0 0
\(988\) −22043.3 4050.52i −0.709808 0.130430i
\(989\) −25184.7 −0.809733
\(990\) 0 0
\(991\) 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
\(993\) 0 0
\(994\) −1491.38 + 2583.15i −0.0475894 + 0.0824272i
\(995\) 18054.9 0.575255
\(996\) 0 0
\(997\) −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
\(999\) 0 0
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 342.4.g.h.235.1 6
3.2 odd 2 114.4.e.d.7.3 6
19.11 even 3 inner 342.4.g.h.163.1 6
57.11 odd 6 114.4.e.d.49.3 yes 6
57.26 odd 6 2166.4.a.u.1.1 3
57.50 even 6 2166.4.a.t.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.4.e.d.7.3 6 3.2 odd 2
114.4.e.d.49.3 yes 6 57.11 odd 6
342.4.g.h.163.1 6 19.11 even 3 inner
342.4.g.h.235.1 6 1.1 even 1 trivial
2166.4.a.t.1.1 3 57.50 even 6
2166.4.a.u.1.1 3 57.26 odd 6