Properties

Label 189.4.e.e.109.3
Level $189$
Weight $4$
Character 189.109
Analytic conductor $11.151$
Analytic rank $0$
Dimension $12$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,4,Mod(109,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, 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("189.109");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.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: \(11.1513609911\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 40x^{10} + 1147x^{8} + 15564x^{6} + 154089x^{4} + 578934x^{2} + 1633284 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.3
Root \(1.02968 - 1.78345i\) of defining polynomial
Character \(\chi\) \(=\) 189.109
Dual form 189.4.e.e.163.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.02968 - 1.78345i) q^{2} +(1.87953 - 3.25543i) q^{4} +(-7.25204 - 12.5609i) q^{5} +(-7.76857 + 16.8122i) q^{7} -24.2161 q^{8} +O(q^{10})\) \(q+(-1.02968 - 1.78345i) q^{2} +(1.87953 - 3.25543i) q^{4} +(-7.25204 - 12.5609i) q^{5} +(-7.76857 + 16.8122i) q^{7} -24.2161 q^{8} +(-14.9345 + 25.8674i) q^{10} +(-14.9047 + 25.8157i) q^{11} -13.3320 q^{13} +(37.9829 - 3.45625i) q^{14} +(9.89856 + 17.1448i) q^{16} +(32.1415 - 55.6707i) q^{17} +(55.1748 + 95.5655i) q^{19} -54.5216 q^{20} +61.3881 q^{22} +(-9.67280 - 16.7538i) q^{23} +(-42.6843 + 73.9314i) q^{25} +(13.7276 + 23.7769i) q^{26} +(40.1297 + 56.8890i) q^{28} -111.113 q^{29} +(-96.4689 + 167.089i) q^{31} +(-76.4797 + 132.467i) q^{32} -132.382 q^{34} +(267.514 - 24.3424i) q^{35} +(35.7607 + 61.9393i) q^{37} +(113.625 - 196.803i) q^{38} +(175.616 + 304.176i) q^{40} -277.562 q^{41} -178.522 q^{43} +(56.0275 + 97.0424i) q^{44} +(-19.9197 + 34.5020i) q^{46} +(265.937 + 460.617i) q^{47} +(-222.299 - 261.213i) q^{49} +175.804 q^{50} +(-25.0578 + 43.4013i) q^{52} +(155.416 - 269.188i) q^{53} +432.357 q^{55} +(188.124 - 407.125i) q^{56} +(114.410 + 198.165i) q^{58} +(-361.012 + 625.290i) q^{59} +(-331.535 - 574.235i) q^{61} +397.328 q^{62} +473.375 q^{64} +(96.6839 + 167.461i) q^{65} +(304.279 - 527.027i) q^{67} +(-120.822 - 209.269i) q^{68} +(-318.867 - 452.035i) q^{70} -976.305 q^{71} +(-130.574 + 226.161i) q^{73} +(73.6440 - 127.555i) q^{74} +414.810 q^{76} +(-318.229 - 451.131i) q^{77} +(-618.075 - 1070.54i) q^{79} +(143.570 - 248.670i) q^{80} +(285.800 + 495.020i) q^{82} -1225.79 q^{83} -932.367 q^{85} +(183.820 + 318.386i) q^{86} +(360.933 - 625.154i) q^{88} +(-395.991 - 685.876i) q^{89} +(103.570 - 224.139i) q^{91} -72.7211 q^{92} +(547.659 - 948.573i) q^{94} +(800.260 - 1386.09i) q^{95} -935.253 q^{97} +(-236.966 + 665.425i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 32 q^{4} - 26 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 32 q^{4} - 26 q^{7} + 20 q^{10} + 104 q^{13} + 148 q^{16} + 62 q^{19} - 712 q^{22} + 46 q^{25} - 348 q^{28} + 82 q^{31} + 840 q^{34} + 1132 q^{37} + 444 q^{40} - 3132 q^{43} + 888 q^{46} + 366 q^{49} + 72 q^{52} + 448 q^{55} - 4 q^{58} - 886 q^{61} - 1848 q^{64} + 2084 q^{67} - 4460 q^{70} + 2398 q^{73} + 6408 q^{76} - 984 q^{79} + 3892 q^{82} - 7200 q^{85} + 5796 q^{88} - 6492 q^{91} - 2772 q^{94} - 1364 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02968 1.78345i −0.364046 0.630546i 0.624576 0.780964i \(-0.285272\pi\)
−0.988623 + 0.150417i \(0.951938\pi\)
\(3\) 0 0
\(4\) 1.87953 3.25543i 0.234941 0.406929i
\(5\) −7.25204 12.5609i −0.648643 1.12348i −0.983447 0.181194i \(-0.942004\pi\)
0.334805 0.942288i \(-0.391330\pi\)
\(6\) 0 0
\(7\) −7.76857 + 16.8122i −0.419463 + 0.907772i
\(8\) −24.2161 −1.07021
\(9\) 0 0
\(10\) −14.9345 + 25.8674i −0.472272 + 0.817999i
\(11\) −14.9047 + 25.8157i −0.408539 + 0.707610i −0.994726 0.102565i \(-0.967295\pi\)
0.586187 + 0.810176i \(0.300628\pi\)
\(12\) 0 0
\(13\) −13.3320 −0.284432 −0.142216 0.989836i \(-0.545423\pi\)
−0.142216 + 0.989836i \(0.545423\pi\)
\(14\) 37.9829 3.45625i 0.725097 0.0659800i
\(15\) 0 0
\(16\) 9.89856 + 17.1448i 0.154665 + 0.267888i
\(17\) 32.1415 55.6707i 0.458557 0.794243i −0.540328 0.841454i \(-0.681700\pi\)
0.998885 + 0.0472110i \(0.0150333\pi\)
\(18\) 0 0
\(19\) 55.1748 + 95.5655i 0.666209 + 1.15391i 0.978956 + 0.204071i \(0.0654173\pi\)
−0.312747 + 0.949836i \(0.601249\pi\)
\(20\) −54.5216 −0.609570
\(21\) 0 0
\(22\) 61.3881 0.594908
\(23\) −9.67280 16.7538i −0.0876921 0.151887i 0.818843 0.574017i \(-0.194616\pi\)
−0.906535 + 0.422130i \(0.861282\pi\)
\(24\) 0 0
\(25\) −42.6843 + 73.9314i −0.341474 + 0.591451i
\(26\) 13.7276 + 23.7769i 0.103546 + 0.179348i
\(27\) 0 0
\(28\) 40.1297 + 56.8890i 0.270850 + 0.383965i
\(29\) −111.113 −0.711487 −0.355744 0.934584i \(-0.615772\pi\)
−0.355744 + 0.934584i \(0.615772\pi\)
\(30\) 0 0
\(31\) −96.4689 + 167.089i −0.558914 + 0.968067i 0.438674 + 0.898646i \(0.355448\pi\)
−0.997587 + 0.0694206i \(0.977885\pi\)
\(32\) −76.4797 + 132.467i −0.422494 + 0.731782i
\(33\) 0 0
\(34\) −132.382 −0.667743
\(35\) 267.514 24.3424i 1.29195 0.117561i
\(36\) 0 0
\(37\) 35.7607 + 61.9393i 0.158892 + 0.275210i 0.934470 0.356043i \(-0.115874\pi\)
−0.775577 + 0.631253i \(0.782541\pi\)
\(38\) 113.625 196.803i 0.485061 0.840151i
\(39\) 0 0
\(40\) 175.616 + 304.176i 0.694183 + 1.20236i
\(41\) −277.562 −1.05727 −0.528634 0.848850i \(-0.677296\pi\)
−0.528634 + 0.848850i \(0.677296\pi\)
\(42\) 0 0
\(43\) −178.522 −0.633124 −0.316562 0.948572i \(-0.602528\pi\)
−0.316562 + 0.948572i \(0.602528\pi\)
\(44\) 56.0275 + 97.0424i 0.191965 + 0.332493i
\(45\) 0 0
\(46\) −19.9197 + 34.5020i −0.0638479 + 0.110588i
\(47\) 265.937 + 460.617i 0.825338 + 1.42953i 0.901660 + 0.432445i \(0.142349\pi\)
−0.0763219 + 0.997083i \(0.524318\pi\)
\(48\) 0 0
\(49\) −222.299 261.213i −0.648101 0.761554i
\(50\) 175.804 0.497250
\(51\) 0 0
\(52\) −25.0578 + 43.4013i −0.0668247 + 0.115744i
\(53\) 155.416 269.188i 0.402793 0.697658i −0.591269 0.806475i \(-0.701373\pi\)
0.994062 + 0.108816i \(0.0347061\pi\)
\(54\) 0 0
\(55\) 432.357 1.05998
\(56\) 188.124 407.125i 0.448913 0.971507i
\(57\) 0 0
\(58\) 114.410 + 198.165i 0.259014 + 0.448626i
\(59\) −361.012 + 625.290i −0.796605 + 1.37976i 0.125210 + 0.992130i \(0.460040\pi\)
−0.921815 + 0.387630i \(0.873294\pi\)
\(60\) 0 0
\(61\) −331.535 574.235i −0.695880 1.20530i −0.969883 0.243571i \(-0.921681\pi\)
0.274003 0.961729i \(-0.411652\pi\)
\(62\) 397.328 0.813882
\(63\) 0 0
\(64\) 473.375 0.924560
\(65\) 96.6839 + 167.461i 0.184495 + 0.319554i
\(66\) 0 0
\(67\) 304.279 527.027i 0.554830 0.960994i −0.443086 0.896479i \(-0.646116\pi\)
0.997917 0.0645154i \(-0.0205502\pi\)
\(68\) −120.822 209.269i −0.215467 0.373200i
\(69\) 0 0
\(70\) −318.867 452.035i −0.544456 0.771836i
\(71\) −976.305 −1.63192 −0.815958 0.578111i \(-0.803790\pi\)
−0.815958 + 0.578111i \(0.803790\pi\)
\(72\) 0 0
\(73\) −130.574 + 226.161i −0.209350 + 0.362605i −0.951510 0.307618i \(-0.900468\pi\)
0.742160 + 0.670223i \(0.233801\pi\)
\(74\) 73.6440 127.555i 0.115688 0.200378i
\(75\) 0 0
\(76\) 414.810 0.626078
\(77\) −318.229 451.131i −0.470982 0.667677i
\(78\) 0 0
\(79\) −618.075 1070.54i −0.880239 1.52462i −0.851075 0.525044i \(-0.824049\pi\)
−0.0291637 0.999575i \(-0.509284\pi\)
\(80\) 143.570 248.670i 0.200645 0.347527i
\(81\) 0 0
\(82\) 285.800 + 495.020i 0.384894 + 0.666656i
\(83\) −1225.79 −1.62106 −0.810529 0.585699i \(-0.800820\pi\)
−0.810529 + 0.585699i \(0.800820\pi\)
\(84\) 0 0
\(85\) −932.367 −1.18976
\(86\) 183.820 + 318.386i 0.230486 + 0.399214i
\(87\) 0 0
\(88\) 360.933 625.154i 0.437222 0.757291i
\(89\) −395.991 685.876i −0.471629 0.816885i 0.527845 0.849341i \(-0.323000\pi\)
−0.999473 + 0.0324564i \(0.989667\pi\)
\(90\) 0 0
\(91\) 103.570 224.139i 0.119309 0.258200i
\(92\) −72.7211 −0.0824098
\(93\) 0 0
\(94\) 547.659 948.573i 0.600923 1.04083i
\(95\) 800.260 1386.09i 0.864263 1.49695i
\(96\) 0 0
\(97\) −935.253 −0.978975 −0.489488 0.872010i \(-0.662816\pi\)
−0.489488 + 0.872010i \(0.662816\pi\)
\(98\) −236.966 + 665.425i −0.244256 + 0.685899i
\(99\) 0 0
\(100\) 160.453 + 277.912i 0.160453 + 0.277912i
\(101\) −221.485 + 383.623i −0.218203 + 0.377940i −0.954259 0.298982i \(-0.903353\pi\)
0.736055 + 0.676921i \(0.236686\pi\)
\(102\) 0 0
\(103\) 349.700 + 605.699i 0.334534 + 0.579430i 0.983395 0.181477i \(-0.0580878\pi\)
−0.648861 + 0.760907i \(0.724754\pi\)
\(104\) 322.848 0.304402
\(105\) 0 0
\(106\) −640.114 −0.586541
\(107\) 955.591 + 1655.13i 0.863369 + 1.49540i 0.868657 + 0.495413i \(0.164983\pi\)
−0.00528834 + 0.999986i \(0.501683\pi\)
\(108\) 0 0
\(109\) 1035.71 1793.90i 0.910118 1.57637i 0.0962224 0.995360i \(-0.469324\pi\)
0.813896 0.581011i \(-0.197343\pi\)
\(110\) −445.189 771.090i −0.385883 0.668369i
\(111\) 0 0
\(112\) −365.139 + 33.2258i −0.308057 + 0.0280316i
\(113\) 2313.34 1.92585 0.962926 0.269767i \(-0.0869467\pi\)
0.962926 + 0.269767i \(0.0869467\pi\)
\(114\) 0 0
\(115\) −140.295 + 242.998i −0.113762 + 0.197041i
\(116\) −208.839 + 361.721i −0.167157 + 0.289525i
\(117\) 0 0
\(118\) 1486.90 1.16000
\(119\) 686.253 + 972.851i 0.528644 + 0.749421i
\(120\) 0 0
\(121\) 221.201 + 383.132i 0.166192 + 0.287853i
\(122\) −682.748 + 1182.55i −0.506665 + 0.877570i
\(123\) 0 0
\(124\) 362.632 + 628.096i 0.262623 + 0.454877i
\(125\) −574.817 −0.411306
\(126\) 0 0
\(127\) −1317.50 −0.920542 −0.460271 0.887778i \(-0.652248\pi\)
−0.460271 + 0.887778i \(0.652248\pi\)
\(128\) 124.414 + 215.491i 0.0859119 + 0.148804i
\(129\) 0 0
\(130\) 199.107 344.863i 0.134329 0.232665i
\(131\) −229.421 397.368i −0.153012 0.265024i 0.779321 0.626624i \(-0.215564\pi\)
−0.932333 + 0.361600i \(0.882231\pi\)
\(132\) 0 0
\(133\) −2035.29 + 185.201i −1.32694 + 0.120744i
\(134\) −1253.24 −0.807935
\(135\) 0 0
\(136\) −778.341 + 1348.13i −0.490752 + 0.850007i
\(137\) 666.378 1154.20i 0.415566 0.719781i −0.579922 0.814672i \(-0.696917\pi\)
0.995488 + 0.0948911i \(0.0302503\pi\)
\(138\) 0 0
\(139\) −406.835 −0.248254 −0.124127 0.992266i \(-0.539613\pi\)
−0.124127 + 0.992266i \(0.539613\pi\)
\(140\) 423.555 916.627i 0.255692 0.553351i
\(141\) 0 0
\(142\) 1005.28 + 1741.20i 0.594093 + 1.02900i
\(143\) 198.708 344.173i 0.116202 0.201267i
\(144\) 0 0
\(145\) 805.795 + 1395.68i 0.461501 + 0.799343i
\(146\) 537.797 0.304852
\(147\) 0 0
\(148\) 268.853 0.149321
\(149\) −217.761 377.174i −0.119730 0.207378i 0.799931 0.600092i \(-0.204869\pi\)
−0.919660 + 0.392714i \(0.871536\pi\)
\(150\) 0 0
\(151\) 982.668 1702.03i 0.529592 0.917280i −0.469812 0.882766i \(-0.655678\pi\)
0.999404 0.0345136i \(-0.0109882\pi\)
\(152\) −1336.12 2314.22i −0.712983 1.23492i
\(153\) 0 0
\(154\) −476.897 + 1032.07i −0.249542 + 0.540041i
\(155\) 2798.39 1.45014
\(156\) 0 0
\(157\) −415.741 + 720.085i −0.211336 + 0.366045i −0.952133 0.305684i \(-0.901115\pi\)
0.740797 + 0.671729i \(0.234448\pi\)
\(158\) −1272.84 + 2204.62i −0.640895 + 1.11006i
\(159\) 0 0
\(160\) 2218.54 1.09619
\(161\) 356.811 32.4680i 0.174663 0.0158934i
\(162\) 0 0
\(163\) 588.061 + 1018.55i 0.282579 + 0.489442i 0.972019 0.234901i \(-0.0754766\pi\)
−0.689440 + 0.724343i \(0.742143\pi\)
\(164\) −521.686 + 903.587i −0.248395 + 0.430233i
\(165\) 0 0
\(166\) 1262.17 + 2186.14i 0.590140 + 1.02215i
\(167\) −1674.29 −0.775809 −0.387905 0.921700i \(-0.626801\pi\)
−0.387905 + 0.921700i \(0.626801\pi\)
\(168\) 0 0
\(169\) −2019.26 −0.919098
\(170\) 960.038 + 1662.83i 0.433127 + 0.750197i
\(171\) 0 0
\(172\) −335.536 + 581.166i −0.148747 + 0.257637i
\(173\) 716.460 + 1240.95i 0.314864 + 0.545360i 0.979409 0.201888i \(-0.0647078\pi\)
−0.664545 + 0.747249i \(0.731374\pi\)
\(174\) 0 0
\(175\) −911.352 1291.96i −0.393667 0.558073i
\(176\) −590.139 −0.252747
\(177\) 0 0
\(178\) −815.486 + 1412.46i −0.343389 + 0.594767i
\(179\) −597.265 + 1034.49i −0.249395 + 0.431965i −0.963358 0.268219i \(-0.913565\pi\)
0.713963 + 0.700183i \(0.246898\pi\)
\(180\) 0 0
\(181\) 741.424 0.304473 0.152236 0.988344i \(-0.451352\pi\)
0.152236 + 0.988344i \(0.451352\pi\)
\(182\) −506.386 + 46.0785i −0.206241 + 0.0187668i
\(183\) 0 0
\(184\) 234.237 + 405.711i 0.0938489 + 0.162551i
\(185\) 518.676 898.373i 0.206129 0.357026i
\(186\) 0 0
\(187\) 958.118 + 1659.51i 0.374676 + 0.648959i
\(188\) 1999.34 0.775623
\(189\) 0 0
\(190\) −3296.04 −1.25853
\(191\) −1951.99 3380.95i −0.739483 1.28082i −0.952728 0.303823i \(-0.901737\pi\)
0.213246 0.976999i \(-0.431597\pi\)
\(192\) 0 0
\(193\) −885.627 + 1533.95i −0.330305 + 0.572104i −0.982572 0.185885i \(-0.940485\pi\)
0.652267 + 0.757989i \(0.273818\pi\)
\(194\) 963.010 + 1667.98i 0.356392 + 0.617289i
\(195\) 0 0
\(196\) −1268.18 + 232.722i −0.462164 + 0.0848113i
\(197\) −830.366 −0.300310 −0.150155 0.988662i \(-0.547977\pi\)
−0.150155 + 0.988662i \(0.547977\pi\)
\(198\) 0 0
\(199\) −531.253 + 920.156i −0.189244 + 0.327780i −0.944998 0.327075i \(-0.893937\pi\)
0.755755 + 0.654855i \(0.227270\pi\)
\(200\) 1033.65 1790.33i 0.365449 0.632977i
\(201\) 0 0
\(202\) 912.232 0.317745
\(203\) 863.187 1868.05i 0.298443 0.645869i
\(204\) 0 0
\(205\) 2012.90 + 3486.44i 0.685789 + 1.18782i
\(206\) 720.158 1247.35i 0.243572 0.421878i
\(207\) 0 0
\(208\) −131.967 228.574i −0.0439917 0.0761958i
\(209\) −3289.45 −1.08869
\(210\) 0 0
\(211\) −3848.67 −1.25570 −0.627851 0.778333i \(-0.716065\pi\)
−0.627851 + 0.778333i \(0.716065\pi\)
\(212\) −584.217 1011.89i −0.189265 0.327817i
\(213\) 0 0
\(214\) 1967.90 3408.51i 0.628612 1.08879i
\(215\) 1294.65 + 2242.40i 0.410671 + 0.711303i
\(216\) 0 0
\(217\) −2059.71 2919.89i −0.644341 0.913435i
\(218\) −4265.79 −1.32530
\(219\) 0 0
\(220\) 812.627 1407.51i 0.249033 0.431338i
\(221\) −428.509 + 742.200i −0.130428 + 0.225908i
\(222\) 0 0
\(223\) 5482.75 1.64642 0.823211 0.567736i \(-0.192181\pi\)
0.823211 + 0.567736i \(0.192181\pi\)
\(224\) −1632.92 2314.87i −0.487070 0.690484i
\(225\) 0 0
\(226\) −2382.00 4125.75i −0.701099 1.21434i
\(227\) 197.418 341.939i 0.0577230 0.0999791i −0.835720 0.549156i \(-0.814949\pi\)
0.893443 + 0.449177i \(0.148283\pi\)
\(228\) 0 0
\(229\) 1911.78 + 3311.30i 0.551678 + 0.955534i 0.998154 + 0.0607380i \(0.0193454\pi\)
−0.446476 + 0.894796i \(0.647321\pi\)
\(230\) 577.835 0.165658
\(231\) 0 0
\(232\) 2690.72 0.761441
\(233\) −1268.77 2197.57i −0.356738 0.617888i 0.630676 0.776046i \(-0.282778\pi\)
−0.987414 + 0.158159i \(0.949444\pi\)
\(234\) 0 0
\(235\) 3857.17 6680.82i 1.07070 1.85451i
\(236\) 1357.06 + 2350.50i 0.374310 + 0.648324i
\(237\) 0 0
\(238\) 1028.42 2225.62i 0.280094 0.606159i
\(239\) −5368.81 −1.45305 −0.726526 0.687139i \(-0.758866\pi\)
−0.726526 + 0.687139i \(0.758866\pi\)
\(240\) 0 0
\(241\) −1054.01 + 1825.60i −0.281721 + 0.487955i −0.971809 0.235771i \(-0.924239\pi\)
0.690088 + 0.723726i \(0.257572\pi\)
\(242\) 455.532 789.005i 0.121003 0.209583i
\(243\) 0 0
\(244\) −2492.51 −0.653962
\(245\) −1668.95 + 4686.60i −0.435206 + 1.22211i
\(246\) 0 0
\(247\) −735.588 1274.08i −0.189491 0.328208i
\(248\) 2336.10 4046.24i 0.598155 1.03603i
\(249\) 0 0
\(250\) 591.877 + 1025.16i 0.149734 + 0.259347i
\(251\) 5717.94 1.43790 0.718951 0.695061i \(-0.244623\pi\)
0.718951 + 0.695061i \(0.244623\pi\)
\(252\) 0 0
\(253\) 576.680 0.143303
\(254\) 1356.60 + 2349.69i 0.335120 + 0.580445i
\(255\) 0 0
\(256\) 2149.71 3723.41i 0.524832 0.909035i
\(257\) 2493.73 + 4319.28i 0.605272 + 1.04836i 0.992008 + 0.126172i \(0.0402690\pi\)
−0.386736 + 0.922190i \(0.626398\pi\)
\(258\) 0 0
\(259\) −1319.14 + 120.035i −0.316477 + 0.0287978i
\(260\) 726.880 0.173381
\(261\) 0 0
\(262\) −472.459 + 818.322i −0.111407 + 0.192962i
\(263\) 307.637 532.842i 0.0721281 0.124930i −0.827706 0.561162i \(-0.810354\pi\)
0.899834 + 0.436233i \(0.143688\pi\)
\(264\) 0 0
\(265\) −4508.34 −1.04508
\(266\) 2426.00 + 3439.16i 0.559200 + 0.792738i
\(267\) 0 0
\(268\) −1143.80 1981.12i −0.260705 0.451553i
\(269\) −396.981 + 687.591i −0.0899790 + 0.155848i −0.907502 0.420048i \(-0.862013\pi\)
0.817523 + 0.575896i \(0.195347\pi\)
\(270\) 0 0
\(271\) −1882.47 3260.54i −0.421964 0.730862i 0.574168 0.818738i \(-0.305326\pi\)
−0.996131 + 0.0878752i \(0.971992\pi\)
\(272\) 1272.62 0.283690
\(273\) 0 0
\(274\) −2744.62 −0.605141
\(275\) −1272.39 2203.85i −0.279011 0.483262i
\(276\) 0 0
\(277\) 1598.27 2768.29i 0.346682 0.600471i −0.638976 0.769227i \(-0.720642\pi\)
0.985658 + 0.168756i \(0.0539750\pi\)
\(278\) 418.909 + 725.571i 0.0903758 + 0.156535i
\(279\) 0 0
\(280\) −6478.15 + 589.478i −1.38265 + 0.125814i
\(281\) 6225.15 1.32157 0.660785 0.750575i \(-0.270223\pi\)
0.660785 + 0.750575i \(0.270223\pi\)
\(282\) 0 0
\(283\) 1858.75 3219.45i 0.390429 0.676242i −0.602077 0.798438i \(-0.705660\pi\)
0.992506 + 0.122195i \(0.0389935\pi\)
\(284\) −1834.99 + 3178.30i −0.383404 + 0.664075i
\(285\) 0 0
\(286\) −818.423 −0.169211
\(287\) 2156.26 4666.43i 0.443485 0.959758i
\(288\) 0 0
\(289\) 390.347 + 676.100i 0.0794518 + 0.137615i
\(290\) 1659.42 2874.20i 0.336015 0.581996i
\(291\) 0 0
\(292\) 490.835 + 850.151i 0.0983696 + 0.170381i
\(293\) 6392.56 1.27460 0.637299 0.770616i \(-0.280052\pi\)
0.637299 + 0.770616i \(0.280052\pi\)
\(294\) 0 0
\(295\) 10472.3 2.06685
\(296\) −865.983 1499.93i −0.170048 0.294532i
\(297\) 0 0
\(298\) −448.448 + 776.735i −0.0871742 + 0.150990i
\(299\) 128.957 + 223.361i 0.0249425 + 0.0432016i
\(300\) 0 0
\(301\) 1386.86 3001.34i 0.265572 0.574732i
\(302\) −4047.33 −0.771183
\(303\) 0 0
\(304\) −1092.30 + 1891.92i −0.206078 + 0.356938i
\(305\) −4808.61 + 8328.76i −0.902755 + 1.56362i
\(306\) 0 0
\(307\) 939.255 0.174613 0.0873063 0.996182i \(-0.472174\pi\)
0.0873063 + 0.996182i \(0.472174\pi\)
\(308\) −2066.75 + 188.063i −0.382350 + 0.0347919i
\(309\) 0 0
\(310\) −2881.44 4990.80i −0.527918 0.914381i
\(311\) −1375.81 + 2382.97i −0.250851 + 0.434487i −0.963760 0.266769i \(-0.914044\pi\)
0.712909 + 0.701257i \(0.247377\pi\)
\(312\) 0 0
\(313\) 318.550 + 551.744i 0.0575255 + 0.0996372i 0.893354 0.449353i \(-0.148346\pi\)
−0.835829 + 0.548991i \(0.815012\pi\)
\(314\) 1712.32 0.307744
\(315\) 0 0
\(316\) −4646.75 −0.827216
\(317\) −1436.10 2487.39i −0.254445 0.440712i 0.710299 0.703900i \(-0.248560\pi\)
−0.964745 + 0.263187i \(0.915226\pi\)
\(318\) 0 0
\(319\) 1656.10 2868.45i 0.290670 0.503456i
\(320\) −3432.93 5946.02i −0.599709 1.03873i
\(321\) 0 0
\(322\) −425.306 602.925i −0.0736068 0.104347i
\(323\) 7093.60 1.22198
\(324\) 0 0
\(325\) 569.065 985.650i 0.0971263 0.168228i
\(326\) 1211.03 2097.56i 0.205744 0.356359i
\(327\) 0 0
\(328\) 6721.47 1.13150
\(329\) −9809.92 + 892.651i −1.64389 + 0.149585i
\(330\) 0 0
\(331\) 3196.80 + 5537.02i 0.530852 + 0.919463i 0.999352 + 0.0359995i \(0.0114615\pi\)
−0.468499 + 0.883464i \(0.655205\pi\)
\(332\) −2303.90 + 3990.47i −0.380852 + 0.659656i
\(333\) 0 0
\(334\) 1723.98 + 2986.01i 0.282430 + 0.489184i
\(335\) −8826.59 −1.43955
\(336\) 0 0
\(337\) −12107.6 −1.95710 −0.978549 0.206016i \(-0.933950\pi\)
−0.978549 + 0.206016i \(0.933950\pi\)
\(338\) 2079.19 + 3601.26i 0.334594 + 0.579534i
\(339\) 0 0
\(340\) −1752.41 + 3035.26i −0.279522 + 0.484147i
\(341\) −2875.68 4980.82i −0.456676 0.790986i
\(342\) 0 0
\(343\) 6118.50 1708.08i 0.963172 0.268884i
\(344\) 4323.10 0.677575
\(345\) 0 0
\(346\) 1475.45 2555.55i 0.229250 0.397073i
\(347\) 1355.07 2347.05i 0.209636 0.363101i −0.741964 0.670440i \(-0.766105\pi\)
0.951600 + 0.307339i \(0.0994386\pi\)
\(348\) 0 0
\(349\) −1175.22 −0.180252 −0.0901261 0.995930i \(-0.528727\pi\)
−0.0901261 + 0.995930i \(0.528727\pi\)
\(350\) −1365.75 + 2955.65i −0.208578 + 0.451390i
\(351\) 0 0
\(352\) −2279.81 3948.74i −0.345211 0.597923i
\(353\) 2638.20 4569.50i 0.397783 0.688980i −0.595669 0.803230i \(-0.703113\pi\)
0.993452 + 0.114250i \(0.0364464\pi\)
\(354\) 0 0
\(355\) 7080.21 + 12263.3i 1.05853 + 1.83343i
\(356\) −2977.10 −0.443219
\(357\) 0 0
\(358\) 2459.96 0.363165
\(359\) −5643.27 9774.43i −0.829639 1.43698i −0.898322 0.439338i \(-0.855213\pi\)
0.0686829 0.997639i \(-0.478120\pi\)
\(360\) 0 0
\(361\) −2659.01 + 4605.55i −0.387668 + 0.671460i
\(362\) −763.428 1322.30i −0.110842 0.191984i
\(363\) 0 0
\(364\) −535.008 758.441i −0.0770385 0.109212i
\(365\) 3787.72 0.543173
\(366\) 0 0
\(367\) −3783.80 + 6553.73i −0.538181 + 0.932158i 0.460821 + 0.887493i \(0.347555\pi\)
−0.999002 + 0.0446643i \(0.985778\pi\)
\(368\) 191.493 331.676i 0.0271258 0.0469832i
\(369\) 0 0
\(370\) −2136.28 −0.300162
\(371\) 3318.29 + 4704.09i 0.464358 + 0.658286i
\(372\) 0 0
\(373\) 3251.99 + 5632.61i 0.451425 + 0.781891i 0.998475 0.0552092i \(-0.0175826\pi\)
−0.547050 + 0.837100i \(0.684249\pi\)
\(374\) 1973.11 3417.52i 0.272799 0.472502i
\(375\) 0 0
\(376\) −6439.95 11154.3i −0.883285 1.52989i
\(377\) 1481.35 0.202370
\(378\) 0 0
\(379\) 10773.8 1.46019 0.730097 0.683344i \(-0.239475\pi\)
0.730097 + 0.683344i \(0.239475\pi\)
\(380\) −3008.22 5210.39i −0.406101 0.703388i
\(381\) 0 0
\(382\) −4019.85 + 6962.58i −0.538412 + 0.932557i
\(383\) −3183.06 5513.23i −0.424666 0.735542i 0.571724 0.820446i \(-0.306275\pi\)
−0.996389 + 0.0849039i \(0.972942\pi\)
\(384\) 0 0
\(385\) −3358.80 + 7268.87i −0.444624 + 0.962223i
\(386\) 3647.64 0.480985
\(387\) 0 0
\(388\) −1757.83 + 3044.66i −0.230001 + 0.398374i
\(389\) −2951.72 + 5112.53i −0.384725 + 0.666363i −0.991731 0.128334i \(-0.959037\pi\)
0.607006 + 0.794697i \(0.292370\pi\)
\(390\) 0 0
\(391\) −1243.59 −0.160847
\(392\) 5383.20 + 6325.56i 0.693604 + 0.815022i
\(393\) 0 0
\(394\) 855.010 + 1480.92i 0.109327 + 0.189360i
\(395\) −8964.62 + 15527.2i −1.14192 + 1.97786i
\(396\) 0 0
\(397\) −1883.39 3262.13i −0.238097 0.412397i 0.722071 0.691819i \(-0.243190\pi\)
−0.960168 + 0.279422i \(0.909857\pi\)
\(398\) 2188.08 0.275574
\(399\) 0 0
\(400\) −1690.05 −0.211256
\(401\) 3626.00 + 6280.42i 0.451556 + 0.782118i 0.998483 0.0550625i \(-0.0175358\pi\)
−0.546927 + 0.837180i \(0.684202\pi\)
\(402\) 0 0
\(403\) 1286.12 2227.62i 0.158973 0.275349i
\(404\) 832.573 + 1442.06i 0.102530 + 0.177587i
\(405\) 0 0
\(406\) −4220.39 + 384.033i −0.515897 + 0.0469440i
\(407\) −2132.01 −0.259655
\(408\) 0 0
\(409\) −6273.70 + 10866.4i −0.758471 + 1.31371i 0.185159 + 0.982709i \(0.440720\pi\)
−0.943630 + 0.331002i \(0.892613\pi\)
\(410\) 4145.27 7179.82i 0.499318 0.864844i
\(411\) 0 0
\(412\) 2629.08 0.314383
\(413\) −7707.95 10927.0i −0.918362 1.30190i
\(414\) 0 0
\(415\) 8889.47 + 15397.0i 1.05149 + 1.82123i
\(416\) 1019.62 1766.04i 0.120171 0.208142i
\(417\) 0 0
\(418\) 3387.07 + 5866.58i 0.396333 + 0.686469i
\(419\) 12631.5 1.47276 0.736381 0.676567i \(-0.236533\pi\)
0.736381 + 0.676567i \(0.236533\pi\)
\(420\) 0 0
\(421\) −3495.94 −0.404707 −0.202354 0.979312i \(-0.564859\pi\)
−0.202354 + 0.979312i \(0.564859\pi\)
\(422\) 3962.89 + 6863.92i 0.457134 + 0.791779i
\(423\) 0 0
\(424\) −3763.57 + 6518.69i −0.431073 + 0.746640i
\(425\) 2743.88 + 4752.53i 0.313171 + 0.542427i
\(426\) 0 0
\(427\) 12229.7 1112.84i 1.38603 0.126122i
\(428\) 7184.23 0.811362
\(429\) 0 0
\(430\) 2666.14 4617.89i 0.299006 0.517894i
\(431\) −1172.59 + 2030.99i −0.131048 + 0.226982i −0.924081 0.382197i \(-0.875168\pi\)
0.793033 + 0.609179i \(0.208501\pi\)
\(432\) 0 0
\(433\) 3250.63 0.360774 0.180387 0.983596i \(-0.442265\pi\)
0.180387 + 0.983596i \(0.442265\pi\)
\(434\) −3086.67 + 6679.94i −0.341393 + 0.738819i
\(435\) 0 0
\(436\) −3893.28 6743.36i −0.427648 0.740708i
\(437\) 1067.39 1848.77i 0.116842 0.202377i
\(438\) 0 0
\(439\) −8120.24 14064.7i −0.882820 1.52909i −0.848192 0.529689i \(-0.822308\pi\)
−0.0346287 0.999400i \(-0.511025\pi\)
\(440\) −10470.0 −1.13440
\(441\) 0 0
\(442\) 1764.91 0.189928
\(443\) 2424.52 + 4199.39i 0.260028 + 0.450382i 0.966249 0.257610i \(-0.0829349\pi\)
−0.706221 + 0.707991i \(0.749602\pi\)
\(444\) 0 0
\(445\) −5743.49 + 9948.01i −0.611837 + 1.05973i
\(446\) −5645.47 9778.23i −0.599373 1.03815i
\(447\) 0 0
\(448\) −3677.44 + 7958.46i −0.387819 + 0.839290i
\(449\) −4139.93 −0.435134 −0.217567 0.976045i \(-0.569812\pi\)
−0.217567 + 0.976045i \(0.569812\pi\)
\(450\) 0 0
\(451\) 4136.98 7165.46i 0.431935 0.748134i
\(452\) 4347.99 7530.94i 0.452461 0.783685i
\(453\) 0 0
\(454\) −813.110 −0.0840553
\(455\) −3566.49 + 324.532i −0.367471 + 0.0334380i
\(456\) 0 0
\(457\) −4616.24 7995.56i −0.472513 0.818417i 0.526992 0.849870i \(-0.323320\pi\)
−0.999505 + 0.0314531i \(0.989987\pi\)
\(458\) 3937.04 6819.16i 0.401672 0.695717i
\(459\) 0 0
\(460\) 527.377 + 913.443i 0.0534545 + 0.0925859i
\(461\) 1274.90 0.128803 0.0644013 0.997924i \(-0.479486\pi\)
0.0644013 + 0.997924i \(0.479486\pi\)
\(462\) 0 0
\(463\) 2061.80 0.206955 0.103477 0.994632i \(-0.467003\pi\)
0.103477 + 0.994632i \(0.467003\pi\)
\(464\) −1099.86 1905.01i −0.110042 0.190599i
\(465\) 0 0
\(466\) −2612.85 + 4525.59i −0.259738 + 0.449879i
\(467\) 484.021 + 838.348i 0.0479610 + 0.0830710i 0.889009 0.457889i \(-0.151394\pi\)
−0.841048 + 0.540960i \(0.818061\pi\)
\(468\) 0 0
\(469\) 6496.66 + 9209.84i 0.639633 + 0.906761i
\(470\) −15886.6 −1.55914
\(471\) 0 0
\(472\) 8742.29 15142.1i 0.852535 1.47663i
\(473\) 2660.81 4608.66i 0.258656 0.448005i
\(474\) 0 0
\(475\) −9420.39 −0.909973
\(476\) 4456.88 405.553i 0.429161 0.0390515i
\(477\) 0 0
\(478\) 5528.15 + 9575.03i 0.528978 + 0.916217i
\(479\) −3100.02 + 5369.40i −0.295707 + 0.512180i −0.975149 0.221549i \(-0.928889\pi\)
0.679442 + 0.733729i \(0.262222\pi\)
\(480\) 0 0
\(481\) −476.760 825.772i −0.0451941 0.0782785i
\(482\) 4341.17 0.410238
\(483\) 0 0
\(484\) 1663.01 0.156181
\(485\) 6782.50 + 11747.6i 0.635005 + 1.09986i
\(486\) 0 0
\(487\) 4914.83 8512.74i 0.457315 0.792092i −0.541503 0.840699i \(-0.682145\pi\)
0.998818 + 0.0486063i \(0.0154780\pi\)
\(488\) 8028.47 + 13905.7i 0.744738 + 1.28992i
\(489\) 0 0
\(490\) 10076.8 1849.19i 0.929030 0.170485i
\(491\) −5053.57 −0.464489 −0.232245 0.972657i \(-0.574607\pi\)
−0.232245 + 0.972657i \(0.574607\pi\)
\(492\) 0 0
\(493\) −3571.33 + 6185.73i −0.326257 + 0.565094i
\(494\) −1514.84 + 2623.77i −0.137967 + 0.238966i
\(495\) 0 0
\(496\) −3819.61 −0.345777
\(497\) 7584.49 16413.8i 0.684529 1.48141i
\(498\) 0 0
\(499\) −7030.82 12177.7i −0.630747 1.09249i −0.987399 0.158249i \(-0.949415\pi\)
0.356652 0.934237i \(-0.383918\pi\)
\(500\) −1080.38 + 1871.28i −0.0966325 + 0.167372i
\(501\) 0 0
\(502\) −5887.64 10197.7i −0.523463 0.906664i
\(503\) 8001.67 0.709298 0.354649 0.934999i \(-0.384600\pi\)
0.354649 + 0.934999i \(0.384600\pi\)
\(504\) 0 0
\(505\) 6424.87 0.566144
\(506\) −593.794 1028.48i −0.0521687 0.0903589i
\(507\) 0 0
\(508\) −2476.27 + 4289.02i −0.216273 + 0.374596i
\(509\) 5456.91 + 9451.65i 0.475193 + 0.823059i 0.999596 0.0284114i \(-0.00904484\pi\)
−0.524403 + 0.851470i \(0.675712\pi\)
\(510\) 0 0
\(511\) −2787.88 3952.18i −0.241348 0.342141i
\(512\) −6863.42 −0.592428
\(513\) 0 0
\(514\) 5135.49 8894.93i 0.440694 0.763304i
\(515\) 5072.08 8785.11i 0.433986 0.751686i
\(516\) 0 0
\(517\) −15854.8 −1.34873
\(518\) 1572.37 + 2229.04i 0.133371 + 0.189070i
\(519\) 0 0
\(520\) −2341.31 4055.26i −0.197448 0.341990i
\(521\) 7901.70 13686.1i 0.664452 1.15087i −0.314981 0.949098i \(-0.601998\pi\)
0.979433 0.201767i \(-0.0646685\pi\)
\(522\) 0 0
\(523\) 323.047 + 559.534i 0.0270093 + 0.0467815i 0.879214 0.476427i \(-0.158068\pi\)
−0.852205 + 0.523208i \(0.824735\pi\)
\(524\) −1724.81 −0.143795
\(525\) 0 0
\(526\) −1267.07 −0.105032
\(527\) 6201.31 + 10741.0i 0.512587 + 0.887827i
\(528\) 0 0
\(529\) 5896.37 10212.8i 0.484620 0.839387i
\(530\) 4642.14 + 8040.41i 0.380456 + 0.658968i
\(531\) 0 0
\(532\) −3222.48 + 6973.86i −0.262617 + 0.568337i
\(533\) 3700.45 0.300721
\(534\) 0 0
\(535\) 13860.0 24006.2i 1.12004 1.93996i
\(536\) −7368.45 + 12762.5i −0.593785 + 1.02847i
\(537\) 0 0
\(538\) 1635.05 0.131026
\(539\) 10056.7 1845.49i 0.803658 0.147479i
\(540\) 0 0
\(541\) −5123.33 8873.86i −0.407152 0.705207i 0.587418 0.809284i \(-0.300145\pi\)
−0.994569 + 0.104077i \(0.966811\pi\)
\(542\) −3876.68 + 6714.61i −0.307228 + 0.532135i
\(543\) 0 0
\(544\) 4916.34 + 8515.36i 0.387475 + 0.671127i
\(545\) −30044.0 −2.36137
\(546\) 0 0
\(547\) 4368.98 0.341506 0.170753 0.985314i \(-0.445380\pi\)
0.170753 + 0.985314i \(0.445380\pi\)
\(548\) −2504.95 4338.70i −0.195267 0.338212i
\(549\) 0 0
\(550\) −2620.31 + 4538.50i −0.203146 + 0.351859i
\(551\) −6130.63 10618.6i −0.473999 0.820990i
\(552\) 0 0
\(553\) 22799.6 2074.65i 1.75323 0.159535i
\(554\) −6582.82 −0.504833
\(555\) 0 0
\(556\) −764.656 + 1324.42i −0.0583249 + 0.101022i
\(557\) 4198.21 7271.52i 0.319361 0.553149i −0.660994 0.750391i \(-0.729865\pi\)
0.980355 + 0.197242i \(0.0631984\pi\)
\(558\) 0 0
\(559\) 2380.04 0.180081
\(560\) 3065.35 + 4345.52i 0.231312 + 0.327914i
\(561\) 0 0
\(562\) −6409.90 11102.3i −0.481113 0.833312i
\(563\) −6071.13 + 10515.5i −0.454472 + 0.787169i −0.998658 0.0517962i \(-0.983505\pi\)
0.544186 + 0.838965i \(0.316839\pi\)
\(564\) 0 0
\(565\) −16776.5 29057.7i −1.24919 2.16366i
\(566\) −7655.66 −0.568536
\(567\) 0 0
\(568\) 23642.3 1.74649
\(569\) −5598.06 9696.12i −0.412448 0.714381i 0.582709 0.812681i \(-0.301993\pi\)
−0.995157 + 0.0983003i \(0.968659\pi\)
\(570\) 0 0
\(571\) −9829.79 + 17025.7i −0.720427 + 1.24782i 0.240402 + 0.970674i \(0.422721\pi\)
−0.960829 + 0.277143i \(0.910612\pi\)
\(572\) −746.955 1293.76i −0.0546010 0.0945717i
\(573\) 0 0
\(574\) −10542.6 + 959.324i −0.766621 + 0.0697586i
\(575\) 1651.51 0.119778
\(576\) 0 0
\(577\) −4258.23 + 7375.46i −0.307231 + 0.532140i −0.977756 0.209748i \(-0.932736\pi\)
0.670525 + 0.741887i \(0.266069\pi\)
\(578\) 803.863 1392.33i 0.0578482 0.100196i
\(579\) 0 0
\(580\) 6058.05 0.433702
\(581\) 9522.62 20608.2i 0.679974 1.47155i
\(582\) 0 0
\(583\) 4632.85 + 8024.33i 0.329113 + 0.570041i
\(584\) 3161.99 5476.73i 0.224048 0.388063i
\(585\) 0 0
\(586\) −6582.28 11400.8i −0.464013 0.803694i
\(587\) −7115.53 −0.500323 −0.250161 0.968204i \(-0.580484\pi\)
−0.250161 + 0.968204i \(0.580484\pi\)
\(588\) 0 0
\(589\) −21290.6 −1.48941
\(590\) −10783.1 18676.9i −0.752428 1.30324i
\(591\) 0 0
\(592\) −707.958 + 1226.22i −0.0491502 + 0.0851306i
\(593\) −3072.24 5321.28i −0.212752 0.368497i 0.739823 0.672802i \(-0.234909\pi\)
−0.952575 + 0.304305i \(0.901576\pi\)
\(594\) 0 0
\(595\) 7243.15 15675.1i 0.499059 1.08003i
\(596\) −1637.15 −0.112517
\(597\) 0 0
\(598\) 265.569 459.979i 0.0181604 0.0314547i
\(599\) −4789.20 + 8295.13i −0.326680 + 0.565826i −0.981851 0.189654i \(-0.939263\pi\)
0.655171 + 0.755481i \(0.272597\pi\)
\(600\) 0 0
\(601\) −19113.8 −1.29728 −0.648642 0.761094i \(-0.724663\pi\)
−0.648642 + 0.761094i \(0.724663\pi\)
\(602\) −6780.77 + 617.015i −0.459076 + 0.0417735i
\(603\) 0 0
\(604\) −3693.90 6398.02i −0.248845 0.431013i
\(605\) 3208.32 5556.98i 0.215598 0.373427i
\(606\) 0 0
\(607\) −10221.3 17703.9i −0.683477 1.18382i −0.973913 0.226923i \(-0.927134\pi\)
0.290435 0.956895i \(-0.406200\pi\)
\(608\) −16879.0 −1.12588
\(609\) 0 0
\(610\) 19805.3 1.31458
\(611\) −3545.46 6140.92i −0.234753 0.406604i
\(612\) 0 0
\(613\) −8711.37 + 15088.5i −0.573978 + 0.994160i 0.422173 + 0.906515i \(0.361267\pi\)
−0.996152 + 0.0876447i \(0.972066\pi\)
\(614\) −967.130 1675.12i −0.0635671 0.110101i
\(615\) 0 0
\(616\) 7706.27 + 10924.6i 0.504049 + 0.714554i
\(617\) −1805.17 −0.117785 −0.0588926 0.998264i \(-0.518757\pi\)
−0.0588926 + 0.998264i \(0.518757\pi\)
\(618\) 0 0
\(619\) −4071.12 + 7051.38i −0.264349 + 0.457866i −0.967393 0.253281i \(-0.918490\pi\)
0.703044 + 0.711146i \(0.251824\pi\)
\(620\) 5259.64 9109.97i 0.340697 0.590105i
\(621\) 0 0
\(622\) 5666.55 0.365286
\(623\) 14607.4 1329.19i 0.939376 0.0854783i
\(624\) 0 0
\(625\) 9504.14 + 16461.7i 0.608265 + 1.05355i
\(626\) 656.007 1136.24i 0.0418839 0.0725451i
\(627\) 0 0
\(628\) 1562.79 + 2706.84i 0.0993029 + 0.171998i
\(629\) 4597.61 0.291445
\(630\) 0 0
\(631\) 3630.07 0.229019 0.114509 0.993422i \(-0.463470\pi\)
0.114509 + 0.993422i \(0.463470\pi\)
\(632\) 14967.4 + 25924.2i 0.942040 + 1.63166i
\(633\) 0 0
\(634\) −2957.43 + 5122.42i −0.185260 + 0.320879i
\(635\) 9554.54 + 16548.9i 0.597103 + 1.03421i
\(636\) 0 0
\(637\) 2963.68 + 3482.48i 0.184341 + 0.216611i
\(638\) −6821.00 −0.423270
\(639\) 0 0
\(640\) 1804.51 3125.50i 0.111452 0.193041i
\(641\) −11111.8 + 19246.2i −0.684696 + 1.18593i 0.288836 + 0.957379i \(0.406732\pi\)
−0.973532 + 0.228550i \(0.926602\pi\)
\(642\) 0 0
\(643\) −5013.00 −0.307455 −0.153727 0.988113i \(-0.549128\pi\)
−0.153727 + 0.988113i \(0.549128\pi\)
\(644\) 564.939 1222.60i 0.0345679 0.0748093i
\(645\) 0 0
\(646\) −7304.13 12651.1i −0.444856 0.770514i
\(647\) −3858.08 + 6682.39i −0.234431 + 0.406046i −0.959107 0.283043i \(-0.908656\pi\)
0.724676 + 0.689090i \(0.241989\pi\)
\(648\) 0 0
\(649\) −10761.5 18639.5i −0.650889 1.12737i
\(650\) −2343.82 −0.141434
\(651\) 0 0
\(652\) 4421.10 0.265558
\(653\) 2822.20 + 4888.20i 0.169129 + 0.292940i 0.938114 0.346327i \(-0.112571\pi\)
−0.768985 + 0.639267i \(0.779238\pi\)
\(654\) 0 0
\(655\) −3327.54 + 5763.46i −0.198500 + 0.343812i
\(656\) −2747.47 4758.75i −0.163522 0.283229i
\(657\) 0 0
\(658\) 11693.1 + 16576.4i 0.692770 + 0.982090i
\(659\) 8812.27 0.520906 0.260453 0.965487i \(-0.416128\pi\)
0.260453 + 0.965487i \(0.416128\pi\)
\(660\) 0 0
\(661\) 3095.51 5361.58i 0.182150 0.315493i −0.760462 0.649382i \(-0.775028\pi\)
0.942613 + 0.333889i \(0.108361\pi\)
\(662\) 6583.35 11402.7i 0.386510 0.669454i
\(663\) 0 0
\(664\) 29683.8 1.73487
\(665\) 17086.3 + 24222.1i 0.996360 + 1.41247i
\(666\) 0 0
\(667\) 1074.77 + 1861.56i 0.0623918 + 0.108066i
\(668\) −3146.86 + 5450.53i −0.182269 + 0.315699i
\(669\) 0 0
\(670\) 9088.54 + 15741.8i 0.524061 + 0.907701i
\(671\) 19765.7 1.13718
\(672\) 0 0
\(673\) 29580.7 1.69428 0.847141 0.531368i \(-0.178322\pi\)
0.847141 + 0.531368i \(0.178322\pi\)
\(674\) 12466.9 + 21593.3i 0.712474 + 1.23404i
\(675\) 0 0
\(676\) −3795.25 + 6573.57i −0.215934 + 0.374008i
\(677\) −13145.0 22767.8i −0.746239 1.29252i −0.949613 0.313423i \(-0.898524\pi\)
0.203374 0.979101i \(-0.434809\pi\)
\(678\) 0 0
\(679\) 7265.58 15723.6i 0.410644 0.888686i
\(680\) 22578.3 1.27329
\(681\) 0 0
\(682\) −5922.04 + 10257.3i −0.332502 + 0.575911i
\(683\) 405.342 702.073i 0.0227086 0.0393325i −0.854448 0.519537i \(-0.826104\pi\)
0.877156 + 0.480205i \(0.159438\pi\)
\(684\) 0 0
\(685\) −19330.4 −1.07821
\(686\) −9346.36 9153.31i −0.520183 0.509439i
\(687\) 0 0
\(688\) −1767.11 3060.72i −0.0979220 0.169606i
\(689\) −2072.00 + 3588.81i −0.114567 + 0.198436i
\(690\) 0 0
\(691\) −585.690 1014.45i −0.0322442 0.0558485i 0.849453 0.527664i \(-0.176932\pi\)
−0.881697 + 0.471816i \(0.843599\pi\)
\(692\) 5386.42 0.295897
\(693\) 0 0
\(694\) −5581.14 −0.305269
\(695\) 2950.38 + 5110.21i 0.161028 + 0.278908i
\(696\) 0 0
\(697\) −8921.28 + 15452.1i −0.484817 + 0.839728i
\(698\) 1210.10 + 2095.95i 0.0656201 + 0.113657i
\(699\) 0 0
\(700\) −5918.79 + 538.579i −0.319585 + 0.0290805i
\(701\) −1057.70 −0.0569885 −0.0284943 0.999594i \(-0.509071\pi\)
−0.0284943 + 0.999594i \(0.509071\pi\)
\(702\) 0 0
\(703\) −3946.18 + 6834.98i −0.211711 + 0.366694i
\(704\) −7055.49 + 12220.5i −0.377719 + 0.654228i
\(705\) 0 0
\(706\) −10866.0 −0.579245
\(707\) −4728.92 6703.84i −0.251555 0.356611i
\(708\) 0 0
\(709\) 14621.9 + 25325.8i 0.774521 + 1.34151i 0.935063 + 0.354481i \(0.115343\pi\)
−0.160542 + 0.987029i \(0.551324\pi\)
\(710\) 14580.7 25254.5i 0.770708 1.33491i
\(711\) 0 0
\(712\) 9589.34 + 16609.2i 0.504741 + 0.874238i
\(713\) 3732.50 0.196049
\(714\) 0 0
\(715\) −5764.17 −0.301493
\(716\) 2245.15 + 3888.72i 0.117186 + 0.202972i
\(717\) 0 0
\(718\) −11621.5 + 20129.0i −0.604054 + 1.04625i
\(719\) −12278.9 21267.6i −0.636890 1.10313i −0.986111 0.166086i \(-0.946887\pi\)
0.349221 0.937040i \(-0.386446\pi\)
\(720\) 0 0
\(721\) −12899.8 + 1173.81i −0.666315 + 0.0606312i
\(722\) 10951.7 0.564516
\(723\) 0 0
\(724\) 1393.53 2413.66i 0.0715331 0.123899i
\(725\) 4742.77 8214.72i 0.242955 0.420810i
\(726\) 0 0
\(727\) −23444.2 −1.19601 −0.598003 0.801494i \(-0.704039\pi\)
−0.598003 + 0.801494i \(0.704039\pi\)
\(728\) −2508.06 + 5427.77i −0.127685 + 0.276328i
\(729\) 0 0
\(730\) −3900.13 6755.22i −0.197740 0.342496i
\(731\) −5737.96 + 9938.44i −0.290323 + 0.502854i
\(732\) 0 0
\(733\) 17985.6 + 31152.0i 0.906296 + 1.56975i 0.819168 + 0.573553i \(0.194436\pi\)
0.0871278 + 0.996197i \(0.472231\pi\)
\(734\) 15584.4 0.783692
\(735\) 0 0
\(736\) 2959.09 0.148198
\(737\) 9070.37 + 15710.3i 0.453340 + 0.785207i
\(738\) 0 0
\(739\) −6034.31 + 10451.7i −0.300373 + 0.520261i −0.976220 0.216780i \(-0.930444\pi\)
0.675848 + 0.737041i \(0.263778\pi\)
\(740\) −1949.73 3377.03i −0.0968561 0.167760i
\(741\) 0 0
\(742\) 4972.77 10761.7i 0.246032 0.532446i
\(743\) −5475.09 −0.270339 −0.135169 0.990823i \(-0.543158\pi\)
−0.135169 + 0.990823i \(0.543158\pi\)
\(744\) 0 0
\(745\) −3158.43 + 5470.56i −0.155323 + 0.269028i
\(746\) 6697.00 11599.5i 0.328679 0.569289i
\(747\) 0 0
\(748\) 7203.23 0.352107
\(749\) −35250.0 + 3207.56i −1.71963 + 0.156478i
\(750\) 0 0
\(751\) −12637.3 21888.4i −0.614036 1.06354i −0.990553 0.137132i \(-0.956212\pi\)
0.376517 0.926410i \(-0.377122\pi\)
\(752\) −5264.79 + 9118.88i −0.255302 + 0.442196i
\(753\) 0 0
\(754\) −1525.31 2641.92i −0.0736720 0.127604i
\(755\) −28505.4 −1.37406
\(756\) 0 0
\(757\) −23583.7 −1.13232 −0.566159 0.824296i \(-0.691571\pi\)
−0.566159 + 0.824296i \(0.691571\pi\)
\(758\) −11093.6 19214.6i −0.531578 0.920720i
\(759\) 0 0
\(760\) −19379.2 + 33565.7i −0.924942 + 1.60205i
\(761\) 8101.35 + 14032.0i 0.385905 + 0.668407i 0.991894 0.127066i \(-0.0405559\pi\)
−0.605989 + 0.795473i \(0.707223\pi\)
\(762\) 0 0
\(763\) 22113.4 + 31348.5i 1.04922 + 1.48741i
\(764\) −14675.3 −0.694939
\(765\) 0 0
\(766\) −6555.06 + 11353.7i −0.309196 + 0.535543i
\(767\) 4812.99 8336.34i 0.226580 0.392448i
\(768\) 0 0
\(769\) −18603.1 −0.872362 −0.436181 0.899859i \(-0.643669\pi\)
−0.436181 + 0.899859i \(0.643669\pi\)
\(770\) 16422.2 1494.33i 0.768590 0.0699377i
\(771\) 0 0
\(772\) 3329.12 + 5766.20i 0.155204 + 0.268821i
\(773\) −13640.7 + 23626.3i −0.634697 + 1.09933i 0.351883 + 0.936044i \(0.385542\pi\)
−0.986579 + 0.163283i \(0.947792\pi\)
\(774\) 0 0
\(775\) −8235.42 14264.2i −0.381709 0.661140i
\(776\) 22648.2 1.04771
\(777\) 0 0
\(778\) 12157.3 0.560231
\(779\) −15314.5 26525.4i −0.704361 1.21999i
\(780\) 0