Properties

Label 98.4.c.a.67.1
Level $98$
Weight $4$
Character 98.67
Analytic conductor $5.782$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.78218718056\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 98.67
Dual form 98.4.c.a.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.50000 + 4.33013i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-4.50000 - 7.79423i) q^{5} +10.0000 q^{6} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.50000 + 4.33013i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-4.50000 - 7.79423i) q^{5} +10.0000 q^{6} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-9.00000 + 15.5885i) q^{10} +(28.5000 - 49.3634i) q^{11} +(-10.0000 - 17.3205i) q^{12} +70.0000 q^{13} +45.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(25.5000 - 44.1673i) q^{17} +(2.00000 - 3.46410i) q^{18} +(2.50000 + 4.33013i) q^{19} +36.0000 q^{20} -114.000 q^{22} +(-34.5000 - 59.7558i) q^{23} +(-20.0000 + 34.6410i) q^{24} +(22.0000 - 38.1051i) q^{25} +(-70.0000 - 121.244i) q^{26} -145.000 q^{27} +114.000 q^{29} +(-45.0000 - 77.9423i) q^{30} +(11.5000 - 19.9186i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(142.500 + 246.817i) q^{33} -102.000 q^{34} -8.00000 q^{36} +(126.500 + 219.104i) q^{37} +(5.00000 - 8.66025i) q^{38} +(-175.000 + 303.109i) q^{39} +(-36.0000 - 62.3538i) q^{40} +42.0000 q^{41} -124.000 q^{43} +(114.000 + 197.454i) q^{44} +(9.00000 - 15.5885i) q^{45} +(-69.0000 + 119.512i) q^{46} +(100.500 + 174.071i) q^{47} +80.0000 q^{48} -88.0000 q^{50} +(127.500 + 220.836i) q^{51} +(-140.000 + 242.487i) q^{52} +(196.500 - 340.348i) q^{53} +(145.000 + 251.147i) q^{54} -513.000 q^{55} -25.0000 q^{57} +(-114.000 - 197.454i) q^{58} +(109.500 - 189.660i) q^{59} +(-90.0000 + 155.885i) q^{60} +(-354.500 - 614.012i) q^{61} -46.0000 q^{62} +64.0000 q^{64} +(-315.000 - 545.596i) q^{65} +(285.000 - 493.634i) q^{66} +(-209.500 + 362.865i) q^{67} +(102.000 + 176.669i) q^{68} +345.000 q^{69} -96.0000 q^{71} +(8.00000 + 13.8564i) q^{72} +(-156.500 + 271.066i) q^{73} +(253.000 - 438.209i) q^{74} +(110.000 + 190.526i) q^{75} -20.0000 q^{76} +700.000 q^{78} +(-230.500 - 399.238i) q^{79} +(-72.0000 + 124.708i) q^{80} +(335.500 - 581.103i) q^{81} +(-42.0000 - 72.7461i) q^{82} +588.000 q^{83} -459.000 q^{85} +(124.000 + 214.774i) q^{86} +(-285.000 + 493.634i) q^{87} +(228.000 - 394.908i) q^{88} +(-508.500 - 880.748i) q^{89} -36.0000 q^{90} +276.000 q^{92} +(57.5000 + 99.5929i) q^{93} +(201.000 - 348.142i) q^{94} +(22.5000 - 38.9711i) q^{95} +(-80.0000 - 138.564i) q^{96} +1834.00 q^{97} +114.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 5 q^{3} - 4 q^{4} - 9 q^{5} + 20 q^{6} + 16 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 5 q^{3} - 4 q^{4} - 9 q^{5} + 20 q^{6} + 16 q^{8} + 2 q^{9} - 18 q^{10} + 57 q^{11} - 20 q^{12} + 140 q^{13} + 90 q^{15} - 16 q^{16} + 51 q^{17} + 4 q^{18} + 5 q^{19} + 72 q^{20} - 228 q^{22} - 69 q^{23} - 40 q^{24} + 44 q^{25} - 140 q^{26} - 290 q^{27} + 228 q^{29} - 90 q^{30} + 23 q^{31} - 32 q^{32} + 285 q^{33} - 204 q^{34} - 16 q^{36} + 253 q^{37} + 10 q^{38} - 350 q^{39} - 72 q^{40} + 84 q^{41} - 248 q^{43} + 228 q^{44} + 18 q^{45} - 138 q^{46} + 201 q^{47} + 160 q^{48} - 176 q^{50} + 255 q^{51} - 280 q^{52} + 393 q^{53} + 290 q^{54} - 1026 q^{55} - 50 q^{57} - 228 q^{58} + 219 q^{59} - 180 q^{60} - 709 q^{61} - 92 q^{62} + 128 q^{64} - 630 q^{65} + 570 q^{66} - 419 q^{67} + 204 q^{68} + 690 q^{69} - 192 q^{71} + 16 q^{72} - 313 q^{73} + 506 q^{74} + 220 q^{75} - 40 q^{76} + 1400 q^{78} - 461 q^{79} - 144 q^{80} + 671 q^{81} - 84 q^{82} + 1176 q^{83} - 918 q^{85} + 248 q^{86} - 570 q^{87} + 456 q^{88} - 1017 q^{89} - 72 q^{90} + 552 q^{92} + 115 q^{93} + 402 q^{94} + 45 q^{95} - 160 q^{96} + 3668 q^{97} + 228 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) −2.50000 + 4.33013i −0.481125 + 0.833333i −0.999765 0.0216593i \(-0.993105\pi\)
0.518640 + 0.854993i \(0.326438\pi\)
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −4.50000 7.79423i −0.402492 0.697137i 0.591534 0.806280i \(-0.298523\pi\)
−0.994026 + 0.109143i \(0.965189\pi\)
\(6\) 10.0000 0.680414
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 1.00000 + 1.73205i 0.0370370 + 0.0641500i
\(10\) −9.00000 + 15.5885i −0.284605 + 0.492950i
\(11\) 28.5000 49.3634i 0.781188 1.35306i −0.150061 0.988677i \(-0.547947\pi\)
0.931250 0.364381i \(-0.118720\pi\)
\(12\) −10.0000 17.3205i −0.240563 0.416667i
\(13\) 70.0000 1.49342 0.746712 0.665148i \(-0.231631\pi\)
0.746712 + 0.665148i \(0.231631\pi\)
\(14\) 0 0
\(15\) 45.0000 0.774597
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 25.5000 44.1673i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 2.00000 3.46410i 0.0261891 0.0453609i
\(19\) 2.50000 + 4.33013i 0.0301863 + 0.0522842i 0.880724 0.473630i \(-0.157057\pi\)
−0.850538 + 0.525914i \(0.823723\pi\)
\(20\) 36.0000 0.402492
\(21\) 0 0
\(22\) −114.000 −1.10477
\(23\) −34.5000 59.7558i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) −20.0000 + 34.6410i −0.170103 + 0.294628i
\(25\) 22.0000 38.1051i 0.176000 0.304841i
\(26\) −70.0000 121.244i −0.528005 0.914531i
\(27\) −145.000 −1.03353
\(28\) 0 0
\(29\) 114.000 0.729975 0.364987 0.931012i \(-0.381073\pi\)
0.364987 + 0.931012i \(0.381073\pi\)
\(30\) −45.0000 77.9423i −0.273861 0.474342i
\(31\) 11.5000 19.9186i 0.0666278 0.115403i −0.830787 0.556590i \(-0.812109\pi\)
0.897415 + 0.441188i \(0.145443\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 142.500 + 246.817i 0.751699 + 1.30198i
\(34\) −102.000 −0.514496
\(35\) 0 0
\(36\) −8.00000 −0.0370370
\(37\) 126.500 + 219.104i 0.562067 + 0.973528i 0.997316 + 0.0732182i \(0.0233270\pi\)
−0.435249 + 0.900310i \(0.643340\pi\)
\(38\) 5.00000 8.66025i 0.0213449 0.0369705i
\(39\) −175.000 + 303.109i −0.718524 + 1.24452i
\(40\) −36.0000 62.3538i −0.142302 0.246475i
\(41\) 42.0000 0.159983 0.0799914 0.996796i \(-0.474511\pi\)
0.0799914 + 0.996796i \(0.474511\pi\)
\(42\) 0 0
\(43\) −124.000 −0.439763 −0.219882 0.975527i \(-0.570567\pi\)
−0.219882 + 0.975527i \(0.570567\pi\)
\(44\) 114.000 + 197.454i 0.390594 + 0.676529i
\(45\) 9.00000 15.5885i 0.0298142 0.0516398i
\(46\) −69.0000 + 119.512i −0.221163 + 0.383065i
\(47\) 100.500 + 174.071i 0.311903 + 0.540231i 0.978774 0.204941i \(-0.0657003\pi\)
−0.666871 + 0.745173i \(0.732367\pi\)
\(48\) 80.0000 0.240563
\(49\) 0 0
\(50\) −88.0000 −0.248902
\(51\) 127.500 + 220.836i 0.350070 + 0.606339i
\(52\) −140.000 + 242.487i −0.373356 + 0.646671i
\(53\) 196.500 340.348i 0.509271 0.882083i −0.490672 0.871345i \(-0.663249\pi\)
0.999942 0.0107383i \(-0.00341816\pi\)
\(54\) 145.000 + 251.147i 0.365407 + 0.632904i
\(55\) −513.000 −1.25769
\(56\) 0 0
\(57\) −25.0000 −0.0580935
\(58\) −114.000 197.454i −0.258085 0.447016i
\(59\) 109.500 189.660i 0.241622 0.418501i −0.719555 0.694436i \(-0.755654\pi\)
0.961176 + 0.275935i \(0.0889873\pi\)
\(60\) −90.0000 + 155.885i −0.193649 + 0.335410i
\(61\) −354.500 614.012i −0.744083 1.28879i −0.950622 0.310351i \(-0.899553\pi\)
0.206539 0.978438i \(-0.433780\pi\)
\(62\) −46.0000 −0.0942259
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −315.000 545.596i −0.601091 1.04112i
\(66\) 285.000 493.634i 0.531531 0.920639i
\(67\) −209.500 + 362.865i −0.382007 + 0.661656i −0.991349 0.131251i \(-0.958100\pi\)
0.609342 + 0.792908i \(0.291434\pi\)
\(68\) 102.000 + 176.669i 0.181902 + 0.315063i
\(69\) 345.000 0.601929
\(70\) 0 0
\(71\) −96.0000 −0.160466 −0.0802331 0.996776i \(-0.525566\pi\)
−0.0802331 + 0.996776i \(0.525566\pi\)
\(72\) 8.00000 + 13.8564i 0.0130946 + 0.0226805i
\(73\) −156.500 + 271.066i −0.250917 + 0.434601i −0.963779 0.266704i \(-0.914065\pi\)
0.712862 + 0.701305i \(0.247399\pi\)
\(74\) 253.000 438.209i 0.397441 0.688388i
\(75\) 110.000 + 190.526i 0.169356 + 0.293333i
\(76\) −20.0000 −0.0301863
\(77\) 0 0
\(78\) 700.000 1.01615
\(79\) −230.500 399.238i −0.328269 0.568579i 0.653899 0.756582i \(-0.273132\pi\)
−0.982169 + 0.188003i \(0.939799\pi\)
\(80\) −72.0000 + 124.708i −0.100623 + 0.174284i
\(81\) 335.500 581.103i 0.460219 0.797124i
\(82\) −42.0000 72.7461i −0.0565625 0.0979691i
\(83\) 588.000 0.777607 0.388804 0.921321i \(-0.372888\pi\)
0.388804 + 0.921321i \(0.372888\pi\)
\(84\) 0 0
\(85\) −459.000 −0.585712
\(86\) 124.000 + 214.774i 0.155480 + 0.269299i
\(87\) −285.000 + 493.634i −0.351209 + 0.608312i
\(88\) 228.000 394.908i 0.276192 0.478378i
\(89\) −508.500 880.748i −0.605628 1.04898i −0.991952 0.126615i \(-0.959589\pi\)
0.386324 0.922363i \(-0.373745\pi\)
\(90\) −36.0000 −0.0421637
\(91\) 0 0
\(92\) 276.000 0.312772
\(93\) 57.5000 + 99.5929i 0.0641126 + 0.111046i
\(94\) 201.000 348.142i 0.220549 0.382001i
\(95\) 22.5000 38.9711i 0.0242995 0.0420879i
\(96\) −80.0000 138.564i −0.0850517 0.147314i
\(97\) 1834.00 1.91974 0.959868 0.280451i \(-0.0904839\pi\)
0.959868 + 0.280451i \(0.0904839\pi\)
\(98\) 0 0
\(99\) 114.000 0.115732
\(100\) 88.0000 + 152.420i 0.0880000 + 0.152420i
\(101\) −142.500 + 246.817i −0.140389 + 0.243161i −0.927643 0.373468i \(-0.878169\pi\)
0.787254 + 0.616629i \(0.211502\pi\)
\(102\) 255.000 441.673i 0.247537 0.428746i
\(103\) −249.500 432.147i −0.238679 0.413405i 0.721656 0.692252i \(-0.243381\pi\)
−0.960336 + 0.278847i \(0.910048\pi\)
\(104\) 560.000 0.528005
\(105\) 0 0
\(106\) −786.000 −0.720218
\(107\) 553.500 + 958.690i 0.500083 + 0.866169i 1.00000 9.56665e-5i \(3.04516e-5\pi\)
−0.499917 + 0.866073i \(0.666636\pi\)
\(108\) 290.000 502.295i 0.258382 0.447531i
\(109\) −461.500 + 799.341i −0.405538 + 0.702413i −0.994384 0.105832i \(-0.966249\pi\)
0.588846 + 0.808246i \(0.299583\pi\)
\(110\) 513.000 + 888.542i 0.444660 + 0.770174i
\(111\) −1265.00 −1.08170
\(112\) 0 0
\(113\) 1542.00 1.28371 0.641855 0.766826i \(-0.278165\pi\)
0.641855 + 0.766826i \(0.278165\pi\)
\(114\) 25.0000 + 43.3013i 0.0205392 + 0.0355749i
\(115\) −310.500 + 537.802i −0.251776 + 0.436089i
\(116\) −228.000 + 394.908i −0.182494 + 0.316088i
\(117\) 70.0000 + 121.244i 0.0553120 + 0.0958032i
\(118\) −438.000 −0.341705
\(119\) 0 0
\(120\) 360.000 0.273861
\(121\) −959.000 1661.04i −0.720511 1.24796i
\(122\) −709.000 + 1228.02i −0.526146 + 0.911312i
\(123\) −105.000 + 181.865i −0.0769718 + 0.133319i
\(124\) 46.0000 + 79.6743i 0.0333139 + 0.0577013i
\(125\) −1521.00 −1.08834
\(126\) 0 0
\(127\) −2056.00 −1.43654 −0.718270 0.695765i \(-0.755066\pi\)
−0.718270 + 0.695765i \(0.755066\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 310.000 536.936i 0.211581 0.366469i
\(130\) −630.000 + 1091.19i −0.425036 + 0.736184i
\(131\) 1024.50 + 1774.49i 0.683290 + 1.18349i 0.973971 + 0.226673i \(0.0727848\pi\)
−0.290681 + 0.956820i \(0.593882\pi\)
\(132\) −1140.00 −0.751699
\(133\) 0 0
\(134\) 838.000 0.540240
\(135\) 652.500 + 1130.16i 0.415987 + 0.720511i
\(136\) 204.000 353.338i 0.128624 0.222783i
\(137\) 70.5000 122.110i 0.0439651 0.0761498i −0.843205 0.537591i \(-0.819334\pi\)
0.887171 + 0.461442i \(0.152668\pi\)
\(138\) −345.000 597.558i −0.212814 0.368605i
\(139\) −1484.00 −0.905548 −0.452774 0.891625i \(-0.649566\pi\)
−0.452774 + 0.891625i \(0.649566\pi\)
\(140\) 0 0
\(141\) −1005.00 −0.600257
\(142\) 96.0000 + 166.277i 0.0567334 + 0.0982651i
\(143\) 1995.00 3455.44i 1.16665 2.02069i
\(144\) 16.0000 27.7128i 0.00925926 0.0160375i
\(145\) −513.000 888.542i −0.293809 0.508892i
\(146\) 626.000 0.354850
\(147\) 0 0
\(148\) −1012.00 −0.562067
\(149\) 28.5000 + 49.3634i 0.0156699 + 0.0271410i 0.873754 0.486368i \(-0.161679\pi\)
−0.858084 + 0.513509i \(0.828345\pi\)
\(150\) 220.000 381.051i 0.119753 0.207418i
\(151\) −419.500 + 726.595i −0.226082 + 0.391586i −0.956644 0.291261i \(-0.905925\pi\)
0.730561 + 0.682847i \(0.239258\pi\)
\(152\) 20.0000 + 34.6410i 0.0106725 + 0.0184852i
\(153\) 102.000 0.0538968
\(154\) 0 0
\(155\) −207.000 −0.107269
\(156\) −700.000 1212.44i −0.359262 0.622260i
\(157\) −1416.50 + 2453.45i −0.720057 + 1.24718i 0.240919 + 0.970545i \(0.422551\pi\)
−0.960976 + 0.276631i \(0.910782\pi\)
\(158\) −461.000 + 798.475i −0.232121 + 0.402046i
\(159\) 982.500 + 1701.74i 0.490046 + 0.848785i
\(160\) 288.000 0.142302
\(161\) 0 0
\(162\) −1342.00 −0.650849
\(163\) 1155.50 + 2001.38i 0.555250 + 0.961721i 0.997884 + 0.0650188i \(0.0207107\pi\)
−0.442634 + 0.896702i \(0.645956\pi\)
\(164\) −84.0000 + 145.492i −0.0399957 + 0.0692746i
\(165\) 1282.50 2221.36i 0.605106 1.04807i
\(166\) −588.000 1018.45i −0.274926 0.476185i
\(167\) −1260.00 −0.583843 −0.291921 0.956442i \(-0.594295\pi\)
−0.291921 + 0.956442i \(0.594295\pi\)
\(168\) 0 0
\(169\) 2703.00 1.23031
\(170\) 459.000 + 795.011i 0.207081 + 0.358674i
\(171\) −5.00000 + 8.66025i −0.00223602 + 0.00387290i
\(172\) 248.000 429.549i 0.109941 0.190423i
\(173\) 1633.50 + 2829.30i 0.717877 + 1.24340i 0.961839 + 0.273615i \(0.0882193\pi\)
−0.243962 + 0.969785i \(0.578447\pi\)
\(174\) 1140.00 0.496685
\(175\) 0 0
\(176\) −912.000 −0.390594
\(177\) 547.500 + 948.298i 0.232501 + 0.402703i
\(178\) −1017.00 + 1761.50i −0.428244 + 0.741740i
\(179\) −643.500 + 1114.57i −0.268701 + 0.465403i −0.968527 0.248910i \(-0.919928\pi\)
0.699826 + 0.714314i \(0.253261\pi\)
\(180\) 36.0000 + 62.3538i 0.0149071 + 0.0258199i
\(181\) 2674.00 1.09810 0.549052 0.835788i \(-0.314989\pi\)
0.549052 + 0.835788i \(0.314989\pi\)
\(182\) 0 0
\(183\) 3545.00 1.43199
\(184\) −276.000 478.046i −0.110581 0.191533i
\(185\) 1138.50 1971.94i 0.452455 0.783675i
\(186\) 115.000 199.186i 0.0453345 0.0785216i
\(187\) −1453.50 2517.54i −0.568398 0.984494i
\(188\) −804.000 −0.311903
\(189\) 0 0
\(190\) −90.0000 −0.0343647
\(191\) −2092.50 3624.32i −0.792712 1.37302i −0.924282 0.381711i \(-0.875335\pi\)
0.131570 0.991307i \(-0.457998\pi\)
\(192\) −160.000 + 277.128i −0.0601407 + 0.104167i
\(193\) 42.5000 73.6122i 0.0158509 0.0274545i −0.857991 0.513664i \(-0.828288\pi\)
0.873842 + 0.486210i \(0.161621\pi\)
\(194\) −1834.00 3176.58i −0.678730 1.17559i
\(195\) 3150.00 1.15680
\(196\) 0 0
\(197\) −390.000 −0.141047 −0.0705237 0.997510i \(-0.522467\pi\)
−0.0705237 + 0.997510i \(0.522467\pi\)
\(198\) −114.000 197.454i −0.0409173 0.0708709i
\(199\) −1416.50 + 2453.45i −0.504588 + 0.873972i 0.495398 + 0.868666i \(0.335022\pi\)
−0.999986 + 0.00530596i \(0.998311\pi\)
\(200\) 176.000 304.841i 0.0622254 0.107778i
\(201\) −1047.50 1814.32i −0.367587 0.636679i
\(202\) 570.000 0.198540
\(203\) 0 0
\(204\) −1020.00 −0.350070
\(205\) −189.000 327.358i −0.0643919 0.111530i
\(206\) −499.000 + 864.293i −0.168772 + 0.292321i
\(207\) 69.0000 119.512i 0.0231683 0.0401286i
\(208\) −560.000 969.948i −0.186678 0.323336i
\(209\) 285.000 0.0943247
\(210\) 0 0
\(211\) −124.000 −0.0404574 −0.0202287 0.999795i \(-0.506439\pi\)
−0.0202287 + 0.999795i \(0.506439\pi\)
\(212\) 786.000 + 1361.39i 0.254635 + 0.441041i
\(213\) 240.000 415.692i 0.0772044 0.133722i
\(214\) 1107.00 1917.38i 0.353612 0.612474i
\(215\) 558.000 + 966.484i 0.177001 + 0.306575i
\(216\) −1160.00 −0.365407
\(217\) 0 0
\(218\) 1846.00 0.573518
\(219\) −782.500 1355.33i −0.241445 0.418195i
\(220\) 1026.00 1777.08i 0.314422 0.544595i
\(221\) 1785.00 3091.71i 0.543313 0.941045i
\(222\) 1265.00 + 2191.04i 0.382438 + 0.662402i
\(223\) −56.0000 −0.0168163 −0.00840816 0.999965i \(-0.502676\pi\)
−0.00840816 + 0.999965i \(0.502676\pi\)
\(224\) 0 0
\(225\) 88.0000 0.0260741
\(226\) −1542.00 2670.82i −0.453860 0.786108i
\(227\) −1528.50 + 2647.44i −0.446917 + 0.774083i −0.998184 0.0602465i \(-0.980811\pi\)
0.551267 + 0.834329i \(0.314145\pi\)
\(228\) 50.0000 86.6025i 0.0145234 0.0251552i
\(229\) −480.500 832.250i −0.138656 0.240160i 0.788332 0.615250i \(-0.210945\pi\)
−0.926988 + 0.375090i \(0.877612\pi\)
\(230\) 1242.00 0.356065
\(231\) 0 0
\(232\) 912.000 0.258085
\(233\) 1414.50 + 2449.99i 0.397712 + 0.688858i 0.993443 0.114326i \(-0.0364709\pi\)
−0.595731 + 0.803184i \(0.703138\pi\)
\(234\) 140.000 242.487i 0.0391115 0.0677431i
\(235\) 904.500 1566.64i 0.251077 0.434878i
\(236\) 438.000 + 758.638i 0.120811 + 0.209251i
\(237\) 2305.00 0.631755
\(238\) 0 0
\(239\) −3540.00 −0.958090 −0.479045 0.877790i \(-0.659017\pi\)
−0.479045 + 0.877790i \(0.659017\pi\)
\(240\) −360.000 623.538i −0.0968246 0.167705i
\(241\) 2615.50 4530.18i 0.699084 1.21085i −0.269701 0.962944i \(-0.586925\pi\)
0.968785 0.247904i \(-0.0797419\pi\)
\(242\) −1918.00 + 3322.07i −0.509478 + 0.882442i
\(243\) −280.000 484.974i −0.0739177 0.128029i
\(244\) 2836.00 0.744083
\(245\) 0 0
\(246\) 420.000 0.108855
\(247\) 175.000 + 303.109i 0.0450809 + 0.0780824i
\(248\) 92.0000 159.349i 0.0235565 0.0408010i
\(249\) −1470.00 + 2546.11i −0.374126 + 0.648006i
\(250\) 1521.00 + 2634.45i 0.384786 + 0.666469i
\(251\) −5040.00 −1.26742 −0.633709 0.773571i \(-0.718468\pi\)
−0.633709 + 0.773571i \(0.718468\pi\)
\(252\) 0 0
\(253\) −3933.00 −0.977334
\(254\) 2056.00 + 3561.10i 0.507893 + 0.879697i
\(255\) 1147.50 1987.53i 0.281801 0.488094i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −718.500 1244.48i −0.174392 0.302056i 0.765559 0.643366i \(-0.222463\pi\)
−0.939951 + 0.341310i \(0.889129\pi\)
\(258\) −1240.00 −0.299221
\(259\) 0 0
\(260\) 2520.00 0.601091
\(261\) 114.000 + 197.454i 0.0270361 + 0.0468279i
\(262\) 2049.00 3548.97i 0.483159 0.836856i
\(263\) 1162.50 2013.51i 0.272558 0.472085i −0.696958 0.717112i \(-0.745464\pi\)
0.969516 + 0.245027i \(0.0787969\pi\)
\(264\) 1140.00 + 1974.54i 0.265766 + 0.460320i
\(265\) −3537.00 −0.819910
\(266\) 0 0
\(267\) 5085.00 1.16553
\(268\) −838.000 1451.46i −0.191004 0.330828i
\(269\) −1192.50 + 2065.47i −0.270290 + 0.468156i −0.968936 0.247311i \(-0.920453\pi\)
0.698646 + 0.715467i \(0.253786\pi\)
\(270\) 1305.00 2260.33i 0.294147 0.509478i
\(271\) −165.500 286.654i −0.0370975 0.0642547i 0.846881 0.531783i \(-0.178478\pi\)
−0.883978 + 0.467528i \(0.845145\pi\)
\(272\) −816.000 −0.181902
\(273\) 0 0
\(274\) −282.000 −0.0621761
\(275\) −1254.00 2171.99i −0.274978 0.476276i
\(276\) −690.000 + 1195.12i −0.150482 + 0.260643i
\(277\) −2435.50 + 4218.41i −0.528285 + 0.915017i 0.471171 + 0.882042i \(0.343831\pi\)
−0.999456 + 0.0329750i \(0.989502\pi\)
\(278\) 1484.00 + 2570.36i 0.320160 + 0.554533i
\(279\) 46.0000 0.00987078
\(280\) 0 0
\(281\) −7026.00 −1.49159 −0.745794 0.666177i \(-0.767930\pi\)
−0.745794 + 0.666177i \(0.767930\pi\)
\(282\) 1005.00 + 1740.71i 0.212223 + 0.367581i
\(283\) −2676.50 + 4635.83i −0.562196 + 0.973752i 0.435109 + 0.900378i \(0.356710\pi\)
−0.997305 + 0.0733738i \(0.976623\pi\)
\(284\) 192.000 332.554i 0.0401166 0.0694839i
\(285\) 112.500 + 194.856i 0.0233822 + 0.0404991i
\(286\) −7980.00 −1.64989
\(287\) 0 0
\(288\) −64.0000 −0.0130946
\(289\) 1156.00 + 2002.25i 0.235294 + 0.407541i
\(290\) −1026.00 + 1777.08i −0.207754 + 0.359841i
\(291\) −4585.00 + 7941.45i −0.923634 + 1.59978i
\(292\) −626.000 1084.26i −0.125458 0.217300i
\(293\) −4158.00 −0.829054 −0.414527 0.910037i \(-0.636053\pi\)
−0.414527 + 0.910037i \(0.636053\pi\)
\(294\) 0 0
\(295\) −1971.00 −0.389004
\(296\) 1012.00 + 1752.84i 0.198721 + 0.344194i
\(297\) −4132.50 + 7157.70i −0.807380 + 1.39842i
\(298\) 57.0000 98.7269i 0.0110803 0.0191916i
\(299\) −2415.00 4182.90i −0.467101 0.809042i
\(300\) −880.000 −0.169356
\(301\) 0 0
\(302\) 1678.00 0.319729
\(303\) −712.500 1234.09i −0.135089 0.233982i
\(304\) 40.0000 69.2820i 0.00754657 0.0130710i
\(305\) −3190.50 + 5526.11i −0.598975 + 1.03746i
\(306\) −102.000 176.669i −0.0190554 0.0330049i
\(307\) 9604.00 1.78544 0.892719 0.450615i \(-0.148795\pi\)
0.892719 + 0.450615i \(0.148795\pi\)
\(308\) 0 0
\(309\) 2495.00 0.459338
\(310\) 207.000 + 358.535i 0.0379252 + 0.0656884i
\(311\) 5065.50 8773.70i 0.923595 1.59971i 0.129791 0.991541i \(-0.458570\pi\)
0.793805 0.608173i \(-0.208097\pi\)
\(312\) −1400.00 + 2424.87i −0.254037 + 0.440004i
\(313\) 5399.50 + 9352.21i 0.975073 + 1.68888i 0.679695 + 0.733495i \(0.262112\pi\)
0.295378 + 0.955380i \(0.404554\pi\)
\(314\) 5666.00 1.01831
\(315\) 0 0
\(316\) 1844.00 0.328269
\(317\) −265.500 459.859i −0.0470409 0.0814772i 0.841546 0.540185i \(-0.181646\pi\)
−0.888587 + 0.458708i \(0.848312\pi\)
\(318\) 1965.00 3403.48i 0.346515 0.600181i
\(319\) 3249.00 5627.43i 0.570248 0.987698i
\(320\) −288.000 498.831i −0.0503115 0.0871421i
\(321\) −5535.00 −0.962410
\(322\) 0 0
\(323\) 255.000 0.0439275
\(324\) 1342.00 + 2324.41i 0.230110 + 0.398562i
\(325\) 1540.00 2667.36i 0.262843 0.455257i
\(326\) 2311.00 4002.77i 0.392621 0.680040i
\(327\) −2307.50 3996.71i −0.390229 0.675897i
\(328\) 336.000 0.0565625
\(329\) 0 0
\(330\) −5130.00 −0.855749
\(331\) 3507.50 + 6075.17i 0.582446 + 1.00883i 0.995189 + 0.0979784i \(0.0312376\pi\)
−0.412743 + 0.910848i \(0.635429\pi\)
\(332\) −1176.00 + 2036.89i −0.194402 + 0.336714i
\(333\) −253.000 + 438.209i −0.0416346 + 0.0721132i
\(334\) 1260.00 + 2182.38i 0.206420 + 0.357529i
\(335\) 3771.00 0.615020
\(336\) 0 0
\(337\) 8990.00 1.45316 0.726582 0.687079i \(-0.241108\pi\)
0.726582 + 0.687079i \(0.241108\pi\)
\(338\) −2703.00 4681.73i −0.434982 0.753410i
\(339\) −3855.00 + 6677.06i −0.617625 + 1.06976i
\(340\) 918.000 1590.02i 0.146428 0.253621i
\(341\) −655.500 1135.36i −0.104098 0.180303i
\(342\) 20.0000 0.00316221
\(343\) 0 0
\(344\) −992.000 −0.155480
\(345\) −1552.50 2689.01i −0.242272 0.419627i
\(346\) 3267.00 5658.61i 0.507616 0.879216i
\(347\) 4354.50 7542.22i 0.673665 1.16682i −0.303192 0.952929i \(-0.598052\pi\)
0.976857 0.213893i \(-0.0686143\pi\)
\(348\) −1140.00 1974.54i −0.175605 0.304156i
\(349\) −6482.00 −0.994193 −0.497097 0.867695i \(-0.665601\pi\)
−0.497097 + 0.867695i \(0.665601\pi\)
\(350\) 0 0
\(351\) −10150.0 −1.54350
\(352\) 912.000 + 1579.63i 0.138096 + 0.239189i
\(353\) −1066.50 + 1847.23i −0.160805 + 0.278522i −0.935158 0.354232i \(-0.884742\pi\)
0.774353 + 0.632754i \(0.218076\pi\)
\(354\) 1095.00 1896.60i 0.164403 0.284754i
\(355\) 432.000 + 748.246i 0.0645864 + 0.111867i
\(356\) 4068.00 0.605628
\(357\) 0 0
\(358\) 2574.00 0.380000
\(359\) −1924.50 3333.33i −0.282928 0.490046i 0.689176 0.724594i \(-0.257972\pi\)
−0.972105 + 0.234548i \(0.924639\pi\)
\(360\) 72.0000 124.708i 0.0105409 0.0182574i
\(361\) 3417.00 5918.42i 0.498178 0.862869i
\(362\) −2674.00 4631.50i −0.388238 0.672449i
\(363\) 9590.00 1.38662
\(364\) 0 0
\(365\) 2817.00 0.403969
\(366\) −3545.00 6140.12i −0.506284 0.876910i
\(367\) 3245.50 5621.37i 0.461618 0.799545i −0.537424 0.843312i \(-0.680603\pi\)
0.999042 + 0.0437668i \(0.0139358\pi\)
\(368\) −552.000 + 956.092i −0.0781929 + 0.135434i
\(369\) 42.0000 + 72.7461i 0.00592529 + 0.0102629i
\(370\) −4554.00 −0.639868
\(371\) 0 0
\(372\) −460.000 −0.0641126
\(373\) −461.500 799.341i −0.0640632 0.110961i 0.832215 0.554453i \(-0.187073\pi\)
−0.896278 + 0.443493i \(0.853739\pi\)
\(374\) −2907.00 + 5035.07i −0.401918 + 0.696143i
\(375\) 3802.50 6586.12i 0.523627 0.906949i
\(376\) 804.000 + 1392.57i 0.110274 + 0.191001i
\(377\) 7980.00 1.09016
\(378\) 0 0
\(379\) 6344.00 0.859814 0.429907 0.902873i \(-0.358546\pi\)
0.429907 + 0.902873i \(0.358546\pi\)
\(380\) 90.0000 + 155.885i 0.0121497 + 0.0210440i
\(381\) 5140.00 8902.74i 0.691155 1.19712i
\(382\) −4185.00 + 7248.63i −0.560532 + 0.970870i
\(383\) −2503.50 4336.19i −0.334002 0.578509i 0.649290 0.760541i \(-0.275066\pi\)
−0.983293 + 0.182032i \(0.941733\pi\)
\(384\) 640.000 0.0850517
\(385\) 0 0
\(386\) −170.000 −0.0224165
\(387\) −124.000 214.774i −0.0162875 0.0282108i
\(388\) −3668.00 + 6353.16i −0.479934 + 0.831270i
\(389\) −6145.50 + 10644.3i −0.801001 + 1.38737i 0.117958 + 0.993019i \(0.462365\pi\)
−0.918958 + 0.394355i \(0.870968\pi\)
\(390\) −3150.00 5455.96i −0.408991 0.708393i
\(391\) −3519.00 −0.455150
\(392\) 0 0
\(393\) −10245.0 −1.31499
\(394\) 390.000 + 675.500i 0.0498678 + 0.0863736i
\(395\) −2074.50 + 3593.14i −0.264252 + 0.457697i
\(396\) −228.000 + 394.908i −0.0289329 + 0.0501133i
\(397\) 443.500 + 768.165i 0.0560671 + 0.0971110i 0.892697 0.450658i \(-0.148811\pi\)
−0.836630 + 0.547769i \(0.815477\pi\)
\(398\) 5666.00 0.713595
\(399\) 0 0
\(400\) −704.000 −0.0880000
\(401\) −5977.50 10353.3i −0.744394 1.28933i −0.950477 0.310794i \(-0.899405\pi\)
0.206083 0.978535i \(-0.433928\pi\)
\(402\) −2095.00 + 3628.65i −0.259923 + 0.450200i
\(403\) 805.000 1394.30i 0.0995035 0.172345i
\(404\) −570.000 987.269i −0.0701945 0.121580i
\(405\) −6039.00 −0.740939
\(406\) 0 0
\(407\) 14421.0 1.75632
\(408\) 1020.00 + 1766.69i 0.123768 + 0.214373i
\(409\) −1710.50 + 2962.67i −0.206794 + 0.358178i −0.950703 0.310103i \(-0.899636\pi\)
0.743909 + 0.668281i \(0.232970\pi\)
\(410\) −378.000 + 654.715i −0.0455319 + 0.0788636i
\(411\) 352.500 + 610.548i 0.0423055 + 0.0732752i
\(412\) 1996.00 0.238679
\(413\) 0 0
\(414\) −276.000 −0.0327649
\(415\) −2646.00 4583.01i −0.312981 0.542099i
\(416\) −1120.00 + 1939.90i −0.132001 + 0.228633i
\(417\) 3710.00 6425.91i 0.435682 0.754624i
\(418\) −285.000 493.634i −0.0333488 0.0577618i
\(419\) 5460.00 0.636607 0.318304 0.947989i \(-0.396887\pi\)
0.318304 + 0.947989i \(0.396887\pi\)
\(420\) 0 0
\(421\) 7730.00 0.894863 0.447431 0.894318i \(-0.352339\pi\)
0.447431 + 0.894318i \(0.352339\pi\)
\(422\) 124.000 + 214.774i 0.0143039 + 0.0247750i
\(423\) −201.000 + 348.142i −0.0231039 + 0.0400171i
\(424\) 1572.00 2722.78i 0.180054 0.311863i
\(425\) −1122.00 1943.36i −0.128059 0.221804i
\(426\) −960.000 −0.109183
\(427\) 0 0
\(428\) −4428.00 −0.500083
\(429\) 9975.00 + 17277.2i 1.12260 + 1.94441i
\(430\) 1116.00 1932.97i 0.125159 0.216781i
\(431\) 5656.50 9797.35i 0.632167 1.09495i −0.354941 0.934889i \(-0.615499\pi\)
0.987108 0.160057i \(-0.0511677\pi\)
\(432\) 1160.00 + 2009.18i 0.129191 + 0.223765i
\(433\) −4214.00 −0.467695 −0.233847 0.972273i \(-0.575132\pi\)
−0.233847 + 0.972273i \(0.575132\pi\)
\(434\) 0 0
\(435\) 5130.00 0.565436
\(436\) −1846.00 3197.37i −0.202769 0.351207i
\(437\) 172.500 298.779i 0.0188828 0.0327060i
\(438\) −1565.00 + 2710.66i −0.170727 + 0.295708i
\(439\) 8276.50 + 14335.3i 0.899808 + 1.55851i 0.827739 + 0.561114i \(0.189627\pi\)
0.0720696 + 0.997400i \(0.477040\pi\)
\(440\) −4104.00 −0.444660
\(441\) 0 0
\(442\) −7140.00 −0.768360
\(443\) 8197.50 + 14198.5i 0.879176 + 1.52278i 0.852247 + 0.523140i \(0.175240\pi\)
0.0269294 + 0.999637i \(0.491427\pi\)
\(444\) 2530.00 4382.09i 0.270425 0.468389i
\(445\) −4576.50 + 7926.73i −0.487521 + 0.844411i
\(446\) 56.0000 + 96.9948i 0.00594546 + 0.0102978i
\(447\) −285.000 −0.0301567
\(448\) 0 0
\(449\) −15090.0 −1.58606 −0.793030 0.609182i \(-0.791498\pi\)
−0.793030 + 0.609182i \(0.791498\pi\)
\(450\) −88.0000 152.420i −0.00921858 0.0159670i
\(451\) 1197.00 2073.26i 0.124977 0.216466i
\(452\) −3084.00 + 5341.64i −0.320927 + 0.555862i
\(453\) −2097.50 3632.98i −0.217548 0.376804i
\(454\) 6114.00 0.632036
\(455\) 0 0
\(456\) −200.000 −0.0205392
\(457\) 7392.50 + 12804.2i 0.756688 + 1.31062i 0.944531 + 0.328423i \(0.106517\pi\)
−0.187842 + 0.982199i \(0.560149\pi\)
\(458\) −961.000 + 1664.50i −0.0980449 + 0.169819i
\(459\) −3697.50 + 6404.26i −0.376001 + 0.651253i
\(460\) −1242.00 2151.21i −0.125888 0.218045i
\(461\) −2898.00 −0.292784 −0.146392 0.989227i \(-0.546766\pi\)
−0.146392 + 0.989227i \(0.546766\pi\)
\(462\) 0 0
\(463\) 464.000 0.0465743 0.0232872 0.999729i \(-0.492587\pi\)
0.0232872 + 0.999729i \(0.492587\pi\)
\(464\) −912.000 1579.63i −0.0912468 0.158044i
\(465\) 517.500 896.336i 0.0516097 0.0893905i
\(466\) 2829.00 4899.97i 0.281225 0.487096i
\(467\) 2116.50 + 3665.89i 0.209721 + 0.363248i 0.951627 0.307256i \(-0.0994109\pi\)
−0.741905 + 0.670505i \(0.766078\pi\)
\(468\) −560.000 −0.0553120
\(469\) 0 0
\(470\) −3618.00 −0.355076
\(471\) −7082.50 12267.2i −0.692876 1.20010i
\(472\) 876.000 1517.28i 0.0854262 0.147963i
\(473\) −3534.00 + 6121.07i −0.343538 + 0.595025i
\(474\) −2305.00 3992.38i −0.223359 0.386869i
\(475\) 220.000 0.0212511
\(476\) 0 0
\(477\) 786.000 0.0754475
\(478\) 3540.00 + 6131.46i 0.338736 + 0.586708i
\(479\) 1369.50 2372.04i 0.130635 0.226266i −0.793287 0.608848i \(-0.791632\pi\)
0.923921 + 0.382582i \(0.124965\pi\)
\(480\) −720.000 + 1247.08i −0.0684653 + 0.118585i
\(481\) 8855.00 + 15337.3i 0.839404 + 1.45389i
\(482\) −10462.0 −0.988654
\(483\) 0 0
\(484\) 7672.00 0.720511
\(485\) −8253.00 14294.6i −0.772679 1.33832i
\(486\) −560.000 + 969.948i −0.0522677 + 0.0905304i
\(487\) −8525.50 + 14766.6i −0.793280 + 1.37400i 0.130646 + 0.991429i \(0.458295\pi\)
−0.923926 + 0.382572i \(0.875038\pi\)
\(488\) −2836.00 4912.10i −0.263073 0.455656i
\(489\) −11555.0 −1.06858
\(490\) 0 0
\(491\) −4296.00 −0.394859 −0.197429 0.980317i \(-0.563259\pi\)
−0.197429 + 0.980317i \(0.563259\pi\)
\(492\) −420.000 727.461i −0.0384859 0.0666595i
\(493\) 2907.00 5035.07i 0.265567 0.459976i
\(494\) 350.000 606.218i 0.0318770 0.0552126i
\(495\) −513.000 888.542i −0.0465811 0.0806808i
\(496\) −368.000 −0.0333139
\(497\) 0 0
\(498\) 5880.00 0.529095
\(499\) −1700.50 2945.35i −0.152555 0.264233i 0.779611 0.626264i \(-0.215417\pi\)
−0.932166 + 0.362031i \(0.882083\pi\)
\(500\) 3042.00 5268.90i 0.272085 0.471265i
\(501\) 3150.00 5455.96i 0.280901 0.486536i
\(502\) 5040.00 + 8729.54i 0.448100 + 0.776132i
\(503\) −16800.0 −1.48921 −0.744607 0.667503i \(-0.767363\pi\)
−0.744607 + 0.667503i \(0.767363\pi\)
\(504\) 0 0
\(505\) 2565.00 0.226022
\(506\) 3933.00 + 6812.16i 0.345540 + 0.598493i
\(507\) −6757.50 + 11704.3i −0.591935 + 1.02526i
\(508\) 4112.00 7122.19i 0.359135 0.622040i
\(509\) 919.500 + 1592.62i 0.0800710 + 0.138687i 0.903280 0.429051i \(-0.141152\pi\)
−0.823209 + 0.567738i \(0.807819\pi\)
\(510\) −4590.00 −0.398527
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) −362.500 627.868i −0.0311984 0.0540372i
\(514\) −1437.00 + 2488.96i −0.123314 + 0.213586i
\(515\) −2245.50 + 3889.32i −0.192133 + 0.332784i
\(516\) 1240.00 + 2147.74i 0.105791 + 0.183235i
\(517\) 11457.0 0.974620
\(518\) 0 0
\(519\) −16335.0 −1.38155
\(520\) −2520.00 4364.77i −0.212518 0.368092i
\(521\) 151.500 262.406i 0.0127396 0.0220656i −0.859585 0.510992i \(-0.829278\pi\)
0.872325 + 0.488927i \(0.162611\pi\)
\(522\) 228.000 394.908i 0.0191174 0.0331123i
\(523\) −10833.5 18764.2i −0.905767 1.56883i −0.819885 0.572528i \(-0.805963\pi\)
−0.0858815 0.996305i \(-0.527371\pi\)
\(524\) −8196.00 −0.683290
\(525\) 0 0
\(526\) −4650.00 −0.385456
\(527\) −586.500 1015.85i −0.0484788 0.0839678i
\(528\) 2280.00 3949.08i 0.187925 0.325495i
\(529\) 3703.00 6413.78i 0.304348 0.527146i
\(530\) 3537.00 + 6126.26i 0.289882 + 0.502090i
\(531\) 438.000 0.0357958
\(532\) 0 0
\(533\) 2940.00 0.238922
\(534\) −5085.00 8807.48i −0.412078 0.713739i
\(535\) 4981.50 8628.21i 0.402559 0.697253i
\(536\) −1676.00 + 2902.92i −0.135060 + 0.233931i
\(537\) −3217.50 5572.87i −0.258557 0.447835i
\(538\) 4770.00 0.382248
\(539\) 0 0
\(540\) −5220.00 −0.415987
\(541\) −2519.50 4363.90i −0.200225 0.346800i 0.748376 0.663275i \(-0.230834\pi\)
−0.948601 + 0.316475i \(0.897501\pi\)
\(542\) −331.000 + 573.309i −0.0262319 + 0.0454349i
\(543\) −6685.00 + 11578.8i −0.528326 + 0.915087i
\(544\) 816.000 + 1413.35i 0.0643120 + 0.111392i
\(545\) 8307.00 0.652904
\(546\) 0 0
\(547\) −2392.00 −0.186974 −0.0934868 0.995621i \(-0.529801\pi\)
−0.0934868 + 0.995621i \(0.529801\pi\)
\(548\) 282.000 + 488.438i 0.0219826 + 0.0380749i
\(549\) 709.000 1228.02i 0.0551173 0.0954659i
\(550\) −2508.00 + 4343.98i −0.194439 + 0.336778i
\(551\) 285.000 + 493.634i 0.0220352 + 0.0381661i
\(552\) 2760.00 0.212814
\(553\) 0 0
\(554\) 9742.00 0.747108
\(555\) 5692.50 + 9859.70i 0.435375 + 0.754092i
\(556\) 2968.00 5140.73i 0.226387 0.392114i
\(557\) 11074.5 19181.6i 0.842445 1.45916i −0.0453775 0.998970i \(-0.514449\pi\)
0.887822 0.460187i \(-0.152218\pi\)
\(558\) −46.0000 79.6743i −0.00348985 0.00604459i
\(559\) −8680.00 −0.656753
\(560\) 0 0
\(561\) 14535.0 1.09388
\(562\) 7026.00 + 12169.4i 0.527356 + 0.913407i
\(563\) −4174.50 + 7230.45i −0.312494 + 0.541256i −0.978902 0.204332i \(-0.934498\pi\)
0.666408 + 0.745588i \(0.267831\pi\)
\(564\) 2010.00 3481.42i 0.150064 0.259919i
\(565\) −6939.00 12018.7i −0.516683 0.894921i
\(566\) 10706.0 0.795065
\(567\) 0 0
\(568\) −768.000 −0.0567334
\(569\) 7672.50 + 13289.2i 0.565286 + 0.979105i 0.997023 + 0.0771050i \(0.0245677\pi\)
−0.431737 + 0.902000i \(0.642099\pi\)
\(570\) 225.000 389.711i 0.0165337 0.0286372i
\(571\) 5796.50 10039.8i 0.424827 0.735821i −0.571578 0.820548i \(-0.693668\pi\)
0.996404 + 0.0847268i \(0.0270017\pi\)
\(572\) 7980.00 + 13821.8i 0.583323 + 1.01034i
\(573\) 20925.0 1.52557
\(574\) 0 0
\(575\) −3036.00 −0.220191
\(576\) 64.0000 + 110.851i 0.00462963 + 0.00801875i
\(577\) −7296.50 + 12637.9i −0.526442 + 0.911825i 0.473083 + 0.881018i \(0.343141\pi\)
−0.999525 + 0.0308071i \(0.990192\pi\)
\(578\) 2312.00 4004.50i 0.166378 0.288175i
\(579\) 212.500 + 368.061i 0.0152525 + 0.0264181i
\(580\) 4104.00 0.293809
\(581\) 0 0
\(582\) 18340.0 1.30622
\(583\) −11200.5 19399.8i −0.795673 1.37815i
\(584\) −1252.00 + 2168.53i −0.0887125 + 0.153655i
\(585\) 630.000 1091.19i 0.0445253 0.0771201i
\(586\) 4158.00 + 7201.87i 0.293115 + 0.507690i
\(587\) 15372.0 1.08087 0.540435 0.841386i \(-0.318260\pi\)
0.540435 + 0.841386i \(0.318260\pi\)
\(588\) 0 0
\(589\) 115.000 0.00804498
\(590\) 1971.00 + 3413.87i 0.137534 + 0.238215i
\(591\) 975.000 1688.75i 0.0678615 0.117540i
\(592\) 2024.00 3505.67i 0.140517 0.243382i
\(593\) −7186.50 12447.4i −0.497663 0.861978i 0.502333 0.864674i \(-0.332475\pi\)
−0.999996 + 0.00269639i \(0.999142\pi\)
\(594\) 16530.0 1.14181
\(595\) 0 0
\(596\) −228.000 −0.0156699
\(597\) −7082.50 12267.2i −0.485540 0.840980i
\(598\) −4830.00 + 8365.81i −0.330290 + 0.572079i
\(599\) −1273.50 + 2205.77i −0.0868678 + 0.150459i −0.906186 0.422880i \(-0.861019\pi\)
0.819318 + 0.573340i \(0.194352\pi\)
\(600\) 880.000 + 1524.20i 0.0598764 + 0.103709i
\(601\) 7042.00 0.477952 0.238976 0.971025i \(-0.423188\pi\)
0.238976 + 0.971025i \(0.423188\pi\)
\(602\) 0 0
\(603\) −838.000 −0.0565937
\(604\) −1678.00 2906.38i −0.113041 0.195793i
\(605\) −8631.00 + 14949.3i −0.580000 + 1.00459i
\(606\) −1425.00 + 2468.17i −0.0955226 + 0.165450i
\(607\) −11295.5 19564.4i −0.755305 1.30823i −0.945223 0.326427i \(-0.894155\pi\)
0.189917 0.981800i \(-0.439178\pi\)
\(608\) −160.000 −0.0106725
\(609\) 0 0
\(610\) 12762.0 0.847079
\(611\) 7035.00 + 12185.0i 0.465803 + 0.806794i
\(612\) −204.000 + 353.338i −0.0134742 + 0.0233380i
\(613\) 4242.50 7348.23i 0.279532 0.484163i −0.691737 0.722150i \(-0.743154\pi\)
0.971268 + 0.237987i \(0.0764874\pi\)
\(614\) −9604.00 16634.6i −0.631247 1.09335i
\(615\) 1890.00 0.123922
\(616\) 0 0
\(617\) −18282.0 −1.19288 −0.596439 0.802658i \(-0.703418\pi\)
−0.596439 + 0.802658i \(0.703418\pi\)
\(618\) −2495.00 4321.47i −0.162401 0.281286i
\(619\) 1145.50 1984.06i 0.0743805 0.128831i −0.826436 0.563030i \(-0.809635\pi\)
0.900817 + 0.434200i \(0.142969\pi\)
\(620\) 414.000 717.069i 0.0268172 0.0464487i
\(621\) 5002.50 + 8664.58i 0.323258 + 0.559900i
\(622\) −20262.0 −1.30616
\(623\) 0 0
\(624\) 5600.00 0.359262
\(625\) 4094.50 + 7091.88i 0.262048 + 0.453880i
\(626\) 10799.0 18704.4i 0.689481 1.19422i
\(627\) −712.500 + 1234.09i −0.0453820 + 0.0786039i
\(628\) −5666.00 9813.80i −0.360029 0.623588i
\(629\) 12903.0 0.817927
\(630\) 0 0
\(631\) −6928.00 −0.437083 −0.218541 0.975828i \(-0.570130\pi\)
−0.218541 + 0.975828i \(0.570130\pi\)
\(632\) −1844.00 3193.90i −0.116061 0.201023i
\(633\) 310.000 536.936i 0.0194651 0.0337145i
\(634\) −531.000 + 919.719i −0.0332629 + 0.0576131i
\(635\) 9252.00 + 16024.9i 0.578196 + 1.00146i
\(636\) −7860.00 −0.490046
\(637\) 0 0
\(638\) −12996.0 −0.806452
\(639\) −96.0000 166.277i −0.00594319 0.0102939i
\(640\) −576.000 + 997.661i −0.0355756 + 0.0616188i
\(641\) −12487.5 + 21629.0i −0.769464 + 1.33275i 0.168390 + 0.985721i \(0.446143\pi\)
−0.937854 + 0.347031i \(0.887190\pi\)
\(642\) 5535.00 + 9586.90i 0.340263 + 0.589353i
\(643\) −9548.00 −0.585593 −0.292797 0.956175i \(-0.594586\pi\)
−0.292797 + 0.956175i \(0.594586\pi\)
\(644\) 0 0
\(645\) −5580.00 −0.340639
\(646\) −255.000 441.673i −0.0155307 0.0269000i
\(647\) 5065.50 8773.70i 0.307798 0.533122i −0.670082 0.742287i \(-0.733741\pi\)
0.977880 + 0.209165i \(0.0670745\pi\)
\(648\) 2684.00 4648.82i 0.162712 0.281826i
\(649\) −6241.50 10810.6i −0.377504 0.653857i
\(650\) −6160.00 −0.371716
\(651\) 0 0
\(652\) −9244.00 −0.555250
\(653\) −8329.50 14427.1i −0.499171 0.864589i 0.500829 0.865546i \(-0.333029\pi\)
−1.00000 0.000957229i \(0.999695\pi\)
\(654\) −4615.00 + 7993.41i −0.275934 + 0.477932i
\(655\) 9220.50 15970.4i 0.550038 0.952693i
\(656\) −336.000 581.969i −0.0199979 0.0346373i
\(657\) −626.000 −0.0371729
\(658\) 0 0
\(659\) 29556.0 1.74710 0.873550 0.486735i \(-0.161812\pi\)
0.873550 + 0.486735i \(0.161812\pi\)
\(660\) 5130.00 + 8885.42i 0.302553 + 0.524037i
\(661\) 95.5000 165.411i 0.00561955 0.00973334i −0.863202 0.504859i \(-0.831545\pi\)
0.868822 + 0.495125i \(0.164878\pi\)
\(662\) 7015.00 12150.3i 0.411852 0.713348i
\(663\) 8925.00 + 15458.6i 0.522803 + 0.905521i
\(664\) 4704.00 0.274926
\(665\) 0 0
\(666\) 1012.00 0.0588802
\(667\) −3933.00 6812.16i −0.228315 0.395454i
\(668\) 2520.00 4364.77i 0.145961 0.252811i
\(669\) 140.000 242.487i 0.00809075 0.0140136i
\(670\) −3771.00 6531.56i −0.217442 0.376621i
\(671\) −40413.0 −2.32508
\(672\) 0 0
\(673\) 2606.00 0.149263 0.0746314 0.997211i \(-0.476222\pi\)
0.0746314 + 0.997211i \(0.476222\pi\)
\(674\) −8990.00 15571.1i −0.513771 0.889878i
\(675\) −3190.00 + 5525.24i −0.181901 + 0.315062i
\(676\) −5406.00 + 9363.47i −0.307579 + 0.532742i
\(677\) −2104.50 3645.10i −0.119472 0.206931i 0.800087 0.599885i \(-0.204787\pi\)
−0.919559 + 0.392953i \(0.871453\pi\)
\(678\) 15420.0 0.873454
\(679\) 0 0
\(680\) −3672.00 −0.207081
\(681\) −7642.50 13237.2i −0.430046 0.744861i
\(682\) −1311.00 + 2270.72i −0.0736082 + 0.127493i
\(683\) −12151.5 + 21047.0i −0.680768 + 1.17912i 0.293979 + 0.955812i \(0.405020\pi\)
−0.974747 + 0.223312i \(0.928313\pi\)
\(684\) −20.0000 34.6410i −0.00111801 0.00193645i
\(685\) −1269.00 −0.0707825
\(686\) 0 0
\(687\) 4805.00 0.266845
\(688\) 992.000 + 1718.19i 0.0549704 + 0.0952116i
\(689\) 13755.0 23824.4i 0.760557 1.31732i
\(690\) −3105.00 + 5378.02i −0.171312 + 0.296721i
\(691\) 7520.50 + 13025.9i 0.414028 + 0.717117i 0.995326 0.0965734i \(-0.0307882\pi\)
−0.581298 + 0.813691i \(0.697455\pi\)
\(692\) −13068.0 −0.717877
\(693\) 0 0
\(694\) −17418.0 −0.952706
\(695\) 6678.00 + 11566.6i 0.364476 + 0.631291i
\(696\) −2280.00 + 3949.08i −0.124171 + 0.215071i
\(697\) 1071.00 1855.03i 0.0582023 0.100809i
\(698\) 6482.00 + 11227.2i 0.351500 + 0.608817i
\(699\) −14145.0 −0.765398
\(700\) 0 0
\(701\) 24726.0 1.33222 0.666111 0.745852i \(-0.267958\pi\)
0.666111 + 0.745852i \(0.267958\pi\)
\(702\) 10150.0 + 17580.3i 0.545708 + 0.945194i
\(703\) −632.500 + 1095.52i −0.0339334 + 0.0587744i
\(704\) 1824.00 3159.26i 0.0976486 0.169132i
\(705\) 4522.50 + 7833.20i 0.241599 + 0.418462i
\(706\) 4266.00 0.227412
\(707\) 0 0
\(708\) −4380.00 −0.232501
\(709\) 2478.50 + 4292.89i 0.131286 + 0.227395i 0.924173 0.381975i \(-0.124756\pi\)
−0.792886 + 0.609370i \(0.791423\pi\)
\(710\) 864.000 1496.49i 0.0456695 0.0791019i
\(711\) 461.000 798.475i 0.0243162 0.0421170i
\(712\) −4068.00 7045.98i −0.214122 0.370870i
\(713\) −1587.00 −0.0833571
\(714\) 0 0
\(715\) −35910.0 −1.87826
\(716\) −2574.00 4458.30i −0.134350 0.232702i
\(717\) 8850.00 15328.6i 0.460961 0.798409i
\(718\) −3849.00 + 6666.66i −0.200060 + 0.346515i
\(719\) 13834.5 + 23962.1i 0.717580 + 1.24288i 0.961956 + 0.273204i \(0.0880834\pi\)
−0.244376 + 0.969680i \(0.578583\pi\)
\(720\) −288.000 −0.0149071
\(721\) 0 0
\(722\) −13668.0 −0.704529
\(723\) 13077.5 + 22650.9i 0.672694 + 1.16514i
\(724\) −5348.00 + 9263.01i −0.274526 + 0.475493i
\(725\) 2508.00 4343.98i 0.128476 0.222526i
\(726\) −9590.00 16610.4i −0.490246 0.849130i
\(727\) 13888.0 0.708497 0.354249 0.935151i \(-0.384737\pi\)
0.354249 + 0.935151i \(0.384737\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) −2817.00 4879.19i −0.142824 0.247379i
\(731\) −3162.00 + 5476.74i −0.159987 + 0.277106i
\(732\) −7090.00 + 12280.2i −0.357997 + 0.620069i
\(733\) 7121.50 + 12334.8i 0.358852 + 0.621550i 0.987769 0.155922i \(-0.0498349\pi\)
−0.628917 + 0.777472i \(0.716502\pi\)
\(734\) −12982.0 −0.652826
\(735\) 0 0
\(736\) 2208.00 0.110581
\(737\) 11941.5 + 20683.3i 0.596840 + 1.03376i
\(738\) 84.0000 145.492i 0.00418981 0.00725697i
\(739\) −18479.5 + 32007.4i −0.919864 + 1.59325i −0.120244 + 0.992744i \(0.538368\pi\)
−0.799620 + 0.600507i \(0.794966\pi\)
\(740\) 4554.00 + 7887.76i 0.226228 + 0.391838i
\(741\) −1750.00 −0.0867582
\(742\) 0 0
\(743\) −12528.0 −0.618584 −0.309292 0.950967i \(-0.600092\pi\)
−0.309292 + 0.950967i \(0.600092\pi\)
\(744\) 460.000 + 796.743i 0.0226672 + 0.0392608i
\(745\) 256.500 444.271i 0.0126140 0.0218481i
\(746\) −923.000 + 1598.68i −0.0452995 + 0.0784610i
\(747\) 588.000 + 1018.45i 0.0288003 + 0.0498835i
\(748\) 11628.0 0.568398
\(749\) 0 0
\(750\) −15210.0 −0.740521
\(751\) 8883.50 + 15386.7i 0.431643 + 0.747627i 0.997015 0.0772090i \(-0.0246009\pi\)
−0.565372 + 0.824836i \(0.691268\pi\)
\(752\) 1608.00 2785.14i 0.0779757 0.135058i
\(753\) 12600.0 21823.8i 0.609787 1.05618i
\(754\) −7980.00 13821.8i −0.385430 0.667585i
\(755\) 7551.00 0.363985
\(756\) 0 0
\(757\) −28726.0 −1.37921 −0.689606 0.724184i \(-0.742216\pi\)
−0.689606 + 0.724184i \(0.742216\pi\)
\(758\) −6344.00 10988.1i −0.303990 0.526526i
\(759\) 9832.50 17030.4i 0.470220 0.814445i
\(760\) 180.000 311.769i 0.00859117 0.0148803i
\(761\) −13234.5 22922.8i −0.630421 1.09192i −0.987466 0.157834i \(-0.949549\pi\)
0.357045 0.934087i \(-0.383784\pi\)
\(762\) −20560.0 −0.977441
\(763\) 0 0
\(764\) 16740.0 0.792712
\(765\) −459.000 795.011i −0.0216930 0.0375735i
\(766\) −5007.00 + 8672.38i −0.236175 + 0.409068i
\(767\) 7665.00 13276.2i 0.360844 0.625000i
\(768\) −640.000 1108.51i −0.0300703 0.0520833i
\(769\) −5054.00 −0.236999 −0.118499 0.992954i \(-0.537808\pi\)
−0.118499 + 0.992954i \(0.537808\pi\)
\(770\) 0 0
\(771\) 7185.00 0.335618
\(772\) 170.000 + 294.449i 0.00792543 + 0.0137273i
\(773\) −17782.5 + 30800.2i −0.827415 + 1.43313i 0.0726439 + 0.997358i \(0.476856\pi\)
−0.900059 + 0.435767i \(0.856477\pi\)
\(774\) −248.000 + 429.549i −0.0115170 + 0.0199481i
\(775\) −506.000 876.418i −0.0234530 0.0406217i
\(776\) 14672.0 0.678730