Properties

Label 147.4.e.n.67.3
Level $147$
Weight $4$
Character 147.67
Analytic conductor $8.673$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Defining polynomial: \(x^{6} - x^{5} + 25 x^{4} + 12 x^{3} + 582 x^{2} - 144 x + 36\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.3
Root \(-2.27818 - 3.94593i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.4.e.n.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.27818 + 3.94593i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-6.38024 + 11.0509i) q^{4} +(8.93660 + 15.4786i) q^{5} -13.6691 q^{6} -21.6905 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(2.27818 + 3.94593i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-6.38024 + 11.0509i) q^{4} +(8.93660 + 15.4786i) q^{5} -13.6691 q^{6} -21.6905 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-40.7184 + 70.5264i) q^{10} +(5.69708 - 9.86762i) q^{11} +(-19.1407 - 33.1527i) q^{12} +13.0987 q^{13} -53.6196 q^{15} +(1.62706 + 2.81815i) q^{16} +(26.6337 - 46.1309i) q^{17} +(20.5036 - 35.5134i) q^{18} +(-21.2111 - 36.7388i) q^{19} -228.071 q^{20} +51.9159 q^{22} +(-76.0427 - 131.710i) q^{23} +(32.5357 - 56.3535i) q^{24} +(-97.2257 + 168.400i) q^{25} +(29.8412 + 51.6864i) q^{26} +27.0000 q^{27} +186.493 q^{29} +(-122.155 - 211.579i) q^{30} +(-78.9369 + 136.723i) q^{31} +(-94.1753 + 163.116i) q^{32} +(17.0912 + 29.6029i) q^{33} +242.706 q^{34} +114.844 q^{36} +(-1.87294 - 3.24403i) q^{37} +(96.6457 - 167.395i) q^{38} +(-19.6480 + 34.0313i) q^{39} +(-193.839 - 335.739i) q^{40} +39.3230 q^{41} +429.439 q^{43} +(72.6974 + 125.916i) q^{44} +(80.4294 - 139.308i) q^{45} +(346.478 - 600.118i) q^{46} +(10.5934 + 18.3484i) q^{47} -9.76236 q^{48} -885.992 q^{50} +(79.9010 + 138.393i) q^{51} +(-83.5726 + 144.752i) q^{52} +(-182.952 + 316.882i) q^{53} +(61.5109 + 106.540i) q^{54} +203.650 q^{55} +127.267 q^{57} +(424.866 + 735.889i) q^{58} +(-113.289 + 196.222i) q^{59} +(342.106 - 592.545i) q^{60} +(325.987 + 564.626i) q^{61} -719.331 q^{62} -832.161 q^{64} +(117.058 + 202.750i) q^{65} +(-77.8739 + 134.882i) q^{66} +(-72.7166 + 125.949i) q^{67} +(339.858 + 588.652i) q^{68} +456.256 q^{69} -368.962 q^{71} +(97.6071 + 169.060i) q^{72} +(304.453 - 527.328i) q^{73} +(8.53380 - 14.7810i) q^{74} +(-291.677 - 505.200i) q^{75} +541.328 q^{76} -179.047 q^{78} +(-455.119 - 788.289i) q^{79} +(-29.0808 + 50.3694i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(89.5850 + 155.166i) q^{82} +327.929 q^{83} +952.058 q^{85} +(978.340 + 1694.53i) q^{86} +(-279.740 + 484.524i) q^{87} +(-123.572 + 214.033i) q^{88} +(-18.8059 - 32.5728i) q^{89} +732.932 q^{90} +1940.68 q^{92} +(-236.811 - 410.168i) q^{93} +(-48.2676 + 83.6019i) q^{94} +(379.111 - 656.640i) q^{95} +(-282.526 - 489.349i) q^{96} -722.013 q^{97} -102.547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 9q^{3} - 25q^{4} + 11q^{5} + 6q^{6} + 78q^{8} - 27q^{9} + O(q^{10}) \) \( 6q - q^{2} - 9q^{3} - 25q^{4} + 11q^{5} + 6q^{6} + 78q^{8} - 27q^{9} - 55q^{10} - 35q^{11} - 75q^{12} - 124q^{13} - 66q^{15} - 241q^{16} + 48q^{17} - 9q^{18} - 202q^{19} - 878q^{20} - 14q^{22} - 216q^{23} - 117q^{24} - 130q^{25} + 274q^{26} + 162q^{27} + 106q^{29} - 165q^{30} - 95q^{31} - 683q^{32} - 105q^{33} + 48q^{34} + 450q^{36} - 262q^{37} - 398q^{38} + 186q^{39} + 21q^{40} - 488q^{41} + 720q^{43} + 905q^{44} + 99q^{45} + 1056q^{46} - 210q^{47} + 1446q^{48} - 2756q^{50} + 144q^{51} + 324q^{52} - 393q^{53} - 27q^{54} + 2062q^{55} + 1212q^{57} + 1249q^{58} + 1143q^{59} + 1317q^{60} - 70q^{61} - 2118q^{62} - 798q^{64} + 472q^{65} + 21q^{66} + 628q^{67} + 1944q^{68} + 1296q^{69} + 636q^{71} - 351q^{72} + 988q^{73} - 1002q^{74} - 390q^{75} + 4680q^{76} - 1644q^{78} - 861q^{79} + 175q^{80} - 243q^{81} + 124q^{82} - 1038q^{83} + 3600q^{85} + 3208q^{86} - 159q^{87} + 891q^{88} + 1766q^{89} + 990q^{90} - 1344q^{92} - 285q^{93} - 3294q^{94} + 736q^{95} - 2049q^{96} - 38q^{97} + 630q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.27818 + 3.94593i 0.805459 + 1.39510i 0.915981 + 0.401223i \(0.131415\pi\)
−0.110521 + 0.993874i \(0.535252\pi\)
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) −6.38024 + 11.0509i −0.797530 + 1.38136i
\(5\) 8.93660 + 15.4786i 0.799314 + 1.38445i 0.920063 + 0.391769i \(0.128137\pi\)
−0.120749 + 0.992683i \(0.538530\pi\)
\(6\) −13.6691 −0.930064
\(7\) 0 0
\(8\) −21.6905 −0.958592
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −40.7184 + 70.5264i −1.28763 + 2.23024i
\(11\) 5.69708 9.86762i 0.156158 0.270473i −0.777322 0.629102i \(-0.783423\pi\)
0.933480 + 0.358630i \(0.116756\pi\)
\(12\) −19.1407 33.1527i −0.460454 0.797530i
\(13\) 13.0987 0.279455 0.139728 0.990190i \(-0.455377\pi\)
0.139728 + 0.990190i \(0.455377\pi\)
\(14\) 0 0
\(15\) −53.6196 −0.922968
\(16\) 1.62706 + 2.81815i 0.0254228 + 0.0440336i
\(17\) 26.6337 46.1309i 0.379977 0.658140i −0.611081 0.791568i \(-0.709265\pi\)
0.991059 + 0.133428i \(0.0425984\pi\)
\(18\) 20.5036 35.5134i 0.268486 0.465032i
\(19\) −21.2111 36.7388i −0.256114 0.443603i 0.709083 0.705125i \(-0.249109\pi\)
−0.965198 + 0.261522i \(0.915776\pi\)
\(20\) −228.071 −2.54991
\(21\) 0 0
\(22\) 51.9159 0.503114
\(23\) −76.0427 131.710i −0.689391 1.19406i −0.972035 0.234836i \(-0.924545\pi\)
0.282644 0.959225i \(-0.408789\pi\)
\(24\) 32.5357 56.3535i 0.276722 0.479296i
\(25\) −97.2257 + 168.400i −0.777806 + 1.34720i
\(26\) 29.8412 + 51.6864i 0.225090 + 0.389867i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 186.493 1.19417 0.597085 0.802178i \(-0.296325\pi\)
0.597085 + 0.802178i \(0.296325\pi\)
\(30\) −122.155 211.579i −0.743413 1.28763i
\(31\) −78.9369 + 136.723i −0.457338 + 0.792133i −0.998819 0.0485801i \(-0.984530\pi\)
0.541481 + 0.840713i \(0.317864\pi\)
\(32\) −94.1753 + 163.116i −0.520250 + 0.901099i
\(33\) 17.0912 + 29.6029i 0.0901576 + 0.156158i
\(34\) 242.706 1.22423
\(35\) 0 0
\(36\) 114.844 0.531686
\(37\) −1.87294 3.24403i −0.00832188 0.0144139i 0.861834 0.507190i \(-0.169316\pi\)
−0.870156 + 0.492776i \(0.835982\pi\)
\(38\) 96.6457 167.395i 0.412579 0.714608i
\(39\) −19.6480 + 34.0313i −0.0806718 + 0.139728i
\(40\) −193.839 335.739i −0.766216 1.32712i
\(41\) 39.3230 0.149786 0.0748930 0.997192i \(-0.476138\pi\)
0.0748930 + 0.997192i \(0.476138\pi\)
\(42\) 0 0
\(43\) 429.439 1.52300 0.761498 0.648168i \(-0.224464\pi\)
0.761498 + 0.648168i \(0.224464\pi\)
\(44\) 72.6974 + 125.916i 0.249080 + 0.431420i
\(45\) 80.4294 139.308i 0.266438 0.461484i
\(46\) 346.478 600.118i 1.11055 1.92354i
\(47\) 10.5934 + 18.3484i 0.0328768 + 0.0569444i 0.881996 0.471258i \(-0.156200\pi\)
−0.849119 + 0.528202i \(0.822866\pi\)
\(48\) −9.76236 −0.0293557
\(49\) 0 0
\(50\) −885.992 −2.50596
\(51\) 79.9010 + 138.393i 0.219380 + 0.379977i
\(52\) −83.5726 + 144.752i −0.222874 + 0.386029i
\(53\) −182.952 + 316.882i −0.474158 + 0.821266i −0.999562 0.0295866i \(-0.990581\pi\)
0.525404 + 0.850853i \(0.323914\pi\)
\(54\) 61.5109 + 106.540i 0.155011 + 0.268486i
\(55\) 203.650 0.499276
\(56\) 0 0
\(57\) 127.267 0.295735
\(58\) 424.866 + 735.889i 0.961856 + 1.66598i
\(59\) −113.289 + 196.222i −0.249982 + 0.432982i −0.963521 0.267634i \(-0.913758\pi\)
0.713538 + 0.700616i \(0.247091\pi\)
\(60\) 342.106 592.545i 0.736095 1.27495i
\(61\) 325.987 + 564.626i 0.684235 + 1.18513i 0.973677 + 0.227934i \(0.0731970\pi\)
−0.289442 + 0.957196i \(0.593470\pi\)
\(62\) −719.331 −1.47347
\(63\) 0 0
\(64\) −832.161 −1.62532
\(65\) 117.058 + 202.750i 0.223372 + 0.386892i
\(66\) −77.8739 + 134.882i −0.145237 + 0.251557i
\(67\) −72.7166 + 125.949i −0.132593 + 0.229658i −0.924675 0.380756i \(-0.875664\pi\)
0.792082 + 0.610414i \(0.208997\pi\)
\(68\) 339.858 + 588.652i 0.606086 + 1.04977i
\(69\) 456.256 0.796041
\(70\) 0 0
\(71\) −368.962 −0.616728 −0.308364 0.951268i \(-0.599782\pi\)
−0.308364 + 0.951268i \(0.599782\pi\)
\(72\) 97.6071 + 169.060i 0.159765 + 0.276722i
\(73\) 304.453 527.328i 0.488130 0.845466i −0.511777 0.859119i \(-0.671012\pi\)
0.999907 + 0.0136522i \(0.00434576\pi\)
\(74\) 8.53380 14.7810i 0.0134059 0.0232197i
\(75\) −291.677 505.200i −0.449066 0.777806i
\(76\) 541.328 0.817034
\(77\) 0 0
\(78\) −179.047 −0.259911
\(79\) −455.119 788.289i −0.648163 1.12265i −0.983561 0.180574i \(-0.942204\pi\)
0.335399 0.942076i \(-0.391129\pi\)
\(80\) −29.0808 + 50.3694i −0.0406416 + 0.0703933i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 89.5850 + 155.166i 0.120646 + 0.208966i
\(83\) 327.929 0.433674 0.216837 0.976208i \(-0.430426\pi\)
0.216837 + 0.976208i \(0.430426\pi\)
\(84\) 0 0
\(85\) 952.058 1.21489
\(86\) 978.340 + 1694.53i 1.22671 + 2.12473i
\(87\) −279.740 + 484.524i −0.344727 + 0.597085i
\(88\) −123.572 + 214.033i −0.149691 + 0.259273i
\(89\) −18.8059 32.5728i −0.0223980 0.0387945i 0.854609 0.519272i \(-0.173797\pi\)
−0.877007 + 0.480477i \(0.840463\pi\)
\(90\) 732.932 0.858420
\(91\) 0 0
\(92\) 1940.68 2.19924
\(93\) −236.811 410.168i −0.264044 0.457338i
\(94\) −48.2676 + 83.6019i −0.0529619 + 0.0917327i
\(95\) 379.111 656.640i 0.409431 0.709156i
\(96\) −282.526 489.349i −0.300366 0.520250i
\(97\) −722.013 −0.755766 −0.377883 0.925853i \(-0.623348\pi\)
−0.377883 + 0.925853i \(0.623348\pi\)
\(98\) 0 0
\(99\) −102.547 −0.104105
\(100\) −1240.65 2148.86i −1.24065 2.14886i
\(101\) 759.336 1315.21i 0.748087 1.29572i −0.200652 0.979663i \(-0.564306\pi\)
0.948739 0.316062i \(-0.102361\pi\)
\(102\) −364.058 + 630.568i −0.353403 + 0.612113i
\(103\) −525.942 910.957i −0.503132 0.871450i −0.999993 0.00361990i \(-0.998848\pi\)
0.496862 0.867830i \(-0.334486\pi\)
\(104\) −284.116 −0.267883
\(105\) 0 0
\(106\) −1667.19 −1.52766
\(107\) −383.260 663.826i −0.346273 0.599762i 0.639312 0.768948i \(-0.279219\pi\)
−0.985584 + 0.169186i \(0.945886\pi\)
\(108\) −172.266 + 298.374i −0.153485 + 0.265843i
\(109\) 713.524 1235.86i 0.627002 1.08600i −0.361148 0.932509i \(-0.617615\pi\)
0.988150 0.153491i \(-0.0490516\pi\)
\(110\) 463.952 + 803.588i 0.402146 + 0.696538i
\(111\) 11.2376 0.00960928
\(112\) 0 0
\(113\) 362.564 0.301833 0.150917 0.988546i \(-0.451778\pi\)
0.150917 + 0.988546i \(0.451778\pi\)
\(114\) 289.937 + 502.186i 0.238203 + 0.412579i
\(115\) 1359.13 2354.08i 1.10208 1.90886i
\(116\) −1189.87 + 2060.92i −0.952386 + 1.64958i
\(117\) −58.9440 102.094i −0.0465759 0.0806718i
\(118\) −1032.37 −0.805402
\(119\) 0 0
\(120\) 1163.03 0.884750
\(121\) 600.587 + 1040.25i 0.451230 + 0.781553i
\(122\) −1485.31 + 2572.64i −1.10225 + 1.90915i
\(123\) −58.9845 + 102.164i −0.0432395 + 0.0748930i
\(124\) −1007.27 1744.65i −0.729481 1.26350i
\(125\) −1241.32 −0.888216
\(126\) 0 0
\(127\) 974.777 0.681082 0.340541 0.940230i \(-0.389390\pi\)
0.340541 + 0.940230i \(0.389390\pi\)
\(128\) −1142.41 1978.72i −0.788875 1.36637i
\(129\) −644.158 + 1115.71i −0.439651 + 0.761498i
\(130\) −533.357 + 923.802i −0.359835 + 0.623252i
\(131\) −896.351 1552.53i −0.597821 1.03546i −0.993142 0.116914i \(-0.962700\pi\)
0.395321 0.918543i \(-0.370633\pi\)
\(132\) −436.184 −0.287613
\(133\) 0 0
\(134\) −662.647 −0.427194
\(135\) 241.288 + 417.924i 0.153828 + 0.266438i
\(136\) −577.697 + 1000.60i −0.364243 + 0.630888i
\(137\) −842.208 + 1458.75i −0.525217 + 0.909702i 0.474352 + 0.880335i \(0.342682\pi\)
−0.999569 + 0.0293665i \(0.990651\pi\)
\(138\) 1039.44 + 1800.35i 0.641178 + 1.11055i
\(139\) −315.089 −0.192270 −0.0961350 0.995368i \(-0.530648\pi\)
−0.0961350 + 0.995368i \(0.530648\pi\)
\(140\) 0 0
\(141\) −63.5606 −0.0379629
\(142\) −840.563 1455.90i −0.496750 0.860396i
\(143\) 74.6241 129.253i 0.0436390 0.0755850i
\(144\) 14.6435 25.3633i 0.00847427 0.0146779i
\(145\) 1666.62 + 2886.67i 0.954517 + 1.65327i
\(146\) 2774.40 1.57268
\(147\) 0 0
\(148\) 47.7992 0.0265478
\(149\) −946.887 1640.06i −0.520617 0.901736i −0.999713 0.0239729i \(-0.992368\pi\)
0.479095 0.877763i \(-0.340965\pi\)
\(150\) 1328.99 2301.87i 0.723409 1.25298i
\(151\) 1005.92 1742.31i 0.542124 0.938986i −0.456658 0.889642i \(-0.650954\pi\)
0.998782 0.0493434i \(-0.0157129\pi\)
\(152\) 460.079 + 796.881i 0.245509 + 0.425234i
\(153\) −479.406 −0.253318
\(154\) 0 0
\(155\) −2821.71 −1.46223
\(156\) −250.718 434.256i −0.128676 0.222874i
\(157\) −1914.25 + 3315.58i −0.973082 + 1.68543i −0.286956 + 0.957944i \(0.592643\pi\)
−0.686125 + 0.727483i \(0.740690\pi\)
\(158\) 2073.69 3591.73i 1.04414 1.80850i
\(159\) −548.856 950.647i −0.273755 0.474158i
\(160\) −3366.43 −1.66337
\(161\) 0 0
\(162\) −369.066 −0.178991
\(163\) 1754.63 + 3039.11i 0.843148 + 1.46038i 0.887220 + 0.461347i \(0.152634\pi\)
−0.0440718 + 0.999028i \(0.514033\pi\)
\(164\) −250.890 + 434.554i −0.119459 + 0.206909i
\(165\) −305.475 + 529.098i −0.144128 + 0.249638i
\(166\) 747.083 + 1293.99i 0.349307 + 0.605017i
\(167\) 343.008 0.158939 0.0794694 0.996837i \(-0.474677\pi\)
0.0794694 + 0.996837i \(0.474677\pi\)
\(168\) 0 0
\(169\) −2025.42 −0.921905
\(170\) 2168.96 + 3756.75i 0.978541 + 1.69488i
\(171\) −190.900 + 330.649i −0.0853714 + 0.147868i
\(172\) −2739.92 + 4745.68i −1.21463 + 2.10381i
\(173\) −2093.61 3626.23i −0.920081 1.59363i −0.799288 0.600949i \(-0.794790\pi\)
−0.120793 0.992678i \(-0.538544\pi\)
\(174\) −2549.20 −1.11066
\(175\) 0 0
\(176\) 37.0779 0.0158798
\(177\) −339.866 588.666i −0.144327 0.249982i
\(178\) 85.6866 148.413i 0.0360813 0.0624947i
\(179\) 985.143 1706.32i 0.411358 0.712493i −0.583681 0.811983i \(-0.698388\pi\)
0.995039 + 0.0994906i \(0.0317213\pi\)
\(180\) 1026.32 + 1777.63i 0.424984 + 0.736095i
\(181\) 3613.10 1.48376 0.741878 0.670535i \(-0.233935\pi\)
0.741878 + 0.670535i \(0.233935\pi\)
\(182\) 0 0
\(183\) −1955.92 −0.790086
\(184\) 1649.40 + 2856.85i 0.660845 + 1.14462i
\(185\) 33.4755 57.9812i 0.0133036 0.0230425i
\(186\) 1079.00 1868.88i 0.425354 0.736734i
\(187\) −303.468 525.622i −0.118673 0.205547i
\(188\) −270.355 −0.104881
\(189\) 0 0
\(190\) 3454.74 1.31912
\(191\) −953.884 1652.18i −0.361365 0.625902i 0.626821 0.779163i \(-0.284356\pi\)
−0.988186 + 0.153261i \(0.951022\pi\)
\(192\) 1248.24 2162.02i 0.469188 0.812658i
\(193\) −1199.96 + 2078.40i −0.447540 + 0.775162i −0.998225 0.0595509i \(-0.981033\pi\)
0.550685 + 0.834713i \(0.314366\pi\)
\(194\) −1644.88 2849.01i −0.608738 1.05437i
\(195\) −702.346 −0.257928
\(196\) 0 0
\(197\) 1514.32 0.547668 0.273834 0.961777i \(-0.411708\pi\)
0.273834 + 0.961777i \(0.411708\pi\)
\(198\) −233.622 404.645i −0.0838524 0.145237i
\(199\) 683.889 1184.53i 0.243616 0.421955i −0.718126 0.695914i \(-0.755000\pi\)
0.961742 + 0.273958i \(0.0883330\pi\)
\(200\) 2108.87 3652.67i 0.745598 1.29141i
\(201\) −218.150 377.847i −0.0765527 0.132593i
\(202\) 6919.63 2.41021
\(203\) 0 0
\(204\) −2039.15 −0.699848
\(205\) 351.414 + 608.667i 0.119726 + 0.207371i
\(206\) 2396.38 4150.66i 0.810504 1.40383i
\(207\) −684.384 + 1185.39i −0.229797 + 0.398020i
\(208\) 21.3123 + 36.9140i 0.00710453 + 0.0123054i
\(209\) −483.366 −0.159977
\(210\) 0 0
\(211\) 4302.52 1.40378 0.701891 0.712285i \(-0.252339\pi\)
0.701891 + 0.712285i \(0.252339\pi\)
\(212\) −2334.55 4043.57i −0.756311 1.30997i
\(213\) 553.443 958.591i 0.178034 0.308364i
\(214\) 1746.27 3024.64i 0.557817 0.966167i
\(215\) 3837.72 + 6647.13i 1.21735 + 2.10851i
\(216\) −585.642 −0.184481
\(217\) 0 0
\(218\) 6502.16 2.02010
\(219\) 913.359 + 1581.98i 0.281822 + 0.488130i
\(220\) −1299.34 + 2250.51i −0.398187 + 0.689680i
\(221\) 348.866 604.253i 0.106187 0.183921i
\(222\) 25.6014 + 44.3429i 0.00773988 + 0.0134059i
\(223\) 1497.19 0.449592 0.224796 0.974406i \(-0.427828\pi\)
0.224796 + 0.974406i \(0.427828\pi\)
\(224\) 0 0
\(225\) 1750.06 0.518537
\(226\) 825.987 + 1430.65i 0.243114 + 0.421086i
\(227\) 801.662 1388.52i 0.234397 0.405988i −0.724700 0.689065i \(-0.758022\pi\)
0.959097 + 0.283076i \(0.0913550\pi\)
\(228\) −811.992 + 1406.41i −0.235858 + 0.408517i
\(229\) 505.261 + 875.137i 0.145802 + 0.252536i 0.929672 0.368389i \(-0.120091\pi\)
−0.783870 + 0.620925i \(0.786757\pi\)
\(230\) 12385.4 3.55072
\(231\) 0 0
\(232\) −4045.13 −1.14472
\(233\) −99.1084 171.661i −0.0278661 0.0482656i 0.851756 0.523939i \(-0.175538\pi\)
−0.879622 + 0.475673i \(0.842205\pi\)
\(234\) 268.571 465.178i 0.0750299 0.129956i
\(235\) −189.339 + 327.944i −0.0525578 + 0.0910329i
\(236\) −1445.62 2503.88i −0.398736 0.690631i
\(237\) 2730.71 0.748434
\(238\) 0 0
\(239\) −1201.19 −0.325098 −0.162549 0.986700i \(-0.551972\pi\)
−0.162549 + 0.986700i \(0.551972\pi\)
\(240\) −87.2423 151.108i −0.0234644 0.0406416i
\(241\) −1366.35 + 2366.58i −0.365204 + 0.632551i −0.988809 0.149188i \(-0.952334\pi\)
0.623605 + 0.781739i \(0.285667\pi\)
\(242\) −2736.49 + 4739.74i −0.726894 + 1.25902i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) −8319.49 −2.18279
\(245\) 0 0
\(246\) −537.510 −0.139311
\(247\) −277.838 481.229i −0.0715724 0.123967i
\(248\) 1712.18 2965.58i 0.438401 0.759332i
\(249\) −491.894 + 851.985i −0.125191 + 0.216837i
\(250\) −2827.95 4898.16i −0.715422 1.23915i
\(251\) −7565.82 −1.90259 −0.951295 0.308281i \(-0.900246\pi\)
−0.951295 + 0.308281i \(0.900246\pi\)
\(252\) 0 0
\(253\) −1732.88 −0.430615
\(254\) 2220.72 + 3846.40i 0.548584 + 0.950175i
\(255\) −1428.09 + 2473.52i −0.350707 + 0.607443i
\(256\) 1876.61 3250.38i 0.458156 0.793550i
\(257\) 2504.34 + 4337.64i 0.607846 + 1.05282i 0.991595 + 0.129382i \(0.0412994\pi\)
−0.383749 + 0.923437i \(0.625367\pi\)
\(258\) −5870.04 −1.41648
\(259\) 0 0
\(260\) −2987.42 −0.712584
\(261\) −839.220 1453.57i −0.199028 0.344727i
\(262\) 4084.10 7073.88i 0.963041 1.66804i
\(263\) 3124.40 5411.63i 0.732544 1.26880i −0.223249 0.974761i \(-0.571666\pi\)
0.955793 0.294042i \(-0.0950004\pi\)
\(264\) −370.716 642.100i −0.0864243 0.149691i
\(265\) −6539.88 −1.51601
\(266\) 0 0
\(267\) 112.835 0.0258630
\(268\) −927.898 1607.17i −0.211494 0.366318i
\(269\) −1794.22 + 3107.69i −0.406676 + 0.704383i −0.994515 0.104595i \(-0.966645\pi\)
0.587839 + 0.808978i \(0.299979\pi\)
\(270\) −1099.40 + 1904.21i −0.247804 + 0.429210i
\(271\) −991.571 1717.45i −0.222264 0.384973i 0.733231 0.679980i \(-0.238012\pi\)
−0.955495 + 0.295007i \(0.904678\pi\)
\(272\) 173.338 0.0386404
\(273\) 0 0
\(274\) −7674.81 −1.69216
\(275\) 1107.80 + 1918.77i 0.242920 + 0.420751i
\(276\) −2911.02 + 5042.04i −0.634866 + 1.09962i
\(277\) −3681.96 + 6377.33i −0.798654 + 1.38331i 0.121838 + 0.992550i \(0.461121\pi\)
−0.920493 + 0.390760i \(0.872212\pi\)
\(278\) −717.831 1243.32i −0.154866 0.268235i
\(279\) 1420.86 0.304892
\(280\) 0 0
\(281\) −5312.05 −1.12772 −0.563861 0.825869i \(-0.690685\pi\)
−0.563861 + 0.825869i \(0.690685\pi\)
\(282\) −144.803 250.806i −0.0305776 0.0529619i
\(283\) −545.882 + 945.495i −0.114662 + 0.198600i −0.917645 0.397402i \(-0.869912\pi\)
0.802983 + 0.596002i \(0.203245\pi\)
\(284\) 2354.06 4077.36i 0.491859 0.851925i
\(285\) 1137.33 + 1969.92i 0.236385 + 0.409431i
\(286\) 680.030 0.140598
\(287\) 0 0
\(288\) 1695.16 0.346833
\(289\) 1037.79 + 1797.51i 0.211234 + 0.365869i
\(290\) −7593.72 + 13152.7i −1.53765 + 2.66329i
\(291\) 1083.02 1875.84i 0.218171 0.377883i
\(292\) 3884.96 + 6728.95i 0.778597 + 1.34857i
\(293\) 7191.86 1.43397 0.716985 0.697089i \(-0.245522\pi\)
0.716985 + 0.697089i \(0.245522\pi\)
\(294\) 0 0
\(295\) −4049.67 −0.799257
\(296\) 40.6249 + 70.3645i 0.00797729 + 0.0138171i
\(297\) 153.821 266.426i 0.0300525 0.0520525i
\(298\) 4314.36 7472.70i 0.838672 1.45262i
\(299\) −996.058 1725.22i −0.192654 0.333687i
\(300\) 7443.88 1.43257
\(301\) 0 0
\(302\) 9166.69 1.74663
\(303\) 2278.01 + 3945.63i 0.431908 + 0.748087i
\(304\) 69.0236 119.552i 0.0130223 0.0225552i
\(305\) −5826.43 + 10091.7i −1.09384 + 1.89458i
\(306\) −1092.18 1891.70i −0.204038 0.353403i
\(307\) −541.355 −0.100641 −0.0503204 0.998733i \(-0.516024\pi\)
−0.0503204 + 0.998733i \(0.516024\pi\)
\(308\) 0 0
\(309\) 3155.65 0.580966
\(310\) −6428.37 11134.3i −1.17776 2.03995i
\(311\) 27.0084 46.7799i 0.00492446 0.00852941i −0.863553 0.504259i \(-0.831766\pi\)
0.868477 + 0.495729i \(0.165099\pi\)
\(312\) 426.174 738.155i 0.0773313 0.133942i
\(313\) 1886.47 + 3267.46i 0.340670 + 0.590058i 0.984557 0.175063i \(-0.0560128\pi\)
−0.643887 + 0.765120i \(0.722679\pi\)
\(314\) −17444.1 −3.13511
\(315\) 0 0
\(316\) 11615.1 2.06772
\(317\) −859.618 1488.90i −0.152306 0.263802i 0.779769 0.626068i \(-0.215337\pi\)
−0.932075 + 0.362266i \(0.882003\pi\)
\(318\) 2500.79 4331.49i 0.440998 0.763831i
\(319\) 1062.47 1840.25i 0.186479 0.322991i
\(320\) −7436.70 12880.7i −1.29914 2.25017i
\(321\) 2299.56 0.399841
\(322\) 0 0
\(323\) −2259.72 −0.389270
\(324\) −516.799 895.122i −0.0886144 0.153485i
\(325\) −1273.53 + 2205.81i −0.217362 + 0.376482i
\(326\) −7994.73 + 13847.3i −1.35824 + 2.35255i
\(327\) 2140.57 + 3707.58i 0.362000 + 0.627002i
\(328\) −852.934 −0.143584
\(329\) 0 0
\(330\) −2783.71 −0.464358
\(331\) −4204.11 7281.73i −0.698123 1.20918i −0.969117 0.246603i \(-0.920686\pi\)
0.270994 0.962581i \(-0.412648\pi\)
\(332\) −2092.27 + 3623.91i −0.345868 + 0.599060i
\(333\) −16.8565 + 29.1963i −0.00277396 + 0.00480464i
\(334\) 781.436 + 1353.49i 0.128019 + 0.221735i
\(335\) −2599.36 −0.423935
\(336\) 0 0
\(337\) 2789.46 0.450894 0.225447 0.974255i \(-0.427616\pi\)
0.225447 + 0.974255i \(0.427616\pi\)
\(338\) −4614.29 7992.18i −0.742557 1.28615i
\(339\) −543.846 + 941.969i −0.0871317 + 0.150917i
\(340\) −6074.36 + 10521.1i −0.968907 + 1.67820i
\(341\) 899.419 + 1557.84i 0.142834 + 0.247395i
\(342\) −1739.62 −0.275053
\(343\) 0 0
\(344\) −9314.72 −1.45993
\(345\) 4077.38 + 7062.23i 0.636286 + 1.10208i
\(346\) 9539.24 16522.4i 1.48217 2.56720i
\(347\) 1735.98 3006.81i 0.268566 0.465170i −0.699926 0.714216i \(-0.746784\pi\)
0.968492 + 0.249046i \(0.0801170\pi\)
\(348\) −3569.61 6182.75i −0.549860 0.952386i
\(349\) 6626.12 1.01630 0.508149 0.861269i \(-0.330330\pi\)
0.508149 + 0.861269i \(0.330330\pi\)
\(350\) 0 0
\(351\) 353.664 0.0537812
\(352\) 1073.05 + 1858.57i 0.162482 + 0.281427i
\(353\) 4734.20 8199.87i 0.713813 1.23636i −0.249603 0.968348i \(-0.580300\pi\)
0.963416 0.268012i \(-0.0863666\pi\)
\(354\) 1548.56 2682.18i 0.232499 0.402701i
\(355\) −3297.27 5711.03i −0.492960 0.853831i
\(356\) 479.944 0.0714522
\(357\) 0 0
\(358\) 8977.35 1.32533
\(359\) 3139.78 + 5438.25i 0.461591 + 0.799499i 0.999040 0.0437971i \(-0.0139455\pi\)
−0.537450 + 0.843296i \(0.680612\pi\)
\(360\) −1744.55 + 3021.65i −0.255405 + 0.442375i
\(361\) 2529.68 4381.53i 0.368811 0.638800i
\(362\) 8231.31 + 14257.0i 1.19510 + 2.06998i
\(363\) −3603.52 −0.521035
\(364\) 0 0
\(365\) 10883.1 1.56068
\(366\) −4455.94 7717.92i −0.636382 1.10225i
\(367\) −5413.91 + 9377.17i −0.770038 + 1.33374i 0.167504 + 0.985871i \(0.446429\pi\)
−0.937542 + 0.347873i \(0.886904\pi\)
\(368\) 247.452 428.599i 0.0350525 0.0607127i
\(369\) −176.954 306.493i −0.0249643 0.0432395i
\(370\) 305.053 0.0428620
\(371\) 0 0
\(372\) 6043.63 0.842332
\(373\) −2619.61 4537.30i −0.363642 0.629846i 0.624915 0.780693i \(-0.285134\pi\)
−0.988557 + 0.150846i \(0.951800\pi\)
\(374\) 1382.71 2394.93i 0.191172 0.331120i
\(375\) 1861.98 3225.04i 0.256406 0.444108i
\(376\) −229.777 397.985i −0.0315155 0.0545864i
\(377\) 2442.81 0.333717
\(378\) 0 0
\(379\) −11050.4 −1.49768 −0.748839 0.662751i \(-0.769389\pi\)
−0.748839 + 0.662751i \(0.769389\pi\)
\(380\) 4837.64 + 8379.03i 0.653067 + 1.13115i
\(381\) −1462.16 + 2532.54i −0.196611 + 0.340541i
\(382\) 4346.25 7527.92i 0.582129 1.00828i
\(383\) −5234.02 9065.59i −0.698292 1.20948i −0.969058 0.246832i \(-0.920610\pi\)
0.270766 0.962645i \(-0.412723\pi\)
\(384\) 6854.48 0.910915
\(385\) 0 0
\(386\) −10934.9 −1.44190
\(387\) −1932.47 3347.14i −0.253833 0.439651i
\(388\) 4606.61 7978.88i 0.602745 1.04399i
\(389\) 5807.02 10058.1i 0.756884 1.31096i −0.187549 0.982255i \(-0.560054\pi\)
0.944432 0.328705i \(-0.106612\pi\)
\(390\) −1600.07 2771.41i −0.207751 0.359835i
\(391\) −8101.19 −1.04781
\(392\) 0 0
\(393\) 5378.11 0.690304
\(394\) 3449.89 + 5975.38i 0.441124 + 0.764049i
\(395\) 8134.43 14089.2i 1.03617 1.79470i
\(396\) 654.276 1133.24i 0.0830268 0.143807i
\(397\) −3353.65 5808.69i −0.423967 0.734332i 0.572356 0.820005i \(-0.306029\pi\)
−0.996323 + 0.0856726i \(0.972696\pi\)
\(398\) 6232.10 0.784892
\(399\) 0 0
\(400\) −632.768 −0.0790960
\(401\) −2763.19 4785.98i −0.344107 0.596011i 0.641084 0.767471i \(-0.278485\pi\)
−0.985191 + 0.171459i \(0.945152\pi\)
\(402\) 993.970 1721.61i 0.123320 0.213597i
\(403\) −1033.97 + 1790.89i −0.127805 + 0.221366i
\(404\) 9689.49 + 16782.7i 1.19324 + 2.06676i
\(405\) −1447.73 −0.177625
\(406\) 0 0
\(407\) −42.6811 −0.00519810
\(408\) −1733.09 3001.80i −0.210296 0.364243i
\(409\) −659.453 + 1142.21i −0.0797258 + 0.138089i −0.903132 0.429364i \(-0.858738\pi\)
0.823406 + 0.567453i \(0.192071\pi\)
\(410\) −1601.17 + 2773.31i −0.192869 + 0.334059i
\(411\) −2526.62 4376.24i −0.303234 0.525217i
\(412\) 13422.5 1.60505
\(413\) 0 0
\(414\) −6236.61 −0.740369
\(415\) 2930.57 + 5075.90i 0.346641 + 0.600401i
\(416\) −1233.57 + 2136.61i −0.145387 + 0.251817i
\(417\) 472.634 818.626i 0.0555036 0.0961350i
\(418\) −1101.20 1907.33i −0.128855 0.223183i
\(419\) −3656.13 −0.426286 −0.213143 0.977021i \(-0.568370\pi\)
−0.213143 + 0.977021i \(0.568370\pi\)
\(420\) 0 0
\(421\) −135.389 −0.0156733 −0.00783663 0.999969i \(-0.502495\pi\)
−0.00783663 + 0.999969i \(0.502495\pi\)
\(422\) 9801.93 + 16977.4i 1.13069 + 1.95841i
\(423\) 95.3409 165.135i 0.0109589 0.0189815i
\(424\) 3968.31 6873.32i 0.454524 0.787259i
\(425\) 5178.96 + 8970.22i 0.591097 + 1.02381i
\(426\) 5043.38 0.573597
\(427\) 0 0
\(428\) 9781.16 1.10465
\(429\) 223.872 + 387.758i 0.0251950 + 0.0436390i
\(430\) −17486.1 + 30286.8i −1.96105 + 3.39665i
\(431\) −4194.58 + 7265.23i −0.468784 + 0.811958i −0.999363 0.0356776i \(-0.988641\pi\)
0.530579 + 0.847635i \(0.321974\pi\)
\(432\) 43.9306 + 76.0900i 0.00489262 + 0.00847427i
\(433\) 8243.02 0.914859 0.457430 0.889246i \(-0.348770\pi\)
0.457430 + 0.889246i \(0.348770\pi\)
\(434\) 0 0
\(435\) −9999.70 −1.10218
\(436\) 9104.91 + 15770.2i 1.00011 + 1.73223i
\(437\) −3225.91 + 5587.43i −0.353126 + 0.611632i
\(438\) −4161.60 + 7208.10i −0.453993 + 0.786338i
\(439\) −9141.59 15833.7i −0.993859 1.72142i −0.592755 0.805383i \(-0.701960\pi\)
−0.401104 0.916032i \(-0.631374\pi\)
\(440\) −4417.26 −0.478602
\(441\) 0 0
\(442\) 3179.12 0.342116
\(443\) −605.218 1048.27i −0.0649092 0.112426i 0.831745 0.555159i \(-0.187342\pi\)
−0.896654 + 0.442733i \(0.854009\pi\)
\(444\) −71.6988 + 124.186i −0.00766368 + 0.0132739i
\(445\) 336.122 582.180i 0.0358061 0.0620179i
\(446\) 3410.86 + 5907.79i 0.362128 + 0.627224i
\(447\) 5681.32 0.601157
\(448\) 0 0
\(449\) −8301.16 −0.872508 −0.436254 0.899824i \(-0.643695\pi\)
−0.436254 + 0.899824i \(0.643695\pi\)
\(450\) 3986.96 + 6905.62i 0.417661 + 0.723409i
\(451\) 224.026 388.025i 0.0233902 0.0405130i
\(452\) −2313.24 + 4006.66i −0.240721 + 0.416941i
\(453\) 3017.76 + 5226.92i 0.312995 + 0.542124i
\(454\) 7305.34 0.755190
\(455\) 0 0
\(456\) −2760.48 −0.283489
\(457\) 6146.88 + 10646.7i 0.629188 + 1.08979i 0.987715 + 0.156266i \(0.0499458\pi\)
−0.358527 + 0.933519i \(0.616721\pi\)
\(458\) −2302.15 + 3987.45i −0.234875 + 0.406815i
\(459\) 719.109 1245.53i 0.0731267 0.126659i
\(460\) 17343.1 + 30039.1i 1.75788 + 3.04474i
\(461\) −19434.2 −1.96343 −0.981717 0.190346i \(-0.939039\pi\)
−0.981717 + 0.190346i \(0.939039\pi\)
\(462\) 0 0
\(463\) −12491.1 −1.25380 −0.626902 0.779098i \(-0.715678\pi\)
−0.626902 + 0.779098i \(0.715678\pi\)
\(464\) 303.436 + 525.566i 0.0303592 + 0.0525836i
\(465\) 4232.56 7331.02i 0.422109 0.731113i
\(466\) 451.574 782.150i 0.0448901 0.0777519i
\(467\) 1692.59 + 2931.65i 0.167716 + 0.290493i 0.937617 0.347671i \(-0.113027\pi\)
−0.769900 + 0.638164i \(0.779694\pi\)
\(468\) 1504.31 0.148583
\(469\) 0 0
\(470\) −1725.39 −0.169333
\(471\) −5742.75 9946.74i −0.561809 0.973082i
\(472\) 2457.29 4256.14i 0.239631 0.415053i
\(473\) 2446.54 4237.54i 0.237827 0.411929i
\(474\) 6221.06 + 10775.2i 0.602833 + 1.04414i
\(475\) 8249.07 0.796828
\(476\) 0 0
\(477\) 3293.14 0.316106
\(478\) −2736.53 4739.80i −0.261853 0.453543i
\(479\) 2989.71 5178.32i 0.285184 0.493953i −0.687470 0.726213i \(-0.741279\pi\)
0.972654 + 0.232260i \(0.0746120\pi\)
\(480\) 5049.64 8746.24i 0.480174 0.831686i
\(481\) −24.5330 42.4925i −0.00232559 0.00402804i
\(482\) −12451.1 −1.17663
\(483\) 0 0
\(484\) −15327.5 −1.43948
\(485\) −6452.34 11175.8i −0.604094 1.04632i
\(486\) 553.598 958.861i 0.0516702 0.0894955i
\(487\) 557.481 965.586i 0.0518725 0.0898457i −0.838923 0.544250i \(-0.816814\pi\)
0.890796 + 0.454404i \(0.150148\pi\)
\(488\) −7070.80 12247.0i −0.655902 1.13606i
\(489\) −10527.8 −0.973583
\(490\) 0 0
\(491\) 1086.23 0.0998387 0.0499194 0.998753i \(-0.484104\pi\)
0.0499194 + 0.998753i \(0.484104\pi\)
\(492\) −752.670 1303.66i −0.0689695 0.119459i
\(493\) 4967.00 8603.10i 0.453758 0.785932i
\(494\) 1265.93 2192.66i 0.115297 0.199701i
\(495\) −916.425 1587.29i −0.0832126 0.144128i
\(496\) −513.740 −0.0465073
\(497\) 0 0
\(498\) −4482.50 −0.403344
\(499\) 1106.75 + 1916.95i 0.0992884 + 0.171973i 0.911390 0.411543i \(-0.135010\pi\)
−0.812102 + 0.583516i \(0.801677\pi\)
\(500\) 7919.92 13717.7i 0.708379 1.22695i
\(501\) −514.512 + 891.162i −0.0458817 + 0.0794694i
\(502\) −17236.3 29854.2i −1.53246 2.65430i
\(503\) 2643.32 0.234314 0.117157 0.993113i \(-0.462622\pi\)
0.117157 + 0.993113i \(0.462622\pi\)
\(504\) 0 0
\(505\) 27143.5 2.39183
\(506\) −3947.83 6837.84i −0.346843 0.600749i
\(507\) 3038.14 5262.21i 0.266131 0.460952i
\(508\) −6219.31 + 10772.2i −0.543183 + 0.940821i
\(509\) −332.584 576.053i −0.0289618 0.0501633i 0.851181 0.524872i \(-0.175887\pi\)
−0.880143 + 0.474709i \(0.842553\pi\)
\(510\) −13013.8 −1.12992
\(511\) 0 0
\(512\) −1177.58 −0.101645
\(513\) −572.701 991.947i −0.0492892 0.0853714i
\(514\) −11410.7 + 19763.9i −0.979190 + 1.69601i
\(515\) 9400.26 16281.7i 0.804320 1.39312i
\(516\) −8219.76 14237.0i −0.701269 1.21463i
\(517\) 241.406 0.0205359
\(518\) 0 0
\(519\) 12561.6 1.06242
\(520\) −2539.03 4397.73i −0.214123 0.370872i
\(521\) −5880.99 + 10186.2i −0.494531 + 0.856554i −0.999980 0.00630307i \(-0.997994\pi\)
0.505449 + 0.862857i \(0.331327\pi\)
\(522\) 3823.79 6623.01i 0.320619 0.555328i
\(523\) 5061.30 + 8766.43i 0.423165 + 0.732943i 0.996247 0.0865547i \(-0.0275857\pi\)
−0.573082 + 0.819498i \(0.694252\pi\)
\(524\) 22875.7 1.90712
\(525\) 0 0
\(526\) 28471.9 2.36014
\(527\) 4204.76 + 7282.85i 0.347556 + 0.601985i
\(528\) −55.6169 + 96.3312i −0.00458412 + 0.00793992i
\(529\) −5481.49 + 9494.22i −0.450521 + 0.780325i
\(530\) −14899.0 25805.9i −1.22108 2.11497i
\(531\) 2039.20 0.166655
\(532\) 0 0
\(533\) 515.079 0.0418585
\(534\) 257.060 + 445.240i 0.0208316 + 0.0360813i
\(535\) 6850.09 11864.7i 0.553561 0.958796i
\(536\) 1577.26 2731.89i 0.127103 0.220148i
\(537\) 2955.43 + 5118.95i 0.237498 + 0.411358i
\(538\) −16350.3 −1.31024
\(539\) 0 0
\(540\) −6157.90 −0.490730
\(541\) −8058.98 13958.6i −0.640449 1.10929i −0.985333 0.170644i \(-0.945415\pi\)
0.344884 0.938645i \(-0.387918\pi\)
\(542\) 4517.96 7825.34i 0.358050 0.620161i
\(543\) −5419.65 + 9387.11i −0.428323 + 0.741878i
\(544\) 5016.47 + 8688.78i 0.395366 + 0.684795i
\(545\) 25505.9 2.00469
\(546\) 0 0
\(547\) −626.100 −0.0489399 −0.0244699 0.999701i \(-0.507790\pi\)
−0.0244699 + 0.999701i \(0.507790\pi\)
\(548\) −10747.0 18614.3i −0.837751 1.45103i
\(549\) 2933.88 5081.63i 0.228078 0.395043i
\(550\) −5047.56 + 8742.64i −0.391325 + 0.677795i
\(551\) −3955.74 6851.54i −0.305844 0.529737i
\(552\) −9896.41 −0.763078
\(553\) 0 0
\(554\) −33552.7 −2.57313
\(555\) 100.426 + 173.944i 0.00768083 + 0.0133036i
\(556\) 2010.34 3482.02i 0.153341 0.265594i
\(557\) −10385.6 + 17988.4i −0.790039 + 1.36839i 0.135903 + 0.990722i \(0.456606\pi\)
−0.925942 + 0.377665i \(0.876727\pi\)
\(558\) 3236.99 + 5606.63i 0.245578 + 0.425354i
\(559\) 5625.08 0.425609
\(560\) 0 0
\(561\) 1820.81 0.137031
\(562\) −12101.8 20961.0i −0.908335 1.57328i
\(563\) −2760.86 + 4781.95i −0.206672 + 0.357966i −0.950664 0.310222i \(-0.899597\pi\)
0.743992 + 0.668188i \(0.232930\pi\)
\(564\) 405.532 702.402i 0.0302765 0.0524405i
\(565\) 3240.09 + 5612.00i 0.241260 + 0.417874i
\(566\) −4974.48 −0.369422
\(567\) 0 0
\(568\) 8002.95 0.591191
\(569\) −3787.40 6559.97i −0.279044 0.483319i 0.692103 0.721799i \(-0.256684\pi\)
−0.971147 + 0.238480i \(0.923351\pi\)
\(570\) −5182.11 + 8975.67i −0.380797 + 0.659560i
\(571\) 165.624 286.869i 0.0121386 0.0210247i −0.859892 0.510476i \(-0.829469\pi\)
0.872031 + 0.489451i \(0.162803\pi\)
\(572\) 952.239 + 1649.33i 0.0696068 + 0.120563i
\(573\) 5723.31 0.417268
\(574\) 0 0
\(575\) 29573.2 2.14485
\(576\) 3744.73 + 6486.06i 0.270886 + 0.469188i
\(577\) 1019.06 1765.06i 0.0735248 0.127349i −0.826919 0.562321i \(-0.809909\pi\)
0.900444 + 0.434972i \(0.143242\pi\)
\(578\) −4728.57 + 8190.13i −0.340281 + 0.589385i
\(579\) −3599.89 6235.19i −0.258387 0.447540i
\(580\) −42533.6 −3.04502
\(581\) 0 0
\(582\) 9869.26 0.702911
\(583\) 2084.58 + 3610.60i 0.148087 + 0.256494i
\(584\) −6603.72 + 11438.0i −0.467918 + 0.810457i
\(585\) 1053.52 1824.75i 0.0744575 0.128964i
\(586\) 16384.4 + 28378.6i 1.15500 + 2.00053i
\(587\) −5232.90 −0.367947 −0.183973 0.982931i \(-0.558896\pi\)
−0.183973 + 0.982931i \(0.558896\pi\)
\(588\) 0 0
\(589\) 6697.36 0.468523
\(590\) −9225.88 15979.7i −0.643769 1.11504i
\(591\) −2271.47 + 3934.31i −0.158098 + 0.273834i
\(592\) 6.09477 10.5565i 0.000423131 0.000732884i
\(593\) −2860.12 4953.87i −0.198062 0.343054i 0.749838 0.661622i \(-0.230132\pi\)
−0.947900 + 0.318568i \(0.896798\pi\)
\(594\) 1401.73 0.0968244
\(595\) 0 0
\(596\) 24165.5 1.66083
\(597\) 2051.67 + 3553.59i 0.140652 + 0.243616i
\(598\) 4538.41 7860.75i 0.310350 0.537542i
\(599\) −9044.21 + 15665.0i −0.616922 + 1.06854i 0.373122 + 0.927782i \(0.378287\pi\)
−0.990044 + 0.140758i \(0.955046\pi\)
\(600\) 6326.61 + 10958.0i 0.430471 + 0.745598i
\(601\) 1821.43 0.123623 0.0618117 0.998088i \(-0.480312\pi\)
0.0618117 + 0.998088i \(0.480312\pi\)
\(602\) 0 0
\(603\) 1308.90 0.0883955
\(604\) 12836.0 + 22232.6i 0.864719 + 1.49774i
\(605\) −10734.4 + 18592.5i −0.721348 + 1.24941i
\(606\) −10379.4 + 17977.7i −0.695769 + 1.20511i
\(607\) 1186.10 + 2054.39i 0.0793120 + 0.137372i 0.902953 0.429739i \(-0.141394\pi\)
−0.823641 + 0.567111i \(0.808061\pi\)
\(608\) 7990.26 0.532974
\(609\) 0 0
\(610\) −53094.7 −3.52416
\(611\) 138.760 + 240.339i 0.00918760 + 0.0159134i
\(612\) 3058.72 5297.87i 0.202029 0.349924i
\(613\) −4862.54 + 8422.16i −0.320385 + 0.554923i −0.980567 0.196182i \(-0.937146\pi\)
0.660182 + 0.751105i \(0.270479\pi\)
\(614\) −1233.30 2136.15i −0.0810621 0.140404i
\(615\) −2108.48 −0.138248
\(616\) 0 0
\(617\) −5329.51 −0.347744 −0.173872 0.984768i \(-0.555628\pi\)
−0.173872 + 0.984768i \(0.555628\pi\)
\(618\) 7189.15 + 12452.0i 0.467945 + 0.810504i
\(619\) −7988.29 + 13836.1i −0.518702 + 0.898418i 0.481062 + 0.876687i \(0.340251\pi\)
−0.999764 + 0.0217314i \(0.993082\pi\)
\(620\) 18003.2 31182.4i 1.16617 2.01986i
\(621\) −2053.15 3556.17i −0.132673 0.229797i
\(622\) 246.120 0.0158658
\(623\) 0 0
\(624\) −127.874 −0.00820361
\(625\) 1060.03 + 1836.03i 0.0678420 + 0.117506i
\(626\) −8595.45 + 14887.8i −0.548791 + 0.950535i
\(627\) 725.049 1255.82i 0.0461813 0.0799883i
\(628\) −24426.7 42308.4i −1.55212 2.68836i
\(629\) −199.533 −0.0126485
\(630\) 0 0
\(631\) −4199.98 −0.264974 −0.132487 0.991185i \(-0.542296\pi\)
−0.132487 + 0.991185i \(0.542296\pi\)
\(632\) 9871.73 + 17098.3i 0.621324 + 1.07616i
\(633\) −6453.78 + 11178.3i −0.405237 + 0.701891i
\(634\) 3916.74 6783.99i 0.245352 0.424963i
\(635\) 8711.19 + 15088.2i 0.544399 + 0.942926i
\(636\) 14007.3 0.873312
\(637\) 0 0
\(638\) 9681.97 0.600804
\(639\) 1660.33 + 2875.77i 0.102788 + 0.178034i
\(640\) 20418.6 35366.0i 1.26112 2.18432i
\(641\) −1324.25 + 2293.67i −0.0815988 + 0.141333i −0.903937 0.427666i \(-0.859336\pi\)
0.822338 + 0.568999i \(0.192669\pi\)
\(642\) 5238.82 + 9073.91i 0.322056 + 0.557817i
\(643\) −13.4305 −0.000823715 −0.000411857 1.00000i \(-0.500131\pi\)
−0.000411857 1.00000i \(0.500131\pi\)
\(644\) 0 0
\(645\) −23026.3 −1.40568
\(646\) −5148.06 8916.70i −0.313541 0.543070i
\(647\) 5812.07 10066.8i 0.353162 0.611695i −0.633639 0.773628i \(-0.718440\pi\)
0.986802 + 0.161934i \(0.0517730\pi\)
\(648\) 878.463 1521.54i 0.0532551 0.0922405i
\(649\) 1290.83 + 2235.78i 0.0780732 + 0.135227i
\(650\) −11605.3 −0.700305
\(651\) 0 0
\(652\) −44779.8 −2.68974
\(653\) 14258.3 + 24696.1i 0.854471 + 1.47999i 0.877135 + 0.480244i \(0.159452\pi\)
−0.0226638 + 0.999743i \(0.507215\pi\)
\(654\) −9753.23 + 16893.1i −0.583152 + 1.01005i
\(655\) 16020.7 27748.6i 0.955694 1.65531i
\(656\) 63.9809 + 110.818i 0.00380798 + 0.00659561i
\(657\) −5480.15 −0.325420
\(658\) 0 0
\(659\) 18048.6 1.06688 0.533440 0.845838i \(-0.320899\pi\)
0.533440 + 0.845838i \(0.320899\pi\)
\(660\) −3898.01 6751.54i −0.229893 0.398187i
\(661\) 8920.72 15451.1i 0.524926 0.909198i −0.474653 0.880173i \(-0.657426\pi\)
0.999579 0.0290250i \(-0.00924023\pi\)
\(662\) 19155.5 33178.2i 1.12462 1.94790i
\(663\) 1046.60 + 1812.76i 0.0613069 + 0.106187i
\(664\) −7112.94 −0.415716
\(665\) 0 0
\(666\) −153.608 −0.00893725
\(667\) −14181.5 24563.0i −0.823251 1.42591i
\(668\) −2188.47 + 3790.55i −0.126758 + 0.219552i
\(669\) −2245.78 + 3889.80i −0.129786 + 0.224796i
\(670\) −5921.81 10256.9i −0.341462 0.591430i
\(671\) 7428.68 0.427394
\(672\) 0 0
\(673\) −6826.13 −0.390978 −0.195489 0.980706i \(-0.562629\pi\)
−0.195489 + 0.980706i \(0.562629\pi\)
\(674\) 6354.89 + 11007.0i 0.363177 + 0.629041i
\(675\) −2625.09 + 4546.80i −0.149689 + 0.259269i
\(676\) 12922.7 22382.8i 0.735246 1.27348i
\(677\) −10643.4 18435.0i −0.604225 1.04655i −0.992173 0.124867i \(-0.960150\pi\)
0.387949 0.921681i \(-0.373184\pi\)
\(678\) −4955.92 −0.280724
\(679\) 0 0
\(680\) −20650.6 −1.16458
\(681\) 2404.99 + 4165.56i 0.135329 + 0.234397i
\(682\) −4098.08 + 7098.08i −0.230093 + 0.398533i
\(683\) 10348.4 17924.0i 0.579753 1.00416i −0.415755 0.909477i \(-0.636483\pi\)
0.995507 0.0946842i \(-0.0301841\pi\)
\(684\) −2435.98 4219.24i −0.136172 0.235858i
\(685\) −30105.9 −1.67925
\(686\) 0 0
\(687\) −3031.56 −0.168357
\(688\) 698.722 + 1210.22i 0.0387188 + 0.0670629i
\(689\) −2396.43 + 4150.74i −0.132506 + 0.229507i
\(690\) −18578.0 + 32178.1i −1.02501 + 1.77536i
\(691\) 15671.0 + 27142.9i 0.862738 + 1.49431i 0.869276 + 0.494327i \(0.164585\pi\)
−0.00653825 + 0.999979i \(0.502081\pi\)
\(692\) 53430.8 2.93517
\(693\) 0 0
\(694\) 15819.5 0.865276
\(695\) −2815.83 4877.16i −0.153684 0.266189i
\(696\) 6067.69 10509.5i 0.330453 0.572361i
\(697\) 1047.32 1814.01i 0.0569153 0.0985801i
\(698\) 15095.5 + 26146.2i 0.818587 + 1.41783i
\(699\) 594.651 0.0321770
\(700\) 0 0
\(701\) −9213.32 −0.496408 −0.248204 0.968708i \(-0.579840\pi\)
−0.248204 + 0.968708i \(0.579840\pi\)
\(702\) 805.712 + 1395.53i 0.0433185 + 0.0750299i
\(703\) −79.4544 + 137.619i −0.00426270 + 0.00738322i
\(704\) −4740.89 + 8211.46i −0.253805 + 0.439604i
\(705\) −568.016 983.833i −0.0303443 0.0525578i
\(706\) 43141.5 2.29979
\(707\) 0 0
\(708\) 8673.71 0.460421
\(709\) −7258.27 12571.7i −0.384471 0.665923i 0.607225 0.794530i \(-0.292283\pi\)
−0.991696 + 0.128607i \(0.958949\pi\)
\(710\) 15023.5 26021.6i 0.794118 1.37545i
\(711\) −4096.07 + 7094.60i −0.216054 + 0.374217i
\(712\) 407.908 + 706.518i 0.0214705 + 0.0371880i
\(713\) 24010.3 1.26114
\(714\) 0 0
\(715\) 2667.54 0.139525
\(716\) 12570.9 + 21773.4i 0.656140 + 1.13647i
\(717\) 1801.78 3120.78i 0.0938477 0.162549i
\(718\) −14306.0 + 24778.7i −0.743585 + 1.28793i
\(719\) 12941.2 + 22414.8i 0.671246 + 1.16263i 0.977551 + 0.210698i \(0.0675737\pi\)
−0.306306 + 0.951933i \(0.599093\pi\)
\(720\) 523.454 0.0270944
\(721\) 0 0
\(722\) 23052.3 1.18825
\(723\) −4099.04 7099.74i −0.210850 0.365204i
\(724\) −23052.4 + 39928.0i −1.18334 + 2.04960i
\(725\) −18132.0 + 31405.5i −0.928833 + 1.60879i
\(726\) −8209.48 14219.2i −0.419673 0.726894i
\(727\) −32181.2 −1.64172 −0.820862 0.571127i \(-0.806506\pi\)
−0.820862 + 0.571127i \(0.806506\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 24793.7 + 42943.9i 1.25706 + 2.17730i
\(731\) 11437.5 19810.4i 0.578704 1.00234i
\(732\) 12479.2 21614.7i 0.630117 1.09139i
\(733\) 10418.1 + 18044.6i 0.524966 + 0.909268i 0.999577 + 0.0290722i \(0.00925528\pi\)
−0.474611 + 0.880195i \(0.657411\pi\)
\(734\) −49335.5 −2.48094
\(735\) 0 0
\(736\) 28645.4 1.43462
\(737\) 828.544 + 1435.08i 0.0414109 + 0.0717257i
\(738\) 806.265 1396.49i 0.0402155 0.0696553i
\(739\) −13217.4 + 22893.3i −0.657931 + 1.13957i 0.323219 + 0.946324i \(0.395235\pi\)
−0.981150 + 0.193246i \(0.938098\pi\)
\(740\) 427.163 + 739.867i 0.0212200 + 0.0367541i
\(741\) 1667.03 0.0826447
\(742\) 0 0
\(743\) 9954.69 0.491524 0.245762 0.969330i \(-0.420962\pi\)
0.245762 + 0.969330i \(0.420962\pi\)
\(744\) 5136.53 + 8896.73i 0.253111 + 0.438401i
\(745\) 16923.9 29313.1i 0.832274 1.44154i
\(746\) 11935.9 20673.6i 0.585798 1.01463i
\(747\) −1475.68 2555.96i −0.0722790 0.125191i
\(748\) 7744.79 0.378580
\(749\) 0 0
\(750\) 16967.7 0.826098
\(751\) 16602.3 + 28756.0i 0.806692 + 1.39723i 0.915143 + 0.403129i \(0.132077\pi\)
−0.108451 + 0.994102i \(0.534589\pi\)
\(752\) −34.4723 + 59.7078i −0.00167164 + 0.00289537i
\(753\) 11348.7 19656.6i 0.549231 0.951295i
\(754\) 5565.18 + 9639.17i 0.268796 + 0.465568i
\(755\) 35958.1 1.73331
\(756\) 0 0
\(757\) 1964.06 0.0942998 0.0471499 0.998888i \(-0.484986\pi\)
0.0471499 + 0.998888i \(0.484986\pi\)
\(758\) −25174.8 43604.0i −1.20632 2.08941i
\(759\) 2599.33 4502.17i 0.124308 0.215307i
\(760\) −8223.09 + 14242.8i −0.392477 + 0.679791i
\(761\) −19276.9 33388.6i −0.918248 1.59045i −0.802075 0.597224i \(-0.796270\pi\)
−0.116174 0.993229i \(-0.537063\pi\)
\(762\) −13324.3 −0.633450
\(763\) 0 0
\(764\) 24344.0 1.15280
\(765\) −4284.26 7420.56i −0.202481 0.350707i
\(766\) 23848.1 41306.1i 1.12489 1.94837i
\(767\) −1483.93 + 2570.25i −0.0698588 + 0.120999i
\(768\) 5629.83 + 9751.15i 0.264517 + 0.458156i
\(769\) 19715.0 0.924501 0.462251 0.886749i \(-0.347042\pi\)
0.462251 + 0.886749i \(0.347042\pi\)
\(770\) 0 0
\(771\) −15026.0 −0.701880
\(772\) −15312.1 26521.3i −0.713853 1.23643i
\(773\) −7350.34 + 12731.2i −0.342010 + 0.592378i −0.984806 0.173659i \(-0.944441\pi\)
0.642796 + 0.766037i \(0.277774\pi\)
\(774\) 8805.06 15250.8i 0.408904 0.708242i
\(775\) −15349.4 26585.9i −0.711440 1.23225i
\(776\) 15660.8 0.724471
\(777\) 0 0
\(778\) 52917.8 2.43856
\(779\) −834.086 1444.68i −0.0383623 0.0664454i
\(780\)