Properties

Label 21.4.e.b.4.3
Level 21
Weight 4
Character 21.4
Analytic conductor 1.239
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 21.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.23904011012\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.3
Root \(-2.27818 - 3.94593i\)
Character \(\chi\) = 21.4
Dual form 21.4.e.b.16.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.27818 + 3.94593i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-6.38024 + 11.0509i) q^{4} +(-8.93660 - 15.4786i) q^{5} +13.6691 q^{6} +(2.26047 + 18.3818i) q^{7} -21.6905 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(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} +(2.26047 + 18.3818i) q^{7} -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} +(-67.3835 + 50.7968i) q^{14} -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} +(51.1480 + 21.6998i) q^{21} +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} +(-217.558 - 92.2999i) q^{28} +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} +(264.324 - 199.260i) q^{35} +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} +(30.8986 + 251.263i) q^{42} +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} +(-332.781 + 83.1031i) q^{49} -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} +(-49.0307 - 398.709i) q^{56} +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} +(133.100 - 100.337i) q^{63} -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} +(1388.44 + 589.055i) q^{70} -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} +(194.263 + 82.4170i) q^{77} -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} +(-566.139 + 426.781i) q^{84} +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} +(-29.6092 - 240.777i) q^{91} +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} +(-1086.05 - 1123.80i) q^{98} -102.547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + 9q^{3} - 25q^{4} - 11q^{5} - 6q^{6} - 13q^{7} + 78q^{8} - 27q^{9} + O(q^{10}) \) \( 6q - q^{2} + 9q^{3} - 25q^{4} - 11q^{5} - 6q^{6} - 13q^{7} + 78q^{8} - 27q^{9} + 55q^{10} - 35q^{11} + 75q^{12} + 124q^{13} - 326q^{14} - 66q^{15} - 241q^{16} - 48q^{17} - 9q^{18} + 202q^{19} + 878q^{20} + 3q^{21} - 14q^{22} - 216q^{23} + 117q^{24} - 130q^{25} - 274q^{26} - 162q^{27} - 201q^{28} + 106q^{29} - 165q^{30} + 95q^{31} - 683q^{32} + 105q^{33} - 48q^{34} + 56q^{35} + 450q^{36} - 262q^{37} + 398q^{38} + 186q^{39} - 21q^{40} + 488q^{41} - 219q^{42} + 720q^{43} + 905q^{44} - 99q^{45} + 1056q^{46} + 210q^{47} - 1446q^{48} - 303q^{49} - 2756q^{50} + 144q^{51} - 324q^{52} - 393q^{53} + 27q^{54} - 2062q^{55} + 1299q^{56} + 1212q^{57} + 1249q^{58} - 1143q^{59} + 1317q^{60} + 70q^{61} + 2118q^{62} + 126q^{63} - 798q^{64} + 472q^{65} - 21q^{66} + 628q^{67} - 1944q^{68} - 1296q^{69} + 3251q^{70} + 636q^{71} - 351q^{72} - 988q^{73} - 1002q^{74} + 390q^{75} - 4680q^{76} + 1073q^{77} - 1644q^{78} - 861q^{79} - 175q^{80} - 243q^{81} - 124q^{82} + 1038q^{83} + 1620q^{84} + 3600q^{85} + 3208q^{86} + 159q^{87} + 891q^{88} - 1766q^{89} - 990q^{90} - 654q^{91} - 1344q^{92} - 285q^{93} + 3294q^{94} + 736q^{95} + 2049q^{96} + 38q^{97} - 4267q^{98} + 630q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.871863\pi\)
0.120749 0.992683i \(-0.461470\pi\)
\(6\) 13.6691 0.930064
\(7\) 2.26047 + 18.3818i 0.122054 + 0.992523i
\(8\) −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 \(-0.544623\pi\)
−0.139728 + 0.990190i \(0.544623\pi\)
\(14\) −67.3835 + 50.7968i −1.28636 + 0.969714i
\(15\) −53.6196 −0.922968
\(16\) 1.62706 + 2.81815i 0.0254228 + 0.0440336i
\(17\) −26.6337 + 46.1309i −0.379977 + 0.658140i −0.991059 0.133428i \(-0.957402\pi\)
0.611081 + 0.791568i \(0.290735\pi\)
\(18\) 20.5036 35.5134i 0.268486 0.465032i
\(19\) 21.2111 + 36.7388i 0.256114 + 0.443603i 0.965198 0.261522i \(-0.0842244\pi\)
−0.709083 + 0.705125i \(0.750891\pi\)
\(20\) 228.071 2.54991
\(21\) 51.1480 + 21.6998i 0.531496 + 0.225490i
\(22\) 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
\(28\) −217.558 92.2999i −1.46838 0.622966i
\(29\) 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 −0.541481 0.840713i \(-0.682136\pi\)
0.998819 + 0.0485801i \(0.0154696\pi\)
\(32\) −94.1753 + 163.116i −0.520250 + 0.901099i
\(33\) −17.0912 29.6029i −0.0901576 0.156158i
\(34\) −242.706 −1.22423
\(35\) 264.324 199.260i 1.27654 0.962316i
\(36\) 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 \(-0.523862\pi\)
−0.0748930 + 0.997192i \(0.523862\pi\)
\(42\) 30.8986 + 251.263i 0.113518 + 0.923111i
\(43\) 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 0.849119 0.528202i \(-0.177134\pi\)
−0.881996 + 0.471258i \(0.843800\pi\)
\(48\) 9.76236 0.0293557
\(49\) −332.781 + 83.1031i −0.970206 + 0.242283i
\(50\) −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
\(56\) −49.0307 398.709i −0.117000 0.951425i
\(57\) 127.267 0.295735
\(58\) 424.866 + 735.889i 0.961856 + 1.66598i
\(59\) 113.289 196.222i 0.249982 0.432982i −0.713538 0.700616i \(-0.752909\pi\)
0.963521 + 0.267634i \(0.0862419\pi\)
\(60\) 342.106 592.545i 0.736095 1.27495i
\(61\) −325.987 564.626i −0.684235 1.18513i −0.973677 0.227934i \(-0.926803\pi\)
0.289442 0.957196i \(-0.406530\pi\)
\(62\) 719.331 1.47347
\(63\) 133.100 100.337i 0.266174 0.200655i
\(64\) −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
\(70\) 1388.44 + 589.055i 2.37073 + 1.00579i
\(71\) −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 −0.999907 0.0136522i \(-0.995654\pi\)
0.511777 + 0.859119i \(0.328988\pi\)
\(74\) 8.53380 14.7810i 0.0134059 0.0232197i
\(75\) 291.677 + 505.200i 0.449066 + 0.777806i
\(76\) −541.328 −0.817034
\(77\) 194.263 + 82.4170i 0.287510 + 0.121978i
\(78\) −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 \(-0.569574\pi\)
−0.216837 + 0.976208i \(0.569574\pi\)
\(84\) −566.139 + 426.781i −0.735367 + 0.554353i
\(85\) 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 0.877007 0.480477i \(-0.159537\pi\)
−0.854609 + 0.519272i \(0.826203\pi\)
\(90\) −732.932 −0.858420
\(91\) −29.6092 240.777i −0.0341086 0.277366i
\(92\) 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 \(-0.376652\pi\)
0.377883 + 0.925853i \(0.376652\pi\)
\(98\) −1086.05 1123.80i −1.11947 1.15838i
\(99\) −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 \(0.435694\pi\)
−0.948739 + 0.316062i \(0.897639\pi\)
\(102\) −364.058 + 630.568i −0.353403 + 0.612113i
\(103\) 525.942 + 910.957i 0.503132 + 0.871450i 0.999993 + 0.00361990i \(0.00115225\pi\)
−0.496862 + 0.867830i \(0.665514\pi\)
\(104\) 284.116 0.267883
\(105\) −121.206 985.625i −0.112652 0.916068i
\(106\) −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
\(112\) −48.1247 + 36.2786i −0.0406014 + 0.0306072i
\(113\) 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
\(119\) −908.173 385.297i −0.699597 0.296808i
\(120\) 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
\(126\) 699.147 + 296.617i 0.494325 + 0.209720i
\(127\) 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 \(0.0373001\pi\)
−0.395321 + 0.918543i \(0.629367\pi\)
\(132\) 436.184 0.287613
\(133\) −627.377 + 472.946i −0.409026 + 0.308343i
\(134\) −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 \(-0.469352\pi\)
0.0961350 + 0.995368i \(0.469352\pi\)
\(140\) 515.547 + 4192.35i 0.311226 + 2.53084i
\(141\) −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
\(147\) −283.263 + 989.244i −0.158933 + 0.555044i
\(148\) 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
\(154\) 117.355 + 954.308i 0.0614071 + 0.499353i
\(155\) −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 \(-0.407357\pi\)
0.686125 0.727483i \(-0.259310\pi\)
\(158\) 2073.69 3591.73i 1.04414 1.80850i
\(159\) 548.856 + 950.647i 0.273755 + 0.474158i
\(160\) 3366.43 1.66337
\(161\) 2249.17 1695.53i 1.10099 0.829977i
\(162\) −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 \(-0.525323\pi\)
−0.0794694 + 0.996837i \(0.525323\pi\)
\(168\) −1109.42 470.679i −0.509487 0.216153i
\(169\) −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 \(0.205210\pi\)
0.120793 + 0.992678i \(0.461456\pi\)
\(174\) 2549.20 1.11066
\(175\) −3315.27 1406.52i −1.43206 0.607559i
\(176\) 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 \(-0.766065\pi\)
−0.741878 + 0.670535i \(0.766065\pi\)
\(182\) 882.634 665.370i 0.359479 0.270992i
\(183\) −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
\(189\) −61.0328 496.308i −0.0234893 0.191011i
\(190\) 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
\(196\) 1204.86 4207.74i 0.439087 1.53343i
\(197\) 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 −0.961742 0.273958i \(-0.911667\pi\)
0.718126 + 0.695914i \(0.245000\pi\)
\(200\) 2108.87 3652.67i 0.745598 1.29141i
\(201\) 218.150 + 377.847i 0.0765527 + 0.132593i
\(202\) −6919.63 −2.41021
\(203\) 421.563 + 3428.08i 0.145753 + 1.18524i
\(204\) −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
\(210\) 3613.08 2723.70i 1.18727 0.895016i
\(211\) 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
\(217\) 2691.64 + 1141.94i 0.842030 + 0.357236i
\(218\) 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 \(-0.572172\pi\)
−0.224796 + 0.974406i \(0.572172\pi\)
\(224\) −3211.25 1362.39i −0.957861 0.406377i
\(225\) 1750.06 0.518537
\(226\) 825.987 + 1430.65i 0.243114 + 0.421086i
\(227\) −801.662 + 1388.52i −0.234397 + 0.405988i −0.959097 0.283076i \(-0.908645\pi\)
0.724700 + 0.689065i \(0.241978\pi\)
\(228\) −811.992 + 1406.41i −0.235858 + 0.408517i
\(229\) −505.261 875.137i −0.145802 0.252536i 0.783870 0.620925i \(-0.213243\pi\)
−0.929672 + 0.368389i \(0.879909\pi\)
\(230\) −12385.4 −3.55072
\(231\) 505.520 381.084i 0.143986 0.108543i
\(232\) −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
\(238\) −548.629 4461.36i −0.149422 1.21507i
\(239\) −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 −0.623605 0.781739i \(-0.714333\pi\)
0.988809 + 0.149188i \(0.0476660\pi\)
\(242\) −2736.49 + 4739.74i −0.726894 + 1.25902i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 8319.49 2.18279
\(245\) 4260.25 + 4408.33i 1.11093 + 1.14954i
\(246\) −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 \(-0.0997537\pi\)
0.951295 + 0.308281i \(0.0997537\pi\)
\(252\) 259.602 + 2111.04i 0.0648945 + 0.527711i
\(253\) −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 \(-0.958701\pi\)
0.383749 0.923437i \(-0.374633\pi\)
\(258\) 5870.04 1.41648
\(259\) 55.3973 41.7610i 0.0132904 0.0100189i
\(260\) −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
\(266\) −3295.49 1398.13i −0.759622 0.322274i
\(267\) 112.835 0.0258630
\(268\) −927.898 1607.17i −0.211494 0.366318i
\(269\) 1794.22 3107.69i 0.406676 0.704383i −0.587839 0.808978i \(-0.700021\pi\)
0.994515 + 0.104595i \(0.0333546\pi\)
\(270\) −1099.40 + 1904.21i −0.247804 + 0.429210i
\(271\) 991.571 + 1717.45i 0.222264 + 0.384973i 0.955495 0.295007i \(-0.0953218\pi\)
−0.733231 + 0.679980i \(0.761988\pi\)
\(272\) −173.338 −0.0386404
\(273\) −669.971 284.239i −0.148529 0.0630143i
\(274\) −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
\(280\) −5733.32 + 4322.04i −1.22368 + 0.922468i
\(281\) −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 −0.802983 0.596002i \(-0.796755\pi\)
0.917645 + 0.397402i \(0.130088\pi\)
\(284\) 2354.06 4077.36i 0.491859 0.851925i
\(285\) −1137.33 1969.92i −0.236385 0.409431i
\(286\) −680.030 −0.140598
\(287\) −88.8886 722.827i −0.0182820 0.148666i
\(288\) 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 \(-0.754478\pi\)
−0.716985 + 0.697089i \(0.754478\pi\)
\(294\) −4548.81 + 1135.94i −0.902354 + 0.225339i
\(295\) −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
\(301\) 970.735 + 7893.85i 0.185888 + 1.51161i
\(302\) 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 \(-0.483976\pi\)
0.0503204 + 0.998733i \(0.483976\pi\)
\(308\) −2150.22 + 1620.94i −0.397793 + 0.299875i
\(309\) 3155.65 0.580966
\(310\) −6428.37 11134.3i −1.17776 2.03995i
\(311\) −27.0084 + 46.7799i −0.00492446 + 0.00852941i −0.868477 0.495729i \(-0.834901\pi\)
0.863553 + 0.504259i \(0.168234\pi\)
\(312\) 426.174 738.155i 0.0773313 0.133942i
\(313\) −1886.47 3267.46i −0.340670 0.590058i 0.643887 0.765120i \(-0.277321\pi\)
−0.984557 + 0.175063i \(0.943987\pi\)
\(314\) 17444.1 3.13511
\(315\) −2742.54 1163.54i −0.490554 0.208120i
\(316\) 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
\(322\) 11814.5 + 5012.34i 2.04470 + 0.867475i
\(323\) −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
\(329\) 313.330 236.202i 0.0525059 0.0395813i
\(330\) −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
\(336\) 22.0675 + 179.450i 0.00358298 + 0.0291362i
\(337\) 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
\(343\) −2279.82 5929.25i −0.358889 0.933380i
\(344\) −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 \(-0.669670\pi\)
−0.508149 + 0.861269i \(0.669670\pi\)
\(350\) −2002.76 16286.1i −0.305863 2.48723i
\(351\) 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 \(0.419700\pi\)
−0.963416 + 0.268012i \(0.913633\pi\)
\(354\) 1548.56 2682.18i 0.232499 0.402701i
\(355\) 3297.27 + 5711.03i 0.492960 + 0.853831i
\(356\) −479.944 −0.0714522
\(357\) −2363.29 + 1781.56i −0.350360 + 0.264118i
\(358\) 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
\(364\) 2849.71 + 1209.01i 0.410345 + 0.174091i
\(365\) 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 \(-0.553571\pi\)
0.937542 0.347873i \(-0.113096\pi\)
\(368\) 247.452 428.599i 0.0350525 0.0607127i
\(369\) 176.954 + 306.493i 0.0249643 + 0.0432395i
\(370\) −305.053 −0.0428620
\(371\) −6238.42 2646.68i −0.872999 0.370374i
\(372\) 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
\(378\) 1819.35 1371.51i 0.247559 0.186622i
\(379\) −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 \(0.0793897\pi\)
−0.270766 + 0.962645i \(0.587277\pi\)
\(384\) −6854.48 −0.910915
\(385\) −460.345 3743.45i −0.0609386 0.495543i
\(386\) −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
\(392\) 7218.16 1802.54i 0.930031 0.232251i
\(393\) 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 0.996323 0.0856726i \(-0.0273039\pi\)
−0.572356 + 0.820005i \(0.693971\pi\)
\(398\) −6232.10 −0.784892
\(399\) 287.683 + 2339.39i 0.0360957 + 0.293524i
\(400\) −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
\(406\) −12566.6 + 9473.26i −1.53613 + 1.15800i
\(407\) −42.6811 −0.00519810
\(408\) −1733.09 3001.80i −0.210296 0.364243i
\(409\) 659.453 1142.21i 0.0797258 0.138089i −0.823406 0.567453i \(-0.807929\pi\)
0.903132 + 0.429364i \(0.141262\pi\)
\(410\) −1601.17 + 2773.31i −0.192869 + 0.334059i
\(411\) 2526.62 + 4376.24i 0.303234 + 0.525217i
\(412\) −13422.5 −1.60505
\(413\) 3863.00 + 1638.90i 0.460256 + 0.195266i
\(414\) −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 \(-0.431630\pi\)
0.213143 + 0.977021i \(0.431630\pi\)
\(420\) 11665.4 + 4949.09i 1.35526 + 0.574978i
\(421\) −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
\(427\) 9641.94 7268.54i 1.09276 0.823769i
\(428\) 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 \(-0.651230\pi\)
−0.457430 + 0.889246i \(0.651230\pi\)
\(434\) 1626.03 + 13222.6i 0.179843 + 1.46245i
\(435\) −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 \(0.298040\pi\)
0.401104 + 0.916032i \(0.368626\pi\)
\(440\) 4417.26 0.478602
\(441\) 2145.24 + 2219.80i 0.231642 + 0.239694i
\(442\) 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
\(448\) −1881.08 15296.6i −0.198376 1.61316i
\(449\) −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
\(455\) −3462.30 + 2610.04i −0.356736 + 0.268924i
\(456\) −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 \(-0.0609609\pi\)
0.981717 + 0.190346i \(0.0609609\pi\)
\(462\) 2655.40 + 1126.57i 0.267403 + 0.113447i
\(463\) −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 0.769900 0.638164i \(-0.220306\pi\)
−0.937617 + 0.347671i \(0.886973\pi\)
\(468\) −1504.31 −0.148583
\(469\) −2479.54 1051.96i −0.244125 0.103571i
\(470\) −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
\(476\) 10052.2 7577.84i 0.967948 0.729684i
\(477\) 3293.14 0.316106
\(478\) −2736.53 4739.80i −0.261853 0.453543i
\(479\) −2989.71 + 5178.32i −0.285184 + 0.493953i −0.972654 0.232260i \(-0.925388\pi\)
0.687470 + 0.726213i \(0.258721\pi\)
\(480\) 5049.64 8746.24i 0.480174 0.831686i
\(481\) 24.5330 + 42.4925i 0.00232559 + 0.00402804i
\(482\) 12451.1 1.17663
\(483\) −1031.35 8386.81i −0.0971600 0.790089i
\(484\) −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
\(490\) −7689.34 + 26853.6i −0.708916 + 2.47576i
\(491\) 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
\(497\) −834.028 6782.18i −0.0752742 0.612117i
\(498\) −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 \(-0.537378\pi\)
−0.117157 + 0.993113i \(0.537378\pi\)
\(504\) −2886.99 + 2176.35i −0.255153 + 0.192346i
\(505\) 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 0.880143 0.474709i \(-0.157447\pi\)
−0.851181 + 0.524872i \(0.824113\pi\)
\(510\) 13013.8 1.12992
\(511\) −10381.4 4404.38i −0.898724 0.381288i
\(512\) −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
\(518\) 290.991 + 123.455i 0.0246823 + 0.0104716i
\(519\) 12561.6 1.06242
\(520\) −2539.03 4397.73i −0.214123 0.370872i
\(521\) 5880.99 10186.2i 0.494531 0.856554i −0.505449 0.862857i \(-0.668673\pi\)
0.999980 + 0.00630307i \(0.00200634\pi\)
\(522\) 3823.79 6623.01i 0.320619 0.555328i
\(523\) −5061.30 8766.43i −0.423165 0.732943i 0.573082 0.819498i \(-0.305748\pi\)
−0.996247 + 0.0865547i \(0.972414\pi\)
\(524\) −22875.7 −1.90712
\(525\) −8627.15 + 6503.54i −0.717180 + 0.540643i
\(526\) 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
\(532\) −1223.66 9950.58i −0.0997224 0.810926i
\(533\) 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
\(539\) −1075.85 + 3757.20i −0.0859740 + 0.300249i
\(540\) −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
\(546\) −404.731 3291.20i −0.0317232 0.257968i
\(547\) −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
\(553\) 13461.4 10147.8i 1.03515 0.780341i
\(554\) −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
\(560\) 991.615 + 420.698i 0.0748275 + 0.0317460i
\(561\) 1820.81 0.137031
\(562\) −12101.8 20961.0i −0.908335 1.57328i
\(563\) 2760.86 4781.95i 0.206672 0.357966i −0.743992 0.668188i \(-0.767070\pi\)
0.950664 + 0.310222i \(0.100403\pi\)
\(564\) 405.532 702.402i 0.0302765 0.0524405i
\(565\) −3240.09 5612.00i −0.241260 0.417874i
\(566\) 4974.48 0.369422
\(567\) −1381.00 585.895i −0.102286 0.0433955i
\(568\) 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
\(574\) 2649.72 1997.48i 0.192678 0.145250i
\(575\) 29573.2 2.14485
\(576\) 3744.73 + 6486.06i 0.270886 + 0.469188i
\(577\) −1019.06 + 1765.06i −0.0735248 + 0.127349i −0.900444 0.434972i \(-0.856758\pi\)
0.826919 + 0.562321i \(0.190091\pi\)
\(578\) −4728.57 + 8190.13i −0.340281 + 0.589385i
\(579\) 3599.89 + 6235.19i 0.258387 + 0.447540i
\(580\) 42533.6 3.04502
\(581\) −741.275 6027.93i −0.0529316 0.430431i
\(582\) 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 \(-0.441104\pi\)
0.183973 + 0.982931i \(0.441104\pi\)
\(588\) −9124.74 9441.91i −0.639963 0.662207i
\(589\) 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 0.947900 0.318568i \(-0.103202\pi\)
−0.749838 + 0.661622i \(0.769868\pi\)
\(594\) −1401.73 −0.0968244
\(595\) 2152.10 + 17500.5i 0.148282 + 1.20580i
\(596\) 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 \(-0.519688\pi\)
−0.0618117 + 0.998088i \(0.519688\pi\)
\(602\) −28937.1 + 21814.1i −1.95911 + 1.47687i
\(603\) 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 0.823641 0.567111i \(-0.191939\pi\)
−0.902953 + 0.429739i \(0.858606\pi\)
\(608\) −7990.26 −0.532974
\(609\) 9538.76 + 4046.87i 0.634696 + 0.269273i
\(610\) −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
\(616\) −4213.65 1787.66i −0.275605 0.116927i
\(617\) −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 \(-0.659749\pi\)
0.999764 0.0217314i \(-0.00691786\pi\)
\(620\) 18003.2 31182.4i 1.16617 2.01986i
\(621\) 2053.15 + 3556.17i 0.132673 + 0.229797i
\(622\) −246.120 −0.0158658
\(623\) −556.236 + 419.316i −0.0357706 + 0.0269656i
\(624\) −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
\(630\) −1656.77 13472.6i −0.104774 0.852002i
\(631\) −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
\(637\) 4358.98 1088.54i 0.271129 0.0677072i
\(638\) 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 \(-0.499869\pi\)
0.000411857 1.00000i \(0.499869\pi\)
\(644\) 4386.86 + 35673.2i 0.268426 + 2.18280i
\(645\) −23026.3 −1.40568
\(646\) −5148.06 8916.70i −0.313541 0.543070i
\(647\) −5812.07 + 10066.8i −0.353162 + 0.611695i −0.986802 0.161934i \(-0.948227\pi\)
0.633639 + 0.773628i \(0.281560\pi\)
\(648\) 878.463 1521.54i 0.0532551 0.0922405i
\(649\) −1290.83 2235.78i −0.0780732 0.135227i
\(650\) 11605.3 0.700305
\(651\) 7004.32 5280.18i 0.421691 0.317890i
\(652\) −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
\(658\) 1645.86 + 698.265i 0.0975111 + 0.0413696i
\(659\) 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 \(0.342574\pi\)
−0.999579 + 0.0290250i \(0.990760\pi\)
\(662\) 19155.5 33178.2i 1.12462 1.94790i
\(663\) −1046.60 1812.76i −0.0613069 0.106187i
\(664\) 7112.94 0.415716
\(665\) 12927.2 + 5484.42i 0.753826 + 0.319815i
\(666\) −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
\(672\) −8356.47 + 6299.49i −0.479699 + 0.361619i
\(673\) −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 \(0.0398505\pi\)
−0.387949 + 0.921681i \(0.626816\pi\)
\(678\) 4955.92 0.280724
\(679\) 1632.09 + 13271.9i 0.0922443 + 0.750115i
\(680\) −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
\(686\) 18202.5 22503.9i 1.01308 1.25248i
\(687\) −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 \(-0.835415\pi\)
0.00653825 0.999979i \(-0.497919\pi\)
\(692\) −53430.8 −2.93517
\(693\) −231.805 1885.00i −0.0127064 0.103327i
\(694\) 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
\(700\) 36695.5 27662.7i 1.98137 1.49365i
\(701\) −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
\(707\) −25892.4 10985.0i −1.37734 0.584345i
\(708\) 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
\(714\) −12413.9 5266.66i −0.650671 0.276050i
\(715\) 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 \(-0.932426\pi\)
0.306306 0.951933i \(-0.400907\pi\)
\(720\) −523.454 −0.0270944
\(721\) −15556.2 + 11726.9i −0.803525 + 0.605734i
\(722\) 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 \(-0.193494\pi\)
0.820862 + 0.571127i \(0.193494\pi\)
\(728\) 642.237 + 5222.56i 0.0326963 + 0.265881i
\(729\) 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 \(-0.990745\pi\)
0.474611 0.880195i \(-0.342589\pi\)
\(734\) 49335.5 2.48094
\(735\) 17843.6 4455.95i 0.895469 0.223620i
\(736\) 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
\(742\) −3768.64 30646.0i −0.186457 1.51624i
\(743\) 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
\(749\) 11336.0 8545.57i 0.553014 0.416887i
\(750\) 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
\(756\) 5874.05 + 2492.10i 0.282589 + 0.119890i
\(757\) 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 \(0.203730\pi\)
0.116174 + 0.993229i \(0.462937\pi\)
\(762\) 13324.3 0.633450
\(763\) 24330.2 + 10322.2i 1.15441 + 0.489764i
\(764\) 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 \(-0.652958\pi\)
−0.462251 + 0.886749i \(0.652958\pi\)
\(770\) 13722.6 10344.8i 0.642246 0.484155i
\(771\) −15026.0 −0.701880
\(772\) −15312.1 26521.3i −0.713853 1.23643i
\(773\) 7350.34 12731.2i 0.342010 0.592378i −0.642796 0.766037i \(-0.722226\pi\)
0.984806 + 0.173659i \(0.0555591\pi\)
\(774\) 8805.06 15250.8i 0.408904 0.708242i
\(775\) 15349.4 + 26585.9i 0.711440 + 1.23225i
\(776\) −15660.8 −0.724471
\(777\) −25.4024 206.568i −0.00117285 0.00953744i
\(778\) 52917.8 2.43856
\(779\) −834.086 1444.68i −0.0383623