Properties

Label 336.4.q.k.193.1
Level $336$
Weight $4$
Character 336.193
Analytic conductor $19.825$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
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: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(-2.27818 - 3.94593i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.4.q.k.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{3} +(-8.93660 - 15.4786i) q^{5} +(-2.26047 - 18.3818i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{3} +(-8.93660 - 15.4786i) q^{5} +(-2.26047 - 18.3818i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-5.69708 + 9.86762i) q^{11} -13.0987 q^{13} +53.6196 q^{15} +(-26.6337 + 46.1309i) q^{17} +(-21.2111 - 36.7388i) q^{19} +(51.1480 + 21.6998i) q^{21} +(76.0427 + 131.710i) q^{23} +(-97.2257 + 168.400i) q^{25} +27.0000 q^{27} +186.493 q^{29} +(-78.9369 + 136.723i) q^{31} +(-17.0912 - 29.6029i) q^{33} +(-264.324 + 199.260i) q^{35} +(-1.87294 - 3.24403i) q^{37} +(19.6480 - 34.0313i) q^{39} -39.3230 q^{41} -429.439 q^{43} +(-80.4294 + 139.308i) q^{45} +(10.5934 + 18.3484i) q^{47} +(-332.781 + 83.1031i) q^{49} +(-79.9010 - 138.393i) q^{51} +(-182.952 + 316.882i) q^{53} +203.650 q^{55} +127.267 q^{57} +(-113.289 + 196.222i) q^{59} +(-325.987 - 564.626i) q^{61} +(-133.100 + 100.337i) q^{63} +(117.058 + 202.750i) q^{65} +(72.7166 - 125.949i) q^{67} -456.256 q^{69} +368.962 q^{71} +(-304.453 + 527.328i) q^{73} +(-291.677 - 505.200i) q^{75} +(194.263 + 82.4170i) q^{77} +(455.119 + 788.289i) q^{79} +(-40.5000 + 70.1481i) q^{81} +327.929 q^{83} +952.058 q^{85} +(-279.740 + 484.524i) q^{87} +(18.8059 + 32.5728i) q^{89} +(29.6092 + 240.777i) q^{91} +(-236.811 - 410.168i) q^{93} +(-379.111 + 656.640i) q^{95} +722.013 q^{97} +102.547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 9q^{3} - 11q^{5} + 13q^{7} - 27q^{9} + O(q^{10}) \) \( 6q - 9q^{3} - 11q^{5} + 13q^{7} - 27q^{9} + 35q^{11} + 124q^{13} + 66q^{15} - 48q^{17} - 202q^{19} + 3q^{21} + 216q^{23} - 130q^{25} + 162q^{27} + 106q^{29} - 95q^{31} + 105q^{33} - 56q^{35} - 262q^{37} - 186q^{39} + 488q^{41} - 720q^{43} - 99q^{45} - 210q^{47} - 303q^{49} - 144q^{51} - 393q^{53} + 2062q^{55} + 1212q^{57} + 1143q^{59} + 70q^{61} - 126q^{63} + 472q^{65} - 628q^{67} - 1296q^{69} - 636q^{71} - 988q^{73} - 390q^{75} + 1073q^{77} + 861q^{79} - 243q^{81} - 1038q^{83} + 3600q^{85} - 159q^{87} - 1766q^{89} + 654q^{91} - 285q^{93} - 736q^{95} + 38q^{97} - 630q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −8.93660 15.4786i −0.799314 1.38445i −0.920063 0.391769i \(-0.871863\pi\)
0.120749 0.992683i \(-0.461470\pi\)
\(6\) 0 0
\(7\) −2.26047 18.3818i −0.122054 0.992523i
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) −5.69708 + 9.86762i −0.156158 + 0.270473i −0.933480 0.358630i \(-0.883244\pi\)
0.777322 + 0.629102i \(0.216577\pi\)
\(12\) 0 0
\(13\) −13.0987 −0.279455 −0.139728 0.990190i \(-0.544623\pi\)
−0.139728 + 0.990190i \(0.544623\pi\)
\(14\) 0 0
\(15\) 53.6196 0.922968
\(16\) 0 0
\(17\) −26.6337 + 46.1309i −0.379977 + 0.658140i −0.991059 0.133428i \(-0.957402\pi\)
0.611081 + 0.791568i \(0.290735\pi\)
\(18\) 0 0
\(19\) −21.2111 36.7388i −0.256114 0.443603i 0.709083 0.705125i \(-0.249109\pi\)
−0.965198 + 0.261522i \(0.915776\pi\)
\(20\) 0 0
\(21\) 51.1480 + 21.6998i 0.531496 + 0.225490i
\(22\) 0 0
\(23\) 76.0427 + 131.710i 0.689391 + 1.19406i 0.972035 + 0.234836i \(0.0754553\pi\)
−0.282644 + 0.959225i \(0.591211\pi\)
\(24\) 0 0
\(25\) −97.2257 + 168.400i −0.777806 + 1.34720i
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 186.493 1.19417 0.597085 0.802178i \(-0.296325\pi\)
0.597085 + 0.802178i \(0.296325\pi\)
\(30\) 0 0
\(31\) −78.9369 + 136.723i −0.457338 + 0.792133i −0.998819 0.0485801i \(-0.984530\pi\)
0.541481 + 0.840713i \(0.317864\pi\)
\(32\) 0 0
\(33\) −17.0912 29.6029i −0.0901576 0.156158i
\(34\) 0 0
\(35\) −264.324 + 199.260i −1.27654 + 0.962316i
\(36\) 0 0
\(37\) −1.87294 3.24403i −0.00832188 0.0144139i 0.861834 0.507190i \(-0.169316\pi\)
−0.870156 + 0.492776i \(0.835982\pi\)
\(38\) 0 0
\(39\) 19.6480 34.0313i 0.0806718 0.139728i
\(40\) 0 0
\(41\) −39.3230 −0.149786 −0.0748930 0.997192i \(-0.523862\pi\)
−0.0748930 + 0.997192i \(0.523862\pi\)
\(42\) 0 0
\(43\) −429.439 −1.52300 −0.761498 0.648168i \(-0.775536\pi\)
−0.761498 + 0.648168i \(0.775536\pi\)
\(44\) 0 0
\(45\) −80.4294 + 139.308i −0.266438 + 0.461484i
\(46\) 0 0
\(47\) 10.5934 + 18.3484i 0.0328768 + 0.0569444i 0.881996 0.471258i \(-0.156200\pi\)
−0.849119 + 0.528202i \(0.822866\pi\)
\(48\) 0 0
\(49\) −332.781 + 83.1031i −0.970206 + 0.242283i
\(50\) 0 0
\(51\) −79.9010 138.393i −0.219380 0.379977i
\(52\) 0 0
\(53\) −182.952 + 316.882i −0.474158 + 0.821266i −0.999562 0.0295866i \(-0.990581\pi\)
0.525404 + 0.850853i \(0.323914\pi\)
\(54\) 0 0
\(55\) 203.650 0.499276
\(56\) 0 0
\(57\) 127.267 0.295735
\(58\) 0 0
\(59\) −113.289 + 196.222i −0.249982 + 0.432982i −0.963521 0.267634i \(-0.913758\pi\)
0.713538 + 0.700616i \(0.247091\pi\)
\(60\) 0 0
\(61\) −325.987 564.626i −0.684235 1.18513i −0.973677 0.227934i \(-0.926803\pi\)
0.289442 0.957196i \(-0.406530\pi\)
\(62\) 0 0
\(63\) −133.100 + 100.337i −0.266174 + 0.200655i
\(64\) 0 0
\(65\) 117.058 + 202.750i 0.223372 + 0.386892i
\(66\) 0 0
\(67\) 72.7166 125.949i 0.132593 0.229658i −0.792082 0.610414i \(-0.791003\pi\)
0.924675 + 0.380756i \(0.124336\pi\)
\(68\) 0 0
\(69\) −456.256 −0.796041
\(70\) 0 0
\(71\) 368.962 0.616728 0.308364 0.951268i \(-0.400218\pi\)
0.308364 + 0.951268i \(0.400218\pi\)
\(72\) 0 0
\(73\) −304.453 + 527.328i −0.488130 + 0.845466i −0.999907 0.0136522i \(-0.995654\pi\)
0.511777 + 0.859119i \(0.328988\pi\)
\(74\) 0 0
\(75\) −291.677 505.200i −0.449066 0.777806i
\(76\) 0 0
\(77\) 194.263 + 82.4170i 0.287510 + 0.121978i
\(78\) 0 0
\(79\) 455.119 + 788.289i 0.648163 + 1.12265i 0.983561 + 0.180574i \(0.0577957\pi\)
−0.335399 + 0.942076i \(0.608871\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 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
\(86\) 0 0
\(87\) −279.740 + 484.524i −0.344727 + 0.597085i
\(88\) 0 0
\(89\) 18.8059 + 32.5728i 0.0223980 + 0.0387945i 0.877007 0.480477i \(-0.159537\pi\)
−0.854609 + 0.519272i \(0.826203\pi\)
\(90\) 0 0
\(91\) 29.6092 + 240.777i 0.0341086 + 0.277366i
\(92\) 0 0
\(93\) −236.811 410.168i −0.264044 0.457338i
\(94\) 0 0
\(95\) −379.111 + 656.640i −0.409431 + 0.709156i
\(96\) 0 0
\(97\) 722.013 0.755766 0.377883 0.925853i \(-0.376652\pi\)
0.377883 + 0.925853i \(0.376652\pi\)
\(98\) 0 0
\(99\) 102.547 0.104105
\(100\) 0 0
\(101\) −759.336 + 1315.21i −0.748087 + 1.29572i 0.200652 + 0.979663i \(0.435694\pi\)
−0.948739 + 0.316062i \(0.897639\pi\)
\(102\) 0 0
\(103\) −525.942 910.957i −0.503132 0.871450i −0.999993 0.00361990i \(-0.998848\pi\)
0.496862 0.867830i \(-0.334486\pi\)
\(104\) 0 0
\(105\) −121.206 985.625i −0.112652 0.916068i
\(106\) 0 0
\(107\) 383.260 + 663.826i 0.346273 + 0.599762i 0.985584 0.169186i \(-0.0541139\pi\)
−0.639312 + 0.768948i \(0.720781\pi\)
\(108\) 0 0
\(109\) 713.524 1235.86i 0.627002 1.08600i −0.361148 0.932509i \(-0.617615\pi\)
0.988150 0.153491i \(-0.0490516\pi\)
\(110\) 0 0
\(111\) 11.2376 0.00960928
\(112\) 0 0
\(113\) 362.564 0.301833 0.150917 0.988546i \(-0.451778\pi\)
0.150917 + 0.988546i \(0.451778\pi\)
\(114\) 0 0
\(115\) 1359.13 2354.08i 1.10208 1.90886i
\(116\) 0 0
\(117\) 58.9440 + 102.094i 0.0465759 + 0.0806718i
\(118\) 0 0
\(119\) 908.173 + 385.297i 0.699597 + 0.296808i
\(120\) 0 0
\(121\) 600.587 + 1040.25i 0.451230 + 0.781553i
\(122\) 0 0
\(123\) 58.9845 102.164i 0.0432395 0.0748930i
\(124\) 0 0
\(125\) 1241.32 0.888216
\(126\) 0 0
\(127\) −974.777 −0.681082 −0.340541 0.940230i \(-0.610610\pi\)
−0.340541 + 0.940230i \(0.610610\pi\)
\(128\) 0 0
\(129\) 644.158 1115.71i 0.439651 0.761498i
\(130\) 0 0
\(131\) −896.351 1552.53i −0.597821 1.03546i −0.993142 0.116914i \(-0.962700\pi\)
0.395321 0.918543i \(-0.370633\pi\)
\(132\) 0 0
\(133\) −627.377 + 472.946i −0.409026 + 0.308343i
\(134\) 0 0
\(135\) −241.288 417.924i −0.153828 0.266438i
\(136\) 0 0
\(137\) −842.208 + 1458.75i −0.525217 + 0.909702i 0.474352 + 0.880335i \(0.342682\pi\)
−0.999569 + 0.0293665i \(0.990651\pi\)
\(138\) 0 0
\(139\) −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
\(142\) 0 0
\(143\) 74.6241 129.253i 0.0436390 0.0755850i
\(144\) 0 0
\(145\) −1666.62 2886.67i −0.954517 1.65327i
\(146\) 0 0
\(147\) 283.263 989.244i 0.158933 0.555044i
\(148\) 0 0
\(149\) −946.887 1640.06i −0.520617 0.901736i −0.999713 0.0239729i \(-0.992368\pi\)
0.479095 0.877763i \(-0.340965\pi\)
\(150\) 0 0
\(151\) −1005.92 + 1742.31i −0.542124 + 0.938986i 0.456658 + 0.889642i \(0.349046\pi\)
−0.998782 + 0.0493434i \(0.984287\pi\)
\(152\) 0 0
\(153\) 479.406 0.253318
\(154\) 0 0
\(155\) 2821.71 1.46223
\(156\) 0 0
\(157\) 1914.25 3315.58i 0.973082 1.68543i 0.286956 0.957944i \(-0.407357\pi\)
0.686125 0.727483i \(-0.259310\pi\)
\(158\) 0 0
\(159\) −548.856 950.647i −0.273755 0.474158i
\(160\) 0 0
\(161\) 2249.17 1695.53i 1.10099 0.829977i
\(162\) 0 0
\(163\) −1754.63 3039.11i −0.843148 1.46038i −0.887220 0.461347i \(-0.847366\pi\)
0.0440718 0.999028i \(-0.485967\pi\)
\(164\) 0 0
\(165\) −305.475 + 529.098i −0.144128 + 0.249638i
\(166\) 0 0
\(167\) 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
\(170\) 0 0
\(171\) −190.900 + 330.649i −0.0853714 + 0.147868i
\(172\) 0 0
\(173\) 2093.61 + 3626.23i 0.920081 + 1.59363i 0.799288 + 0.600949i \(0.205210\pi\)
0.120793 + 0.992678i \(0.461456\pi\)
\(174\) 0 0
\(175\) 3315.27 + 1406.52i 1.43206 + 0.607559i
\(176\) 0 0
\(177\) −339.866 588.666i −0.144327 0.249982i
\(178\) 0 0
\(179\) −985.143 + 1706.32i −0.411358 + 0.712493i −0.995039 0.0994906i \(-0.968279\pi\)
0.583681 + 0.811983i \(0.301612\pi\)
\(180\) 0 0
\(181\) −3613.10 −1.48376 −0.741878 0.670535i \(-0.766065\pi\)
−0.741878 + 0.670535i \(0.766065\pi\)
\(182\) 0 0
\(183\) 1955.92 0.790086
\(184\) 0 0
\(185\) −33.4755 + 57.9812i −0.0133036 + 0.0230425i
\(186\) 0 0
\(187\) −303.468 525.622i −0.118673 0.205547i
\(188\) 0 0
\(189\) −61.0328 496.308i −0.0234893 0.191011i
\(190\) 0 0
\(191\) 953.884 + 1652.18i 0.361365 + 0.625902i 0.988186 0.153261i \(-0.0489776\pi\)
−0.626821 + 0.779163i \(0.715644\pi\)
\(192\) 0 0
\(193\) −1199.96 + 2078.40i −0.447540 + 0.775162i −0.998225 0.0595509i \(-0.981033\pi\)
0.550685 + 0.834713i \(0.314366\pi\)
\(194\) 0 0
\(195\) −702.346 −0.257928
\(196\) 0 0
\(197\) 1514.32 0.547668 0.273834 0.961777i \(-0.411708\pi\)
0.273834 + 0.961777i \(0.411708\pi\)
\(198\) 0 0
\(199\) 683.889 1184.53i 0.243616 0.421955i −0.718126 0.695914i \(-0.755000\pi\)
0.961742 + 0.273958i \(0.0883330\pi\)
\(200\) 0 0
\(201\) 218.150 + 377.847i 0.0765527 + 0.132593i
\(202\) 0 0
\(203\) −421.563 3428.08i −0.145753 1.18524i
\(204\) 0 0
\(205\) 351.414 + 608.667i 0.119726 + 0.207371i
\(206\) 0 0
\(207\) 684.384 1185.39i 0.229797 0.398020i
\(208\) 0 0
\(209\) 483.366 0.159977
\(210\) 0 0
\(211\) −4302.52 −1.40378 −0.701891 0.712285i \(-0.747661\pi\)
−0.701891 + 0.712285i \(0.747661\pi\)
\(212\) 0 0
\(213\) −553.443 + 958.591i −0.178034 + 0.308364i
\(214\) 0 0
\(215\) 3837.72 + 6647.13i 1.21735 + 2.10851i
\(216\) 0 0
\(217\) 2691.64 + 1141.94i 0.842030 + 0.357236i
\(218\) 0 0
\(219\) −913.359 1581.98i −0.281822 0.488130i
\(220\) 0 0
\(221\) 348.866 604.253i 0.106187 0.183921i
\(222\) 0 0
\(223\) 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
\(226\) 0 0
\(227\) 801.662 1388.52i 0.234397 0.405988i −0.724700 0.689065i \(-0.758022\pi\)
0.959097 + 0.283076i \(0.0913550\pi\)
\(228\) 0 0
\(229\) −505.261 875.137i −0.145802 0.252536i 0.783870 0.620925i \(-0.213243\pi\)
−0.929672 + 0.368389i \(0.879909\pi\)
\(230\) 0 0
\(231\) −505.520 + 381.084i −0.143986 + 0.108543i
\(232\) 0 0
\(233\) −99.1084 171.661i −0.0278661 0.0482656i 0.851756 0.523939i \(-0.175538\pi\)
−0.879622 + 0.475673i \(0.842205\pi\)
\(234\) 0 0
\(235\) 189.339 327.944i 0.0525578 0.0910329i
\(236\) 0 0
\(237\) −2730.71 −0.748434
\(238\) 0 0
\(239\) 1201.19 0.325098 0.162549 0.986700i \(-0.448028\pi\)
0.162549 + 0.986700i \(0.448028\pi\)
\(240\) 0 0
\(241\) 1366.35 2366.58i 0.365204 0.632551i −0.623605 0.781739i \(-0.714333\pi\)
0.988809 + 0.149188i \(0.0476660\pi\)
\(242\) 0 0
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 4260.25 + 4408.33i 1.11093 + 1.14954i
\(246\) 0 0
\(247\) 277.838 + 481.229i 0.0715724 + 0.123967i
\(248\) 0 0
\(249\) −491.894 + 851.985i −0.125191 + 0.216837i
\(250\) 0 0
\(251\) −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
\(254\) 0 0
\(255\) −1428.09 + 2473.52i −0.350707 + 0.607443i
\(256\) 0 0
\(257\) −2504.34 4337.64i −0.607846 1.05282i −0.991595 0.129382i \(-0.958701\pi\)
0.383749 0.923437i \(-0.374633\pi\)
\(258\) 0 0
\(259\) −55.3973 + 41.7610i −0.0132904 + 0.0100189i
\(260\) 0 0
\(261\) −839.220 1453.57i −0.199028 0.344727i
\(262\) 0 0
\(263\) −3124.40 + 5411.63i −0.732544 + 1.26880i 0.223249 + 0.974761i \(0.428334\pi\)
−0.955793 + 0.294042i \(0.905000\pi\)
\(264\) 0 0
\(265\) 6539.88 1.51601
\(266\) 0 0
\(267\) −112.835 −0.0258630
\(268\) 0 0
\(269\) 1794.22 3107.69i 0.406676 0.704383i −0.587839 0.808978i \(-0.700021\pi\)
0.994515 + 0.104595i \(0.0333546\pi\)
\(270\) 0 0
\(271\) −991.571 1717.45i −0.222264 0.384973i 0.733231 0.679980i \(-0.238012\pi\)
−0.955495 + 0.295007i \(0.904678\pi\)
\(272\) 0 0
\(273\) −669.971 284.239i −0.148529 0.0630143i
\(274\) 0 0
\(275\) −1107.80 1918.77i −0.242920 0.420751i
\(276\) 0 0
\(277\) −3681.96 + 6377.33i −0.798654 + 1.38331i 0.121838 + 0.992550i \(0.461121\pi\)
−0.920493 + 0.390760i \(0.872212\pi\)
\(278\) 0 0
\(279\) 1420.86 0.304892
\(280\) 0 0
\(281\) −5312.05 −1.12772 −0.563861 0.825869i \(-0.690685\pi\)
−0.563861 + 0.825869i \(0.690685\pi\)
\(282\) 0 0
\(283\) −545.882 + 945.495i −0.114662 + 0.198600i −0.917645 0.397402i \(-0.869912\pi\)
0.802983 + 0.596002i \(0.203245\pi\)
\(284\) 0 0
\(285\) −1137.33 1969.92i −0.236385 0.409431i
\(286\) 0 0
\(287\) 88.8886 + 722.827i 0.0182820 + 0.148666i
\(288\) 0 0
\(289\) 1037.79 + 1797.51i 0.211234 + 0.365869i
\(290\) 0 0
\(291\) −1083.02 + 1875.84i −0.218171 + 0.377883i
\(292\) 0 0
\(293\) −7191.86 −1.43397 −0.716985 0.697089i \(-0.754478\pi\)
−0.716985 + 0.697089i \(0.754478\pi\)
\(294\) 0 0
\(295\) 4049.67 0.799257
\(296\) 0 0
\(297\) −153.821 + 266.426i −0.0300525 + 0.0520525i
\(298\) 0 0
\(299\) −996.058 1725.22i −0.192654 0.333687i
\(300\) 0 0
\(301\) 970.735 + 7893.85i 0.185888 + 1.51161i
\(302\) 0 0
\(303\) −2278.01 3945.63i −0.431908 0.748087i
\(304\) 0 0
\(305\) −5826.43 + 10091.7i −1.09384 + 1.89458i
\(306\) 0 0
\(307\) −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
\(310\) 0 0
\(311\) 27.0084 46.7799i 0.00492446 0.00852941i −0.863553 0.504259i \(-0.831766\pi\)
0.868477 + 0.495729i \(0.165099\pi\)
\(312\) 0 0
\(313\) −1886.47 3267.46i −0.340670 0.590058i 0.643887 0.765120i \(-0.277321\pi\)
−0.984557 + 0.175063i \(0.943987\pi\)
\(314\) 0 0
\(315\) 2742.54 + 1163.54i 0.490554 + 0.208120i
\(316\) 0 0
\(317\) −859.618 1488.90i −0.152306 0.263802i 0.779769 0.626068i \(-0.215337\pi\)
−0.932075 + 0.362266i \(0.882003\pi\)
\(318\) 0 0
\(319\) −1062.47 + 1840.25i −0.186479 + 0.322991i
\(320\) 0 0
\(321\) −2299.56 −0.399841
\(322\) 0 0
\(323\) 2259.72 0.389270
\(324\) 0 0
\(325\) 1273.53 2205.81i 0.217362 0.376482i
\(326\) 0 0
\(327\) 2140.57 + 3707.58i 0.362000 + 0.627002i
\(328\) 0 0
\(329\) 313.330 236.202i 0.0525059 0.0395813i
\(330\) 0 0
\(331\) 4204.11 + 7281.73i 0.698123 + 1.20918i 0.969117 + 0.246603i \(0.0793143\pi\)
−0.270994 + 0.962581i \(0.587352\pi\)
\(332\) 0 0
\(333\) −16.8565 + 29.1963i −0.00277396 + 0.00480464i
\(334\) 0 0
\(335\) −2599.36 −0.423935
\(336\) 0 0
\(337\) 2789.46 0.450894 0.225447 0.974255i \(-0.427616\pi\)
0.225447 + 0.974255i \(0.427616\pi\)
\(338\) 0 0
\(339\) −543.846 + 941.969i −0.0871317 + 0.150917i
\(340\) 0 0
\(341\) −899.419 1557.84i −0.142834 0.247395i
\(342\) 0 0
\(343\) 2279.82 + 5929.25i 0.358889 + 0.933380i
\(344\) 0 0
\(345\) 4077.38 + 7062.23i 0.636286 + 1.10208i
\(346\) 0 0
\(347\) −1735.98 + 3006.81i −0.268566 + 0.465170i −0.968492 0.249046i \(-0.919883\pi\)
0.699926 + 0.714216i \(0.253216\pi\)
\(348\) 0 0
\(349\) −6626.12 −1.01630 −0.508149 0.861269i \(-0.669670\pi\)
−0.508149 + 0.861269i \(0.669670\pi\)
\(350\) 0 0
\(351\) −353.664 −0.0537812
\(352\) 0 0
\(353\) −4734.20 + 8199.87i −0.713813 + 1.23636i 0.249603 + 0.968348i \(0.419700\pi\)
−0.963416 + 0.268012i \(0.913633\pi\)
\(354\) 0 0
\(355\) −3297.27 5711.03i −0.492960 0.853831i
\(356\) 0 0
\(357\) −2363.29 + 1781.56i −0.350360 + 0.264118i
\(358\) 0 0
\(359\) −3139.78 5438.25i −0.461591 0.799499i 0.537450 0.843296i \(-0.319388\pi\)
−0.999040 + 0.0437971i \(0.986054\pi\)
\(360\) 0 0
\(361\) 2529.68 4381.53i 0.368811 0.638800i
\(362\) 0 0
\(363\) −3603.52 −0.521035
\(364\) 0 0
\(365\) 10883.1 1.56068
\(366\) 0 0
\(367\) −5413.91 + 9377.17i −0.770038 + 1.33374i 0.167504 + 0.985871i \(0.446429\pi\)
−0.937542 + 0.347873i \(0.886904\pi\)
\(368\) 0 0
\(369\) 176.954 + 306.493i 0.0249643 + 0.0432395i
\(370\) 0 0
\(371\) 6238.42 + 2646.68i 0.872999 + 0.370374i
\(372\) 0 0
\(373\) −2619.61 4537.30i −0.363642 0.629846i 0.624915 0.780693i \(-0.285134\pi\)
−0.988557 + 0.150846i \(0.951800\pi\)
\(374\) 0 0
\(375\) −1861.98 + 3225.04i −0.256406 + 0.444108i
\(376\) 0 0
\(377\) −2442.81 −0.333717
\(378\) 0 0
\(379\) 11050.4 1.49768 0.748839 0.662751i \(-0.230611\pi\)
0.748839 + 0.662751i \(0.230611\pi\)
\(380\) 0 0
\(381\) 1462.16 2532.54i 0.196611 0.340541i
\(382\) 0 0
\(383\) −5234.02 9065.59i −0.698292 1.20948i −0.969058 0.246832i \(-0.920610\pi\)
0.270766 0.962645i \(-0.412723\pi\)
\(384\) 0 0
\(385\) −460.345 3743.45i −0.0609386 0.495543i
\(386\) 0 0
\(387\) 1932.47 + 3347.14i 0.253833 + 0.439651i
\(388\) 0 0
\(389\) 5807.02 10058.1i 0.756884 1.31096i −0.187549 0.982255i \(-0.560054\pi\)
0.944432 0.328705i \(-0.106612\pi\)
\(390\) 0 0
\(391\) −8101.19 −1.04781
\(392\) 0 0
\(393\) 5378.11 0.690304
\(394\) 0 0
\(395\) 8134.43 14089.2i 1.03617 1.79470i
\(396\) 0 0
\(397\) 3353.65 + 5808.69i 0.423967 + 0.734332i 0.996323 0.0856726i \(-0.0273039\pi\)
−0.572356 + 0.820005i \(0.693971\pi\)
\(398\) 0 0
\(399\) −287.683 2339.39i −0.0360957 0.293524i
\(400\) 0 0
\(401\) −2763.19 4785.98i −0.344107 0.596011i 0.641084 0.767471i \(-0.278485\pi\)
−0.985191 + 0.171459i \(0.945152\pi\)
\(402\) 0 0
\(403\) 1033.97 1790.89i 0.127805 0.221366i
\(404\) 0 0
\(405\) 1447.73 0.177625
\(406\) 0 0
\(407\) 42.6811 0.00519810
\(408\) 0 0
\(409\) 659.453 1142.21i 0.0797258 0.138089i −0.823406 0.567453i \(-0.807929\pi\)
0.903132 + 0.429364i \(0.141262\pi\)
\(410\) 0 0
\(411\) −2526.62 4376.24i −0.303234 0.525217i
\(412\) 0 0
\(413\) 3863.00 + 1638.90i 0.460256 + 0.195266i
\(414\) 0 0
\(415\) −2930.57 5075.90i −0.346641 0.600401i
\(416\) 0 0
\(417\) 472.634 818.626i 0.0555036 0.0961350i
\(418\) 0 0
\(419\) −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 \(0.502495\pi\)
\(422\) 0 0
\(423\) 95.3409 165.135i 0.0109589 0.0189815i
\(424\) 0 0
\(425\) −5178.96 8970.22i −0.591097 1.02381i
\(426\) 0 0
\(427\) −9641.94 + 7268.54i −1.09276 + 0.823769i
\(428\) 0 0
\(429\) 223.872 + 387.758i 0.0251950 + 0.0436390i
\(430\) 0 0
\(431\) 4194.58 7265.23i 0.468784 0.811958i −0.530579 0.847635i \(-0.678026\pi\)
0.999363 + 0.0356776i \(0.0113589\pi\)
\(432\) 0 0
\(433\) −8243.02 −0.914859 −0.457430 0.889246i \(-0.651230\pi\)
−0.457430 + 0.889246i \(0.651230\pi\)
\(434\) 0 0
\(435\) 9999.70 1.10218
\(436\) 0 0
\(437\) 3225.91 5587.43i 0.353126 0.611632i
\(438\) 0 0
\(439\) −9141.59 15833.7i −0.993859 1.72142i −0.592755 0.805383i \(-0.701960\pi\)
−0.401104 0.916032i \(-0.631374\pi\)
\(440\) 0 0
\(441\) 2145.24 + 2219.80i 0.231642 + 0.239694i
\(442\) 0 0
\(443\) 605.218 + 1048.27i 0.0649092 + 0.112426i 0.896654 0.442733i \(-0.145991\pi\)
−0.831745 + 0.555159i \(0.812658\pi\)
\(444\) 0 0
\(445\) 336.122 582.180i 0.0358061 0.0620179i
\(446\) 0 0
\(447\) 5681.32 0.601157
\(448\) 0 0
\(449\) −8301.16 −0.872508 −0.436254 0.899824i \(-0.643695\pi\)
−0.436254 + 0.899824i \(0.643695\pi\)
\(450\) 0 0
\(451\) 224.026 388.025i 0.0233902 0.0405130i
\(452\) 0 0
\(453\) −3017.76 5226.92i −0.312995 0.542124i
\(454\) 0 0
\(455\) 3462.30 2610.04i 0.356736 0.268924i
\(456\) 0 0
\(457\) 6146.88 + 10646.7i 0.629188 + 1.08979i 0.987715 + 0.156266i \(0.0499458\pi\)
−0.358527 + 0.933519i \(0.616721\pi\)
\(458\) 0 0
\(459\) −719.109 + 1245.53i −0.0731267 + 0.126659i
\(460\) 0 0
\(461\) 19434.2 1.96343 0.981717 0.190346i \(-0.0609609\pi\)
0.981717 + 0.190346i \(0.0609609\pi\)
\(462\) 0 0
\(463\) 12491.1 1.25380 0.626902 0.779098i \(-0.284322\pi\)
0.626902 + 0.779098i \(0.284322\pi\)
\(464\) 0 0
\(465\) −4232.56 + 7331.02i −0.422109 + 0.731113i
\(466\) 0 0
\(467\) 1692.59 + 2931.65i 0.167716 + 0.290493i 0.937617 0.347671i \(-0.113027\pi\)
−0.769900 + 0.638164i \(0.779694\pi\)
\(468\) 0 0
\(469\) −2479.54 1051.96i −0.244125 0.103571i
\(470\) 0 0
\(471\) 5742.75 + 9946.74i 0.561809 + 0.973082i
\(472\) 0 0
\(473\) 2446.54 4237.54i 0.237827 0.411929i
\(474\) 0 0
\(475\) 8249.07 0.796828
\(476\) 0 0
\(477\) 3293.14 0.316106
\(478\) 0 0
\(479\) 2989.71 5178.32i 0.285184 0.493953i −0.687470 0.726213i \(-0.741279\pi\)
0.972654 + 0.232260i \(0.0746120\pi\)
\(480\) 0 0
\(481\) 24.5330 + 42.4925i 0.00232559 + 0.00402804i
\(482\) 0 0
\(483\) 1031.35 + 8386.81i 0.0971600 + 0.790089i
\(484\) 0 0
\(485\) −6452.34 11175.8i −0.604094 1.04632i
\(486\) 0 0
\(487\) −557.481 + 965.586i −0.0518725 + 0.0898457i −0.890796 0.454404i \(-0.849852\pi\)
0.838923 + 0.544250i \(0.183186\pi\)
\(488\) 0 0
\(489\) 10527.8 0.973583
\(490\) 0 0
\(491\) −1086.23 −0.0998387 −0.0499194 0.998753i \(-0.515896\pi\)
−0.0499194 + 0.998753i \(0.515896\pi\)
\(492\) 0 0
\(493\) −4967.00 + 8603.10i −0.453758 + 0.785932i
\(494\) 0 0
\(495\) −916.425 1587.29i −0.0832126 0.144128i
\(496\) 0 0
\(497\) −834.028 6782.18i −0.0752742 0.612117i
\(498\) 0 0
\(499\) −1106.75 1916.95i −0.0992884 0.171973i 0.812102 0.583516i \(-0.198323\pi\)
−0.911390 + 0.411543i \(0.864990\pi\)
\(500\) 0 0
\(501\) −514.512 + 891.162i −0.0458817 + 0.0794694i
\(502\) 0 0
\(503\) 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
\(506\) 0 0
\(507\) 3038.14 5262.21i 0.266131 0.460952i
\(508\) 0 0
\(509\) 332.584 + 576.053i 0.0289618 + 0.0501633i 0.880143 0.474709i \(-0.157447\pi\)
−0.851181 + 0.524872i \(0.824113\pi\)
\(510\) 0 0
\(511\) 10381.4 + 4404.38i 0.898724 + 0.381288i
\(512\) 0 0
\(513\) −572.701 991.947i −0.0492892 0.0853714i
\(514\) 0 0
\(515\) −9400.26 + 16281.7i −0.804320 + 1.39312i
\(516\) 0 0
\(517\) −241.406 −0.0205359
\(518\) 0 0
\(519\) −12561.6 −1.06242
\(520\) 0 0
\(521\) 5880.99 10186.2i 0.494531 0.856554i −0.505449 0.862857i \(-0.668673\pi\)
0.999980 + 0.00630307i \(0.00200634\pi\)
\(522\) 0 0
\(523\) 5061.30 + 8766.43i 0.423165 + 0.732943i 0.996247 0.0865547i \(-0.0275857\pi\)
−0.573082 + 0.819498i \(0.694252\pi\)
\(524\) 0 0
\(525\) −8627.15 + 6503.54i −0.717180 + 0.540643i
\(526\) 0 0
\(527\) −4204.76 7282.85i −0.347556 0.601985i
\(528\) 0 0
\(529\) −5481.49 + 9494.22i −0.450521 + 0.780325i
\(530\) 0 0
\(531\) 2039.20 0.166655
\(532\) 0 0
\(533\) 515.079 0.0418585
\(534\) 0 0
\(535\) 6850.09 11864.7i 0.553561 0.958796i
\(536\) 0 0
\(537\) −2955.43 5118.95i −0.237498 0.411358i
\(538\) 0 0
\(539\) 1075.85 3757.20i 0.0859740 0.300249i
\(540\) 0 0
\(541\) −8058.98 13958.6i −0.640449 1.10929i −0.985333 0.170644i \(-0.945415\pi\)
0.344884 0.938645i \(-0.387918\pi\)
\(542\) 0 0
\(543\) 5419.65 9387.11i 0.428323 0.741878i
\(544\) 0 0
\(545\) −25505.9 −2.00469
\(546\) 0 0
\(547\) 626.100 0.0489399 0.0244699 0.999701i \(-0.492210\pi\)
0.0244699 + 0.999701i \(0.492210\pi\)
\(548\) 0 0
\(549\) −2933.88 + 5081.63i −0.228078 + 0.395043i
\(550\) 0 0
\(551\) −3955.74 6851.54i −0.305844 0.529737i
\(552\) 0 0
\(553\) 13461.4 10147.8i 1.03515 0.780341i
\(554\) 0 0
\(555\) −100.426 173.944i −0.00768083 0.0133036i
\(556\) 0 0
\(557\) −10385.6 + 17988.4i −0.790039 + 1.36839i 0.135903 + 0.990722i \(0.456606\pi\)
−0.925942 + 0.377665i \(0.876727\pi\)
\(558\) 0 0
\(559\) 5625.08 0.425609
\(560\) 0 0
\(561\) 1820.81 0.137031
\(562\) 0 0
\(563\) −2760.86 + 4781.95i −0.206672 + 0.357966i −0.950664 0.310222i \(-0.899597\pi\)
0.743992 + 0.668188i \(0.232930\pi\)
\(564\) 0 0
\(565\) −3240.09 5612.00i −0.241260 0.417874i
\(566\) 0 0
\(567\) 1381.00 + 585.895i 0.102286 + 0.0433955i
\(568\) 0 0
\(569\) −3787.40 6559.97i −0.279044 0.483319i 0.692103 0.721799i \(-0.256684\pi\)
−0.971147 + 0.238480i \(0.923351\pi\)
\(570\) 0 0
\(571\) −165.624 + 286.869i −0.0121386 + 0.0210247i −0.872031 0.489451i \(-0.837197\pi\)
0.859892 + 0.510476i \(0.170531\pi\)
\(572\) 0 0
\(573\) −5723.31 −0.417268
\(574\) 0 0
\(575\) −29573.2 −2.14485
\(576\) 0 0
\(577\) −1019.06 + 1765.06i −0.0735248 + 0.127349i −0.900444 0.434972i \(-0.856758\pi\)
0.826919 + 0.562321i \(0.190091\pi\)
\(578\) 0 0
\(579\) −3599.89 6235.19i −0.258387 0.447540i
\(580\) 0 0
\(581\) −741.275 6027.93i −0.0529316 0.430431i
\(582\) 0 0
\(583\) −2084.58 3610.60i −0.148087 0.256494i
\(584\) 0 0
\(585\) 1053.52 1824.75i 0.0744575 0.128964i
\(586\) 0 0
\(587\) −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
\(590\) 0 0
\(591\) −2271.47 + 3934.31i −0.158098 + 0.273834i
\(592\) 0 0
\(593\) 2860.12 + 4953.87i 0.198062 + 0.343054i 0.947900 0.318568i \(-0.103202\pi\)
−0.749838 + 0.661622i \(0.769868\pi\)
\(594\) 0 0
\(595\) −2152.10 17500.5i −0.148282 1.20580i
\(596\) 0 0
\(597\) 2051.67 + 3553.59i 0.140652 + 0.243616i
\(598\) 0 0
\(599\) 9044.21 15665.0i 0.616922 1.06854i −0.373122 0.927782i \(-0.621713\pi\)
0.990044 0.140758i \(-0.0449540\pi\)
\(600\) 0 0
\(601\) −1821.43 −0.123623 −0.0618117 0.998088i \(-0.519688\pi\)
−0.0618117 + 0.998088i \(0.519688\pi\)
\(602\) 0 0
\(603\) −1308.90 −0.0883955
\(604\) 0 0
\(605\) 10734.4 18592.5i 0.721348 1.24941i
\(606\) 0 0
\(607\) 1186.10 + 2054.39i 0.0793120 + 0.137372i 0.902953 0.429739i \(-0.141394\pi\)
−0.823641 + 0.567111i \(0.808061\pi\)
\(608\) 0 0
\(609\) 9538.76 + 4046.87i 0.634696 + 0.269273i
\(610\) 0 0
\(611\) −138.760 240.339i −0.00918760 0.0159134i
\(612\) 0 0
\(613\) −4862.54 + 8422.16i −0.320385 + 0.554923i −0.980567 0.196182i \(-0.937146\pi\)
0.660182 + 0.751105i \(0.270479\pi\)
\(614\) 0 0
\(615\) −2108.48 −0.138248
\(616\) 0 0
\(617\) −5329.51 −0.347744 −0.173872 0.984768i \(-0.555628\pi\)
−0.173872 + 0.984768i \(0.555628\pi\)
\(618\) 0 0
\(619\) −7988.29 + 13836.1i −0.518702 + 0.898418i 0.481062 + 0.876687i \(0.340251\pi\)
−0.999764 + 0.0217314i \(0.993082\pi\)
\(620\) 0 0
\(621\) 2053.15 + 3556.17i 0.132673 + 0.229797i
\(622\) 0 0
\(623\) 556.236 419.316i 0.0357706 0.0269656i
\(624\) 0 0
\(625\) 1060.03 + 1836.03i 0.0678420 + 0.117506i
\(626\) 0 0
\(627\) −725.049 + 1255.82i −0.0461813 + 0.0799883i
\(628\) 0 0
\(629\) 199.533 0.0126485
\(630\) 0 0
\(631\) 4199.98 0.264974 0.132487 0.991185i \(-0.457704\pi\)
0.132487 + 0.991185i \(0.457704\pi\)
\(632\) 0 0
\(633\) 6453.78 11178.3i 0.405237 0.701891i
\(634\) 0 0
\(635\) 8711.19 + 15088.2i 0.544399 + 0.942926i
\(636\) 0 0
\(637\) 4358.98 1088.54i 0.271129 0.0677072i
\(638\) 0 0
\(639\) −1660.33 2875.77i −0.102788 0.178034i
\(640\) 0 0
\(641\) −1324.25 + 2293.67i −0.0815988 + 0.141333i −0.903937 0.427666i \(-0.859336\pi\)
0.822338 + 0.568999i \(0.192669\pi\)
\(642\) 0 0
\(643\) −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
\(646\) 0 0
\(647\) 5812.07 10066.8i 0.353162 0.611695i −0.633639 0.773628i \(-0.718440\pi\)
0.986802 + 0.161934i \(0.0517730\pi\)
\(648\) 0 0
\(649\) −1290.83 2235.78i −0.0780732 0.135227i
\(650\) 0 0
\(651\) −7004.32 + 5280.18i −0.421691 + 0.317890i
\(652\) 0 0
\(653\) 14258.3 + 24696.1i 0.854471 + 1.47999i 0.877135 + 0.480244i \(0.159452\pi\)
−0.0226638 + 0.999743i \(0.507215\pi\)
\(654\) 0 0
\(655\) −16020.7 + 27748.6i −0.955694 + 1.65531i
\(656\) 0 0
\(657\) 5480.15 0.325420
\(658\) 0 0
\(659\) −18048.6 −1.06688 −0.533440 0.845838i \(-0.679101\pi\)
−0.533440 + 0.845838i \(0.679101\pi\)
\(660\) 0 0
\(661\) −8920.72 + 15451.1i −0.524926 + 0.909198i 0.474653 + 0.880173i \(0.342574\pi\)
−0.999579 + 0.0290250i \(0.990760\pi\)
\(662\) 0 0
\(663\) 1046.60 + 1812.76i 0.0613069 + 0.106187i
\(664\) 0 0
\(665\) 12927.2 + 5484.42i 0.753826 + 0.319815i
\(666\) 0 0
\(667\) 14181.5 + 24563.0i 0.823251 + 1.42591i
\(668\) 0 0
\(669\) −2245.78 + 3889.80i −0.129786 + 0.224796i
\(670\) 0 0
\(671\) 7428.68 0.427394
\(672\) 0 0
\(673\) −6826.13 −0.390978 −0.195489 0.980706i \(-0.562629\pi\)
−0.195489 + 0.980706i \(0.562629\pi\)
\(674\) 0 0
\(675\) −2625.09 + 4546.80i −0.149689 + 0.259269i
\(676\) 0 0
\(677\) 10643.4 + 18435.0i 0.604225 + 1.04655i 0.992173 + 0.124867i \(0.0398505\pi\)
−0.387949 + 0.921681i \(0.626816\pi\)
\(678\) 0 0
\(679\) −1632.09 13271.9i −0.0922443 0.750115i
\(680\) 0 0
\(681\) 2404.99 + 4165.56i 0.135329 + 0.234397i
\(682\) 0 0
\(683\) −10348.4 + 17924.0i −0.579753 + 1.00416i 0.415755 + 0.909477i \(0.363517\pi\)
−0.995507 + 0.0946842i \(0.969816\pi\)
\(684\) 0 0
\(685\) 30105.9 1.67925
\(686\) 0 0
\(687\) 3031.56 0.168357
\(688\) 0 0
\(689\) 2396.43 4150.74i 0.132506 0.229507i
\(690\) 0 0
\(691\) 15671.0 + 27142.9i 0.862738 + 1.49431i 0.869276 + 0.494327i \(0.164585\pi\)
−0.00653825 + 0.999979i \(0.502081\pi\)
\(692\) 0 0
\(693\) −231.805 1885.00i −0.0127064 0.103327i
\(694\) 0 0
\(695\) 2815.83 + 4877.16i 0.153684 + 0.266189i
\(696\) 0 0
\(697\) 1047.32 1814.01i 0.0569153 0.0985801i
\(698\) 0 0
\(699\) 594.651 0.0321770
\(700\) 0 0
\(701\) −9213.32 −0.496408 −0.248204 0.968708i \(-0.579840\pi\)
−0.248204 + 0.968708i \(0.579840\pi\)
\(702\) 0 0
\(703\) −79.4544 + 137.619i −0.00426270 + 0.00738322i
\(704\) 0 0
\(705\) 568.016 + 983.833i 0.0303443 + 0.0525578i
\(706\) 0 0
\(707\) 25892.4 + 10985.0i 1.37734 + 0.584345i
\(708\) 0 0
\(709\) −7258.27 12571.7i −0.384471 0.665923i 0.607225 0.794530i \(-0.292283\pi\)
−0.991696 + 0.128607i \(0.958949\pi\)
\(710\) 0 0
\(711\) 4096.07 7094.60i 0.216054 0.374217i
\(712\) 0 0
\(713\) −24010.3 −1.26114
\(714\) 0 0
\(715\) −2667.54 −0.139525
\(716\) 0 0
\(717\) −1801.78 + 3120.78i −0.0938477 + 0.162549i
\(718\) 0 0
\(719\) 12941.2 + 22414.8i 0.671246 + 1.16263i 0.977551 + 0.210698i \(0.0675737\pi\)
−0.306306 + 0.951933i \(0.599093\pi\)
\(720\) 0 0
\(721\) −15556.2 + 11726.9i −0.803525 + 0.605734i
\(722\) 0 0
\(723\) 4099.04 + 7099.74i 0.210850 + 0.365204i
\(724\) 0 0
\(725\) −18132.0 + 31405.5i −0.928833 + 1.60879i
\(726\) 0 0
\(727\) −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
\(730\) 0 0
\(731\) 11437.5 19810.4i 0.578704 1.00234i
\(732\) 0 0
\(733\) −10418.1 18044.6i −0.524966 0.909268i −0.999577 0.0290722i \(-0.990745\pi\)
0.474611 0.880195i \(-0.342589\pi\)
\(734\) 0 0
\(735\) −17843.6 + 4455.95i −0.895469 + 0.223620i
\(736\) 0 0
\(737\) 828.544 + 1435.08i 0.0414109 + 0.0717257i
\(738\) 0 0
\(739\) 13217.4 22893.3i 0.657931 1.13957i −0.323219 0.946324i \(-0.604765\pi\)
0.981150 0.193246i \(-0.0619016\pi\)
\(740\) 0 0
\(741\) −1667.03 −0.0826447
\(742\) 0 0
\(743\) −9954.69 −0.491524 −0.245762 0.969330i \(-0.579038\pi\)
−0.245762 + 0.969330i \(0.579038\pi\)
\(744\) 0 0
\(745\) −16923.9 + 29313.1i −0.832274 + 1.44154i
\(746\) 0 0
\(747\) −1475.68 2555.96i −0.0722790 0.125191i
\(748\) 0 0
\(749\) 11336.0 8545.57i 0.553014 0.416887i
\(750\) 0 0
\(751\) −16602.3 28756.0i −0.806692 1.39723i −0.915143 0.403129i \(-0.867923\pi\)
0.108451 0.994102i \(-0.465411\pi\)
\(752\) 0 0
\(753\) 11348.7 19656.6i 0.549231 0.951295i
\(754\) 0 0
\(755\) 35958.1 1.73331
\(756\) 0 0
\(757\) 1964.06 0.0942998 0.0471499 0.998888i \(-0.484986\pi\)
0.0471499 + 0.998888i \(0.484986\pi\)
\(758\) 0 0
\(759\) 2599.33 4502.17i 0.124308 0.215307i
\(760\) 0 0
\(761\) 19276.9 + 33388.6i 0.918248 + 1.59045i 0.802075 + 0.597224i \(0.203730\pi\)
0.116174 + 0.993229i \(0.462937\pi\)
\(762\) 0 0
\(763\) −24330.2 10322.2i −1.15441 0.489764i
\(764\) 0 0
\(765\) −4284.26 7420.56i −0.202481 0.350707i
\(766\) 0 0
\(767\) 1483.93 2570.25i 0.0698588 0.120999i
\(768\) 0 0
\(769\) −19715.0 −0.924501 −0.462251 0.886749i \(-0.652958\pi\)
−0.462251 + 0.886749i \(0.652958\pi\)
\(770\) 0 0
\(771\) 15026.0 0.701880
\(772\) 0 0
\(773\) 7350.34 12731.2i 0.342010 0.592378i −0.642796 0.766037i \(-0.722226\pi\)
0.984806 + 0.173659i \(0.0555591\pi\)
\(774\) 0 0
\(775\) −15349.4 26585.9i −0.711440 1.23225i
\(776\) 0 0
\(777\) −25.4024 206.568i −0.00117285 0.00953744i
\(778\) 0 0
\(779\) 834.086 + 1444.68i 0.0383623 + 0.0664454i
\(780\) 0 0
\(781\) −2102.00 + 3640.78i −0.0963068 + 0.166808i
\(782\) 0 0
\(783\) 5035.32 0.229818
\(784\) 0 0
\(785\) −68427.6 −3.11119
\(786\) 0 0
\(787\) −11959.3 + 20714.1i −0.541681 + 0.938218i 0.457127 + 0.889401i \(0.348878\pi\)
−0.998808 + 0.0488169i \(0.984455\pi\)
\(788\) 0 0
\(789\) −9373.21 16234.9i −0.422934 0.732544i
\(790\) 0 0
\(791\) −819.566 6664.58i −0.0368400 0.299577i
\(792\) 0 0