Properties

Label 336.4.q.k.289.1
Level $336$
Weight $4$
Character 336.289
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 289.1
Root \(-2.27818 + 3.94593i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.4.q.k.193.1

$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

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

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 0.120749 + 0.992683i \(0.461470\pi\)
−0.920063 + 0.391769i \(0.871863\pi\)
\(6\) 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 0.777322 0.629102i \(-0.216577\pi\)
−0.933480 + 0.358630i \(0.883244\pi\)
\(12\) 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 0.611081 0.791568i \(-0.290735\pi\)
−0.991059 + 0.133428i \(0.957402\pi\)
\(18\) 0 0
\(19\) −21.2111 + 36.7388i −0.256114 + 0.443603i −0.965198 0.261522i \(-0.915776\pi\)
0.709083 + 0.705125i \(0.249109\pi\)
\(20\) 0 0
\(21\) 51.1480 21.6998i 0.531496 0.225490i
\(22\) 0 0
\(23\) 76.0427 131.710i 0.689391 1.19406i −0.282644 0.959225i \(-0.591211\pi\)
0.972035 0.234836i \(-0.0754553\pi\)
\(24\) 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 0.541481 0.840713i \(-0.317864\pi\)
−0.998819 + 0.0485801i \(0.984530\pi\)
\(32\) 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 −0.870156 0.492776i \(-0.835982\pi\)
0.861834 + 0.507190i \(0.169316\pi\)
\(38\) 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 −0.849119 0.528202i \(-0.822866\pi\)
0.881996 + 0.471258i \(0.156200\pi\)
\(48\) 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 0.525404 0.850853i \(-0.323914\pi\)
−0.999562 + 0.0295866i \(0.990581\pi\)
\(54\) 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 0.713538 0.700616i \(-0.247091\pi\)
−0.963521 + 0.267634i \(0.913758\pi\)
\(60\) 0 0
\(61\) −325.987 + 564.626i −0.684235 + 1.18513i 0.289442 + 0.957196i \(0.406530\pi\)
−0.973677 + 0.227934i \(0.926803\pi\)
\(62\) 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 0.924675 0.380756i \(-0.124336\pi\)
−0.792082 + 0.610414i \(0.791003\pi\)
\(68\) 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 0.511777 0.859119i \(-0.328988\pi\)
−0.999907 + 0.0136522i \(0.995654\pi\)
\(74\) 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 −0.335399 0.942076i \(-0.608871\pi\)
0.983561 0.180574i \(-0.0577957\pi\)
\(80\) 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 −0.854609 0.519272i \(-0.826203\pi\)
0.877007 + 0.480477i \(0.159537\pi\)
\(90\) 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 −0.948739 0.316062i \(-0.897639\pi\)
0.200652 0.979663i \(-0.435694\pi\)
\(102\) 0 0
\(103\) −525.942 + 910.957i −0.503132 + 0.871450i 0.496862 + 0.867830i \(0.334486\pi\)
−0.999993 + 0.00361990i \(0.998848\pi\)
\(104\) 0 0
\(105\) −121.206 + 985.625i −0.112652 + 0.916068i
\(106\) 0 0
\(107\) 383.260 663.826i 0.346273 0.599762i −0.639312 0.768948i \(-0.720781\pi\)
0.985584 + 0.169186i \(0.0541139\pi\)
\(108\) 0 0
\(109\) 713.524 + 1235.86i 0.627002 + 1.08600i 0.988150 + 0.153491i \(0.0490516\pi\)
−0.361148 + 0.932509i \(0.617615\pi\)
\(110\) 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 0.395321 + 0.918543i \(0.370633\pi\)
−0.993142 + 0.116914i \(0.962700\pi\)
\(132\) 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 −0.999569 0.0293665i \(-0.990651\pi\)
0.474352 0.880335i \(-0.342682\pi\)
\(138\) 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 0.479095 + 0.877763i \(0.340965\pi\)
−0.999713 + 0.0239729i \(0.992368\pi\)
\(150\) 0 0
\(151\) −1005.92 1742.31i −0.542124 0.938986i −0.998782 0.0493434i \(-0.984287\pi\)
0.456658 0.889642i \(-0.349046\pi\)
\(152\) 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 0.686125 + 0.727483i \(0.259310\pi\)
0.286956 + 0.957944i \(0.407357\pi\)
\(158\) 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 0.0440718 + 0.999028i \(0.485967\pi\)
−0.887220 + 0.461347i \(0.847366\pi\)
\(164\) 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 0.120793 0.992678i \(-0.461456\pi\)
0.799288 0.600949i \(-0.205210\pi\)
\(174\) 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 0.583681 0.811983i \(-0.301612\pi\)
−0.995039 + 0.0994906i \(0.968279\pi\)
\(180\) 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 −0.626821 0.779163i \(-0.715644\pi\)
0.988186 + 0.153261i \(0.0489776\pi\)
\(192\) 0 0
\(193\) −1199.96 2078.40i −0.447540 0.775162i 0.550685 0.834713i \(-0.314366\pi\)
−0.998225 + 0.0595509i \(0.981033\pi\)
\(194\) 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 0.961742 0.273958i \(-0.0883330\pi\)
−0.718126 + 0.695914i \(0.755000\pi\)
\(200\) 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 0.959097 0.283076i \(-0.0913550\pi\)
−0.724700 + 0.689065i \(0.758022\pi\)
\(228\) 0 0
\(229\) −505.261 + 875.137i −0.145802 + 0.252536i −0.929672 0.368389i \(-0.879909\pi\)
0.783870 + 0.620925i \(0.213243\pi\)
\(230\) 0 0
\(231\) −505.520 381.084i −0.143986 0.108543i
\(232\) 0 0
\(233\) −99.1084 + 171.661i −0.0278661 + 0.0482656i −0.879622 0.475673i \(-0.842205\pi\)
0.851756 + 0.523939i \(0.175538\pi\)
\(234\) 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 0.988809 0.149188i \(-0.0476660\pi\)
−0.623605 + 0.781739i \(0.714333\pi\)
\(242\) 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 0.383749 + 0.923437i \(0.374633\pi\)
−0.991595 + 0.129382i \(0.958701\pi\)
\(258\) 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 −0.955793 0.294042i \(-0.905000\pi\)
0.223249 0.974761i \(-0.428334\pi\)
\(264\) 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 0.994515 0.104595i \(-0.0333546\pi\)
−0.587839 + 0.808978i \(0.700021\pi\)
\(270\) 0 0
\(271\) −991.571 + 1717.45i −0.222264 + 0.384973i −0.955495 0.295007i \(-0.904678\pi\)
0.733231 + 0.679980i \(0.238012\pi\)
\(272\) 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 −0.920493 0.390760i \(-0.872212\pi\)
0.121838 0.992550i \(-0.461121\pi\)
\(278\) 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 0.802983 0.596002i \(-0.203245\pi\)
−0.917645 + 0.397402i \(0.869912\pi\)
\(284\) 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 0.868477 0.495729i \(-0.165099\pi\)
−0.863553 + 0.504259i \(0.831766\pi\)
\(312\) 0 0
\(313\) −1886.47 + 3267.46i −0.340670 + 0.590058i −0.984557 0.175063i \(-0.943987\pi\)
0.643887 + 0.765120i \(0.277321\pi\)
\(314\) 0 0
\(315\) 2742.54 1163.54i 0.490554 0.208120i
\(316\) 0 0
\(317\) −859.618 + 1488.90i −0.152306 + 0.263802i −0.932075 0.362266i \(-0.882003\pi\)
0.779769 + 0.626068i \(0.215337\pi\)
\(318\) 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 −0.270994 0.962581i \(-0.587352\pi\)
0.969117 0.246603i \(-0.0793143\pi\)
\(332\) 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 0.699926 0.714216i \(-0.253216\pi\)
−0.968492 + 0.249046i \(0.919883\pi\)
\(348\) 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 −0.963416 0.268012i \(-0.913633\pi\)
0.249603 0.968348i \(-0.419700\pi\)
\(354\) 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 −0.999040 0.0437971i \(-0.986054\pi\)
0.537450 + 0.843296i \(0.319388\pi\)
\(360\) 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 −0.937542 0.347873i \(-0.886904\pi\)
0.167504 0.985871i \(-0.446429\pi\)
\(368\) 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 −0.988557 0.150846i \(-0.951800\pi\)
0.624915 + 0.780693i \(0.285134\pi\)
\(374\) 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 0.270766 + 0.962645i \(0.412723\pi\)
−0.969058 + 0.246832i \(0.920610\pi\)
\(384\) 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 0.944432 + 0.328705i \(0.106612\pi\)
−0.187549 + 0.982255i \(0.560054\pi\)
\(390\) 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 −0.572356 0.820005i \(-0.693971\pi\)
0.996323 + 0.0856726i \(0.0273039\pi\)
\(398\) 0 0
\(399\) −287.683 + 2339.39i −0.0360957 + 0.293524i
\(400\) 0 0
\(401\) −2763.19 + 4785.98i −0.344107 + 0.596011i −0.985191 0.171459i \(-0.945152\pi\)
0.641084 + 0.767471i \(0.278485\pi\)
\(402\) 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 0.903132 0.429364i \(-0.141262\pi\)
−0.823406 + 0.567453i \(0.807929\pi\)
\(410\) 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 0.999363 0.0356776i \(-0.0113589\pi\)
−0.530579 + 0.847635i \(0.678026\pi\)
\(432\) 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 −0.401104 + 0.916032i \(0.631374\pi\)
−0.592755 + 0.805383i \(0.701960\pi\)
\(440\) 0 0
\(441\) 2145.24 2219.80i 0.231642 0.239694i
\(442\) 0 0
\(443\) 605.218 1048.27i 0.0649092 0.112426i −0.831745 0.555159i \(-0.812658\pi\)
0.896654 + 0.442733i \(0.145991\pi\)
\(444\) 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 −0.358527 0.933519i \(-0.616721\pi\)
0.987715 0.156266i \(-0.0499458\pi\)
\(458\) 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 −0.769900 0.638164i \(-0.779694\pi\)
0.937617 + 0.347671i \(0.113027\pi\)
\(468\) 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 0.972654 0.232260i \(-0.0746120\pi\)
−0.687470 + 0.726213i \(0.741279\pi\)
\(480\) 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 0.838923 0.544250i \(-0.183186\pi\)
−0.890796 + 0.454404i \(0.849852\pi\)
\(488\) 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 −0.911390 0.411543i \(-0.864990\pi\)
0.812102 + 0.583516i \(0.198323\pi\)
\(500\) 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 −0.851181 0.524872i \(-0.824113\pi\)
0.880143 + 0.474709i \(0.157447\pi\)
\(510\) 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 0.999980 0.00630307i \(-0.00200634\pi\)
−0.505449 + 0.862857i \(0.668673\pi\)
\(522\) 0 0
\(523\) 5061.30 8766.43i 0.423165 0.732943i −0.573082 0.819498i \(-0.694252\pi\)
0.996247 + 0.0865547i \(0.0275857\pi\)
\(524\) 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 0.344884 + 0.938645i \(0.387918\pi\)
−0.985333 + 0.170644i \(0.945415\pi\)
\(542\) 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 −0.925942 0.377665i \(-0.876727\pi\)
0.135903 0.990722i \(-0.456606\pi\)
\(558\) 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 0.743992 0.668188i \(-0.232930\pi\)
−0.950664 + 0.310222i \(0.899597\pi\)
\(564\) 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 −0.971147 0.238480i \(-0.923351\pi\)
0.692103 + 0.721799i \(0.256684\pi\)
\(570\) 0 0
\(571\) −165.624 286.869i −0.0121386 0.0210247i 0.859892 0.510476i \(-0.170531\pi\)
−0.872031 + 0.489451i \(0.837197\pi\)
\(572\) 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 0.826919 0.562321i \(-0.190091\pi\)
−0.900444 + 0.434972i \(0.856758\pi\)
\(578\) 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 −0.749838 0.661622i \(-0.769868\pi\)
0.947900 + 0.318568i \(0.103202\pi\)
\(594\) 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 0.990044 + 0.140758i \(0.0449540\pi\)
−0.373122 + 0.927782i \(0.621713\pi\)
\(600\) 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 −0.823641 0.567111i \(-0.808061\pi\)
0.902953 + 0.429739i \(0.141394\pi\)
\(608\) 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 0.660182 0.751105i \(-0.270479\pi\)
−0.980567 + 0.196182i \(0.937146\pi\)
\(614\) 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 −0.999764 0.0217314i \(-0.993082\pi\)
0.481062 0.876687i \(-0.340251\pi\)
\(620\) 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 0.822338 0.568999i \(-0.192669\pi\)
−0.903937 + 0.427666i \(0.859336\pi\)
\(642\) 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 0.986802 0.161934i \(-0.0517730\pi\)
−0.633639 + 0.773628i \(0.718440\pi\)
\(648\) 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 −0.0226638 0.999743i \(-0.507215\pi\)
0.877135 0.480244i \(-0.159452\pi\)
\(654\) 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 −0.999579 0.0290250i \(-0.990760\pi\)
0.474653 0.880173i \(-0.342574\pi\)
\(662\) 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 −0.387949 0.921681i \(-0.626816\pi\)
0.992173 0.124867i \(-0.0398505\pi\)
\(678\) 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 −0.995507 0.0946842i \(-0.969816\pi\)
0.415755 0.909477i \(-0.363517\pi\)
\(684\) 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 −0.00653825 0.999979i \(-0.502081\pi\)
0.869276 0.494327i \(-0.164585\pi\)
\(692\) 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 −0.991696 0.128607i \(-0.958949\pi\)
0.607225 + 0.794530i \(0.292283\pi\)
\(710\) 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 −0.306306 0.951933i \(-0.599093\pi\)
0.977551 0.210698i \(-0.0675737\pi\)
\(720\) 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 0.474611 + 0.880195i \(0.342589\pi\)
−0.999577 + 0.0290722i \(0.990745\pi\)
\(734\) 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 0.981150 + 0.193246i \(0.0619016\pi\)
−0.323219 + 0.946324i \(0.604765\pi\)
\(740\) 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 0.108451 + 0.994102i \(0.465411\pi\)
−0.915143 + 0.403129i \(0.867923\pi\)
\(752\) 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 0.116174 0.993229i \(-0.462937\pi\)
0.802075 0.597224i \(-0.203730\pi\)
\(762\) 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 0.984806 0.173659i \(-0.0555591\pi\)
−0.642796 + 0.766037i \(0.722226\pi\)
\(774\) 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 −0.998808 0.0488169i \(-0.984455\pi\)
0.457127 0.889401i \(-0.348878\pi\)
\(788\) 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