Properties

Label 810.3.j.c.539.2
Level $810$
Weight $3$
Character 810.539
Analytic conductor $22.071$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.0709014132\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.443364212736.6
Defining polynomial: \( x^{8} - 16x^{6} + 175x^{4} - 1296x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 539.2
Root \(2.87843 - 0.845366i\) of defining polynomial
Character \(\chi\) \(=\) 810.539
Dual form 810.3.j.c.269.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.98493 - 0.387937i) q^{5} +(-5.04975 + 2.91548i) q^{7} +2.82843 q^{8} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.98493 - 0.387937i) q^{5} +(-5.04975 + 2.91548i) q^{7} +2.82843 q^{8} +(-4.00000 - 5.83095i) q^{10} +(14.2829 - 8.24621i) q^{11} +(7.14143 + 4.12311i) q^{14} +(-2.00000 - 3.46410i) q^{16} -11.3137 q^{17} +12.0000 q^{19} +(-4.31300 + 9.02209i) q^{20} +(-20.1990 - 11.6619i) q^{22} +(-12.0208 + 20.8207i) q^{23} +(24.6990 - 3.86768i) q^{25} -11.6619i q^{28} +(16.0000 - 27.7128i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.00000 + 13.8564i) q^{34} +(-24.0416 + 16.4924i) q^{35} -23.3238i q^{37} +(-8.48528 - 14.6969i) q^{38} +(14.0995 - 1.09725i) q^{40} +(49.9900 + 28.8617i) q^{41} +(35.3483 - 20.4083i) q^{43} +32.9848i q^{44} +34.0000 q^{46} +(17.6777 + 30.6186i) q^{47} +(-7.50000 + 12.9904i) q^{49} +(-22.2018 - 27.5151i) q^{50} +67.8823 q^{53} +(68.0000 - 46.6476i) q^{55} +(-14.2829 + 8.24621i) q^{56} +(-14.2829 - 8.24621i) q^{59} +(8.00000 + 13.8564i) q^{61} -45.2548 q^{62} +8.00000 q^{64} +(-5.04975 - 2.91548i) q^{67} +(11.3137 - 19.5959i) q^{68} +(37.1990 + 17.7830i) q^{70} -116.619i q^{73} +(-28.5657 + 16.4924i) q^{74} +(-12.0000 + 20.7846i) q^{76} +(-48.0833 + 83.2827i) q^{77} +(36.0000 + 62.3538i) q^{79} +(-11.3137 - 16.4924i) q^{80} -81.6333i q^{82} +(21.9203 + 37.9671i) q^{83} +(-56.3980 + 4.38901i) q^{85} +(-49.9900 - 28.8617i) q^{86} +(40.3980 - 23.3238i) q^{88} -65.9697i q^{89} +(-24.0416 - 41.6413i) q^{92} +(25.0000 - 43.3013i) q^{94} +(59.8191 - 4.65524i) q^{95} +(141.393 - 81.6333i) q^{97} +21.2132 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} - 32 q^{10} - 16 q^{16} + 96 q^{19} + 36 q^{25} + 128 q^{31} + 64 q^{34} + 32 q^{40} + 272 q^{46} - 60 q^{49} + 544 q^{55} + 64 q^{61} + 64 q^{64} + 136 q^{70} - 96 q^{76} + 288 q^{79} - 128 q^{85} + 200 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 4.98493 0.387937i 0.996986 0.0775874i
\(6\) 0 0
\(7\) −5.04975 + 2.91548i −0.721393 + 0.416497i −0.815265 0.579088i \(-0.803409\pi\)
0.0938720 + 0.995584i \(0.470076\pi\)
\(8\) 2.82843 0.353553
\(9\) 0 0
\(10\) −4.00000 5.83095i −0.400000 0.583095i
\(11\) 14.2829 8.24621i 1.29844 0.749656i 0.318307 0.947988i \(-0.396886\pi\)
0.980135 + 0.198332i \(0.0635525\pi\)
\(12\) 0 0
\(13\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 7.14143 + 4.12311i 0.510102 + 0.294508i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −11.3137 −0.665512 −0.332756 0.943013i \(-0.607979\pi\)
−0.332756 + 0.943013i \(0.607979\pi\)
\(18\) 0 0
\(19\) 12.0000 0.631579 0.315789 0.948829i \(-0.397731\pi\)
0.315789 + 0.948829i \(0.397731\pi\)
\(20\) −4.31300 + 9.02209i −0.215650 + 0.451104i
\(21\) 0 0
\(22\) −20.1990 11.6619i −0.918137 0.530087i
\(23\) −12.0208 + 20.8207i −0.522644 + 0.905246i 0.477009 + 0.878899i \(0.341721\pi\)
−0.999653 + 0.0263476i \(0.991612\pi\)
\(24\) 0 0
\(25\) 24.6990 3.86768i 0.987960 0.154707i
\(26\) 0 0
\(27\) 0 0
\(28\) 11.6619i 0.416497i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 16.0000 27.7128i 0.516129 0.893962i −0.483696 0.875236i \(-0.660706\pi\)
0.999825 0.0187254i \(-0.00596084\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 8.00000 + 13.8564i 0.235294 + 0.407541i
\(35\) −24.0416 + 16.4924i −0.686904 + 0.471212i
\(36\) 0 0
\(37\) 23.3238i 0.630373i −0.949030 0.315187i \(-0.897933\pi\)
0.949030 0.315187i \(-0.102067\pi\)
\(38\) −8.48528 14.6969i −0.223297 0.386762i
\(39\) 0 0
\(40\) 14.0995 1.09725i 0.352488 0.0274313i
\(41\) 49.9900 + 28.8617i 1.21927 + 0.703945i 0.964761 0.263126i \(-0.0847535\pi\)
0.254507 + 0.967071i \(0.418087\pi\)
\(42\) 0 0
\(43\) 35.3483 20.4083i 0.822053 0.474612i −0.0290711 0.999577i \(-0.509255\pi\)
0.851124 + 0.524965i \(0.175922\pi\)
\(44\) 32.9848i 0.749656i
\(45\) 0 0
\(46\) 34.0000 0.739130
\(47\) 17.6777 + 30.6186i 0.376121 + 0.651460i 0.990494 0.137555i \(-0.0439245\pi\)
−0.614373 + 0.789015i \(0.710591\pi\)
\(48\) 0 0
\(49\) −7.50000 + 12.9904i −0.153061 + 0.265110i
\(50\) −22.2018 27.5151i −0.444035 0.550303i
\(51\) 0 0
\(52\) 0 0
\(53\) 67.8823 1.28080 0.640399 0.768043i \(-0.278769\pi\)
0.640399 + 0.768043i \(0.278769\pi\)
\(54\) 0 0
\(55\) 68.0000 46.6476i 1.23636 0.848138i
\(56\) −14.2829 + 8.24621i −0.255051 + 0.147254i
\(57\) 0 0
\(58\) 0 0
\(59\) −14.2829 8.24621i −0.242082 0.139766i 0.374051 0.927408i \(-0.377968\pi\)
−0.616133 + 0.787642i \(0.711302\pi\)
\(60\) 0 0
\(61\) 8.00000 + 13.8564i 0.131148 + 0.227154i 0.924119 0.382104i \(-0.124801\pi\)
−0.792972 + 0.609259i \(0.791467\pi\)
\(62\) −45.2548 −0.729917
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −5.04975 2.91548i −0.0753694 0.0435146i 0.461842 0.886962i \(-0.347189\pi\)
−0.537211 + 0.843448i \(0.680522\pi\)
\(68\) 11.3137 19.5959i 0.166378 0.288175i
\(69\) 0 0
\(70\) 37.1990 + 17.7830i 0.531414 + 0.254042i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 116.619i 1.59752i −0.601649 0.798761i \(-0.705489\pi\)
0.601649 0.798761i \(-0.294511\pi\)
\(74\) −28.5657 + 16.4924i −0.386023 + 0.222871i
\(75\) 0 0
\(76\) −12.0000 + 20.7846i −0.157895 + 0.273482i
\(77\) −48.0833 + 83.2827i −0.624458 + 1.08159i
\(78\) 0 0
\(79\) 36.0000 + 62.3538i 0.455696 + 0.789289i 0.998728 0.0504232i \(-0.0160570\pi\)
−0.543032 + 0.839712i \(0.682724\pi\)
\(80\) −11.3137 16.4924i −0.141421 0.206155i
\(81\) 0 0
\(82\) 81.6333i 0.995528i
\(83\) 21.9203 + 37.9671i 0.264100 + 0.457435i 0.967327 0.253530i \(-0.0815917\pi\)
−0.703227 + 0.710965i \(0.748258\pi\)
\(84\) 0 0
\(85\) −56.3980 + 4.38901i −0.663506 + 0.0516354i
\(86\) −49.9900 28.8617i −0.581279 0.335602i
\(87\) 0 0
\(88\) 40.3980 23.3238i 0.459068 0.265043i
\(89\) 65.9697i 0.741232i −0.928786 0.370616i \(-0.879147\pi\)
0.928786 0.370616i \(-0.120853\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −24.0416 41.6413i −0.261322 0.452623i
\(93\) 0 0
\(94\) 25.0000 43.3013i 0.265957 0.460652i
\(95\) 59.8191 4.65524i 0.629675 0.0490026i
\(96\) 0 0
\(97\) 141.393 81.6333i 1.45766 0.841581i 0.458765 0.888558i \(-0.348292\pi\)
0.998896 + 0.0469772i \(0.0149588\pi\)
\(98\) 21.2132 0.216461
\(99\) 0 0
\(100\) −18.0000 + 46.6476i −0.180000 + 0.466476i
\(101\) 114.263 65.9697i 1.13132 0.653165i 0.187050 0.982350i \(-0.440107\pi\)
0.944265 + 0.329185i \(0.106774\pi\)
\(102\) 0 0
\(103\) −85.8458 49.5631i −0.833454 0.481195i 0.0215796 0.999767i \(-0.493130\pi\)
−0.855034 + 0.518572i \(0.826464\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −48.0000 83.1384i −0.452830 0.784325i
\(107\) −55.1543 −0.515461 −0.257731 0.966217i \(-0.582975\pi\)
−0.257731 + 0.966217i \(0.582975\pi\)
\(108\) 0 0
\(109\) 80.0000 0.733945 0.366972 0.930232i \(-0.380394\pi\)
0.366972 + 0.930232i \(0.380394\pi\)
\(110\) −105.215 50.2978i −0.956497 0.457253i
\(111\) 0 0
\(112\) 20.1990 + 11.6619i 0.180348 + 0.104124i
\(113\) 76.3675 132.272i 0.675819 1.17055i −0.300410 0.953810i \(-0.597123\pi\)
0.976229 0.216742i \(-0.0695432\pi\)
\(114\) 0 0
\(115\) −51.8458 + 108.453i −0.450833 + 0.943068i
\(116\) 0 0
\(117\) 0 0
\(118\) 23.3238i 0.197659i
\(119\) 57.1314 32.9848i 0.480096 0.277184i
\(120\) 0 0
\(121\) 75.5000 130.770i 0.623967 1.08074i
\(122\) 11.3137 19.5959i 0.0927353 0.160622i
\(123\) 0 0
\(124\) 32.0000 + 55.4256i 0.258065 + 0.446981i
\(125\) 121.622 28.8617i 0.972979 0.230894i
\(126\) 0 0
\(127\) 40.8167i 0.321391i −0.987004 0.160696i \(-0.948626\pi\)
0.987004 0.160696i \(-0.0513737\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −42.8486 24.7386i −0.327088 0.188845i 0.327459 0.944865i \(-0.393808\pi\)
−0.654548 + 0.756021i \(0.727141\pi\)
\(132\) 0 0
\(133\) −60.5970 + 34.9857i −0.455617 + 0.263050i
\(134\) 8.24621i 0.0615389i
\(135\) 0 0
\(136\) −32.0000 −0.235294
\(137\) 25.4558 + 44.0908i 0.185809 + 0.321831i 0.943849 0.330378i \(-0.107176\pi\)
−0.758040 + 0.652208i \(0.773843\pi\)
\(138\) 0 0
\(139\) −22.0000 + 38.1051i −0.158273 + 0.274138i −0.934246 0.356629i \(-0.883926\pi\)
0.775973 + 0.630766i \(0.217259\pi\)
\(140\) −4.52408 58.1337i −0.0323149 0.415241i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) −142.829 + 82.4621i −0.978278 + 0.564809i
\(147\) 0 0
\(148\) 40.3980 + 23.3238i 0.272960 + 0.157593i
\(149\) 7.14143 + 4.12311i 0.0479290 + 0.0276718i 0.523773 0.851858i \(-0.324524\pi\)
−0.475844 + 0.879530i \(0.657857\pi\)
\(150\) 0 0
\(151\) −68.0000 117.779i −0.450331 0.779996i 0.548075 0.836429i \(-0.315361\pi\)
−0.998406 + 0.0564326i \(0.982027\pi\)
\(152\) 33.9411 0.223297
\(153\) 0 0
\(154\) 136.000 0.883117
\(155\) 69.0080 144.353i 0.445213 0.931312i
\(156\) 0 0
\(157\) 100.995 + 58.3095i 0.643281 + 0.371398i 0.785877 0.618383i \(-0.212212\pi\)
−0.142597 + 0.989781i \(0.545545\pi\)
\(158\) 50.9117 88.1816i 0.322226 0.558112i
\(159\) 0 0
\(160\) −12.1990 + 25.5183i −0.0762438 + 0.159489i
\(161\) 140.186i 0.870718i
\(162\) 0 0
\(163\) 99.1262i 0.608136i 0.952650 + 0.304068i \(0.0983450\pi\)
−0.952650 + 0.304068i \(0.901655\pi\)
\(164\) −99.9800 + 57.7235i −0.609634 + 0.351972i
\(165\) 0 0
\(166\) 31.0000 53.6936i 0.186747 0.323455i
\(167\) −146.371 + 253.522i −0.876474 + 1.51810i −0.0212891 + 0.999773i \(0.506777\pi\)
−0.855185 + 0.518324i \(0.826556\pi\)
\(168\) 0 0
\(169\) −84.5000 146.358i −0.500000 0.866025i
\(170\) 45.2548 + 65.9697i 0.266205 + 0.388057i
\(171\) 0 0
\(172\) 81.6333i 0.474612i
\(173\) 82.0244 + 142.070i 0.474129 + 0.821216i 0.999561 0.0296195i \(-0.00942955\pi\)
−0.525432 + 0.850836i \(0.676096\pi\)
\(174\) 0 0
\(175\) −113.448 + 91.5402i −0.648273 + 0.523087i
\(176\) −57.1314 32.9848i −0.324610 0.187414i
\(177\) 0 0
\(178\) −80.7960 + 46.6476i −0.453910 + 0.262065i
\(179\) 16.4924i 0.0921364i 0.998938 + 0.0460682i \(0.0146692\pi\)
−0.998938 + 0.0460682i \(0.985331\pi\)
\(180\) 0 0
\(181\) −82.0000 −0.453039 −0.226519 0.974007i \(-0.572735\pi\)
−0.226519 + 0.974007i \(0.572735\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −34.0000 + 58.8897i −0.184783 + 0.320053i
\(185\) −9.04817 116.267i −0.0489090 0.628473i
\(186\) 0 0
\(187\) −161.592 + 93.2952i −0.864129 + 0.498905i
\(188\) −70.7107 −0.376121
\(189\) 0 0
\(190\) −48.0000 69.9714i −0.252632 0.368271i
\(191\) −257.091 + 148.432i −1.34603 + 0.777130i −0.987684 0.156460i \(-0.949992\pi\)
−0.358344 + 0.933590i \(0.616659\pi\)
\(192\) 0 0
\(193\) 100.995 + 58.3095i 0.523290 + 0.302122i 0.738280 0.674495i \(-0.235638\pi\)
−0.214989 + 0.976616i \(0.568972\pi\)
\(194\) −199.960 115.447i −1.03072 0.595087i
\(195\) 0 0
\(196\) −15.0000 25.9808i −0.0765306 0.132555i
\(197\) −192.333 −0.976310 −0.488155 0.872757i \(-0.662330\pi\)
−0.488155 + 0.872757i \(0.662330\pi\)
\(198\) 0 0
\(199\) −312.000 −1.56784 −0.783920 0.620862i \(-0.786783\pi\)
−0.783920 + 0.620862i \(0.786783\pi\)
\(200\) 69.8593 10.9394i 0.349297 0.0546972i
\(201\) 0 0
\(202\) −161.592 93.2952i −0.799961 0.461858i
\(203\) 0 0
\(204\) 0 0
\(205\) 260.393 + 124.481i 1.27021 + 0.607223i
\(206\) 140.186i 0.680513i
\(207\) 0 0
\(208\) 0 0
\(209\) 171.394 98.9545i 0.820068 0.473467i
\(210\) 0 0
\(211\) 6.00000 10.3923i 0.0284360 0.0492526i −0.851457 0.524424i \(-0.824281\pi\)
0.879893 + 0.475171i \(0.157614\pi\)
\(212\) −67.8823 + 117.576i −0.320199 + 0.554601i
\(213\) 0 0
\(214\) 39.0000 + 67.5500i 0.182243 + 0.315654i
\(215\) 168.291 115.447i 0.782751 0.536963i
\(216\) 0 0
\(217\) 186.590i 0.859864i
\(218\) −56.5685 97.9796i −0.259489 0.449448i
\(219\) 0 0
\(220\) 12.7960 + 164.427i 0.0581638 + 0.747396i
\(221\) 0 0
\(222\) 0 0
\(223\) 35.3483 20.4083i 0.158512 0.0915172i −0.418646 0.908150i \(-0.637495\pi\)
0.577158 + 0.816633i \(0.304162\pi\)
\(224\) 32.9848i 0.147254i
\(225\) 0 0
\(226\) −216.000 −0.955752
\(227\) 79.9031 + 138.396i 0.351996 + 0.609675i 0.986599 0.163163i \(-0.0521698\pi\)
−0.634603 + 0.772838i \(0.718836\pi\)
\(228\) 0 0
\(229\) −41.0000 + 71.0141i −0.179039 + 0.310105i −0.941552 0.336868i \(-0.890632\pi\)
0.762512 + 0.646974i \(0.223966\pi\)
\(230\) 169.488 13.1899i 0.736902 0.0573472i
\(231\) 0 0
\(232\) 0 0
\(233\) 192.333 0.825464 0.412732 0.910853i \(-0.364575\pi\)
0.412732 + 0.910853i \(0.364575\pi\)
\(234\) 0 0
\(235\) 100.000 + 145.774i 0.425532 + 0.620314i
\(236\) 28.5657 16.4924i 0.121041 0.0698831i
\(237\) 0 0
\(238\) −80.7960 46.6476i −0.339479 0.195998i
\(239\) 399.920 + 230.894i 1.67331 + 0.966083i 0.965768 + 0.259407i \(0.0835273\pi\)
0.707537 + 0.706676i \(0.249806\pi\)
\(240\) 0 0
\(241\) −152.000 263.272i −0.630705 1.09241i −0.987408 0.158196i \(-0.949432\pi\)
0.356702 0.934218i \(-0.383901\pi\)
\(242\) −213.546 −0.882423
\(243\) 0 0
\(244\) −32.0000 −0.131148
\(245\) −32.3475 + 67.6656i −0.132031 + 0.276186i
\(246\) 0 0
\(247\) 0 0
\(248\) 45.2548 78.3837i 0.182479 0.316063i
\(249\) 0 0
\(250\) −121.348 128.548i −0.485393 0.514192i
\(251\) 346.341i 1.37984i 0.723884 + 0.689922i \(0.242355\pi\)
−0.723884 + 0.689922i \(0.757645\pi\)
\(252\) 0 0
\(253\) 396.505i 1.56721i
\(254\) −49.9900 + 28.8617i −0.196811 + 0.113629i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −195.161 + 338.030i −0.759383 + 1.31529i 0.183782 + 0.982967i \(0.441166\pi\)
−0.943166 + 0.332323i \(0.892168\pi\)
\(258\) 0 0
\(259\) 68.0000 + 117.779i 0.262548 + 0.454747i
\(260\) 0 0
\(261\) 0 0
\(262\) 69.9714i 0.267066i
\(263\) −147.785 255.972i −0.561921 0.973276i −0.997329 0.0730428i \(-0.976729\pi\)
0.435407 0.900234i \(-0.356604\pi\)
\(264\) 0 0
\(265\) 338.388 26.3340i 1.27694 0.0993737i
\(266\) 85.6971 + 49.4773i 0.322170 + 0.186005i
\(267\) 0 0
\(268\) 10.0995 5.83095i 0.0376847 0.0217573i
\(269\) 74.2159i 0.275896i 0.990440 + 0.137948i \(0.0440506\pi\)
−0.990440 + 0.137948i \(0.955949\pi\)
\(270\) 0 0
\(271\) 40.0000 0.147601 0.0738007 0.997273i \(-0.476487\pi\)
0.0738007 + 0.997273i \(0.476487\pi\)
\(272\) 22.6274 + 39.1918i 0.0831890 + 0.144088i
\(273\) 0 0
\(274\) 36.0000 62.3538i 0.131387 0.227569i
\(275\) 320.879 258.915i 1.16683 0.941508i
\(276\) 0 0
\(277\) −383.781 + 221.576i −1.38549 + 0.799914i −0.992803 0.119758i \(-0.961788\pi\)
−0.392688 + 0.919672i \(0.628455\pi\)
\(278\) 62.2254 0.223832
\(279\) 0 0
\(280\) −68.0000 + 46.6476i −0.242857 + 0.166599i
\(281\) 449.910 259.756i 1.60110 0.924397i 0.609836 0.792528i \(-0.291235\pi\)
0.991267 0.131870i \(-0.0420981\pi\)
\(282\) 0 0
\(283\) 277.736 + 160.351i 0.981401 + 0.566612i 0.902693 0.430286i \(-0.141587\pi\)
0.0787079 + 0.996898i \(0.474921\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −336.583 −1.17276
\(288\) 0 0
\(289\) −161.000 −0.557093
\(290\) 0 0
\(291\) 0 0
\(292\) 201.990 + 116.619i 0.691747 + 0.399380i
\(293\) −42.4264 + 73.4847i −0.144800 + 0.250801i −0.929298 0.369330i \(-0.879587\pi\)
0.784498 + 0.620131i \(0.212921\pi\)
\(294\) 0 0
\(295\) −74.3980 35.5659i −0.252197 0.120562i
\(296\) 65.9697i 0.222871i
\(297\) 0 0
\(298\) 11.6619i 0.0391339i
\(299\) 0 0
\(300\) 0 0
\(301\) −119.000 + 206.114i −0.395349 + 0.684764i
\(302\) −96.1665 + 166.565i −0.318432 + 0.551541i
\(303\) 0 0
\(304\) −24.0000 41.5692i −0.0789474 0.136741i
\(305\) 45.2548 + 65.9697i 0.148377 + 0.216294i
\(306\) 0 0
\(307\) 367.350i 1.19658i 0.801280 + 0.598290i \(0.204153\pi\)
−0.801280 + 0.598290i \(0.795847\pi\)
\(308\) −96.1665 166.565i −0.312229 0.540796i
\(309\) 0 0
\(310\) −225.592 + 17.5560i −0.727716 + 0.0566323i
\(311\) 85.6971 + 49.4773i 0.275554 + 0.159091i 0.631409 0.775450i \(-0.282477\pi\)
−0.355855 + 0.934541i \(0.615810\pi\)
\(312\) 0 0
\(313\) −161.592 + 93.2952i −0.516269 + 0.298068i −0.735407 0.677626i \(-0.763009\pi\)
0.219138 + 0.975694i \(0.429675\pi\)
\(314\) 164.924i 0.525236i
\(315\) 0 0
\(316\) −144.000 −0.455696
\(317\) 260.215 + 450.706i 0.820868 + 1.42179i 0.905036 + 0.425334i \(0.139843\pi\)
−0.0841679 + 0.996452i \(0.526823\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 39.8794 3.10350i 0.124623 0.00969842i
\(321\) 0 0
\(322\) −171.692 + 99.1262i −0.533204 + 0.307845i
\(323\) −135.765 −0.420324
\(324\) 0 0
\(325\) 0 0
\(326\) 121.404 70.0928i 0.372406 0.215009i
\(327\) 0 0
\(328\) 141.393 + 81.6333i 0.431076 + 0.248882i
\(329\) −178.536 103.078i −0.542662 0.313306i
\(330\) 0 0
\(331\) −146.000 252.879i −0.441088 0.763986i 0.556683 0.830725i \(-0.312074\pi\)
−0.997770 + 0.0667389i \(0.978741\pi\)
\(332\) −87.6812 −0.264100
\(333\) 0 0
\(334\) 414.000 1.23952
\(335\) −26.3037 12.5745i −0.0785184 0.0375357i
\(336\) 0 0
\(337\) −282.786 163.267i −0.839128 0.484471i 0.0178397 0.999841i \(-0.494321\pi\)
−0.856968 + 0.515370i \(0.827654\pi\)
\(338\) −119.501 + 206.982i −0.353553 + 0.612372i
\(339\) 0 0
\(340\) 48.7960 102.073i 0.143518 0.300215i
\(341\) 527.758i 1.54768i
\(342\) 0 0
\(343\) 373.181i 1.08799i
\(344\) 99.9800 57.7235i 0.290640 0.167801i
\(345\) 0 0
\(346\) 116.000 200.918i 0.335260 0.580688i
\(347\) −197.283 + 341.704i −0.568538 + 0.984737i 0.428173 + 0.903697i \(0.359158\pi\)
−0.996711 + 0.0810402i \(0.974176\pi\)
\(348\) 0 0
\(349\) −127.000 219.970i −0.363897 0.630288i 0.624702 0.780864i \(-0.285221\pi\)
−0.988598 + 0.150576i \(0.951887\pi\)
\(350\) 192.333 + 74.2159i 0.549523 + 0.212045i
\(351\) 0 0
\(352\) 93.2952i 0.265043i
\(353\) −172.534 298.838i −0.488765 0.846566i 0.511151 0.859491i \(-0.329219\pi\)
−0.999916 + 0.0129248i \(0.995886\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 114.263 + 65.9697i 0.320963 + 0.185308i
\(357\) 0 0
\(358\) 20.1990 11.6619i 0.0564218 0.0325752i
\(359\) 395.818i 1.10256i 0.834321 + 0.551279i \(0.185860\pi\)
−0.834321 + 0.551279i \(0.814140\pi\)
\(360\) 0 0
\(361\) −217.000 −0.601108
\(362\) 57.9828 + 100.429i 0.160173 + 0.277428i
\(363\) 0 0
\(364\) 0 0
\(365\) −45.2408 581.337i −0.123947 1.59271i
\(366\) 0 0
\(367\) 358.532 206.999i 0.976928 0.564029i 0.0755864 0.997139i \(-0.475917\pi\)
0.901341 + 0.433110i \(0.142584\pi\)
\(368\) 96.1665 0.261322
\(369\) 0 0
\(370\) −136.000 + 93.2952i −0.367568 + 0.252149i
\(371\) −342.789 + 197.909i −0.923958 + 0.533448i
\(372\) 0 0
\(373\) −545.373 314.871i −1.46213 0.844159i −0.463017 0.886349i \(-0.653233\pi\)
−0.999110 + 0.0421901i \(0.986566\pi\)
\(374\) 228.526 + 131.939i 0.611031 + 0.352779i
\(375\) 0 0
\(376\) 50.0000 + 86.6025i 0.132979 + 0.230326i
\(377\) 0 0
\(378\) 0 0
\(379\) −572.000 −1.50923 −0.754617 0.656165i \(-0.772178\pi\)
−0.754617 + 0.656165i \(0.772178\pi\)
\(380\) −51.7560 + 108.265i −0.136200 + 0.284908i
\(381\) 0 0
\(382\) 363.582 + 209.914i 0.951786 + 0.549514i
\(383\) 96.8736 167.790i 0.252934 0.438094i −0.711398 0.702789i \(-0.751938\pi\)
0.964332 + 0.264695i \(0.0852712\pi\)
\(384\) 0 0
\(385\) −207.383 + 433.811i −0.538658 + 1.12678i
\(386\) 164.924i 0.427265i
\(387\) 0 0
\(388\) 326.533i 0.841581i
\(389\) −335.647 + 193.786i −0.862846 + 0.498164i −0.864964 0.501833i \(-0.832659\pi\)
0.00211824 + 0.999998i \(0.499326\pi\)
\(390\) 0 0
\(391\) 136.000 235.559i 0.347826 0.602452i
\(392\) −21.2132 + 36.7423i −0.0541153 + 0.0937305i
\(393\) 0 0
\(394\) 136.000 + 235.559i 0.345178 + 0.597865i
\(395\) 203.647 + 296.864i 0.515561 + 0.751553i
\(396\) 0 0
\(397\) 513.124i 1.29250i −0.763124 0.646252i \(-0.776336\pi\)
0.763124 0.646252i \(-0.223664\pi\)
\(398\) 220.617 + 382.120i 0.554315 + 0.960102i
\(399\) 0 0
\(400\) −62.7960 77.8245i −0.156990 0.194561i
\(401\) 57.1314 + 32.9848i 0.142472 + 0.0822565i 0.569542 0.821962i \(-0.307121\pi\)
−0.427069 + 0.904219i \(0.640454\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 263.879i 0.653165i
\(405\) 0 0
\(406\) 0 0
\(407\) −192.333 333.131i −0.472563 0.818503i
\(408\) 0 0
\(409\) −320.000 + 554.256i −0.782396 + 1.35515i 0.148146 + 0.988965i \(0.452669\pi\)
−0.930542 + 0.366184i \(0.880664\pi\)
\(410\) −31.6686 406.936i −0.0772404 0.992527i
\(411\) 0 0
\(412\) 171.692 99.1262i 0.416727 0.240598i
\(413\) 96.1665 0.232849
\(414\) 0 0
\(415\) 124.000 + 180.760i 0.298795 + 0.435565i
\(416\) 0 0
\(417\) 0 0
\(418\) −242.388 139.943i −0.579876 0.334791i
\(419\) −499.900 288.617i −1.19308 0.688824i −0.234075 0.972218i \(-0.575206\pi\)
−0.959004 + 0.283394i \(0.908540\pi\)
\(420\) 0 0
\(421\) 328.000 + 568.113i 0.779097 + 1.34944i 0.932463 + 0.361267i \(0.117656\pi\)
−0.153365 + 0.988170i \(0.549011\pi\)
\(422\) −16.9706 −0.0402146
\(423\) 0 0
\(424\) 192.000 0.452830
\(425\) −279.437 + 43.7577i −0.657500 + 0.102959i
\(426\) 0 0
\(427\) −80.7960 46.6476i −0.189218 0.109245i
\(428\) 55.1543 95.5301i 0.128865 0.223201i
\(429\) 0 0
\(430\) −260.393 124.481i −0.605565 0.289490i
\(431\) 362.833i 0.841841i 0.907098 + 0.420920i \(0.138293\pi\)
−0.907098 + 0.420920i \(0.861707\pi\)
\(432\) 0 0
\(433\) 163.267i 0.377059i 0.982068 + 0.188530i \(0.0603722\pi\)
−0.982068 + 0.188530i \(0.939628\pi\)
\(434\) 228.526 131.939i 0.526557 0.304008i
\(435\) 0 0
\(436\) −80.0000 + 138.564i −0.183486 + 0.317807i
\(437\) −144.250 + 249.848i −0.330091 + 0.571734i
\(438\) 0 0
\(439\) −216.000 374.123i −0.492027 0.852216i 0.507931 0.861398i \(-0.330411\pi\)
−0.999958 + 0.00918170i \(0.997077\pi\)
\(440\) 192.333 131.939i 0.437121 0.299862i
\(441\) 0 0
\(442\) 0 0
\(443\) −61.5183 106.553i −0.138867 0.240526i 0.788201 0.615418i \(-0.211013\pi\)
−0.927068 + 0.374893i \(0.877680\pi\)
\(444\) 0 0
\(445\) −25.5921 328.854i −0.0575103 0.738998i
\(446\) −49.9900 28.8617i −0.112085 0.0647124i
\(447\) 0 0
\(448\) −40.3980 + 23.3238i −0.0901742 + 0.0520621i
\(449\) 865.852i 1.92840i −0.265174 0.964201i \(-0.585429\pi\)
0.265174 0.964201i \(-0.414571\pi\)
\(450\) 0 0
\(451\) 952.000 2.11086
\(452\) 152.735 + 264.545i 0.337909 + 0.585276i
\(453\) 0 0
\(454\) 113.000 195.722i 0.248899 0.431105i
\(455\) 0 0
\(456\) 0 0
\(457\) 403.980 233.238i 0.883983 0.510368i 0.0120133 0.999928i \(-0.496176\pi\)
0.871970 + 0.489560i \(0.162843\pi\)
\(458\) 115.966 0.253200
\(459\) 0 0
\(460\) −136.000 198.252i −0.295652 0.430983i
\(461\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) 530.224 + 306.125i 1.14519 + 0.661177i 0.947711 0.319130i \(-0.103391\pi\)
0.197481 + 0.980307i \(0.436724\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −136.000 235.559i −0.291845 0.505491i
\(467\) −767.918 −1.64436 −0.822182 0.569225i \(-0.807243\pi\)
−0.822182 + 0.569225i \(0.807243\pi\)
\(468\) 0 0
\(469\) 34.0000 0.0724947
\(470\) 107.825 225.552i 0.229415 0.479898i
\(471\) 0 0
\(472\) −40.3980 23.3238i −0.0855890 0.0494148i
\(473\) 336.583 582.979i 0.711592 1.23251i
\(474\) 0 0
\(475\) 296.388 46.4121i 0.623975 0.0977097i
\(476\) 131.939i 0.277184i
\(477\) 0 0
\(478\) 653.067i 1.36625i
\(479\) −485.617 + 280.371i −1.01381 + 0.585326i −0.912306 0.409509i \(-0.865700\pi\)
−0.101508 + 0.994835i \(0.532367\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −214.960 + 372.322i −0.445976 + 0.772453i
\(483\) 0 0
\(484\) 151.000 + 261.540i 0.311983 + 0.540371i
\(485\) 673.166 461.788i 1.38797 0.952140i
\(486\) 0 0
\(487\) 647.236i 1.32903i −0.747277 0.664513i \(-0.768639\pi\)
0.747277 0.664513i \(-0.231361\pi\)
\(488\) 22.6274 + 39.1918i 0.0463677 + 0.0803111i
\(489\) 0 0
\(490\) 105.746 8.22939i 0.215809 0.0167947i
\(491\) −299.940 173.170i −0.610876 0.352689i 0.162432 0.986720i \(-0.448066\pi\)
−0.773308 + 0.634030i \(0.781399\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −128.000 −0.258065
\(497\) 0 0
\(498\) 0 0
\(499\) 330.000 571.577i 0.661323 1.14544i −0.318946 0.947773i \(-0.603329\pi\)
0.980268 0.197671i \(-0.0633379\pi\)
\(500\) −71.6324 + 239.518i −0.143265 + 0.479036i
\(501\) 0 0
\(502\) 424.179 244.900i 0.844979 0.487849i
\(503\) −182.434 −0.362691 −0.181345 0.983419i \(-0.558045\pi\)
−0.181345 + 0.983419i \(0.558045\pi\)
\(504\) 0 0
\(505\) 544.000 373.181i 1.07723 0.738972i
\(506\) 485.617 280.371i 0.959718 0.554093i
\(507\) 0 0
\(508\) 70.6965 + 40.8167i 0.139166 + 0.0803478i
\(509\) −342.789 197.909i −0.673455 0.388819i 0.123930 0.992291i \(-0.460450\pi\)
−0.797384 + 0.603472i \(0.793784\pi\)
\(510\) 0 0
\(511\) 340.000 + 588.897i 0.665362 + 1.15244i
\(512\) 22.6274 0.0441942
\(513\) 0 0
\(514\) 552.000 1.07393
\(515\) −447.162 213.766i −0.868277 0.415079i
\(516\) 0 0
\(517\) 504.975 + 291.548i 0.976741 + 0.563922i
\(518\) 96.1665 166.565i 0.185650 0.321555i
\(519\) 0 0
\(520\) 0 0
\(521\) 131.939i 0.253243i 0.991951 + 0.126621i \(0.0404133\pi\)
−0.991951 + 0.126621i \(0.959587\pi\)
\(522\) 0 0
\(523\) 145.774i 0.278726i −0.990241 0.139363i \(-0.955494\pi\)
0.990241 0.139363i \(-0.0445055\pi\)
\(524\) 85.6971 49.4773i 0.163544 0.0944223i
\(525\) 0 0
\(526\) −209.000 + 361.999i −0.397338 + 0.688210i
\(527\) −181.019 + 313.535i −0.343490 + 0.594942i
\(528\) 0 0
\(529\) −24.5000 42.4352i −0.0463138 0.0802179i
\(530\) −271.529 395.818i −0.512319 0.746827i
\(531\) 0 0
\(532\) 139.943i 0.263050i
\(533\) 0 0
\(534\) 0 0
\(535\) −274.940 + 21.3964i −0.513907 + 0.0399933i
\(536\) −14.2829 8.24621i −0.0266471 0.0153847i
\(537\) 0 0
\(538\) 90.8955 52.4786i 0.168951 0.0975438i
\(539\) 247.386i 0.458973i
\(540\) 0 0
\(541\) 418.000 0.772643 0.386322 0.922364i \(-0.373745\pi\)
0.386322 + 0.922364i \(0.373745\pi\)
\(542\) −28.2843 48.9898i −0.0521850 0.0903871i
\(543\) 0 0
\(544\) 32.0000 55.4256i 0.0588235 0.101885i
\(545\) 398.794 31.0350i 0.731733 0.0569449i
\(546\) 0 0
\(547\) −247.438 + 142.858i −0.452354 + 0.261167i −0.708824 0.705385i \(-0.750774\pi\)
0.256470 + 0.966552i \(0.417441\pi\)
\(548\) −101.823 −0.185809
\(549\) 0 0
\(550\) −544.000 209.914i −0.989091 0.381662i
\(551\) 0 0
\(552\) 0 0
\(553\) −363.582 209.914i −0.657472 0.379592i
\(554\) 542.749 + 313.356i 0.979691 + 0.565625i
\(555\) 0 0
\(556\) −44.0000 76.2102i −0.0791367 0.137069i
\(557\) 424.264 0.761695 0.380847 0.924638i \(-0.375632\pi\)
0.380847 + 0.924638i \(0.375632\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 105.215 + 50.2978i 0.187883 + 0.0898175i
\(561\) 0 0
\(562\) −636.269 367.350i −1.13215 0.653648i
\(563\) 406.586 704.228i 0.722178 1.25085i −0.237947 0.971278i \(-0.576474\pi\)
0.960125 0.279571i \(-0.0901923\pi\)
\(564\) 0 0
\(565\) 329.373 688.994i 0.582962 1.21946i
\(566\) 453.542i 0.801310i
\(567\) 0 0
\(568\) 0 0
\(569\) 392.779 226.771i 0.690296 0.398543i −0.113427 0.993546i \(-0.536183\pi\)
0.803723 + 0.595004i \(0.202849\pi\)
\(570\) 0 0
\(571\) −110.000 + 190.526i −0.192644 + 0.333670i −0.946126 0.323799i \(-0.895040\pi\)
0.753481 + 0.657469i \(0.228373\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 238.000 + 412.228i 0.414634 + 0.718167i
\(575\) −216.375 + 560.742i −0.376304 + 0.975204i
\(576\) 0 0
\(577\) 46.6476i 0.0808451i 0.999183 + 0.0404225i \(0.0128704\pi\)
−0.999183 + 0.0404225i \(0.987130\pi\)
\(578\) 113.844 + 197.184i 0.196962 + 0.341149i
\(579\) 0 0
\(580\) 0 0
\(581\) −221.384 127.816i −0.381040 0.219994i
\(582\) 0 0
\(583\) 969.552 559.771i 1.66304 0.960157i
\(584\) 329.848i 0.564809i
\(585\) 0 0
\(586\) 120.000 0.204778
\(587\) −27.5772 47.7650i −0.0469798 0.0813715i 0.841579 0.540134i \(-0.181626\pi\)
−0.888559 + 0.458762i \(0.848293\pi\)
\(588\) 0 0
\(589\) 192.000 332.554i 0.325976 0.564607i
\(590\) 9.04817 + 116.267i 0.0153359 + 0.197064i
\(591\) 0 0
\(592\) −80.7960 + 46.6476i −0.136480 + 0.0787966i
\(593\) 390.323 0.658217 0.329109 0.944292i \(-0.393252\pi\)
0.329109 + 0.944292i \(0.393252\pi\)
\(594\) 0 0
\(595\) 272.000 186.590i 0.457143 0.313597i
\(596\) −14.2829 + 8.24621i −0.0239645 + 0.0138359i
\(597\) 0 0
\(598\) 0 0
\(599\) 85.6971 + 49.4773i 0.143067 + 0.0825998i 0.569825 0.821766i \(-0.307011\pi\)
−0.426758 + 0.904366i \(0.640344\pi\)
\(600\) 0 0
\(601\) 440.000 + 762.102i 0.732113 + 1.26806i 0.955978 + 0.293437i \(0.0947991\pi\)
−0.223865 + 0.974620i \(0.571868\pi\)
\(602\) 336.583 0.559108
\(603\) 0 0
\(604\) 272.000 0.450331
\(605\) 325.632 681.167i 0.538234 1.12590i
\(606\) 0 0
\(607\) −368.632 212.830i −0.607301 0.350626i 0.164607 0.986359i \(-0.447364\pi\)
−0.771909 + 0.635734i \(0.780698\pi\)
\(608\) −33.9411 + 58.7878i −0.0558242 + 0.0966904i
\(609\) 0 0
\(610\) 48.7960 102.073i 0.0799935 0.167333i
\(611\) 0 0
\(612\) 0 0
\(613\) 606.419i 0.989264i −0.869102 0.494632i \(-0.835303\pi\)
0.869102 0.494632i \(-0.164697\pi\)
\(614\) 449.910 259.756i 0.732752 0.423055i
\(615\) 0 0
\(616\) −136.000 + 235.559i −0.220779 + 0.382401i
\(617\) 56.5685 97.9796i 0.0916832 0.158800i −0.816536 0.577294i \(-0.804109\pi\)
0.908220 + 0.418494i \(0.137442\pi\)
\(618\) 0 0
\(619\) −26.0000 45.0333i −0.0420032 0.0727517i 0.844259 0.535935i \(-0.180041\pi\)
−0.886263 + 0.463183i \(0.846707\pi\)
\(620\) 181.019 + 263.879i 0.291967 + 0.425611i
\(621\) 0 0
\(622\) 139.943i 0.224988i
\(623\) 192.333 + 333.131i 0.308721 + 0.534720i
\(624\) 0 0
\(625\) 595.082 191.055i 0.952131 0.305689i
\(626\) 228.526 + 131.939i 0.365057 + 0.210766i
\(627\) 0 0
\(628\) −201.990 + 116.619i −0.321640 + 0.185699i
\(629\) 263.879i 0.419521i
\(630\) 0 0
\(631\) −544.000 −0.862124 −0.431062 0.902322i \(-0.641861\pi\)
−0.431062 + 0.902322i \(0.641861\pi\)
\(632\) 101.823 + 176.363i 0.161113 + 0.279056i
\(633\) 0 0
\(634\) 368.000 637.395i 0.580442 1.00535i
\(635\) −15.8343 203.468i −0.0249359 0.320422i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −32.0000 46.6476i −0.0500000 0.0728869i
\(641\) −735.567 + 424.680i −1.14753 + 0.662527i −0.948284 0.317422i \(-0.897183\pi\)
−0.199246 + 0.979949i \(0.563849\pi\)
\(642\) 0 0
\(643\) −318.134 183.675i −0.494766 0.285653i 0.231784 0.972767i \(-0.425544\pi\)
−0.726549 + 0.687114i \(0.758877\pi\)
\(644\) 242.809 + 140.186i 0.377032 + 0.217679i
\(645\) 0 0
\(646\) 96.0000 + 166.277i 0.148607 + 0.257395i
\(647\) −971.565 −1.50165 −0.750823 0.660504i \(-0.770343\pi\)
−0.750823 + 0.660504i \(0.770343\pi\)
\(648\) 0 0
\(649\) −272.000 −0.419106
\(650\) 0 0
\(651\) 0 0
\(652\) −171.692 99.1262i −0.263331 0.152034i
\(653\) −175.362 + 303.737i −0.268549 + 0.465140i −0.968487 0.249063i \(-0.919877\pi\)
0.699938 + 0.714203i \(0.253211\pi\)
\(654\) 0 0
\(655\) −223.194 106.698i −0.340754 0.162897i
\(656\) 230.894i 0.351972i
\(657\) 0 0
\(658\) 291.548i 0.443081i
\(659\) −499.900 + 288.617i −0.758574 + 0.437963i −0.828783 0.559570i \(-0.810966\pi\)
0.0702098 + 0.997532i \(0.477633\pi\)
\(660\) 0 0
\(661\) −40.0000 + 69.2820i −0.0605144 + 0.104814i −0.894695 0.446677i \(-0.852607\pi\)
0.834181 + 0.551491i \(0.185941\pi\)
\(662\) −206.475 + 357.626i −0.311896 + 0.540220i
\(663\) 0 0
\(664\) 62.0000 + 107.387i 0.0933735 + 0.161728i
\(665\) −288.500 + 197.909i −0.433834 + 0.297608i
\(666\) 0 0
\(667\) 0 0
\(668\) −292.742 507.044i −0.438237 0.759048i
\(669\) 0 0
\(670\) 3.19901 + 41.1068i 0.00477464 + 0.0613534i
\(671\) 228.526 + 131.939i 0.340575 + 0.196631i
\(672\) 0 0
\(673\) −424.179 + 244.900i −0.630281 + 0.363893i −0.780861 0.624705i \(-0.785219\pi\)
0.150580 + 0.988598i \(0.451886\pi\)
\(674\) 461.788i 0.685145i
\(675\) 0 0
\(676\) 338.000 0.500000
\(677\) −96.1665 166.565i −0.142048 0.246034i 0.786220 0.617947i \(-0.212035\pi\)
−0.928268 + 0.371913i \(0.878702\pi\)
\(678\) 0 0
\(679\) −476.000 + 824.456i −0.701031 + 1.21422i
\(680\) −159.518 + 12.4140i −0.234585 + 0.0182559i
\(681\) 0 0
\(682\) −646.368 + 373.181i −0.947754 + 0.547186i
\(683\) 236.174 0.345789 0.172894 0.984940i \(-0.444688\pi\)
0.172894 + 0.984940i \(0.444688\pi\)
\(684\) 0 0
\(685\) 144.000 + 209.914i 0.210219 + 0.306444i
\(686\) −457.051 + 263.879i −0.666256 + 0.384663i
\(687\) 0 0
\(688\) −141.393 81.6333i −0.205513 0.118653i
\(689\) 0 0
\(690\) 0 0
\(691\) 274.000 + 474.582i 0.396527 + 0.686805i 0.993295 0.115609i \(-0.0368821\pi\)
−0.596768 + 0.802414i \(0.703549\pi\)
\(692\) −328.098 −0.474129
\(693\) 0 0
\(694\) 558.000 0.804035
\(695\) −94.8860 + 198.486i −0.136527 + 0.285591i
\(696\) 0 0
\(697\) −565.572 326.533i −0.811438 0.468484i
\(698\) −179.605 + 311.085i −0.257314 + 0.445681i
\(699\) 0 0
\(700\) −45.1045 288.037i −0.0644349 0.411482i
\(701\) 57.7235i 0.0823445i −0.999152 0.0411722i \(-0.986891\pi\)
0.999152 0.0411722i \(-0.0131092\pi\)
\(702\) 0 0
\(703\) 279.886i 0.398130i
\(704\) 114.263 65.9697i 0.162305 0.0937069i
\(705\) 0 0
\(706\) −244.000 + 422.620i −0.345609 + 0.598612i
\(707\) −384.666 + 666.261i −0.544082 + 0.942378i
\(708\) 0 0
\(709\) −615.000 1065.21i −0.867419 1.50241i −0.864625 0.502418i \(-0.832444\pi\)
−0.00279375 0.999996i \(-0.500889\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 186.590i 0.262065i
\(713\) 384.666 + 666.261i 0.539504 + 0.934448i
\(714\) 0 0
\(715\) 0 0
\(716\) −28.5657 16.4924i −0.0398962 0.0230341i
\(717\) 0 0
\(718\) 484.776 279.886i 0.675176 0.389813i
\(719\) 626.712i 0.871644i 0.900033 + 0.435822i \(0.143542\pi\)
−0.900033 + 0.435822i \(0.856458\pi\)
\(720\) 0 0
\(721\) 578.000 0.801664
\(722\) 153.442 + 265.770i 0.212524 + 0.368102i
\(723\) 0 0
\(724\) 82.0000 142.028i 0.113260 0.196172i
\(725\) 0 0
\(726\) 0 0
\(727\) −318.134 + 183.675i −0.437599 + 0.252648i −0.702579 0.711606i \(-0.747968\pi\)
0.264980 + 0.964254i \(0.414635\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −680.000 + 466.476i −0.931507 + 0.639008i
\(731\) −399.920 + 230.894i −0.547086 + 0.315860i
\(732\) 0 0
\(733\) 868.557 + 501.462i 1.18494 + 0.684123i 0.957151 0.289589i \(-0.0935186\pi\)
0.227784 + 0.973712i \(0.426852\pi\)
\(734\) −507.041 292.740i −0.690792 0.398829i
\(735\) 0 0
\(736\) −68.0000 117.779i −0.0923913 0.160026i
\(737\) −96.1665 −0.130484
\(738\) 0 0
\(739\) −340.000 −0.460081 −0.230041 0.973181i \(-0.573886\pi\)
−0.230041 + 0.973181i \(0.573886\pi\)
\(740\) 210.429 + 100.596i 0.284364 + 0.135940i
\(741\) 0 0
\(742\) 484.776 + 279.886i 0.653337 + 0.377204i
\(743\) −621.547 + 1076.55i −0.836537 + 1.44892i 0.0562362 + 0.998417i \(0.482090\pi\)
−0.892773 + 0.450507i \(0.851243\pi\)
\(744\) 0 0
\(745\) 37.1990 + 17.7830i 0.0499316 + 0.0238697i
\(746\) 890.591i 1.19382i
\(747\) 0 0
\(748\) 373.181i 0.498905i
\(749\) 278.516 160.801i 0.371850 0.214688i
\(750\) 0 0
\(751\) 260.000 450.333i 0.346205 0.599645i −0.639367 0.768902i \(-0.720803\pi\)
0.985572 + 0.169257i \(0.0541368\pi\)
\(752\) 70.7107 122.474i 0.0940302 0.162865i
\(753\) 0 0
\(754\) 0 0
\(755\) −384.666 560.742i −0.509492 0.742705i
\(756\) 0 0
\(757\) 816.333i 1.07838i 0.842184 + 0.539190i \(0.181269\pi\)
−0.842184 + 0.539190i \(0.818731\pi\)
\(758\) 404.465 + 700.554i 0.533595 + 0.924214i
\(759\) 0 0
\(760\) 169.194 13.1670i 0.222624 0.0173250i
\(761\) −342.789 197.909i −0.450445 0.260064i 0.257573 0.966259i \(-0.417077\pi\)
−0.708018 + 0.706194i \(0.750410\pi\)
\(762\) 0 0
\(763\) −403.980 + 233.238i −0.529463 + 0.305686i
\(764\) 593.727i 0.777130i
\(765\) 0 0
\(766\) −274.000 −0.357702
\(767\) 0 0
\(768\) 0 0
\(769\) 153.000 265.004i 0.198960 0.344608i −0.749232 0.662308i \(-0.769577\pi\)
0.948191 + 0.317700i \(0.102910\pi\)
\(770\) 677.950 52.7594i 0.880455 0.0685187i
\(771\) 0 0
\(772\) −201.990 + 116.619i −0.261645 + 0.151061i
\(773\) 305.470 0.395175 0.197587 0.980285i \(-0.436689\pi\)
0.197587 + 0.980285i \(0.436689\pi\)
\(774\) 0 0
\(775\) 288.000 746.362i 0.371613 0.963048i
\(776\) 399.920 230.894i 0.515361 0.297544i
\(777\) 0 0
\(778\) 474.677 + 274.055i 0.610124 + 0.352255i
\(779\) 599.880 + 346.341i 0.770064 + 0.444597i
\(780\) 0 0
\(781\) 0 0
\(782\) −384.666 −0.491900
\(783\) 0 0
\(784\) 60.0000 0.0765306
\(785\) 526.073 + 251.489i 0.670157 + 0.320368i
\(786\) 0 0
\(787\) 489.826 + 282.801i 0.622396 + 0.359341i 0.777801 0.628510i \(-0.216335\pi\)
−0.155405 + 0.987851i \(0.549668\pi\)
\(788\) 192.333 333.131i 0.244077 0.422755i
\(789\) 0 0