Properties

Label 810.3.j.c.269.1
Level $810$
Weight $3$
Character 810.269
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 269.1
Root \(-2.17132 - 2.07011i\) of defining polynomial
Character \(\chi\) \(=\) 810.269
Dual form 810.3.j.c.539.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-2.15650 + 4.51104i) q^{5} +(5.04975 + 2.91548i) q^{7} +2.82843 q^{8} +O(q^{10})\) \(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-2.15650 + 4.51104i) q^{5} +(5.04975 + 2.91548i) q^{7} +2.82843 q^{8} +(-4.00000 - 5.83095i) q^{10} +(-14.2829 - 8.24621i) q^{11} +(-7.14143 + 4.12311i) q^{14} +(-2.00000 + 3.46410i) q^{16} -11.3137 q^{17} +12.0000 q^{19} +(9.96986 - 0.775874i) q^{20} +(20.1990 - 11.6619i) q^{22} +(-12.0208 - 20.8207i) q^{23} +(-15.6990 - 19.4561i) q^{25} -11.6619i q^{28} +(16.0000 + 27.7128i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(8.00000 - 13.8564i) q^{34} +(-24.0416 + 16.4924i) q^{35} -23.3238i q^{37} +(-8.48528 + 14.6969i) q^{38} +(-6.09950 + 12.7592i) q^{40} +(-49.9900 + 28.8617i) q^{41} +(-35.3483 - 20.4083i) q^{43} +32.9848i q^{44} +34.0000 q^{46} +(17.6777 - 30.6186i) q^{47} +(-7.50000 - 12.9904i) q^{49} +(34.9297 - 5.46972i) q^{50} +67.8823 q^{53} +(68.0000 - 46.6476i) q^{55} +(14.2829 + 8.24621i) q^{56} +(14.2829 - 8.24621i) q^{59} +(8.00000 - 13.8564i) q^{61} -45.2548 q^{62} +8.00000 q^{64} +(5.04975 - 2.91548i) q^{67} +(11.3137 + 19.5959i) q^{68} +(-3.19901 - 41.1068i) q^{70} -116.619i q^{73} +(28.5657 + 16.4924i) q^{74} +(-12.0000 - 20.7846i) q^{76} +(-48.0833 - 83.2827i) q^{77} +(36.0000 - 62.3538i) q^{79} +(-11.3137 - 16.4924i) q^{80} -81.6333i q^{82} +(21.9203 - 37.9671i) q^{83} +(24.3980 - 51.0366i) q^{85} +(49.9900 - 28.8617i) q^{86} +(-40.3980 - 23.3238i) q^{88} -65.9697i q^{89} +(-24.0416 + 41.6413i) q^{92} +(25.0000 + 43.3013i) q^{94} +(-25.8780 + 54.1325i) q^{95} +(-141.393 - 81.6333i) q^{97} +21.2132 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

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

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
\(5\) −2.15650 + 4.51104i −0.431300 + 0.902209i
\(6\) 0 0
\(7\) 5.04975 + 2.91548i 0.721393 + 0.416497i 0.815265 0.579088i \(-0.196591\pi\)
−0.0938720 + 0.995584i \(0.529924\pi\)
\(8\) 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 \(-0.603114\pi\)
−0.980135 + 0.198332i \(0.936448\pi\)
\(12\) 0 0
\(13\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) −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 \(0.397731\pi\)
\(20\) 9.96986 0.775874i 0.498493 0.0387937i
\(21\) 0 0
\(22\) 20.1990 11.6619i 0.918137 0.530087i
\(23\) −12.0208 20.8207i −0.522644 0.905246i −0.999653 0.0263476i \(-0.991612\pi\)
0.477009 0.878899i \(-0.341721\pi\)
\(24\) 0 0
\(25\) −15.6990 19.4561i −0.627960 0.778245i
\(26\) 0 0
\(27\) 0 0
\(28\) 11.6619i 0.416497i
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 16.0000 + 27.7128i 0.516129 + 0.893962i 0.999825 + 0.0187254i \(0.00596084\pi\)
−0.483696 + 0.875236i \(0.660706\pi\)
\(32\) −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
\(40\) −6.09950 + 12.7592i −0.152488 + 0.318979i
\(41\) −49.9900 + 28.8617i −1.21927 + 0.703945i −0.964761 0.263126i \(-0.915246\pi\)
−0.254507 + 0.967071i \(0.581913\pi\)
\(42\) 0 0
\(43\) −35.3483 20.4083i −0.822053 0.474612i 0.0290711 0.999577i \(-0.490745\pi\)
−0.851124 + 0.524965i \(0.824078\pi\)
\(44\) 32.9848i 0.749656i
\(45\) 0 0
\(46\) 34.0000 0.739130
\(47\) 17.6777 30.6186i 0.376121 0.651460i −0.614373 0.789015i \(-0.710591\pi\)
0.990494 + 0.137555i \(0.0439245\pi\)
\(48\) 0 0
\(49\) −7.50000 12.9904i −0.153061 0.265110i
\(50\) 34.9297 5.46972i 0.698593 0.109394i
\(51\) 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 \(-0.622032\pi\)
0.616133 + 0.787642i \(0.288698\pi\)
\(60\) 0 0
\(61\) 8.00000 13.8564i 0.131148 0.227154i −0.792972 0.609259i \(-0.791467\pi\)
0.924119 + 0.382104i \(0.124801\pi\)
\(62\) −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 \(-0.652811\pi\)
0.537211 + 0.843448i \(0.319478\pi\)
\(68\) 11.3137 + 19.5959i 0.166378 + 0.288175i
\(69\) 0 0
\(70\) −3.19901 41.1068i −0.0457001 0.587240i
\(71\) 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 −0.543032 0.839712i \(-0.682724\pi\)
0.998728 + 0.0504232i \(0.0160570\pi\)
\(80\) −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 −0.703227 0.710965i \(-0.748258\pi\)
0.967327 + 0.253530i \(0.0815917\pi\)
\(84\) 0 0
\(85\) 24.3980 51.0366i 0.287036 0.600431i
\(86\) 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
\(95\) −25.8780 + 54.1325i −0.272400 + 0.569816i
\(96\) 0 0
\(97\) −141.393 81.6333i −1.45766 0.841581i −0.458765 0.888558i \(-0.651708\pi\)
−0.998896 + 0.0469772i \(0.985041\pi\)
\(98\) 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 \(-0.559893\pi\)
−0.944265 + 0.329185i \(0.893226\pi\)
\(102\) 0 0
\(103\) 85.8458 49.5631i 0.833454 0.481195i −0.0215796 0.999767i \(-0.506870\pi\)
0.855034 + 0.518572i \(0.173536\pi\)
\(104\) 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 \(0.380394\pi\)
\(110\) 9.04817 + 116.267i 0.0822561 + 1.05698i
\(111\) 0 0
\(112\) −20.1990 + 11.6619i −0.180348 + 0.104124i
\(113\) 76.3675 + 132.272i 0.675819 + 1.17055i 0.976229 + 0.216742i \(0.0695432\pi\)
−0.300410 + 0.953810i \(0.597123\pi\)
\(114\) 0 0
\(115\) 119.846 9.32664i 1.04214 0.0811012i
\(116\) 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 \(-0.606192\pi\)
0.654548 + 0.756021i \(0.272859\pi\)
\(132\) 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 −0.758040 0.652208i \(-0.773843\pi\)
0.943849 + 0.330378i \(0.107176\pi\)
\(138\) 0 0
\(139\) −22.0000 38.1051i −0.158273 0.274138i 0.775973 0.630766i \(-0.217259\pi\)
−0.934246 + 0.356629i \(0.883926\pi\)
\(140\) 52.6073 + 25.1489i 0.375767 + 0.179635i
\(141\) 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 \(-0.675476\pi\)
0.475844 + 0.879530i \(0.342143\pi\)
\(150\) 0 0
\(151\) −68.0000 + 117.779i −0.450331 + 0.779996i −0.998406 0.0564326i \(-0.982027\pi\)
0.548075 + 0.836429i \(0.315361\pi\)
\(152\) 33.9411 0.223297
\(153\) 0 0
\(154\) 136.000 0.883117
\(155\) −159.518 + 12.4140i −1.02915 + 0.0800902i
\(156\) 0 0
\(157\) −100.995 + 58.3095i −0.643281 + 0.371398i −0.785877 0.618383i \(-0.787788\pi\)
0.142597 + 0.989781i \(0.454455\pi\)
\(158\) 50.9117 + 88.1816i 0.322226 + 0.558112i
\(159\) 0 0
\(160\) 28.1990 2.19450i 0.176244 0.0137156i
\(161\) 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 −0.855185 0.518324i \(-0.826556\pi\)
−0.0212891 0.999773i \(-0.506777\pi\)
\(168\) 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 −0.525432 0.850836i \(-0.676096\pi\)
0.999561 + 0.0296195i \(0.00942955\pi\)
\(174\) 0 0
\(175\) −22.5522 144.019i −0.128870 0.822964i
\(176\) 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
\(185\) 105.215 + 50.2978i 0.568728 + 0.271880i
\(186\) 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 \(-0.0500081\pi\)
0.358344 + 0.933590i \(0.383341\pi\)
\(192\) 0 0
\(193\) −100.995 + 58.3095i −0.523290 + 0.302122i −0.738280 0.674495i \(-0.764362\pi\)
0.214989 + 0.976616i \(0.431028\pi\)
\(194\) 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 \(0.786783\pi\)
\(200\) −44.4035 55.0303i −0.222018 0.275151i
\(201\) 0 0
\(202\) 161.592 93.2952i 0.799961 0.461858i
\(203\) 0 0
\(204\) 0 0
\(205\) −22.3931 287.747i −0.109234 1.40365i
\(206\) 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 0.879893 0.475171i \(-0.157614\pi\)
−0.851457 + 0.524424i \(0.824281\pi\)
\(212\) −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
\(220\) −148.796 71.1318i −0.676346 0.323327i
\(221\) 0 0
\(222\) 0 0
\(223\) −35.3483 20.4083i −0.158512 0.0915172i 0.418646 0.908150i \(-0.362505\pi\)
−0.577158 + 0.816633i \(0.695838\pi\)
\(224\) 32.9848i 0.147254i
\(225\) 0 0
\(226\) −216.000 −0.955752
\(227\) 79.9031 138.396i 0.351996 0.609675i −0.634603 0.772838i \(-0.718836\pi\)
0.986599 + 0.163163i \(0.0521698\pi\)
\(228\) 0 0
\(229\) −41.0000 71.0141i −0.179039 0.310105i 0.762512 0.646974i \(-0.223966\pi\)
−0.941552 + 0.336868i \(0.890632\pi\)
\(230\) −73.3210 + 153.375i −0.318787 + 0.666850i
\(231\) 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 −0.707537 + 0.706676i \(0.750194\pi\)
−0.965768 + 0.259407i \(0.916473\pi\)
\(240\) 0 0
\(241\) −152.000 + 263.272i −0.630705 + 1.09241i 0.356702 + 0.934218i \(0.383901\pi\)
−0.987408 + 0.158196i \(0.949432\pi\)
\(242\) −213.546 −0.882423
\(243\) 0 0
\(244\) −32.0000 −0.131148
\(245\) 74.7739 5.81905i 0.305200 0.0237512i
\(246\) 0 0
\(247\) 0 0
\(248\) 45.2548 + 78.3837i 0.182479 + 0.316063i
\(249\) 0 0
\(250\) −50.6517 + 169.365i −0.202607 + 0.677459i
\(251\) 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 −0.943166 0.332323i \(-0.892168\pi\)
0.183782 0.982967i \(-0.441166\pi\)
\(258\) 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 0.435407 + 0.900234i \(0.356604\pi\)
−0.997329 + 0.0730428i \(0.976729\pi\)
\(264\) 0 0
\(265\) −146.388 + 306.220i −0.552408 + 1.15555i
\(266\) −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
\(275\) 63.7873 + 407.347i 0.231954 + 1.48126i
\(276\) 0 0
\(277\) 383.781 + 221.576i 1.38549 + 0.799914i 0.992803 0.119758i \(-0.0382117\pi\)
0.392688 + 0.919672i \(0.371545\pi\)
\(278\) 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 −0.991267 0.131870i \(-0.957902\pi\)
−0.609836 0.792528i \(-0.708765\pi\)
\(282\) 0 0
\(283\) −277.736 + 160.351i −0.981401 + 0.566612i −0.902693 0.430286i \(-0.858413\pi\)
−0.0787079 + 0.996898i \(0.525079\pi\)
\(284\) 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 0.784498 0.620131i \(-0.212921\pi\)
−0.929298 + 0.369330i \(0.879587\pi\)
\(294\) 0 0
\(295\) 6.39802 + 82.2135i 0.0216882 + 0.278690i
\(296\) 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
\(310\) 97.5921 204.146i 0.314813 0.658537i
\(311\) −85.6971 + 49.4773i −0.275554 + 0.159091i −0.631409 0.775450i \(-0.717523\pi\)
0.355855 + 0.934541i \(0.384190\pi\)
\(312\) 0 0
\(313\) 161.592 + 93.2952i 0.516269 + 0.298068i 0.735407 0.677626i \(-0.236991\pi\)
−0.219138 + 0.975694i \(0.570325\pi\)
\(314\) 164.924i 0.525236i
\(315\) 0 0
\(316\) −144.000 −0.455696
\(317\) 260.215 450.706i 0.820868 1.42179i −0.0841679 0.996452i \(-0.526823\pi\)
0.905036 0.425334i \(-0.139843\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −17.2520 + 36.0883i −0.0539125 + 0.112776i
\(321\) 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 −0.997770 0.0667389i \(-0.978741\pi\)
0.556683 + 0.830725i \(0.312074\pi\)
\(332\) −87.6812 −0.264100
\(333\) 0 0
\(334\) 414.000 1.23952
\(335\) 2.26204 + 29.0669i 0.00675236 + 0.0867668i
\(336\) 0 0
\(337\) 282.786 163.267i 0.839128 0.484471i −0.0178397 0.999841i \(-0.505679\pi\)
0.856968 + 0.515370i \(0.172346\pi\)
\(338\) −119.501 206.982i −0.353553 0.612372i
\(339\) 0 0
\(340\) −112.796 + 8.77801i −0.331753 + 0.0258177i
\(341\) 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 −0.996711 0.0810402i \(-0.974176\pi\)
0.428173 0.903697i \(-0.359158\pi\)
\(348\) 0 0
\(349\) −127.000 + 219.970i −0.363897 + 0.630288i −0.988598 0.150576i \(-0.951887\pi\)
0.624702 + 0.780864i \(0.285221\pi\)
\(350\) 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 −0.999916 0.0129248i \(-0.995886\pi\)
0.511151 + 0.859491i \(0.329219\pi\)
\(354\) 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
\(365\) 526.073 + 251.489i 1.44130 + 0.689011i
\(366\) 0 0
\(367\) −358.532 206.999i −0.976928 0.564029i −0.0755864 0.997139i \(-0.524083\pi\)
−0.901341 + 0.433110i \(0.857416\pi\)
\(368\) 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 \(-0.346767\pi\)
0.999110 + 0.0421901i \(0.0134335\pi\)
\(374\) −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 \(0.772178\pi\)
\(380\) 119.638 9.31049i 0.314838 0.0245013i
\(381\) 0 0
\(382\) −363.582 + 209.914i −0.951786 + 0.549514i
\(383\) 96.8736 + 167.790i 0.252934 + 0.438094i 0.964332 0.264695i \(-0.0852712\pi\)
−0.711398 + 0.702789i \(0.751938\pi\)
\(384\) 0 0
\(385\) 479.383 37.3065i 1.24515 0.0969001i
\(386\) 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 \(-0.167341\pi\)
−0.00211824 + 0.999998i \(0.500674\pi\)
\(390\) 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
\(400\) 98.7960 15.4707i 0.246990 0.0386768i
\(401\) −57.1314 + 32.9848i −0.142472 + 0.0822565i −0.569542 0.821962i \(-0.692879\pi\)
0.427069 + 0.904219i \(0.359546\pi\)
\(402\) 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 −0.930542 0.366184i \(-0.880664\pi\)
0.148146 0.988965i \(-0.452669\pi\)
\(410\) 368.251 + 176.042i 0.898174 + 0.429372i
\(411\) 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 \(-0.424794\pi\)
0.959004 + 0.283394i \(0.0914605\pi\)
\(420\) 0 0
\(421\) 328.000 568.113i 0.779097 1.34944i −0.153365 0.988170i \(-0.549011\pi\)
0.932463 0.361267i \(-0.117656\pi\)
\(422\) −16.9706 −0.0402146
\(423\) 0 0
\(424\) 192.000 0.452830
\(425\) 177.614 + 220.121i 0.417915 + 0.517932i
\(426\) 0 0
\(427\) 80.7960 46.6476i 0.189218 0.109245i
\(428\) 55.1543 + 95.5301i 0.128865 + 0.223201i
\(429\) 0 0
\(430\) 22.3931 + 287.747i 0.0520769 + 0.669180i
\(431\) 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 −0.999958 0.00918170i \(-0.997077\pi\)
0.507931 + 0.861398i \(0.330411\pi\)
\(440\) 192.333 131.939i 0.437121 0.299862i
\(441\) 0 0
\(442\) 0 0
\(443\) −61.5183 + 106.553i −0.138867 + 0.240526i −0.927068 0.374893i \(-0.877680\pi\)
0.788201 + 0.615418i \(0.211013\pi\)
\(444\) 0 0
\(445\) 297.592 + 142.264i 0.668746 + 0.319694i
\(446\) 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 \(-0.503824\pi\)
−0.871970 + 0.489560i \(0.837157\pi\)
\(458\) 115.966 0.253200
\(459\) 0 0
\(460\) −136.000 198.252i −0.295652 0.430983i
\(461\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 0 0
\(463\) −530.224 + 306.125i −1.14519 + 0.661177i −0.947711 0.319130i \(-0.896609\pi\)
−0.197481 + 0.980307i \(0.563276\pi\)
\(464\) 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
\(470\) −249.246 + 19.3968i −0.530311 + 0.0412699i
\(471\) 0 0
\(472\) 40.3980 23.3238i 0.0855890 0.0494148i
\(473\) 336.583 + 582.979i 0.711592 + 1.23251i
\(474\) 0 0
\(475\) −188.388 233.474i −0.396607 0.491523i
\(476\) 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 \(-0.134300\pi\)
0.101508 + 0.994835i \(0.467633\pi\)
\(480\) 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
\(490\) −45.7463 + 95.6937i −0.0933598 + 0.195293i
\(491\) 299.940 173.170i 0.610876 0.352689i −0.162432 0.986720i \(-0.551934\pi\)
0.773308 + 0.634030i \(0.218601\pi\)
\(492\) 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 0.980268 + 0.197671i \(0.0633379\pi\)
−0.318946 + 0.947773i \(0.603329\pi\)
\(500\) −171.612 181.794i −0.343225 0.363589i
\(501\) 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 \(-0.539550\pi\)
0.797384 + 0.603472i \(0.206216\pi\)
\(510\) 0 0
\(511\) 340.000 588.897i 0.665362 1.15244i
\(512\) 22.6274 0.0441942
\(513\) 0 0
\(514\) 552.000 1.07393
\(515\) 38.4547 + 494.137i 0.0746693 + 0.959489i
\(516\) 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
\(535\) 118.940 248.804i 0.222318 0.465053i
\(536\) 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
\(545\) −172.520 + 360.883i −0.316551 + 0.662171i
\(546\) 0 0
\(547\) 247.438 + 142.858i 0.452354 + 0.261167i 0.708824 0.705385i \(-0.249226\pi\)
−0.256470 + 0.966552i \(0.582559\pi\)
\(548\) −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
\(560\) −9.04817 116.267i −0.0161574 0.207621i
\(561\) 0 0
\(562\) 636.269 367.350i 1.13215 0.653648i
\(563\) 406.586 + 704.228i 0.722178 + 1.25085i 0.960125 + 0.279571i \(0.0901923\pi\)
−0.237947 + 0.971278i \(0.576474\pi\)
\(564\) 0 0
\(565\) −761.373 + 59.2516i −1.34756 + 0.104870i
\(566\) 453.542i 0.801310i
\(567\) 0 0
\(568\) 0 0
\(569\) −392.779 226.771i −0.690296 0.398543i 0.113427 0.993546i \(-0.463817\pi\)
−0.803723 + 0.595004i \(0.797151\pi\)
\(570\) 0 0
\(571\) −110.000 190.526i −0.192644 0.333670i 0.753481 0.657469i \(-0.228373\pi\)
−0.946126 + 0.323799i \(0.895040\pi\)
\(572\) 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 −0.888559 0.458762i \(-0.848293\pi\)
0.841579 + 0.540134i \(0.181626\pi\)
\(588\) 0 0
\(589\) 192.000 + 332.554i 0.325976 + 0.564607i
\(590\) −105.215 50.2978i −0.178330 0.0852505i
\(591\) 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 \(-0.692989\pi\)
0.426758 + 0.904366i \(0.359656\pi\)
\(600\) 0 0
\(601\) 440.000 762.102i 0.732113 1.26806i −0.223865 0.974620i \(-0.571868\pi\)
0.955978 0.293437i \(-0.0947991\pi\)
\(602\) 336.583 0.559108
\(603\) 0 0
\(604\) 272.000 0.450331
\(605\) −752.724 + 58.5785i −1.24417 + 0.0968239i
\(606\) 0 0
\(607\) 368.632 212.830i 0.607301 0.350626i −0.164607 0.986359i \(-0.552636\pi\)
0.771909 + 0.635734i \(0.219302\pi\)
\(608\) −33.9411 58.7878i −0.0558242 0.0966904i
\(609\) 0 0
\(610\) −112.796 + 8.77801i −0.184912 + 0.0143902i
\(611\) 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 0.908220 0.418494i \(-0.137442\pi\)
−0.816536 + 0.577294i \(0.804109\pi\)
\(618\) 0 0
\(619\) −26.0000 + 45.0333i −0.0420032 + 0.0727517i −0.886263 0.463183i \(-0.846707\pi\)
0.844259 + 0.535935i \(0.180041\pi\)
\(620\) 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
\(625\) −132.082 + 610.884i −0.211331 + 0.977414i
\(626\) −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
\(635\) 184.126 + 88.0212i 0.289962 + 0.138616i
\(636\) 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 \(-0.102817\pi\)
0.199246 + 0.979949i \(0.436151\pi\)
\(642\) 0 0
\(643\) 318.134 183.675i 0.494766 0.285653i −0.231784 0.972767i \(-0.574456\pi\)
0.726549 + 0.687114i \(0.241123\pi\)
\(644\) −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 0.699938 0.714203i \(-0.253211\pi\)
−0.968487 + 0.249063i \(0.919877\pi\)
\(654\) 0 0
\(655\) 19.1941 + 246.641i 0.0293039 + 0.376551i
\(656\) 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 \(-0.189034\pi\)
−0.0702098 + 0.997532i \(0.522367\pi\)
\(660\) 0 0
\(661\) −40.0000 69.2820i −0.0605144 0.104814i 0.834181 0.551491i \(-0.185941\pi\)
−0.894695 + 0.446677i \(0.852607\pi\)
\(662\) −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
\(670\) −37.1990 17.7830i −0.0555209 0.0265417i
\(671\) −228.526 + 131.939i −0.340575 + 0.196631i
\(672\) 0 0
\(673\) 424.179 + 244.900i 0.630281 + 0.363893i 0.780861 0.624705i \(-0.214781\pi\)
−0.150580 + 0.988598i \(0.548114\pi\)
\(674\) 461.788i 0.685145i
\(675\) 0 0
\(676\) 338.000 0.500000
\(677\) −96.1665 + 166.565i −0.142048 + 0.246034i −0.928268 0.371913i \(-0.878702\pi\)
0.786220 + 0.617947i \(0.212035\pi\)
\(678\) 0 0
\(679\) −476.000 824.456i −0.701031 1.21422i
\(680\) 69.0080 144.353i 0.101482 0.212284i
\(681\) 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 −0.596768 0.802414i \(-0.703549\pi\)
0.993295 + 0.115609i \(0.0368821\pi\)
\(692\) −328.098 −0.474129
\(693\) 0 0
\(694\) 558.000 0.804035
\(695\) 219.337 17.0692i 0.315593 0.0245600i
\(696\) 0 0
\(697\) 565.572 326.533i 0.811438 0.468484i
\(698\) −179.605 311.085i −0.257314 0.445681i
\(699\) 0 0
\(700\) −226.896 + 183.080i −0.324136 + 0.261543i
\(701\) 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 −0.00279375 + 0.999996i \(0.500889\pi\)
−0.864625 + 0.502418i \(0.832444\pi\)
\(710\) 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 \(-0.252032\pi\)
−0.264980 + 0.964254i \(0.585365\pi\)
\(728\) 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 \(-0.906481\pi\)
−0.227784 + 0.973712i \(0.573148\pi\)
\(734\) 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 \(0.573886\pi\)
\(740\) −18.0963 232.535i −0.0244545 0.314236i
\(741\) 0 0
\(742\) −484.776 + 279.886i −0.653337 + 0.377204i
\(743\) −621.547 1076.55i −0.836537 1.44892i −0.892773 0.450507i \(-0.851243\pi\)
0.0562362 0.998417i \(-0.482090\pi\)
\(744\) 0 0
\(745\) −3.19901 41.1068i −0.00429397 0.0551769i
\(746\) 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 0.985572 0.169257i \(-0.0541368\pi\)
−0.639367 + 0.768902i \(0.720803\pi\)
\(752\) 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
\(760\) −73.1941 + 153.110i −0.0963080 + 0.201460i
\(761\) 342.789 197.909i 0.450445 0.260064i −0.257573 0.966259i \(-0.582923\pi\)
0.708018 + 0.706194i \(0.249590\pi\)
\(762\) 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 0.948191 0.317700i \(-0.102910\pi\)
−0.749232 + 0.662308i \(0.769577\pi\)
\(770\) −293.284 + 613.502i −0.380888 + 0.796756i
\(771\) 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
\(785\) −45.2408 581.337i −0.0576316 0.740557i
\(786\) 0 0
\(787\) −489.826 + 282.801i −0.622396 + 0.359341i −0.777801 0.628510i \(-0.783665\pi\)
0.155405 + 0.987851i \(0.450332\pi\)
\(788\) 192.333 + 333.131i 0.244077 + 0.422755i
\(789\) 0 0