Properties

Label 1078.2.c.b.1077.10
Level $1078$
Weight $2$
Character 1078.1077
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1077.10
Root \(2.24352 + 0.601150i\) of defining polynomial
Character \(\chi\) \(=\) 1078.1077
Dual form 1078.2.c.b.1077.7

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -2.59518i q^{3} -1.00000 q^{4} -3.53900i q^{5} +2.59518 q^{6} -1.00000i q^{8} -3.73495 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -2.59518i q^{3} -1.00000 q^{4} -3.53900i q^{5} +2.59518 q^{6} -1.00000i q^{8} -3.73495 q^{9} +3.53900 q^{10} +(-2.29457 - 2.39477i) q^{11} +2.59518i q^{12} -5.01680 q^{13} -9.18432 q^{15} +1.00000 q^{16} +3.89362 q^{17} -3.73495i q^{18} +4.65637 q^{19} +3.53900i q^{20} +(2.39477 - 2.29457i) q^{22} -1.55962 q^{23} -2.59518 q^{24} -7.52450 q^{25} -5.01680i q^{26} +1.90732i q^{27} +0.100205i q^{29} -9.18432i q^{30} +0.279729i q^{31} +1.00000i q^{32} +(-6.21487 + 5.95482i) q^{33} +3.89362i q^{34} +3.73495 q^{36} +0.705430 q^{37} +4.65637i q^{38} +13.0195i q^{39} -3.53900 q^{40} +2.94809 q^{41} +9.03556i q^{43} +(2.29457 + 2.39477i) q^{44} +13.2180i q^{45} -1.55962i q^{46} +6.56949i q^{47} -2.59518i q^{48} -7.52450i q^{50} -10.1046i q^{51} +5.01680 q^{52} +5.54058 q^{53} -1.90732 q^{54} +(-8.47510 + 8.12048i) q^{55} -12.0841i q^{57} -0.100205 q^{58} -14.5344i q^{59} +9.18432 q^{60} -11.1272 q^{61} -0.279729 q^{62} -1.00000 q^{64} +17.7544i q^{65} +(-5.95482 - 6.21487i) q^{66} +3.98392 q^{67} -3.89362 q^{68} +4.04750i q^{69} -8.45381 q^{71} +3.73495i q^{72} -3.89771 q^{73} +0.705430i q^{74} +19.5274i q^{75} -4.65637 q^{76} -13.0195 q^{78} +7.69982i q^{79} -3.53900i q^{80} -6.25501 q^{81} +2.94809i q^{82} +2.87320 q^{83} -13.7795i q^{85} -9.03556 q^{86} +0.260049 q^{87} +(-2.39477 + 2.29457i) q^{88} -5.94902i q^{89} -13.2180 q^{90} +1.55962 q^{92} +0.725946 q^{93} -6.56949 q^{94} -16.4789i q^{95} +2.59518 q^{96} -16.7587i q^{97} +(8.57010 + 8.94436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 2.59518i 1.49833i −0.662385 0.749163i \(-0.730456\pi\)
0.662385 0.749163i \(-0.269544\pi\)
\(4\) −1.00000 −0.500000
\(5\) 3.53900i 1.58269i −0.611372 0.791344i \(-0.709382\pi\)
0.611372 0.791344i \(-0.290618\pi\)
\(6\) 2.59518 1.05948
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −3.73495 −1.24498
\(10\) 3.53900 1.11913
\(11\) −2.29457 2.39477i −0.691839 0.722052i
\(12\) 2.59518i 0.749163i
\(13\) −5.01680 −1.39141 −0.695704 0.718328i \(-0.744908\pi\)
−0.695704 + 0.718328i \(0.744908\pi\)
\(14\) 0 0
\(15\) −9.18432 −2.37138
\(16\) 1.00000 0.250000
\(17\) 3.89362 0.944342 0.472171 0.881507i \(-0.343471\pi\)
0.472171 + 0.881507i \(0.343471\pi\)
\(18\) 3.73495i 0.880335i
\(19\) 4.65637 1.06825 0.534123 0.845407i \(-0.320642\pi\)
0.534123 + 0.845407i \(0.320642\pi\)
\(20\) 3.53900i 0.791344i
\(21\) 0 0
\(22\) 2.39477 2.29457i 0.510568 0.489204i
\(23\) −1.55962 −0.325204 −0.162602 0.986692i \(-0.551989\pi\)
−0.162602 + 0.986692i \(0.551989\pi\)
\(24\) −2.59518 −0.529738
\(25\) −7.52450 −1.50490
\(26\) 5.01680i 0.983875i
\(27\) 1.90732i 0.367064i
\(28\) 0 0
\(29\) 0.100205i 0.0186075i 0.999957 + 0.00930376i \(0.00296152\pi\)
−0.999957 + 0.00930376i \(0.997038\pi\)
\(30\) 9.18432i 1.67682i
\(31\) 0.279729i 0.0502408i 0.999684 + 0.0251204i \(0.00799691\pi\)
−0.999684 + 0.0251204i \(0.992003\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −6.21487 + 5.95482i −1.08187 + 1.03660i
\(34\) 3.89362i 0.667750i
\(35\) 0 0
\(36\) 3.73495 0.622491
\(37\) 0.705430 0.115972 0.0579860 0.998317i \(-0.481532\pi\)
0.0579860 + 0.998317i \(0.481532\pi\)
\(38\) 4.65637i 0.755364i
\(39\) 13.0195i 2.08478i
\(40\) −3.53900 −0.559564
\(41\) 2.94809 0.460415 0.230207 0.973142i \(-0.426060\pi\)
0.230207 + 0.973142i \(0.426060\pi\)
\(42\) 0 0
\(43\) 9.03556i 1.37791i 0.724804 + 0.688955i \(0.241930\pi\)
−0.724804 + 0.688955i \(0.758070\pi\)
\(44\) 2.29457 + 2.39477i 0.345919 + 0.361026i
\(45\) 13.2180i 1.97042i
\(46\) 1.55962i 0.229954i
\(47\) 6.56949i 0.958259i 0.877744 + 0.479129i \(0.159048\pi\)
−0.877744 + 0.479129i \(0.840952\pi\)
\(48\) 2.59518i 0.374582i
\(49\) 0 0
\(50\) 7.52450i 1.06412i
\(51\) 10.1046i 1.41493i
\(52\) 5.01680 0.695704
\(53\) 5.54058 0.761057 0.380529 0.924769i \(-0.375742\pi\)
0.380529 + 0.924769i \(0.375742\pi\)
\(54\) −1.90732 −0.259553
\(55\) −8.47510 + 8.12048i −1.14278 + 1.09496i
\(56\) 0 0
\(57\) 12.0841i 1.60058i
\(58\) −0.100205 −0.0131575
\(59\) 14.5344i 1.89222i −0.323853 0.946108i \(-0.604978\pi\)
0.323853 0.946108i \(-0.395022\pi\)
\(60\) 9.18432 1.18569
\(61\) −11.1272 −1.42469 −0.712346 0.701828i \(-0.752367\pi\)
−0.712346 + 0.701828i \(0.752367\pi\)
\(62\) −0.279729 −0.0355256
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 17.7544i 2.20217i
\(66\) −5.95482 6.21487i −0.732987 0.764997i
\(67\) 3.98392 0.486713 0.243356 0.969937i \(-0.421752\pi\)
0.243356 + 0.969937i \(0.421752\pi\)
\(68\) −3.89362 −0.472171
\(69\) 4.04750i 0.487262i
\(70\) 0 0
\(71\) −8.45381 −1.00328 −0.501641 0.865076i \(-0.667270\pi\)
−0.501641 + 0.865076i \(0.667270\pi\)
\(72\) 3.73495i 0.440168i
\(73\) −3.89771 −0.456192 −0.228096 0.973639i \(-0.573250\pi\)
−0.228096 + 0.973639i \(0.573250\pi\)
\(74\) 0.705430i 0.0820045i
\(75\) 19.5274i 2.25483i
\(76\) −4.65637 −0.534123
\(77\) 0 0
\(78\) −13.0195 −1.47417
\(79\) 7.69982i 0.866297i 0.901322 + 0.433149i \(0.142598\pi\)
−0.901322 + 0.433149i \(0.857402\pi\)
\(80\) 3.53900i 0.395672i
\(81\) −6.25501 −0.695001
\(82\) 2.94809i 0.325562i
\(83\) 2.87320 0.315375 0.157687 0.987489i \(-0.449596\pi\)
0.157687 + 0.987489i \(0.449596\pi\)
\(84\) 0 0
\(85\) 13.7795i 1.49460i
\(86\) −9.03556 −0.974330
\(87\) 0.260049 0.0278801
\(88\) −2.39477 + 2.29457i −0.255284 + 0.244602i
\(89\) 5.94902i 0.630595i −0.948993 0.315297i \(-0.897896\pi\)
0.948993 0.315297i \(-0.102104\pi\)
\(90\) −13.2180 −1.39330
\(91\) 0 0
\(92\) 1.55962 0.162602
\(93\) 0.725946 0.0752771
\(94\) −6.56949 −0.677591
\(95\) 16.4789i 1.69070i
\(96\) 2.59518 0.264869
\(97\) 16.7587i 1.70159i −0.525502 0.850793i \(-0.676122\pi\)
0.525502 0.850793i \(-0.323878\pi\)
\(98\) 0 0
\(99\) 8.57010 + 8.94436i 0.861327 + 0.898942i
\(100\) 7.52450 0.752450
\(101\) −1.40290 −0.139594 −0.0697971 0.997561i \(-0.522235\pi\)
−0.0697971 + 0.997561i \(0.522235\pi\)
\(102\) 10.1046 1.00051
\(103\) 2.06291i 0.203264i 0.994822 + 0.101632i \(0.0324064\pi\)
−0.994822 + 0.101632i \(0.967594\pi\)
\(104\) 5.01680i 0.491937i
\(105\) 0 0
\(106\) 5.54058i 0.538149i
\(107\) 12.2655i 1.18575i −0.805295 0.592875i \(-0.797993\pi\)
0.805295 0.592875i \(-0.202007\pi\)
\(108\) 1.90732i 0.183532i
\(109\) 6.72491i 0.644129i −0.946718 0.322065i \(-0.895623\pi\)
0.946718 0.322065i \(-0.104377\pi\)
\(110\) −8.12048 8.47510i −0.774257 0.808069i
\(111\) 1.83072i 0.173764i
\(112\) 0 0
\(113\) −11.9900 −1.12792 −0.563960 0.825802i \(-0.690723\pi\)
−0.563960 + 0.825802i \(0.690723\pi\)
\(114\) 12.0841 1.13178
\(115\) 5.51950i 0.514696i
\(116\) 0.100205i 0.00930376i
\(117\) 18.7375 1.73228
\(118\) 14.5344 1.33800
\(119\) 0 0
\(120\) 9.18432i 0.838410i
\(121\) −0.469894 + 10.9900i −0.0427176 + 0.999087i
\(122\) 11.1272i 1.00741i
\(123\) 7.65083i 0.689852i
\(124\) 0.279729i 0.0251204i
\(125\) 8.93419i 0.799098i
\(126\) 0 0
\(127\) 13.2199i 1.17308i −0.809922 0.586538i \(-0.800491\pi\)
0.809922 0.586538i \(-0.199509\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 23.4489 2.06456
\(130\) −17.7544 −1.55717
\(131\) 16.4986 1.44149 0.720746 0.693200i \(-0.243800\pi\)
0.720746 + 0.693200i \(0.243800\pi\)
\(132\) 6.21487 5.95482i 0.540935 0.518300i
\(133\) 0 0
\(134\) 3.98392i 0.344158i
\(135\) 6.74999 0.580947
\(136\) 3.89362i 0.333875i
\(137\) 6.64374 0.567613 0.283807 0.958882i \(-0.408403\pi\)
0.283807 + 0.958882i \(0.408403\pi\)
\(138\) −4.04750 −0.344546
\(139\) −14.3533 −1.21743 −0.608716 0.793388i \(-0.708315\pi\)
−0.608716 + 0.793388i \(0.708315\pi\)
\(140\) 0 0
\(141\) 17.0490 1.43578
\(142\) 8.45381i 0.709428i
\(143\) 11.5114 + 12.0141i 0.962631 + 1.00467i
\(144\) −3.73495 −0.311246
\(145\) 0.354624 0.0294499
\(146\) 3.89771i 0.322577i
\(147\) 0 0
\(148\) −0.705430 −0.0579860
\(149\) 2.66587i 0.218397i −0.994020 0.109198i \(-0.965172\pi\)
0.994020 0.109198i \(-0.0348284\pi\)
\(150\) −19.5274 −1.59441
\(151\) 10.3903i 0.845554i 0.906234 + 0.422777i \(0.138945\pi\)
−0.906234 + 0.422777i \(0.861055\pi\)
\(152\) 4.65637i 0.377682i
\(153\) −14.5425 −1.17569
\(154\) 0 0
\(155\) 0.989959 0.0795154
\(156\) 13.0195i 1.04239i
\(157\) 8.37473i 0.668376i −0.942506 0.334188i \(-0.891538\pi\)
0.942506 0.334188i \(-0.108462\pi\)
\(158\) −7.69982 −0.612565
\(159\) 14.3788i 1.14031i
\(160\) 3.53900 0.279782
\(161\) 0 0
\(162\) 6.25501i 0.491440i
\(163\) 3.06508 0.240075 0.120038 0.992769i \(-0.461698\pi\)
0.120038 + 0.992769i \(0.461698\pi\)
\(164\) −2.94809 −0.230207
\(165\) 21.0741 + 21.9944i 1.64061 + 1.71226i
\(166\) 2.87320i 0.223003i
\(167\) 10.0731 0.779482 0.389741 0.920925i \(-0.372565\pi\)
0.389741 + 0.920925i \(0.372565\pi\)
\(168\) 0 0
\(169\) 12.1682 0.936018
\(170\) 13.7795 1.05684
\(171\) −17.3913 −1.32995
\(172\) 9.03556i 0.688955i
\(173\) 0.0766026 0.00582399 0.00291200 0.999996i \(-0.499073\pi\)
0.00291200 + 0.999996i \(0.499073\pi\)
\(174\) 0.260049i 0.0197142i
\(175\) 0 0
\(176\) −2.29457 2.39477i −0.172960 0.180513i
\(177\) −37.7193 −2.83516
\(178\) 5.94902 0.445898
\(179\) −8.97491 −0.670817 −0.335408 0.942073i \(-0.608874\pi\)
−0.335408 + 0.942073i \(0.608874\pi\)
\(180\) 13.2180i 0.985209i
\(181\) 15.1450i 1.12572i −0.826554 0.562858i \(-0.809702\pi\)
0.826554 0.562858i \(-0.190298\pi\)
\(182\) 0 0
\(183\) 28.8771i 2.13465i
\(184\) 1.55962i 0.114977i
\(185\) 2.49651i 0.183547i
\(186\) 0.725946i 0.0532289i
\(187\) −8.93419 9.32434i −0.653332 0.681864i
\(188\) 6.56949i 0.479129i
\(189\) 0 0
\(190\) 16.4789 1.19550
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 2.59518i 0.187291i
\(193\) 14.8281i 1.06735i −0.845690 0.533674i \(-0.820811\pi\)
0.845690 0.533674i \(-0.179189\pi\)
\(194\) 16.7587 1.20320
\(195\) 46.0759 3.29956
\(196\) 0 0
\(197\) 14.4745i 1.03126i 0.856811 + 0.515631i \(0.172443\pi\)
−0.856811 + 0.515631i \(0.827557\pi\)
\(198\) −8.94436 + 8.57010i −0.635648 + 0.609050i
\(199\) 11.2259i 0.795780i 0.917433 + 0.397890i \(0.130258\pi\)
−0.917433 + 0.397890i \(0.869742\pi\)
\(200\) 7.52450i 0.532062i
\(201\) 10.3390i 0.729255i
\(202\) 1.40290i 0.0987080i
\(203\) 0 0
\(204\) 10.1046i 0.707466i
\(205\) 10.4333i 0.728693i
\(206\) −2.06291 −0.143729
\(207\) 5.82511 0.404873
\(208\) −5.01680 −0.347852
\(209\) −10.6844 11.1510i −0.739054 0.771329i
\(210\) 0 0
\(211\) 6.44038i 0.443374i −0.975118 0.221687i \(-0.928844\pi\)
0.975118 0.221687i \(-0.0711563\pi\)
\(212\) −5.54058 −0.380529
\(213\) 21.9391i 1.50324i
\(214\) 12.2655 0.838451
\(215\) 31.9768 2.18080
\(216\) 1.90732 0.129777
\(217\) 0 0
\(218\) 6.72491 0.455468
\(219\) 10.1152i 0.683525i
\(220\) 8.47510 8.12048i 0.571391 0.547482i
\(221\) −19.5335 −1.31397
\(222\) 1.83072 0.122870
\(223\) 4.01793i 0.269061i −0.990909 0.134530i \(-0.957047\pi\)
0.990909 0.134530i \(-0.0429526\pi\)
\(224\) 0 0
\(225\) 28.1036 1.87357
\(226\) 11.9900i 0.797560i
\(227\) 12.7293 0.844874 0.422437 0.906392i \(-0.361175\pi\)
0.422437 + 0.906392i \(0.361175\pi\)
\(228\) 12.0841i 0.800290i
\(229\) 6.01345i 0.397380i −0.980062 0.198690i \(-0.936331\pi\)
0.980062 0.198690i \(-0.0636687\pi\)
\(230\) −5.51950 −0.363945
\(231\) 0 0
\(232\) 0.100205 0.00657875
\(233\) 6.46694i 0.423663i −0.977306 0.211832i \(-0.932057\pi\)
0.977306 0.211832i \(-0.0679428\pi\)
\(234\) 18.7375i 1.22491i
\(235\) 23.2494 1.51662
\(236\) 14.5344i 0.946108i
\(237\) 19.9824 1.29800
\(238\) 0 0
\(239\) 15.5775i 1.00762i 0.863813 + 0.503812i \(0.168070\pi\)
−0.863813 + 0.503812i \(0.831930\pi\)
\(240\) −9.18432 −0.592846
\(241\) −23.4762 −1.51224 −0.756119 0.654434i \(-0.772907\pi\)
−0.756119 + 0.654434i \(0.772907\pi\)
\(242\) −10.9900 0.469894i −0.706461 0.0302059i
\(243\) 21.9548i 1.40840i
\(244\) 11.1272 0.712346
\(245\) 0 0
\(246\) 7.65083 0.487799
\(247\) −23.3601 −1.48637
\(248\) 0.279729 0.0177628
\(249\) 7.45646i 0.472534i
\(250\) −8.93419 −0.565048
\(251\) 18.2818i 1.15394i 0.816766 + 0.576968i \(0.195764\pi\)
−0.816766 + 0.576968i \(0.804236\pi\)
\(252\) 0 0
\(253\) 3.57867 + 3.73495i 0.224989 + 0.234814i
\(254\) 13.2199 0.829489
\(255\) −35.7603 −2.23940
\(256\) 1.00000 0.0625000
\(257\) 9.61966i 0.600058i −0.953930 0.300029i \(-0.903004\pi\)
0.953930 0.300029i \(-0.0969964\pi\)
\(258\) 23.4489i 1.45986i
\(259\) 0 0
\(260\) 17.7544i 1.10108i
\(261\) 0.374259i 0.0231660i
\(262\) 16.4986i 1.01929i
\(263\) 0.578666i 0.0356820i 0.999841 + 0.0178410i \(0.00567928\pi\)
−0.999841 + 0.0178410i \(0.994321\pi\)
\(264\) 5.95482 + 6.21487i 0.366494 + 0.382499i
\(265\) 19.6081i 1.20452i
\(266\) 0 0
\(267\) −15.4388 −0.944837
\(268\) −3.98392 −0.243356
\(269\) 22.0896i 1.34683i −0.739266 0.673413i \(-0.764827\pi\)
0.739266 0.673413i \(-0.235173\pi\)
\(270\) 6.74999i 0.410791i
\(271\) 4.26222 0.258911 0.129456 0.991585i \(-0.458677\pi\)
0.129456 + 0.991585i \(0.458677\pi\)
\(272\) 3.89362 0.236085
\(273\) 0 0
\(274\) 6.64374i 0.401363i
\(275\) 17.2655 + 18.0195i 1.04115 + 1.08662i
\(276\) 4.04750i 0.243631i
\(277\) 18.3653i 1.10346i −0.834022 0.551731i \(-0.813968\pi\)
0.834022 0.551731i \(-0.186032\pi\)
\(278\) 14.3533i 0.860855i
\(279\) 1.04477i 0.0625489i
\(280\) 0 0
\(281\) 3.72890i 0.222448i 0.993795 + 0.111224i \(0.0354771\pi\)
−0.993795 + 0.111224i \(0.964523\pi\)
\(282\) 17.0490i 1.01525i
\(283\) 12.7315 0.756811 0.378405 0.925640i \(-0.376473\pi\)
0.378405 + 0.925640i \(0.376473\pi\)
\(284\) 8.45381 0.501641
\(285\) −42.7657 −2.53322
\(286\) −12.0141 + 11.5114i −0.710408 + 0.680683i
\(287\) 0 0
\(288\) 3.73495i 0.220084i
\(289\) −1.83972 −0.108219
\(290\) 0.354624i 0.0208242i
\(291\) −43.4917 −2.54953
\(292\) 3.89771 0.228096
\(293\) −26.2251 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(294\) 0 0
\(295\) −51.4371 −2.99478
\(296\) 0.705430i 0.0410023i
\(297\) 4.56760 4.37648i 0.265039 0.253949i
\(298\) 2.66587 0.154430
\(299\) 7.82431 0.452492
\(300\) 19.5274i 1.12742i
\(301\) 0 0
\(302\) −10.3903 −0.597897
\(303\) 3.64079i 0.209158i
\(304\) 4.65637 0.267061
\(305\) 39.3791i 2.25484i
\(306\) 14.5425i 0.831337i
\(307\) 25.5942 1.46074 0.730369 0.683053i \(-0.239348\pi\)
0.730369 + 0.683053i \(0.239348\pi\)
\(308\) 0 0
\(309\) 5.35360 0.304556
\(310\) 0.989959i 0.0562259i
\(311\) 1.90970i 0.108289i 0.998533 + 0.0541446i \(0.0172432\pi\)
−0.998533 + 0.0541446i \(0.982757\pi\)
\(312\) 13.0195 0.737083
\(313\) 30.4503i 1.72115i −0.509323 0.860576i \(-0.670104\pi\)
0.509323 0.860576i \(-0.329896\pi\)
\(314\) 8.37473 0.472613
\(315\) 0 0
\(316\) 7.69982i 0.433149i
\(317\) 34.3942 1.93177 0.965885 0.258973i \(-0.0833841\pi\)
0.965885 + 0.258973i \(0.0833841\pi\)
\(318\) 14.3788 0.806323
\(319\) 0.239967 0.229926i 0.0134356 0.0128734i
\(320\) 3.53900i 0.197836i
\(321\) −31.8311 −1.77664
\(322\) 0 0
\(323\) 18.1302 1.00879
\(324\) 6.25501 0.347501
\(325\) 37.7489 2.09393
\(326\) 3.06508i 0.169759i
\(327\) −17.4523 −0.965116
\(328\) 2.94809i 0.162781i
\(329\) 0 0
\(330\) −21.9944 + 21.0741i −1.21075 + 1.16009i
\(331\) 15.5128 0.852663 0.426332 0.904567i \(-0.359806\pi\)
0.426332 + 0.904567i \(0.359806\pi\)
\(332\) −2.87320 −0.157687
\(333\) −2.63474 −0.144383
\(334\) 10.0731i 0.551177i
\(335\) 14.0991i 0.770314i
\(336\) 0 0
\(337\) 7.70882i 0.419926i −0.977709 0.209963i \(-0.932666\pi\)
0.977709 0.209963i \(-0.0673344\pi\)
\(338\) 12.1682i 0.661865i
\(339\) 31.1161i 1.68999i
\(340\) 13.7795i 0.747299i
\(341\) 0.669887 0.641857i 0.0362764 0.0347585i
\(342\) 17.3913i 0.940415i
\(343\) 0 0
\(344\) 9.03556 0.487165
\(345\) 14.3241 0.771183
\(346\) 0.0766026i 0.00411818i
\(347\) 21.7413i 1.16713i 0.812065 + 0.583567i \(0.198343\pi\)
−0.812065 + 0.583567i \(0.801657\pi\)
\(348\) −0.260049 −0.0139401
\(349\) 13.4565 0.720307 0.360154 0.932893i \(-0.382724\pi\)
0.360154 + 0.932893i \(0.382724\pi\)
\(350\) 0 0
\(351\) 9.56862i 0.510735i
\(352\) 2.39477 2.29457i 0.127642 0.122301i
\(353\) 6.70769i 0.357014i −0.983939 0.178507i \(-0.942873\pi\)
0.983939 0.178507i \(-0.0571267\pi\)
\(354\) 37.7193i 2.00476i
\(355\) 29.9180i 1.58788i
\(356\) 5.94902i 0.315297i
\(357\) 0 0
\(358\) 8.97491i 0.474339i
\(359\) 31.0463i 1.63856i 0.573391 + 0.819282i \(0.305627\pi\)
−0.573391 + 0.819282i \(0.694373\pi\)
\(360\) 13.2180 0.696648
\(361\) 2.68183 0.141149
\(362\) 15.1450 0.796002
\(363\) 28.5209 + 1.21946i 1.49696 + 0.0640050i
\(364\) 0 0
\(365\) 13.7940i 0.722010i
\(366\) −28.8771 −1.50943
\(367\) 29.6492i 1.54768i −0.633384 0.773838i \(-0.718335\pi\)
0.633384 0.773838i \(-0.281665\pi\)
\(368\) −1.55962 −0.0813010
\(369\) −11.0110 −0.573208
\(370\) 2.49651 0.129788
\(371\) 0 0
\(372\) −0.725946 −0.0376385
\(373\) 8.78055i 0.454640i −0.973820 0.227320i \(-0.927004\pi\)
0.973820 0.227320i \(-0.0729963\pi\)
\(374\) 9.32434 8.93419i 0.482150 0.461976i
\(375\) 23.1858 1.19731
\(376\) 6.56949 0.338796
\(377\) 0.502706i 0.0258907i
\(378\) 0 0
\(379\) 30.8135 1.58278 0.791391 0.611311i \(-0.209358\pi\)
0.791391 + 0.611311i \(0.209358\pi\)
\(380\) 16.4789i 0.845349i
\(381\) −34.3080 −1.75765
\(382\) 6.00000i 0.306987i
\(383\) 5.29482i 0.270553i 0.990808 + 0.135276i \(0.0431922\pi\)
−0.990808 + 0.135276i \(0.956808\pi\)
\(384\) −2.59518 −0.132435
\(385\) 0 0
\(386\) 14.8281 0.754729
\(387\) 33.7473i 1.71547i
\(388\) 16.7587i 0.850793i
\(389\) 0.860237 0.0436158 0.0218079 0.999762i \(-0.493058\pi\)
0.0218079 + 0.999762i \(0.493058\pi\)
\(390\) 46.0759i 2.33314i
\(391\) −6.07258 −0.307104
\(392\) 0 0
\(393\) 42.8168i 2.15982i
\(394\) −14.4745 −0.729213
\(395\) 27.2496 1.37108
\(396\) −8.57010 8.94436i −0.430664 0.449471i
\(397\) 12.3473i 0.619695i 0.950786 + 0.309847i \(0.100278\pi\)
−0.950786 + 0.309847i \(0.899722\pi\)
\(398\) −11.2259 −0.562702
\(399\) 0 0
\(400\) −7.52450 −0.376225
\(401\) 33.7252 1.68416 0.842078 0.539355i \(-0.181332\pi\)
0.842078 + 0.539355i \(0.181332\pi\)
\(402\) 10.3390 0.515661
\(403\) 1.40334i 0.0699054i
\(404\) 1.40290 0.0697971
\(405\) 22.1365i 1.09997i
\(406\) 0 0
\(407\) −1.61866 1.68935i −0.0802339 0.0837377i
\(408\) −10.1046 −0.500254
\(409\) −38.3692 −1.89723 −0.948616 0.316428i \(-0.897516\pi\)
−0.948616 + 0.316428i \(0.897516\pi\)
\(410\) 10.4333 0.515264
\(411\) 17.2417i 0.850470i
\(412\) 2.06291i 0.101632i
\(413\) 0 0
\(414\) 5.82511i 0.286289i
\(415\) 10.1682i 0.499139i
\(416\) 5.01680i 0.245969i
\(417\) 37.2494i 1.82411i
\(418\) 11.1510 10.6844i 0.545412 0.522590i
\(419\) 33.5023i 1.63670i 0.574723 + 0.818348i \(0.305110\pi\)
−0.574723 + 0.818348i \(0.694890\pi\)
\(420\) 0 0
\(421\) −23.0155 −1.12171 −0.560853 0.827915i \(-0.689527\pi\)
−0.560853 + 0.827915i \(0.689527\pi\)
\(422\) 6.44038 0.313513
\(423\) 24.5367i 1.19302i
\(424\) 5.54058i 0.269074i
\(425\) −29.2975 −1.42114
\(426\) −21.9391 −1.06295
\(427\) 0 0
\(428\) 12.2655i 0.592875i
\(429\) 31.1787 29.8741i 1.50532 1.44234i
\(430\) 31.9768i 1.54206i
\(431\) 26.8381i 1.29275i −0.763021 0.646373i \(-0.776285\pi\)
0.763021 0.646373i \(-0.223715\pi\)
\(432\) 1.90732i 0.0917659i
\(433\) 30.6912i 1.47493i 0.675387 + 0.737463i \(0.263976\pi\)
−0.675387 + 0.737463i \(0.736024\pi\)
\(434\) 0 0
\(435\) 0.920312i 0.0441256i
\(436\) 6.72491i 0.322065i
\(437\) −7.26219 −0.347398
\(438\) −10.1152 −0.483325
\(439\) −16.8452 −0.803976 −0.401988 0.915645i \(-0.631681\pi\)
−0.401988 + 0.915645i \(0.631681\pi\)
\(440\) 8.12048 + 8.47510i 0.387129 + 0.404035i
\(441\) 0 0
\(442\) 19.5335i 0.929114i
\(443\) −0.790590 −0.0375620 −0.0187810 0.999824i \(-0.505979\pi\)
−0.0187810 + 0.999824i \(0.505979\pi\)
\(444\) 1.83072i 0.0868819i
\(445\) −21.0536 −0.998035
\(446\) 4.01793 0.190255
\(447\) −6.91841 −0.327230
\(448\) 0 0
\(449\) 15.9734 0.753833 0.376917 0.926247i \(-0.376984\pi\)
0.376917 + 0.926247i \(0.376984\pi\)
\(450\) 28.1036i 1.32482i
\(451\) −6.76461 7.06002i −0.318533 0.332443i
\(452\) 11.9900 0.563960
\(453\) 26.9648 1.26692
\(454\) 12.7293i 0.597416i
\(455\) 0 0
\(456\) −12.0841 −0.565891
\(457\) 34.9331i 1.63410i −0.576564 0.817052i \(-0.695607\pi\)
0.576564 0.817052i \(-0.304393\pi\)
\(458\) 6.01345 0.280990
\(459\) 7.42637i 0.346633i
\(460\) 5.51950i 0.257348i
\(461\) 20.8346 0.970364 0.485182 0.874413i \(-0.338753\pi\)
0.485182 + 0.874413i \(0.338753\pi\)
\(462\) 0 0
\(463\) 13.1724 0.612172 0.306086 0.952004i \(-0.400981\pi\)
0.306086 + 0.952004i \(0.400981\pi\)
\(464\) 0.100205i 0.00465188i
\(465\) 2.56912i 0.119140i
\(466\) 6.46694 0.299575
\(467\) 16.8184i 0.778262i −0.921182 0.389131i \(-0.872775\pi\)
0.921182 0.389131i \(-0.127225\pi\)
\(468\) −18.7375 −0.866140
\(469\) 0 0
\(470\) 23.2494i 1.07241i
\(471\) −21.7339 −1.00145
\(472\) −14.5344 −0.668999
\(473\) 21.6381 20.7327i 0.994922 0.953292i
\(474\) 19.9824i 0.917822i
\(475\) −35.0369 −1.60760
\(476\) 0 0
\(477\) −20.6938 −0.947503
\(478\) −15.5775 −0.712498
\(479\) −22.8582 −1.04442 −0.522208 0.852818i \(-0.674891\pi\)
−0.522208 + 0.852818i \(0.674891\pi\)
\(480\) 9.18432i 0.419205i
\(481\) −3.53900 −0.161364
\(482\) 23.4762i 1.06931i
\(483\) 0 0
\(484\) 0.469894 10.9900i 0.0213588 0.499544i
\(485\) −59.3089 −2.69308
\(486\) −21.9548 −0.995891
\(487\) 31.2628 1.41665 0.708327 0.705884i \(-0.249450\pi\)
0.708327 + 0.705884i \(0.249450\pi\)
\(488\) 11.1272i 0.503705i
\(489\) 7.95442i 0.359711i
\(490\) 0 0
\(491\) 22.4979i 1.01532i −0.861558 0.507659i \(-0.830511\pi\)
0.861558 0.507659i \(-0.169489\pi\)
\(492\) 7.65083i 0.344926i
\(493\) 0.390159i 0.0175719i
\(494\) 23.3601i 1.05102i
\(495\) 31.6541 30.3295i 1.42274 1.36321i
\(496\) 0.279729i 0.0125602i
\(497\) 0 0
\(498\) 7.45646 0.334132
\(499\) −31.9097 −1.42847 −0.714236 0.699905i \(-0.753226\pi\)
−0.714236 + 0.699905i \(0.753226\pi\)
\(500\) 8.93419i 0.399549i
\(501\) 26.1415i 1.16792i
\(502\) −18.2818 −0.815957
\(503\) −30.2687 −1.34962 −0.674808 0.737994i \(-0.735773\pi\)
−0.674808 + 0.737994i \(0.735773\pi\)
\(504\) 0 0
\(505\) 4.96487i 0.220934i
\(506\) −3.73495 + 3.57867i −0.166039 + 0.159091i
\(507\) 31.5787i 1.40246i
\(508\) 13.2199i 0.586538i
\(509\) 23.0542i 1.02186i −0.859622 0.510930i \(-0.829301\pi\)
0.859622 0.510930i \(-0.170699\pi\)
\(510\) 35.7603i 1.58349i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 8.88119i 0.392114i
\(514\) 9.61966 0.424305
\(515\) 7.30061 0.321703
\(516\) −23.4489 −1.03228
\(517\) 15.7325 15.0742i 0.691912 0.662961i
\(518\) 0 0
\(519\) 0.198797i 0.00872624i
\(520\) 17.7544 0.778583
\(521\) 7.98303i 0.349743i 0.984591 + 0.174872i \(0.0559510\pi\)
−0.984591 + 0.174872i \(0.944049\pi\)
\(522\) 0.374259 0.0163809
\(523\) 5.58280 0.244119 0.122059 0.992523i \(-0.461050\pi\)
0.122059 + 0.992523i \(0.461050\pi\)
\(524\) −16.4986 −0.720746
\(525\) 0 0
\(526\) −0.578666 −0.0252310
\(527\) 1.08916i 0.0474444i
\(528\) −6.21487 + 5.95482i −0.270467 + 0.259150i
\(529\) −20.5676 −0.894242
\(530\) 19.6081 0.851721
\(531\) 54.2851i 2.35577i
\(532\) 0 0
\(533\) −14.7900 −0.640625
\(534\) 15.4388i 0.668101i
\(535\) −43.4075 −1.87667
\(536\) 3.98392i 0.172079i
\(537\) 23.2915i 1.00510i
\(538\) 22.0896 0.952350
\(539\) 0 0
\(540\) −6.74999 −0.290473
\(541\) 13.4022i 0.576204i −0.957600 0.288102i \(-0.906976\pi\)
0.957600 0.288102i \(-0.0930242\pi\)
\(542\) 4.26222i 0.183078i
\(543\) −39.3039 −1.68669
\(544\) 3.89362i 0.166938i
\(545\) −23.7994 −1.01946
\(546\) 0 0
\(547\) 24.5161i 1.04823i 0.851647 + 0.524116i \(0.175604\pi\)
−0.851647 + 0.524116i \(0.824396\pi\)
\(548\) −6.64374 −0.283807
\(549\) 41.5595 1.77372
\(550\) −18.0195 + 17.2655i −0.768353 + 0.736203i
\(551\) 0.466590i 0.0198774i
\(552\) 4.04750 0.172273
\(553\) 0 0
\(554\) 18.3653 0.780265
\(555\) −6.47890 −0.275014
\(556\) 14.3533 0.608716
\(557\) 3.61157i 0.153027i 0.997069 + 0.0765137i \(0.0243789\pi\)
−0.997069 + 0.0765137i \(0.975621\pi\)
\(558\) 1.04477 0.0442287
\(559\) 45.3296i 1.91724i
\(560\) 0 0
\(561\) −24.1983 + 23.1858i −1.02165 + 0.978905i
\(562\) −3.72890 −0.157294
\(563\) 5.85803 0.246887 0.123443 0.992352i \(-0.460606\pi\)
0.123443 + 0.992352i \(0.460606\pi\)
\(564\) −17.0490 −0.717892
\(565\) 42.4324i 1.78515i
\(566\) 12.7315i 0.535146i
\(567\) 0 0
\(568\) 8.45381i 0.354714i
\(569\) 34.6147i 1.45112i 0.688158 + 0.725561i \(0.258420\pi\)
−0.688158 + 0.725561i \(0.741580\pi\)
\(570\) 42.7657i 1.79126i
\(571\) 7.96636i 0.333382i −0.986009 0.166691i \(-0.946692\pi\)
0.986009 0.166691i \(-0.0533082\pi\)
\(572\) −11.5114 12.0141i −0.481315 0.502335i
\(573\) 15.5711i 0.650491i
\(574\) 0 0
\(575\) 11.7354 0.489399
\(576\) 3.73495 0.155623
\(577\) 18.3764i 0.765018i −0.923952 0.382509i \(-0.875060\pi\)
0.923952 0.382509i \(-0.124940\pi\)
\(578\) 1.83972i 0.0765223i
\(579\) −38.4815 −1.59924
\(580\) −0.354624 −0.0147249
\(581\) 0 0
\(582\) 43.4917i 1.80279i
\(583\) −12.7133 13.2684i −0.526529 0.549523i
\(584\) 3.89771i 0.161288i
\(585\) 66.3118i 2.74166i
\(586\) 26.2251i 1.08335i
\(587\) 17.2267i 0.711021i −0.934672 0.355511i \(-0.884307\pi\)
0.934672 0.355511i \(-0.115693\pi\)
\(588\) 0 0
\(589\) 1.30252i 0.0536695i
\(590\) 51.4371i 2.11763i
\(591\) 37.5638 1.54517
\(592\) 0.705430 0.0289930
\(593\) 41.2427 1.69363 0.846817 0.531884i \(-0.178516\pi\)
0.846817 + 0.531884i \(0.178516\pi\)
\(594\) 4.37648 + 4.56760i 0.179569 + 0.187411i
\(595\) 0 0
\(596\) 2.66587i 0.109198i
\(597\) 29.1331 1.19234
\(598\) 7.82431i 0.319960i
\(599\) 9.95440 0.406726 0.203363 0.979103i \(-0.434813\pi\)
0.203363 + 0.979103i \(0.434813\pi\)
\(600\) 19.5274 0.797203
\(601\) −4.76767 −0.194477 −0.0972386 0.995261i \(-0.531001\pi\)
−0.0972386 + 0.995261i \(0.531001\pi\)
\(602\) 0 0
\(603\) −14.8797 −0.605949
\(604\) 10.3903i 0.422777i
\(605\) 38.8934 + 1.66295i 1.58124 + 0.0676087i
\(606\) −3.64079 −0.147897
\(607\) −4.55345 −0.184819 −0.0924094 0.995721i \(-0.529457\pi\)
−0.0924094 + 0.995721i \(0.529457\pi\)
\(608\) 4.65637i 0.188841i
\(609\) 0 0
\(610\) −39.3791 −1.59441
\(611\) 32.9578i 1.33333i
\(612\) 14.5425 0.587844
\(613\) 1.44894i 0.0585223i 0.999572 + 0.0292611i \(0.00931544\pi\)
−0.999572 + 0.0292611i \(0.990685\pi\)
\(614\) 25.5942i 1.03290i
\(615\) −27.0762 −1.09182
\(616\) 0 0
\(617\) −2.96752 −0.119468 −0.0597340 0.998214i \(-0.519025\pi\)
−0.0597340 + 0.998214i \(0.519025\pi\)
\(618\) 5.35360i 0.215354i
\(619\) 11.5475i 0.464133i 0.972700 + 0.232067i \(0.0745488\pi\)
−0.972700 + 0.232067i \(0.925451\pi\)
\(620\) −0.989959 −0.0397577
\(621\) 2.97470i 0.119371i
\(622\) −1.90970 −0.0765720
\(623\) 0 0
\(624\) 13.0195i 0.521196i
\(625\) −6.00443 −0.240177
\(626\) 30.4503 1.21704
\(627\) −28.9387 + 27.7279i −1.15570 + 1.10734i
\(628\) 8.37473i 0.334188i
\(629\) 2.74668 0.109517
\(630\) 0 0
\(631\) −27.5215 −1.09562 −0.547808 0.836604i \(-0.684537\pi\)
−0.547808 + 0.836604i \(0.684537\pi\)
\(632\) 7.69982 0.306282
\(633\) −16.7139 −0.664319
\(634\) 34.3942i 1.36597i
\(635\) −46.7851 −1.85661
\(636\) 14.3788i 0.570156i
\(637\) 0 0
\(638\) 0.229926 + 0.239967i 0.00910288 + 0.00950040i
\(639\) 31.5745 1.24907
\(640\) −3.53900 −0.139891
\(641\) 33.6547 1.32928 0.664639 0.747164i \(-0.268585\pi\)
0.664639 + 0.747164i \(0.268585\pi\)
\(642\) 31.8311i 1.25627i
\(643\) 5.95261i 0.234748i 0.993088 + 0.117374i \(0.0374476\pi\)
−0.993088 + 0.117374i \(0.962552\pi\)
\(644\) 0 0
\(645\) 82.9855i 3.26755i
\(646\) 18.1302i 0.713321i
\(647\) 11.7737i 0.462873i −0.972850 0.231437i \(-0.925657\pi\)
0.972850 0.231437i \(-0.0743426\pi\)
\(648\) 6.25501i 0.245720i
\(649\) −34.8066 + 33.3502i −1.36628 + 1.30911i
\(650\) 37.7489i 1.48063i
\(651\) 0 0
\(652\) −3.06508 −0.120038
\(653\) 28.8670 1.12965 0.564827 0.825209i \(-0.308943\pi\)
0.564827 + 0.825209i \(0.308943\pi\)
\(654\) 17.4523i 0.682440i
\(655\) 58.3886i 2.28143i
\(656\) 2.94809 0.115104
\(657\) 14.5577 0.567952
\(658\) 0 0
\(659\) 44.6812i 1.74053i −0.492581 0.870266i \(-0.663947\pi\)
0.492581 0.870266i \(-0.336053\pi\)
\(660\) −21.0741 21.9944i −0.820307 0.856130i
\(661\) 39.6341i 1.54159i 0.637084 + 0.770794i \(0.280140\pi\)
−0.637084 + 0.770794i \(0.719860\pi\)
\(662\) 15.5128i 0.602924i
\(663\) 50.6929i 1.96875i
\(664\) 2.87320i 0.111502i
\(665\) 0 0
\(666\) 2.63474i 0.102094i
\(667\) 0.156281i 0.00605124i
\(668\) −10.0731 −0.389741
\(669\) −10.4272 −0.403141
\(670\) 14.0991 0.544694
\(671\) 25.5321 + 26.6471i 0.985657 + 1.02870i
\(672\) 0 0
\(673\) 2.71886i 0.104804i 0.998626 + 0.0524022i \(0.0166878\pi\)
−0.998626 + 0.0524022i \(0.983312\pi\)
\(674\) 7.70882 0.296933
\(675\) 14.3516i 0.552394i
\(676\) −12.1682 −0.468009
\(677\) −6.05945 −0.232884 −0.116442 0.993198i \(-0.537149\pi\)
−0.116442 + 0.993198i \(0.537149\pi\)
\(678\) −31.1161 −1.19501
\(679\) 0 0
\(680\) −13.7795 −0.528420
\(681\) 33.0348i 1.26590i
\(682\) 0.641857 + 0.669887i 0.0245780 + 0.0256513i
\(683\) −6.03409 −0.230888 −0.115444 0.993314i \(-0.536829\pi\)
−0.115444 + 0.993314i \(0.536829\pi\)
\(684\) 17.3913 0.664973
\(685\) 23.5122i 0.898354i
\(686\) 0 0
\(687\) −15.6060 −0.595405
\(688\) 9.03556i 0.344478i
\(689\) −27.7960 −1.05894
\(690\) 14.3241i 0.545309i
\(691\) 19.8053i 0.753427i −0.926330 0.376714i \(-0.877054\pi\)
0.926330 0.376714i \(-0.122946\pi\)
\(692\) −0.0766026 −0.00291200
\(693\) 0 0
\(694\) −21.7413 −0.825288
\(695\) 50.7963i 1.92681i
\(696\) 0.260049i 0.00985712i
\(697\) 11.4788 0.434789
\(698\) 13.4565i 0.509334i
\(699\) −16.7828 −0.634786
\(700\) 0 0
\(701\) 26.0155i 0.982591i 0.870993 + 0.491296i \(0.163476\pi\)
−0.870993 + 0.491296i \(0.836524\pi\)
\(702\) 9.56862 0.361144
\(703\) 3.28475 0.123887
\(704\) 2.29457 + 2.39477i 0.0864799 + 0.0902565i
\(705\) 60.3363i 2.27240i
\(706\) 6.70769 0.252447
\(707\) 0 0
\(708\) 37.7193 1.41758
\(709\) −24.8917 −0.934826 −0.467413 0.884039i \(-0.654814\pi\)
−0.467413 + 0.884039i \(0.654814\pi\)
\(710\) −29.9180 −1.12280
\(711\) 28.7584i 1.07853i
\(712\) −5.94902 −0.222949
\(713\) 0.436271i 0.0163385i
\(714\) 0 0
\(715\) 42.5178 40.7388i 1.59008 1.52354i
\(716\) 8.97491 0.335408
\(717\) 40.4263 1.50975
\(718\) −31.0463 −1.15864
\(719\) 13.2970i 0.495895i −0.968773 0.247948i \(-0.920244\pi\)
0.968773 0.247948i \(-0.0797561\pi\)
\(720\) 13.2180i 0.492604i
\(721\) 0 0
\(722\) 2.68183i 0.0998073i
\(723\) 60.9250i 2.26583i
\(724\) 15.1450i 0.562858i
\(725\) 0.753989i 0.0280025i
\(726\) −1.21946 + 28.5209i −0.0452583 + 1.05851i
\(727\) 5.67083i 0.210319i 0.994455 + 0.105160i \(0.0335354\pi\)
−0.994455 + 0.105160i \(0.966465\pi\)
\(728\) 0 0
\(729\) 38.2116 1.41525
\(730\) −13.7940 −0.510538
\(731\) 35.1810i 1.30122i
\(732\) 28.8771i 1.06733i
\(733\) 41.3759 1.52825 0.764127 0.645066i \(-0.223170\pi\)
0.764127 + 0.645066i \(0.223170\pi\)
\(734\) 29.6492 1.09437
\(735\) 0 0
\(736\) 1.55962i 0.0574885i
\(737\) −9.14137 9.54058i −0.336727 0.351432i
\(738\) 11.0110i 0.405320i
\(739\) 41.5403i 1.52808i 0.645167 + 0.764042i \(0.276788\pi\)
−0.645167 + 0.764042i \(0.723212\pi\)
\(740\) 2.49651i 0.0917736i
\(741\) 60.6236i 2.22706i
\(742\) 0 0
\(743\) 39.7404i 1.45793i 0.684549 + 0.728967i \(0.259999\pi\)
−0.684549 + 0.728967i \(0.740001\pi\)
\(744\) 0.725946i 0.0266145i
\(745\) −9.43451 −0.345654
\(746\) 8.78055 0.321479
\(747\) −10.7312 −0.392636
\(748\) 8.93419 + 9.32434i 0.326666 + 0.340932i
\(749\) 0 0
\(750\) 23.1858i 0.846626i
\(751\) 5.36526 0.195781 0.0978905 0.995197i \(-0.468791\pi\)
0.0978905 + 0.995197i \(0.468791\pi\)
\(752\) 6.56949i 0.239565i
\(753\) 47.4445 1.72897
\(754\) 0.502706 0.0183075
\(755\) 36.7714 1.33825
\(756\) 0 0
\(757\) 25.8962 0.941215 0.470607 0.882343i \(-0.344035\pi\)
0.470607 + 0.882343i \(0.344035\pi\)
\(758\) 30.8135i 1.11920i
\(759\) 9.69285 9.28727i 0.351828 0.337107i
\(760\) −16.4789 −0.597752
\(761\) −15.2206 −0.551747 −0.275873 0.961194i \(-0.588967\pi\)
−0.275873 + 0.961194i \(0.588967\pi\)
\(762\) 34.3080i 1.24285i
\(763\) 0 0
\(764\) −6.00000 −0.217072
\(765\) 51.4657i 1.86075i
\(766\) −5.29482 −0.191310
\(767\) 72.9160i 2.63284i
\(768\) 2.59518i 0.0936454i
\(769\) −22.5146 −0.811898 −0.405949 0.913896i \(-0.633059\pi\)
−0.405949 + 0.913896i \(0.633059\pi\)
\(770\) 0 0
\(771\) −24.9647 −0.899083
\(772\) 14.8281i 0.533674i
\(773\) 28.0333i 1.00829i −0.863619 0.504144i \(-0.831808\pi\)
0.863619 0.504144i \(-0.168192\pi\)
\(774\) 33.7473 1.21302
\(775\) 2.10482i 0.0756073i
\(776\) −16.7587 −0.601601
\(777\) 0 0
\(778\) 0.860237i 0.0308410i
\(779\) 13.7274 0.491836
\(780\) −46.0759 −1.64978
\(781\) 19.3979 + 20.2450i 0.694110 + 0.724422i
\(782\) 6.07258i 0.217155i
\(783\) −0.191122 −0.00683014
\(784\) 0 0
\(785\) −29.6381 −1.05783
\(786\) 42.8168 1.52723
\(787\) −12.7432 −0.454246 −0.227123 0.973866i \(-0.572932\pi\)
−0.227123 + 0.973866i \(0.572932\pi\)
\(788\) 14.4745i 0.515631i
\(789\) 1.50174 0.0534634
\(790\) 27.2496i 0.969499i
\(791\) 0 0
\(792\) 8.94436 8.57010i 0.317824 0.304525i