Properties

Label 1764.2.b.b.1567.1
Level 1764
Weight 2
Character 1764.1567
Analytic conductor 14.086
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-7})\)
Defining polynomial: \(x^{4} - x^{3} - x^{2} - 2 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1567.1
Root \(-0.895644 - 1.09445i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.b.1567.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 1.32288i) q^{2} +(-1.50000 + 1.32288i) q^{4} -1.73205i q^{5} +(2.50000 + 1.32288i) q^{8} +O(q^{10})\) \(q+(-0.500000 - 1.32288i) q^{2} +(-1.50000 + 1.32288i) q^{4} -1.73205i q^{5} +(2.50000 + 1.32288i) q^{8} +(-2.29129 + 0.866025i) q^{10} +2.64575i q^{11} -3.46410i q^{13} +(0.500000 - 3.96863i) q^{16} +6.92820i q^{17} +(2.29129 + 2.59808i) q^{20} +(3.50000 - 1.32288i) q^{22} +5.29150i q^{23} +2.00000 q^{25} +(-4.58258 + 1.73205i) q^{26} -5.00000 q^{29} -4.58258 q^{31} +(-5.50000 + 1.32288i) q^{32} +(9.16515 - 3.46410i) q^{34} +(2.29129 - 4.33013i) q^{40} +3.46410i q^{41} +10.5830i q^{43} +(-3.50000 - 3.96863i) q^{44} +(7.00000 - 2.64575i) q^{46} +9.16515 q^{47} +(-1.00000 - 2.64575i) q^{50} +(4.58258 + 5.19615i) q^{52} -7.00000 q^{53} +4.58258 q^{55} +(2.50000 + 6.61438i) q^{58} +13.7477 q^{59} -10.3923i q^{61} +(2.29129 + 6.06218i) q^{62} +(4.50000 + 6.61438i) q^{64} -6.00000 q^{65} +(-9.16515 - 10.3923i) q^{68} +5.29150i q^{71} +6.92820i q^{73} +7.93725i q^{79} +(-6.87386 - 0.866025i) q^{80} +(4.58258 - 1.73205i) q^{82} -4.58258 q^{83} +12.0000 q^{85} +(14.0000 - 5.29150i) q^{86} +(-3.50000 + 6.61438i) q^{88} +10.3923i q^{89} +(-7.00000 - 7.93725i) q^{92} +(-4.58258 - 12.1244i) q^{94} -8.66025i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 6q^{4} + 10q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 6q^{4} + 10q^{8} + 2q^{16} + 14q^{22} + 8q^{25} - 20q^{29} - 22q^{32} - 14q^{44} + 28q^{46} - 4q^{50} - 28q^{53} + 10q^{58} + 18q^{64} - 24q^{65} + 48q^{85} + 56q^{86} - 14q^{88} - 28q^{92} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 1.32288i −0.353553 0.935414i
\(3\) 0 0
\(4\) −1.50000 + 1.32288i −0.750000 + 0.661438i
\(5\) 1.73205i 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.50000 + 1.32288i 0.883883 + 0.467707i
\(9\) 0 0
\(10\) −2.29129 + 0.866025i −0.724569 + 0.273861i
\(11\) 2.64575i 0.797724i 0.917011 + 0.398862i \(0.130595\pi\)
−0.917011 + 0.398862i \(0.869405\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i −0.877058 0.480384i \(-0.840497\pi\)
0.877058 0.480384i \(-0.159503\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.500000 3.96863i 0.125000 0.992157i
\(17\) 6.92820i 1.68034i 0.542326 + 0.840168i \(0.317544\pi\)
−0.542326 + 0.840168i \(0.682456\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 2.29129 + 2.59808i 0.512348 + 0.580948i
\(21\) 0 0
\(22\) 3.50000 1.32288i 0.746203 0.282038i
\(23\) 5.29150i 1.10335i 0.834058 + 0.551677i \(0.186012\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 0 0
\(25\) 2.00000 0.400000
\(26\) −4.58258 + 1.73205i −0.898717 + 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) −4.58258 −0.823055 −0.411527 0.911397i \(-0.635005\pi\)
−0.411527 + 0.911397i \(0.635005\pi\)
\(32\) −5.50000 + 1.32288i −0.972272 + 0.233854i
\(33\) 0 0
\(34\) 9.16515 3.46410i 1.57181 0.594089i
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 2.29129 4.33013i 0.362284 0.684653i
\(41\) 3.46410i 0.541002i 0.962720 + 0.270501i \(0.0871893\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(42\) 0 0
\(43\) 10.5830i 1.61389i 0.590624 + 0.806947i \(0.298881\pi\)
−0.590624 + 0.806947i \(0.701119\pi\)
\(44\) −3.50000 3.96863i −0.527645 0.598293i
\(45\) 0 0
\(46\) 7.00000 2.64575i 1.03209 0.390095i
\(47\) 9.16515 1.33687 0.668437 0.743768i \(-0.266963\pi\)
0.668437 + 0.743768i \(0.266963\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.00000 2.64575i −0.141421 0.374166i
\(51\) 0 0
\(52\) 4.58258 + 5.19615i 0.635489 + 0.720577i
\(53\) −7.00000 −0.961524 −0.480762 0.876851i \(-0.659640\pi\)
−0.480762 + 0.876851i \(0.659640\pi\)
\(54\) 0 0
\(55\) 4.58258 0.617914
\(56\) 0 0
\(57\) 0 0
\(58\) 2.50000 + 6.61438i 0.328266 + 0.868510i
\(59\) 13.7477 1.78980 0.894901 0.446265i \(-0.147246\pi\)
0.894901 + 0.446265i \(0.147246\pi\)
\(60\) 0 0
\(61\) 10.3923i 1.33060i −0.746577 0.665299i \(-0.768304\pi\)
0.746577 0.665299i \(-0.231696\pi\)
\(62\) 2.29129 + 6.06218i 0.290994 + 0.769897i
\(63\) 0 0
\(64\) 4.50000 + 6.61438i 0.562500 + 0.826797i
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −9.16515 10.3923i −1.11144 1.26025i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.29150i 0.627986i 0.949425 + 0.313993i \(0.101667\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) 0 0
\(73\) 6.92820i 0.810885i 0.914121 + 0.405442i \(0.132883\pi\)
−0.914121 + 0.405442i \(0.867117\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 7.93725i 0.893011i 0.894781 + 0.446505i \(0.147332\pi\)
−0.894781 + 0.446505i \(0.852668\pi\)
\(80\) −6.87386 0.866025i −0.768521 0.0968246i
\(81\) 0 0
\(82\) 4.58258 1.73205i 0.506061 0.191273i
\(83\) −4.58258 −0.503003 −0.251502 0.967857i \(-0.580924\pi\)
−0.251502 + 0.967857i \(0.580924\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) 14.0000 5.29150i 1.50966 0.570597i
\(87\) 0 0
\(88\) −3.50000 + 6.61438i −0.373101 + 0.705095i
\(89\) 10.3923i 1.10158i 0.834643 + 0.550791i \(0.185674\pi\)
−0.834643 + 0.550791i \(0.814326\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −7.00000 7.93725i −0.729800 0.827516i
\(93\) 0 0
\(94\) −4.58258 12.1244i −0.472657 1.25053i
\(95\) 0 0
\(96\) 0 0
\(97\) 8.66025i 0.879316i −0.898165 0.439658i \(-0.855100\pi\)
0.898165 0.439658i \(-0.144900\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.00000 + 2.64575i −0.300000 + 0.264575i
\(101\) 6.92820i 0.689382i −0.938716 0.344691i \(-0.887984\pi\)
0.938716 0.344691i \(-0.112016\pi\)
\(102\) 0 0
\(103\) 18.3303 1.80614 0.903069 0.429495i \(-0.141308\pi\)
0.903069 + 0.429495i \(0.141308\pi\)
\(104\) 4.58258 8.66025i 0.449359 0.849208i
\(105\) 0 0
\(106\) 3.50000 + 9.26013i 0.339950 + 0.899423i
\(107\) 18.5203i 1.79042i 0.445644 + 0.895211i \(0.352975\pi\)
−0.445644 + 0.895211i \(0.647025\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −2.29129 6.06218i −0.218466 0.578006i
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) 9.16515 0.854655
\(116\) 7.50000 6.61438i 0.696358 0.614130i
\(117\) 0 0
\(118\) −6.87386 18.1865i −0.632790 1.67421i
\(119\) 0 0
\(120\) 0 0
\(121\) 4.00000 0.363636
\(122\) −13.7477 + 5.19615i −1.24466 + 0.470438i
\(123\) 0 0
\(124\) 6.87386 6.06218i 0.617291 0.544400i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 7.93725i 0.704317i −0.935940 0.352159i \(-0.885448\pi\)
0.935940 0.352159i \(-0.114552\pi\)
\(128\) 6.50000 9.26013i 0.574524 0.818488i
\(129\) 0 0
\(130\) 3.00000 + 7.93725i 0.263117 + 0.696143i
\(131\) 13.7477 1.20114 0.600572 0.799570i \(-0.294939\pi\)
0.600572 + 0.799570i \(0.294939\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −9.16515 + 17.3205i −0.785905 + 1.48522i
\(137\) 4.00000 0.341743 0.170872 0.985293i \(-0.445342\pi\)
0.170872 + 0.985293i \(0.445342\pi\)
\(138\) 0 0
\(139\) 9.16515 0.777378 0.388689 0.921369i \(-0.372928\pi\)
0.388689 + 0.921369i \(0.372928\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.00000 2.64575i 0.587427 0.222027i
\(143\) 9.16515 0.766428
\(144\) 0 0
\(145\) 8.66025i 0.719195i
\(146\) 9.16515 3.46410i 0.758513 0.286691i
\(147\) 0 0
\(148\) 0 0
\(149\) −14.0000 −1.14692 −0.573462 0.819232i \(-0.694400\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(150\) 0 0
\(151\) 13.2288i 1.07654i 0.842772 + 0.538270i \(0.180922\pi\)
−0.842772 + 0.538270i \(0.819078\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.93725i 0.637536i
\(156\) 0 0
\(157\) 6.92820i 0.552931i −0.961024 0.276465i \(-0.910837\pi\)
0.961024 0.276465i \(-0.0891631\pi\)
\(158\) 10.5000 3.96863i 0.835335 0.315727i
\(159\) 0 0
\(160\) 2.29129 + 9.52628i 0.181142 + 0.753119i
\(161\) 0 0
\(162\) 0 0
\(163\) 15.8745i 1.24339i −0.783260 0.621694i \(-0.786445\pi\)
0.783260 0.621694i \(-0.213555\pi\)
\(164\) −4.58258 5.19615i −0.357839 0.405751i
\(165\) 0 0
\(166\) 2.29129 + 6.06218i 0.177838 + 0.470516i
\(167\) −18.3303 −1.41844 −0.709221 0.704987i \(-0.750953\pi\)
−0.709221 + 0.704987i \(0.750953\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −6.00000 15.8745i −0.460179 1.21752i
\(171\) 0 0
\(172\) −14.0000 15.8745i −1.06749 1.21042i
\(173\) 13.8564i 1.05348i 0.850026 + 0.526742i \(0.176586\pi\)
−0.850026 + 0.526742i \(0.823414\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 10.5000 + 1.32288i 0.791467 + 0.0997155i
\(177\) 0 0
\(178\) 13.7477 5.19615i 1.03044 0.389468i
\(179\) 5.29150i 0.395505i 0.980252 + 0.197753i \(0.0633643\pi\)
−0.980252 + 0.197753i \(0.936636\pi\)
\(180\) 0 0
\(181\) 3.46410i 0.257485i 0.991678 + 0.128742i \(0.0410940\pi\)
−0.991678 + 0.128742i \(0.958906\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −7.00000 + 13.2288i −0.516047 + 0.975237i
\(185\) 0 0
\(186\) 0 0
\(187\) −18.3303 −1.34044
\(188\) −13.7477 + 12.1244i −1.00266 + 0.884260i
\(189\) 0 0
\(190\) 0 0
\(191\) 10.5830i 0.765759i 0.923798 + 0.382880i \(0.125068\pi\)
−0.923798 + 0.382880i \(0.874932\pi\)
\(192\) 0 0
\(193\) 3.00000 0.215945 0.107972 0.994154i \(-0.465564\pi\)
0.107972 + 0.994154i \(0.465564\pi\)
\(194\) −11.4564 + 4.33013i −0.822524 + 0.310885i
\(195\) 0 0
\(196\) 0 0
\(197\) −14.0000 −0.997459 −0.498729 0.866758i \(-0.666200\pi\)
−0.498729 + 0.866758i \(0.666200\pi\)
\(198\) 0 0
\(199\) −18.3303 −1.29940 −0.649700 0.760190i \(-0.725106\pi\)
−0.649700 + 0.760190i \(0.725106\pi\)
\(200\) 5.00000 + 2.64575i 0.353553 + 0.187083i
\(201\) 0 0
\(202\) −9.16515 + 3.46410i −0.644858 + 0.243733i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 0.419058
\(206\) −9.16515 24.2487i −0.638566 1.68949i
\(207\) 0 0
\(208\) −13.7477 1.73205i −0.953233 0.120096i
\(209\) 0 0
\(210\) 0 0
\(211\) 5.29150i 0.364282i 0.983272 + 0.182141i \(0.0583027\pi\)
−0.983272 + 0.182141i \(0.941697\pi\)
\(212\) 10.5000 9.26013i 0.721143 0.635988i
\(213\) 0 0
\(214\) 24.5000 9.26013i 1.67479 0.633009i
\(215\) 18.3303 1.25012
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −6.87386 + 6.06218i −0.463436 + 0.408712i
\(221\) 24.0000 1.61441
\(222\) 0 0
\(223\) 4.58258 0.306872 0.153436 0.988159i \(-0.450966\pi\)
0.153436 + 0.988159i \(0.450966\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.00000 18.5203i −0.465633 1.23195i
\(227\) −4.58258 −0.304156 −0.152078 0.988368i \(-0.548597\pi\)
−0.152078 + 0.988368i \(0.548597\pi\)
\(228\) 0 0
\(229\) 10.3923i 0.686743i −0.939200 0.343371i \(-0.888431\pi\)
0.939200 0.343371i \(-0.111569\pi\)
\(230\) −4.58258 12.1244i −0.302166 0.799456i
\(231\) 0 0
\(232\) −12.5000 6.61438i −0.820665 0.434255i
\(233\) 20.0000 1.31024 0.655122 0.755523i \(-0.272617\pi\)
0.655122 + 0.755523i \(0.272617\pi\)
\(234\) 0 0
\(235\) 15.8745i 1.03554i
\(236\) −20.6216 + 18.1865i −1.34235 + 1.18384i
\(237\) 0 0
\(238\) 0 0
\(239\) 5.29150i 0.342279i −0.985247 0.171139i \(-0.945255\pi\)
0.985247 0.171139i \(-0.0547449\pi\)
\(240\) 0 0
\(241\) 5.19615i 0.334714i 0.985896 + 0.167357i \(0.0535232\pi\)
−0.985896 + 0.167357i \(0.946477\pi\)
\(242\) −2.00000 5.29150i −0.128565 0.340151i
\(243\) 0 0
\(244\) 13.7477 + 15.5885i 0.880108 + 0.997949i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −11.4564 6.06218i −0.727485 0.384949i
\(249\) 0 0
\(250\) −16.0390 + 6.06218i −1.01440 + 0.383406i
\(251\) 4.58258 0.289250 0.144625 0.989487i \(-0.453802\pi\)
0.144625 + 0.989487i \(0.453802\pi\)
\(252\) 0 0
\(253\) −14.0000 −0.880172
\(254\) −10.5000 + 3.96863i −0.658829 + 0.249014i
\(255\) 0 0
\(256\) −15.5000 3.96863i −0.968750 0.248039i
\(257\) 10.3923i 0.648254i −0.946014 0.324127i \(-0.894929\pi\)
0.946014 0.324127i \(-0.105071\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 9.00000 7.93725i 0.558156 0.492248i
\(261\) 0 0
\(262\) −6.87386 18.1865i −0.424669 1.12357i
\(263\) 10.5830i 0.652576i −0.945270 0.326288i \(-0.894202\pi\)
0.945270 0.326288i \(-0.105798\pi\)
\(264\) 0 0
\(265\) 12.1244i 0.744793i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 19.0526i 1.16166i 0.814027 + 0.580828i \(0.197271\pi\)
−0.814027 + 0.580828i \(0.802729\pi\)
\(270\) 0 0
\(271\) −13.7477 −0.835115 −0.417557 0.908651i \(-0.637114\pi\)
−0.417557 + 0.908651i \(0.637114\pi\)
\(272\) 27.4955 + 3.46410i 1.66716 + 0.210042i
\(273\) 0 0
\(274\) −2.00000 5.29150i −0.120824 0.319671i
\(275\) 5.29150i 0.319090i
\(276\) 0 0
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) −4.58258 12.1244i −0.274845 0.727171i
\(279\) 0 0
\(280\) 0 0
\(281\) −16.0000 −0.954480 −0.477240 0.878773i \(-0.658363\pi\)
−0.477240 + 0.878773i \(0.658363\pi\)
\(282\) 0 0
\(283\) 18.3303 1.08962 0.544812 0.838558i \(-0.316601\pi\)
0.544812 + 0.838558i \(0.316601\pi\)
\(284\) −7.00000 7.93725i −0.415374 0.470989i
\(285\) 0 0
\(286\) −4.58258 12.1244i −0.270973 0.716928i
\(287\) 0 0
\(288\) 0 0
\(289\) −31.0000 −1.82353
\(290\) 11.4564 4.33013i 0.672745 0.254274i
\(291\) 0 0
\(292\) −9.16515 10.3923i −0.536350 0.608164i
\(293\) 15.5885i 0.910687i −0.890316 0.455344i \(-0.849516\pi\)
0.890316 0.455344i \(-0.150484\pi\)
\(294\) 0 0
\(295\) 23.8118i 1.38637i
\(296\) 0 0
\(297\) 0 0
\(298\) 7.00000 + 18.5203i 0.405499 + 1.07285i
\(299\) 18.3303 1.06007
\(300\) 0 0
\(301\) 0 0
\(302\) 17.5000 6.61438i 1.00701 0.380615i
\(303\) 0 0
\(304\) 0 0
\(305\) −18.0000 −1.03068
\(306\) 0 0
\(307\) −27.4955 −1.56925 −0.784624 0.619972i \(-0.787144\pi\)
−0.784624 + 0.619972i \(0.787144\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 10.5000 3.96863i 0.596360 0.225403i
\(311\) 9.16515 0.519708 0.259854 0.965648i \(-0.416326\pi\)
0.259854 + 0.965648i \(0.416326\pi\)
\(312\) 0 0
\(313\) 22.5167i 1.27272i 0.771393 + 0.636358i \(0.219560\pi\)
−0.771393 + 0.636358i \(0.780440\pi\)
\(314\) −9.16515 + 3.46410i −0.517219 + 0.195491i
\(315\) 0 0
\(316\) −10.5000 11.9059i −0.590671 0.669758i
\(317\) −7.00000 −0.393159 −0.196580 0.980488i \(-0.562983\pi\)
−0.196580 + 0.980488i \(0.562983\pi\)
\(318\) 0 0
\(319\) 13.2288i 0.740668i
\(320\) 11.4564 7.79423i 0.640434 0.435711i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 6.92820i 0.384308i
\(326\) −21.0000 + 7.93725i −1.16308 + 0.439604i
\(327\) 0 0
\(328\) −4.58258 + 8.66025i −0.253030 + 0.478183i
\(329\) 0 0
\(330\) 0 0
\(331\) 10.5830i 0.581695i 0.956769 + 0.290847i \(0.0939372\pi\)
−0.956769 + 0.290847i \(0.906063\pi\)
\(332\) 6.87386 6.06218i 0.377252 0.332705i
\(333\) 0 0
\(334\) 9.16515 + 24.2487i 0.501495 + 1.32683i
\(335\) 0 0
\(336\) 0 0
\(337\) −21.0000 −1.14394 −0.571971 0.820274i \(-0.693821\pi\)
−0.571971 + 0.820274i \(0.693821\pi\)
\(338\) −0.500000 1.32288i −0.0271964 0.0719549i
\(339\) 0 0
\(340\) −18.0000 + 15.8745i −0.976187 + 0.860916i
\(341\) 12.1244i 0.656571i
\(342\) 0 0
\(343\) 0 0
\(344\) −14.0000 + 26.4575i −0.754829 + 1.42649i
\(345\) 0 0
\(346\) 18.3303 6.92820i 0.985443 0.372463i
\(347\) 5.29150i 0.284063i 0.989862 + 0.142031i \(0.0453634\pi\)
−0.989862 + 0.142031i \(0.954637\pi\)
\(348\) 0 0
\(349\) 20.7846i 1.11257i 0.830990 + 0.556287i \(0.187775\pi\)
−0.830990 + 0.556287i \(0.812225\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.50000 14.5516i −0.186551 0.775605i
\(353\) 6.92820i 0.368751i −0.982856 0.184376i \(-0.940974\pi\)
0.982856 0.184376i \(-0.0590263\pi\)
\(354\) 0 0
\(355\) 9.16515 0.486436
\(356\) −13.7477 15.5885i −0.728628 0.826187i
\(357\) 0 0
\(358\) 7.00000 2.64575i 0.369961 0.139832i
\(359\) 10.5830i 0.558550i 0.960211 + 0.279275i \(0.0900940\pi\)
−0.960211 + 0.279275i \(0.909906\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 4.58258 1.73205i 0.240855 0.0910346i
\(363\) 0 0
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) 0 0
\(367\) 4.58258 0.239209 0.119604 0.992822i \(-0.461837\pi\)
0.119604 + 0.992822i \(0.461837\pi\)
\(368\) 21.0000 + 2.64575i 1.09470 + 0.137919i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 34.0000 1.76045 0.880227 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(374\) 9.16515 + 24.2487i 0.473919 + 1.25387i
\(375\) 0 0
\(376\) 22.9129 + 12.1244i 1.18164 + 0.625266i
\(377\) 17.3205i 0.892052i
\(378\) 0 0
\(379\) 5.29150i 0.271806i 0.990722 + 0.135903i \(0.0433936\pi\)
−0.990722 + 0.135903i \(0.956606\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 14.0000 5.29150i 0.716302 0.270737i
\(383\) −27.4955 −1.40495 −0.702476 0.711707i \(-0.747922\pi\)
−0.702476 + 0.711707i \(0.747922\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.50000 3.96863i −0.0763480 0.201998i
\(387\) 0 0
\(388\) 11.4564 + 12.9904i 0.581613 + 0.659487i
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) 0 0
\(391\) −36.6606 −1.85401
\(392\) 0 0
\(393\) 0 0
\(394\) 7.00000 + 18.5203i 0.352655 + 0.933037i
\(395\) 13.7477 0.691723
\(396\) 0 0
\(397\) 13.8564i 0.695433i 0.937600 + 0.347717i \(0.113043\pi\)
−0.937600 + 0.347717i \(0.886957\pi\)
\(398\) 9.16515 + 24.2487i 0.459408 + 1.21548i
\(399\) 0 0
\(400\) 1.00000 7.93725i 0.0500000 0.396863i
\(401\) −8.00000 −0.399501 −0.199750 0.979847i \(-0.564013\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(402\) 0 0
\(403\) 15.8745i 0.790766i
\(404\) 9.16515 + 10.3923i 0.455983 + 0.517036i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 5.19615i 0.256933i −0.991714 0.128467i \(-0.958994\pi\)
0.991714 0.128467i \(-0.0410055\pi\)
\(410\) −3.00000 7.93725i −0.148159 0.391993i
\(411\) 0 0
\(412\) −27.4955 + 24.2487i −1.35460 + 1.19465i
\(413\) 0 0
\(414\) 0 0
\(415\) 7.93725i 0.389624i
\(416\) 4.58258 + 19.0526i 0.224679 + 0.934129i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 7.00000 2.64575i 0.340755 0.128793i
\(423\) 0 0
\(424\) −17.5000 9.26013i −0.849875 0.449712i
\(425\) 13.8564i 0.672134i
\(426\) 0 0
\(427\) 0 0
\(428\) −24.5000 27.7804i −1.18425 1.34282i
\(429\) 0 0
\(430\) −9.16515 24.2487i −0.441983 1.16938i
\(431\) 26.4575i 1.27441i 0.770693 + 0.637207i \(0.219910\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) 20.7846i 0.998845i −0.866359 0.499422i \(-0.833546\pi\)
0.866359 0.499422i \(-0.166454\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 4.58258 0.218714 0.109357 0.994003i \(-0.465121\pi\)
0.109357 + 0.994003i \(0.465121\pi\)
\(440\) 11.4564 + 6.06218i 0.546164 + 0.289003i
\(441\) 0 0
\(442\) −12.0000 31.7490i −0.570782 1.51015i
\(443\) 18.5203i 0.879924i −0.898016 0.439962i \(-0.854992\pi\)
0.898016 0.439962i \(-0.145008\pi\)
\(444\) 0 0
\(445\) 18.0000 0.853282
\(446\) −2.29129 6.06218i −0.108496 0.287052i
\(447\) 0 0
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) −9.16515 −0.431570
\(452\) −21.0000 + 18.5203i −0.987757 + 0.871120i
\(453\) 0 0
\(454\) 2.29129 + 6.06218i 0.107535 + 0.284512i
\(455\) 0 0
\(456\) 0 0
\(457\) −27.0000 −1.26301 −0.631503 0.775373i \(-0.717562\pi\)
−0.631503 + 0.775373i \(0.717562\pi\)
\(458\) −13.7477 + 5.19615i −0.642389 + 0.242800i
\(459\) 0 0
\(460\) −13.7477 + 12.1244i −0.640991 + 0.565301i
\(461\) 27.7128i 1.29071i 0.763881 + 0.645357i \(0.223291\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(462\) 0 0
\(463\) 15.8745i 0.737751i 0.929479 + 0.368875i \(0.120257\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) −2.50000 + 19.8431i −0.116060 + 0.921194i
\(465\) 0 0
\(466\) −10.0000 26.4575i −0.463241 1.22562i
\(467\) −36.6606 −1.69645 −0.848225 0.529636i \(-0.822329\pi\)
−0.848225 + 0.529636i \(0.822329\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −21.0000 + 7.93725i −0.968658 + 0.366118i
\(471\) 0 0
\(472\) 34.3693 + 18.1865i 1.58198 + 0.837103i
\(473\) −28.0000 −1.28744
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −7.00000 + 2.64575i −0.320173 + 0.121014i
\(479\) −18.3303 −0.837533 −0.418766 0.908094i \(-0.637537\pi\)
−0.418766 + 0.908094i \(0.637537\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 6.87386 2.59808i 0.313096 0.118339i
\(483\) 0 0
\(484\) −6.00000 + 5.29150i −0.272727 + 0.240523i
\(485\) −15.0000 −0.681115
\(486\) 0 0
\(487\) 2.64575i 0.119890i 0.998202 + 0.0599452i \(0.0190926\pi\)
−0.998202 + 0.0599452i \(0.980907\pi\)
\(488\) 13.7477 25.9808i 0.622330 1.17609i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.64575i 0.119401i 0.998216 + 0.0597005i \(0.0190146\pi\)
−0.998216 + 0.0597005i \(0.980985\pi\)
\(492\) 0 0
\(493\) 34.6410i 1.56015i
\(494\) 0 0
\(495\) 0 0
\(496\) −2.29129 + 18.1865i −0.102882 + 0.816599i
\(497\) 0 0
\(498\) 0 0
\(499\) 5.29150i 0.236880i 0.992961 + 0.118440i \(0.0377894\pi\)
−0.992961 + 0.118440i \(0.962211\pi\)
\(500\) 16.0390 + 18.1865i 0.717287 + 0.813327i
\(501\) 0 0
\(502\) −2.29129 6.06218i −0.102265 0.270568i
\(503\) 36.6606 1.63462 0.817308 0.576201i \(-0.195466\pi\)
0.817308 + 0.576201i \(0.195466\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 7.00000 + 18.5203i 0.311188 + 0.823326i
\(507\) 0 0
\(508\) 10.5000 + 11.9059i 0.465862 + 0.528238i
\(509\) 1.73205i 0.0767718i 0.999263 + 0.0383859i \(0.0122216\pi\)
−0.999263 + 0.0383859i \(0.987778\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 2.50000 + 22.4889i 0.110485 + 0.993878i
\(513\) 0 0
\(514\) −13.7477 + 5.19615i −0.606386 + 0.229192i
\(515\) 31.7490i 1.39903i
\(516\) 0 0
\(517\) 24.2487i 1.06646i
\(518\) 0 0
\(519\) 0 0
\(520\) −15.0000 7.93725i −0.657794 0.348072i
\(521\) 6.92820i 0.303530i −0.988417 0.151765i \(-0.951504\pi\)
0.988417 0.151765i \(-0.0484957\pi\)
\(522\) 0 0
\(523\) −27.4955 −1.20229 −0.601146 0.799139i \(-0.705289\pi\)
−0.601146 + 0.799139i \(0.705289\pi\)
\(524\) −20.6216 + 18.1865i −0.900858 + 0.794482i
\(525\) 0 0
\(526\) −14.0000 + 5.29150i −0.610429 + 0.230720i
\(527\) 31.7490i 1.38301i
\(528\) 0 0
\(529\) −5.00000 −0.217391
\(530\) 16.0390 6.06218i 0.696690 0.263324i
\(531\) 0 0
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 32.0780 1.38685
\(536\) 0 0
\(537\) 0 0
\(538\) 25.2042 9.52628i 1.08663 0.410707i
\(539\) 0 0
\(540\) 0 0
\(541\) 8.00000 0.343947 0.171973 0.985102i \(-0.444986\pi\)
0.171973 + 0.985102i \(0.444986\pi\)
\(542\) 6.87386 + 18.1865i 0.295258 + 0.781179i
\(543\) 0 0
\(544\) −9.16515 38.1051i −0.392953 1.63374i
\(545\) 0 0
\(546\) 0 0
\(547\) 31.7490i 1.35749i −0.734374 0.678745i \(-0.762524\pi\)
0.734374 0.678745i \(-0.237476\pi\)
\(548\) −6.00000 + 5.29150i −0.256307 + 0.226042i
\(549\) 0 0
\(550\) 7.00000 2.64575i 0.298481 0.112815i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 2.00000 + 5.29150i 0.0849719 + 0.224814i
\(555\) 0 0
\(556\) −13.7477 + 12.1244i −0.583033 + 0.514187i
\(557\) 7.00000 0.296600 0.148300 0.988942i \(-0.452620\pi\)
0.148300 + 0.988942i \(0.452620\pi\)
\(558\) 0 0
\(559\) 36.6606 1.55058
\(560\) 0 0
\(561\) 0 0
\(562\) 8.00000 + 21.1660i 0.337460 + 0.892834i
\(563\) −22.9129 −0.965663 −0.482831 0.875713i \(-0.660392\pi\)
−0.482831 + 0.875713i \(0.660392\pi\)
\(564\) 0 0
\(565\) 24.2487i 1.02015i
\(566\) −9.16515 24.2487i −0.385240 1.01925i
\(567\) 0 0
\(568\) −7.00000 + 13.2288i −0.293713 + 0.555066i
\(569\) 8.00000 0.335377 0.167689 0.985840i \(-0.446370\pi\)
0.167689 + 0.985840i \(0.446370\pi\)
\(570\) 0 0
\(571\) 15.8745i 0.664327i −0.943222 0.332164i \(-0.892221\pi\)
0.943222 0.332164i \(-0.107779\pi\)
\(572\) −13.7477 + 12.1244i −0.574821 + 0.506945i
\(573\) 0 0
\(574\) 0 0
\(575\) 10.5830i 0.441342i
\(576\) 0 0
\(577\) 43.3013i 1.80266i 0.433138 + 0.901328i \(0.357406\pi\)
−0.433138 + 0.901328i \(0.642594\pi\)
\(578\) 15.5000 + 41.0091i 0.644715 + 1.70576i
\(579\) 0 0
\(580\) −11.4564 12.9904i −0.475703 0.539396i
\(581\) 0 0
\(582\) 0 0
\(583\) 18.5203i 0.767031i
\(584\) −9.16515 + 17.3205i −0.379257 + 0.716728i
\(585\) 0 0
\(586\) −20.6216 + 7.79423i −0.851870 + 0.321977i
\(587\) −22.9129 −0.945716 −0.472858 0.881139i \(-0.656778\pi\)
−0.472858 + 0.881139i \(0.656778\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −31.5000 + 11.9059i −1.29683 + 0.490157i
\(591\) 0 0
\(592\) 0 0
\(593\) 10.3923i 0.426761i −0.976969 0.213380i \(-0.931553\pi\)
0.976969 0.213380i \(-0.0684474\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 21.0000 18.5203i 0.860194 0.758619i
\(597\) 0 0
\(598\) −9.16515 24.2487i −0.374791 0.991604i
\(599\) 10.5830i 0.432410i 0.976348 + 0.216205i \(0.0693679\pi\)
−0.976348 + 0.216205i \(0.930632\pi\)
\(600\) 0 0
\(601\) 8.66025i 0.353259i 0.984277 + 0.176630i \(0.0565195\pi\)
−0.984277 + 0.176630i \(0.943481\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −17.5000 19.8431i −0.712065 0.807406i
\(605\) 6.92820i 0.281672i
\(606\) 0 0
\(607\) −13.7477 −0.558003 −0.279002 0.960291i \(-0.590003\pi\)
−0.279002 + 0.960291i \(0.590003\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 9.00000 + 23.8118i 0.364399 + 0.964110i
\(611\) 31.7490i 1.28443i
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 13.7477 + 36.3731i 0.554813 + 1.46790i
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 0 0
\(619\) −27.4955 −1.10514 −0.552568 0.833468i \(-0.686352\pi\)
−0.552568 + 0.833468i \(0.686352\pi\)
\(620\) −10.5000 11.9059i −0.421690 0.478152i
\(621\) 0 0
\(622\) −4.58258 12.1244i −0.183745 0.486142i
\(623\) 0 0
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 29.7867 11.2583i 1.19052 0.449973i
\(627\) 0 0
\(628\) 9.16515 + 10.3923i 0.365729 + 0.414698i
\(629\) 0 0
\(630\) 0 0
\(631\) 7.93725i 0.315977i −0.987441 0.157989i \(-0.949499\pi\)
0.987441 0.157989i \(-0.0505009\pi\)
\(632\) −10.5000 + 19.8431i −0.417668 + 0.789318i
\(633\) 0 0
\(634\) 3.50000 + 9.26013i 0.139003 + 0.367767i
\(635\) −13.7477 −0.545562
\(636\) 0 0
\(637\) 0 0
\(638\) −17.5000 + 6.61438i −0.692832 + 0.261866i
\(639\) 0 0
\(640\) −16.0390 11.2583i −0.633998 0.445025i
\(641\) 38.0000 1.50091 0.750455 0.660922i \(-0.229834\pi\)
0.750455 + 0.660922i \(0.229834\pi\)
\(642\) 0 0
\(643\) 18.3303 0.722877 0.361438 0.932396i \(-0.382286\pi\)
0.361438 + 0.932396i \(0.382286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.16515 0.360319 0.180160 0.983637i \(-0.442339\pi\)
0.180160 + 0.983637i \(0.442339\pi\)
\(648\) 0 0
\(649\) 36.3731i 1.42777i
\(650\) −9.16515 + 3.46410i −0.359487 + 0.135873i
\(651\) 0 0
\(652\) 21.0000 + 23.8118i 0.822423 + 0.932541i
\(653\) 43.0000 1.68272 0.841360 0.540475i \(-0.181755\pi\)
0.841360 + 0.540475i \(0.181755\pi\)
\(654\) 0 0
\(655\) 23.8118i 0.930403i
\(656\) 13.7477 + 1.73205i 0.536759 + 0.0676252i
\(657\) 0 0
\(658\) 0 0
\(659\) 26.4575i 1.03064i −0.856998 0.515319i \(-0.827673\pi\)
0.856998 0.515319i \(-0.172327\pi\)
\(660\) 0 0
\(661\) 6.92820i 0.269476i −0.990881 0.134738i \(-0.956981\pi\)
0.990881 0.134738i \(-0.0430193\pi\)
\(662\) 14.0000 5.29150i 0.544125 0.205660i
\(663\) 0 0
\(664\) −11.4564 6.06218i −0.444596 0.235258i
\(665\) 0 0
\(666\) 0 0
\(667\) 26.4575i 1.02444i
\(668\) 27.4955 24.2487i 1.06383 0.938211i
\(669\) 0 0
\(670\) 0 0
\(671\) 27.4955 1.06145
\(672\) 0 0
\(673\) 21.0000 0.809491 0.404745 0.914429i \(-0.367360\pi\)
0.404745 + 0.914429i \(0.367360\pi\)
\(674\) 10.5000 + 27.7804i 0.404445 + 1.07006i
\(675\) 0 0
\(676\) −1.50000 + 1.32288i −0.0576923 + 0.0508798i
\(677\) 22.5167i 0.865386i −0.901541 0.432693i \(-0.857563\pi\)
0.901541 0.432693i \(-0.142437\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 30.0000 + 15.8745i 1.15045 + 0.608760i
\(681\) 0 0
\(682\) −16.0390 + 6.06218i −0.614166 + 0.232133i
\(683\) 2.64575i 0.101237i 0.998718 + 0.0506184i \(0.0161192\pi\)
−0.998718 + 0.0506184i \(0.983881\pi\)
\(684\) 0 0
\(685\) 6.92820i 0.264713i
\(686\) 0 0
\(687\) 0 0
\(688\) 42.0000 + 5.29150i 1.60123 + 0.201737i
\(689\) 24.2487i 0.923802i
\(690\) 0 0
\(691\) 45.8258 1.74329 0.871647 0.490134i \(-0.163052\pi\)
0.871647 + 0.490134i \(0.163052\pi\)
\(692\) −18.3303 20.7846i −0.696814 0.790112i
\(693\) 0 0
\(694\) 7.00000 2.64575i 0.265716 0.100431i
\(695\) 15.8745i 0.602154i
\(696\) 0 0
\(697\) −24.0000 −0.909065
\(698\) 27.4955 10.3923i 1.04072 0.393355i
\(699\) 0 0
\(700\) 0 0
\(701\) −23.0000 −0.868698 −0.434349 0.900745i \(-0.643022\pi\)
−0.434349 + 0.900745i \(0.643022\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −17.5000 + 11.9059i −0.659556 + 0.448720i
\(705\) 0 0
\(706\) −9.16515 + 3.46410i −0.344935 + 0.130373i
\(707\) 0 0
\(708\) 0 0
\(709\) 42.0000 1.57734 0.788672 0.614815i \(-0.210769\pi\)
0.788672 + 0.614815i \(0.210769\pi\)
\(710\) −4.58258 12.1244i −0.171981 0.455019i
\(711\) 0 0
\(712\) −13.7477 + 25.9808i −0.515218 + 0.973670i
\(713\) 24.2487i 0.908121i
\(714\) 0 0
\(715\) 15.8745i 0.593673i
\(716\) −7.00000 7.93725i −0.261602 0.296629i
\(717\) 0 0
\(718\) 14.0000 5.29150i 0.522475 0.197477i
\(719\) −27.4955 −1.02541 −0.512704 0.858566i \(-0.671356\pi\)
−0.512704 + 0.858566i \(0.671356\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 9.50000 + 25.1346i 0.353553 + 0.935414i
\(723\) 0 0
\(724\) −4.58258 5.19615i −0.170310 0.193113i
\(725\) −10.0000 −0.371391
\(726\) 0 0
\(727\) −13.7477 −0.509875 −0.254937 0.966958i \(-0.582055\pi\)
−0.254937 + 0.966958i \(0.582055\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −6.00000 15.8745i −0.222070 0.587542i
\(731\) −73.3212 −2.71188
\(732\) 0 0
\(733\) 34.6410i 1.27950i −0.768585 0.639748i \(-0.779039\pi\)
0.768585 0.639748i \(-0.220961\pi\)
\(734\) −2.29129 6.06218i −0.0845730 0.223759i
\(735\) 0 0
\(736\) −7.00000 29.1033i −0.258023 1.07276i
\(737\) 0 0
\(738\) 0 0
\(739\) 47.6235i 1.75186i 0.482439 + 0.875930i \(0.339751\pi\)
−0.482439 + 0.875930i \(0.660249\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 21.1660i 0.776506i −0.921553 0.388253i \(-0.873079\pi\)
0.921553 0.388253i \(-0.126921\pi\)
\(744\) 0 0
\(745\) 24.2487i 0.888404i
\(746\) −17.0000 44.9778i −0.622414 1.64675i
\(747\) 0 0
\(748\) 27.4955 24.2487i 1.00533 0.886621i
\(749\) 0 0
\(750\) 0 0
\(751\) 13.2288i 0.482724i −0.970435 0.241362i \(-0.922406\pi\)
0.970435 0.241362i \(-0.0775941\pi\)
\(752\) 4.58258 36.3731i 0.167109 1.32639i
\(753\) 0 0
\(754\) 22.9129 8.66025i 0.834438 0.315388i
\(755\) 22.9129 0.833885
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 7.00000 2.64575i 0.254251 0.0960980i
\(759\) 0 0
\(760\) 0 0
\(761\) 38.1051i 1.38131i −0.723185 0.690655i \(-0.757322\pi\)
0.723185 0.690655i \(-0.242678\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −14.0000 15.8745i −0.506502 0.574320i
\(765\) 0 0
\(766\) 13.7477 + 36.3731i 0.496726 + 1.31421i
\(767\) 47.6235i 1.71959i
\(768\) 0 0
\(769\) 32.9090i 1.18673i −0.804934 0.593364i \(-0.797800\pi\)
0.804934 0.593364i \(-0.202200\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.50000 + 3.96863i −0.161959 + 0.142834i
\(773\) 41.5692i 1.49514i −0.664183 0.747570i \(-0.731220\pi\)
0.664183 0.747570i \(-0.268780\pi\)
\(774\) 0 0
\(775\) −9.16515 −0.329222
\(776\) 11.4564 21.6506i 0.411262 0.777213i
\(777\) 0 0
\(778\) 5.00000 + 13.2288i 0.179259 + 0.474274i
\(779\) 0 0
\(780\) 0 0
\(781\) −14.0000 −0.500959
\(782\) 18.3303 + 48.4974i 0.655490 + 1.73426i
\(783\) 0 0
\(784\) 0 0
\(785\) −12.0000 −0.428298
\(786\) 0 0
\(787\) −27.4955 −0.980107 −0.490054 0.871692i \(-0.663023\pi\)
−0.490054 + 0.871692i \(0.663023\pi\)
\(788\) 21.0000 18.5203i 0.748094 0.659757i
\(789\) 0 0
\(790\) −6.87386 18.1865i −0.244561 0.647048i
\(791\) 0 0
\(792\) 0 0
\(793\) −36.0000 −1.27840
\(794\) 18.3303 6.92820i 0.650518 0.245873i
\(795\) 0 0
\(796\) 27.4955 24.2487i 0.974551 0.859473i
\(797\) 15.5885i 0.552171i −0.961133 0.276086i \(-0.910963\pi\)
0.961133 0.276086i \(-0.0890374\pi\)
\(798\) 0 0
\(799\) 63.4980i 2.24640i
\(800\) −11.0000 + 2.64575i −0.388909 + 0.0935414i
\(801\) 0 0
\(802\) 4.00000 + 10.5830i 0.141245 + 0.373699i
\(803\) −18.3303 −0.646862
\(804\) 0 0
\(805\) 0 0