Properties

Label 560.2.bj.a.97.2
Level 560
Weight 2
Character 560.97
Analytic conductor 4.472
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bj (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{10})\)
Defining polynomial: \(x^{4} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.2
Root \(1.58114 + 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 560.97
Dual form 560.2.bj.a.433.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.58114 + 1.58114i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-2.58114 + 0.581139i) q^{7} +2.00000i q^{9} +O(q^{10})\) \(q+(1.58114 + 1.58114i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-2.58114 + 0.581139i) q^{7} +2.00000i q^{9} +1.00000 q^{11} +(1.58114 + 1.58114i) q^{13} +5.00000i q^{15} +(-1.58114 + 1.58114i) q^{17} +3.16228 q^{19} +(-5.00000 - 3.16228i) q^{21} +(-2.00000 + 2.00000i) q^{23} +5.00000i q^{25} +(1.58114 - 1.58114i) q^{27} +3.00000i q^{29} -3.16228i q^{31} +(1.58114 + 1.58114i) q^{33} +(-5.00000 - 3.16228i) q^{35} +(-6.00000 - 6.00000i) q^{37} +5.00000i q^{39} -9.48683i q^{41} +(3.00000 - 3.00000i) q^{43} +(-3.16228 + 3.16228i) q^{45} +(-4.74342 + 4.74342i) q^{47} +(6.32456 - 3.00000i) q^{49} -5.00000 q^{51} +(1.00000 - 1.00000i) q^{53} +(1.58114 + 1.58114i) q^{55} +(5.00000 + 5.00000i) q^{57} +9.48683 q^{59} +6.32456i q^{61} +(-1.16228 - 5.16228i) q^{63} +5.00000i q^{65} +(1.00000 + 1.00000i) q^{67} -6.32456 q^{69} +6.00000 q^{71} +(-7.90569 + 7.90569i) q^{75} +(-2.58114 + 0.581139i) q^{77} -13.0000i q^{79} +11.0000 q^{81} +(-3.16228 - 3.16228i) q^{83} -5.00000 q^{85} +(-4.74342 + 4.74342i) q^{87} +6.32456 q^{89} +(-5.00000 - 3.16228i) q^{91} +(5.00000 - 5.00000i) q^{93} +(5.00000 + 5.00000i) q^{95} +(1.58114 - 1.58114i) q^{97} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{7} + O(q^{10}) \) \( 4q - 4q^{7} + 4q^{11} - 20q^{21} - 8q^{23} - 20q^{35} - 24q^{37} + 12q^{43} - 20q^{51} + 4q^{53} + 20q^{57} + 8q^{63} + 4q^{67} + 24q^{71} - 4q^{77} + 44q^{81} - 20q^{85} - 20q^{91} + 20q^{93} + 20q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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 0
\(3\) 1.58114 + 1.58114i 0.912871 + 0.912871i 0.996497 0.0836263i \(-0.0266502\pi\)
−0.0836263 + 0.996497i \(0.526650\pi\)
\(4\) 0 0
\(5\) 1.58114 + 1.58114i 0.707107 + 0.707107i
\(6\) 0 0
\(7\) −2.58114 + 0.581139i −0.975579 + 0.219650i
\(8\) 0 0
\(9\) 2.00000i 0.666667i
\(10\) 0 0
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 0 0
\(13\) 1.58114 + 1.58114i 0.438529 + 0.438529i 0.891517 0.452988i \(-0.149642\pi\)
−0.452988 + 0.891517i \(0.649642\pi\)
\(14\) 0 0
\(15\) 5.00000i 1.29099i
\(16\) 0 0
\(17\) −1.58114 + 1.58114i −0.383482 + 0.383482i −0.872355 0.488873i \(-0.837408\pi\)
0.488873 + 0.872355i \(0.337408\pi\)
\(18\) 0 0
\(19\) 3.16228 0.725476 0.362738 0.931891i \(-0.381842\pi\)
0.362738 + 0.931891i \(0.381842\pi\)
\(20\) 0 0
\(21\) −5.00000 3.16228i −1.09109 0.690066i
\(22\) 0 0
\(23\) −2.00000 + 2.00000i −0.417029 + 0.417029i −0.884178 0.467150i \(-0.845281\pi\)
0.467150 + 0.884178i \(0.345281\pi\)
\(24\) 0 0
\(25\) 5.00000i 1.00000i
\(26\) 0 0
\(27\) 1.58114 1.58114i 0.304290 0.304290i
\(28\) 0 0
\(29\) 3.00000i 0.557086i 0.960424 + 0.278543i \(0.0898515\pi\)
−0.960424 + 0.278543i \(0.910149\pi\)
\(30\) 0 0
\(31\) 3.16228i 0.567962i −0.958830 0.283981i \(-0.908345\pi\)
0.958830 0.283981i \(-0.0916552\pi\)
\(32\) 0 0
\(33\) 1.58114 + 1.58114i 0.275241 + 0.275241i
\(34\) 0 0
\(35\) −5.00000 3.16228i −0.845154 0.534522i
\(36\) 0 0
\(37\) −6.00000 6.00000i −0.986394 0.986394i 0.0135147 0.999909i \(-0.495698\pi\)
−0.999909 + 0.0135147i \(0.995698\pi\)
\(38\) 0 0
\(39\) 5.00000i 0.800641i
\(40\) 0 0
\(41\) 9.48683i 1.48159i −0.671729 0.740797i \(-0.734448\pi\)
0.671729 0.740797i \(-0.265552\pi\)
\(42\) 0 0
\(43\) 3.00000 3.00000i 0.457496 0.457496i −0.440337 0.897833i \(-0.645141\pi\)
0.897833 + 0.440337i \(0.145141\pi\)
\(44\) 0 0
\(45\) −3.16228 + 3.16228i −0.471405 + 0.471405i
\(46\) 0 0
\(47\) −4.74342 + 4.74342i −0.691898 + 0.691898i −0.962649 0.270751i \(-0.912728\pi\)
0.270751 + 0.962649i \(0.412728\pi\)
\(48\) 0 0
\(49\) 6.32456 3.00000i 0.903508 0.428571i
\(50\) 0 0
\(51\) −5.00000 −0.700140
\(52\) 0 0
\(53\) 1.00000 1.00000i 0.137361 0.137361i −0.635083 0.772444i \(-0.719034\pi\)
0.772444 + 0.635083i \(0.219034\pi\)
\(54\) 0 0
\(55\) 1.58114 + 1.58114i 0.213201 + 0.213201i
\(56\) 0 0
\(57\) 5.00000 + 5.00000i 0.662266 + 0.662266i
\(58\) 0 0
\(59\) 9.48683 1.23508 0.617540 0.786539i \(-0.288129\pi\)
0.617540 + 0.786539i \(0.288129\pi\)
\(60\) 0 0
\(61\) 6.32456i 0.809776i 0.914366 + 0.404888i \(0.132690\pi\)
−0.914366 + 0.404888i \(0.867310\pi\)
\(62\) 0 0
\(63\) −1.16228 5.16228i −0.146433 0.650386i
\(64\) 0 0
\(65\) 5.00000i 0.620174i
\(66\) 0 0
\(67\) 1.00000 + 1.00000i 0.122169 + 0.122169i 0.765548 0.643379i \(-0.222468\pi\)
−0.643379 + 0.765548i \(0.722468\pi\)
\(68\) 0 0
\(69\) −6.32456 −0.761387
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 0 0
\(75\) −7.90569 + 7.90569i −0.912871 + 0.912871i
\(76\) 0 0
\(77\) −2.58114 + 0.581139i −0.294148 + 0.0662269i
\(78\) 0 0
\(79\) 13.0000i 1.46261i −0.682048 0.731307i \(-0.738911\pi\)
0.682048 0.731307i \(-0.261089\pi\)
\(80\) 0 0
\(81\) 11.0000 1.22222
\(82\) 0 0
\(83\) −3.16228 3.16228i −0.347105 0.347105i 0.511925 0.859030i \(-0.328933\pi\)
−0.859030 + 0.511925i \(0.828933\pi\)
\(84\) 0 0
\(85\) −5.00000 −0.542326
\(86\) 0 0
\(87\) −4.74342 + 4.74342i −0.508548 + 0.508548i
\(88\) 0 0
\(89\) 6.32456 0.670402 0.335201 0.942147i \(-0.391196\pi\)
0.335201 + 0.942147i \(0.391196\pi\)
\(90\) 0 0
\(91\) −5.00000 3.16228i −0.524142 0.331497i
\(92\) 0 0
\(93\) 5.00000 5.00000i 0.518476 0.518476i
\(94\) 0 0
\(95\) 5.00000 + 5.00000i 0.512989 + 0.512989i
\(96\) 0 0
\(97\) 1.58114 1.58114i 0.160540 0.160540i −0.622266 0.782806i \(-0.713788\pi\)
0.782806 + 0.622266i \(0.213788\pi\)
\(98\) 0 0
\(99\) 2.00000i 0.201008i
\(100\) 0 0
\(101\) 3.16228i 0.314658i −0.987546 0.157329i \(-0.949712\pi\)
0.987546 0.157329i \(-0.0502884\pi\)
\(102\) 0 0
\(103\) 11.0680 + 11.0680i 1.09056 + 1.09056i 0.995469 + 0.0950911i \(0.0303142\pi\)
0.0950911 + 0.995469i \(0.469686\pi\)
\(104\) 0 0
\(105\) −2.90569 12.9057i −0.283567 1.25947i
\(106\) 0 0
\(107\) 3.00000 + 3.00000i 0.290021 + 0.290021i 0.837088 0.547068i \(-0.184256\pi\)
−0.547068 + 0.837088i \(0.684256\pi\)
\(108\) 0 0
\(109\) 7.00000i 0.670478i −0.942133 0.335239i \(-0.891183\pi\)
0.942133 0.335239i \(-0.108817\pi\)
\(110\) 0 0
\(111\) 18.9737i 1.80090i
\(112\) 0 0
\(113\) 12.0000 12.0000i 1.12887 1.12887i 0.138503 0.990362i \(-0.455771\pi\)
0.990362 0.138503i \(-0.0442291\pi\)
\(114\) 0 0
\(115\) −6.32456 −0.589768
\(116\) 0 0
\(117\) −3.16228 + 3.16228i −0.292353 + 0.292353i
\(118\) 0 0
\(119\) 3.16228 5.00000i 0.289886 0.458349i
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) 15.0000 15.0000i 1.35250 1.35250i
\(124\) 0 0
\(125\) −7.90569 + 7.90569i −0.707107 + 0.707107i
\(126\) 0 0
\(127\) −9.00000 9.00000i −0.798621 0.798621i 0.184257 0.982878i \(-0.441012\pi\)
−0.982878 + 0.184257i \(0.941012\pi\)
\(128\) 0 0
\(129\) 9.48683 0.835269
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −8.16228 + 1.83772i −0.707759 + 0.159351i
\(134\) 0 0
\(135\) 5.00000 0.430331
\(136\) 0 0
\(137\) 2.00000 + 2.00000i 0.170872 + 0.170872i 0.787362 0.616491i \(-0.211446\pi\)
−0.616491 + 0.787362i \(0.711446\pi\)
\(138\) 0 0
\(139\) −18.9737 −1.60933 −0.804663 0.593732i \(-0.797654\pi\)
−0.804663 + 0.593732i \(0.797654\pi\)
\(140\) 0 0
\(141\) −15.0000 −1.26323
\(142\) 0 0
\(143\) 1.58114 + 1.58114i 0.132221 + 0.132221i
\(144\) 0 0
\(145\) −4.74342 + 4.74342i −0.393919 + 0.393919i
\(146\) 0 0
\(147\) 14.7434 + 5.25658i 1.21602 + 0.433556i
\(148\) 0 0
\(149\) 12.0000i 0.983078i −0.870855 0.491539i \(-0.836434\pi\)
0.870855 0.491539i \(-0.163566\pi\)
\(150\) 0 0
\(151\) −9.00000 −0.732410 −0.366205 0.930534i \(-0.619343\pi\)
−0.366205 + 0.930534i \(0.619343\pi\)
\(152\) 0 0
\(153\) −3.16228 3.16228i −0.255655 0.255655i
\(154\) 0 0
\(155\) 5.00000 5.00000i 0.401610 0.401610i
\(156\) 0 0
\(157\) −6.32456 + 6.32456i −0.504754 + 0.504754i −0.912912 0.408157i \(-0.866172\pi\)
0.408157 + 0.912912i \(0.366172\pi\)
\(158\) 0 0
\(159\) 3.16228 0.250785
\(160\) 0 0
\(161\) 4.00000 6.32456i 0.315244 0.498445i
\(162\) 0 0
\(163\) −6.00000 + 6.00000i −0.469956 + 0.469956i −0.901900 0.431944i \(-0.857828\pi\)
0.431944 + 0.901900i \(0.357828\pi\)
\(164\) 0 0
\(165\) 5.00000i 0.389249i
\(166\) 0 0
\(167\) 11.0680 11.0680i 0.856465 0.856465i −0.134454 0.990920i \(-0.542928\pi\)
0.990920 + 0.134454i \(0.0429282\pi\)
\(168\) 0 0
\(169\) 8.00000i 0.615385i
\(170\) 0 0
\(171\) 6.32456i 0.483651i
\(172\) 0 0
\(173\) 11.0680 + 11.0680i 0.841482 + 0.841482i 0.989052 0.147569i \(-0.0471450\pi\)
−0.147569 + 0.989052i \(0.547145\pi\)
\(174\) 0 0
\(175\) −2.90569 12.9057i −0.219650 0.975579i
\(176\) 0 0
\(177\) 15.0000 + 15.0000i 1.12747 + 1.12747i
\(178\) 0 0
\(179\) 6.00000i 0.448461i 0.974536 + 0.224231i \(0.0719869\pi\)
−0.974536 + 0.224231i \(0.928013\pi\)
\(180\) 0 0
\(181\) 22.1359i 1.64535i −0.568511 0.822676i \(-0.692480\pi\)
0.568511 0.822676i \(-0.307520\pi\)
\(182\) 0 0
\(183\) −10.0000 + 10.0000i −0.739221 + 0.739221i
\(184\) 0 0
\(185\) 18.9737i 1.39497i
\(186\) 0 0
\(187\) −1.58114 + 1.58114i −0.115624 + 0.115624i
\(188\) 0 0
\(189\) −3.16228 + 5.00000i −0.230022 + 0.363696i
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 0 0
\(193\) −8.00000 + 8.00000i −0.575853 + 0.575853i −0.933758 0.357905i \(-0.883491\pi\)
0.357905 + 0.933758i \(0.383491\pi\)
\(194\) 0 0
\(195\) −7.90569 + 7.90569i −0.566139 + 0.566139i
\(196\) 0 0
\(197\) −1.00000 1.00000i −0.0712470 0.0712470i 0.670585 0.741832i \(-0.266043\pi\)
−0.741832 + 0.670585i \(0.766043\pi\)
\(198\) 0 0
\(199\) −9.48683 −0.672504 −0.336252 0.941772i \(-0.609159\pi\)
−0.336252 + 0.941772i \(0.609159\pi\)
\(200\) 0 0
\(201\) 3.16228i 0.223050i
\(202\) 0 0
\(203\) −1.74342 7.74342i −0.122364 0.543481i
\(204\) 0 0
\(205\) 15.0000 15.0000i 1.04765 1.04765i
\(206\) 0 0
\(207\) −4.00000 4.00000i −0.278019 0.278019i
\(208\) 0 0
\(209\) 3.16228 0.218739
\(210\) 0 0
\(211\) −17.0000 −1.17033 −0.585164 0.810915i \(-0.698970\pi\)
−0.585164 + 0.810915i \(0.698970\pi\)
\(212\) 0 0
\(213\) 9.48683 + 9.48683i 0.650027 + 0.650027i
\(214\) 0 0
\(215\) 9.48683 0.646997
\(216\) 0 0
\(217\) 1.83772 + 8.16228i 0.124753 + 0.554092i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −5.00000 −0.336336
\(222\) 0 0
\(223\) 14.2302 + 14.2302i 0.952928 + 0.952928i 0.998941 0.0460129i \(-0.0146515\pi\)
−0.0460129 + 0.998941i \(0.514652\pi\)
\(224\) 0 0
\(225\) −10.0000 −0.666667
\(226\) 0 0
\(227\) −1.58114 + 1.58114i −0.104944 + 0.104944i −0.757629 0.652685i \(-0.773642\pi\)
0.652685 + 0.757629i \(0.273642\pi\)
\(228\) 0 0
\(229\) −15.8114 −1.04485 −0.522423 0.852686i \(-0.674972\pi\)
−0.522423 + 0.852686i \(0.674972\pi\)
\(230\) 0 0
\(231\) −5.00000 3.16228i −0.328976 0.208063i
\(232\) 0 0
\(233\) −18.0000 + 18.0000i −1.17922 + 1.17922i −0.199276 + 0.979943i \(0.563859\pi\)
−0.979943 + 0.199276i \(0.936141\pi\)
\(234\) 0 0
\(235\) −15.0000 −0.978492
\(236\) 0 0
\(237\) 20.5548 20.5548i 1.33518 1.33518i
\(238\) 0 0
\(239\) 19.0000i 1.22901i −0.788914 0.614504i \(-0.789356\pi\)
0.788914 0.614504i \(-0.210644\pi\)
\(240\) 0 0
\(241\) 25.2982i 1.62960i 0.579741 + 0.814801i \(0.303154\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 0 0
\(243\) 12.6491 + 12.6491i 0.811441 + 0.811441i
\(244\) 0 0
\(245\) 14.7434 + 5.25658i 0.941922 + 0.335831i
\(246\) 0 0
\(247\) 5.00000 + 5.00000i 0.318142 + 0.318142i
\(248\) 0 0
\(249\) 10.0000i 0.633724i
\(250\) 0 0
\(251\) 12.6491i 0.798405i −0.916863 0.399202i \(-0.869287\pi\)
0.916863 0.399202i \(-0.130713\pi\)
\(252\) 0 0
\(253\) −2.00000 + 2.00000i −0.125739 + 0.125739i
\(254\) 0 0
\(255\) −7.90569 7.90569i −0.495074 0.495074i
\(256\) 0 0
\(257\) −12.6491 + 12.6491i −0.789030 + 0.789030i −0.981335 0.192305i \(-0.938404\pi\)
0.192305 + 0.981335i \(0.438404\pi\)
\(258\) 0 0
\(259\) 18.9737 + 12.0000i 1.17897 + 0.745644i
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) −7.00000 + 7.00000i −0.431638 + 0.431638i −0.889185 0.457547i \(-0.848728\pi\)
0.457547 + 0.889185i \(0.348728\pi\)
\(264\) 0 0
\(265\) 3.16228 0.194257
\(266\) 0 0
\(267\) 10.0000 + 10.0000i 0.611990 + 0.611990i
\(268\) 0 0
\(269\) 18.9737 1.15684 0.578422 0.815737i \(-0.303669\pi\)
0.578422 + 0.815737i \(0.303669\pi\)
\(270\) 0 0
\(271\) 12.6491i 0.768379i 0.923254 + 0.384189i \(0.125519\pi\)
−0.923254 + 0.384189i \(0.874481\pi\)
\(272\) 0 0
\(273\) −2.90569 12.9057i −0.175861 0.781088i
\(274\) 0 0
\(275\) 5.00000i 0.301511i
\(276\) 0 0
\(277\) −18.0000 18.0000i −1.08152 1.08152i −0.996368 0.0851468i \(-0.972864\pi\)
−0.0851468 0.996368i \(-0.527136\pi\)
\(278\) 0 0
\(279\) 6.32456 0.378641
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 0 0
\(283\) −4.74342 4.74342i −0.281967 0.281967i 0.551926 0.833893i \(-0.313893\pi\)
−0.833893 + 0.551926i \(0.813893\pi\)
\(284\) 0 0
\(285\) 15.8114i 0.936586i
\(286\) 0 0
\(287\) 5.51317 + 24.4868i 0.325432 + 1.44541i
\(288\) 0 0
\(289\) 12.0000i 0.705882i
\(290\) 0 0
\(291\) 5.00000 0.293105
\(292\) 0 0
\(293\) 7.90569 + 7.90569i 0.461856 + 0.461856i 0.899263 0.437408i \(-0.144103\pi\)
−0.437408 + 0.899263i \(0.644103\pi\)
\(294\) 0 0
\(295\) 15.0000 + 15.0000i 0.873334 + 0.873334i
\(296\) 0 0
\(297\) 1.58114 1.58114i 0.0917470 0.0917470i
\(298\) 0 0
\(299\) −6.32456 −0.365758
\(300\) 0 0
\(301\) −6.00000 + 9.48683i −0.345834 + 0.546812i
\(302\) 0 0
\(303\) 5.00000 5.00000i 0.287242 0.287242i
\(304\) 0 0
\(305\) −10.0000 + 10.0000i −0.572598 + 0.572598i
\(306\) 0 0
\(307\) −4.74342 + 4.74342i −0.270721 + 0.270721i −0.829390 0.558669i \(-0.811312\pi\)
0.558669 + 0.829390i \(0.311312\pi\)
\(308\) 0 0
\(309\) 35.0000i 1.99108i
\(310\) 0 0
\(311\) 22.1359i 1.25521i 0.778530 + 0.627607i \(0.215966\pi\)
−0.778530 + 0.627607i \(0.784034\pi\)
\(312\) 0 0
\(313\) 14.2302 + 14.2302i 0.804341 + 0.804341i 0.983771 0.179430i \(-0.0574252\pi\)
−0.179430 + 0.983771i \(0.557425\pi\)
\(314\) 0 0
\(315\) 6.32456 10.0000i 0.356348 0.563436i
\(316\) 0 0
\(317\) 19.0000 + 19.0000i 1.06715 + 1.06715i 0.997577 + 0.0695692i \(0.0221625\pi\)
0.0695692 + 0.997577i \(0.477838\pi\)
\(318\) 0 0
\(319\) 3.00000i 0.167968i
\(320\) 0 0
\(321\) 9.48683i 0.529503i
\(322\) 0 0
\(323\) −5.00000 + 5.00000i −0.278207 + 0.278207i
\(324\) 0 0
\(325\) −7.90569 + 7.90569i −0.438529 + 0.438529i
\(326\) 0 0
\(327\) 11.0680 11.0680i 0.612060 0.612060i
\(328\) 0 0
\(329\) 9.48683 15.0000i 0.523026 0.826977i
\(330\) 0 0
\(331\) 6.00000 0.329790 0.164895 0.986311i \(-0.447272\pi\)
0.164895 + 0.986311i \(0.447272\pi\)
\(332\) 0 0
\(333\) 12.0000 12.0000i 0.657596 0.657596i
\(334\) 0 0
\(335\) 3.16228i 0.172774i
\(336\) 0 0
\(337\) −8.00000 8.00000i −0.435788 0.435788i 0.454804 0.890592i \(-0.349709\pi\)
−0.890592 + 0.454804i \(0.849709\pi\)
\(338\) 0 0
\(339\) 37.9473 2.06102
\(340\) 0 0
\(341\) 3.16228i 0.171247i
\(342\) 0 0
\(343\) −14.5811 + 11.4189i −0.787307 + 0.616561i
\(344\) 0 0
\(345\) −10.0000 10.0000i −0.538382 0.538382i
\(346\) 0 0
\(347\) −24.0000 24.0000i −1.28839 1.28839i −0.935766 0.352621i \(-0.885290\pi\)
−0.352621 0.935766i \(-0.614710\pi\)
\(348\) 0 0
\(349\) −34.7851 −1.86200 −0.931001 0.365018i \(-0.881063\pi\)
−0.931001 + 0.365018i \(0.881063\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) −14.2302 14.2302i −0.757400 0.757400i 0.218449 0.975848i \(-0.429900\pi\)
−0.975848 + 0.218449i \(0.929900\pi\)
\(354\) 0 0
\(355\) 9.48683 + 9.48683i 0.503509 + 0.503509i
\(356\) 0 0
\(357\) 12.9057 2.90569i 0.683042 0.153786i
\(358\) 0 0
\(359\) 22.0000i 1.16112i 0.814219 + 0.580558i \(0.197165\pi\)
−0.814219 + 0.580558i \(0.802835\pi\)
\(360\) 0 0
\(361\) −9.00000 −0.473684
\(362\) 0 0
\(363\) −15.8114 15.8114i −0.829883 0.829883i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −17.3925 + 17.3925i −0.907883 + 0.907883i −0.996101 0.0882186i \(-0.971883\pi\)
0.0882186 + 0.996101i \(0.471883\pi\)
\(368\) 0 0
\(369\) 18.9737 0.987730
\(370\) 0 0
\(371\) −2.00000 + 3.16228i −0.103835 + 0.164177i
\(372\) 0 0
\(373\) 12.0000 12.0000i 0.621336 0.621336i −0.324537 0.945873i \(-0.605208\pi\)
0.945873 + 0.324537i \(0.105208\pi\)
\(374\) 0 0
\(375\) −25.0000 −1.29099
\(376\) 0 0
\(377\) −4.74342 + 4.74342i −0.244298 + 0.244298i
\(378\) 0 0
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) 0 0
\(381\) 28.4605i 1.45808i
\(382\) 0 0
\(383\) −15.8114 15.8114i −0.807924 0.807924i 0.176395 0.984319i \(-0.443556\pi\)
−0.984319 + 0.176395i \(0.943556\pi\)
\(384\) 0 0
\(385\) −5.00000 3.16228i −0.254824 0.161165i
\(386\) 0 0
\(387\) 6.00000 + 6.00000i 0.304997 + 0.304997i
\(388\) 0 0
\(389\) 23.0000i 1.16615i 0.812420 + 0.583073i \(0.198150\pi\)
−0.812420 + 0.583073i \(0.801850\pi\)
\(390\) 0 0
\(391\) 6.32456i 0.319847i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 20.5548 20.5548i 1.03422 1.03422i
\(396\) 0 0
\(397\) 23.7171 23.7171i 1.19033 1.19033i 0.213351 0.976976i \(-0.431562\pi\)
0.976976 0.213351i \(-0.0684376\pi\)
\(398\) 0 0
\(399\) −15.8114 10.0000i −0.791559 0.500626i
\(400\) 0 0
\(401\) −1.00000 −0.0499376 −0.0249688 0.999688i \(-0.507949\pi\)
−0.0249688 + 0.999688i \(0.507949\pi\)
\(402\) 0 0
\(403\) 5.00000 5.00000i 0.249068 0.249068i
\(404\) 0 0
\(405\) 17.3925 + 17.3925i 0.864242 + 0.864242i
\(406\) 0 0
\(407\) −6.00000 6.00000i −0.297409 0.297409i
\(408\) 0 0
\(409\) −3.16228 −0.156365 −0.0781823 0.996939i \(-0.524912\pi\)
−0.0781823 + 0.996939i \(0.524912\pi\)
\(410\) 0 0
\(411\) 6.32456i 0.311967i
\(412\) 0 0
\(413\) −24.4868 + 5.51317i −1.20492 + 0.271285i
\(414\) 0 0
\(415\) 10.0000i 0.490881i
\(416\) 0 0
\(417\) −30.0000 30.0000i −1.46911 1.46911i
\(418\) 0 0
\(419\) −15.8114 −0.772437 −0.386218 0.922407i \(-0.626219\pi\)
−0.386218 + 0.922407i \(0.626219\pi\)
\(420\) 0 0
\(421\) 19.0000 0.926003 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(422\) 0 0
\(423\) −9.48683 9.48683i −0.461266 0.461266i
\(424\) 0 0
\(425\) −7.90569 7.90569i −0.383482 0.383482i
\(426\) 0 0
\(427\) −3.67544 16.3246i −0.177867 0.790001i
\(428\) 0 0
\(429\) 5.00000i 0.241402i
\(430\) 0 0
\(431\) 23.0000 1.10787 0.553936 0.832560i \(-0.313125\pi\)
0.553936 + 0.832560i \(0.313125\pi\)
\(432\) 0 0
\(433\) −9.48683 9.48683i −0.455908 0.455908i 0.441402 0.897310i \(-0.354481\pi\)
−0.897310 + 0.441402i \(0.854481\pi\)
\(434\) 0 0
\(435\) −15.0000 −0.719195
\(436\) 0 0
\(437\) −6.32456 + 6.32456i −0.302545 + 0.302545i
\(438\) 0 0
\(439\) −12.6491 −0.603709 −0.301855 0.953354i \(-0.597606\pi\)
−0.301855 + 0.953354i \(0.597606\pi\)
\(440\) 0 0
\(441\) 6.00000 + 12.6491i 0.285714 + 0.602339i
\(442\) 0 0
\(443\) −1.00000 + 1.00000i −0.0475114 + 0.0475114i −0.730463 0.682952i \(-0.760696\pi\)
0.682952 + 0.730463i \(0.260696\pi\)
\(444\) 0 0
\(445\) 10.0000 + 10.0000i 0.474045 + 0.474045i
\(446\) 0 0
\(447\) 18.9737 18.9737i 0.897424 0.897424i
\(448\) 0 0
\(449\) 17.0000i 0.802280i −0.916017 0.401140i \(-0.868614\pi\)
0.916017 0.401140i \(-0.131386\pi\)
\(450\) 0 0
\(451\) 9.48683i 0.446718i
\(452\) 0 0
\(453\) −14.2302 14.2302i −0.668595 0.668595i
\(454\) 0 0
\(455\) −2.90569 12.9057i −0.136221 0.605028i
\(456\) 0 0
\(457\) −1.00000 1.00000i −0.0467780 0.0467780i 0.683331 0.730109i \(-0.260531\pi\)
−0.730109 + 0.683331i \(0.760531\pi\)
\(458\) 0 0
\(459\) 5.00000i 0.233380i
\(460\) 0 0
\(461\) 6.32456i 0.294564i −0.989095 0.147282i \(-0.952948\pi\)
0.989095 0.147282i \(-0.0470525\pi\)
\(462\) 0 0
\(463\) 4.00000 4.00000i 0.185896 0.185896i −0.608023 0.793919i \(-0.708037\pi\)
0.793919 + 0.608023i \(0.208037\pi\)
\(464\) 0 0
\(465\) 15.8114 0.733236
\(466\) 0 0
\(467\) −11.0680 + 11.0680i −0.512165 + 0.512165i −0.915189 0.403025i \(-0.867959\pi\)
0.403025 + 0.915189i \(0.367959\pi\)
\(468\) 0 0
\(469\) −3.16228 2.00000i −0.146020 0.0923514i
\(470\) 0 0
\(471\) −20.0000 −0.921551
\(472\) 0 0
\(473\) 3.00000 3.00000i 0.137940 0.137940i
\(474\) 0 0
\(475\) 15.8114i 0.725476i
\(476\) 0 0
\(477\) 2.00000 + 2.00000i 0.0915737 + 0.0915737i
\(478\) 0 0
\(479\) −6.32456 −0.288976 −0.144488 0.989507i \(-0.546154\pi\)
−0.144488 + 0.989507i \(0.546154\pi\)
\(480\) 0 0
\(481\) 18.9737i 0.865125i
\(482\) 0 0
\(483\) 16.3246 3.67544i 0.742793 0.167239i
\(484\) 0 0
\(485\) 5.00000 0.227038
\(486\) 0 0
\(487\) −4.00000 4.00000i −0.181257 0.181257i 0.610646 0.791904i \(-0.290910\pi\)
−0.791904 + 0.610646i \(0.790910\pi\)
\(488\) 0 0
\(489\) −18.9737 −0.858019
\(490\) 0 0
\(491\) 41.0000 1.85030 0.925152 0.379597i \(-0.123937\pi\)
0.925152 + 0.379597i \(0.123937\pi\)
\(492\) 0 0
\(493\) −4.74342 4.74342i −0.213633 0.213633i
\(494\) 0 0
\(495\) −3.16228 + 3.16228i −0.142134 + 0.142134i
\(496\) 0 0
\(497\) −15.4868 + 3.48683i −0.694679 + 0.156406i
\(498\) 0 0
\(499\) 19.0000i 0.850557i −0.905063 0.425278i \(-0.860176\pi\)
0.905063 0.425278i \(-0.139824\pi\)
\(500\) 0 0
\(501\) 35.0000 1.56368
\(502\) 0 0
\(503\) 7.90569 + 7.90569i 0.352497 + 0.352497i 0.861038 0.508541i \(-0.169815\pi\)
−0.508541 + 0.861038i \(0.669815\pi\)
\(504\) 0 0
\(505\) 5.00000 5.00000i 0.222497 0.222497i
\(506\) 0 0
\(507\) 12.6491 12.6491i 0.561767 0.561767i
\(508\) 0 0
\(509\) −18.9737 −0.840993 −0.420496 0.907294i \(-0.638144\pi\)
−0.420496 + 0.907294i \(0.638144\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 5.00000 5.00000i 0.220755 0.220755i
\(514\) 0 0
\(515\) 35.0000i 1.54228i
\(516\) 0 0
\(517\) −4.74342 + 4.74342i −0.208615 + 0.208615i
\(518\) 0 0
\(519\) 35.0000i 1.53633i
\(520\) 0 0
\(521\) 41.1096i 1.80104i 0.434810 + 0.900522i \(0.356816\pi\)
−0.434810 + 0.900522i \(0.643184\pi\)
\(522\) 0 0
\(523\) −18.9737 18.9737i −0.829660 0.829660i 0.157809 0.987470i \(-0.449557\pi\)
−0.987470 + 0.157809i \(0.949557\pi\)
\(524\) 0 0
\(525\) 15.8114 25.0000i 0.690066 1.09109i
\(526\) 0 0
\(527\) 5.00000 + 5.00000i 0.217803 + 0.217803i
\(528\) 0 0
\(529\) 15.0000i 0.652174i
\(530\) 0 0
\(531\) 18.9737i 0.823387i
\(532\) 0 0
\(533\) 15.0000 15.0000i 0.649722 0.649722i
\(534\) 0 0
\(535\) 9.48683i 0.410152i
\(536\) 0 0
\(537\) −9.48683 + 9.48683i −0.409387 + 0.409387i
\(538\) 0 0
\(539\) 6.32456 3.00000i 0.272418 0.129219i
\(540\) 0 0
\(541\) 9.00000 0.386940 0.193470 0.981106i \(-0.438026\pi\)
0.193470 + 0.981106i \(0.438026\pi\)
\(542\) 0 0
\(543\) 35.0000 35.0000i 1.50199 1.50199i
\(544\) 0 0
\(545\) 11.0680 11.0680i 0.474100 0.474100i
\(546\) 0 0
\(547\) −14.0000 14.0000i −0.598597 0.598597i 0.341342 0.939939i \(-0.389118\pi\)
−0.939939 + 0.341342i \(0.889118\pi\)
\(548\) 0 0
\(549\) −12.6491 −0.539851
\(550\) 0 0
\(551\) 9.48683i 0.404153i
\(552\) 0 0
\(553\) 7.55480 + 33.5548i 0.321263 + 1.42690i
\(554\) 0 0
\(555\) 30.0000 30.0000i 1.27343 1.27343i
\(556\) 0 0
\(557\) −6.00000 6.00000i −0.254228 0.254228i 0.568473 0.822702i \(-0.307534\pi\)
−0.822702 + 0.568473i \(0.807534\pi\)
\(558\) 0 0
\(559\) 9.48683 0.401250
\(560\) 0 0
\(561\) −5.00000 −0.211100
\(562\) 0 0
\(563\) 9.48683 + 9.48683i 0.399822 + 0.399822i 0.878170 0.478348i \(-0.158764\pi\)
−0.478348 + 0.878170i \(0.658764\pi\)
\(564\) 0 0
\(565\) 37.9473 1.59646
\(566\) 0 0
\(567\) −28.3925 + 6.39253i −1.19237 + 0.268461i
\(568\) 0 0
\(569\) 32.0000i 1.34151i −0.741679 0.670755i \(-0.765970\pi\)
0.741679 0.670755i \(-0.234030\pi\)
\(570\) 0 0
\(571\) 26.0000 1.08807 0.544033 0.839064i \(-0.316897\pi\)
0.544033 + 0.839064i \(0.316897\pi\)
\(572\) 0 0
\(573\) 4.74342 + 4.74342i 0.198159 + 0.198159i
\(574\) 0 0
\(575\) −10.0000 10.0000i −0.417029 0.417029i
\(576\) 0 0
\(577\) −20.5548 + 20.5548i −0.855708 + 0.855708i −0.990829 0.135121i \(-0.956858\pi\)
0.135121 + 0.990829i \(0.456858\pi\)
\(578\) 0 0
\(579\) −25.2982 −1.05136
\(580\) 0 0
\(581\) 10.0000 + 6.32456i 0.414870 + 0.262387i
\(582\) 0 0
\(583\) 1.00000 1.00000i 0.0414158 0.0414158i
\(584\) 0 0
\(585\) −10.0000 −0.413449
\(586\) 0 0
\(587\) −15.8114 + 15.8114i −0.652606 + 0.652606i −0.953620 0.301014i \(-0.902675\pi\)
0.301014 + 0.953620i \(0.402675\pi\)
\(588\) 0 0
\(589\) 10.0000i 0.412043i
\(590\) 0 0
\(591\) 3.16228i 0.130079i
\(592\) 0 0
\(593\) −20.5548 20.5548i −0.844085 0.844085i 0.145303 0.989387i \(-0.453584\pi\)
−0.989387 + 0.145303i \(0.953584\pi\)
\(594\) 0 0
\(595\) 12.9057 2.90569i 0.529082 0.119122i
\(596\) 0 0
\(597\) −15.0000 15.0000i −0.613909 0.613909i
\(598\) 0 0
\(599\) 13.0000i 0.531166i −0.964088 0.265583i \(-0.914436\pi\)
0.964088 0.265583i \(-0.0855644\pi\)
\(600\) 0 0
\(601\) 22.1359i 0.902944i 0.892285 + 0.451472i \(0.149101\pi\)
−0.892285 + 0.451472i \(0.850899\pi\)
\(602\) 0 0
\(603\) −2.00000 + 2.00000i −0.0814463 + 0.0814463i
\(604\) 0 0
\(605\) −15.8114 15.8114i −0.642824 0.642824i
\(606\) 0 0
\(607\) 14.2302 14.2302i 0.577588 0.577588i −0.356650 0.934238i \(-0.616081\pi\)
0.934238 + 0.356650i \(0.116081\pi\)
\(608\) 0 0
\(609\) 9.48683 15.0000i 0.384426 0.607831i
\(610\) 0 0
\(611\) −15.0000 −0.606835
\(612\) 0 0
\(613\) 17.0000 17.0000i 0.686624 0.686624i −0.274861 0.961484i \(-0.588632\pi\)
0.961484 + 0.274861i \(0.0886317\pi\)
\(614\) 0 0
\(615\) 47.4342 1.91273
\(616\) 0 0
\(617\) 4.00000 + 4.00000i 0.161034 + 0.161034i 0.783025 0.621991i \(-0.213676\pi\)
−0.621991 + 0.783025i \(0.713676\pi\)
\(618\) 0 0
\(619\) −25.2982 −1.01682 −0.508411 0.861115i \(-0.669767\pi\)
−0.508411 + 0.861115i \(0.669767\pi\)
\(620\) 0 0
\(621\) 6.32456i 0.253796i
\(622\) 0 0
\(623\) −16.3246 + 3.67544i −0.654029 + 0.147254i
\(624\) 0 0
\(625\) −25.0000 −1.00000
\(626\) 0 0
\(627\) 5.00000 + 5.00000i 0.199681 + 0.199681i
\(628\) 0 0
\(629\) 18.9737 0.756530
\(630\) 0 0
\(631\) 31.0000 1.23409 0.617045 0.786928i \(-0.288330\pi\)
0.617045 + 0.786928i \(0.288330\pi\)
\(632\) 0 0
\(633\) −26.8794 26.8794i −1.06836 1.06836i
\(634\) 0 0
\(635\) 28.4605i 1.12942i
\(636\) 0 0
\(637\) 14.7434 + 5.25658i 0.584155 + 0.208273i
\(638\) 0 0
\(639\) 12.0000i 0.474713i
\(640\) 0 0
\(641\) 44.0000 1.73790 0.868948 0.494904i \(-0.164797\pi\)
0.868948 + 0.494904i \(0.164797\pi\)
\(642\) 0 0
\(643\) 4.74342 + 4.74342i 0.187062 + 0.187062i 0.794425 0.607363i \(-0.207772\pi\)
−0.607363 + 0.794425i \(0.707772\pi\)
\(644\) 0 0
\(645\) 15.0000 + 15.0000i 0.590624 + 0.590624i
\(646\) 0 0
\(647\) 12.6491 12.6491i 0.497288 0.497288i −0.413305 0.910593i \(-0.635626\pi\)
0.910593 + 0.413305i \(0.135626\pi\)
\(648\) 0 0
\(649\) 9.48683 0.372391
\(650\) 0 0
\(651\) −10.0000 + 15.8114i −0.391931 + 0.619697i
\(652\) 0 0
\(653\) −19.0000 + 19.0000i −0.743527 + 0.743527i −0.973255 0.229728i \(-0.926216\pi\)
0.229728 + 0.973255i \(0.426216\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.00000i 0.0389545i 0.999810 + 0.0194772i \(0.00620019\pi\)
−0.999810 + 0.0194772i \(0.993800\pi\)
\(660\) 0 0
\(661\) 12.6491i 0.491993i −0.969271 0.245997i \(-0.920885\pi\)
0.969271 0.245997i \(-0.0791152\pi\)
\(662\) 0 0
\(663\) −7.90569 7.90569i −0.307032 0.307032i
\(664\) 0 0
\(665\) −15.8114 10.0000i −0.613139 0.387783i
\(666\) 0 0
\(667\) −6.00000 6.00000i −0.232321 0.232321i
\(668\) 0 0
\(669\) 45.0000i 1.73980i
\(670\) 0 0
\(671\) 6.32456i 0.244157i
\(672\) 0 0
\(673\) −24.0000 + 24.0000i −0.925132 + 0.925132i −0.997386 0.0722542i \(-0.976981\pi\)
0.0722542 + 0.997386i \(0.476981\pi\)
\(674\) 0 0
\(675\) 7.90569 + 7.90569i 0.304290 + 0.304290i
\(676\) 0 0
\(677\) 14.2302 14.2302i 0.546913 0.546913i −0.378634 0.925547i \(-0.623606\pi\)
0.925547 + 0.378634i \(0.123606\pi\)
\(678\) 0 0
\(679\) −3.16228 + 5.00000i −0.121357 + 0.191882i
\(680\) 0 0
\(681\) −5.00000 −0.191600
\(682\) 0 0
\(683\) −32.0000 + 32.0000i −1.22445 + 1.22445i −0.258411 + 0.966035i \(0.583199\pi\)
−0.966035 + 0.258411i \(0.916801\pi\)
\(684\) 0 0
\(685\) 6.32456i 0.241649i
\(686\) 0 0
\(687\) −25.0000 25.0000i −0.953809 0.953809i
\(688\) 0 0
\(689\) 3.16228 0.120473
\(690\) 0 0
\(691\) 31.6228i 1.20299i −0.798878 0.601494i \(-0.794573\pi\)
0.798878 0.601494i \(-0.205427\pi\)
\(692\) 0 0
\(693\) −1.16228 5.16228i −0.0441513 0.196099i
\(694\) 0 0
\(695\) −30.0000 30.0000i −1.13796 1.13796i
\(696\) 0 0
\(697\) 15.0000 + 15.0000i 0.568166 + 0.568166i
\(698\) 0 0
\(699\) −56.9210 −2.15295
\(700\) 0 0
\(701\) −13.0000 −0.491003 −0.245502 0.969396i \(-0.578953\pi\)
−0.245502 + 0.969396i \(0.578953\pi\)
\(702\) 0 0
\(703\) −18.9737 18.9737i −0.715605 0.715605i
\(704\) 0 0
\(705\) −23.7171 23.7171i −0.893237 0.893237i
\(706\) 0 0
\(707\) 1.83772 + 8.16228i 0.0691147 + 0.306974i
\(708\) 0 0
\(709\) 9.00000i 0.338002i 0.985616 + 0.169001i \(0.0540541\pi\)
−0.985616 + 0.169001i \(0.945946\pi\)
\(710\) 0 0
\(711\) 26.0000 0.975076
\(712\) 0 0
\(713\) 6.32456 + 6.32456i 0.236856 + 0.236856i
\(714\) 0 0
\(715\) 5.00000i 0.186989i
\(716\) 0 0
\(717\) 30.0416 30.0416i 1.12193 1.12193i
\(718\) 0 0
\(719\) 31.6228 1.17933 0.589665 0.807648i \(-0.299260\pi\)
0.589665 + 0.807648i \(0.299260\pi\)
\(720\) 0 0
\(721\) −35.0000 22.1359i −1.30347 0.824386i
\(722\) 0 0
\(723\) −40.0000 + 40.0000i −1.48762 + 1.48762i
\(724\) 0 0
\(725\) −15.0000 −0.557086
\(726\) 0 0
\(727\) 9.48683 9.48683i 0.351847 0.351847i −0.508949 0.860796i \(-0.669966\pi\)
0.860796 + 0.508949i \(0.169966\pi\)
\(728\) 0 0
\(729\) 7.00000i 0.259259i
\(730\) 0 0
\(731\) 9.48683i 0.350883i
\(732\) 0 0
\(733\) −17.3925 17.3925i −0.642408 0.642408i 0.308739 0.951147i \(-0.400093\pi\)
−0.951147 + 0.308739i \(0.900093\pi\)
\(734\) 0 0
\(735\) 15.0000 + 31.6228i 0.553283 + 1.16642i
\(736\) 0 0
\(737\) 1.00000 + 1.00000i 0.0368355 + 0.0368355i
\(738\) 0 0
\(739\) 37.0000i 1.36107i 0.732717 + 0.680534i \(0.238252\pi\)
−0.732717 + 0.680534i \(0.761748\pi\)
\(740\) 0 0
\(741\) 15.8114i 0.580846i
\(742\) 0 0
\(743\) 9.00000 9.00000i 0.330178 0.330178i −0.522476 0.852654i \(-0.674992\pi\)
0.852654 + 0.522476i \(0.174992\pi\)
\(744\) 0 0
\(745\) 18.9737 18.9737i 0.695141 0.695141i
\(746\) 0 0
\(747\) 6.32456 6.32456i 0.231403 0.231403i
\(748\) 0 0
\(749\) −9.48683 6.00000i −0.346641 0.219235i
\(750\) 0 0
\(751\) −37.0000 −1.35015 −0.675075 0.737749i \(-0.735889\pi\)
−0.675075 + 0.737749i \(0.735889\pi\)
\(752\) 0 0
\(753\) 20.0000 20.0000i 0.728841 0.728841i
\(754\) 0 0
\(755\) −14.2302 14.2302i −0.517892 0.517892i
\(756\) 0 0
\(757\) −16.0000 16.0000i −0.581530 0.581530i 0.353794 0.935324i \(-0.384892\pi\)
−0.935324 + 0.353794i \(0.884892\pi\)
\(758\) 0 0
\(759\) −6.32456 −0.229567
\(760\) 0 0
\(761\) 25.2982i 0.917060i 0.888679 + 0.458530i \(0.151624\pi\)
−0.888679 + 0.458530i \(0.848376\pi\)
\(762\) 0 0
\(763\) 4.06797 + 18.0680i 0.147270 + 0.654104i
\(764\) 0 0
\(765\) 10.0000i 0.361551i
\(766\) 0 0
\(767\) 15.0000 + 15.0000i 0.541619 + 0.541619i
\(768\) 0 0
\(769\) 22.1359 0.798243 0.399121 0.916898i \(-0.369315\pi\)
0.399121 + 0.916898i \(0.369315\pi\)
\(770\) 0 0
\(771\) −40.0000 −1.44056
\(772\) 0 0
\(773\) 36.3662 + 36.3662i 1.30800 + 1.30800i 0.922856 + 0.385145i \(0.125849\pi\)
0.385145 + 0.922856i \(0.374151\pi\)
\(774\) 0 0
\(775\) 15.8114 0.567962
\(776\) 0 0
\(777\) 11.0263 + 48.9737i 0.395568 + 1.75692i
\(778\) 0 0
\(779\) 30.0000i 1.07486i
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) 0 0
\(783\) 4.74342 + 4.74342i 0.169516 + 0.169516i
\(784\) 0 0
\(785\) −20.0000 −0.713831
\(786\) 0 0
\(787\) 17.3925 17.3925i 0.619977 0.619977i −0.325549 0.945525i \(-0.605549\pi\)
0.945525 + 0.325549i \(0.105549\pi\)
\(788\) 0 0
\(789\) −22.1359 −0.788060
\(790\) 0 0
\(791\) −24.0000 + 37.9473i −0.853342 + 1.34925i
\(792\) 0 0
\(793\) −10.0000 + 10.0000i −0.355110 + 0.355110i
\(794\) 0 0
\(795\) 5.00000 + 5.00000i 0.177332 + 0.177332i
\(796\) 0 0
\(797\) −1.58114 + 1.58114i −0.0560068 + 0.0560068i −0.734555 0.678549i \(-0.762609\pi\)
0.678549 + 0.734555i \(0.262609\pi\)
\(798\) 0 0
\(799\) 15.0000i 0.530662i
\(800\) 0 0
\(801\) 12.6491i 0.446934i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 16.3246 3.67544i 0.575365 0.129542i
\(806\) 0 0
\(807\) 30.0000 +