Properties

Label 1764.2.b.a.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: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1567.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.a.1567.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -1.73205i q^{5} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -1.73205i q^{5} +(2.00000 - 2.00000i) q^{8} +(-1.73205 + 1.73205i) q^{10} -1.00000i q^{11} +3.46410i q^{13} -4.00000 q^{16} +1.73205i q^{17} +5.19615 q^{19} +3.46410 q^{20} +(-1.00000 + 1.00000i) q^{22} +1.00000i q^{23} +2.00000 q^{25} +(3.46410 - 3.46410i) q^{26} -4.00000 q^{29} +1.73205 q^{31} +(4.00000 + 4.00000i) q^{32} +(1.73205 - 1.73205i) q^{34} +3.00000 q^{37} +(-5.19615 - 5.19615i) q^{38} +(-3.46410 - 3.46410i) q^{40} +3.46410i q^{41} -2.00000i q^{43} +2.00000 q^{44} +(1.00000 - 1.00000i) q^{46} +8.66025 q^{47} +(-2.00000 - 2.00000i) q^{50} -6.92820 q^{52} +1.00000 q^{53} -1.73205 q^{55} +(4.00000 + 4.00000i) q^{58} -5.19615 q^{59} +5.19615i q^{61} +(-1.73205 - 1.73205i) q^{62} -8.00000i q^{64} +6.00000 q^{65} +3.00000i q^{67} -3.46410 q^{68} -14.0000i q^{71} +8.66025i q^{73} +(-3.00000 - 3.00000i) q^{74} +10.3923i q^{76} -9.00000i q^{79} +6.92820i q^{80} +(3.46410 - 3.46410i) q^{82} +13.8564 q^{83} +3.00000 q^{85} +(-2.00000 + 2.00000i) q^{86} +(-2.00000 - 2.00000i) q^{88} +15.5885i q^{89} -2.00000 q^{92} +(-8.66025 - 8.66025i) q^{94} -9.00000i q^{95} -17.3205i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} + 8q^{8} + O(q^{10}) \) \( 4q - 4q^{2} + 8q^{8} - 16q^{16} - 4q^{22} + 8q^{25} - 16q^{29} + 16q^{32} + 12q^{37} + 8q^{44} + 4q^{46} - 8q^{50} + 4q^{53} + 16q^{58} + 24q^{65} - 12q^{74} + 12q^{85} - 8q^{86} - 8q^{88} - 8q^{92} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.707107 0.707107i
\(3\) 0 0
\(4\) 2.00000i 1.00000i
\(5\) 1.73205i 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 0 0
\(10\) −1.73205 + 1.73205i −0.547723 + 0.547723i
\(11\) 1.00000i 0.301511i −0.988571 0.150756i \(-0.951829\pi\)
0.988571 0.150756i \(-0.0481707\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 1.73205i 0.420084i 0.977692 + 0.210042i \(0.0673601\pi\)
−0.977692 + 0.210042i \(0.932640\pi\)
\(18\) 0 0
\(19\) 5.19615 1.19208 0.596040 0.802955i \(-0.296740\pi\)
0.596040 + 0.802955i \(0.296740\pi\)
\(20\) 3.46410 0.774597
\(21\) 0 0
\(22\) −1.00000 + 1.00000i −0.213201 + 0.213201i
\(23\) 1.00000i 0.208514i 0.994550 + 0.104257i \(0.0332465\pi\)
−0.994550 + 0.104257i \(0.966753\pi\)
\(24\) 0 0
\(25\) 2.00000 0.400000
\(26\) 3.46410 3.46410i 0.679366 0.679366i
\(27\) 0 0
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 1.73205 0.311086 0.155543 0.987829i \(-0.450287\pi\)
0.155543 + 0.987829i \(0.450287\pi\)
\(32\) 4.00000 + 4.00000i 0.707107 + 0.707107i
\(33\) 0 0
\(34\) 1.73205 1.73205i 0.297044 0.297044i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) −5.19615 5.19615i −0.842927 0.842927i
\(39\) 0 0
\(40\) −3.46410 3.46410i −0.547723 0.547723i
\(41\) 3.46410i 0.541002i 0.962720 + 0.270501i \(0.0871893\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) 1.00000 1.00000i 0.147442 0.147442i
\(47\) 8.66025 1.26323 0.631614 0.775283i \(-0.282393\pi\)
0.631614 + 0.775283i \(0.282393\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.00000 2.00000i −0.282843 0.282843i
\(51\) 0 0
\(52\) −6.92820 −0.960769
\(53\) 1.00000 0.137361 0.0686803 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) 0 0
\(55\) −1.73205 −0.233550
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 + 4.00000i 0.525226 + 0.525226i
\(59\) −5.19615 −0.676481 −0.338241 0.941060i \(-0.609832\pi\)
−0.338241 + 0.941060i \(0.609832\pi\)
\(60\) 0 0
\(61\) 5.19615i 0.665299i 0.943051 + 0.332650i \(0.107943\pi\)
−0.943051 + 0.332650i \(0.892057\pi\)
\(62\) −1.73205 1.73205i −0.219971 0.219971i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) 3.00000i 0.366508i 0.983066 + 0.183254i \(0.0586631\pi\)
−0.983066 + 0.183254i \(0.941337\pi\)
\(68\) −3.46410 −0.420084
\(69\) 0 0
\(70\) 0 0
\(71\) 14.0000i 1.66149i −0.556650 0.830747i \(-0.687914\pi\)
0.556650 0.830747i \(-0.312086\pi\)
\(72\) 0 0
\(73\) 8.66025i 1.01361i 0.862062 + 0.506803i \(0.169173\pi\)
−0.862062 + 0.506803i \(0.830827\pi\)
\(74\) −3.00000 3.00000i −0.348743 0.348743i
\(75\) 0 0
\(76\) 10.3923i 1.19208i
\(77\) 0 0
\(78\) 0 0
\(79\) 9.00000i 1.01258i −0.862364 0.506290i \(-0.831017\pi\)
0.862364 0.506290i \(-0.168983\pi\)
\(80\) 6.92820i 0.774597i
\(81\) 0 0
\(82\) 3.46410 3.46410i 0.382546 0.382546i
\(83\) 13.8564 1.52094 0.760469 0.649374i \(-0.224969\pi\)
0.760469 + 0.649374i \(0.224969\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) −2.00000 + 2.00000i −0.215666 + 0.215666i
\(87\) 0 0
\(88\) −2.00000 2.00000i −0.213201 0.213201i
\(89\) 15.5885i 1.65237i 0.563397 + 0.826187i \(0.309494\pi\)
−0.563397 + 0.826187i \(0.690506\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) 0 0
\(94\) −8.66025 8.66025i −0.893237 0.893237i
\(95\) 9.00000i 0.923381i
\(96\) 0 0
\(97\) 17.3205i 1.75863i −0.476240 0.879316i \(-0.658000\pi\)
0.476240 0.879316i \(-0.342000\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 4.00000i 0.400000i
\(101\) 8.66025i 0.861727i 0.902417 + 0.430864i \(0.141791\pi\)
−0.902417 + 0.430864i \(0.858209\pi\)
\(102\) 0 0
\(103\) 8.66025 0.853320 0.426660 0.904412i \(-0.359690\pi\)
0.426660 + 0.904412i \(0.359690\pi\)
\(104\) 6.92820 + 6.92820i 0.679366 + 0.679366i
\(105\) 0 0
\(106\) −1.00000 1.00000i −0.0971286 0.0971286i
\(107\) 13.0000i 1.25676i −0.777908 0.628379i \(-0.783719\pi\)
0.777908 0.628379i \(-0.216281\pi\)
\(108\) 0 0
\(109\) 9.00000 0.862044 0.431022 0.902342i \(-0.358153\pi\)
0.431022 + 0.902342i \(0.358153\pi\)
\(110\) 1.73205 + 1.73205i 0.165145 + 0.165145i
\(111\) 0 0
\(112\) 0 0
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 0 0
\(115\) 1.73205 0.161515
\(116\) 8.00000i 0.742781i
\(117\) 0 0
\(118\) 5.19615 + 5.19615i 0.478345 + 0.478345i
\(119\) 0 0
\(120\) 0 0
\(121\) 10.0000 0.909091
\(122\) 5.19615 5.19615i 0.470438 0.470438i
\(123\) 0 0
\(124\) 3.46410i 0.311086i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 6.00000i 0.532414i −0.963916 0.266207i \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) −8.00000 + 8.00000i −0.707107 + 0.707107i
\(129\) 0 0
\(130\) −6.00000 6.00000i −0.526235 0.526235i
\(131\) 5.19615 0.453990 0.226995 0.973896i \(-0.427110\pi\)
0.226995 + 0.973896i \(0.427110\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.00000 3.00000i 0.259161 0.259161i
\(135\) 0 0
\(136\) 3.46410 + 3.46410i 0.297044 + 0.297044i
\(137\) −1.00000 −0.0854358 −0.0427179 0.999087i \(-0.513602\pi\)
−0.0427179 + 0.999087i \(0.513602\pi\)
\(138\) 0 0
\(139\) 6.92820 0.587643 0.293821 0.955860i \(-0.405073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −14.0000 + 14.0000i −1.17485 + 1.17485i
\(143\) 3.46410 0.289683
\(144\) 0 0
\(145\) 6.92820i 0.575356i
\(146\) 8.66025 8.66025i 0.716728 0.716728i
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) −1.00000 −0.0819232 −0.0409616 0.999161i \(-0.513042\pi\)
−0.0409616 + 0.999161i \(0.513042\pi\)
\(150\) 0 0
\(151\) 7.00000i 0.569652i −0.958579 0.284826i \(-0.908064\pi\)
0.958579 0.284826i \(-0.0919358\pi\)
\(152\) 10.3923 10.3923i 0.842927 0.842927i
\(153\) 0 0
\(154\) 0 0
\(155\) 3.00000i 0.240966i
\(156\) 0 0
\(157\) 1.73205i 0.138233i 0.997609 + 0.0691164i \(0.0220180\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) −9.00000 + 9.00000i −0.716002 + 0.716002i
\(159\) 0 0
\(160\) 6.92820 6.92820i 0.547723 0.547723i
\(161\) 0 0
\(162\) 0 0
\(163\) 21.0000i 1.64485i −0.568876 0.822423i \(-0.692621\pi\)
0.568876 0.822423i \(-0.307379\pi\)
\(164\) −6.92820 −0.541002
\(165\) 0 0
\(166\) −13.8564 13.8564i −1.07547 1.07547i
\(167\) −17.3205 −1.34030 −0.670151 0.742225i \(-0.733770\pi\)
−0.670151 + 0.742225i \(0.733770\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −3.00000 3.00000i −0.230089 0.230089i
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) 12.1244i 0.921798i −0.887453 0.460899i \(-0.847527\pi\)
0.887453 0.460899i \(-0.152473\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.00000i 0.301511i
\(177\) 0 0
\(178\) 15.5885 15.5885i 1.16840 1.16840i
\(179\) 19.0000i 1.42013i 0.704138 + 0.710063i \(0.251334\pi\)
−0.704138 + 0.710063i \(0.748666\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.00000 + 2.00000i 0.147442 + 0.147442i
\(185\) 5.19615i 0.382029i
\(186\) 0 0
\(187\) 1.73205 0.126660
\(188\) 17.3205i 1.26323i
\(189\) 0 0
\(190\) −9.00000 + 9.00000i −0.652929 + 0.652929i
\(191\) 1.00000i 0.0723575i −0.999345 0.0361787i \(-0.988481\pi\)
0.999345 0.0361787i \(-0.0115186\pi\)
\(192\) 0 0
\(193\) −15.0000 −1.07972 −0.539862 0.841754i \(-0.681524\pi\)
−0.539862 + 0.841754i \(0.681524\pi\)
\(194\) −17.3205 + 17.3205i −1.24354 + 1.24354i
\(195\) 0 0
\(196\) 0 0
\(197\) −16.0000 −1.13995 −0.569976 0.821661i \(-0.693048\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(198\) 0 0
\(199\) 22.5167 1.59616 0.798082 0.602549i \(-0.205848\pi\)
0.798082 + 0.602549i \(0.205848\pi\)
\(200\) 4.00000 4.00000i 0.282843 0.282843i
\(201\) 0 0
\(202\) 8.66025 8.66025i 0.609333 0.609333i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 0.419058
\(206\) −8.66025 8.66025i −0.603388 0.603388i
\(207\) 0 0
\(208\) 13.8564i 0.960769i
\(209\) 5.19615i 0.359425i
\(210\) 0 0
\(211\) 10.0000i 0.688428i −0.938891 0.344214i \(-0.888145\pi\)
0.938891 0.344214i \(-0.111855\pi\)
\(212\) 2.00000i 0.137361i
\(213\) 0 0
\(214\) −13.0000 + 13.0000i −0.888662 + 0.888662i
\(215\) −3.46410 −0.236250
\(216\) 0 0
\(217\) 0 0
\(218\) −9.00000 9.00000i −0.609557 0.609557i
\(219\) 0 0
\(220\) 3.46410i 0.233550i
\(221\) −6.00000 −0.403604
\(222\) 0 0
\(223\) −6.92820 −0.463947 −0.231973 0.972722i \(-0.574518\pi\)
−0.231973 + 0.972722i \(0.574518\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −16.0000 16.0000i −1.06430 1.06430i
\(227\) 19.0526 1.26456 0.632281 0.774739i \(-0.282119\pi\)
0.632281 + 0.774739i \(0.282119\pi\)
\(228\) 0 0
\(229\) 15.5885i 1.03011i 0.857156 + 0.515057i \(0.172229\pi\)
−0.857156 + 0.515057i \(0.827771\pi\)
\(230\) −1.73205 1.73205i −0.114208 0.114208i
\(231\) 0 0
\(232\) −8.00000 + 8.00000i −0.525226 + 0.525226i
\(233\) 7.00000 0.458585 0.229293 0.973358i \(-0.426359\pi\)
0.229293 + 0.973358i \(0.426359\pi\)
\(234\) 0 0
\(235\) 15.0000i 0.978492i
\(236\) 10.3923i 0.676481i
\(237\) 0 0
\(238\) 0 0
\(239\) 20.0000i 1.29369i 0.762620 + 0.646846i \(0.223912\pi\)
−0.762620 + 0.646846i \(0.776088\pi\)
\(240\) 0 0
\(241\) 5.19615i 0.334714i −0.985896 0.167357i \(-0.946477\pi\)
0.985896 0.167357i \(-0.0535232\pi\)
\(242\) −10.0000 10.0000i −0.642824 0.642824i
\(243\) 0 0
\(244\) −10.3923 −0.665299
\(245\) 0 0
\(246\) 0 0
\(247\) 18.0000i 1.14531i
\(248\) 3.46410 3.46410i 0.219971 0.219971i
\(249\) 0 0
\(250\) −12.1244 + 12.1244i −0.766812 + 0.766812i
\(251\) −3.46410 −0.218652 −0.109326 0.994006i \(-0.534869\pi\)
−0.109326 + 0.994006i \(0.534869\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) −6.00000 + 6.00000i −0.376473 + 0.376473i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 5.19615i 0.324127i 0.986780 + 0.162064i \(0.0518150\pi\)
−0.986780 + 0.162064i \(0.948185\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 12.0000i 0.744208i
\(261\) 0 0
\(262\) −5.19615 5.19615i −0.321019 0.321019i
\(263\) 23.0000i 1.41824i −0.705087 0.709120i \(-0.749092\pi\)
0.705087 0.709120i \(-0.250908\pi\)
\(264\) 0 0
\(265\) 1.73205i 0.106399i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.00000 −0.366508
\(269\) 22.5167i 1.37287i −0.727194 0.686433i \(-0.759176\pi\)
0.727194 0.686433i \(-0.240824\pi\)
\(270\) 0 0
\(271\) 15.5885 0.946931 0.473466 0.880812i \(-0.343003\pi\)
0.473466 + 0.880812i \(0.343003\pi\)
\(272\) 6.92820i 0.420084i
\(273\) 0 0
\(274\) 1.00000 + 1.00000i 0.0604122 + 0.0604122i
\(275\) 2.00000i 0.120605i
\(276\) 0 0
\(277\) −13.0000 −0.781094 −0.390547 0.920583i \(-0.627714\pi\)
−0.390547 + 0.920583i \(0.627714\pi\)
\(278\) −6.92820 6.92820i −0.415526 0.415526i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.00000 0.238620 0.119310 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 0 0
\(283\) −12.1244 −0.720718 −0.360359 0.932814i \(-0.617346\pi\)
−0.360359 + 0.932814i \(0.617346\pi\)
\(284\) 28.0000 1.66149
\(285\) 0 0
\(286\) −3.46410 3.46410i −0.204837 0.204837i
\(287\) 0 0
\(288\) 0 0
\(289\) 14.0000 0.823529
\(290\) 6.92820 6.92820i 0.406838 0.406838i
\(291\) 0 0
\(292\) −17.3205 −1.01361
\(293\) 20.7846i 1.21425i 0.794606 + 0.607125i \(0.207677\pi\)
−0.794606 + 0.607125i \(0.792323\pi\)
\(294\) 0 0
\(295\) 9.00000i 0.524000i
\(296\) 6.00000 6.00000i 0.348743 0.348743i
\(297\) 0 0
\(298\) 1.00000 + 1.00000i 0.0579284 + 0.0579284i
\(299\) −3.46410 −0.200334
\(300\) 0 0
\(301\) 0 0
\(302\) −7.00000 + 7.00000i −0.402805 + 0.402805i
\(303\) 0 0
\(304\) −20.7846 −1.19208
\(305\) 9.00000 0.515339
\(306\) 0 0
\(307\) −20.7846 −1.18624 −0.593120 0.805114i \(-0.702104\pi\)
−0.593120 + 0.805114i \(0.702104\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.00000 + 3.00000i −0.170389 + 0.170389i
\(311\) 8.66025 0.491078 0.245539 0.969387i \(-0.421035\pi\)
0.245539 + 0.969387i \(0.421035\pi\)
\(312\) 0 0
\(313\) 1.73205i 0.0979013i −0.998801 0.0489506i \(-0.984412\pi\)
0.998801 0.0489506i \(-0.0155877\pi\)
\(314\) 1.73205 1.73205i 0.0977453 0.0977453i
\(315\) 0 0
\(316\) 18.0000 1.01258
\(317\) −11.0000 −0.617822 −0.308911 0.951091i \(-0.599964\pi\)
−0.308911 + 0.951091i \(0.599964\pi\)
\(318\) 0 0
\(319\) 4.00000i 0.223957i
\(320\) −13.8564 −0.774597
\(321\) 0 0
\(322\) 0 0
\(323\) 9.00000i 0.500773i
\(324\) 0 0
\(325\) 6.92820i 0.384308i
\(326\) −21.0000 + 21.0000i −1.16308 + 1.16308i
\(327\) 0 0
\(328\) 6.92820 + 6.92820i 0.382546 + 0.382546i
\(329\) 0 0
\(330\) 0 0
\(331\) 7.00000i 0.384755i 0.981321 + 0.192377i \(0.0616198\pi\)
−0.981321 + 0.192377i \(0.938380\pi\)
\(332\) 27.7128i 1.52094i
\(333\) 0 0
\(334\) 17.3205 + 17.3205i 0.947736 + 0.947736i
\(335\) 5.19615 0.283896
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −1.00000 1.00000i −0.0543928 0.0543928i
\(339\) 0 0
\(340\) 6.00000i 0.325396i
\(341\) 1.73205i 0.0937958i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 4.00000i −0.215666 0.215666i
\(345\) 0 0
\(346\) −12.1244 + 12.1244i −0.651809 + 0.651809i
\(347\) 13.0000i 0.697877i 0.937146 + 0.348938i \(0.113458\pi\)
−0.937146 + 0.348938i \(0.886542\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.00000 4.00000i 0.213201 0.213201i
\(353\) 29.4449i 1.56719i 0.621271 + 0.783596i \(0.286617\pi\)
−0.621271 + 0.783596i \(0.713383\pi\)
\(354\) 0 0
\(355\) −24.2487 −1.28699
\(356\) −31.1769 −1.65237
\(357\) 0 0
\(358\) 19.0000 19.0000i 1.00418 1.00418i
\(359\) 23.0000i 1.21389i 0.794742 + 0.606947i \(0.207606\pi\)
−0.794742 + 0.606947i \(0.792394\pi\)
\(360\) 0 0
\(361\) 8.00000 0.421053
\(362\) 6.92820 6.92820i 0.364138 0.364138i
\(363\) 0 0
\(364\) 0 0
\(365\) 15.0000 0.785136
\(366\) 0 0
\(367\) −1.73205 −0.0904123 −0.0452062 0.998978i \(-0.514394\pi\)
−0.0452062 + 0.998978i \(0.514394\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 0 0
\(370\) −5.19615 + 5.19615i −0.270135 + 0.270135i
\(371\) 0 0
\(372\) 0 0
\(373\) −29.0000 −1.50156 −0.750782 0.660551i \(-0.770323\pi\)
−0.750782 + 0.660551i \(0.770323\pi\)
\(374\) −1.73205 1.73205i −0.0895622 0.0895622i
\(375\) 0 0
\(376\) 17.3205 17.3205i 0.893237 0.893237i
\(377\) 13.8564i 0.713641i
\(378\) 0 0
\(379\) 8.00000i 0.410932i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) 18.0000 0.923381
\(381\) 0 0
\(382\) −1.00000 + 1.00000i −0.0511645 + 0.0511645i
\(383\) −5.19615 −0.265511 −0.132755 0.991149i \(-0.542383\pi\)
−0.132755 + 0.991149i \(0.542383\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15.0000 + 15.0000i 0.763480 + 0.763480i
\(387\) 0 0
\(388\) 34.6410 1.75863
\(389\) 19.0000 0.963338 0.481669 0.876353i \(-0.340031\pi\)
0.481669 + 0.876353i \(0.340031\pi\)
\(390\) 0 0
\(391\) −1.73205 −0.0875936
\(392\) 0 0
\(393\) 0 0
\(394\) 16.0000 + 16.0000i 0.806068 + 0.806068i
\(395\) −15.5885 −0.784340
\(396\) 0 0
\(397\) 19.0526i 0.956221i −0.878300 0.478110i \(-0.841322\pi\)
0.878300 0.478110i \(-0.158678\pi\)
\(398\) −22.5167 22.5167i −1.12866 1.12866i
\(399\) 0 0
\(400\) −8.00000 −0.400000
\(401\) 23.0000 1.14857 0.574283 0.818657i \(-0.305281\pi\)
0.574283 + 0.818657i \(0.305281\pi\)
\(402\) 0 0
\(403\) 6.00000i 0.298881i
\(404\) −17.3205 −0.861727
\(405\) 0 0
\(406\) 0 0
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) 25.9808i 1.28467i 0.766426 + 0.642333i \(0.222033\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) −6.00000 6.00000i −0.296319 0.296319i
\(411\) 0 0
\(412\) 17.3205i 0.853320i
\(413\) 0 0
\(414\) 0 0
\(415\) 24.0000i 1.17811i
\(416\) −13.8564 + 13.8564i −0.679366 + 0.679366i
\(417\) 0 0
\(418\) −5.19615 + 5.19615i −0.254152 + 0.254152i
\(419\) −20.7846 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −10.0000 + 10.0000i −0.486792 + 0.486792i
\(423\) 0 0
\(424\) 2.00000 2.00000i 0.0971286 0.0971286i
\(425\) 3.46410i 0.168034i
\(426\) 0 0
\(427\) 0 0
\(428\) 26.0000 1.25676
\(429\) 0 0
\(430\) 3.46410 + 3.46410i 0.167054 + 0.167054i
\(431\) 23.0000i 1.10787i 0.832560 + 0.553936i \(0.186875\pi\)
−0.832560 + 0.553936i \(0.813125\pi\)
\(432\) 0 0
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 18.0000i 0.862044i
\(437\) 5.19615i 0.248566i
\(438\) 0 0
\(439\) −22.5167 −1.07466 −0.537331 0.843372i \(-0.680567\pi\)
−0.537331 + 0.843372i \(0.680567\pi\)
\(440\) −3.46410 + 3.46410i −0.165145 + 0.165145i
\(441\) 0 0
\(442\) 6.00000 + 6.00000i 0.285391 + 0.285391i
\(443\) 17.0000i 0.807694i −0.914826 0.403847i \(-0.867673\pi\)
0.914826 0.403847i \(-0.132327\pi\)
\(444\) 0 0
\(445\) 27.0000 1.27992
\(446\) 6.92820 + 6.92820i 0.328060 + 0.328060i
\(447\) 0 0
\(448\) 0 0
\(449\) −8.00000 −0.377543 −0.188772 0.982021i \(-0.560451\pi\)
−0.188772 + 0.982021i \(0.560451\pi\)
\(450\) 0 0
\(451\) 3.46410 0.163118
\(452\) 32.0000i 1.50515i
\(453\) 0 0
\(454\) −19.0526 19.0526i −0.894181 0.894181i
\(455\) 0 0
\(456\) 0 0
\(457\) 15.0000 0.701670 0.350835 0.936437i \(-0.385898\pi\)
0.350835 + 0.936437i \(0.385898\pi\)
\(458\) 15.5885 15.5885i 0.728401 0.728401i
\(459\) 0 0
\(460\) 3.46410i 0.161515i
\(461\) 17.3205i 0.806696i 0.915047 + 0.403348i \(0.132154\pi\)
−0.915047 + 0.403348i \(0.867846\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i 0.716965 + 0.697109i \(0.245531\pi\)
−0.716965 + 0.697109i \(0.754469\pi\)
\(464\) 16.0000 0.742781
\(465\) 0 0
\(466\) −7.00000 7.00000i −0.324269 0.324269i
\(467\) −8.66025 −0.400749 −0.200374 0.979719i \(-0.564216\pi\)
−0.200374 + 0.979719i \(0.564216\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −15.0000 + 15.0000i −0.691898 + 0.691898i
\(471\) 0 0
\(472\) −10.3923 + 10.3923i −0.478345 + 0.478345i
\(473\) −2.00000 −0.0919601
\(474\) 0 0
\(475\) 10.3923 0.476832
\(476\) 0 0
\(477\) 0 0
\(478\) 20.0000 20.0000i 0.914779 0.914779i
\(479\) −12.1244 −0.553976 −0.276988 0.960873i \(-0.589336\pi\)
−0.276988 + 0.960873i \(0.589336\pi\)
\(480\) 0 0
\(481\) 10.3923i 0.473848i
\(482\) −5.19615 + 5.19615i −0.236678 + 0.236678i
\(483\) 0 0
\(484\) 20.0000i 0.909091i
\(485\) −30.0000 −1.36223
\(486\) 0 0
\(487\) 31.0000i 1.40474i 0.711810 + 0.702372i \(0.247876\pi\)
−0.711810 + 0.702372i \(0.752124\pi\)
\(488\) 10.3923 + 10.3923i 0.470438 + 0.470438i
\(489\) 0 0
\(490\) 0 0
\(491\) 32.0000i 1.44414i 0.691820 + 0.722070i \(0.256809\pi\)
−0.691820 + 0.722070i \(0.743191\pi\)
\(492\) 0 0
\(493\) 6.92820i 0.312031i
\(494\) 18.0000 18.0000i 0.809858 0.809858i
\(495\) 0 0
\(496\) −6.92820 −0.311086
\(497\) 0 0
\(498\) 0 0
\(499\) 35.0000i 1.56682i 0.621508 + 0.783408i \(0.286520\pi\)
−0.621508 + 0.783408i \(0.713480\pi\)
\(500\) 24.2487 1.08444
\(501\) 0 0
\(502\) 3.46410 + 3.46410i 0.154610 + 0.154610i
\(503\) −6.92820 −0.308913 −0.154457 0.988000i \(-0.549363\pi\)
−0.154457 + 0.988000i \(0.549363\pi\)
\(504\) 0 0
\(505\) 15.0000 0.667491
\(506\) −1.00000 1.00000i −0.0444554 0.0444554i
\(507\) 0 0
\(508\) 12.0000 0.532414
\(509\) 12.1244i 0.537403i 0.963224 + 0.268701i \(0.0865945\pi\)
−0.963224 + 0.268701i \(0.913406\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 0 0
\(514\) 5.19615 5.19615i 0.229192 0.229192i
\(515\) 15.0000i 0.660979i
\(516\) 0 0
\(517\) 8.66025i 0.380878i
\(518\) 0 0
\(519\) 0 0
\(520\) 12.0000 12.0000i 0.526235 0.526235i
\(521\) 1.73205i 0.0758825i −0.999280 0.0379413i \(-0.987920\pi\)
0.999280 0.0379413i \(-0.0120800\pi\)
\(522\) 0 0
\(523\) 25.9808 1.13606 0.568030 0.823008i \(-0.307706\pi\)
0.568030 + 0.823008i \(0.307706\pi\)
\(524\) 10.3923i 0.453990i
\(525\) 0 0
\(526\) −23.0000 + 23.0000i −1.00285 + 1.00285i
\(527\) 3.00000i 0.130682i
\(528\) 0 0
\(529\) 22.0000 0.956522
\(530\) −1.73205 + 1.73205i −0.0752355 + 0.0752355i
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) −22.5167 −0.973480
\(536\) 6.00000 + 6.00000i 0.259161 + 0.259161i
\(537\) 0 0
\(538\) −22.5167 + 22.5167i −0.970762 + 0.970762i
\(539\) 0 0
\(540\) 0 0
\(541\) −19.0000 −0.816874 −0.408437 0.912787i \(-0.633926\pi\)
−0.408437 + 0.912787i \(0.633926\pi\)
\(542\) −15.5885 15.5885i −0.669582 0.669582i
\(543\) 0 0
\(544\) −6.92820 + 6.92820i −0.297044 + 0.297044i
\(545\) 15.5885i 0.667736i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 0 0
\(550\) −2.00000 + 2.00000i −0.0852803 + 0.0852803i
\(551\) −20.7846 −0.885454
\(552\) 0 0
\(553\) 0 0
\(554\) 13.0000 + 13.0000i 0.552317 + 0.552317i
\(555\) 0 0
\(556\) 13.8564i 0.587643i
\(557\) −37.0000 −1.56774 −0.783870 0.620925i \(-0.786757\pi\)
−0.783870 + 0.620925i \(0.786757\pi\)
\(558\) 0 0
\(559\) 6.92820 0.293032
\(560\) 0 0
\(561\) 0 0
\(562\) −4.00000 4.00000i −0.168730 0.168730i
\(563\) 22.5167 0.948964 0.474482 0.880265i \(-0.342635\pi\)
0.474482 + 0.880265i \(0.342635\pi\)
\(564\) 0 0
\(565\) 27.7128i 1.16589i
\(566\) 12.1244 + 12.1244i 0.509625 + 0.509625i
\(567\) 0 0
\(568\) −28.0000 28.0000i −1.17485 1.17485i
\(569\) 13.0000 0.544988 0.272494 0.962157i \(-0.412151\pi\)
0.272494 + 0.962157i \(0.412151\pi\)
\(570\) 0 0
\(571\) 21.0000i 0.878823i 0.898286 + 0.439411i \(0.144813\pi\)
−0.898286 + 0.439411i \(0.855187\pi\)
\(572\) 6.92820i 0.289683i
\(573\) 0 0
\(574\) 0 0
\(575\) 2.00000i 0.0834058i
\(576\) 0 0
\(577\) 32.9090i 1.37002i −0.728535 0.685009i \(-0.759798\pi\)
0.728535 0.685009i \(-0.240202\pi\)
\(578\) −14.0000 14.0000i −0.582323 0.582323i
\(579\) 0 0
\(580\) −13.8564 −0.575356
\(581\) 0 0
\(582\) 0 0
\(583\) 1.00000i 0.0414158i
\(584\) 17.3205 + 17.3205i 0.716728 + 0.716728i
\(585\) 0 0
\(586\) 20.7846 20.7846i 0.858604 0.858604i
\(587\) 6.92820 0.285958 0.142979 0.989726i \(-0.454332\pi\)
0.142979 + 0.989726i \(0.454332\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) 9.00000 9.00000i 0.370524 0.370524i
\(591\) 0 0
\(592\) −12.0000 −0.493197
\(593\) 15.5885i 0.640141i −0.947394 0.320071i \(-0.896293\pi\)
0.947394 0.320071i \(-0.103707\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.00000i 0.0819232i
\(597\) 0 0
\(598\) 3.46410 + 3.46410i 0.141658 + 0.141658i
\(599\) 17.0000i 0.694601i 0.937754 + 0.347301i \(0.112902\pi\)
−0.937754 + 0.347301i \(0.887098\pi\)
\(600\) 0 0
\(601\) 38.1051i 1.55434i 0.629291 + 0.777170i \(0.283346\pi\)
−0.629291 + 0.777170i \(0.716654\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 14.0000 0.569652
\(605\) 17.3205i 0.704179i
\(606\) 0 0
\(607\) −15.5885 −0.632716 −0.316358 0.948640i \(-0.602460\pi\)
−0.316358 + 0.948640i \(0.602460\pi\)
\(608\) 20.7846 + 20.7846i 0.842927 + 0.842927i
\(609\) 0 0
\(610\) −9.00000 9.00000i −0.364399 0.364399i
\(611\) 30.0000i 1.21367i
\(612\) 0 0
\(613\) −31.0000 −1.25208 −0.626039 0.779792i \(-0.715325\pi\)
−0.626039 + 0.779792i \(0.715325\pi\)
\(614\) 20.7846 + 20.7846i 0.838799 + 0.838799i
\(615\) 0 0
\(616\) 0 0
\(617\) −20.0000 −0.805170 −0.402585 0.915383i \(-0.631888\pi\)
−0.402585 + 0.915383i \(0.631888\pi\)
\(618\) 0 0
\(619\) −15.5885 −0.626553 −0.313276 0.949662i \(-0.601427\pi\)
−0.313276 + 0.949662i \(0.601427\pi\)
\(620\) 6.00000 0.240966
\(621\) 0 0
\(622\) −8.66025 8.66025i −0.347245 0.347245i
\(623\) 0 0
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) −1.73205 + 1.73205i −0.0692267 + 0.0692267i
\(627\) 0 0
\(628\) −3.46410 −0.138233
\(629\) 5.19615i 0.207184i
\(630\) 0 0
\(631\) 30.0000i 1.19428i −0.802137 0.597141i \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) −18.0000 18.0000i −0.716002 0.716002i
\(633\) 0 0
\(634\) 11.0000 + 11.0000i 0.436866 + 0.436866i
\(635\) −10.3923 −0.412406
\(636\) 0 0
\(637\) 0 0
\(638\) 4.00000 4.00000i 0.158362 0.158362i
\(639\) 0 0
\(640\) 13.8564 + 13.8564i 0.547723 + 0.547723i
\(641\) 13.0000 0.513469 0.256735 0.966482i \(-0.417353\pi\)
0.256735 + 0.966482i \(0.417353\pi\)
\(642\) 0 0
\(643\) 13.8564 0.546443 0.273222 0.961951i \(-0.411911\pi\)
0.273222 + 0.961951i \(0.411911\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 9.00000 9.00000i 0.354100 0.354100i
\(647\) −32.9090 −1.29378 −0.646892 0.762581i \(-0.723932\pi\)
−0.646892 + 0.762581i \(0.723932\pi\)
\(648\) 0 0
\(649\) 5.19615i 0.203967i
\(650\) 6.92820 6.92820i 0.271746 0.271746i
\(651\) 0 0
\(652\) 42.0000 1.64485
\(653\) −31.0000 −1.21312 −0.606562 0.795036i \(-0.707452\pi\)
−0.606562 + 0.795036i \(0.707452\pi\)
\(654\) 0 0
\(655\) 9.00000i 0.351659i
\(656\) 13.8564i 0.541002i
\(657\) 0 0
\(658\) 0 0
\(659\) 38.0000i 1.48027i −0.672458 0.740135i \(-0.734762\pi\)
0.672458 0.740135i \(-0.265238\pi\)
\(660\) 0 0
\(661\) 39.8372i 1.54949i −0.632276 0.774743i \(-0.717879\pi\)
0.632276 0.774743i \(-0.282121\pi\)
\(662\) 7.00000 7.00000i 0.272063 0.272063i
\(663\) 0 0
\(664\) 27.7128 27.7128i 1.07547 1.07547i
\(665\) 0 0
\(666\) 0 0
\(667\) 4.00000i 0.154881i
\(668\) 34.6410i 1.34030i
\(669\) 0 0
\(670\) −5.19615 5.19615i −0.200745 0.200745i
\(671\) 5.19615 0.200595
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 2.00000i 0.0769231i
\(677\) 43.3013i 1.66420i −0.554623 0.832102i \(-0.687138\pi\)
0.554623 0.832102i \(-0.312862\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6.00000 6.00000i 0.230089 0.230089i
\(681\) 0 0
\(682\) −1.73205 + 1.73205i −0.0663237 + 0.0663237i
\(683\) 25.0000i 0.956598i −0.878197 0.478299i \(-0.841253\pi\)
0.878197 0.478299i \(-0.158747\pi\)
\(684\) 0 0
\(685\) 1.73205i 0.0661783i
\(686\) 0 0
\(687\) 0 0
\(688\) 8.00000i 0.304997i
\(689\) 3.46410i 0.131972i
\(690\) 0 0
\(691\) −12.1244 −0.461232 −0.230616 0.973045i \(-0.574074\pi\)
−0.230616 + 0.973045i \(0.574074\pi\)
\(692\) 24.2487 0.921798
\(693\) 0 0
\(694\) 13.0000 13.0000i 0.493473 0.493473i
\(695\) 12.0000i 0.455186i
\(696\) 0 0
\(697\) −6.00000 −0.227266
\(698\) 10.3923 10.3923i 0.393355 0.393355i
\(699\) 0 0
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) 15.5885 0.587930
\(704\) −8.00000 −0.301511
\(705\) 0 0
\(706\) 29.4449 29.4449i 1.10817 1.10817i
\(707\) 0 0
\(708\) 0 0
\(709\) −9.00000 −0.338002 −0.169001 0.985616i \(-0.554054\pi\)
−0.169001 + 0.985616i \(0.554054\pi\)
\(710\) 24.2487 + 24.2487i 0.910038 + 0.910038i
\(711\) 0 0
\(712\) 31.1769 + 31.1769i 1.16840 + 1.16840i
\(713\) 1.73205i 0.0648658i
\(714\) 0 0
\(715\) 6.00000i 0.224387i
\(716\) −38.0000 −1.42013
\(717\) 0 0
\(718\) 23.0000 23.0000i 0.858352 0.858352i
\(719\) 25.9808 0.968919 0.484459 0.874814i \(-0.339016\pi\)
0.484459 + 0.874814i \(0.339016\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −8.00000 8.00000i −0.297729 0.297729i
\(723\) 0 0
\(724\) −13.8564 −0.514969
\(725\) −8.00000 −0.297113
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −15.0000 15.0000i −0.555175 0.555175i
\(731\) 3.46410 0.128124
\(732\) 0 0
\(733\) 43.3013i 1.59937i −0.600420 0.799684i \(-0.705000\pi\)
0.600420 0.799684i \(-0.295000\pi\)
\(734\) 1.73205 + 1.73205i 0.0639312 + 0.0639312i
\(735\) 0 0
\(736\) −4.00000 + 4.00000i −0.147442 + 0.147442i
\(737\) 3.00000 0.110506
\(738\) 0 0
\(739\) 51.0000i 1.87607i −0.346547 0.938033i \(-0.612646\pi\)
0.346547 0.938033i \(-0.387354\pi\)
\(740\) 10.3923 0.382029
\(741\) 0 0
\(742\) 0 0
\(743\) 34.0000i 1.24734i −0.781688 0.623670i \(-0.785641\pi\)
0.781688 0.623670i \(-0.214359\pi\)
\(744\) 0 0
\(745\) 1.73205i 0.0634574i
\(746\) 29.0000 + 29.0000i 1.06177 + 1.06177i
\(747\) 0 0
\(748\) 3.46410i 0.126660i
\(749\) 0 0
\(750\) 0 0
\(751\) 25.0000i 0.912263i 0.889912 + 0.456131i \(0.150765\pi\)
−0.889912 + 0.456131i \(0.849235\pi\)
\(752\) −34.6410 −1.26323
\(753\) 0 0
\(754\) −13.8564 + 13.8564i −0.504621 + 0.504621i
\(755\) −12.1244 −0.441250
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) 8.00000 8.00000i 0.290573 0.290573i
\(759\) 0 0
\(760\) −18.0000 18.0000i −0.652929 0.652929i
\(761\) 19.0526i 0.690655i 0.938482 + 0.345327i \(0.112232\pi\)
−0.938482 + 0.345327i \(0.887768\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 2.00000 0.0723575
\(765\) 0 0
\(766\) 5.19615 + 5.19615i 0.187745 + 0.187745i
\(767\) 18.0000i 0.649942i
\(768\) 0 0
\(769\) 3.46410i 0.124919i −0.998048 0.0624593i \(-0.980106\pi\)
0.998048 0.0624593i \(-0.0198944\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 30.0000i 1.07972i
\(773\) 25.9808i 0.934463i −0.884135 0.467232i \(-0.845251\pi\)
0.884135 0.467232i \(-0.154749\pi\)
\(774\) 0 0
\(775\) 3.46410 0.124434
\(776\) −34.6410 34.6410i −1.24354 1.24354i
\(777\) 0 0
\(778\) −19.0000 19.0000i −0.681183 0.681183i
\(779\) 18.0000i 0.644917i
\(780\) 0 0
\(781\) −14.0000 −0.500959
\(782\) 1.73205 + 1.73205i 0.0619380 + 0.0619380i
\(783\) 0 0
\(784\) 0 0
\(785\) 3.00000 0.107075
\(786\) 0 0
\(787\) 5.19615 0.185223 0.0926114 0.995702i \(-0.470479\pi\)
0.0926114 + 0.995702i \(0.470479\pi\)
\(788\) 32.0000i 1.13995i
\(789\) 0 0
\(790\) 15.5885 + 15.5885i 0.554612 + 0.554612i
\(791\) 0 0
\(792\) 0 0
\(793\) −18.0000 −0.639199
\(794\) −19.0526 + 19.0526i −0.676150 + 0.676150i
\(795\) 0 0
\(796\) 45.0333i 1.59616i
\(797\) 10.3923i 0.368114i 0.982916 + 0.184057i \(0.0589232\pi\)
−0.982916 + 0.184057i \(0.941077\pi\)
\(798\) 0 0
\(799\) 15.0000i 0.530662i
\(800\) 8.00000 + 8.00000i 0.282843 + 0.282843i
\(801\) 0 0
\(802\) −23.0000 23.0000i −0.812158 0.812158i
\(803\) 8.66025 0.305614
\(804\) 0 0
\(805\) 0