Properties

Label 1024.2.e.i.257.1
Level $1024$
Weight $2$
Character 1024.257
Analytic conductor $8.177$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1024 = 2^{10} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1024.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17668116698\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 128)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 257.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1024.257
Dual form 1024.2.e.i.769.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41421 - 1.41421i) q^{3} +(1.41421 - 1.41421i) q^{5} +4.00000i q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(-1.41421 - 1.41421i) q^{3} +(1.41421 - 1.41421i) q^{5} +4.00000i q^{7} +1.00000i q^{9} +(1.41421 - 1.41421i) q^{11} +(1.41421 + 1.41421i) q^{13} -4.00000 q^{15} +2.00000 q^{17} +(1.41421 + 1.41421i) q^{19} +(5.65685 - 5.65685i) q^{21} +4.00000i q^{23} +1.00000i q^{25} +(-2.82843 + 2.82843i) q^{27} +(4.24264 + 4.24264i) q^{29} -4.00000 q^{33} +(5.65685 + 5.65685i) q^{35} +(7.07107 - 7.07107i) q^{37} -4.00000i q^{39} -6.00000i q^{41} +(-4.24264 + 4.24264i) q^{43} +(1.41421 + 1.41421i) q^{45} +8.00000 q^{47} -9.00000 q^{49} +(-2.82843 - 2.82843i) q^{51} +(4.24264 - 4.24264i) q^{53} -4.00000i q^{55} -4.00000i q^{57} +(9.89949 - 9.89949i) q^{59} +(-1.41421 - 1.41421i) q^{61} -4.00000 q^{63} +4.00000 q^{65} +(-7.07107 - 7.07107i) q^{67} +(5.65685 - 5.65685i) q^{69} -12.0000i q^{71} +14.0000i q^{73} +(1.41421 - 1.41421i) q^{75} +(5.65685 + 5.65685i) q^{77} +8.00000 q^{79} +11.0000 q^{81} +(-4.24264 - 4.24264i) q^{83} +(2.82843 - 2.82843i) q^{85} -12.0000i q^{87} +2.00000i q^{89} +(-5.65685 + 5.65685i) q^{91} +4.00000 q^{95} -2.00000 q^{97} +(1.41421 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + O(q^{10}) \) \( 4q - 16q^{15} + 8q^{17} - 16q^{33} + 32q^{47} - 36q^{49} - 16q^{63} + 16q^{65} + 32q^{79} + 44q^{81} + 16q^{95} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(1023\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) −1.41421 1.41421i −0.816497 0.816497i 0.169102 0.985599i \(-0.445913\pi\)
−0.985599 + 0.169102i \(0.945913\pi\)
\(4\) 0 0
\(5\) 1.41421 1.41421i 0.632456 0.632456i −0.316228 0.948683i \(-0.602416\pi\)
0.948683 + 0.316228i \(0.102416\pi\)
\(6\) 0 0
\(7\) 4.00000i 1.51186i 0.654654 + 0.755929i \(0.272814\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 1.41421 1.41421i 0.426401 0.426401i −0.460999 0.887401i \(-0.652509\pi\)
0.887401 + 0.460999i \(0.152509\pi\)
\(12\) 0 0
\(13\) 1.41421 + 1.41421i 0.392232 + 0.392232i 0.875482 0.483250i \(-0.160544\pi\)
−0.483250 + 0.875482i \(0.660544\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 1.41421 + 1.41421i 0.324443 + 0.324443i 0.850469 0.526026i \(-0.176318\pi\)
−0.526026 + 0.850469i \(0.676318\pi\)
\(20\) 0 0
\(21\) 5.65685 5.65685i 1.23443 1.23443i
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) 0 0
\(27\) −2.82843 + 2.82843i −0.544331 + 0.544331i
\(28\) 0 0
\(29\) 4.24264 + 4.24264i 0.787839 + 0.787839i 0.981140 0.193301i \(-0.0619194\pi\)
−0.193301 + 0.981140i \(0.561919\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −4.00000 −0.696311
\(34\) 0 0
\(35\) 5.65685 + 5.65685i 0.956183 + 0.956183i
\(36\) 0 0
\(37\) 7.07107 7.07107i 1.16248 1.16248i 0.178545 0.983932i \(-0.442861\pi\)
0.983932 0.178545i \(-0.0571389\pi\)
\(38\) 0 0
\(39\) 4.00000i 0.640513i
\(40\) 0 0
\(41\) 6.00000i 0.937043i −0.883452 0.468521i \(-0.844787\pi\)
0.883452 0.468521i \(-0.155213\pi\)
\(42\) 0 0
\(43\) −4.24264 + 4.24264i −0.646997 + 0.646997i −0.952266 0.305269i \(-0.901253\pi\)
0.305269 + 0.952266i \(0.401253\pi\)
\(44\) 0 0
\(45\) 1.41421 + 1.41421i 0.210819 + 0.210819i
\(46\) 0 0
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) −9.00000 −1.28571
\(50\) 0 0
\(51\) −2.82843 2.82843i −0.396059 0.396059i
\(52\) 0 0
\(53\) 4.24264 4.24264i 0.582772 0.582772i −0.352892 0.935664i \(-0.614802\pi\)
0.935664 + 0.352892i \(0.114802\pi\)
\(54\) 0 0
\(55\) 4.00000i 0.539360i
\(56\) 0 0
\(57\) 4.00000i 0.529813i
\(58\) 0 0
\(59\) 9.89949 9.89949i 1.28880 1.28880i 0.353291 0.935513i \(-0.385063\pi\)
0.935513 0.353291i \(-0.114937\pi\)
\(60\) 0 0
\(61\) −1.41421 1.41421i −0.181071 0.181071i 0.610751 0.791823i \(-0.290868\pi\)
−0.791823 + 0.610751i \(0.790868\pi\)
\(62\) 0 0
\(63\) −4.00000 −0.503953
\(64\) 0 0
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) −7.07107 7.07107i −0.863868 0.863868i 0.127917 0.991785i \(-0.459171\pi\)
−0.991785 + 0.127917i \(0.959171\pi\)
\(68\) 0 0
\(69\) 5.65685 5.65685i 0.681005 0.681005i
\(70\) 0 0
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) 0 0
\(73\) 14.0000i 1.63858i 0.573382 + 0.819288i \(0.305631\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(74\) 0 0
\(75\) 1.41421 1.41421i 0.163299 0.163299i
\(76\) 0 0
\(77\) 5.65685 + 5.65685i 0.644658 + 0.644658i
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 11.0000 1.22222
\(82\) 0 0
\(83\) −4.24264 4.24264i −0.465690 0.465690i 0.434825 0.900515i \(-0.356810\pi\)
−0.900515 + 0.434825i \(0.856810\pi\)
\(84\) 0 0
\(85\) 2.82843 2.82843i 0.306786 0.306786i
\(86\) 0 0
\(87\) 12.0000i 1.28654i
\(88\) 0 0
\(89\) 2.00000i 0.212000i 0.994366 + 0.106000i \(0.0338043\pi\)
−0.994366 + 0.106000i \(0.966196\pi\)
\(90\) 0 0
\(91\) −5.65685 + 5.65685i −0.592999 + 0.592999i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 0.410391
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 1.41421 + 1.41421i 0.142134 + 0.142134i
\(100\) 0 0
\(101\) −4.24264 + 4.24264i −0.422159 + 0.422159i −0.885946 0.463788i \(-0.846490\pi\)
0.463788 + 0.885946i \(0.346490\pi\)
\(102\) 0 0
\(103\) 4.00000i 0.394132i 0.980390 + 0.197066i \(0.0631413\pi\)
−0.980390 + 0.197066i \(0.936859\pi\)
\(104\) 0 0
\(105\) 16.0000i 1.56144i
\(106\) 0 0
\(107\) 1.41421 1.41421i 0.136717 0.136717i −0.635436 0.772153i \(-0.719180\pi\)
0.772153 + 0.635436i \(0.219180\pi\)
\(108\) 0 0
\(109\) −4.24264 4.24264i −0.406371 0.406371i 0.474100 0.880471i \(-0.342774\pi\)
−0.880471 + 0.474100i \(0.842774\pi\)
\(110\) 0 0
\(111\) −20.0000 −1.89832
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) 5.65685 + 5.65685i 0.527504 + 0.527504i
\(116\) 0 0
\(117\) −1.41421 + 1.41421i −0.130744 + 0.130744i
\(118\) 0 0
\(119\) 8.00000i 0.733359i
\(120\) 0 0
\(121\) 7.00000i 0.636364i
\(122\) 0 0
\(123\) −8.48528 + 8.48528i −0.765092 + 0.765092i
\(124\) 0 0
\(125\) 8.48528 + 8.48528i 0.758947 + 0.758947i
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 12.0000 1.05654
\(130\) 0 0
\(131\) 4.24264 + 4.24264i 0.370681 + 0.370681i 0.867725 0.497044i \(-0.165581\pi\)
−0.497044 + 0.867725i \(0.665581\pi\)
\(132\) 0 0
\(133\) −5.65685 + 5.65685i −0.490511 + 0.490511i
\(134\) 0 0
\(135\) 8.00000i 0.688530i
\(136\) 0 0
\(137\) 10.0000i 0.854358i 0.904167 + 0.427179i \(0.140493\pi\)
−0.904167 + 0.427179i \(0.859507\pi\)
\(138\) 0 0
\(139\) 7.07107 7.07107i 0.599760 0.599760i −0.340489 0.940249i \(-0.610592\pi\)
0.940249 + 0.340489i \(0.110592\pi\)
\(140\) 0 0
\(141\) −11.3137 11.3137i −0.952786 0.952786i
\(142\) 0 0
\(143\) 4.00000 0.334497
\(144\) 0 0
\(145\) 12.0000 0.996546
\(146\) 0 0
\(147\) 12.7279 + 12.7279i 1.04978 + 1.04978i
\(148\) 0 0
\(149\) −12.7279 + 12.7279i −1.04271 + 1.04271i −0.0436658 + 0.999046i \(0.513904\pi\)
−0.999046 + 0.0436658i \(0.986096\pi\)
\(150\) 0 0
\(151\) 4.00000i 0.325515i 0.986666 + 0.162758i \(0.0520389\pi\)
−0.986666 + 0.162758i \(0.947961\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.7279 12.7279i −1.01580 1.01580i −0.999873 0.0159256i \(-0.994931\pi\)
−0.0159256 0.999873i \(-0.505069\pi\)
\(158\) 0 0
\(159\) −12.0000 −0.951662
\(160\) 0 0
\(161\) −16.0000 −1.26098
\(162\) 0 0
\(163\) −1.41421 1.41421i −0.110770 0.110770i 0.649550 0.760319i \(-0.274958\pi\)
−0.760319 + 0.649550i \(0.774958\pi\)
\(164\) 0 0
\(165\) −5.65685 + 5.65685i −0.440386 + 0.440386i
\(166\) 0 0
\(167\) 20.0000i 1.54765i 0.633402 + 0.773823i \(0.281658\pi\)
−0.633402 + 0.773823i \(0.718342\pi\)
\(168\) 0 0
\(169\) 9.00000i 0.692308i
\(170\) 0 0
\(171\) −1.41421 + 1.41421i −0.108148 + 0.108148i
\(172\) 0 0
\(173\) 12.7279 + 12.7279i 0.967686 + 0.967686i 0.999494 0.0318080i \(-0.0101265\pi\)
−0.0318080 + 0.999494i \(0.510127\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) −28.0000 −2.10461
\(178\) 0 0
\(179\) −4.24264 4.24264i −0.317110 0.317110i 0.530546 0.847656i \(-0.321987\pi\)
−0.847656 + 0.530546i \(0.821987\pi\)
\(180\) 0 0
\(181\) −1.41421 + 1.41421i −0.105118 + 0.105118i −0.757710 0.652592i \(-0.773682\pi\)
0.652592 + 0.757710i \(0.273682\pi\)
\(182\) 0 0
\(183\) 4.00000i 0.295689i
\(184\) 0 0
\(185\) 20.0000i 1.47043i
\(186\) 0 0
\(187\) 2.82843 2.82843i 0.206835 0.206835i
\(188\) 0 0
\(189\) −11.3137 11.3137i −0.822951 0.822951i
\(190\) 0 0
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 0 0
\(195\) −5.65685 5.65685i −0.405096 0.405096i
\(196\) 0 0
\(197\) −9.89949 + 9.89949i −0.705310 + 0.705310i −0.965545 0.260235i \(-0.916200\pi\)
0.260235 + 0.965545i \(0.416200\pi\)
\(198\) 0 0
\(199\) 4.00000i 0.283552i 0.989899 + 0.141776i \(0.0452813\pi\)
−0.989899 + 0.141776i \(0.954719\pi\)
\(200\) 0 0
\(201\) 20.0000i 1.41069i
\(202\) 0 0
\(203\) −16.9706 + 16.9706i −1.19110 + 1.19110i
\(204\) 0 0
\(205\) −8.48528 8.48528i −0.592638 0.592638i
\(206\) 0 0
\(207\) −4.00000 −0.278019
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) −15.5563 15.5563i −1.07094 1.07094i −0.997283 0.0736598i \(-0.976532\pi\)
−0.0736598 0.997283i \(-0.523468\pi\)
\(212\) 0 0
\(213\) −16.9706 + 16.9706i −1.16280 + 1.16280i
\(214\) 0 0
\(215\) 12.0000i 0.818393i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 19.7990 19.7990i 1.33789 1.33789i
\(220\) 0 0
\(221\) 2.82843 + 2.82843i 0.190261 + 0.190261i
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 0 0
\(227\) −12.7279 12.7279i −0.844782 0.844782i 0.144695 0.989476i \(-0.453780\pi\)
−0.989476 + 0.144695i \(0.953780\pi\)
\(228\) 0 0
\(229\) −9.89949 + 9.89949i −0.654177 + 0.654177i −0.953996 0.299819i \(-0.903074\pi\)
0.299819 + 0.953996i \(0.403074\pi\)
\(230\) 0 0
\(231\) 16.0000i 1.05272i
\(232\) 0 0
\(233\) 18.0000i 1.17922i −0.807688 0.589610i \(-0.799282\pi\)
0.807688 0.589610i \(-0.200718\pi\)
\(234\) 0 0
\(235\) 11.3137 11.3137i 0.738025 0.738025i
\(236\) 0 0
\(237\) −11.3137 11.3137i −0.734904 0.734904i
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) −7.07107 7.07107i −0.453609 0.453609i
\(244\) 0 0
\(245\) −12.7279 + 12.7279i −0.813157 + 0.813157i
\(246\) 0 0
\(247\) 4.00000i 0.254514i
\(248\) 0 0
\(249\) 12.0000i 0.760469i
\(250\) 0 0
\(251\) −12.7279 + 12.7279i −0.803379 + 0.803379i −0.983622 0.180243i \(-0.942312\pi\)
0.180243 + 0.983622i \(0.442312\pi\)
\(252\) 0 0
\(253\) 5.65685 + 5.65685i 0.355643 + 0.355643i
\(254\) 0 0
\(255\) −8.00000 −0.500979
\(256\) 0 0
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 28.2843 + 28.2843i 1.75750 + 1.75750i
\(260\) 0 0
\(261\) −4.24264 + 4.24264i −0.262613 + 0.262613i
\(262\) 0 0
\(263\) 12.0000i 0.739952i −0.929041 0.369976i \(-0.879366\pi\)
0.929041 0.369976i \(-0.120634\pi\)
\(264\) 0 0
\(265\) 12.0000i 0.737154i
\(266\) 0 0
\(267\) 2.82843 2.82843i 0.173097 0.173097i
\(268\) 0 0
\(269\) 7.07107 + 7.07107i 0.431131 + 0.431131i 0.889013 0.457882i \(-0.151392\pi\)
−0.457882 + 0.889013i \(0.651392\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 16.0000 0.968364
\(274\) 0 0
\(275\) 1.41421 + 1.41421i 0.0852803 + 0.0852803i
\(276\) 0 0
\(277\) 4.24264 4.24264i 0.254916 0.254916i −0.568067 0.822982i \(-0.692309\pi\)
0.822982 + 0.568067i \(0.192309\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 18.0000i 1.07379i 0.843649 + 0.536895i \(0.180403\pi\)
−0.843649 + 0.536895i \(0.819597\pi\)
\(282\) 0 0
\(283\) 4.24264 4.24264i 0.252199 0.252199i −0.569673 0.821872i \(-0.692930\pi\)
0.821872 + 0.569673i \(0.192930\pi\)
\(284\) 0 0
\(285\) −5.65685 5.65685i −0.335083 0.335083i
\(286\) 0 0
\(287\) 24.0000 1.41668
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 2.82843 + 2.82843i 0.165805 + 0.165805i
\(292\) 0 0
\(293\) −9.89949 + 9.89949i −0.578335 + 0.578335i −0.934444 0.356110i \(-0.884103\pi\)
0.356110 + 0.934444i \(0.384103\pi\)
\(294\) 0 0
\(295\) 28.0000i 1.63022i
\(296\) 0 0
\(297\) 8.00000i 0.464207i
\(298\) 0 0
\(299\) −5.65685 + 5.65685i −0.327144 + 0.327144i
\(300\) 0 0
\(301\) −16.9706 16.9706i −0.978167 0.978167i
\(302\) 0 0
\(303\) 12.0000 0.689382
\(304\) 0 0
\(305\) −4.00000 −0.229039
\(306\) 0 0
\(307\) 12.7279 + 12.7279i 0.726421 + 0.726421i 0.969905 0.243484i \(-0.0782903\pi\)
−0.243484 + 0.969905i \(0.578290\pi\)
\(308\) 0 0
\(309\) 5.65685 5.65685i 0.321807 0.321807i
\(310\) 0 0
\(311\) 28.0000i 1.58773i −0.608091 0.793867i \(-0.708065\pi\)
0.608091 0.793867i \(-0.291935\pi\)
\(312\) 0 0
\(313\) 10.0000i 0.565233i −0.959233 0.282617i \(-0.908798\pi\)
0.959233 0.282617i \(-0.0912024\pi\)
\(314\) 0 0
\(315\) −5.65685 + 5.65685i −0.318728 + 0.318728i
\(316\) 0 0
\(317\) 4.24264 + 4.24264i 0.238290 + 0.238290i 0.816142 0.577851i \(-0.196109\pi\)
−0.577851 + 0.816142i \(0.696109\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) 2.82843 + 2.82843i 0.157378 + 0.157378i
\(324\) 0 0
\(325\) −1.41421 + 1.41421i −0.0784465 + 0.0784465i
\(326\) 0 0
\(327\) 12.0000i 0.663602i
\(328\) 0 0
\(329\) 32.0000i 1.76422i
\(330\) 0 0
\(331\) −9.89949 + 9.89949i −0.544125 + 0.544125i −0.924736 0.380610i \(-0.875714\pi\)
0.380610 + 0.924736i \(0.375714\pi\)
\(332\) 0 0
\(333\) 7.07107 + 7.07107i 0.387492 + 0.387492i
\(334\) 0 0
\(335\) −20.0000 −1.09272
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 2.82843 + 2.82843i 0.153619 + 0.153619i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 8.00000i 0.431959i
\(344\) 0 0
\(345\) 16.0000i 0.861411i
\(346\) 0 0
\(347\) −12.7279 + 12.7279i −0.683271 + 0.683271i −0.960736 0.277465i \(-0.910506\pi\)
0.277465 + 0.960736i \(0.410506\pi\)
\(348\) 0 0
\(349\) −7.07107 7.07107i −0.378506 0.378506i 0.492057 0.870563i \(-0.336245\pi\)
−0.870563 + 0.492057i \(0.836245\pi\)
\(350\) 0 0
\(351\) −8.00000 −0.427008
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) −16.9706 16.9706i −0.900704 0.900704i
\(356\) 0 0
\(357\) 11.3137 11.3137i 0.598785 0.598785i
\(358\) 0 0
\(359\) 4.00000i 0.211112i 0.994413 + 0.105556i \(0.0336622\pi\)
−0.994413 + 0.105556i \(0.966338\pi\)
\(360\) 0 0
\(361\) 15.0000i 0.789474i
\(362\) 0 0
\(363\) 9.89949 9.89949i 0.519589 0.519589i
\(364\) 0 0
\(365\) 19.7990 + 19.7990i 1.03633 + 1.03633i
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) 16.9706 + 16.9706i 0.881068 + 0.881068i
\(372\) 0 0
\(373\) −7.07107 + 7.07107i −0.366126 + 0.366126i −0.866062 0.499936i \(-0.833357\pi\)
0.499936 + 0.866062i \(0.333357\pi\)
\(374\) 0 0
\(375\) 24.0000i 1.23935i
\(376\) 0 0
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) −1.41421 + 1.41421i −0.0726433 + 0.0726433i −0.742495 0.669852i \(-0.766358\pi\)
0.669852 + 0.742495i \(0.266358\pi\)
\(380\) 0 0
\(381\) −22.6274 22.6274i −1.15924 1.15924i
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 16.0000 0.815436
\(386\) 0 0
\(387\) −4.24264 4.24264i −0.215666 0.215666i
\(388\) 0 0
\(389\) 7.07107 7.07107i 0.358517 0.358517i −0.504749 0.863266i \(-0.668415\pi\)
0.863266 + 0.504749i \(0.168415\pi\)
\(390\) 0 0
\(391\) 8.00000i 0.404577i
\(392\) 0 0
\(393\) 12.0000i 0.605320i
\(394\) 0 0
\(395\) 11.3137 11.3137i 0.569254 0.569254i
\(396\) 0 0
\(397\) −4.24264 4.24264i −0.212932 0.212932i 0.592580 0.805512i \(-0.298110\pi\)
−0.805512 + 0.592580i \(0.798110\pi\)
\(398\) 0 0
\(399\) 16.0000 0.801002
\(400\) 0 0
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 15.5563 15.5563i 0.773001 0.773001i
\(406\) 0 0
\(407\) 20.0000i 0.991363i
\(408\) 0 0
\(409\) 10.0000i 0.494468i −0.968956 0.247234i \(-0.920478\pi\)
0.968956 0.247234i \(-0.0795217\pi\)
\(410\) 0 0
\(411\) 14.1421 14.1421i 0.697580 0.697580i
\(412\) 0 0
\(413\) 39.5980 + 39.5980i 1.94849 + 1.94849i
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) −20.0000 −0.979404
\(418\) 0 0
\(419\) −18.3848 18.3848i −0.898155 0.898155i 0.0971178 0.995273i \(-0.469038\pi\)
−0.995273 + 0.0971178i \(0.969038\pi\)
\(420\) 0 0
\(421\) 24.0416 24.0416i 1.17172 1.17172i 0.189917 0.981800i \(-0.439178\pi\)
0.981800 0.189917i \(-0.0608220\pi\)
\(422\) 0 0
\(423\) 8.00000i 0.388973i
\(424\) 0 0
\(425\) 2.00000i 0.0970143i
\(426\) 0 0
\(427\) 5.65685 5.65685i 0.273754 0.273754i
\(428\) 0 0
\(429\) −5.65685 5.65685i −0.273115 0.273115i
\(430\) 0 0
\(431\) −40.0000 −1.92673 −0.963366 0.268190i \(-0.913575\pi\)
−0.963366 + 0.268190i \(0.913575\pi\)
\(432\) 0 0
\(433\) −30.0000 −1.44171 −0.720854 0.693087i \(-0.756250\pi\)
−0.720854 + 0.693087i \(0.756250\pi\)
\(434\) 0 0
\(435\) −16.9706 16.9706i −0.813676 0.813676i
\(436\) 0 0
\(437\) −5.65685 + 5.65685i −0.270604 + 0.270604i
\(438\) 0 0
\(439\) 36.0000i 1.71819i 0.511819 + 0.859093i \(0.328972\pi\)
−0.511819 + 0.859093i \(0.671028\pi\)
\(440\) 0 0
\(441\) 9.00000i 0.428571i
\(442\) 0 0
\(443\) 4.24264 4.24264i 0.201574 0.201574i −0.599100 0.800674i \(-0.704475\pi\)
0.800674 + 0.599100i \(0.204475\pi\)
\(444\) 0 0
\(445\) 2.82843 + 2.82843i 0.134080 + 0.134080i
\(446\) 0 0
\(447\) 36.0000 1.70274
\(448\) 0 0
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) −8.48528 8.48528i −0.399556 0.399556i
\(452\) 0 0
\(453\) 5.65685 5.65685i 0.265782 0.265782i
\(454\) 0 0
\(455\) 16.0000i 0.750092i
\(456\) 0 0
\(457\) 6.00000i 0.280668i −0.990104 0.140334i \(-0.955182\pi\)
0.990104 0.140334i \(-0.0448177\pi\)
\(458\) 0 0
\(459\) −5.65685 + 5.65685i −0.264039 + 0.264039i
\(460\) 0 0
\(461\) 7.07107 + 7.07107i 0.329332 + 0.329332i 0.852333 0.523000i \(-0.175187\pi\)
−0.523000 + 0.852333i \(0.675187\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.89949 9.89949i −0.458094 0.458094i 0.439935 0.898029i \(-0.355001\pi\)
−0.898029 + 0.439935i \(0.855001\pi\)
\(468\) 0 0
\(469\) 28.2843 28.2843i 1.30605 1.30605i
\(470\) 0 0
\(471\) 36.0000i 1.65879i
\(472\) 0 0
\(473\) 12.0000i 0.551761i
\(474\) 0 0
\(475\) −1.41421 + 1.41421i −0.0648886 + 0.0648886i
\(476\) 0 0
\(477\) 4.24264 + 4.24264i 0.194257 + 0.194257i
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 20.0000 0.911922
\(482\) 0 0
\(483\) 22.6274 + 22.6274i 1.02958 + 1.02958i
\(484\) 0 0
\(485\) −2.82843 + 2.82843i −0.128432 + 0.128432i
\(486\) 0 0
\(487\) 20.0000i 0.906287i 0.891438 + 0.453143i \(0.149697\pi\)
−0.891438 + 0.453143i \(0.850303\pi\)
\(488\) 0 0
\(489\) 4.00000i 0.180886i
\(490\) 0 0
\(491\) 7.07107 7.07107i 0.319113 0.319113i −0.529313 0.848426i \(-0.677550\pi\)
0.848426 + 0.529313i \(0.177550\pi\)
\(492\) 0 0
\(493\) 8.48528 + 8.48528i 0.382158 + 0.382158i
\(494\) 0 0
\(495\) 4.00000 0.179787
\(496\) 0 0
\(497\) 48.0000 2.15309
\(498\) 0 0
\(499\) −15.5563 15.5563i −0.696398 0.696398i 0.267234 0.963632i \(-0.413890\pi\)
−0.963632 + 0.267234i \(0.913890\pi\)
\(500\) 0 0
\(501\) 28.2843 28.2843i 1.26365 1.26365i
\(502\) 0 0
\(503\) 20.0000i 0.891756i 0.895094 + 0.445878i \(0.147108\pi\)
−0.895094 + 0.445878i \(0.852892\pi\)
\(504\) 0 0
\(505\) 12.0000i 0.533993i
\(506\) 0 0
\(507\) −12.7279 + 12.7279i −0.565267 + 0.565267i
\(508\) 0 0
\(509\) 9.89949 + 9.89949i 0.438787 + 0.438787i 0.891604 0.452816i \(-0.149581\pi\)
−0.452816 + 0.891604i \(0.649581\pi\)
\(510\) 0 0
\(511\) −56.0000 −2.47729
\(512\) 0 0
\(513\) −8.00000 −0.353209
\(514\) 0 0
\(515\) 5.65685 + 5.65685i 0.249271 + 0.249271i
\(516\) 0 0
\(517\) 11.3137 11.3137i 0.497576 0.497576i
\(518\) 0 0
\(519\) 36.0000i 1.58022i
\(520\) 0 0
\(521\) 22.0000i 0.963837i −0.876216 0.481919i \(-0.839940\pi\)
0.876216 0.481919i \(-0.160060\pi\)
\(522\) 0 0
\(523\) −9.89949 + 9.89949i −0.432875 + 0.432875i −0.889605 0.456730i \(-0.849020\pi\)
0.456730 + 0.889605i \(0.349020\pi\)
\(524\) 0 0
\(525\) 5.65685 + 5.65685i 0.246885 + 0.246885i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 9.89949 + 9.89949i 0.429601 + 0.429601i
\(532\) 0 0
\(533\) 8.48528 8.48528i 0.367538 0.367538i
\(534\) 0 0
\(535\) 4.00000i 0.172935i
\(536\) 0 0
\(537\) 12.0000i 0.517838i
\(538\) 0 0
\(539\) −12.7279 + 12.7279i −0.548230 + 0.548230i
\(540\) 0 0
\(541\) −24.0416 24.0416i −1.03363 1.03363i −0.999414 0.0342160i \(-0.989107\pi\)
−0.0342160 0.999414i \(-0.510893\pi\)
\(542\) 0 0
\(543\) 4.00000 0.171656
\(544\) 0 0
\(545\) −12.0000 −0.514024
\(546\) 0 0
\(547\) 26.8701 + 26.8701i 1.14888 + 1.14888i 0.986773 + 0.162108i \(0.0518292\pi\)
0.162108 + 0.986773i \(0.448171\pi\)
\(548\) 0 0
\(549\) 1.41421 1.41421i 0.0603572 0.0603572i
\(550\) 0 0
\(551\) 12.0000i 0.511217i
\(552\) 0 0
\(553\) 32.0000i 1.36078i
\(554\) 0 0
\(555\) −28.2843 + 28.2843i −1.20060 + 1.20060i
\(556\) 0 0
\(557\) 1.41421 + 1.41421i 0.0599222 + 0.0599222i 0.736433 0.676511i \(-0.236509\pi\)
−0.676511 + 0.736433i \(0.736509\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) 0 0
\(561\) −8.00000 −0.337760
\(562\) 0 0
\(563\) 12.7279 + 12.7279i 0.536418 + 0.536418i 0.922475 0.386057i \(-0.126163\pi\)
−0.386057 + 0.922475i \(0.626163\pi\)
\(564\) 0 0
\(565\) −2.82843 + 2.82843i −0.118993 + 0.118993i
\(566\) 0 0
\(567\) 44.0000i 1.84783i
\(568\) 0 0
\(569\) 26.0000i 1.08998i −0.838444 0.544988i \(-0.816534\pi\)
0.838444 0.544988i \(-0.183466\pi\)
\(570\) 0 0
\(571\) 26.8701 26.8701i 1.12448 1.12448i 0.133417 0.991060i \(-0.457405\pi\)
0.991060 0.133417i \(-0.0425949\pi\)
\(572\) 0 0
\(573\) 22.6274 + 22.6274i 0.945274 + 0.945274i
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 0 0
\(579\) 2.82843 + 2.82843i 0.117545 + 0.117545i
\(580\) 0 0
\(581\) 16.9706 16.9706i 0.704058 0.704058i
\(582\) 0 0
\(583\) 12.0000i 0.496989i
\(584\) 0 0
\(585\) 4.00000i 0.165380i
\(586\) 0 0
\(587\) 24.0416 24.0416i 0.992304 0.992304i −0.00766632 0.999971i \(-0.502440\pi\)
0.999971 + 0.00766632i \(0.00244029\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 28.0000 1.15177
\(592\) 0 0
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) 11.3137 + 11.3137i 0.463817 + 0.463817i
\(596\) 0 0
\(597\) 5.65685 5.65685i 0.231520 0.231520i
\(598\) 0 0
\(599\) 12.0000i 0.490307i −0.969484 0.245153i \(-0.921162\pi\)
0.969484 0.245153i \(-0.0788383\pi\)
\(600\) 0 0
\(601\) 30.0000i 1.22373i −0.790964 0.611863i \(-0.790420\pi\)
0.790964 0.611863i \(-0.209580\pi\)
\(602\) 0 0
\(603\) 7.07107 7.07107i 0.287956 0.287956i
\(604\) 0 0
\(605\) 9.89949 + 9.89949i 0.402472 + 0.402472i
\(606\) 0 0
\(607\) −16.0000 −0.649420 −0.324710 0.945814i \(-0.605267\pi\)
−0.324710 + 0.945814i \(0.605267\pi\)
\(608\) 0 0
\(609\) 48.0000 1.94506
\(610\) 0 0
\(611\) 11.3137 + 11.3137i 0.457704 + 0.457704i
\(612\) 0 0
\(613\) 24.0416 24.0416i 0.971032 0.971032i −0.0285598 0.999592i \(-0.509092\pi\)
0.999592 + 0.0285598i \(0.00909209\pi\)
\(614\) 0 0
\(615\) 24.0000i 0.967773i
\(616\) 0 0
\(617\) 2.00000i 0.0805170i −0.999189 0.0402585i \(-0.987182\pi\)
0.999189 0.0402585i \(-0.0128181\pi\)
\(618\) 0 0
\(619\) −32.5269 + 32.5269i −1.30737 + 1.30737i −0.384058 + 0.923309i \(0.625474\pi\)
−0.923309 + 0.384058i \(0.874526\pi\)
\(620\) 0 0
\(621\) −11.3137 11.3137i −0.454003 0.454003i
\(622\) 0 0
\(623\) −8.00000 −0.320513
\(624\) 0 0
\(625\) 19.0000 0.760000
\(626\) 0 0
\(627\) −5.65685 5.65685i −0.225913 0.225913i
\(628\) 0 0
\(629\) 14.1421 14.1421i 0.563884 0.563884i
\(630\) 0 0
\(631\) 44.0000i 1.75161i −0.482663 0.875806i \(-0.660330\pi\)
0.482663 0.875806i \(-0.339670\pi\)
\(632\) 0 0
\(633\) 44.0000i 1.74884i
\(634\) 0 0
\(635\) 22.6274 22.6274i 0.897942 0.897942i
\(636\) 0 0
\(637\) −12.7279 12.7279i −0.504299 0.504299i
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) −29.6985 29.6985i −1.17119 1.17119i −0.981925 0.189269i \(-0.939388\pi\)
−0.189269 0.981925i \(-0.560612\pi\)
\(644\) 0 0
\(645\) 16.9706 16.9706i 0.668215 0.668215i
\(646\) 0 0
\(647\) 12.0000i 0.471769i −0.971781 0.235884i \(-0.924201\pi\)
0.971781 0.235884i \(-0.0757987\pi\)
\(648\) 0 0
\(649\) 28.0000i 1.09910i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 29.6985 + 29.6985i 1.16219 + 1.16219i 0.983995 + 0.178197i \(0.0570263\pi\)
0.178197 + 0.983995i \(0.442974\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) 0 0
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) −4.24264 4.24264i −0.165270 0.165270i 0.619627 0.784897i \(-0.287284\pi\)
−0.784897 + 0.619627i \(0.787284\pi\)
\(660\) 0 0
\(661\) −24.0416 + 24.0416i −0.935111 + 0.935111i −0.998019 0.0629083i \(-0.979962\pi\)
0.0629083 + 0.998019i \(0.479962\pi\)
\(662\) 0 0
\(663\) 8.00000i 0.310694i
\(664\) 0 0
\(665\) 16.0000i 0.620453i
\(666\) 0 0
\(667\) −16.9706 + 16.9706i −0.657103 + 0.657103i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) −2.82843 2.82843i −0.108866 0.108866i
\(676\) 0 0
\(677\) −15.5563 + 15.5563i −0.597879 + 0.597879i −0.939748 0.341869i \(-0.888940\pi\)
0.341869 + 0.939748i \(0.388940\pi\)
\(678\) 0 0
\(679\) 8.00000i 0.307012i
\(680\) 0 0
\(681\) 36.0000i 1.37952i
\(682\) 0 0
\(683\) 29.6985 29.6985i 1.13638 1.13638i 0.147287 0.989094i \(-0.452946\pi\)
0.989094 0.147287i \(-0.0470541\pi\)
\(684\) 0 0
\(685\) 14.1421 + 14.1421i 0.540343 + 0.540343i
\(686\) 0 0
\(687\) 28.0000 1.06827
\(688\) 0 0
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) −4.24264 4.24264i −0.161398 0.161398i 0.621788 0.783186i \(-0.286407\pi\)
−0.783186 + 0.621788i \(0.786407\pi\)
\(692\) 0 0
\(693\) −5.65685 + 5.65685i −0.214886 + 0.214886i
\(694\) 0 0
\(695\) 20.0000i 0.758643i
\(696\) 0 0
\(697\) 12.0000i 0.454532i
\(698\) 0 0
\(699\) −25.4558 + 25.4558i −0.962828 + 0.962828i
\(700\) 0 0
\(701\) −1.41421 1.41421i −0.0534141 0.0534141i 0.679895 0.733309i \(-0.262025\pi\)
−0.733309 + 0.679895i \(0.762025\pi\)
\(702\) 0 0
\(703\) 20.0000 0.754314
\(704\) 0 0
\(705\) −32.0000 −1.20519
\(706\) 0 0
\(707\) −16.9706 16.9706i −0.638244 0.638244i
\(708\) 0 0
\(709\) −15.5563 + 15.5563i −0.584231 + 0.584231i −0.936063 0.351832i \(-0.885559\pi\)
0.351832 + 0.936063i \(0.385559\pi\)
\(710\) 0 0
\(711\) 8.00000i 0.300023i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 5.65685 5.65685i 0.211554 0.211554i
\(716\) 0 0
\(717\) −33.9411 33.9411i −1.26755 1.26755i
\(718\) 0 0
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) −16.0000 −0.595871
\(722\) 0 0
\(723\) −2.82843 2.82843i −0.105190 0.105190i
\(724\) 0 0
\(725\) −4.24264 + 4.24264i −0.157568 + 0.157568i
\(726\) 0 0
\(727\) 12.0000i 0.445055i −0.974926 0.222528i \(-0.928569\pi\)
0.974926 0.222528i \(-0.0714308\pi\)
\(728\) 0 0
\(729\) 13.0000i 0.481481i
\(730\) 0 0
\(731\) −8.48528 + 8.48528i −0.313839 + 0.313839i
\(732\) 0 0
\(733\) 4.24264 + 4.24264i 0.156706 + 0.156706i 0.781105 0.624400i \(-0.214656\pi\)
−0.624400 + 0.781105i \(0.714656\pi\)
\(734\) 0 0
\(735\) 36.0000 1.32788
\(736\) 0 0
\(737\) −20.0000 −0.736709
\(738\) 0 0
\(739\) −12.7279 12.7279i −0.468204 0.468204i 0.433128 0.901332i \(-0.357410\pi\)
−0.901332 + 0.433128i \(0.857410\pi\)
\(740\) 0 0
\(741\) 5.65685 5.65685i 0.207810 0.207810i
\(742\) 0 0
\(743\) 44.0000i 1.61420i −0.590412 0.807102i \(-0.701035\pi\)
0.590412 0.807102i \(-0.298965\pi\)
\(744\) 0 0
\(745\) 36.0000i 1.31894i
\(746\) 0 0
\(747\) 4.24264 4.24264i 0.155230 0.155230i
\(748\) 0 0
\(749\) 5.65685 + 5.65685i 0.206697 + 0.206697i
\(750\) 0 0
\(751\) −8.00000 −0.291924 −0.145962 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 0 0
\(753\) 36.0000 1.31191
\(754\) 0 0
\(755\) 5.65685 + 5.65685i 0.205874 + 0.205874i
\(756\) 0 0
\(757\) 32.5269 32.5269i 1.18221 1.18221i 0.203040 0.979170i \(-0.434918\pi\)
0.979170 0.203040i \(-0.0650823\pi\)
\(758\) 0 0
\(759\) 16.0000i 0.580763i
\(760\) 0 0
\(761\) 10.0000i 0.362500i −0.983437 0.181250i \(-0.941986\pi\)
0.983437 0.181250i \(-0.0580143\pi\)
\(762\) 0 0
\(763\) 16.9706 16.9706i 0.614376 0.614376i
\(764\) 0 0
\(765\) 2.82843 + 2.82843i 0.102262 + 0.102262i
\(766\) 0 0
\(767\) 28.0000 1.01102
\(768\) 0 0
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −25.4558 25.4558i −0.916770 0.916770i
\(772\) 0 0
\(773\) −38.1838 + 38.1838i −1.37337 + 1.37337i −0.517985 + 0.855390i \(0.673318\pi\)
−0.855390 + 0.517985i \(0.826682\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 80.0000i 2.86998i
\(778\) 0 0
\(779\) 8.48528 8.48528i 0.304017 0.304017i
\(780\) 0 0
\(781\) −16.9706 16.9706i −0.607254 0.607254i
\(782\) 0 0
\(783\) −24.0000 −0.857690
\(784\) 0 0
\(785\) −36.0000 −1.28490
\(786\) 0 0
\(787\) −15.5563 15.5563i −0.554524 0.554524i 0.373219 0.927743i \(-0.378254\pi\)
−0.927743 + 0.373219i \(0.878254\pi\)
\(788\) 0 0
\(789\) −16.9706 + 16.9706i −0.604168 + 0.604168i
\(790\) 0 0
\(791\) 8.00000i 0.284447i
\(792\) 0 0
\(793\) 4.00000i 0.142044i
\(794\) 0 0
\(795\) −16.9706 + 16.9706i −0.601884 + 0.601884i
\(796\) 0 0
\(797\) −12.7279 12.7279i −0.450846 0.450846i 0.444789 0.895635i \(-0.353279\pi\)
−0.895635 + 0.444789i \(0.853279\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039