Properties

Label 1024.2.e.i.769.1
Level $1024$
Weight $2$
Character 1024.769
Analytic conductor $8.177$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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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 769.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1024.769
Dual form 1024.2.e.i.257.1

$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).

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

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 −0.985599 0.169102i \(-0.945913\pi\)
0.169102 + 0.985599i \(0.445913\pi\)
\(4\) 0 0
\(5\) 1.41421 + 1.41421i 0.632456 + 0.632456i 0.948683 0.316228i \(-0.102416\pi\)
−0.316228 + 0.948683i \(0.602416\pi\)
\(6\) 0 0
\(7\) 4.00000i 1.51186i −0.654654 0.755929i \(-0.727186\pi\)
0.654654 0.755929i \(-0.272814\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 1.41421 + 1.41421i 0.426401 + 0.426401i 0.887401 0.460999i \(-0.152509\pi\)
−0.460999 + 0.887401i \(0.652509\pi\)
\(12\) 0 0
\(13\) 1.41421 1.41421i 0.392232 0.392232i −0.483250 0.875482i \(-0.660544\pi\)
0.875482 + 0.483250i \(0.160544\pi\)
\(14\) 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 −0.526026 0.850469i \(-0.676318\pi\)
0.850469 + 0.526026i \(0.176318\pi\)
\(20\) 0 0
\(21\) 5.65685 + 5.65685i 1.23443 + 1.23443i
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 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 −0.193301 0.981140i \(-0.561919\pi\)
0.981140 + 0.193301i \(0.0619194\pi\)
\(30\) 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 0.983932 + 0.178545i \(0.0571389\pi\)
0.178545 + 0.983932i \(0.442861\pi\)
\(38\) 0 0
\(39\) 4.00000i 0.640513i
\(40\) 0 0
\(41\) 6.00000i 0.937043i 0.883452 + 0.468521i \(0.155213\pi\)
−0.883452 + 0.468521i \(0.844787\pi\)
\(42\) 0 0
\(43\) −4.24264 4.24264i −0.646997 0.646997i 0.305269 0.952266i \(-0.401253\pi\)
−0.952266 + 0.305269i \(0.901253\pi\)
\(44\) 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 0.935664 0.352892i \(-0.114802\pi\)
−0.352892 + 0.935664i \(0.614802\pi\)
\(54\) 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 0.935513 + 0.353291i \(0.114937\pi\)
0.353291 + 0.935513i \(0.385063\pi\)
\(60\) 0 0
\(61\) −1.41421 + 1.41421i −0.181071 + 0.181071i −0.791823 0.610751i \(-0.790868\pi\)
0.610751 + 0.791823i \(0.290868\pi\)
\(62\) 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 −0.991785 0.127917i \(-0.959171\pi\)
0.127917 + 0.991785i \(0.459171\pi\)
\(68\) 0 0
\(69\) 5.65685 + 5.65685i 0.681005 + 0.681005i
\(70\) 0 0
\(71\) 12.0000i 1.42414i 0.702109 + 0.712069i \(0.252242\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(72\) 0 0
\(73\) 14.0000i 1.63858i −0.573382 0.819288i \(-0.694369\pi\)
0.573382 0.819288i \(-0.305631\pi\)
\(74\) 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 −0.900515 0.434825i \(-0.856810\pi\)
0.434825 + 0.900515i \(0.356810\pi\)
\(84\) 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 \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 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 0.463788 0.885946i \(-0.346490\pi\)
−0.885946 + 0.463788i \(0.846490\pi\)
\(102\) 0 0
\(103\) 4.00000i 0.394132i −0.980390 0.197066i \(-0.936859\pi\)
0.980390 0.197066i \(-0.0631413\pi\)
\(104\) 0 0
\(105\) 16.0000i 1.56144i
\(106\) 0 0
\(107\) 1.41421 + 1.41421i 0.136717 + 0.136717i 0.772153 0.635436i \(-0.219180\pi\)
−0.635436 + 0.772153i \(0.719180\pi\)
\(108\) 0 0
\(109\) −4.24264 + 4.24264i −0.406371 + 0.406371i −0.880471 0.474100i \(-0.842774\pi\)
0.474100 + 0.880471i \(0.342774\pi\)
\(110\) 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 −0.497044 0.867725i \(-0.665581\pi\)
0.867725 + 0.497044i \(0.165581\pi\)
\(132\) 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 \(-0.859507\pi\)
0.904167 0.427179i \(-0.140493\pi\)
\(138\) 0 0
\(139\) 7.07107 + 7.07107i 0.599760 + 0.599760i 0.940249 0.340489i \(-0.110592\pi\)
−0.340489 + 0.940249i \(0.610592\pi\)
\(140\) 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 −0.999046 0.0436658i \(-0.986096\pi\)
−0.0436658 0.999046i \(-0.513904\pi\)
\(150\) 0 0
\(151\) 4.00000i 0.325515i −0.986666 0.162758i \(-0.947961\pi\)
0.986666 0.162758i \(-0.0520389\pi\)
\(152\) 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 −0.0159256 + 0.999873i \(0.505069\pi\)
−0.999873 + 0.0159256i \(0.994931\pi\)
\(158\) 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 −0.760319 0.649550i \(-0.774958\pi\)
0.649550 + 0.760319i \(0.274958\pi\)
\(164\) 0 0
\(165\) −5.65685 5.65685i −0.440386 0.440386i
\(166\) 0 0
\(167\) 20.0000i 1.54765i −0.633402 0.773823i \(-0.718342\pi\)
0.633402 0.773823i \(-0.281658\pi\)
\(168\) 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 −0.0318080 0.999494i \(-0.510127\pi\)
0.999494 + 0.0318080i \(0.0101265\pi\)
\(174\) 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 −0.847656 0.530546i \(-0.821987\pi\)
0.530546 + 0.847656i \(0.321987\pi\)
\(180\) 0 0
\(181\) −1.41421 1.41421i −0.105118 0.105118i 0.652592 0.757710i \(-0.273682\pi\)
−0.757710 + 0.652592i \(0.773682\pi\)
\(182\) 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 0.260235 0.965545i \(-0.416200\pi\)
−0.965545 + 0.260235i \(0.916200\pi\)
\(198\) 0 0
\(199\) 4.00000i 0.283552i −0.989899 0.141776i \(-0.954719\pi\)
0.989899 0.141776i \(-0.0452813\pi\)
\(200\) 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 −0.0736598 + 0.997283i \(0.523468\pi\)
−0.997283 + 0.0736598i \(0.976532\pi\)
\(212\) 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 −0.989476 0.144695i \(-0.953780\pi\)
0.144695 + 0.989476i \(0.453780\pi\)
\(228\) 0 0
\(229\) −9.89949 9.89949i −0.654177 0.654177i 0.299819 0.953996i \(-0.403074\pi\)
−0.953996 + 0.299819i \(0.903074\pi\)
\(230\) 0 0
\(231\) 16.0000i 1.05272i
\(232\) 0 0
\(233\) 18.0000i 1.17922i 0.807688 + 0.589610i \(0.200718\pi\)
−0.807688 + 0.589610i \(0.799282\pi\)
\(234\) 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 0.180243 0.983622i \(-0.442312\pi\)
−0.983622 + 0.180243i \(0.942312\pi\)
\(252\) 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 \(0.120634\pi\)
−0.929041 + 0.369976i \(0.879366\pi\)
\(264\) 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 −0.457882 0.889013i \(-0.651392\pi\)
0.889013 + 0.457882i \(0.151392\pi\)
\(270\) 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 0.822982 0.568067i \(-0.192309\pi\)
−0.568067 + 0.822982i \(0.692309\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 18.0000i 1.07379i −0.843649 0.536895i \(-0.819597\pi\)
0.843649 0.536895i \(-0.180403\pi\)
\(282\) 0 0
\(283\) 4.24264 + 4.24264i 0.252199 + 0.252199i 0.821872 0.569673i \(-0.192930\pi\)
−0.569673 + 0.821872i \(0.692930\pi\)
\(284\) 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 0.356110 0.934444i \(-0.384103\pi\)
−0.934444 + 0.356110i \(0.884103\pi\)
\(294\) 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 −0.243484 0.969905i \(-0.578290\pi\)
0.969905 + 0.243484i \(0.0782903\pi\)
\(308\) 0 0
\(309\) 5.65685 + 5.65685i 0.321807 + 0.321807i
\(310\) 0 0
\(311\) 28.0000i 1.58773i 0.608091 + 0.793867i \(0.291935\pi\)
−0.608091 + 0.793867i \(0.708065\pi\)
\(312\) 0 0
\(313\) 10.0000i 0.565233i 0.959233 + 0.282617i \(0.0912024\pi\)
−0.959233 + 0.282617i \(0.908798\pi\)
\(314\) 0 0
\(315\) −5.65685 5.65685i −0.318728 0.318728i
\(316\) 0 0
\(317\) 4.24264 4.24264i 0.238290 0.238290i −0.577851 0.816142i \(-0.696109\pi\)
0.816142 + 0.577851i \(0.196109\pi\)
\(318\) 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 0.380610 0.924736i \(-0.375714\pi\)
−0.924736 + 0.380610i \(0.875714\pi\)
\(332\) 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 0.277465 0.960736i \(-0.410506\pi\)
−0.960736 + 0.277465i \(0.910506\pi\)
\(348\) 0 0
\(349\) −7.07107 + 7.07107i −0.378506 + 0.378506i −0.870563 0.492057i \(-0.836245\pi\)
0.492057 + 0.870563i \(0.336245\pi\)
\(350\) 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 \(-0.966338\pi\)
0.994413 0.105556i \(-0.0336622\pi\)
\(360\) 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 0.499936 0.866062i \(-0.333357\pi\)
−0.866062 + 0.499936i \(0.833357\pi\)
\(374\) 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 0.669852 0.742495i \(-0.266358\pi\)
−0.742495 + 0.669852i \(0.766358\pi\)
\(380\) 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 0.863266 0.504749i \(-0.168415\pi\)
−0.504749 + 0.863266i \(0.668415\pi\)
\(390\) 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 −0.805512 0.592580i \(-0.798110\pi\)
0.592580 + 0.805512i \(0.298110\pi\)
\(398\) 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 \(0.0795217\pi\)
−0.968956 + 0.247234i \(0.920478\pi\)
\(410\) 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 −0.995273 0.0971178i \(-0.969038\pi\)
0.0971178 + 0.995273i \(0.469038\pi\)
\(420\) 0 0
\(421\) 24.0416 + 24.0416i 1.17172 + 1.17172i 0.981800 + 0.189917i \(0.0608220\pi\)
0.189917 + 0.981800i \(0.439178\pi\)
\(422\) 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 \(-0.671028\pi\)
0.511819 0.859093i \(-0.328972\pi\)
\(440\) 0 0
\(441\) 9.00000i 0.428571i
\(442\) 0 0
\(443\) 4.24264 + 4.24264i 0.201574 + 0.201574i 0.800674 0.599100i \(-0.204475\pi\)
−0.599100 + 0.800674i \(0.704475\pi\)
\(444\) 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 \(0.0448177\pi\)
−0.990104 + 0.140334i \(0.955182\pi\)
\(458\) 0 0
\(459\) −5.65685 5.65685i −0.264039 0.264039i
\(460\) 0 0
\(461\) 7.07107 7.07107i 0.329332 0.329332i −0.523000 0.852333i \(-0.675187\pi\)
0.852333 + 0.523000i \(0.175187\pi\)
\(462\) 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 −0.898029 0.439935i \(-0.855001\pi\)
0.439935 + 0.898029i \(0.355001\pi\)
\(468\) 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 \(-0.850303\pi\)
0.891438 0.453143i \(-0.149697\pi\)
\(488\) 0 0
\(489\) 4.00000i 0.180886i
\(490\) 0 0
\(491\) 7.07107 + 7.07107i 0.319113 + 0.319113i 0.848426 0.529313i \(-0.177550\pi\)
−0.529313 + 0.848426i \(0.677550\pi\)
\(492\) 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 −0.963632 0.267234i \(-0.913890\pi\)
0.267234 + 0.963632i \(0.413890\pi\)
\(500\) 0 0
\(501\) 28.2843 + 28.2843i 1.26365 + 1.26365i
\(502\) 0 0
\(503\) 20.0000i 0.891756i −0.895094 0.445878i \(-0.852892\pi\)
0.895094 0.445878i \(-0.147108\pi\)
\(504\) 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 −0.452816 0.891604i \(-0.649581\pi\)
0.891604 + 0.452816i \(0.149581\pi\)
\(510\) 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 \(0.160060\pi\)
−0.876216 + 0.481919i \(0.839940\pi\)
\(522\) 0 0
\(523\) −9.89949 9.89949i −0.432875 0.432875i 0.456730 0.889605i \(-0.349020\pi\)
−0.889605 + 0.456730i \(0.849020\pi\)
\(524\) 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 −0.0342160 + 0.999414i \(0.510893\pi\)
−0.999414 + 0.0342160i \(0.989107\pi\)
\(542\) 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 0.162108 0.986773i \(-0.448171\pi\)
0.986773 0.162108i \(-0.0518292\pi\)
\(548\) 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 −0.676511 0.736433i \(-0.736509\pi\)
0.736433 + 0.676511i \(0.236509\pi\)
\(558\) 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 −0.386057 0.922475i \(-0.626163\pi\)
0.922475 + 0.386057i \(0.126163\pi\)
\(564\) 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 \(0.183466\pi\)
−0.838444 + 0.544988i \(0.816534\pi\)
\(570\) 0 0
\(571\) 26.8701 + 26.8701i 1.12448 + 1.12448i 0.991060 + 0.133417i \(0.0425949\pi\)
0.133417 + 0.991060i \(0.457405\pi\)
\(572\) 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 0.999971 0.00766632i \(-0.00244029\pi\)
−0.00766632 + 0.999971i \(0.502440\pi\)
\(588\) 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 \(0.0788383\pi\)
−0.969484 + 0.245153i \(0.921162\pi\)
\(600\) 0 0
\(601\) 30.0000i 1.22373i 0.790964 + 0.611863i \(0.209580\pi\)
−0.790964 + 0.611863i \(0.790420\pi\)
\(602\) 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 0.999592 0.0285598i \(-0.00909209\pi\)
−0.0285598 + 0.999592i \(0.509092\pi\)
\(614\) 0 0
\(615\) 24.0000i 0.967773i
\(616\) 0 0
\(617\) 2.00000i 0.0805170i 0.999189 + 0.0402585i \(0.0128181\pi\)
−0.999189 + 0.0402585i \(0.987182\pi\)
\(618\) 0 0
\(619\) −32.5269 32.5269i −1.30737 1.30737i −0.923309 0.384058i \(-0.874526\pi\)
−0.384058 0.923309i \(-0.625474\pi\)
\(620\) 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 \(0.339670\pi\)
−0.482663 + 0.875806i \(0.660330\pi\)
\(632\) 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 −0.189269 + 0.981925i \(0.560612\pi\)
−0.981925 + 0.189269i \(0.939388\pi\)
\(644\) 0 0
\(645\) 16.9706 + 16.9706i 0.668215 + 0.668215i
\(646\) 0 0
\(647\) 12.0000i 0.471769i 0.971781 + 0.235884i \(0.0757987\pi\)
−0.971781 + 0.235884i \(0.924201\pi\)
\(648\) 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 0.178197 0.983995i \(-0.442974\pi\)
0.983995 0.178197i \(-0.0570263\pi\)
\(654\) 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 −0.784897 0.619627i \(-0.787284\pi\)
0.619627 + 0.784897i \(0.287284\pi\)
\(660\) 0 0
\(661\) −24.0416 24.0416i −0.935111 0.935111i 0.0629083 0.998019i \(-0.479962\pi\)
−0.998019 + 0.0629083i \(0.979962\pi\)
\(662\) 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 0.341869 0.939748i \(-0.388940\pi\)
−0.939748 + 0.341869i \(0.888940\pi\)
\(678\) 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 0.989094 + 0.147287i \(0.0470541\pi\)
0.147287 + 0.989094i \(0.452946\pi\)
\(684\) 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 −0.783186 0.621788i \(-0.786407\pi\)
0.621788 + 0.783186i \(0.286407\pi\)
\(692\) 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 −0.733309 0.679895i \(-0.762025\pi\)
0.679895 + 0.733309i \(0.262025\pi\)
\(702\) 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 0.351832 0.936063i \(-0.385559\pi\)
−0.936063 + 0.351832i \(0.885559\pi\)
\(710\) 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 \(0.0714308\pi\)
−0.974926 + 0.222528i \(0.928569\pi\)
\(728\) 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 −0.624400 0.781105i \(-0.714656\pi\)
0.781105 + 0.624400i \(0.214656\pi\)
\(734\) 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 −0.901332 0.433128i \(-0.857410\pi\)
0.433128 + 0.901332i \(0.357410\pi\)
\(740\) 0 0
\(741\) 5.65685 + 5.65685i 0.207810 + 0.207810i
\(742\) 0 0
\(743\) 44.0000i 1.61420i 0.590412 + 0.807102i \(0.298965\pi\)
−0.590412 + 0.807102i \(0.701035\pi\)
\(744\) 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 0.979170 + 0.203040i \(0.0650823\pi\)
0.203040 + 0.979170i \(0.434918\pi\)
\(758\) 0 0
\(759\) 16.0000i 0.580763i
\(760\) 0 0
\(761\) 10.0000i 0.362500i 0.983437 + 0.181250i \(0.0580143\pi\)
−0.983437 + 0.181250i \(0.941986\pi\)
\(762\) 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 −0.855390 0.517985i \(-0.826682\pi\)
−0.517985 0.855390i \(-0.673318\pi\)
\(774\) 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 −0.927743 0.373219i \(-0.878254\pi\)
0.373219 + 0.927743i \(0.378254\pi\)
\(788\) 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 −0.895635 0.444789i \(-0.853279\pi\)
0.444789 + 0.895635i \(0.353279\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039