Properties

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

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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: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 512)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 769.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1024.769
Dual form 1024.2.e.e.257.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{3} +(2.00000 + 2.00000i) q^{5} -4.00000i q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{3} +(2.00000 + 2.00000i) q^{5} -4.00000i q^{7} +1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(-2.00000 + 2.00000i) q^{13} +4.00000 q^{15} +4.00000 q^{17} +(5.00000 - 5.00000i) q^{19} +(-4.00000 - 4.00000i) q^{21} +4.00000i q^{23} +3.00000i q^{25} +(4.00000 + 4.00000i) q^{27} +(6.00000 - 6.00000i) q^{29} -8.00000 q^{31} +2.00000 q^{33} +(8.00000 - 8.00000i) q^{35} +(-2.00000 - 2.00000i) q^{37} +4.00000i q^{39} -2.00000i q^{41} +(3.00000 + 3.00000i) q^{43} +(-2.00000 + 2.00000i) q^{45} -9.00000 q^{49} +(4.00000 - 4.00000i) q^{51} +(2.00000 + 2.00000i) q^{53} +4.00000i q^{55} -10.0000i q^{57} +(-3.00000 - 3.00000i) q^{59} +(-6.00000 + 6.00000i) q^{61} +4.00000 q^{63} -8.00000 q^{65} +(3.00000 - 3.00000i) q^{67} +(4.00000 + 4.00000i) q^{69} +4.00000i q^{71} +4.00000i q^{73} +(3.00000 + 3.00000i) q^{75} +(4.00000 - 4.00000i) q^{77} -8.00000 q^{79} +5.00000 q^{81} +(7.00000 - 7.00000i) q^{83} +(8.00000 + 8.00000i) q^{85} -12.0000i q^{87} +12.0000i q^{89} +(8.00000 + 8.00000i) q^{91} +(-8.00000 + 8.00000i) q^{93} +20.0000 q^{95} -4.00000 q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} + 4q^{5} + O(q^{10}) \) \( 2q + 2q^{3} + 4q^{5} + 2q^{11} - 4q^{13} + 8q^{15} + 8q^{17} + 10q^{19} - 8q^{21} + 8q^{27} + 12q^{29} - 16q^{31} + 4q^{33} + 16q^{35} - 4q^{37} + 6q^{43} - 4q^{45} - 18q^{49} + 8q^{51} + 4q^{53} - 6q^{59} - 12q^{61} + 8q^{63} - 16q^{65} + 6q^{67} + 8q^{69} + 6q^{75} + 8q^{77} - 16q^{79} + 10q^{81} + 14q^{83} + 16q^{85} + 16q^{91} - 16q^{93} + 40q^{95} - 8q^{97} - 2q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 1.00000i 0.577350 0.577350i −0.356822 0.934172i \(-0.616140\pi\)
0.934172 + 0.356822i \(0.116140\pi\)
\(4\) 0 0
\(5\) 2.00000 + 2.00000i 0.894427 + 0.894427i 0.994936 0.100509i \(-0.0320471\pi\)
−0.100509 + 0.994936i \(0.532047\pi\)
\(6\) 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
\(11\) 1.00000 + 1.00000i 0.301511 + 0.301511i 0.841605 0.540094i \(-0.181611\pi\)
−0.540094 + 0.841605i \(0.681611\pi\)
\(12\) 0 0
\(13\) −2.00000 + 2.00000i −0.554700 + 0.554700i −0.927794 0.373094i \(-0.878297\pi\)
0.373094 + 0.927794i \(0.378297\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 5.00000 5.00000i 1.14708 1.14708i 0.159954 0.987124i \(-0.448865\pi\)
0.987124 0.159954i \(-0.0511347\pi\)
\(20\) 0 0
\(21\) −4.00000 4.00000i −0.872872 0.872872i
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 0 0
\(25\) 3.00000i 0.600000i
\(26\) 0 0
\(27\) 4.00000 + 4.00000i 0.769800 + 0.769800i
\(28\) 0 0
\(29\) 6.00000 6.00000i 1.11417 1.11417i 0.121592 0.992580i \(-0.461200\pi\)
0.992580 0.121592i \(-0.0387999\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 0 0
\(33\) 2.00000 0.348155
\(34\) 0 0
\(35\) 8.00000 8.00000i 1.35225 1.35225i
\(36\) 0 0
\(37\) −2.00000 2.00000i −0.328798 0.328798i 0.523331 0.852129i \(-0.324689\pi\)
−0.852129 + 0.523331i \(0.824689\pi\)
\(38\) 0 0
\(39\) 4.00000i 0.640513i
\(40\) 0 0
\(41\) 2.00000i 0.312348i −0.987730 0.156174i \(-0.950084\pi\)
0.987730 0.156174i \(-0.0499160\pi\)
\(42\) 0 0
\(43\) 3.00000 + 3.00000i 0.457496 + 0.457496i 0.897833 0.440337i \(-0.145141\pi\)
−0.440337 + 0.897833i \(0.645141\pi\)
\(44\) 0 0
\(45\) −2.00000 + 2.00000i −0.298142 + 0.298142i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −9.00000 −1.28571
\(50\) 0 0
\(51\) 4.00000 4.00000i 0.560112 0.560112i
\(52\) 0 0
\(53\) 2.00000 + 2.00000i 0.274721 + 0.274721i 0.830997 0.556276i \(-0.187770\pi\)
−0.556276 + 0.830997i \(0.687770\pi\)
\(54\) 0 0
\(55\) 4.00000i 0.539360i
\(56\) 0 0
\(57\) 10.0000i 1.32453i
\(58\) 0 0
\(59\) −3.00000 3.00000i −0.390567 0.390567i 0.484323 0.874889i \(-0.339066\pi\)
−0.874889 + 0.484323i \(0.839066\pi\)
\(60\) 0 0
\(61\) −6.00000 + 6.00000i −0.768221 + 0.768221i −0.977793 0.209572i \(-0.932793\pi\)
0.209572 + 0.977793i \(0.432793\pi\)
\(62\) 0 0
\(63\) 4.00000 0.503953
\(64\) 0 0
\(65\) −8.00000 −0.992278
\(66\) 0 0
\(67\) 3.00000 3.00000i 0.366508 0.366508i −0.499694 0.866202i \(-0.666554\pi\)
0.866202 + 0.499694i \(0.166554\pi\)
\(68\) 0 0
\(69\) 4.00000 + 4.00000i 0.481543 + 0.481543i
\(70\) 0 0
\(71\) 4.00000i 0.474713i 0.971423 + 0.237356i \(0.0762809\pi\)
−0.971423 + 0.237356i \(0.923719\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) 0 0
\(75\) 3.00000 + 3.00000i 0.346410 + 0.346410i
\(76\) 0 0
\(77\) 4.00000 4.00000i 0.455842 0.455842i
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) 7.00000 7.00000i 0.768350 0.768350i −0.209466 0.977816i \(-0.567173\pi\)
0.977816 + 0.209466i \(0.0671726\pi\)
\(84\) 0 0
\(85\) 8.00000 + 8.00000i 0.867722 + 0.867722i
\(86\) 0 0
\(87\) 12.0000i 1.28654i
\(88\) 0 0
\(89\) 12.0000i 1.27200i 0.771690 + 0.635999i \(0.219412\pi\)
−0.771690 + 0.635999i \(0.780588\pi\)
\(90\) 0 0
\(91\) 8.00000 + 8.00000i 0.838628 + 0.838628i
\(92\) 0 0
\(93\) −8.00000 + 8.00000i −0.829561 + 0.829561i
\(94\) 0 0
\(95\) 20.0000 2.05196
\(96\) 0 0
\(97\) −4.00000 −0.406138 −0.203069 0.979164i \(-0.565092\pi\)
−0.203069 + 0.979164i \(0.565092\pi\)
\(98\) 0 0
\(99\) −1.00000 + 1.00000i −0.100504 + 0.100504i
\(100\) 0 0
\(101\) −2.00000 2.00000i −0.199007 0.199007i 0.600567 0.799574i \(-0.294942\pi\)
−0.799574 + 0.600567i \(0.794942\pi\)
\(102\) 0 0
\(103\) 12.0000i 1.18240i −0.806527 0.591198i \(-0.798655\pi\)
0.806527 0.591198i \(-0.201345\pi\)
\(104\) 0 0
\(105\) 16.0000i 1.56144i
\(106\) 0 0
\(107\) −7.00000 7.00000i −0.676716 0.676716i 0.282540 0.959256i \(-0.408823\pi\)
−0.959256 + 0.282540i \(0.908823\pi\)
\(108\) 0 0
\(109\) 10.0000 10.0000i 0.957826 0.957826i −0.0413197 0.999146i \(-0.513156\pi\)
0.999146 + 0.0413197i \(0.0131562\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) −8.00000 + 8.00000i −0.746004 + 0.746004i
\(116\) 0 0
\(117\) −2.00000 2.00000i −0.184900 0.184900i
\(118\) 0 0
\(119\) 16.0000i 1.46672i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) 0 0
\(123\) −2.00000 2.00000i −0.180334 0.180334i
\(124\) 0 0
\(125\) 4.00000 4.00000i 0.357771 0.357771i
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 6.00000 0.528271
\(130\) 0 0
\(131\) −5.00000 + 5.00000i −0.436852 + 0.436852i −0.890951 0.454099i \(-0.849961\pi\)
0.454099 + 0.890951i \(0.349961\pi\)
\(132\) 0 0
\(133\) −20.0000 20.0000i −1.73422 1.73422i
\(134\) 0 0
\(135\) 16.0000i 1.37706i
\(136\) 0 0
\(137\) 18.0000i 1.53784i 0.639343 + 0.768922i \(0.279207\pi\)
−0.639343 + 0.768922i \(0.720793\pi\)
\(138\) 0 0
\(139\) 3.00000 + 3.00000i 0.254457 + 0.254457i 0.822795 0.568338i \(-0.192414\pi\)
−0.568338 + 0.822795i \(0.692414\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.00000 −0.334497
\(144\) 0 0
\(145\) 24.0000 1.99309
\(146\) 0 0
\(147\) −9.00000 + 9.00000i −0.742307 + 0.742307i
\(148\) 0 0
\(149\) −2.00000 2.00000i −0.163846 0.163846i 0.620422 0.784268i \(-0.286961\pi\)
−0.784268 + 0.620422i \(0.786961\pi\)
\(150\) 0 0
\(151\) 4.00000i 0.325515i 0.986666 + 0.162758i \(0.0520389\pi\)
−0.986666 + 0.162758i \(0.947961\pi\)
\(152\) 0 0
\(153\) 4.00000i 0.323381i
\(154\) 0 0
\(155\) −16.0000 16.0000i −1.28515 1.28515i
\(156\) 0 0
\(157\) −6.00000 + 6.00000i −0.478852 + 0.478852i −0.904764 0.425912i \(-0.859953\pi\)
0.425912 + 0.904764i \(0.359953\pi\)
\(158\) 0 0
\(159\) 4.00000 0.317221
\(160\) 0 0
\(161\) 16.0000 1.26098
\(162\) 0 0
\(163\) −7.00000 + 7.00000i −0.548282 + 0.548282i −0.925944 0.377661i \(-0.876728\pi\)
0.377661 + 0.925944i \(0.376728\pi\)
\(164\) 0 0
\(165\) 4.00000 + 4.00000i 0.311400 + 0.311400i
\(166\) 0 0
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 5.00000 + 5.00000i 0.382360 + 0.382360i
\(172\) 0 0
\(173\) −10.0000 + 10.0000i −0.760286 + 0.760286i −0.976374 0.216088i \(-0.930670\pi\)
0.216088 + 0.976374i \(0.430670\pi\)
\(174\) 0 0
\(175\) 12.0000 0.907115
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) 0 0
\(179\) −1.00000 + 1.00000i −0.0747435 + 0.0747435i −0.743490 0.668747i \(-0.766831\pi\)
0.668747 + 0.743490i \(0.266831\pi\)
\(180\) 0 0
\(181\) 6.00000 + 6.00000i 0.445976 + 0.445976i 0.894015 0.448038i \(-0.147877\pi\)
−0.448038 + 0.894015i \(0.647877\pi\)
\(182\) 0 0
\(183\) 12.0000i 0.887066i
\(184\) 0 0
\(185\) 8.00000i 0.588172i
\(186\) 0 0
\(187\) 4.00000 + 4.00000i 0.292509 + 0.292509i
\(188\) 0 0
\(189\) 16.0000 16.0000i 1.16383 1.16383i
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0 0
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 0 0
\(195\) −8.00000 + 8.00000i −0.572892 + 0.572892i
\(196\) 0 0
\(197\) 10.0000 + 10.0000i 0.712470 + 0.712470i 0.967051 0.254581i \(-0.0819375\pi\)
−0.254581 + 0.967051i \(0.581938\pi\)
\(198\) 0 0
\(199\) 4.00000i 0.283552i −0.989899 0.141776i \(-0.954719\pi\)
0.989899 0.141776i \(-0.0452813\pi\)
\(200\) 0 0
\(201\) 6.00000i 0.423207i
\(202\) 0 0
\(203\) −24.0000 24.0000i −1.68447 1.68447i
\(204\) 0 0
\(205\) 4.00000 4.00000i 0.279372 0.279372i
\(206\) 0 0
\(207\) −4.00000 −0.278019
\(208\) 0 0
\(209\) 10.0000 0.691714
\(210\) 0 0
\(211\) −17.0000 + 17.0000i −1.17033 + 1.17033i −0.188197 + 0.982131i \(0.560264\pi\)
−0.982131 + 0.188197i \(0.939736\pi\)
\(212\) 0 0
\(213\) 4.00000 + 4.00000i 0.274075 + 0.274075i
\(214\) 0 0
\(215\) 12.0000i 0.818393i
\(216\) 0 0
\(217\) 32.0000i 2.17230i
\(218\) 0 0
\(219\) 4.00000 + 4.00000i 0.270295 + 0.270295i
\(220\) 0 0
\(221\) −8.00000 + 8.00000i −0.538138 + 0.538138i
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) −15.0000 + 15.0000i −0.995585 + 0.995585i −0.999990 0.00440533i \(-0.998598\pi\)
0.00440533 + 0.999990i \(0.498598\pi\)
\(228\) 0 0
\(229\) 18.0000 + 18.0000i 1.18947 + 1.18947i 0.977213 + 0.212260i \(0.0680825\pi\)
0.212260 + 0.977213i \(0.431918\pi\)
\(230\) 0 0
\(231\) 8.00000i 0.526361i
\(232\) 0 0
\(233\) 12.0000i 0.786146i −0.919507 0.393073i \(-0.871412\pi\)
0.919507 0.393073i \(-0.128588\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −8.00000 + 8.00000i −0.519656 + 0.519656i
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) −12.0000 −0.772988 −0.386494 0.922292i \(-0.626314\pi\)
−0.386494 + 0.922292i \(0.626314\pi\)
\(242\) 0 0
\(243\) −7.00000 + 7.00000i −0.449050 + 0.449050i
\(244\) 0 0
\(245\) −18.0000 18.0000i −1.14998 1.14998i
\(246\) 0 0
\(247\) 20.0000i 1.27257i
\(248\) 0 0
\(249\) 14.0000i 0.887214i
\(250\) 0 0
\(251\) −3.00000 3.00000i −0.189358 0.189358i 0.606060 0.795419i \(-0.292749\pi\)
−0.795419 + 0.606060i \(0.792749\pi\)
\(252\) 0 0
\(253\) −4.00000 + 4.00000i −0.251478 + 0.251478i
\(254\) 0 0
\(255\) 16.0000 1.00196
\(256\) 0 0
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) −8.00000 + 8.00000i −0.497096 + 0.497096i
\(260\) 0 0
\(261\) 6.00000 + 6.00000i 0.371391 + 0.371391i
\(262\) 0 0
\(263\) 28.0000i 1.72655i −0.504730 0.863277i \(-0.668408\pi\)
0.504730 0.863277i \(-0.331592\pi\)
\(264\) 0 0
\(265\) 8.00000i 0.491436i
\(266\) 0 0
\(267\) 12.0000 + 12.0000i 0.734388 + 0.734388i
\(268\) 0 0
\(269\) −14.0000 + 14.0000i −0.853595 + 0.853595i −0.990574 0.136979i \(-0.956261\pi\)
0.136979 + 0.990574i \(0.456261\pi\)
\(270\) 0 0
\(271\) 32.0000 1.94386 0.971931 0.235267i \(-0.0755965\pi\)
0.971931 + 0.235267i \(0.0755965\pi\)
\(272\) 0 0
\(273\) 16.0000 0.968364
\(274\) 0 0
\(275\) −3.00000 + 3.00000i −0.180907 + 0.180907i
\(276\) 0 0
\(277\) −6.00000 6.00000i −0.360505 0.360505i 0.503494 0.863999i \(-0.332048\pi\)
−0.863999 + 0.503494i \(0.832048\pi\)
\(278\) 0 0
\(279\) 8.00000i 0.478947i
\(280\) 0 0
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) 0 0
\(283\) −17.0000 17.0000i −1.01055 1.01055i −0.999944 0.0106013i \(-0.996625\pi\)
−0.0106013 0.999944i \(-0.503375\pi\)
\(284\) 0 0
\(285\) 20.0000 20.0000i 1.18470 1.18470i
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −4.00000 + 4.00000i −0.234484 + 0.234484i
\(292\) 0 0
\(293\) −6.00000 6.00000i −0.350524 0.350524i 0.509781 0.860304i \(-0.329727\pi\)
−0.860304 + 0.509781i \(0.829727\pi\)
\(294\) 0 0
\(295\) 12.0000i 0.698667i
\(296\) 0 0
\(297\) 8.00000i 0.464207i
\(298\) 0 0
\(299\) −8.00000 8.00000i −0.462652 0.462652i
\(300\) 0 0
\(301\) 12.0000 12.0000i 0.691669 0.691669i
\(302\) 0 0
\(303\) −4.00000 −0.229794
\(304\) 0 0
\(305\) −24.0000 −1.37424
\(306\) 0 0
\(307\) 5.00000 5.00000i 0.285365 0.285365i −0.549879 0.835244i \(-0.685326\pi\)
0.835244 + 0.549879i \(0.185326\pi\)
\(308\) 0 0
\(309\) −12.0000 12.0000i −0.682656 0.682656i
\(310\) 0 0
\(311\) 20.0000i 1.13410i −0.823685 0.567048i \(-0.808085\pi\)
0.823685 0.567048i \(-0.191915\pi\)
\(312\) 0 0
\(313\) 14.0000i 0.791327i −0.918396 0.395663i \(-0.870515\pi\)
0.918396 0.395663i \(-0.129485\pi\)
\(314\) 0 0
\(315\) 8.00000 + 8.00000i 0.450749 + 0.450749i
\(316\) 0 0
\(317\) −2.00000 + 2.00000i −0.112331 + 0.112331i −0.761038 0.648707i \(-0.775310\pi\)
0.648707 + 0.761038i \(0.275310\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) −14.0000 −0.781404
\(322\) 0 0
\(323\) 20.0000 20.0000i 1.11283 1.11283i
\(324\) 0 0
\(325\) −6.00000 6.00000i −0.332820 0.332820i
\(326\) 0 0
\(327\) 20.0000i 1.10600i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 9.00000 + 9.00000i 0.494685 + 0.494685i 0.909779 0.415094i \(-0.136251\pi\)
−0.415094 + 0.909779i \(0.636251\pi\)
\(332\) 0 0
\(333\) 2.00000 2.00000i 0.109599 0.109599i
\(334\) 0 0
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) −30.0000 −1.63420 −0.817102 0.576493i \(-0.804421\pi\)
−0.817102 + 0.576493i \(0.804421\pi\)
\(338\) 0 0
\(339\) −14.0000 + 14.0000i −0.760376 + 0.760376i
\(340\) 0 0
\(341\) −8.00000 8.00000i −0.433224 0.433224i
\(342\) 0 0
\(343\) 8.00000i 0.431959i
\(344\) 0 0
\(345\) 16.0000i 0.861411i
\(346\) 0 0
\(347\) −11.0000 11.0000i −0.590511 0.590511i 0.347259 0.937769i \(-0.387113\pi\)
−0.937769 + 0.347259i \(0.887113\pi\)
\(348\) 0 0
\(349\) 14.0000 14.0000i 0.749403 0.749403i −0.224964 0.974367i \(-0.572227\pi\)
0.974367 + 0.224964i \(0.0722265\pi\)
\(350\) 0 0
\(351\) −16.0000 −0.854017
\(352\) 0 0
\(353\) −14.0000 −0.745145 −0.372572 0.928003i \(-0.621524\pi\)
−0.372572 + 0.928003i \(0.621524\pi\)
\(354\) 0 0
\(355\) −8.00000 + 8.00000i −0.424596 + 0.424596i
\(356\) 0 0
\(357\) −16.0000 16.0000i −0.846810 0.846810i
\(358\) 0 0
\(359\) 36.0000i 1.90001i 0.312239 + 0.950004i \(0.398921\pi\)
−0.312239 + 0.950004i \(0.601079\pi\)
\(360\) 0 0
\(361\) 31.0000i 1.63158i
\(362\) 0 0
\(363\) −9.00000 9.00000i −0.472377 0.472377i
\(364\) 0 0
\(365\) −8.00000 + 8.00000i −0.418739 + 0.418739i
\(366\) 0 0
\(367\) 16.0000 0.835193 0.417597 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) 0 0
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) 8.00000 8.00000i 0.415339 0.415339i
\(372\) 0 0
\(373\) 26.0000 + 26.0000i 1.34623 + 1.34623i 0.889718 + 0.456511i \(0.150901\pi\)
0.456511 + 0.889718i \(0.349099\pi\)
\(374\) 0 0
\(375\) 8.00000i 0.413118i
\(376\) 0 0
\(377\) 24.0000i 1.23606i
\(378\) 0 0
\(379\) 21.0000 + 21.0000i 1.07870 + 1.07870i 0.996626 + 0.0820711i \(0.0261534\pi\)
0.0820711 + 0.996626i \(0.473847\pi\)
\(380\) 0 0
\(381\) −8.00000 + 8.00000i −0.409852 + 0.409852i
\(382\) 0 0
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 0 0
\(385\) 16.0000 0.815436
\(386\) 0 0
\(387\) −3.00000 + 3.00000i −0.152499 + 0.152499i
\(388\) 0 0
\(389\) 14.0000 + 14.0000i 0.709828 + 0.709828i 0.966499 0.256671i \(-0.0826256\pi\)
−0.256671 + 0.966499i \(0.582626\pi\)
\(390\) 0 0
\(391\) 16.0000i 0.809155i
\(392\) 0 0
\(393\) 10.0000i 0.504433i
\(394\) 0 0
\(395\) −16.0000 16.0000i −0.805047 0.805047i
\(396\) 0 0
\(397\) 2.00000 2.00000i 0.100377 0.100377i −0.655135 0.755512i \(-0.727388\pi\)
0.755512 + 0.655135i \(0.227388\pi\)
\(398\) 0 0
\(399\) −40.0000 −2.00250
\(400\) 0 0
\(401\) 36.0000 1.79775 0.898877 0.438201i \(-0.144384\pi\)
0.898877 + 0.438201i \(0.144384\pi\)
\(402\) 0 0
\(403\) 16.0000 16.0000i 0.797017 0.797017i
\(404\) 0 0
\(405\) 10.0000 + 10.0000i 0.496904 + 0.496904i
\(406\) 0 0
\(407\) 4.00000i 0.198273i
\(408\) 0 0
\(409\) 14.0000i 0.692255i −0.938187 0.346128i \(-0.887496\pi\)
0.938187 0.346128i \(-0.112504\pi\)
\(410\) 0 0
\(411\) 18.0000 + 18.0000i 0.887875 + 0.887875i
\(412\) 0 0
\(413\) −12.0000 + 12.0000i −0.590481 + 0.590481i
\(414\) 0 0
\(415\) 28.0000 1.37447
\(416\) 0 0
\(417\) 6.00000 0.293821
\(418\) 0 0
\(419\) 19.0000 19.0000i 0.928211 0.928211i −0.0693796 0.997590i \(-0.522102\pi\)
0.997590 + 0.0693796i \(0.0221020\pi\)
\(420\) 0 0
\(421\) −6.00000 6.00000i −0.292422 0.292422i 0.545614 0.838036i \(-0.316296\pi\)
−0.838036 + 0.545614i \(0.816296\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 12.0000i 0.582086i
\(426\) 0 0
\(427\) 24.0000 + 24.0000i 1.16144 + 1.16144i
\(428\) 0 0
\(429\) −4.00000 + 4.00000i −0.193122 + 0.193122i
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) 20.0000 0.961139 0.480569 0.876957i \(-0.340430\pi\)
0.480569 + 0.876957i \(0.340430\pi\)
\(434\) 0 0
\(435\) 24.0000 24.0000i 1.15071 1.15071i
\(436\) 0 0
\(437\) 20.0000 + 20.0000i 0.956730 + 0.956730i
\(438\) 0 0
\(439\) 4.00000i 0.190910i −0.995434 0.0954548i \(-0.969569\pi\)
0.995434 0.0954548i \(-0.0304305\pi\)
\(440\) 0 0
\(441\) 9.00000i 0.428571i
\(442\) 0 0
\(443\) −25.0000 25.0000i −1.18779 1.18779i −0.977678 0.210108i \(-0.932619\pi\)
−0.210108 0.977678i \(-0.567381\pi\)
\(444\) 0 0
\(445\) −24.0000 + 24.0000i −1.13771 + 1.13771i
\(446\) 0 0
\(447\) −4.00000 −0.189194
\(448\) 0 0
\(449\) −20.0000 −0.943858 −0.471929 0.881636i \(-0.656442\pi\)
−0.471929 + 0.881636i \(0.656442\pi\)
\(450\) 0 0
\(451\) 2.00000 2.00000i 0.0941763 0.0941763i
\(452\) 0 0
\(453\) 4.00000 + 4.00000i 0.187936 + 0.187936i
\(454\) 0 0
\(455\) 32.0000i 1.50018i
\(456\) 0 0
\(457\) 2.00000i 0.0935561i −0.998905 0.0467780i \(-0.985105\pi\)
0.998905 0.0467780i \(-0.0148953\pi\)
\(458\) 0 0
\(459\) 16.0000 + 16.0000i 0.746816 + 0.746816i
\(460\) 0 0
\(461\) 10.0000 10.0000i 0.465746 0.465746i −0.434787 0.900533i \(-0.643176\pi\)
0.900533 + 0.434787i \(0.143176\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) −32.0000 −1.48396
\(466\) 0 0
\(467\) 13.0000 13.0000i 0.601568 0.601568i −0.339160 0.940729i \(-0.610143\pi\)
0.940729 + 0.339160i \(0.110143\pi\)
\(468\) 0 0
\(469\) −12.0000 12.0000i −0.554109 0.554109i
\(470\) 0 0
\(471\) 12.0000i 0.552931i
\(472\) 0 0
\(473\) 6.00000i 0.275880i
\(474\) 0 0
\(475\) 15.0000 + 15.0000i 0.688247 + 0.688247i
\(476\) 0 0
\(477\) −2.00000 + 2.00000i −0.0915737 + 0.0915737i
\(478\) 0 0
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 0 0
\(483\) 16.0000 16.0000i 0.728025 0.728025i
\(484\) 0 0
\(485\) −8.00000 8.00000i −0.363261 0.363261i
\(486\) 0 0
\(487\) 12.0000i 0.543772i 0.962329 + 0.271886i \(0.0876473\pi\)
−0.962329 + 0.271886i \(0.912353\pi\)
\(488\) 0 0
\(489\) 14.0000i 0.633102i
\(490\) 0 0
\(491\) 11.0000 + 11.0000i 0.496423 + 0.496423i 0.910323 0.413900i \(-0.135834\pi\)
−0.413900 + 0.910323i \(0.635834\pi\)
\(492\) 0 0
\(493\) 24.0000 24.0000i 1.08091 1.08091i
\(494\) 0 0
\(495\) −4.00000 −0.179787
\(496\) 0 0
\(497\) 16.0000 0.717698
\(498\) 0 0
\(499\) −9.00000 + 9.00000i −0.402895 + 0.402895i −0.879252 0.476357i \(-0.841957\pi\)
0.476357 + 0.879252i \(0.341957\pi\)
\(500\) 0 0
\(501\) 12.0000 + 12.0000i 0.536120 + 0.536120i
\(502\) 0 0
\(503\) 20.0000i 0.891756i 0.895094 + 0.445878i \(0.147108\pi\)
−0.895094 + 0.445878i \(0.852892\pi\)
\(504\) 0 0
\(505\) 8.00000i 0.355995i
\(506\) 0 0
\(507\) 5.00000 + 5.00000i 0.222058 + 0.222058i
\(508\) 0 0
\(509\) 2.00000 2.00000i 0.0886484 0.0886484i −0.661392 0.750040i \(-0.730034\pi\)
0.750040 + 0.661392i \(0.230034\pi\)
\(510\) 0 0
\(511\) 16.0000 0.707798
\(512\) 0 0
\(513\) 40.0000 1.76604
\(514\) 0 0
\(515\) 24.0000 24.0000i 1.05757 1.05757i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 20.0000i 0.877903i
\(520\) 0 0
\(521\) 14.0000i 0.613351i −0.951814 0.306676i \(-0.900783\pi\)
0.951814 0.306676i \(-0.0992167\pi\)
\(522\) 0 0
\(523\) −7.00000 7.00000i −0.306089 0.306089i 0.537302 0.843390i \(-0.319444\pi\)
−0.843390 + 0.537302i \(0.819444\pi\)
\(524\) 0 0
\(525\) 12.0000 12.0000i 0.523723 0.523723i
\(526\) 0 0
\(527\) −32.0000 −1.39394
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 3.00000 3.00000i 0.130189 0.130189i
\(532\) 0 0
\(533\) 4.00000 + 4.00000i 0.173259 + 0.173259i
\(534\) 0 0
\(535\) 28.0000i 1.21055i
\(536\) 0 0
\(537\) 2.00000i 0.0863064i
\(538\) 0 0
\(539\) −9.00000 9.00000i −0.387657 0.387657i
\(540\) 0 0
\(541\) −6.00000 + 6.00000i −0.257960 + 0.257960i −0.824224 0.566264i \(-0.808388\pi\)
0.566264 + 0.824224i \(0.308388\pi\)
\(542\) 0 0
\(543\) 12.0000 0.514969
\(544\) 0 0
\(545\) 40.0000 1.71341
\(546\) 0 0
\(547\) 19.0000 19.0000i 0.812381 0.812381i −0.172609 0.984990i \(-0.555220\pi\)
0.984990 + 0.172609i \(0.0552197\pi\)
\(548\) 0 0
\(549\) −6.00000 6.00000i −0.256074 0.256074i
\(550\) 0 0
\(551\) 60.0000i 2.55609i
\(552\) 0 0
\(553\) 32.0000i 1.36078i
\(554\) 0 0
\(555\) −8.00000 8.00000i −0.339581 0.339581i
\(556\) 0 0
\(557\) 22.0000 22.0000i 0.932170 0.932170i −0.0656714 0.997841i \(-0.520919\pi\)
0.997841 + 0.0656714i \(0.0209189\pi\)
\(558\) 0 0
\(559\) −12.0000 −0.507546
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 0 0
\(563\) 5.00000 5.00000i 0.210725 0.210725i −0.593851 0.804575i \(-0.702393\pi\)
0.804575 + 0.593851i \(0.202393\pi\)
\(564\) 0 0
\(565\) −28.0000 28.0000i −1.17797 1.17797i
\(566\) 0 0
\(567\) 20.0000i 0.839921i
\(568\) 0 0
\(569\) 30.0000i 1.25767i 0.777541 + 0.628833i \(0.216467\pi\)
−0.777541 + 0.628833i \(0.783533\pi\)
\(570\) 0 0
\(571\) 23.0000 + 23.0000i 0.962520 + 0.962520i 0.999323 0.0368025i \(-0.0117173\pi\)
−0.0368025 + 0.999323i \(0.511717\pi\)
\(572\) 0 0
\(573\) −8.00000 + 8.00000i −0.334205 + 0.334205i
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) 0 0
\(579\) −4.00000 + 4.00000i −0.166234 + 0.166234i
\(580\) 0 0
\(581\) −28.0000 28.0000i −1.16164 1.16164i
\(582\) 0 0
\(583\) 4.00000i 0.165663i
\(584\) 0 0
\(585\) 8.00000i 0.330759i
\(586\) 0 0
\(587\) 1.00000 + 1.00000i 0.0412744 + 0.0412744i 0.727443 0.686168i \(-0.240709\pi\)
−0.686168 + 0.727443i \(0.740709\pi\)
\(588\) 0 0
\(589\) −40.0000 + 40.0000i −1.64817 + 1.64817i
\(590\) 0 0
\(591\) 20.0000 0.822690
\(592\) 0 0
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) 32.0000 32.0000i 1.31187 1.31187i
\(596\) 0 0
\(597\) −4.00000 4.00000i −0.163709 0.163709i
\(598\) 0 0
\(599\) 36.0000i 1.47092i −0.677568 0.735460i \(-0.736966\pi\)
0.677568 0.735460i \(-0.263034\pi\)
\(600\) 0 0
\(601\) 4.00000i 0.163163i −0.996667 0.0815817i \(-0.974003\pi\)
0.996667 0.0815817i \(-0.0259972\pi\)
\(602\) 0 0
\(603\) 3.00000 + 3.00000i 0.122169 + 0.122169i
\(604\) 0 0
\(605\) 18.0000 18.0000i 0.731804 0.731804i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) −48.0000 −1.94506
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −6.00000 6.00000i −0.242338 0.242338i 0.575479 0.817817i \(-0.304816\pi\)
−0.817817 + 0.575479i \(0.804816\pi\)
\(614\) 0 0
\(615\) 8.00000i 0.322591i
\(616\) 0 0
\(617\) 28.0000i 1.12724i −0.826035 0.563619i \(-0.809409\pi\)
0.826035 0.563619i \(-0.190591\pi\)
\(618\) 0 0
\(619\) 1.00000 + 1.00000i 0.0401934 + 0.0401934i 0.726918 0.686724i \(-0.240952\pi\)
−0.686724 + 0.726918i \(0.740952\pi\)
\(620\) 0 0
\(621\) −16.0000 + 16.0000i −0.642058 + 0.642058i
\(622\) 0 0
\(623\) 48.0000 1.92308
\(624\) 0 0
\(625\) 31.0000 1.24000
\(626\) 0 0
\(627\) 10.0000 10.0000i 0.399362 0.399362i
\(628\) 0 0
\(629\) −8.00000 8.00000i −0.318981 0.318981i
\(630\) 0 0
\(631\) 4.00000i 0.159237i 0.996825 + 0.0796187i \(0.0253703\pi\)
−0.996825 + 0.0796187i \(0.974630\pi\)
\(632\) 0 0
\(633\) 34.0000i 1.35138i
\(634\) 0 0
\(635\) −16.0000 16.0000i −0.634941 0.634941i
\(636\) 0 0
\(637\) 18.0000 18.0000i 0.713186 0.713186i
\(638\) 0 0
\(639\) −4.00000 −0.158238
\(640\) 0 0
\(641\) −4.00000 −0.157991 −0.0789953 0.996875i \(-0.525171\pi\)
−0.0789953 + 0.996875i \(0.525171\pi\)
\(642\) 0 0
\(643\) 3.00000 3.00000i 0.118308 0.118308i −0.645474 0.763782i \(-0.723340\pi\)
0.763782 + 0.645474i \(0.223340\pi\)
\(644\) 0 0
\(645\) 12.0000 + 12.0000i 0.472500 + 0.472500i
\(646\) 0 0
\(647\) 12.0000i 0.471769i −0.971781 0.235884i \(-0.924201\pi\)
0.971781 0.235884i \(-0.0757987\pi\)
\(648\) 0 0
\(649\) 6.00000i 0.235521i
\(650\) 0 0
\(651\) 32.0000 + 32.0000i 1.25418 + 1.25418i
\(652\) 0 0
\(653\) 34.0000 34.0000i 1.33052 1.33052i 0.425622 0.904901i \(-0.360055\pi\)
0.904901 0.425622i \(-0.139945\pi\)
\(654\) 0 0
\(655\) −20.0000 −0.781465
\(656\) 0 0
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) 23.0000 23.0000i 0.895953 0.895953i −0.0991224 0.995075i \(-0.531604\pi\)
0.995075 + 0.0991224i \(0.0316036\pi\)
\(660\) 0 0
\(661\) 22.0000 + 22.0000i 0.855701 + 0.855701i 0.990828 0.135127i \(-0.0431444\pi\)
−0.135127 + 0.990828i \(0.543144\pi\)
\(662\) 0 0
\(663\) 16.0000i 0.621389i
\(664\) 0 0
\(665\) 80.0000i 3.10227i
\(666\) 0 0
\(667\) 24.0000 + 24.0000i 0.929284 + 0.929284i
\(668\) 0 0
\(669\) −24.0000 + 24.0000i −0.927894 + 0.927894i
\(670\) 0 0
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) −20.0000 −0.770943 −0.385472 0.922720i \(-0.625961\pi\)
−0.385472 + 0.922720i \(0.625961\pi\)
\(674\) 0 0
\(675\) −12.0000 + 12.0000i −0.461880 + 0.461880i
\(676\) 0 0
\(677\) 30.0000 + 30.0000i 1.15299 + 1.15299i 0.985949 + 0.167044i \(0.0534223\pi\)
0.167044 + 0.985949i \(0.446578\pi\)
\(678\) 0 0
\(679\) 16.0000i 0.614024i
\(680\) 0 0
\(681\) 30.0000i 1.14960i
\(682\) 0 0
\(683\) −21.0000 21.0000i −0.803543 0.803543i 0.180105 0.983647i \(-0.442356\pi\)
−0.983647 + 0.180105i \(0.942356\pi\)
\(684\) 0 0
\(685\) −36.0000 + 36.0000i −1.37549 + 1.37549i
\(686\) 0 0
\(687\) 36.0000 1.37349
\(688\) 0 0
\(689\) −8.00000 −0.304776
\(690\) 0 0
\(691\) −33.0000 + 33.0000i −1.25538 + 1.25538i −0.302104 + 0.953275i \(0.597689\pi\)
−0.953275 + 0.302104i \(0.902311\pi\)
\(692\) 0 0
\(693\) 4.00000 + 4.00000i 0.151947 + 0.151947i
\(694\) 0 0
\(695\) 12.0000i 0.455186i
\(696\) 0 0
\(697\) 8.00000i 0.303022i
\(698\) 0 0
\(699\) −12.0000 12.0000i −0.453882 0.453882i
\(700\) 0 0
\(701\) 34.0000 34.0000i 1.28416 1.28416i 0.345886 0.938277i \(-0.387579\pi\)
0.938277 0.345886i \(-0.112421\pi\)
\(702\) 0 0
\(703\) −20.0000 −0.754314
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.00000 + 8.00000i −0.300871 + 0.300871i
\(708\) 0 0
\(709\) 6.00000 + 6.00000i 0.225335 + 0.225335i 0.810740 0.585406i \(-0.199065\pi\)
−0.585406 + 0.810740i \(0.699065\pi\)
\(710\) 0 0
\(711\) 8.00000i 0.300023i
\(712\) 0 0
\(713\) 32.0000i 1.19841i
\(714\) 0 0
\(715\) −8.00000 8.00000i −0.299183 0.299183i
\(716\) 0 0
\(717\) −8.00000 + 8.00000i −0.298765 + 0.298765i
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) −48.0000 −1.78761
\(722\) 0 0
\(723\) −12.0000 + 12.0000i −0.446285 + 0.446285i
\(724\) 0 0
\(725\) 18.0000 + 18.0000i 0.668503 + 0.668503i
\(726\) 0 0
\(727\) 28.0000i 1.03846i 0.854634 + 0.519231i \(0.173782\pi\)
−0.854634 + 0.519231i \(0.826218\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 12.0000 + 12.0000i 0.443836 + 0.443836i
\(732\) 0 0
\(733\) 14.0000 14.0000i 0.517102 0.517102i −0.399592 0.916693i \(-0.630848\pi\)
0.916693 + 0.399592i \(0.130848\pi\)
\(734\) 0 0
\(735\) −36.0000 −1.32788
\(736\) 0 0
\(737\) 6.00000 0.221013
\(738\) 0 0
\(739\) 17.0000 17.0000i 0.625355 0.625355i −0.321541 0.946896i \(-0.604201\pi\)
0.946896 + 0.321541i \(0.104201\pi\)
\(740\) 0 0
\(741\) 20.0000 + 20.0000i 0.734718 + 0.734718i
\(742\) 0 0
\(743\) 4.00000i 0.146746i −0.997305 0.0733729i \(-0.976624\pi\)
0.997305 0.0733729i \(-0.0233763\pi\)
\(744\) 0 0
\(745\) 8.00000i 0.293097i
\(746\) 0 0
\(747\) 7.00000 + 7.00000i 0.256117 + 0.256117i
\(748\) 0 0
\(749\) −28.0000 + 28.0000i −1.02310 + 1.02310i
\(750\) 0 0
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 0 0
\(753\) −6.00000 −0.218652
\(754\) 0 0
\(755\) −8.00000 + 8.00000i −0.291150 + 0.291150i
\(756\) 0 0
\(757\) −18.0000 18.0000i −0.654221 0.654221i 0.299786 0.954007i \(-0.403085\pi\)
−0.954007 + 0.299786i \(0.903085\pi\)
\(758\) 0 0
\(759\) 8.00000i 0.290382i
\(760\) 0 0
\(761\) 18.0000i 0.652499i 0.945284 + 0.326250i \(0.105785\pi\)
−0.945284 + 0.326250i \(0.894215\pi\)
\(762\) 0 0
\(763\) −40.0000 40.0000i −1.44810 1.44810i
\(764\) 0 0
\(765\) −8.00000 + 8.00000i −0.289241 + 0.289241i
\(766\) 0 0
\(767\) 12.0000 0.433295
\(768\) 0 0
\(769\) 44.0000 1.58668 0.793340 0.608778i \(-0.208340\pi\)
0.793340 + 0.608778i \(0.208340\pi\)
\(770\) 0 0
\(771\) −2.00000 + 2.00000i −0.0720282 + 0.0720282i
\(772\) 0 0
\(773\) 6.00000 + 6.00000i 0.215805 + 0.215805i 0.806728 0.590923i \(-0.201236\pi\)
−0.590923 + 0.806728i \(0.701236\pi\)
\(774\) 0 0
\(775\) 24.0000i 0.862105i
\(776\) 0 0
\(777\) 16.0000i 0.573997i
\(778\) 0 0
\(779\) −10.0000 10.0000i −0.358287 0.358287i
\(780\) 0 0
\(781\) −4.00000 + 4.00000i −0.143131 + 0.143131i
\(782\) 0 0
\(783\) 48.0000 1.71538
\(784\) 0 0
\(785\) −24.0000 −0.856597
\(786\) 0 0
\(787\) −33.0000 + 33.0000i −1.17632 + 1.17632i −0.195649 + 0.980674i \(0.562681\pi\)
−0.980674 + 0.195649i \(0.937319\pi\)
\(788\) 0 0
\(789\) −28.0000 28.0000i −0.996826 0.996826i
\(790\) 0 0
\(791\) 56.0000i 1.99113i
\(792\) 0 0
\(793\) 24.0000i 0.852265i
\(794\) 0 0
\(795\) 8.00000 + 8.00000i 0.283731 + 0.283731i
\(796\) 0 0
\(797\) −14.0000 + 14.0000i −0.495905 + 0.495905i −0.910161 0.414255i \(-0.864042\pi\)
0.414255 +