Properties

Label 1024.2.e.d.257.1
Level $1024$
Weight $2$
Character 1024.257
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 257.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1024.257
Dual form 1024.2.e.d.769.1

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

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

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
\(3\) 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i \(-0.116140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) 0 0
\(5\) −2.00000 + 2.00000i −0.894427 + 0.894427i −0.994936 0.100509i \(-0.967953\pi\)
0.100509 + 0.994936i \(0.467953\pi\)
\(6\) 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 −0.540094 0.841605i \(-0.681611\pi\)
0.841605 + 0.540094i \(0.181611\pi\)
\(12\) 0 0
\(13\) 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i \(-0.121703\pi\)
−0.373094 + 0.927794i \(0.621703\pi\)
\(14\) 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 0.987124 + 0.159954i \(0.0511347\pi\)
0.159954 + 0.987124i \(0.448865\pi\)
\(20\) 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 −0.992580 0.121592i \(-0.961200\pi\)
−0.121592 0.992580i \(-0.538800\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 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 \(-0.675311\pi\)
0.852129 + 0.523331i \(0.175311\pi\)
\(38\) 0 0
\(39\) 4.00000i 0.640513i
\(40\) 0 0
\(41\) 2.00000i 0.312348i 0.987730 + 0.156174i \(0.0499160\pi\)
−0.987730 + 0.156174i \(0.950084\pi\)
\(42\) 0 0
\(43\) 3.00000 3.00000i 0.457496 0.457496i −0.440337 0.897833i \(-0.645141\pi\)
0.897833 + 0.440337i \(0.145141\pi\)
\(44\) 0 0
\(45\) 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 \(-0.812230\pi\)
0.556276 + 0.830997i \(0.312230\pi\)
\(54\) 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 −0.874889 0.484323i \(-0.839066\pi\)
0.484323 + 0.874889i \(0.339066\pi\)
\(60\) 0 0
\(61\) 6.00000 + 6.00000i 0.768221 + 0.768221i 0.977793 0.209572i \(-0.0672070\pi\)
−0.209572 + 0.977793i \(0.567207\pi\)
\(62\) 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 0.866202 0.499694i \(-0.166554\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(68\) 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 \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 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 \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) 7.00000 + 7.00000i 0.768350 + 0.768350i 0.977816 0.209466i \(-0.0671726\pi\)
−0.209466 + 0.977816i \(0.567173\pi\)
\(84\) 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 \(-0.780588\pi\)
0.771690 0.635999i \(-0.219412\pi\)
\(90\) 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 \(-0.705058\pi\)
0.799574 + 0.600567i \(0.205058\pi\)
\(102\) 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 −0.959256 0.282540i \(-0.908823\pi\)
0.282540 + 0.959256i \(0.408823\pi\)
\(108\) 0 0
\(109\) −10.0000 10.0000i −0.957826 0.957826i 0.0413197 0.999146i \(-0.486844\pi\)
−0.999146 + 0.0413197i \(0.986844\pi\)
\(110\) 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 \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 6.00000 0.528271
\(130\) 0 0
\(131\) −5.00000 5.00000i −0.436852 0.436852i 0.454099 0.890951i \(-0.349961\pi\)
−0.890951 + 0.454099i \(0.849961\pi\)
\(132\) 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 \(-0.720793\pi\)
0.639343 0.768922i \(-0.279207\pi\)
\(138\) 0 0
\(139\) 3.00000 3.00000i 0.254457 0.254457i −0.568338 0.822795i \(-0.692414\pi\)
0.822795 + 0.568338i \(0.192414\pi\)
\(140\) 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 \(-0.713039\pi\)
0.784268 + 0.620422i \(0.213039\pi\)
\(150\) 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 \(-0.140047\pi\)
−0.425912 + 0.904764i \(0.640047\pi\)
\(158\) 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 0.377661 0.925944i \(-0.376728\pi\)
−0.925944 + 0.377661i \(0.876728\pi\)
\(164\) 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 \(-0.0693298\pi\)
−0.216088 + 0.976374i \(0.569330\pi\)
\(174\) 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 0.668747 0.743490i \(-0.266831\pi\)
−0.743490 + 0.668747i \(0.766831\pi\)
\(180\) 0 0
\(181\) −6.00000 + 6.00000i −0.445976 + 0.445976i −0.894015 0.448038i \(-0.852123\pi\)
0.448038 + 0.894015i \(0.352123\pi\)
\(182\) 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 \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 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 \(-0.918062\pi\)
0.254581 + 0.967051i \(0.418062\pi\)
\(198\) 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 −0.982131 0.188197i \(-0.939736\pi\)
−0.188197 0.982131i \(-0.560264\pi\)
\(212\) 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 \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 0 0
\(227\) −15.0000 15.0000i −0.995585 0.995585i 0.00440533 0.999990i \(-0.498598\pi\)
−0.999990 + 0.00440533i \(0.998598\pi\)
\(228\) 0 0
\(229\) −18.0000 + 18.0000i −1.18947 + 1.18947i −0.212260 + 0.977213i \(0.568082\pi\)
−0.977213 + 0.212260i \(0.931918\pi\)
\(230\) 0 0
\(231\) 8.00000i 0.526361i
\(232\) 0 0
\(233\) 12.0000i 0.786146i 0.919507 + 0.393073i \(0.128588\pi\)
−0.919507 + 0.393073i \(0.871412\pi\)
\(234\) 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 \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 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 −0.795419 0.606060i \(-0.792749\pi\)
0.606060 + 0.795419i \(0.292749\pi\)
\(252\) 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 \(-0.0437393\pi\)
−0.136979 + 0.990574i \(0.543739\pi\)
\(270\) 0 0
\(271\) −32.0000 −1.94386 −0.971931 0.235267i \(-0.924404\pi\)
−0.971931 + 0.235267i \(0.924404\pi\)
\(272\) 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 \(-0.667952\pi\)
0.863999 + 0.503494i \(0.167952\pi\)
\(278\) 0 0
\(279\) 8.00000i 0.478947i
\(280\) 0 0
\(281\) 20.0000i 1.19310i 0.802576 + 0.596550i \(0.203462\pi\)
−0.802576 + 0.596550i \(0.796538\pi\)
\(282\) 0 0
\(283\) −17.0000 + 17.0000i −1.01055 + 1.01055i −0.0106013 + 0.999944i \(0.503375\pi\)
−0.999944 + 0.0106013i \(0.996625\pi\)
\(284\) 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 \(-0.670273\pi\)
0.860304 + 0.509781i \(0.170273\pi\)
\(294\) 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 0.835244 0.549879i \(-0.185326\pi\)
−0.549879 + 0.835244i \(0.685326\pi\)
\(308\) 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 \(0.129485\pi\)
−0.918396 + 0.395663i \(0.870515\pi\)
\(314\) 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 \(-0.224690\pi\)
−0.648707 + 0.761038i \(0.724690\pi\)
\(318\) 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 −0.415094 0.909779i \(-0.636251\pi\)
0.909779 + 0.415094i \(0.136251\pi\)
\(332\) 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 −0.937769 0.347259i \(-0.887113\pi\)
0.347259 + 0.937769i \(0.387113\pi\)
\(348\) 0 0
\(349\) −14.0000 14.0000i −0.749403 0.749403i 0.224964 0.974367i \(-0.427773\pi\)
−0.974367 + 0.224964i \(0.927773\pi\)
\(350\) 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 \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 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 −0.456511 + 0.889718i \(0.650901\pi\)
−0.889718 + 0.456511i \(0.849099\pi\)
\(374\) 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 0.0820711 0.996626i \(-0.473847\pi\)
0.996626 0.0820711i \(-0.0261534\pi\)
\(380\) 0 0
\(381\) 8.00000 + 8.00000i 0.409852 + 0.409852i
\(382\) 0 0
\(383\) 16.0000 0.817562 0.408781 0.912633i \(-0.365954\pi\)
0.408781 + 0.912633i \(0.365954\pi\)
\(384\) 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 \(-0.917374\pi\)
0.256671 + 0.966499i \(0.417374\pi\)
\(390\) 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 \(-0.272612\pi\)
−0.755512 + 0.655135i \(0.772612\pi\)
\(398\) 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 \(0.112504\pi\)
−0.938187 + 0.346128i \(0.887496\pi\)
\(410\) 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 0.997590 0.0693796i \(-0.0221020\pi\)
−0.0693796 + 0.997590i \(0.522102\pi\)
\(420\) 0 0
\(421\) 6.00000 6.00000i 0.292422 0.292422i −0.545614 0.838036i \(-0.683704\pi\)
0.838036 + 0.545614i \(0.183704\pi\)
\(422\) 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 \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 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 −0.210108 + 0.977678i \(0.567381\pi\)
−0.977678 + 0.210108i \(0.932619\pi\)
\(444\) 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 \(0.0148953\pi\)
−0.998905 + 0.0467780i \(0.985105\pi\)
\(458\) 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 \(-0.356824\pi\)
−0.900533 + 0.434787i \(0.856824\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 0 0
\(465\) −32.0000 −1.48396
\(466\) 0 0
\(467\) 13.0000 + 13.0000i 0.601568 + 0.601568i 0.940729 0.339160i \(-0.110143\pi\)
−0.339160 + 0.940729i \(0.610143\pi\)
\(468\) 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 \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 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 −0.413900 0.910323i \(-0.635834\pi\)
0.910323 + 0.413900i \(0.135834\pi\)
\(492\) 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 0.476357 0.879252i \(-0.341957\pi\)
−0.879252 + 0.476357i \(0.841957\pi\)
\(500\) 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 \(-0.269966\pi\)
−0.750040 + 0.661392i \(0.769966\pi\)
\(510\) 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 \(0.0992167\pi\)
−0.951814 + 0.306676i \(0.900783\pi\)
\(522\) 0 0
\(523\) −7.00000 + 7.00000i −0.306089 + 0.306089i −0.843390 0.537302i \(-0.819444\pi\)
0.537302 + 0.843390i \(0.319444\pi\)
\(524\) 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 \(-0.191612\pi\)
−0.566264 + 0.824224i \(0.691612\pi\)
\(542\) 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 0.984990 0.172609i \(-0.0552197\pi\)
−0.172609 + 0.984990i \(0.555220\pi\)
\(548\) 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 \(-0.479081\pi\)
−0.997841 + 0.0656714i \(0.979081\pi\)
\(558\) 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 0.804575 0.593851i \(-0.202393\pi\)
−0.593851 + 0.804575i \(0.702393\pi\)
\(564\) 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 \(-0.783533\pi\)
0.777541 0.628833i \(-0.216467\pi\)
\(570\) 0 0
\(571\) 23.0000 23.0000i 0.962520 0.962520i −0.0368025 0.999323i \(-0.511717\pi\)
0.999323 + 0.0368025i \(0.0117173\pi\)
\(572\) 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 −0.686168 0.727443i \(-0.740709\pi\)
0.727443 + 0.686168i \(0.240709\pi\)
\(588\) 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 \(0.0259972\pi\)
−0.996667 + 0.0815817i \(0.974003\pi\)
\(602\) 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 \(-0.695184\pi\)
0.817817 + 0.575479i \(0.195184\pi\)
\(614\) 0 0
\(615\) 8.00000i 0.322591i
\(616\) 0 0
\(617\) 28.0000i 1.12724i 0.826035 + 0.563619i \(0.190591\pi\)
−0.826035 + 0.563619i \(0.809409\pi\)
\(618\) 0 0
\(619\) 1.00000 1.00000i 0.0401934 0.0401934i −0.686724 0.726918i \(-0.740952\pi\)
0.726918 + 0.686724i \(0.240952\pi\)
\(620\) 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 0.763782 0.645474i \(-0.223340\pi\)
−0.645474 + 0.763782i \(0.723340\pi\)
\(644\) 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 −0.904901 0.425622i \(-0.860055\pi\)
−0.425622 0.904901i \(-0.639945\pi\)
\(654\) 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 0.995075 0.0991224i \(-0.0316036\pi\)
−0.0991224 + 0.995075i \(0.531604\pi\)
\(660\) 0 0
\(661\) −22.0000 + 22.0000i −0.855701 + 0.855701i −0.990828 0.135127i \(-0.956856\pi\)
0.135127 + 0.990828i \(0.456856\pi\)
\(662\) 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 −0.167044 + 0.985949i \(0.553422\pi\)
−0.985949 + 0.167044i \(0.946578\pi\)
\(678\) 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 −0.983647 0.180105i \(-0.942356\pi\)
0.180105 + 0.983647i \(0.442356\pi\)
\(684\) 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 −0.953275 0.302104i \(-0.902311\pi\)
−0.302104 0.953275i \(-0.597689\pi\)
\(692\) 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 −0.938277 0.345886i \(-0.887579\pi\)
−0.345886 0.938277i \(-0.612421\pi\)
\(702\) 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 \(-0.800935\pi\)
0.585406 + 0.810740i \(0.300935\pi\)
\(710\) 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 \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 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 \(-0.369152\pi\)
−0.916693 + 0.399592i \(0.869152\pi\)
\(734\) 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 0.946896 0.321541i \(-0.104201\pi\)
−0.321541 + 0.946896i \(0.604201\pi\)
\(740\) 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 \(-0.239608\pi\)
0.729810 + 0.683650i \(0.239608\pi\)
\(752\) 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 \(-0.596915\pi\)
0.954007 + 0.299786i \(0.0969151\pi\)
\(758\) 0 0
\(759\) 8.00000i 0.290382i
\(760\) 0 0
\(761\) 18.0000i 0.652499i −0.945284 0.326250i \(-0.894215\pi\)
0.945284 0.326250i \(-0.105785\pi\)
\(762\) 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 \(-0.798764\pi\)
0.590923 + 0.806728i \(0.298764\pi\)
\(774\) 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 −0.980674 0.195649i \(-0.937319\pi\)
−0.195649 0.980674i \(-0.562681\pi\)
\(788\) 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 \(-0.135958\pi\)