Properties

Label 1734.2.f.e.1483.1
Level $1734$
Weight $2$
Character 1734.1483
Analytic conductor $13.846$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1734.f (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.8460597105\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 102)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1483.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1734.1483
Dual form 1734.2.f.e.829.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.41421 + 1.41421i) q^{5} +(-0.707107 - 0.707107i) q^{6} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.41421 + 1.41421i) q^{5} +(-0.707107 - 0.707107i) q^{6} -1.00000i q^{8} -1.00000i q^{9} +(-1.41421 - 1.41421i) q^{10} +(2.82843 + 2.82843i) q^{11} +(0.707107 - 0.707107i) q^{12} +2.00000 q^{13} -2.00000i q^{15} +1.00000 q^{16} +1.00000 q^{18} +4.00000i q^{19} +(1.41421 - 1.41421i) q^{20} +(-2.82843 + 2.82843i) q^{22} +(0.707107 + 0.707107i) q^{24} +1.00000i q^{25} +2.00000i q^{26} +(0.707107 + 0.707107i) q^{27} +(-7.07107 + 7.07107i) q^{29} +2.00000 q^{30} +(-5.65685 + 5.65685i) q^{31} +1.00000i q^{32} -4.00000 q^{33} +1.00000i q^{36} +(1.41421 - 1.41421i) q^{37} -4.00000 q^{38} +(-1.41421 + 1.41421i) q^{39} +(1.41421 + 1.41421i) q^{40} +(7.07107 + 7.07107i) q^{41} -12.0000i q^{43} +(-2.82843 - 2.82843i) q^{44} +(1.41421 + 1.41421i) q^{45} +(-0.707107 + 0.707107i) q^{48} -7.00000i q^{49} -1.00000 q^{50} -2.00000 q^{52} +6.00000i q^{53} +(-0.707107 + 0.707107i) q^{54} -8.00000 q^{55} +(-2.82843 - 2.82843i) q^{57} +(-7.07107 - 7.07107i) q^{58} -12.0000i q^{59} +2.00000i q^{60} +(-7.07107 - 7.07107i) q^{61} +(-5.65685 - 5.65685i) q^{62} -1.00000 q^{64} +(-2.82843 + 2.82843i) q^{65} -4.00000i q^{66} -12.0000 q^{67} -1.00000 q^{72} +(7.07107 - 7.07107i) q^{73} +(1.41421 + 1.41421i) q^{74} +(-0.707107 - 0.707107i) q^{75} -4.00000i q^{76} +(-1.41421 - 1.41421i) q^{78} +(5.65685 + 5.65685i) q^{79} +(-1.41421 + 1.41421i) q^{80} -1.00000 q^{81} +(-7.07107 + 7.07107i) q^{82} +4.00000i q^{83} +12.0000 q^{86} -10.0000i q^{87} +(2.82843 - 2.82843i) q^{88} +6.00000 q^{89} +(-1.41421 + 1.41421i) q^{90} -8.00000i q^{93} +(-5.65685 - 5.65685i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-9.89949 + 9.89949i) q^{97} +7.00000 q^{98} +(2.82843 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + O(q^{10}) \) \( 4q - 4q^{4} + 8q^{13} + 4q^{16} + 4q^{18} + 8q^{30} - 16q^{33} - 16q^{38} - 4q^{50} - 8q^{52} - 32q^{55} - 4q^{64} - 48q^{67} - 4q^{72} - 4q^{81} + 48q^{86} + 24q^{89} + 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times\).

\(n\) \(1157\) \(1159\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −1.41421 + 1.41421i −0.632456 + 0.632456i −0.948683 0.316228i \(-0.897584\pi\)
0.316228 + 0.948683i \(0.397584\pi\)
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −1.41421 1.41421i −0.447214 0.447214i
\(11\) 2.82843 + 2.82843i 0.852803 + 0.852803i 0.990478 0.137675i \(-0.0439628\pi\)
−0.137675 + 0.990478i \(0.543963\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 2.00000i 0.516398i
\(16\) 1.00000 0.250000
\(17\) 0 0
\(18\) 1.00000 0.235702
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) 1.41421 1.41421i 0.316228 0.316228i
\(21\) 0 0
\(22\) −2.82843 + 2.82843i −0.603023 + 0.603023i
\(23\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) 1.00000i 0.200000i
\(26\) 2.00000i 0.392232i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0 0
\(29\) −7.07107 + 7.07107i −1.31306 + 1.31306i −0.393919 + 0.919145i \(0.628881\pi\)
−0.919145 + 0.393919i \(0.871119\pi\)
\(30\) 2.00000 0.365148
\(31\) −5.65685 + 5.65685i −1.01600 + 1.01600i −0.0161311 + 0.999870i \(0.505135\pi\)
−0.999870 + 0.0161311i \(0.994865\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −4.00000 −0.696311
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000i 0.166667i
\(37\) 1.41421 1.41421i 0.232495 0.232495i −0.581238 0.813733i \(-0.697432\pi\)
0.813733 + 0.581238i \(0.197432\pi\)
\(38\) −4.00000 −0.648886
\(39\) −1.41421 + 1.41421i −0.226455 + 0.226455i
\(40\) 1.41421 + 1.41421i 0.223607 + 0.223607i
\(41\) 7.07107 + 7.07107i 1.10432 + 1.10432i 0.993884 + 0.110432i \(0.0352233\pi\)
0.110432 + 0.993884i \(0.464777\pi\)
\(42\) 0 0
\(43\) 12.0000i 1.82998i −0.403473 0.914991i \(-0.632197\pi\)
0.403473 0.914991i \(-0.367803\pi\)
\(44\) −2.82843 2.82843i −0.426401 0.426401i
\(45\) 1.41421 + 1.41421i 0.210819 + 0.210819i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 7.00000i 1.00000i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) −2.82843 2.82843i −0.374634 0.374634i
\(58\) −7.07107 7.07107i −0.928477 0.928477i
\(59\) 12.0000i 1.56227i −0.624364 0.781133i \(-0.714642\pi\)
0.624364 0.781133i \(-0.285358\pi\)
\(60\) 2.00000i 0.258199i
\(61\) −7.07107 7.07107i −0.905357 0.905357i 0.0905357 0.995893i \(-0.471142\pi\)
−0.995893 + 0.0905357i \(0.971142\pi\)
\(62\) −5.65685 5.65685i −0.718421 0.718421i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −2.82843 + 2.82843i −0.350823 + 0.350823i
\(66\) 4.00000i 0.492366i
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(72\) −1.00000 −0.117851
\(73\) 7.07107 7.07107i 0.827606 0.827606i −0.159579 0.987185i \(-0.551014\pi\)
0.987185 + 0.159579i \(0.0510137\pi\)
\(74\) 1.41421 + 1.41421i 0.164399 + 0.164399i
\(75\) −0.707107 0.707107i −0.0816497 0.0816497i
\(76\) 4.00000i 0.458831i
\(77\) 0 0
\(78\) −1.41421 1.41421i −0.160128 0.160128i
\(79\) 5.65685 + 5.65685i 0.636446 + 0.636446i 0.949677 0.313231i \(-0.101411\pi\)
−0.313231 + 0.949677i \(0.601411\pi\)
\(80\) −1.41421 + 1.41421i −0.158114 + 0.158114i
\(81\) −1.00000 −0.111111
\(82\) −7.07107 + 7.07107i −0.780869 + 0.780869i
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 12.0000 1.29399
\(87\) 10.0000i 1.07211i
\(88\) 2.82843 2.82843i 0.301511 0.301511i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.41421 + 1.41421i −0.149071 + 0.149071i
\(91\) 0 0
\(92\) 0 0
\(93\) 8.00000i 0.829561i
\(94\) 0 0
\(95\) −5.65685 5.65685i −0.580381 0.580381i
\(96\) −0.707107 0.707107i −0.0721688 0.0721688i
\(97\) −9.89949 + 9.89949i −1.00514 + 1.00514i −0.00515471 + 0.999987i \(0.501641\pi\)
−0.999987 + 0.00515471i \(0.998359\pi\)
\(98\) 7.00000 0.707107
\(99\) 2.82843 2.82843i 0.284268 0.284268i
\(100\) 1.00000i 0.100000i
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 2.00000i 0.196116i
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −2.82843 + 2.82843i −0.273434 + 0.273434i −0.830481 0.557047i \(-0.811934\pi\)
0.557047 + 0.830481i \(0.311934\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −7.07107 7.07107i −0.677285 0.677285i 0.282100 0.959385i \(-0.408969\pi\)
−0.959385 + 0.282100i \(0.908969\pi\)
\(110\) 8.00000i 0.762770i
\(111\) 2.00000i 0.189832i
\(112\) 0 0
\(113\) −1.41421 1.41421i −0.133038 0.133038i 0.637452 0.770490i \(-0.279988\pi\)
−0.770490 + 0.637452i \(0.779988\pi\)
\(114\) 2.82843 2.82843i 0.264906 0.264906i
\(115\) 0 0
\(116\) 7.07107 7.07107i 0.656532 0.656532i
\(117\) 2.00000i 0.184900i
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) −2.00000 −0.182574
\(121\) 5.00000i 0.454545i
\(122\) 7.07107 7.07107i 0.640184 0.640184i
\(123\) −10.0000 −0.901670
\(124\) 5.65685 5.65685i 0.508001 0.508001i
\(125\) −8.48528 8.48528i −0.758947 0.758947i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.48528 + 8.48528i 0.747087 + 0.747087i
\(130\) −2.82843 2.82843i −0.248069 0.248069i
\(131\) −8.48528 + 8.48528i −0.741362 + 0.741362i −0.972840 0.231478i \(-0.925644\pi\)
0.231478 + 0.972840i \(0.425644\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) 12.0000i 1.03664i
\(135\) −2.00000 −0.172133
\(136\) 0 0
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) 2.82843 2.82843i 0.239904 0.239904i −0.576906 0.816810i \(-0.695740\pi\)
0.816810 + 0.576906i \(0.195740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.65685 + 5.65685i 0.473050 + 0.473050i
\(144\) 1.00000i 0.0833333i
\(145\) 20.0000i 1.66091i
\(146\) 7.07107 + 7.07107i 0.585206 + 0.585206i
\(147\) 4.94975 + 4.94975i 0.408248 + 0.408248i
\(148\) −1.41421 + 1.41421i −0.116248 + 0.116248i
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0.707107 0.707107i 0.0577350 0.0577350i
\(151\) 24.0000i 1.95309i 0.215308 + 0.976546i \(0.430924\pi\)
−0.215308 + 0.976546i \(0.569076\pi\)
\(152\) 4.00000 0.324443
\(153\) 0 0
\(154\) 0 0
\(155\) 16.0000i 1.28515i
\(156\) 1.41421 1.41421i 0.113228 0.113228i
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −5.65685 + 5.65685i −0.450035 + 0.450035i
\(159\) −4.24264 4.24264i −0.336463 0.336463i
\(160\) −1.41421 1.41421i −0.111803 0.111803i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 2.82843 + 2.82843i 0.221540 + 0.221540i 0.809146 0.587607i \(-0.199930\pi\)
−0.587607 + 0.809146i \(0.699930\pi\)
\(164\) −7.07107 7.07107i −0.552158 0.552158i
\(165\) 5.65685 5.65685i 0.440386 0.440386i
\(166\) −4.00000 −0.310460
\(167\) −11.3137 + 11.3137i −0.875481 + 0.875481i −0.993063 0.117582i \(-0.962486\pi\)
0.117582 + 0.993063i \(0.462486\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) 12.0000i 0.914991i
\(173\) −4.24264 + 4.24264i −0.322562 + 0.322562i −0.849749 0.527187i \(-0.823247\pi\)
0.527187 + 0.849749i \(0.323247\pi\)
\(174\) 10.0000 0.758098
\(175\) 0 0
\(176\) 2.82843 + 2.82843i 0.213201 + 0.213201i
\(177\) 8.48528 + 8.48528i 0.637793 + 0.637793i
\(178\) 6.00000i 0.449719i
\(179\) 12.0000i 0.896922i 0.893802 + 0.448461i \(0.148028\pi\)
−0.893802 + 0.448461i \(0.851972\pi\)
\(180\) −1.41421 1.41421i −0.105409 0.105409i
\(181\) −9.89949 9.89949i −0.735824 0.735824i 0.235943 0.971767i \(-0.424182\pi\)
−0.971767 + 0.235943i \(0.924182\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 4.00000i 0.294086i
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 5.65685 5.65685i 0.410391 0.410391i
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −12.7279 12.7279i −0.916176 0.916176i 0.0805728 0.996749i \(-0.474325\pi\)
−0.996749 + 0.0805728i \(0.974325\pi\)
\(194\) −9.89949 9.89949i −0.710742 0.710742i
\(195\) 4.00000i 0.286446i
\(196\) 7.00000i 0.500000i
\(197\) 9.89949 + 9.89949i 0.705310 + 0.705310i 0.965545 0.260235i \(-0.0838002\pi\)
−0.260235 + 0.965545i \(0.583800\pi\)
\(198\) 2.82843 + 2.82843i 0.201008 + 0.201008i
\(199\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(200\) 1.00000 0.0707107
\(201\) 8.48528 8.48528i 0.598506 0.598506i
\(202\) 10.0000i 0.703598i
\(203\) 0 0
\(204\) 0 0
\(205\) −20.0000 −1.39686
\(206\) 8.00000i 0.557386i
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) −11.3137 + 11.3137i −0.782586 + 0.782586i
\(210\) 0 0
\(211\) −19.7990 19.7990i −1.36302 1.36302i −0.870043 0.492975i \(-0.835909\pi\)
−0.492975 0.870043i \(-0.664091\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) −2.82843 2.82843i −0.193347 0.193347i
\(215\) 16.9706 + 16.9706i 1.15738 + 1.15738i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) 0 0
\(218\) 7.07107 7.07107i 0.478913 0.478913i
\(219\) 10.0000i 0.675737i
\(220\) 8.00000 0.539360
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 1.41421 1.41421i 0.0940721 0.0940721i
\(227\) −2.82843 2.82843i −0.187729 0.187729i 0.606984 0.794714i \(-0.292379\pi\)
−0.794714 + 0.606984i \(0.792379\pi\)
\(228\) 2.82843 + 2.82843i 0.187317 + 0.187317i
\(229\) 26.0000i 1.71813i 0.511868 + 0.859064i \(0.328954\pi\)
−0.511868 + 0.859064i \(0.671046\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 7.07107 + 7.07107i 0.464238 + 0.464238i
\(233\) 18.3848 18.3848i 1.20443 1.20443i 0.231621 0.972806i \(-0.425597\pi\)
0.972806 0.231621i \(-0.0744028\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) 12.0000i 0.781133i
\(237\) −8.00000 −0.519656
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 2.00000i 0.129099i
\(241\) −1.41421 + 1.41421i −0.0910975 + 0.0910975i −0.751187 0.660089i \(-0.770518\pi\)
0.660089 + 0.751187i \(0.270518\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 7.07107 + 7.07107i 0.452679 + 0.452679i
\(245\) 9.89949 + 9.89949i 0.632456 + 0.632456i
\(246\) 10.0000i 0.637577i
\(247\) 8.00000i 0.509028i
\(248\) 5.65685 + 5.65685i 0.359211 + 0.359211i
\(249\) −2.82843 2.82843i −0.179244 0.179244i
\(250\) 8.48528 8.48528i 0.536656 0.536656i
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 2.00000i 0.124757i 0.998053 + 0.0623783i \(0.0198685\pi\)
−0.998053 + 0.0623783i \(0.980131\pi\)
\(258\) −8.48528 + 8.48528i −0.528271 + 0.528271i
\(259\) 0 0
\(260\) 2.82843 2.82843i 0.175412 0.175412i
\(261\) 7.07107 + 7.07107i 0.437688 + 0.437688i
\(262\) −8.48528 8.48528i −0.524222 0.524222i
\(263\) 8.00000i 0.493301i 0.969104 + 0.246651i \(0.0793300\pi\)
−0.969104 + 0.246651i \(0.920670\pi\)
\(264\) 4.00000i 0.246183i
\(265\) −8.48528 8.48528i −0.521247 0.521247i
\(266\) 0 0
\(267\) −4.24264 + 4.24264i −0.259645 + 0.259645i
\(268\) 12.0000 0.733017
\(269\) −4.24264 + 4.24264i −0.258678 + 0.258678i −0.824516 0.565838i \(-0.808553\pi\)
0.565838 + 0.824516i \(0.308553\pi\)
\(270\) 2.00000i 0.121716i
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 10.0000i 0.604122i
\(275\) −2.82843 + 2.82843i −0.170561 + 0.170561i
\(276\) 0 0
\(277\) 21.2132 21.2132i 1.27458 1.27458i 0.330919 0.943659i \(-0.392641\pi\)
0.943659 0.330919i \(-0.107359\pi\)
\(278\) 2.82843 + 2.82843i 0.169638 + 0.169638i
\(279\) 5.65685 + 5.65685i 0.338667 + 0.338667i
\(280\) 0 0
\(281\) 6.00000i 0.357930i 0.983855 + 0.178965i \(0.0572749\pi\)
−0.983855 + 0.178965i \(0.942725\pi\)
\(282\) 0 0
\(283\) −8.48528 8.48528i −0.504398 0.504398i 0.408404 0.912801i \(-0.366086\pi\)
−0.912801 + 0.408404i \(0.866086\pi\)
\(284\) 0 0
\(285\) 8.00000 0.473879
\(286\) −5.65685 + 5.65685i −0.334497 + 0.334497i
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 0 0
\(290\) 20.0000 1.17444
\(291\) 14.0000i 0.820695i
\(292\) −7.07107 + 7.07107i −0.413803 + 0.413803i
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) −4.94975 + 4.94975i −0.288675 + 0.288675i
\(295\) 16.9706 + 16.9706i 0.988064 + 0.988064i
\(296\) −1.41421 1.41421i −0.0821995 0.0821995i
\(297\) 4.00000i 0.232104i
\(298\) 10.0000i 0.579284i
\(299\) 0 0
\(300\) 0.707107 + 0.707107i 0.0408248 + 0.0408248i
\(301\) 0 0
\(302\) −24.0000 −1.38104
\(303\) 7.07107 7.07107i 0.406222 0.406222i
\(304\) 4.00000i 0.229416i
\(305\) 20.0000 1.14520
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 5.65685 5.65685i 0.321807 0.321807i
\(310\) 16.0000 0.908739
\(311\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(312\) 1.41421 + 1.41421i 0.0800641 + 0.0800641i
\(313\) 7.07107 + 7.07107i 0.399680 + 0.399680i 0.878120 0.478440i \(-0.158798\pi\)
−0.478440 + 0.878120i \(0.658798\pi\)
\(314\) 2.00000i 0.112867i
\(315\) 0 0
\(316\) −5.65685 5.65685i −0.318223 0.318223i
\(317\) −4.24264 4.24264i −0.238290 0.238290i 0.577851 0.816142i \(-0.303891\pi\)
−0.816142 + 0.577851i \(0.803891\pi\)
\(318\) 4.24264 4.24264i 0.237915 0.237915i
\(319\) −40.0000 −2.23957
\(320\) 1.41421 1.41421i 0.0790569 0.0790569i
\(321\) 4.00000i 0.223258i
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 2.00000i 0.110940i
\(326\) −2.82843 + 2.82843i −0.156652 + 0.156652i
\(327\) 10.0000 0.553001
\(328\) 7.07107 7.07107i 0.390434 0.390434i
\(329\) 0 0
\(330\) 5.65685 + 5.65685i 0.311400 + 0.311400i
\(331\) 20.0000i 1.09930i 0.835395 + 0.549650i \(0.185239\pi\)
−0.835395 + 0.549650i \(0.814761\pi\)
\(332\) 4.00000i 0.219529i
\(333\) −1.41421 1.41421i −0.0774984 0.0774984i
\(334\) −11.3137 11.3137i −0.619059 0.619059i
\(335\) 16.9706 16.9706i 0.927201 0.927201i
\(336\) 0 0
\(337\) 9.89949 9.89949i 0.539260 0.539260i −0.384052 0.923312i \(-0.625472\pi\)
0.923312 + 0.384052i \(0.125472\pi\)
\(338\) 9.00000i 0.489535i
\(339\) 2.00000 0.108625
\(340\) 0 0
\(341\) −32.0000 −1.73290
\(342\) 4.00000i 0.216295i
\(343\) 0 0
\(344\) −12.0000 −0.646997
\(345\) 0 0
\(346\) −4.24264 4.24264i −0.228086 0.228086i
\(347\) 19.7990 + 19.7990i 1.06287 + 1.06287i 0.997887 + 0.0649788i \(0.0206980\pi\)
0.0649788 + 0.997887i \(0.479302\pi\)
\(348\) 10.0000i 0.536056i
\(349\) 14.0000i 0.749403i −0.927146 0.374701i \(-0.877745\pi\)
0.927146 0.374701i \(-0.122255\pi\)
\(350\) 0 0
\(351\) 1.41421 + 1.41421i 0.0754851 + 0.0754851i
\(352\) −2.82843 + 2.82843i −0.150756 + 0.150756i
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) −8.48528 + 8.48528i −0.450988 + 0.450988i
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 24.0000i 1.26667i −0.773877 0.633336i \(-0.781685\pi\)
0.773877 0.633336i \(-0.218315\pi\)
\(360\) 1.41421 1.41421i 0.0745356 0.0745356i
\(361\) 3.00000 0.157895
\(362\) 9.89949 9.89949i 0.520306 0.520306i
\(363\) −3.53553 3.53553i −0.185567 0.185567i
\(364\) 0 0
\(365\) 20.0000i 1.04685i
\(366\) 10.0000i 0.522708i
\(367\) 16.9706 + 16.9706i 0.885856 + 0.885856i 0.994122 0.108266i \(-0.0345298\pi\)
−0.108266 + 0.994122i \(0.534530\pi\)
\(368\) 0 0
\(369\) 7.07107 7.07107i 0.368105 0.368105i
\(370\) −4.00000 −0.207950
\(371\) 0 0
\(372\) 8.00000i 0.414781i
\(373\) 6.00000 0.310668 0.155334 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 0 0
\(375\) 12.0000 0.619677
\(376\) 0 0
\(377\) −14.1421 + 14.1421i −0.728357 + 0.728357i
\(378\) 0 0
\(379\) −2.82843 + 2.82843i −0.145287 + 0.145287i −0.776009 0.630722i \(-0.782759\pi\)
0.630722 + 0.776009i \(0.282759\pi\)
\(380\) 5.65685 + 5.65685i 0.290191 + 0.290191i
\(381\) 0 0
\(382\) 16.0000i 0.818631i
\(383\) 16.0000i 0.817562i 0.912633 + 0.408781i \(0.134046\pi\)
−0.912633 + 0.408781i \(0.865954\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) 0 0
\(386\) 12.7279 12.7279i 0.647834 0.647834i
\(387\) −12.0000 −0.609994
\(388\) 9.89949 9.89949i 0.502571 0.502571i
\(389\) 26.0000i 1.31825i −0.752032 0.659126i \(-0.770926\pi\)
0.752032 0.659126i \(-0.229074\pi\)
\(390\) 4.00000 0.202548
\(391\) 0 0
\(392\) −7.00000 −0.353553
\(393\) 12.0000i 0.605320i
\(394\) −9.89949 + 9.89949i −0.498729 + 0.498729i
\(395\) −16.0000 −0.805047
\(396\) −2.82843 + 2.82843i −0.142134 + 0.142134i
\(397\) 18.3848 + 18.3848i 0.922705 + 0.922705i 0.997220 0.0745145i \(-0.0237407\pi\)
−0.0745145 + 0.997220i \(0.523741\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000i 0.0500000i
\(401\) −9.89949 9.89949i −0.494357 0.494357i 0.415319 0.909676i \(-0.363670\pi\)
−0.909676 + 0.415319i \(0.863670\pi\)
\(402\) 8.48528 + 8.48528i 0.423207 + 0.423207i
\(403\) −11.3137 + 11.3137i −0.563576 + 0.563576i
\(404\) 10.0000 0.497519
\(405\) 1.41421 1.41421i 0.0702728 0.0702728i
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 20.0000i 0.987730i
\(411\) −7.07107 + 7.07107i −0.348790 + 0.348790i
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) −5.65685 5.65685i −0.277684 0.277684i
\(416\) 2.00000i 0.0980581i
\(417\) 4.00000i 0.195881i
\(418\) −11.3137 11.3137i −0.553372 0.553372i
\(419\) −2.82843 2.82843i −0.138178 0.138178i 0.634635 0.772812i \(-0.281151\pi\)
−0.772812 + 0.634635i \(0.781151\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 19.7990 19.7990i 0.963800 0.963800i
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 2.82843 2.82843i 0.136717 0.136717i
\(429\) −8.00000 −0.386244
\(430\) −16.9706 + 16.9706i −0.818393 + 0.818393i
\(431\) 5.65685 + 5.65685i 0.272481 + 0.272481i 0.830098 0.557617i \(-0.188284\pi\)
−0.557617 + 0.830098i \(0.688284\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 14.0000i 0.672797i 0.941720 + 0.336399i \(0.109209\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) 0 0
\(435\) 14.1421 + 14.1421i 0.678064 + 0.678064i
\(436\) 7.07107 + 7.07107i 0.338643 + 0.338643i
\(437\) 0 0
\(438\) −10.0000 −0.477818
\(439\) −11.3137 + 11.3137i −0.539974 + 0.539974i −0.923521 0.383547i \(-0.874702\pi\)
0.383547 + 0.923521i \(0.374702\pi\)
\(440\) 8.00000i 0.381385i
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 2.00000i 0.0949158i
\(445\) −8.48528 + 8.48528i −0.402241 + 0.402241i
\(446\) −16.0000 −0.757622
\(447\) −7.07107 + 7.07107i −0.334450 + 0.334450i
\(448\) 0 0
\(449\) 1.41421 + 1.41421i 0.0667409 + 0.0667409i 0.739689 0.672948i \(-0.234972\pi\)
−0.672948 + 0.739689i \(0.734972\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 40.0000i 1.88353i
\(452\) 1.41421 + 1.41421i 0.0665190 + 0.0665190i
\(453\) −16.9706 16.9706i −0.797347 0.797347i
\(454\) 2.82843 2.82843i 0.132745 0.132745i
\(455\) 0 0
\(456\) −2.82843 + 2.82843i −0.132453 + 0.132453i
\(457\) 10.0000i 0.467780i 0.972263 + 0.233890i \(0.0751456\pi\)
−0.972263 + 0.233890i \(0.924854\pi\)
\(458\) −26.0000 −1.21490
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0000i 1.39724i 0.715493 + 0.698620i \(0.246202\pi\)
−0.715493 + 0.698620i \(0.753798\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) −7.07107 + 7.07107i −0.328266 + 0.328266i
\(465\) 11.3137 + 11.3137i 0.524661 + 0.524661i
\(466\) 18.3848 + 18.3848i 0.851658 + 0.851658i
\(467\) 12.0000i 0.555294i 0.960683 + 0.277647i \(0.0895545\pi\)
−0.960683 + 0.277647i \(0.910445\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 0 0
\(470\) 0 0
\(471\) −1.41421 + 1.41421i −0.0651635 + 0.0651635i
\(472\) −12.0000 −0.552345
\(473\) 33.9411 33.9411i 1.56061 1.56061i
\(474\) 8.00000i 0.367452i
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −16.9706 + 16.9706i −0.775405 + 0.775405i −0.979046 0.203641i \(-0.934723\pi\)
0.203641 + 0.979046i \(0.434723\pi\)
\(480\) 2.00000 0.0912871
\(481\) 2.82843 2.82843i 0.128965 0.128965i
\(482\) −1.41421 1.41421i −0.0644157 0.0644157i
\(483\) 0 0
\(484\) 5.00000i 0.227273i
\(485\) 28.0000i 1.27141i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) 11.3137 + 11.3137i 0.512673 + 0.512673i 0.915345 0.402671i \(-0.131918\pi\)
−0.402671 + 0.915345i \(0.631918\pi\)
\(488\) −7.07107 + 7.07107i −0.320092 + 0.320092i
\(489\) −4.00000 −0.180886
\(490\) −9.89949 + 9.89949i −0.447214 + 0.447214i
\(491\) 12.0000i 0.541552i 0.962642 + 0.270776i \(0.0872803\pi\)
−0.962642 + 0.270776i \(0.912720\pi\)
\(492\) 10.0000 0.450835
\(493\) 0 0
\(494\) −8.00000 −0.359937
\(495\) 8.00000i 0.359573i
\(496\) −5.65685 + 5.65685i −0.254000 + 0.254000i
\(497\) 0 0
\(498\) 2.82843 2.82843i 0.126745 0.126745i
\(499\) −2.82843 2.82843i −0.126618 0.126618i 0.640958 0.767576i \(-0.278537\pi\)
−0.767576 + 0.640958i \(0.778537\pi\)
\(500\) 8.48528 + 8.48528i 0.379473 + 0.379473i
\(501\) 16.0000i 0.714827i
\(502\) 28.0000i 1.24970i
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 0 0
\(505\) 14.1421 14.1421i 0.629317 0.629317i
\(506\) 0 0
\(507\) 6.36396 6.36396i 0.282633 0.282633i
\(508\) 0 0
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −2.82843 + 2.82843i −0.124878 + 0.124878i
\(514\) −2.00000 −0.0882162
\(515\) 11.3137 11.3137i 0.498542 0.498542i
\(516\) −8.48528 8.48528i −0.373544 0.373544i
\(517\) 0 0
\(518\) 0 0
\(519\) 6.00000i 0.263371i
\(520\) 2.82843 + 2.82843i 0.124035 + 0.124035i
\(521\) 15.5563 + 15.5563i 0.681536 + 0.681536i 0.960346 0.278810i \(-0.0899400\pi\)
−0.278810 + 0.960346i \(0.589940\pi\)
\(522\) −7.07107 + 7.07107i −0.309492 + 0.309492i
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 8.48528 8.48528i 0.370681 0.370681i
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) 0 0
\(528\) −4.00000 −0.174078
\(529\) 23.0000i 1.00000i
\(530\) 8.48528 8.48528i 0.368577 0.368577i
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 14.1421 + 14.1421i 0.612564 + 0.612564i
\(534\) −4.24264 4.24264i −0.183597 0.183597i
\(535\) 8.00000i 0.345870i
\(536\) 12.0000i 0.518321i
\(537\) −8.48528 8.48528i −0.366167 0.366167i
\(538\) −4.24264 4.24264i −0.182913 0.182913i
\(539\) 19.7990 19.7990i 0.852803 0.852803i
\(540\) 2.00000 0.0860663
\(541\) 7.07107 7.07107i 0.304009 0.304009i −0.538571 0.842580i \(-0.681036\pi\)
0.842580 + 0.538571i \(0.181036\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 14.0000 0.600798
\(544\) 0 0
\(545\) 20.0000 0.856706
\(546\) 0 0
\(547\) 8.48528 8.48528i 0.362804 0.362804i −0.502040 0.864844i \(-0.667417\pi\)
0.864844 + 0.502040i \(0.167417\pi\)
\(548\) −10.0000 −0.427179
\(549\) −7.07107 + 7.07107i −0.301786 + 0.301786i
\(550\) −2.82843 2.82843i −0.120605 0.120605i
\(551\) −28.2843 28.2843i −1.20495 1.20495i
\(552\) 0 0
\(553\) 0 0
\(554\) 21.2132 + 21.2132i 0.901263 + 0.901263i
\(555\) −2.82843 2.82843i −0.120060 0.120060i
\(556\) −2.82843 + 2.82843i −0.119952 + 0.119952i
\(557\) 34.0000 1.44063 0.720313 0.693649i \(-0.243998\pi\)
0.720313 + 0.693649i \(0.243998\pi\)
\(558\) −5.65685 + 5.65685i −0.239474 + 0.239474i
\(559\) 24.0000i 1.01509i
\(560\) 0 0
\(561\) 0 0
\(562\) −6.00000 −0.253095
\(563\) 36.0000i 1.51722i 0.651546 + 0.758610i \(0.274121\pi\)
−0.651546 + 0.758610i \(0.725879\pi\)
\(564\) 0 0
\(565\) 4.00000 0.168281
\(566\) 8.48528 8.48528i 0.356663 0.356663i
\(567\) 0 0
\(568\) 0 0
\(569\) 6.00000i 0.251533i 0.992060 + 0.125767i \(0.0401390\pi\)
−0.992060 + 0.125767i \(0.959861\pi\)
\(570\) 8.00000i 0.335083i
\(571\) 19.7990 + 19.7990i 0.828562 + 0.828562i 0.987318 0.158756i \(-0.0507483\pi\)
−0.158756 + 0.987318i \(0.550748\pi\)
\(572\) −5.65685 5.65685i −0.236525 0.236525i
\(573\) −11.3137 + 11.3137i −0.472637 + 0.472637i
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000i 0.0416667i
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 0 0
\(579\) 18.0000 0.748054
\(580\) 20.0000i 0.830455i
\(581\) 0 0
\(582\) 14.0000 0.580319
\(583\) −16.9706 + 16.9706i −0.702849 + 0.702849i
\(584\) −7.07107 7.07107i −0.292603 0.292603i
\(585\) 2.82843 + 2.82843i 0.116941 + 0.116941i
\(586\) 26.0000i 1.07405i
\(587\) 20.0000i 0.825488i 0.910847 + 0.412744i \(0.135430\pi\)
−0.910847 + 0.412744i \(0.864570\pi\)
\(588\) −4.94975 4.94975i −0.204124 0.204124i
\(589\) −22.6274 22.6274i −0.932346 0.932346i
\(590\) −16.9706 + 16.9706i −0.698667 + 0.698667i
\(591\) −14.0000 −0.575883
\(592\) 1.41421 1.41421i 0.0581238 0.0581238i
\(593\) 14.0000i 0.574911i −0.957794 0.287456i \(-0.907191\pi\)
0.957794 0.287456i \(-0.0928094\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 0 0
\(598\) 0 0
\(599\) 8.00000 0.326871 0.163436 0.986554i \(-0.447742\pi\)
0.163436 + 0.986554i \(0.447742\pi\)
\(600\) −0.707107 + 0.707107i −0.0288675 + 0.0288675i
\(601\) 4.24264 + 4.24264i 0.173061 + 0.173061i 0.788323 0.615262i \(-0.210950\pi\)
−0.615262 + 0.788323i \(0.710950\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) 24.0000i 0.976546i
\(605\) −7.07107 7.07107i −0.287480 0.287480i
\(606\) 7.07107 + 7.07107i 0.287242 + 0.287242i
\(607\) −16.9706 + 16.9706i −0.688814 + 0.688814i −0.961970 0.273156i \(-0.911933\pi\)
0.273156 + 0.961970i \(0.411933\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) 20.0000i 0.809776i
\(611\) 0 0
\(612\) 0 0
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) 12.0000i 0.484281i
\(615\) 14.1421 14.1421i 0.570266 0.570266i
\(616\) 0 0
\(617\) −4.24264 + 4.24264i −0.170802 + 0.170802i −0.787332 0.616530i \(-0.788538\pi\)
0.616530 + 0.787332i \(0.288538\pi\)
\(618\) 5.65685 + 5.65685i 0.227552 + 0.227552i
\(619\) −14.1421 14.1421i −0.568420 0.568420i 0.363265 0.931686i \(-0.381662\pi\)
−0.931686 + 0.363265i \(0.881662\pi\)
\(620\) 16.0000i 0.642575i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −1.41421 + 1.41421i −0.0566139 + 0.0566139i
\(625\) 19.0000 0.760000
\(626\) −7.07107 + 7.07107i −0.282617 + 0.282617i
\(627\) 16.0000i 0.638978i
\(628\) −2.00000 −0.0798087
\(629\) 0 0
\(630\) 0 0
\(631\) 24.0000i 0.955425i −0.878516 0.477712i \(-0.841466\pi\)
0.878516 0.477712i \(-0.158534\pi\)
\(632\) 5.65685 5.65685i 0.225018 0.225018i
\(633\) 28.0000 1.11290
\(634\) 4.24264 4.24264i 0.168497 0.168497i
\(635\) 0 0
\(636\) 4.24264 + 4.24264i 0.168232 + 0.168232i
\(637\) 14.0000i 0.554700i
\(638\) 40.0000i 1.58362i
\(639\) 0 0
\(640\) 1.41421 + 1.41421i 0.0559017 + 0.0559017i
\(641\) 1.41421 1.41421i 0.0558581 0.0558581i −0.678626 0.734484i \(-0.737424\pi\)
0.734484 + 0.678626i \(0.237424\pi\)
\(642\) 4.00000 0.157867
\(643\) 19.7990 19.7990i 0.780796 0.780796i −0.199169 0.979965i \(-0.563824\pi\)
0.979965 + 0.199169i \(0.0638243\pi\)
\(644\) 0 0
\(645\) −24.0000 −0.944999
\(646\) 0 0
\(647\) −40.0000 −1.57256 −0.786281 0.617869i \(-0.787996\pi\)
−0.786281 + 0.617869i \(0.787996\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 33.9411 33.9411i 1.33231 1.33231i
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −2.82843 2.82843i −0.110770 0.110770i
\(653\) 4.24264 + 4.24264i 0.166027 + 0.166027i 0.785231 0.619203i \(-0.212544\pi\)
−0.619203 + 0.785231i \(0.712544\pi\)
\(654\) 10.0000i 0.391031i
\(655\) 24.0000i 0.937758i
\(656\) 7.07107 + 7.07107i 0.276079 + 0.276079i
\(657\) −7.07107 7.07107i −0.275869 0.275869i
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) −5.65685 + 5.65685i −0.220193 + 0.220193i
\(661\) 6.00000i 0.233373i 0.993169 + 0.116686i \(0.0372273\pi\)
−0.993169 + 0.116686i \(0.962773\pi\)
\(662\) −20.0000 −0.777322
\(663\) 0 0
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) 1.41421 1.41421i 0.0547997 0.0547997i
\(667\) 0 0
\(668\) 11.3137 11.3137i 0.437741 0.437741i
\(669\) −11.3137 11.3137i −0.437413 0.437413i
\(670\) 16.9706 + 16.9706i 0.655630 + 0.655630i
\(671\) 40.0000i 1.54418i
\(672\) 0 0
\(673\) −32.5269 32.5269i −1.25382 1.25382i −0.953994 0.299827i \(-0.903071\pi\)
−0.299827 0.953994i \(-0.596929\pi\)
\(674\) 9.89949 + 9.89949i 0.381314 + 0.381314i
\(675\) −0.707107 + 0.707107i −0.0272166 + 0.0272166i
\(676\) 9.00000 0.346154
\(677\) −32.5269 + 32.5269i −1.25011 + 1.25011i −0.294441 + 0.955670i \(0.595134\pi\)
−0.955670 + 0.294441i \(0.904866\pi\)
\(678\) 2.00000i 0.0768095i
\(679\) 0 0
\(680\) 0 0
\(681\) 4.00000 0.153280
\(682\) 32.0000i 1.22534i
\(683\) 14.1421 14.1421i 0.541134 0.541134i −0.382727 0.923861i \(-0.625015\pi\)
0.923861 + 0.382727i \(0.125015\pi\)
\(684\) −4.00000 −0.152944
\(685\) −14.1421 + 14.1421i −0.540343 + 0.540343i
\(686\) 0 0
\(687\) −18.3848 18.3848i −0.701423 0.701423i
\(688\) 12.0000i 0.457496i
\(689\) 12.0000i 0.457164i
\(690\) 0 0
\(691\) 19.7990 + 19.7990i 0.753189 + 0.753189i 0.975073 0.221884i \(-0.0712206\pi\)
−0.221884 + 0.975073i \(0.571221\pi\)
\(692\) 4.24264 4.24264i 0.161281 0.161281i
\(693\) 0 0
\(694\) −19.7990 + 19.7990i −0.751559 + 0.751559i
\(695\) 8.00000i 0.303457i
\(696\) −10.0000 −0.379049
\(697\) 0 0
\(698\) 14.0000 0.529908
\(699\) 26.0000i 0.983410i
\(700\) 0 0
\(701\) −46.0000 −1.73740 −0.868698 0.495342i \(-0.835043\pi\)
−0.868698 + 0.495342i \(0.835043\pi\)
\(702\) −1.41421 + 1.41421i −0.0533761 + 0.0533761i
\(703\) 5.65685 + 5.65685i 0.213352 + 0.213352i
\(704\) −2.82843 2.82843i −0.106600 0.106600i
\(705\) 0 0
\(706\) 30.0000i 1.12906i
\(707\) 0 0
\(708\) −8.48528 8.48528i −0.318896 0.318896i
\(709\) 32.5269 32.5269i 1.22157 1.22157i 0.254501 0.967072i \(-0.418089\pi\)
0.967072 0.254501i \(-0.0819114\pi\)
\(710\) 0 0
\(711\) 5.65685 5.65685i 0.212149 0.212149i
\(712\) 6.00000i 0.224860i
\(713\) 0 0
\(714\) 0 0
\(715\) −16.0000 −0.598366
\(716\) 12.0000i 0.448461i
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) 28.2843 28.2843i 1.05483 1.05483i 0.0564181 0.998407i \(-0.482032\pi\)
0.998407 0.0564181i \(-0.0179680\pi\)
\(720\) 1.41421 + 1.41421i 0.0527046 + 0.0527046i
\(721\) 0 0
\(722\) 3.00000i 0.111648i
\(723\) 2.00000i 0.0743808i
\(724\) 9.89949 + 9.89949i 0.367912 + 0.367912i
\(725\) −7.07107 7.07107i −0.262613 0.262613i
\(726\) 3.53553 3.53553i 0.131216 0.131216i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) −20.0000 −0.740233
\(731\) 0 0
\(732\) −10.0000 −0.369611
\(733\) 46.0000i 1.69905i 0.527549 + 0.849524i \(0.323111\pi\)
−0.527549 + 0.849524i \(0.676889\pi\)
\(734\) −16.9706 + 16.9706i −0.626395 + 0.626395i
\(735\) −14.0000 −0.516398
\(736\) 0 0
\(737\) −33.9411 33.9411i −1.25024 1.25024i
\(738\) 7.07107 + 7.07107i 0.260290 + 0.260290i
\(739\) 52.0000i 1.91285i −0.291977 0.956425i \(-0.594313\pi\)
0.291977 0.956425i \(-0.405687\pi\)
\(740\) 4.00000i 0.147043i
\(741\) −5.65685 5.65685i −0.207810 0.207810i
\(742\) 0 0
\(743\) −11.3137 + 11.3137i −0.415060 + 0.415060i −0.883497 0.468437i \(-0.844817\pi\)
0.468437 + 0.883497i \(0.344817\pi\)
\(744\) −8.00000 −0.293294
\(745\) −14.1421 + 14.1421i −0.518128 + 0.518128i
\(746\) 6.00000i 0.219676i
\(747\) 4.00000 0.146352
\(748\) 0 0
\(749\) 0 0
\(750\) 12.0000i 0.438178i
\(751\) −5.65685 + 5.65685i −0.206422 + 0.206422i −0.802745 0.596323i \(-0.796628\pi\)
0.596323 + 0.802745i \(0.296628\pi\)
\(752\) 0 0
\(753\) 19.7990 19.7990i 0.721515 0.721515i
\(754\) −14.1421 14.1421i −0.515026 0.515026i
\(755\) −33.9411 33.9411i −1.23524 1.23524i
\(756\) 0 0
\(757\) 10.0000i 0.363456i 0.983349 + 0.181728i \(0.0581691\pi\)
−0.983349 + 0.181728i \(0.941831\pi\)
\(758\) −2.82843 2.82843i −0.102733 0.102733i
\(759\) 0 0
\(760\) −5.65685 + 5.65685i −0.205196 + 0.205196i
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) 24.0000i 0.866590i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) −1.41421 1.41421i −0.0509317 0.0509317i
\(772\) 12.7279 + 12.7279i 0.458088 + 0.458088i
\(773\) 38.0000i 1.36677i −0.730061 0.683383i \(-0.760508\pi\)
0.730061 0.683383i \(-0.239492\pi\)
\(774\) 12.0000i 0.431331i
\(775\) −5.65685 5.65685i −0.203200 0.203200i
\(776\) 9.89949 + 9.89949i 0.355371 + 0.355371i
\(777\) 0 0
\(778\) 26.0000 0.932145
\(779\) −28.2843 + 28.2843i −1.01339 + 1.01339i
\(780\) 4.00000i 0.143223i
\(781\) 0 0
\(782\) 0 0
\(783\) −10.0000 −0.357371
\(784\) 7.00000i 0.250000i
\(785\) −2.82843 + 2.82843i −0.100951 + 0.100951i
\(786\) 12.0000 0.428026
\(787\) 2.82843 2.82843i 0.100823 0.100823i −0.654896 0.755719i \(-0.727288\pi\)
0.755719 + 0.654896i \(0.227288\pi\)
\(788\) −9.89949 9.89949i −0.352655 0.352655i
\(789\) −5.65685 5.65685i −0.201389 0.201389i
\(790\) 16.0000i 0.569254i
\(791\) 0