Properties

Label 1734.2.f.e.829.1
Level $1734$
Weight $2$
Character 1734.829
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 829.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1734.829
Dual form 1734.2.f.e.1483.1

$q$-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 \(\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times\).

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

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 0.316228 0.948683i \(-0.397584\pi\)
−0.948683 + 0.316228i \(0.897584\pi\)
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(8\) 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 −0.137675 0.990478i \(-0.543963\pi\)
0.990478 + 0.137675i \(0.0439628\pi\)
\(12\) 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 \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(24\) 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 −0.919145 0.393919i \(-0.871119\pi\)
−0.393919 0.919145i \(-0.628881\pi\)
\(30\) 2.00000 0.365148
\(31\) −5.65685 5.65685i −1.01600 1.01600i −0.999870 0.0161311i \(-0.994865\pi\)
−0.0161311 0.999870i \(-0.505135\pi\)
\(32\) 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 0.813733 0.581238i \(-0.197432\pi\)
−0.581238 + 0.813733i \(0.697432\pi\)
\(38\) −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 0.110432 0.993884i \(-0.464777\pi\)
0.993884 0.110432i \(-0.0352233\pi\)
\(42\) 0 0
\(43\) 12.0000i 1.82998i 0.403473 + 0.914991i \(0.367803\pi\)
−0.403473 + 0.914991i \(0.632197\pi\)
\(44\) −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 \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) −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 \(0.285358\pi\)
−0.624364 + 0.781133i \(0.714642\pi\)
\(60\) 2.00000i 0.258199i
\(61\) −7.07107 + 7.07107i −0.905357 + 0.905357i −0.995893 0.0905357i \(-0.971142\pi\)
0.0905357 + 0.995893i \(0.471142\pi\)
\(62\) −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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(72\) −1.00000 −0.117851
\(73\) 7.07107 + 7.07107i 0.827606 + 0.827606i 0.987185 0.159579i \(-0.0510137\pi\)
−0.159579 + 0.987185i \(0.551014\pi\)
\(74\) 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 −0.313231 0.949677i \(-0.601411\pi\)
0.949677 + 0.313231i \(0.101411\pi\)
\(80\) −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 \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 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 −0.999987 0.00515471i \(-0.998359\pi\)
−0.00515471 0.999987i \(-0.501641\pi\)
\(98\) 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 0.557047 0.830481i \(-0.311934\pi\)
−0.830481 + 0.557047i \(0.811934\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −7.07107 + 7.07107i −0.677285 + 0.677285i −0.959385 0.282100i \(-0.908969\pi\)
0.282100 + 0.959385i \(0.408969\pi\)
\(110\) 8.00000i 0.762770i
\(111\) 2.00000i 0.189832i
\(112\) 0 0
\(113\) −1.41421 + 1.41421i −0.133038 + 0.133038i −0.770490 0.637452i \(-0.779988\pi\)
0.637452 + 0.770490i \(0.279988\pi\)
\(114\) 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 0.231478 0.972840i \(-0.425644\pi\)
−0.972840 + 0.231478i \(0.925644\pi\)
\(132\) 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 0.816810 0.576906i \(-0.195740\pi\)
−0.576906 + 0.816810i \(0.695740\pi\)
\(140\) 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 \(-0.569076\pi\)
0.215308 0.976546i \(-0.430924\pi\)
\(152\) 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 −0.587607 0.809146i \(-0.699930\pi\)
0.809146 + 0.587607i \(0.199930\pi\)
\(164\) −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 0.117582 0.993063i \(-0.462486\pi\)
−0.993063 + 0.117582i \(0.962486\pi\)
\(168\) 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 0.527187 0.849749i \(-0.323247\pi\)
−0.849749 + 0.527187i \(0.823247\pi\)
\(174\) 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 \(-0.851972\pi\)
0.893802 0.448461i \(-0.148028\pi\)
\(180\) −1.41421 + 1.41421i −0.105409 + 0.105409i
\(181\) −9.89949 + 9.89949i −0.735824 + 0.735824i −0.971767 0.235943i \(-0.924182\pi\)
0.235943 + 0.971767i \(0.424182\pi\)
\(182\) 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 −0.996749 0.0805728i \(-0.974325\pi\)
0.0805728 + 0.996749i \(0.474325\pi\)
\(194\) −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 −0.260235 0.965545i \(-0.583800\pi\)
0.965545 + 0.260235i \(0.0838002\pi\)
\(198\) 2.82843 2.82843i 0.201008 0.201008i
\(199\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(200\) 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 −0.492975 + 0.870043i \(0.664091\pi\)
−0.870043 + 0.492975i \(0.835909\pi\)
\(212\) 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 \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) 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 −0.794714 0.606984i \(-0.792379\pi\)
0.606984 + 0.794714i \(0.292379\pi\)
\(228\) 2.82843 2.82843i 0.187317 0.187317i
\(229\) 26.0000i 1.71813i −0.511868 0.859064i \(-0.671046\pi\)
0.511868 0.859064i \(-0.328954\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 7.07107 7.07107i 0.464238 0.464238i
\(233\) 18.3848 + 18.3848i 1.20443 + 1.20443i 0.972806 + 0.231621i \(0.0744028\pi\)
0.231621 + 0.972806i \(0.425597\pi\)
\(234\) 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 0.660089 0.751187i \(-0.270518\pi\)
−0.751187 + 0.660089i \(0.770518\pi\)
\(242\) −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 \(-0.980131\pi\)
0.998053 0.0623783i \(-0.0198685\pi\)
\(258\) −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 \(-0.920670\pi\)
0.969104 0.246651i \(-0.0793300\pi\)
\(264\) 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 0.565838 0.824516i \(-0.308553\pi\)
−0.824516 + 0.565838i \(0.808553\pi\)
\(270\) 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 0.943659 + 0.330919i \(0.107359\pi\)
0.330919 + 0.943659i \(0.392641\pi\)
\(278\) 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 \(-0.942725\pi\)
0.983855 0.178965i \(-0.0572749\pi\)
\(282\) 0 0
\(283\) −8.48528 + 8.48528i −0.504398 + 0.504398i −0.912801 0.408404i \(-0.866086\pi\)
0.408404 + 0.912801i \(0.366086\pi\)
\(284\) 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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(312\) 1.41421 1.41421i 0.0800641 0.0800641i
\(313\) 7.07107 7.07107i 0.399680 0.399680i −0.478440 0.878120i \(-0.658798\pi\)
0.878120 + 0.478440i \(0.158798\pi\)
\(314\) 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 −0.816142 0.577851i \(-0.803891\pi\)
0.577851 + 0.816142i \(0.303891\pi\)
\(318\) 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 \(-0.814761\pi\)
0.835395 0.549650i \(-0.185239\pi\)
\(332\) 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 0.923312 0.384052i \(-0.125472\pi\)
−0.384052 + 0.923312i \(0.625472\pi\)
\(338\) 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 0.0649788 0.997887i \(-0.479302\pi\)
0.997887 0.0649788i \(-0.0206980\pi\)
\(348\) 10.0000i 0.536056i
\(349\) 14.0000i 0.749403i 0.927146 + 0.374701i \(0.122255\pi\)
−0.927146 + 0.374701i \(0.877745\pi\)
\(350\) 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 \(0.218315\pi\)
−0.773877 + 0.633336i \(0.781685\pi\)
\(360\) 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 −0.108266 0.994122i \(-0.534530\pi\)
0.994122 + 0.108266i \(0.0345298\pi\)
\(368\) 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 0.630722 0.776009i \(-0.282759\pi\)
−0.776009 + 0.630722i \(0.782759\pi\)
\(380\) 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 \(-0.865954\pi\)
0.912633 0.408781i \(-0.134046\pi\)
\(384\) 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 \(0.229074\pi\)
−0.752032 + 0.659126i \(0.770926\pi\)
\(390\) 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 −0.0745145 0.997220i \(-0.523741\pi\)
0.997220 + 0.0745145i \(0.0237407\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000i 0.0500000i
\(401\) −9.89949 + 9.89949i −0.494357 + 0.494357i −0.909676 0.415319i \(-0.863670\pi\)
0.415319 + 0.909676i \(0.363670\pi\)
\(402\) 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 −0.772812 0.634635i \(-0.781151\pi\)
0.634635 + 0.772812i \(0.281151\pi\)
\(420\) 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 −0.557617 0.830098i \(-0.688284\pi\)
0.830098 + 0.557617i \(0.188284\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 14.0000i 0.672797i −0.941720 0.336399i \(-0.890791\pi\)
0.941720 0.336399i \(-0.109209\pi\)
\(434\) 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 0.383547 0.923521i \(-0.374702\pi\)
−0.923521 + 0.383547i \(0.874702\pi\)
\(440\) 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 −0.672948 0.739689i \(-0.734972\pi\)
0.739689 + 0.672948i \(0.234972\pi\)
\(450\) 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 \(-0.924854\pi\)
0.972263 0.233890i \(-0.0751456\pi\)
\(458\) −26.0000 −1.21490
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0000i 1.39724i −0.715493 0.698620i \(-0.753798\pi\)
0.715493 0.698620i \(-0.246202\pi\)
\(462\) 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 \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 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 0.203641 0.979046i \(-0.434723\pi\)
−0.979046 + 0.203641i \(0.934723\pi\)
\(480\) 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 −0.402671 0.915345i \(-0.631918\pi\)
0.915345 + 0.402671i \(0.131918\pi\)
\(488\) −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 \(-0.912720\pi\)
0.962642 0.270776i \(-0.0872803\pi\)
\(492\) 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 −0.767576 0.640958i \(-0.778537\pi\)
0.640958 + 0.767576i \(0.278537\pi\)
\(500\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 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 −0.278810 0.960346i \(-0.589940\pi\)
0.960346 + 0.278810i \(0.0899400\pi\)
\(522\) −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 0.842580 0.538571i \(-0.181036\pi\)
−0.538571 + 0.842580i \(0.681036\pi\)
\(542\) 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 0.864844 0.502040i \(-0.167417\pi\)
−0.502040 + 0.864844i \(0.667417\pi\)
\(548\) −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 \(-0.725879\pi\)
0.651546 0.758610i \(-0.274121\pi\)
\(564\) 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 \(-0.959861\pi\)
0.992060 0.125767i \(-0.0401390\pi\)
\(570\) 8.00000i 0.335083i
\(571\) 19.7990 19.7990i 0.828562 0.828562i −0.158756 0.987318i \(-0.550748\pi\)
0.987318 + 0.158756i \(0.0507483\pi\)
\(572\) −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 \(-0.864570\pi\)
0.910847 0.412744i \(-0.135430\pi\)
\(588\) −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 \(0.0928094\pi\)
−0.957794 + 0.287456i \(0.907191\pi\)
\(594\) −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 −0.615262 0.788323i \(-0.710950\pi\)
0.788323 + 0.615262i \(0.210950\pi\)
\(602\) 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 0.273156 0.961970i \(-0.411933\pi\)
−0.961970 + 0.273156i \(0.911933\pi\)
\(608\) −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 0.616530 0.787332i \(-0.288538\pi\)
−0.787332 + 0.616530i \(0.788538\pi\)
\(618\) 5.65685 5.65685i 0.227552 0.227552i
\(619\) −14.1421 + 14.1421i −0.568420 + 0.568420i −0.931686 0.363265i \(-0.881662\pi\)
0.363265 + 0.931686i \(0.381662\pi\)
\(620\) 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 \(0.158534\pi\)
−0.878516 + 0.477712i \(0.841466\pi\)
\(632\) 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 0.734484 0.678626i \(-0.237424\pi\)
−0.678626 + 0.734484i \(0.737424\pi\)
\(642\) 4.00000 0.157867
\(643\) 19.7990 + 19.7990i 0.780796 + 0.780796i 0.979965 0.199169i \(-0.0638243\pi\)
−0.199169 + 0.979965i \(0.563824\pi\)
\(644\) 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 −0.619203 0.785231i \(-0.712544\pi\)
0.785231 + 0.619203i \(0.212544\pi\)
\(654\) 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 \(-0.962773\pi\)
0.993169 0.116686i \(-0.0372273\pi\)
\(662\) −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 −0.299827 + 0.953994i \(0.596929\pi\)
−0.953994 + 0.299827i \(0.903071\pi\)
\(674\) 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 −0.955670 0.294441i \(-0.904866\pi\)
−0.294441 0.955670i \(-0.595134\pi\)
\(678\) 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 0.923861 0.382727i \(-0.125015\pi\)
−0.382727 + 0.923861i \(0.625015\pi\)
\(684\) −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 −0.221884 0.975073i \(-0.571221\pi\)
0.975073 + 0.221884i \(0.0712206\pi\)
\(692\) 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 0.967072 + 0.254501i \(0.0819114\pi\)
0.254501 + 0.967072i \(0.418089\pi\)
\(710\) 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 0.998407 + 0.0564181i \(0.0179680\pi\)
0.0564181 + 0.998407i \(0.482032\pi\)
\(720\) 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 \(-0.676889\pi\)
0.527549 0.849524i \(-0.323111\pi\)
\(734\) −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 \(0.405687\pi\)
−0.291977 + 0.956425i \(0.594313\pi\)
\(740\) 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 0.468437 0.883497i \(-0.344817\pi\)
−0.883497 + 0.468437i \(0.844817\pi\)
\(744\) −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 0.596323 0.802745i \(-0.296628\pi\)
−0.802745 + 0.596323i \(0.796628\pi\)
\(752\) 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 \(-0.941831\pi\)
0.983349 0.181728i \(-0.0581691\pi\)
\(758\) −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 \(0.239492\pi\)
−0.730061 + 0.683383i \(0.760508\pi\)
\(774\) 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 0.755719 0.654896i \(-0.227288\pi\)
−0.654896 + 0.755719i \(0.727288\pi\)
\(788\) −9.89949 + 9.89949i −0.352655 + 0.352655i
\(789\) −5.65685 + 5.65685i −0.201389 + 0.201389i
\(790\) 16.0000i 0.569254i