Properties

Label 144.2.i.c.49.1
Level $144$
Weight $2$
Character 144.49
Analytic conductor $1.150$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 144.49
Dual form 144.2.i.c.97.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{13} -3.00000 q^{17} +1.00000 q^{19} +(3.00000 + 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} -5.19615i q^{27} +(-3.00000 - 5.19615i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-4.50000 - 2.59808i) q^{33} -4.00000 q^{37} +3.46410i q^{39} +(-4.50000 + 7.79423i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{47} +(1.50000 - 2.59808i) q^{49} +(-4.50000 + 2.59808i) q^{51} +12.0000 q^{53} +(1.50000 - 0.866025i) q^{57} +(1.50000 - 2.59808i) q^{59} +(-4.00000 - 6.92820i) q^{61} +6.00000 q^{63} +(2.50000 - 4.33013i) q^{67} +10.3923i q^{69} +12.0000 q^{71} +11.0000 q^{73} +(7.50000 + 4.33013i) q^{75} +(3.00000 - 5.19615i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{83} +(-9.00000 - 5.19615i) q^{87} +6.00000 q^{89} -4.00000 q^{91} +6.92820i q^{93} +(-2.50000 - 4.33013i) q^{97} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} + 2q^{7} + 3q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + 2q^{7} + 3q^{9} - 3q^{11} - 2q^{13} - 6q^{17} + 2q^{19} + 6q^{21} - 6q^{23} + 5q^{25} - 6q^{29} - 4q^{31} - 9q^{33} - 8q^{37} - 9q^{41} - q^{43} - 6q^{47} + 3q^{49} - 9q^{51} + 24q^{53} + 3q^{57} + 3q^{59} - 8q^{61} + 12q^{63} + 5q^{67} + 24q^{71} + 22q^{73} + 15q^{75} + 6q^{77} - 4q^{79} - 9q^{81} + 12q^{83} - 18q^{87} + 12q^{89} - 8q^{91} - 5q^{97} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 0 0
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 3.00000 + 1.73205i 0.654654 + 0.377964i
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) −4.50000 2.59808i −0.783349 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 3.46410i 0.554700i
\(40\) 0 0
\(41\) −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) 0 0
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0 0
\(51\) −4.50000 + 2.59808i −0.630126 + 0.363803i
\(52\) 0 0
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.50000 0.866025i 0.198680 0.114708i
\(58\) 0 0
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 0 0
\(63\) 6.00000 0.755929
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i \(-0.734535\pi\)
0.977356 + 0.211604i \(0.0678686\pi\)
\(68\) 0 0
\(69\) 10.3923i 1.25109i
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 0 0
\(75\) 7.50000 + 4.33013i 0.866025 + 0.500000i
\(76\) 0 0
\(77\) 3.00000 5.19615i 0.341882 0.592157i
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −9.00000 5.19615i −0.964901 0.557086i
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 6.92820i 0.718421i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.50000 4.33013i −0.253837 0.439658i 0.710742 0.703452i \(-0.248359\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) 0 0
\(99\) −9.00000 −0.904534
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i \(-0.591062\pi\)
0.971925 0.235291i \(-0.0756043\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) −6.00000 + 3.46410i −0.569495 + 0.328798i
\(112\) 0 0
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.00000 + 5.19615i 0.277350 + 0.480384i
\(118\) 0 0
\(119\) −3.00000 5.19615i −0.275010 0.476331i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) 15.5885i 1.40556i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 0 0
\(129\) −1.50000 0.866025i −0.132068 0.0762493i
\(130\) 0 0
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 0 0
\(133\) 1.00000 + 1.73205i 0.0867110 + 0.150188i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.50000 + 2.59808i 0.128154 + 0.221969i 0.922961 0.384893i \(-0.125762\pi\)
−0.794808 + 0.606861i \(0.792428\pi\)
\(138\) 0 0
\(139\) −9.50000 + 16.4545i −0.805779 + 1.39565i 0.109984 + 0.993933i \(0.464920\pi\)
−0.915764 + 0.401718i \(0.868413\pi\)
\(140\) 0 0
\(141\) −9.00000 5.19615i −0.757937 0.437595i
\(142\) 0 0
\(143\) 6.00000 0.501745
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.19615i 0.428571i
\(148\) 0 0
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) 0 0
\(153\) −4.50000 + 7.79423i −0.363803 + 0.630126i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) 0 0
\(159\) 18.0000 10.3923i 1.42749 0.824163i
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) 1.50000 2.59808i 0.114708 0.198680i
\(172\) 0 0
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) −5.00000 + 8.66025i −0.377964 + 0.654654i
\(176\) 0 0
\(177\) 5.19615i 0.390567i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) −12.0000 6.92820i −0.887066 0.512148i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 4.50000 + 7.79423i 0.329073 + 0.569970i
\(188\) 0 0
\(189\) 9.00000 5.19615i 0.654654 0.377964i
\(190\) 0 0
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) 8.66025i 0.610847i
\(202\) 0 0
\(203\) 6.00000 10.3923i 0.421117 0.729397i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 9.00000 + 15.5885i 0.625543 + 1.08347i
\(208\) 0 0
\(209\) −1.50000 2.59808i −0.103757 0.179713i
\(210\) 0 0
\(211\) 10.0000 17.3205i 0.688428 1.19239i −0.283918 0.958849i \(-0.591634\pi\)
0.972346 0.233544i \(-0.0750324\pi\)
\(212\) 0 0
\(213\) 18.0000 10.3923i 1.23334 0.712069i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) 0 0
\(219\) 16.5000 9.52628i 1.11497 0.643726i
\(220\) 0 0
\(221\) 3.00000 5.19615i 0.201802 0.349531i
\(222\) 0 0
\(223\) 13.0000 + 22.5167i 0.870544 + 1.50783i 0.861435 + 0.507869i \(0.169566\pi\)
0.00910984 + 0.999959i \(0.497100\pi\)
\(224\) 0 0
\(225\) 15.0000 1.00000
\(226\) 0 0
\(227\) 10.5000 + 18.1865i 0.696909 + 1.20708i 0.969533 + 0.244962i \(0.0787754\pi\)
−0.272623 + 0.962121i \(0.587891\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) 10.3923i 0.683763i
\(232\) 0 0
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −6.00000 3.46410i −0.389742 0.225018i
\(238\) 0 0
\(239\) 3.00000 5.19615i 0.194054 0.336111i −0.752536 0.658551i \(-0.771170\pi\)
0.946590 + 0.322440i \(0.104503\pi\)
\(240\) 0 0
\(241\) 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.00000 + 1.73205i −0.0636285 + 0.110208i
\(248\) 0 0
\(249\) 18.0000 + 10.3923i 1.14070 + 0.658586i
\(250\) 0 0
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.5000 18.1865i 0.654972 1.13444i −0.326929 0.945049i \(-0.606014\pi\)
0.981901 0.189396i \(-0.0606529\pi\)
\(258\) 0 0
\(259\) −4.00000 6.92820i −0.248548 0.430498i
\(260\) 0 0
\(261\) −18.0000 −1.11417
\(262\) 0 0
\(263\) 9.00000 + 15.5885i 0.554964 + 0.961225i 0.997906 + 0.0646755i \(0.0206012\pi\)
−0.442943 + 0.896550i \(0.646065\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.00000 5.19615i 0.550791 0.317999i
\(268\) 0 0
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) 0 0
\(273\) −6.00000 + 3.46410i −0.363137 + 0.209657i
\(274\) 0 0
\(275\) 7.50000 12.9904i 0.452267 0.783349i
\(276\) 0 0
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 0 0
\(279\) 6.00000 + 10.3923i 0.359211 + 0.622171i
\(280\) 0 0
\(281\) −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i \(-0.223942\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(282\) 0 0
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.0000 −1.06251
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −7.50000 4.33013i −0.439658 0.253837i
\(292\) 0 0
\(293\) −15.0000 + 25.9808i −0.876309 + 1.51781i −0.0209480 + 0.999781i \(0.506668\pi\)
−0.855361 + 0.518032i \(0.826665\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −13.5000 + 7.79423i −0.783349 + 0.452267i
\(298\) 0 0
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 0 0
\(301\) 1.00000 1.73205i 0.0576390 0.0998337i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) 0 0
\(309\) 24.2487i 1.37946i
\(310\) 0 0
\(311\) −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i \(0.337148\pi\)
−0.999928 + 0.0119847i \(0.996185\pi\)
\(312\) 0 0
\(313\) −14.5000 25.1147i −0.819588 1.41957i −0.905986 0.423308i \(-0.860869\pi\)
0.0863973 0.996261i \(-0.472465\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) −9.00000 + 15.5885i −0.503903 + 0.872786i
\(320\) 0 0
\(321\) −4.50000 + 2.59808i −0.251166 + 0.145010i
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) 0 0
\(325\) −10.0000 −0.554700
\(326\) 0 0
\(327\) −24.0000 + 13.8564i −1.32720 + 0.766261i
\(328\) 0 0
\(329\) 6.00000 10.3923i 0.330791 0.572946i
\(330\) 0 0
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) 0 0
\(333\) −6.00000 + 10.3923i −0.328798 + 0.569495i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.500000 0.866025i 0.0272367 0.0471754i −0.852086 0.523402i \(-0.824663\pi\)
0.879322 + 0.476227i \(0.157996\pi\)
\(338\) 0 0
\(339\) 10.3923i 0.564433i
\(340\) 0 0
\(341\) 12.0000 0.649836
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 16.5000 28.5788i 0.885766 1.53419i 0.0409337 0.999162i \(-0.486967\pi\)
0.844833 0.535031i \(-0.179700\pi\)
\(348\) 0 0
\(349\) 8.00000 + 13.8564i 0.428230 + 0.741716i 0.996716 0.0809766i \(-0.0258039\pi\)
−0.568486 + 0.822693i \(0.692471\pi\)
\(350\) 0 0
\(351\) 9.00000 + 5.19615i 0.480384 + 0.277350i
\(352\) 0 0
\(353\) 10.5000 + 18.1865i 0.558859 + 0.967972i 0.997592 + 0.0693543i \(0.0220939\pi\)
−0.438733 + 0.898617i \(0.644573\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −9.00000 5.19615i −0.476331 0.275010i
\(358\) 0 0
\(359\) 18.0000 0.950004 0.475002 0.879985i \(-0.342447\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 3.46410i 0.181818i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −14.0000 24.2487i −0.730794 1.26577i −0.956544 0.291587i \(-0.905817\pi\)
0.225750 0.974185i \(-0.427517\pi\)
\(368\) 0 0
\(369\) 13.5000 + 23.3827i 0.702782 + 1.21725i
\(370\) 0 0
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) 0 0
\(373\) 17.0000 29.4449i 0.880227 1.52460i 0.0291379 0.999575i \(-0.490724\pi\)
0.851089 0.525022i \(-0.175943\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 0 0
\(381\) −3.00000 + 1.73205i −0.153695 + 0.0887357i
\(382\) 0 0
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.00000 −0.152499
\(388\) 0 0
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 0 0
\(391\) 9.00000 15.5885i 0.455150 0.788342i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 0 0
\(399\) 3.00000 + 1.73205i 0.150188 + 0.0867110i
\(400\) 0 0
\(401\) 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i \(-0.597840\pi\)
0.976714 0.214544i \(-0.0688266\pi\)
\(402\) 0 0
\(403\) −4.00000 6.92820i −0.199254 0.345118i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 + 10.3923i 0.297409 + 0.515127i
\(408\) 0 0
\(409\) −8.50000 + 14.7224i −0.420298 + 0.727977i −0.995968 0.0897044i \(-0.971408\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(410\) 0 0
\(411\) 4.50000 + 2.59808i 0.221969 + 0.128154i
\(412\) 0 0
\(413\) 6.00000 0.295241
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 32.9090i 1.61156i
\(418\) 0 0
\(419\) −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i \(-0.928027\pi\)
0.681426 + 0.731887i \(0.261360\pi\)
\(420\) 0 0
\(421\) −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i \(-0.328710\pi\)
−0.999895 + 0.0145228i \(0.995377\pi\)
\(422\) 0 0
\(423\) −18.0000 −0.875190
\(424\) 0 0
\(425\) −7.50000 12.9904i −0.363803 0.630126i
\(426\) 0 0
\(427\) 8.00000 13.8564i 0.387147 0.670559i
\(428\) 0 0
\(429\) 9.00000 5.19615i 0.434524 0.250873i
\(430\) 0 0
\(431\) 30.0000 1.44505 0.722525 0.691345i \(-0.242982\pi\)
0.722525 + 0.691345i \(0.242982\pi\)
\(432\) 0 0
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.00000 + 5.19615i −0.143509 + 0.248566i
\(438\) 0 0
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 0 0
\(441\) −4.50000 7.79423i −0.214286 0.371154i
\(442\) 0 0
\(443\) 1.50000 + 2.59808i 0.0712672 + 0.123438i 0.899457 0.437009i \(-0.143962\pi\)
−0.828190 + 0.560448i \(0.810629\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 10.3923i 0.491539i
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) 27.0000 1.27138
\(452\) 0 0
\(453\) −15.0000 8.66025i −0.704761 0.406894i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.50000 14.7224i −0.397613 0.688686i 0.595818 0.803120i \(-0.296828\pi\)
−0.993431 + 0.114433i \(0.963495\pi\)
\(458\) 0 0
\(459\) 15.5885i 0.727607i
\(460\) 0 0
\(461\) 15.0000 + 25.9808i 0.698620 + 1.21004i 0.968945 + 0.247276i \(0.0795353\pi\)
−0.270326 + 0.962769i \(0.587131\pi\)
\(462\) 0 0
\(463\) 10.0000 17.3205i 0.464739 0.804952i −0.534450 0.845200i \(-0.679481\pi\)
0.999190 + 0.0402476i \(0.0128147\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.0000 0.694117 0.347059 0.937843i \(-0.387180\pi\)
0.347059 + 0.937843i \(0.387180\pi\)
\(468\) 0 0
\(469\) 10.0000 0.461757
\(470\) 0 0
\(471\) 6.92820i 0.319235i
\(472\) 0 0
\(473\) −1.50000 + 2.59808i −0.0689701 + 0.119460i
\(474\) 0 0
\(475\) 2.50000 + 4.33013i 0.114708 + 0.198680i
\(476\) 0 0
\(477\) 18.0000 31.1769i 0.824163 1.42749i
\(478\) 0 0
\(479\) −21.0000 36.3731i −0.959514 1.66193i −0.723681 0.690134i \(-0.757551\pi\)
−0.235833 0.971794i \(-0.575782\pi\)
\(480\) 0 0
\(481\) 4.00000 6.92820i 0.182384 0.315899i
\(482\) 0 0
\(483\) −18.0000 + 10.3923i −0.819028 + 0.472866i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −26.0000 −1.17817 −0.589086 0.808070i \(-0.700512\pi\)
−0.589086 + 0.808070i \(0.700512\pi\)
\(488\) 0 0
\(489\) 6.00000 3.46410i 0.271329 0.156652i
\(490\) 0 0
\(491\) −7.50000 + 12.9904i −0.338470 + 0.586248i −0.984145 0.177365i \(-0.943243\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(492\) 0 0
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.0000 + 20.7846i 0.538274 + 0.932317i
\(498\) 0 0
\(499\) −6.50000 + 11.2583i −0.290980 + 0.503992i −0.974042 0.226369i \(-0.927315\pi\)
0.683062 + 0.730361i \(0.260648\pi\)
\(500\) 0 0
\(501\) 20.7846i 0.928588i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 13.5000 + 7.79423i 0.599556 + 0.346154i
\(508\) 0 0
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) 11.0000 + 19.0526i 0.486611 + 0.842836i
\(512\) 0 0
\(513\) 5.19615i 0.229416i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −9.00000 + 15.5885i −0.395820 + 0.685580i
\(518\) 0 0
\(519\) 9.00000 + 5.19615i 0.395056 + 0.228086i
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) 17.3205i 0.755929i
\(526\) 0 0
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) −4.50000 7.79423i −0.195283 0.338241i
\(532\) 0 0
\(533\) −9.00000 15.5885i −0.389833 0.675211i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −18.0000 + 10.3923i −0.776757 + 0.448461i
\(538\) 0 0
\(539\) −9.00000 −0.387657
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) 0 0
\(543\) 21.0000 12.1244i 0.901196 0.520306i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.500000 0.866025i −0.0213785 0.0370286i 0.855138 0.518400i \(-0.173472\pi\)
−0.876517 + 0.481371i \(0.840139\pi\)
\(548\) 0 0
\(549\) −24.0000 −1.02430
\(550\) 0 0
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) 0 0
\(553\) 4.00000 6.92820i 0.170097 0.294617i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) 13.5000 + 7.79423i 0.569970 + 0.329073i
\(562\) 0 0
\(563\) −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i \(0.473712\pi\)
−0.904320 + 0.426855i \(0.859622\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 9.00000 15.5885i 0.377964 0.654654i
\(568\) 0 0
\(569\) −22.5000 38.9711i −0.943249 1.63376i −0.759220 0.650835i \(-0.774419\pi\)
−0.184030 0.982921i \(-0.558914\pi\)
\(570\) 0 0
\(571\) −18.5000 + 32.0429i −0.774201 + 1.34096i 0.161042 + 0.986948i \(0.448515\pi\)
−0.935243 + 0.354008i \(0.884819\pi\)
\(572\) 0 0
\(573\) −27.0000 15.5885i −1.12794 0.651217i
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) 0 0
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 0 0
\(579\) 8.66025i 0.359908i
\(580\) 0 0
\(581\) −12.0000 + 20.7846i −0.497844 + 0.862291i
\(582\) 0 0
\(583\) −18.0000 31.1769i −0.745484 1.29122i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.50000 7.79423i −0.185735 0.321702i 0.758089 0.652151i \(-0.226133\pi\)
−0.943824 + 0.330449i \(0.892800\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 0 0
\(591\) −18.0000 + 10.3923i −0.740421 + 0.427482i
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 15.0000 8.66025i 0.613909 0.354441i
\(598\) 0 0
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) 18.5000 + 32.0429i 0.754631 + 1.30706i 0.945558 + 0.325455i \(0.105517\pi\)
−0.190927 + 0.981604i \(0.561149\pi\)
\(602\) 0 0
\(603\) −7.50000 12.9904i −0.305424 0.529009i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −14.0000 + 24.2487i −0.568242 + 0.984225i 0.428497 + 0.903543i \(0.359043\pi\)
−0.996740 + 0.0806818i \(0.974290\pi\)
\(608\) 0 0
\(609\) 20.7846i 0.842235i
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13.5000 + 23.3827i −0.543490 + 0.941351i 0.455211 + 0.890384i \(0.349564\pi\)
−0.998700 + 0.0509678i \(0.983769\pi\)
\(618\) 0 0
\(619\) 17.5000 + 30.3109i 0.703384 + 1.21830i 0.967271 + 0.253744i \(0.0816620\pi\)
−0.263887 + 0.964554i \(0.585005\pi\)
\(620\) 0 0
\(621\) 27.0000 + 15.5885i 1.08347 + 0.625543i
\(622\) 0 0
\(623\) 6.00000 + 10.3923i 0.240385 + 0.416359i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) −4.50000 2.59808i −0.179713 0.103757i
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) 34.6410i 1.37686i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 + 5.19615i 0.118864 + 0.205879i
\(638\) 0 0
\(639\) 18.0000 31.1769i 0.712069 1.23334i
\(640\) 0 0
\(641\) 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) 0 0
\(643\) 11.5000 19.9186i 0.453516 0.785512i −0.545086 0.838380i \(-0.683503\pi\)
0.998602 + 0.0528680i \(0.0168363\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.0000 −0.707653 −0.353827 0.935311i \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) 0 0
\(649\) −9.00000 −0.353281
\(650\) 0 0
\(651\) −12.0000 + 6.92820i −0.470317 + 0.271538i
\(652\) 0 0
\(653\) 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 16.5000 28.5788i 0.643726 1.11497i
\(658\) 0 0
\(659\) −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 0 0
\(661\) 2.00000 3.46410i 0.0777910 0.134738i −0.824506 0.565854i \(-0.808547\pi\)
0.902297 + 0.431116i \(0.141880\pi\)
\(662\) 0 0
\(663\) 10.3923i 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 36.0000 1.39393
\(668\) 0 0
\(669\) 39.0000 + 22.5167i 1.50783 + 0.870544i
\(670\) 0 0
\(671\) −12.0000 + 20.7846i −0.463255 + 0.802381i
\(672\) 0 0
\(673\) 11.0000 + 19.0526i 0.424019 + 0.734422i 0.996328 0.0856156i \(-0.0272857\pi\)
−0.572309 + 0.820038i \(0.693952\pi\)
\(674\) 0 0
\(675\) 22.5000 12.9904i 0.866025 0.500000i
\(676\) 0 0
\(677\) −18.0000 31.1769i −0.691796 1.19823i −0.971249 0.238067i \(-0.923486\pi\)
0.279453 0.960159i \(-0.409847\pi\)
\(678\) 0 0
\(679\) 5.00000 8.66025i 0.191882 0.332350i
\(680\) 0 0
\(681\) 31.5000 + 18.1865i 1.20708 + 0.696909i
\(682\) 0 0
\(683\) 9.00000 0.344375 0.172188 0.985064i \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 24.2487i 0.925146i
\(688\) 0 0
\(689\) −12.0000 + 20.7846i −0.457164 + 0.791831i
\(690\) 0 0
\(691\) 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i \(-0.118041\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 0 0
\(693\) −9.00000 15.5885i −0.341882 0.592157i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 13.5000 23.3827i 0.511349 0.885682i
\(698\) 0 0
\(699\) 4.50000 2.59808i 0.170206 0.0982683i
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) −4.00000 −0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) 0 0
\(711\) −12.0000 −0.450035
\(712\) 0 0
\(713\) −12.0000 20.7846i −0.449404 0.778390i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.3923i 0.388108i
\(718\) 0 0
\(719\) 36.0000 1.34257 0.671287 0.741198i \(-0.265742\pi\)
0.671287 + 0.741198i \(0.265742\pi\)
\(720\) 0 0
\(721\) 28.0000 1.04277
\(722\) 0 0
\(723\) 10.5000 + 6.06218i 0.390499 + 0.225455i
\(724\) 0 0
\(725\) 15.0000 25.9808i 0.557086 0.964901i
\(726\) 0 0
\(727\) 13.0000 + 22.5167i 0.482143 + 0.835097i 0.999790 0.0204978i \(-0.00652512\pi\)
−0.517647 + 0.855595i \(0.673192\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 1.50000 + 2.59808i 0.0554795 + 0.0960933i
\(732\) 0 0
\(733\) −7.00000 + 12.1244i −0.258551 + 0.447823i −0.965854 0.259087i \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −15.0000 −0.552532
\(738\) 0 0
\(739\) −47.0000 −1.72892 −0.864461 0.502699i \(-0.832340\pi\)
−0.864461 + 0.502699i \(0.832340\pi\)
\(740\) 0 0
\(741\) 3.46410i 0.127257i
\(742\) 0 0
\(743\) 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i \(-0.798229\pi\)
0.915794 + 0.401648i \(0.131563\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 36.0000 1.31717
\(748\) 0 0
\(749\) −3.00000 5.19615i −0.109618 0.189863i
\(750\) 0 0
\(751\) 4.00000 6.92820i 0.145962 0.252814i −0.783769 0.621052i \(-0.786706\pi\)
0.929731 + 0.368238i \(0.120039\pi\)
\(752\) 0 0
\(753\) −31.5000 + 18.1865i −1.14792 + 0.662754i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 27.0000 15.5885i 0.980038 0.565825i
\(760\) 0 0
\(761\) −21.0000 + 36.3731i −0.761249 + 1.31852i 0.180957 + 0.983491i \(0.442080\pi\)
−0.942207 + 0.335032i \(0.891253\pi\)
\(762\) 0 0
\(763\) −16.0000 27.7128i −0.579239 1.00327i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.00000 + 5.19615i 0.108324 + 0.187622i
\(768\) 0 0
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 0 0
\(771\) 36.3731i 1.30994i
\(772\) 0 0
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) −20.0000 −0.718421
\(776\) 0 0
\(777\) −12.0000 6.92820i −0.430498 0.248548i
\(778\) 0 0
\(779\) −4.50000 + 7.79423i −0.161229 + 0.279257i
\(780\) 0 0
\(781\) −18.0000 31.1769i −0.644091 1.11560i
\(782\) 0 0
\(783\) −27.0000 + 15.5885i −0.964901 + 0.557086i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −2.00000 + 3.46410i −0.0712923 + 0.123482i −0.899468 0.436987i \(-0.856046\pi\)
0.828176 + 0.560469i \(0.189379\pi\)
\(788\) 0 0
\(789\) 27.0000 + 15.5885i 0.961225 + 0.554964i
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 16.0000 0.568177
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.00000 10.3923i 0.212531 0.368114i −0.739975 0.672634i \(-0.765163\pi\)
0.952506 + 0.304520i \(0.0984960\pi\)
\(798\) 0 0
\(799\) 9.00000 + 15.5885i 0.318397 + 0.551480i
\(800\) 0 0