Properties

Label 1232.2.q.f.177.2
Level $1232$
Weight $2$
Character 1232.177
Analytic conductor $9.838$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.83756952902\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1232.177
Dual form 1232.2.q.f.529.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.207107 + 0.358719i) q^{3} +(1.70711 - 2.95680i) q^{5} +(2.62132 + 0.358719i) q^{7} +(1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q+(0.207107 + 0.358719i) q^{3} +(1.70711 - 2.95680i) q^{5} +(2.62132 + 0.358719i) q^{7} +(1.41421 - 2.44949i) q^{9} +(0.500000 + 0.866025i) q^{11} +1.82843 q^{13} +1.41421 q^{15} +(3.82843 + 6.63103i) q^{17} +(-1.70711 + 2.95680i) q^{19} +(0.414214 + 1.01461i) q^{21} +(1.12132 - 1.94218i) q^{23} +(-3.32843 - 5.76500i) q^{25} +2.41421 q^{27} -8.65685 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.207107 + 0.358719i) q^{33} +(5.53553 - 7.13834i) q^{35} +(3.29289 - 5.70346i) q^{37} +(0.378680 + 0.655892i) q^{39} -2.58579 q^{41} -5.65685 q^{43} +(-4.82843 - 8.36308i) q^{45} +(3.24264 - 5.61642i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-1.58579 + 2.74666i) q^{51} +(5.94975 + 10.3053i) q^{53} +3.41421 q^{55} -1.41421 q^{57} +(-4.20711 - 7.28692i) q^{59} +(-3.08579 + 5.34474i) q^{61} +(4.58579 - 5.91359i) q^{63} +(3.12132 - 5.40629i) q^{65} +(5.62132 + 9.73641i) q^{67} +0.928932 q^{69} -3.07107 q^{71} +(3.29289 + 5.70346i) q^{73} +(1.37868 - 2.38794i) q^{75} +(1.00000 + 2.44949i) q^{77} +(-2.37868 + 4.11999i) q^{79} +(-3.74264 - 6.48244i) q^{81} -16.1421 q^{83} +26.1421 q^{85} +(-1.79289 - 3.10538i) q^{87} +(2.24264 - 3.88437i) q^{89} +(4.79289 + 0.655892i) q^{91} +(0.828427 - 1.43488i) q^{93} +(5.82843 + 10.0951i) q^{95} +1.82843 q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 4q^{5} + 2q^{7} + O(q^{10}) \) \( 4q - 2q^{3} + 4q^{5} + 2q^{7} + 2q^{11} - 4q^{13} + 4q^{17} - 4q^{19} - 4q^{21} - 4q^{23} - 2q^{25} + 4q^{27} - 12q^{29} - 8q^{31} + 2q^{33} + 8q^{35} + 16q^{37} + 10q^{39} - 16q^{41} - 8q^{45} - 4q^{47} + 10q^{49} - 12q^{51} + 4q^{53} + 8q^{55} - 14q^{59} - 18q^{61} + 24q^{63} + 4q^{65} + 14q^{67} + 32q^{69} + 16q^{71} + 16q^{73} + 14q^{75} + 4q^{77} - 18q^{79} + 2q^{81} - 8q^{83} + 48q^{85} - 10q^{87} - 8q^{89} + 22q^{91} - 8q^{93} + 12q^{95} - 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).

\(n\) \(309\) \(353\) \(463\) \(673\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.207107 + 0.358719i 0.119573 + 0.207107i 0.919599 0.392859i \(-0.128514\pi\)
−0.800025 + 0.599966i \(0.795181\pi\)
\(4\) 0 0
\(5\) 1.70711 2.95680i 0.763441 1.32232i −0.177625 0.984098i \(-0.556842\pi\)
0.941067 0.338221i \(-0.109825\pi\)
\(6\) 0 0
\(7\) 2.62132 + 0.358719i 0.990766 + 0.135583i
\(8\) 0 0
\(9\) 1.41421 2.44949i 0.471405 0.816497i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0 0
\(13\) 1.82843 0.507114 0.253557 0.967320i \(-0.418399\pi\)
0.253557 + 0.967320i \(0.418399\pi\)
\(14\) 0 0
\(15\) 1.41421 0.365148
\(16\) 0 0
\(17\) 3.82843 + 6.63103i 0.928530 + 1.60826i 0.785783 + 0.618502i \(0.212260\pi\)
0.142747 + 0.989759i \(0.454407\pi\)
\(18\) 0 0
\(19\) −1.70711 + 2.95680i −0.391637 + 0.678335i −0.992666 0.120892i \(-0.961424\pi\)
0.601028 + 0.799228i \(0.294758\pi\)
\(20\) 0 0
\(21\) 0.414214 + 1.01461i 0.0903888 + 0.221406i
\(22\) 0 0
\(23\) 1.12132 1.94218i 0.233811 0.404973i −0.725115 0.688628i \(-0.758213\pi\)
0.958927 + 0.283654i \(0.0915468\pi\)
\(24\) 0 0
\(25\) −3.32843 5.76500i −0.665685 1.15300i
\(26\) 0 0
\(27\) 2.41421 0.464616
\(28\) 0 0
\(29\) −8.65685 −1.60754 −0.803769 0.594942i \(-0.797175\pi\)
−0.803769 + 0.594942i \(0.797175\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0 0
\(33\) −0.207107 + 0.358719i −0.0360527 + 0.0624450i
\(34\) 0 0
\(35\) 5.53553 7.13834i 0.935676 1.20660i
\(36\) 0 0
\(37\) 3.29289 5.70346i 0.541348 0.937643i −0.457479 0.889221i \(-0.651247\pi\)
0.998827 0.0484222i \(-0.0154193\pi\)
\(38\) 0 0
\(39\) 0.378680 + 0.655892i 0.0606373 + 0.105027i
\(40\) 0 0
\(41\) −2.58579 −0.403832 −0.201916 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(42\) 0 0
\(43\) −5.65685 −0.862662 −0.431331 0.902194i \(-0.641956\pi\)
−0.431331 + 0.902194i \(0.641956\pi\)
\(44\) 0 0
\(45\) −4.82843 8.36308i −0.719779 1.24669i
\(46\) 0 0
\(47\) 3.24264 5.61642i 0.472988 0.819239i −0.526534 0.850154i \(-0.676509\pi\)
0.999522 + 0.0309151i \(0.00984215\pi\)
\(48\) 0 0
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) 0 0
\(51\) −1.58579 + 2.74666i −0.222055 + 0.384610i
\(52\) 0 0
\(53\) 5.94975 + 10.3053i 0.817261 + 1.41554i 0.907693 + 0.419634i \(0.137842\pi\)
−0.0904325 + 0.995903i \(0.528825\pi\)
\(54\) 0 0
\(55\) 3.41421 0.460372
\(56\) 0 0
\(57\) −1.41421 −0.187317
\(58\) 0 0
\(59\) −4.20711 7.28692i −0.547719 0.948677i −0.998430 0.0560070i \(-0.982163\pi\)
0.450712 0.892670i \(-0.351170\pi\)
\(60\) 0 0
\(61\) −3.08579 + 5.34474i −0.395094 + 0.684324i −0.993113 0.117158i \(-0.962621\pi\)
0.598019 + 0.801482i \(0.295955\pi\)
\(62\) 0 0
\(63\) 4.58579 5.91359i 0.577755 0.745042i
\(64\) 0 0
\(65\) 3.12132 5.40629i 0.387152 0.670567i
\(66\) 0 0
\(67\) 5.62132 + 9.73641i 0.686754 + 1.18949i 0.972882 + 0.231301i \(0.0742982\pi\)
−0.286129 + 0.958191i \(0.592368\pi\)
\(68\) 0 0
\(69\) 0.928932 0.111830
\(70\) 0 0
\(71\) −3.07107 −0.364469 −0.182234 0.983255i \(-0.558333\pi\)
−0.182234 + 0.983255i \(0.558333\pi\)
\(72\) 0 0
\(73\) 3.29289 + 5.70346i 0.385404 + 0.667539i 0.991825 0.127604i \(-0.0407288\pi\)
−0.606421 + 0.795144i \(0.707395\pi\)
\(74\) 0 0
\(75\) 1.37868 2.38794i 0.159196 0.275736i
\(76\) 0 0
\(77\) 1.00000 + 2.44949i 0.113961 + 0.279145i
\(78\) 0 0
\(79\) −2.37868 + 4.11999i −0.267622 + 0.463536i −0.968247 0.249994i \(-0.919571\pi\)
0.700625 + 0.713530i \(0.252905\pi\)
\(80\) 0 0
\(81\) −3.74264 6.48244i −0.415849 0.720272i
\(82\) 0 0
\(83\) −16.1421 −1.77183 −0.885915 0.463848i \(-0.846468\pi\)
−0.885915 + 0.463848i \(0.846468\pi\)
\(84\) 0 0
\(85\) 26.1421 2.83551
\(86\) 0 0
\(87\) −1.79289 3.10538i −0.192218 0.332932i
\(88\) 0 0
\(89\) 2.24264 3.88437i 0.237719 0.411742i −0.722340 0.691538i \(-0.756933\pi\)
0.960060 + 0.279796i \(0.0902668\pi\)
\(90\) 0 0
\(91\) 4.79289 + 0.655892i 0.502432 + 0.0687562i
\(92\) 0 0
\(93\) 0.828427 1.43488i 0.0859039 0.148790i
\(94\) 0 0
\(95\) 5.82843 + 10.0951i 0.597984 + 1.03574i
\(96\) 0 0
\(97\) 1.82843 0.185649 0.0928243 0.995683i \(-0.470411\pi\)
0.0928243 + 0.995683i \(0.470411\pi\)
\(98\) 0 0
\(99\) 2.82843 0.284268
\(100\) 0 0
\(101\) −5.91421 10.2437i −0.588486 1.01929i −0.994431 0.105390i \(-0.966391\pi\)
0.405945 0.913898i \(-0.366943\pi\)
\(102\) 0 0
\(103\) 5.29289 9.16756i 0.521524 0.903307i −0.478162 0.878271i \(-0.658697\pi\)
0.999687 0.0250350i \(-0.00796973\pi\)
\(104\) 0 0
\(105\) 3.70711 + 0.507306i 0.361777 + 0.0495080i
\(106\) 0 0
\(107\) 5.53553 9.58783i 0.535140 0.926890i −0.464016 0.885827i \(-0.653592\pi\)
0.999157 0.0410635i \(-0.0130746\pi\)
\(108\) 0 0
\(109\) 0.242641 + 0.420266i 0.0232408 + 0.0402542i 0.877412 0.479738i \(-0.159268\pi\)
−0.854171 + 0.519992i \(0.825935\pi\)
\(110\) 0 0
\(111\) 2.72792 0.258923
\(112\) 0 0
\(113\) −13.8284 −1.30087 −0.650434 0.759562i \(-0.725413\pi\)
−0.650434 + 0.759562i \(0.725413\pi\)
\(114\) 0 0
\(115\) −3.82843 6.63103i −0.357003 0.618347i
\(116\) 0 0
\(117\) 2.58579 4.47871i 0.239056 0.414057i
\(118\) 0 0
\(119\) 7.65685 + 18.7554i 0.701903 + 1.71930i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 0 0
\(123\) −0.535534 0.927572i −0.0482875 0.0836363i
\(124\) 0 0
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) 9.72792 0.863213 0.431607 0.902062i \(-0.357947\pi\)
0.431607 + 0.902062i \(0.357947\pi\)
\(128\) 0 0
\(129\) −1.17157 2.02922i −0.103151 0.178663i
\(130\) 0 0
\(131\) −1.70711 + 2.95680i −0.149151 + 0.258336i −0.930914 0.365239i \(-0.880987\pi\)
0.781763 + 0.623575i \(0.214321\pi\)
\(132\) 0 0
\(133\) −5.53553 + 7.13834i −0.479992 + 0.618972i
\(134\) 0 0
\(135\) 4.12132 7.13834i 0.354707 0.614370i
\(136\) 0 0
\(137\) 2.67157 + 4.62730i 0.228248 + 0.395337i 0.957289 0.289133i \(-0.0933670\pi\)
−0.729041 + 0.684470i \(0.760034\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 2.68629 0.226227
\(142\) 0 0
\(143\) 0.914214 + 1.58346i 0.0764504 + 0.132416i
\(144\) 0 0
\(145\) −14.7782 + 25.5965i −1.22726 + 2.12568i
\(146\) 0 0
\(147\) 0.721825 + 2.80821i 0.0595352 + 0.231617i
\(148\) 0 0
\(149\) −3.17157 + 5.49333i −0.259825 + 0.450031i −0.966195 0.257812i \(-0.916998\pi\)
0.706370 + 0.707843i \(0.250332\pi\)
\(150\) 0 0
\(151\) 4.86396 + 8.42463i 0.395824 + 0.685586i 0.993206 0.116370i \(-0.0371259\pi\)
−0.597382 + 0.801957i \(0.703793\pi\)
\(152\) 0 0
\(153\) 21.6569 1.75085
\(154\) 0 0
\(155\) −13.6569 −1.09694
\(156\) 0 0
\(157\) −3.17157 5.49333i −0.253119 0.438415i 0.711264 0.702925i \(-0.248123\pi\)
−0.964383 + 0.264510i \(0.914790\pi\)
\(158\) 0 0
\(159\) −2.46447 + 4.26858i −0.195445 + 0.338520i
\(160\) 0 0
\(161\) 3.63604 4.68885i 0.286560 0.369533i
\(162\) 0 0
\(163\) −7.86396 + 13.6208i −0.615953 + 1.06686i 0.374264 + 0.927322i \(0.377896\pi\)
−0.990217 + 0.139539i \(0.955438\pi\)
\(164\) 0 0
\(165\) 0.707107 + 1.22474i 0.0550482 + 0.0953463i
\(166\) 0 0
\(167\) 11.7279 0.907534 0.453767 0.891120i \(-0.350080\pi\)
0.453767 + 0.891120i \(0.350080\pi\)
\(168\) 0 0
\(169\) −9.65685 −0.742835
\(170\) 0 0
\(171\) 4.82843 + 8.36308i 0.369239 + 0.639541i
\(172\) 0 0
\(173\) 2.08579 3.61269i 0.158579 0.274668i −0.775777 0.631007i \(-0.782642\pi\)
0.934357 + 0.356339i \(0.115975\pi\)
\(174\) 0 0
\(175\) −6.65685 16.3059i −0.503211 1.23261i
\(176\) 0 0
\(177\) 1.74264 3.01834i 0.130985 0.226872i
\(178\) 0 0
\(179\) −9.44975 16.3674i −0.706307 1.22336i −0.966218 0.257727i \(-0.917026\pi\)
0.259910 0.965633i \(-0.416307\pi\)
\(180\) 0 0
\(181\) 3.65685 0.271812 0.135906 0.990722i \(-0.456606\pi\)
0.135906 + 0.990722i \(0.456606\pi\)
\(182\) 0 0
\(183\) −2.55635 −0.188971
\(184\) 0 0
\(185\) −11.2426 19.4728i −0.826575 1.43167i
\(186\) 0 0
\(187\) −3.82843 + 6.63103i −0.279962 + 0.484909i
\(188\) 0 0
\(189\) 6.32843 + 0.866025i 0.460325 + 0.0629941i
\(190\) 0 0
\(191\) −6.41421 + 11.1097i −0.464116 + 0.803873i −0.999161 0.0409507i \(-0.986961\pi\)
0.535045 + 0.844824i \(0.320295\pi\)
\(192\) 0 0
\(193\) −1.05025 1.81909i −0.0755988 0.130941i 0.825748 0.564040i \(-0.190754\pi\)
−0.901347 + 0.433099i \(0.857420\pi\)
\(194\) 0 0
\(195\) 2.58579 0.185172
\(196\) 0 0
\(197\) −17.4853 −1.24577 −0.622887 0.782312i \(-0.714041\pi\)
−0.622887 + 0.782312i \(0.714041\pi\)
\(198\) 0 0
\(199\) 9.94975 + 17.2335i 0.705319 + 1.22165i 0.966576 + 0.256379i \(0.0825295\pi\)
−0.261257 + 0.965269i \(0.584137\pi\)
\(200\) 0 0
\(201\) −2.32843 + 4.03295i −0.164235 + 0.284463i
\(202\) 0 0
\(203\) −22.6924 3.10538i −1.59269 0.217955i
\(204\) 0 0
\(205\) −4.41421 + 7.64564i −0.308302 + 0.533995i
\(206\) 0 0
\(207\) −3.17157 5.49333i −0.220440 0.381813i
\(208\) 0 0
\(209\) −3.41421 −0.236166
\(210\) 0 0
\(211\) −4.58579 −0.315699 −0.157849 0.987463i \(-0.550456\pi\)
−0.157849 + 0.987463i \(0.550456\pi\)
\(212\) 0 0
\(213\) −0.636039 1.10165i −0.0435807 0.0754839i
\(214\) 0 0
\(215\) −9.65685 + 16.7262i −0.658592 + 1.14071i
\(216\) 0 0
\(217\) −4.00000 9.79796i −0.271538 0.665129i
\(218\) 0 0
\(219\) −1.36396 + 2.36245i −0.0921679 + 0.159640i
\(220\) 0 0
\(221\) 7.00000 + 12.1244i 0.470871 + 0.815572i
\(222\) 0 0
\(223\) −11.4142 −0.764352 −0.382176 0.924089i \(-0.624825\pi\)
−0.382176 + 0.924089i \(0.624825\pi\)
\(224\) 0 0
\(225\) −18.8284 −1.25523
\(226\) 0 0
\(227\) −11.5858 20.0672i −0.768976 1.33190i −0.938119 0.346313i \(-0.887433\pi\)
0.169143 0.985591i \(-0.445900\pi\)
\(228\) 0 0
\(229\) −0.343146 + 0.594346i −0.0226757 + 0.0392755i −0.877141 0.480234i \(-0.840552\pi\)
0.854465 + 0.519509i \(0.173885\pi\)
\(230\) 0 0
\(231\) −0.671573 + 0.866025i −0.0441863 + 0.0569803i
\(232\) 0 0
\(233\) 0.707107 1.22474i 0.0463241 0.0802357i −0.841934 0.539581i \(-0.818583\pi\)
0.888258 + 0.459345i \(0.151916\pi\)
\(234\) 0 0
\(235\) −11.0711 19.1757i −0.722197 1.25088i
\(236\) 0 0
\(237\) −1.97056 −0.128002
\(238\) 0 0
\(239\) 22.2132 1.43685 0.718426 0.695603i \(-0.244863\pi\)
0.718426 + 0.695603i \(0.244863\pi\)
\(240\) 0 0
\(241\) −1.87868 3.25397i −0.121016 0.209607i 0.799152 0.601129i \(-0.205282\pi\)
−0.920169 + 0.391522i \(0.871949\pi\)
\(242\) 0 0
\(243\) 5.17157 8.95743i 0.331757 0.574619i
\(244\) 0 0
\(245\) 17.0711 16.7262i 1.09063 1.06860i
\(246\) 0 0
\(247\) −3.12132 + 5.40629i −0.198605 + 0.343994i
\(248\) 0 0
\(249\) −3.34315 5.79050i −0.211863 0.366958i
\(250\) 0 0
\(251\) −2.14214 −0.135210 −0.0676052 0.997712i \(-0.521536\pi\)
−0.0676052 + 0.997712i \(0.521536\pi\)
\(252\) 0 0
\(253\) 2.24264 0.140994
\(254\) 0 0
\(255\) 5.41421 + 9.37769i 0.339051 + 0.587254i
\(256\) 0 0
\(257\) −1.57107 + 2.72117i −0.0980005 + 0.169742i −0.910857 0.412722i \(-0.864578\pi\)
0.812856 + 0.582464i \(0.197911\pi\)
\(258\) 0 0
\(259\) 10.6777 13.7694i 0.663478 0.855587i
\(260\) 0 0
\(261\) −12.2426 + 21.2049i −0.757800 + 1.31255i
\(262\) 0 0
\(263\) 15.5208 + 26.8828i 0.957054 + 1.65767i 0.729595 + 0.683879i \(0.239709\pi\)
0.227459 + 0.973788i \(0.426958\pi\)
\(264\) 0 0
\(265\) 40.6274 2.49572
\(266\) 0 0
\(267\) 1.85786 0.113699
\(268\) 0 0
\(269\) −6.82843 11.8272i −0.416337 0.721116i 0.579231 0.815163i \(-0.303353\pi\)
−0.995568 + 0.0940473i \(0.970020\pi\)
\(270\) 0 0
\(271\) −13.2782 + 22.9985i −0.806592 + 1.39706i 0.108620 + 0.994083i \(0.465357\pi\)
−0.915211 + 0.402974i \(0.867976\pi\)
\(272\) 0 0
\(273\) 0.757359 + 1.85514i 0.0458375 + 0.112278i
\(274\) 0 0
\(275\) 3.32843 5.76500i 0.200712 0.347643i
\(276\) 0 0
\(277\) 1.91421 + 3.31552i 0.115014 + 0.199210i 0.917785 0.397077i \(-0.129975\pi\)
−0.802771 + 0.596287i \(0.796642\pi\)
\(278\) 0 0
\(279\) −11.3137 −0.677334
\(280\) 0 0
\(281\) −16.7279 −0.997904 −0.498952 0.866630i \(-0.666282\pi\)
−0.498952 + 0.866630i \(0.666282\pi\)
\(282\) 0 0
\(283\) −10.2929 17.8278i −0.611849 1.05975i −0.990929 0.134389i \(-0.957093\pi\)
0.379080 0.925364i \(-0.376241\pi\)
\(284\) 0 0
\(285\) −2.41421 + 4.18154i −0.143006 + 0.247693i
\(286\) 0 0
\(287\) −6.77817 0.927572i −0.400103 0.0547528i
\(288\) 0 0
\(289\) −20.8137 + 36.0504i −1.22434 + 2.12061i
\(290\) 0 0
\(291\) 0.378680 + 0.655892i 0.0221986 + 0.0384491i
\(292\) 0 0
\(293\) −5.17157 −0.302127 −0.151063 0.988524i \(-0.548270\pi\)
−0.151063 + 0.988524i \(0.548270\pi\)
\(294\) 0 0
\(295\) −28.7279 −1.67260
\(296\) 0 0
\(297\) 1.20711 + 2.09077i 0.0700434 + 0.121319i
\(298\) 0 0
\(299\) 2.05025 3.55114i 0.118569 0.205368i
\(300\) 0 0
\(301\) −14.8284 2.02922i −0.854696 0.116963i
\(302\) 0 0
\(303\) 2.44975 4.24309i 0.140734 0.243759i
\(304\) 0 0
\(305\) 10.5355 + 18.2481i 0.603263 + 1.04488i
\(306\) 0 0
\(307\) 9.89949 0.564994 0.282497 0.959268i \(-0.408837\pi\)
0.282497 + 0.959268i \(0.408837\pi\)
\(308\) 0 0
\(309\) 4.38478 0.249441
\(310\) 0 0
\(311\) −4.36396 7.55860i −0.247458 0.428609i 0.715362 0.698754i \(-0.246262\pi\)
−0.962820 + 0.270145i \(0.912928\pi\)
\(312\) 0 0
\(313\) 4.67157 8.09140i 0.264053 0.457353i −0.703262 0.710931i \(-0.748274\pi\)
0.967315 + 0.253578i \(0.0816073\pi\)
\(314\) 0 0
\(315\) −9.65685 23.6544i −0.544102 1.33277i
\(316\) 0 0
\(317\) −15.6569 + 27.1185i −0.879377 + 1.52312i −0.0273502 + 0.999626i \(0.508707\pi\)
−0.852026 + 0.523499i \(0.824626\pi\)
\(318\) 0 0
\(319\) −4.32843 7.49706i −0.242345 0.419755i
\(320\) 0 0
\(321\) 4.58579 0.255954
\(322\) 0 0
\(323\) −26.1421 −1.45459
\(324\) 0 0
\(325\) −6.08579 10.5409i −0.337579 0.584703i
\(326\) 0 0
\(327\) −0.100505 + 0.174080i −0.00555794 + 0.00962664i
\(328\) 0 0
\(329\) 10.5147 13.5592i 0.579695 0.747545i
\(330\) 0 0
\(331\) −4.96447 + 8.59871i −0.272872 + 0.472628i −0.969596 0.244711i \(-0.921307\pi\)
0.696724 + 0.717339i \(0.254640\pi\)
\(332\) 0 0
\(333\) −9.31371 16.1318i −0.510388 0.884018i
\(334\) 0 0
\(335\) 38.3848 2.09718
\(336\) 0 0
\(337\) −19.7574 −1.07625 −0.538126 0.842864i \(-0.680868\pi\)
−0.538126 + 0.842864i \(0.680868\pi\)
\(338\) 0 0
\(339\) −2.86396 4.96053i −0.155549 0.269419i
\(340\) 0 0
\(341\) 2.00000 3.46410i 0.108306 0.187592i
\(342\) 0 0
\(343\) 17.0000 + 7.34847i 0.917914 + 0.396780i
\(344\) 0 0
\(345\) 1.58579 2.74666i 0.0853759 0.147875i
\(346\) 0 0
\(347\) 7.29289 + 12.6317i 0.391503 + 0.678103i 0.992648 0.121037i \(-0.0386219\pi\)
−0.601145 + 0.799140i \(0.705289\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 4.41421 0.235613
\(352\) 0 0
\(353\) 12.6569 + 21.9223i 0.673656 + 1.16681i 0.976860 + 0.213881i \(0.0686105\pi\)
−0.303203 + 0.952926i \(0.598056\pi\)
\(354\) 0 0
\(355\) −5.24264 + 9.08052i −0.278250 + 0.481944i
\(356\) 0 0
\(357\) −5.14214 + 6.63103i −0.272151 + 0.350951i
\(358\) 0 0
\(359\) 5.37868 9.31615i 0.283876 0.491687i −0.688460 0.725274i \(-0.741713\pi\)
0.972336 + 0.233587i \(0.0750463\pi\)
\(360\) 0 0
\(361\) 3.67157 + 6.35935i 0.193241 + 0.334703i
\(362\) 0 0
\(363\) −0.414214 −0.0217406
\(364\) 0 0
\(365\) 22.4853 1.17693
\(366\) 0 0
\(367\) 7.36396 + 12.7548i 0.384396 + 0.665793i 0.991685 0.128688i \(-0.0410765\pi\)
−0.607290 + 0.794481i \(0.707743\pi\)
\(368\) 0 0
\(369\) −3.65685 + 6.33386i −0.190368 + 0.329727i
\(370\) 0 0
\(371\) 11.8995 + 29.1477i 0.617791 + 1.51327i
\(372\) 0 0
\(373\) −6.98528 + 12.0989i −0.361684 + 0.626455i −0.988238 0.152923i \(-0.951131\pi\)
0.626554 + 0.779378i \(0.284465\pi\)
\(374\) 0 0
\(375\) −1.17157 2.02922i −0.0604998 0.104789i
\(376\) 0 0
\(377\) −15.8284 −0.815205
\(378\) 0 0
\(379\) 25.8701 1.32886 0.664428 0.747352i \(-0.268675\pi\)
0.664428 + 0.747352i \(0.268675\pi\)
\(380\) 0 0
\(381\) 2.01472 + 3.48960i 0.103217 + 0.178777i
\(382\) 0 0
\(383\) 15.1924 26.3140i 0.776295 1.34458i −0.157769 0.987476i \(-0.550430\pi\)
0.934064 0.357106i \(-0.116236\pi\)
\(384\) 0 0
\(385\) 8.94975 + 1.22474i 0.456121 + 0.0624188i
\(386\) 0 0
\(387\) −8.00000 + 13.8564i −0.406663 + 0.704361i
\(388\) 0 0
\(389\) −1.36396 2.36245i −0.0691556 0.119781i 0.829374 0.558693i \(-0.188697\pi\)
−0.898530 + 0.438912i \(0.855364\pi\)
\(390\) 0 0
\(391\) 17.1716 0.868404
\(392\) 0 0
\(393\) −1.41421 −0.0713376
\(394\) 0 0
\(395\) 8.12132 + 14.0665i 0.408628 + 0.707764i
\(396\) 0 0
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 0 0
\(399\) −3.70711 0.507306i −0.185587 0.0253971i
\(400\) 0 0
\(401\) 2.15685 3.73578i 0.107708 0.186556i −0.807133 0.590369i \(-0.798982\pi\)
0.914841 + 0.403813i \(0.132315\pi\)
\(402\) 0 0
\(403\) −3.65685 6.33386i −0.182161 0.315512i
\(404\) 0 0
\(405\) −25.5563 −1.26991
\(406\) 0 0
\(407\) 6.58579 0.326445
\(408\) 0 0
\(409\) 11.3640 + 19.6830i 0.561912 + 0.973260i 0.997330 + 0.0730312i \(0.0232673\pi\)
−0.435418 + 0.900228i \(0.643399\pi\)
\(410\) 0 0
\(411\) −1.10660 + 1.91669i −0.0545846 + 0.0945434i
\(412\) 0 0
\(413\) −8.41421 20.6105i −0.414036 1.01418i
\(414\) 0 0
\(415\) −27.5563 + 47.7290i −1.35269 + 2.34292i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.14214 −0.104650 −0.0523251 0.998630i \(-0.516663\pi\)
−0.0523251 + 0.998630i \(0.516663\pi\)
\(420\) 0 0
\(421\) 23.3137 1.13624 0.568120 0.822946i \(-0.307671\pi\)
0.568120 + 0.822946i \(0.307671\pi\)
\(422\) 0 0
\(423\) −9.17157 15.8856i −0.445937 0.772386i
\(424\) 0 0
\(425\) 25.4853 44.1418i 1.23622 2.14119i
\(426\) 0 0
\(427\) −10.0061 + 12.9033i −0.484229 + 0.624436i
\(428\) 0 0
\(429\) −0.378680 + 0.655892i −0.0182828 + 0.0316668i
\(430\) 0 0
\(431\) −10.2071 17.6792i −0.491659 0.851578i 0.508295 0.861183i \(-0.330276\pi\)
−0.999954 + 0.00960469i \(0.996943\pi\)
\(432\) 0 0
\(433\) −2.14214 −0.102944 −0.0514722 0.998674i \(-0.516391\pi\)
−0.0514722 + 0.998674i \(0.516391\pi\)
\(434\) 0 0
\(435\) −12.2426 −0.586990
\(436\) 0 0
\(437\) 3.82843 + 6.63103i 0.183139 + 0.317205i
\(438\) 0 0
\(439\) 4.69239 8.12745i 0.223955 0.387902i −0.732050 0.681251i \(-0.761436\pi\)
0.956006 + 0.293349i \(0.0947696\pi\)
\(440\) 0 0
\(441\) 14.1421 13.8564i 0.673435 0.659829i
\(442\) 0 0
\(443\) −16.3137 + 28.2562i −0.775088 + 1.34249i 0.159658 + 0.987172i \(0.448961\pi\)
−0.934745 + 0.355319i \(0.884372\pi\)
\(444\) 0 0
\(445\) −7.65685 13.2621i −0.362970 0.628682i
\(446\) 0 0
\(447\) −2.62742 −0.124273
\(448\) 0 0
\(449\) 33.6569 1.58837 0.794183 0.607679i \(-0.207899\pi\)
0.794183 + 0.607679i \(0.207899\pi\)
\(450\) 0 0
\(451\) −1.29289 2.23936i −0.0608800 0.105447i
\(452\) 0 0
\(453\) −2.01472 + 3.48960i −0.0946597 + 0.163955i
\(454\) 0 0
\(455\) 10.1213 13.0519i 0.474495 0.611884i
\(456\) 0 0
\(457\) 0.171573 0.297173i 0.00802584 0.0139012i −0.861985 0.506934i \(-0.830779\pi\)
0.870010 + 0.493033i \(0.164112\pi\)
\(458\) 0 0
\(459\) 9.24264 + 16.0087i 0.431410 + 0.747223i
\(460\) 0 0
\(461\) 14.3137 0.666656 0.333328 0.942811i \(-0.391828\pi\)
0.333328 + 0.942811i \(0.391828\pi\)
\(462\) 0 0
\(463\) −7.17157 −0.333291 −0.166646 0.986017i \(-0.553294\pi\)
−0.166646 + 0.986017i \(0.553294\pi\)
\(464\) 0 0
\(465\) −2.82843 4.89898i −0.131165 0.227185i
\(466\) 0 0
\(467\) −17.0000 + 29.4449i −0.786666 + 1.36255i 0.141332 + 0.989962i \(0.454861\pi\)
−0.927999 + 0.372584i \(0.878472\pi\)
\(468\) 0 0
\(469\) 11.2426 + 27.5387i 0.519137 + 1.27162i
\(470\) 0 0
\(471\) 1.31371 2.27541i 0.0605325 0.104845i
\(472\) 0 0
\(473\) −2.82843 4.89898i −0.130051 0.225255i
\(474\) 0 0
\(475\) 22.7279 1.04283
\(476\) 0 0
\(477\) 33.6569 1.54104
\(478\) 0 0
\(479\) −13.0355 22.5782i −0.595609 1.03162i −0.993461 0.114175i \(-0.963578\pi\)
0.397852 0.917450i \(-0.369756\pi\)
\(480\) 0 0
\(481\) 6.02082 10.4284i 0.274526 0.475492i
\(482\) 0 0
\(483\) 2.43503 + 0.333226i 0.110798 + 0.0151623i
\(484\) 0 0
\(485\) 3.12132 5.40629i 0.141732 0.245487i
\(486\) 0 0
\(487\) 0.828427 + 1.43488i 0.0375396 + 0.0650205i 0.884185 0.467137i \(-0.154715\pi\)
−0.846645 + 0.532158i \(0.821381\pi\)
\(488\) 0 0
\(489\) −6.51472 −0.294606
\(490\) 0 0
\(491\) −24.8284 −1.12049 −0.560246 0.828327i \(-0.689293\pi\)
−0.560246 + 0.828327i \(0.689293\pi\)
\(492\) 0 0
\(493\) −33.1421 57.4039i −1.49265 2.58534i
\(494\) 0 0
\(495\) 4.82843 8.36308i 0.217022 0.375893i
\(496\) 0 0
\(497\) −8.05025 1.10165i −0.361103 0.0494158i
\(498\) 0 0
\(499\) −3.07107 + 5.31925i −0.137480 + 0.238122i −0.926542 0.376191i \(-0.877234\pi\)
0.789062 + 0.614313i \(0.210567\pi\)
\(500\) 0 0
\(501\) 2.42893 + 4.20703i 0.108517 + 0.187956i
\(502\) 0 0
\(503\) 38.2132 1.70384 0.851921 0.523670i \(-0.175437\pi\)
0.851921 + 0.523670i \(0.175437\pi\)
\(504\) 0 0
\(505\) −40.3848 −1.79710
\(506\) 0 0
\(507\) −2.00000 3.46410i −0.0888231 0.153846i
\(508\) 0 0
\(509\) 6.65685 11.5300i 0.295060 0.511059i −0.679939 0.733269i \(-0.737994\pi\)
0.974999 + 0.222210i \(0.0713271\pi\)
\(510\) 0 0
\(511\) 6.58579 + 16.1318i 0.291338 + 0.713630i
\(512\) 0 0
\(513\) −4.12132 + 7.13834i −0.181961 + 0.315165i
\(514\) 0 0
\(515\) −18.0711 31.3000i −0.796306 1.37924i
\(516\) 0 0
\(517\) 6.48528 0.285222
\(518\) 0 0
\(519\) 1.72792 0.0758474
\(520\) 0 0
\(521\) −14.1421 24.4949i −0.619578 1.07314i −0.989563 0.144103i \(-0.953970\pi\)
0.369984 0.929038i \(-0.379363\pi\)
\(522\) 0 0
\(523\) 6.36396 11.0227i 0.278277 0.481989i −0.692680 0.721245i \(-0.743570\pi\)
0.970957 + 0.239256i \(0.0769035\pi\)
\(524\) 0 0
\(525\) 4.47056 5.76500i 0.195111 0.251605i
\(526\) 0 0
\(527\) 15.3137 26.5241i 0.667076 1.15541i
\(528\) 0 0
\(529\) 8.98528 + 15.5630i 0.390664 + 0.676651i
\(530\) 0 0
\(531\) −23.7990 −1.03279
\(532\) 0 0
\(533\) −4.72792 −0.204789
\(534\) 0 0
\(535\) −18.8995 32.7349i −0.817096 1.41525i
\(536\) 0 0
\(537\) 3.91421 6.77962i 0.168911 0.292562i
\(538\) 0 0
\(539\) 1.74264 + 6.77962i 0.0750608 + 0.292019i
\(540\) 0 0
\(541\) 20.5711 35.6301i 0.884419 1.53186i 0.0380415 0.999276i \(-0.487888\pi\)
0.846378 0.532583i \(-0.178779\pi\)
\(542\) 0 0
\(543\) 0.757359 + 1.31178i 0.0325014 + 0.0562941i
\(544\) 0 0
\(545\) 1.65685 0.0709718
\(546\) 0 0
\(547\) 18.8701 0.806825 0.403413 0.915018i \(-0.367824\pi\)
0.403413 + 0.915018i \(0.367824\pi\)
\(548\) 0 0
\(549\) 8.72792 + 15.1172i 0.372499 + 0.645187i
\(550\) 0 0
\(551\) 14.7782 25.5965i 0.629571 1.09045i
\(552\) 0 0
\(553\) −7.71320 + 9.94655i −0.327999 + 0.422970i
\(554\) 0 0
\(555\) 4.65685 8.06591i 0.197672 0.342379i
\(556\) 0 0
\(557\) −12.2426 21.2049i −0.518737 0.898479i −0.999763 0.0217729i \(-0.993069\pi\)
0.481026 0.876707i \(-0.340264\pi\)
\(558\) 0 0
\(559\) −10.3431 −0.437468
\(560\) 0 0
\(561\) −3.17157 −0.133904
\(562\) 0 0
\(563\) −2.53553 4.39167i −0.106860 0.185087i 0.807637 0.589681i \(-0.200746\pi\)
−0.914497 + 0.404594i \(0.867413\pi\)
\(564\) 0 0
\(565\) −23.6066 + 40.8878i −0.993137 + 1.72016i
\(566\) 0 0
\(567\) −7.48528 18.3351i −0.314352 0.770003i
\(568\) 0 0
\(569\) 2.00000 3.46410i 0.0838444 0.145223i −0.821054 0.570851i \(-0.806613\pi\)
0.904898 + 0.425628i \(0.139947\pi\)
\(570\) 0 0
\(571\) −5.19239 8.99348i −0.217295 0.376365i 0.736685 0.676236i \(-0.236390\pi\)
−0.953980 + 0.299870i \(0.903057\pi\)
\(572\) 0 0
\(573\) −5.31371 −0.221983
\(574\) 0 0
\(575\) −14.9289 −0.622580
\(576\) 0 0
\(577\) 16.1569 + 27.9845i 0.672619 + 1.16501i 0.977159 + 0.212510i \(0.0681639\pi\)
−0.304540 + 0.952499i \(0.598503\pi\)
\(578\) 0 0
\(579\) 0.435029 0.753492i 0.0180792 0.0313141i
\(580\) 0 0
\(581\) −42.3137 5.79050i −1.75547 0.240230i
\(582\) 0 0
\(583\) −5.94975 + 10.3053i −0.246413 + 0.426800i
\(584\) 0 0
\(585\) −8.82843 15.2913i −0.365011 0.632217i
\(586\) 0 0
\(587\) 44.8995 1.85320 0.926600 0.376048i \(-0.122717\pi\)
0.926600 + 0.376048i \(0.122717\pi\)
\(588\) 0 0
\(589\) 13.6569 0.562721
\(590\) 0 0
\(591\) −3.62132 6.27231i −0.148961 0.258008i
\(592\) 0 0
\(593\) 17.8492 30.9158i 0.732981 1.26956i −0.222623 0.974905i \(-0.571462\pi\)
0.955604 0.294655i \(-0.0952047\pi\)
\(594\) 0 0
\(595\) 68.5269 + 9.37769i 2.80933 + 0.384448i
\(596\) 0 0
\(597\) −4.12132 + 7.13834i −0.168674 + 0.292153i
\(598\) 0 0
\(599\) −1.31371 2.27541i −0.0536767 0.0929707i 0.837939 0.545765i \(-0.183761\pi\)
−0.891615 + 0.452794i \(0.850427\pi\)
\(600\) 0 0
\(601\) −35.9411 −1.46607 −0.733035 0.680191i \(-0.761897\pi\)
−0.733035 + 0.680191i \(0.761897\pi\)
\(602\) 0 0
\(603\) 31.7990 1.29495
\(604\) 0 0
\(605\) 1.70711 + 2.95680i 0.0694038 + 0.120211i
\(606\) 0 0
\(607\) −4.51472 + 7.81972i −0.183247 + 0.317393i −0.942984 0.332837i \(-0.891994\pi\)
0.759738 + 0.650230i \(0.225327\pi\)
\(608\) 0 0
\(609\) −3.58579 8.78335i −0.145303 0.355919i
\(610\) 0 0
\(611\) 5.92893 10.2692i 0.239859 0.415448i
\(612\) 0 0
\(613\) 8.31371 + 14.3998i 0.335788 + 0.581601i 0.983636 0.180168i \(-0.0576643\pi\)
−0.647848 + 0.761769i \(0.724331\pi\)
\(614\) 0 0
\(615\) −3.65685 −0.147459
\(616\) 0 0
\(617\) −8.02944 −0.323253 −0.161626 0.986852i \(-0.551674\pi\)
−0.161626 + 0.986852i \(0.551674\pi\)
\(618\) 0 0
\(619\) 22.9706 + 39.7862i 0.923265 + 1.59914i 0.794328 + 0.607489i \(0.207823\pi\)
0.128937 + 0.991653i \(0.458844\pi\)
\(620\) 0 0
\(621\) 2.70711 4.68885i 0.108632 0.188157i
\(622\) 0 0
\(623\) 7.27208 9.37769i 0.291350 0.375709i
\(624\) 0 0
\(625\) 6.98528 12.0989i 0.279411 0.483954i
\(626\) 0 0
\(627\) −0.707107 1.22474i −0.0282391 0.0489116i
\(628\) 0 0
\(629\) 50.4264 2.01063
\(630\) 0 0
\(631\) −48.7279 −1.93983 −0.969914 0.243448i \(-0.921722\pi\)
−0.969914 + 0.243448i \(0.921722\pi\)
\(632\) 0 0
\(633\) −0.949747 1.64501i −0.0377491 0.0653833i
\(634\) 0 0
\(635\) 16.6066 28.7635i 0.659013 1.14144i
\(636\) 0 0
\(637\) 12.3284 + 3.43861i 0.488470 + 0.136243i
\(638\) 0 0
\(639\) −4.34315 + 7.52255i −0.171812 + 0.297587i
\(640\) 0 0
\(641\) 20.6421 + 35.7532i 0.815315 + 1.41217i 0.909101 + 0.416575i \(0.136770\pi\)
−0.0937859 + 0.995592i \(0.529897\pi\)
\(642\) 0 0
\(643\) −4.41421 −0.174080 −0.0870398 0.996205i \(-0.527741\pi\)
−0.0870398 + 0.996205i \(0.527741\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) −23.0919 39.9963i −0.907836 1.57242i −0.817065 0.576546i \(-0.804400\pi\)
−0.0907706 0.995872i \(-0.528933\pi\)
\(648\) 0 0
\(649\) 4.20711 7.28692i 0.165143 0.286037i
\(650\) 0 0
\(651\) 2.68629 3.46410i 0.105284 0.135769i
\(652\) 0 0
\(653\) −9.19239 + 15.9217i −0.359726 + 0.623064i −0.987915 0.154997i \(-0.950463\pi\)
0.628189 + 0.778061i \(0.283796\pi\)
\(654\) 0 0
\(655\) 5.82843 + 10.0951i 0.227735 + 0.394449i
\(656\) 0 0
\(657\) 18.6274 0.726725
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) 7.48528 + 12.9649i 0.291144 + 0.504276i 0.974080 0.226202i \(-0.0726309\pi\)
−0.682937 + 0.730478i \(0.739298\pi\)
\(662\) 0 0
\(663\) −2.89949 + 5.02207i −0.112607 + 0.195041i
\(664\) 0 0
\(665\) 11.6569 + 28.5533i 0.452033 + 1.10725i
\(666\) 0 0
\(667\) −9.70711 + 16.8132i −0.375861 + 0.651010i
\(668\) 0 0
\(669\) −2.36396 4.09450i −0.0913960 0.158303i
\(670\) 0 0
\(671\) −6.17157 −0.238251
\(672\) 0 0
\(673\) −25.5563 −0.985125 −0.492562 0.870277i \(-0.663940\pi\)
−0.492562 + 0.870277i \(0.663940\pi\)
\(674\) 0 0
\(675\) −8.03553 13.9180i −0.309288 0.535702i
\(676\) 0 0
\(677\) 6.34315 10.9867i 0.243787 0.422251i −0.718003 0.696040i \(-0.754944\pi\)
0.961790 + 0.273789i \(0.0882769\pi\)
\(678\) 0 0
\(679\) 4.79289 + 0.655892i 0.183934 + 0.0251708i
\(680\) 0 0
\(681\) 4.79899 8.31209i 0.183898 0.318520i
\(682\) 0 0
\(683\) 8.20711 + 14.2151i 0.314036 + 0.543927i 0.979232 0.202742i \(-0.0649853\pi\)
−0.665196 + 0.746669i \(0.731652\pi\)
\(684\) 0 0
\(685\) 18.2426 0.697015
\(686\) 0 0
\(687\) −0.284271 −0.0108456
\(688\) 0 0
\(689\) 10.8787 + 18.8424i 0.414445 + 0.717839i
\(690\) 0 0
\(691\) 6.96447 12.0628i 0.264941 0.458891i −0.702607 0.711578i \(-0.747981\pi\)
0.967548 + 0.252687i \(0.0813143\pi\)
\(692\) 0 0
\(693\) 7.41421 + 1.01461i 0.281643 + 0.0385419i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9.89949 17.1464i −0.374970 0.649467i
\(698\) 0 0
\(699\) 0.585786 0.0221565
\(700\) 0 0
\(701\) 36.1127 1.36396 0.681979 0.731372i \(-0.261120\pi\)
0.681979 + 0.731372i \(0.261120\pi\)
\(702\) 0 0
\(703\) 11.2426 + 19.4728i 0.424024 + 0.734432i
\(704\) 0 0
\(705\) 4.58579 7.94282i 0.172711 0.299144i
\(706\) 0 0
\(707\) −11.8284 28.9736i −0.444854 1.08966i
\(708\) 0 0
\(709\) −18.0208 + 31.2130i −0.676786 + 1.17223i 0.299158 + 0.954204i \(0.403294\pi\)
−0.975943 + 0.218024i \(0.930039\pi\)
\(710\) 0 0
\(711\) 6.72792 + 11.6531i 0.252317 + 0.437026i
\(712\) 0 0
\(713\) −8.97056 −0.335950
\(714\) 0 0
\(715\) 6.24264 0.233462
\(716\) 0 0
\(717\) 4.60051 + 7.96831i 0.171809 + 0.297582i
\(718\) 0 0
\(719\) −9.24264 + 16.0087i −0.344692 + 0.597025i −0.985298 0.170846i \(-0.945350\pi\)
0.640605 + 0.767870i \(0.278683\pi\)
\(720\) 0 0
\(721\) 17.1630 22.1324i 0.639182 0.824255i
\(722\) 0 0
\(723\) 0.778175 1.34784i 0.0289406 0.0501266i
\(724\) 0 0
\(725\) 28.8137 + 49.9068i 1.07011 + 1.85349i
\(726\) 0 0
\(727\) 48.4264 1.79604 0.898018 0.439959i \(-0.145007\pi\)
0.898018 + 0.439959i \(0.145007\pi\)
\(728\) 0 0
\(729\) −18.1716 −0.673021
\(730\) 0 0
\(731\) −21.6569 37.5108i −0.801008 1.38739i
\(732\) 0 0
\(733\) 6.50000 11.2583i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) 0 0
\(735\) 9.53553 + 2.65962i 0.351723 + 0.0981017i
\(736\) 0 0
\(737\) −5.62132 + 9.73641i −0.207064 + 0.358645i
\(738\) 0 0
\(739\) 16.2132 + 28.0821i 0.596412 + 1.03302i 0.993346 + 0.115169i \(0.0367410\pi\)
−0.396934 + 0.917847i \(0.629926\pi\)
\(740\) 0 0
\(741\) −2.58579 −0.0949912
\(742\) 0 0
\(743\) −9.31371 −0.341687 −0.170843 0.985298i \(-0.554649\pi\)
−0.170843 + 0.985298i \(0.554649\pi\)
\(744\) 0 0
\(745\) 10.8284 + 18.7554i 0.396723 + 0.687144i
\(746\) 0 0
\(747\) −22.8284 + 39.5400i −0.835248 + 1.44669i
\(748\) 0 0
\(749\) 17.9497 23.1471i 0.655869 0.845775i
\(750\) 0 0
\(751\) 17.1716 29.7420i 0.626600 1.08530i −0.361630 0.932322i \(-0.617780\pi\)
0.988229 0.152980i \(-0.0488872\pi\)
\(752\) 0 0
\(753\) −0.443651 0.768426i −0.0161675 0.0280030i
\(754\) 0 0
\(755\) 33.2132 1.20875
\(756\) 0 0
\(757\) 19.6569 0.714441 0.357220 0.934020i \(-0.383725\pi\)
0.357220 + 0.934020i \(0.383725\pi\)
\(758\) 0 0
\(759\) 0.464466 + 0.804479i 0.0168591 + 0.0292007i
\(760\) 0 0
\(761\) 1.48528 2.57258i 0.0538414 0.0932561i −0.837849 0.545903i \(-0.816187\pi\)
0.891690 + 0.452647i \(0.149520\pi\)
\(762\) 0 0
\(763\) 0.485281 + 1.18869i 0.0175684 + 0.0430335i
\(764\) 0 0
\(765\) 36.9706 64.0349i 1.33667 2.31519i
\(766\) 0 0
\(767\) −7.69239 13.3236i −0.277756 0.481088i
\(768\) 0 0
\(769\) −10.9706 −0.395609 −0.197804 0.980242i \(-0.563381\pi\)
−0.197804 + 0.980242i \(0.563381\pi\)
\(770\) 0 0
\(771\) −1.30152 −0.0468729
\(772\) 0 0
\(773\) −22.9706 39.7862i −0.826194 1.43101i −0.901004 0.433812i \(-0.857168\pi\)
0.0748099 0.997198i \(-0.476165\pi\)
\(774\) 0 0
\(775\) −13.3137 + 23.0600i −0.478243 + 0.828340i
\(776\) 0 0
\(777\) 7.15076 + 0.978559i 0.256532 + 0.0351056i
\(778\) 0 0
\(779\) 4.41421 7.64564i 0.158156 0.273934i
\(780\) 0 0
\(781\) −1.53553 2.65962i −0.0549457 0.0951688i
\(782\) 0 0
\(783\) −20.8995 −0.746887
\(784\) 0 0
\(785\) −21.6569 −0.772966
\(786\) 0 0
\(787\) −8.77817 15.2042i −0.312908 0.541973i 0.666082 0.745878i \(-0.267970\pi\)
−0.978991 + 0.203905i \(0.934637\pi\)
\(788\) 0 0
\(789\) −6.42893 + 11.1352i −0.228876 + 0.396425i
\(790\) 0 0
\(791\) −36.2487 4.96053i −1.28886 0.176376i
\(792\) 0 0
\(793\) −5.64214 + 9.77247i −0.200358 + 0.347030i
\(794\) 0 0
\(795\) 8.41421 + 14.5738i 0.298421 + 0.516881i
\(796\) 0 0
\(797\) 3.65685