Properties

Label 637.2.e.d.508.1
Level $637$
Weight $2$
Character 637.508
Analytic conductor $5.086$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.d.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{10} +(3.00000 - 5.19615i) q^{11} +1.00000 q^{13} +(2.00000 + 3.46410i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(2.50000 + 4.33013i) q^{19} +6.00000 q^{20} +12.0000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} -5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(-4.00000 + 6.92820i) q^{32} +8.00000 q^{34} -6.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-5.00000 + 8.66025i) q^{38} +6.00000 q^{41} -1.00000 q^{43} +(6.00000 + 10.3923i) q^{44} +(4.50000 - 7.79423i) q^{45} +(3.00000 - 5.19615i) q^{46} +(3.50000 + 6.06218i) q^{47} -8.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(4.50000 - 7.79423i) q^{53} -18.0000 q^{55} +(-5.00000 - 8.66025i) q^{58} +(4.00000 - 6.92820i) q^{59} +(-5.00000 - 8.66025i) q^{61} -6.00000 q^{62} -8.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(3.00000 - 5.19615i) q^{67} +(4.00000 + 6.92820i) q^{68} -8.00000 q^{71} +(-6.50000 + 11.2583i) q^{73} +(-4.00000 + 6.92820i) q^{74} -10.0000 q^{76} +(-1.50000 - 2.59808i) q^{79} +(6.00000 - 10.3923i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{82} -15.0000 q^{83} -12.0000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(1.50000 + 2.59808i) q^{89} +18.0000 q^{90} +6.00000 q^{92} +(-7.00000 + 12.1244i) q^{94} +(7.50000 - 12.9904i) q^{95} -7.00000 q^{97} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 2 q^{4} - 3 q^{5} + 3 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{2} - 2 q^{4} - 3 q^{5} + 3 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 12 q^{20} + 24 q^{22} - 3 q^{23} - 4 q^{25} + 2 q^{26} - 10 q^{29} - 3 q^{31} - 8 q^{32} + 16 q^{34} - 12 q^{36} + 4 q^{37} - 10 q^{38} + 12 q^{41} - 2 q^{43} + 12 q^{44} + 9 q^{45} + 6 q^{46} + 7 q^{47} - 16 q^{50} - 2 q^{52} + 9 q^{53} - 36 q^{55} - 10 q^{58} + 8 q^{59} - 10 q^{61} - 12 q^{62} - 16 q^{64} - 3 q^{65} + 6 q^{67} + 8 q^{68} - 16 q^{71} - 13 q^{73} - 8 q^{74} - 20 q^{76} - 3 q^{79} + 12 q^{80} - 9 q^{81} + 12 q^{82} - 30 q^{83} - 24 q^{85} - 2 q^{86} + 3 q^{89} + 36 q^{90} + 12 q^{92} - 14 q^{94} + 15 q^{95} - 14 q^{97} + 36 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 3.00000 5.19615i 0.948683 1.64317i
\(11\) 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) −3.00000 + 5.19615i −0.707107 + 1.22474i
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) 6.00000 1.34164
\(21\) 0 0
\(22\) 12.0000 2.55841
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) −1.50000 + 2.59808i −0.269408 + 0.466628i −0.968709 0.248199i \(-0.920161\pi\)
0.699301 + 0.714827i \(0.253495\pi\)
\(32\) −4.00000 + 6.92820i −0.707107 + 1.22474i
\(33\) 0 0
\(34\) 8.00000 1.37199
\(35\) 0 0
\(36\) −6.00000 −1.00000
\(37\) 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) −5.00000 + 8.66025i −0.811107 + 1.40488i
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 6.00000 + 10.3923i 0.904534 + 1.56670i
\(45\) 4.50000 7.79423i 0.670820 1.16190i
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i \(0.00388317\pi\)
−0.489398 + 0.872060i \(0.662783\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −8.00000 −1.13137
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i \(-0.621227\pi\)
0.989828 0.142269i \(-0.0454398\pi\)
\(54\) 0 0
\(55\) −18.0000 −2.42712
\(56\) 0 0
\(57\) 0 0
\(58\) −5.00000 8.66025i −0.656532 1.13715i
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −1.50000 2.59808i −0.186052 0.322252i
\(66\) 0 0
\(67\) 3.00000 5.19615i 0.366508 0.634811i −0.622509 0.782613i \(-0.713886\pi\)
0.989017 + 0.147802i \(0.0472198\pi\)
\(68\) 4.00000 + 6.92820i 0.485071 + 0.840168i
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −6.50000 + 11.2583i −0.760767 + 1.31769i 0.181688 + 0.983356i \(0.441844\pi\)
−0.942455 + 0.334332i \(0.891489\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) 0 0
\(76\) −10.0000 −1.14708
\(77\) 0 0
\(78\) 0 0
\(79\) −1.50000 2.59808i −0.168763 0.292306i 0.769222 0.638982i \(-0.220644\pi\)
−0.937985 + 0.346675i \(0.887311\pi\)
\(80\) 6.00000 10.3923i 0.670820 1.16190i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 6.00000 + 10.3923i 0.662589 + 1.14764i
\(83\) −15.0000 −1.64646 −0.823232 0.567705i \(-0.807831\pi\)
−0.823232 + 0.567705i \(0.807831\pi\)
\(84\) 0 0
\(85\) −12.0000 −1.30158
\(86\) −1.00000 1.73205i −0.107833 0.186772i
\(87\) 0 0
\(88\) 0 0
\(89\) 1.50000 + 2.59808i 0.159000 + 0.275396i 0.934508 0.355942i \(-0.115840\pi\)
−0.775509 + 0.631337i \(0.782506\pi\)
\(90\) 18.0000 1.89737
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) −7.00000 + 12.1244i −0.721995 + 1.25053i
\(95\) 7.50000 12.9904i 0.769484 1.33278i
\(96\) 0 0
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 0 0
\(99\) 18.0000 1.80907
\(100\) −4.00000 6.92820i −0.400000 0.692820i
\(101\) −7.00000 + 12.1244i −0.696526 + 1.20642i 0.273138 + 0.961975i \(0.411939\pi\)
−0.969664 + 0.244443i \(0.921395\pi\)
\(102\) 0 0
\(103\) −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i \(-0.229808\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 18.0000 1.74831
\(107\) 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) −18.0000 31.1769i −1.71623 2.97260i
\(111\) 0 0
\(112\) 0 0
\(113\) −3.00000 −0.282216 −0.141108 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) 0 0
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) 5.00000 8.66025i 0.464238 0.804084i
\(117\) 1.50000 + 2.59808i 0.138675 + 0.240192i
\(118\) 16.0000 1.47292
\(119\) 0 0
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 10.0000 17.3205i 0.905357 1.56813i
\(123\) 0 0
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 3.00000 5.19615i 0.263117 0.455733i
\(131\) 4.00000 + 6.92820i 0.349482 + 0.605320i 0.986157 0.165812i \(-0.0530244\pi\)
−0.636676 + 0.771132i \(0.719691\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 0 0
\(137\) −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i \(-0.887992\pi\)
0.767853 + 0.640626i \(0.221325\pi\)
\(138\) 0 0
\(139\) 18.0000 1.52674 0.763370 0.645961i \(-0.223543\pi\)
0.763370 + 0.645961i \(0.223543\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.00000 13.8564i −0.671345 1.16280i
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) −6.00000 + 10.3923i −0.500000 + 0.866025i
\(145\) 7.50000 + 12.9904i 0.622841 + 1.07879i
\(146\) −26.0000 −2.15178
\(147\) 0 0
\(148\) −8.00000 −0.657596
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) 9.00000 0.722897
\(156\) 0 0
\(157\) −4.00000 + 6.92820i −0.319235 + 0.552931i −0.980329 0.197372i \(-0.936759\pi\)
0.661094 + 0.750303i \(0.270093\pi\)
\(158\) 3.00000 5.19615i 0.238667 0.413384i
\(159\) 0 0
\(160\) 24.0000 1.89737
\(161\) 0 0
\(162\) −18.0000 −1.41421
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) −6.00000 + 10.3923i −0.468521 + 0.811503i
\(165\) 0 0
\(166\) −15.0000 25.9808i −1.16423 2.01650i
\(167\) −5.00000 −0.386912 −0.193456 0.981109i \(-0.561970\pi\)
−0.193456 + 0.981109i \(0.561970\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −12.0000 20.7846i −0.920358 1.59411i
\(171\) −7.50000 + 12.9904i −0.573539 + 0.993399i
\(172\) 1.00000 1.73205i 0.0762493 0.132068i
\(173\) −4.00000 6.92820i −0.304114 0.526742i 0.672949 0.739689i \(-0.265027\pi\)
−0.977064 + 0.212947i \(0.931694\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 24.0000 1.80907
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −11.5000 + 19.9186i −0.859550 + 1.48878i 0.0128080 + 0.999918i \(0.495923\pi\)
−0.872358 + 0.488867i \(0.837410\pi\)
\(180\) 9.00000 + 15.5885i 0.670820 + 1.16190i
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 10.3923i 0.441129 0.764057i
\(186\) 0 0
\(187\) −12.0000 20.7846i −0.877527 1.51992i
\(188\) −14.0000 −1.02105
\(189\) 0 0
\(190\) 30.0000 2.17643
\(191\) 4.00000 + 6.92820i 0.289430 + 0.501307i 0.973674 0.227946i \(-0.0732010\pi\)
−0.684244 + 0.729253i \(0.739868\pi\)
\(192\) 0 0
\(193\) −11.0000 + 19.0526i −0.791797 + 1.37143i 0.133056 + 0.991109i \(0.457521\pi\)
−0.924853 + 0.380325i \(0.875812\pi\)
\(194\) −7.00000 12.1244i −0.502571 0.870478i
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 18.0000 + 31.1769i 1.27920 + 2.21565i
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −28.0000 −1.97007
\(203\) 0 0
\(204\) 0 0
\(205\) −9.00000 15.5885i −0.628587 1.08875i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 4.50000 7.79423i 0.312772 0.541736i
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 30.0000 2.07514
\(210\) 0 0
\(211\) −5.00000 −0.344214 −0.172107 0.985078i \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) 9.00000 + 15.5885i 0.618123 + 1.07062i
\(213\) 0 0
\(214\) −4.00000 + 6.92820i −0.273434 + 0.473602i
\(215\) 1.50000 + 2.59808i 0.102299 + 0.177187i
\(216\) 0 0
\(217\) 0 0
\(218\) 4.00000 0.270914
\(219\) 0 0
\(220\) 18.0000 31.1769i 1.21356 2.10195i
\(221\) 2.00000 3.46410i 0.134535 0.233021i
\(222\) 0 0
\(223\) −15.0000 −1.00447 −0.502237 0.864730i \(-0.667490\pi\)
−0.502237 + 0.864730i \(0.667490\pi\)
\(224\) 0 0
\(225\) −12.0000 −0.800000
\(226\) −3.00000 5.19615i −0.199557 0.345643i
\(227\) 10.0000 17.3205i 0.663723 1.14960i −0.315906 0.948790i \(-0.602309\pi\)
0.979630 0.200812i \(-0.0643581\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) −18.0000 −1.18688
\(231\) 0 0
\(232\) 0 0
\(233\) −7.50000 12.9904i −0.491341 0.851028i 0.508609 0.860998i \(-0.330160\pi\)
−0.999950 + 0.00996947i \(0.996827\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) 10.5000 18.1865i 0.684944 1.18636i
\(236\) 8.00000 + 13.8564i 0.520756 + 0.901975i
\(237\) 0 0
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 0 0
\(241\) −8.50000 + 14.7224i −0.547533 + 0.948355i 0.450910 + 0.892570i \(0.351100\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 25.0000 43.3013i 1.60706 2.78351i
\(243\) 0 0
\(244\) 20.0000 1.28037
\(245\) 0 0
\(246\) 0 0
\(247\) 2.50000 + 4.33013i 0.159071 + 0.275519i
\(248\) 0 0
\(249\) 0 0
\(250\) −3.00000 5.19615i −0.189737 0.328634i
\(251\) 26.0000 1.64111 0.820553 0.571571i \(-0.193666\pi\)
0.820553 + 0.571571i \(0.193666\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) −4.00000 6.92820i −0.250982 0.434714i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −1.00000 1.73205i −0.0623783 0.108042i 0.833150 0.553047i \(-0.186535\pi\)
−0.895528 + 0.445005i \(0.853202\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) −7.50000 12.9904i −0.464238 0.804084i
\(262\) −8.00000 + 13.8564i −0.494242 + 0.856052i
\(263\) 7.50000 12.9904i 0.462470 0.801021i −0.536614 0.843828i \(-0.680297\pi\)
0.999083 + 0.0428069i \(0.0136300\pi\)
\(264\) 0 0
\(265\) −27.0000 −1.65860
\(266\) 0 0
\(267\) 0 0
\(268\) 6.00000 + 10.3923i 0.366508 + 0.634811i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 16.0000 0.970143
\(273\) 0 0
\(274\) −8.00000 −0.483298
\(275\) 12.0000 + 20.7846i 0.723627 + 1.25336i
\(276\) 0 0
\(277\) −0.500000 + 0.866025i −0.0300421 + 0.0520344i −0.880656 0.473757i \(-0.842897\pi\)
0.850613 + 0.525792i \(0.176231\pi\)
\(278\) 18.0000 + 31.1769i 1.07957 + 1.86987i
\(279\) −9.00000 −0.538816
\(280\) 0 0
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) 8.00000 13.8564i 0.475551 0.823678i −0.524057 0.851683i \(-0.675582\pi\)
0.999608 + 0.0280052i \(0.00891551\pi\)
\(284\) 8.00000 13.8564i 0.474713 0.822226i
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) −24.0000 −1.41421
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −15.0000 + 25.9808i −0.880830 + 1.52564i
\(291\) 0 0
\(292\) −13.0000 22.5167i −0.760767 1.31769i
\(293\) 19.0000 1.10999 0.554996 0.831853i \(-0.312720\pi\)
0.554996 + 0.831853i \(0.312720\pi\)
\(294\) 0 0
\(295\) −24.0000 −1.39733
\(296\) 0 0
\(297\) 0 0
\(298\) −18.0000 + 31.1769i −1.04271 + 1.80603i
\(299\) −1.50000 2.59808i −0.0867472 0.150251i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −10.0000 + 17.3205i −0.573539 + 0.993399i
\(305\) −15.0000 + 25.9808i −0.858898 + 1.48765i
\(306\) 12.0000 + 20.7846i 0.685994 + 1.18818i
\(307\) 33.0000 1.88341 0.941705 0.336440i \(-0.109223\pi\)
0.941705 + 0.336440i \(0.109223\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 9.00000 + 15.5885i 0.511166 + 0.885365i
\(311\) −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) 0 0
\(313\) 11.0000 + 19.0526i 0.621757 + 1.07691i 0.989158 + 0.146852i \(0.0469141\pi\)
−0.367402 + 0.930062i \(0.619753\pi\)
\(314\) −16.0000 −0.902932
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) 0 0
\(319\) −15.0000 + 25.9808i −0.839839 + 1.45464i
\(320\) 12.0000 + 20.7846i 0.670820 + 1.16190i
\(321\) 0 0
\(322\) 0 0
\(323\) 20.0000 1.11283
\(324\) −9.00000 15.5885i −0.500000 0.866025i
\(325\) −2.00000 + 3.46410i −0.110940 + 0.192154i
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −11.0000 19.0526i −0.604615 1.04722i −0.992112 0.125353i \(-0.959994\pi\)
0.387498 0.921871i \(-0.373340\pi\)
\(332\) 15.0000 25.9808i 0.823232 1.42588i
\(333\) −6.00000 + 10.3923i −0.328798 + 0.569495i
\(334\) −5.00000 8.66025i −0.273588 0.473868i
\(335\) −18.0000 −0.983445
\(336\) 0 0
\(337\) 17.0000 0.926049 0.463025 0.886345i \(-0.346764\pi\)
0.463025 + 0.886345i \(0.346764\pi\)
\(338\) 1.00000 + 1.73205i 0.0543928 + 0.0942111i
\(339\) 0 0
\(340\) 12.0000 20.7846i 0.650791 1.12720i
\(341\) 9.00000 + 15.5885i 0.487377 + 0.844162i
\(342\) −30.0000 −1.62221
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 8.00000 13.8564i 0.430083 0.744925i
\(347\) 16.0000 27.7128i 0.858925 1.48770i −0.0140303 0.999902i \(-0.504466\pi\)
0.872955 0.487800i \(-0.162201\pi\)
\(348\) 0 0
\(349\) −11.0000 −0.588817 −0.294408 0.955680i \(-0.595123\pi\)
−0.294408 + 0.955680i \(0.595123\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 24.0000 + 41.5692i 1.27920 + 2.21565i
\(353\) −5.00000 + 8.66025i −0.266123 + 0.460939i −0.967857 0.251500i \(-0.919076\pi\)
0.701734 + 0.712439i \(0.252409\pi\)
\(354\) 0 0
\(355\) 12.0000 + 20.7846i 0.636894 + 1.10313i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −46.0000 −2.43118
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) −14.0000 24.2487i −0.735824 1.27448i
\(363\) 0 0
\(364\) 0 0
\(365\) 39.0000 2.04135
\(366\) 0 0
\(367\) 7.00000 12.1244i 0.365397 0.632886i −0.623443 0.781869i \(-0.714267\pi\)
0.988840 + 0.148983i \(0.0475999\pi\)
\(368\) 6.00000 10.3923i 0.312772 0.541736i
\(369\) 9.00000 + 15.5885i 0.468521 + 0.811503i
\(370\) 24.0000 1.24770
\(371\) 0 0
\(372\) 0 0
\(373\) −15.0000 25.9808i −0.776671 1.34523i −0.933851 0.357663i \(-0.883574\pi\)
0.157180 0.987570i \(-0.449760\pi\)
\(374\) 24.0000 41.5692i 1.24101 2.14949i
\(375\) 0 0
\(376\) 0 0
\(377\) −5.00000 −0.257513
\(378\) 0 0
\(379\) −6.00000 −0.308199 −0.154100 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(380\) 15.0000 + 25.9808i 0.769484 + 1.33278i
\(381\) 0 0
\(382\) −8.00000 + 13.8564i −0.409316 + 0.708955i
\(383\) −18.0000 31.1769i −0.919757 1.59307i −0.799783 0.600289i \(-0.795052\pi\)
−0.119974 0.992777i \(-0.538281\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −44.0000 −2.23954
\(387\) −1.50000 2.59808i −0.0762493 0.132068i
\(388\) 7.00000 12.1244i 0.355371 0.615521i
\(389\) −15.0000 + 25.9808i −0.760530 + 1.31728i 0.182047 + 0.983290i \(0.441728\pi\)
−0.942578 + 0.333987i \(0.891606\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 0 0
\(393\) 0 0
\(394\) 2.00000 + 3.46410i 0.100759 + 0.174519i
\(395\) −4.50000 + 7.79423i −0.226420 + 0.392170i
\(396\) −18.0000 + 31.1769i −0.904534 + 1.56670i
\(397\) −6.50000 11.2583i −0.326226 0.565039i 0.655534 0.755166i \(-0.272444\pi\)
−0.981760 + 0.190126i \(0.939110\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) −16.0000 −0.800000
\(401\) 16.0000 + 27.7128i 0.799002 + 1.38391i 0.920267 + 0.391292i \(0.127972\pi\)
−0.121265 + 0.992620i \(0.538695\pi\)
\(402\) 0 0
\(403\) −1.50000 + 2.59808i −0.0747203 + 0.129419i
\(404\) −14.0000 24.2487i −0.696526 1.20642i
\(405\) 27.0000 1.34164
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −6.50000 + 11.2583i −0.321404 + 0.556689i −0.980778 0.195127i \(-0.937488\pi\)
0.659374 + 0.751815i \(0.270822\pi\)
\(410\) 18.0000 31.1769i 0.888957 1.53972i
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 18.0000 0.884652
\(415\) 22.5000 + 38.9711i 1.10448 + 1.91302i
\(416\) −4.00000 + 6.92820i −0.196116 + 0.339683i
\(417\) 0 0
\(418\) 30.0000 + 51.9615i 1.46735 + 2.54152i
\(419\) 10.0000 0.488532 0.244266 0.969708i \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) 0 0
\(421\) −12.0000 −0.584844 −0.292422 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) −5.00000 8.66025i −0.243396 0.421575i
\(423\) −10.5000 + 18.1865i −0.510527 + 0.884260i
\(424\) 0 0
\(425\) 8.00000 + 13.8564i 0.388057 + 0.672134i
\(426\) 0 0
\(427\) 0 0
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) −3.00000 + 5.19615i −0.144673 + 0.250581i
\(431\) −3.00000 + 5.19615i −0.144505 + 0.250290i −0.929188 0.369607i \(-0.879492\pi\)
0.784683 + 0.619897i \(0.212826\pi\)
\(432\) 0 0
\(433\) −12.0000 −0.576683 −0.288342 0.957528i \(-0.593104\pi\)
−0.288342 + 0.957528i \(0.593104\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) 7.50000 12.9904i 0.358774 0.621414i
\(438\) 0 0
\(439\) −11.0000 19.0526i −0.525001 0.909329i −0.999576 0.0291138i \(-0.990731\pi\)
0.474575 0.880215i \(-0.342602\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 8.00000 0.380521
\(443\) −9.50000 16.4545i −0.451359 0.781776i 0.547112 0.837059i \(-0.315727\pi\)
−0.998471 + 0.0552833i \(0.982394\pi\)
\(444\) 0 0
\(445\) 4.50000 7.79423i 0.213320 0.369482i
\(446\) −15.0000 25.9808i −0.710271 1.23022i
\(447\) 0 0
\(448\) 0 0
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) −12.0000 20.7846i −0.565685 0.979796i
\(451\) 18.0000 31.1769i 0.847587 1.46806i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 0 0
\(454\) 40.0000 1.87729
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(458\) −14.0000 + 24.2487i −0.654177 + 1.13307i
\(459\) 0 0
\(460\) −9.00000 15.5885i −0.419627 0.726816i
\(461\) 22.0000 1.02464 0.512321 0.858794i \(-0.328786\pi\)
0.512321 + 0.858794i \(0.328786\pi\)
\(462\) 0 0
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) −10.0000 17.3205i −0.464238 0.804084i
\(465\) 0 0
\(466\) 15.0000 25.9808i 0.694862 1.20354i
\(467\) −11.0000 19.0526i −0.509019 0.881647i −0.999945 0.0104461i \(-0.996675\pi\)
0.490926 0.871201i \(-0.336658\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) 42.0000 1.93732
\(471\) 0 0
\(472\) 0 0
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) 0 0
\(475\) −20.0000 −0.917663
\(476\) 0 0
\(477\) 27.0000 1.23625
\(478\) −4.00000 6.92820i −0.182956 0.316889i
\(479\) −5.50000 + 9.52628i −0.251301 + 0.435267i −0.963884 0.266321i \(-0.914192\pi\)
0.712583 + 0.701588i \(0.247525\pi\)
\(480\) 0 0
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) −34.0000 −1.54866
\(483\) 0 0
\(484\) 50.0000 2.27273
\(485\) 10.5000 + 18.1865i 0.476780 + 0.825808i
\(486\) 0 0
\(487\) 13.0000 22.5167i 0.589086 1.02033i −0.405266 0.914199i \(-0.632821\pi\)
0.994352 0.106129i \(-0.0338455\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) −10.0000 + 17.3205i −0.450377 + 0.780076i
\(494\) −5.00000 + 8.66025i −0.224961 + 0.389643i
\(495\) −27.0000 46.7654i −1.21356 2.10195i
\(496\) −12.0000 −0.538816
\(497\) 0 0
\(498\) 0 0
\(499\) 8.00000 + 13.8564i 0.358129 + 0.620298i 0.987648 0.156687i \(-0.0500814\pi\)
−0.629519 + 0.776985i \(0.716748\pi\)
\(500\) 3.00000 5.19615i 0.134164 0.232379i
\(501\) 0 0
\(502\) 26.0000 + 45.0333i 1.16044 + 2.00994i
\(503\) −2.00000 −0.0891756 −0.0445878 0.999005i \(-0.514197\pi\)
−0.0445878 + 0.999005i \(0.514197\pi\)
\(504\) 0 0
\(505\) 42.0000 1.86898
\(506\) −18.0000 31.1769i −0.800198 1.38598i
\(507\) 0 0
\(508\) 4.00000 6.92820i 0.177471 0.307389i
\(509\) −9.50000 16.4545i −0.421080 0.729332i 0.574965 0.818178i \(-0.305016\pi\)
−0.996045 + 0.0888457i \(0.971682\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −32.0000 −1.41421
\(513\) 0 0
\(514\) 2.00000 3.46410i 0.0882162 0.152795i
\(515\) −6.00000 + 10.3923i −0.264392 + 0.457940i
\(516\) 0 0
\(517\) 42.0000 1.84716
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 20.0000 34.6410i 0.876216 1.51765i 0.0207541 0.999785i \(-0.493393\pi\)
0.855462 0.517866i \(-0.173273\pi\)
\(522\) 15.0000 25.9808i 0.656532 1.13715i
\(523\) 5.00000 + 8.66025i 0.218635 + 0.378686i 0.954391 0.298560i \(-0.0965063\pi\)
−0.735756 + 0.677247i \(0.763173\pi\)
\(524\) −16.0000 −0.698963
\(525\) 0 0
\(526\) 30.0000 1.30806
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) −27.0000 46.7654i −1.17281 2.03136i
\(531\) 24.0000 1.04151
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) 6.00000 10.3923i 0.259403 0.449299i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000 + 34.6410i 0.859867 + 1.48933i 0.872055 + 0.489408i \(0.162787\pi\)
−0.0121878 + 0.999926i \(0.503880\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 0 0
\(544\) 16.0000 + 27.7128i 0.685994 + 1.18818i
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) −7.00000 −0.299298 −0.149649 0.988739i \(-0.547814\pi\)
−0.149649 + 0.988739i \(0.547814\pi\)
\(548\) −4.00000 6.92820i −0.170872 0.295958i
\(549\) 15.0000 25.9808i 0.640184 1.10883i
\(550\) −24.0000 + 41.5692i −1.02336 + 1.77252i
\(551\) −12.5000 21.6506i −0.532518 0.922348i
\(552\) 0 0
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) −18.0000 + 31.1769i −0.763370 + 1.32220i
\(557\) 6.00000 10.3923i 0.254228 0.440336i −0.710457 0.703740i \(-0.751512\pi\)
0.964686 + 0.263404i \(0.0848453\pi\)
\(558\) −9.00000 15.5885i −0.381000 0.659912i
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) 0 0
\(562\) −30.0000 51.9615i −1.26547 2.19186i
\(563\) 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 0 0
\(565\) 4.50000 + 7.79423i 0.189316 + 0.327906i
\(566\) 32.0000 1.34506
\(567\) 0 0
\(568\) 0 0
\(569\) −3.50000 6.06218i −0.146728 0.254140i 0.783289 0.621658i \(-0.213541\pi\)
−0.930016 + 0.367519i \(0.880207\pi\)
\(570\) 0 0
\(571\) 8.50000 14.7224i 0.355714 0.616115i −0.631526 0.775355i \(-0.717571\pi\)
0.987240 + 0.159240i \(0.0509044\pi\)
\(572\) 6.00000 + 10.3923i 0.250873 + 0.434524i
\(573\) 0 0
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) −12.0000 20.7846i −0.500000 0.866025i
\(577\) 1.00000 1.73205i 0.0416305 0.0721062i −0.844459 0.535620i \(-0.820078\pi\)
0.886090 + 0.463513i \(0.153411\pi\)
\(578\) −1.00000 + 1.73205i −0.0415945 + 0.0720438i
\(579\) 0 0
\(580\) −30.0000 −1.24568
\(581\) 0 0
\(582\) 0 0
\(583\) −27.0000 46.7654i −1.11823 1.93682i
\(584\) 0 0
\(585\) 4.50000 7.79423i 0.186052 0.322252i
\(586\) 19.0000 + 32.9090i 0.784883 + 1.35946i
\(587\) −39.0000 −1.60970 −0.804851 0.593477i \(-0.797755\pi\)
−0.804851 + 0.593477i \(0.797755\pi\)
\(588\) 0 0
\(589\) −15.0000 −0.618064
\(590\) −24.0000 41.5692i −0.988064 1.71138i
\(591\) 0 0
\(592\) −8.00000 + 13.8564i −0.328798 + 0.569495i
\(593\) −13.5000 23.3827i −0.554379 0.960212i −0.997952 0.0639736i \(-0.979623\pi\)
0.443573 0.896238i \(-0.353711\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −36.0000 −1.47462
\(597\) 0 0
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) −5.50000 + 9.52628i −0.224724 + 0.389233i −0.956237 0.292595i \(-0.905481\pi\)
0.731513 + 0.681828i \(0.238815\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 18.0000 0.733017
\(604\) 0 0
\(605\) −37.5000 + 64.9519i −1.52459 + 2.64067i
\(606\) 0 0
\(607\) 1.00000 + 1.73205i 0.0405887 + 0.0703018i 0.885606 0.464437i \(-0.153743\pi\)
−0.845017 + 0.534739i \(0.820410\pi\)
\(608\) −40.0000 −1.62221
\(609\) 0 0
\(610\) −60.0000 −2.42933
\(611\) 3.50000 + 6.06218i 0.141595 + 0.245249i
\(612\) −12.0000 + 20.7846i −0.485071 + 0.840168i
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) 33.0000 + 57.1577i 1.33177 + 2.30670i
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) −9.00000 + 15.5885i −0.361449 + 0.626048i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 0 0
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −22.0000 + 38.1051i −0.879297 + 1.52299i
\(627\) 0 0
\(628\) −8.00000 13.8564i −0.319235 0.552931i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) 22.0000 0.875806 0.437903 0.899022i \(-0.355721\pi\)
0.437903 + 0.899022i \(0.355721\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −24.0000 + 41.5692i −0.953162 + 1.65092i
\(635\) 6.00000 + 10.3923i 0.238103 + 0.412406i
\(636\) 0 0
\(637\) 0 0
\(638\) −60.0000 −2.37542
\(639\) −12.0000 20.7846i −0.474713 0.822226i
\(640\) 0 0
\(641\) −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i \(-0.890212\pi\)
0.763367 + 0.645966i \(0.223545\pi\)
\(642\) 0 0
\(643\) −8.00000 −0.315489 −0.157745 0.987480i \(-0.550422\pi\)
−0.157745 + 0.987480i \(0.550422\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 20.0000 + 34.6410i 0.786889 + 1.36293i
\(647\) 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i \(-0.718214\pi\)
0.986916 + 0.161233i \(0.0515470\pi\)
\(648\) 0 0
\(649\) −24.0000 41.5692i −0.942082 1.63173i
\(650\) −8.00000 −0.313786
\(651\) 0 0
\(652\) −8.00000 −0.313304
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 0 0
\(655\) 12.0000 20.7846i 0.468879 0.812122i
\(656\) 12.0000 + 20.7846i 0.468521 + 0.811503i
\(657\) −39.0000 −1.52153
\(658\) 0 0
\(659\) 17.0000 0.662226 0.331113 0.943591i \(-0.392576\pi\)
0.331113 + 0.943591i \(0.392576\pi\)
\(660\) 0 0
\(661\) −16.5000 + 28.5788i −0.641776 + 1.11159i 0.343261 + 0.939240i \(0.388469\pi\)
−0.985036 + 0.172348i \(0.944865\pi\)
\(662\) 22.0000 38.1051i 0.855054 1.48100i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −24.0000 −0.929981
\(667\) 7.50000 + 12.9904i 0.290401 + 0.502990i
\(668\) 5.00000 8.66025i 0.193456 0.335075i
\(669\) 0 0
\(670\) −18.0000 31.1769i −0.695401 1.20447i
\(671\) −60.0000 −2.31627
\(672\) 0 0
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) 17.0000 + 29.4449i 0.654816 + 1.13417i
\(675\) 0 0
\(676\) −1.00000 + 1.73205i −0.0384615 + 0.0666173i
\(677\) 11.0000 + 19.0526i 0.422764 + 0.732249i 0.996209 0.0869952i \(-0.0277265\pi\)
−0.573444 + 0.819244i \(0.694393\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −18.0000 + 31.1769i −0.689256 + 1.19383i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) −15.0000 25.9808i −0.573539 0.993399i
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) 4.50000 7.79423i 0.171436 0.296936i
\(690\) 0 0
\(691\) 5.50000 + 9.52628i 0.209230 + 0.362397i 0.951472 0.307735i \(-0.0995710\pi\)
−0.742242 + 0.670132i \(0.766238\pi\)
\(692\) 16.0000 0.608229
\(693\) 0 0
\(694\) 64.0000 2.42941
\(695\) −27.0000 46.7654i −1.02417 1.77391i
\(696\) 0 0
\(697\) 12.0000 20.7846i 0.454532 0.787273i
\(698\) −11.0000 19.0526i −0.416356 0.721150i
\(699\) 0 0
\(700\) 0 0
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 0 0
\(703\) −10.0000 + 17.3205i −0.377157 + 0.653255i
\(704\) −24.0000 + 41.5692i −0.904534 + 1.56670i
\(705\) 0 0
\(706\) −20.0000 −0.752710
\(707\) 0 0
\(708\) 0 0
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) −24.0000 + 41.5692i −0.900704 + 1.56007i
\(711\) 4.50000 7.79423i 0.168763 0.292306i
\(712\) 0 0
\(713\) 9.00000 0.337053
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) −23.0000 39.8372i −0.859550 1.48878i
\(717\) 0 0
\(718\) 20.0000 34.6410i 0.746393 1.29279i
\(719\) 9.00000 + 15.5885i 0.335643 + 0.581351i 0.983608 0.180319i \(-0.0577130\pi\)
−0.647965 + 0.761670i \(0.724380\pi\)
\(720\) 36.0000 1.34164
\(721\) 0 0
\(722\) −12.0000 −0.446594
\(723\) 0 0
\(724\) 14.0000 24.2487i 0.520306 0.901196i
\(725\) 10.0000 17.3205i 0.371391 0.643268i
\(726\) 0 0
\(727\) −46.0000 −1.70605 −0.853023 0.521874i \(-0.825233\pi\)
−0.853023 + 0.521874i \(0.825233\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 39.0000 + 67.5500i 1.44345 + 2.50014i
\(731\) −2.00000 + 3.46410i −0.0739727 + 0.128124i
\(732\) 0 0
\(733\) 25.5000 + 44.1673i 0.941864 + 1.63136i 0.761912 + 0.647681i \(0.224261\pi\)
0.179952 + 0.983675i \(0.442406\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) 24.0000 0.884652
\(737\) −18.0000 31.1769i −0.663039 1.14842i
\(738\) −18.0000 + 31.1769i −0.662589 + 1.14764i
\(739\) 13.0000 22.5167i 0.478213 0.828289i −0.521475 0.853266i \(-0.674618\pi\)
0.999688 + 0.0249776i \(0.00795146\pi\)
\(740\) 12.0000 + 20.7846i 0.441129 + 0.764057i
\(741\) 0 0
\(742\) 0 0
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) 27.0000 46.7654i 0.989203 1.71335i
\(746\) 30.0000 51.9615i 1.09838 1.90245i
\(747\) −22.5000 38.9711i −0.823232 1.42588i
\(748\) 48.0000 1.75505
\(749\) 0 0
\(750\) 0 0
\(751\) 8.50000 + 14.7224i 0.310169 + 0.537229i 0.978399 0.206726i \(-0.0662809\pi\)
−0.668229 + 0.743955i \(0.732948\pi\)
\(752\) −14.0000 + 24.2487i −0.510527 + 0.884260i
\(753\) 0 0
\(754\) −5.00000 8.66025i −0.182089 0.315388i
\(755\) 0 0
\(756\) 0 0
\(757\) −15.0000 −0.545184 −0.272592 0.962130i \(-0.587881\pi\)
−0.272592 + 0.962130i \(0.587881\pi\)
\(758\) −6.00000 10.3923i −0.217930 0.377466i
\(759\) 0 0
\(760\) 0 0
\(761\) 4.50000 + 7.79423i 0.163125 + 0.282541i 0.935988 0.352032i \(-0.114509\pi\)
−0.772863 + 0.634573i \(0.781176\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) −18.0000 31.1769i −0.650791 1.12720i
\(766\) 36.0000 62.3538i 1.30073 2.25294i
\(767\) 4.00000 6.92820i 0.144432 0.250163i
\(768\) 0 0
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −22.0000 38.1051i −0.791797 1.37143i
\(773\) 27.0000 46.7654i 0.971123 1.68203i 0.278944 0.960307i \(-0.410016\pi\)
0.692179 0.721726i \(-0.256651\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) −6.00000 10.3923i −0.215526 0.373303i
\(776\) 0 0
\(777\) 0 0
\(778\) −60.0000 −2.15110
\(779\) 15.0000 + 25.9808i 0.537431 + 0.930857i
\(780\) 0 0
\(781\) −24.0000 + 41.5692i −0.858788 + 1.48746i
\(782\) −12.0000 20.7846i −0.429119 0.743256i
\(783\) 0 0
\(784\) 0 0
\(785\) 24.0000 0.856597
\(786\) 0 0
\(787\) 18.5000 32.0429i 0.659454 1.14221i −0.321303 0.946976i \(-0.604121\pi\)
0.980757 0.195231i \(-0.0625457\pi\)
\(788\) −2.00000 + 3.46410i −0.0712470 + 0.123404i
\(789\) 0 0
\(790\) −18.0000 −0.640411
\(791\) 0 0
\(792\) 0 0