Properties

Label 637.2.e.e.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.e.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 \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 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 −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) −3.00000 + 5.19615i −0.707107 + 1.22474i
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) −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 −0.699301 0.714827i \(-0.746505\pi\)
0.968709 + 0.248199i \(0.0798387\pi\)
\(32\) −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 \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 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 \(-0.996117\pi\)
0.489398 0.872060i \(-0.337217\pi\)
\(48\) 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 \(0.341016\pi\)
−0.999709 + 0.0241347i \(0.992317\pi\)
\(60\) 0 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 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 \(-0.558156\pi\)
0.942455 0.334332i \(-0.108511\pi\)
\(74\) −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 \(-0.192169\pi\)
0.823232 + 0.567705i \(0.192169\pi\)
\(84\) 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 0.775509 0.631337i \(-0.217494\pi\)
−0.934508 + 0.355942i \(0.884160\pi\)
\(90\) −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 \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 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 \(-0.588061\pi\)
0.969664 0.244443i \(-0.0786053\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 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 0.636676 0.771132i \(-0.280309\pi\)
−0.986157 + 0.165812i \(0.946976\pi\)
\(132\) 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 \(-0.776457\pi\)
−0.763370 + 0.645961i \(0.776457\pi\)
\(140\) 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 −0.661094 0.750303i \(-0.729907\pi\)
0.980329 + 0.197372i \(0.0632408\pi\)
\(158\) 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 \(-0.438030\pi\)
0.193456 + 0.981109i \(0.438030\pi\)
\(168\) 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 0.977064 0.212947i \(-0.0683062\pi\)
−0.672949 + 0.739689i \(0.734973\pi\)
\(174\) 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 \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 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 −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 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 \(-0.332510\pi\)
0.502237 + 0.864730i \(0.332510\pi\)
\(224\) 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 \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 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 \(-0.648900\pi\)
0.998443 0.0557856i \(-0.0177663\pi\)
\(242\) 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 \(-0.806334\pi\)
−0.820553 + 0.571571i \(0.806334\pi\)
\(252\) 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 0.895528 0.445005i \(-0.146798\pi\)
−0.833150 + 0.553047i \(0.813465\pi\)
\(258\) 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 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) −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 −0.999608 0.0280052i \(-0.991084\pi\)
0.524057 + 0.851683i \(0.324418\pi\)
\(284\) 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 \(-0.687280\pi\)
−0.554996 + 0.831853i \(0.687280\pi\)
\(294\) 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 \(-0.890777\pi\)
−0.941705 + 0.336440i \(0.890777\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 9.00000 + 15.5885i 0.511166 + 0.885365i
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0 0
\(313\) −11.0000 19.0526i −0.621757 1.07691i −0.989158 0.146852i \(-0.953086\pi\)
0.367402 0.930062i \(-0.380247\pi\)
\(314\) 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 \(-0.404877\pi\)
0.294408 + 0.955680i \(0.404877\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 24.0000 + 41.5692i 1.27920 + 2.21565i
\(353\) 5.00000 8.66025i 0.266123 0.460939i −0.701734 0.712439i \(-0.747591\pi\)
0.967857 + 0.251500i \(0.0809239\pi\)
\(354\) 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 −0.988840 0.148983i \(-0.952400\pi\)
0.623443 + 0.781869i \(0.285733\pi\)
\(368\) 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 \(0.204948\pi\)
0.119974 + 0.992777i \(0.461719\pi\)
\(384\) 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 0.981760 0.190126i \(-0.0608897\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(398\) −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 −0.659374 0.751815i \(-0.729178\pi\)
0.980778 + 0.195127i \(0.0625118\pi\)
\(410\) 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 \(-0.578547\pi\)
−0.244266 + 0.969708i \(0.578547\pi\)
\(420\) 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 \(-0.406896\pi\)
0.288342 + 0.957528i \(0.406896\pi\)
\(434\) 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 \(0.00926853\pi\)
−0.474575 + 0.880215i \(0.657398\pi\)
\(440\) 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 \(-0.671214\pi\)
−0.512321 + 0.858794i \(0.671214\pi\)
\(462\) 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 \(0.00332515\pi\)
−0.490926 + 0.871201i \(0.663342\pi\)
\(468\) 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 −0.712583 0.701588i \(-0.752475\pi\)
0.963884 + 0.266321i \(0.0858081\pi\)
\(480\) 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 \(-0.485803\pi\)
0.0445878 + 0.999005i \(0.485803\pi\)
\(504\) 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 0.996045 0.0888457i \(-0.0283178\pi\)
−0.574965 + 0.818178i \(0.694984\pi\)
\(510\) 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 \(0.506607\pi\)
−0.855462 + 0.517866i \(0.826727\pi\)
\(522\) 15.0000 25.9808i 0.656532 1.13715i
\(523\) −5.00000 8.66025i −0.218635 0.378686i 0.735756 0.677247i \(-0.236827\pi\)
−0.954391 + 0.298560i \(0.903494\pi\)
\(524\) 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 −0.905088 0.425223i \(-0.860196\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(564\) 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 −0.886090 0.463513i \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) −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 \(-0.202245\pi\)
0.804851 + 0.593477i \(0.202245\pi\)
\(588\) 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 \(0.0203773\pi\)
−0.443573 + 0.896238i \(0.646289\pi\)
\(594\) 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 \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 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 0.845017 0.534739i \(-0.179590\pi\)
−0.885606 + 0.464437i \(0.846257\pi\)
\(608\) 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 −0.993959 0.109749i \(-0.964995\pi\)
0.592025 + 0.805919i \(0.298329\pi\)
\(620\) −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 \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 20.0000 + 34.6410i 0.786889 + 1.36293i
\(647\) −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i \(-0.948453\pi\)
0.633090 + 0.774078i \(0.281786\pi\)
\(648\) 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 \(-0.611531\pi\)
0.985036 0.172348i \(-0.0551353\pi\)
\(662\) 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 0.573444 0.819244i \(-0.305607\pi\)
−0.996209 + 0.0869952i \(0.972274\pi\)
\(678\) 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 0.742242 0.670132i \(-0.233762\pi\)
−0.951472 + 0.307735i \(0.900429\pi\)
\(692\) −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 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) −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 \(-0.174767\pi\)
0.853023 + 0.521874i \(0.174767\pi\)
\(728\) 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 \(-0.775739\pi\)
−0.179952 0.983675i \(-0.557594\pi\)
\(734\) −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 0.772863 0.634573i \(-0.218824\pi\)
−0.935988 + 0.352032i \(0.885491\pi\)
\(762\) 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 \(-0.717382\pi\)
−0.631066 + 0.775729i \(0.717382\pi\)
\(770\) 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 \(0.589984\pi\)
−0.692179 + 0.721726i \(0.743349\pi\)
\(774\) 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 \(0.395879\pi\)
−0.980757 + 0.195231i \(0.937454\pi\)
\(788\) −2.00000 + 3.46410i −0.0712470 + 0.123404i
\(789\) 0 0
\(790\) 18.0000 0.640411
\(791\) 0 0
\(792\) 0 0