Properties

Label 525.2.bc.a.418.1
Level 525
Weight 2
Character 525.418
Analytic conductor 4.192
Analytic rank 0
Dimension 8
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 525.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 418.1
Root \(0.258819 - 0.965926i\)
Character \(\chi\) = 525.418
Dual form 525.2.bc.a.157.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.63896 - 0.189469i) q^{7} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.63896 - 0.189469i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(-1.93185 + 0.517638i) q^{12} +(-1.41421 + 1.41421i) q^{13} +(2.00000 - 3.46410i) q^{16} +(1.55291 - 5.79555i) q^{17} +(-1.73205 + 3.00000i) q^{19} +(2.50000 + 0.866025i) q^{21} +(-0.707107 - 0.707107i) q^{27} +(-4.76028 + 2.31079i) q^{28} +(-4.50000 + 2.59808i) q^{31} +(1.55291 + 5.79555i) q^{33} +2.00000 q^{36} +(-2.24144 - 8.36516i) q^{37} +(1.73205 - 1.00000i) q^{39} -10.3923i q^{41} +(3.67423 + 3.67423i) q^{43} +(-10.3923 - 6.00000i) q^{44} +(-5.79555 + 1.55291i) q^{47} +(-2.82843 + 2.82843i) q^{48} +(6.92820 + 1.00000i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(-1.03528 + 3.86370i) q^{52} +(2.68973 - 10.0382i) q^{53} +(2.44949 - 2.44949i) q^{57} +(5.19615 + 9.00000i) q^{59} +(7.50000 + 4.33013i) q^{61} +(-2.19067 - 1.48356i) q^{63} -8.00000i q^{64} +(3.34607 + 0.896575i) q^{67} +(-3.10583 - 11.5911i) q^{68} -6.00000 q^{71} +(0.965926 + 0.258819i) q^{73} +6.92820i q^{76} +(6.93237 + 14.2808i) q^{77} +(-4.33013 - 2.50000i) q^{79} +(0.500000 + 0.866025i) q^{81} +(4.24264 - 4.24264i) q^{83} +(5.19615 - 1.00000i) q^{84} +(-5.19615 + 9.00000i) q^{89} +(4.00000 - 3.46410i) q^{91} +(5.01910 - 1.34486i) q^{93} +(9.19239 + 9.19239i) q^{97} -6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 24q^{11} + 16q^{16} + 20q^{21} - 36q^{31} + 16q^{36} - 24q^{51} + 60q^{61} - 48q^{71} + 4q^{81} + 32q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.63896 0.189469i −0.997433 0.0716124i
\(8\) 0 0
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0 0
\(11\) −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i \(-0.806886\pi\)
−0.0829925 0.996550i \(-0.526448\pi\)
\(12\) −1.93185 + 0.517638i −0.557678 + 0.149429i
\(13\) −1.41421 + 1.41421i −0.392232 + 0.392232i −0.875482 0.483250i \(-0.839456\pi\)
0.483250 + 0.875482i \(0.339456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 1.55291 5.79555i 0.376637 1.40563i −0.474301 0.880363i \(-0.657299\pi\)
0.850938 0.525266i \(-0.176034\pi\)
\(18\) 0 0
\(19\) −1.73205 + 3.00000i −0.397360 + 0.688247i −0.993399 0.114708i \(-0.963407\pi\)
0.596040 + 0.802955i \(0.296740\pi\)
\(20\) 0 0
\(21\) 2.50000 + 0.866025i 0.545545 + 0.188982i
\(22\) 0 0
\(23\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −4.76028 + 2.31079i −0.899608 + 0.436698i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −4.50000 + 2.59808i −0.808224 + 0.466628i −0.846339 0.532645i \(-0.821198\pi\)
0.0381148 + 0.999273i \(0.487865\pi\)
\(32\) 0 0
\(33\) 1.55291 + 5.79555i 0.270328 + 1.00888i
\(34\) 0 0
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) −2.24144 8.36516i −0.368490 1.37522i −0.862627 0.505840i \(-0.831183\pi\)
0.494137 0.869384i \(-0.335484\pi\)
\(38\) 0 0
\(39\) 1.73205 1.00000i 0.277350 0.160128i
\(40\) 0 0
\(41\) 10.3923i 1.62301i −0.584349 0.811503i \(-0.698650\pi\)
0.584349 0.811503i \(-0.301350\pi\)
\(42\) 0 0
\(43\) 3.67423 + 3.67423i 0.560316 + 0.560316i 0.929397 0.369082i \(-0.120328\pi\)
−0.369082 + 0.929397i \(0.620328\pi\)
\(44\) −10.3923 6.00000i −1.56670 0.904534i
\(45\) 0 0
\(46\) 0 0
\(47\) −5.79555 + 1.55291i −0.845369 + 0.226516i −0.655407 0.755276i \(-0.727503\pi\)
−0.189961 + 0.981792i \(0.560836\pi\)
\(48\) −2.82843 + 2.82843i −0.408248 + 0.408248i
\(49\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(50\) 0 0
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) −1.03528 + 3.86370i −0.143567 + 0.535799i
\(53\) 2.68973 10.0382i 0.369462 1.37885i −0.491807 0.870704i \(-0.663664\pi\)
0.861270 0.508148i \(-0.169670\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.44949 2.44949i 0.324443 0.324443i
\(58\) 0 0
\(59\) 5.19615 + 9.00000i 0.676481 + 1.17170i 0.976034 + 0.217620i \(0.0698294\pi\)
−0.299552 + 0.954080i \(0.596837\pi\)
\(60\) 0 0
\(61\) 7.50000 + 4.33013i 0.960277 + 0.554416i 0.896258 0.443533i \(-0.146275\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 0 0
\(63\) −2.19067 1.48356i −0.275999 0.186911i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 3.34607 + 0.896575i 0.408787 + 0.109534i 0.457352 0.889286i \(-0.348798\pi\)
−0.0485648 + 0.998820i \(0.515465\pi\)
\(68\) −3.10583 11.5911i −0.376637 1.40563i
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 0.965926 + 0.258819i 0.113053 + 0.0302925i 0.314902 0.949124i \(-0.398028\pi\)
−0.201849 + 0.979417i \(0.564695\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 6.92820i 0.794719i
\(77\) 6.93237 + 14.2808i 0.790017 + 1.62745i
\(78\) 0 0
\(79\) −4.33013 2.50000i −0.487177 0.281272i 0.236225 0.971698i \(-0.424090\pi\)
−0.723403 + 0.690426i \(0.757423\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 4.24264 4.24264i 0.465690 0.465690i −0.434825 0.900515i \(-0.643190\pi\)
0.900515 + 0.434825i \(0.143190\pi\)
\(84\) 5.19615 1.00000i 0.566947 0.109109i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.19615 + 9.00000i −0.550791 + 0.953998i 0.447427 + 0.894321i \(0.352341\pi\)
−0.998218 + 0.0596775i \(0.980993\pi\)
\(90\) 0 0
\(91\) 4.00000 3.46410i 0.419314 0.363137i
\(92\) 0 0
\(93\) 5.01910 1.34486i 0.520456 0.139456i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 9.19239 + 9.19239i 0.933346 + 0.933346i 0.997913 0.0645677i \(-0.0205669\pi\)
−0.0645677 + 0.997913i \(0.520567\pi\)
\(98\) 0 0
\(99\) 6.00000i 0.603023i
\(100\) 0 0
\(101\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 0 0
\(103\) 1.81173 + 6.76148i 0.178515 + 0.666228i 0.995926 + 0.0901732i \(0.0287421\pi\)
−0.817411 + 0.576055i \(0.804591\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(108\) −1.93185 0.517638i −0.185893 0.0498097i
\(109\) 8.66025 5.00000i 0.829502 0.478913i −0.0241802 0.999708i \(-0.507698\pi\)
0.853682 + 0.520794i \(0.174364\pi\)
\(110\) 0 0
\(111\) 8.66025i 0.821995i
\(112\) −5.93426 + 8.76268i −0.560734 + 0.827996i
\(113\) 7.34847 + 7.34847i 0.691286 + 0.691286i 0.962515 0.271229i \(-0.0874301\pi\)
−0.271229 + 0.962515i \(0.587430\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.93185 + 0.517638i −0.178600 + 0.0478557i
\(118\) 0 0
\(119\) −5.19615 + 15.0000i −0.476331 + 1.37505i
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 0 0
\(123\) −2.68973 + 10.0382i −0.242524 + 0.905114i
\(124\) −5.19615 + 9.00000i −0.466628 + 0.808224i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.57321 8.57321i 0.760750 0.760750i −0.215708 0.976458i \(-0.569206\pi\)
0.976458 + 0.215708i \(0.0692060\pi\)
\(128\) 0 0
\(129\) −2.59808 4.50000i −0.228748 0.396203i
\(130\) 0 0
\(131\) 9.00000 + 5.19615i 0.786334 + 0.453990i 0.838670 0.544640i \(-0.183334\pi\)
−0.0523366 + 0.998630i \(0.516667\pi\)
\(132\) 8.48528 + 8.48528i 0.738549 + 0.738549i
\(133\) 5.13922 7.58871i 0.445627 0.658024i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 20.0764 + 5.37945i 1.71524 + 0.459598i 0.976700 0.214610i \(-0.0688480\pi\)
0.738542 + 0.674207i \(0.235515\pi\)
\(138\) 0 0
\(139\) −1.73205 −0.146911 −0.0734553 0.997299i \(-0.523403\pi\)
−0.0734553 + 0.997299i \(0.523403\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 11.5911 + 3.10583i 0.969297 + 0.259722i
\(144\) 3.46410 2.00000i 0.288675 0.166667i
\(145\) 0 0
\(146\) 0 0
\(147\) −6.43331 2.75908i −0.530611 0.227565i
\(148\) −12.2474 12.2474i −1.00673 1.00673i
\(149\) −10.3923 6.00000i −0.851371 0.491539i 0.00974235 0.999953i \(-0.496899\pi\)
−0.861113 + 0.508413i \(0.830232\pi\)
\(150\) 0 0
\(151\) −2.50000 4.33013i −0.203447 0.352381i 0.746190 0.665733i \(-0.231881\pi\)
−0.949637 + 0.313353i \(0.898548\pi\)
\(152\) 0 0
\(153\) 4.24264 4.24264i 0.342997 0.342997i
\(154\) 0 0
\(155\) 0 0
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) 1.81173 6.76148i 0.144592 0.539625i −0.855181 0.518329i \(-0.826554\pi\)
0.999773 0.0212957i \(-0.00677914\pi\)
\(158\) 0 0
\(159\) −5.19615 + 9.00000i −0.412082 + 0.713746i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 8.36516 2.24144i 0.655210 0.175563i 0.0841267 0.996455i \(-0.473190\pi\)
0.571083 + 0.820892i \(0.306523\pi\)
\(164\) −10.3923 18.0000i −0.811503 1.40556i
\(165\) 0 0
\(166\) 0 0
\(167\) −8.48528 8.48528i −0.656611 0.656611i 0.297966 0.954577i \(-0.403692\pi\)
−0.954577 + 0.297966i \(0.903692\pi\)
\(168\) 0 0
\(169\) 9.00000i 0.692308i
\(170\) 0 0
\(171\) −3.00000 + 1.73205i −0.229416 + 0.132453i
\(172\) 10.0382 + 2.68973i 0.765405 + 0.205090i
\(173\) −4.65874 17.3867i −0.354198 1.32188i −0.881491 0.472200i \(-0.843460\pi\)
0.527294 0.849683i \(-0.323207\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −24.0000 −1.80907
\(177\) −2.68973 10.0382i −0.202172 0.754517i
\(178\) 0 0
\(179\) 20.7846 12.0000i 1.55351 0.896922i 0.555663 0.831408i \(-0.312464\pi\)
0.997852 0.0655145i \(-0.0208689\pi\)
\(180\) 0 0
\(181\) 5.19615i 0.386227i −0.981176 0.193113i \(-0.938141\pi\)
0.981176 0.193113i \(-0.0618586\pi\)
\(182\) 0 0
\(183\) −6.12372 6.12372i −0.452679 0.452679i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −34.7733 + 9.31749i −2.54288 + 0.681362i
\(188\) −8.48528 + 8.48528i −0.618853 + 0.618853i
\(189\) 1.73205 + 2.00000i 0.125988 + 0.145479i
\(190\) 0 0
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −2.07055 + 7.72741i −0.149429 + 0.557678i
\(193\) −4.03459 + 15.0573i −0.290416 + 1.08385i 0.654374 + 0.756171i \(0.272932\pi\)
−0.944790 + 0.327677i \(0.893734\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 13.0000 5.19615i 0.928571 0.371154i
\(197\) −7.34847 + 7.34847i −0.523557 + 0.523557i −0.918644 0.395087i \(-0.870714\pi\)
0.395087 + 0.918644i \(0.370714\pi\)
\(198\) 0 0
\(199\) −9.52628 16.5000i −0.675300 1.16965i −0.976381 0.216055i \(-0.930681\pi\)
0.301081 0.953599i \(-0.402653\pi\)
\(200\) 0 0
\(201\) −3.00000 1.73205i −0.211604 0.122169i
\(202\) 0 0
\(203\) 0 0
\(204\) 12.0000i 0.840168i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 2.07055 + 7.72741i 0.143567 + 0.535799i
\(209\) 20.7846 1.43770
\(210\) 0 0
\(211\) 7.00000 0.481900 0.240950 0.970538i \(-0.422541\pi\)
0.240950 + 0.970538i \(0.422541\pi\)
\(212\) −5.37945 20.0764i −0.369462 1.37885i
\(213\) 5.79555 + 1.55291i 0.397105 + 0.106404i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 12.3676 6.00361i 0.839565 0.407551i
\(218\) 0 0
\(219\) −0.866025 0.500000i −0.0585206 0.0337869i
\(220\) 0 0
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 0 0
\(223\) 3.53553 3.53553i 0.236757 0.236757i −0.578749 0.815506i \(-0.696459\pi\)
0.815506 + 0.578749i \(0.196459\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.55291 5.79555i 0.103071 0.384664i −0.895049 0.445969i \(-0.852859\pi\)
0.998119 + 0.0613041i \(0.0195260\pi\)
\(228\) 1.79315 6.69213i 0.118754 0.443197i
\(229\) −3.46410 + 6.00000i −0.228914 + 0.396491i −0.957487 0.288478i \(-0.906851\pi\)
0.728572 + 0.684969i \(0.240184\pi\)
\(230\) 0 0
\(231\) −3.00000 15.5885i −0.197386 1.02565i
\(232\) 0 0
\(233\) −20.0764 + 5.37945i −1.31525 + 0.352420i −0.847196 0.531281i \(-0.821711\pi\)
−0.468052 + 0.883701i \(0.655044\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 18.0000 + 10.3923i 1.17170 + 0.676481i
\(237\) 3.53553 + 3.53553i 0.229658 + 0.229658i
\(238\) 0 0
\(239\) 18.0000i 1.16432i −0.813073 0.582162i \(-0.802207\pi\)
0.813073 0.582162i \(-0.197793\pi\)
\(240\) 0 0
\(241\) 16.5000 9.52628i 1.06286 0.613642i 0.136637 0.990621i \(-0.456371\pi\)
0.926222 + 0.376980i \(0.123037\pi\)
\(242\) 0 0
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) 17.3205 1.10883
\(245\) 0 0
\(246\) 0 0
\(247\) −1.79315 6.69213i −0.114095 0.425810i
\(248\) 0 0
\(249\) −5.19615 + 3.00000i −0.329293 + 0.190117i
\(250\) 0 0
\(251\) 20.7846i 1.31191i −0.754799 0.655956i \(-0.772265\pi\)
0.754799 0.655956i \(-0.227735\pi\)
\(252\) −5.27792 0.378937i −0.332478 0.0238708i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 5.79555 1.55291i 0.361517 0.0968681i −0.0734884 0.997296i \(-0.523413\pi\)
0.435005 + 0.900428i \(0.356747\pi\)
\(258\) 0 0
\(259\) 4.33013 + 22.5000i 0.269061 + 1.39808i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −8.06918 + 30.1146i −0.497567 + 1.85694i 0.0175838 + 0.999845i \(0.494403\pi\)
−0.515151 + 0.857100i \(0.672264\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 7.34847 7.34847i 0.449719 0.449719i
\(268\) 6.69213 1.79315i 0.408787 0.109534i
\(269\) 10.3923 + 18.0000i 0.633630 + 1.09748i 0.986804 + 0.161922i \(0.0517692\pi\)
−0.353174 + 0.935558i \(0.614898\pi\)
\(270\) 0 0
\(271\) −27.0000 15.5885i −1.64013 0.946931i −0.980785 0.195094i \(-0.937499\pi\)
−0.659349 0.751837i \(-0.729168\pi\)
\(272\) −16.9706 16.9706i −1.02899 1.02899i
\(273\) −4.76028 + 2.31079i −0.288105 + 0.139855i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −13.3843 3.58630i −0.804182 0.215480i −0.166763 0.985997i \(-0.553331\pi\)
−0.637419 + 0.770517i \(0.719998\pi\)
\(278\) 0 0
\(279\) −5.19615 −0.311086
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −15.4548 4.14110i −0.918693 0.246163i −0.231667 0.972795i \(-0.574418\pi\)
−0.687027 + 0.726632i \(0.741084\pi\)
\(284\) −10.3923 + 6.00000i −0.616670 + 0.356034i
\(285\) 0 0
\(286\) 0 0
\(287\) −1.96902 + 27.4249i −0.116227 + 1.61884i
\(288\) 0 0
\(289\) −16.4545 9.50000i −0.967911 0.558824i
\(290\) 0 0
\(291\) −6.50000 11.2583i −0.381037 0.659975i
\(292\) 1.93185 0.517638i 0.113053 0.0302925i
\(293\) −12.7279 + 12.7279i −0.743573 + 0.743573i −0.973264 0.229691i \(-0.926229\pi\)
0.229691 + 0.973264i \(0.426229\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1.55291 + 5.79555i −0.0901092 + 0.336292i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −9.00000 10.3923i −0.518751 0.599002i
\(302\) 0 0
\(303\) 0 0
\(304\) 6.92820 + 12.0000i 0.397360 + 0.688247i
\(305\) 0 0
\(306\) 0 0
\(307\) −4.94975 4.94975i −0.282497 0.282497i 0.551607 0.834104i \(-0.314015\pi\)
−0.834104 + 0.551607i \(0.814015\pi\)
\(308\) 26.2880 + 17.8028i 1.49790 + 1.01441i
\(309\) 7.00000i 0.398216i
\(310\) 0 0
\(311\) 18.0000 10.3923i 1.02069 0.589294i 0.106384 0.994325i \(-0.466073\pi\)
0.914303 + 0.405032i \(0.132739\pi\)
\(312\) 0 0
\(313\) −4.91756 18.3526i −0.277957 1.03735i −0.953834 0.300335i \(-0.902902\pi\)
0.675877 0.737015i \(-0.263765\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −2.68973 10.0382i −0.151070 0.563801i −0.999410 0.0343491i \(-0.989064\pi\)
0.848340 0.529452i \(-0.177602\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 14.6969 + 14.6969i 0.817760 + 0.817760i
\(324\) 1.73205 + 1.00000i 0.0962250 + 0.0555556i
\(325\) 0 0
\(326\) 0 0
\(327\) −9.65926 + 2.58819i −0.534158 + 0.143127i
\(328\) 0 0
\(329\) 15.5885 3.00000i 0.859419 0.165395i
\(330\) 0 0
\(331\) 2.50000 4.33013i 0.137412 0.238005i −0.789104 0.614260i \(-0.789455\pi\)
0.926516 + 0.376254i \(0.122788\pi\)
\(332\) 3.10583 11.5911i 0.170454 0.636145i
\(333\) 2.24144 8.36516i 0.122830 0.458408i
\(334\) 0 0
\(335\) 0 0
\(336\) 8.00000 6.92820i 0.436436 0.377964i
\(337\) 18.3712 18.3712i 1.00074 1.00074i 0.000741840 1.00000i \(-0.499764\pi\)
1.00000 0.000741840i \(-0.000236135\pi\)
\(338\) 0 0
\(339\) −5.19615 9.00000i −0.282216 0.488813i
\(340\) 0 0
\(341\) 27.0000 + 15.5885i 1.46213 + 0.844162i
\(342\) 0 0
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.0382 2.68973i −0.538879 0.144392i −0.0208935 0.999782i \(-0.506651\pi\)
−0.517985 + 0.855390i \(0.673318\pi\)
\(348\) 0 0
\(349\) −20.7846 −1.11257 −0.556287 0.830990i \(-0.687775\pi\)
−0.556287 + 0.830990i \(0.687775\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) −34.7733 9.31749i −1.85080 0.495920i −0.851215 0.524817i \(-0.824134\pi\)
−0.999582 + 0.0288971i \(0.990800\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 20.7846i 1.10158i
\(357\) 8.90138 13.1440i 0.471111 0.695656i
\(358\) 0 0
\(359\) 15.5885 + 9.00000i 0.822727 + 0.475002i 0.851356 0.524588i \(-0.175781\pi\)
−0.0286287 + 0.999590i \(0.509114\pi\)
\(360\) 0 0
\(361\) 3.50000 + 6.06218i 0.184211 + 0.319062i
\(362\) 0 0
\(363\) 17.6777 17.6777i 0.927837 0.927837i
\(364\) 3.46410 10.0000i 0.181568 0.524142i
\(365\) 0 0
\(366\) 0 0
\(367\) −4.39992 + 16.4207i −0.229674 + 0.857156i 0.750804 + 0.660526i \(0.229666\pi\)
−0.980478 + 0.196630i \(0.937000\pi\)
\(368\) 0 0
\(369\) 5.19615 9.00000i 0.270501 0.468521i
\(370\) 0 0
\(371\) −9.00000 + 25.9808i −0.467257 + 1.34885i
\(372\) 7.34847 7.34847i 0.381000 0.381000i
\(373\) 6.69213 1.79315i 0.346505 0.0928458i −0.0813690 0.996684i \(-0.525929\pi\)
0.427874 + 0.903838i \(0.359263\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 28.0000i 1.43826i −0.694874 0.719132i \(-0.744540\pi\)
0.694874 0.719132i \(-0.255460\pi\)
\(380\) 0 0
\(381\) −10.5000 + 6.06218i −0.537931 + 0.310575i
\(382\) 0 0
\(383\) 6.21166 + 23.1822i 0.317401 + 1.18456i 0.921733 + 0.387824i \(0.126773\pi\)
−0.604333 + 0.796732i \(0.706560\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.34486 + 5.01910i 0.0683632 + 0.255135i
\(388\) 25.1141 + 6.72930i 1.27497 + 0.341628i
\(389\) −5.19615 + 3.00000i −0.263455 + 0.152106i −0.625910 0.779895i \(-0.715272\pi\)
0.362454 + 0.932002i \(0.381939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −7.34847 7.34847i −0.370681 0.370681i
\(394\) 0 0
\(395\) 0 0
\(396\) −6.00000 10.3923i −0.301511 0.522233i
\(397\) 6.76148 1.81173i 0.339349 0.0909283i −0.0851201 0.996371i \(-0.527127\pi\)
0.424469 + 0.905442i \(0.360461\pi\)
\(398\) 0 0
\(399\) −6.92820 + 6.00000i −0.346844 + 0.300376i
\(400\) 0 0
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 0 0
\(403\) 2.68973 10.0382i 0.133985 0.500038i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −36.7423 + 36.7423i −1.82125 + 1.82125i
\(408\) 0 0
\(409\) −3.46410 6.00000i −0.171289 0.296681i 0.767582 0.640951i \(-0.221460\pi\)
−0.938871 + 0.344270i \(0.888126\pi\)
\(410\) 0 0
\(411\) −18.0000 10.3923i −0.887875 0.512615i
\(412\) 9.89949 + 9.89949i 0.487713 + 0.487713i
\(413\) −12.0072 24.7351i −0.590836 1.21714i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.67303 + 0.448288i 0.0819288 + 0.0219527i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 31.0000 1.51085 0.755424 0.655237i \(-0.227431\pi\)
0.755424 + 0.655237i \(0.227431\pi\)
\(422\) 0 0
\(423\) −5.79555 1.55291i −0.281790 0.0755053i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −18.9718 12.8480i −0.918108 0.621760i
\(428\) 0 0
\(429\) −10.3923 6.00000i −0.501745 0.289683i
\(430\) 0 0
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) −3.86370 + 1.03528i −0.185893 + 0.0498097i
\(433\) 20.5061 20.5061i 0.985460 0.985460i −0.0144357 0.999896i \(-0.504595\pi\)
0.999896 + 0.0144357i \(0.00459518\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 10.0000 17.3205i 0.478913 0.829502i
\(437\) 0 0
\(438\) 0 0
\(439\) 4.33013 7.50000i 0.206666 0.357955i −0.743996 0.668184i \(-0.767072\pi\)
0.950662 + 0.310228i \(0.100405\pi\)
\(440\) 0 0
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) 10.0382 2.68973i 0.476929 0.127793i −0.0123433 0.999924i \(-0.503929\pi\)
0.489272 + 0.872131i \(0.337262\pi\)
\(444\) 8.66025 + 15.0000i 0.410997 + 0.711868i
\(445\) 0 0
\(446\) 0 0
\(447\) 8.48528 + 8.48528i 0.401340 + 0.401340i
\(448\) −1.51575 + 21.1117i −0.0716124 + 0.997433i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) −54.0000 + 31.1769i −2.54276 + 1.46806i
\(452\) 20.0764 + 5.37945i 0.944314 + 0.253028i
\(453\) 1.29410 + 4.82963i 0.0608019 + 0.226916i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4.93117 + 18.4034i 0.230670 + 0.860873i 0.980053 + 0.198736i \(0.0636836\pi\)
−0.749383 + 0.662137i \(0.769650\pi\)
\(458\) 0 0
\(459\) −5.19615 + 3.00000i −0.242536 + 0.140028i
\(460\) 0 0
\(461\) 31.1769i 1.45205i −0.687666 0.726027i \(-0.741365\pi\)
0.687666 0.726027i \(-0.258635\pi\)
\(462\) 0 0
\(463\) 1.22474 + 1.22474i 0.0569187 + 0.0569187i 0.734993 0.678074i \(-0.237185\pi\)
−0.678074 + 0.734993i \(0.737185\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.9778 7.76457i 1.34093 0.359302i 0.484152 0.874984i \(-0.339128\pi\)
0.856780 + 0.515683i \(0.172462\pi\)
\(468\) −2.82843 + 2.82843i −0.130744 + 0.130744i
\(469\) −8.66025 3.00000i −0.399893 0.138527i
\(470\) 0 0
\(471\) −3.50000 + 6.06218i −0.161271 + 0.279330i
\(472\) 0 0
\(473\) 8.06918 30.1146i 0.371021 1.38467i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.00000 + 31.1769i 0.275010 + 1.42899i
\(477\) 7.34847 7.34847i 0.336463 0.336463i
\(478\) 0 0
\(479\) −10.3923 18.0000i −0.474837 0.822441i 0.524748 0.851258i \(-0.324159\pi\)
−0.999585 + 0.0288165i \(0.990826\pi\)
\(480\) 0 0
\(481\) 15.0000 + 8.66025i 0.683941 + 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 50.0000i 2.27273i
\(485\) 0 0
\(486\) 0 0
\(487\) 35.1337 + 9.41404i 1.59206 + 0.426591i 0.942632 0.333833i \(-0.108342\pi\)
0.649427 + 0.760424i \(0.275009\pi\)
\(488\) 0 0
\(489\) −8.66025 −0.391630
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 5.37945 + 20.0764i 0.242524 + 0.905114i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 20.7846i 0.933257i
\(497\) 15.8338 + 1.13681i 0.710241 + 0.0509930i
\(498\) 0 0
\(499\) 17.3205 + 10.0000i 0.775372 + 0.447661i 0.834788 0.550572i \(-0.185590\pi\)
−0.0594153 + 0.998233i \(0.518924\pi\)
\(500\) 0 0
\(501\) 6.00000 + 10.3923i 0.268060 + 0.464294i
\(502\) 0 0
\(503\) −25.4558 + 25.4558i −1.13502 + 1.13502i −0.145690 + 0.989330i \(0.546540\pi\)
−0.989330 + 0.145690i \(0.953460\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.32937 8.69333i 0.103451 0.386084i
\(508\) 6.27603 23.4225i 0.278454 1.03920i
\(509\) −5.19615 + 9.00000i −0.230315 + 0.398918i −0.957901 0.287099i \(-0.907309\pi\)
0.727586 + 0.686017i \(0.240642\pi\)
\(510\) 0 0
\(511\) −2.50000 0.866025i −0.110593 0.0383107i
\(512\) 0 0
\(513\) 3.34607 0.896575i 0.147732 0.0395848i
\(514\) 0 0
\(515\) 0 0
\(516\) −9.00000 5.19615i −0.396203 0.228748i
\(517\) 25.4558 + 25.4558i 1.11955 + 1.11955i
\(518\) 0 0
\(519\) 18.0000i 0.790112i
\(520\) 0 0
\(521\) −9.00000 + 5.19615i −0.394297 + 0.227648i −0.684020 0.729463i \(-0.739770\pi\)
0.289723 + 0.957110i \(0.406437\pi\)
\(522\) 0 0
\(523\) 1.81173 + 6.76148i 0.0792216 + 0.295659i 0.994157 0.107941i \(-0.0344256\pi\)
−0.914936 + 0.403599i \(0.867759\pi\)
\(524\) 20.7846 0.907980
\(525\) 0 0
\(526\) 0 0
\(527\) 8.06918 + 30.1146i 0.351499 + 1.31181i
\(528\) 23.1822 + 6.21166i 1.00888 + 0.270328i
\(529\) −19.9186 + 11.5000i −0.866025 + 0.500000i
\(530\) 0 0
\(531\) 10.3923i 0.450988i
\(532\) 1.31268 18.2832i 0.0569118 0.792679i
\(533\) 14.6969 + 14.6969i 0.636595 + 0.636595i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −23.1822 + 6.21166i −1.00039 + 0.268053i
\(538\) 0 0
\(539\) −15.5885 39.0000i −0.671442 1.67985i
\(540\) 0 0
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) 0 0
\(543\) −1.34486 + 5.01910i −0.0577136 + 0.215390i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −22.0454 + 22.0454i −0.942594 + 0.942594i −0.998439 0.0558458i \(-0.982214\pi\)
0.0558458 + 0.998439i \(0.482214\pi\)
\(548\) 40.1528 10.7589i 1.71524 0.459598i
\(549\) 4.33013 + 7.50000i 0.184805 + 0.320092i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 10.9534 + 7.41782i 0.465784 + 0.315438i
\(554\) 0 0
\(555\) 0 0
\(556\) −3.00000 + 1.73205i −0.127228 + 0.0734553i
\(557\) −10.0382 2.68973i −0.425332 0.113967i 0.0398021 0.999208i \(-0.487327\pi\)
−0.465134 + 0.885240i \(0.653994\pi\)
\(558\) 0 0
\(559\) −10.3923 −0.439548
\(560\) 0 0
\(561\) 36.0000 1.51992
\(562\) 0 0
\(563\) −5.79555 1.55291i −0.244254 0.0654475i 0.134615 0.990898i \(-0.457020\pi\)
−0.378869 + 0.925450i \(0.623687\pi\)
\(564\) 10.3923 6.00000i 0.437595 0.252646i
\(565\) 0 0
\(566\) 0 0
\(567\) −1.15539 2.38014i −0.0485220 0.0999565i
\(568\) 0 0
\(569\) 20.7846 + 12.0000i 0.871336 + 0.503066i 0.867792 0.496928i \(-0.165539\pi\)
0.00354413 + 0.999994i \(0.498872\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 23.1822 6.21166i 0.969297 0.259722i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) −1.81173 + 6.76148i −0.0754234 + 0.281484i −0.993329 0.115315i \(-0.963212\pi\)
0.917906 + 0.396799i \(0.129879\pi\)
\(578\) 0 0
\(579\) 7.79423 13.5000i 0.323917 0.561041i
\(580\) 0 0
\(581\) −12.0000 + 10.3923i −0.497844 + 0.431145i
\(582\) 0 0
\(583\) −60.2292 + 16.1384i −2.49444 + 0.668383i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.7279 12.7279i −0.525338 0.525338i 0.393841 0.919179i \(-0.371146\pi\)
−0.919179 + 0.393841i \(0.871146\pi\)
\(588\) −13.9019 + 1.65445i −0.573305 + 0.0682284i
\(589\) 18.0000i 0.741677i
\(590\) 0 0
\(591\) 9.00000 5.19615i 0.370211 0.213741i
\(592\) −33.4607 8.96575i −1.37522 0.368490i
\(593\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −24.0000 −0.983078
\(597\) 4.93117 + 18.4034i 0.201819 + 0.753199i
\(598\) 0 0
\(599\) 10.3923 6.00000i 0.424618 0.245153i −0.272433 0.962175i \(-0.587828\pi\)
0.697051 + 0.717021i \(0.254495\pi\)
\(600\) 0 0
\(601\) 34.6410i 1.41304i 0.707695 + 0.706518i \(0.249735\pi\)
−0.707695 + 0.706518i \(0.750265\pi\)
\(602\) 0 0
\(603\) 2.44949 + 2.44949i 0.0997509 + 0.0997509i
\(604\) −8.66025 5.00000i −0.352381 0.203447i
\(605\) 0 0
\(606\) 0 0
\(607\) 24.1481 6.47048i 0.980143 0.262629i 0.267038 0.963686i \(-0.413955\pi\)
0.713105 + 0.701057i \(0.247288\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) 3.10583 11.5911i 0.125546 0.468543i
\(613\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.34847 + 7.34847i −0.295838 + 0.295838i −0.839381 0.543543i \(-0.817082\pi\)
0.543543 + 0.839381i \(0.317082\pi\)
\(618\) 0 0
\(619\) 23.3827 + 40.5000i 0.939829 + 1.62783i 0.765787 + 0.643094i \(0.222350\pi\)
0.174042 + 0.984738i \(0.444317\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 15.4176 22.7661i 0.617695 0.912105i
\(624\) 8.00000i 0.320256i
\(625\) 0 0
\(626\) 0 0
\(627\) −20.0764 5.37945i −0.801774 0.214835i
\(628\) −3.62347 13.5230i −0.144592 0.539625i
\(629\) −51.9615 −2.07184
\(630\) 0 0
\(631\) −1.00000 −0.0398094 −0.0199047 0.999802i \(-0.506336\pi\)
−0.0199047 + 0.999802i \(0.506336\pi\)
\(632\) 0 0
\(633\) −6.76148 1.81173i −0.268745 0.0720099i
\(634\) 0 0
\(635\) 0 0
\(636\) 20.7846i 0.824163i
\(637\) −11.2122 + 8.38375i −0.444242 + 0.332176i
\(638\) 0 0
\(639\) −5.19615 3.00000i −0.205557 0.118678i
\(640\) 0 0
\(641\) 9.00000 + 15.5885i 0.355479 + 0.615707i 0.987200 0.159489i \(-0.0509845\pi\)
−0.631721 + 0.775196i \(0.717651\pi\)
\(642\) 0 0
\(643\) 20.5061 20.5061i 0.808682 0.808682i −0.175753 0.984434i \(-0.556236\pi\)
0.984434 + 0.175753i \(0.0562359\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.65874 17.3867i 0.183154 0.683540i −0.811864 0.583846i \(-0.801547\pi\)
0.995018 0.0996938i \(-0.0317863\pi\)
\(648\) 0 0
\(649\) 31.1769 54.0000i 1.22380 2.11969i
\(650\) 0 0
\(651\) −13.5000 + 2.59808i −0.529107 + 0.101827i
\(652\) 12.2474 12.2474i 0.479647 0.479647i
\(653\) −10.0382 + 2.68973i −0.392825 + 0.105257i −0.449824 0.893117i \(-0.648513\pi\)
0.0569993 + 0.998374i \(0.481847\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −36.0000 20.7846i −1.40556 0.811503i
\(657\) 0.707107 + 0.707107i 0.0275869 + 0.0275869i
\(658\) 0 0
\(659\) 6.00000i 0.233727i −0.993148 0.116863i \(-0.962716\pi\)
0.993148 0.116863i \(-0.0372840\pi\)
\(660\) 0 0
\(661\) 37.5000 21.6506i 1.45858 0.842112i 0.459639 0.888106i \(-0.347979\pi\)
0.998942 + 0.0459936i \(0.0146454\pi\)
\(662\) 0 0
\(663\) −3.10583 11.5911i −0.120620 0.450161i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −23.1822 6.21166i −0.896947 0.240336i
\(669\) −4.33013 + 2.50000i −0.167412 + 0.0966556i
\(670\) 0 0
\(671\) 51.9615i 2.00595i
\(672\) 0 0
\(673\) −8.57321 8.57321i −0.330473 0.330473i 0.522293 0.852766i \(-0.325077\pi\)
−0.852766 + 0.522293i \(0.825077\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 9.00000 + 15.5885i 0.346154 + 0.599556i
\(677\) 46.3644 12.4233i 1.78193 0.477467i 0.790997 0.611820i \(-0.209562\pi\)
0.990933 + 0.134354i \(0.0428958\pi\)
\(678\) 0 0
\(679\) −22.5167 26.0000i −0.864110 0.997788i
\(680\) 0 0
\(681\) −3.00000 + 5.19615i −0.114960 + 0.199117i
\(682\) 0 0
\(683\) 8.06918 30.1146i 0.308759 1.15230i −0.620903 0.783888i \(-0.713234\pi\)
0.929661 0.368415i \(-0.120099\pi\)
\(684\) −3.46410 + 6.00000i −0.132453 + 0.229416i
\(685\) 0 0
\(686\) 0 0
\(687\) 4.89898 4.89898i 0.186908 0.186908i
\(688\) 20.0764 5.37945i 0.765405 0.205090i
\(689\) 10.3923 + 18.0000i 0.395915 + 0.685745i
\(690\) 0 0
\(691\) 10.5000 + 6.06218i 0.399439 + 0.230616i 0.686242 0.727373i \(-0.259259\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(692\) −25.4558 25.4558i −0.967686 0.967686i
\(693\) −1.13681 + 15.8338i −0.0431839 + 0.601474i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −60.2292 16.1384i −2.28134 0.611284i
\(698\) 0 0
\(699\) 20.7846 0.786146
\(700\) 0 0
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 0 0
\(703\) 28.9778 + 7.76457i 1.09292 + 0.292846i
\(704\) −41.5692 + 24.0000i −1.56670 + 0.904534i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) −14.6969 14.6969i −0.552345 0.552345i
\(709\) 26.8468 + 15.5000i 1.00825 + 0.582115i 0.910679 0.413114i \(-0.135559\pi\)
0.0975728 + 0.995228i \(0.468892\pi\)
\(710\) 0 0
\(711\) −2.50000 4.33013i −0.0937573 0.162392i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 24.0000 41.5692i 0.896922 1.55351i
\(717\) −4.65874 + 17.3867i −0.173984 + 0.649317i
\(718\) 0 0
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) −3.50000 18.1865i −0.130347 0.677302i
\(722\) 0 0
\(723\) −18.4034 + 4.93117i −0.684428 + 0.183392i
\(724\) −5.19615 9.00000i −0.193113 0.334482i
\(725\) 0 0
\(726\) 0 0
\(727\) −28.2843 28.2843i −1.04901 1.04901i −0.998736 0.0502699i \(-0.983992\pi\)
−0.0502699 0.998736i \(-0.516008\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 27.0000 15.5885i 0.998631 0.576560i
\(732\) −16.7303 4.48288i −0.618371 0.165692i
\(733\) 12.1645 + 45.3985i 0.449306 + 1.67683i 0.704310 + 0.709892i \(0.251256\pi\)
−0.255004 + 0.966940i \(0.582077\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.37945 20.0764i −0.198155 0.739523i
\(738\) 0 0
\(739\) 0.866025 0.500000i 0.0318573 0.0183928i −0.483987 0.875075i \(-0.660812\pi\)
0.515844 + 0.856683i \(0.327478\pi\)
\(740\) 0 0
\(741\) 6.92820i 0.254514i
\(742\) 0 0
\(743\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 5.79555 1.55291i 0.212048 0.0568182i
\(748\) −50.9117 + 50.9117i −1.86152 + 1.86152i
\(749\) 0 0
\(750\) 0 0
\(751\) −5.50000 + 9.52628i −0.200698 + 0.347619i −0.948753 0.316017i \(-0.897654\pi\)
0.748056 + 0.663636i \(0.230988\pi\)
\(752\) −6.21166 + 23.1822i −0.226516 + 0.845369i
\(753\) −5.37945 + 20.0764i −0.196038 + 0.731624i
\(754\) 0 0
\(755\) 0 0
\(756\) 5.00000 + 1.73205i 0.181848 + 0.0629941i
\(757\) 20.8207 20.8207i 0.756740 0.756740i −0.218988 0.975728i \(-0.570275\pi\)
0.975728 + 0.218988i \(0.0702755\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 10.3923i −0.652499 0.376721i 0.136914 0.990583i \(-0.456282\pi\)
−0.789413 + 0.613862i \(0.789615\pi\)
\(762\) 0 0
\(763\) −23.8014 + 11.5539i −0.861668 + 0.418281i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −20.0764 5.37945i −0.724916 0.194241i
\(768\) 4.14110 + 15.4548i 0.149429 + 0.557678i
\(769\) −5.19615 −0.187378 −0.0936890 0.995602i \(-0.529866\pi\)
−0.0936890 + 0.995602i \(0.529866\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 8.06918 + 30.1146i 0.290416 + 1.08385i
\(773\) 23.1822 + 6.21166i 0.833806 + 0.223418i 0.650374 0.759614i \(-0.274612\pi\)
0.183433 + 0.983032i \(0.441279\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.64085 22.8541i 0.0588651 0.819884i
\(778\) 0 0
\(779\) 31.1769 + 18.0000i 1.11703 + 0.644917i
\(780\) 0 0
\(781\) 18.0000 + 31.1769i 0.644091 + 1.11560i
\(782\) 0 0
\(783\) 0 0
\(784\) 17.3205 22.0000i 0.618590 0.785714i
\(785\) 0 0
\(786\) 0 0
\(787\) 2.84701 10.6252i 0.101485 0.378747i −0.896438 0.443170i \(-0.853854\pi\)
0.997923 + 0.0644227i \(0.0205206\pi\)
\(788\) −5.37945 + 20.0764i −0.191635 + 0.715192i
\(789\) 15.5885 27.0000i 0.554964 0.961225i
\(790\) 0 0
\(791\) −18.0000 20.7846i −0.640006 0.739016i
\(792\) 0 0
\(793\) −16.7303 + 4.48288i −0.594111 + 0.159192i
\(794\) 0 0
\(795\) 0 0
\(796\) −33.0000 19.0526i −1.16965 0.675300i
\(797\) −8.48528