Properties

Label 525.2.bc.a.82.1
Level 525
Weight 2
Character 525.82
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 82.1
Root \(0.965926 + 0.258819i\)
Character \(\chi\) = 525.82
Dual form 525.2.bc.a.493.1

$q$-expansion

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

Character values

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

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

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 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) −0.258819 + 0.965926i −0.149429 + 0.557678i
\(4\) −1.73205 + 1.00000i −0.866025 + 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.189469 2.63896i 0.0716124 0.997433i
\(8\) 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 \(-0.526448\pi\)
\(12\) −0.517638 1.93185i −0.149429 0.557678i
\(13\) 1.41421 + 1.41421i 0.392232 + 0.392232i 0.875482 0.483250i \(-0.160544\pi\)
−0.483250 + 0.875482i \(0.660544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 5.79555 + 1.55291i 1.40563 + 0.376637i 0.880363 0.474301i \(-0.157299\pi\)
0.525266 + 0.850938i \(0.323966\pi\)
\(18\) 0 0
\(19\) 1.73205 3.00000i 0.397360 0.688247i −0.596040 0.802955i \(-0.703260\pi\)
0.993399 + 0.114708i \(0.0365932\pi\)
\(20\) 0 0
\(21\) 2.50000 + 0.866025i 0.545545 + 0.188982i
\(22\) 0 0
\(23\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 2.31079 + 4.76028i 0.436698 + 0.899608i
\(29\) 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
\(33\) 5.79555 1.55291i 1.00888 0.270328i
\(34\) 0 0
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 8.36516 2.24144i 1.37522 0.368490i 0.505840 0.862627i \(-0.331183\pi\)
0.869384 + 0.494137i \(0.164516\pi\)
\(38\) 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 −0.369082 0.929397i \(-0.620328\pi\)
0.929397 + 0.369082i \(0.120328\pi\)
\(44\) 10.3923 + 6.00000i 1.56670 + 0.904534i
\(45\) 0 0
\(46\) 0 0
\(47\) −1.55291 5.79555i −0.226516 0.845369i −0.981792 0.189961i \(-0.939164\pi\)
0.755276 0.655407i \(-0.227503\pi\)
\(48\) 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
\(52\) −3.86370 1.03528i −0.535799 0.143567i
\(53\) −10.0382 2.68973i −1.37885 0.369462i −0.508148 0.861270i \(-0.669670\pi\)
−0.870704 + 0.491807i \(0.836336\pi\)
\(54\) 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 \(-0.930171\pi\)
0.299552 0.954080i \(-0.403163\pi\)
\(60\) 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
\(63\) −1.48356 + 2.19067i −0.186911 + 0.275999i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.896575 + 3.34607i −0.109534 + 0.408787i −0.998820 0.0485648i \(-0.984535\pi\)
0.889286 + 0.457352i \(0.151202\pi\)
\(68\) −11.5911 + 3.10583i −1.40563 + 0.376637i
\(69\) 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
\(73\) 0.258819 0.965926i 0.0302925 0.113053i −0.949124 0.314902i \(-0.898028\pi\)
0.979417 + 0.201849i \(0.0646950\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 6.92820i 0.794719i
\(77\) −14.2808 + 6.93237i −1.62745 + 0.790017i
\(78\) 0 0
\(79\) 4.33013 + 2.50000i 0.487177 + 0.281272i 0.723403 0.690426i \(-0.242577\pi\)
−0.236225 + 0.971698i \(0.575910\pi\)
\(80\) 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 \(-0.356810\pi\)
−0.900515 + 0.434825i \(0.856810\pi\)
\(84\) −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 \(-0.647659\pi\)
0.998218 0.0596775i \(-0.0190072\pi\)
\(90\) 0 0
\(91\) 4.00000 3.46410i 0.419314 0.363137i
\(92\) 0 0
\(93\) −1.34486 5.01910i −0.139456 0.520456i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.19239 + 9.19239i −0.933346 + 0.933346i −0.997913 0.0645677i \(-0.979433\pi\)
0.0645677 + 0.997913i \(0.479433\pi\)
\(98\) 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
\(103\) 6.76148 1.81173i 0.666228 0.178515i 0.0901732 0.995926i \(-0.471258\pi\)
0.576055 + 0.817411i \(0.304591\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(108\) −0.517638 + 1.93185i −0.0498097 + 0.185893i
\(109\) −8.66025 + 5.00000i −0.829502 + 0.478913i −0.853682 0.520794i \(-0.825636\pi\)
0.0241802 + 0.999708i \(0.492302\pi\)
\(110\) 0 0
\(111\) 8.66025i 0.821995i
\(112\) −8.76268 5.93426i −0.827996 0.560734i
\(113\) 7.34847 7.34847i 0.691286 0.691286i −0.271229 0.962515i \(-0.587430\pi\)
0.962515 + 0.271229i \(0.0874301\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.517638 1.93185i −0.0478557 0.178600i
\(118\) 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
\(123\) 10.0382 + 2.68973i 0.905114 + 0.242524i
\(124\) 5.19615 9.00000i 0.466628 0.808224i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.57321 + 8.57321i 0.760750 + 0.760750i 0.976458 0.215708i \(-0.0692060\pi\)
−0.215708 + 0.976458i \(0.569206\pi\)
\(128\) 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
\(133\) −7.58871 5.13922i −0.658024 0.445627i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.37945 + 20.0764i −0.459598 + 1.71524i 0.214610 + 0.976700i \(0.431152\pi\)
−0.674207 + 0.738542i \(0.735515\pi\)
\(138\) 0 0
\(139\) 1.73205 0.146911 0.0734553 0.997299i \(-0.476597\pi\)
0.0734553 + 0.997299i \(0.476597\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 3.10583 11.5911i 0.259722 0.969297i
\(144\) −3.46410 + 2.00000i −0.288675 + 0.166667i
\(145\) 0 0
\(146\) 0 0
\(147\) 2.75908 6.43331i 0.227565 0.530611i
\(148\) −12.2474 + 12.2474i −1.00673 + 1.00673i
\(149\) 10.3923 + 6.00000i 0.851371 + 0.491539i 0.861113 0.508413i \(-0.169768\pi\)
−0.00974235 + 0.999953i \(0.503101\pi\)
\(150\) 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
\(157\) 6.76148 + 1.81173i 0.539625 + 0.144592i 0.518329 0.855181i \(-0.326554\pi\)
0.0212957 + 0.999773i \(0.493221\pi\)
\(158\) 0 0
\(159\) 5.19615 9.00000i 0.412082 0.713746i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.24144 8.36516i −0.175563 0.655210i −0.996455 0.0841267i \(-0.973190\pi\)
0.820892 0.571083i \(-0.193477\pi\)
\(164\) 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 \(-0.596308\pi\)
0.954577 + 0.297966i \(0.0963081\pi\)
\(168\) 0 0
\(169\) 9.00000i 0.692308i
\(170\) 0 0
\(171\) −3.00000 + 1.73205i −0.229416 + 0.132453i
\(172\) −2.68973 + 10.0382i −0.205090 + 0.765405i
\(173\) −17.3867 + 4.65874i −1.32188 + 0.354198i −0.849683 0.527294i \(-0.823207\pi\)
−0.472200 + 0.881491i \(0.656540\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −24.0000 −1.80907
\(177\) 10.0382 2.68973i 0.754517 0.202172i
\(178\) 0 0
\(179\) −20.7846 + 12.0000i −1.55351 + 0.896922i −0.555663 + 0.831408i \(0.687536\pi\)
−0.997852 + 0.0655145i \(0.979131\pi\)
\(180\) 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
\(187\) −9.31749 34.7733i −0.681362 2.54288i
\(188\) 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 \(0.166667\pi\)
\(192\) −7.72741 2.07055i −0.557678 0.149429i
\(193\) 15.0573 + 4.03459i 1.08385 + 0.290416i 0.756171 0.654374i \(-0.227068\pi\)
0.327677 + 0.944790i \(0.393734\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 13.0000 5.19615i 0.928571 0.371154i
\(197\) −7.34847 7.34847i −0.523557 0.523557i 0.395087 0.918644i \(-0.370714\pi\)
−0.918644 + 0.395087i \(0.870714\pi\)
\(198\) 0 0
\(199\) 9.52628 + 16.5000i 0.675300 + 1.16965i 0.976381 + 0.216055i \(0.0693192\pi\)
−0.301081 + 0.953599i \(0.597347\pi\)
\(200\) 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
\(208\) 7.72741 2.07055i 0.535799 0.143567i
\(209\) −20.7846 −1.43770
\(210\) 0 0
\(211\) 7.00000 0.481900 0.240950 0.970538i \(-0.422541\pi\)
0.240950 + 0.970538i \(0.422541\pi\)
\(212\) 20.0764 5.37945i 1.37885 0.369462i
\(213\) 1.55291 5.79555i 0.106404 0.397105i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 6.00361 + 12.3676i 0.407551 + 0.839565i
\(218\) 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 \(-0.303541\pi\)
−0.815506 + 0.578749i \(0.803541\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.79555 + 1.55291i 0.384664 + 0.103071i 0.445969 0.895049i \(-0.352859\pi\)
−0.0613041 + 0.998119i \(0.519526\pi\)
\(228\) −6.69213 1.79315i −0.443197 0.118754i
\(229\) 3.46410 6.00000i 0.228914 0.396491i −0.728572 0.684969i \(-0.759816\pi\)
0.957487 + 0.288478i \(0.0931491\pi\)
\(230\) 0 0
\(231\) −3.00000 15.5885i −0.197386 1.02565i
\(232\) 0 0
\(233\) 5.37945 + 20.0764i 0.352420 + 1.31525i 0.883701 + 0.468052i \(0.155044\pi\)
−0.531281 + 0.847196i \(0.678289\pi\)
\(234\) 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 \(0.197793\pi\)
−0.813073 + 0.582162i \(0.802207\pi\)
\(240\) 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
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) −17.3205 −1.10883
\(245\) 0 0
\(246\) 0 0
\(247\) 6.69213 1.79315i 0.425810 0.114095i
\(248\) 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 \(-0.227735\pi\)
\(252\) 0.378937 5.27792i 0.0238708 0.332478i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 1.55291 + 5.79555i 0.0968681 + 0.361517i 0.997296 0.0734884i \(-0.0234132\pi\)
−0.900428 + 0.435005i \(0.856747\pi\)
\(258\) 0 0
\(259\) −4.33013 22.5000i −0.269061 1.39808i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 30.1146 + 8.06918i 1.85694 + 0.497567i 0.999845 0.0175838i \(-0.00559740\pi\)
0.857100 + 0.515151i \(0.172264\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 7.34847 + 7.34847i 0.449719 + 0.449719i
\(268\) −1.79315 6.69213i −0.109534 0.408787i
\(269\) −10.3923 18.0000i −0.633630 1.09748i −0.986804 0.161922i \(-0.948231\pi\)
0.353174 0.935558i \(-0.385102\pi\)
\(270\) 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
\(273\) 2.31079 + 4.76028i 0.139855 + 0.288105i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 3.58630 13.3843i 0.215480 0.804182i −0.770517 0.637419i \(-0.780002\pi\)
0.985997 0.166763i \(-0.0533314\pi\)
\(278\) 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
\(283\) −4.14110 + 15.4548i −0.246163 + 0.918693i 0.726632 + 0.687027i \(0.241084\pi\)
−0.972795 + 0.231667i \(0.925582\pi\)
\(284\) 10.3923 6.00000i 0.616670 0.356034i
\(285\) 0 0
\(286\) 0 0
\(287\) −27.4249 1.96902i −1.61884 0.116227i
\(288\) 0 0
\(289\) 16.4545 + 9.50000i 0.967911 + 0.558824i
\(290\) 0 0
\(291\) −6.50000 11.2583i −0.381037 0.659975i
\(292\) 0.517638 + 1.93185i 0.0302925 + 0.113053i
\(293\) 12.7279 + 12.7279i 0.743573 + 0.743573i 0.973264 0.229691i \(-0.0737714\pi\)
−0.229691 + 0.973264i \(0.573771\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.79555 1.55291i −0.336292 0.0901092i
\(298\) 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 \(-0.685985\pi\)
0.834104 + 0.551607i \(0.185985\pi\)
\(308\) 17.8028 26.2880i 1.01441 1.49790i
\(309\) 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
\(313\) −18.3526 + 4.91756i −1.03735 + 0.277957i −0.737015 0.675877i \(-0.763765\pi\)
−0.300335 + 0.953834i \(0.597098\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 10.0382 2.68973i 0.563801 0.151070i 0.0343491 0.999410i \(-0.489064\pi\)
0.529452 + 0.848340i \(0.322398\pi\)
\(318\) 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
\(327\) −2.58819 9.65926i −0.143127 0.534158i
\(328\) 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 \(0.122788\pi\)
\(332\) 11.5911 + 3.10583i 0.636145 + 0.170454i
\(333\) −8.36516 2.24144i −0.458408 0.122830i
\(334\) 0 0
\(335\) 0 0
\(336\) 8.00000 6.92820i 0.436436 0.377964i
\(337\) 18.3712 + 18.3712i 1.00074 + 1.00074i 1.00000 0.000741840i \(0.000236135\pi\)
0.000741840 1.00000i \(0.499764\pi\)
\(338\) 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
\(343\) −3.95164 + 18.0938i −0.213368 + 0.976972i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.68973 10.0382i 0.144392 0.538879i −0.855390 0.517985i \(-0.826682\pi\)
0.999782 0.0208935i \(-0.00665108\pi\)
\(348\) 0 0
\(349\) 20.7846 1.11257 0.556287 0.830990i \(-0.312225\pi\)
0.556287 + 0.830990i \(0.312225\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) −9.31749 + 34.7733i −0.495920 + 1.85080i 0.0288971 + 0.999582i \(0.490800\pi\)
−0.524817 + 0.851215i \(0.675866\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 20.7846i 1.10158i
\(357\) 13.1440 + 8.90138i 0.695656 + 0.471111i
\(358\) 0 0
\(359\) −15.5885 9.00000i −0.822727 0.475002i 0.0286287 0.999590i \(-0.490886\pi\)
−0.851356 + 0.524588i \(0.824219\pi\)
\(360\) 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
\(367\) −16.4207 4.39992i −0.857156 0.229674i −0.196630 0.980478i \(-0.563000\pi\)
−0.660526 + 0.750804i \(0.729666\pi\)
\(368\) 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
\(373\) −1.79315 6.69213i −0.0928458 0.346505i 0.903838 0.427874i \(-0.140737\pi\)
−0.996684 + 0.0813690i \(0.974071\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 28.0000i 1.43826i 0.694874 + 0.719132i \(0.255460\pi\)
−0.694874 + 0.719132i \(0.744540\pi\)
\(380\) 0 0
\(381\) −10.5000 + 6.06218i −0.537931 + 0.310575i
\(382\) 0 0
\(383\) 23.1822 6.21166i 1.18456 0.317401i 0.387824 0.921733i \(-0.373227\pi\)
0.796732 + 0.604333i \(0.206560\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.01910 + 1.34486i −0.255135 + 0.0683632i
\(388\) 6.72930 25.1141i 0.341628 1.27497i
\(389\) 5.19615 3.00000i 0.263455 0.152106i −0.362454 0.932002i \(-0.618061\pi\)
0.625910 + 0.779895i \(0.284728\pi\)
\(390\) 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
\(397\) 1.81173 + 6.76148i 0.0909283 + 0.339349i 0.996371 0.0851201i \(-0.0271274\pi\)
−0.905442 + 0.424469i \(0.860461\pi\)
\(398\) 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
\(403\) −10.0382 2.68973i −0.500038 0.133985i
\(404\) 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 0.938871 0.344270i \(-0.111874\pi\)
−0.767582 + 0.640951i \(0.778540\pi\)
\(410\) 0 0
\(411\) −18.0000 10.3923i −0.887875 0.512615i
\(412\) −9.89949 + 9.89949i −0.487713 + 0.487713i
\(413\) −24.7351 + 12.0072i −1.21714 + 0.590836i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.448288 + 1.67303i −0.0219527 + 0.0819288i
\(418\) 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
\(423\) −1.55291 + 5.79555i −0.0755053 + 0.281790i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 12.8480 18.9718i 0.621760 0.918108i
\(428\) 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 \(0.740007\pi\)
\(432\) −1.03528 3.86370i −0.0498097 0.185893i
\(433\) −20.5061 20.5061i −0.985460 0.985460i 0.0144357 0.999896i \(-0.495405\pi\)
−0.999896 + 0.0144357i \(0.995405\pi\)
\(434\) 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 −0.950662 0.310228i \(-0.899595\pi\)
0.743996 + 0.668184i \(0.232928\pi\)
\(440\) 0 0
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) −2.68973 10.0382i −0.127793 0.476929i 0.872131 0.489272i \(-0.162738\pi\)
−0.999924 + 0.0123433i \(0.996071\pi\)
\(444\) −8.66025 15.0000i −0.410997 0.711868i
\(445\) 0 0
\(446\) 0 0
\(447\) −8.48528 + 8.48528i −0.401340 + 0.401340i
\(448\) 21.1117 + 1.51575i 0.997433 + 0.0716124i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) −54.0000 + 31.1769i −2.54276 + 1.46806i
\(452\) −5.37945 + 20.0764i −0.253028 + 0.944314i
\(453\) 4.82963 1.29410i 0.226916 0.0608019i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.4034 + 4.93117i −0.860873 + 0.230670i −0.662137 0.749383i \(-0.730350\pi\)
−0.198736 + 0.980053i \(0.563684\pi\)
\(458\) 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 −0.678074 0.734993i \(-0.737185\pi\)
0.734993 + 0.678074i \(0.237185\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.76457 + 28.9778i 0.359302 + 1.34093i 0.874984 + 0.484152i \(0.160872\pi\)
−0.515683 + 0.856780i \(0.672462\pi\)
\(468\) 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
\(473\) −30.1146 8.06918i −1.38467 0.371021i
\(474\) 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 0.999585 0.0288165i \(-0.00917385\pi\)
−0.524748 + 0.851258i \(0.675841\pi\)
\(480\) 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
\(487\) −9.41404 + 35.1337i −0.426591 + 1.59206i 0.333833 + 0.942632i \(0.391658\pi\)
−0.760424 + 0.649427i \(0.775009\pi\)
\(488\) 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 \(0.412720\pi\)
\(492\) −20.0764 + 5.37945i −0.905114 + 0.242524i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 20.7846i 0.933257i
\(497\) −1.13681 + 15.8338i −0.0509930 + 0.710241i
\(498\) 0 0
\(499\) −17.3205 10.0000i −0.775372 0.447661i 0.0594153 0.998233i \(-0.481076\pi\)
−0.834788 + 0.550572i \(0.814410\pi\)
\(500\) 0 0
\(501\) 6.00000 + 10.3923i 0.268060 + 0.464294i
\(502\) 0 0
\(503\) 25.4558 + 25.4558i 1.13502 + 1.13502i 0.989330 + 0.145690i \(0.0465401\pi\)
0.145690 + 0.989330i \(0.453460\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 8.69333 + 2.32937i 0.386084 + 0.103451i
\(508\) −23.4225 6.27603i −1.03920 0.278454i
\(509\) 5.19615 9.00000i 0.230315 0.398918i −0.727586 0.686017i \(-0.759358\pi\)
0.957901 + 0.287099i \(0.0926909\pi\)
\(510\) 0 0
\(511\) −2.50000 0.866025i −0.110593 0.0383107i
\(512\) 0 0
\(513\) −0.896575 3.34607i −0.0395848 0.147732i
\(514\) 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
\(523\) 6.76148 1.81173i 0.295659 0.0792216i −0.107941 0.994157i \(-0.534426\pi\)
0.403599 + 0.914936i \(0.367759\pi\)
\(524\) −20.7846 −0.907980
\(525\) 0 0
\(526\) 0 0
\(527\) −30.1146 + 8.06918i −1.31181 + 0.351499i
\(528\) 6.21166 23.1822i 0.270328 1.00888i
\(529\) 19.9186 11.5000i 0.866025 0.500000i
\(530\) 0 0
\(531\) 10.3923i 0.450988i
\(532\) 18.2832 + 1.31268i 0.792679 + 0.0569118i
\(533\) 14.6969 14.6969i 0.636595 0.636595i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −6.21166 23.1822i −0.268053 1.00039i
\(538\) 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
\(543\) 5.01910 + 1.34486i 0.215390 + 0.0577136i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −22.0454 22.0454i −0.942594 0.942594i 0.0558458 0.998439i \(-0.482214\pi\)
−0.998439 + 0.0558458i \(0.982214\pi\)
\(548\) −10.7589 40.1528i −0.459598 1.71524i
\(549\) −4.33013 7.50000i −0.184805 0.320092i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 7.41782 10.9534i 0.315438 0.465784i
\(554\) 0 0
\(555\) 0 0
\(556\) −3.00000 + 1.73205i −0.127228 + 0.0734553i
\(557\) 2.68973 10.0382i 0.113967 0.425332i −0.885240 0.465134i \(-0.846006\pi\)
0.999208 + 0.0398021i \(0.0126728\pi\)
\(558\) 0 0
\(559\) 10.3923 0.439548
\(560\) 0 0
\(561\) 36.0000 1.51992
\(562\) 0 0
\(563\) −1.55291 + 5.79555i −0.0654475 + 0.244254i −0.990898 0.134615i \(-0.957020\pi\)
0.925450 + 0.378869i \(0.123687\pi\)
\(564\) −10.3923 + 6.00000i −0.437595 + 0.252646i
\(565\) 0 0
\(566\) 0 0
\(567\) 2.38014 1.15539i 0.0999565 0.0485220i
\(568\) 0 0
\(569\) −20.7846 12.0000i −0.871336 0.503066i −0.00354413 0.999994i \(-0.501128\pi\)
−0.867792 + 0.496928i \(0.834461\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 6.21166 + 23.1822i 0.259722 + 0.969297i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) −6.76148 1.81173i −0.281484 0.0754234i 0.115315 0.993329i \(-0.463212\pi\)
−0.396799 + 0.917906i \(0.629879\pi\)
\(578\) 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
\(583\) 16.1384 + 60.2292i 0.668383 + 2.49444i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.7279 12.7279i 0.525338 0.525338i −0.393841 0.919179i \(-0.628854\pi\)
0.919179 + 0.393841i \(0.128854\pi\)
\(588\) 1.65445 + 13.9019i 0.0682284 + 0.573305i
\(589\) 18.0000i 0.741677i
\(590\) 0 0
\(591\) 9.00000 5.19615i 0.370211 0.213741i
\(592\) 8.96575 33.4607i 0.368490 1.37522i
\(593\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −24.0000 −0.983078
\(597\) −18.4034 + 4.93117i −0.753199 + 0.201819i
\(598\) 0 0
\(599\) −10.3923 + 6.00000i −0.424618 + 0.245153i −0.697051 0.717021i \(-0.745505\pi\)
0.272433 + 0.962175i \(0.412172\pi\)
\(600\) 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
\(607\) 6.47048 + 24.1481i 0.262629 + 0.980143i 0.963686 + 0.267038i \(0.0860450\pi\)
−0.701057 + 0.713105i \(0.747288\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) 11.5911 + 3.10583i 0.468543 + 0.125546i
\(613\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.34847 7.34847i −0.295838 0.295838i 0.543543 0.839381i \(-0.317082\pi\)
−0.839381 + 0.543543i \(0.817082\pi\)
\(618\) 0 0
\(619\) −23.3827 40.5000i −0.939829 1.62783i −0.765787 0.643094i \(-0.777650\pi\)
−0.174042 0.984738i \(-0.555683\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −22.7661 15.4176i −0.912105 0.617695i
\(624\) 8.00000i 0.320256i
\(625\) 0 0
\(626\) 0 0
\(627\) 5.37945 20.0764i 0.214835 0.801774i
\(628\) −13.5230 + 3.62347i −0.539625 + 0.144592i
\(629\) 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
\(633\) −1.81173 + 6.76148i −0.0720099 + 0.268745i
\(634\) 0 0
\(635\) 0 0
\(636\) 20.7846i 0.824163i
\(637\) −8.38375 11.2122i −0.332176 0.444242i
\(638\) 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 \(-0.443764\pi\)
−0.984434 + 0.175753i \(0.943764\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.3867 + 4.65874i 0.683540 + 0.183154i 0.583846 0.811864i \(-0.301547\pi\)
0.0996938 + 0.995018i \(0.468214\pi\)
\(648\) 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
\(653\) 2.68973 + 10.0382i 0.105257 + 0.392825i 0.998374 0.0569993i \(-0.0181533\pi\)
−0.893117 + 0.449824i \(0.851487\pi\)
\(654\) 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 \(0.0372840\pi\)
−0.993148 + 0.116863i \(0.962716\pi\)
\(660\) 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
\(663\) −11.5911 + 3.10583i −0.450161 + 0.120620i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −6.21166 + 23.1822i −0.240336 + 0.896947i
\(669\) 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 −0.852766 0.522293i \(-0.825077\pi\)
0.522293 + 0.852766i \(0.325077\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 9.00000 + 15.5885i 0.346154 + 0.599556i
\(677\) 12.4233 + 46.3644i 0.477467 + 1.78193i 0.611820 + 0.790997i \(0.290438\pi\)
−0.134354 + 0.990933i \(0.542896\pi\)
\(678\) 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
\(683\) −30.1146 8.06918i −1.15230 0.308759i −0.368415 0.929661i \(-0.620099\pi\)
−0.783888 + 0.620903i \(0.786766\pi\)
\(684\) 3.46410 6.00000i 0.132453 0.229416i
\(685\) 0 0
\(686\) 0 0
\(687\) 4.89898 + 4.89898i 0.186908 + 0.186908i
\(688\) −5.37945 20.0764i −0.205090 0.765405i
\(689\) −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
\(693\) 15.8338 + 1.13681i 0.601474 + 0.0431839i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 16.1384 60.2292i 0.611284 2.28134i
\(698\) 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
\(703\) 7.76457 28.9778i 0.292846 1.09292i
\(704\) 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 −0.0975728 0.995228i \(-0.531108\pi\)
−0.910679 + 0.413114i \(0.864441\pi\)
\(710\) 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
\(717\) −17.3867 4.65874i −0.649317 0.173984i
\(718\) 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
\(723\) 4.93117 + 18.4034i 0.183392 + 0.684428i
\(724\) 5.19615 + 9.00000i 0.193113 + 0.334482i
\(725\) 0 0
\(726\) 0 0
\(727\) 28.2843 28.2843i 1.04901 1.04901i 0.0502699 0.998736i \(-0.483992\pi\)
0.998736 0.0502699i \(-0.0160081\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 27.0000 15.5885i 0.998631 0.576560i
\(732\) 4.48288 16.7303i 0.165692 0.618371i
\(733\) 45.3985 12.1645i 1.67683 0.449306i 0.709892 0.704310i \(-0.248744\pi\)
0.966940 + 0.255004i \(0.0820769\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 20.0764 5.37945i 0.739523 0.198155i
\(738\) 0 0
\(739\) −0.866025 + 0.500000i −0.0318573 + 0.0183928i −0.515844 0.856683i \(-0.672522\pi\)
0.483987 + 0.875075i \(0.339188\pi\)
\(740\) 0 0
\(741\) 6.92820i 0.254514i
\(742\) 0 0
\(743\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.55291 + 5.79555i 0.0568182 + 0.212048i
\(748\) 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 \(0.230988\pi\)
\(752\) −23.1822 6.21166i −0.845369 0.226516i
\(753\) 20.0764 + 5.37945i 0.731624 + 0.196038i
\(754\) 0 0
\(755\) 0 0
\(756\) 5.00000 + 1.73205i 0.181848 + 0.0629941i
\(757\) 20.8207 + 20.8207i 0.756740 + 0.756740i 0.975728 0.218988i \(-0.0702755\pi\)
−0.218988 + 0.975728i \(0.570275\pi\)
\(758\) 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
\(763\) 11.5539 + 23.8014i 0.418281 + 0.861668i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.37945 20.0764i 0.194241 0.724916i
\(768\) 15.4548 4.14110i 0.557678 0.149429i
\(769\) 5.19615 0.187378 0.0936890 0.995602i \(-0.470134\pi\)
0.0936890 + 0.995602i \(0.470134\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) −30.1146 + 8.06918i −1.08385 + 0.290416i
\(773\) 6.21166 23.1822i 0.223418 0.833806i −0.759614 0.650374i \(-0.774612\pi\)
0.983032 0.183433i \(-0.0587210\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 22.8541 + 1.64085i 0.819884 + 0.0588651i
\(778\) 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
\(787\) 10.6252 + 2.84701i 0.378747 + 0.101485i 0.443170 0.896438i \(-0.353854\pi\)
−0.0644227 + 0.997923i \(0.520521\pi\)
\(788\) 20.0764 + 5.37945i 0.715192 + 0.191635i
\(789\) −15.5885 + 27.0000i −0.554964 + 0.961225i
\(790\) 0 0
\(791\) −18.0000 20.7846i −0.640006 0.739016i
\(792\) 0 0
\(793\) 4.48288 + 16.7303i 0.159192 + 0.594111i
\(794\) 0 0
\(795\) 0 0
\(796\) −33.0000 19.0526i −1.16965 0.675300i
\(797\) 8.48528 8.48528i 0.300564 0.300564i