Properties

Label 1134.2.t.a.593.1
Level $1134$
Weight $2$
Character 1134.593
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 593.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.593
Dual form 1134.2.t.a.1025.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +3.00000i q^{11} +(3.00000 - 1.73205i) q^{13} +(2.59808 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{22} -5.00000 q^{25} +(-1.73205 + 3.00000i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(7.79423 + 4.50000i) q^{29} +(1.50000 + 0.866025i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.00000 - 6.92820i) q^{37} +(5.19615 + 9.00000i) q^{41} +(-2.00000 + 3.46410i) q^{43} +(2.59808 + 1.50000i) q^{44} +(5.19615 + 9.00000i) q^{47} +(5.50000 + 4.33013i) q^{49} +(4.33013 - 2.50000i) q^{50} -3.46410i q^{52} +(-5.19615 + 3.00000i) q^{53} +(0.866025 - 2.50000i) q^{56} -9.00000 q^{58} +(2.59808 - 4.50000i) q^{59} +(12.0000 - 6.92820i) q^{61} -1.73205 q^{62} -1.00000 q^{64} +(-1.00000 + 1.73205i) q^{67} -12.0000i q^{71} +(4.50000 - 2.59808i) q^{73} +8.00000i q^{74} +(2.59808 - 7.50000i) q^{77} +(6.50000 + 11.2583i) q^{79} +(-9.00000 - 5.19615i) q^{82} +(-2.59808 + 4.50000i) q^{83} -4.00000i q^{86} -3.00000 q^{88} +(-5.19615 + 9.00000i) q^{89} +(-9.00000 + 1.73205i) q^{91} +(-9.00000 - 5.19615i) q^{94} +(7.50000 + 4.33013i) q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 10 q^{7} + O(q^{10}) \) \( 4 q + 2 q^{4} - 10 q^{7} + 12 q^{13} - 2 q^{16} - 6 q^{22} - 20 q^{25} - 8 q^{28} + 6 q^{31} + 16 q^{37} - 8 q^{43} + 22 q^{49} - 36 q^{58} + 48 q^{61} - 4 q^{64} - 4 q^{67} + 18 q^{73} + 26 q^{79} - 36 q^{82} - 12 q^{88} - 36 q^{91} - 36 q^{94} + 30 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 3.00000i 0.904534i 0.891883 + 0.452267i \(0.149385\pi\)
−0.891883 + 0.452267i \(0.850615\pi\)
\(12\) 0 0
\(13\) 3.00000 1.73205i 0.832050 0.480384i −0.0225039 0.999747i \(-0.507164\pi\)
0.854554 + 0.519362i \(0.173830\pi\)
\(14\) 2.59808 0.500000i 0.694365 0.133631i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) −1.73205 + 3.00000i −0.339683 + 0.588348i
\(27\) 0 0
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) 7.79423 + 4.50000i 1.44735 + 0.835629i 0.998323 0.0578882i \(-0.0184367\pi\)
0.449029 + 0.893517i \(0.351770\pi\)
\(30\) 0 0
\(31\) 1.50000 + 0.866025i 0.269408 + 0.155543i 0.628619 0.777714i \(-0.283621\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.19615 + 9.00000i 0.811503 + 1.40556i 0.911812 + 0.410608i \(0.134683\pi\)
−0.100309 + 0.994956i \(0.531983\pi\)
\(42\) 0 0
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) 2.59808 + 1.50000i 0.391675 + 0.226134i
\(45\) 0 0
\(46\) 0 0
\(47\) 5.19615 + 9.00000i 0.757937 + 1.31278i 0.943901 + 0.330228i \(0.107126\pi\)
−0.185964 + 0.982556i \(0.559541\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 4.33013 2.50000i 0.612372 0.353553i
\(51\) 0 0
\(52\) 3.46410i 0.480384i
\(53\) −5.19615 + 3.00000i −0.713746 + 0.412082i −0.812447 0.583036i \(-0.801865\pi\)
0.0987002 + 0.995117i \(0.468532\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.866025 2.50000i 0.115728 0.334077i
\(57\) 0 0
\(58\) −9.00000 −1.18176
\(59\) 2.59808 4.50000i 0.338241 0.585850i −0.645861 0.763455i \(-0.723502\pi\)
0.984102 + 0.177605i \(0.0568349\pi\)
\(60\) 0 0
\(61\) 12.0000 6.92820i 1.53644 0.887066i 0.537400 0.843328i \(-0.319407\pi\)
0.999043 0.0437377i \(-0.0139266\pi\)
\(62\) −1.73205 −0.219971
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) 0 0
\(73\) 4.50000 2.59808i 0.526685 0.304082i −0.212980 0.977056i \(-0.568317\pi\)
0.739666 + 0.672975i \(0.234984\pi\)
\(74\) 8.00000i 0.929981i
\(75\) 0 0
\(76\) 0 0
\(77\) 2.59808 7.50000i 0.296078 0.854704i
\(78\) 0 0
\(79\) 6.50000 + 11.2583i 0.731307 + 1.26666i 0.956325 + 0.292306i \(0.0944227\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −9.00000 5.19615i −0.993884 0.573819i
\(83\) −2.59808 + 4.50000i −0.285176 + 0.493939i −0.972652 0.232268i \(-0.925385\pi\)
0.687476 + 0.726207i \(0.258719\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.00000i 0.431331i
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) −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
\(91\) −9.00000 + 1.73205i −0.943456 + 0.181568i
\(92\) 0 0
\(93\) 0 0
\(94\) −9.00000 5.19615i −0.928279 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) 7.50000 + 4.33013i 0.761510 + 0.439658i 0.829837 0.558005i \(-0.188433\pi\)
−0.0683279 + 0.997663i \(0.521766\pi\)
\(98\) −6.92820 1.00000i −0.699854 0.101015i
\(99\) 0 0
\(100\) −2.50000 + 4.33013i −0.250000 + 0.433013i
\(101\) −5.19615 −0.517036 −0.258518 0.966006i \(-0.583234\pi\)
−0.258518 + 0.966006i \(0.583234\pi\)
\(102\) 0 0
\(103\) 17.3205i 1.70664i 0.521387 + 0.853320i \(0.325415\pi\)
−0.521387 + 0.853320i \(0.674585\pi\)
\(104\) 1.73205 + 3.00000i 0.169842 + 0.294174i
\(105\) 0 0
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) 10.3923 + 6.00000i 1.00466 + 0.580042i 0.909624 0.415432i \(-0.136370\pi\)
0.0950377 + 0.995474i \(0.469703\pi\)
\(108\) 0 0
\(109\) 4.00000 + 6.92820i 0.383131 + 0.663602i 0.991508 0.130046i \(-0.0415126\pi\)
−0.608377 + 0.793648i \(0.708179\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) 10.3923 6.00000i 0.977626 0.564433i 0.0760733 0.997102i \(-0.475762\pi\)
0.901553 + 0.432670i \(0.142428\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.79423 4.50000i 0.723676 0.417815i
\(117\) 0 0
\(118\) 5.19615i 0.478345i
\(119\) 0 0
\(120\) 0 0
\(121\) 2.00000 0.181818
\(122\) −6.92820 + 12.0000i −0.627250 + 1.08643i
\(123\) 0 0
\(124\) 1.50000 0.866025i 0.134704 0.0777714i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −15.5885 −1.36197 −0.680985 0.732297i \(-0.738448\pi\)
−0.680985 + 0.732297i \(0.738448\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) 0 0
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) 0 0
\(139\) 6.00000 3.46410i 0.508913 0.293821i −0.223474 0.974710i \(-0.571740\pi\)
0.732387 + 0.680889i \(0.238406\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) 5.19615 + 9.00000i 0.434524 + 0.752618i
\(144\) 0 0
\(145\) 0 0
\(146\) −2.59808 + 4.50000i −0.215018 + 0.372423i
\(147\) 0 0
\(148\) −4.00000 6.92820i −0.328798 0.569495i
\(149\) 15.0000i 1.22885i 0.788976 + 0.614424i \(0.210612\pi\)
−0.788976 + 0.614424i \(0.789388\pi\)
\(150\) 0 0
\(151\) −23.0000 −1.87171 −0.935857 0.352381i \(-0.885372\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 1.50000 + 7.79423i 0.120873 + 0.628077i
\(155\) 0 0
\(156\) 0 0
\(157\) −9.00000 5.19615i −0.718278 0.414698i 0.0958404 0.995397i \(-0.469446\pi\)
−0.814119 + 0.580699i \(0.802779\pi\)
\(158\) −11.2583 6.50000i −0.895665 0.517112i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.00000 8.66025i 0.391630 0.678323i −0.601035 0.799223i \(-0.705245\pi\)
0.992665 + 0.120900i \(0.0385779\pi\)
\(164\) 10.3923 0.811503
\(165\) 0 0
\(166\) 5.19615i 0.403300i
\(167\) 5.19615 + 9.00000i 0.402090 + 0.696441i 0.993978 0.109580i \(-0.0349504\pi\)
−0.591888 + 0.806020i \(0.701617\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 0 0
\(171\) 0 0
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −12.9904 22.5000i −0.987640 1.71064i −0.629558 0.776953i \(-0.716764\pi\)
−0.358082 0.933690i \(-0.616569\pi\)
\(174\) 0 0
\(175\) 12.5000 + 4.33013i 0.944911 + 0.327327i
\(176\) 2.59808 1.50000i 0.195837 0.113067i
\(177\) 0 0
\(178\) 10.3923i 0.778936i
\(179\) −7.79423 + 4.50000i −0.582568 + 0.336346i −0.762153 0.647397i \(-0.775858\pi\)
0.179585 + 0.983742i \(0.442524\pi\)
\(180\) 0 0
\(181\) 20.7846i 1.54491i 0.635071 + 0.772454i \(0.280971\pi\)
−0.635071 + 0.772454i \(0.719029\pi\)
\(182\) 6.92820 6.00000i 0.513553 0.444750i
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 10.3923 0.757937
\(189\) 0 0
\(190\) 0 0
\(191\) 5.19615 3.00000i 0.375980 0.217072i −0.300088 0.953912i \(-0.597016\pi\)
0.676068 + 0.736839i \(0.263683\pi\)
\(192\) 0 0
\(193\) 5.50000 9.52628i 0.395899 0.685717i −0.597317 0.802005i \(-0.703766\pi\)
0.993215 + 0.116289i \(0.0370998\pi\)
\(194\) −8.66025 −0.621770
\(195\) 0 0
\(196\) 6.50000 2.59808i 0.464286 0.185577i
\(197\) 15.0000i 1.06871i −0.845262 0.534353i \(-0.820555\pi\)
0.845262 0.534353i \(-0.179445\pi\)
\(198\) 0 0
\(199\) 1.50000 0.866025i 0.106332 0.0613909i −0.445891 0.895087i \(-0.647113\pi\)
0.552223 + 0.833696i \(0.313780\pi\)
\(200\) 5.00000i 0.353553i
\(201\) 0 0
\(202\) 4.50000 2.59808i 0.316619 0.182800i
\(203\) −15.5885 18.0000i −1.09410 1.26335i
\(204\) 0 0
\(205\) 0 0
\(206\) −8.66025 15.0000i −0.603388 1.04510i
\(207\) 0 0
\(208\) −3.00000 1.73205i −0.208013 0.120096i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.00000 + 1.73205i 0.0688428 + 0.119239i 0.898392 0.439194i \(-0.144736\pi\)
−0.829549 + 0.558433i \(0.811403\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 0 0
\(216\) 0 0
\(217\) −3.00000 3.46410i −0.203653 0.235159i
\(218\) −6.92820 4.00000i −0.469237 0.270914i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −4.50000 2.59808i −0.301342 0.173980i 0.341703 0.939808i \(-0.388996\pi\)
−0.643046 + 0.765828i \(0.722329\pi\)
\(224\) −1.73205 2.00000i −0.115728 0.133631i
\(225\) 0 0
\(226\) −6.00000 + 10.3923i −0.399114 + 0.691286i
\(227\) −25.9808 −1.72440 −0.862202 0.506565i \(-0.830915\pi\)
−0.862202 + 0.506565i \(0.830915\pi\)
\(228\) 0 0
\(229\) 6.92820i 0.457829i −0.973447 0.228914i \(-0.926482\pi\)
0.973447 0.228914i \(-0.0735176\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.50000 + 7.79423i −0.295439 + 0.511716i
\(233\) −15.5885 9.00000i −1.02123 0.589610i −0.106773 0.994283i \(-0.534052\pi\)
−0.914461 + 0.404674i \(0.867385\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2.59808 4.50000i −0.169120 0.292925i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.3923 6.00000i 0.672222 0.388108i −0.124696 0.992195i \(-0.539796\pi\)
0.796918 + 0.604087i \(0.206462\pi\)
\(240\) 0 0
\(241\) 12.1244i 0.780998i −0.920603 0.390499i \(-0.872302\pi\)
0.920603 0.390499i \(-0.127698\pi\)
\(242\) −1.73205 + 1.00000i −0.111340 + 0.0642824i
\(243\) 0 0
\(244\) 13.8564i 0.887066i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.866025 + 1.50000i −0.0549927 + 0.0952501i
\(249\) 0 0
\(250\) 0 0
\(251\) 25.9808 1.63989 0.819946 0.572441i \(-0.194004\pi\)
0.819946 + 0.572441i \(0.194004\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −6.92820 + 4.00000i −0.434714 + 0.250982i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −20.7846 −1.29651 −0.648254 0.761424i \(-0.724501\pi\)
−0.648254 + 0.761424i \(0.724501\pi\)
\(258\) 0 0
\(259\) −16.0000 + 13.8564i −0.994192 + 0.860995i
\(260\) 0 0
\(261\) 0 0
\(262\) 13.5000 7.79423i 0.834033 0.481529i
\(263\) 24.0000i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 7.79423 + 13.5000i 0.475223 + 0.823110i 0.999597 0.0283781i \(-0.00903423\pi\)
−0.524375 + 0.851488i \(0.675701\pi\)
\(270\) 0 0
\(271\) 3.00000 + 1.73205i 0.182237 + 0.105215i 0.588343 0.808611i \(-0.299780\pi\)
−0.406106 + 0.913826i \(0.633114\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 6.00000 + 10.3923i 0.362473 + 0.627822i
\(275\) 15.0000i 0.904534i
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) −3.46410 + 6.00000i −0.207763 + 0.359856i
\(279\) 0 0
\(280\) 0 0
\(281\) −5.19615 3.00000i −0.309976 0.178965i 0.336939 0.941526i \(-0.390608\pi\)
−0.646916 + 0.762561i \(0.723942\pi\)
\(282\) 0 0
\(283\) −6.00000 3.46410i −0.356663 0.205919i 0.310953 0.950425i \(-0.399352\pi\)
−0.667616 + 0.744506i \(0.732685\pi\)
\(284\) −10.3923 6.00000i −0.616670 0.356034i
\(285\) 0 0
\(286\) −9.00000 5.19615i −0.532181 0.307255i
\(287\) −5.19615 27.0000i −0.306719 1.59376i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 5.19615i 0.304082i
\(293\) 2.59808 + 4.50000i 0.151781 + 0.262893i 0.931882 0.362761i \(-0.118166\pi\)
−0.780101 + 0.625653i \(0.784832\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 6.92820 + 4.00000i 0.402694 + 0.232495i
\(297\) 0 0
\(298\) −7.50000 12.9904i −0.434463 0.752513i
\(299\) 0 0
\(300\) 0 0
\(301\) 8.00000 6.92820i 0.461112 0.399335i
\(302\) 19.9186 11.5000i 1.14619 0.661751i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 17.3205i 0.988534i −0.869310 0.494267i \(-0.835437\pi\)
0.869310 0.494267i \(-0.164563\pi\)
\(308\) −5.19615 6.00000i −0.296078 0.341882i
\(309\) 0 0
\(310\) 0 0
\(311\) −15.5885 + 27.0000i −0.883940 + 1.53103i −0.0370169 + 0.999315i \(0.511786\pi\)
−0.846923 + 0.531715i \(0.821548\pi\)
\(312\) 0 0
\(313\) 18.0000 10.3923i 1.01742 0.587408i 0.104065 0.994571i \(-0.466815\pi\)
0.913356 + 0.407163i \(0.133482\pi\)
\(314\) 10.3923 0.586472
\(315\) 0 0
\(316\) 13.0000 0.731307
\(317\) 7.79423 4.50000i 0.437767 0.252745i −0.264883 0.964281i \(-0.585333\pi\)
0.702650 + 0.711535i \(0.252000\pi\)
\(318\) 0 0
\(319\) −13.5000 + 23.3827i −0.755855 + 1.30918i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −15.0000 + 8.66025i −0.832050 + 0.480384i
\(326\) 10.0000i 0.553849i
\(327\) 0 0
\(328\) −9.00000 + 5.19615i −0.496942 + 0.286910i
\(329\) −5.19615 27.0000i −0.286473 1.48856i
\(330\) 0 0
\(331\) −14.0000 24.2487i −0.769510 1.33283i −0.937829 0.347097i \(-0.887167\pi\)
0.168320 0.985732i \(-0.446166\pi\)
\(332\) 2.59808 + 4.50000i 0.142588 + 0.246970i
\(333\) 0 0
\(334\) −9.00000 5.19615i −0.492458 0.284321i
\(335\) 0 0
\(336\) 0 0
\(337\) −6.50000 11.2583i −0.354078 0.613280i 0.632882 0.774248i \(-0.281872\pi\)
−0.986960 + 0.160968i \(0.948538\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 0 0
\(340\) 0 0
\(341\) −2.59808 + 4.50000i −0.140694 + 0.243689i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −3.46410 2.00000i −0.186772 0.107833i
\(345\) 0 0
\(346\) 22.5000 + 12.9904i 1.20961 + 0.698367i
\(347\) 2.59808 + 1.50000i 0.139472 + 0.0805242i 0.568112 0.822951i \(-0.307674\pi\)
−0.428640 + 0.903475i \(0.641007\pi\)
\(348\) 0 0
\(349\) 24.0000 + 13.8564i 1.28469 + 0.741716i 0.977702 0.209997i \(-0.0673454\pi\)
0.306988 + 0.951713i \(0.400679\pi\)
\(350\) −12.9904 + 2.50000i −0.694365 + 0.133631i
\(351\) 0 0
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 10.3923 0.553127 0.276563 0.960996i \(-0.410804\pi\)
0.276563 + 0.960996i \(0.410804\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 5.19615 + 9.00000i 0.275396 + 0.476999i
\(357\) 0 0
\(358\) 4.50000 7.79423i 0.237832 0.411938i
\(359\) −10.3923 6.00000i −0.548485 0.316668i 0.200026 0.979791i \(-0.435897\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(360\) 0 0
\(361\) −9.50000 16.4545i −0.500000 0.866025i
\(362\) −10.3923 18.0000i −0.546207 0.946059i
\(363\) 0 0
\(364\) −3.00000 + 8.66025i −0.157243 + 0.453921i
\(365\) 0 0
\(366\) 0 0
\(367\) 10.3923i 0.542474i 0.962513 + 0.271237i \(0.0874327\pi\)
−0.962513 + 0.271237i \(0.912567\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 15.5885 3.00000i 0.809312 0.155752i
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −9.00000 + 5.19615i −0.464140 + 0.267971i
\(377\) 31.1769 1.60569
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −3.00000 + 5.19615i −0.153493 + 0.265858i
\(383\) −20.7846 −1.06204 −0.531022 0.847358i \(-0.678192\pi\)
−0.531022 + 0.847358i \(0.678192\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 11.0000i 0.559885i
\(387\) 0 0
\(388\) 7.50000 4.33013i 0.380755 0.219829i
\(389\) 9.00000i 0.456318i 0.973624 + 0.228159i \(0.0732706\pi\)
−0.973624 + 0.228159i \(0.926729\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −4.33013 + 5.50000i −0.218704 + 0.277792i
\(393\) 0 0
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) 0 0
\(396\) 0 0
\(397\) 21.0000 + 12.1244i 1.05396 + 0.608504i 0.923755 0.382983i \(-0.125103\pi\)
0.130204 + 0.991487i \(0.458437\pi\)
\(398\) −0.866025 + 1.50000i −0.0434099 + 0.0751882i
\(399\) 0 0
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) 30.0000i 1.49813i 0.662497 + 0.749064i \(0.269497\pi\)
−0.662497 + 0.749064i \(0.730503\pi\)
\(402\) 0 0
\(403\) 6.00000 0.298881
\(404\) −2.59808 + 4.50000i −0.129259 + 0.223883i
\(405\) 0 0
\(406\) 22.5000 + 7.79423i 1.11666 + 0.386821i
\(407\) 20.7846 + 12.0000i 1.03025 + 0.594818i
\(408\) 0 0
\(409\) −6.00000 3.46410i −0.296681 0.171289i 0.344270 0.938871i \(-0.388126\pi\)
−0.640951 + 0.767582i \(0.721460\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 15.0000 + 8.66025i 0.738997 + 0.426660i
\(413\) −10.3923 + 9.00000i −0.511372 + 0.442861i
\(414\) 0 0
\(415\) 0 0
\(416\) 3.46410 0.169842
\(417\) 0 0
\(418\) 0 0
\(419\) 15.5885 + 27.0000i 0.761546 + 1.31904i 0.942053 + 0.335463i \(0.108893\pi\)
−0.180508 + 0.983574i \(0.557774\pi\)
\(420\) 0 0
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) −1.73205 1.00000i −0.0843149 0.0486792i
\(423\) 0 0
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 0 0
\(426\) 0 0
\(427\) −36.0000 + 6.92820i −1.74216 + 0.335279i
\(428\) 10.3923 6.00000i 0.502331 0.290021i
\(429\) 0 0
\(430\) 0 0
\(431\) −15.5885 + 9.00000i −0.750870 + 0.433515i −0.826008 0.563658i \(-0.809393\pi\)
0.0751385 + 0.997173i \(0.476060\pi\)
\(432\) 0 0
\(433\) 12.1244i 0.582659i 0.956623 + 0.291330i \(0.0940977\pi\)
−0.956623 + 0.291330i \(0.905902\pi\)
\(434\) 4.33013 + 1.50000i 0.207853 + 0.0720023i
\(435\) 0 0
\(436\) 8.00000 0.383131
\(437\) 0 0
\(438\) 0 0
\(439\) −13.5000 + 7.79423i −0.644320 + 0.371998i −0.786277 0.617875i \(-0.787994\pi\)
0.141957 + 0.989873i \(0.454661\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −23.3827 + 13.5000i −1.11094 + 0.641404i −0.939074 0.343715i \(-0.888315\pi\)
−0.171871 + 0.985119i \(0.554981\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 5.19615 0.246045
\(447\) 0 0
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) 30.0000i 1.41579i −0.706319 0.707894i \(-0.749646\pi\)
0.706319 0.707894i \(-0.250354\pi\)
\(450\) 0 0
\(451\) −27.0000 + 15.5885i −1.27138 + 0.734032i
\(452\) 12.0000i 0.564433i
\(453\) 0 0
\(454\) 22.5000 12.9904i 1.05598 0.609669i
\(455\) 0 0
\(456\) 0 0
\(457\) −11.0000 19.0526i −0.514558 0.891241i −0.999857 0.0168929i \(-0.994623\pi\)
0.485299 0.874348i \(-0.338711\pi\)
\(458\) 3.46410 + 6.00000i 0.161867 + 0.280362i
\(459\) 0 0
\(460\) 0 0
\(461\) −7.79423 + 13.5000i −0.363013 + 0.628758i −0.988455 0.151513i \(-0.951585\pi\)
0.625442 + 0.780271i \(0.284919\pi\)
\(462\) 0 0
\(463\) −2.50000 4.33013i −0.116185 0.201238i 0.802068 0.597233i \(-0.203733\pi\)
−0.918253 + 0.395995i \(0.870400\pi\)
\(464\) 9.00000i 0.417815i
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) 2.59808 4.50000i 0.120225 0.208235i −0.799632 0.600491i \(-0.794972\pi\)
0.919856 + 0.392256i \(0.128305\pi\)
\(468\) 0 0
\(469\) 4.00000 3.46410i 0.184703 0.159957i
\(470\) 0 0
\(471\) 0 0
\(472\) 4.50000 + 2.59808i 0.207129 + 0.119586i
\(473\) −10.3923 6.00000i −0.477839 0.275880i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) 10.3923 0.474837 0.237418 0.971408i \(-0.423699\pi\)
0.237418 + 0.971408i \(0.423699\pi\)
\(480\) 0 0
\(481\) 27.7128i 1.26360i
\(482\) 6.06218 + 10.5000i 0.276125 + 0.478262i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 0 0
\(486\) 0 0
\(487\) 5.50000 + 9.52628i 0.249229 + 0.431677i 0.963312 0.268384i \(-0.0864896\pi\)
−0.714083 + 0.700061i \(0.753156\pi\)
\(488\) 6.92820 + 12.0000i 0.313625 + 0.543214i
\(489\) 0 0
\(490\) 0 0
\(491\) 31.1769 18.0000i 1.40699 0.812329i 0.411897 0.911230i \(-0.364866\pi\)
0.995097 + 0.0989017i \(0.0315329\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.73205i 0.0777714i
\(497\) −10.3923 + 30.0000i −0.466159 + 1.34568i
\(498\) 0 0
\(499\) 16.0000 0.716258 0.358129 0.933672i \(-0.383415\pi\)
0.358129 + 0.933672i \(0.383415\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −22.5000 + 12.9904i −1.00422 + 0.579789i
\(503\) −31.1769 −1.39011 −0.695055 0.718957i \(-0.744620\pi\)
−0.695055 + 0.718957i \(0.744620\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 4.00000 6.92820i 0.177471 0.307389i
\(509\) 5.19615 0.230315 0.115158 0.993347i \(-0.463263\pi\)
0.115158 + 0.993347i \(0.463263\pi\)
\(510\) 0 0
\(511\) −13.5000 + 2.59808i −0.597205 + 0.114932i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.0000 10.3923i 0.793946 0.458385i
\(515\) 0 0
\(516\) 0 0
\(517\) −27.0000 + 15.5885i −1.18746 + 0.685580i
\(518\) 6.92820 20.0000i 0.304408 0.878750i
\(519\) 0 0
\(520\) 0 0
\(521\) 10.3923 + 18.0000i 0.455295 + 0.788594i 0.998705 0.0508731i \(-0.0162004\pi\)
−0.543410 + 0.839467i \(0.682867\pi\)
\(522\) 0 0
\(523\) 33.0000 + 19.0526i 1.44299 + 0.833110i 0.998048 0.0624496i \(-0.0198913\pi\)
0.444941 + 0.895560i \(0.353225\pi\)
\(524\) −7.79423 + 13.5000i −0.340492 + 0.589750i
\(525\) 0 0
\(526\) 12.0000 + 20.7846i 0.523225 + 0.906252i
\(527\) 0 0
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 31.1769 + 18.0000i 1.35042 + 0.779667i
\(534\) 0 0
\(535\) 0 0
\(536\) −1.73205 1.00000i −0.0748132 0.0431934i
\(537\) 0 0
\(538\) −13.5000 7.79423i −0.582026 0.336033i
\(539\) −12.9904 + 16.5000i −0.559535 + 0.710705i
\(540\) 0 0
\(541\) −19.0000 + 32.9090i −0.816874 + 1.41487i 0.0911008 + 0.995842i \(0.470961\pi\)
−0.907975 + 0.419025i \(0.862372\pi\)
\(542\) −3.46410 −0.148796
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −7.00000 + 12.1244i −0.299298 + 0.518400i −0.975976 0.217880i \(-0.930086\pi\)
0.676677 + 0.736280i \(0.263419\pi\)
\(548\) −10.3923 6.00000i −0.443937 0.256307i
\(549\) 0 0
\(550\) 7.50000 + 12.9904i 0.319801 + 0.553912i
\(551\) 0 0
\(552\) 0 0
\(553\) −6.50000 33.7750i −0.276408 1.43626i
\(554\) −12.1244 + 7.00000i −0.515115 + 0.297402i
\(555\) 0 0
\(556\) 6.92820i 0.293821i
\(557\) 18.1865 10.5000i 0.770588 0.444899i −0.0624962 0.998045i \(-0.519906\pi\)
0.833084 + 0.553146i \(0.186573\pi\)
\(558\) 0 0
\(559\) 13.8564i 0.586064i
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 15.5885 27.0000i 0.656975 1.13791i −0.324420 0.945913i \(-0.605169\pi\)
0.981395 0.192001i \(-0.0614977\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 6.92820 0.291214
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) 10.3923 6.00000i 0.435668 0.251533i −0.266090 0.963948i \(-0.585732\pi\)
0.701758 + 0.712415i \(0.252399\pi\)
\(570\) 0 0
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) 10.3923 0.434524
\(573\) 0 0
\(574\) 18.0000 + 20.7846i 0.751305 + 0.867533i
\(575\) 0 0
\(576\) 0 0
\(577\) −7.50000 + 4.33013i −0.312229 + 0.180266i −0.647924 0.761705i \(-0.724362\pi\)
0.335694 + 0.941971i \(0.391029\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 0 0
\(580\) 0 0
\(581\) 10.3923 9.00000i 0.431145 0.373383i
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) 2.59808 + 4.50000i 0.107509 + 0.186211i
\(585\) 0 0
\(586\) −4.50000 2.59808i −0.185893 0.107326i
\(587\) −5.19615 + 9.00000i −0.214468 + 0.371470i −0.953108 0.302631i \(-0.902135\pi\)
0.738640 + 0.674100i \(0.235468\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −8.00000 −0.328798
\(593\) −10.3923 + 18.0000i −0.426761 + 0.739171i −0.996583 0.0825966i \(-0.973679\pi\)
0.569822 + 0.821768i \(0.307012\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.9904 + 7.50000i 0.532107 + 0.307212i
\(597\) 0 0
\(598\) 0 0
\(599\) 25.9808 + 15.0000i 1.06155 + 0.612883i 0.925859 0.377869i \(-0.123343\pi\)
0.135686 + 0.990752i \(0.456676\pi\)
\(600\) 0 0
\(601\) −30.0000 17.3205i −1.22373 0.706518i −0.258015 0.966141i \(-0.583069\pi\)
−0.965710 + 0.259623i \(0.916402\pi\)
\(602\) −3.46410 + 10.0000i −0.141186 + 0.407570i
\(603\) 0 0
\(604\) −11.5000 + 19.9186i −0.467928 + 0.810476i
\(605\) 0 0
\(606\) 0 0
\(607\) 5.19615i 0.210905i 0.994424 + 0.105453i \(0.0336291\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 31.1769 + 18.0000i 1.26128 + 0.728202i
\(612\) 0 0
\(613\) 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i \(-0.101939\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(614\) 8.66025 + 15.0000i 0.349499 + 0.605351i
\(615\) 0 0
\(616\) 7.50000 + 2.59808i 0.302184 + 0.104679i
\(617\) 15.5885 9.00000i 0.627568 0.362326i −0.152242 0.988343i \(-0.548649\pi\)
0.779809 + 0.626017i \(0.215316\pi\)
\(618\) 0 0
\(619\) 34.6410i 1.39234i 0.717877 + 0.696170i \(0.245114\pi\)
−0.717877 + 0.696170i \(0.754886\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 31.1769i 1.25008i
\(623\) 20.7846 18.0000i 0.832718 0.721155i
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −10.3923 + 18.0000i −0.415360 + 0.719425i
\(627\) 0 0
\(628\) −9.00000 + 5.19615i −0.359139 + 0.207349i
\(629\) 0 0
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) −11.2583 + 6.50000i −0.447832 + 0.258556i
\(633\) 0 0
\(634\) −4.50000 + 7.79423i −0.178718 + 0.309548i
\(635\) 0 0
\(636\) 0 0
\(637\) 24.0000 + 3.46410i 0.950915 + 0.137253i
\(638\) 27.0000i 1.06894i
\(639\) 0 0
\(640\) 0 0
\(641\) 42.0000i 1.65890i 0.558581 + 0.829450i \(0.311346\pi\)
−0.558581 + 0.829450i \(0.688654\pi\)
\(642\) 0 0
\(643\) −3.00000 + 1.73205i −0.118308 + 0.0683054i −0.557986 0.829850i \(-0.688426\pi\)
0.439678 + 0.898155i \(0.355093\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.19615 + 9.00000i 0.204282 + 0.353827i 0.949904 0.312543i \(-0.101181\pi\)
−0.745622 + 0.666369i \(0.767847\pi\)
\(648\) 0 0
\(649\) 13.5000 + 7.79423i 0.529921 + 0.305950i
\(650\) 8.66025 15.0000i 0.339683 0.588348i
\(651\) 0 0
\(652\) −5.00000 8.66025i −0.195815 0.339162i
\(653\) 30.0000i 1.17399i −0.809590 0.586995i \(-0.800311\pi\)
0.809590 0.586995i \(-0.199689\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 5.19615 9.00000i 0.202876 0.351391i
\(657\) 0 0
\(658\) 18.0000 + 20.7846i 0.701713 + 0.810268i
\(659\) −12.9904 7.50000i −0.506033 0.292159i 0.225168 0.974320i \(-0.427707\pi\)
−0.731202 + 0.682161i \(0.761040\pi\)
\(660\) 0 0
\(661\) −9.00000 5.19615i −0.350059 0.202107i 0.314652 0.949207i \(-0.398112\pi\)
−0.664711 + 0.747100i \(0.731446\pi\)
\(662\) 24.2487 + 14.0000i 0.942453 + 0.544125i
\(663\) 0 0
\(664\) −4.50000 2.59808i −0.174634 0.100825i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 10.3923 0.402090
\(669\) 0 0
\(670\) 0 0
\(671\) 20.7846 + 36.0000i 0.802381 + 1.38976i
\(672\) 0 0
\(673\) 13.0000 22.5167i 0.501113 0.867953i −0.498886 0.866668i \(-0.666257\pi\)
0.999999 0.00128586i \(-0.000409302\pi\)
\(674\) 11.2583 + 6.50000i 0.433655 + 0.250371i
\(675\) 0 0
\(676\) 0.500000 + 0.866025i 0.0192308 + 0.0333087i
\(677\) 7.79423 + 13.5000i 0.299557 + 0.518847i 0.976035 0.217616i \(-0.0698279\pi\)
−0.676478 + 0.736463i \(0.736495\pi\)
\(678\) 0 0
\(679\) −15.0000 17.3205i −0.575647 0.664700i
\(680\) 0 0
\(681\) 0 0
\(682\) 5.19615i 0.198971i
\(683\) −18.1865 + 10.5000i −0.695888 + 0.401771i −0.805814 0.592168i \(-0.798272\pi\)
0.109926 + 0.993940i \(0.464939\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 16.4545 + 8.50000i 0.628235 + 0.324532i
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) −10.3923 + 18.0000i −0.395915 + 0.685745i
\(690\) 0 0
\(691\) −12.0000 + 6.92820i −0.456502 + 0.263561i −0.710572 0.703624i \(-0.751564\pi\)
0.254071 + 0.967186i \(0.418230\pi\)
\(692\) −25.9808 −0.987640
\(693\) 0 0
\(694\) −3.00000 −0.113878
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −27.7128 −1.04895
\(699\) 0 0
\(700\) 10.0000 8.66025i 0.377964 0.327327i
\(701\) 6.00000i 0.226617i 0.993560 + 0.113308i \(0.0361448\pi\)
−0.993560 + 0.113308i \(0.963855\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 3.00000i 0.113067i
\(705\) 0 0
\(706\) −9.00000 + 5.19615i −0.338719 + 0.195560i
\(707\) 12.9904 + 4.50000i 0.488554 + 0.169240i
\(708\) 0 0
\(709\) −2.00000 3.46410i −0.0751116 0.130097i 0.826023 0.563636i \(-0.190598\pi\)
−0.901135 + 0.433539i \(0.857265\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −9.00000 5.19615i −0.337289 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 9.00000i 0.336346i
\(717\) 0 0
\(718\) 12.0000 0.447836
\(719\) −5.19615 + 9.00000i −0.193784 + 0.335643i −0.946501 0.322700i \(-0.895409\pi\)
0.752717 + 0.658344i \(0.228743\pi\)
\(720\) 0 0
\(721\) 15.0000 43.3013i 0.558629 1.61262i
\(722\) 16.4545 + 9.50000i 0.612372 + 0.353553i
\(723\) 0 0
\(724\) 18.0000 + 10.3923i 0.668965 + 0.386227i
\(725\) −38.9711 22.5000i −1.44735 0.835629i
\(726\) 0 0
\(727\) 21.0000 + 12.1244i 0.778847 + 0.449667i 0.836021 0.548697i \(-0.184876\pi\)
−0.0571746 + 0.998364i \(0.518209\pi\)
\(728\) −1.73205 9.00000i −0.0641941 0.333562i
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 13.8564i 0.511798i −0.966704 0.255899i \(-0.917629\pi\)
0.966704 0.255899i \(-0.0823715\pi\)
\(734\) −5.19615 9.00000i −0.191793 0.332196i
\(735\) 0 0
\(736\) 0 0
\(737\) −5.19615 3.00000i −0.191403 0.110506i
\(738\) 0 0
\(739\) −13.0000 22.5167i −0.478213 0.828289i 0.521475 0.853266i \(-0.325382\pi\)
−0.999688 + 0.0249776i \(0.992049\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −12.0000 + 10.3923i −0.440534 + 0.381514i
\(743\) 5.19615 3.00000i 0.190628 0.110059i −0.401648 0.915794i \(-0.631563\pi\)
0.592277 + 0.805735i \(0.298229\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.46410 2.00000i 0.126830 0.0732252i
\(747\) 0 0
\(748\) 0 0
\(749\) −20.7846 24.0000i −0.759453 0.876941i
\(750\) 0 0
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 5.19615 9.00000i 0.189484 0.328196i
\(753\) 0 0
\(754\) −27.0000 + 15.5885i −0.983282 + 0.567698i
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 22.5167 13.0000i 0.817842 0.472181i
\(759\) 0 0
\(760\) 0 0
\(761\) 41.5692 1.50688 0.753442 0.657515i \(-0.228392\pi\)
0.753442 + 0.657515i \(0.228392\pi\)
\(762\) 0 0
\(763\) −4.00000 20.7846i −0.144810 0.752453i
\(764\) 6.00000i 0.217072i
\(765\) 0 0
\(766\) 18.0000 10.3923i 0.650366 0.375489i
\(767\) 18.0000i 0.649942i
\(768\) 0 0
\(769\) −13.5000 + 7.79423i −0.486822 + 0.281067i −0.723255 0.690581i \(-0.757355\pi\)
0.236433 + 0.971648i \(0.424022\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.50000 9.52628i −0.197949 0.342858i
\(773\) −20.7846 36.0000i −0.747570 1.29483i −0.948984 0.315324i \(-0.897887\pi\)
0.201414 0.979506i \(-0.435446\pi\)
\(774\) 0 0
\(775\) −7.50000 4.33013i −0.269408 0.155543i
\(776\) −4.33013 + 7.50000i −0.155443 + 0.269234i
\(777\) 0 0
\(778\) −4.50000 7.79423i −0.161333 0.279437i
\(779\) 0 0
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 0 0
\(786\) 0 0
\(787\) 21.0000 + 12.1244i 0.748569 + 0.432187i 0.825177 0.564875i \(-0.191076\pi\)
−0.0766075 + 0.997061i \(0.524409\pi\)
\(788\) −12.9904 7.50000i −0.462763 0.267176i
\(789\) 0 0
\(790\) 0 0
\(791\) −31.1769 + 6.00000i −1.10852 + 0.213335i
\(792\) 0 0
\(793\) 24.0000 41.5692i 0.852265 1.47617i
\(794\) −24.2487 −0.860555
\(795\) 0 0