Properties

Label 1134.2.l.d.215.1
Level $1134$
Weight $2$
Character 1134.215
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.l (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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.215
Dual form 1134.2.l.d.269.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.73205i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.73205i) q^{7} +1.00000i q^{8} +(-2.59808 - 1.50000i) q^{11} +(-3.00000 - 1.73205i) q^{13} +(-1.73205 - 2.00000i) q^{14} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{22} +(2.50000 - 4.33013i) q^{25} +(-1.73205 + 3.00000i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(-7.79423 + 4.50000i) q^{29} -1.73205i q^{31} -1.00000i q^{32} +(4.00000 - 6.92820i) q^{37} +(5.19615 - 9.00000i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(2.59808 + 1.50000i) q^{44} -10.3923 q^{47} +(1.00000 - 6.92820i) q^{49} +(-4.33013 - 2.50000i) q^{50} +(3.00000 + 1.73205i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(1.73205 + 2.00000i) q^{56} +(4.50000 + 7.79423i) q^{58} -5.19615 q^{59} +13.8564i q^{61} -1.73205 q^{62} -1.00000 q^{64} +2.00000 q^{67} -12.0000i q^{71} +(4.50000 - 2.59808i) q^{73} +(-6.92820 - 4.00000i) q^{74} +(-7.79423 + 1.50000i) q^{77} -13.0000 q^{79} +(-9.00000 - 5.19615i) q^{82} +(-2.59808 - 4.50000i) q^{83} +(-3.46410 + 2.00000i) q^{86} +(1.50000 - 2.59808i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(-9.00000 + 1.73205i) q^{91} +10.3923i q^{94} +(-7.50000 + 4.33013i) q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 8 q^{7} + O(q^{10}) \) \( 4 q - 4 q^{4} + 8 q^{7} - 12 q^{13} + 4 q^{16} - 6 q^{22} + 10 q^{25} - 8 q^{28} + 16 q^{37} - 8 q^{43} + 4 q^{49} + 12 q^{52} + 18 q^{58} - 4 q^{64} + 8 q^{67} + 18 q^{73} - 52 q^{79} - 36 q^{82} + 6 q^{88} - 36 q^{91} - 30 q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −2.59808 1.50000i −0.783349 0.452267i 0.0542666 0.998526i \(-0.482718\pi\)
−0.837616 + 0.546259i \(0.816051\pi\)
\(12\) 0 0
\(13\) −3.00000 1.73205i −0.832050 0.480384i 0.0225039 0.999747i \(-0.492836\pi\)
−0.854554 + 0.519362i \(0.826170\pi\)
\(14\) −1.73205 2.00000i −0.462910 0.534522i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 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 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) −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 \(-0.981563\pi\)
−0.449029 + 0.893517i \(0.648230\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i −0.987829 0.155543i \(-0.950287\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 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 −0.100309 0.994956i \(-0.531983\pi\)
0.911812 0.410608i \(-0.134683\pi\)
\(42\) 0 0
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) 2.59808 + 1.50000i 0.391675 + 0.226134i
\(45\) 0 0
\(46\) 0 0
\(47\) −10.3923 −1.51587 −0.757937 0.652328i \(-0.773792\pi\)
−0.757937 + 0.652328i \(0.773792\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) −4.33013 2.50000i −0.612372 0.353553i
\(51\) 0 0
\(52\) 3.00000 + 1.73205i 0.416025 + 0.240192i
\(53\) −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
\(56\) 1.73205 + 2.00000i 0.231455 + 0.267261i
\(57\) 0 0
\(58\) 4.50000 + 7.79423i 0.590879 + 1.02343i
\(59\) −5.19615 −0.676481 −0.338241 0.941060i \(-0.609832\pi\)
−0.338241 + 0.941060i \(0.609832\pi\)
\(60\) 0 0
\(61\) 13.8564i 1.77413i 0.461644 + 0.887066i \(0.347260\pi\)
−0.461644 + 0.887066i \(0.652740\pi\)
\(62\) −1.73205 −0.219971
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 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 \(0.234984\pi\)
\(74\) −6.92820 4.00000i −0.805387 0.464991i
\(75\) 0 0
\(76\) 0 0
\(77\) −7.79423 + 1.50000i −0.888235 + 0.170941i
\(78\) 0 0
\(79\) −13.0000 −1.46261 −0.731307 0.682048i \(-0.761089\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −9.00000 5.19615i −0.993884 0.573819i
\(83\) −2.59808 4.50000i −0.285176 0.493939i 0.687476 0.726207i \(-0.258719\pi\)
−0.972652 + 0.232268i \(0.925385\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −3.46410 + 2.00000i −0.373544 + 0.215666i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −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
\(94\) 10.3923i 1.07188i
\(95\) 0 0
\(96\) 0 0
\(97\) −7.50000 + 4.33013i −0.761510 + 0.439658i −0.829837 0.558005i \(-0.811567\pi\)
0.0683279 + 0.997663i \(0.478234\pi\)
\(98\) −6.92820 1.00000i −0.699854 0.101015i
\(99\) 0 0
\(100\) −2.50000 + 4.33013i −0.250000 + 0.433013i
\(101\) 2.59808 4.50000i 0.258518 0.447767i −0.707327 0.706887i \(-0.750099\pi\)
0.965845 + 0.259120i \(0.0834325\pi\)
\(102\) 0 0
\(103\) 15.0000 8.66025i 1.47799 0.853320i 0.478303 0.878195i \(-0.341252\pi\)
0.999691 + 0.0248745i \(0.00791862\pi\)
\(104\) 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
\(112\) 2.00000 1.73205i 0.188982 0.163663i
\(113\) −10.3923 6.00000i −0.977626 0.564433i −0.0760733 0.997102i \(-0.524238\pi\)
−0.901553 + 0.432670i \(0.857572\pi\)
\(114\) 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
\(121\) −1.00000 1.73205i −0.0909091 0.157459i
\(122\) 13.8564 1.25450
\(123\) 0 0
\(124\) 1.73205i 0.155543i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.79423 + 13.5000i 0.680985 + 1.17950i 0.974681 + 0.223602i \(0.0717814\pi\)
−0.293696 + 0.955899i \(0.594885\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) 0 0
\(137\) 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) 0 0
\(139\) −6.00000 3.46410i −0.508913 0.293821i 0.223474 0.974710i \(-0.428260\pi\)
−0.732387 + 0.680889i \(0.761594\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) 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
\(149\) 12.9904 7.50000i 1.06421 0.614424i 0.137619 0.990485i \(-0.456055\pi\)
0.926595 + 0.376061i \(0.122722\pi\)
\(150\) 0 0
\(151\) 11.5000 19.9186i 0.935857 1.62095i 0.162758 0.986666i \(-0.447961\pi\)
0.773099 0.634285i \(-0.218706\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 1.50000 + 7.79423i 0.120873 + 0.628077i
\(155\) 0 0
\(156\) 0 0
\(157\) 10.3923i 0.829396i 0.909959 + 0.414698i \(0.136113\pi\)
−0.909959 + 0.414698i \(0.863887\pi\)
\(158\) 13.0000i 1.03422i
\(159\) 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 \(0.0385779\pi\)
\(164\) −5.19615 + 9.00000i −0.405751 + 0.702782i
\(165\) 0 0
\(166\) −4.50000 + 2.59808i −0.349268 + 0.201650i
\(167\) 5.19615 9.00000i 0.402090 0.696441i −0.591888 0.806020i \(-0.701617\pi\)
0.993978 + 0.109580i \(0.0349504\pi\)
\(168\) 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
\(173\) 25.9808 1.97528 0.987640 0.156737i \(-0.0500975\pi\)
0.987640 + 0.156737i \(0.0500975\pi\)
\(174\) 0 0
\(175\) −2.50000 12.9904i −0.188982 0.981981i
\(176\) −2.59808 1.50000i −0.195837 0.113067i
\(177\) 0 0
\(178\) 9.00000 + 5.19615i 0.674579 + 0.389468i
\(179\) −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 \(0.719029\pi\)
\(182\) 1.73205 + 9.00000i 0.128388 + 0.667124i
\(183\) 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
\(191\) 6.00000i 0.434145i 0.976156 + 0.217072i \(0.0696508\pi\)
−0.976156 + 0.217072i \(0.930349\pi\)
\(192\) 0 0
\(193\) −11.0000 −0.791797 −0.395899 0.918294i \(-0.629567\pi\)
−0.395899 + 0.918294i \(0.629567\pi\)
\(194\) 4.33013 + 7.50000i 0.310885 + 0.538469i
\(195\) 0 0
\(196\) −1.00000 + 6.92820i −0.0714286 + 0.494872i
\(197\) 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 \(0.313780\pi\)
\(200\) 4.33013 + 2.50000i 0.306186 + 0.176777i
\(201\) 0 0
\(202\) −4.50000 2.59808i −0.316619 0.182800i
\(203\) −7.79423 + 22.5000i −0.547048 + 1.57919i
\(204\) 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 −0.829549 0.558433i \(-0.811403\pi\)
0.898392 + 0.439194i \(0.144736\pi\)
\(212\) 5.19615 3.00000i 0.356873 0.206041i
\(213\) 0 0
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) 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 \(-0.611004\pi\)
0.643046 + 0.765828i \(0.277671\pi\)
\(224\) −1.73205 2.00000i −0.115728 0.133631i
\(225\) 0 0
\(226\) −6.00000 + 10.3923i −0.399114 + 0.691286i
\(227\) 12.9904 22.5000i 0.862202 1.49338i −0.00759708 0.999971i \(-0.502418\pi\)
0.869799 0.493406i \(-0.164248\pi\)
\(228\) 0 0
\(229\) −6.00000 + 3.46410i −0.396491 + 0.228914i −0.684969 0.728572i \(-0.740184\pi\)
0.288478 + 0.957487i \(0.406851\pi\)
\(230\) 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
\(236\) 5.19615 0.338241
\(237\) 0 0
\(238\) 0 0
\(239\) −10.3923 6.00000i −0.672222 0.388108i 0.124696 0.992195i \(-0.460204\pi\)
−0.796918 + 0.604087i \(0.793538\pi\)
\(240\) 0 0
\(241\) 10.5000 + 6.06218i 0.676364 + 0.390499i 0.798484 0.602016i \(-0.205636\pi\)
−0.122119 + 0.992515i \(0.538969\pi\)
\(242\) −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
\(248\) 1.73205 0.109985
\(249\) 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
\(254\) 8.00000i 0.501965i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 10.3923 + 18.0000i 0.648254 + 1.12281i 0.983540 + 0.180693i \(0.0578339\pi\)
−0.335285 + 0.942117i \(0.608833\pi\)
\(258\) 0 0
\(259\) −4.00000 20.7846i −0.248548 1.29149i
\(260\) 0 0
\(261\) 0 0
\(262\) 13.5000 7.79423i 0.834033 0.481529i
\(263\) 20.7846 + 12.0000i 1.28163 + 0.739952i 0.977147 0.212565i \(-0.0681817\pi\)
0.304487 + 0.952517i \(0.401515\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −2.00000 −0.122169
\(269\) 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
\(275\) −12.9904 + 7.50000i −0.783349 + 0.452267i
\(276\) 0 0
\(277\) −7.00000 + 12.1244i −0.420589 + 0.728482i −0.995997 0.0893846i \(-0.971510\pi\)
0.575408 + 0.817867i \(0.304843\pi\)
\(278\) −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 \(-0.609392\pi\)
0.646916 + 0.762561i \(0.276058\pi\)
\(282\) 0 0
\(283\) 6.92820i 0.411839i 0.978569 + 0.205919i \(0.0660185\pi\)
−0.978569 + 0.205919i \(0.933982\pi\)
\(284\) 12.0000i 0.712069i
\(285\) 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
\(292\) −4.50000 + 2.59808i −0.263343 + 0.152041i
\(293\) 2.59808 4.50000i 0.151781 0.262893i −0.780101 0.625653i \(-0.784832\pi\)
0.931882 + 0.362761i \(0.118166\pi\)
\(294\) 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
\(301\) −10.0000 3.46410i −0.576390 0.199667i
\(302\) −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 \(-0.164563\pi\)
\(308\) 7.79423 1.50000i 0.444117 0.0854704i
\(309\) 0 0
\(310\) 0 0
\(311\) 31.1769 1.76788 0.883940 0.467600i \(-0.154881\pi\)
0.883940 + 0.467600i \(0.154881\pi\)
\(312\) 0 0
\(313\) 20.7846i 1.17482i 0.809291 + 0.587408i \(0.199852\pi\)
−0.809291 + 0.587408i \(0.800148\pi\)
\(314\) 10.3923 0.586472
\(315\) 0 0
\(316\) 13.0000 0.731307
\(317\) 9.00000i 0.505490i 0.967533 + 0.252745i \(0.0813334\pi\)
−0.967533 + 0.252745i \(0.918667\pi\)
\(318\) 0 0
\(319\) 27.0000 1.51171
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −15.0000 + 8.66025i −0.832050 + 0.480384i
\(326\) −8.66025 5.00000i −0.479647 0.276924i
\(327\) 0 0
\(328\) 9.00000 + 5.19615i 0.496942 + 0.286910i
\(329\) −20.7846 + 18.0000i −1.14589 + 0.992372i
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 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 −0.986960 0.160968i \(-0.948538\pi\)
0.632882 + 0.774248i \(0.281872\pi\)
\(338\) −0.866025 + 0.500000i −0.0471056 + 0.0271964i
\(339\) 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
\(346\) 25.9808i 1.39673i
\(347\) 3.00000i 0.161048i −0.996753 0.0805242i \(-0.974341\pi\)
0.996753 0.0805242i \(-0.0256594\pi\)
\(348\) 0 0
\(349\) −24.0000 + 13.8564i −1.28469 + 0.741716i −0.977702 0.209997i \(-0.932655\pi\)
−0.306988 + 0.951713i \(0.599321\pi\)
\(350\) −12.9904 + 2.50000i −0.694365 + 0.133631i
\(351\) 0 0
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) −5.19615 + 9.00000i −0.276563 + 0.479022i −0.970528 0.240987i \(-0.922529\pi\)
0.693965 + 0.720009i \(0.255862\pi\)
\(354\) 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
\(362\) 20.7846 1.09241
\(363\) 0 0
\(364\) 9.00000 1.73205i 0.471728 0.0907841i
\(365\) 0 0
\(366\) 0 0
\(367\) −9.00000 5.19615i −0.469796 0.271237i 0.246358 0.969179i \(-0.420766\pi\)
−0.716154 + 0.697942i \(0.754099\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.19615 + 15.0000i −0.269771 + 0.778761i
\(372\) 0 0
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 10.3923i 0.535942i
\(377\) 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
\(382\) 6.00000 0.306987
\(383\) 10.3923 + 18.0000i 0.531022 + 0.919757i 0.999345 + 0.0361995i \(0.0115252\pi\)
−0.468323 + 0.883558i \(0.655141\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 11.0000i 0.559885i
\(387\) 0 0
\(388\) 7.50000 4.33013i 0.380755 0.219829i
\(389\) −7.79423 4.50000i −0.395183 0.228159i 0.289220 0.957263i \(-0.406604\pi\)
−0.684403 + 0.729103i \(0.739937\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 6.92820 + 1.00000i 0.349927 + 0.0505076i
\(393\) 0 0
\(394\) −15.0000 −0.755689
\(395\) 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
\(401\) 25.9808 15.0000i 1.29742 0.749064i 0.317460 0.948272i \(-0.397170\pi\)
0.979957 + 0.199207i \(0.0638367\pi\)
\(402\) 0 0
\(403\) −3.00000 + 5.19615i −0.149441 + 0.258839i
\(404\) −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
\(409\) 6.92820i 0.342578i 0.985221 + 0.171289i \(0.0547931\pi\)
−0.985221 + 0.171289i \(0.945207\pi\)
\(410\) 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
\(416\) −1.73205 + 3.00000i −0.0849208 + 0.147087i
\(417\) 0 0
\(418\) 0 0
\(419\) 15.5885 27.0000i 0.761546 1.31904i −0.180508 0.983574i \(-0.557774\pi\)
0.942053 0.335463i \(-0.108893\pi\)
\(420\) 0 0
\(421\) 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i \(-0.0883103\pi\)
−0.718076 + 0.695965i \(0.754977\pi\)
\(422\) −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
\(427\) 24.0000 + 27.7128i 1.16144 + 1.34112i
\(428\) −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 \(0.905902\pi\)
\(434\) −3.46410 + 3.00000i −0.166282 + 0.144005i
\(435\) 0 0
\(436\) −4.00000 6.92820i −0.191565 0.331801i
\(437\) 0 0
\(438\) 0 0
\(439\) 15.5885i 0.743996i −0.928233 0.371998i \(-0.878673\pi\)
0.928233 0.371998i \(-0.121327\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 27.0000i 1.28281i −0.767203 0.641404i \(-0.778352\pi\)
0.767203 0.641404i \(-0.221648\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −2.59808 4.50000i −0.123022 0.213081i
\(447\) 0 0
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) 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
\(452\) 10.3923 + 6.00000i 0.488813 + 0.282216i
\(453\) 0 0
\(454\) −22.5000 12.9904i −1.05598 0.609669i
\(455\) 0 0
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 3.46410 + 6.00000i 0.161867 + 0.280362i
\(459\) 0 0
\(460\) 0 0
\(461\) −7.79423 13.5000i −0.363013 0.628758i 0.625442 0.780271i \(-0.284919\pi\)
−0.988455 + 0.151513i \(0.951585\pi\)
\(462\) 0 0
\(463\) −2.50000 + 4.33013i −0.116185 + 0.201238i −0.918253 0.395995i \(-0.870400\pi\)
0.802068 + 0.597233i \(0.203733\pi\)
\(464\) −7.79423 + 4.50000i −0.361838 + 0.208907i
\(465\) 0 0
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) 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
\(472\) 5.19615i 0.239172i
\(473\) 12.0000i 0.551761i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) −5.19615 + 9.00000i −0.237418 + 0.411220i −0.959973 0.280094i \(-0.909635\pi\)
0.722554 + 0.691314i \(0.242968\pi\)
\(480\) 0 0
\(481\) −24.0000 + 13.8564i −1.09431 + 0.631798i
\(482\) 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 \(0.753156\pi\)
\(488\) −13.8564 −0.627250
\(489\) 0 0
\(490\) 0 0
\(491\) −31.1769 18.0000i −1.40699 0.812329i −0.411897 0.911230i \(-0.635134\pi\)
−0.995097 + 0.0989017i \(0.968467\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.73205i 0.0777714i
\(497\) −20.7846 24.0000i −0.932317 1.07655i
\(498\) 0 0
\(499\) −8.00000 13.8564i −0.358129 0.620298i 0.629519 0.776985i \(-0.283252\pi\)
−0.987648 + 0.156687i \(0.949919\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 25.9808i 1.15958i
\(503\) −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
\(508\) −8.00000 −0.354943
\(509\) −2.59808 4.50000i −0.115158 0.199459i 0.802685 0.596403i \(-0.203404\pi\)
−0.917843 + 0.396944i \(0.870071\pi\)
\(510\) 0 0
\(511\) 4.50000 12.9904i 0.199068 0.574661i
\(512\) 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
\(518\) −20.7846 + 4.00000i −0.913223 + 0.175750i
\(519\) 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
\(529\) −11.5000 + 19.9186i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −31.1769 + 18.0000i −1.35042 + 0.779667i
\(534\) 0 0
\(535\) 0 0
\(536\) 2.00000i 0.0863868i
\(537\) 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 \(0.862372\pi\)
\(542\) 1.73205 3.00000i 0.0743980 0.128861i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −7.00000 12.1244i −0.299298 0.518400i 0.676677 0.736280i \(-0.263419\pi\)
−0.975976 + 0.217880i \(0.930086\pi\)
\(548\) −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
\(553\) −26.0000 + 22.5167i −1.10563 + 0.957506i
\(554\) 12.1244 + 7.00000i 0.515115 + 0.297402i
\(555\) 0 0
\(556\) 6.00000 + 3.46410i 0.254457 + 0.146911i
\(557\) 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
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) −31.1769 −1.31395 −0.656975 0.753912i \(-0.728164\pi\)
−0.656975 + 0.753912i \(0.728164\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 6.92820 0.291214
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) 12.0000i 0.503066i 0.967849 + 0.251533i \(0.0809347\pi\)
−0.967849 + 0.251533i \(0.919065\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) −5.19615 9.00000i −0.217262 0.376309i
\(573\) 0 0
\(574\) −27.0000 + 5.19615i −1.12696 + 0.216883i
\(575\) 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 \(0.391029\pi\)
\(578\) −14.7224 8.50000i −0.612372 0.353553i
\(579\) 0 0
\(580\) 0 0
\(581\) −12.9904 4.50000i −0.538932 0.186691i
\(582\) 0 0
\(583\) 18.0000 0.745484
\(584\) 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 0.738640 0.674100i \(-0.235468\pi\)
−0.953108 + 0.302631i \(0.902135\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 4.00000 6.92820i 0.164399 0.284747i
\(593\) −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
\(599\) 30.0000i 1.22577i −0.790173 0.612883i \(-0.790010\pi\)
0.790173 0.612883i \(-0.209990\pi\)
\(600\) 0 0
\(601\) 30.0000 17.3205i 1.22373 0.706518i 0.258015 0.966141i \(-0.416931\pi\)
0.965710 + 0.259623i \(0.0835982\pi\)
\(602\) −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
\(607\) 4.50000 2.59808i 0.182649 0.105453i −0.405887 0.913923i \(-0.633038\pi\)
0.588537 + 0.808470i \(0.299704\pi\)
\(608\) 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 \(0.768606\pi\)
\(614\) −17.3205 −0.698999
\(615\) 0 0
\(616\) −1.50000 7.79423i −0.0604367 0.314038i
\(617\) −15.5885 9.00000i −0.627568 0.362326i 0.152242 0.988343i \(-0.451351\pi\)
−0.779809 + 0.626017i \(0.784684\pi\)
\(618\) 0 0
\(619\) −30.0000 17.3205i −1.20580 0.696170i −0.243962 0.969785i \(-0.578447\pi\)
−0.961839 + 0.273615i \(0.911781\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 31.1769i 1.25008i
\(623\) 5.19615 + 27.0000i 0.208179 + 1.08173i
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 20.7846 0.830720
\(627\) 0 0
\(628\) 10.3923i 0.414698i
\(629\) 0 0
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) 13.0000i 0.517112i
\(633\) 0 0
\(634\) 9.00000 0.357436
\(635\) 0 0
\(636\) 0 0
\(637\) −15.0000 + 19.0526i −0.594322 + 0.754890i
\(638\) 27.0000i 1.06894i
\(639\) 0 0
\(640\) 0 0
\(641\) −36.3731 21.0000i −1.43665 0.829450i −0.439034 0.898470i \(-0.644679\pi\)
−0.997615 + 0.0690201i \(0.978013\pi\)
\(642\) 0 0
\(643\) 3.00000 + 1.73205i 0.118308 + 0.0683054i 0.557986 0.829850i \(-0.311574\pi\)
−0.439678 + 0.898155i \(0.644907\pi\)
\(644\) 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
\(653\) −25.9808 + 15.0000i −1.01671 + 0.586995i −0.913148 0.407628i \(-0.866356\pi\)
−0.103558 + 0.994623i \(0.533023\pi\)
\(654\) 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 \(-0.572293\pi\)
0.731202 + 0.682161i \(0.238960\pi\)
\(660\) 0 0
\(661\) 10.3923i 0.404214i 0.979363 + 0.202107i \(0.0647788\pi\)
−0.979363 + 0.202107i \(0.935221\pi\)
\(662\) 28.0000i 1.08825i
\(663\) 0 0
\(664\) 4.50000 2.59808i 0.174634 0.100825i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −5.19615 + 9.00000i −0.201045 + 0.348220i
\(669\) 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 0.999999 + 0.00128586i \(0.000409302\pi\)
−0.498886 + 0.866668i \(0.666257\pi\)
\(674\) 11.2583 + 6.50000i 0.433655 + 0.250371i
\(675\) 0 0
\(676\) 0.500000 + 0.866025i 0.0192308 + 0.0333087i
\(677\) −15.5885 −0.599113 −0.299557 0.954079i \(-0.596839\pi\)
−0.299557 + 0.954079i \(0.596839\pi\)
\(678\) 0 0
\(679\) −7.50000 + 21.6506i −0.287824 + 0.830875i
\(680\) 0 0
\(681\) 0 0
\(682\) 4.50000 + 2.59808i 0.172314 + 0.0994855i
\(683\) −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
\(686\) −15.5885 + 10.0000i −0.595170 + 0.381802i
\(687\) 0 0
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) 20.7846 0.791831
\(690\) 0 0
\(691\) 13.8564i 0.527123i −0.964643 0.263561i \(-0.915103\pi\)
0.964643 0.263561i \(-0.0848971\pi\)
\(692\) −25.9808 −0.987640
\(693\) 0 0
\(694\) −3.00000 −0.113878
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 13.8564 + 24.0000i 0.524473 + 0.908413i
\(699\) 0 0
\(700\) 2.50000 + 12.9904i 0.0944911 + 0.490990i
\(701\) 6.00000i 0.226617i 0.993560 + 0.113308i \(0.0361448\pi\)
−0.993560 + 0.113308i \(0.963855\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 2.59808 + 1.50000i 0.0979187 + 0.0565334i
\(705\) 0 0
\(706\) 9.00000 + 5.19615i 0.338719 + 0.195560i
\(707\) −2.59808 13.5000i −0.0977107 0.507720i
\(708\) 0 0
\(709\) 4.00000 0.150223 0.0751116 0.997175i \(-0.476069\pi\)
0.0751116 + 0.997175i \(0.476069\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −9.00000 5.19615i −0.337289 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 7.79423 4.50000i 0.291284 0.168173i
\(717\) 0 0
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) −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
\(724\) 20.7846i 0.772454i
\(725\) 45.0000i 1.67126i
\(726\) 0 0
\(727\) −21.0000 + 12.1244i −0.778847 + 0.449667i −0.836021 0.548697i \(-0.815124\pi\)
0.0571746 + 0.998364i \(0.481791\pi\)
\(728\) −1.73205 9.00000i −0.0641941 0.333562i
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −12.0000 + 6.92820i −0.443230 + 0.255899i −0.704967 0.709240i \(-0.749038\pi\)
0.261737 + 0.965139i \(0.415705\pi\)
\(734\) −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
\(742\) 15.0000 + 5.19615i 0.550667 + 0.190757i
\(743\) −5.19615 3.00000i −0.190628 0.110059i 0.401648 0.915794i \(-0.368437\pi\)
−0.592277 + 0.805735i \(0.701771\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.46410 2.00000i 0.126830 0.0732252i
\(747\) 0 0
\(748\) 0 0
\(749\) 31.1769 6.00000i 1.13918 0.219235i
\(750\) 0 0
\(751\) −2.00000 3.46410i −0.0729810 0.126407i 0.827225 0.561870i \(-0.189918\pi\)
−0.900207 + 0.435463i \(0.856585\pi\)
\(752\) −10.3923 −0.378968
\(753\) 0 0
\(754\) 31.1769i 1.13540i
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 26.0000i 0.944363i
\(759\) 0 0
\(760\) 0 0
\(761\) −20.7846 36.0000i −0.753442 1.30500i −0.946145 0.323742i \(-0.895059\pi\)
0.192704 0.981257i \(-0.438274\pi\)
\(762\) 0 0
\(763\) 20.0000 + 6.92820i 0.724049 + 0.250818i
\(764\) 6.00000i 0.217072i
\(765\) 0 0
\(766\) 18.0000 10.3923i 0.650366 0.375489i
\(767\) 15.5885 + 9.00000i 0.562867 + 0.324971i
\(768\) 0 0
\(769\) 13.5000 + 7.79423i 0.486822 + 0.281067i 0.723255 0.690581i \(-0.242645\pi\)
−0.236433 + 0.971648i \(0.575978\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.0000 0.395899
\(773\) −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
\(781\) −18.0000 + 31.1769i −0.644091 + 1.11560i
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 0 0
\(786\) 0 0
\(787\) 24.2487i 0.864373i −0.901784 0.432187i \(-0.857742\pi\)
0.901784 0.432187i \(-0.142258\pi\)
\(788\) 15.0000i 0.534353i
\(789\) 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
\(794\) 12.1244 21.0000i 0.430277 0.745262i
\(795\) 0 0
\(796\) −1.50000 + 0.866025i