Properties

Label 378.2.k.a.215.1
Level $378$
Weight $2$
Character 378.215
Analytic conductor $3.018$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.01834519640\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 378.215
Dual form 378.2.k.a.269.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 2.59808i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 2.59808i) q^{7} -1.00000i q^{8} +(-2.59808 + 1.50000i) q^{11} +3.46410i q^{13} +(0.866025 - 2.50000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{22} +(2.50000 + 4.33013i) q^{25} +(1.73205 - 3.00000i) q^{26} +(-2.00000 + 1.73205i) q^{28} +9.00000i q^{29} +(-1.50000 + 0.866025i) q^{31} +(0.866025 - 0.500000i) q^{32} +(4.00000 - 6.92820i) q^{37} +10.3923 q^{41} +4.00000 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-5.19615 + 9.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} -5.00000i q^{50} +(-3.00000 + 1.73205i) q^{52} +(5.19615 - 3.00000i) q^{53} +(2.59808 - 0.500000i) q^{56} +(4.50000 - 7.79423i) q^{58} +(-2.59808 - 4.50000i) q^{59} +(-12.0000 - 6.92820i) q^{61} +1.73205 q^{62} -1.00000 q^{64} +(-1.00000 - 1.73205i) q^{67} +12.0000i q^{71} +(4.50000 - 2.59808i) q^{73} +(-6.92820 + 4.00000i) q^{74} +(-5.19615 - 6.00000i) q^{77} +(6.50000 - 11.2583i) q^{79} +(-9.00000 - 5.19615i) q^{82} -5.19615 q^{83} +(-3.46410 - 2.00000i) q^{86} +(1.50000 + 2.59808i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-9.00000 + 1.73205i) q^{91} +(9.00000 - 5.19615i) q^{94} -8.66025i q^{97} +(6.92820 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 2 q^{7} + O(q^{10}) \) \( 4 q + 2 q^{4} + 2 q^{7} - 2 q^{16} + 12 q^{22} + 10 q^{25} - 8 q^{28} - 6 q^{31} + 16 q^{37} + 16 q^{43} - 26 q^{49} - 12 q^{52} + 18 q^{58} - 48 q^{61} - 4 q^{64} - 4 q^{67} + 18 q^{73} + 26 q^{79} - 36 q^{82} + 6 q^{88} - 36 q^{91} + 36 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −2.59808 + 1.50000i −0.783349 + 0.452267i −0.837616 0.546259i \(-0.816051\pi\)
0.0542666 + 0.998526i \(0.482718\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) 0.866025 2.50000i 0.231455 0.668153i
\(15\) 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
\(22\) 3.00000 0.639602
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 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
\(29\) 9.00000i 1.67126i 0.549294 + 0.835629i \(0.314897\pi\)
−0.549294 + 0.835629i \(0.685103\pi\)
\(30\) 0 0
\(31\) −1.50000 + 0.866025i −0.269408 + 0.155543i −0.628619 0.777714i \(-0.716379\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 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
\(41\) 10.3923 1.62301 0.811503 0.584349i \(-0.198650\pi\)
0.811503 + 0.584349i \(0.198650\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −2.59808 1.50000i −0.391675 0.226134i
\(45\) 0 0
\(46\) 0 0
\(47\) −5.19615 + 9.00000i −0.757937 + 1.31278i 0.185964 + 0.982556i \(0.440459\pi\)
−0.943901 + 0.330228i \(0.892874\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 5.00000i 0.707107i
\(51\) 0 0
\(52\) −3.00000 + 1.73205i −0.416025 + 0.240192i
\(53\) 5.19615 3.00000i 0.713746 0.412082i −0.0987002 0.995117i \(-0.531468\pi\)
0.812447 + 0.583036i \(0.198135\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.59808 0.500000i 0.347183 0.0668153i
\(57\) 0 0
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −2.59808 4.50000i −0.338241 0.585850i 0.645861 0.763455i \(-0.276498\pi\)
−0.984102 + 0.177605i \(0.943165\pi\)
\(60\) 0 0
\(61\) −12.0000 6.92820i −1.53644 0.887066i −0.999043 0.0437377i \(-0.986073\pi\)
−0.537400 0.843328i \(-0.680593\pi\)
\(62\) 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 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000i 1.42414i 0.702109 + 0.712069i \(0.252242\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(72\) 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
\(77\) −5.19615 6.00000i −0.592157 0.683763i
\(78\) 0 0
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −9.00000 5.19615i −0.993884 0.573819i
\(83\) −5.19615 −0.570352 −0.285176 0.958475i \(-0.592052\pi\)
−0.285176 + 0.958475i \(0.592052\pi\)
\(84\) 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 \(-0.647659\pi\)
0.998218 0.0596775i \(-0.0190072\pi\)
\(90\) 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
\(97\) 8.66025i 0.879316i −0.898165 0.439658i \(-0.855100\pi\)
0.898165 0.439658i \(-0.144900\pi\)
\(98\) 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 \(-0.249901\pi\)
−0.965845 + 0.259120i \(0.916568\pi\)
\(102\) 0 0
\(103\) −15.0000 8.66025i −1.47799 0.853320i −0.478303 0.878195i \(-0.658748\pi\)
−0.999691 + 0.0248745i \(0.992081\pi\)
\(104\) 3.46410 0.339683
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −10.3923 6.00000i −1.00466 0.580042i −0.0950377 0.995474i \(-0.530297\pi\)
−0.909624 + 0.415432i \(0.863630\pi\)
\(108\) 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
\(112\) −2.50000 0.866025i −0.236228 0.0818317i
\(113\) 12.0000i 1.12887i −0.825479 0.564433i \(-0.809095\pi\)
0.825479 0.564433i \(-0.190905\pi\)
\(114\) 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
\(122\) 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
\(131\) −7.79423 + 13.5000i −0.680985 + 1.17950i 0.293696 + 0.955899i \(0.405115\pi\)
−0.974681 + 0.223602i \(0.928219\pi\)
\(132\) 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 0.0146279 0.999893i \(-0.495344\pi\)
0.873247 + 0.487278i \(0.162010\pi\)
\(138\) 0 0
\(139\) 6.92820i 0.587643i 0.955860 + 0.293821i \(0.0949270\pi\)
−0.955860 + 0.293821i \(0.905073\pi\)
\(140\) 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
\(146\) −5.19615 −0.430037
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 12.9904 + 7.50000i 1.06421 + 0.614424i 0.926595 0.376061i \(-0.122722\pi\)
0.137619 + 0.990485i \(0.456055\pi\)
\(150\) 0 0
\(151\) 11.5000 + 19.9186i 0.935857 + 1.62095i 0.773099 + 0.634285i \(0.218706\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 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 \(-0.530554\pi\)
0.814119 + 0.580699i \(0.197221\pi\)
\(158\) −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 \(0.0385779\pi\)
\(164\) 5.19615 + 9.00000i 0.405751 + 0.702782i
\(165\) 0 0
\(166\) 4.50000 + 2.59808i 0.349268 + 0.201650i
\(167\) 10.3923 0.804181 0.402090 0.915600i \(-0.368284\pi\)
0.402090 + 0.915600i \(0.368284\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) 12.9904 22.5000i 0.987640 1.71064i 0.358082 0.933690i \(-0.383431\pi\)
0.629558 0.776953i \(-0.283236\pi\)
\(174\) 0 0
\(175\) −10.0000 + 8.66025i −0.755929 + 0.654654i
\(176\) 3.00000i 0.226134i
\(177\) 0 0
\(178\) −9.00000 + 5.19615i −0.674579 + 0.389468i
\(179\) 7.79423 4.50000i 0.582568 0.336346i −0.179585 0.983742i \(-0.557476\pi\)
0.762153 + 0.647397i \(0.224142\pi\)
\(180\) 0 0
\(181\) 20.7846i 1.54491i 0.635071 + 0.772454i \(0.280971\pi\)
−0.635071 + 0.772454i \(0.719029\pi\)
\(182\) 8.66025 + 3.00000i 0.641941 + 0.222375i
\(183\) 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 0.676068 0.736839i \(-0.263683\pi\)
−0.300088 + 0.953912i \(0.597016\pi\)
\(192\) 0 0
\(193\) 5.50000 + 9.52628i 0.395899 + 0.685717i 0.993215 0.116289i \(-0.0370998\pi\)
−0.597317 + 0.802005i \(0.703766\pi\)
\(194\) −4.33013 + 7.50000i −0.310885 + 0.538469i
\(195\) 0 0
\(196\) −5.50000 4.33013i −0.392857 0.309295i
\(197\) 15.0000i 1.06871i 0.845262 + 0.534353i \(0.179445\pi\)
−0.845262 + 0.534353i \(0.820555\pi\)
\(198\) 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
\(202\) 5.19615i 0.365600i
\(203\) −23.3827 + 4.50000i −1.64114 + 0.315838i
\(204\) 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
\(211\) −2.00000 −0.137686 −0.0688428 0.997628i \(-0.521931\pi\)
−0.0688428 + 0.997628i \(0.521931\pi\)
\(212\) 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
\(218\) 8.00000i 0.541828i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 5.19615i 0.347960i 0.984749 + 0.173980i \(0.0556628\pi\)
−0.984749 + 0.173980i \(0.944337\pi\)
\(224\) 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 −0.869799 0.493406i \(-0.835752\pi\)
0.00759708 0.999971i \(-0.497582\pi\)
\(228\) 0 0
\(229\) 6.00000 + 3.46410i 0.396491 + 0.228914i 0.684969 0.728572i \(-0.259816\pi\)
−0.288478 + 0.957487i \(0.593149\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 9.00000 0.590879
\(233\) 15.5885 + 9.00000i 1.02123 + 0.589610i 0.914461 0.404674i \(-0.132615\pi\)
0.106773 + 0.994283i \(0.465948\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.59808 4.50000i 0.169120 0.292925i
\(237\) 0 0
\(238\) 0 0
\(239\) 12.0000i 0.776215i −0.921614 0.388108i \(-0.873129\pi\)
0.921614 0.388108i \(-0.126871\pi\)
\(240\) 0 0
\(241\) −10.5000 + 6.06218i −0.676364 + 0.390499i −0.798484 0.602016i \(-0.794364\pi\)
0.122119 + 0.992515i \(0.461031\pi\)
\(242\) 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 \(-0.805996\pi\)
−0.819946 + 0.572441i \(0.805996\pi\)
\(252\) 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
\(257\) −10.3923 + 18.0000i −0.648254 + 1.12281i 0.335285 + 0.942117i \(0.391167\pi\)
−0.983540 + 0.180693i \(0.942166\pi\)
\(258\) 0 0
\(259\) 20.0000 + 6.92820i 1.24274 + 0.430498i
\(260\) 0 0
\(261\) 0 0
\(262\) 13.5000 7.79423i 0.834033 0.481529i
\(263\) 20.7846 12.0000i 1.28163 0.739952i 0.304487 0.952517i \(-0.401515\pi\)
0.977147 + 0.212565i \(0.0681817\pi\)
\(264\) 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 0.524375 0.851488i \(-0.324299\pi\)
−0.999597 + 0.0283781i \(0.990966\pi\)
\(270\) 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
\(274\) −12.0000 −0.724947
\(275\) −12.9904 7.50000i −0.783349 0.452267i
\(276\) 0 0
\(277\) −7.00000 12.1244i −0.420589 0.728482i 0.575408 0.817867i \(-0.304843\pi\)
−0.995997 + 0.0893846i \(0.971510\pi\)
\(278\) 3.46410 6.00000i 0.207763 0.359856i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000i 0.357930i −0.983855 0.178965i \(-0.942725\pi\)
0.983855 0.178965i \(-0.0572749\pi\)
\(282\) 0 0
\(283\) 6.00000 3.46410i 0.356663 0.205919i −0.310953 0.950425i \(-0.600648\pi\)
0.667616 + 0.744506i \(0.267315\pi\)
\(284\) −10.3923 + 6.00000i −0.616670 + 0.356034i
\(285\) 0 0
\(286\) 10.3923i 0.614510i
\(287\) 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
\(293\) 5.19615 0.303562 0.151781 0.988414i \(-0.451499\pi\)
0.151781 + 0.988414i \(0.451499\pi\)
\(294\) 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
\(301\) 2.00000 + 10.3923i 0.115278 + 0.599002i
\(302\) 23.0000i 1.32350i
\(303\) 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 \(-0.164563\pi\)
\(308\) 2.59808 7.50000i 0.148039 0.427352i
\(309\) 0 0
\(310\) 0 0
\(311\) 15.5885 + 27.0000i 0.883940 + 1.53103i 0.846923 + 0.531715i \(0.178452\pi\)
0.0370169 + 0.999315i \(0.488214\pi\)
\(312\) 0 0
\(313\) −18.0000 10.3923i −1.01742 0.587408i −0.104065 0.994571i \(-0.533185\pi\)
−0.913356 + 0.407163i \(0.866518\pi\)
\(314\) −10.3923 −0.586472
\(315\) 0 0
\(316\) 13.0000 0.731307
\(317\) 7.79423 + 4.50000i 0.437767 + 0.252745i 0.702650 0.711535i \(-0.252000\pi\)
−0.264883 + 0.964281i \(0.585333\pi\)
\(318\) 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
\(326\) −8.66025 + 5.00000i −0.479647 + 0.276924i
\(327\) 0 0
\(328\) 10.3923i 0.573819i
\(329\) −25.9808 9.00000i −1.43237 0.496186i
\(330\) 0 0
\(331\) −14.0000 + 24.2487i −0.769510 + 1.33283i 0.168320 + 0.985732i \(0.446166\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(332\) −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
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) −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
\(344\) 4.00000i 0.215666i
\(345\) 0 0
\(346\) −22.5000 + 12.9904i −1.20961 + 0.698367i
\(347\) 2.59808 1.50000i 0.139472 0.0805242i −0.428640 0.903475i \(-0.641007\pi\)
0.568112 + 0.822951i \(0.307674\pi\)
\(348\) 0 0
\(349\) 27.7128i 1.48343i −0.670714 0.741716i \(-0.734012\pi\)
0.670714 0.741716i \(-0.265988\pi\)
\(350\) 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 \(-0.0774711\pi\)
−0.693965 + 0.720009i \(0.744138\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 10.3923 0.550791
\(357\) 0 0
\(358\) −9.00000 −0.475665
\(359\) 10.3923 + 6.00000i 0.548485 + 0.316668i 0.748511 0.663123i \(-0.230769\pi\)
−0.200026 + 0.979791i \(0.564103\pi\)
\(360\) 0 0
\(361\) −9.50000 16.4545i −0.500000 0.866025i
\(362\) 10.3923 18.0000i 0.546207 0.946059i
\(363\) 0 0
\(364\) −6.00000 6.92820i −0.314485 0.363137i
\(365\) 0 0
\(366\) 0 0
\(367\) 9.00000 5.19615i 0.469796 0.271237i −0.246358 0.969179i \(-0.579234\pi\)
0.716154 + 0.697942i \(0.245901\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.3923 + 12.0000i 0.539542 + 0.623009i
\(372\) 0 0
\(373\) 2.00000 3.46410i 0.103556 0.179364i −0.809591 0.586994i \(-0.800311\pi\)
0.913147 + 0.407630i \(0.133645\pi\)
\(374\) 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
\(383\) −10.3923 + 18.0000i −0.531022 + 0.919757i 0.468323 + 0.883558i \(0.344859\pi\)
−0.999345 + 0.0361995i \(0.988475\pi\)
\(384\) 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 −0.684403 0.729103i \(-0.739937\pi\)
0.289220 + 0.957263i \(0.406604\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 2.59808 + 6.50000i 0.131223 + 0.328300i
\(393\) 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 \(0.458437\pi\)
\(398\) −1.73205 −0.0868199
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 25.9808 + 15.0000i 1.29742 + 0.749064i 0.979957 0.199207i \(-0.0638367\pi\)
0.317460 + 0.948272i \(0.397170\pi\)
\(402\) 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
\(407\) 24.0000i 1.18964i
\(408\) 0 0
\(409\) 6.00000 3.46410i 0.296681 0.171289i −0.344270 0.938871i \(-0.611874\pi\)
0.640951 + 0.767582i \(0.278540\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 17.3205i 0.853320i
\(413\) 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
\(419\) 31.1769 1.52309 0.761546 0.648111i \(-0.224441\pi\)
0.761546 + 0.648111i \(0.224441\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 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
\(427\) 12.0000 34.6410i 0.580721 1.67640i
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 0 0
\(431\) 15.5885 9.00000i 0.750870 0.433515i −0.0751385 0.997173i \(-0.523940\pi\)
0.826008 + 0.563658i \(0.190607\pi\)
\(432\) 0 0
\(433\) 12.1244i 0.582659i 0.956623 + 0.291330i \(0.0940977\pi\)
−0.956623 + 0.291330i \(0.905902\pi\)
\(434\) 0.866025 + 4.50000i 0.0415705 + 0.216007i
\(435\) 0 0
\(436\) −4.00000 + 6.92820i −0.191565 + 0.331801i
\(437\) 0 0
\(438\) 0 0
\(439\) 13.5000 + 7.79423i 0.644320 + 0.371998i 0.786277 0.617875i \(-0.212006\pi\)
−0.141957 + 0.989873i \(0.545339\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −23.3827 13.5000i −1.11094 0.641404i −0.171871 0.985119i \(-0.554981\pi\)
−0.939074 + 0.343715i \(0.888315\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2.59808 4.50000i 0.123022 0.213081i
\(447\) 0 0
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) 30.0000i 1.41579i 0.706319 + 0.707894i \(0.250354\pi\)
−0.706319 + 0.707894i \(0.749646\pi\)
\(450\) 0 0
\(451\) −27.0000 + 15.5885i −1.27138 + 0.734032i
\(452\) 10.3923 6.00000i 0.488813 0.282216i
\(453\) 0 0
\(454\) 25.9808i 1.21934i
\(455\) 0 0
\(456\) 0 0
\(457\) −11.0000 + 19.0526i −0.514558 + 0.891241i 0.485299 + 0.874348i \(0.338711\pi\)
−0.999857 + 0.0168929i \(0.994623\pi\)
\(458\) −3.46410 6.00000i −0.161867 0.280362i
\(459\) 0 0
\(460\) 0 0
\(461\) −15.5885 −0.726027 −0.363013 0.931784i \(-0.618252\pi\)
−0.363013 + 0.931784i \(0.618252\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) −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 −0.919856 0.392256i \(-0.871695\pi\)
0.799632 + 0.600491i \(0.205028\pi\)
\(468\) 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
\(479\) 5.19615 + 9.00000i 0.237418 + 0.411220i 0.959973 0.280094i \(-0.0903655\pi\)
−0.722554 + 0.691314i \(0.757032\pi\)
\(480\) 0 0
\(481\) 24.0000 + 13.8564i 1.09431 + 0.631798i
\(482\) 12.1244 0.552249
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 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
\(491\) 36.0000i 1.62466i −0.583200 0.812329i \(-0.698200\pi\)
0.583200 0.812329i \(-0.301800\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.73205i 0.0777714i
\(497\) −31.1769 + 6.00000i −1.39848 + 0.269137i
\(498\) 0 0
\(499\) −8.00000 + 13.8564i −0.358129 + 0.620298i −0.987648 0.156687i \(-0.949919\pi\)
0.629519 + 0.776985i \(0.283252\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 22.5000 + 12.9904i 1.00422 + 0.579789i
\(503\) 31.1769 1.39011 0.695055 0.718957i \(-0.255380\pi\)
0.695055 + 0.718957i \(0.255380\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 4.00000 + 6.92820i 0.177471 + 0.307389i
\(509\) 2.59808 4.50000i 0.115158 0.199459i −0.802685 0.596403i \(-0.796596\pi\)
0.917843 + 0.396944i \(0.129929\pi\)
\(510\) 0 0
\(511\) 9.00000 + 10.3923i 0.398137 + 0.459728i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.0000 10.3923i 0.793946 0.458385i
\(515\) 0 0
\(516\) 0 0
\(517\) 31.1769i 1.37116i
\(518\) −13.8564 16.0000i −0.608816 0.703000i
\(519\) 0 0
\(520\) 0 0
\(521\) −10.3923 18.0000i −0.455295 0.788594i 0.543410 0.839467i \(-0.317133\pi\)
−0.998705 + 0.0508731i \(0.983800\pi\)
\(522\) 0 0
\(523\) 33.0000 + 19.0526i 1.44299 + 0.833110i 0.998048 0.0624496i \(-0.0198913\pi\)
0.444941 + 0.895560i \(0.353225\pi\)
\(524\) −15.5885 −0.680985
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 36.0000i 1.55933i
\(534\) 0 0
\(535\) 0 0
\(536\) −1.73205 + 1.00000i −0.0748132 + 0.0431934i
\(537\) 0 0
\(538\) 15.5885i 0.672066i
\(539\) 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
\(547\) 14.0000 0.598597 0.299298 0.954160i \(-0.403247\pi\)
0.299298 + 0.954160i \(0.403247\pi\)
\(548\) 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
\(553\) 32.5000 + 11.2583i 1.38204 + 0.478753i
\(554\) 14.0000i 0.594803i
\(555\) 0 0
\(556\) −6.00000 + 3.46410i −0.254457 + 0.146911i
\(557\) −18.1865 + 10.5000i −0.770588 + 0.444899i −0.833084 0.553146i \(-0.813427\pi\)
0.0624962 + 0.998045i \(0.480094\pi\)
\(558\) 0 0
\(559\) 13.8564i 0.586064i
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 + 5.19615i −0.126547 + 0.219186i
\(563\) −15.5885 27.0000i −0.656975 1.13791i −0.981395 0.192001i \(-0.938502\pi\)
0.324420 0.945913i \(-0.394831\pi\)
\(564\) 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 0.701758 0.712415i \(-0.252399\pi\)
−0.266090 + 0.963948i \(0.585732\pi\)
\(570\) 0 0
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) 5.19615 9.00000i 0.217262 0.376309i
\(573\) 0 0
\(574\) 9.00000 25.9808i 0.375653 1.08442i
\(575\) 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
\(581\) −2.59808 13.5000i −0.107786 0.560074i
\(582\) 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
\(587\) −10.3923 −0.428936 −0.214468 0.976731i \(-0.568802\pi\)
−0.214468 + 0.976731i \(0.568802\pi\)
\(588\) 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 −0.569822 0.821768i \(-0.692988\pi\)
0.996583 + 0.0825966i \(0.0263213\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.0000i 0.614424i
\(597\) 0 0
\(598\) 0 0
\(599\) 25.9808 15.0000i 1.06155 0.612883i 0.135686 0.990752i \(-0.456676\pi\)
0.925859 + 0.377869i \(0.123343\pi\)
\(600\) 0 0
\(601\) 34.6410i 1.41304i 0.707695 + 0.706518i \(0.249735\pi\)
−0.707695 + 0.706518i \(0.750265\pi\)
\(602\) 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 \(-0.366962\pi\)
−0.588537 + 0.808470i \(0.700296\pi\)
\(608\) 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
\(616\) −6.00000 + 5.19615i −0.241747 + 0.209359i
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) 0 0
\(619\) 30.0000 17.3205i 1.20580 0.696170i 0.243962 0.969785i \(-0.421553\pi\)
0.961839 + 0.273615i \(0.0882193\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 31.1769i 1.25008i
\(623\) 25.9808 + 9.00000i 1.04090 + 0.360577i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 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
\(637\) −9.00000 22.5167i −0.356593 0.892143i
\(638\) 27.0000i 1.06894i
\(639\) 0 0
\(640\) 0 0
\(641\) −36.3731 + 21.0000i −1.43665 + 0.829450i −0.997615 0.0690201i \(-0.978013\pi\)
−0.439034 + 0.898470i \(0.644679\pi\)
\(642\) 0 0
\(643\) 3.46410i 0.136611i −0.997664 0.0683054i \(-0.978241\pi\)
0.997664 0.0683054i \(-0.0217592\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.19615 9.00000i −0.204282 0.353827i 0.745622 0.666369i \(-0.232153\pi\)
−0.949904 + 0.312543i \(0.898819\pi\)
\(648\) 0 0
\(649\) 13.5000 + 7.79423i 0.529921 + 0.305950i
\(650\) 17.3205 0.679366
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) −25.9808 15.0000i −1.01671 0.586995i −0.103558 0.994623i \(-0.533023\pi\)
−0.913148 + 0.407628i \(0.866356\pi\)
\(654\) 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
\(659\) 15.0000i 0.584317i −0.956370 0.292159i \(-0.905627\pi\)
0.956370 0.292159i \(-0.0943735\pi\)
\(660\) 0 0
\(661\) 9.00000 5.19615i 0.350059 0.202107i −0.314652 0.949207i \(-0.601888\pi\)
0.664711 + 0.747100i \(0.268554\pi\)
\(662\) 24.2487 14.0000i 0.942453 0.544125i
\(663\) 0 0
\(664\) 5.19615i 0.201650i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 5.19615 + 9.00000i 0.201045 + 0.348220i
\(669\) 0 0
\(670\) 0 0
\(671\) 41.5692 1.60476
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) −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 \(-0.930172\pi\)
0.676478 + 0.736463i \(0.263505\pi\)
\(678\) 0 0
\(679\) 22.5000 4.33013i 0.863471 0.166175i
\(680\) 0 0
\(681\) 0 0
\(682\) −4.50000 + 2.59808i −0.172314 + 0.0994855i
\(683\) 18.1865 10.5000i 0.695888 0.401771i −0.109926 0.993940i \(-0.535061\pi\)
0.805814 + 0.592168i \(0.201728\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.866025 + 18.5000i 0.0330650 + 0.706333i
\(687\) 0 0
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) 10.3923 + 18.0000i 0.395915 + 0.685745i
\(690\) 0 0
\(691\) 12.0000 + 6.92820i 0.456502 + 0.263561i 0.710572 0.703624i \(-0.248436\pi\)
−0.254071 + 0.967186i \(0.581770\pi\)
\(692\) 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
\(700\) −12.5000 4.33013i −0.472456 0.163663i
\(701\) 6.00000i 0.226617i −0.993560 0.113308i \(-0.963855\pi\)
0.993560 0.113308i \(-0.0361448\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 2.59808 1.50000i 0.0979187 0.0565334i
\(705\) 0 0
\(706\) 10.3923i 0.391120i
\(707\) 10.3923 9.00000i 0.390843 0.338480i
\(708\) 0 0
\(709\) −2.00000 + 3.46410i −0.0751116 + 0.130097i −0.901135 0.433539i \(-0.857265\pi\)
0.826023 + 0.563636i \(0.190598\pi\)
\(710\) 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 −0.752717 0.658344i \(-0.771257\pi\)
0.946501 + 0.322700i \(0.104591\pi\)
\(720\) 0 0
\(721\) 15.0000 43.3013i 0.558629 1.61262i
\(722\) 19.0000i 0.707107i
\(723\) 0 0
\(724\) −18.0000 + 10.3923i −0.668965 + 0.386227i
\(725\) −38.9711 + 22.5000i −1.44735 + 0.835629i
\(726\) 0 0
\(727\) 24.2487i 0.899335i −0.893196 0.449667i \(-0.851542\pi\)
0.893196 0.449667i \(-0.148458\pi\)
\(728\) 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 \(-0.250962\pi\)
−0.261737 + 0.965139i \(0.584295\pi\)
\(734\) −10.3923 −0.383587
\(735\) 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
\(742\) −3.00000 15.5885i −0.110133 0.572270i
\(743\) 6.00000i 0.220119i −0.993925 0.110059i \(-0.964896\pi\)
0.993925 0.110059i \(-0.0351041\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −3.46410 + 2.00000i −0.126830 + 0.0732252i
\(747\) 0 0
\(748\) 0 0
\(749\) 10.3923 30.0000i 0.379727 1.09618i
\(750\) 0 0
\(751\) −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i \(-0.856585\pi\)
0.827225 + 0.561870i \(0.189918\pi\)
\(752\) −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
\(761\) 20.7846 36.0000i 0.753442 1.30500i −0.192704 0.981257i \(-0.561726\pi\)
0.946145 0.323742i \(-0.104941\pi\)
\(762\) 0 0
\(763\) −16.0000 + 13.8564i −0.579239 + 0.501636i
\(764\) 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
\(769\) 15.5885i 0.562134i −0.959688 0.281067i \(-0.909312\pi\)
0.959688 0.281067i \(-0.0906883\pi\)
\(770\) 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 \(0.102113\pi\)
−0.201414 + 0.979506i \(0.564554\pi\)
\(774\) 0 0
\(775\) −7.50000 4.33013i −0.269408 0.155543i
\(776\) −8.66025 −0.310885
\(777\) 0 0
\(778\) 9.00000 0.322666
\(779\) 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
\(787\) −21.0000 + 12.1244i −0.748569 + 0.432187i −0.825177 0.564875i \(-0.808924\pi\)
0.0766075 + 0.997061i \(0.475591\pi\)
\(788\) −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
\(794\) −12.1244 21.0000i −0.430277 0.745262i
\(795\) 0 0
\(796\) 1.50000 + 0.866025i 0.0531661 + 0.0306955i
\(797\) 15.5885 0.552171 0.276086 0.961133i \(-0.410963\pi\)