Properties

Label 152.2.i.b.121.1
Level $152$
Weight $2$
Character 152.121
Analytic conductor $1.214$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.21372611072\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 152.121
Dual form 152.2.i.b.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(2.00000 + 3.46410i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(2.00000 + 3.46410i) q^{5} +(1.00000 - 1.73205i) q^{9} +3.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(2.00000 - 3.46410i) q^{15} +(-1.00000 - 1.73205i) q^{17} +(0.500000 - 4.33013i) q^{19} +(-3.00000 + 5.19615i) q^{23} +(-5.50000 + 9.52628i) q^{25} -5.00000 q^{27} +(2.00000 - 3.46410i) q^{29} -10.0000 q^{31} +(-1.50000 - 2.59808i) q^{33} +2.00000 q^{37} +2.00000 q^{39} +(-4.50000 - 7.79423i) q^{41} +(2.00000 + 3.46410i) q^{43} +8.00000 q^{45} +(6.00000 - 10.3923i) q^{47} -7.00000 q^{49} +(-1.00000 + 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{53} +(6.00000 + 10.3923i) q^{55} +(-4.00000 + 1.73205i) q^{57} +(0.500000 + 0.866025i) q^{59} +(4.00000 - 6.92820i) q^{61} -8.00000 q^{65} +(-4.50000 + 7.79423i) q^{67} +6.00000 q^{69} +(3.00000 + 5.19615i) q^{71} +(4.50000 + 7.79423i) q^{73} +11.0000 q^{75} +(2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} -5.00000 q^{83} +(4.00000 - 6.92820i) q^{85} -4.00000 q^{87} +(9.00000 - 15.5885i) q^{89} +(5.00000 + 8.66025i) q^{93} +(16.0000 - 6.92820i) q^{95} +(-0.500000 - 0.866025i) q^{97} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} + 4q^{5} + 2q^{9} + O(q^{10}) \) \( 2q - q^{3} + 4q^{5} + 2q^{9} + 6q^{11} - 2q^{13} + 4q^{15} - 2q^{17} + q^{19} - 6q^{23} - 11q^{25} - 10q^{27} + 4q^{29} - 20q^{31} - 3q^{33} + 4q^{37} + 4q^{39} - 9q^{41} + 4q^{43} + 16q^{45} + 12q^{47} - 14q^{49} - 2q^{51} + 2q^{53} + 12q^{55} - 8q^{57} + q^{59} + 8q^{61} - 16q^{65} - 9q^{67} + 12q^{69} + 6q^{71} + 9q^{73} + 22q^{75} + 4q^{79} - q^{81} - 10q^{83} + 8q^{85} - 8q^{87} + 18q^{89} + 10q^{93} + 32q^{95} - q^{97} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).

\(n\) \(39\) \(77\) \(97\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) 0 0
\(5\) 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i \(0.185750\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 2.00000 3.46410i 0.516398 0.894427i
\(16\) 0 0
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) 0.500000 4.33013i 0.114708 0.993399i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) −5.50000 + 9.52628i −1.10000 + 1.90526i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 2.00000 3.46410i 0.371391 0.643268i −0.618389 0.785872i \(-0.712214\pi\)
0.989780 + 0.142605i \(0.0455477\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0 0
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) −4.50000 7.79423i −0.702782 1.21725i −0.967486 0.252924i \(-0.918608\pi\)
0.264704 0.964330i \(-0.414726\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 0 0
\(45\) 8.00000 1.19257
\(46\) 0 0
\(47\) 6.00000 10.3923i 0.875190 1.51587i 0.0186297 0.999826i \(-0.494070\pi\)
0.856560 0.516047i \(-0.172597\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) −1.00000 + 1.73205i −0.140028 + 0.242536i
\(52\) 0 0
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 0 0
\(55\) 6.00000 + 10.3923i 0.809040 + 1.40130i
\(56\) 0 0
\(57\) −4.00000 + 1.73205i −0.529813 + 0.229416i
\(58\) 0 0
\(59\) 0.500000 + 0.866025i 0.0650945 + 0.112747i 0.896736 0.442566i \(-0.145932\pi\)
−0.831641 + 0.555313i \(0.812598\pi\)
\(60\) 0 0
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.00000 −0.992278
\(66\) 0 0
\(67\) −4.50000 + 7.79423i −0.549762 + 0.952217i 0.448528 + 0.893769i \(0.351948\pi\)
−0.998290 + 0.0584478i \(0.981385\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) 0 0
\(73\) 4.50000 + 7.79423i 0.526685 + 0.912245i 0.999517 + 0.0310925i \(0.00989865\pi\)
−0.472831 + 0.881153i \(0.656768\pi\)
\(74\) 0 0
\(75\) 11.0000 1.27017
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −5.00000 −0.548821 −0.274411 0.961613i \(-0.588483\pi\)
−0.274411 + 0.961613i \(0.588483\pi\)
\(84\) 0 0
\(85\) 4.00000 6.92820i 0.433861 0.751469i
\(86\) 0 0
\(87\) −4.00000 −0.428845
\(88\) 0 0
\(89\) 9.00000 15.5885i 0.953998 1.65237i 0.217354 0.976093i \(-0.430258\pi\)
0.736644 0.676280i \(-0.236409\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 5.00000 + 8.66025i 0.518476 + 0.898027i
\(94\) 0 0
\(95\) 16.0000 6.92820i 1.64157 0.710819i
\(96\) 0 0
\(97\) −0.500000 0.866025i −0.0507673 0.0879316i 0.839525 0.543321i \(-0.182833\pi\)
−0.890292 + 0.455389i \(0.849500\pi\)
\(98\) 0 0
\(99\) 3.00000 5.19615i 0.301511 0.522233i
\(100\) 0 0
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.0000 1.54678 0.773389 0.633932i \(-0.218560\pi\)
0.773389 + 0.633932i \(0.218560\pi\)
\(108\) 0 0
\(109\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(110\) 0 0
\(111\) −1.00000 1.73205i −0.0949158 0.164399i
\(112\) 0 0
\(113\) −1.00000 −0.0940721 −0.0470360 0.998893i \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(114\) 0 0
\(115\) −24.0000 −2.23801
\(116\) 0 0
\(117\) 2.00000 + 3.46410i 0.184900 + 0.320256i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −4.50000 + 7.79423i −0.405751 + 0.702782i
\(124\) 0 0
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) 3.00000 5.19615i 0.266207 0.461084i −0.701672 0.712500i \(-0.747563\pi\)
0.967879 + 0.251416i \(0.0808962\pi\)
\(128\) 0 0
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 0 0
\(131\) 7.50000 + 12.9904i 0.655278 + 1.13497i 0.981824 + 0.189794i \(0.0607819\pi\)
−0.326546 + 0.945181i \(0.605885\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −10.0000 17.3205i −0.860663 1.49071i
\(136\) 0 0
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) 0 0
\(139\) 6.50000 11.2583i 0.551323 0.954919i −0.446857 0.894606i \(-0.647457\pi\)
0.998179 0.0603135i \(-0.0192101\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) 0 0
\(145\) 16.0000 1.32873
\(146\) 0 0
\(147\) 3.50000 + 6.06218i 0.288675 + 0.500000i
\(148\) 0 0
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −20.0000 34.6410i −1.60644 2.78243i
\(156\) 0 0
\(157\) −4.00000 6.92820i −0.319235 0.552931i 0.661094 0.750303i \(-0.270093\pi\)
−0.980329 + 0.197372i \(0.936759\pi\)
\(158\) 0 0
\(159\) −2.00000 −0.158610
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 0 0
\(165\) 6.00000 10.3923i 0.467099 0.809040i
\(166\) 0 0
\(167\) −8.00000 + 13.8564i −0.619059 + 1.07224i 0.370599 + 0.928793i \(0.379152\pi\)
−0.989658 + 0.143448i \(0.954181\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) −7.00000 5.19615i −0.535303 0.397360i
\(172\) 0 0
\(173\) 13.0000 + 22.5167i 0.988372 + 1.71191i 0.625871 + 0.779926i \(0.284744\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.500000 0.866025i 0.0375823 0.0650945i
\(178\) 0 0
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 0 0
\(181\) −7.00000 + 12.1244i −0.520306 + 0.901196i 0.479415 + 0.877588i \(0.340849\pi\)
−0.999721 + 0.0236082i \(0.992485\pi\)
\(182\) 0 0
\(183\) −8.00000 −0.591377
\(184\) 0 0
\(185\) 4.00000 + 6.92820i 0.294086 + 0.509372i
\(186\) 0 0
\(187\) −3.00000 5.19615i −0.219382 0.379980i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) 0 0
\(195\) 4.00000 + 6.92820i 0.286446 + 0.496139i
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 9.00000 15.5885i 0.637993 1.10504i −0.347879 0.937539i \(-0.613098\pi\)
0.985873 0.167497i \(-0.0535685\pi\)
\(200\) 0 0
\(201\) 9.00000 0.634811
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 18.0000 31.1769i 1.25717 2.17749i
\(206\) 0 0
\(207\) 6.00000 + 10.3923i 0.417029 + 0.722315i
\(208\) 0 0
\(209\) 1.50000 12.9904i 0.103757 0.898563i
\(210\) 0 0
\(211\) 6.00000 + 10.3923i 0.413057 + 0.715436i 0.995222 0.0976347i \(-0.0311277\pi\)
−0.582165 + 0.813070i \(0.697794\pi\)
\(212\) 0 0
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) 0 0
\(215\) −8.00000 + 13.8564i −0.545595 + 0.944999i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 4.50000 7.79423i 0.304082 0.526685i
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) −5.00000 8.66025i −0.334825 0.579934i 0.648626 0.761107i \(-0.275344\pi\)
−0.983451 + 0.181173i \(0.942010\pi\)
\(224\) 0 0
\(225\) 11.0000 + 19.0526i 0.733333 + 1.27017i
\(226\) 0 0
\(227\) 19.0000 1.26107 0.630537 0.776159i \(-0.282835\pi\)
0.630537 + 0.776159i \(0.282835\pi\)
\(228\) 0 0
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.50000 9.52628i −0.360317 0.624087i 0.627696 0.778459i \(-0.283998\pi\)
−0.988013 + 0.154371i \(0.950665\pi\)
\(234\) 0 0
\(235\) 48.0000 3.13117
\(236\) 0 0
\(237\) 2.00000 3.46410i 0.129914 0.225018i
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −10.5000 + 18.1865i −0.676364 + 1.17150i 0.299704 + 0.954032i \(0.403112\pi\)
−0.976068 + 0.217465i \(0.930221\pi\)
\(242\) 0 0
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) 0 0
\(245\) −14.0000 24.2487i −0.894427 1.54919i
\(246\) 0 0
\(247\) 7.00000 + 5.19615i 0.445399 + 0.330623i
\(248\) 0 0
\(249\) 2.50000 + 4.33013i 0.158431 + 0.274411i
\(250\) 0 0
\(251\) −2.50000 + 4.33013i −0.157799 + 0.273315i −0.934075 0.357078i \(-0.883773\pi\)
0.776276 + 0.630393i \(0.217106\pi\)
\(252\) 0 0
\(253\) −9.00000 + 15.5885i −0.565825 + 0.980038i
\(254\) 0 0
\(255\) −8.00000 −0.500979
\(256\) 0 0
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −4.00000 6.92820i −0.247594 0.428845i
\(262\) 0 0
\(263\) −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i \(-0.330877\pi\)
−0.999970 + 0.00771799i \(0.997543\pi\)
\(264\) 0 0
\(265\) 8.00000 0.491436
\(266\) 0 0
\(267\) −18.0000 −1.10158
\(268\) 0 0
\(269\) −2.00000 3.46410i −0.121942 0.211210i 0.798591 0.601874i \(-0.205579\pi\)
−0.920534 + 0.390664i \(0.872246\pi\)
\(270\) 0 0
\(271\) 10.0000 + 17.3205i 0.607457 + 1.05215i 0.991658 + 0.128897i \(0.0411435\pi\)
−0.384201 + 0.923249i \(0.625523\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −16.5000 + 28.5788i −0.994987 + 1.72337i
\(276\) 0 0
\(277\) 12.0000 0.721010 0.360505 0.932757i \(-0.382604\pi\)
0.360505 + 0.932757i \(0.382604\pi\)
\(278\) 0 0
\(279\) −10.0000 + 17.3205i −0.598684 + 1.03695i
\(280\) 0 0
\(281\) 6.50000 11.2583i 0.387757 0.671616i −0.604390 0.796689i \(-0.706583\pi\)
0.992148 + 0.125073i \(0.0399165\pi\)
\(282\) 0 0
\(283\) −6.50000 11.2583i −0.386385 0.669238i 0.605575 0.795788i \(-0.292943\pi\)
−0.991960 + 0.126550i \(0.959610\pi\)
\(284\) 0 0
\(285\) −14.0000 10.3923i −0.829288 0.615587i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) −0.500000 + 0.866025i −0.0293105 + 0.0507673i
\(292\) 0 0
\(293\) −4.00000 −0.233682 −0.116841 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) −2.00000 + 3.46410i −0.116445 + 0.201688i
\(296\) 0 0
\(297\) −15.0000 −0.870388
\(298\) 0 0
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 12.0000 0.689382
\(304\) 0 0
\(305\) 32.0000 1.83231
\(306\) 0 0
\(307\) −12.5000 21.6506i −0.713413 1.23567i −0.963569 0.267461i \(-0.913815\pi\)
0.250156 0.968206i \(-0.419518\pi\)
\(308\) 0 0
\(309\) 7.00000 + 12.1244i 0.398216 + 0.689730i
\(310\) 0 0
\(311\) −2.00000 −0.113410 −0.0567048 0.998391i \(-0.518059\pi\)
−0.0567048 + 0.998391i \(0.518059\pi\)
\(312\) 0 0
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 0 0
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) 0 0
\(321\) −8.00000 13.8564i −0.446516 0.773389i
\(322\) 0 0
\(323\) −8.00000 + 3.46410i −0.445132 + 0.192748i
\(324\) 0 0
\(325\) −11.0000 19.0526i −0.610170 1.05685i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 13.0000 0.714545 0.357272 0.934000i \(-0.383707\pi\)
0.357272 + 0.934000i \(0.383707\pi\)
\(332\) 0 0
\(333\) 2.00000 3.46410i 0.109599 0.189832i
\(334\) 0 0
\(335\) −36.0000 −1.96689
\(336\) 0 0
\(337\) −1.50000 2.59808i −0.0817102 0.141526i 0.822274 0.569091i \(-0.192705\pi\)
−0.903985 + 0.427565i \(0.859372\pi\)
\(338\) 0 0
\(339\) 0.500000 + 0.866025i 0.0271563 + 0.0470360i
\(340\) 0 0
\(341\) −30.0000 −1.62459
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 12.0000 + 20.7846i 0.646058 + 1.11901i
\(346\) 0 0
\(347\) 4.50000 + 7.79423i 0.241573 + 0.418416i 0.961162 0.275983i \(-0.0890035\pi\)
−0.719590 + 0.694399i \(0.755670\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) 5.00000 8.66025i 0.266880 0.462250i
\(352\) 0 0
\(353\) 11.0000 0.585471 0.292735 0.956193i \(-0.405434\pi\)
0.292735 + 0.956193i \(0.405434\pi\)
\(354\) 0 0
\(355\) −12.0000 + 20.7846i −0.636894 + 1.10313i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.00000 + 1.73205i 0.0527780 + 0.0914141i 0.891207 0.453596i \(-0.149859\pi\)
−0.838429 + 0.545010i \(0.816526\pi\)
\(360\) 0 0
\(361\) −18.5000 4.33013i −0.973684 0.227901i
\(362\) 0 0
\(363\) 1.00000 + 1.73205i 0.0524864 + 0.0909091i
\(364\) 0 0
\(365\) −18.0000 + 31.1769i −0.942163 + 1.63187i
\(366\) 0 0
\(367\) 13.0000 22.5167i 0.678594 1.17536i −0.296810 0.954937i \(-0.595923\pi\)
0.975404 0.220423i \(-0.0707439\pi\)
\(368\) 0 0
\(369\) −18.0000 −0.937043
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 12.0000 + 20.7846i 0.619677 + 1.07331i
\(376\) 0 0
\(377\) 4.00000 + 6.92820i 0.206010 + 0.356821i
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) −6.00000 −0.307389
\(382\) 0 0
\(383\) 4.00000 + 6.92820i 0.204390 + 0.354015i 0.949938 0.312437i \(-0.101145\pi\)
−0.745548 + 0.666452i \(0.767812\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8.00000 0.406663
\(388\) 0 0
\(389\) −2.00000 + 3.46410i −0.101404 + 0.175637i −0.912263 0.409604i \(-0.865667\pi\)
0.810859 + 0.585241i \(0.199000\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) 0 0
\(393\) 7.50000 12.9904i 0.378325 0.655278i
\(394\) 0 0
\(395\) −8.00000 + 13.8564i −0.402524 + 0.697191i
\(396\) 0 0
\(397\) 7.00000 + 12.1244i 0.351320 + 0.608504i 0.986481 0.163876i \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i \(-0.142801\pi\)
−0.826139 + 0.563466i \(0.809468\pi\)
\(402\) 0 0
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) 0 0
\(405\) 2.00000 3.46410i 0.0993808 0.172133i
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) 17.5000 30.3109i 0.865319 1.49878i −0.00141047 0.999999i \(-0.500449\pi\)
0.866730 0.498778i \(-0.166218\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −10.0000 17.3205i −0.490881 0.850230i
\(416\) 0 0
\(417\) −13.0000 −0.636613
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 11.0000 + 19.0526i 0.536107 + 0.928565i 0.999109 + 0.0422075i \(0.0134391\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 0 0
\(423\) −12.0000 20.7846i −0.583460 1.01058i
\(424\) 0 0
\(425\) 22.0000 1.06716
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 6.00000 0.289683
\(430\) 0 0
\(431\) 15.0000 25.9808i 0.722525 1.25145i −0.237460 0.971397i \(-0.576315\pi\)
0.959985 0.280052i \(-0.0903517\pi\)
\(432\) 0 0
\(433\) −5.00000 + 8.66025i −0.240285 + 0.416185i −0.960795 0.277259i \(-0.910574\pi\)
0.720511 + 0.693444i \(0.243907\pi\)
\(434\) 0 0
\(435\) −8.00000 13.8564i −0.383571 0.664364i
\(436\) 0 0
\(437\) 21.0000 + 15.5885i 1.00457 + 0.745697i
\(438\) 0 0
\(439\) 7.00000 + 12.1244i 0.334092 + 0.578664i 0.983310 0.181938i \(-0.0582371\pi\)
−0.649218 + 0.760602i \(0.724904\pi\)
\(440\) 0 0
\(441\) −7.00000 + 12.1244i −0.333333 + 0.577350i
\(442\) 0 0
\(443\) −0.500000 + 0.866025i −0.0237557 + 0.0411461i −0.877659 0.479286i \(-0.840896\pi\)
0.853903 + 0.520432i \(0.174229\pi\)
\(444\) 0 0
\(445\) 72.0000 3.41313
\(446\) 0 0
\(447\) 5.00000 8.66025i 0.236492 0.409616i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) −13.5000 23.3827i −0.635690 1.10105i
\(452\) 0 0
\(453\) −1.00000 1.73205i −0.0469841 0.0813788i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −11.0000 −0.514558 −0.257279 0.966337i \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(458\) 0 0
\(459\) 5.00000 + 8.66025i 0.233380 + 0.404226i
\(460\) 0 0
\(461\) −3.00000 5.19615i −0.139724 0.242009i 0.787668 0.616100i \(-0.211288\pi\)
−0.927392 + 0.374091i \(0.877955\pi\)
\(462\) 0 0
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) 0 0
\(465\) −20.0000 + 34.6410i −0.927478 + 1.60644i
\(466\) 0 0
\(467\) 5.00000 0.231372 0.115686 0.993286i \(-0.463093\pi\)
0.115686 + 0.993286i \(0.463093\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −4.00000 + 6.92820i −0.184310 + 0.319235i
\(472\) 0 0
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) 0 0
\(475\) 38.5000 + 28.5788i 1.76650 + 1.31129i
\(476\) 0 0
\(477\) −2.00000 3.46410i −0.0915737 0.158610i
\(478\) 0 0
\(479\) −10.0000 + 17.3205i −0.456912 + 0.791394i −0.998796 0.0490589i \(-0.984378\pi\)
0.541884 + 0.840453i \(0.317711\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.00000 3.46410i 0.0908153 0.157297i
\(486\) 0 0
\(487\) −26.0000 −1.17817 −0.589086 0.808070i \(-0.700512\pi\)
−0.589086 + 0.808070i \(0.700512\pi\)
\(488\) 0 0
\(489\) 5.50000 + 9.52628i 0.248719 + 0.430793i
\(490\) 0 0
\(491\) −8.00000 13.8564i −0.361035 0.625331i 0.627096 0.778942i \(-0.284243\pi\)
−0.988131 + 0.153611i \(0.950910\pi\)
\(492\) 0 0
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) 24.0000 1.07872
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −3.50000 6.06218i −0.156682 0.271380i 0.776989 0.629515i \(-0.216746\pi\)
−0.933670 + 0.358134i \(0.883413\pi\)
\(500\) 0 0
\(501\) 16.0000 0.714827
\(502\) 0 0
\(503\) 3.00000 5.19615i 0.133763 0.231685i −0.791361 0.611349i \(-0.790627\pi\)
0.925124 + 0.379664i \(0.123960\pi\)
\(504\) 0 0
\(505\) −48.0000 −2.13597
\(506\) 0 0
\(507\) 4.50000 7.79423i 0.199852 0.346154i
\(508\) 0 0
\(509\) −8.00000 + 13.8564i −0.354594 + 0.614174i −0.987048 0.160423i \(-0.948714\pi\)
0.632455 + 0.774597i \(0.282047\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.50000 + 21.6506i −0.110378 + 0.955899i
\(514\) 0 0
\(515\) −28.0000 48.4974i −1.23383 2.13705i
\(516\) 0 0
\(517\) 18.0000 31.1769i 0.791639 1.37116i
\(518\) 0 0
\(519\) 13.0000 22.5167i 0.570637 0.988372i
\(520\) 0 0
\(521\) 1.00000 0.0438108 0.0219054 0.999760i \(-0.493027\pi\)
0.0219054 + 0.999760i \(0.493027\pi\)
\(522\) 0 0
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.0000 + 17.3205i 0.435607 + 0.754493i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 2.00000 0.0867926
\(532\) 0 0
\(533\) 18.0000 0.779667
\(534\) 0 0
\(535\) 32.0000 + 55.4256i 1.38348 + 2.39626i
\(536\) 0 0
\(537\) −4.50000 7.79423i −0.194189 0.336346i
\(538\) 0 0
\(539\) −21.0000 −0.904534
\(540\) 0 0
\(541\) −2.00000 + 3.46410i −0.0859867 + 0.148933i −0.905811 0.423681i \(-0.860738\pi\)
0.819825 + 0.572615i \(0.194071\pi\)
\(542\) 0 0
\(543\) 14.0000 0.600798
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −14.0000 + 24.2487i −0.598597 + 1.03680i 0.394432 + 0.918925i \(0.370941\pi\)
−0.993028 + 0.117875i \(0.962392\pi\)
\(548\) 0 0
\(549\) −8.00000 13.8564i −0.341432 0.591377i
\(550\) 0 0
\(551\) −14.0000 10.3923i −0.596420 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 4.00000 6.92820i 0.169791 0.294086i
\(556\) 0 0
\(557\) 20.0000 34.6410i 0.847427 1.46779i −0.0360693 0.999349i \(-0.511484\pi\)
0.883497 0.468438i \(-0.155183\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) −3.00000 + 5.19615i −0.126660 + 0.219382i
\(562\) 0 0
\(563\) 11.0000 0.463595 0.231797 0.972764i \(-0.425539\pi\)
0.231797 + 0.972764i \(0.425539\pi\)
\(564\) 0 0
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −46.0000 −1.92842 −0.964210 0.265139i \(-0.914582\pi\)
−0.964210 + 0.265139i \(0.914582\pi\)
\(570\) 0 0
\(571\) 17.0000 0.711428 0.355714 0.934595i \(-0.384238\pi\)
0.355714 + 0.934595i \(0.384238\pi\)
\(572\) 0 0
\(573\) −6.00000 10.3923i −0.250654 0.434145i
\(574\) 0 0
\(575\) −33.0000 57.1577i −1.37620 2.38364i
\(576\) 0 0
\(577\) −37.0000 −1.54033 −0.770165 0.637845i \(-0.779826\pi\)
−0.770165 + 0.637845i \(0.779826\pi\)
\(578\) 0 0
\(579\) 3.00000 5.19615i 0.124676 0.215945i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 3.00000 5.19615i 0.124247 0.215203i
\(584\) 0 0
\(585\) −8.00000 + 13.8564i −0.330759 + 0.572892i
\(586\) 0 0
\(587\) −2.00000 3.46410i −0.0825488 0.142979i 0.821795 0.569783i \(-0.192973\pi\)
−0.904344 + 0.426804i \(0.859639\pi\)
\(588\) 0 0
\(589\) −5.00000 + 43.3013i −0.206021 + 1.78420i
\(590\) 0 0
\(591\) 9.00000 + 15.5885i 0.370211 + 0.641223i
\(592\) 0 0
\(593\) 10.5000 18.1865i 0.431183 0.746831i −0.565792 0.824548i \(-0.691430\pi\)
0.996976 + 0.0777165i \(0.0247629\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −18.0000 −0.736691
\(598\) 0 0
\(599\) −19.0000 + 32.9090i −0.776319 + 1.34462i 0.157731 + 0.987482i \(0.449582\pi\)
−0.934050 + 0.357142i \(0.883751\pi\)
\(600\) 0 0
\(601\) −13.0000 −0.530281 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) 0 0
\(603\) 9.00000 + 15.5885i 0.366508 + 0.634811i
\(604\) 0 0
\(605\) −4.00000 6.92820i −0.162623 0.281672i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 + 20.7846i 0.485468 + 0.840855i
\(612\) 0 0
\(613\) 11.0000 + 19.0526i 0.444286 + 0.769526i 0.998002 0.0631797i \(-0.0201241\pi\)
−0.553716 + 0.832705i \(0.686791\pi\)
\(614\) 0 0
\(615\) −36.0000 −1.45166
\(616\) 0 0
\(617\) −1.50000 + 2.59808i −0.0603877 + 0.104595i −0.894639 0.446790i \(-0.852567\pi\)
0.834251 + 0.551385i \(0.185900\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) 15.0000 25.9808i 0.601929 1.04257i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −20.5000 35.5070i −0.820000 1.42028i
\(626\) 0 0
\(627\) −12.0000 + 5.19615i −0.479234 + 0.207514i
\(628\) 0 0
\(629\) −2.00000 3.46410i −0.0797452 0.138123i
\(630\) 0 0
\(631\) 4.00000 6.92820i 0.159237 0.275807i −0.775356 0.631524i \(-0.782430\pi\)
0.934594 + 0.355716i \(0.115763\pi\)
\(632\) 0 0
\(633\) 6.00000 10.3923i 0.238479 0.413057i
\(634\) 0 0
\(635\) 24.0000 0.952411
\(636\) 0 0
\(637\) 7.00000 12.1244i 0.277350 0.480384i
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) 0 0
\(643\) −2.50000 4.33013i −0.0985904 0.170764i 0.812511 0.582946i \(-0.198100\pi\)
−0.911101 + 0.412182i \(0.864767\pi\)
\(644\) 0 0
\(645\) 16.0000 0.629999
\(646\) 0 0
\(647\) −14.0000 −0.550397 −0.275198 0.961387i \(-0.588744\pi\)
−0.275198 + 0.961387i \(0.588744\pi\)
\(648\) 0 0
\(649\) 1.50000 + 2.59808i 0.0588802 + 0.101983i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) 0 0
\(655\) −30.0000 + 51.9615i −1.17220 + 2.03030i
\(656\) 0 0
\(657\) 18.0000 0.702247
\(658\) 0 0
\(659\) −6.00000 + 10.3923i −0.233727 + 0.404827i −0.958902 0.283738i \(-0.908425\pi\)
0.725175 + 0.688565i \(0.241759\pi\)
\(660\) 0 0
\(661\) −10.0000 + 17.3205i −0.388955 + 0.673690i −0.992309 0.123784i \(-0.960497\pi\)
0.603354 + 0.797473i \(0.293830\pi\)
\(662\) 0 0
\(663\) −2.00000 3.46410i −0.0776736 0.134535i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 + 20.7846i 0.464642 + 0.804783i
\(668\) 0 0
\(669\) −5.00000 + 8.66025i −0.193311 + 0.334825i
\(670\) 0 0
\(671\) 12.0000 20.7846i 0.463255 0.802381i
\(672\) 0 0
\(673\) 30.0000 1.15642 0.578208 0.815890i \(-0.303752\pi\)
0.578208 + 0.815890i \(0.303752\pi\)
\(674\) 0 0
\(675\) 27.5000 47.6314i 1.05848 1.83333i
\(676\) 0 0
\(677\) −2.00000 −0.0768662 −0.0384331 0.999261i \(-0.512237\pi\)
−0.0384331 + 0.999261i \(0.512237\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −9.50000 16.4545i −0.364041 0.630537i
\(682\) 0 0
\(683\) −28.0000 −1.07139 −0.535695 0.844411i \(-0.679950\pi\)
−0.535695 + 0.844411i \(0.679950\pi\)
\(684\) 0 0
\(685\) −36.0000 −1.37549
\(686\) 0 0
\(687\) 4.00000 + 6.92820i 0.152610 + 0.264327i
\(688\) 0 0
\(689\) 2.00000 + 3.46410i 0.0761939 + 0.131972i
\(690\) 0 0
\(691\) 36.0000 1.36950 0.684752 0.728776i \(-0.259910\pi\)
0.684752 + 0.728776i \(0.259910\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 52.0000 1.97247
\(696\) 0 0
\(697\) −9.00000 + 15.5885i −0.340899 + 0.590455i
\(698\) 0 0
\(699\) −5.50000 + 9.52628i −0.208029 + 0.360317i
\(700\) 0 0
\(701\) 6.00000 + 10.3923i 0.226617 + 0.392512i 0.956803 0.290736i \(-0.0939001\pi\)
−0.730186 + 0.683248i \(0.760567\pi\)
\(702\) 0 0
\(703\) 1.00000 8.66025i 0.0377157 0.326628i
\(704\) 0 0
\(705\) −24.0000 41.5692i −0.903892 1.56559i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −9.00000 + 15.5885i −0.338002 + 0.585437i −0.984057 0.177854i \(-0.943084\pi\)
0.646055 + 0.763291i \(0.276418\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) 30.0000 51.9615i 1.12351 1.94597i
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) 0 0
\(717\) −6.00000 10.3923i −0.224074 0.388108i
\(718\) 0 0
\(719\) 17.0000 + 29.4449i 0.633993 + 1.09811i 0.986728 + 0.162385i \(0.0519185\pi\)
−0.352735 + 0.935723i \(0.614748\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 21.0000 0.780998
\(724\) 0 0
\(725\) 22.0000 + 38.1051i 0.817059 + 1.41519i
\(726\) 0 0
\(727\) 4.00000 + 6.92820i 0.148352 + 0.256953i 0.930618 0.365991i \(-0.119270\pi\)
−0.782267 + 0.622944i \(0.785937\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) 0 0
\(733\) 22.0000 0.812589 0.406294 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 0 0
\(735\) −14.0000 + 24.2487i −0.516398 + 0.894427i
\(736\) 0 0
\(737\) −13.5000 + 23.3827i −0.497279 + 0.861312i
\(738\) 0 0
\(739\) 2.50000 + 4.33013i 0.0919640 + 0.159286i 0.908337 0.418238i \(-0.137352\pi\)
−0.816373 + 0.577524i \(0.804019\pi\)
\(740\) 0 0
\(741\) 1.00000 8.66025i 0.0367359 0.318142i
\(742\) 0 0
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) 0 0
\(745\) −20.0000 + 34.6410i −0.732743 + 1.26915i
\(746\) 0 0
\(747\) −5.00000 + 8.66025i −0.182940 + 0.316862i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −19.0000 + 32.9090i −0.693320 + 1.20087i 0.277424 + 0.960748i \(0.410519\pi\)
−0.970744 + 0.240118i \(0.922814\pi\)
\(752\) 0 0
\(753\) 5.00000 0.182210
\(754\) 0 0
\(755\) 4.00000 + 6.92820i 0.145575 + 0.252143i
\(756\) 0 0
\(757\) −7.00000 12.1244i −0.254419 0.440667i 0.710318 0.703881i \(-0.248551\pi\)
−0.964738 + 0.263213i \(0.915218\pi\)
\(758\) 0 0
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) 17.0000 0.616250 0.308125 0.951346i \(-0.400299\pi\)
0.308125 + 0.951346i \(0.400299\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −8.00000 13.8564i −0.289241 0.500979i
\(766\) 0 0
\(767\) −2.00000 −0.0722158
\(768\) 0 0
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) 0 0
\(773\) −26.0000 + 45.0333i −0.935155 + 1.61974i −0.160798 + 0.986987i \(0.551407\pi\)
−0.774357 + 0.632749i \(0.781927\pi\)
\(774\) 0 0
\(775\) 55.0000 95.2628i 1.97566 3.42194i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −36.0000 + 15.5885i −1.28983 + 0.558514i
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) 0 0
\(783\) −10.0000 + 17.3205i −0.357371 + 0.618984i
\(784\) 0 0
\(785\) 16.0000 27.7128i 0.571064 0.989113i
\(786\) 0 0
\(787\) 41.0000 1.46149 0.730746 0.682649i \(-0.239172\pi\)
0.730746 + 0.682649i \(0.239172\pi\)
\(788\) 0 0
\(789\) −8.00000 + 13.8564i −0.284808 + 0.493301i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 8.00000 + 13.8564i 0.284088 + 0.492055i
\(794\) 0 0
\(795\) −4.00000 6.92820i −0.141865 0.245718i
\(796\) 0 0
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\)