Properties

Label 336.2.bl.d.31.1
Level $336$
Weight $2$
Character 336.31
Analytic conductor $2.683$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bl (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
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: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 336.31
Dual form 336.2.bl.d.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(3.00000 - 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(3.00000 - 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} -1.73205i q^{13} +3.46410i q^{15} +(2.50000 + 4.33013i) q^{19} +(2.00000 + 1.73205i) q^{21} +(6.00000 - 3.46410i) q^{23} +(3.50000 - 6.06218i) q^{25} +1.00000 q^{27} +(-2.50000 + 4.33013i) q^{31} +(3.00000 - 1.73205i) q^{33} +(-3.00000 - 8.66025i) q^{35} +(5.50000 + 9.52628i) q^{37} +(1.50000 + 0.866025i) q^{39} -3.46410i q^{41} +8.66025i q^{43} +(-3.00000 - 1.73205i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-6.00000 + 10.3923i) q^{53} -12.0000 q^{55} -5.00000 q^{57} +(6.00000 - 10.3923i) q^{59} +(-12.0000 + 6.92820i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(7.50000 + 4.33013i) q^{67} +6.92820i q^{69} +3.46410i q^{71} +(-4.50000 - 2.59808i) q^{73} +(3.50000 + 6.06218i) q^{75} +(-6.00000 + 6.92820i) q^{77} +(10.5000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} -18.0000 q^{83} +(6.00000 - 3.46410i) q^{89} +(-4.50000 - 0.866025i) q^{91} +(-2.50000 - 4.33013i) q^{93} +(15.0000 + 8.66025i) q^{95} +6.92820i q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} + 6q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} + 6q^{5} + q^{7} - q^{9} - 6q^{11} + 5q^{19} + 4q^{21} + 12q^{23} + 7q^{25} + 2q^{27} - 5q^{31} + 6q^{33} - 6q^{35} + 11q^{37} + 3q^{39} - 6q^{45} - 6q^{47} - 13q^{49} - 12q^{53} - 24q^{55} - 10q^{57} + 12q^{59} - 24q^{61} - 5q^{63} - 6q^{65} + 15q^{67} - 9q^{73} + 7q^{75} - 12q^{77} + 21q^{79} - q^{81} - 36q^{83} + 12q^{89} - 9q^{91} - 5q^{93} + 30q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) 3.00000 1.73205i 1.34164 0.774597i 0.354593 0.935021i \(-0.384620\pi\)
0.987048 + 0.160424i \(0.0512862\pi\)
\(6\) 0 0
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.00000 1.73205i −0.904534 0.522233i −0.0258656 0.999665i \(-0.508234\pi\)
−0.878668 + 0.477432i \(0.841568\pi\)
\(12\) 0 0
\(13\) 1.73205i 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 0 0
\(15\) 3.46410i 0.894427i
\(16\) 0 0
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0 0
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) 0 0
\(21\) 2.00000 + 1.73205i 0.436436 + 0.377964i
\(22\) 0 0
\(23\) 6.00000 3.46410i 1.25109 0.722315i 0.279761 0.960070i \(-0.409745\pi\)
0.971325 + 0.237754i \(0.0764114\pi\)
\(24\) 0 0
\(25\) 3.50000 6.06218i 0.700000 1.21244i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 0 0
\(33\) 3.00000 1.73205i 0.522233 0.301511i
\(34\) 0 0
\(35\) −3.00000 8.66025i −0.507093 1.46385i
\(36\) 0 0
\(37\) 5.50000 + 9.52628i 0.904194 + 1.56611i 0.821995 + 0.569495i \(0.192861\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 0 0
\(39\) 1.50000 + 0.866025i 0.240192 + 0.138675i
\(40\) 0 0
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) 0 0
\(43\) 8.66025i 1.32068i 0.750968 + 0.660338i \(0.229587\pi\)
−0.750968 + 0.660338i \(0.770413\pi\)
\(44\) 0 0
\(45\) −3.00000 1.73205i −0.447214 0.258199i
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) 0 0
\(57\) −5.00000 −0.662266
\(58\) 0 0
\(59\) 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i \(-0.547975\pi\)
0.931282 0.364299i \(-0.118692\pi\)
\(60\) 0 0
\(61\) −12.0000 + 6.92820i −1.53644 + 0.887066i −0.537400 + 0.843328i \(0.680593\pi\)
−0.999043 + 0.0437377i \(0.986073\pi\)
\(62\) 0 0
\(63\) −2.50000 + 0.866025i −0.314970 + 0.109109i
\(64\) 0 0
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0 0
\(67\) 7.50000 + 4.33013i 0.916271 + 0.529009i 0.882443 0.470418i \(-0.155897\pi\)
0.0338274 + 0.999428i \(0.489230\pi\)
\(68\) 0 0
\(69\) 6.92820i 0.834058i
\(70\) 0 0
\(71\) 3.46410i 0.411113i 0.978645 + 0.205557i \(0.0659005\pi\)
−0.978645 + 0.205557i \(0.934100\pi\)
\(72\) 0 0
\(73\) −4.50000 2.59808i −0.526685 0.304082i 0.212980 0.977056i \(-0.431683\pi\)
−0.739666 + 0.672975i \(0.765016\pi\)
\(74\) 0 0
\(75\) 3.50000 + 6.06218i 0.404145 + 0.700000i
\(76\) 0 0
\(77\) −6.00000 + 6.92820i −0.683763 + 0.789542i
\(78\) 0 0
\(79\) 10.5000 6.06218i 1.18134 0.682048i 0.225018 0.974355i \(-0.427756\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −18.0000 −1.97576 −0.987878 0.155230i \(-0.950388\pi\)
−0.987878 + 0.155230i \(0.950388\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 3.46410i 0.635999 0.367194i −0.147073 0.989126i \(-0.546985\pi\)
0.783072 + 0.621932i \(0.213652\pi\)
\(90\) 0 0
\(91\) −4.50000 0.866025i −0.471728 0.0907841i
\(92\) 0 0
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) 0 0
\(95\) 15.0000 + 8.66025i 1.53897 + 0.888523i
\(96\) 0 0
\(97\) 6.92820i 0.703452i 0.936103 + 0.351726i \(0.114405\pi\)
−0.936103 + 0.351726i \(0.885595\pi\)
\(98\) 0 0
\(99\) 3.46410i 0.348155i
\(100\) 0 0
\(101\) 9.00000 + 5.19615i 0.895533 + 0.517036i 0.875748 0.482768i \(-0.160368\pi\)
0.0197851 + 0.999804i \(0.493702\pi\)
\(102\) 0 0
\(103\) −2.50000 4.33013i −0.246332 0.426660i 0.716173 0.697923i \(-0.245892\pi\)
−0.962505 + 0.271263i \(0.912559\pi\)
\(104\) 0 0
\(105\) 9.00000 + 1.73205i 0.878310 + 0.169031i
\(106\) 0 0
\(107\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 0 0
\(109\) 3.50000 6.06218i 0.335239 0.580651i −0.648292 0.761392i \(-0.724516\pi\)
0.983531 + 0.180741i \(0.0578495\pi\)
\(110\) 0 0
\(111\) −11.0000 −1.04407
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 12.0000 20.7846i 1.11901 1.93817i
\(116\) 0 0
\(117\) −1.50000 + 0.866025i −0.138675 + 0.0800641i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 0 0
\(123\) 3.00000 + 1.73205i 0.270501 + 0.156174i
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 12.1244i 1.07586i 0.842989 + 0.537931i \(0.180794\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0 0
\(129\) −7.50000 4.33013i −0.660338 0.381246i
\(130\) 0 0
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 0 0
\(133\) 12.5000 4.33013i 1.08389 0.375470i
\(134\) 0 0
\(135\) 3.00000 1.73205i 0.258199 0.149071i
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) −7.00000 −0.593732 −0.296866 0.954919i \(-0.595942\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.50000 4.33013i 0.453632 0.357143i
\(148\) 0 0
\(149\) −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i \(-0.330232\pi\)
−0.999953 + 0.00974235i \(0.996899\pi\)
\(150\) 0 0
\(151\) 3.00000 + 1.73205i 0.244137 + 0.140952i 0.617076 0.786903i \(-0.288317\pi\)
−0.372940 + 0.927855i \(0.621650\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 17.3205i 1.39122i
\(156\) 0 0
\(157\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) −6.00000 10.3923i −0.475831 0.824163i
\(160\) 0 0
\(161\) −6.00000 17.3205i −0.472866 1.36505i
\(162\) 0 0
\(163\) −3.00000 + 1.73205i −0.234978 + 0.135665i −0.612866 0.790186i \(-0.709984\pi\)
0.377888 + 0.925851i \(0.376650\pi\)
\(164\) 0 0
\(165\) 6.00000 10.3923i 0.467099 0.809040i
\(166\) 0 0
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) 10.0000 0.769231
\(170\) 0 0
\(171\) 2.50000 4.33013i 0.191180 0.331133i
\(172\) 0 0
\(173\) 6.00000 3.46410i 0.456172 0.263371i −0.254262 0.967135i \(-0.581832\pi\)
0.710433 + 0.703765i \(0.248499\pi\)
\(174\) 0 0
\(175\) −14.0000 12.1244i −1.05830 0.916515i
\(176\) 0 0
\(177\) 6.00000 + 10.3923i 0.450988 + 0.781133i
\(178\) 0 0
\(179\) −9.00000 5.19615i −0.672692 0.388379i 0.124404 0.992232i \(-0.460298\pi\)
−0.797096 + 0.603853i \(0.793631\pi\)
\(180\) 0 0
\(181\) 5.19615i 0.386227i −0.981176 0.193113i \(-0.938141\pi\)
0.981176 0.193113i \(-0.0618586\pi\)
\(182\) 0 0
\(183\) 13.8564i 1.02430i
\(184\) 0 0
\(185\) 33.0000 + 19.0526i 2.42621 + 1.40077i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.500000 2.59808i 0.0363696 0.188982i
\(190\) 0 0
\(191\) 15.0000 8.66025i 1.08536 0.626634i 0.153024 0.988222i \(-0.451099\pi\)
0.932338 + 0.361588i \(0.117765\pi\)
\(192\) 0 0
\(193\) 5.50000 9.52628i 0.395899 0.685717i −0.597317 0.802005i \(-0.703766\pi\)
0.993215 + 0.116289i \(0.0370998\pi\)
\(194\) 0 0
\(195\) 6.00000 0.429669
\(196\) 0 0
\(197\) 24.0000 1.70993 0.854965 0.518686i \(-0.173579\pi\)
0.854965 + 0.518686i \(0.173579\pi\)
\(198\) 0 0
\(199\) −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i \(0.358603\pi\)
−0.996850 + 0.0793045i \(0.974730\pi\)
\(200\) 0 0
\(201\) −7.50000 + 4.33013i −0.529009 + 0.305424i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) 0 0
\(207\) −6.00000 3.46410i −0.417029 0.240772i
\(208\) 0 0
\(209\) 17.3205i 1.19808i
\(210\) 0 0
\(211\) 3.46410i 0.238479i 0.992866 + 0.119239i \(0.0380456\pi\)
−0.992866 + 0.119239i \(0.961954\pi\)
\(212\) 0 0
\(213\) −3.00000 1.73205i −0.205557 0.118678i
\(214\) 0 0
\(215\) 15.0000 + 25.9808i 1.02299 + 1.77187i
\(216\) 0 0
\(217\) 10.0000 + 8.66025i 0.678844 + 0.587896i
\(218\) 0 0
\(219\) 4.50000 2.59808i 0.304082 0.175562i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) −7.00000 −0.466667
\(226\) 0 0
\(227\) −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i \(0.370447\pi\)
−0.993210 + 0.116331i \(0.962887\pi\)
\(228\) 0 0
\(229\) 7.50000 4.33013i 0.495614 0.286143i −0.231287 0.972886i \(-0.574293\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) −3.00000 8.66025i −0.197386 0.569803i
\(232\) 0 0
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) −18.0000 10.3923i −1.17419 0.677919i
\(236\) 0 0
\(237\) 12.1244i 0.787562i
\(238\) 0 0
\(239\) 10.3923i 0.672222i 0.941822 + 0.336111i \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) 0 0
\(241\) −12.0000 6.92820i −0.772988 0.446285i 0.0609515 0.998141i \(-0.480586\pi\)
−0.833939 + 0.551856i \(0.813920\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) −24.0000 + 3.46410i −1.53330 + 0.221313i
\(246\) 0 0
\(247\) 7.50000 4.33013i 0.477214 0.275519i
\(248\) 0 0
\(249\) 9.00000 15.5885i 0.570352 0.987878i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) −24.0000 −1.50887
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −15.0000 + 8.66025i −0.935674 + 0.540212i −0.888602 0.458680i \(-0.848323\pi\)
−0.0470726 + 0.998891i \(0.514989\pi\)
\(258\) 0 0
\(259\) 27.5000 9.52628i 1.70877 0.591934i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.0000 + 6.92820i 0.739952 + 0.427211i 0.822052 0.569413i \(-0.192829\pi\)
−0.0821001 + 0.996624i \(0.526163\pi\)
\(264\) 0 0
\(265\) 41.5692i 2.55358i
\(266\) 0 0
\(267\) 6.92820i 0.423999i
\(268\) 0 0
\(269\) −15.0000 8.66025i −0.914566 0.528025i −0.0326687 0.999466i \(-0.510401\pi\)
−0.881897 + 0.471441i \(0.843734\pi\)
\(270\) 0 0
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 0 0
\(273\) 3.00000 3.46410i 0.181568 0.209657i
\(274\) 0 0
\(275\) −21.0000 + 12.1244i −1.26635 + 0.731126i
\(276\) 0 0
\(277\) −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i \(0.360033\pi\)
−0.996484 + 0.0837823i \(0.973300\pi\)
\(278\) 0 0
\(279\) 5.00000 0.299342
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −3.50000 + 6.06218i −0.208053 + 0.360359i −0.951101 0.308879i \(-0.900046\pi\)
0.743048 + 0.669238i \(0.233379\pi\)
\(284\) 0 0
\(285\) −15.0000 + 8.66025i −0.888523 + 0.512989i
\(286\) 0 0
\(287\) −9.00000 1.73205i −0.531253 0.102240i
\(288\) 0 0
\(289\) −8.50000 14.7224i −0.500000 0.866025i
\(290\) 0 0
\(291\) −6.00000 3.46410i −0.351726 0.203069i
\(292\) 0 0
\(293\) 20.7846i 1.21425i −0.794606 0.607125i \(-0.792323\pi\)
0.794606 0.607125i \(-0.207677\pi\)
\(294\) 0 0
\(295\) 41.5692i 2.42025i
\(296\) 0 0
\(297\) −3.00000 1.73205i −0.174078 0.100504i
\(298\) 0 0
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 0 0
\(301\) 22.5000 + 4.33013i 1.29688 + 0.249584i
\(302\) 0 0
\(303\) −9.00000 + 5.19615i −0.517036 + 0.298511i
\(304\) 0 0
\(305\) −24.0000 + 41.5692i −1.37424 + 2.38025i
\(306\) 0 0
\(307\) −11.0000 −0.627803 −0.313902 0.949456i \(-0.601636\pi\)
−0.313902 + 0.949456i \(0.601636\pi\)
\(308\) 0 0
\(309\) 5.00000 0.284440
\(310\) 0 0
\(311\) −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i \(0.337148\pi\)
−0.999928 + 0.0119847i \(0.996185\pi\)
\(312\) 0 0
\(313\) 13.5000 7.79423i 0.763065 0.440556i −0.0673300 0.997731i \(-0.521448\pi\)
0.830395 + 0.557175i \(0.188115\pi\)
\(314\) 0 0
\(315\) −6.00000 + 6.92820i −0.338062 + 0.390360i
\(316\) 0 0
\(317\) 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −10.5000 6.06218i −0.582435 0.336269i
\(326\) 0 0
\(327\) 3.50000 + 6.06218i 0.193550 + 0.335239i
\(328\) 0 0
\(329\) −15.0000 + 5.19615i −0.826977 + 0.286473i
\(330\) 0 0
\(331\) 13.5000 7.79423i 0.742027 0.428410i −0.0807788 0.996732i \(-0.525741\pi\)
0.822806 + 0.568323i \(0.192407\pi\)
\(332\) 0 0
\(333\) 5.50000 9.52628i 0.301398 0.522037i
\(334\) 0 0
\(335\) 30.0000 1.63908
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 0 0
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 0 0
\(341\) 15.0000 8.66025i 0.812296 0.468979i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 12.0000 + 20.7846i 0.646058 + 1.11901i
\(346\) 0 0
\(347\) −24.0000 13.8564i −1.28839 0.743851i −0.310021 0.950730i \(-0.600336\pi\)
−0.978367 + 0.206879i \(0.933669\pi\)
\(348\) 0 0
\(349\) 13.8564i 0.741716i −0.928689 0.370858i \(-0.879064\pi\)
0.928689 0.370858i \(-0.120936\pi\)
\(350\) 0 0
\(351\) 1.73205i 0.0924500i
\(352\) 0 0
\(353\) 21.0000 + 12.1244i 1.11772 + 0.645314i 0.940817 0.338914i \(-0.110060\pi\)
0.176900 + 0.984229i \(0.443393\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −18.0000 + 10.3923i −0.950004 + 0.548485i −0.893082 0.449894i \(-0.851462\pi\)
−0.0569216 + 0.998379i \(0.518129\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 0 0
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) −18.0000 −0.942163
\(366\) 0 0
\(367\) 5.50000 9.52628i 0.287098 0.497268i −0.686018 0.727585i \(-0.740643\pi\)
0.973116 + 0.230317i \(0.0739762\pi\)
\(368\) 0 0
\(369\) −3.00000 + 1.73205i −0.156174 + 0.0901670i
\(370\) 0 0
\(371\) 24.0000 + 20.7846i 1.24602 + 1.07908i
\(372\) 0 0
\(373\) 0.500000 + 0.866025i 0.0258890 + 0.0448411i 0.878680 0.477412i \(-0.158425\pi\)
−0.852791 + 0.522253i \(0.825092\pi\)
\(374\) 0 0
\(375\) 6.00000 + 3.46410i 0.309839 + 0.178885i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 8.66025i 0.444847i 0.974950 + 0.222424i \(0.0713968\pi\)
−0.974950 + 0.222424i \(0.928603\pi\)
\(380\) 0 0
\(381\) −10.5000 6.06218i −0.537931 0.310575i
\(382\) 0 0
\(383\) −12.0000 20.7846i −0.613171 1.06204i −0.990702 0.136047i \(-0.956560\pi\)
0.377531 0.925997i \(1.62323\pi\)
\(384\) 0 0
\(385\) −6.00000 + 31.1769i −0.305788 + 1.58892i
\(386\) 0 0
\(387\) 7.50000 4.33013i 0.381246 0.220113i
\(388\) 0 0
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 0 0
\(395\) 21.0000 36.3731i 1.05662 1.83013i
\(396\) 0 0
\(397\) −1.50000 + 0.866025i −0.0752828 + 0.0434646i −0.537169 0.843475i \(-0.680506\pi\)
0.461886 + 0.886939i \(0.347173\pi\)
\(398\) 0 0
\(399\) −2.50000 + 12.9904i −0.125157 + 0.650332i
\(400\) 0 0
\(401\) −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i \(-0.263528\pi\)
−0.976050 + 0.217545i \(0.930195\pi\)
\(402\) 0 0
\(403\) 7.50000 + 4.33013i 0.373602 + 0.215699i
\(404\) 0 0
\(405\) 3.46410i 0.172133i
\(406\) 0 0
\(407\) 38.1051i 1.88880i
\(408\) 0 0
\(409\) −19.5000 11.2583i −0.964213 0.556689i −0.0667458 0.997770i \(-0.521262\pi\)
−0.897467 + 0.441081i \(0.854595\pi\)
\(410\) 0 0
\(411\) −6.00000 10.3923i −0.295958 0.512615i
\(412\) 0 0
\(413\) −24.0000 20.7846i −1.18096 1.02274i
\(414\) 0 0
\(415\) −54.0000 + 31.1769i −2.65076 + 1.53041i
\(416\) 0 0
\(417\) 3.50000 6.06218i 0.171396 0.296866i
\(418\) 0 0
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) 0 0
\(421\) 7.00000 0.341159 0.170580 0.985344i \(-0.445436\pi\)
0.170580 + 0.985344i \(0.445436\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 12.0000 + 34.6410i 0.580721 + 1.67640i
\(428\) 0 0
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) 0 0
\(431\) 21.0000 + 12.1244i 1.01153 + 0.584010i 0.911641 0.410988i \(-0.134816\pi\)
0.0998939 + 0.994998i \(0.468150\pi\)
\(432\) 0 0
\(433\) 1.73205i 0.0832370i −0.999134 0.0416185i \(-0.986749\pi\)
0.999134 0.0416185i \(-0.0132514\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 30.0000 + 17.3205i 1.43509 + 0.828552i
\(438\) 0 0
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) 12.0000 6.92820i 0.570137 0.329169i −0.187067 0.982347i \(-0.559898\pi\)
0.757204 + 0.653178i \(0.226565\pi\)
\(444\) 0 0
\(445\) 12.0000 20.7846i 0.568855 0.985285i
\(446\) 0 0
\(447\) 12.0000 0.567581
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) −6.00000 + 10.3923i −0.282529 + 0.489355i
\(452\) 0 0
\(453\) −3.00000 + 1.73205i −0.140952 + 0.0813788i
\(454\) 0 0
\(455\) −15.0000 + 5.19615i −0.703211 + 0.243599i
\(456\) 0 0
\(457\) 9.50000 + 16.4545i 0.444391 + 0.769708i 0.998010 0.0630623i \(-0.0200867\pi\)
−0.553618 + 0.832771i \(0.686753\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.8564i 0.645357i −0.946509 0.322679i \(-0.895417\pi\)
0.946509 0.322679i \(-0.104583\pi\)
\(462\) 0 0
\(463\) 15.5885i 0.724457i −0.932089 0.362229i \(-0.882016\pi\)
0.932089 0.362229i \(-0.117984\pi\)
\(464\) 0 0
\(465\) −15.0000 8.66025i −0.695608 0.401610i
\(466\) 0 0
\(467\) −15.0000 25.9808i −0.694117 1.20225i −0.970477 0.241192i \(-0.922462\pi\)
0.276360 0.961054i \(1.58913\pi\)
\(468\) 0 0
\(469\) 15.0000 17.3205i 0.692636 0.799787i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.0000 25.9808i 0.689701 1.19460i
\(474\) 0 0
\(475\) 35.0000 1.60591
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) 0 0
\(479\) 6.00000 10.3923i 0.274147 0.474837i −0.695773 0.718262i \(-0.744938\pi\)
0.969920 + 0.243426i \(0.0782712\pi\)
\(480\) 0 0
\(481\) 16.5000 9.52628i 0.752335 0.434361i
\(482\) 0 0
\(483\) 18.0000 + 3.46410i 0.819028 + 0.157622i
\(484\) 0 0
\(485\) 12.0000 + 20.7846i 0.544892 + 0.943781i
\(486\) 0 0
\(487\) 22.5000 + 12.9904i 1.01957 + 0.588650i 0.913980 0.405759i \(-0.132993\pi\)
0.105592 + 0.994410i \(0.466326\pi\)
\(488\) 0 0
\(489\) 3.46410i 0.156652i
\(490\) 0 0
\(491\) 34.6410i 1.56333i −0.623700 0.781664i \(-0.714371\pi\)
0.623700 0.781664i \(-0.285629\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 6.00000 + 10.3923i 0.269680 + 0.467099i
\(496\) 0 0
\(497\) 9.00000 + 1.73205i 0.403705 + 0.0776931i
\(498\) 0 0
\(499\) −28.5000 + 16.4545i −1.27584 + 0.736604i −0.976080 0.217412i \(-0.930238\pi\)
−0.299755 + 0.954016i \(0.596905\pi\)
\(500\) 0 0
\(501\) 3.00000 5.19615i 0.134030 0.232147i
\(502\) 0 0
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) −5.00000 + 8.66025i −0.222058 + 0.384615i
\(508\) 0 0
\(509\) 27.0000 15.5885i 1.19675 0.690946i 0.236924 0.971528i \(-0.423861\pi\)
0.959830 + 0.280582i \(0.0905275\pi\)
\(510\) 0 0
\(511\) −9.00000 + 10.3923i −0.398137 + 0.459728i
\(512\) 0 0
\(513\) 2.50000 + 4.33013i 0.110378 + 0.191180i
\(514\) 0 0
\(515\) −15.0000 8.66025i −0.660979 0.381616i
\(516\) 0 0
\(517\) 20.7846i 0.914106i
\(518\) 0 0
\(519\) 6.92820i 0.304114i
\(520\) 0 0
\(521\) −12.0000 6.92820i −0.525730 0.303530i 0.213546 0.976933i \(-0.431499\pi\)
−0.739276 + 0.673403i \(0.764832\pi\)
\(522\) 0 0
\(523\) −5.50000 9.52628i −0.240498 0.416555i 0.720358 0.693602i \(-0.243977\pi\)
−0.960856 + 0.277047i \(0.910644\pi\)
\(524\) 0 0
\(525\) 17.5000 6.06218i 0.763763 0.264575i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 12.5000 21.6506i 0.543478 0.941332i
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9.00000 5.19615i 0.388379 0.224231i
\(538\) 0 0
\(539\) 15.0000 + 19.0526i 0.646096 + 0.820652i
\(540\) 0 0
\(541\) 2.50000 + 4.33013i 0.107483 + 0.186167i 0.914750 0.404020i \(-0.132387\pi\)
−0.807267 + 0.590187i \(0.799054\pi\)
\(542\) 0 0
\(543\) 4.50000 + 2.59808i 0.193113 + 0.111494i
\(544\) 0 0
\(545\) 24.2487i 1.03870i
\(546\) 0 0
\(547\) 3.46410i 0.148114i −0.997254 0.0740571i \(-0.976405\pi\)
0.997254 0.0740571i \(-0.0235947\pi\)
\(548\) 0 0
\(549\) 12.0000 + 6.92820i 0.512148 + 0.295689i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −10.5000 30.3109i −0.446505 1.28895i
\(554\) 0 0
\(555\) −33.0000 + 19.0526i −1.40077 + 0.808736i
\(556\) 0 0
\(557\) −21.0000 + 36.3731i −0.889799 + 1.54118i −0.0496855 + 0.998765i \(0.515822\pi\)
−0.840113 + 0.542411i \(0.817511\pi\)
\(558\) 0 0
\(559\) 15.0000 0.634432
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.00000 + 5.19615i −0.126435 + 0.218992i −0.922293 0.386492i \(-0.873687\pi\)
0.795858 + 0.605483i \(0.207020\pi\)
\(564\) 0 0
\(565\) −18.0000 + 10.3923i −0.757266 + 0.437208i
\(566\) 0 0
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) −21.0000 36.3731i −0.880366 1.52484i −0.850935 0.525271i \(-0.823964\pi\)
−0.0294311 0.999567i \(-0.509370\pi\)
\(570\) 0 0
\(571\) −40.5000 23.3827i −1.69487 0.978535i −0.950477 0.310796i \(-0.899404\pi\)
−0.744396 0.667739i \(1.23274\pi\)
\(572\) 0 0
\(573\) 17.3205i 0.723575i
\(574\) 0 0
\(575\) 48.4974i 2.02248i
\(576\) 0 0
\(577\) 10.5000 + 6.06218i 0.437121 + 0.252372i 0.702376 0.711807i \(-0.252123\pi\)
−0.265255 + 0.964178i \(0.585456\pi\)
\(578\) 0 0
\(579\) 5.50000 + 9.52628i 0.228572 + 0.395899i
\(580\) 0 0
\(581\) −9.00000 + 46.7654i −0.373383 + 1.94015i
\(582\) 0 0
\(583\) 36.0000 20.7846i 1.49097 0.860811i
\(584\) 0 0
\(585\) −3.00000 + 5.19615i −0.124035 + 0.214834i
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) −25.0000 −1.03011
\(590\) 0 0
\(591\) −12.0000 + 20.7846i −0.493614 + 0.854965i
\(592\) 0 0
\(593\) 3.00000 1.73205i 0.123195 0.0711268i −0.437136 0.899395i \(-0.644007\pi\)
0.560331 + 0.828269i \(0.310674\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.00000 13.8564i −0.327418 0.567105i
\(598\) 0 0
\(599\) −42.0000 24.2487i −1.71607 0.990775i −0.925794 0.378030i \(-0.876602\pi\)
−0.790280 0.612746i \(1.20994\pi\)
\(600\) 0 0
\(601\) 39.8372i 1.62499i −0.582967 0.812496i \(-0.698108\pi\)
0.582967 0.812496i \(-0.301892\pi\)
\(602\) 0 0
\(603\) 8.66025i 0.352673i
\(604\) 0 0
\(605\) 3.00000 + 1.73205i 0.121967 + 0.0704179i
\(606\) 0 0
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −9.00000 + 5.19615i −0.364101 + 0.210214i
\(612\) 0 0
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 0 0
\(615\) 12.0000 0.483887
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) 0.500000 0.866025i 0.0200967 0.0348085i −0.855802 0.517303i \(-0.826936\pi\)
0.875899 + 0.482495i \(0.160269\pi\)
\(620\) 0 0
\(621\) 6.00000 3.46410i 0.240772 0.139010i
\(622\) 0 0
\(623\) −6.00000 17.3205i −0.240385 0.693932i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) 15.0000 + 8.66025i 0.599042 + 0.345857i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 3.46410i 0.137904i 0.997620 + 0.0689519i \(0.0219655\pi\)
−0.997620 + 0.0689519i \(0.978035\pi\)
\(632\) 0 0
\(633\) −3.00000 1.73205i −0.119239 0.0688428i
\(634\) 0 0
\(635\) 21.0000 + 36.3731i 0.833360 + 1.44342i
\(636\) 0 0
\(637\) −4.50000 + 11.2583i −0.178296 + 0.446071i
\(638\) 0 0
\(639\) 3.00000 1.73205i 0.118678 0.0685189i
\(640\) 0 0
\(641\) −12.0000 + 20.7846i −0.473972 + 0.820943i −0.999556 0.0297987i \(-0.990513\pi\)
0.525584 + 0.850741i \(0.323847\pi\)
\(642\) 0 0
\(643\) 31.0000 1.22252 0.611260 0.791430i \(-0.290663\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(644\) 0 0
\(645\) −30.0000 −1.18125
\(646\) 0 0
\(647\) −15.0000 + 25.9808i −0.589711 + 1.02141i 0.404559 + 0.914512i \(0.367425\pi\)
−0.994270 + 0.106897i \(0.965908\pi\)
\(648\) 0 0
\(649\) −36.0000 + 20.7846i −1.41312 + 0.815867i
\(650\) 0 0
\(651\) −12.5000 + 4.33013i −0.489914 + 0.169711i
\(652\) 0 0
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 0 0
\(655\) 18.0000 + 10.3923i 0.703318 + 0.406061i
\(656\) 0 0
\(657\) 5.19615i 0.202721i
\(658\) 0 0
\(659\) 13.8564i 0.539769i 0.962893 + 0.269884i \(0.0869855\pi\)
−0.962893 + 0.269884i \(0.913014\pi\)
\(660\) 0 0
\(661\) 22.5000 + 12.9904i 0.875149 + 0.505267i 0.869056 0.494714i \(-0.164727\pi\)
0.00609283 + 0.999981i \(0.498061\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 30.0000 34.6410i 1.16335 1.34332i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) 0 0
\(671\) 48.0000 1.85302
\(672\) 0 0
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) 0 0
\(675\) 3.50000 6.06218i 0.134715 0.233333i
\(676\) 0 0
\(677\) −6.00000 + 3.46410i −0.230599 + 0.133136i −0.610848 0.791748i \(-0.709171\pi\)
0.380250 + 0.924884i \(0.375838\pi\)
\(678\) 0 0
\(679\) 18.0000 + 3.46410i 0.690777 + 0.132940i
\(680\) 0 0
\(681\) −9.00000 15.5885i −0.344881 0.597351i
\(682\) 0 0
\(683\) 6.00000 + 3.46410i 0.229584 + 0.132550i 0.610380 0.792109i \(-0.291017\pi\)
−0.380796 + 0.924659i \(0.624350\pi\)
\(684\) 0 0
\(685\) 41.5692i 1.58828i
\(686\) 0 0
\(687\) 8.66025i 0.330409i
\(688\) 0 0
\(689\) 18.0000 + 10.3923i 0.685745 + 0.395915i
\(690\) 0 0
\(691\) −11.5000 19.9186i −0.437481 0.757739i 0.560014 0.828483i \(-0.310796\pi\)
−0.997494 + 0.0707446i \(0.977462\pi\)
\(692\) 0 0
\(693\) 9.00000 + 1.73205i 0.341882 + 0.0657952i
\(694\) 0 0
\(695\) −21.0000 + 12.1244i −0.796575 + 0.459903i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0 0
\(703\) −27.5000 + 47.6314i −1.03718 + 1.79645i
\(704\) 0 0
\(705\) 18.0000 10.3923i 0.677919 0.391397i
\(706\) 0 0
\(707\) 18.0000 20.7846i 0.676960 0.781686i
\(708\) 0 0
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) −10.5000 6.06218i −0.393781 0.227349i
\(712\) 0 0
\(713\) 34.6410i 1.29732i
\(714\) 0 0
\(715\) 20.7846i 0.777300i
\(716\) 0 0
\(717\) −9.00000 5.19615i −0.336111 0.194054i
\(718\) 0 0
\(719\) −15.0000 25.9808i −0.559406 0.968919i −0.997546 0.0700124i \(-0.977696\pi\)
0.438141 0.898906i \(1.64436\pi\)
\(720\) 0 0
\(721\) −12.5000 + 4.33013i −0.465524 + 0.161262i
\(722\) 0 0
\(723\) 12.0000 6.92820i 0.446285 0.257663i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −25.5000 + 14.7224i −0.941864 + 0.543785i −0.890544 0.454897i \(-0.849676\pi\)
−0.0513199 + 0.998682i \(0.516343\pi\)
\(734\) 0 0
\(735\) 9.00000 22.5167i 0.331970 0.830540i
\(736\) 0 0
\(737\) −15.0000 25.9808i −0.552532 0.957014i
\(738\) 0 0
\(739\) −46.5000 26.8468i −1.71053 0.987575i −0.933839 0.357693i \(-0.883563\pi\)
−0.776691 0.629882i \(1.21690\pi\)
\(740\) 0 0
\(741\) 8.66025i 0.318142i
\(742\) 0 0
\(743\) 3.46410i 0.127086i 0.997979 + 0.0635428i \(0.0202399\pi\)
−0.997979 + 0.0635428i \(0.979760\pi\)
\(744\) 0 0
\(745\) −36.0000 20.7846i −1.31894 0.761489i
\(746\) 0 0
\(747\) 9.00000 + 15.5885i 0.329293 + 0.570352i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −4.50000 + 2.59808i −0.164207 + 0.0948051i −0.579852 0.814722i \(-0.696889\pi\)
0.415644 + 0.909527i \(0.363556\pi\)
\(752\) 0 0
\(753\) −6.00000 + 10.3923i −0.218652 + 0.378717i
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 0 0
\(759\) 12.0000 20.7846i 0.435572 0.754434i
\(760\) 0 0
\(761\) −36.0000 + 20.7846i −1.30500 + 0.753442i −0.981257 0.192704i \(-0.938274\pi\)
−0.323742 + 0.946145i \(0.604941\pi\)
\(762\) 0 0
\(763\) −14.0000 12.1244i −0.506834 0.438931i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −18.0000 10.3923i −0.649942 0.375244i
\(768\) 0 0
\(769\) 15.5885i 0.562134i −0.959688 0.281067i \(-0.909312\pi\)
0.959688 0.281067i \(-0.0906883\pi\)
\(770\) 0 0
\(771\) 17.3205i 0.623783i
\(772\) 0 0
\(773\) −39.0000 22.5167i −1.40273 0.809868i −0.408060 0.912955i \(-0.633795\pi\)
−0.994672 + 0.103087i \(0.967128\pi\)
\(774\) 0 0
\(775\) 17.5000 + 30.3109i 0.628619 + 1.08880i
\(776\) 0 0
\(777\) −5.50000 + 28.5788i −0.197311 + 1.02526i
\(778\) 0 0
\(779\) 15.0000 8.66025i 0.537431 0.310286i
\(780\) 0 0
\(781\) 6.00000 10.3923i 0.214697 0.371866i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 8.00000 13.8564i 0.285169 0.493928i −0.687481 0.726202i \(-0.741284\pi\)
0.972650 + 0.232275i \(0.0746169\pi\)
\(788\) 0 0
\(789\) −12.0000 + 6.92820i −0.427211 + 0.246651i
\(790\) 0 0
\(791\) −3.00000 + 15.5885i −0.106668 + 0.554262i
\(792\) 0 0
\(793\) 12.0000 + 20.7846i 0.426132 + 0.738083i
\(794\) 0 0
\(795\) −36.0000 20.7846i −1.27679 0.737154i
\(796\) 0 0
\(797\) 34.6410i 1.22705i