Properties

Label 144.2.s.a.47.1
Level $144$
Weight $2$
Character 144.47
Analytic conductor $1.150$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(1\)
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 47.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 144.47
Dual form 144.2.s.a.95.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(-3.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(-3.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-2.00000 - 3.46410i) q^{13} +6.00000 q^{15} -1.73205i q^{17} +1.73205i q^{19} +(3.00000 + 5.19615i) q^{21} +(3.50000 - 6.06218i) q^{25} -5.19615i q^{27} +(-3.00000 - 1.73205i) q^{29} +(4.50000 - 2.59808i) q^{33} +12.0000 q^{35} +2.00000 q^{37} +6.92820i q^{39} +(-4.50000 + 2.59808i) q^{41} +(4.50000 + 2.59808i) q^{43} +(-9.00000 - 5.19615i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(2.50000 + 4.33013i) q^{49} +(-1.50000 + 2.59808i) q^{51} -10.3923i q^{55} +(1.50000 - 2.59808i) q^{57} +(-7.50000 - 12.9904i) q^{59} +(-4.00000 + 6.92820i) q^{61} -10.3923i q^{63} +(12.0000 + 6.92820i) q^{65} +(-7.50000 + 4.33013i) q^{67} -6.00000 q^{71} -11.0000 q^{73} +(-10.5000 + 6.06218i) q^{75} +(9.00000 - 5.19615i) q^{77} +(3.00000 + 1.73205i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 10.3923i) q^{83} +(3.00000 + 5.19615i) q^{85} +(3.00000 + 5.19615i) q^{87} -13.8564i q^{89} +13.8564i q^{91} +(-3.00000 - 5.19615i) q^{95} +(-6.50000 + 11.2583i) q^{97} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{3} - 6q^{5} - 6q^{7} + 3q^{9} + O(q^{10}) \) \( 2q - 3q^{3} - 6q^{5} - 6q^{7} + 3q^{9} - 3q^{11} - 4q^{13} + 12q^{15} + 6q^{21} + 7q^{25} - 6q^{29} + 9q^{33} + 24q^{35} + 4q^{37} - 9q^{41} + 9q^{43} - 18q^{45} - 12q^{47} + 5q^{49} - 3q^{51} + 3q^{57} - 15q^{59} - 8q^{61} + 24q^{65} - 15q^{67} - 12q^{71} - 22q^{73} - 21q^{75} + 18q^{77} + 6q^{79} - 9q^{81} + 12q^{83} + 6q^{85} + 6q^{87} - 6q^{95} - 13q^{97} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) 0 0
\(5\) −3.00000 + 1.73205i −1.34164 + 0.774597i −0.987048 0.160424i \(-0.948714\pi\)
−0.354593 + 0.935021i \(0.615380\pi\)
\(6\) 0 0
\(7\) −3.00000 1.73205i −1.13389 0.654654i −0.188982 0.981981i \(-0.560519\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) −2.00000 3.46410i −0.554700 0.960769i −0.997927 0.0643593i \(-0.979500\pi\)
0.443227 0.896410i \(-0.353834\pi\)
\(14\) 0 0
\(15\) 6.00000 1.54919
\(16\) 0 0
\(17\) 1.73205i 0.420084i −0.977692 0.210042i \(-0.932640\pi\)
0.977692 0.210042i \(-0.0673601\pi\)
\(18\) 0 0
\(19\) 1.73205i 0.397360i 0.980064 + 0.198680i \(0.0636654\pi\)
−0.980064 + 0.198680i \(0.936335\pi\)
\(20\) 0 0
\(21\) 3.00000 + 5.19615i 0.654654 + 1.13389i
\(22\) 0 0
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 3.50000 6.06218i 0.700000 1.21244i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −3.00000 1.73205i −0.557086 0.321634i 0.194889 0.980825i \(-0.437565\pi\)
−0.751975 + 0.659192i \(0.770899\pi\)
\(30\) 0 0
\(31\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) 0 0
\(33\) 4.50000 2.59808i 0.783349 0.452267i
\(34\) 0 0
\(35\) 12.0000 2.02837
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 6.92820i 1.10940i
\(40\) 0 0
\(41\) −4.50000 + 2.59808i −0.702782 + 0.405751i −0.808383 0.588657i \(-0.799657\pi\)
0.105601 + 0.994409i \(0.466323\pi\)
\(42\) 0 0
\(43\) 4.50000 + 2.59808i 0.686244 + 0.396203i 0.802203 0.597051i \(-0.203661\pi\)
−0.115960 + 0.993254i \(0.536994\pi\)
\(44\) 0 0
\(45\) −9.00000 5.19615i −1.34164 0.774597i
\(46\) 0 0
\(47\) −6.00000 + 10.3923i −0.875190 + 1.51587i −0.0186297 + 0.999826i \(0.505930\pi\)
−0.856560 + 0.516047i \(0.827403\pi\)
\(48\) 0 0
\(49\) 2.50000 + 4.33013i 0.357143 + 0.618590i
\(50\) 0 0
\(51\) −1.50000 + 2.59808i −0.210042 + 0.363803i
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 10.3923i 1.40130i
\(56\) 0 0
\(57\) 1.50000 2.59808i 0.198680 0.344124i
\(58\) 0 0
\(59\) −7.50000 12.9904i −0.976417 1.69120i −0.675178 0.737655i \(-0.735933\pi\)
−0.301239 0.953549i \(-0.597400\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 0 0
\(63\) 10.3923i 1.30931i
\(64\) 0 0
\(65\) 12.0000 + 6.92820i 1.48842 + 0.859338i
\(66\) 0 0
\(67\) −7.50000 + 4.33013i −0.916271 + 0.529009i −0.882443 0.470418i \(-0.844103\pi\)
−0.0338274 + 0.999428i \(0.510770\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) 0 0
\(75\) −10.5000 + 6.06218i −1.21244 + 0.700000i
\(76\) 0 0
\(77\) 9.00000 5.19615i 1.02565 0.592157i
\(78\) 0 0
\(79\) 3.00000 + 1.73205i 0.337526 + 0.194871i 0.659178 0.751987i \(-0.270905\pi\)
−0.321651 + 0.946858i \(0.604238\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) 3.00000 + 5.19615i 0.325396 + 0.563602i
\(86\) 0 0
\(87\) 3.00000 + 5.19615i 0.321634 + 0.557086i
\(88\) 0 0
\(89\) 13.8564i 1.46878i −0.678730 0.734388i \(-0.737469\pi\)
0.678730 0.734388i \(-0.262531\pi\)
\(90\) 0 0
\(91\) 13.8564i 1.45255i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 0 0
\(97\) −6.50000 + 11.2583i −0.659975 + 1.14311i 0.320647 + 0.947199i \(0.396100\pi\)
−0.980622 + 0.195911i \(0.937234\pi\)
\(98\) 0 0
\(99\) −9.00000 −0.904534
\(100\) 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
\(103\) 12.0000 6.92820i 1.18240 0.682656i 0.225828 0.974167i \(-0.427491\pi\)
0.956567 + 0.291511i \(0.0941580\pi\)
\(104\) 0 0
\(105\) −18.0000 10.3923i −1.75662 1.01419i
\(106\) 0 0
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 0 0
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) −3.00000 1.73205i −0.284747 0.164399i
\(112\) 0 0
\(113\) −6.00000 + 3.46410i −0.564433 + 0.325875i −0.754923 0.655814i \(-0.772326\pi\)
0.190490 + 0.981689i \(0.438992\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 6.00000 10.3923i 0.554700 0.960769i
\(118\) 0 0
\(119\) −3.00000 + 5.19615i −0.275010 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 9.00000 0.811503
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) −4.50000 7.79423i −0.396203 0.686244i
\(130\) 0 0
\(131\) 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) 0 0
\(133\) 3.00000 5.19615i 0.260133 0.450564i
\(134\) 0 0
\(135\) 9.00000 + 15.5885i 0.774597 + 1.34164i
\(136\) 0 0
\(137\) −1.50000 0.866025i −0.128154 0.0739895i 0.434553 0.900646i \(-0.356906\pi\)
−0.562706 + 0.826657i \(0.690240\pi\)
\(138\) 0 0
\(139\) 16.5000 9.52628i 1.39951 0.808008i 0.405170 0.914241i \(-0.367212\pi\)
0.994341 + 0.106233i \(0.0338788\pi\)
\(140\) 0 0
\(141\) 18.0000 10.3923i 1.51587 0.875190i
\(142\) 0 0
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) 12.0000 0.996546
\(146\) 0 0
\(147\) 8.66025i 0.714286i
\(148\) 0 0
\(149\) 12.0000 6.92820i 0.983078 0.567581i 0.0798802 0.996804i \(-0.474546\pi\)
0.903198 + 0.429224i \(0.141213\pi\)
\(150\) 0 0
\(151\) −6.00000 3.46410i −0.488273 0.281905i 0.235585 0.971854i \(-0.424299\pi\)
−0.723858 + 0.689949i \(0.757633\pi\)
\(152\) 0 0
\(153\) 4.50000 2.59808i 0.363803 0.210042i
\(154\) 0 0
\(155\) 0 0
\(156\) 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
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 3.46410i 0.271329i 0.990755 + 0.135665i \(0.0433170\pi\)
−0.990755 + 0.135665i \(0.956683\pi\)
\(164\) 0 0
\(165\) −9.00000 + 15.5885i −0.700649 + 1.21356i
\(166\) 0 0
\(167\) −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i \(-0.241242\pi\)
−0.958440 + 0.285295i \(0.907908\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) 0 0
\(171\) −4.50000 + 2.59808i −0.344124 + 0.198680i
\(172\) 0 0
\(173\) −21.0000 12.1244i −1.59660 0.921798i −0.992136 0.125166i \(-0.960054\pi\)
−0.604465 0.796632i \(-0.706613\pi\)
\(174\) 0 0
\(175\) −21.0000 + 12.1244i −1.58745 + 0.916515i
\(176\) 0 0
\(177\) 25.9808i 1.95283i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) 12.0000 6.92820i 0.887066 0.512148i
\(184\) 0 0
\(185\) −6.00000 + 3.46410i −0.441129 + 0.254686i
\(186\) 0 0
\(187\) 4.50000 + 2.59808i 0.329073 + 0.189990i
\(188\) 0 0
\(189\) −9.00000 + 15.5885i −0.654654 + 1.13389i
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) −11.5000 19.9186i −0.827788 1.43377i −0.899770 0.436365i \(-0.856266\pi\)
0.0719816 0.997406i \(-0.477068\pi\)
\(194\) 0 0
\(195\) −12.0000 20.7846i −0.859338 1.48842i
\(196\) 0 0
\(197\) 13.8564i 0.987228i 0.869681 + 0.493614i \(0.164324\pi\)
−0.869681 + 0.493614i \(0.835676\pi\)
\(198\) 0 0
\(199\) 3.46410i 0.245564i 0.992434 + 0.122782i \(0.0391815\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 0 0
\(201\) 15.0000 1.05802
\(202\) 0 0
\(203\) 6.00000 + 10.3923i 0.421117 + 0.729397i
\(204\) 0 0
\(205\) 9.00000 15.5885i 0.628587 1.08875i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.50000 2.59808i −0.311272 0.179713i
\(210\) 0 0
\(211\) −15.0000 + 8.66025i −1.03264 + 0.596196i −0.917741 0.397180i \(-0.869989\pi\)
−0.114902 + 0.993377i \(0.536655\pi\)
\(212\) 0 0
\(213\) 9.00000 + 5.19615i 0.616670 + 0.356034i
\(214\) 0 0
\(215\) −18.0000 −1.22759
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 16.5000 + 9.52628i 1.11497 + 0.643726i
\(220\) 0 0
\(221\) −6.00000 + 3.46410i −0.403604 + 0.233021i
\(222\) 0 0
\(223\) −18.0000 10.3923i −1.20537 0.695920i −0.243625 0.969870i \(-0.578337\pi\)
−0.961744 + 0.273949i \(0.911670\pi\)
\(224\) 0 0
\(225\) 21.0000 1.40000
\(226\) 0 0
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 0 0
\(229\) 13.0000 + 22.5167i 0.859064 + 1.48794i 0.872823 + 0.488037i \(0.162287\pi\)
−0.0137585 + 0.999905i \(0.504380\pi\)
\(230\) 0 0
\(231\) −18.0000 −1.18431
\(232\) 0 0
\(233\) 12.1244i 0.794293i 0.917755 + 0.397146i \(0.130000\pi\)
−0.917755 + 0.397146i \(0.870000\pi\)
\(234\) 0 0
\(235\) 41.5692i 2.71168i
\(236\) 0 0
\(237\) −3.00000 5.19615i −0.194871 0.337526i
\(238\) 0 0
\(239\) 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i \(0.116196\pi\)
−0.157893 + 0.987456i \(0.550470\pi\)
\(240\) 0 0
\(241\) 8.50000 14.7224i 0.547533 0.948355i −0.450910 0.892570i \(-0.648900\pi\)
0.998443 0.0557856i \(-0.0177663\pi\)
\(242\) 0 0
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 0 0
\(245\) −15.0000 8.66025i −0.958315 0.553283i
\(246\) 0 0
\(247\) 6.00000 3.46410i 0.381771 0.220416i
\(248\) 0 0
\(249\) −18.0000 + 10.3923i −1.14070 + 0.658586i
\(250\) 0 0
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 10.3923i 0.650791i
\(256\) 0 0
\(257\) −16.5000 + 9.52628i −1.02924 + 0.594233i −0.916767 0.399422i \(-0.869211\pi\)
−0.112474 + 0.993655i \(0.535878\pi\)
\(258\) 0 0
\(259\) −6.00000 3.46410i −0.372822 0.215249i
\(260\) 0 0
\(261\) 10.3923i 0.643268i
\(262\) 0 0
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −12.0000 + 20.7846i −0.734388 + 1.27200i
\(268\) 0 0
\(269\) 6.92820i 0.422420i 0.977441 + 0.211210i \(0.0677404\pi\)
−0.977441 + 0.211210i \(0.932260\pi\)
\(270\) 0 0
\(271\) 6.92820i 0.420858i 0.977609 + 0.210429i \(0.0674861\pi\)
−0.977609 + 0.210429i \(0.932514\pi\)
\(272\) 0 0
\(273\) 12.0000 20.7846i 0.726273 1.25794i
\(274\) 0 0
\(275\) 10.5000 + 18.1865i 0.633174 + 1.09669i
\(276\) 0 0
\(277\) 4.00000 6.92820i 0.240337 0.416275i −0.720473 0.693482i \(-0.756075\pi\)
0.960810 + 0.277207i \(0.0894088\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 + 3.46410i 0.357930 + 0.206651i 0.668172 0.744007i \(-0.267077\pi\)
−0.310242 + 0.950657i \(0.600410\pi\)
\(282\) 0 0
\(283\) −9.00000 + 5.19615i −0.534994 + 0.308879i −0.743048 0.669238i \(-0.766621\pi\)
0.208053 + 0.978117i \(0.433287\pi\)
\(284\) 0 0
\(285\) 10.3923i 0.615587i
\(286\) 0 0
\(287\) 18.0000 1.06251
\(288\) 0 0
\(289\) 14.0000 0.823529
\(290\) 0 0
\(291\) 19.5000 11.2583i 1.14311 0.659975i
\(292\) 0 0
\(293\) −3.00000 + 1.73205i −0.175262 + 0.101187i −0.585065 0.810987i \(-0.698931\pi\)
0.409803 + 0.912174i \(0.365598\pi\)
\(294\) 0 0
\(295\) 45.0000 + 25.9808i 2.62000 + 1.51266i
\(296\) 0 0
\(297\) 13.5000 + 7.79423i 0.783349 + 0.452267i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −9.00000 15.5885i −0.518751 0.898504i
\(302\) 0 0
\(303\) −9.00000 15.5885i −0.517036 0.895533i
\(304\) 0 0
\(305\) 27.7128i 1.58683i
\(306\) 0 0
\(307\) 25.9808i 1.48280i 0.671063 + 0.741400i \(0.265838\pi\)
−0.671063 + 0.741400i \(0.734162\pi\)
\(308\) 0 0
\(309\) −24.0000 −1.36531
\(310\) 0 0
\(311\) 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 0 0
\(315\) 18.0000 + 31.1769i 1.01419 + 1.75662i
\(316\) 0 0
\(317\) −6.00000 3.46410i −0.336994 0.194563i 0.321948 0.946757i \(-0.395662\pi\)
−0.658942 + 0.752194i \(0.728996\pi\)
\(318\) 0 0
\(319\) 9.00000 5.19615i 0.503903 0.290929i
\(320\) 0 0
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) −28.0000 −1.55316
\(326\) 0 0
\(327\) −6.00000 3.46410i −0.331801 0.191565i
\(328\) 0 0
\(329\) 36.0000 20.7846i 1.98474 1.14589i
\(330\) 0 0
\(331\) −21.0000 12.1244i −1.15426 0.666415i −0.204342 0.978900i \(-0.565505\pi\)
−0.949923 + 0.312485i \(0.898839\pi\)
\(332\) 0 0
\(333\) 3.00000 + 5.19615i 0.164399 + 0.284747i
\(334\) 0 0
\(335\) 15.0000 25.9808i 0.819538 1.41948i
\(336\) 0 0
\(337\) 5.50000 + 9.52628i 0.299604 + 0.518930i 0.976045 0.217567i \(-0.0698121\pi\)
−0.676441 + 0.736497i \(0.736479\pi\)
\(338\) 0 0
\(339\) 12.0000 0.651751
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 6.92820i 0.374088i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.5000 23.3827i −0.724718 1.25525i −0.959090 0.283101i \(-0.908637\pi\)
0.234372 0.972147i \(-0.424697\pi\)
\(348\) 0 0
\(349\) −16.0000 + 27.7128i −0.856460 + 1.48343i 0.0188232 + 0.999823i \(0.494008\pi\)
−0.875284 + 0.483610i \(0.839325\pi\)
\(350\) 0 0
\(351\) −18.0000 + 10.3923i −0.960769 + 0.554700i
\(352\) 0 0
\(353\) 22.5000 + 12.9904i 1.19755 + 0.691408i 0.960009 0.279968i \(-0.0903240\pi\)
0.237545 + 0.971377i \(0.423657\pi\)
\(354\) 0 0
\(355\) 18.0000 10.3923i 0.955341 0.551566i
\(356\) 0 0
\(357\) 9.00000 5.19615i 0.476331 0.275010i
\(358\) 0 0
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) 0 0
\(361\) 16.0000 0.842105
\(362\) 0 0
\(363\) 3.46410i 0.181818i
\(364\) 0 0
\(365\) 33.0000 19.0526i 1.72730 0.997257i
\(366\) 0 0
\(367\) −3.00000 1.73205i −0.156599 0.0904123i 0.419653 0.907685i \(-0.362152\pi\)
−0.576252 + 0.817272i \(0.695485\pi\)
\(368\) 0 0
\(369\) −13.5000 7.79423i −0.702782 0.405751i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.0000 17.3205i −0.517780 0.896822i −0.999787 0.0206542i \(-0.993425\pi\)
0.482006 0.876168i \(-0.339908\pi\)
\(374\) 0 0
\(375\) 6.00000 10.3923i 0.309839 0.536656i
\(376\) 0 0
\(377\) 13.8564i 0.713641i
\(378\) 0 0
\(379\) 19.0526i 0.978664i −0.872098 0.489332i \(-0.837241\pi\)
0.872098 0.489332i \(-0.162759\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i \(-0.0145596\pi\)
−0.539076 + 0.842257i \(0.681226\pi\)
\(384\) 0 0
\(385\) −18.0000 + 31.1769i −0.917365 + 1.58892i
\(386\) 0 0
\(387\) 15.5885i 0.792406i
\(388\) 0 0
\(389\) −9.00000 5.19615i −0.456318 0.263455i 0.254177 0.967158i \(-0.418196\pi\)
−0.710495 + 0.703702i \(0.751529\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 20.7846i 1.04844i
\(394\) 0 0
\(395\) −12.0000 −0.603786
\(396\) 0 0
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 0 0
\(399\) −9.00000 + 5.19615i −0.450564 + 0.260133i
\(400\) 0 0
\(401\) −7.50000 + 4.33013i −0.374532 + 0.216236i −0.675437 0.737418i \(-0.736045\pi\)
0.300904 + 0.953654i \(0.402711\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 31.1769i 1.54919i
\(406\) 0 0
\(407\) −3.00000 + 5.19615i −0.148704 + 0.257564i
\(408\) 0 0
\(409\) 11.5000 + 19.9186i 0.568638 + 0.984911i 0.996701 + 0.0811615i \(0.0258630\pi\)
−0.428063 + 0.903749i \(0.640804\pi\)
\(410\) 0 0
\(411\) 1.50000 + 2.59808i 0.0739895 + 0.128154i
\(412\) 0 0
\(413\) 51.9615i 2.55686i
\(414\) 0 0
\(415\) 41.5692i 2.04055i
\(416\) 0 0
\(417\) −33.0000 −1.61602
\(418\) 0 0
\(419\) −6.00000 10.3923i −0.293119 0.507697i 0.681426 0.731887i \(-0.261360\pi\)
−0.974546 + 0.224189i \(0.928027\pi\)
\(420\) 0 0
\(421\) −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i \(-0.911690\pi\)
0.718076 + 0.695965i \(0.245023\pi\)
\(422\) 0 0
\(423\) −36.0000 −1.75038
\(424\) 0 0
\(425\) −10.5000 6.06218i −0.509325 0.294059i
\(426\) 0 0
\(427\) 24.0000 13.8564i 1.16144 0.670559i
\(428\) 0 0
\(429\) −18.0000 10.3923i −0.869048 0.501745i
\(430\) 0 0
\(431\) 18.0000 0.867029 0.433515 0.901146i \(-0.357273\pi\)
0.433515 + 0.901146i \(0.357273\pi\)
\(432\) 0 0
\(433\) −31.0000 −1.48976 −0.744882 0.667196i \(-0.767494\pi\)
−0.744882 + 0.667196i \(0.767494\pi\)
\(434\) 0 0
\(435\) −18.0000 10.3923i −0.863034 0.498273i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −18.0000 10.3923i −0.859093 0.495998i 0.00461537 0.999989i \(-0.498531\pi\)
−0.863708 + 0.503992i \(0.831864\pi\)
\(440\) 0 0
\(441\) −7.50000 + 12.9904i −0.357143 + 0.618590i
\(442\) 0 0
\(443\) −4.50000 + 7.79423i −0.213801 + 0.370315i −0.952901 0.303281i \(-0.901918\pi\)
0.739100 + 0.673596i \(0.235251\pi\)
\(444\) 0 0
\(445\) 24.0000 + 41.5692i 1.13771 + 1.97057i
\(446\) 0 0
\(447\) −24.0000 −1.13516
\(448\) 0 0
\(449\) 25.9808i 1.22611i −0.790041 0.613054i \(-0.789941\pi\)
0.790041 0.613054i \(-0.210059\pi\)
\(450\) 0 0
\(451\) 15.5885i 0.734032i
\(452\) 0 0
\(453\) 6.00000 + 10.3923i 0.281905 + 0.488273i
\(454\) 0 0
\(455\) −24.0000 41.5692i −1.12514 1.94880i
\(456\) 0 0
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 0 0
\(459\) −9.00000 −0.420084
\(460\) 0 0
\(461\) 18.0000 + 10.3923i 0.838344 + 0.484018i 0.856701 0.515814i \(-0.172510\pi\)
−0.0183573 + 0.999831i \(0.505844\pi\)
\(462\) 0 0
\(463\) −15.0000 + 8.66025i −0.697109 + 0.402476i −0.806270 0.591548i \(-0.798517\pi\)
0.109161 + 0.994024i \(0.465184\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.00000 0.138823 0.0694117 0.997588i \(-0.477888\pi\)
0.0694117 + 0.997588i \(0.477888\pi\)
\(468\) 0 0
\(469\) 30.0000 1.38527
\(470\) 0 0
\(471\) 13.8564i 0.638470i
\(472\) 0 0
\(473\) −13.5000 + 7.79423i −0.620731 + 0.358379i
\(474\) 0 0
\(475\) 10.5000 + 6.06218i 0.481773 + 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.0000 25.9808i 0.685367 1.18709i −0.287954 0.957644i \(-0.592975\pi\)
0.973321 0.229447i \(-0.0736918\pi\)
\(480\) 0 0
\(481\) −4.00000 6.92820i −0.182384 0.315899i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 45.0333i 2.04486i
\(486\) 0 0
\(487\) 17.3205i 0.784867i −0.919780 0.392434i \(-0.871633\pi\)
0.919780 0.392434i \(-0.128367\pi\)
\(488\) 0 0
\(489\) 3.00000 5.19615i 0.135665 0.234978i
\(490\) 0 0
\(491\) 7.50000 + 12.9904i 0.338470 + 0.586248i 0.984145 0.177365i \(-0.0567572\pi\)
−0.645675 + 0.763612i \(0.723424\pi\)
\(492\) 0 0
\(493\) −3.00000 + 5.19615i −0.135113 + 0.234023i
\(494\) 0 0
\(495\) 27.0000 15.5885i 1.21356 0.700649i
\(496\) 0 0
\(497\) 18.0000 + 10.3923i 0.807410 + 0.466159i
\(498\) 0 0
\(499\) −13.5000 + 7.79423i −0.604343 + 0.348918i −0.770748 0.637140i \(-0.780117\pi\)
0.166405 + 0.986057i \(0.446784\pi\)
\(500\) 0 0
\(501\) 10.3923i 0.464294i
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) 0 0
\(507\) 4.50000 2.59808i 0.199852 0.115385i
\(508\) 0 0
\(509\) 18.0000 10.3923i 0.797836 0.460631i −0.0448779 0.998992i \(-0.514290\pi\)
0.842714 + 0.538362i \(0.180957\pi\)
\(510\) 0 0
\(511\) 33.0000 + 19.0526i 1.45983 + 0.842836i
\(512\) 0 0
\(513\) 9.00000 0.397360
\(514\) 0 0
\(515\) −24.0000 + 41.5692i −1.05757 + 1.83176i
\(516\) 0 0
\(517\) −18.0000 31.1769i −0.791639 1.37116i
\(518\) 0 0
\(519\) 21.0000 + 36.3731i 0.921798 + 1.59660i
\(520\) 0 0
\(521\) 15.5885i 0.682943i 0.939892 + 0.341471i \(0.110925\pi\)
−0.939892 + 0.341471i \(0.889075\pi\)
\(522\) 0 0
\(523\) 17.3205i 0.757373i 0.925525 + 0.378686i \(0.123624\pi\)
−0.925525 + 0.378686i \(0.876376\pi\)
\(524\) 0 0
\(525\) 42.0000 1.83303
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 0 0
\(531\) 22.5000 38.9711i 0.976417 1.69120i
\(532\) 0 0
\(533\) 18.0000 + 10.3923i 0.779667 + 0.450141i
\(534\) 0 0
\(535\) −9.00000 + 5.19615i −0.389104 + 0.224649i
\(536\) 0 0
\(537\) 18.0000 + 10.3923i 0.776757 + 0.448461i
\(538\) 0 0
\(539\) −15.0000 −0.646096
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) 12.0000 + 6.92820i 0.514969 + 0.297318i
\(544\) 0 0
\(545\) −12.0000 + 6.92820i −0.514024 + 0.296772i
\(546\) 0 0
\(547\) −7.50000 4.33013i −0.320677 0.185143i 0.331017 0.943625i \(-0.392608\pi\)
−0.651694 + 0.758482i \(0.725941\pi\)
\(548\) 0 0
\(549\) −24.0000 −1.02430
\(550\) 0 0
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 0 0
\(553\) −6.00000 10.3923i −0.255146 0.441926i
\(554\) 0 0
\(555\) 12.0000 0.509372
\(556\) 0 0
\(557\) 38.1051i 1.61457i −0.590165 0.807283i \(-0.700937\pi\)
0.590165 0.807283i \(-0.299063\pi\)
\(558\) 0 0
\(559\) 20.7846i 0.879095i
\(560\) 0 0
\(561\) −4.50000 7.79423i −0.189990 0.329073i
\(562\) 0 0
\(563\) 4.50000 + 7.79423i 0.189652 + 0.328488i 0.945134 0.326682i \(-0.105931\pi\)
−0.755482 + 0.655169i \(0.772597\pi\)
\(564\) 0 0
\(565\) 12.0000 20.7846i 0.504844 0.874415i
\(566\) 0 0
\(567\) 27.0000 15.5885i 1.13389 0.654654i
\(568\) 0 0
\(569\) −16.5000 9.52628i −0.691716 0.399362i 0.112539 0.993647i \(-0.464102\pi\)
−0.804255 + 0.594285i \(0.797435\pi\)
\(570\) 0 0
\(571\) 10.5000 6.06218i 0.439411 0.253694i −0.263937 0.964540i \(-0.585021\pi\)
0.703348 + 0.710846i \(0.251688\pi\)
\(572\) 0 0
\(573\) −9.00000 + 5.19615i −0.375980 + 0.217072i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) 0 0
\(579\) 39.8372i 1.65558i
\(580\) 0 0
\(581\) −36.0000 + 20.7846i −1.49353 + 0.862291i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 41.5692i 1.71868i
\(586\) 0 0
\(587\) −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i \(-0.853053\pi\)
0.833408 + 0.552658i \(0.186386\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 12.0000 20.7846i 0.493614 0.854965i
\(592\) 0 0
\(593\) 6.92820i 0.284507i 0.989830 + 0.142254i \(0.0454349\pi\)
−0.989830 + 0.142254i \(0.954565\pi\)
\(594\) 0 0
\(595\) 20.7846i 0.852086i
\(596\) 0 0
\(597\) 3.00000 5.19615i 0.122782 0.212664i
\(598\) 0 0
\(599\) 9.00000 + 15.5885i 0.367730 + 0.636927i 0.989210 0.146503i \(-0.0468017\pi\)
−0.621480 + 0.783430i \(0.713468\pi\)
\(600\) 0 0
\(601\) 3.50000 6.06218i 0.142768 0.247281i −0.785770 0.618519i \(-0.787733\pi\)
0.928538 + 0.371237i \(0.121066\pi\)
\(602\) 0 0
\(603\) −22.5000 12.9904i −0.916271 0.529009i
\(604\) 0 0
\(605\) −6.00000 3.46410i −0.243935 0.140836i
\(606\) 0 0
\(607\) −24.0000 + 13.8564i −0.974130 + 0.562414i −0.900493 0.434871i \(-0.856794\pi\)
−0.0736371 + 0.997285i \(0.523461\pi\)
\(608\) 0 0
\(609\) 20.7846i 0.842235i
\(610\) 0 0
\(611\) 48.0000 1.94187
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) −27.0000 + 15.5885i −1.08875 + 0.628587i
\(616\) 0 0
\(617\) −25.5000 + 14.7224i −1.02659 + 0.592703i −0.916006 0.401164i \(-0.868606\pi\)
−0.110585 + 0.993867i \(0.535272\pi\)
\(618\) 0 0
\(619\) 25.5000 + 14.7224i 1.02493 + 0.591744i 0.915529 0.402253i \(-0.131773\pi\)
0.109403 + 0.993997i \(0.465106\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −24.0000 + 41.5692i −0.961540 + 1.66544i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) 4.50000 + 7.79423i 0.179713 + 0.311272i
\(628\) 0 0
\(629\) 3.46410i 0.138123i
\(630\) 0 0
\(631\) 3.46410i 0.137904i −0.997620 0.0689519i \(-0.978035\pi\)
0.997620 0.0689519i \(-0.0219655\pi\)
\(632\) 0 0
\(633\) 30.0000 1.19239
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 10.0000 17.3205i 0.396214 0.686264i
\(638\) 0 0
\(639\) −9.00000 15.5885i −0.356034 0.616670i
\(640\) 0 0
\(641\) −37.5000 21.6506i −1.48116 0.855149i −0.481389 0.876507i \(-0.659868\pi\)
−0.999772 + 0.0213584i \(0.993201\pi\)
\(642\) 0 0
\(643\) −22.5000 + 12.9904i −0.887313 + 0.512291i −0.873063 0.487608i \(-0.837870\pi\)
−0.0142506 + 0.999898i \(0.504536\pi\)
\(644\) 0 0
\(645\) 27.0000 + 15.5885i 1.06312 + 0.613795i
\(646\) 0 0
\(647\) 42.0000 1.65119 0.825595 0.564263i \(-0.190840\pi\)
0.825595 + 0.564263i \(0.190840\pi\)
\(648\) 0 0
\(649\) 45.0000 1.76640
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −27.0000 + 15.5885i −1.05659 + 0.610023i −0.924487 0.381212i \(-0.875507\pi\)
−0.132104 + 0.991236i \(0.542173\pi\)
\(654\) 0 0
\(655\) −36.0000 20.7846i −1.40664 0.812122i
\(656\) 0 0
\(657\) −16.5000 28.5788i −0.643726 1.11497i
\(658\) 0 0
\(659\) 12.0000 20.7846i 0.467454 0.809653i −0.531855 0.846836i \(-0.678505\pi\)
0.999309 + 0.0371821i \(0.0118382\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 0 0
\(663\) 12.0000 0.466041
\(664\) 0 0
\(665\) 20.7846i 0.805993i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 18.0000 + 31.1769i 0.695920 + 1.20537i
\(670\) 0 0
\(671\) −12.0000 20.7846i −0.463255 0.802381i
\(672\) 0 0
\(673\) 23.0000 39.8372i 0.886585 1.53561i 0.0426985 0.999088i \(-0.486405\pi\)
0.843886 0.536522i \(-0.180262\pi\)
\(674\) 0 0
\(675\) −31.5000 18.1865i −1.21244 0.700000i
\(676\) 0 0
\(677\) 18.0000 + 10.3923i 0.691796 + 0.399409i 0.804285 0.594244i \(-0.202549\pi\)
−0.112488 + 0.993653i \(0.535882\pi\)
\(678\) 0 0
\(679\) 39.0000 22.5167i 1.49668 0.864110i
\(680\) 0 0
\(681\) 4.50000 2.59808i 0.172440 0.0995585i
\(682\) 0 0
\(683\) −15.0000 −0.573959 −0.286980 0.957937i \(-0.592651\pi\)
−0.286980 + 0.957937i \(0.592651\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) 45.0333i 1.71813i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −27.0000 15.5885i −1.02713 0.593013i −0.110968 0.993824i \(-0.535395\pi\)
−0.916161 + 0.400811i \(0.868728\pi\)
\(692\) 0 0
\(693\) 27.0000 + 15.5885i 1.02565 + 0.592157i
\(694\) 0 0
\(695\) −33.0000 + 57.1577i −1.25176 + 2.16811i
\(696\) 0 0
\(697\) 4.50000 + 7.79423i 0.170450 + 0.295227i
\(698\) 0 0
\(699\) 10.5000 18.1865i 0.397146 0.687878i
\(700\) 0 0
\(701\) 27.7128i 1.04670i 0.852118 + 0.523349i \(0.175318\pi\)
−0.852118 + 0.523349i \(0.824682\pi\)
\(702\) 0 0
\(703\) 3.46410i 0.130651i
\(704\) 0 0
\(705\) −36.0000 + 62.3538i −1.35584 + 2.34838i
\(706\) 0 0
\(707\) −18.0000 31.1769i −0.676960 1.17253i
\(708\) 0 0
\(709\) −14.0000 + 24.2487i −0.525781 + 0.910679i 0.473768 + 0.880650i \(0.342894\pi\)
−0.999549 + 0.0300298i \(0.990440\pi\)
\(710\) 0 0
\(711\) 10.3923i 0.389742i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −36.0000 + 20.7846i −1.34632 + 0.777300i
\(716\) 0 0
\(717\) 41.5692i 1.55243i
\(718\) 0 0
\(719\) −42.0000 −1.56634 −0.783168 0.621810i \(-0.786397\pi\)
−0.783168 + 0.621810i \(0.786397\pi\)
\(720\) 0 0
\(721\) −48.0000 −1.78761
\(722\) 0 0
\(723\) −25.5000 + 14.7224i −0.948355 + 0.547533i
\(724\) 0 0
\(725\) −21.0000 + 12.1244i −0.779920 + 0.450287i
\(726\) 0 0
\(727\) −36.0000 20.7846i −1.33517 0.770859i −0.349080 0.937093i \(-0.613506\pi\)
−0.986086 + 0.166234i \(0.946839\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 4.50000 7.79423i 0.166439 0.288280i
\(732\) 0 0
\(733\) −11.0000 19.0526i −0.406294 0.703722i 0.588177 0.808732i \(-0.299846\pi\)
−0.994471 + 0.105010i \(0.966513\pi\)
\(734\) 0 0
\(735\) 15.0000 + 25.9808i 0.553283 + 0.958315i
\(736\) 0 0
\(737\) 25.9808i 0.957014i
\(738\) 0 0
\(739\) 25.9808i 0.955718i 0.878437 + 0.477859i \(0.158587\pi\)
−0.878437 + 0.477859i \(0.841413\pi\)
\(740\) 0 0
\(741\) −12.0000 −0.440831
\(742\) 0 0
\(743\) −9.00000 15.5885i −0.330178 0.571885i 0.652369 0.757902i \(-0.273775\pi\)
−0.982547 + 0.186017i \(0.940442\pi\)
\(744\) 0 0
\(745\) −24.0000 + 41.5692i −0.879292 + 1.52298i
\(746\) 0 0
\(747\) 36.0000 1.31717
\(748\) 0 0
\(749\) −9.00000 5.19615i −0.328853 0.189863i
\(750\) 0 0
\(751\) 33.0000 19.0526i 1.20419 0.695238i 0.242704 0.970100i \(-0.421966\pi\)
0.961483 + 0.274863i \(0.0886324\pi\)
\(752\) 0 0
\(753\) 31.5000 + 18.1865i 1.14792 + 0.662754i
\(754\) 0 0
\(755\) 24.0000 0.873449
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 42.0000 24.2487i 1.52250 0.879015i 0.522852 0.852423i \(-0.324868\pi\)
0.999646 0.0265919i \(-0.00846546\pi\)
\(762\) 0 0
\(763\) −12.0000 6.92820i −0.434429 0.250818i
\(764\) 0 0
\(765\) −9.00000 + 15.5885i −0.325396 + 0.563602i
\(766\) 0 0
\(767\) −30.0000 + 51.9615i −1.08324 + 1.87622i
\(768\) 0 0
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) 0 0
\(771\) 33.0000 1.18847
\(772\) 0 0
\(773\) 6.92820i 0.249190i −0.992208 0.124595i \(-0.960237\pi\)
0.992208 0.124595i \(-0.0397632\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.00000 + 10.3923i 0.215249 + 0.372822i
\(778\) 0 0
\(779\) −4.50000 7.79423i −0.161229 0.279257i
\(780\) 0 0
\(781\) 9.00000 15.5885i 0.322045 0.557799i
\(782\) 0 0
\(783\) −9.00000 + 15.5885i −0.321634 + 0.557086i
\(784\) 0 0
\(785\) 24.0000 + 13.8564i 0.856597 + 0.494556i
\(786\) 0 0
\(787\) 15.0000 8.66025i 0.534692 0.308705i −0.208233 0.978079i \(-0.566771\pi\)
0.742925 + 0.669375i \(0.233438\pi\)
\(788\) 0 0
\(789\) −27.0000 + 15.5885i −0.961225 + 0.554964i
\(790\) 0 0
\(791\) 24.0000 0.853342
\(792\) 0 0
\(793\) 32.0000 1.13635
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.00000