Properties

Label 560.2.bw.d.529.1
Level $560$
Weight $2$
Character 560.529
Analytic conductor $4.472$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bw (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 529.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 560.529
Dual form 560.2.bw.d.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +5.00000i q^{13} +(1.73205 + 1.00000i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-6.06218 + 3.50000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +4.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-4.23205 + 4.13397i) q^{35} +(0.866025 - 0.500000i) q^{37} +3.00000 q^{41} +2.00000i q^{43} +(5.59808 - 3.69615i) q^{45} +(6.06218 - 3.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(7.79423 + 4.50000i) q^{53} +(6.00000 + 3.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(2.59808 - 7.50000i) q^{63} +(-11.1603 + 0.669873i) q^{65} +(1.73205 + 1.00000i) q^{67} +6.00000 q^{71} +(-13.8564 - 8.00000i) q^{73} +(7.79423 - 1.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} -6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +(1.00000 + 1.73205i) q^{89} +(-10.0000 + 8.66025i) q^{91} +(-9.33013 + 6.16025i) q^{95} -12.0000i q^{97} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{5} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{5} - 6 q^{9} + 6 q^{11} + 10 q^{19} - 6 q^{25} + 16 q^{29} - 4 q^{31} - 10 q^{35} + 12 q^{41} + 12 q^{45} - 4 q^{49} + 24 q^{55} + 8 q^{59} - 12 q^{61} - 10 q^{65} + 24 q^{71} - 28 q^{79} - 18 q^{81} - 8 q^{85} + 4 q^{89} - 40 q^{91} - 20 q^{95} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(1\)

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
\(3\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 0 0
\(5\) 0.133975 + 2.23205i 0.0599153 + 0.998203i
\(6\) 0 0
\(7\) 1.73205 + 2.00000i 0.654654 + 0.755929i
\(8\) 0 0
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) 5.00000i 1.38675i 0.720577 + 0.693375i \(0.243877\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i \(-0.255354\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) 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
\(21\) 0 0
\(22\) 0 0
\(23\) −6.06218 + 3.50000i −1.26405 + 0.729800i −0.973856 0.227167i \(-0.927054\pi\)
−0.290196 + 0.956967i \(0.593720\pi\)
\(24\) 0 0
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.23205 + 4.13397i −0.715347 + 0.698769i
\(36\) 0 0
\(37\) 0.866025 0.500000i 0.142374 0.0821995i −0.427121 0.904194i \(-0.640472\pi\)
0.569495 + 0.821995i \(0.307139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) 0 0
\(45\) 5.59808 3.69615i 0.834512 0.550990i
\(46\) 0 0
\(47\) 6.06218 3.50000i 0.884260 0.510527i 0.0121990 0.999926i \(-0.496117\pi\)
0.872060 + 0.489398i \(0.162783\pi\)
\(48\) 0 0
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.79423 + 4.50000i 1.07062 + 0.618123i 0.928351 0.371706i \(-0.121227\pi\)
0.142269 + 0.989828i \(0.454560\pi\)
\(54\) 0 0
\(55\) 6.00000 + 3.00000i 0.809040 + 0.404520i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 0 0
\(63\) 2.59808 7.50000i 0.327327 0.944911i
\(64\) 0 0
\(65\) −11.1603 + 0.669873i −1.38426 + 0.0830875i
\(66\) 0 0
\(67\) 1.73205 + 1.00000i 0.211604 + 0.122169i 0.602056 0.798454i \(-0.294348\pi\)
−0.390453 + 0.920623i \(0.627682\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −13.8564 8.00000i −1.62177 0.936329i −0.986447 0.164083i \(-0.947534\pi\)
−0.635323 0.772246i \(-0.719133\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.79423 1.50000i 0.888235 0.170941i
\(78\) 0 0
\(79\) −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 0 0
\(85\) −2.00000 + 4.00000i −0.216930 + 0.433861i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.00000 + 1.73205i 0.106000 + 0.183597i 0.914146 0.405385i \(-0.132862\pi\)
−0.808146 + 0.588982i \(0.799529\pi\)
\(90\) 0 0
\(91\) −10.0000 + 8.66025i −1.04828 + 0.907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −9.33013 + 6.16025i −0.957251 + 0.632029i
\(96\) 0 0
\(97\) 12.0000i 1.21842i −0.793011 0.609208i \(-0.791488\pi\)
0.793011 0.609208i \(-0.208512\pi\)
\(98\) 0 0
\(99\) −9.00000 −0.904534
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −6.92820 + 4.00000i −0.682656 + 0.394132i −0.800855 0.598858i \(-0.795621\pi\)
0.118199 + 0.992990i \(0.462288\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.8564 8.00000i 1.33955 0.773389i 0.352809 0.935695i \(-0.385227\pi\)
0.986740 + 0.162306i \(0.0518932\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000i 1.31701i −0.752577 0.658505i \(-0.771189\pi\)
0.752577 0.658505i \(-0.228811\pi\)
\(114\) 0 0
\(115\) −8.62436 13.0622i −0.804225 1.21805i
\(116\) 0 0
\(117\) 12.9904 7.50000i 1.20096 0.693375i
\(118\) 0 0
\(119\) 1.00000 + 5.19615i 0.0916698 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 7.00000i 0.621150i −0.950549 0.310575i \(-0.899478\pi\)
0.950549 0.310575i \(-0.100522\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i \(-0.180577\pi\)
−0.887041 + 0.461690i \(0.847243\pi\)
\(132\) 0 0
\(133\) −4.33013 + 12.5000i −0.375470 + 1.08389i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.92820 + 4.00000i 0.591916 + 0.341743i 0.765855 0.643013i \(-0.222316\pi\)
−0.173939 + 0.984757i \(0.555649\pi\)
\(138\) 0 0
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 12.9904 + 7.50000i 1.08631 + 0.627182i
\(144\) 0 0
\(145\) 0.535898 + 8.92820i 0.0445039 + 0.741447i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 0 0
\(151\) −3.00000 + 5.19615i −0.244137 + 0.422857i −0.961888 0.273442i \(-0.911838\pi\)
0.717752 + 0.696299i \(0.245171\pi\)
\(152\) 0 0
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) −4.00000 2.00000i −0.321288 0.160644i
\(156\) 0 0
\(157\) 7.79423 + 4.50000i 0.622047 + 0.359139i 0.777666 0.628678i \(-0.216404\pi\)
−0.155618 + 0.987817i \(0.549737\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −17.5000 6.06218i −1.37919 0.477767i
\(162\) 0 0
\(163\) −10.3923 + 6.00000i −0.813988 + 0.469956i −0.848339 0.529454i \(-0.822397\pi\)
0.0343508 + 0.999410i \(0.489064\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.0000i 1.16073i −0.814355 0.580367i \(-0.802909\pi\)
0.814355 0.580367i \(-0.197091\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 7.50000 12.9904i 0.573539 0.993399i
\(172\) 0 0
\(173\) −7.79423 + 4.50000i −0.592584 + 0.342129i −0.766119 0.642699i \(-0.777815\pi\)
0.173534 + 0.984828i \(0.444481\pi\)
\(174\) 0 0
\(175\) −9.79423 8.89230i −0.740374 0.672195i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −6.50000 + 11.2583i −0.485833 + 0.841487i −0.999867 0.0162823i \(-0.994817\pi\)
0.514035 + 0.857769i \(0.328150\pi\)
\(180\) 0 0
\(181\) 26.0000 1.93256 0.966282 0.257485i \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.23205 + 1.86603i 0.0905822 + 0.137193i
\(186\) 0 0
\(187\) 5.19615 3.00000i 0.379980 0.219382i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −10.0000 17.3205i −0.723575 1.25327i −0.959558 0.281511i \(-0.909164\pi\)
0.235983 0.971757i \(-0.424169\pi\)
\(192\) 0 0
\(193\) −8.66025 5.00000i −0.623379 0.359908i 0.154805 0.987945i \(-0.450525\pi\)
−0.778183 + 0.628037i \(0.783859\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.00000i 0.356235i −0.984009 0.178118i \(-0.942999\pi\)
0.984009 0.178118i \(-0.0570008\pi\)
\(198\) 0 0
\(199\) −9.00000 + 15.5885i −0.637993 + 1.10504i 0.347879 + 0.937539i \(0.386902\pi\)
−0.985873 + 0.167497i \(0.946431\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.92820 + 8.00000i 0.486265 + 0.561490i
\(204\) 0 0
\(205\) 0.401924 + 6.69615i 0.0280716 + 0.467680i
\(206\) 0 0
\(207\) 18.1865 + 10.5000i 1.26405 + 0.729800i
\(208\) 0 0
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) 9.00000 0.619586 0.309793 0.950804i \(-0.399740\pi\)
0.309793 + 0.950804i \(0.399740\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.46410 + 0.267949i −0.304449 + 0.0182740i
\(216\) 0 0
\(217\) −5.19615 + 1.00000i −0.352738 + 0.0678844i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −5.00000 + 8.66025i −0.336336 + 0.582552i
\(222\) 0 0
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0 0
\(225\) 9.00000 + 12.0000i 0.600000 + 0.800000i
\(226\) 0 0
\(227\) −5.19615 3.00000i −0.344881 0.199117i 0.317547 0.948242i \(-0.397141\pi\)
−0.662428 + 0.749125i \(0.730474\pi\)
\(228\) 0 0
\(229\) 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i \(0.0106368\pi\)
−0.470787 + 0.882247i \(0.656030\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.92820 4.00000i 0.453882 0.262049i −0.255586 0.966786i \(-0.582269\pi\)
0.709468 + 0.704737i \(0.248935\pi\)
\(234\) 0 0
\(235\) 8.62436 + 13.0622i 0.562591 + 0.852083i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 4.50000 7.79423i 0.289870 0.502070i −0.683908 0.729568i \(-0.739721\pi\)
0.973779 + 0.227498i \(0.0730544\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −15.5981 1.30385i −0.996525 0.0832998i
\(246\) 0 0
\(247\) −21.6506 + 12.5000i −1.37760 + 0.795356i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.00000 −0.315597 −0.157799 0.987471i \(-0.550440\pi\)
−0.157799 + 0.987471i \(0.550440\pi\)
\(252\) 0 0
\(253\) 21.0000i 1.32026i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.19615 + 3.00000i −0.324127 + 0.187135i −0.653231 0.757159i \(-0.726587\pi\)
0.329104 + 0.944294i \(0.393253\pi\)
\(258\) 0 0
\(259\) 2.50000 + 0.866025i 0.155342 + 0.0538122i
\(260\) 0 0
\(261\) −6.00000 10.3923i −0.371391 0.643268i
\(262\) 0 0
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) −9.00000 + 18.0000i −0.552866 + 1.10573i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5.00000 + 8.66025i −0.304855 + 0.528025i −0.977229 0.212187i \(-0.931941\pi\)
0.672374 + 0.740212i \(0.265275\pi\)
\(270\) 0 0
\(271\) 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i \(0.0933238\pi\)
−0.228380 + 0.973572i \(0.573343\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.89230 + 13.7942i −0.355319 + 0.831823i
\(276\) 0 0
\(277\) 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i \(-0.314196\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 0 0
\(283\) −12.1244 7.00000i −0.720718 0.416107i 0.0942988 0.995544i \(-0.469939\pi\)
−0.815017 + 0.579437i \(0.803272\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.19615 + 6.00000i 0.306719 + 0.354169i
\(288\) 0 0
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9.00000i 0.525786i 0.964825 + 0.262893i \(0.0846766\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(294\) 0 0
\(295\) 8.00000 + 4.00000i 0.465778 + 0.232889i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −17.5000 30.3109i −1.01205 1.75292i
\(300\) 0 0
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 11.1962 7.39230i 0.641090 0.423282i
\(306\) 0 0
\(307\) 22.0000i 1.25561i 0.778372 + 0.627803i \(0.216046\pi\)
−0.778372 + 0.627803i \(0.783954\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0 0
\(313\) 19.0526 11.0000i 1.07691 0.621757i 0.146852 0.989158i \(-0.453086\pi\)
0.930062 + 0.367402i \(0.119753\pi\)
\(314\) 0 0
\(315\) 17.0885 + 4.79423i 0.962825 + 0.270124i
\(316\) 0 0
\(317\) −1.73205 + 1.00000i −0.0972817 + 0.0561656i −0.547852 0.836576i \(-0.684554\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(318\) 0 0
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 10.0000i 0.556415i
\(324\) 0 0
\(325\) −2.99038 24.8205i −0.165876 1.37679i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 17.5000 + 6.06218i 0.964806 + 0.334219i
\(330\) 0 0
\(331\) 2.50000 + 4.33013i 0.137412 + 0.238005i 0.926516 0.376254i \(-0.122788\pi\)
−0.789104 + 0.614260i \(0.789455\pi\)
\(332\) 0 0
\(333\) −2.59808 1.50000i −0.142374 0.0821995i
\(334\) 0 0
\(335\) −2.00000 + 4.00000i −0.109272 + 0.218543i
\(336\) 0 0
\(337\) 10.0000i 0.544735i 0.962193 + 0.272367i \(0.0878066\pi\)
−0.962193 + 0.272367i \(0.912193\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.00000 + 5.19615i 0.162459 + 0.281387i
\(342\) 0 0
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.3923 6.00000i −0.557888 0.322097i 0.194409 0.980921i \(-0.437721\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 20.7846 + 12.0000i 1.10625 + 0.638696i 0.937856 0.347024i \(-0.112808\pi\)
0.168397 + 0.985719i \(0.446141\pi\)
\(354\) 0 0
\(355\) 0.803848 + 13.3923i 0.0426638 + 0.710790i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8.00000 13.8564i −0.422224 0.731313i 0.573933 0.818902i \(-0.305417\pi\)
−0.996157 + 0.0875892i \(0.972084\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 16.0000 32.0000i 0.837478 1.67496i
\(366\) 0 0
\(367\) 11.2583 + 6.50000i 0.587680 + 0.339297i 0.764180 0.645003i \(-0.223144\pi\)
−0.176500 + 0.984301i \(0.556477\pi\)
\(368\) 0 0
\(369\) −4.50000 7.79423i −0.234261 0.405751i
\(370\) 0 0
\(371\) 4.50000 + 23.3827i 0.233628 + 1.21397i
\(372\) 0 0
\(373\) −22.5167 + 13.0000i −1.16587 + 0.673114i −0.952703 0.303902i \(-0.901711\pi\)
−0.213165 + 0.977016i \(0.568377\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 20.0000i 1.03005i
\(378\) 0 0
\(379\) −29.0000 −1.48963 −0.744815 0.667271i \(-0.767462\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 18.1865 10.5000i 0.929288 0.536525i 0.0427020 0.999088i \(-0.486403\pi\)
0.886586 + 0.462563i \(0.153070\pi\)
\(384\) 0 0
\(385\) 4.39230 + 17.1962i 0.223853 + 0.876397i
\(386\) 0 0
\(387\) 5.19615 3.00000i 0.264135 0.152499i
\(388\) 0 0
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) −14.0000 −0.708010
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 26.1244 17.2487i 1.31446 0.867877i
\(396\) 0 0
\(397\) −12.1244 + 7.00000i −0.608504 + 0.351320i −0.772380 0.635161i \(-0.780934\pi\)
0.163876 + 0.986481i \(0.447600\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) 0 0
\(403\) −8.66025 5.00000i −0.431398 0.249068i
\(404\) 0 0
\(405\) −18.0000 9.00000i −0.894427 0.447214i
\(406\) 0 0
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.3923 2.00000i 0.511372 0.0984136i
\(414\) 0 0
\(415\) 13.3923 0.803848i 0.657402 0.0394593i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 35.0000 1.70986 0.854931 0.518742i \(-0.173599\pi\)
0.854931 + 0.518742i \(0.173599\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 0 0
\(423\) −18.1865 10.5000i −0.884260 0.510527i
\(424\) 0 0
\(425\) −9.19615 3.92820i −0.446079 0.190546i
\(426\) 0 0
\(427\) 5.19615 15.0000i 0.251459 0.725901i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.00000 1.73205i 0.0481683 0.0834300i −0.840936 0.541135i \(-0.817995\pi\)
0.889104 + 0.457705i \(0.151328\pi\)
\(432\) 0 0
\(433\) 28.0000i 1.34559i −0.739827 0.672797i \(-0.765093\pi\)
0.739827 0.672797i \(-0.234907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −30.3109 17.5000i −1.44997 0.837139i
\(438\) 0 0
\(439\) 14.0000 + 24.2487i 0.668184 + 1.15733i 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 0 0
\(441\) 19.5000 7.79423i 0.928571 0.371154i
\(442\) 0 0
\(443\) 25.9808 15.0000i 1.23438 0.712672i 0.266443 0.963851i \(-0.414152\pi\)
0.967941 + 0.251179i \(0.0808184\pi\)
\(444\) 0 0
\(445\) −3.73205 + 2.46410i −0.176916 + 0.116810i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.00000 −0.235965 −0.117982 0.993016i \(-0.537643\pi\)
−0.117982 + 0.993016i \(0.537643\pi\)
\(450\) 0 0
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −20.6699 21.1603i −0.969019 0.992008i
\(456\) 0 0
\(457\) −8.66025 + 5.00000i −0.405110 + 0.233890i −0.688686 0.725059i \(-0.741812\pi\)
0.283577 + 0.958950i \(0.408479\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −32.0000 −1.49039 −0.745194 0.666847i \(-0.767643\pi\)
−0.745194 + 0.666847i \(0.767643\pi\)
\(462\) 0 0
\(463\) 17.0000i 0.790057i −0.918669 0.395029i \(-0.870735\pi\)
0.918669 0.395029i \(-0.129265\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −29.4449 + 17.0000i −1.36255 + 0.786666i −0.989962 0.141332i \(-0.954861\pi\)
−0.372584 + 0.927999i \(0.621528\pi\)
\(468\) 0 0
\(469\) 1.00000 + 5.19615i 0.0461757 + 0.239936i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.19615 + 3.00000i 0.238919 + 0.137940i
\(474\) 0 0
\(475\) −15.0000 20.0000i −0.688247 0.917663i
\(476\) 0 0
\(477\) 27.0000i 1.23625i
\(478\) 0 0
\(479\) −18.0000 + 31.1769i −0.822441 + 1.42451i 0.0814184 + 0.996680i \(0.474055\pi\)
−0.903859 + 0.427830i \(0.859278\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 26.7846 1.60770i 1.21623 0.0730017i
\(486\) 0 0
\(487\) −27.7128 16.0000i −1.25579 0.725029i −0.283535 0.958962i \(-0.591507\pi\)
−0.972253 + 0.233933i \(0.924840\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 6.92820 + 4.00000i 0.312031 + 0.180151i
\(494\) 0 0
\(495\) −1.20577 20.0885i −0.0541954 0.902909i
\(496\) 0 0
\(497\) 10.3923 + 12.0000i 0.466159 + 0.538274i
\(498\) 0 0
\(499\) −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i \(-0.195204\pi\)
−0.907314 + 0.420455i \(0.861871\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 40.0000i 1.78351i 0.452517 + 0.891756i \(0.350526\pi\)
−0.452517 + 0.891756i \(0.649474\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −17.0000 29.4449i −0.753512 1.30512i −0.946111 0.323843i \(-0.895025\pi\)
0.192599 0.981278i \(-0.438308\pi\)
\(510\) 0 0
\(511\) −8.00000 41.5692i −0.353899 1.83891i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.85641 14.9282i −0.434325 0.657815i
\(516\) 0 0
\(517\) 21.0000i 0.923579i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.5000 23.3827i 0.591446 1.02441i −0.402592 0.915379i \(-0.631891\pi\)
0.994038 0.109035i \(-0.0347759\pi\)
\(522\) 0 0
\(523\) 13.8564 8.00000i 0.605898 0.349816i −0.165460 0.986216i \(-0.552911\pi\)
0.771358 + 0.636401i \(0.219578\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.46410 + 2.00000i −0.150899 + 0.0871214i
\(528\) 0 0
\(529\) 13.0000 22.5167i 0.565217 0.978985i
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 15.0000i 0.649722i
\(534\) 0 0
\(535\) 19.7128 + 29.8564i 0.852259 + 1.29081i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) 0 0
\(541\) 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.00000 + 2.00000i 0.171341 + 0.0856706i
\(546\) 0 0
\(547\) 26.0000i 1.11168i 0.831289 + 0.555840i \(0.187603\pi\)
−0.831289 + 0.555840i \(0.812397\pi\)
\(548\) 0 0
\(549\) −9.00000 + 15.5885i −0.384111 + 0.665299i
\(550\) 0 0
\(551\) 10.0000 + 17.3205i 0.426014 + 0.737878i
\(552\) 0 0
\(553\) 12.1244 35.0000i 0.515580 1.48835i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.9186 11.5000i −0.843978 0.487271i 0.0146368 0.999893i \(-0.495341\pi\)
−0.858614 + 0.512622i \(0.828674\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.73205 1.00000i −0.0729972 0.0421450i 0.463057 0.886328i \(-0.346752\pi\)
−0.536054 + 0.844183i \(0.680086\pi\)
\(564\) 0 0
\(565\) 31.2487 1.87564i 1.31464 0.0789090i
\(566\) 0 0
\(567\) −23.3827 + 4.50000i −0.981981 + 0.188982i
\(568\) 0 0
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) 16.0000 27.7128i 0.669579 1.15975i −0.308443 0.951243i \(-0.599808\pi\)
0.978022 0.208502i \(-0.0668588\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 28.0000 21.0000i 1.16768 0.875761i
\(576\) 0 0
\(577\) 3.46410 + 2.00000i 0.144212 + 0.0832611i 0.570370 0.821388i \(-0.306800\pi\)
−0.426158 + 0.904649i \(0.640133\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 10.3923i 0.497844 0.431145i
\(582\) 0 0
\(583\) 23.3827 13.5000i 0.968412 0.559113i
\(584\) 0 0
\(585\) 18.4808 + 27.9904i 0.764085 + 1.15726i
\(586\) 0 0
\(587\) 34.0000i 1.40333i −0.712507 0.701665i \(-0.752440\pi\)
0.712507 0.701665i \(-0.247560\pi\)
\(588\) 0 0
\(589\) −10.0000 −0.412043
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.19615 3.00000i 0.213380 0.123195i −0.389501 0.921026i \(-0.627353\pi\)
0.602881 + 0.797831i \(0.294019\pi\)
\(594\) 0 0
\(595\) −11.4641 + 2.92820i −0.469982 + 0.120045i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 6.00000i 0.244339i
\(604\) 0 0
\(605\) −3.73205 + 2.46410i −0.151729 + 0.100180i
\(606\) 0 0
\(607\) 11.2583 6.50000i 0.456962 0.263827i −0.253804 0.967256i \(-0.581682\pi\)
0.710766 + 0.703429i \(0.248349\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 17.5000 + 30.3109i 0.707974 + 1.22625i
\(612\) 0 0
\(613\) −12.9904 7.50000i −0.524677 0.302922i 0.214169 0.976797i \(-0.431296\pi\)
−0.738846 + 0.673874i \(0.764629\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.0000i 0.563619i 0.959470 + 0.281809i \(0.0909346\pi\)
−0.959470 + 0.281809i \(0.909065\pi\)
\(618\) 0 0
\(619\) −9.50000 + 16.4545i −0.381837 + 0.661361i −0.991325 0.131434i \(-0.958042\pi\)
0.609488 + 0.792796i \(0.291375\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.73205 + 5.00000i −0.0693932 + 0.200321i
\(624\) 0 0
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.00000 0.0797452
\(630\) 0 0
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 15.6244 0.937822i 0.620034 0.0372163i
\(636\) 0 0
\(637\) −34.6410 5.00000i −1.37253 0.198107i
\(638\) 0 0
\(639\) −9.00000 15.5885i −0.356034 0.616670i
\(640\) 0 0
\(641\) 2.50000 4.33013i 0.0987441 0.171030i −0.812421 0.583071i \(-0.801851\pi\)
0.911165 + 0.412042i \(0.135184\pi\)
\(642\) 0 0
\(643\) 14.0000i 0.552106i −0.961142 0.276053i \(-0.910973\pi\)
0.961142 0.276053i \(-0.0890266\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23.3827 13.5000i −0.919268 0.530740i −0.0358667 0.999357i \(-0.511419\pi\)
−0.883402 + 0.468617i \(0.844753\pi\)
\(648\) 0 0
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.59808 + 1.50000i −0.101671 + 0.0586995i −0.549973 0.835182i \(-0.685362\pi\)
0.448303 + 0.893882i \(0.352029\pi\)
\(654\) 0 0
\(655\) 1.86603 1.23205i 0.0729116 0.0481402i
\(656\) 0 0
\(657\) 48.0000i 1.87266i
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −8.00000 + 13.8564i −0.311164 + 0.538952i −0.978615 0.205702i \(-0.934052\pi\)
0.667451 + 0.744654i \(0.267385\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −28.4808 7.99038i −1.10444 0.309854i
\(666\) 0 0
\(667\) −24.2487 + 14.0000i −0.938914 + 0.542082i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −18.0000 −0.694882
\(672\) 0 0
\(673\) 32.0000i 1.23351i −0.787155 0.616755i \(-0.788447\pi\)
0.787155 0.616755i \(-0.211553\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14.7224 + 8.50000i −0.565829 + 0.326682i −0.755482 0.655170i \(-0.772597\pi\)
0.189653 + 0.981851i \(0.439264\pi\)
\(678\) 0 0
\(679\) 24.0000 20.7846i 0.921035 0.797640i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 38.1051 + 22.0000i 1.45805 + 0.841807i 0.998916 0.0465592i \(-0.0148256\pi\)
0.459136 + 0.888366i \(0.348159\pi\)
\(684\) 0 0
\(685\) −8.00000 + 16.0000i −0.305664 + 0.611329i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −22.5000 + 38.9711i −0.857182 + 1.48468i
\(690\) 0 0
\(691\) −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i \(-0.851021\pi\)
0.0555386 0.998457i \(-0.482312\pi\)
\(692\) 0 0
\(693\) −15.5885 18.0000i −0.592157 0.683763i
\(694\) 0 0
\(695\) 2.14359 + 35.7128i 0.0813111 + 1.35466i
\(696\) 0 0
\(697\) 5.19615 + 3.00000i 0.196818 + 0.113633i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) 4.33013 + 2.50000i 0.163314 + 0.0942893i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 6.00000 + 10.3923i 0.225335 + 0.390291i 0.956420 0.291995i \(-0.0943191\pi\)
−0.731085 + 0.682286i \(0.760986\pi\)
\(710\) 0 0
\(711\) −21.0000 + 36.3731i −0.787562 + 1.36410i
\(712\) 0 0
\(713\) 14.0000i 0.524304i
\(714\) 0 0
\(715\) −15.0000 + 30.0000i −0.560968 + 1.12194i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −13.0000 22.5167i −0.484818 0.839730i 0.515030 0.857172i \(-0.327781\pi\)
−0.999848 + 0.0174426i \(0.994448\pi\)
\(720\) 0 0
\(721\) −20.0000 6.92820i −0.744839 0.258020i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −19.8564 + 2.39230i −0.737448 + 0.0888480i
\(726\) 0 0
\(727\) 29.0000i 1.07555i 0.843088 + 0.537775i \(0.180735\pi\)
−0.843088 + 0.537775i \(0.819265\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −2.00000 + 3.46410i −0.0739727 + 0.128124i
\(732\) 0 0
\(733\) −35.5070 + 20.5000i −1.31148 + 0.757185i −0.982342 0.187096i \(-0.940092\pi\)
−0.329141 + 0.944281i \(0.606759\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.19615 3.00000i 0.191403 0.110506i
\(738\) 0 0
\(739\) 14.5000 25.1147i 0.533391 0.923861i −0.465848 0.884865i \(-0.654251\pi\)
0.999239 0.0389959i \(-0.0124159\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 21.0000i 0.770415i −0.922830 0.385208i \(-0.874130\pi\)
0.922830 0.385208i \(-0.125870\pi\)
\(744\) 0 0
\(745\) 33.5885 22.1769i 1.23059 0.812499i
\(746\) 0 0
\(747\) −15.5885 + 9.00000i −0.570352 + 0.329293i
\(748\) 0 0
\(749\) 40.0000 + 13.8564i 1.46157 + 0.506302i
\(750\) 0 0
\(751\) 14.0000 + 24.2487i 0.510867 + 0.884848i 0.999921 + 0.0125942i \(0.00400897\pi\)
−0.489053 + 0.872254i \(0.662658\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12.0000 6.00000i −0.436725 0.218362i
\(756\) 0 0
\(757\) 42.0000i 1.52652i 0.646094 + 0.763258i \(0.276401\pi\)
−0.646094 + 0.763258i \(0.723599\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.500000 0.866025i −0.0181250 0.0313934i 0.856821 0.515615i \(-0.172436\pi\)
−0.874946 + 0.484221i \(0.839103\pi\)
\(762\) 0 0
\(763\) 5.19615 1.00000i 0.188113 0.0362024i
\(764\) 0 0
\(765\) 13.3923 0.803848i 0.484200 0.0290632i
\(766\) 0 0
\(767\) 17.3205 + 10.0000i 0.625407 + 0.361079i
\(768\) 0 0
\(769\) 29.0000 1.04577 0.522883 0.852404i \(-0.324856\pi\)
0.522883 + 0.852404i \(0.324856\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 38.9711 + 22.5000i 1.40169 + 0.809269i 0.994567 0.104102i \(-0.0331970\pi\)
0.407128 + 0.913371i \(0.366530\pi\)
\(774\) 0 0
\(775\) 3.92820 9.19615i 0.141105 0.330336i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.50000 + 12.9904i 0.268715 + 0.465429i
\(780\) 0 0
\(781\) 9.00000 15.5885i 0.322045 0.557799i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −9.00000 + 18.0000i −0.321224 + 0.642448i
\(786\) 0 0
\(787\) 15.5885 + 9.00000i 0.555668 + 0.320815i 0.751405 0.659841i \(-0.229376\pi\)
−0.195737 + 0.980656i \(0.562710\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 28.0000 24.2487i 0.995565 0.862185i
\(792\) 0 0
\(793\) 25.9808 15.0000i 0.922604 0.532666i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.00000i 0.0708436i −0.999372 0.0354218i \(-0.988723\pi\)
0.999372 0.0354218i \(-0.0112775\pi\)
\(798\) 0 0