Properties

Label 768.2.o.b.95.9
Level 768
Weight 2
Character 768.95
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 95.9
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.266294 - 1.71146i) q^{3} +(3.14689 - 1.30348i) q^{5} +(0.663471 + 0.663471i) q^{7} +(-2.85817 - 0.911503i) q^{9} +O(q^{10})\) \(q+(0.266294 - 1.71146i) q^{3} +(3.14689 - 1.30348i) q^{5} +(0.663471 + 0.663471i) q^{7} +(-2.85817 - 0.911503i) q^{9} +(-1.91929 + 0.794997i) q^{11} +(2.31672 - 5.59306i) q^{13} +(-1.39286 - 5.73287i) q^{15} +2.24987 q^{17} +(-3.08841 - 1.27926i) q^{19} +(1.31218 - 0.958824i) q^{21} +(4.32171 + 4.32171i) q^{23} +(4.66830 - 4.66830i) q^{25} +(-2.32111 + 4.64892i) q^{27} +(-0.546766 + 1.32001i) q^{29} -2.34273i q^{31} +(0.849507 + 3.49649i) q^{33} +(2.95269 + 1.22305i) q^{35} +(0.324682 + 0.783851i) q^{37} +(-8.95535 - 5.45437i) q^{39} +(-4.73908 + 4.73908i) q^{41} +(-0.951664 - 2.29752i) q^{43} +(-10.1825 + 0.857185i) q^{45} -3.02812i q^{47} -6.11961i q^{49} +(0.599128 - 3.85056i) q^{51} +(3.49549 + 8.43885i) q^{53} +(-5.00353 + 5.00353i) q^{55} +(-3.01183 + 4.94502i) q^{57} +(-3.11165 - 7.51220i) q^{59} +(1.01639 + 0.421005i) q^{61} +(-1.29156 - 2.50107i) q^{63} -20.6205i q^{65} +(-3.46052 + 8.35443i) q^{67} +(8.54728 - 6.24558i) q^{69} +(0.167408 - 0.167408i) q^{71} +(3.86922 + 3.86922i) q^{73} +(-6.74645 - 9.23273i) q^{75} +(-1.80085 - 0.745938i) q^{77} +2.44740 q^{79} +(7.33832 + 5.21047i) q^{81} +(5.17660 - 12.4974i) q^{83} +(7.08008 - 2.93267i) q^{85} +(2.11354 + 1.28728i) q^{87} +(6.63254 + 6.63254i) q^{89} +(5.24791 - 2.17376i) q^{91} +(-4.00949 - 0.623856i) q^{93} -11.3864 q^{95} +4.48787 q^{97} +(6.21032 - 0.522799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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
\(3\) 0.266294 1.71146i 0.153745 0.988111i
\(4\) 0 0
\(5\) 3.14689 1.30348i 1.40733 0.582935i 0.455687 0.890140i \(-0.349394\pi\)
0.951644 + 0.307205i \(0.0993936\pi\)
\(6\) 0 0
\(7\) 0.663471 + 0.663471i 0.250769 + 0.250769i 0.821286 0.570517i \(-0.193257\pi\)
−0.570517 + 0.821286i \(0.693257\pi\)
\(8\) 0 0
\(9\) −2.85817 0.911503i −0.952725 0.303834i
\(10\) 0 0
\(11\) −1.91929 + 0.794997i −0.578689 + 0.239701i −0.652776 0.757551i \(-0.726396\pi\)
0.0740873 + 0.997252i \(0.476396\pi\)
\(12\) 0 0
\(13\) 2.31672 5.59306i 0.642543 1.55123i −0.180696 0.983539i \(-0.557835\pi\)
0.823238 0.567696i \(-0.192165\pi\)
\(14\) 0 0
\(15\) −1.39286 5.73287i −0.359634 1.48022i
\(16\) 0 0
\(17\) 2.24987 0.545673 0.272837 0.962060i \(-0.412038\pi\)
0.272837 + 0.962060i \(0.412038\pi\)
\(18\) 0 0
\(19\) −3.08841 1.27926i −0.708530 0.293483i −0.000833646 1.00000i \(-0.500265\pi\)
−0.707696 + 0.706517i \(0.750265\pi\)
\(20\) 0 0
\(21\) 1.31218 0.958824i 0.286342 0.209233i
\(22\) 0 0
\(23\) 4.32171 + 4.32171i 0.901140 + 0.901140i 0.995535 0.0943951i \(-0.0300917\pi\)
−0.0943951 + 0.995535i \(0.530092\pi\)
\(24\) 0 0
\(25\) 4.66830 4.66830i 0.933659 0.933659i
\(26\) 0 0
\(27\) −2.32111 + 4.64892i −0.446699 + 0.894684i
\(28\) 0 0
\(29\) −0.546766 + 1.32001i −0.101532 + 0.245120i −0.966480 0.256741i \(-0.917351\pi\)
0.864948 + 0.501861i \(0.167351\pi\)
\(30\) 0 0
\(31\) 2.34273i 0.420767i −0.977619 0.210384i \(-0.932529\pi\)
0.977619 0.210384i \(-0.0674713\pi\)
\(32\) 0 0
\(33\) 0.849507 + 3.49649i 0.147880 + 0.608661i
\(34\) 0 0
\(35\) 2.95269 + 1.22305i 0.499096 + 0.206732i
\(36\) 0 0
\(37\) 0.324682 + 0.783851i 0.0533774 + 0.128864i 0.948319 0.317319i \(-0.102783\pi\)
−0.894941 + 0.446184i \(0.852783\pi\)
\(38\) 0 0
\(39\) −8.95535 5.45437i −1.43400 0.873398i
\(40\) 0 0
\(41\) −4.73908 + 4.73908i −0.740120 + 0.740120i −0.972601 0.232481i \(-0.925316\pi\)
0.232481 + 0.972601i \(0.425316\pi\)
\(42\) 0 0
\(43\) −0.951664 2.29752i −0.145127 0.350369i 0.834555 0.550925i \(-0.185725\pi\)
−0.979682 + 0.200556i \(0.935725\pi\)
\(44\) 0 0
\(45\) −10.1825 + 0.857185i −1.51791 + 0.127782i
\(46\) 0 0
\(47\) 3.02812i 0.441696i −0.975308 0.220848i \(-0.929117\pi\)
0.975308 0.220848i \(-0.0708825\pi\)
\(48\) 0 0
\(49\) 6.11961i 0.874230i
\(50\) 0 0
\(51\) 0.599128 3.85056i 0.0838946 0.539186i
\(52\) 0 0
\(53\) 3.49549 + 8.43885i 0.480142 + 1.15916i 0.959541 + 0.281568i \(0.0908545\pi\)
−0.479399 + 0.877597i \(0.659145\pi\)
\(54\) 0 0
\(55\) −5.00353 + 5.00353i −0.674676 + 0.674676i
\(56\) 0 0
\(57\) −3.01183 + 4.94502i −0.398926 + 0.654984i
\(58\) 0 0
\(59\) −3.11165 7.51220i −0.405103 0.978005i −0.986407 0.164318i \(-0.947458\pi\)
0.581305 0.813686i \(1.69746\pi\)
\(60\) 0 0
\(61\) 1.01639 + 0.421005i 0.130136 + 0.0539041i 0.446801 0.894633i \(-0.352563\pi\)
−0.316665 + 0.948537i \(0.602563\pi\)
\(62\) 0 0
\(63\) −1.29156 2.50107i −0.162721 0.315106i
\(64\) 0 0
\(65\) 20.6205i 2.55766i
\(66\) 0 0
\(67\) −3.46052 + 8.35443i −0.422770 + 1.02066i 0.558757 + 0.829331i \(0.311278\pi\)
−0.981527 + 0.191325i \(0.938722\pi\)
\(68\) 0 0
\(69\) 8.54728 6.24558i 1.02897 0.751880i
\(70\) 0 0
\(71\) 0.167408 0.167408i 0.0198677 0.0198677i −0.697103 0.716971i \(-0.745528\pi\)
0.716971 + 0.697103i \(0.245528\pi\)
\(72\) 0 0
\(73\) 3.86922 + 3.86922i 0.452858 + 0.452858i 0.896302 0.443444i \(-0.146244\pi\)
−0.443444 + 0.896302i \(0.646244\pi\)
\(74\) 0 0
\(75\) −6.74645 9.23273i −0.779013 1.06610i
\(76\) 0 0
\(77\) −1.80085 0.745938i −0.205226 0.0850075i
\(78\) 0 0
\(79\) 2.44740 0.275354 0.137677 0.990477i \(-0.456036\pi\)
0.137677 + 0.990477i \(0.456036\pi\)
\(80\) 0 0
\(81\) 7.33832 + 5.21047i 0.815369 + 0.578941i
\(82\) 0 0
\(83\) 5.17660 12.4974i 0.568206 1.37177i −0.334860 0.942268i \(-0.608689\pi\)
0.903066 0.429502i \(-0.141311\pi\)
\(84\) 0 0
\(85\) 7.08008 2.93267i 0.767943 0.318092i
\(86\) 0 0
\(87\) 2.11354 + 1.28728i 0.226595 + 0.138011i
\(88\) 0 0
\(89\) 6.63254 + 6.63254i 0.703048 + 0.703048i 0.965064 0.262016i \(-0.0843872\pi\)
−0.262016 + 0.965064i \(0.584387\pi\)
\(90\) 0 0
\(91\) 5.24791 2.17376i 0.550130 0.227871i
\(92\) 0 0
\(93\) −4.00949 0.623856i −0.415764 0.0646909i
\(94\) 0 0
\(95\) −11.3864 −1.16822
\(96\) 0 0
\(97\) 4.48787 0.455674 0.227837 0.973699i \(-0.426835\pi\)
0.227837 + 0.973699i \(0.426835\pi\)
\(98\) 0 0
\(99\) 6.21032 0.522799i 0.624160 0.0525433i
\(100\) 0 0
\(101\) −12.6091 + 5.22285i −1.25465 + 0.519693i −0.908263 0.418399i \(-0.862591\pi\)
−0.346386 + 0.938092i \(0.612591\pi\)
\(102\) 0 0
\(103\) 5.37192 + 5.37192i 0.529311 + 0.529311i 0.920367 0.391056i \(-0.127890\pi\)
−0.391056 + 0.920367i \(0.627890\pi\)
\(104\) 0 0
\(105\) 2.87948 4.72772i 0.281008 0.461378i
\(106\) 0 0
\(107\) −13.4838 + 5.58517i −1.30353 + 0.539939i −0.922989 0.384826i \(-0.874261\pi\)
−0.380538 + 0.924765i \(0.624261\pi\)
\(108\) 0 0
\(109\) 1.82205 4.39883i 0.174521 0.421331i −0.812280 0.583268i \(-0.801774\pi\)
0.986801 + 0.161936i \(0.0517739\pi\)
\(110\) 0 0
\(111\) 1.42799 0.346944i 0.135539 0.0329305i
\(112\) 0 0
\(113\) −5.85162 −0.550475 −0.275237 0.961376i \(-0.588756\pi\)
−0.275237 + 0.961376i \(0.588756\pi\)
\(114\) 0 0
\(115\) 19.2332 + 7.96666i 1.79351 + 0.742895i
\(116\) 0 0
\(117\) −11.7197 + 13.8742i −1.08348 + 1.28267i
\(118\) 0 0
\(119\) 1.49272 + 1.49272i 0.136838 + 0.136838i
\(120\) 0 0
\(121\) −4.72651 + 4.72651i −0.429683 + 0.429683i
\(122\) 0 0
\(123\) 6.84875 + 9.37273i 0.617531 + 0.845110i
\(124\) 0 0
\(125\) 2.08814 5.04121i 0.186769 0.450899i
\(126\) 0 0
\(127\) 10.2914i 0.913216i 0.889668 + 0.456608i \(0.150936\pi\)
−0.889668 + 0.456608i \(0.849064\pi\)
\(128\) 0 0
\(129\) −4.18553 + 1.01692i −0.368516 + 0.0895345i
\(130\) 0 0
\(131\) 16.3968 + 6.79177i 1.43259 + 0.593400i 0.957990 0.286800i \(-0.0925915\pi\)
0.474603 + 0.880200i \(0.342592\pi\)
\(132\) 0 0
\(133\) −1.20032 2.89782i −0.104081 0.251273i
\(134\) 0 0
\(135\) −1.24450 + 17.6551i −0.107110 + 1.51951i
\(136\) 0 0
\(137\) −8.43673 + 8.43673i −0.720799 + 0.720799i −0.968768 0.247969i \(-0.920237\pi\)
0.247969 + 0.968768i \(0.420237\pi\)
\(138\) 0 0
\(139\) 7.74040 + 18.6870i 0.656532 + 1.58501i 0.803124 + 0.595812i \(0.203169\pi\)
−0.146592 + 0.989197i \(0.546831\pi\)
\(140\) 0 0
\(141\) −5.18249 0.806371i −0.436445 0.0679086i
\(142\) 0 0
\(143\) 12.5765i 1.05170i
\(144\) 0 0
\(145\) 4.86662i 0.404151i
\(146\) 0 0
\(147\) −10.4735 1.62962i −0.863836 0.134409i
\(148\) 0 0
\(149\) −4.26837 10.3048i −0.349678 0.844198i −0.996658 0.0816908i \(-0.973968\pi\)
0.646979 0.762508i \(1.72397\pi\)
\(150\) 0 0
\(151\) 12.1716 12.1716i 0.990514 0.990514i −0.00944142 0.999955i \(-0.503005\pi\)
0.999955 + 0.00944142i \(0.00300534\pi\)
\(152\) 0 0
\(153\) −6.43052 2.05076i −0.519877 0.165794i
\(154\) 0 0
\(155\) −3.05371 7.37231i −0.245280 0.592159i
\(156\) 0 0
\(157\) 10.1467 + 4.20290i 0.809795 + 0.335428i 0.748872 0.662714i \(-0.230596\pi\)
0.0609231 + 0.998142i \(0.480596\pi\)
\(158\) 0 0
\(159\) 15.3736 3.73516i 1.21920 0.296217i
\(160\) 0 0
\(161\) 5.73467i 0.451955i
\(162\) 0 0
\(163\) 4.03936 9.75187i 0.316387 0.763826i −0.683053 0.730369i \(-0.739348\pi\)
0.999440 0.0334571i \(-0.0106517\pi\)
\(164\) 0 0
\(165\) 7.23092 + 9.89575i 0.562926 + 0.770383i
\(166\) 0 0
\(167\) 12.8761 12.8761i 0.996385 0.996385i −0.00360853 0.999993i \(-0.501149\pi\)
0.999993 + 0.00360853i \(0.00114863\pi\)
\(168\) 0 0
\(169\) −16.7227 16.7227i −1.28636 1.28636i
\(170\) 0 0
\(171\) 7.66116 + 6.47145i 0.585864 + 0.494884i
\(172\) 0 0
\(173\) 9.91155 + 4.10550i 0.753561 + 0.312135i 0.726194 0.687490i \(-0.241288\pi\)
0.0273673 + 0.999625i \(0.491288\pi\)
\(174\) 0 0
\(175\) 6.19456 0.468265
\(176\) 0 0
\(177\) −13.6854 + 3.32501i −1.02866 + 0.249923i
\(178\) 0 0
\(179\) −9.52280 + 22.9901i −0.711768 + 1.71836i −0.0162316 + 0.999868i \(0.505167\pi\)
−0.695536 + 0.718491i \(0.744833\pi\)
\(180\) 0 0
\(181\) −11.0607 + 4.58151i −0.822139 + 0.340541i −0.753786 0.657120i \(-0.771774\pi\)
−0.0683528 + 0.997661i \(0.521774\pi\)
\(182\) 0 0
\(183\) 0.991192 1.62741i 0.0732710 0.120301i
\(184\) 0 0
\(185\) 2.04347 + 2.04347i 0.150239 + 0.150239i
\(186\) 0 0
\(187\) −4.31816 + 1.78864i −0.315775 + 0.130798i
\(188\) 0 0
\(189\) −4.62442 + 1.54443i −0.336377 + 0.112341i
\(190\) 0 0
\(191\) 0.133706 0.00967461 0.00483731 0.999988i \(-0.498460\pi\)
0.00483731 + 0.999988i \(0.498460\pi\)
\(192\) 0 0
\(193\) 7.48776 0.538981 0.269490 0.963003i \(-0.413145\pi\)
0.269490 + 0.963003i \(0.413145\pi\)
\(194\) 0 0
\(195\) −35.2912 5.49113i −2.52725 0.393228i
\(196\) 0 0
\(197\) 4.23540 1.75436i 0.301759 0.124993i −0.226666 0.973973i \(-0.572783\pi\)
0.528425 + 0.848980i \(0.322783\pi\)
\(198\) 0 0
\(199\) 3.74082 + 3.74082i 0.265179 + 0.265179i 0.827154 0.561975i \(-0.189958\pi\)
−0.561975 + 0.827154i \(0.689958\pi\)
\(200\) 0 0
\(201\) 13.3767 + 8.14727i 0.943522 + 0.574664i
\(202\) 0 0
\(203\) −1.23855 + 0.513025i −0.0869293 + 0.0360073i
\(204\) 0 0
\(205\) −8.73604 + 21.0907i −0.610152 + 1.47304i
\(206\) 0 0
\(207\) −8.41296 16.2915i −0.584741 1.13234i
\(208\) 0 0
\(209\) 6.94457 0.480366
\(210\) 0 0
\(211\) −0.564367 0.233768i −0.0388526 0.0160933i 0.363173 0.931722i \(-0.381694\pi\)
−0.402025 + 0.915629i \(0.631694\pi\)
\(212\) 0 0
\(213\) −0.241932 0.331092i −0.0165769 0.0226861i
\(214\) 0 0
\(215\) −5.98956 5.98956i −0.408485 0.408485i
\(216\) 0 0
\(217\) 1.55434 1.55434i 0.105515 0.105515i
\(218\) 0 0
\(219\) 7.65236 5.59165i 0.517098 0.377849i
\(220\) 0 0
\(221\) 5.21232 12.5836i 0.350618 0.846468i
\(222\) 0 0
\(223\) 10.6887i 0.715768i 0.933766 + 0.357884i \(0.116502\pi\)
−0.933766 + 0.357884i \(0.883498\pi\)
\(224\) 0 0
\(225\) −17.5980 + 9.08764i −1.17320 + 0.605842i
\(226\) 0 0
\(227\) −1.76729 0.732035i −0.117299 0.0485869i 0.323262 0.946309i \(-0.395220\pi\)
−0.440561 + 0.897723i \(0.645220\pi\)
\(228\) 0 0
\(229\) 4.83167 + 11.6647i 0.319286 + 0.770824i 0.999292 + 0.0376176i \(0.0119769\pi\)
−0.680007 + 0.733206i \(0.738023\pi\)
\(230\) 0 0
\(231\) −1.75620 + 2.88345i −0.115549 + 0.189717i
\(232\) 0 0
\(233\) 6.98725 6.98725i 0.457750 0.457750i −0.440166 0.897916i \(-0.645080\pi\)
0.897916 + 0.440166i \(0.145080\pi\)
\(234\) 0 0
\(235\) −3.94710 9.52914i −0.257480 0.621613i
\(236\) 0 0
\(237\) 0.651729 4.18862i 0.0423344 0.272080i
\(238\) 0 0
\(239\) 6.60970i 0.427546i −0.976883 0.213773i \(-0.931425\pi\)
0.976883 0.213773i \(-0.0685752\pi\)
\(240\) 0 0
\(241\) 13.3092i 0.857322i 0.903466 + 0.428661i \(0.141014\pi\)
−0.903466 + 0.428661i \(0.858986\pi\)
\(242\) 0 0
\(243\) 10.8717 11.1717i 0.697417 0.716666i
\(244\) 0 0
\(245\) −7.97681 19.2577i −0.509620 1.23033i
\(246\) 0 0
\(247\) −14.3100 + 14.3100i −0.910521 + 0.910521i
\(248\) 0 0
\(249\) −20.0103 12.1875i −1.26810 0.772353i
\(250\) 0 0
\(251\) 5.55430 + 13.4093i 0.350584 + 0.846385i 0.996548 + 0.0830174i \(0.0264557\pi\)
−0.645964 + 0.763368i \(0.723544\pi\)
\(252\) 0 0
\(253\) −11.7304 4.85889i −0.737483 0.305476i
\(254\) 0 0
\(255\) −3.13375 12.8982i −0.196243 0.807718i
\(256\) 0 0
\(257\) 12.0491i 0.751605i 0.926700 + 0.375803i \(0.122633\pi\)
−0.926700 + 0.375803i \(0.877367\pi\)
\(258\) 0 0
\(259\) −0.304646 + 0.735480i −0.0189298 + 0.0457005i
\(260\) 0 0
\(261\) 2.76595 3.27444i 0.171208 0.202683i
\(262\) 0 0
\(263\) 2.42769 2.42769i 0.149698 0.149698i −0.628285 0.777983i \(-0.716243\pi\)
0.777983 + 0.628285i \(0.216243\pi\)
\(264\) 0 0
\(265\) 21.9998 + 21.9998i 1.35144 + 1.35144i
\(266\) 0 0
\(267\) 13.1175 9.58511i 0.802780 0.586599i
\(268\) 0 0
\(269\) 11.0872 + 4.59246i 0.675997 + 0.280007i 0.694153 0.719828i \(-0.255779\pi\)
−0.0181552 + 0.999835i \(0.505779\pi\)
\(270\) 0 0
\(271\) 16.6609 1.01208 0.506038 0.862511i \(-0.331109\pi\)
0.506038 + 0.862511i \(0.331109\pi\)
\(272\) 0 0
\(273\) −2.32280 9.56043i −0.140582 0.578624i
\(274\) 0 0
\(275\) −5.24854 + 12.6711i −0.316499 + 0.764097i
\(276\) 0 0
\(277\) 26.2888 10.8892i 1.57954 0.654267i 0.591199 0.806526i \(-0.298655\pi\)
0.988341 + 0.152259i \(0.0486547\pi\)
\(278\) 0 0
\(279\) −2.13541 + 6.69594i −0.127844 + 0.400875i
\(280\) 0 0
\(281\) −0.109141 0.109141i −0.00651081 0.00651081i 0.703844 0.710355i \(-0.251465\pi\)
−0.710355 + 0.703844i \(0.751465\pi\)
\(282\) 0 0
\(283\) −11.5159 + 4.77003i −0.684547 + 0.283549i −0.697726 0.716364i \(-0.745805\pi\)
0.0131791 + 0.999913i \(0.495805\pi\)
\(284\) 0 0
\(285\) −3.03213 + 19.4873i −0.179608 + 1.15433i
\(286\) 0 0
\(287\) −6.28849 −0.371198
\(288\) 0 0
\(289\) −11.9381 −0.702240
\(290\) 0 0
\(291\) 1.19510 7.68080i 0.0700577 0.450257i
\(292\) 0 0
\(293\) −14.6551 + 6.07035i −0.856161 + 0.354634i −0.767205 0.641402i \(-0.778353\pi\)
−0.0889561 + 0.996036i \(0.528353\pi\)
\(294\) 0 0
\(295\) −19.5840 19.5840i −1.14023 1.14023i
\(296\) 0 0
\(297\) 0.759024 10.7679i 0.0440430 0.624818i
\(298\) 0 0
\(299\) 34.1838 14.1594i 1.97690 0.818859i
\(300\) 0 0
\(301\) 0.892937 2.15574i 0.0514680 0.124255i
\(302\) 0 0
\(303\) 5.58096 + 22.9707i 0.320618 + 1.31963i
\(304\) 0 0
\(305\) 3.74725 0.214567
\(306\) 0 0
\(307\) −17.9759 7.44586i −1.02594 0.424958i −0.194694 0.980864i \(-0.562371\pi\)
−0.831245 + 0.555906i \(0.812371\pi\)
\(308\) 0 0
\(309\) 10.6243 7.76330i 0.604397 0.441639i
\(310\) 0 0
\(311\) −14.7567 14.7567i −0.836776 0.836776i 0.151657 0.988433i \(-0.451539\pi\)
−0.988433 + 0.151657i \(0.951539\pi\)
\(312\) 0 0
\(313\) −3.76309 + 3.76309i −0.212703 + 0.212703i −0.805415 0.592712i \(-0.798057\pi\)
0.592712 + 0.805415i \(0.298057\pi\)
\(314\) 0 0
\(315\) −7.32450 6.18707i −0.412689 0.348602i
\(316\) 0 0
\(317\) −5.65481 + 13.6519i −0.317606 + 0.766768i 0.681774 + 0.731562i \(0.261209\pi\)
−0.999380 + 0.0352055i \(0.988791\pi\)
\(318\) 0 0
\(319\) 2.96816i 0.166185i
\(320\) 0 0
\(321\) 5.96812 + 24.5642i 0.333108 + 1.37104i
\(322\) 0 0
\(323\) −6.94852 2.87817i −0.386626 0.160146i
\(324\) 0 0
\(325\) −15.2949 36.9252i −0.848409 2.04824i
\(326\) 0 0
\(327\) −7.04321 4.28975i −0.389490 0.237224i
\(328\) 0 0
\(329\) 2.00907 2.00907i 0.110764 0.110764i
\(330\) 0 0
\(331\) −3.87845 9.36340i −0.213179 0.514659i 0.780730 0.624869i \(-0.214848\pi\)
−0.993908 + 0.110210i \(0.964848\pi\)
\(332\) 0 0
\(333\) −0.213514 2.53633i −0.0117005 0.138990i
\(334\) 0 0
\(335\) 30.8012i 1.68285i
\(336\) 0 0
\(337\) 18.4557i 1.00535i −0.864476 0.502674i \(-0.832350\pi\)
0.864476 0.502674i \(-0.167650\pi\)
\(338\) 0 0
\(339\) −1.55825 + 10.0148i −0.0846328 + 0.543930i
\(340\) 0 0
\(341\) 1.86247 + 4.49639i 0.100858 + 0.243493i
\(342\) 0 0
\(343\) 8.70449 8.70449i 0.469998 0.469998i
\(344\) 0 0
\(345\) 18.7563 30.7954i 1.00981 1.65797i
\(346\) 0 0
\(347\) −2.01715 4.86983i −0.108286 0.261426i 0.860443 0.509547i \(-0.170187\pi\)
−0.968729 + 0.248121i \(0.920187\pi\)
\(348\) 0 0
\(349\) −19.0402 7.88672i −1.01920 0.422166i −0.190397 0.981707i \(-0.560977\pi\)
−0.828803 + 0.559541i \(0.810977\pi\)
\(350\) 0 0
\(351\) 20.6243 + 23.7524i 1.10084 + 1.26781i
\(352\) 0 0
\(353\) 13.3595i 0.711053i −0.934666 0.355527i \(-0.884301\pi\)
0.934666 0.355527i \(-0.115699\pi\)
\(354\) 0 0
\(355\) 0.308601 0.745029i 0.0163788 0.0395420i
\(356\) 0 0
\(357\) 2.95224 2.15723i 0.156249 0.114173i
\(358\) 0 0
\(359\) −0.514805 + 0.514805i −0.0271704 + 0.0271704i −0.720561 0.693391i \(-0.756116\pi\)
0.693391 + 0.720561i \(0.256116\pi\)
\(360\) 0 0
\(361\) −5.53327 5.53327i −0.291225 0.291225i
\(362\) 0 0
\(363\) 6.83058 + 9.34786i 0.358512 + 0.490636i
\(364\) 0 0
\(365\) 17.2195 + 7.13254i 0.901308 + 0.373334i
\(366\) 0 0
\(367\) −37.5921 −1.96229 −0.981145 0.193271i \(-0.938090\pi\)
−0.981145 + 0.193271i \(0.938090\pi\)
\(368\) 0 0
\(369\) 17.8648 9.22543i 0.930005 0.480257i
\(370\) 0 0
\(371\) −3.27978 + 7.91809i −0.170278 + 0.411087i
\(372\) 0 0
\(373\) −22.6229 + 9.37070i −1.17137 + 0.485196i −0.881644 0.471914i \(-0.843563\pi\)
−0.289723 + 0.957111i \(0.593563\pi\)
\(374\) 0 0
\(375\) −8.07176 4.91620i −0.416824 0.253872i
\(376\) 0 0
\(377\) 6.11619 + 6.11619i 0.315000 + 0.315000i
\(378\) 0 0
\(379\) 14.1576 5.86429i 0.727229 0.301228i 0.0118165 0.999930i \(-0.496239\pi\)
0.715413 + 0.698702i \(0.246239\pi\)
\(380\) 0 0
\(381\) 17.6133 + 2.74055i 0.902359 + 0.140403i
\(382\) 0 0
\(383\) 16.0682 0.821048 0.410524 0.911850i \(-0.365346\pi\)
0.410524 + 0.911850i \(0.365346\pi\)
\(384\) 0 0
\(385\) −6.63940 −0.338375
\(386\) 0 0
\(387\) 0.625825 + 7.43416i 0.0318125 + 0.377900i
\(388\) 0 0
\(389\) −31.0923 + 12.8788i −1.57644 + 0.652983i −0.987845 0.155444i \(-0.950319\pi\)
−0.588596 + 0.808427i \(0.700319\pi\)
\(390\) 0 0
\(391\) 9.72329 + 9.72329i 0.491728 + 0.491728i
\(392\) 0 0
\(393\) 15.9902 26.2538i 0.806599 1.32433i
\(394\) 0 0
\(395\) 7.70170 3.19015i 0.387514 0.160514i
\(396\) 0 0
\(397\) 8.21223 19.8261i 0.412160 0.995042i −0.572397 0.819977i \(-0.693986\pi\)
0.984557 0.175065i \(-0.0560136\pi\)
\(398\) 0 0
\(399\) −5.27914 + 1.28262i −0.264288 + 0.0642113i
\(400\) 0 0
\(401\) −15.2053 −0.759315 −0.379657 0.925127i \(-0.623958\pi\)
−0.379657 + 0.925127i \(0.623958\pi\)
\(402\) 0 0
\(403\) −13.1030 5.42745i −0.652709 0.270361i
\(404\) 0 0
\(405\) 29.8846 + 6.83138i 1.48498 + 0.339454i
\(406\) 0 0
\(407\) −1.24632 1.24632i −0.0617777 0.0617777i
\(408\) 0 0
\(409\) 23.0147 23.0147i 1.13800 1.13800i 0.149193 0.988808i \(-0.452332\pi\)
0.988808 0.149193i \(-0.0476677\pi\)
\(410\) 0 0
\(411\) 12.1925 + 16.6858i 0.601410 + 0.823048i
\(412\) 0 0
\(413\) 2.91963 7.04862i 0.143666 0.346840i
\(414\) 0 0
\(415\) 46.0756i 2.26176i
\(416\) 0 0
\(417\) 34.0432 8.27113i 1.66710 0.405039i
\(418\) 0 0
\(419\) −10.8187 4.48124i −0.528527 0.218923i 0.102431 0.994740i \(-0.467338\pi\)
−0.630958 + 0.775817i \(0.717338\pi\)
\(420\) 0 0
\(421\) 11.0208 + 26.6066i 0.537121 + 1.29673i 0.926724 + 0.375742i \(0.122612\pi\)
−0.389603 + 0.920983i \(0.627388\pi\)
\(422\) 0 0
\(423\) −2.76014 + 8.65489i −0.134203 + 0.420815i
\(424\) 0 0
\(425\) 10.5031 10.5031i 0.509473 0.509473i
\(426\) 0 0
\(427\) 0.395024 + 0.953673i 0.0191166 + 0.0461515i
\(428\) 0 0
\(429\) 21.5241 + 3.34905i 1.03920 + 0.161694i
\(430\) 0 0
\(431\) 0.278342i 0.0134073i 0.999978 + 0.00670363i \(0.00213385\pi\)
−0.999978 + 0.00670363i \(0.997866\pi\)
\(432\) 0 0
\(433\) 11.0862i 0.532769i −0.963867 0.266385i \(-0.914171\pi\)
0.963867 0.266385i \(-0.0858292\pi\)
\(434\) 0 0
\(435\) 8.32902 + 1.29595i 0.399346 + 0.0621362i
\(436\) 0 0
\(437\) −7.81862 18.8758i −0.374015 0.902953i
\(438\) 0 0
\(439\) 18.4802 18.4802i 0.882011 0.882011i −0.111728 0.993739i \(-0.535639\pi\)
0.993739 + 0.111728i \(0.0356386\pi\)
\(440\) 0 0
\(441\) −5.57805 + 17.4909i −0.265621 + 0.832901i
\(442\) 0 0
\(443\) −15.7855 38.1095i −0.749991 1.81064i −0.559251 0.828998i \(-0.688911\pi\)
−0.190740 0.981641i \(1.43891\pi\)
\(444\) 0 0
\(445\) 29.5173 + 12.2265i 1.39925 + 0.579590i
\(446\) 0 0
\(447\) −18.7728 + 4.56103i −0.887923 + 0.215730i
\(448\) 0 0
\(449\) 23.9532i 1.13042i 0.824946 + 0.565211i \(0.191205\pi\)
−0.824946 + 0.565211i \(0.808795\pi\)
\(450\) 0 0
\(451\) 5.32813 12.8632i 0.250892 0.605706i
\(452\) 0 0
\(453\) −17.5900 24.0725i −0.826451 1.13102i
\(454\) 0 0
\(455\) 13.6811 13.6811i 0.641381 0.641381i
\(456\) 0 0
\(457\) −3.61836 3.61836i −0.169260 0.169260i 0.617394 0.786654i \(-0.288188\pi\)
−0.786654 + 0.617394i \(0.788188\pi\)
\(458\) 0 0
\(459\) −5.22221 + 10.4595i −0.243752 + 0.488206i
\(460\) 0 0
\(461\) 11.0476 + 4.57608i 0.514539 + 0.213129i 0.624816 0.780772i \(-0.285174\pi\)
−0.110277 + 0.993901i \(0.535174\pi\)
\(462\) 0 0
\(463\) −27.8395 −1.29381 −0.646906 0.762569i \(-0.723938\pi\)
−0.646906 + 0.762569i \(0.723938\pi\)
\(464\) 0 0
\(465\) −13.4306 + 3.26309i −0.622829 + 0.151322i
\(466\) 0 0
\(467\) 15.3748 37.1181i 0.711462 1.71762i 0.0151469 0.999885i \(-0.495178\pi\)
0.696315 0.717736i \(-0.254822\pi\)
\(468\) 0 0
\(469\) −7.83888 + 3.24697i −0.361966 + 0.149931i
\(470\) 0 0
\(471\) 9.89510 16.2465i 0.455942 0.748597i
\(472\) 0 0
\(473\) 3.65304 + 3.65304i 0.167967 + 0.167967i
\(474\) 0 0
\(475\) −20.3896 + 8.44564i −0.935538 + 0.387512i
\(476\) 0 0
\(477\) −2.29867 27.3058i −0.105249 1.25025i
\(478\) 0 0
\(479\) −23.6720 −1.08160 −0.540800 0.841151i \(-0.681878\pi\)
−0.540800 + 0.841151i \(0.681878\pi\)
\(480\) 0 0
\(481\) 5.13632 0.234196
\(482\) 0 0
\(483\) 9.81464 + 1.52711i 0.446582 + 0.0694859i
\(484\) 0 0
\(485\) 14.1228 5.84987i 0.641284 0.265629i
\(486\) 0 0
\(487\) −1.06704 1.06704i −0.0483522 0.0483522i 0.682517 0.730869i \(-0.260885\pi\)
−0.730869 + 0.682517i \(0.760885\pi\)
\(488\) 0 0
\(489\) −15.6143 9.51006i −0.706101 0.430060i
\(490\) 0 0
\(491\) −24.4454 + 10.1256i −1.10321 + 0.456964i −0.858594 0.512657i \(-0.828661\pi\)
−0.244614 + 0.969621i \(0.578661\pi\)
\(492\) 0 0
\(493\) −1.23015 + 2.96985i −0.0554033 + 0.133755i
\(494\) 0 0
\(495\) 18.8617 9.74023i 0.847771 0.437791i
\(496\) 0 0
\(497\) 0.222141 0.00996439
\(498\) 0 0
\(499\) −23.7276 9.82828i −1.06219 0.439974i −0.217963 0.975957i \(-0.569941\pi\)
−0.844229 + 0.535983i \(0.819941\pi\)
\(500\) 0 0
\(501\) −18.6081 25.4658i −0.831349 1.13773i
\(502\) 0 0
\(503\) −8.35178 8.35178i −0.372387 0.372387i 0.495959 0.868346i \(-0.334817\pi\)
−0.868346 + 0.495959i \(0.834817\pi\)
\(504\) 0 0
\(505\) −32.8714 + 32.8714i −1.46276 + 1.46276i
\(506\) 0 0
\(507\) −33.0734 + 24.1670i −1.46884 + 1.07330i
\(508\) 0 0
\(509\) 2.98703 7.21134i 0.132398 0.319637i −0.843752 0.536733i \(-0.819658\pi\)
0.976150 + 0.217096i \(0.0696584\pi\)
\(510\) 0 0
\(511\) 5.13423i 0.227125i
\(512\) 0 0
\(513\) 13.1157 11.3884i 0.579074 0.502812i
\(514\) 0 0
\(515\) 23.9070 + 9.90262i 1.05347 + 0.436361i
\(516\) 0 0
\(517\) 2.40734 + 5.81184i 0.105875 + 0.255605i
\(518\) 0 0
\(519\) 9.66577 15.8699i 0.424280 0.696612i
\(520\) 0 0
\(521\) −5.48494 + 5.48494i −0.240299 + 0.240299i −0.816974 0.576675i \(-0.804350\pi\)
0.576675 + 0.816974i \(0.304350\pi\)
\(522\) 0 0
\(523\) −6.43166 15.5274i −0.281237 0.678966i 0.718628 0.695394i \(-0.244770\pi\)
−0.999865 + 0.0164288i \(0.994770\pi\)
\(524\) 0 0
\(525\) 1.64958 10.6017i 0.0719934 0.462697i
\(526\) 0 0
\(527\) 5.27084i 0.229601i
\(528\) 0 0
\(529\) 14.3544i 0.624106i
\(530\) 0 0
\(531\) 2.04626 + 24.3074i 0.0888000 + 1.05485i
\(532\) 0 0
\(533\) 15.5268 + 37.4851i 0.672542 + 1.62366i
\(534\) 0 0
\(535\) −35.1518 + 35.1518i −1.51974 + 1.51974i
\(536\) 0 0
\(537\) 36.8107 + 22.4200i 1.58850 + 0.967495i
\(538\) 0 0
\(539\) 4.86507 + 11.7453i 0.209554 + 0.505907i
\(540\) 0 0
\(541\) 3.57097 + 1.47914i 0.153528 + 0.0635934i 0.458124 0.888888i \(-0.348522\pi\)
−0.304596 + 0.952482i \(0.598522\pi\)
\(542\) 0 0
\(543\) 4.89565 + 20.1500i 0.210092 + 0.864720i
\(544\) 0 0
\(545\) 16.2176i 0.694687i
\(546\) 0 0
\(547\) −1.97916 + 4.77812i −0.0846228 + 0.204298i −0.960527 0.278188i \(-0.910266\pi\)
0.875904 + 0.482486i \(0.160266\pi\)
\(548\) 0 0
\(549\) −2.52129 2.12975i −0.107606 0.0908956i
\(550\) 0 0
\(551\) 3.37727 3.37727i 0.143877 0.143877i
\(552\) 0 0
\(553\) 1.62378 + 1.62378i 0.0690502 + 0.0690502i
\(554\) 0 0
\(555\) 4.04148 2.95315i 0.171551 0.125354i
\(556\) 0 0
\(557\) −30.8826 12.7920i −1.30854 0.542014i −0.384080 0.923300i \(-0.625481\pi\)
−0.924457 + 0.381286i \(0.875481\pi\)
\(558\) 0 0
\(559\) −15.0549 −0.636755
\(560\) 0 0
\(561\) 1.91128 + 7.86665i 0.0806943 + 0.332130i
\(562\) 0 0
\(563\) −6.06412 + 14.6401i −0.255572 + 0.617005i −0.998636 0.0522151i \(-0.983372\pi\)
0.743064 + 0.669221i \(0.233372\pi\)
\(564\) 0 0
\(565\) −18.4144 + 7.62750i −0.774700 + 0.320891i
\(566\) 0 0
\(567\) 1.41177 + 8.32577i 0.0592888 + 0.349649i
\(568\) 0 0
\(569\) −24.5419 24.5419i −1.02885 1.02885i −0.999571 0.0292808i \(-0.990678\pi\)
−0.0292808 0.999571i \(1.49068\pi\)
\(570\) 0 0
\(571\) 37.5798 15.5661i 1.57266 0.651419i 0.585435 0.810720i \(-0.300924\pi\)
0.987230 + 0.159301i \(0.0509239\pi\)
\(572\) 0 0
\(573\) 0.0356051 0.228832i 0.00148743 0.00955959i
\(574\) 0 0
\(575\) 40.3501 1.68271
\(576\) 0 0
\(577\) −37.6825 −1.56874 −0.784371 0.620292i \(-0.787014\pi\)
−0.784371 + 0.620292i \(0.787014\pi\)
\(578\) 0 0
\(579\) 1.99395 12.8150i 0.0828657 0.532573i
\(580\) 0 0
\(581\) 11.7262 4.85715i 0.486485 0.201509i
\(582\) 0 0
\(583\) −13.4177 13.4177i −0.555705 0.555705i
\(584\) 0 0
\(585\) −18.7957 + 58.9371i −0.777105 + 2.43675i
\(586\) 0 0
\(587\) −16.1148 + 6.67499i −0.665131 + 0.275506i −0.689596 0.724195i \(-0.742212\pi\)
0.0244651 + 0.999701i \(0.492212\pi\)
\(588\) 0 0
\(589\) −2.99697 + 7.23532i −0.123488 + 0.298126i
\(590\) 0 0
\(591\) −1.87465 7.71588i −0.0771127 0.317389i
\(592\) 0 0
\(593\) −35.2533 −1.44768 −0.723839 0.689969i \(-0.757624\pi\)
−0.723839 + 0.689969i \(0.757624\pi\)
\(594\) 0 0
\(595\) 6.64317 + 2.75169i 0.272344 + 0.112808i
\(596\) 0 0
\(597\) 7.39841 5.40609i 0.302797 0.221257i
\(598\) 0 0
\(599\) 12.1323 + 12.1323i 0.495712 + 0.495712i 0.910100 0.414388i \(-0.136004\pi\)
−0.414388 + 0.910100i \(0.636004\pi\)
\(600\) 0 0
\(601\) 0.0132863 0.0132863i 0.000541959 0.000541959i −0.706836 0.707378i \(-0.749878\pi\)
0.707378 + 0.706836i \(0.249878\pi\)
\(602\) 0 0
\(603\) 17.5059 20.7241i 0.712894 0.843953i
\(604\) 0 0
\(605\) −8.71287 + 21.0347i −0.354228 + 0.855183i
\(606\) 0 0
\(607\) 5.69469i 0.231140i 0.993299 + 0.115570i \(0.0368695\pi\)
−0.993299 + 0.115570i \(0.963130\pi\)
\(608\) 0 0
\(609\) 0.548201 + 2.25635i 0.0222142 + 0.0914317i
\(610\) 0 0
\(611\) −16.9364 7.01530i −0.685175 0.283809i
\(612\) 0 0
\(613\) 12.0221 + 29.0239i 0.485567 + 1.17226i 0.956929 + 0.290322i \(0.0937626\pi\)
−0.471362 + 0.881940i \(0.656237\pi\)
\(614\) 0 0
\(615\) 33.7694 + 20.5677i 1.36171 + 0.829369i
\(616\) 0 0
\(617\) −12.5126 + 12.5126i −0.503739 + 0.503739i −0.912598 0.408859i \(-0.865927\pi\)
0.408859 + 0.912598i \(0.365927\pi\)
\(618\) 0 0
\(619\) −9.64869 23.2940i −0.387814 0.936265i −0.990402 0.138213i \(-0.955864\pi\)
0.602589 0.798052i \(-0.294136\pi\)
\(620\) 0 0
\(621\) −30.1225 + 10.0601i −1.20877 + 0.403698i
\(622\) 0 0
\(623\) 8.80100i 0.352605i
\(624\) 0 0
\(625\) 14.4239i 0.576955i
\(626\) 0 0
\(627\) 1.84930 11.8853i 0.0738539 0.474655i
\(628\) 0 0
\(629\) 0.730492 + 1.76356i 0.0291266 + 0.0703178i
\(630\) 0 0
\(631\) 14.0643 14.0643i 0.559893 0.559893i −0.369384 0.929277i \(-0.620431\pi\)
0.929277 + 0.369384i \(0.120431\pi\)
\(632\) 0 0
\(633\) −0.550373 + 0.903639i −0.0218753 + 0.0359164i
\(634\) 0 0
\(635\) 13.4147 + 32.3860i 0.532346 + 1.28520i
\(636\) 0 0
\(637\) −34.2273 14.1774i −1.35614 0.561730i
\(638\) 0 0
\(639\) −0.631075 + 0.325889i −0.0249649 + 0.0128920i
\(640\) 0 0
\(641\) 2.18451i 0.0862828i −0.999069 0.0431414i \(-0.986263\pi\)
0.999069 0.0431414i \(-0.0137366\pi\)
\(642\) 0 0
\(643\) −10.9947 + 26.5434i −0.433587 + 1.04677i 0.544535 + 0.838738i \(0.316706\pi\)
−0.978122 + 0.208033i \(0.933294\pi\)
\(644\) 0 0
\(645\) −11.8459 + 8.65589i −0.466430 + 0.340825i
\(646\) 0 0
\(647\) −18.0436 + 18.0436i −0.709366 + 0.709366i −0.966402 0.257036i \(-0.917254\pi\)
0.257036 + 0.966402i \(0.417254\pi\)
\(648\) 0 0
\(649\) 11.9443 + 11.9443i 0.468857 + 0.468857i
\(650\) 0 0
\(651\) −2.24627 3.07409i −0.0880382 0.120483i
\(652\) 0 0
\(653\) 9.04305 + 3.74575i 0.353882 + 0.146583i 0.552540 0.833486i \(-0.313658\pi\)
−0.198659 + 0.980069i \(0.563658\pi\)
\(654\) 0 0
\(655\) 60.4518 2.36205
\(656\) 0 0
\(657\) −7.53210 14.5857i −0.293855 0.569043i
\(658\) 0 0
\(659\) −6.74648 + 16.2874i −0.262805 + 0.634468i −0.999110 0.0421820i \(-0.986569\pi\)
0.736305 + 0.676650i \(0.236569\pi\)
\(660\) 0 0
\(661\) 20.2135 8.37271i 0.786215 0.325661i 0.0467942 0.998905i \(-0.485100\pi\)
0.739421 + 0.673244i \(0.235100\pi\)
\(662\) 0 0
\(663\) −20.1484 12.2716i −0.782498 0.476590i
\(664\) 0 0
\(665\) −7.55453 7.55453i −0.292952 0.292952i
\(666\) 0 0
\(667\) −8.06767 + 3.34174i −0.312381 + 0.129393i
\(668\) 0 0
\(669\) 18.2933 + 2.84634i 0.707258 + 0.110046i
\(670\) 0 0
\(671\) −2.28546 −0.0882291
\(672\) 0 0
\(673\) −12.4887 −0.481404 −0.240702 0.970599i \(-0.577378\pi\)
−0.240702 + 0.970599i \(0.577378\pi\)
\(674\) 0 0
\(675\) 10.8669 + 32.5382i 0.418266 + 1.25239i
\(676\) 0 0
\(677\) 40.9040 16.9430i 1.57207 0.651173i 0.584937 0.811078i \(-0.301119\pi\)
0.987132 + 0.159906i \(0.0511190\pi\)
\(678\) 0 0
\(679\) 2.97757 + 2.97757i 0.114269 + 0.114269i
\(680\) 0 0
\(681\) −1.72347 + 2.82970i −0.0660433 + 0.108434i
\(682\) 0 0
\(683\) −8.56803 + 3.54899i −0.327846 + 0.135798i −0.540535 0.841322i \(-0.681778\pi\)
0.212688 + 0.977120i \(0.431778\pi\)
\(684\) 0 0
\(685\) −15.5523 + 37.5466i −0.594223 + 1.43458i
\(686\) 0 0
\(687\) 21.2502 5.16296i 0.810748 0.196979i
\(688\) 0 0
\(689\) 55.2970 2.10665
\(690\) 0 0
\(691\) 32.2776 + 13.3698i 1.22790 + 0.508611i 0.899912 0.436072i \(-0.143631\pi\)
0.327984 + 0.944683i \(0.393631\pi\)
\(692\) 0 0
\(693\) 4.46723 + 3.77350i 0.169696 + 0.143344i
\(694\) 0 0
\(695\) 48.7163 + 48.7163i 1.84792 + 1.84792i
\(696\) 0 0
\(697\) −10.6623 + 10.6623i −0.403864 + 0.403864i
\(698\) 0 0
\(699\) −10.0977 13.8191i −0.381931 0.522685i
\(700\) 0 0
\(701\) 7.31376 17.6570i 0.276237 0.666895i −0.723488 0.690337i \(-0.757462\pi\)
0.999725 + 0.0234415i \(0.00746235\pi\)
\(702\) 0 0
\(703\) 2.83621i 0.106970i
\(704\) 0 0
\(705\) −17.3598 + 4.21774i −0.653808 + 0.158849i
\(706\) 0 0
\(707\) −11.8310 4.90055i −0.444949 0.184304i
\(708\) 0 0
\(709\) −17.1483 41.3997i −0.644019 1.55480i −0.821212 0.570624i \(-0.806701\pi\)
0.177192 0.984176i \(-0.443299\pi\)
\(710\) 0 0
\(711\) −6.99510 2.23081i −0.262337 0.0836621i
\(712\) 0 0
\(713\) 10.1246 10.1246i 0.379170 0.379170i
\(714\) 0 0
\(715\) 16.3933 + 39.5768i 0.613073 + 1.48009i
\(716\) 0 0
\(717\) −11.3122 1.76013i −0.422462 0.0657331i
\(718\) 0 0
\(719\) 41.1609i 1.53504i −0.641023 0.767522i \(-0.721490\pi\)
0.641023 0.767522i \(-0.278510\pi\)
\(720\) 0 0
\(721\) 7.12823i 0.265469i
\(722\) 0 0
\(723\) 22.7781 + 3.54417i 0.847128 + 0.131809i
\(724\) 0 0
\(725\) 3.60973 + 8.71466i 0.134062 + 0.323654i
\(726\) 0 0
\(727\) −2.53270 + 2.53270i −0.0939328 + 0.0939328i −0.752512 0.658579i \(-0.771158\pi\)
0.658579 + 0.752512i \(0.271158\pi\)
\(728\) 0 0
\(729\) −16.2249 21.5813i −0.600920 0.799309i
\(730\) 0 0
\(731\) −2.14112 5.16912i −0.0791922 0.191187i
\(732\) 0 0
\(733\) 12.2518 + 5.07484i 0.452529 + 0.187444i 0.597294 0.802023i \(-0.296243\pi\)
−0.144765 + 0.989466i \(0.546243\pi\)
\(734\) 0 0
\(735\) −35.0830 + 8.52375i −1.29405 + 0.314403i
\(736\) 0 0
\(737\) 18.7857i 0.691980i
\(738\) 0 0
\(739\) −0.871699 + 2.10447i −0.0320659 + 0.0774141i −0.939101 0.343640i \(-0.888340\pi\)
0.907035 + 0.421054i \(0.138340\pi\)
\(740\) 0 0
\(741\) 20.6802 + 28.3015i 0.759707 + 1.03968i
\(742\) 0 0
\(743\) −37.5946 + 37.5946i −1.37921 + 1.37921i −0.533262 + 0.845950i \(0.679034\pi\)
−0.845950 + 0.533262i \(0.820966\pi\)
\(744\) 0 0
\(745\) −26.8642 26.8642i −0.984226 0.984226i
\(746\) 0 0
\(747\) −26.1871 + 31.0013i −0.958134 + 1.13428i
\(748\) 0 0
\(749\) −12.6517 5.24051i −0.462283 0.191484i
\(750\) 0 0
\(751\) 33.5914 1.22577 0.612885 0.790172i \(-0.290009\pi\)
0.612885 + 0.790172i \(0.290009\pi\)
\(752\) 0 0
\(753\) 24.4285 5.93514i 0.890223 0.216288i
\(754\) 0 0
\(755\) 22.4372 54.1683i 0.816575 1.97139i
\(756\) 0 0
\(757\) −30.7254 + 12.7269i −1.11673 + 0.462567i −0.863252 0.504773i \(-0.831576\pi\)
−0.253483 + 0.967340i \(0.581576\pi\)
\(758\) 0 0
\(759\) −11.4395 + 18.7822i −0.415228 + 0.681749i
\(760\) 0 0
\(761\) 8.23145 + 8.23145i 0.298390 + 0.298390i 0.840383 0.541993i \(-0.182330\pi\)
−0.541993 + 0.840383i \(0.682330\pi\)
\(762\) 0 0
\(763\) 4.12738 1.70962i 0.149421 0.0618922i
\(764\) 0 0
\(765\) −22.9093 + 1.92856i −0.828286 + 0.0697271i
\(766\) 0 0
\(767\) −49.2250 −1.77741
\(768\) 0 0
\(769\) 28.7476 1.03667 0.518333 0.855179i \(-0.326553\pi\)
0.518333 + 0.855179i \(0.326553\pi\)
\(770\) 0 0
\(771\) 20.6216 + 3.20862i 0.742669 + 0.115556i
\(772\) 0 0
\(773\) 19.1137 7.91717i 0.687474 0.284761i −0.0114736 0.999934i \(-0.503652\pi\)
0.698947 + 0.715173i \(0.253652\pi\)
\(774\) 0 0
\(775\) −10.9366 10.9366i −0.392853 0.392853i
\(776\) 0 0
\(777\) 1.17762 + 0.717242i 0.0422468 + 0.0257309i
\(778\) 0 0
\(779\) 20.6987 8.57370i 0.741609 0.307185i
\(780\) 0 0
\(781\) −0.188216 + 0.454395i −0.00673491 + 0.0162595i
\(782\) 0 0
\(783\) −4.86751 5.60576i