Properties

Label 768.2.o.b.95.10
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 95.10
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.02188 - 1.39848i) q^{3} +(-3.14689 + 1.30348i) q^{5} +(0.663471 + 0.663471i) q^{7} +(-0.911503 - 2.85817i) q^{9} +O(q^{10})\) \(q+(1.02188 - 1.39848i) q^{3} +(-3.14689 + 1.30348i) q^{5} +(0.663471 + 0.663471i) q^{7} +(-0.911503 - 2.85817i) q^{9} +(1.91929 - 0.794997i) q^{11} +(2.31672 - 5.59306i) q^{13} +(-1.39286 + 5.73287i) q^{15} -2.24987 q^{17} +(-3.08841 - 1.27926i) q^{19} +(1.60584 - 0.249861i) q^{21} +(-4.32171 - 4.32171i) q^{23} +(4.66830 - 4.66830i) q^{25} +(-4.92856 - 1.64600i) q^{27} +(0.546766 - 1.32001i) q^{29} -2.34273i q^{31} +(0.849507 - 3.49649i) q^{33} +(-2.95269 - 1.22305i) q^{35} +(0.324682 + 0.783851i) q^{37} +(-5.45437 - 8.95535i) q^{39} +(4.73908 - 4.73908i) q^{41} +(-0.951664 - 2.29752i) q^{43} +(6.59398 + 7.80622i) q^{45} +3.02812i q^{47} -6.11961i q^{49} +(-2.29911 + 3.14640i) q^{51} +(-3.49549 - 8.43885i) q^{53} +(-5.00353 + 5.00353i) q^{55} +(-4.94502 + 3.01183i) q^{57} +(3.11165 + 7.51220i) q^{59} +(1.01639 + 0.421005i) q^{61} +(1.29156 - 2.50107i) q^{63} +20.6205i q^{65} +(-3.46052 + 8.35443i) q^{67} +(-10.4601 + 1.62755i) q^{69} +(-0.167408 + 0.167408i) q^{71} +(3.86922 + 3.86922i) q^{73} +(-1.75807 - 11.2990i) q^{75} +(1.80085 + 0.745938i) q^{77} +2.44740 q^{79} +(-7.33832 + 5.21047i) q^{81} +(-5.17660 + 12.4974i) q^{83} +(7.08008 - 2.93267i) q^{85} +(-1.28728 - 2.11354i) q^{87} +(-6.63254 - 6.63254i) q^{89} +(5.24791 - 2.17376i) q^{91} +(-3.27627 - 2.39400i) q^{93} +11.3864 q^{95} +4.48787 q^{97} +(-4.02168 - 4.76103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) 1.02188 1.39848i 0.589985 0.807414i
\(4\) 0 0
\(5\) −3.14689 + 1.30348i −1.40733 + 0.582935i −0.951644 0.307205i \(-0.900606\pi\)
−0.455687 + 0.890140i \(0.650606\pi\)
\(6\) 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
\(9\) −0.911503 2.85817i −0.303834 0.952725i
\(10\) 0 0
\(11\) 1.91929 0.794997i 0.578689 0.239701i −0.0740873 0.997252i \(-0.523604\pi\)
0.652776 + 0.757551i \(0.273604\pi\)
\(12\) 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 \(-0.587962\pi\)
−0.272837 + 0.962060i \(0.587962\pi\)
\(18\) 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
\(21\) 1.60584 0.249861i 0.350424 0.0545242i
\(22\) 0 0
\(23\) −4.32171 4.32171i −0.901140 0.901140i 0.0943951 0.995535i \(-0.469908\pi\)
−0.995535 + 0.0943951i \(0.969908\pi\)
\(24\) 0 0
\(25\) 4.66830 4.66830i 0.933659 0.933659i
\(26\) 0 0
\(27\) −4.92856 1.64600i −0.948501 0.316774i
\(28\) 0 0
\(29\) 0.546766 1.32001i 0.101532 0.245120i −0.864948 0.501861i \(-0.832649\pi\)
0.966480 + 0.256741i \(0.0826489\pi\)
\(30\) 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
\(39\) −5.45437 8.95535i −0.873398 1.43400i
\(40\) 0 0
\(41\) 4.73908 4.73908i 0.740120 0.740120i −0.232481 0.972601i \(-0.574684\pi\)
0.972601 + 0.232481i \(0.0746843\pi\)
\(42\) 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
\(45\) 6.59398 + 7.80622i 0.982973 + 1.16368i
\(46\) 0 0
\(47\) 3.02812i 0.441696i 0.975308 + 0.220848i \(0.0708825\pi\)
−0.975308 + 0.220848i \(0.929117\pi\)
\(48\) 0 0
\(49\) 6.11961i 0.874230i
\(50\) 0 0
\(51\) −2.29911 + 3.14640i −0.321939 + 0.440584i
\(52\) 0 0
\(53\) −3.49549 8.43885i −0.480142 1.15916i −0.959541 0.281568i \(-0.909145\pi\)
0.479399 0.877597i \(1.65915\pi\)
\(54\) 0 0
\(55\) −5.00353 + 5.00353i −0.674676 + 0.674676i
\(56\) 0 0
\(57\) −4.94502 + 3.01183i −0.654984 + 0.398926i
\(58\) 0 0
\(59\) 3.11165 + 7.51220i 0.405103 + 0.978005i 0.986407 + 0.164318i \(0.0525425\pi\)
−0.581305 + 0.813686i \(0.697458\pi\)
\(60\) 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
\(69\) −10.4601 + 1.62755i −1.25925 + 0.195933i
\(70\) 0 0
\(71\) −0.167408 + 0.167408i −0.0198677 + 0.0198677i −0.716971 0.697103i \(-0.754472\pi\)
0.697103 + 0.716971i \(0.254472\pi\)
\(72\) 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
\(75\) −1.75807 11.2990i −0.203004 1.30469i
\(76\) 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 \(0.391311\pi\)
−0.903066 + 0.429502i \(0.858689\pi\)
\(84\) 0 0
\(85\) 7.08008 2.93267i 0.767943 0.318092i
\(86\) 0 0
\(87\) −1.28728 2.11354i −0.138011 0.226595i
\(88\) 0 0
\(89\) −6.63254 6.63254i −0.703048 0.703048i 0.262016 0.965064i \(-0.415613\pi\)
−0.965064 + 0.262016i \(0.915613\pi\)
\(90\) 0 0
\(91\) 5.24791 2.17376i 0.550130 0.227871i
\(92\) 0 0
\(93\) −3.27627 2.39400i −0.339733 0.248246i
\(94\) 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
\(99\) −4.02168 4.76103i −0.404194 0.478502i
\(100\) 0 0
\(101\) 12.6091 5.22285i 1.25465 0.519693i 0.346386 0.938092i \(-0.387409\pi\)
0.908263 + 0.418399i \(0.137409\pi\)
\(102\) 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
\(105\) −4.72772 + 2.87948i −0.461378 + 0.281008i
\(106\) 0 0
\(107\) 13.4838 5.58517i 1.30353 0.539939i 0.380538 0.924765i \(-0.375739\pi\)
0.922989 + 0.384826i \(0.125739\pi\)
\(108\) 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 \(-0.411244\pi\)
0.275237 + 0.961376i \(0.411244\pi\)
\(114\) 0 0
\(115\) 19.2332 + 7.96666i 1.79351 + 0.742895i
\(116\) 0 0
\(117\) −18.0976 1.52350i −1.67313 0.140848i
\(118\) 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
\(123\) −1.78472 11.4703i −0.160923 1.03424i
\(124\) 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 −0.474603 0.880200i \(-0.657408\pi\)
−0.957990 + 0.286800i \(0.907408\pi\)
\(132\) 0 0
\(133\) −1.20032 2.89782i −0.104081 0.251273i
\(134\) 0 0
\(135\) 17.6551 1.24450i 1.51951 0.107110i
\(136\) 0 0
\(137\) 8.43673 8.43673i 0.720799 0.720799i −0.247969 0.968768i \(-0.579763\pi\)
0.968768 + 0.247969i \(0.0797631\pi\)
\(138\) 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
\(141\) 4.23477 + 3.09439i 0.356632 + 0.260594i
\(142\) 0 0
\(143\) 12.5765i 1.05170i
\(144\) 0 0
\(145\) 4.86662i 0.404151i
\(146\) 0 0
\(147\) −8.55817 6.25354i −0.705866 0.515783i
\(148\) 0 0
\(149\) 4.26837 + 10.3048i 0.349678 + 0.844198i 0.996658 + 0.0816908i \(0.0260320\pi\)
−0.646979 + 0.762508i \(0.723968\pi\)
\(150\) 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
\(153\) 2.05076 + 6.43052i 0.165794 + 0.519877i
\(154\) 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
\(165\) 1.88432 + 12.1104i 0.146694 + 0.942792i
\(166\) 0 0
\(167\) −12.8761 + 12.8761i −0.996385 + 0.996385i −0.999993 0.00360853i \(-0.998851\pi\)
0.00360853 + 0.999993i \(0.498851\pi\)
\(168\) 0 0
\(169\) −16.7227 16.7227i −1.28636 1.28636i
\(170\) 0 0
\(171\) −0.841256 + 9.99326i −0.0643325 + 0.764204i
\(172\) 0 0
\(173\) −9.91155 4.10550i −0.753561 0.312135i −0.0273673 0.999625i \(-0.508712\pi\)
−0.726194 + 0.687490i \(0.758712\pi\)
\(174\) 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 \(-0.494833\pi\)
0.695536 0.718491i \(-0.255167\pi\)
\(180\) 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
\(183\) 1.62741 0.991192i 0.120301 0.0732710i
\(184\) 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
\(189\) −2.17788 4.36203i −0.158417 0.317291i
\(190\) 0 0
\(191\) −0.133706 −0.00967461 −0.00483731 0.999988i \(-0.501540\pi\)
−0.00483731 + 0.999988i \(0.501540\pi\)
\(192\) 0 0
\(193\) 7.48776 0.538981 0.269490 0.963003i \(-0.413145\pi\)
0.269490 + 0.963003i \(0.413145\pi\)
\(194\) 0 0
\(195\) 28.8374 + 21.0718i 2.06509 + 1.50898i
\(196\) 0 0
\(197\) −4.23540 + 1.75436i −0.301759 + 0.124993i −0.528425 0.848980i \(-0.677217\pi\)
0.226666 + 0.973973i \(0.427217\pi\)
\(198\) 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
\(201\) 8.14727 + 13.3767i 0.574664 + 0.943522i
\(202\) 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
\(213\) 0.0630455 + 0.405189i 0.00431980 + 0.0277631i
\(214\) 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
\(219\) 9.36493 1.45714i 0.632823 0.0984642i
\(220\) 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 0.440561 0.897723i \(-0.354780\pi\)
−0.323262 + 0.946309i \(0.604780\pi\)
\(228\) 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
\(231\) 2.88345 1.75620i 0.189717 0.115549i
\(232\) 0 0
\(233\) −6.98725 + 6.98725i −0.457750 + 0.457750i −0.897916 0.440166i \(-0.854920\pi\)
0.440166 + 0.897916i \(0.354920\pi\)
\(234\) 0 0
\(235\) −3.94710 9.52914i −0.257480 0.621613i
\(236\) 0 0
\(237\) 2.50096 3.42265i 0.162455 0.222325i
\(238\) 0 0
\(239\) 6.60970i 0.427546i 0.976883 + 0.213773i \(0.0685752\pi\)
−0.976883 + 0.213773i \(0.931425\pi\)
\(240\) 0 0
\(241\) 13.3092i 0.857322i 0.903466 + 0.428661i \(0.141014\pi\)
−0.903466 + 0.428661i \(0.858986\pi\)
\(242\) 0 0
\(243\) −0.212173 + 15.5870i −0.0136109 + 0.999907i
\(244\) 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
\(249\) 12.1875 + 20.0103i 0.772353 + 1.26810i
\(250\) 0 0
\(251\) −5.55430 13.4093i −0.350584 0.846385i −0.996548 0.0830174i \(-0.973544\pi\)
0.645964 0.763368i \(1.72354\pi\)
\(252\) 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 \(-0.877367\pi\)
0.926700 0.375803i \(-0.122633\pi\)
\(258\) 0 0
\(259\) −0.304646 + 0.735480i −0.0189298 + 0.0457005i
\(260\) 0 0
\(261\) −4.27120 0.359559i −0.264380 0.0222562i
\(262\) 0 0
\(263\) −2.42769 + 2.42769i −0.149698 + 0.149698i −0.777983 0.628285i \(-0.783757\pi\)
0.628285 + 0.777983i \(0.283757\pi\)
\(264\) 0 0
\(265\) 21.9998 + 21.9998i 1.35144 + 1.35144i
\(266\) 0 0
\(267\) −16.0532 + 2.49780i −0.982439 + 0.152863i
\(268\) 0 0
\(269\) −11.0872 4.59246i −0.675997 0.280007i 0.0181552 0.999835i \(-0.494221\pi\)
−0.694153 + 0.719828i \(0.744221\pi\)
\(270\) 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
\(279\) −6.69594 + 2.13541i −0.400875 + 0.127844i
\(280\) 0 0
\(281\) 0.109141 + 0.109141i 0.00651081 + 0.00651081i 0.710355 0.703844i \(-0.248535\pi\)
−0.703844 + 0.710355i \(0.748535\pi\)
\(282\) 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
\(285\) 11.6356 15.9236i 0.689231 0.943235i
\(286\) 0 0
\(287\) 6.28849 0.371198
\(288\) 0 0
\(289\) −11.9381 −0.702240
\(290\) 0 0
\(291\) 4.58609 6.27621i 0.268841 0.367918i
\(292\) 0 0
\(293\) 14.6551 6.07035i 0.856161 0.354634i 0.0889561 0.996036i \(-0.471647\pi\)
0.767205 + 0.641402i \(0.221647\pi\)
\(294\) 0 0
\(295\) −19.5840 19.5840i −1.14023 1.14023i
\(296\) 0 0
\(297\) −10.7679 + 0.759024i −0.624818 + 0.0440430i
\(298\) 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
\(309\) 13.0020 2.02305i 0.739659 0.115087i
\(310\) 0 0
\(311\) 14.7567 + 14.7567i 0.836776 + 0.836776i 0.988433 0.151657i \(-0.0484609\pi\)
−0.151657 + 0.988433i \(0.548461\pi\)
\(312\) 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
\(315\) −0.804289 + 9.55412i −0.0453165 + 0.538314i
\(316\) 0 0
\(317\) 5.65481 13.6519i 0.317606 0.766768i −0.681774 0.731562i \(-0.738791\pi\)
0.999380 0.0352055i \(-0.0112086\pi\)
\(318\) 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
\(327\) −4.28975 7.04321i −0.237224 0.389490i
\(328\) 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
\(333\) 1.94443 1.64248i 0.106554 0.0900073i
\(334\) 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
\(339\) 5.97969 8.18339i 0.324772 0.444461i
\(340\) 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
\(345\) 30.7954 18.7563i 1.65797 1.00981i
\(346\) 0 0
\(347\) 2.01715 + 4.86983i 0.108286 + 0.261426i 0.968729 0.248121i \(-0.0798130\pi\)
−0.860443 + 0.509547i \(0.829813\pi\)
\(348\) 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 \(0.115699\pi\)
−0.934666 + 0.355527i \(0.884301\pi\)
\(354\) 0 0
\(355\) 0.308601 0.745029i 0.0163788 0.0395420i
\(356\) 0 0
\(357\) −3.61294 + 0.562156i −0.191217 + 0.0297524i
\(358\) 0 0
\(359\) 0.514805 0.514805i 0.0271704 0.0271704i −0.693391 0.720561i \(-0.743884\pi\)
0.720561 + 0.693391i \(0.243884\pi\)
\(360\) 0 0
\(361\) −5.53327 5.53327i −0.291225 0.291225i
\(362\) 0 0
\(363\) 1.77999 + 11.4399i 0.0934252 + 0.600438i
\(364\) 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
\(375\) 4.91620 + 8.07176i 0.253872 + 0.416824i
\(376\) 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
\(381\) 14.3924 + 10.5167i 0.737344 + 0.538784i
\(382\) 0 0
\(383\) −16.0682 −0.821048 −0.410524 0.911850i \(-0.634654\pi\)
−0.410524 + 0.911850i \(0.634654\pi\)
\(384\) 0 0
\(385\) −6.63940 −0.338375
\(386\) 0 0
\(387\) −5.69927 + 4.81422i −0.289710 + 0.244721i
\(388\) 0 0
\(389\) 31.0923 12.8788i 1.57644 0.652983i 0.588596 0.808427i \(-0.299681\pi\)
0.987845 + 0.155444i \(0.0496807\pi\)
\(390\) 0 0
\(391\) 9.72329 + 9.72329i 0.491728 + 0.491728i
\(392\) 0 0
\(393\) −26.2538 + 15.9902i −1.32433 + 0.806599i
\(394\) 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 \(-0.376042\pi\)
0.379657 + 0.925127i \(0.376042\pi\)
\(402\) 0 0
\(403\) −13.1030 5.42745i −0.652709 0.270361i
\(404\) 0 0
\(405\) 16.3011 25.9621i 0.810009 1.29007i
\(406\) 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
\(411\) −3.17725 20.4200i −0.156722 1.00724i
\(412\) 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 0.630958 0.775817i \(-0.282662\pi\)
−0.102431 + 0.994740i \(0.532662\pi\)
\(420\) 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
\(423\) 8.65489 2.76014i 0.420815 0.134203i
\(424\) 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
\(429\) −17.5880 12.8517i −0.849157 0.620488i
\(430\) 0 0
\(431\) 0.278342i 0.0134073i −0.999978 0.00670363i \(-0.997866\pi\)
0.999978 0.00670363i \(-0.00213385\pi\)
\(432\) 0 0
\(433\) 11.0862i 0.532769i −0.963867 0.266385i \(-0.914171\pi\)
0.963867 0.266385i \(-0.0858292\pi\)
\(434\) 0 0
\(435\) 6.80588 + 4.97313i 0.326317 + 0.238443i
\(436\) 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
\(441\) −17.4909 + 5.57805i −0.832901 + 0.265621i
\(442\) 0 0
\(443\) 15.7855 + 38.1095i 0.749991 + 1.81064i 0.559251 + 0.828998i \(0.311089\pi\)
0.190740 + 0.981641i \(0.438911\pi\)
\(444\) 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 \(-0.808795\pi\)
0.824946 0.565211i \(-0.191205\pi\)
\(450\) 0 0
\(451\) 5.32813 12.8632i 0.250892 0.605706i
\(452\) 0 0
\(453\) −4.58380 29.4598i −0.215366 1.38414i
\(454\) 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
\(459\) 11.0886 + 3.70329i 0.517572 + 0.172855i
\(460\) 0 0
\(461\) −11.0476 4.57608i −0.514539 0.213129i 0.110277 0.993901i \(-0.464826\pi\)
−0.624816 + 0.780772i \(0.714826\pi\)
\(462\) 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 \(0.504822\pi\)
−0.696315 + 0.717736i \(0.745178\pi\)
\(468\) 0 0
\(469\) −7.83888 + 3.24697i −0.361966 + 0.149931i
\(470\) 0 0
\(471\) 16.2465 9.89510i 0.748597 0.455942i
\(472\) 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
\(477\) −20.9336 + 17.6827i −0.958482 + 0.809637i
\(478\) 0 0
\(479\) 23.6720 1.08160 0.540800 0.841151i \(-0.318122\pi\)
0.540800 + 0.841151i \(0.318122\pi\)
\(480\) 0 0
\(481\) 5.13632 0.234196
\(482\) 0 0
\(483\) −8.01983 5.86017i −0.364915 0.266647i
\(484\) 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
\(489\) −9.51006 15.6143i −0.430060 0.706101i
\(490\) 0 0
\(491\) 24.4454 10.1256i 1.10321 0.456964i 0.244614 0.969621i \(-0.421339\pi\)
0.858594 + 0.512657i \(0.171339\pi\)
\(492\) 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
\(501\) 4.84911 + 31.1650i 0.216642 + 1.39235i
\(502\) 0 0
\(503\) 8.35178 + 8.35178i 0.372387 + 0.372387i 0.868346 0.495959i \(-0.165183\pi\)
−0.495959 + 0.868346i \(0.665183\pi\)
\(504\) 0 0
\(505\) −32.8714 + 32.8714i −1.46276 + 1.46276i
\(506\) 0 0
\(507\) −40.4751 + 6.29772i −1.79756 + 0.279692i
\(508\) 0 0
\(509\) −2.98703 + 7.21134i −0.132398 + 0.319637i −0.976150 0.217096i \(-0.930342\pi\)
0.843752 + 0.536733i \(0.180342\pi\)
\(510\) 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
\(519\) −15.8699 + 9.66577i −0.696612 + 0.424280i
\(520\) 0 0
\(521\) 5.48494 5.48494i 0.240299 0.240299i −0.576675 0.816974i \(-0.695650\pi\)
0.816974 + 0.576675i \(0.195650\pi\)
\(522\) 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
\(525\) 6.33013 8.66298i 0.276269 0.378083i
\(526\) 0 0
\(527\) 5.27084i 0.229601i
\(528\) 0 0
\(529\) 14.3544i 0.624106i
\(530\) 0 0
\(531\) 18.6349 15.7410i 0.808685 0.683103i
\(532\) 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
\(537\) −22.4200 36.8107i −0.967495 1.58850i
\(538\) 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
\(549\) 0.276857 3.28878i 0.0118160 0.140362i
\(550\) 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
\(555\) −4.94596 + 0.769566i −0.209944 + 0.0326663i
\(556\) 0 0
\(557\) 30.8826 + 12.7920i 1.30854 + 0.542014i 0.924457 0.381286i \(-0.124519\pi\)
0.384080 + 0.923300i \(0.374519\pi\)
\(558\) 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 −0.743064 0.669221i \(-0.766628\pi\)
0.998636 + 0.0522151i \(0.0166281\pi\)
\(564\) 0 0
\(565\) −18.4144 + 7.62750i −0.774700 + 0.320891i
\(566\) 0 0
\(567\) −8.32577 1.41177i −0.349649 0.0592888i
\(568\) 0 0
\(569\) 24.5419 + 24.5419i 1.02885 + 1.02885i 0.999571 + 0.0292808i \(0.00932170\pi\)
0.0292808 + 0.999571i \(0.490678\pi\)
\(570\) 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
\(573\) −0.136632 + 0.186985i −0.00570788 + 0.00781142i
\(574\) 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
\(579\) 7.65163 10.4715i 0.317991 0.435181i
\(580\) 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
\(585\) 58.9371 18.7957i 2.43675 0.777105i
\(586\) 0 0
\(587\) 16.1148 6.67499i 0.665131 0.275506i −0.0244651 0.999701i \(-0.507788\pi\)
0.689596 + 0.724195i \(0.257788\pi\)
\(588\) 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 \(-0.242376\pi\)
0.723839 + 0.689969i \(0.242376\pi\)
\(594\) 0 0
\(595\) 6.64317 + 2.75169i 0.272344 + 0.112808i
\(596\) 0 0
\(597\) 9.05415 1.40878i 0.370562 0.0576576i
\(598\) 0 0
\(599\) −12.1323 12.1323i −0.495712 0.495712i 0.414388 0.910100i \(-0.363996\pi\)
−0.910100 + 0.414388i \(0.863996\pi\)
\(600\) 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
\(603\) 27.0327 + 2.27568i 1.10086 + 0.0926727i
\(604\) 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
\(615\) 20.5677 + 33.7694i 0.829369 + 1.36171i
\(616\) 0 0
\(617\) 12.5126 12.5126i 0.503739 0.503739i −0.408859 0.912598i \(-0.634073\pi\)
0.912598 + 0.408859i \(0.134073\pi\)
\(618\) 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
\(621\) 14.1863 + 28.4134i 0.569275 + 1.14019i
\(622\) 0 0
\(623\) 8.80100i 0.352605i
\(624\) 0 0
\(625\) 14.4239i 0.576955i
\(626\) 0 0
\(627\) −7.09655 + 9.71186i −0.283409 + 0.387854i
\(628\) 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
\(633\) −0.903639 + 0.550373i −0.0359164 + 0.0218753i
\(634\) 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 \(0.0137366\pi\)
−0.999069 + 0.0431414i \(0.986263\pi\)
\(642\) 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
\(645\) 14.4969 2.25565i 0.570816 0.0888162i
\(646\) 0 0
\(647\) 18.0436 18.0436i 0.709366 0.709366i −0.257036 0.966402i \(-0.582746\pi\)
0.966402 + 0.257036i \(0.0827458\pi\)
\(648\) 0 0
\(649\) 11.9443 + 11.9443i 0.468857 + 0.468857i
\(650\) 0 0
\(651\) −0.585358 3.76206i −0.0229420 0.147447i
\(652\) 0 0
\(653\) −9.04305 3.74575i −0.353882 0.146583i 0.198659 0.980069i \(-0.436342\pi\)
−0.552540 + 0.833486i \(0.686342\pi\)
\(654\) 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 −0.736305 0.676650i \(-0.763431\pi\)
0.999110 + 0.0421820i \(0.0134309\pi\)
\(660\) 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
\(663\) 12.2716 + 20.1484i 0.476590 + 0.782498i
\(664\) 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
\(669\) 14.9480 + 10.9226i 0.577921 + 0.422293i
\(670\) 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
\(675\) −30.6920 + 15.3239i −1.18134 + 0.589818i
\(676\) 0 0
\(677\) −40.9040 + 16.9430i −1.57207 + 0.651173i −0.987132 0.159906i \(-0.948881\pi\)
−0.584937 + 0.811078i \(0.698881\pi\)
\(678\) 0 0
\(679\) 2.97757 + 2.97757i 0.114269 + 0.114269i
\(680\) 0 0
\(681\) 2.82970 1.72347i 0.108434 0.0660433i
\(682\) 0 0
\(683\) 8.56803 3.54899i 0.327846 0.135798i −0.212688 0.977120i \(-0.568222\pi\)
0.540535 + 0.841322i \(0.318222\pi\)
\(684\) 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
\(693\) 0.490537 5.82708i 0.0186340 0.221352i
\(694\) 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
\(699\) 2.63138 + 16.9117i 0.0995279 + 0.639660i
\(700\) 0 0
\(701\) −7.31376 + 17.6570i −0.276237 + 0.666895i −0.999725 0.0234415i \(-0.992538\pi\)
0.723488 + 0.690337i \(0.242538\pi\)
\(702\) 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
\(711\) −2.23081 6.99510i −0.0836621 0.262337i
\(712\) 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
\(717\) 9.24354 + 6.75435i 0.345206 + 0.252246i
\(718\) 0 0
\(719\) 41.1609i 1.53504i 0.641023 + 0.767522i \(0.278510\pi\)
−0.641023 + 0.767522i \(0.721490\pi\)
\(720\) 0 0
\(721\) 7.12823i 0.265469i
\(722\) 0 0
\(723\) 18.6127 + 13.6005i 0.692213 + 0.505807i
\(724\) 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
\(729\) 21.5813 + 16.2249i 0.799309 + 0.600920i
\(730\) 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
\(741\) 5.38909 + 34.6353i 0.197973 + 1.27236i
\(742\) 0 0
\(743\) 37.5946 37.5946i 1.37921 1.37921i 0.533262 0.845950i \(-0.320966\pi\)
0.845950 0.533262i \(-0.179034\pi\)
\(744\) 0 0
\(745\) −26.8642 26.8642i −0.984226 0.984226i
\(746\) 0 0
\(747\) 40.4383 + 3.40419i 1.47956 + 0.124553i
\(748\) 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
\(759\) −18.7822 + 11.4395i −0.681749 + 0.415228i
\(760\) 0 0
\(761\) −8.23145 8.23145i −0.298390 0.298390i 0.541993 0.840383i \(-0.317670\pi\)
−0.840383 + 0.541993i \(0.817670\pi\)
\(762\) 0 0
\(763\) 4.12738 1.70962i 0.149421 0.0618922i
\(764\) 0 0
\(765\) −14.8356 17.5630i −0.536382 0.634991i
\(766\) 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
\(771\) −16.8505 12.3128i −0.606856 0.443436i
\(772\) 0 0
\(773\) −19.1137 + 7.91717i −0.687474 + 0.284761i −0.698947 0.715173i \(-0.746348\pi\)
0.0114736 + 0.999934i \(0.496348\pi\)
\(774\) 0 0
\(775\) −10.9366 10.9366i −0.392853 0.392853i
\(776\) 0 0
\(777\) 0.717242 + 1.17762i 0.0257309 + 0.0422468i
\(778\) 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 −0.173951