Properties

Label 1152.2.r.g.193.3
Level $1152$
Weight $2$
Character 1152.193
Analytic conductor $9.199$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 193.3
Character \(\chi\) \(=\) 1152.193
Dual form 1152.2.r.g.961.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.37296 + 1.05593i) q^{3} +(-3.35903 - 1.93934i) q^{5} +(1.14978 + 1.99147i) q^{7} +(0.770012 - 2.89950i) q^{9} +O(q^{10})\) \(q+(-1.37296 + 1.05593i) q^{3} +(-3.35903 - 1.93934i) q^{5} +(1.14978 + 1.99147i) q^{7} +(0.770012 - 2.89950i) q^{9} +(-3.60542 + 2.08159i) q^{11} +(0.846691 + 0.488838i) q^{13} +(6.65962 - 0.884289i) q^{15} -6.79209 q^{17} -0.729224i q^{19} +(-3.68146 - 1.52012i) q^{21} +(2.94585 - 5.10236i) q^{23} +(5.02208 + 8.69849i) q^{25} +(2.00448 + 4.79396i) q^{27} +(4.32630 - 2.49779i) q^{29} +(1.53163 - 2.65287i) q^{31} +(2.75206 - 6.66502i) q^{33} -8.91924i q^{35} +1.11690i q^{37} +(-1.67865 + 0.222897i) q^{39} +(-3.12603 + 5.41445i) q^{41} +(4.80283 - 2.77291i) q^{43} +(-8.20961 + 8.24620i) q^{45} +(4.86355 + 8.42391i) q^{47} +(0.856020 - 1.48267i) q^{49} +(9.32523 - 7.17199i) q^{51} -6.81170i q^{53} +16.1477 q^{55} +(0.770012 + 1.00119i) q^{57} +(10.6458 + 6.14633i) q^{59} +(10.8032 - 6.23724i) q^{61} +(6.65962 - 1.80032i) q^{63} +(-1.89604 - 3.28404i) q^{65} +(-0.0524343 - 0.0302730i) q^{67} +(1.34323 + 10.1159i) q^{69} +12.7904 q^{71} -1.71204 q^{73} +(-16.0801 - 6.63966i) q^{75} +(-8.29088 - 4.78674i) q^{77} +(-5.77427 - 10.0013i) q^{79} +(-7.81416 - 4.46529i) q^{81} +(-6.35637 + 3.66985i) q^{83} +(22.8149 + 13.1722i) q^{85} +(-3.30232 + 7.99764i) q^{87} +10.3321 q^{89} +2.24822i q^{91} +(0.698385 + 5.25957i) q^{93} +(-1.41421 + 2.44949i) q^{95} +(-4.66606 - 8.08185i) q^{97} +(3.25935 + 12.0568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{9} + O(q^{10}) \) \( 24 q + 4 q^{9} - 40 q^{17} + 12 q^{25} - 28 q^{33} - 28 q^{41} - 12 q^{49} + 4 q^{57} + 16 q^{65} + 24 q^{73} + 44 q^{81} + 96 q^{89} - 36 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.37296 + 1.05593i −0.792676 + 0.609643i
\(4\) 0 0
\(5\) −3.35903 1.93934i −1.50221 0.867299i −0.999997 0.00255286i \(-0.999187\pi\)
−0.502209 0.864746i \(-0.667479\pi\)
\(6\) 0 0
\(7\) 1.14978 + 1.99147i 0.434575 + 0.752707i 0.997261 0.0739645i \(-0.0235651\pi\)
−0.562686 + 0.826671i \(0.690232\pi\)
\(8\) 0 0
\(9\) 0.770012 2.89950i 0.256671 0.966499i
\(10\) 0 0
\(11\) −3.60542 + 2.08159i −1.08708 + 0.627624i −0.932797 0.360403i \(-0.882639\pi\)
−0.154280 + 0.988027i \(0.549306\pi\)
\(12\) 0 0
\(13\) 0.846691 + 0.488838i 0.234830 + 0.135579i 0.612798 0.790239i \(-0.290044\pi\)
−0.377968 + 0.925819i \(0.623377\pi\)
\(14\) 0 0
\(15\) 6.65962 0.884289i 1.71951 0.228322i
\(16\) 0 0
\(17\) −6.79209 −1.64732 −0.823662 0.567082i \(-0.808072\pi\)
−0.823662 + 0.567082i \(0.808072\pi\)
\(18\) 0 0
\(19\) 0.729224i 0.167296i −0.996495 0.0836478i \(-0.973343\pi\)
0.996495 0.0836478i \(-0.0266571\pi\)
\(20\) 0 0
\(21\) −3.68146 1.52012i −0.803360 0.331717i
\(22\) 0 0
\(23\) 2.94585 5.10236i 0.614251 1.06391i −0.376264 0.926513i \(-0.622791\pi\)
0.990515 0.137402i \(-0.0438753\pi\)
\(24\) 0 0
\(25\) 5.02208 + 8.69849i 1.00442 + 1.73970i
\(26\) 0 0
\(27\) 2.00448 + 4.79396i 0.385763 + 0.922598i
\(28\) 0 0
\(29\) 4.32630 2.49779i 0.803374 0.463828i −0.0412755 0.999148i \(-0.513142\pi\)
0.844650 + 0.535320i \(0.179809\pi\)
\(30\) 0 0
\(31\) 1.53163 2.65287i 0.275089 0.476469i −0.695068 0.718944i \(-0.744626\pi\)
0.970158 + 0.242475i \(0.0779592\pi\)
\(32\) 0 0
\(33\) 2.75206 6.66502i 0.479073 1.16023i
\(34\) 0 0
\(35\) 8.91924i 1.50763i
\(36\) 0 0
\(37\) 1.11690i 0.183618i 0.995777 + 0.0918089i \(0.0292649\pi\)
−0.995777 + 0.0918089i \(0.970735\pi\)
\(38\) 0 0
\(39\) −1.67865 + 0.222897i −0.268799 + 0.0356921i
\(40\) 0 0
\(41\) −3.12603 + 5.41445i −0.488204 + 0.845594i −0.999908 0.0135675i \(-0.995681\pi\)
0.511704 + 0.859162i \(0.329015\pi\)
\(42\) 0 0
\(43\) 4.80283 2.77291i 0.732424 0.422865i −0.0868842 0.996218i \(-0.527691\pi\)
0.819308 + 0.573353i \(0.194358\pi\)
\(44\) 0 0
\(45\) −8.20961 + 8.24620i −1.22382 + 1.22927i
\(46\) 0 0
\(47\) 4.86355 + 8.42391i 0.709421 + 1.22875i 0.965072 + 0.261985i \(0.0843770\pi\)
−0.255651 + 0.966769i \(0.582290\pi\)
\(48\) 0 0
\(49\) 0.856020 1.48267i 0.122289 0.211810i
\(50\) 0 0
\(51\) 9.32523 7.17199i 1.30579 1.00428i
\(52\) 0 0
\(53\) 6.81170i 0.935660i −0.883819 0.467830i \(-0.845036\pi\)
0.883819 0.467830i \(-0.154964\pi\)
\(54\) 0 0
\(55\) 16.1477 2.17735
\(56\) 0 0
\(57\) 0.770012 + 1.00119i 0.101991 + 0.132611i
\(58\) 0 0
\(59\) 10.6458 + 6.14633i 1.38596 + 0.800184i 0.992857 0.119311i \(-0.0380686\pi\)
0.393102 + 0.919495i \(0.371402\pi\)
\(60\) 0 0
\(61\) 10.8032 6.23724i 1.38321 0.798597i 0.390672 0.920530i \(-0.372243\pi\)
0.992538 + 0.121933i \(0.0389093\pi\)
\(62\) 0 0
\(63\) 6.65962 1.80032i 0.839033 0.226819i
\(64\) 0 0
\(65\) −1.89604 3.28404i −0.235175 0.407336i
\(66\) 0 0
\(67\) −0.0524343 0.0302730i −0.00640587 0.00369843i 0.496794 0.867869i \(-0.334511\pi\)
−0.503200 + 0.864170i \(0.667844\pi\)
\(68\) 0 0
\(69\) 1.34323 + 10.1159i 0.161706 + 1.21781i
\(70\) 0 0
\(71\) 12.7904 1.51794 0.758968 0.651128i \(-0.225704\pi\)
0.758968 + 0.651128i \(0.225704\pi\)
\(72\) 0 0
\(73\) −1.71204 −0.200379 −0.100190 0.994968i \(-0.531945\pi\)
−0.100190 + 0.994968i \(0.531945\pi\)
\(74\) 0 0
\(75\) −16.0801 6.63966i −1.85677 0.766682i
\(76\) 0 0
\(77\) −8.29088 4.78674i −0.944833 0.545500i
\(78\) 0 0
\(79\) −5.77427 10.0013i −0.649657 1.12524i −0.983205 0.182505i \(-0.941579\pi\)
0.333548 0.942733i \(-0.391754\pi\)
\(80\) 0 0
\(81\) −7.81416 4.46529i −0.868240 0.496144i
\(82\) 0 0
\(83\) −6.35637 + 3.66985i −0.697702 + 0.402818i −0.806491 0.591246i \(-0.798636\pi\)
0.108789 + 0.994065i \(0.465303\pi\)
\(84\) 0 0
\(85\) 22.8149 + 13.1722i 2.47462 + 1.42872i
\(86\) 0 0
\(87\) −3.30232 + 7.99764i −0.354046 + 0.857437i
\(88\) 0 0
\(89\) 10.3321 1.09520 0.547601 0.836740i \(-0.315541\pi\)
0.547601 + 0.836740i \(0.315541\pi\)
\(90\) 0 0
\(91\) 2.24822i 0.235677i
\(92\) 0 0
\(93\) 0.698385 + 5.25957i 0.0724191 + 0.545392i
\(94\) 0 0
\(95\) −1.41421 + 2.44949i −0.145095 + 0.251312i
\(96\) 0 0
\(97\) −4.66606 8.08185i −0.473766 0.820587i 0.525783 0.850619i \(-0.323772\pi\)
−0.999549 + 0.0300318i \(0.990439\pi\)
\(98\) 0 0
\(99\) 3.25935 + 12.0568i 0.327577 + 1.21175i
\(100\) 0 0
\(101\) 5.29357 3.05624i 0.526730 0.304108i −0.212954 0.977062i \(-0.568308\pi\)
0.739684 + 0.672955i \(0.234975\pi\)
\(102\) 0 0
\(103\) −5.39242 + 9.33994i −0.531331 + 0.920292i 0.468000 + 0.883728i \(0.344975\pi\)
−0.999331 + 0.0365638i \(0.988359\pi\)
\(104\) 0 0
\(105\) 9.41812 + 12.2457i 0.919114 + 1.19506i
\(106\) 0 0
\(107\) 0.608132i 0.0587904i −0.999568 0.0293952i \(-0.990642\pi\)
0.999568 0.0293952i \(-0.00935813\pi\)
\(108\) 0 0
\(109\) 14.8475i 1.42213i 0.703124 + 0.711067i \(0.251788\pi\)
−0.703124 + 0.711067i \(0.748212\pi\)
\(110\) 0 0
\(111\) −1.17938 1.53346i −0.111941 0.145549i
\(112\) 0 0
\(113\) 5.98205 10.3612i 0.562744 0.974701i −0.434512 0.900666i \(-0.643079\pi\)
0.997256 0.0740351i \(-0.0235877\pi\)
\(114\) 0 0
\(115\) −19.7904 + 11.4260i −1.84546 + 1.06548i
\(116\) 0 0
\(117\) 2.06935 2.07857i 0.191311 0.192164i
\(118\) 0 0
\(119\) −7.80939 13.5263i −0.715886 1.23995i
\(120\) 0 0
\(121\) 3.16606 5.48377i 0.287823 0.498524i
\(122\) 0 0
\(123\) −1.42539 10.7347i −0.128523 0.967913i
\(124\) 0 0
\(125\) 19.5646i 1.74992i
\(126\) 0 0
\(127\) 8.48528 0.752947 0.376473 0.926427i \(-0.377137\pi\)
0.376473 + 0.926427i \(0.377137\pi\)
\(128\) 0 0
\(129\) −3.66606 + 8.87855i −0.322778 + 0.781713i
\(130\) 0 0
\(131\) 6.69741 + 3.86675i 0.585155 + 0.337839i 0.763179 0.646187i \(-0.223637\pi\)
−0.178024 + 0.984026i \(0.556971\pi\)
\(132\) 0 0
\(133\) 1.45223 0.838446i 0.125924 0.0727025i
\(134\) 0 0
\(135\) 2.56399 19.9904i 0.220673 1.72050i
\(136\) 0 0
\(137\) 3.91812 + 6.78638i 0.334748 + 0.579800i 0.983436 0.181254i \(-0.0580156\pi\)
−0.648689 + 0.761054i \(0.724682\pi\)
\(138\) 0 0
\(139\) −3.33004 1.92260i −0.282450 0.163073i 0.352082 0.935969i \(-0.385474\pi\)
−0.634532 + 0.772897i \(0.718807\pi\)
\(140\) 0 0
\(141\) −15.5725 6.43007i −1.31144 0.541510i
\(142\) 0 0
\(143\) −4.07024 −0.340371
\(144\) 0 0
\(145\) −19.3763 −1.60911
\(146\) 0 0
\(147\) 0.390323 + 2.93954i 0.0321933 + 0.242449i
\(148\) 0 0
\(149\) −7.32361 4.22829i −0.599973 0.346395i 0.169058 0.985606i \(-0.445928\pi\)
−0.769031 + 0.639211i \(0.779261\pi\)
\(150\) 0 0
\(151\) −2.71101 4.69560i −0.220619 0.382123i 0.734377 0.678741i \(-0.237474\pi\)
−0.954996 + 0.296619i \(0.904141\pi\)
\(152\) 0 0
\(153\) −5.22999 + 19.6936i −0.422819 + 1.59214i
\(154\) 0 0
\(155\) −10.2896 + 5.94071i −0.826482 + 0.477169i
\(156\) 0 0
\(157\) 3.50734 + 2.02496i 0.279916 + 0.161610i 0.633386 0.773836i \(-0.281665\pi\)
−0.353469 + 0.935446i \(0.614998\pi\)
\(158\) 0 0
\(159\) 7.19270 + 9.35216i 0.570418 + 0.741675i
\(160\) 0 0
\(161\) 13.5483 1.06775
\(162\) 0 0
\(163\) 9.39102i 0.735562i 0.929913 + 0.367781i \(0.119882\pi\)
−0.929913 + 0.367781i \(0.880118\pi\)
\(164\) 0 0
\(165\) −22.1700 + 17.0508i −1.72593 + 1.32741i
\(166\) 0 0
\(167\) −7.92681 + 13.7296i −0.613395 + 1.06243i 0.377269 + 0.926104i \(0.376863\pi\)
−0.990664 + 0.136328i \(0.956470\pi\)
\(168\) 0 0
\(169\) −6.02208 10.4305i −0.463237 0.802349i
\(170\) 0 0
\(171\) −2.11438 0.561511i −0.161691 0.0429398i
\(172\) 0 0
\(173\) −3.21073 + 1.85371i −0.244107 + 0.140935i −0.617063 0.786914i \(-0.711678\pi\)
0.372956 + 0.927849i \(0.378344\pi\)
\(174\) 0 0
\(175\) −11.5485 + 20.0027i −0.872988 + 1.51206i
\(176\) 0 0
\(177\) −21.1063 + 2.80257i −1.58644 + 0.210654i
\(178\) 0 0
\(179\) 22.1833i 1.65806i −0.559206 0.829029i \(-0.688894\pi\)
0.559206 0.829029i \(-0.311106\pi\)
\(180\) 0 0
\(181\) 20.1998i 1.50144i −0.660620 0.750720i \(-0.729707\pi\)
0.660620 0.750720i \(-0.270293\pi\)
\(182\) 0 0
\(183\) −8.24623 + 19.9709i −0.609579 + 1.47629i
\(184\) 0 0
\(185\) 2.16606 3.75172i 0.159252 0.275832i
\(186\) 0 0
\(187\) 24.4884 14.1384i 1.79077 1.03390i
\(188\) 0 0
\(189\) −7.24234 + 9.50387i −0.526803 + 0.691304i
\(190\) 0 0
\(191\) −6.27776 10.8734i −0.454243 0.786772i 0.544401 0.838825i \(-0.316757\pi\)
−0.998644 + 0.0520530i \(0.983424\pi\)
\(192\) 0 0
\(193\) 3.66606 6.34979i 0.263888 0.457068i −0.703383 0.710811i \(-0.748328\pi\)
0.967272 + 0.253742i \(0.0816616\pi\)
\(194\) 0 0
\(195\) 6.07091 + 2.50675i 0.434747 + 0.179512i
\(196\) 0 0
\(197\) 25.5059i 1.81722i −0.417647 0.908609i \(-0.637145\pi\)
0.417647 0.908609i \(-0.362855\pi\)
\(198\) 0 0
\(199\) −20.6876 −1.46650 −0.733252 0.679957i \(-0.761998\pi\)
−0.733252 + 0.679957i \(0.761998\pi\)
\(200\) 0 0
\(201\) 0.103956 0.0138037i 0.00733250 0.000973637i
\(202\) 0 0
\(203\) 9.94857 + 5.74381i 0.698253 + 0.403137i
\(204\) 0 0
\(205\) 21.0009 12.1249i 1.46677 0.846838i
\(206\) 0 0
\(207\) −12.5259 12.4703i −0.870612 0.866749i
\(208\) 0 0
\(209\) 1.51795 + 2.62916i 0.104999 + 0.181863i
\(210\) 0 0
\(211\) 6.18585 + 3.57140i 0.425851 + 0.245865i 0.697578 0.716509i \(-0.254261\pi\)
−0.271726 + 0.962375i \(0.587595\pi\)
\(212\) 0 0
\(213\) −17.5606 + 13.5058i −1.20323 + 0.925400i
\(214\) 0 0
\(215\) −21.5105 −1.46700
\(216\) 0 0
\(217\) 7.04415 0.478188
\(218\) 0 0
\(219\) 2.35055 1.80780i 0.158836 0.122160i
\(220\) 0 0
\(221\) −5.75080 3.32023i −0.386841 0.223343i
\(222\) 0 0
\(223\) −2.32915 4.03421i −0.155972 0.270151i 0.777441 0.628956i \(-0.216518\pi\)
−0.933412 + 0.358805i \(0.883184\pi\)
\(224\) 0 0
\(225\) 29.0883 7.86355i 1.93922 0.524237i
\(226\) 0 0
\(227\) 8.39503 4.84688i 0.557198 0.321698i −0.194822 0.980839i \(-0.562413\pi\)
0.752020 + 0.659140i \(0.229080\pi\)
\(228\) 0 0
\(229\) 3.26619 + 1.88574i 0.215836 + 0.124613i 0.604021 0.796969i \(-0.293564\pi\)
−0.388185 + 0.921582i \(0.626898\pi\)
\(230\) 0 0
\(231\) 16.4375 2.18263i 1.08151 0.143606i
\(232\) 0 0
\(233\) 1.95585 0.128132 0.0640659 0.997946i \(-0.479593\pi\)
0.0640659 + 0.997946i \(0.479593\pi\)
\(234\) 0 0
\(235\) 37.7283i 2.46112i
\(236\) 0 0
\(237\) 18.4886 + 7.63414i 1.20096 + 0.495891i
\(238\) 0 0
\(239\) 6.78125 11.7455i 0.438643 0.759751i −0.558942 0.829206i \(-0.688793\pi\)
0.997585 + 0.0694552i \(0.0221261\pi\)
\(240\) 0 0
\(241\) −1.21204 2.09932i −0.0780744 0.135229i 0.824345 0.566088i \(-0.191544\pi\)
−0.902419 + 0.430859i \(0.858210\pi\)
\(242\) 0 0
\(243\) 15.4435 2.12058i 0.990704 0.136035i
\(244\) 0 0
\(245\) −5.75080 + 3.32023i −0.367405 + 0.212122i
\(246\) 0 0
\(247\) 0.356472 0.617428i 0.0226818 0.0392860i
\(248\) 0 0
\(249\) 4.85189 11.7504i 0.307476 0.744654i
\(250\) 0 0
\(251\) 22.7914i 1.43858i 0.694708 + 0.719291i \(0.255533\pi\)
−0.694708 + 0.719291i \(0.744467\pi\)
\(252\) 0 0
\(253\) 24.5282i 1.54208i
\(254\) 0 0
\(255\) −45.2327 + 6.00617i −2.83258 + 0.376121i
\(256\) 0 0
\(257\) 1.78796 3.09684i 0.111530 0.193175i −0.804857 0.593468i \(-0.797758\pi\)
0.916387 + 0.400293i \(0.131092\pi\)
\(258\) 0 0
\(259\) −2.22429 + 1.28419i −0.138210 + 0.0797958i
\(260\) 0 0
\(261\) −3.91103 14.4674i −0.242087 0.895511i
\(262\) 0 0
\(263\) 13.0802 + 22.6555i 0.806558 + 1.39700i 0.915234 + 0.402923i \(0.132006\pi\)
−0.108676 + 0.994077i \(0.534661\pi\)
\(264\) 0 0
\(265\) −13.2102 + 22.8808i −0.811497 + 1.40555i
\(266\) 0 0
\(267\) −14.1855 + 10.9100i −0.868140 + 0.667682i
\(268\) 0 0
\(269\) 14.5691i 0.888291i −0.895955 0.444146i \(-0.853507\pi\)
0.895955 0.444146i \(-0.146493\pi\)
\(270\) 0 0
\(271\) 12.3714 0.751512 0.375756 0.926719i \(-0.377383\pi\)
0.375756 + 0.926719i \(0.377383\pi\)
\(272\) 0 0
\(273\) −2.37397 3.08670i −0.143679 0.186816i
\(274\) 0 0
\(275\) −36.2134 20.9078i −2.18375 1.26079i
\(276\) 0 0
\(277\) −10.0771 + 5.81802i −0.605474 + 0.349571i −0.771192 0.636602i \(-0.780339\pi\)
0.165718 + 0.986173i \(0.447006\pi\)
\(278\) 0 0
\(279\) −6.51260 6.48370i −0.389899 0.388169i
\(280\) 0 0
\(281\) −4.89604 8.48020i −0.292073 0.505886i 0.682226 0.731141i \(-0.261012\pi\)
−0.974300 + 0.225255i \(0.927679\pi\)
\(282\) 0 0
\(283\) 15.0400 + 8.68335i 0.894036 + 0.516172i 0.875260 0.483652i \(-0.160690\pi\)
0.0187752 + 0.999824i \(0.494023\pi\)
\(284\) 0 0
\(285\) −0.644845 4.85635i −0.0381973 0.287666i
\(286\) 0 0
\(287\) −14.3770 −0.848646
\(288\) 0 0
\(289\) 29.1325 1.71367
\(290\) 0 0
\(291\) 14.9402 + 6.16897i 0.875808 + 0.361631i
\(292\) 0 0
\(293\) 5.14526 + 2.97062i 0.300589 + 0.173545i 0.642708 0.766112i \(-0.277811\pi\)
−0.342118 + 0.939657i \(0.611144\pi\)
\(294\) 0 0
\(295\) −23.8396 41.2915i −1.38800 2.40408i
\(296\) 0 0
\(297\) −17.2061 13.1117i −0.998398 0.760821i
\(298\) 0 0
\(299\) 4.98845 2.88008i 0.288489 0.166559i
\(300\) 0 0
\(301\) 11.0444 + 6.37647i 0.636587 + 0.367534i
\(302\) 0 0
\(303\) −4.04065 + 9.78574i −0.232129 + 0.562176i
\(304\) 0 0
\(305\) −48.3845 −2.77049
\(306\) 0 0
\(307\) 29.3867i 1.67718i 0.544759 + 0.838592i \(0.316621\pi\)
−0.544759 + 0.838592i \(0.683379\pi\)
\(308\) 0 0
\(309\) −2.45880 18.5174i −0.139876 1.05342i
\(310\) 0 0
\(311\) −7.18849 + 12.4508i −0.407622 + 0.706021i −0.994623 0.103565i \(-0.966975\pi\)
0.587001 + 0.809586i \(0.300308\pi\)
\(312\) 0 0
\(313\) 2.50000 + 4.33013i 0.141308 + 0.244753i 0.927990 0.372606i \(-0.121536\pi\)
−0.786681 + 0.617359i \(0.788202\pi\)
\(314\) 0 0
\(315\) −25.8613 6.86792i −1.45712 0.386964i
\(316\) 0 0
\(317\) −2.54007 + 1.46651i −0.142665 + 0.0823675i −0.569633 0.821899i \(-0.692915\pi\)
0.426969 + 0.904266i \(0.359581\pi\)
\(318\) 0 0
\(319\) −10.3988 + 18.0112i −0.582219 + 1.00843i
\(320\) 0 0
\(321\) 0.642147 + 0.834939i 0.0358412 + 0.0466017i
\(322\) 0 0
\(323\) 4.95296i 0.275590i
\(324\) 0 0
\(325\) 9.81992i 0.544711i
\(326\) 0 0
\(327\) −15.6780 20.3850i −0.866994 1.12729i
\(328\) 0 0
\(329\) −11.1840 + 19.3713i −0.616594 + 1.06797i
\(330\) 0 0
\(331\) −11.2381 + 6.48830i −0.617700 + 0.356629i −0.775973 0.630766i \(-0.782741\pi\)
0.158273 + 0.987395i \(0.449407\pi\)
\(332\) 0 0
\(333\) 3.23846 + 0.860029i 0.177466 + 0.0471293i
\(334\) 0 0
\(335\) 0.117419 + 0.203376i 0.00641529 + 0.0111116i
\(336\) 0 0
\(337\) −6.54415 + 11.3348i −0.356483 + 0.617446i −0.987371 0.158428i \(-0.949357\pi\)
0.630888 + 0.775874i \(0.282691\pi\)
\(338\) 0 0
\(339\) 2.72766 + 20.5421i 0.148146 + 1.11570i
\(340\) 0 0
\(341\) 12.7529i 0.690610i
\(342\) 0 0
\(343\) 20.0338 1.08173
\(344\) 0 0
\(345\) 15.1063 36.5847i 0.813293 1.96965i
\(346\) 0 0
\(347\) −12.1842 7.03455i −0.654082 0.377634i 0.135936 0.990718i \(-0.456596\pi\)
−0.790018 + 0.613083i \(0.789929\pi\)
\(348\) 0 0
\(349\) −1.81396 + 1.04729i −0.0970990 + 0.0560601i −0.547763 0.836633i \(-0.684521\pi\)
0.450664 + 0.892694i \(0.351187\pi\)
\(350\) 0 0
\(351\) −0.646290 + 5.03887i −0.0344964 + 0.268955i
\(352\) 0 0
\(353\) 12.0901 + 20.9407i 0.643493 + 1.11456i 0.984647 + 0.174555i \(0.0558488\pi\)
−0.341154 + 0.940007i \(0.610818\pi\)
\(354\) 0 0
\(355\) −42.9633 24.8049i −2.28025 1.31650i
\(356\) 0 0
\(357\) 25.0048 + 10.3248i 1.32339 + 0.546444i
\(358\) 0 0
\(359\) −0.469676 −0.0247886 −0.0123943 0.999923i \(-0.503945\pi\)
−0.0123943 + 0.999923i \(0.503945\pi\)
\(360\) 0 0
\(361\) 18.4682 0.972012
\(362\) 0 0
\(363\) 1.44364 + 10.8721i 0.0757714 + 0.570638i
\(364\) 0 0
\(365\) 5.75080 + 3.32023i 0.301011 + 0.173789i
\(366\) 0 0
\(367\) −2.71101 4.69560i −0.141513 0.245109i 0.786553 0.617522i \(-0.211864\pi\)
−0.928067 + 0.372414i \(0.878530\pi\)
\(368\) 0 0
\(369\) 13.2921 + 13.2331i 0.691958 + 0.688888i
\(370\) 0 0
\(371\) 13.5653 7.83195i 0.704277 0.406615i
\(372\) 0 0
\(373\) 17.6141 + 10.1695i 0.912025 + 0.526558i 0.881082 0.472963i \(-0.156816\pi\)
0.0309430 + 0.999521i \(0.490149\pi\)
\(374\) 0 0
\(375\) 20.6590 + 26.8614i 1.06682 + 1.38712i
\(376\) 0 0
\(377\) 4.88406 0.251542
\(378\) 0 0
\(379\) 18.7646i 0.963873i 0.876206 + 0.481937i \(0.160066\pi\)
−0.876206 + 0.481937i \(0.839934\pi\)
\(380\) 0 0
\(381\) −11.6499 + 8.95989i −0.596843 + 0.459029i
\(382\) 0 0
\(383\) 6.68500 11.5788i 0.341587 0.591647i −0.643140 0.765748i \(-0.722369\pi\)
0.984728 + 0.174102i \(0.0557021\pi\)
\(384\) 0 0
\(385\) 18.5662 + 32.1576i 0.946223 + 1.63891i
\(386\) 0 0
\(387\) −4.34182 16.0610i −0.220707 0.816424i
\(388\) 0 0
\(389\) 15.0089 8.66542i 0.760984 0.439354i −0.0686651 0.997640i \(-0.521874\pi\)
0.829649 + 0.558286i \(0.188541\pi\)
\(390\) 0 0
\(391\) −20.0084 + 34.6556i −1.01187 + 1.75261i
\(392\) 0 0
\(393\) −13.2783 + 1.76314i −0.669800 + 0.0889385i
\(394\) 0 0
\(395\) 44.7931i 2.25379i
\(396\) 0 0
\(397\) 26.6228i 1.33616i −0.744090 0.668080i \(-0.767117\pi\)
0.744090 0.668080i \(-0.232883\pi\)
\(398\) 0 0
\(399\) −1.10851 + 2.68461i −0.0554947 + 0.134399i
\(400\) 0 0
\(401\) −7.71021 + 13.3545i −0.385029 + 0.666890i −0.991773 0.128007i \(-0.959142\pi\)
0.606744 + 0.794897i \(0.292475\pi\)
\(402\) 0 0
\(403\) 2.59364 1.49744i 0.129198 0.0745927i
\(404\) 0 0
\(405\) 17.5883 + 30.1534i 0.873971 + 1.49833i
\(406\) 0 0
\(407\) −2.32494 4.02691i −0.115243 0.199607i
\(408\) 0 0
\(409\) 2.50000 4.33013i 0.123617 0.214111i −0.797574 0.603220i \(-0.793884\pi\)
0.921192 + 0.389109i \(0.127217\pi\)
\(410\) 0 0
\(411\) −12.5454 5.18013i −0.618817 0.255517i
\(412\) 0 0
\(413\) 28.2677i 1.39096i
\(414\) 0 0
\(415\) 28.4683 1.39746
\(416\) 0 0
\(417\) 6.60212 0.876654i 0.323307 0.0429300i
\(418\) 0 0
\(419\) −1.39624 0.806118i −0.0682107 0.0393815i 0.465507 0.885044i \(-0.345872\pi\)
−0.533717 + 0.845663i \(0.679205\pi\)
\(420\) 0 0
\(421\) 19.5487 11.2864i 0.952744 0.550067i 0.0588116 0.998269i \(-0.481269\pi\)
0.893932 + 0.448202i \(0.147936\pi\)
\(422\) 0 0
\(423\) 28.1701 7.61533i 1.36968 0.370270i
\(424\) 0 0
\(425\) −34.1104 59.0809i −1.65460 2.86585i
\(426\) 0 0
\(427\) 24.8426 + 14.3429i 1.20222 + 0.694101i
\(428\) 0 0
\(429\) 5.58826 4.29790i 0.269804 0.207505i
\(430\) 0 0
\(431\) 11.7834 0.567586 0.283793 0.958886i \(-0.408407\pi\)
0.283793 + 0.958886i \(0.408407\pi\)
\(432\) 0 0
\(433\) 2.28796 0.109952 0.0549762 0.998488i \(-0.482492\pi\)
0.0549762 + 0.998488i \(0.482492\pi\)
\(434\) 0 0
\(435\) 26.6027 20.4600i 1.27550 0.980983i
\(436\) 0 0
\(437\) −3.72076 2.14818i −0.177988 0.102762i
\(438\) 0 0
\(439\) −7.71736 13.3669i −0.368329 0.637965i 0.620975 0.783830i \(-0.286737\pi\)
−0.989304 + 0.145865i \(0.953403\pi\)
\(440\) 0 0
\(441\) −3.63985 3.62370i −0.173326 0.172557i
\(442\) 0 0
\(443\) 17.8566 10.3095i 0.848393 0.489820i −0.0117155 0.999931i \(-0.503729\pi\)
0.860108 + 0.510112i \(0.170396\pi\)
\(444\) 0 0
\(445\) −34.7059 20.0375i −1.64522 0.949867i
\(446\) 0 0
\(447\) 14.5198 1.92799i 0.686762 0.0911908i
\(448\) 0 0
\(449\) 2.95218 0.139322 0.0696611 0.997571i \(-0.477808\pi\)
0.0696611 + 0.997571i \(0.477808\pi\)
\(450\) 0 0
\(451\) 26.0285i 1.22563i
\(452\) 0 0
\(453\) 8.68033 + 3.58421i 0.407838 + 0.168401i
\(454\) 0 0
\(455\) 4.36006 7.55185i 0.204403 0.354036i
\(456\) 0 0
\(457\) −6.37810 11.0472i −0.298355 0.516766i 0.677405 0.735610i \(-0.263105\pi\)
−0.975760 + 0.218845i \(0.929771\pi\)
\(458\) 0 0
\(459\) −13.6146 32.5610i −0.635476 1.51982i
\(460\) 0 0
\(461\) 17.6141 10.1695i 0.820372 0.473642i −0.0301727 0.999545i \(-0.509606\pi\)
0.850545 + 0.525903i \(0.176272\pi\)
\(462\) 0 0
\(463\) −4.24686 + 7.35577i −0.197368 + 0.341852i −0.947674 0.319239i \(-0.896573\pi\)
0.750306 + 0.661091i \(0.229906\pi\)
\(464\) 0 0
\(465\) 7.85419 19.0215i 0.364229 0.882100i
\(466\) 0 0
\(467\) 10.8773i 0.503342i −0.967813 0.251671i \(-0.919020\pi\)
0.967813 0.251671i \(-0.0809801\pi\)
\(468\) 0 0
\(469\) 0.139229i 0.00642899i
\(470\) 0 0
\(471\) −6.95365 + 0.923331i −0.320407 + 0.0425449i
\(472\) 0 0
\(473\) −11.5442 + 19.9951i −0.530801 + 0.919374i
\(474\) 0 0
\(475\) 6.34315 3.66222i 0.291044 0.168034i
\(476\) 0 0
\(477\) −19.7505 5.24509i −0.904314 0.240156i
\(478\) 0 0
\(479\) −8.66514 15.0085i −0.395920 0.685754i 0.597298 0.802020i \(-0.296241\pi\)
−0.993218 + 0.116265i \(0.962908\pi\)
\(480\) 0 0
\(481\) −0.545984 + 0.945673i −0.0248947 + 0.0431190i
\(482\) 0 0
\(483\) −18.6012 + 14.3061i −0.846383 + 0.650949i
\(484\) 0 0
\(485\) 36.1963i 1.64359i
\(486\) 0 0
\(487\) 32.2953 1.46344 0.731720 0.681605i \(-0.238718\pi\)
0.731720 + 0.681605i \(0.238718\pi\)
\(488\) 0 0
\(489\) −9.91629 12.8935i −0.448430 0.583062i
\(490\) 0 0
\(491\) 19.2245 + 11.0993i 0.867591 + 0.500904i 0.866547 0.499096i \(-0.166334\pi\)
0.00104378 + 0.999999i \(0.499668\pi\)
\(492\) 0 0
\(493\) −29.3846 + 16.9652i −1.32342 + 0.764075i
\(494\) 0 0
\(495\) 12.4339 46.8201i 0.558862 2.10441i
\(496\) 0 0
\(497\) 14.7061 + 25.4717i 0.659658 + 1.14256i
\(498\) 0 0
\(499\) 21.0686 + 12.1639i 0.943158 + 0.544532i 0.890949 0.454104i \(-0.150040\pi\)
0.0522091 + 0.998636i \(0.483374\pi\)
\(500\) 0 0
\(501\) −3.61442 27.2204i −0.161480 1.21612i
\(502\) 0 0
\(503\) −3.36573 −0.150070 −0.0750352 0.997181i \(-0.523907\pi\)
−0.0750352 + 0.997181i \(0.523907\pi\)
\(504\) 0 0
\(505\) −23.7084 −1.05501
\(506\) 0 0
\(507\) 19.2820 + 7.96176i 0.856343 + 0.353594i
\(508\) 0 0
\(509\) 0.753847 + 0.435234i 0.0334137 + 0.0192914i 0.516614 0.856219i \(-0.327192\pi\)
−0.483200 + 0.875510i \(0.660526\pi\)
\(510\) 0 0
\(511\) −1.96847 3.40948i −0.0870798 0.150827i
\(512\) 0 0
\(513\) 3.49587 1.46172i 0.154347 0.0645364i
\(514\) 0 0
\(515\) 36.2266 20.9155i 1.59634 0.921645i
\(516\) 0 0
\(517\) −35.0703 20.2479i −1.54239 0.890500i
\(518\) 0 0
\(519\) 2.45079 5.93538i 0.107578 0.260534i
\(520\) 0 0
\(521\) 19.9558 0.874282 0.437141 0.899393i \(-0.355991\pi\)
0.437141 + 0.899393i \(0.355991\pi\)
\(522\) 0 0
\(523\) 15.1185i 0.661085i −0.943791 0.330543i \(-0.892768\pi\)
0.943791 0.330543i \(-0.107232\pi\)
\(524\) 0 0
\(525\) −5.26584 39.6573i −0.229820 1.73078i
\(526\) 0 0
\(527\) −10.4030 + 18.0185i −0.453161 + 0.784898i
\(528\) 0 0
\(529\) −5.85602 10.1429i −0.254610 0.440997i
\(530\) 0 0
\(531\) 26.0186 26.1346i 1.12911 1.13414i
\(532\) 0 0
\(533\) −5.29357 + 3.05624i −0.229290 + 0.132381i
\(534\) 0 0
\(535\) −1.17938 + 2.04274i −0.0509888 + 0.0883153i
\(536\) 0 0
\(537\) 23.4241 + 30.4567i 1.01082 + 1.31430i
\(538\) 0 0
\(539\) 7.12754i 0.307005i
\(540\) 0 0
\(541\) 12.0537i 0.518230i −0.965846 0.259115i \(-0.916569\pi\)
0.965846 0.259115i \(-0.0834309\pi\)
\(542\) 0 0
\(543\) 21.3297 + 27.7334i 0.915343 + 1.19016i
\(544\) 0 0
\(545\) 28.7944 49.8733i 1.23342 2.13634i
\(546\) 0 0
\(547\) −24.4510 + 14.1168i −1.04545 + 0.603591i −0.921372 0.388682i \(-0.872931\pi\)
−0.124078 + 0.992272i \(0.539597\pi\)
\(548\) 0 0
\(549\) −9.76626 36.1267i −0.416814 1.54185i
\(550\) 0 0
\(551\) −1.82145 3.15484i −0.0775964 0.134401i
\(552\) 0 0
\(553\) 13.2783 22.9986i 0.564649 0.978001i
\(554\) 0 0
\(555\) 0.987665 + 7.43815i 0.0419241 + 0.315732i
\(556\) 0 0
\(557\) 20.4351i 0.865864i 0.901427 + 0.432932i \(0.142521\pi\)
−0.901427 + 0.432932i \(0.857479\pi\)
\(558\) 0 0
\(559\) 5.42202 0.229327
\(560\) 0 0
\(561\) −18.6923 + 45.2694i −0.789188 + 1.91128i
\(562\) 0 0
\(563\) −23.8436 13.7661i −1.00489 0.580173i −0.0951975 0.995458i \(-0.530348\pi\)
−0.909691 + 0.415286i \(0.863682\pi\)
\(564\) 0 0
\(565\) −40.1878 + 23.2025i −1.69072 + 0.976135i
\(566\) 0 0
\(567\) −0.0920369 20.6958i −0.00386518 0.869142i
\(568\) 0 0
\(569\) 8.25619 + 14.3001i 0.346118 + 0.599493i 0.985556 0.169349i \(-0.0541665\pi\)
−0.639439 + 0.768842i \(0.720833\pi\)
\(570\) 0 0
\(571\) −40.5817 23.4298i −1.69829 0.980508i −0.947384 0.320100i \(-0.896283\pi\)
−0.750907 0.660408i \(-0.770383\pi\)
\(572\) 0 0
\(573\) 20.1007 + 8.29980i 0.839717 + 0.346729i
\(574\) 0 0
\(575\) 59.1771 2.46785
\(576\) 0 0
\(577\) 4.95218 0.206162 0.103081 0.994673i \(-0.467130\pi\)
0.103081 + 0.994673i \(0.467130\pi\)
\(578\) 0 0
\(579\) 1.67163 + 12.5891i 0.0694704 + 0.523185i
\(580\) 0 0
\(581\) −14.6168 8.43903i −0.606408 0.350110i
\(582\) 0 0
\(583\) 14.1792 + 24.5591i 0.587242 + 1.01713i
\(584\) 0 0
\(585\) −10.9821 + 2.96882i −0.454052 + 0.122746i
\(586\) 0 0
\(587\) 2.06698 1.19337i 0.0853135 0.0492558i −0.456736 0.889602i \(-0.650982\pi\)
0.542050 + 0.840346i \(0.317648\pi\)
\(588\) 0 0
\(589\) −1.93453 1.11690i −0.0797111 0.0460212i
\(590\) 0 0
\(591\) 26.9325 + 35.0184i 1.10785 + 1.44047i
\(592\) 0 0
\(593\) 25.4287 1.04423 0.522115 0.852875i \(-0.325143\pi\)
0.522115 + 0.852875i \(0.325143\pi\)
\(594\) 0 0
\(595\) 60.5803i 2.48355i
\(596\) 0 0
\(597\) 28.4031 21.8447i 1.16246 0.894044i
\(598\) 0 0
\(599\) 23.3108 40.3754i 0.952452 1.64970i 0.212358 0.977192i \(-0.431886\pi\)
0.740094 0.672503i \(-0.234781\pi\)
\(600\) 0 0
\(601\) −17.7102 30.6750i −0.722414 1.25126i −0.960029 0.279899i \(-0.909699\pi\)
0.237615 0.971359i \(-0.423634\pi\)
\(602\) 0 0
\(603\) −0.128151 + 0.128723i −0.00521873 + 0.00524199i
\(604\) 0 0
\(605\) −21.2698 + 12.2801i −0.864740 + 0.499258i
\(606\) 0 0
\(607\) 11.8754 20.5688i 0.482009 0.834863i −0.517778 0.855515i \(-0.673241\pi\)
0.999787 + 0.0206517i \(0.00657410\pi\)
\(608\) 0 0
\(609\) −19.7240 + 2.61903i −0.799258 + 0.106128i
\(610\) 0 0
\(611\) 9.50994i 0.384731i
\(612\) 0 0
\(613\) 21.5983i 0.872345i 0.899863 + 0.436173i \(0.143666\pi\)
−0.899863 + 0.436173i \(0.856334\pi\)
\(614\) 0 0
\(615\) −16.0302 + 38.8224i −0.646402 + 1.56547i
\(616\) 0 0
\(617\) 4.17018 7.22297i 0.167885 0.290786i −0.769791 0.638296i \(-0.779640\pi\)
0.937676 + 0.347510i \(0.112973\pi\)
\(618\) 0 0
\(619\) 31.0809 17.9446i 1.24925 0.721253i 0.278287 0.960498i \(-0.410233\pi\)
0.970959 + 0.239245i \(0.0768999\pi\)
\(620\) 0 0
\(621\) 30.3654 + 3.89469i 1.21852 + 0.156289i
\(622\) 0 0
\(623\) 11.8796 + 20.5761i 0.475948 + 0.824365i
\(624\) 0 0
\(625\) −12.8321 + 22.2259i −0.513284 + 0.889035i
\(626\) 0 0
\(627\) −4.86029 2.00687i −0.194101 0.0801467i
\(628\) 0 0
\(629\) 7.58611i 0.302478i
\(630\) 0 0
\(631\) 31.5824 1.25727 0.628637 0.777699i \(-0.283613\pi\)
0.628637 + 0.777699i \(0.283613\pi\)
\(632\) 0 0
\(633\) −12.2641 + 1.62847i −0.487452 + 0.0647257i
\(634\) 0 0
\(635\) −28.5024 16.4558i −1.13108 0.653030i
\(636\) 0 0
\(637\) 1.44957 0.836909i 0.0574340 0.0331596i
\(638\) 0 0
\(639\) 9.84873 37.0856i 0.389610 1.46708i
\(640\) 0 0
\(641\) 21.6242 + 37.4542i 0.854105 + 1.47935i 0.877473 + 0.479625i \(0.159227\pi\)
−0.0233688 + 0.999727i \(0.507439\pi\)
\(642\) 0 0
\(643\) 10.9211 + 6.30532i 0.430688 + 0.248658i 0.699640 0.714496i \(-0.253344\pi\)
−0.268952 + 0.963154i \(0.586677\pi\)
\(644\) 0 0
\(645\) 29.5329 22.7136i 1.16286 0.894348i
\(646\) 0 0
\(647\) 37.3641 1.46893 0.734467 0.678644i \(-0.237432\pi\)
0.734467 + 0.678644i \(0.237432\pi\)
\(648\) 0 0
\(649\) −51.1766 −2.00886
\(650\) 0 0
\(651\) −9.67130 + 7.43815i −0.379048 + 0.291524i
\(652\) 0 0
\(653\) 21.7270 + 12.5441i 0.850244 + 0.490888i 0.860733 0.509057i \(-0.170006\pi\)
−0.0104893 + 0.999945i \(0.503339\pi\)
\(654\) 0 0
\(655\) −14.9979 25.9771i −0.586016 1.01501i
\(656\) 0 0
\(657\) −1.31829 + 4.96405i −0.0514314 + 0.193666i
\(658\) 0 0
\(659\) −35.0292 + 20.2241i −1.36455 + 0.787821i −0.990225 0.139479i \(-0.955457\pi\)
−0.374320 + 0.927299i \(0.622124\pi\)
\(660\) 0 0
\(661\) −33.8592 19.5486i −1.31697 0.760354i −0.333731 0.942668i \(-0.608308\pi\)
−0.983240 + 0.182315i \(0.941641\pi\)
\(662\) 0 0
\(663\) 11.4015 1.51394i 0.442799 0.0587965i
\(664\) 0 0
\(665\) −6.50413 −0.252219
\(666\) 0 0
\(667\) 29.4324i 1.13963i
\(668\) 0 0
\(669\) 7.45768 + 3.07936i 0.288331 + 0.119055i
\(670\) 0 0
\(671\) −25.9668 + 44.9758i −1.00244 + 1.73627i
\(672\) 0 0
\(673\) −7.26405 12.5817i −0.280009 0.484989i 0.691378 0.722493i \(-0.257004\pi\)
−0.971387 + 0.237504i \(0.923671\pi\)
\(674\) 0 0
\(675\) −31.6336 + 41.5116i −1.21758 + 1.59778i
\(676\) 0 0
\(677\) −40.9668 + 23.6522i −1.57448 + 0.909027i −0.578871 + 0.815419i \(0.696507\pi\)
−0.995609 + 0.0936076i \(0.970160\pi\)
\(678\) 0 0
\(679\) 10.7299 18.5847i 0.411774 0.713214i
\(680\) 0 0
\(681\) −6.40803 + 15.5191i −0.245556 + 0.594695i
\(682\) 0 0
\(683\) 2.97962i 0.114012i −0.998374 0.0570059i \(-0.981845\pi\)
0.998374 0.0570059i \(-0.0181554\pi\)
\(684\) 0 0
\(685\) 30.3943i 1.16130i
\(686\) 0 0
\(687\) −6.47554 + 0.859847i −0.247057 + 0.0328052i
\(688\) 0 0
\(689\) 3.32982 5.76741i 0.126856 0.219721i
\(690\) 0 0
\(691\) −8.27507 + 4.77761i −0.314798 + 0.181749i −0.649072 0.760727i \(-0.724842\pi\)
0.334273 + 0.942476i \(0.391509\pi\)
\(692\) 0 0
\(693\) −20.2632 + 20.3535i −0.769736 + 0.773166i
\(694\) 0 0
\(695\) 7.45714 + 12.9161i 0.282865 + 0.489937i
\(696\) 0 0
\(697\) 21.2323 36.7754i 0.804230 1.39297i
\(698\) 0 0
\(699\) −2.68529 + 2.06524i −0.101567 + 0.0781147i
\(700\) 0 0
\(701\) 14.7403i 0.556734i 0.960475 + 0.278367i \(0.0897931\pi\)
−0.960475 + 0.278367i \(0.910207\pi\)
\(702\) 0 0
\(703\) 0.814473 0.0307184
\(704\) 0 0
\(705\) 39.8385 + 51.7992i 1.50041 + 1.95087i
\(706\) 0 0
\(707\) 12.1729 + 7.02800i 0.457808 + 0.264315i
\(708\) 0 0
\(709\) 13.5013 7.79495i 0.507050 0.292746i −0.224570 0.974458i \(-0.572098\pi\)
0.731620 + 0.681712i \(0.238764\pi\)
\(710\) 0 0
\(711\) −33.4451 + 9.04134i −1.25429 + 0.339077i
\(712\) 0 0
\(713\) −9.02391 15.6299i −0.337948 0.585343i
\(714\) 0 0
\(715\) 13.6721 + 7.89358i 0.511307 + 0.295203i
\(716\) 0 0
\(717\) 3.09207 + 23.2865i 0.115476 + 0.869652i
\(718\) 0 0
\(719\) −37.7089 −1.40630 −0.703152 0.711039i \(-0.748225\pi\)
−0.703152 + 0.711039i \(0.748225\pi\)
\(720\) 0 0
\(721\) −24.8003 −0.923613
\(722\) 0 0
\(723\) 3.88081 + 1.60243i 0.144329 + 0.0595951i
\(724\) 0 0
\(725\) 43.4540 + 25.0882i 1.61384 + 0.931752i
\(726\) 0 0
\(727\) 8.83754 + 15.3071i 0.327766 + 0.567708i 0.982068 0.188526i \(-0.0603709\pi\)
−0.654302 + 0.756233i \(0.727038\pi\)
\(728\) 0 0
\(729\) −18.9641 + 19.2188i −0.702374 + 0.711808i
\(730\) 0 0
\(731\) −32.6212 + 18.8339i −1.20654 + 0.696596i
\(732\) 0 0
\(733\) 4.02969 + 2.32654i 0.148840 + 0.0859328i 0.572570 0.819856i \(-0.305946\pi\)
−0.423730 + 0.905788i \(0.639280\pi\)
\(734\) 0 0
\(735\) 4.38966 10.6310i 0.161915 0.392130i
\(736\) 0 0
\(737\) 0.252064 0.00928489
\(738\) 0 0
\(739\) 41.1901i 1.51520i −0.652718 0.757601i \(-0.726371\pi\)
0.652718 0.757601i \(-0.273629\pi\)
\(740\) 0 0
\(741\) 0.162542 + 1.22411i 0.00597113 + 0.0449689i
\(742\) 0 0
\(743\) 3.91901 6.78793i 0.143775 0.249025i −0.785141 0.619318i \(-0.787409\pi\)
0.928915 + 0.370293i \(0.120743\pi\)
\(744\) 0 0
\(745\) 16.4002 + 28.4059i 0.600856 + 1.04071i
\(746\) 0 0
\(747\) 5.74624 + 21.2561i 0.210244 + 0.777720i
\(748\) 0 0
\(749\) 1.21108 0.699217i 0.0442519 0.0255489i
\(750\) 0 0
\(751\) −0.0295971 + 0.0512637i −0.00108001 + 0.00187064i −0.866565 0.499064i \(-0.833677\pi\)
0.865485 + 0.500935i \(0.167010\pi\)
\(752\) 0 0
\(753\) −24.0662 31.2916i −0.877022 1.14033i
\(754\) 0 0
\(755\) 21.0303i 0.765370i
\(756\) 0 0
\(757\) 35.2826i 1.28237i −0.767387 0.641185i \(-0.778443\pi\)
0.767387 0.641185i \(-0.221557\pi\)
\(758\) 0 0
\(759\) −25.9001 33.6761i −0.940115 1.22237i
\(760\) 0 0
\(761\) 18.4443 31.9465i 0.668606 1.15806i −0.309688 0.950838i \(-0.600225\pi\)
0.978294 0.207222i \(-0.0664421\pi\)
\(762\) 0 0
\(763\) −29.5685 + 17.0714i −1.07045 + 0.618025i
\(764\) 0 0
\(765\) 55.7604 56.0089i 2.01602 2.02501i
\(766\) 0 0
\(767\) 6.00911 + 10.4081i 0.216976 + 0.375814i
\(768\) 0 0
\(769\) 8.52208 14.7607i 0.307314 0.532283i −0.670460 0.741946i \(-0.733903\pi\)
0.977774 + 0.209662i \(0.0672365\pi\)
\(770\) 0 0
\(771\) 0.815263 + 6.13978i 0.0293610 + 0.221119i
\(772\) 0 0
\(773\) 32.1463i 1.15622i 0.815958 + 0.578112i \(0.196210\pi\)
−0.815958 + 0.578112i \(0.803790\pi\)
\(774\) 0 0
\(775\) 30.7679 1.10522
\(776\) 0 0
\(777\) 1.69782 4.11183i 0.0609091 0.147511i
\(778\) 0 0
\(779\) 3.94835 + 2.27958i 0.141464 + 0.0816744i
\(780\) 0 0
\(781\) −46.1147 + 26.6243i −1.65011 + 0.952693i
\(782\) 0 0
\(783\) 20.6463 + 15.7333i 0.737839 + 0.562264i
\(784\) 0 0
\(785\) −7.85419 13.6039i −0.280328 0.485542i
\(786\) 0 0
\(787\) −7.85559 4.53543i −0.280022 0.161671i 0.353412 0.935468i \(-0.385022\pi\)
−0.633433 + 0.773797i \(0.718355\pi\)
\(788\) 0 0
\(789\) −41.8812 17.2932i −1.49101 0.615656i
\(790\) 0 0
\(791\) 27.5121 0.978219
\(792\) 0 0
\(793\) 12.1960 0.433092
\(794\) 0 0
\(795\) −6.02351 45.3633i −0.213632 1.60887i
\(796\) 0 0
\(797\) 42.5519 + 24.5673i 1.50726 + 0.870220i 0.999964 + 0.00845051i \(0