Properties

Label 768.2.n.b.481.1
Level $768$
Weight $2$
Character 768.481
Analytic conductor $6.133$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 481.1
Character \(\chi\) \(=\) 768.481
Dual form 768.2.n.b.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.382683 - 0.923880i) q^{3} +(-2.14986 - 0.890503i) q^{5} +(1.10001 + 1.10001i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.382683 - 0.923880i) q^{3} +(-2.14986 - 0.890503i) q^{5} +(1.10001 + 1.10001i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(0.999449 - 2.41288i) q^{11} +(2.03123 - 0.841362i) q^{13} +2.32700i q^{15} -5.68481i q^{17} +(-6.02698 + 2.49646i) q^{19} +(0.595322 - 1.43723i) q^{21} +(-3.60241 + 3.60241i) q^{23} +(0.293385 + 0.293385i) q^{25} +(0.923880 + 0.382683i) q^{27} +(-3.82608 - 9.23698i) q^{29} -1.98933 q^{31} -2.61168 q^{33} +(-1.38531 - 3.34444i) q^{35} +(-5.97179 - 2.47360i) q^{37} +(-1.55463 - 1.55463i) q^{39} +(-4.33228 + 4.33228i) q^{41} +(-4.39793 + 10.6175i) q^{43} +(2.14986 - 0.890503i) q^{45} -5.32331i q^{47} -4.57995i q^{49} +(-5.25208 + 2.17548i) q^{51} +(-0.802971 + 1.93854i) q^{53} +(-4.29736 + 4.29736i) q^{55} +(4.61285 + 4.61285i) q^{57} +(5.97225 + 2.47379i) q^{59} +(3.53897 + 8.54384i) q^{61} -1.55565 q^{63} -5.11610 q^{65} +(-2.25745 - 5.44997i) q^{67} +(4.70677 + 1.94961i) q^{69} +(-2.57276 - 2.57276i) q^{71} +(8.01131 - 8.01131i) q^{73} +(0.158779 - 0.383327i) q^{75} +(3.75360 - 1.55479i) q^{77} -14.4931i q^{79} -1.00000i q^{81} +(2.50672 - 1.03832i) q^{83} +(-5.06234 + 12.2216i) q^{85} +(-7.06968 + 7.06968i) q^{87} +(-2.98746 - 2.98746i) q^{89} +(3.15988 + 1.30887i) q^{91} +(0.761282 + 1.83790i) q^{93} +15.1803 q^{95} -5.81093 q^{97} +(0.999449 + 2.41288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} - 48q^{35} - 16q^{43} + 16q^{51} + 32q^{53} - 32q^{55} + 64q^{59} + 32q^{61} - 16q^{63} + 16q^{67} + 32q^{69} - 64q^{71} + 32q^{75} + 32q^{77} - 48q^{91} + O(q^{100}) \)

Character values

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

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

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
\(3\) −0.382683 0.923880i −0.220942 0.533402i
\(4\) 0 0
\(5\) −2.14986 0.890503i −0.961448 0.398245i −0.153926 0.988082i \(-0.549192\pi\)
−0.807522 + 0.589837i \(0.799192\pi\)
\(6\) 0 0
\(7\) 1.10001 + 1.10001i 0.415765 + 0.415765i 0.883741 0.467976i \(-0.155017\pi\)
−0.467976 + 0.883741i \(0.655017\pi\)
\(8\) 0 0
\(9\) −0.707107 + 0.707107i −0.235702 + 0.235702i
\(10\) 0 0
\(11\) 0.999449 2.41288i 0.301345 0.727511i −0.698583 0.715529i \(-0.746186\pi\)
0.999928 0.0119825i \(-0.00381423\pi\)
\(12\) 0 0
\(13\) 2.03123 0.841362i 0.563361 0.233352i −0.0827824 0.996568i \(-0.526381\pi\)
0.646144 + 0.763216i \(0.276381\pi\)
\(14\) 0 0
\(15\) 2.32700i 0.600828i
\(16\) 0 0
\(17\) 5.68481i 1.37877i −0.724396 0.689384i \(-0.757881\pi\)
0.724396 0.689384i \(-0.242119\pi\)
\(18\) 0 0
\(19\) −6.02698 + 2.49646i −1.38268 + 0.572726i −0.945197 0.326499i \(-0.894131\pi\)
−0.437486 + 0.899225i \(0.644131\pi\)
\(20\) 0 0
\(21\) 0.595322 1.43723i 0.129910 0.313630i
\(22\) 0 0
\(23\) −3.60241 + 3.60241i −0.751154 + 0.751154i −0.974695 0.223541i \(-0.928238\pi\)
0.223541 + 0.974695i \(0.428238\pi\)
\(24\) 0 0
\(25\) 0.293385 + 0.293385i 0.0586771 + 0.0586771i
\(26\) 0 0
\(27\) 0.923880 + 0.382683i 0.177801 + 0.0736475i
\(28\) 0 0
\(29\) −3.82608 9.23698i −0.710485 1.71526i −0.698785 0.715332i \(-0.746275\pi\)
−0.0117007 0.999932i \(-0.503725\pi\)
\(30\) 0 0
\(31\) −1.98933 −0.357294 −0.178647 0.983913i \(-0.557172\pi\)
−0.178647 + 0.983913i \(0.557172\pi\)
\(32\) 0 0
\(33\) −2.61168 −0.454636
\(34\) 0 0
\(35\) −1.38531 3.34444i −0.234160 0.565313i
\(36\) 0 0
\(37\) −5.97179 2.47360i −0.981756 0.406657i −0.166681 0.986011i \(-0.553305\pi\)
−0.815076 + 0.579354i \(0.803305\pi\)
\(38\) 0 0
\(39\) −1.55463 1.55463i −0.248941 0.248941i
\(40\) 0 0
\(41\) −4.33228 + 4.33228i −0.676589 + 0.676589i −0.959227 0.282638i \(-0.908791\pi\)
0.282638 + 0.959227i \(0.408791\pi\)
\(42\) 0 0
\(43\) −4.39793 + 10.6175i −0.670678 + 1.61916i 0.109784 + 0.993955i \(0.464984\pi\)
−0.780462 + 0.625204i \(0.785016\pi\)
\(44\) 0 0
\(45\) 2.14986 0.890503i 0.320483 0.132748i
\(46\) 0 0
\(47\) 5.32331i 0.776485i −0.921557 0.388242i \(-0.873082\pi\)
0.921557 0.388242i \(-0.126918\pi\)
\(48\) 0 0
\(49\) 4.57995i 0.654278i
\(50\) 0 0
\(51\) −5.25208 + 2.17548i −0.735438 + 0.304628i
\(52\) 0 0
\(53\) −0.802971 + 1.93854i −0.110297 + 0.266279i −0.969384 0.245549i \(-0.921032\pi\)
0.859088 + 0.511829i \(0.171032\pi\)
\(54\) 0 0
\(55\) −4.29736 + 4.29736i −0.579455 + 0.579455i
\(56\) 0 0
\(57\) 4.61285 + 4.61285i 0.610987 + 0.610987i
\(58\) 0 0
\(59\) 5.97225 + 2.47379i 0.777521 + 0.322060i 0.735915 0.677074i \(-0.236752\pi\)
0.0416066 + 0.999134i \(0.486752\pi\)
\(60\) 0 0
\(61\) 3.53897 + 8.54384i 0.453119 + 1.09393i 0.971130 + 0.238552i \(0.0766728\pi\)
−0.518010 + 0.855374i \(0.673327\pi\)
\(62\) 0 0
\(63\) −1.55565 −0.195994
\(64\) 0 0
\(65\) −5.11610 −0.634574
\(66\) 0 0
\(67\) −2.25745 5.44997i −0.275792 0.665820i 0.723919 0.689885i \(-0.242339\pi\)
−0.999710 + 0.0240652i \(0.992339\pi\)
\(68\) 0 0
\(69\) 4.70677 + 1.94961i 0.566629 + 0.234705i
\(70\) 0 0
\(71\) −2.57276 2.57276i −0.305330 0.305330i 0.537765 0.843095i \(-0.319269\pi\)
−0.843095 + 0.537765i \(0.819269\pi\)
\(72\) 0 0
\(73\) 8.01131 8.01131i 0.937653 0.937653i −0.0605139 0.998167i \(-0.519274\pi\)
0.998167 + 0.0605139i \(0.0192740\pi\)
\(74\) 0 0
\(75\) 0.158779 0.383327i 0.0183342 0.0442627i
\(76\) 0 0
\(77\) 3.75360 1.55479i 0.427763 0.177185i
\(78\) 0 0
\(79\) 14.4931i 1.63060i −0.579039 0.815300i \(-0.696572\pi\)
0.579039 0.815300i \(-0.303428\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 2.50672 1.03832i 0.275148 0.113970i −0.240843 0.970564i \(-0.577424\pi\)
0.515991 + 0.856594i \(0.327424\pi\)
\(84\) 0 0
\(85\) −5.06234 + 12.2216i −0.549088 + 1.32561i
\(86\) 0 0
\(87\) −7.06968 + 7.06968i −0.757949 + 0.757949i
\(88\) 0 0
\(89\) −2.98746 2.98746i −0.316670 0.316670i 0.530817 0.847487i \(-0.321885\pi\)
−0.847487 + 0.530817i \(0.821885\pi\)
\(90\) 0 0
\(91\) 3.15988 + 1.30887i 0.331246 + 0.137206i
\(92\) 0 0
\(93\) 0.761282 + 1.83790i 0.0789413 + 0.190581i
\(94\) 0 0
\(95\) 15.1803 1.55746
\(96\) 0 0
\(97\) −5.81093 −0.590010 −0.295005 0.955496i \(-0.595321\pi\)
−0.295005 + 0.955496i \(0.595321\pi\)
\(98\) 0 0
\(99\) 0.999449 + 2.41288i 0.100448 + 0.242504i
\(100\) 0 0
\(101\) −2.91259 1.20644i −0.289814 0.120045i 0.233040 0.972467i \(-0.425133\pi\)
−0.522854 + 0.852422i \(0.675133\pi\)
\(102\) 0 0
\(103\) 5.84034 + 5.84034i 0.575466 + 0.575466i 0.933651 0.358185i \(-0.116604\pi\)
−0.358185 + 0.933651i \(0.616604\pi\)
\(104\) 0 0
\(105\) −2.55972 + 2.55972i −0.249803 + 0.249803i
\(106\) 0 0
\(107\) 3.26727 7.88789i 0.315859 0.762551i −0.683606 0.729851i \(-0.739589\pi\)
0.999465 0.0327002i \(-0.0104107\pi\)
\(108\) 0 0
\(109\) 12.3255 5.10538i 1.18057 0.489006i 0.295894 0.955221i \(-0.404382\pi\)
0.884672 + 0.466214i \(0.154382\pi\)
\(110\) 0 0
\(111\) 6.46382i 0.613519i
\(112\) 0 0
\(113\) 13.6962i 1.28843i −0.764844 0.644216i \(-0.777184\pi\)
0.764844 0.644216i \(-0.222816\pi\)
\(114\) 0 0
\(115\) 10.9526 4.53673i 1.02134 0.423052i
\(116\) 0 0
\(117\) −0.841362 + 2.03123i −0.0777840 + 0.187787i
\(118\) 0 0
\(119\) 6.25336 6.25336i 0.573244 0.573244i
\(120\) 0 0
\(121\) 2.95507 + 2.95507i 0.268643 + 0.268643i
\(122\) 0 0
\(123\) 5.66040 + 2.34461i 0.510381 + 0.211407i
\(124\) 0 0
\(125\) 4.08304 + 9.85732i 0.365198 + 0.881665i
\(126\) 0 0
\(127\) −4.61080 −0.409142 −0.204571 0.978852i \(-0.565580\pi\)
−0.204571 + 0.978852i \(0.565580\pi\)
\(128\) 0 0
\(129\) 11.4923 1.01184
\(130\) 0 0
\(131\) 0.640651 + 1.54667i 0.0559740 + 0.135133i 0.949393 0.314092i \(-0.101700\pi\)
−0.893419 + 0.449225i \(0.851700\pi\)
\(132\) 0 0
\(133\) −9.37587 3.88361i −0.812991 0.336752i
\(134\) 0 0
\(135\) −1.64543 1.64543i −0.141616 0.141616i
\(136\) 0 0
\(137\) −2.84955 + 2.84955i −0.243454 + 0.243454i −0.818277 0.574824i \(-0.805071\pi\)
0.574824 + 0.818277i \(0.305071\pi\)
\(138\) 0 0
\(139\) −0.112341 + 0.271215i −0.00952863 + 0.0230041i −0.928572 0.371152i \(-0.878963\pi\)
0.919044 + 0.394156i \(0.128963\pi\)
\(140\) 0 0
\(141\) −4.91810 + 2.03714i −0.414178 + 0.171558i
\(142\) 0 0
\(143\) 5.74201i 0.480171i
\(144\) 0 0
\(145\) 23.2654i 1.93208i
\(146\) 0 0
\(147\) −4.23132 + 1.75267i −0.348993 + 0.144558i
\(148\) 0 0
\(149\) 5.19437 12.5403i 0.425539 1.02734i −0.555147 0.831752i \(-0.687338\pi\)
0.980686 0.195590i \(-0.0626621\pi\)
\(150\) 0 0
\(151\) 1.03696 1.03696i 0.0843863 0.0843863i −0.663654 0.748040i \(-0.730995\pi\)
0.748040 + 0.663654i \(0.230995\pi\)
\(152\) 0 0
\(153\) 4.01977 + 4.01977i 0.324979 + 0.324979i
\(154\) 0 0
\(155\) 4.27678 + 1.77150i 0.343519 + 0.142290i
\(156\) 0 0
\(157\) −0.319782 0.772022i −0.0255214 0.0616140i 0.910605 0.413278i \(-0.135616\pi\)
−0.936126 + 0.351664i \(0.885616\pi\)
\(158\) 0 0
\(159\) 2.09826 0.166403
\(160\) 0 0
\(161\) −7.92538 −0.624607
\(162\) 0 0
\(163\) 1.96818 + 4.75161i 0.154160 + 0.372175i 0.982025 0.188753i \(-0.0604446\pi\)
−0.827865 + 0.560928i \(0.810445\pi\)
\(164\) 0 0
\(165\) 5.61477 + 2.32571i 0.437109 + 0.181056i
\(166\) 0 0
\(167\) 4.63248 + 4.63248i 0.358472 + 0.358472i 0.863249 0.504778i \(-0.168426\pi\)
−0.504778 + 0.863249i \(0.668426\pi\)
\(168\) 0 0
\(169\) −5.77439 + 5.77439i −0.444184 + 0.444184i
\(170\) 0 0
\(171\) 2.49646 6.02698i 0.190909 0.460894i
\(172\) 0 0
\(173\) −12.6684 + 5.24743i −0.963163 + 0.398955i −0.808163 0.588959i \(-0.799538\pi\)
−0.155000 + 0.987914i \(0.549538\pi\)
\(174\) 0 0
\(175\) 0.645455i 0.0487918i
\(176\) 0 0
\(177\) 6.46432i 0.485888i
\(178\) 0 0
\(179\) −8.55352 + 3.54299i −0.639320 + 0.264815i −0.678707 0.734409i \(-0.737460\pi\)
0.0393869 + 0.999224i \(0.487460\pi\)
\(180\) 0 0
\(181\) 0.495989 1.19742i 0.0368666 0.0890039i −0.904374 0.426741i \(-0.859662\pi\)
0.941240 + 0.337737i \(0.109662\pi\)
\(182\) 0 0
\(183\) 6.53917 6.53917i 0.483390 0.483390i
\(184\) 0 0
\(185\) 10.6358 + 10.6358i 0.781959 + 0.781959i
\(186\) 0 0
\(187\) −13.7168 5.68167i −1.00307 0.415485i
\(188\) 0 0
\(189\) 0.595322 + 1.43723i 0.0433033 + 0.104543i
\(190\) 0 0
\(191\) 0.646843 0.0468039 0.0234019 0.999726i \(-0.492550\pi\)
0.0234019 + 0.999726i \(0.492550\pi\)
\(192\) 0 0
\(193\) 18.7195 1.34746 0.673730 0.738978i \(-0.264691\pi\)
0.673730 + 0.738978i \(0.264691\pi\)
\(194\) 0 0
\(195\) 1.95785 + 4.72666i 0.140204 + 0.338483i
\(196\) 0 0
\(197\) 0.597874 + 0.247647i 0.0425967 + 0.0176441i 0.403880 0.914812i \(-0.367661\pi\)
−0.361283 + 0.932456i \(0.617661\pi\)
\(198\) 0 0
\(199\) 13.5447 + 13.5447i 0.960158 + 0.960158i 0.999236 0.0390782i \(-0.0124421\pi\)
−0.0390782 + 0.999236i \(0.512442\pi\)
\(200\) 0 0
\(201\) −4.17123 + 4.17123i −0.294216 + 0.294216i
\(202\) 0 0
\(203\) 5.95205 14.3695i 0.417752 1.00854i
\(204\) 0 0
\(205\) 13.1717 5.45591i 0.919953 0.381057i
\(206\) 0 0
\(207\) 5.09457i 0.354097i
\(208\) 0 0
\(209\) 17.0375i 1.17851i
\(210\) 0 0
\(211\) 23.9743 9.93047i 1.65046 0.683642i 0.653168 0.757213i \(-0.273440\pi\)
0.997290 + 0.0735712i \(0.0234396\pi\)
\(212\) 0 0
\(213\) −1.39237 + 3.36147i −0.0954034 + 0.230324i
\(214\) 0 0
\(215\) 18.9099 18.9099i 1.28964 1.28964i
\(216\) 0 0
\(217\) −2.18828 2.18828i −0.148550 0.148550i
\(218\) 0 0
\(219\) −10.4673 4.33569i −0.707314 0.292979i
\(220\) 0 0
\(221\) −4.78298 11.5471i −0.321738 0.776745i
\(222\) 0 0
\(223\) −1.90075 −0.127284 −0.0636420 0.997973i \(-0.520272\pi\)
−0.0636420 + 0.997973i \(0.520272\pi\)
\(224\) 0 0
\(225\) −0.414910 −0.0276606
\(226\) 0 0
\(227\) −6.11900 14.7726i −0.406132 0.980490i −0.986145 0.165883i \(-0.946953\pi\)
0.580013 0.814607i \(-0.303047\pi\)
\(228\) 0 0
\(229\) 11.9674 + 4.95706i 0.790828 + 0.327572i 0.741277 0.671200i \(-0.234221\pi\)
0.0495519 + 0.998772i \(0.484221\pi\)
\(230\) 0 0
\(231\) −2.87288 2.87288i −0.189022 0.189022i
\(232\) 0 0
\(233\) 5.40070 5.40070i 0.353811 0.353811i −0.507714 0.861526i \(-0.669509\pi\)
0.861526 + 0.507714i \(0.169509\pi\)
\(234\) 0 0
\(235\) −4.74042 + 11.4444i −0.309231 + 0.746550i
\(236\) 0 0
\(237\) −13.3899 + 5.54626i −0.869765 + 0.360268i
\(238\) 0 0
\(239\) 22.6418i 1.46458i 0.680995 + 0.732288i \(0.261547\pi\)
−0.680995 + 0.732288i \(0.738453\pi\)
\(240\) 0 0
\(241\) 20.4844i 1.31951i 0.751479 + 0.659757i \(0.229341\pi\)
−0.751479 + 0.659757i \(0.770659\pi\)
\(242\) 0 0
\(243\) −0.923880 + 0.382683i −0.0592669 + 0.0245492i
\(244\) 0 0
\(245\) −4.07846 + 9.84627i −0.260563 + 0.629055i
\(246\) 0 0
\(247\) −10.1417 + 10.1417i −0.645303 + 0.645303i
\(248\) 0 0
\(249\) −1.91856 1.91856i −0.121584 0.121584i
\(250\) 0 0
\(251\) 12.6079 + 5.22237i 0.795804 + 0.329633i 0.743275 0.668986i \(-0.233272\pi\)
0.0525298 + 0.998619i \(0.483272\pi\)
\(252\) 0 0
\(253\) 5.09176 + 12.2926i 0.320116 + 0.772829i
\(254\) 0 0
\(255\) 13.2285 0.828402
\(256\) 0 0
\(257\) 12.4131 0.774307 0.387153 0.922015i \(-0.373458\pi\)
0.387153 + 0.922015i \(0.373458\pi\)
\(258\) 0 0
\(259\) −3.84805 9.29003i −0.239106 0.577254i
\(260\) 0 0
\(261\) 9.23698 + 3.82608i 0.571755 + 0.236828i
\(262\) 0 0
\(263\) −17.4830 17.4830i −1.07805 1.07805i −0.996684 0.0813652i \(-0.974072\pi\)
−0.0813652 0.996684i \(-0.525928\pi\)
\(264\) 0 0
\(265\) 3.45256 3.45256i 0.212089 0.212089i
\(266\) 0 0
\(267\) −1.61680 + 3.90330i −0.0989466 + 0.238878i
\(268\) 0 0
\(269\) −11.1213 + 4.60660i −0.678079 + 0.280869i −0.695023 0.718987i \(-0.744606\pi\)
0.0169449 + 0.999856i \(0.494606\pi\)
\(270\) 0 0
\(271\) 18.4077i 1.11819i 0.829105 + 0.559093i \(0.188850\pi\)
−0.829105 + 0.559093i \(0.811150\pi\)
\(272\) 0 0
\(273\) 3.42023i 0.207002i
\(274\) 0 0
\(275\) 1.00113 0.414681i 0.0603703 0.0250062i
\(276\) 0 0
\(277\) 4.36873 10.5471i 0.262492 0.633711i −0.736600 0.676329i \(-0.763570\pi\)
0.999091 + 0.0426179i \(0.0135698\pi\)
\(278\) 0 0
\(279\) 1.40667 1.40667i 0.0842149 0.0842149i
\(280\) 0 0
\(281\) −5.71168 5.71168i −0.340730 0.340730i 0.515912 0.856642i \(-0.327453\pi\)
−0.856642 + 0.515912i \(0.827453\pi\)
\(282\) 0 0
\(283\) −8.28088 3.43005i −0.492247 0.203896i 0.122730 0.992440i \(-0.460835\pi\)
−0.614978 + 0.788545i \(0.710835\pi\)
\(284\) 0 0
\(285\) −5.80924 14.0247i −0.344110 0.830754i
\(286\) 0 0
\(287\) −9.53112 −0.562604
\(288\) 0 0
\(289\) −15.3170 −0.901003
\(290\) 0 0
\(291\) 2.22374 + 5.36860i 0.130358 + 0.314713i
\(292\) 0 0
\(293\) 17.2497 + 7.14508i 1.00774 + 0.417420i 0.824630 0.565672i \(-0.191383\pi\)
0.183111 + 0.983092i \(0.441383\pi\)
\(294\) 0 0
\(295\) −10.6366 10.6366i −0.619288 0.619288i
\(296\) 0 0
\(297\) 1.84674 1.84674i 0.107159 0.107159i
\(298\) 0 0
\(299\) −4.28638 + 10.3482i −0.247888 + 0.598454i
\(300\) 0 0
\(301\) −16.5172 + 6.84164i −0.952035 + 0.394346i
\(302\) 0 0
\(303\) 3.15257i 0.181110i
\(304\) 0 0
\(305\) 21.5196i 1.23221i
\(306\) 0 0
\(307\) −0.294424 + 0.121954i −0.0168036 + 0.00696030i −0.391069 0.920361i \(-0.627895\pi\)
0.374266 + 0.927321i \(0.377895\pi\)
\(308\) 0 0
\(309\) 3.16077 7.63077i 0.179810 0.434099i
\(310\) 0 0
\(311\) −9.49039 + 9.49039i −0.538151 + 0.538151i −0.922986 0.384835i \(-0.874258\pi\)
0.384835 + 0.922986i \(0.374258\pi\)
\(312\) 0 0
\(313\) −23.1330 23.1330i −1.30756 1.30756i −0.923174 0.384383i \(-0.874414\pi\)
−0.384383 0.923174i \(-0.625586\pi\)
\(314\) 0 0
\(315\) 3.34444 + 1.38531i 0.188438 + 0.0780535i
\(316\) 0 0
\(317\) 1.17141 + 2.82804i 0.0657931 + 0.158839i 0.953356 0.301848i \(-0.0976034\pi\)
−0.887563 + 0.460686i \(0.847603\pi\)
\(318\) 0 0
\(319\) −26.1117 −1.46198
\(320\) 0 0
\(321\) −8.53779 −0.476533
\(322\) 0 0
\(323\) 14.1919 + 34.2622i 0.789657 + 1.90640i
\(324\) 0 0
\(325\) 0.842776 + 0.349089i 0.0467488 + 0.0193640i
\(326\) 0 0
\(327\) −9.43351 9.43351i −0.521674 0.521674i
\(328\) 0 0
\(329\) 5.85570 5.85570i 0.322835 0.322835i
\(330\) 0 0
\(331\) 5.82090 14.0529i 0.319946 0.772417i −0.679310 0.733851i \(-0.737721\pi\)
0.999256 0.0385662i \(-0.0122791\pi\)
\(332\) 0 0
\(333\) 5.97179 2.47360i 0.327252 0.135552i
\(334\) 0 0
\(335\) 13.7270i 0.749984i
\(336\) 0 0
\(337\) 4.16517i 0.226891i 0.993544 + 0.113446i \(0.0361888\pi\)
−0.993544 + 0.113446i \(0.963811\pi\)
\(338\) 0 0
\(339\) −12.6537 + 5.24132i −0.687252 + 0.284669i
\(340\) 0 0
\(341\) −1.98823 + 4.80001i −0.107669 + 0.259935i
\(342\) 0 0
\(343\) 12.7381 12.7381i 0.687792 0.687792i
\(344\) 0 0
\(345\) −8.38278 8.38278i −0.451314 0.451314i
\(346\) 0 0
\(347\) −29.5450 12.2380i −1.58606 0.656968i −0.596702 0.802463i \(-0.703522\pi\)
−0.989359 + 0.145495i \(0.953522\pi\)
\(348\) 0 0
\(349\) −11.3566 27.4173i −0.607907 1.46762i −0.865272 0.501302i \(-0.832854\pi\)
0.257365 0.966314i \(-0.417146\pi\)
\(350\) 0 0
\(351\) 2.19859 0.117352
\(352\) 0 0
\(353\) 4.26063 0.226771 0.113385 0.993551i \(-0.463831\pi\)
0.113385 + 0.993551i \(0.463831\pi\)
\(354\) 0 0
\(355\) 3.24003 + 7.82213i 0.171963 + 0.415156i
\(356\) 0 0
\(357\) −8.17040 3.38429i −0.432424 0.179116i
\(358\) 0 0
\(359\) −4.97012 4.97012i −0.262313 0.262313i 0.563680 0.825993i \(-0.309385\pi\)
−0.825993 + 0.563680i \(0.809385\pi\)
\(360\) 0 0
\(361\) 16.6571 16.6571i 0.876691 0.876691i
\(362\) 0 0
\(363\) 1.59927 3.86099i 0.0839401 0.202649i
\(364\) 0 0
\(365\) −24.3573 + 10.0891i −1.27492 + 0.528090i
\(366\) 0 0
\(367\) 15.0671i 0.786495i −0.919433 0.393247i \(-0.871352\pi\)
0.919433 0.393247i \(-0.128648\pi\)
\(368\) 0 0
\(369\) 6.12677i 0.318947i
\(370\) 0 0
\(371\) −3.01570 + 1.24914i −0.156567 + 0.0648523i
\(372\) 0 0
\(373\) 6.17375 14.9048i 0.319665 0.771739i −0.679607 0.733577i \(-0.737850\pi\)
0.999272 0.0381624i \(-0.0121504\pi\)
\(374\) 0 0
\(375\) 7.54447 7.54447i 0.389595 0.389595i
\(376\) 0 0
\(377\) −15.5433 15.5433i −0.800520 0.800520i
\(378\) 0 0
\(379\) 0.511585 + 0.211905i 0.0262783 + 0.0108848i 0.395784 0.918344i \(-0.370473\pi\)
−0.369506 + 0.929229i \(0.620473\pi\)
\(380\) 0 0
\(381\) 1.76448 + 4.25983i 0.0903969 + 0.218237i
\(382\) 0 0
\(383\) −6.05003 −0.309142 −0.154571 0.987982i \(-0.549400\pi\)
−0.154571 + 0.987982i \(0.549400\pi\)
\(384\) 0 0
\(385\) −9.45429 −0.481835
\(386\) 0 0
\(387\) −4.39793 10.6175i −0.223559 0.539720i
\(388\) 0 0
\(389\) 10.1717 + 4.21324i 0.515724 + 0.213620i 0.625338 0.780354i \(-0.284961\pi\)
−0.109613 + 0.993974i \(0.534961\pi\)
\(390\) 0 0
\(391\) 20.4790 + 20.4790i 1.03567 + 1.03567i
\(392\) 0 0
\(393\) 1.18377 1.18377i 0.0597133 0.0597133i
\(394\) 0 0
\(395\) −12.9061 + 31.1582i −0.649378 + 1.56774i
\(396\) 0 0
\(397\) 22.5585 9.34403i 1.13218 0.468963i 0.263657 0.964616i \(-0.415071\pi\)
0.868521 + 0.495653i \(0.165071\pi\)
\(398\) 0 0
\(399\) 10.1484i 0.508054i
\(400\) 0 0
\(401\) 26.6309i 1.32988i 0.746895 + 0.664942i \(0.231544\pi\)
−0.746895 + 0.664942i \(0.768456\pi\)
\(402\) 0 0
\(403\) −4.04077 + 1.67374i −0.201285 + 0.0833751i
\(404\) 0 0
\(405\) −0.890503 + 2.14986i −0.0442494 + 0.106828i
\(406\) 0 0
\(407\) −11.9370 + 11.9370i −0.591695 + 0.591695i
\(408\) 0 0
\(409\) −15.3022 15.3022i −0.756647 0.756647i 0.219064 0.975710i \(-0.429700\pi\)
−0.975710 + 0.219064i \(0.929700\pi\)
\(410\) 0 0
\(411\) 3.72312 + 1.54217i 0.183648 + 0.0760695i
\(412\) 0 0
\(413\) 3.84835 + 9.29075i 0.189365 + 0.457168i
\(414\) 0 0
\(415\) −6.31374 −0.309929
\(416\) 0 0
\(417\) 0.293561 0.0143757
\(418\) 0 0
\(419\) 7.92030 + 19.1213i 0.386932 + 0.934136i 0.990586 + 0.136890i \(0.0437107\pi\)
−0.603654 + 0.797246i \(0.706289\pi\)
\(420\) 0 0
\(421\) −29.2323 12.1084i −1.42469 0.590128i −0.468659 0.883379i \(-0.655263\pi\)
−0.956035 + 0.293251i \(0.905263\pi\)
\(422\) 0 0
\(423\) 3.76415 + 3.76415i 0.183019 + 0.183019i
\(424\) 0 0
\(425\) 1.66784 1.66784i 0.0809021 0.0809021i
\(426\) 0 0
\(427\) −5.50541 + 13.2912i −0.266425 + 0.643208i
\(428\) 0 0
\(429\) −5.30493 + 2.19737i −0.256124 + 0.106090i
\(430\) 0 0
\(431\) 1.99673i 0.0961789i −0.998843 0.0480895i \(-0.984687\pi\)
0.998843 0.0480895i \(-0.0153133\pi\)
\(432\) 0 0
\(433\) 16.8123i 0.807948i −0.914770 0.403974i \(-0.867629\pi\)
0.914770 0.403974i \(-0.132371\pi\)
\(434\) 0 0
\(435\) 21.4944 8.90328i 1.03058 0.426879i
\(436\) 0 0
\(437\) 12.7184 30.7049i 0.608402 1.46881i
\(438\) 0 0
\(439\) 23.5940 23.5940i 1.12608 1.12608i 0.135274 0.990808i \(-0.456809\pi\)
0.990808 0.135274i \(-0.0431914\pi\)
\(440\) 0 0
\(441\) 3.23851 + 3.23851i 0.154215 + 0.154215i
\(442\) 0 0
\(443\) −21.0559 8.72163i −1.00039 0.414377i −0.178453 0.983948i \(-0.557109\pi\)
−0.821942 + 0.569571i \(0.807109\pi\)
\(444\) 0 0
\(445\) 3.76229 + 9.08297i 0.178350 + 0.430574i
\(446\) 0 0
\(447\) −13.5735 −0.642006
\(448\) 0 0
\(449\) 29.2703 1.38135 0.690675 0.723165i \(-0.257314\pi\)
0.690675 + 0.723165i \(0.257314\pi\)
\(450\) 0 0
\(451\) 6.12339 + 14.7832i 0.288339 + 0.696113i
\(452\) 0 0
\(453\) −1.35485 0.561197i −0.0636564 0.0263673i
\(454\) 0 0
\(455\) −5.62777 5.62777i −0.263834 0.263834i
\(456\) 0 0
\(457\) −13.2549 + 13.2549i −0.620040 + 0.620040i −0.945541 0.325502i \(-0.894467\pi\)
0.325502 + 0.945541i \(0.394467\pi\)
\(458\) 0 0
\(459\) 2.17548 5.25208i 0.101543 0.245146i
\(460\) 0 0
\(461\) 36.5469 15.1382i 1.70216 0.705057i 0.702182 0.711997i \(-0.252209\pi\)
0.999976 + 0.00694059i \(0.00220928\pi\)
\(462\) 0 0
\(463\) 18.4673i 0.858250i −0.903245 0.429125i \(-0.858822\pi\)
0.903245 0.429125i \(-0.141178\pi\)
\(464\) 0 0
\(465\) 4.62915i 0.214672i
\(466\) 0 0
\(467\) 0.983296 0.407295i 0.0455015 0.0188474i −0.359817 0.933023i \(-0.617161\pi\)
0.405318 + 0.914176i \(0.367161\pi\)
\(468\) 0 0
\(469\) 3.51181 8.47826i 0.162160 0.391490i
\(470\) 0 0
\(471\) −0.590880 + 0.590880i −0.0272263 + 0.0272263i
\(472\) 0 0
\(473\) 21.2234 + 21.2234i 0.975851 + 0.975851i
\(474\) 0 0
\(475\) −2.50065 1.03580i −0.114738 0.0475259i
\(476\) 0 0
\(477\) −0.802971 1.93854i −0.0367655 0.0887598i
\(478\) 0 0
\(479\) −19.1585 −0.875375 −0.437687 0.899127i \(-0.644202\pi\)
−0.437687 + 0.899127i \(0.644202\pi\)
\(480\) 0 0
\(481\) −14.2113 −0.647978
\(482\) 0 0
\(483\) 3.03291 + 7.32209i 0.138002 + 0.333167i
\(484\) 0 0
\(485\) 12.4927 + 5.17465i 0.567264 + 0.234969i
\(486\) 0 0
\(487\) −26.4107 26.4107i −1.19678 1.19678i −0.975124 0.221660i \(-0.928852\pi\)
−0.221660 0.975124i \(-0.571148\pi\)
\(488\) 0 0
\(489\) 3.63672 3.63672i 0.164458 0.164458i
\(490\) 0 0
\(491\) 9.74865 23.5353i 0.439951 1.06213i −0.536015 0.844209i \(-0.680071\pi\)
0.975965 0.217926i \(-0.0699292\pi\)
\(492\) 0 0
\(493\) −52.5104 + 21.7505i −2.36495 + 0.979595i
\(494\) 0 0
\(495\) 6.07738i 0.273158i
\(496\) 0 0
\(497\) 5.66013i 0.253892i
\(498\) 0 0
\(499\) 12.2231 5.06299i 0.547183 0.226651i −0.0919272 0.995766i \(-0.529303\pi\)
0.639110 + 0.769115i \(0.279303\pi\)
\(500\) 0 0
\(501\) 2.50708 6.05262i 0.112008 0.270411i
\(502\) 0 0
\(503\) −21.6420 + 21.6420i −0.964970 + 0.964970i −0.999407 0.0344366i \(-0.989036\pi\)
0.0344366 + 0.999407i \(0.489036\pi\)
\(504\) 0 0
\(505\) 5.18734 + 5.18734i 0.230834 + 0.230834i
\(506\) 0 0
\(507\) 7.54461 + 3.12508i 0.335068 + 0.138790i
\(508\) 0 0
\(509\) −1.14400 2.76185i −0.0507067 0.122417i 0.896496 0.443051i \(-0.146104\pi\)
−0.947203 + 0.320634i \(0.896104\pi\)
\(510\) 0 0
\(511\) 17.6251 0.779688
\(512\) 0 0
\(513\) −6.52355 −0.288022
\(514\) 0 0
\(515\) −7.35510 17.7568i −0.324104 0.782457i
\(516\) 0 0
\(517\) −12.8445 5.32037i −0.564901 0.233990i
\(518\) 0 0
\(519\) 9.69599 + 9.69599i 0.425607 + 0.425607i
\(520\) 0 0
\(521\) −16.6745 + 16.6745i −0.730525 + 0.730525i −0.970724 0.240199i \(-0.922787\pi\)
0.240199 + 0.970724i \(0.422787\pi\)
\(522\) 0 0
\(523\) 0.461277 1.11362i 0.0201703 0.0486953i −0.913474 0.406898i \(-0.866610\pi\)
0.933644 + 0.358203i \(0.116610\pi\)
\(524\) 0 0
\(525\) 0.596323 0.247005i 0.0260256 0.0107802i
\(526\) 0 0
\(527\) 11.3089i 0.492625i
\(528\) 0 0
\(529\) 2.95466i 0.128463i
\(530\) 0 0
\(531\) −5.97225 + 2.47379i −0.259174 + 0.107353i
\(532\) 0 0
\(533\) −5.15484 + 12.4449i −0.223281 + 0.539047i
\(534\) 0 0
\(535\) −14.0484 + 14.0484i −0.607364 + 0.607364i
\(536\) 0 0
\(537\) 6.54658 + 6.54658i 0.282506 + 0.282506i
\(538\) 0 0
\(539\) −11.0509 4.57742i −0.475995 0.197164i
\(540\) 0 0
\(541\) 4.79193 + 11.5687i 0.206021 + 0.497379i 0.992790 0.119869i \(-0.0382474\pi\)
−0.786768 + 0.617248i \(0.788247\pi\)
\(542\) 0 0
\(543\) −1.29608 −0.0556202
\(544\) 0 0
\(545\) −31.0444 −1.32980
\(546\) 0 0
\(547\) −10.4863 25.3162i −0.448363 1.08244i −0.972935 0.231078i \(-0.925775\pi\)
0.524573 0.851366i \(-0.324225\pi\)
\(548\) 0 0
\(549\) −8.54384 3.53897i −0.364642 0.151040i
\(550\) 0 0
\(551\) 46.1194 + 46.1194i 1.96475 + 1.96475i
\(552\) 0 0
\(553\) 15.9426 15.9426i 0.677947 0.677947i
\(554\) 0 0
\(555\) 5.75605 13.8963i 0.244331 0.589867i
\(556\) 0 0
\(557\) 10.9293 4.52708i 0.463091 0.191818i −0.138925 0.990303i \(-0.544365\pi\)
0.602015 + 0.798485i \(0.294365\pi\)
\(558\) 0 0
\(559\) 25.2669i 1.06868i
\(560\) 0 0
\(561\) 14.8469i 0.626838i
\(562\) 0 0
\(563\) −33.9735 + 14.0723i −1.43181 + 0.593076i −0.957798 0.287442i \(-0.907195\pi\)
−0.474014 + 0.880518i \(0.657195\pi\)
\(564\) 0 0
\(565\) −12.1965 + 29.4450i −0.513112 + 1.23876i
\(566\) 0 0
\(567\) 1.10001 1.10001i 0.0461961 0.0461961i
\(568\) 0 0
\(569\) −3.61769 3.61769i −0.151661 0.151661i 0.627198 0.778860i \(-0.284202\pi\)
−0.778860 + 0.627198i \(0.784202\pi\)
\(570\) 0 0
\(571\) −14.7686 6.11734i −0.618045 0.256003i 0.0516188 0.998667i \(-0.483562\pi\)
−0.669664 + 0.742664i \(0.733562\pi\)
\(572\) 0 0
\(573\) −0.247536 0.597605i −0.0103410 0.0249653i
\(574\) 0 0
\(575\) −2.11379 −0.0881510
\(576\) 0 0
\(577\) 42.0367 1.75001 0.875005 0.484114i \(-0.160858\pi\)
0.875005 + 0.484114i \(0.160858\pi\)
\(578\) 0 0
\(579\) −7.16365 17.2946i −0.297711 0.718738i
\(580\) 0 0
\(581\) 3.89959 + 1.61526i 0.161782 + 0.0670123i
\(582\) 0 0
\(583\) 3.87495 + 3.87495i 0.160484 + 0.160484i
\(584\) 0 0
\(585\) 3.61763 3.61763i 0.149571 0.149571i
\(586\) 0 0
\(587\) −8.05275 + 19.4411i −0.332372 + 0.802418i 0.666031 + 0.745925i \(0.267992\pi\)
−0.998403 + 0.0564936i \(0.982008\pi\)
\(588\) 0 0
\(589\) 11.9896 4.96626i 0.494024 0.204631i
\(590\) 0 0
\(591\) 0.647134i 0.0266195i
\(592\) 0 0
\(593\) 24.6856i 1.01372i 0.862029 + 0.506858i \(0.169193\pi\)
−0.862029 + 0.506858i \(0.830807\pi\)
\(594\) 0 0
\(595\) −19.0125 + 7.87523i −0.779436 + 0.322853i
\(596\) 0 0
\(597\) 7.33034 17.6970i 0.300011 0.724290i
\(598\) 0 0
\(599\) 0.292862 0.292862i 0.0119660 0.0119660i −0.701098 0.713064i \(-0.747307\pi\)
0.713064 + 0.701098i \(0.247307\pi\)
\(600\) 0 0
\(601\) 17.9233 + 17.9233i 0.731107 + 0.731107i 0.970839 0.239732i \(-0.0770595\pi\)
−0.239732 + 0.970839i \(0.577059\pi\)
\(602\) 0 0
\(603\) 5.44997 + 2.25745i 0.221940 + 0.0919306i
\(604\) 0 0
\(605\) −3.72150 8.98450i −0.151301 0.365272i
\(606\) 0 0
\(607\) 30.0813 1.22096 0.610481 0.792031i \(-0.290976\pi\)
0.610481 + 0.792031i \(0.290976\pi\)
\(608\) 0 0
\(609\) −15.5535 −0.630258
\(610\) 0 0
\(611\) −4.47883 10.8129i −0.181194 0.437441i
\(612\) 0 0
\(613\) 8.13147 + 3.36816i 0.328427 + 0.136039i 0.540803 0.841149i \(-0.318120\pi\)
−0.212377 + 0.977188i \(0.568120\pi\)
\(614\) 0 0
\(615\) −10.0812 10.0812i −0.406513 0.406513i
\(616\) 0 0
\(617\) −13.3355 + 13.3355i −0.536869 + 0.536869i −0.922608 0.385739i \(-0.873946\pi\)
0.385739 + 0.922608i \(0.373946\pi\)
\(618\) 0 0
\(619\) 9.84872 23.7769i 0.395853 0.955674i −0.592785 0.805361i \(-0.701972\pi\)
0.988638 0.150314i \(-0.0480284\pi\)
\(620\) 0 0
\(621\) −4.70677 + 1.94961i −0.188876 + 0.0782351i
\(622\) 0 0
\(623\) 6.57248i 0.263321i
\(624\) 0 0
\(625\) 26.9024i 1.07610i
\(626\) 0 0
\(627\) 15.7406 6.51995i 0.628618 0.260382i
\(628\) 0 0
\(629\) −14.0619 + 33.9485i −0.560686 + 1.35361i
\(630\) 0 0
\(631\) −3.24320 + 3.24320i −0.129110 + 0.129110i −0.768709 0.639599i \(-0.779100\pi\)
0.639599 + 0.768709i \(0.279100\pi\)
\(632\) 0 0
\(633\) −18.3491 18.3491i −0.729312 0.729312i
\(634\) 0 0
\(635\) 9.91260 + 4.10593i 0.393369 + 0.162939i
\(636\) 0 0
\(637\) −3.85340 9.30292i −0.152677 0.368595i
\(638\) 0 0
\(639\) 3.63843 0.143934
\(640\) 0 0
\(641\) 27.4171 1.08291 0.541455 0.840729i \(-0.317874\pi\)
0.541455 + 0.840729i \(0.317874\pi\)
\(642\) 0 0
\(643\) −0.821316 1.98283i −0.0323896 0.0781953i 0.906857 0.421438i \(-0.138475\pi\)
−0.939247 + 0.343243i \(0.888475\pi\)
\(644\) 0 0
\(645\) −24.7070 10.2340i −0.972836 0.402962i
\(646\) 0 0
\(647\) −13.6349 13.6349i −0.536044 0.536044i 0.386321 0.922365i \(-0.373746\pi\)
−0.922365 + 0.386321i \(0.873746\pi\)
\(648\) 0 0
\(649\) 11.9379 11.9379i 0.468604 0.468604i
\(650\) 0 0
\(651\) −1.18429 + 2.85913i −0.0464160 + 0.112058i
\(652\) 0 0
\(653\) 12.3455 5.11368i 0.483118 0.200114i −0.127813 0.991798i \(-0.540796\pi\)
0.610930 + 0.791684i \(0.290796\pi\)
\(654\) 0 0
\(655\) 3.89563i 0.152215i
\(656\) 0 0
\(657\) 11.3297i 0.442014i
\(658\) 0 0
\(659\) 26.7406 11.0763i 1.04166 0.431472i 0.204755 0.978813i \(-0.434360\pi\)
0.836909 + 0.547342i \(0.184360\pi\)
\(660\) 0 0
\(661\) −5.00939 + 12.0937i −0.194843 + 0.470392i −0.990862 0.134879i \(-0.956935\pi\)
0.796019 + 0.605271i \(0.206935\pi\)
\(662\) 0 0
\(663\) −8.83780 + 8.83780i −0.343232 + 0.343232i
\(664\) 0 0
\(665\) 16.6985 + 16.6985i 0.647539 + 0.647539i
\(666\) 0 0
\(667\) 47.0584 + 19.4922i 1.82211 + 0.754743i
\(668\) 0 0
\(669\) 0.727387 + 1.75607i 0.0281224 + 0.0678935i
\(670\) 0 0
\(671\) 24.1523 0.932389
\(672\) 0 0
\(673\) −25.2282 −0.972477 −0.486239 0.873826i \(-0.661631\pi\)
−0.486239 + 0.873826i \(0.661631\pi\)
\(674\) 0 0
\(675\) 0.158779 + 0.383327i 0.00611141 + 0.0147542i
\(676\) 0 0
\(677\) −10.3092 4.27021i −0.396214 0.164117i 0.175675 0.984448i \(-0.443789\pi\)
−0.571889 + 0.820331i \(0.693789\pi\)
\(678\) 0 0
\(679\) −6.39209 6.39209i −0.245306 0.245306i
\(680\) 0 0
\(681\) −11.3064 + 11.3064i −0.433264 + 0.433264i
\(682\) 0 0
\(683\) −4.79116 + 11.5669i −0.183329 + 0.442595i −0.988649 0.150246i \(-0.951994\pi\)
0.805320 + 0.592840i \(0.201994\pi\)
\(684\) 0 0
\(685\) 8.66369 3.58862i 0.331023 0.137114i
\(686\) 0 0
\(687\) 12.9534i 0.494204i
\(688\) 0 0
\(689\) 4.61321i 0.175749i
\(690\) 0 0
\(691\) 5.63700 2.33492i 0.214441 0.0888245i −0.272877 0.962049i \(-0.587975\pi\)
0.487318 + 0.873224i \(0.337975\pi\)
\(692\) 0 0
\(693\) −1.55479 + 3.75360i −0.0590617 + 0.142588i
\(694\) 0 0
\(695\) 0.483035 0.483035i 0.0183226 0.0183226i
\(696\) 0 0
\(697\) 24.6282 + 24.6282i 0.932860 + 0.932860i
\(698\) 0 0
\(699\) −7.05635 2.92284i −0.266896 0.110552i
\(700\) 0 0
\(701\) 9.95368 + 24.0303i 0.375945 + 0.907612i 0.992717 + 0.120470i \(0.0384402\pi\)
−0.616772 + 0.787142i \(0.711560\pi\)
\(702\) 0 0
\(703\) 42.1671 1.59036
\(704\) 0 0
\(705\) 12.3873 0.466533
\(706\) 0 0
\(707\) −1.87679 4.53098i −0.0705840 0.170405i
\(708\) 0 0
\(709\) 36.9193 + 15.2925i 1.38653 + 0.574322i 0.946221 0.323522i \(-0.104867\pi\)
0.440314 + 0.897844i \(0.354867\pi\)
\(710\) 0 0
\(711\) 10.2482 + 10.2482i 0.384336 + 0.384336i
\(712\) 0 0
\(713\) 7.16636 7.16636i 0.268382 0.268382i
\(714\) 0 0
\(715\) −5.11328 + 12.3445i −0.191226 + 0.461660i
\(716\) 0 0
\(717\) 20.9183 8.66464i 0.781208 0.323587i
\(718\) 0 0
\(719\) 38.7035i 1.44340i −0.692208 0.721698i \(-0.743362\pi\)
0.692208 0.721698i \(-0.256638\pi\)
\(720\) 0 0
\(721\) 12.8489i 0.478518i
\(722\) 0 0
\(723\) 18.9251 7.83903i 0.703832 0.291537i
\(724\) 0 0
\(725\) 1.58748 3.83251i 0.0589575 0.142336i
\(726\) 0 0
\(727\) 8.44191 8.44191i 0.313093 0.313093i −0.533014 0.846107i \(-0.678941\pi\)
0.846107 + 0.533014i \(0.178941\pi\)
\(728\) 0 0
\(729\) 0.707107 + 0.707107i 0.0261891 + 0.0261891i
\(730\) 0 0
\(731\) 60.3587 + 25.0014i 2.23245 + 0.924709i
\(732\) 0 0
\(733\) −8.42070 20.3294i −0.311026 0.750883i −0.999668 0.0257810i \(-0.991793\pi\)
0.688642 0.725102i \(-0.258207\pi\)
\(734\) 0 0
\(735\) 10.6575 0.393109
\(736\) 0 0
\(737\) −15.4064 −0.567500
\(738\) 0 0
\(739\) 6.97881 + 16.8483i 0.256720 + 0.619776i 0.998718 0.0506261i \(-0.0161217\pi\)
−0.741998 + 0.670402i \(0.766122\pi\)
\(740\) 0 0
\(741\) 13.2508 + 5.48867i 0.486781 + 0.201631i
\(742\) 0 0
\(743\) −12.3355 12.3355i −0.452546 0.452546i 0.443653 0.896199i \(-0.353682\pi\)
−0.896199 + 0.443653i \(0.853682\pi\)
\(744\) 0 0
\(745\) −22.3344 + 22.3344i −0.818267 + 0.818267i
\(746\) 0 0
\(747\) −1.03832 + 2.50672i −0.0379901 + 0.0917162i
\(748\) 0 0
\(749\) 12.2708 5.08274i 0.448366 0.185719i
\(750\) 0 0
\(751\) 17.5511i 0.640449i −0.947342 0.320224i \(-0.896242\pi\)
0.947342 0.320224i \(-0.103758\pi\)
\(752\) 0 0
\(753\) 13.6467i 0.497314i
\(754\) 0 0
\(755\) −3.15273 + 1.30590i −0.114740 + 0.0475267i
\(756\) 0 0
\(757\) −2.89105 + 6.97962i −0.105077 + 0.253679i −0.967670 0.252220i \(-0.918839\pi\)
0.862593 + 0.505899i \(0.168839\pi\)
\(758\) 0 0
\(759\) 9.40835 9.40835i 0.341501 0.341501i
\(760\) 0 0
\(761\) 22.3535 + 22.3535i 0.810314 + 0.810314i 0.984681 0.174367i \(-0.0557879\pi\)
−0.174367 + 0.984681i \(0.555788\pi\)
\(762\) 0 0
\(763\) 19.1741 + 7.94219i 0.694150 + 0.287527i
\(764\) 0 0
\(765\) −5.06234 12.2216i −0.183029 0.441872i
\(766\) 0 0
\(767\) 14.2124 0.513179
\(768\) 0 0
\(769\) −3.22764 −0.116392 −0.0581958 0.998305i \(-0.518535\pi\)
−0.0581958 + 0.998305i \(0.518535\pi\)
\(770\) 0 0
\(771\) −4.75028 11.4682i −0.171077 0.413017i
\(772\) 0 0
\(773\) −6.48169 2.68480i −0.233130 0.0965656i 0.263060 0.964779i \(-0.415268\pi\)
−0.496190 + 0.868214i \(0.665268\pi\)
\(774\) 0 0
\(775\) −0.583639 0.583639i −0.0209649 0.0209649i
\(776\) 0 0
\(777\) −7.11028 + 7.11028i −0.255080 + 0.255080i
\(778\) 0 0
\(779\) 15.2952 36.9259i 0.548008 1.32301i
\(780\) 0 0
\(781\) −8.77910 + 3.63642i −0.314141 + 0.130121i
\(782\) 0 0
\(783\) 9.99803i 0.357301i
\(784\) 0 0
\(785\) 1.94451i 0.0694025i
\(786\) 0 0
\(787\) −44.8838 + 18.5915i −1.59994 + 0.662715i −0.991407 0.130816i \(-0.958240\pi\)
−0.608530 + 0.793531i \(0.708240\pi\)
\(788\) 0 0
\(789\) −9.46175 + 22.8427i −0.336847 + 0.813221i
\(790\) 0 0
\(791\) 15.0660 15.0660i 0.535685 0.535685i
\(792\) 0 0
\(793\) 14.3769 + 14.3769i 0.510540 + 0.510540i
\(794\) 0 0
\(795\) −4.51098 1.86851i −0.159988 0.0662692i
\(796\) 0 0
\(797\) 9.68913 + 23.3916i 0.343207 + 0.828574i 0.997388 + 0.0722361i \(0.0230135\pi\)
−0.654181 + 0.756338i \(0.726986\pi\)
\(798\) <