Properties

Label 912.2.q.k.49.2
Level $912$
Weight $2$
Character 912.49
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 456)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.2
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 912.49
Dual form 912.2.q.k.577.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.347296 + 0.601535i) q^{5} -0.305407 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.347296 + 0.601535i) q^{5} -0.305407 q^{7} +(-0.500000 - 0.866025i) q^{9} -4.82295 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.347296 - 0.601535i) q^{15} +(3.75877 - 6.51038i) q^{17} +(-3.06418 - 3.10013i) q^{19} +(0.152704 - 0.264490i) q^{21} +(0.347296 + 0.601535i) q^{23} +(2.25877 + 3.91231i) q^{25} +1.00000 q^{27} +(-5.06418 - 8.77141i) q^{29} +1.82295 q^{31} +(2.41147 - 4.17680i) q^{33} +(0.106067 - 0.183713i) q^{35} +6.51754 q^{37} +1.00000 q^{39} +(-2.69459 + 4.66717i) q^{41} +(1.84730 - 3.19961i) q^{43} +0.694593 q^{45} +(-3.00000 - 5.19615i) q^{47} -6.90673 q^{49} +(3.75877 + 6.51038i) q^{51} +(-2.71688 - 4.70578i) q^{53} +(1.67499 - 2.90117i) q^{55} +(4.21688 - 1.10359i) q^{57} +(-2.04189 + 3.53666i) q^{59} +(-0.194593 - 0.337044i) q^{61} +(0.152704 + 0.264490i) q^{63} +0.694593 q^{65} +(-3.91147 - 6.77487i) q^{67} -0.694593 q^{69} +(5.45336 - 9.44550i) q^{71} +(2.19459 - 3.80115i) q^{73} -4.51754 q^{75} +1.47296 q^{77} +(7.21688 - 12.5000i) q^{79} +(-0.500000 + 0.866025i) q^{81} -0.739170 q^{83} +(2.61081 + 4.52206i) q^{85} +10.1284 q^{87} +(0.411474 + 0.712694i) q^{89} +(0.152704 + 0.264490i) q^{91} +(-0.911474 + 1.57872i) q^{93} +(2.92902 - 0.766546i) q^{95} +(-5.45336 + 9.44550i) q^{97} +(2.41147 + 4.17680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{3} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{3} - 6 q^{7} - 3 q^{9} + 12 q^{11} - 3 q^{13} + 3 q^{21} - 9 q^{25} + 6 q^{27} - 12 q^{29} - 30 q^{31} - 6 q^{33} - 24 q^{35} - 6 q^{37} + 6 q^{39} - 12 q^{41} + 9 q^{43} - 18 q^{47} + 12 q^{49} + 9 q^{57} - 6 q^{59} + 3 q^{61} + 3 q^{63} - 3 q^{67} + 6 q^{71} + 9 q^{73} + 18 q^{75} - 12 q^{77} + 27 q^{79} - 3 q^{81} + 24 q^{83} + 24 q^{85} + 24 q^{87} - 18 q^{89} + 3 q^{91} + 15 q^{93} - 48 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −0.347296 + 0.601535i −0.155316 + 0.269015i −0.933174 0.359425i \(-0.882973\pi\)
0.777858 + 0.628440i \(0.216306\pi\)
\(6\) 0 0
\(7\) −0.305407 −0.115433 −0.0577166 0.998333i \(-0.518382\pi\)
−0.0577166 + 0.998333i \(0.518382\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −4.82295 −1.45417 −0.727087 0.686546i \(-0.759126\pi\)
−0.727087 + 0.686546i \(0.759126\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) −0.347296 0.601535i −0.0896715 0.155316i
\(16\) 0 0
\(17\) 3.75877 6.51038i 0.911636 1.57900i 0.0998822 0.994999i \(-0.468153\pi\)
0.811754 0.584000i \(-0.198513\pi\)
\(18\) 0 0
\(19\) −3.06418 3.10013i −0.702971 0.711219i
\(20\) 0 0
\(21\) 0.152704 0.264490i 0.0333227 0.0577166i
\(22\) 0 0
\(23\) 0.347296 + 0.601535i 0.0724163 + 0.125429i 0.899960 0.435973i \(-0.143596\pi\)
−0.827544 + 0.561402i \(0.810262\pi\)
\(24\) 0 0
\(25\) 2.25877 + 3.91231i 0.451754 + 0.782461i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −5.06418 8.77141i −0.940394 1.62881i −0.764721 0.644362i \(-0.777123\pi\)
−0.175674 0.984448i \(-0.556210\pi\)
\(30\) 0 0
\(31\) 1.82295 0.327411 0.163706 0.986509i \(-0.447655\pi\)
0.163706 + 0.986509i \(0.447655\pi\)
\(32\) 0 0
\(33\) 2.41147 4.17680i 0.419784 0.727087i
\(34\) 0 0
\(35\) 0.106067 0.183713i 0.0179286 0.0310532i
\(36\) 0 0
\(37\) 6.51754 1.07148 0.535739 0.844384i \(-0.320033\pi\)
0.535739 + 0.844384i \(0.320033\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −2.69459 + 4.66717i −0.420825 + 0.728890i −0.996020 0.0891261i \(-0.971593\pi\)
0.575196 + 0.818016i \(0.304926\pi\)
\(42\) 0 0
\(43\) 1.84730 3.19961i 0.281710 0.487936i −0.690096 0.723718i \(-0.742432\pi\)
0.971806 + 0.235782i \(0.0757650\pi\)
\(44\) 0 0
\(45\) 0.694593 0.103544
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) −6.90673 −0.986675
\(50\) 0 0
\(51\) 3.75877 + 6.51038i 0.526333 + 0.911636i
\(52\) 0 0
\(53\) −2.71688 4.70578i −0.373192 0.646388i 0.616862 0.787071i \(-0.288404\pi\)
−0.990055 + 0.140683i \(0.955070\pi\)
\(54\) 0 0
\(55\) 1.67499 2.90117i 0.225856 0.391194i
\(56\) 0 0
\(57\) 4.21688 1.10359i 0.558540 0.146174i
\(58\) 0 0
\(59\) −2.04189 + 3.53666i −0.265831 + 0.460433i −0.967781 0.251793i \(-0.918980\pi\)
0.701950 + 0.712226i \(0.252313\pi\)
\(60\) 0 0
\(61\) −0.194593 0.337044i −0.0249150 0.0431541i 0.853299 0.521422i \(-0.174598\pi\)
−0.878214 + 0.478268i \(0.841265\pi\)
\(62\) 0 0
\(63\) 0.152704 + 0.264490i 0.0192389 + 0.0333227i
\(64\) 0 0
\(65\) 0.694593 0.0861536
\(66\) 0 0
\(67\) −3.91147 6.77487i −0.477863 0.827682i 0.521815 0.853058i \(-0.325255\pi\)
−0.999678 + 0.0253761i \(0.991922\pi\)
\(68\) 0 0
\(69\) −0.694593 −0.0836191
\(70\) 0 0
\(71\) 5.45336 9.44550i 0.647195 1.12097i −0.336595 0.941650i \(-0.609275\pi\)
0.983790 0.179325i \(-0.0573914\pi\)
\(72\) 0 0
\(73\) 2.19459 3.80115i 0.256858 0.444890i −0.708541 0.705670i \(-0.750646\pi\)
0.965398 + 0.260779i \(0.0839795\pi\)
\(74\) 0 0
\(75\) −4.51754 −0.521641
\(76\) 0 0
\(77\) 1.47296 0.167860
\(78\) 0 0
\(79\) 7.21688 12.5000i 0.811963 1.40636i −0.0995259 0.995035i \(-0.531733\pi\)
0.911489 0.411326i \(-0.134934\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −0.739170 −0.0811345 −0.0405672 0.999177i \(-0.512916\pi\)
−0.0405672 + 0.999177i \(0.512916\pi\)
\(84\) 0 0
\(85\) 2.61081 + 4.52206i 0.283183 + 0.490487i
\(86\) 0 0
\(87\) 10.1284 1.08587
\(88\) 0 0
\(89\) 0.411474 + 0.712694i 0.0436162 + 0.0755454i 0.887009 0.461751i \(-0.152779\pi\)
−0.843393 + 0.537297i \(0.819445\pi\)
\(90\) 0 0
\(91\) 0.152704 + 0.264490i 0.0160077 + 0.0277261i
\(92\) 0 0
\(93\) −0.911474 + 1.57872i −0.0945155 + 0.163706i
\(94\) 0 0
\(95\) 2.92902 0.766546i 0.300511 0.0786459i
\(96\) 0 0
\(97\) −5.45336 + 9.44550i −0.553705 + 0.959045i 0.444298 + 0.895879i \(0.353453\pi\)
−0.998003 + 0.0631663i \(0.979880\pi\)
\(98\) 0 0
\(99\) 2.41147 + 4.17680i 0.242362 + 0.419784i
\(100\) 0 0
\(101\) −4.75877 8.24243i −0.473515 0.820153i 0.526025 0.850469i \(-0.323682\pi\)
−0.999540 + 0.0303164i \(0.990348\pi\)
\(102\) 0 0
\(103\) 2.30541 0.227159 0.113579 0.993529i \(-0.463768\pi\)
0.113579 + 0.993529i \(0.463768\pi\)
\(104\) 0 0
\(105\) 0.106067 + 0.183713i 0.0103511 + 0.0179286i
\(106\) 0 0
\(107\) −9.51754 −0.920095 −0.460048 0.887894i \(-0.652168\pi\)
−0.460048 + 0.887894i \(0.652168\pi\)
\(108\) 0 0
\(109\) −6.75877 + 11.7065i −0.647373 + 1.12128i 0.336375 + 0.941728i \(0.390799\pi\)
−0.983748 + 0.179555i \(0.942534\pi\)
\(110\) 0 0
\(111\) −3.25877 + 5.64436i −0.309309 + 0.535739i
\(112\) 0 0
\(113\) −21.0797 −1.98301 −0.991504 0.130078i \(-0.958477\pi\)
−0.991504 + 0.130078i \(0.958477\pi\)
\(114\) 0 0
\(115\) −0.482459 −0.0449895
\(116\) 0 0
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) 0 0
\(119\) −1.14796 + 1.98832i −0.105233 + 0.182269i
\(120\) 0 0
\(121\) 12.2608 1.11462
\(122\) 0 0
\(123\) −2.69459 4.66717i −0.242963 0.420825i
\(124\) 0 0
\(125\) −6.61081 −0.591289
\(126\) 0 0
\(127\) 4.69459 + 8.13127i 0.416578 + 0.721534i 0.995593 0.0937831i \(-0.0298960\pi\)
−0.579015 + 0.815317i \(0.696563\pi\)
\(128\) 0 0
\(129\) 1.84730 + 3.19961i 0.162645 + 0.281710i
\(130\) 0 0
\(131\) −4.06418 + 7.03936i −0.355089 + 0.615032i −0.987133 0.159900i \(-0.948883\pi\)
0.632044 + 0.774932i \(0.282216\pi\)
\(132\) 0 0
\(133\) 0.935822 + 0.946803i 0.0811461 + 0.0820982i
\(134\) 0 0
\(135\) −0.347296 + 0.601535i −0.0298905 + 0.0517719i
\(136\) 0 0
\(137\) 2.67499 + 4.63322i 0.228540 + 0.395843i 0.957376 0.288846i \(-0.0932715\pi\)
−0.728836 + 0.684689i \(0.759938\pi\)
\(138\) 0 0
\(139\) 6.97565 + 12.0822i 0.591667 + 1.02480i 0.994008 + 0.109308i \(0.0348633\pi\)
−0.402341 + 0.915490i \(0.631803\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 2.41147 + 4.17680i 0.201658 + 0.349281i
\(144\) 0 0
\(145\) 7.03508 0.584232
\(146\) 0 0
\(147\) 3.45336 5.98140i 0.284829 0.493338i
\(148\) 0 0
\(149\) −5.34730 + 9.26179i −0.438068 + 0.758755i −0.997540 0.0700934i \(-0.977670\pi\)
0.559473 + 0.828849i \(0.311004\pi\)
\(150\) 0 0
\(151\) 17.6459 1.43600 0.718001 0.696042i \(-0.245057\pi\)
0.718001 + 0.696042i \(0.245057\pi\)
\(152\) 0 0
\(153\) −7.51754 −0.607757
\(154\) 0 0
\(155\) −0.633103 + 1.09657i −0.0508521 + 0.0880784i
\(156\) 0 0
\(157\) −7.95336 + 13.7756i −0.634747 + 1.09941i 0.351821 + 0.936067i \(0.385563\pi\)
−0.986569 + 0.163348i \(0.947771\pi\)
\(158\) 0 0
\(159\) 5.43376 0.430925
\(160\) 0 0
\(161\) −0.106067 0.183713i −0.00835924 0.0144786i
\(162\) 0 0
\(163\) 2.17705 0.170520 0.0852599 0.996359i \(-0.472828\pi\)
0.0852599 + 0.996359i \(0.472828\pi\)
\(164\) 0 0
\(165\) 1.67499 + 2.90117i 0.130398 + 0.225856i
\(166\) 0 0
\(167\) −5.47565 9.48411i −0.423719 0.733902i 0.572581 0.819848i \(-0.305942\pi\)
−0.996300 + 0.0859458i \(0.972609\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) −1.15270 + 4.20372i −0.0881495 + 0.321467i
\(172\) 0 0
\(173\) 5.06418 8.77141i 0.385022 0.666878i −0.606750 0.794893i \(-0.707527\pi\)
0.991772 + 0.128015i \(0.0408604\pi\)
\(174\) 0 0
\(175\) −0.689845 1.19485i −0.0521474 0.0903219i
\(176\) 0 0
\(177\) −2.04189 3.53666i −0.153478 0.265831i
\(178\) 0 0
\(179\) −8.69459 −0.649864 −0.324932 0.945737i \(-0.605341\pi\)
−0.324932 + 0.945737i \(0.605341\pi\)
\(180\) 0 0
\(181\) −3.93582 6.81704i −0.292547 0.506707i 0.681864 0.731479i \(-0.261170\pi\)
−0.974411 + 0.224772i \(0.927836\pi\)
\(182\) 0 0
\(183\) 0.389185 0.0287694
\(184\) 0 0
\(185\) −2.26352 + 3.92053i −0.166417 + 0.288243i
\(186\) 0 0
\(187\) −18.1284 + 31.3992i −1.32568 + 2.29614i
\(188\) 0 0
\(189\) −0.305407 −0.0222151
\(190\) 0 0
\(191\) −13.8580 −1.00273 −0.501366 0.865235i \(-0.667169\pi\)
−0.501366 + 0.865235i \(0.667169\pi\)
\(192\) 0 0
\(193\) −1.04664 + 1.81283i −0.0753386 + 0.130490i −0.901233 0.433334i \(-0.857337\pi\)
0.825895 + 0.563824i \(0.190670\pi\)
\(194\) 0 0
\(195\) −0.347296 + 0.601535i −0.0248704 + 0.0430768i
\(196\) 0 0
\(197\) 14.0446 1.00063 0.500317 0.865842i \(-0.333217\pi\)
0.500317 + 0.865842i \(0.333217\pi\)
\(198\) 0 0
\(199\) −10.9953 19.0443i −0.779433 1.35002i −0.932269 0.361766i \(-0.882174\pi\)
0.152836 0.988252i \(-0.451159\pi\)
\(200\) 0 0
\(201\) 7.82295 0.551788
\(202\) 0 0
\(203\) 1.54664 + 2.67885i 0.108553 + 0.188019i
\(204\) 0 0
\(205\) −1.87164 3.24178i −0.130721 0.226416i
\(206\) 0 0
\(207\) 0.347296 0.601535i 0.0241388 0.0418096i
\(208\) 0 0
\(209\) 14.7784 + 14.9518i 1.02224 + 1.03424i
\(210\) 0 0
\(211\) −7.97565 + 13.8142i −0.549067 + 0.951011i 0.449272 + 0.893395i \(0.351683\pi\)
−0.998339 + 0.0576162i \(0.981650\pi\)
\(212\) 0 0
\(213\) 5.45336 + 9.44550i 0.373658 + 0.647195i
\(214\) 0 0
\(215\) 1.28312 + 2.22243i 0.0875080 + 0.151568i
\(216\) 0 0
\(217\) −0.556742 −0.0377941
\(218\) 0 0
\(219\) 2.19459 + 3.80115i 0.148297 + 0.256858i
\(220\) 0 0
\(221\) −7.51754 −0.505685
\(222\) 0 0
\(223\) −13.2520 + 22.9531i −0.887417 + 1.53705i −0.0444991 + 0.999009i \(0.514169\pi\)
−0.842918 + 0.538042i \(0.819164\pi\)
\(224\) 0 0
\(225\) 2.25877 3.91231i 0.150585 0.260820i
\(226\) 0 0
\(227\) −2.65539 −0.176245 −0.0881223 0.996110i \(-0.528087\pi\)
−0.0881223 + 0.996110i \(0.528087\pi\)
\(228\) 0 0
\(229\) 21.2567 1.40468 0.702342 0.711840i \(-0.252138\pi\)
0.702342 + 0.711840i \(0.252138\pi\)
\(230\) 0 0
\(231\) −0.736482 + 1.27562i −0.0484569 + 0.0839299i
\(232\) 0 0
\(233\) −6.75877 + 11.7065i −0.442782 + 0.766921i −0.997895 0.0648544i \(-0.979342\pi\)
0.555113 + 0.831775i \(0.312675\pi\)
\(234\) 0 0
\(235\) 4.16756 0.271861
\(236\) 0 0
\(237\) 7.21688 + 12.5000i 0.468787 + 0.811963i
\(238\) 0 0
\(239\) 24.4688 1.58276 0.791379 0.611326i \(-0.209364\pi\)
0.791379 + 0.611326i \(0.209364\pi\)
\(240\) 0 0
\(241\) −5.93376 10.2776i −0.382227 0.662037i 0.609153 0.793053i \(-0.291510\pi\)
−0.991380 + 0.131016i \(0.958176\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 2.39868 4.15464i 0.153246 0.265430i
\(246\) 0 0
\(247\) −1.15270 + 4.20372i −0.0733448 + 0.267476i
\(248\) 0 0
\(249\) 0.369585 0.640140i 0.0234215 0.0405672i
\(250\) 0 0
\(251\) 3.69459 + 6.39922i 0.233201 + 0.403915i 0.958748 0.284257i \(-0.0917468\pi\)
−0.725548 + 0.688172i \(0.758413\pi\)
\(252\) 0 0
\(253\) −1.67499 2.90117i −0.105306 0.182395i
\(254\) 0 0
\(255\) −5.22163 −0.326991
\(256\) 0 0
\(257\) −2.67230 4.62857i −0.166694 0.288722i 0.770562 0.637365i \(-0.219976\pi\)
−0.937255 + 0.348643i \(0.886642\pi\)
\(258\) 0 0
\(259\) −1.99050 −0.123684
\(260\) 0 0
\(261\) −5.06418 + 8.77141i −0.313465 + 0.542937i
\(262\) 0 0
\(263\) −12.0642 + 20.8958i −0.743909 + 1.28849i 0.206794 + 0.978385i \(0.433697\pi\)
−0.950703 + 0.310104i \(0.899636\pi\)
\(264\) 0 0
\(265\) 3.77425 0.231850
\(266\) 0 0
\(267\) −0.822948 −0.0503636
\(268\) 0 0
\(269\) 1.80066 3.11883i 0.109788 0.190159i −0.805896 0.592057i \(-0.798316\pi\)
0.915684 + 0.401898i \(0.131649\pi\)
\(270\) 0 0
\(271\) 9.38919 16.2625i 0.570352 0.987879i −0.426177 0.904640i \(-0.640140\pi\)
0.996530 0.0832396i \(-0.0265267\pi\)
\(272\) 0 0
\(273\) −0.305407 −0.0184841
\(274\) 0 0
\(275\) −10.8939 18.8688i −0.656929 1.13783i
\(276\) 0 0
\(277\) 20.1284 1.20940 0.604698 0.796455i \(-0.293294\pi\)
0.604698 + 0.796455i \(0.293294\pi\)
\(278\) 0 0
\(279\) −0.911474 1.57872i −0.0545685 0.0945155i
\(280\) 0 0
\(281\) 7.17024 + 12.4192i 0.427741 + 0.740869i 0.996672 0.0815162i \(-0.0259762\pi\)
−0.568931 + 0.822385i \(0.692643\pi\)
\(282\) 0 0
\(283\) 3.38919 5.87024i 0.201466 0.348950i −0.747535 0.664223i \(-0.768763\pi\)
0.949001 + 0.315273i \(0.102096\pi\)
\(284\) 0 0
\(285\) −0.800660 + 2.91987i −0.0474270 + 0.172958i
\(286\) 0 0
\(287\) 0.822948 1.42539i 0.0485771 0.0841380i
\(288\) 0 0
\(289\) −19.7567 34.2196i −1.16216 2.01292i
\(290\) 0 0
\(291\) −5.45336 9.44550i −0.319682 0.553705i
\(292\) 0 0
\(293\) 16.7784 0.980203 0.490101 0.871665i \(-0.336960\pi\)
0.490101 + 0.871665i \(0.336960\pi\)
\(294\) 0 0
\(295\) −1.41828 2.45654i −0.0825755 0.143025i
\(296\) 0 0
\(297\) −4.82295 −0.279856
\(298\) 0 0
\(299\) 0.347296 0.601535i 0.0200847 0.0347877i
\(300\) 0 0
\(301\) −0.564178 + 0.977185i −0.0325187 + 0.0563240i
\(302\) 0 0
\(303\) 9.51754 0.546768
\(304\) 0 0
\(305\) 0.270325 0.0154788
\(306\) 0 0
\(307\) −8.58172 + 14.8640i −0.489785 + 0.848332i −0.999931 0.0117559i \(-0.996258\pi\)
0.510146 + 0.860088i \(0.329591\pi\)
\(308\) 0 0
\(309\) −1.15270 + 1.99654i −0.0655750 + 0.113579i
\(310\) 0 0
\(311\) 12.1729 0.690264 0.345132 0.938554i \(-0.387834\pi\)
0.345132 + 0.938554i \(0.387834\pi\)
\(312\) 0 0
\(313\) −1.85204 3.20783i −0.104684 0.181318i 0.808925 0.587912i \(-0.200050\pi\)
−0.913609 + 0.406594i \(0.866716\pi\)
\(314\) 0 0
\(315\) −0.212134 −0.0119524
\(316\) 0 0
\(317\) −11.7811 20.4054i −0.661690 1.14608i −0.980171 0.198152i \(-0.936506\pi\)
0.318481 0.947929i \(-0.396827\pi\)
\(318\) 0 0
\(319\) 24.4243 + 42.3041i 1.36750 + 2.36857i
\(320\) 0 0
\(321\) 4.75877 8.24243i 0.265609 0.460048i
\(322\) 0 0
\(323\) −31.7006 + 8.29628i −1.76387 + 0.461618i
\(324\) 0 0
\(325\) 2.25877 3.91231i 0.125294 0.217016i
\(326\) 0 0
\(327\) −6.75877 11.7065i −0.373761 0.647373i
\(328\) 0 0
\(329\) 0.916222 + 1.58694i 0.0505129 + 0.0874910i
\(330\) 0 0
\(331\) 4.30541 0.236647 0.118323 0.992975i \(-0.462248\pi\)
0.118323 + 0.992975i \(0.462248\pi\)
\(332\) 0 0
\(333\) −3.25877 5.64436i −0.178580 0.309309i
\(334\) 0 0
\(335\) 5.43376 0.296878
\(336\) 0 0
\(337\) −9.77631 + 16.9331i −0.532550 + 0.922403i 0.466728 + 0.884401i \(0.345433\pi\)
−0.999278 + 0.0380021i \(0.987901\pi\)
\(338\) 0 0
\(339\) 10.5398 18.2555i 0.572445 0.991504i
\(340\) 0 0
\(341\) −8.79199 −0.476113
\(342\) 0 0
\(343\) 4.24722 0.229328
\(344\) 0 0
\(345\) 0.241230 0.417822i 0.0129874 0.0224948i
\(346\) 0 0
\(347\) 16.8452 29.1768i 0.904300 1.56629i 0.0824452 0.996596i \(-0.473727\pi\)
0.821855 0.569697i \(-0.192940\pi\)
\(348\) 0 0
\(349\) 12.5567 0.672147 0.336073 0.941836i \(-0.390901\pi\)
0.336073 + 0.941836i \(0.390901\pi\)
\(350\) 0 0
\(351\) −0.500000 0.866025i −0.0266880 0.0462250i
\(352\) 0 0
\(353\) −5.65951 −0.301225 −0.150613 0.988593i \(-0.548125\pi\)
−0.150613 + 0.988593i \(0.548125\pi\)
\(354\) 0 0
\(355\) 3.78787 + 6.56078i 0.201039 + 0.348210i
\(356\) 0 0
\(357\) −1.14796 1.98832i −0.0607563 0.105233i
\(358\) 0 0
\(359\) 11.3892 19.7266i 0.601098 1.04113i −0.391557 0.920154i \(-0.628063\pi\)
0.992655 0.120979i \(-0.0386033\pi\)
\(360\) 0 0
\(361\) −0.221629 + 18.9987i −0.0116647 + 0.999932i
\(362\) 0 0
\(363\) −6.13041 + 10.6182i −0.321763 + 0.557310i
\(364\) 0 0
\(365\) 1.52435 + 2.64025i 0.0797880 + 0.138197i
\(366\) 0 0
\(367\) −13.5574 23.4821i −0.707689 1.22575i −0.965712 0.259615i \(-0.916404\pi\)
0.258023 0.966139i \(-0.416929\pi\)
\(368\) 0 0
\(369\) 5.38919 0.280550
\(370\) 0 0
\(371\) 0.829755 + 1.43718i 0.0430788 + 0.0746146i
\(372\) 0 0
\(373\) −13.9418 −0.721879 −0.360940 0.932589i \(-0.617544\pi\)
−0.360940 + 0.932589i \(0.617544\pi\)
\(374\) 0 0
\(375\) 3.30541 5.72513i 0.170690 0.295645i
\(376\) 0 0
\(377\) −5.06418 + 8.77141i −0.260818 + 0.451751i
\(378\) 0 0
\(379\) −1.08378 −0.0556699 −0.0278350 0.999613i \(-0.508861\pi\)
−0.0278350 + 0.999613i \(0.508861\pi\)
\(380\) 0 0
\(381\) −9.38919 −0.481023
\(382\) 0 0
\(383\) 16.5398 28.6478i 0.845146 1.46384i −0.0403487 0.999186i \(-0.512847\pi\)
0.885495 0.464650i \(-0.153820\pi\)
\(384\) 0 0
\(385\) −0.511555 + 0.886039i −0.0260713 + 0.0451567i
\(386\) 0 0
\(387\) −3.69459 −0.187807
\(388\) 0 0
\(389\) 1.41147 + 2.44474i 0.0715646 + 0.123953i 0.899587 0.436741i \(-0.143867\pi\)
−0.828023 + 0.560695i \(0.810534\pi\)
\(390\) 0 0
\(391\) 5.22163 0.264069
\(392\) 0 0
\(393\) −4.06418 7.03936i −0.205011 0.355089i
\(394\) 0 0
\(395\) 5.01279 + 8.68241i 0.252221 + 0.436860i
\(396\) 0 0
\(397\) 14.7567 25.5594i 0.740618 1.28279i −0.211596 0.977357i \(-0.567866\pi\)
0.952214 0.305431i \(-0.0988005\pi\)
\(398\) 0 0
\(399\) −1.28787 + 0.337044i −0.0644740 + 0.0168733i
\(400\) 0 0
\(401\) −11.1506 + 19.3135i −0.556837 + 0.964469i 0.440922 + 0.897546i \(0.354652\pi\)
−0.997758 + 0.0669236i \(0.978682\pi\)
\(402\) 0 0
\(403\) −0.911474 1.57872i −0.0454038 0.0786416i
\(404\) 0 0
\(405\) −0.347296 0.601535i −0.0172573 0.0298905i
\(406\) 0 0
\(407\) −31.4338 −1.55811
\(408\) 0 0
\(409\) −14.8871 25.7853i −0.736121 1.27500i −0.954230 0.299075i \(-0.903322\pi\)
0.218109 0.975924i \(-0.430011\pi\)
\(410\) 0 0
\(411\) −5.34998 −0.263895
\(412\) 0 0
\(413\) 0.623608 1.08012i 0.0306857 0.0531493i
\(414\) 0 0
\(415\) 0.256711 0.444637i 0.0126015 0.0218264i
\(416\) 0 0
\(417\) −13.9513 −0.683198
\(418\) 0 0
\(419\) 40.1147 1.95973 0.979867 0.199653i \(-0.0639815\pi\)
0.979867 + 0.199653i \(0.0639815\pi\)
\(420\) 0 0
\(421\) −17.0155 + 29.4717i −0.829284 + 1.43636i 0.0693170 + 0.997595i \(0.477918\pi\)
−0.898601 + 0.438767i \(0.855415\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 33.9608 1.64734
\(426\) 0 0
\(427\) 0.0594300 + 0.102936i 0.00287602 + 0.00498141i
\(428\) 0 0
\(429\) −4.82295 −0.232854
\(430\) 0 0
\(431\) 5.12836 + 8.88257i 0.247024 + 0.427858i 0.962699 0.270575i \(-0.0872140\pi\)
−0.715675 + 0.698434i \(0.753881\pi\)
\(432\) 0 0
\(433\) −15.9979 27.7092i −0.768812 1.33162i −0.938208 0.346073i \(-0.887515\pi\)
0.169396 0.985548i \(-0.445818\pi\)
\(434\) 0 0
\(435\) −3.51754 + 6.09256i −0.168653 + 0.292116i
\(436\) 0 0
\(437\) 0.800660 2.91987i 0.0383007 0.139677i
\(438\) 0 0
\(439\) 6.05943 10.4952i 0.289201 0.500911i −0.684418 0.729089i \(-0.739944\pi\)
0.973619 + 0.228179i \(0.0732771\pi\)
\(440\) 0 0
\(441\) 3.45336 + 5.98140i 0.164446 + 0.284829i
\(442\) 0 0
\(443\) 2.45336 + 4.24935i 0.116563 + 0.201893i 0.918403 0.395645i \(-0.129479\pi\)
−0.801841 + 0.597538i \(0.796146\pi\)
\(444\) 0 0
\(445\) −0.571614 −0.0270971
\(446\) 0 0
\(447\) −5.34730 9.26179i −0.252918 0.438068i
\(448\) 0 0
\(449\) −6.12836 −0.289215 −0.144607 0.989489i \(-0.546192\pi\)
−0.144607 + 0.989489i \(0.546192\pi\)
\(450\) 0 0
\(451\) 12.9959 22.5095i 0.611952 1.05993i
\(452\) 0 0
\(453\) −8.82295 + 15.2818i −0.414538 + 0.718001i
\(454\) 0 0
\(455\) −0.212134 −0.00994498
\(456\) 0 0
\(457\) 29.9959 1.40315 0.701574 0.712597i \(-0.252481\pi\)
0.701574 + 0.712597i \(0.252481\pi\)
\(458\) 0 0
\(459\) 3.75877 6.51038i 0.175444 0.303879i
\(460\) 0 0
\(461\) 8.53983 14.7914i 0.397740 0.688905i −0.595707 0.803202i \(-0.703128\pi\)
0.993447 + 0.114297i \(0.0364614\pi\)
\(462\) 0 0
\(463\) −28.3756 −1.31872 −0.659362 0.751825i \(-0.729174\pi\)
−0.659362 + 0.751825i \(0.729174\pi\)
\(464\) 0 0
\(465\) −0.633103 1.09657i −0.0293595 0.0508521i
\(466\) 0 0
\(467\) −6.61081 −0.305912 −0.152956 0.988233i \(-0.548879\pi\)
−0.152956 + 0.988233i \(0.548879\pi\)
\(468\) 0 0
\(469\) 1.19459 + 2.06910i 0.0551612 + 0.0955419i
\(470\) 0 0
\(471\) −7.95336 13.7756i −0.366472 0.634747i
\(472\) 0 0
\(473\) −8.90941 + 15.4316i −0.409655 + 0.709544i
\(474\) 0 0
\(475\) 5.20739 18.9905i 0.238931 0.871343i
\(476\) 0 0
\(477\) −2.71688 + 4.70578i −0.124397 + 0.215463i
\(478\) 0 0
\(479\) 5.45336 + 9.44550i 0.249171 + 0.431576i 0.963296 0.268442i \(-0.0865087\pi\)
−0.714125 + 0.700018i \(0.753175\pi\)
\(480\) 0 0
\(481\) −3.25877 5.64436i −0.148587 0.257360i
\(482\) 0 0
\(483\) 0.212134 0.00965242
\(484\) 0 0
\(485\) −3.78787 6.56078i −0.171998 0.297910i
\(486\) 0 0
\(487\) −11.8324 −0.536179 −0.268090 0.963394i \(-0.586392\pi\)
−0.268090 + 0.963394i \(0.586392\pi\)
\(488\) 0 0
\(489\) −1.08853 + 1.88538i −0.0492248 + 0.0852599i
\(490\) 0 0
\(491\) −7.45336 + 12.9096i −0.336366 + 0.582602i −0.983746 0.179565i \(-0.942531\pi\)
0.647381 + 0.762167i \(0.275864\pi\)
\(492\) 0 0
\(493\) −76.1403 −3.42919
\(494\) 0 0
\(495\) −3.34998 −0.150571
\(496\) 0 0
\(497\) −1.66550 + 2.88473i −0.0747077 + 0.129398i
\(498\) 0 0
\(499\) 19.9115 34.4877i 0.891360 1.54388i 0.0531141 0.998588i \(-0.483085\pi\)
0.838246 0.545292i \(-0.183581\pi\)
\(500\) 0 0
\(501\) 10.9513 0.489268
\(502\) 0 0
\(503\) −5.06418 8.77141i −0.225801 0.391098i 0.730759 0.682636i \(-0.239166\pi\)
−0.956559 + 0.291538i \(0.905833\pi\)
\(504\) 0 0
\(505\) 6.61081 0.294177
\(506\) 0 0
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 0 0
\(509\) −12.5175 21.6810i −0.554830 0.960994i −0.997917 0.0645153i \(-0.979450\pi\)
0.443086 0.896479i \(-0.353883\pi\)
\(510\) 0 0
\(511\) −0.670245 + 1.16090i −0.0296499 + 0.0513551i
\(512\) 0 0
\(513\) −3.06418 3.10013i −0.135287 0.136874i
\(514\) 0 0
\(515\) −0.800660 + 1.38678i −0.0352813 + 0.0611090i
\(516\) 0 0
\(517\) 14.4688 + 25.0608i 0.636339 + 1.10217i
\(518\) 0 0
\(519\) 5.06418 + 8.77141i 0.222293 + 0.385022i
\(520\) 0 0
\(521\) 23.9162 1.04779 0.523894 0.851783i \(-0.324479\pi\)
0.523894 + 0.851783i \(0.324479\pi\)
\(522\) 0 0
\(523\) −18.4290 31.9200i −0.805845 1.39576i −0.915719 0.401818i \(-0.868378\pi\)
0.109875 0.993945i \(-0.464955\pi\)
\(524\) 0 0
\(525\) 1.37969 0.0602146
\(526\) 0 0
\(527\) 6.85204 11.8681i 0.298480 0.516982i
\(528\) 0 0
\(529\) 11.2588 19.5008i 0.489512 0.847859i
\(530\) 0 0
\(531\) 4.08378 0.177221
\(532\) 0 0
\(533\) 5.38919 0.233432
\(534\) 0 0
\(535\) 3.30541 5.72513i 0.142905 0.247519i
\(536\) 0 0
\(537\) 4.34730 7.52974i 0.187600 0.324932i
\(538\) 0 0
\(539\) 33.3108 1.43480
\(540\) 0 0
\(541\) −11.2101 19.4164i −0.481959 0.834777i 0.517827 0.855485i \(-0.326741\pi\)
−0.999786 + 0.0207084i \(0.993408\pi\)
\(542\) 0 0
\(543\) 7.87164 0.337805
\(544\) 0 0
\(545\) −4.69459 8.13127i −0.201094 0.348305i
\(546\) 0 0
\(547\) −3.18779 5.52141i −0.136300 0.236078i 0.789793 0.613373i \(-0.210188\pi\)
−0.926093 + 0.377295i \(0.876854\pi\)
\(548\) 0 0
\(549\) −0.194593 + 0.337044i −0.00830501 + 0.0143847i
\(550\) 0 0
\(551\) −11.6750 + 42.5768i −0.497371 + 1.81383i
\(552\) 0 0
\(553\) −2.20409 + 3.81759i −0.0937274 + 0.162341i
\(554\) 0 0
\(555\) −2.26352 3.92053i −0.0960810 0.166417i
\(556\) 0 0
\(557\) 8.97090 + 15.5381i 0.380109 + 0.658369i 0.991078 0.133286i \(-0.0425530\pi\)
−0.610968 + 0.791655i \(0.709220\pi\)
\(558\) 0 0
\(559\) −3.69459 −0.156265
\(560\) 0 0
\(561\) −18.1284 31.3992i −0.765380 1.32568i
\(562\) 0 0
\(563\) 17.5175 0.738276 0.369138 0.929375i \(-0.379653\pi\)
0.369138 + 0.929375i \(0.379653\pi\)
\(564\) 0 0
\(565\) 7.32089 12.6802i 0.307992 0.533458i
\(566\) 0 0
\(567\) 0.152704 0.264490i 0.00641295 0.0111076i
\(568\) 0 0
\(569\) 12.6810 0.531614 0.265807 0.964026i \(-0.414362\pi\)
0.265807 + 0.964026i \(0.414362\pi\)
\(570\) 0 0
\(571\) −39.0256 −1.63317 −0.816585 0.577225i \(-0.804135\pi\)
−0.816585 + 0.577225i \(0.804135\pi\)
\(572\) 0 0
\(573\) 6.92902 12.0014i 0.289464 0.501366i
\(574\) 0 0
\(575\) −1.56893 + 2.71746i −0.0654287 + 0.113326i
\(576\) 0 0
\(577\) 28.2959 1.17797 0.588987 0.808142i \(-0.299527\pi\)
0.588987 + 0.808142i \(0.299527\pi\)
\(578\) 0 0
\(579\) −1.04664 1.81283i −0.0434967 0.0753386i
\(580\) 0 0
\(581\) 0.225748 0.00936560
\(582\) 0 0
\(583\) 13.1034 + 22.6957i 0.542686 + 0.939961i
\(584\) 0 0
\(585\) −0.347296 0.601535i −0.0143589 0.0248704i
\(586\) 0 0
\(587\) 12.8648 22.2826i 0.530989 0.919699i −0.468357 0.883539i \(-0.655154\pi\)
0.999346 0.0361602i \(-0.0115127\pi\)
\(588\) 0 0
\(589\) −5.58584 5.65138i −0.230160 0.232861i
\(590\) 0 0
\(591\) −7.02229 + 12.1630i −0.288858 + 0.500317i
\(592\) 0 0
\(593\) 6.49525 + 11.2501i 0.266728 + 0.461987i 0.968015 0.250893i \(-0.0807241\pi\)
−0.701287 + 0.712879i \(0.747391\pi\)
\(594\) 0 0
\(595\) −0.797362 1.38107i −0.0326886 0.0566184i
\(596\) 0 0
\(597\) 21.9905 0.900011
\(598\) 0 0
\(599\) −5.18984 8.98908i −0.212051 0.367284i 0.740305 0.672271i \(-0.234681\pi\)
−0.952356 + 0.304987i \(0.901348\pi\)
\(600\) 0 0
\(601\) −7.29591 −0.297606 −0.148803 0.988867i \(-0.547542\pi\)
−0.148803 + 0.988867i \(0.547542\pi\)
\(602\) 0 0
\(603\) −3.91147 + 6.77487i −0.159288 + 0.275894i
\(604\) 0 0
\(605\) −4.25814 + 7.37532i −0.173118 + 0.299849i
\(606\) 0 0
\(607\) −39.1147 −1.58762 −0.793809 0.608167i \(-0.791905\pi\)
−0.793809 + 0.608167i \(0.791905\pi\)
\(608\) 0 0
\(609\) −3.09327 −0.125346
\(610\) 0 0
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) 0 0
\(613\) −20.3209 + 35.1968i −0.820753 + 1.42159i 0.0843693 + 0.996435i \(0.473112\pi\)
−0.905122 + 0.425151i \(0.860221\pi\)
\(614\) 0 0
\(615\) 3.74329 0.150944
\(616\) 0 0
\(617\) 8.38238 + 14.5187i 0.337462 + 0.584501i 0.983955 0.178419i \(-0.0570983\pi\)
−0.646493 + 0.762920i \(0.723765\pi\)
\(618\) 0 0
\(619\) 14.0797 0.565909 0.282955 0.959133i \(-0.408685\pi\)
0.282955 + 0.959133i \(0.408685\pi\)
\(620\) 0 0
\(621\) 0.347296 + 0.601535i 0.0139365 + 0.0241388i
\(622\) 0 0
\(623\) −0.125667 0.217662i −0.00503475 0.00872044i
\(624\) 0 0
\(625\) −8.99794 + 15.5849i −0.359918 + 0.623396i
\(626\) 0 0
\(627\) −20.3378 + 5.32256i −0.812214 + 0.212562i
\(628\) 0 0
\(629\) 24.4979 42.4317i 0.976797 1.69186i
\(630\) 0 0
\(631\) 10.4486 + 18.0975i 0.415953 + 0.720451i 0.995528 0.0944674i \(-0.0301148\pi\)
−0.579575 + 0.814919i \(0.696781\pi\)
\(632\) 0 0
\(633\) −7.97565 13.8142i −0.317004 0.549067i
\(634\) 0 0
\(635\) −6.52166 −0.258804
\(636\) 0 0
\(637\) 3.45336 + 5.98140i 0.136827 + 0.236992i
\(638\) 0 0
\(639\) −10.9067 −0.431463
\(640\) 0 0
\(641\) −1.69459 + 2.93512i −0.0669324 + 0.115930i −0.897550 0.440914i \(-0.854655\pi\)
0.830617 + 0.556844i \(0.187988\pi\)
\(642\) 0 0
\(643\) −8.82770 + 15.2900i −0.348130 + 0.602979i −0.985917 0.167233i \(-0.946517\pi\)
0.637787 + 0.770213i \(0.279850\pi\)
\(644\) 0 0
\(645\) −2.56624 −0.101045
\(646\) 0 0
\(647\) 16.6500 0.654580 0.327290 0.944924i \(-0.393865\pi\)
0.327290 + 0.944924i \(0.393865\pi\)
\(648\) 0 0
\(649\) 9.84793 17.0571i 0.386565 0.669550i
\(650\) 0 0
\(651\) 0.278371 0.482152i 0.0109102 0.0188970i
\(652\) 0 0
\(653\) −35.5877 −1.39265 −0.696327 0.717724i \(-0.745184\pi\)
−0.696327 + 0.717724i \(0.745184\pi\)
\(654\) 0 0
\(655\) −2.82295 4.88949i −0.110302 0.191048i
\(656\) 0 0
\(657\) −4.38919 −0.171238
\(658\) 0 0
\(659\) 20.4561 + 35.4309i 0.796855 + 1.38019i 0.921655 + 0.388011i \(0.126838\pi\)
−0.124800 + 0.992182i \(0.539829\pi\)
\(660\) 0 0
\(661\) 0.645897 + 1.11873i 0.0251225 + 0.0435134i 0.878313 0.478085i \(-0.158669\pi\)
−0.853191 + 0.521599i \(0.825336\pi\)
\(662\) 0 0
\(663\) 3.75877 6.51038i 0.145979 0.252842i
\(664\) 0 0
\(665\) −0.894543 + 0.234109i −0.0346889 + 0.00907834i
\(666\) 0 0
\(667\) 3.51754 6.09256i 0.136200 0.235905i
\(668\) 0 0
\(669\) −13.2520 22.9531i −0.512351 0.887417i
\(670\) 0 0
\(671\) 0.938511 + 1.62555i 0.0362308 + 0.0627536i
\(672\) 0 0
\(673\) 7.99588 0.308219 0.154109 0.988054i \(-0.450749\pi\)
0.154109 + 0.988054i \(0.450749\pi\)
\(674\) 0 0
\(675\) 2.25877 + 3.91231i 0.0869401 + 0.150585i
\(676\) 0 0
\(677\) 46.7701 1.79752 0.898761 0.438439i \(-0.144468\pi\)
0.898761 + 0.438439i \(0.144468\pi\)
\(678\) 0 0
\(679\) 1.66550 2.88473i 0.0639159 0.110706i
\(680\) 0 0
\(681\) 1.32770 2.29964i 0.0508774 0.0881223i
\(682\) 0 0
\(683\) 5.69047 0.217740 0.108870 0.994056i \(-0.465277\pi\)
0.108870 + 0.994056i \(0.465277\pi\)
\(684\) 0 0
\(685\) −3.71606 −0.141983
\(686\) 0 0
\(687\) −10.6284 + 18.4089i −0.405497 + 0.702342i
\(688\) 0 0
\(689\) −2.71688 + 4.70578i −0.103505 + 0.179276i
\(690\) 0 0
\(691\) 28.8485 1.09745 0.548725 0.836003i \(-0.315113\pi\)
0.548725 + 0.836003i \(0.315113\pi\)
\(692\) 0 0
\(693\) −0.736482 1.27562i −0.0279766 0.0484569i
\(694\) 0 0
\(695\) −9.69047 −0.367581
\(696\) 0 0
\(697\) 20.2567 + 35.0857i 0.767278 + 1.32896i
\(698\) 0 0
\(699\) −6.75877 11.7065i −0.255640 0.442782i
\(700\) 0 0
\(701\) 22.7716 39.4415i 0.860070 1.48969i −0.0117902 0.999930i \(-0.503753\pi\)
0.871860 0.489755i \(-0.162914\pi\)
\(702\) 0 0
\(703\) −19.9709 20.2052i −0.753217 0.762055i
\(704\) 0 0
\(705\) −2.08378 + 3.60921i −0.0784796 + 0.135931i
\(706\) 0 0
\(707\) 1.45336 + 2.51730i 0.0546593 + 0.0946728i
\(708\) 0 0
\(709\) 15.1013 + 26.1563i 0.567142 + 0.982319i 0.996847 + 0.0793493i \(0.0252842\pi\)
−0.429705 + 0.902969i \(0.641382\pi\)
\(710\) 0 0
\(711\) −14.4338 −0.541308
\(712\) 0 0
\(713\) 0.633103 + 1.09657i 0.0237099 + 0.0410668i
\(714\) 0 0
\(715\) −3.34998 −0.125282
\(716\) 0 0
\(717\) −12.2344 + 21.1906i −0.456903 + 0.791379i
\(718\) 0 0
\(719\) −18.0770 + 31.3102i −0.674157 + 1.16767i 0.302557 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214543i \(0.931174\pi\)
\(720\) 0 0
\(721\) −0.704088 −0.0262216
\(722\) 0 0
\(723\) 11.8675 0.441358
\(724\) 0 0
\(725\) 22.8776 39.6252i 0.849654 1.47164i
\(726\) 0 0
\(727\) −3.65064 + 6.32310i −0.135395 + 0.234511i −0.925748 0.378140i \(-0.876564\pi\)
0.790353 + 0.612651i \(0.209897\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −13.8871 24.0532i −0.513634 0.889640i
\(732\) 0 0
\(733\) 51.4986 1.90214 0.951071 0.308972i \(-0.0999849\pi\)
0.951071 + 0.308972i \(0.0999849\pi\)
\(734\) 0 0
\(735\) 2.39868 + 4.15464i 0.0884767 + 0.153246i
\(736\) 0 0
\(737\) 18.8648 + 32.6749i 0.694895 + 1.20359i
\(738\) 0 0
\(739\) 16.3452 28.3108i 0.601269 1.04143i −0.391360 0.920238i \(-0.627995\pi\)
0.992629 0.121191i \(-0.0386714\pi\)
\(740\) 0 0
\(741\) −3.06418 3.10013i −0.112565 0.113886i
\(742\) 0 0
\(743\) −22.7965 + 39.4848i −0.836324 + 1.44856i 0.0566239 + 0.998396i \(0.481966\pi\)
−0.892948 + 0.450160i \(0.851367\pi\)
\(744\) 0 0
\(745\) −3.71419 6.43317i −0.136078 0.235693i
\(746\) 0 0
\(747\) 0.369585 + 0.640140i 0.0135224 + 0.0234215i
\(748\) 0 0
\(749\) 2.90673 0.106209
\(750\) 0 0
\(751\) −9.15270 15.8529i −0.333987 0.578482i 0.649303 0.760530i \(-0.275061\pi\)
−0.983290 + 0.182048i \(0.941727\pi\)
\(752\) 0 0
\(753\) −7.38919 −0.269277
\(754\) 0 0
\(755\) −6.12836 + 10.6146i −0.223034 + 0.386306i
\(756\) 0 0
\(757\) 15.7121 27.2142i 0.571067 0.989117i −0.425390 0.905010i \(-0.639863\pi\)
0.996457 0.0841071i \(-0.0268038\pi\)
\(758\) 0 0
\(759\) 3.34998 0.121597
\(760\) 0 0
\(761\) 38.5580 1.39773 0.698863 0.715255i \(-0.253690\pi\)
0.698863 + 0.715255i \(0.253690\pi\)
\(762\) 0 0
\(763\) 2.06418 3.57526i 0.0747283 0.129433i
\(764\) 0 0
\(765\) 2.61081 4.52206i 0.0943942 0.163496i
\(766\) 0 0
\(767\) 4.08378 0.147457
\(768\) 0 0
\(769\) −7.37164 12.7681i −0.265828 0.460428i 0.701952 0.712224i \(-0.252312\pi\)
−0.967780 + 0.251796i \(0.918979\pi\)
\(770\) 0 0
\(771\) 5.34461 0.192481
\(772\) 0 0
\(773\) 1.95130 + 3.37976i 0.0701835 + 0.121561i 0.898982 0.437986i \(-0.144308\pi\)
−0.828798 + 0.559548i \(0.810975\pi\)
\(774\) 0 0
\(775\) 4.11762 + 7.13193i 0.147909 + 0.256186i
\(776\) 0 0
\(777\) 0.995252 1.72383i 0.0357045 0.0618420i
\(778\) 0 0
\(779\) 22.7256 5.94745i 0.814228 0.213090i
\(780\) 0 0
\(781\) −26.3013 + 45.5552i −0.941134 + 1.63009i
\(782\) 0 0
\(783\) −5.06418 8.77141i −0.180979 0.313465i
\(784\) 0 0
\(785\) −5.52435 9.56845i −0.197172 0.341513i
\(786\) 0 0
\(787\) 10.7879 0.384546 0.192273 0.981341i \(-0.438414\pi\)
0.192273 + 0.981341i \(0.438414\pi\)
\(788\) 0 0
\(789\) −12.0642 20.8958i −0.429496 0.743909i
\(790\) 0 0
\(791\) 6.43788 0.228905
\(792\) 0 0
\(793\) −0.194593 + 0.337044i −0.00691019 + 0.0119688i
\(794\) 0 0