Properties

Label 720.2.q.i.241.1
Level $720$
Weight $2$
Character 720.241
Analytic conductor $5.749$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 241.1
Root \(0.403374 - 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 720.241
Dual form 720.2.q.i.481.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.25707 - 1.19154i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.257068 + 0.445256i) q^{7} +(0.160442 + 2.99571i) q^{9} +O(q^{10})\) \(q+(-1.25707 - 1.19154i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.257068 + 0.445256i) q^{7} +(0.160442 + 2.99571i) q^{9} +(-1.66044 + 2.87597i) q^{11} +(0.660442 + 1.14392i) q^{13} +(-0.403374 + 1.68443i) q^{15} -3.32088 q^{17} +1.32088 q^{19} +(0.853695 - 0.253408i) q^{21} +(2.06382 + 3.57463i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.36783 - 3.95698i) q^{27} +(0.693252 - 1.20075i) q^{29} +(4.36783 + 7.56531i) q^{31} +(5.51414 - 1.63680i) q^{33} +0.514137 q^{35} +0.292611 q^{37} +(0.532810 - 2.22493i) q^{39} +(5.67458 + 9.82866i) q^{41} +(5.17458 - 8.96263i) q^{43} +(2.51414 - 1.63680i) q^{45} +(-2.43165 + 4.21174i) q^{47} +(3.36783 + 5.83326i) q^{49} +(4.17458 + 3.95698i) q^{51} -5.02827 q^{53} +3.32088 q^{55} +(-1.66044 - 1.57389i) q^{57} +(-2.51414 - 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} +(-1.37510 - 0.698664i) q^{63} +(0.660442 - 1.14392i) q^{65} +(4.72426 + 8.18266i) q^{67} +(1.66498 - 6.95269i) q^{69} -8.99093 q^{71} +6.05655 q^{73} +(1.66044 - 0.492881i) q^{75} +(-0.853695 - 1.47864i) q^{77} +(-4.02827 + 6.97717i) q^{79} +(-8.94852 + 0.961276i) q^{81} +(0.771205 - 1.33577i) q^{83} +(1.66044 + 2.87597i) q^{85} +(-2.30221 + 0.683382i) q^{87} -3.00000 q^{89} -0.679116 q^{91} +(3.52374 - 14.7146i) q^{93} +(-0.660442 - 1.14392i) q^{95} +(6.12763 - 10.6134i) q^{97} +(-8.88197 - 4.51277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9} - 2 q^{11} - 4 q^{13} - q^{15} - 4 q^{17} - 8 q^{19} + 3 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 8 q^{31} + 20 q^{33} - 10 q^{35} + 12 q^{37} + 14 q^{39} + 13 q^{41} + 10 q^{43} + 2 q^{45} + 13 q^{47} + 2 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{55} - 2 q^{57} - 2 q^{59} - q^{61} - 33 q^{63} - 4 q^{65} + 11 q^{67} + 39 q^{69} + 20 q^{71} - 16 q^{73} + 2 q^{75} + 2 q^{79} - 19 q^{81} - 15 q^{83} + 2 q^{85} + 26 q^{87} - 18 q^{89} - 20 q^{91} - 42 q^{93} + 4 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.25707 1.19154i −0.725769 0.687939i
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −0.257068 + 0.445256i −0.0971627 + 0.168291i −0.910509 0.413489i \(-0.864310\pi\)
0.813346 + 0.581780i \(0.197643\pi\)
\(8\) 0 0
\(9\) 0.160442 + 2.99571i 0.0534807 + 0.998569i
\(10\) 0 0
\(11\) −1.66044 + 2.87597i −0.500642 + 0.867138i 0.499358 + 0.866396i \(0.333569\pi\)
−1.00000 0.000741679i \(0.999764\pi\)
\(12\) 0 0
\(13\) 0.660442 + 1.14392i 0.183174 + 0.317266i 0.942960 0.332907i \(-0.108030\pi\)
−0.759786 + 0.650173i \(0.774696\pi\)
\(14\) 0 0
\(15\) −0.403374 + 1.68443i −0.104151 + 0.434917i
\(16\) 0 0
\(17\) −3.32088 −0.805433 −0.402716 0.915325i \(-0.631934\pi\)
−0.402716 + 0.915325i \(0.631934\pi\)
\(18\) 0 0
\(19\) 1.32088 0.303032 0.151516 0.988455i \(-0.451585\pi\)
0.151516 + 0.988455i \(0.451585\pi\)
\(20\) 0 0
\(21\) 0.853695 0.253408i 0.186291 0.0552982i
\(22\) 0 0
\(23\) 2.06382 + 3.57463i 0.430335 + 0.745363i 0.996902 0.0786532i \(-0.0250620\pi\)
−0.566567 + 0.824016i \(0.691729\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 3.36783 3.95698i 0.648139 0.761522i
\(28\) 0 0
\(29\) 0.693252 1.20075i 0.128734 0.222973i −0.794453 0.607326i \(-0.792242\pi\)
0.923186 + 0.384353i \(0.125575\pi\)
\(30\) 0 0
\(31\) 4.36783 + 7.56531i 0.784486 + 1.35877i 0.929306 + 0.369311i \(0.120406\pi\)
−0.144820 + 0.989458i \(0.546260\pi\)
\(32\) 0 0
\(33\) 5.51414 1.63680i 0.959888 0.284930i
\(34\) 0 0
\(35\) 0.514137 0.0869050
\(36\) 0 0
\(37\) 0.292611 0.0481049 0.0240524 0.999711i \(-0.492343\pi\)
0.0240524 + 0.999711i \(0.492343\pi\)
\(38\) 0 0
\(39\) 0.532810 2.22493i 0.0853179 0.356274i
\(40\) 0 0
\(41\) 5.67458 + 9.82866i 0.886220 + 1.53498i 0.844308 + 0.535857i \(0.180012\pi\)
0.0419119 + 0.999121i \(0.486655\pi\)
\(42\) 0 0
\(43\) 5.17458 8.96263i 0.789116 1.36679i −0.137393 0.990517i \(-0.543872\pi\)
0.926509 0.376272i \(-0.122794\pi\)
\(44\) 0 0
\(45\) 2.51414 1.63680i 0.374785 0.244000i
\(46\) 0 0
\(47\) −2.43165 + 4.21174i −0.354692 + 0.614345i −0.987065 0.160319i \(-0.948748\pi\)
0.632373 + 0.774664i \(0.282081\pi\)
\(48\) 0 0
\(49\) 3.36783 + 5.83326i 0.481119 + 0.833322i
\(50\) 0 0
\(51\) 4.17458 + 3.95698i 0.584558 + 0.554088i
\(52\) 0 0
\(53\) −5.02827 −0.690687 −0.345343 0.938476i \(-0.612238\pi\)
−0.345343 + 0.938476i \(0.612238\pi\)
\(54\) 0 0
\(55\) 3.32088 0.447788
\(56\) 0 0
\(57\) −1.66044 1.57389i −0.219931 0.208467i
\(58\) 0 0
\(59\) −2.51414 4.35461i −0.327313 0.566922i 0.654665 0.755919i \(-0.272810\pi\)
−0.981978 + 0.188997i \(0.939476\pi\)
\(60\) 0 0
\(61\) −3.67458 + 6.36456i −0.470482 + 0.814898i −0.999430 0.0337558i \(-0.989253\pi\)
0.528948 + 0.848654i \(0.322586\pi\)
\(62\) 0 0
\(63\) −1.37510 0.698664i −0.173246 0.0880234i
\(64\) 0 0
\(65\) 0.660442 1.14392i 0.0819178 0.141886i
\(66\) 0 0
\(67\) 4.72426 + 8.18266i 0.577160 + 0.999670i 0.995803 + 0.0915197i \(0.0291724\pi\)
−0.418643 + 0.908151i \(0.637494\pi\)
\(68\) 0 0
\(69\) 1.66498 6.95269i 0.200440 0.837005i
\(70\) 0 0
\(71\) −8.99093 −1.06703 −0.533513 0.845792i \(-0.679129\pi\)
−0.533513 + 0.845792i \(0.679129\pi\)
\(72\) 0 0
\(73\) 6.05655 0.708865 0.354433 0.935082i \(-0.384674\pi\)
0.354433 + 0.935082i \(0.384674\pi\)
\(74\) 0 0
\(75\) 1.66044 0.492881i 0.191731 0.0569130i
\(76\) 0 0
\(77\) −0.853695 1.47864i −0.0972875 0.168507i
\(78\) 0 0
\(79\) −4.02827 + 6.97717i −0.453216 + 0.784994i −0.998584 0.0532036i \(-0.983057\pi\)
0.545367 + 0.838197i \(0.316390\pi\)
\(80\) 0 0
\(81\) −8.94852 + 0.961276i −0.994280 + 0.106808i
\(82\) 0 0
\(83\) 0.771205 1.33577i 0.0846508 0.146619i −0.820592 0.571515i \(-0.806356\pi\)
0.905242 + 0.424896i \(0.139689\pi\)
\(84\) 0 0
\(85\) 1.66044 + 2.87597i 0.180100 + 0.311943i
\(86\) 0 0
\(87\) −2.30221 + 0.683382i −0.246823 + 0.0732662i
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) −0.679116 −0.0711906
\(92\) 0 0
\(93\) 3.52374 14.7146i 0.365395 1.52583i
\(94\) 0 0
\(95\) −0.660442 1.14392i −0.0677599 0.117364i
\(96\) 0 0
\(97\) 6.12763 10.6134i 0.622167 1.07762i −0.366915 0.930255i \(-0.619586\pi\)
0.989081 0.147370i \(-0.0470808\pi\)
\(98\) 0 0
\(99\) −8.88197 4.51277i −0.892671 0.453551i
\(100\) 0 0
\(101\) −5.83502 + 10.1066i −0.580606 + 1.00564i 0.414801 + 0.909912i \(0.363851\pi\)
−0.995408 + 0.0957276i \(0.969482\pi\)
\(102\) 0 0
\(103\) 0.146305 + 0.253408i 0.0144159 + 0.0249691i 0.873143 0.487464i \(-0.162078\pi\)
−0.858727 + 0.512433i \(0.828744\pi\)
\(104\) 0 0
\(105\) −0.646305 0.612617i −0.0630729 0.0597853i
\(106\) 0 0
\(107\) −1.87237 −0.181009 −0.0905043 0.995896i \(-0.528848\pi\)
−0.0905043 + 0.995896i \(0.528848\pi\)
\(108\) 0 0
\(109\) 5.54787 0.531390 0.265695 0.964057i \(-0.414399\pi\)
0.265695 + 0.964057i \(0.414399\pi\)
\(110\) 0 0
\(111\) −0.367832 0.348659i −0.0349130 0.0330932i
\(112\) 0 0
\(113\) −3.90064 6.75611i −0.366942 0.635561i 0.622144 0.782903i \(-0.286262\pi\)
−0.989086 + 0.147341i \(0.952928\pi\)
\(114\) 0 0
\(115\) 2.06382 3.57463i 0.192452 0.333336i
\(116\) 0 0
\(117\) −3.32088 + 2.16202i −0.307016 + 0.199879i
\(118\) 0 0
\(119\) 0.853695 1.47864i 0.0782581 0.135547i
\(120\) 0 0
\(121\) −0.0141369 0.0244859i −0.00128518 0.00222599i
\(122\) 0 0
\(123\) 4.57795 19.1168i 0.412780 1.72370i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −17.8916 −1.58762 −0.793810 0.608166i \(-0.791906\pi\)
−0.793810 + 0.608166i \(0.791906\pi\)
\(128\) 0 0
\(129\) −17.1842 + 5.10090i −1.51298 + 0.449109i
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) −0.339558 + 0.588131i −0.0294434 + 0.0509974i
\(134\) 0 0
\(135\) −5.11076 0.938136i −0.439864 0.0807419i
\(136\) 0 0
\(137\) −2.83502 + 4.91040i −0.242212 + 0.419524i −0.961344 0.275350i \(-0.911206\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(138\) 0 0
\(139\) 4.00000 + 6.92820i 0.339276 + 0.587643i 0.984297 0.176522i \(-0.0564848\pi\)
−0.645021 + 0.764165i \(0.723151\pi\)
\(140\) 0 0
\(141\) 8.07522 2.39703i 0.680056 0.201866i
\(142\) 0 0
\(143\) −4.38650 −0.366818
\(144\) 0 0
\(145\) −1.38650 −0.115143
\(146\) 0 0
\(147\) 2.71699 11.3457i 0.224094 0.935780i
\(148\) 0 0
\(149\) −8.83049 15.2948i −0.723422 1.25300i −0.959620 0.281298i \(-0.909235\pi\)
0.236199 0.971705i \(-0.424098\pi\)
\(150\) 0 0
\(151\) 0.632168 1.09495i 0.0514451 0.0891056i −0.839156 0.543891i \(-0.816951\pi\)
0.890601 + 0.454785i \(0.150284\pi\)
\(152\) 0 0
\(153\) −0.532810 9.94840i −0.0430752 0.804280i
\(154\) 0 0
\(155\) 4.36783 7.56531i 0.350833 0.607660i
\(156\) 0 0
\(157\) 7.83502 + 13.5707i 0.625303 + 1.08306i 0.988482 + 0.151337i \(0.0483579\pi\)
−0.363179 + 0.931719i \(0.618309\pi\)
\(158\) 0 0
\(159\) 6.32088 + 5.99141i 0.501279 + 0.475150i
\(160\) 0 0
\(161\) −2.12217 −0.167250
\(162\) 0 0
\(163\) −15.7074 −1.23030 −0.615149 0.788411i \(-0.710904\pi\)
−0.615149 + 0.788411i \(0.710904\pi\)
\(164\) 0 0
\(165\) −4.17458 3.95698i −0.324991 0.308051i
\(166\) 0 0
\(167\) 3.08249 + 5.33903i 0.238530 + 0.413146i 0.960293 0.278994i \(-0.0900011\pi\)
−0.721763 + 0.692141i \(0.756668\pi\)
\(168\) 0 0
\(169\) 5.62763 9.74734i 0.432895 0.749796i
\(170\) 0 0
\(171\) 0.211926 + 3.95698i 0.0162064 + 0.302598i
\(172\) 0 0
\(173\) −4.29261 + 7.43502i −0.326361 + 0.565274i −0.981787 0.189986i \(-0.939156\pi\)
0.655426 + 0.755260i \(0.272489\pi\)
\(174\) 0 0
\(175\) −0.257068 0.445256i −0.0194325 0.0336582i
\(176\) 0 0
\(177\) −2.02827 + 8.46975i −0.152454 + 0.636626i
\(178\) 0 0
\(179\) 1.06562 0.0796482 0.0398241 0.999207i \(-0.487320\pi\)
0.0398241 + 0.999207i \(0.487320\pi\)
\(180\) 0 0
\(181\) −12.6700 −0.941757 −0.470878 0.882198i \(-0.656063\pi\)
−0.470878 + 0.882198i \(0.656063\pi\)
\(182\) 0 0
\(183\) 12.2029 3.62226i 0.902061 0.267765i
\(184\) 0 0
\(185\) −0.146305 0.253408i −0.0107566 0.0186309i
\(186\) 0 0
\(187\) 5.51414 9.55077i 0.403234 0.698421i
\(188\) 0 0
\(189\) 0.896105 + 2.51676i 0.0651821 + 0.183067i
\(190\) 0 0
\(191\) −8.46719 + 14.6656i −0.612664 + 1.06117i 0.378125 + 0.925754i \(0.376569\pi\)
−0.990789 + 0.135411i \(0.956764\pi\)
\(192\) 0 0
\(193\) −13.3588 23.1380i −0.961585 1.66551i −0.718524 0.695502i \(-0.755182\pi\)
−0.243060 0.970011i \(-0.578151\pi\)
\(194\) 0 0
\(195\) −2.19325 + 0.651039i −0.157062 + 0.0466218i
\(196\) 0 0
\(197\) −14.2553 −1.01565 −0.507823 0.861462i \(-0.669550\pi\)
−0.507823 + 0.861462i \(0.669550\pi\)
\(198\) 0 0
\(199\) 24.6610 1.74817 0.874085 0.485773i \(-0.161462\pi\)
0.874085 + 0.485773i \(0.161462\pi\)
\(200\) 0 0
\(201\) 3.81128 15.9153i 0.268827 1.12258i
\(202\) 0 0
\(203\) 0.356427 + 0.617349i 0.0250162 + 0.0433294i
\(204\) 0 0
\(205\) 5.67458 9.82866i 0.396330 0.686463i
\(206\) 0 0
\(207\) −10.3774 + 6.75611i −0.721281 + 0.469582i
\(208\) 0 0
\(209\) −2.19325 + 3.79882i −0.151710 + 0.262770i
\(210\) 0 0
\(211\) −2.68872 4.65699i −0.185099 0.320601i 0.758511 0.651660i \(-0.225927\pi\)
−0.943610 + 0.331060i \(0.892594\pi\)
\(212\) 0 0
\(213\) 11.3022 + 10.7131i 0.774415 + 0.734049i
\(214\) 0 0
\(215\) −10.3492 −0.705807
\(216\) 0 0
\(217\) −4.49133 −0.304891
\(218\) 0 0
\(219\) −7.61350 7.21665i −0.514472 0.487656i
\(220\) 0 0
\(221\) −2.19325 3.79882i −0.147534 0.255537i
\(222\) 0 0
\(223\) 4.33229 7.50375i 0.290112 0.502488i −0.683724 0.729740i \(-0.739641\pi\)
0.973836 + 0.227252i \(0.0729743\pi\)
\(224\) 0 0
\(225\) −2.67458 1.35891i −0.178305 0.0905938i
\(226\) 0 0
\(227\) 1.66044 2.87597i 0.110207 0.190885i −0.805646 0.592397i \(-0.798182\pi\)
0.915854 + 0.401512i \(0.131515\pi\)
\(228\) 0 0
\(229\) 12.6559 + 21.9207i 0.836326 + 1.44856i 0.892946 + 0.450163i \(0.148634\pi\)
−0.0566206 + 0.998396i \(0.518033\pi\)
\(230\) 0 0
\(231\) −0.688716 + 2.87597i −0.0453142 + 0.189225i
\(232\) 0 0
\(233\) 27.6327 1.81028 0.905139 0.425116i \(-0.139767\pi\)
0.905139 + 0.425116i \(0.139767\pi\)
\(234\) 0 0
\(235\) 4.86330 0.317246
\(236\) 0 0
\(237\) 13.3774 3.97092i 0.868958 0.257939i
\(238\) 0 0
\(239\) −2.09936 3.63620i −0.135796 0.235206i 0.790105 0.612971i \(-0.210026\pi\)
−0.925901 + 0.377765i \(0.876693\pi\)
\(240\) 0 0
\(241\) −1.80221 + 3.12152i −0.116091 + 0.201075i −0.918215 0.396082i \(-0.870370\pi\)
0.802125 + 0.597157i \(0.203703\pi\)
\(242\) 0 0
\(243\) 12.3943 + 9.45417i 0.795095 + 0.606485i
\(244\) 0 0
\(245\) 3.36783 5.83326i 0.215163 0.372673i
\(246\) 0 0
\(247\) 0.872368 + 1.51099i 0.0555074 + 0.0961417i
\(248\) 0 0
\(249\) −2.56108 + 0.760225i −0.162302 + 0.0481773i
\(250\) 0 0
\(251\) 6.87783 0.434125 0.217062 0.976158i \(-0.430352\pi\)
0.217062 + 0.976158i \(0.430352\pi\)
\(252\) 0 0
\(253\) −13.7074 −0.861776
\(254\) 0 0
\(255\) 1.33956 5.59378i 0.0838864 0.350296i
\(256\) 0 0
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 0 0
\(259\) −0.0752210 + 0.130287i −0.00467400 + 0.00809561i
\(260\) 0 0
\(261\) 3.70832 + 1.88413i 0.229539 + 0.116625i
\(262\) 0 0
\(263\) 3.11803 5.40059i 0.192266 0.333015i −0.753735 0.657179i \(-0.771750\pi\)
0.946001 + 0.324164i \(0.105083\pi\)
\(264\) 0 0
\(265\) 2.51414 + 4.35461i 0.154442 + 0.267502i
\(266\) 0 0
\(267\) 3.77121 + 3.57463i 0.230794 + 0.218764i
\(268\) 0 0
\(269\) 9.92345 0.605044 0.302522 0.953142i \(-0.402172\pi\)
0.302522 + 0.953142i \(0.402172\pi\)
\(270\) 0 0
\(271\) −6.60442 −0.401190 −0.200595 0.979674i \(-0.564288\pi\)
−0.200595 + 0.979674i \(0.564288\pi\)
\(272\) 0 0
\(273\) 0.853695 + 0.809197i 0.0516680 + 0.0489748i
\(274\) 0 0
\(275\) −1.66044 2.87597i −0.100128 0.173428i
\(276\) 0 0
\(277\) −11.3305 + 19.6250i −0.680783 + 1.17915i 0.293959 + 0.955818i \(0.405027\pi\)
−0.974742 + 0.223333i \(0.928306\pi\)
\(278\) 0 0
\(279\) −21.9627 + 14.2985i −1.31487 + 0.856031i
\(280\) 0 0
\(281\) 7.77394 13.4649i 0.463754 0.803246i −0.535390 0.844605i \(-0.679835\pi\)
0.999144 + 0.0413590i \(0.0131687\pi\)
\(282\) 0 0
\(283\) 0.322689 + 0.558913i 0.0191819 + 0.0332240i 0.875457 0.483296i \(-0.160561\pi\)
−0.856275 + 0.516520i \(0.827227\pi\)
\(284\) 0 0
\(285\) −0.532810 + 2.22493i −0.0315610 + 0.131794i
\(286\) 0 0
\(287\) −5.83502 −0.344430
\(288\) 0 0
\(289\) −5.97173 −0.351278
\(290\) 0 0
\(291\) −20.3492 + 6.04039i −1.19289 + 0.354094i
\(292\) 0 0
\(293\) 0.688716 + 1.19289i 0.0402352 + 0.0696895i 0.885442 0.464750i \(-0.153856\pi\)
−0.845207 + 0.534440i \(0.820523\pi\)
\(294\) 0 0
\(295\) −2.51414 + 4.35461i −0.146379 + 0.253535i
\(296\) 0 0
\(297\) 5.78807 + 16.2561i 0.335858 + 0.943276i
\(298\) 0 0
\(299\) −2.72606 + 4.72168i −0.157652 + 0.273062i
\(300\) 0 0
\(301\) 2.66044 + 4.60802i 0.153345 + 0.265602i
\(302\) 0 0
\(303\) 19.3774 5.75194i 1.11320 0.330440i
\(304\) 0 0
\(305\) 7.34916 0.420812
\(306\) 0 0
\(307\) 7.98546 0.455754 0.227877 0.973690i \(-0.426822\pi\)
0.227877 + 0.973690i \(0.426822\pi\)
\(308\) 0 0
\(309\) 0.118031 0.492881i 0.00671458 0.0280390i
\(310\) 0 0
\(311\) 4.81635 + 8.34216i 0.273110 + 0.473040i 0.969657 0.244471i \(-0.0786143\pi\)
−0.696547 + 0.717512i \(0.745281\pi\)
\(312\) 0 0
\(313\) 12.2685 21.2496i 0.693455 1.20110i −0.277244 0.960800i \(-0.589421\pi\)
0.970699 0.240300i \(-0.0772458\pi\)
\(314\) 0 0
\(315\) 0.0824893 + 1.54020i 0.00464774 + 0.0867806i
\(316\) 0 0
\(317\) 10.1746 17.6229i 0.571461 0.989800i −0.424955 0.905215i \(-0.639710\pi\)
0.996416 0.0845855i \(-0.0269566\pi\)
\(318\) 0 0
\(319\) 2.30221 + 3.98755i 0.128899 + 0.223260i
\(320\) 0 0
\(321\) 2.35369 + 2.23101i 0.131370 + 0.124523i
\(322\) 0 0
\(323\) −4.38650 −0.244072
\(324\) 0 0
\(325\) −1.32088 −0.0732695
\(326\) 0 0
\(327\) −6.97406 6.61054i −0.385666 0.365564i
\(328\) 0 0
\(329\) −1.25020 2.16541i −0.0689257 0.119383i
\(330\) 0 0
\(331\) 8.22153 14.2401i 0.451896 0.782707i −0.546608 0.837389i \(-0.684081\pi\)
0.998504 + 0.0546819i \(0.0174145\pi\)
\(332\) 0 0
\(333\) 0.0469471 + 0.876576i 0.00257269 + 0.0480360i
\(334\) 0 0
\(335\) 4.72426 8.18266i 0.258114 0.447066i
\(336\) 0 0
\(337\) −2.44852 4.24096i −0.133379 0.231020i 0.791598 0.611042i \(-0.209249\pi\)
−0.924977 + 0.380023i \(0.875916\pi\)
\(338\) 0 0
\(339\) −3.14683 + 13.1407i −0.170913 + 0.713704i
\(340\) 0 0
\(341\) −29.0101 −1.57099
\(342\) 0 0
\(343\) −7.06201 −0.381313
\(344\) 0 0
\(345\) −6.85369 + 2.03443i −0.368991 + 0.109530i
\(346\) 0 0
\(347\) 11.1372 + 19.2903i 0.597878 + 1.03556i 0.993134 + 0.116984i \(0.0373226\pi\)
−0.395256 + 0.918571i \(0.629344\pi\)
\(348\) 0 0
\(349\) 1.47173 2.54910i 0.0787797 0.136450i −0.823944 0.566671i \(-0.808231\pi\)
0.902724 + 0.430221i \(0.141564\pi\)
\(350\) 0 0
\(351\) 6.75073 + 1.23917i 0.360327 + 0.0661420i
\(352\) 0 0
\(353\) −9.41478 + 16.3069i −0.501098 + 0.867927i 0.498901 + 0.866659i \(0.333737\pi\)
−0.999999 + 0.00126845i \(0.999596\pi\)
\(354\) 0 0
\(355\) 4.49546 + 7.78637i 0.238594 + 0.413258i
\(356\) 0 0
\(357\) −2.83502 + 0.841540i −0.150045 + 0.0445390i
\(358\) 0 0
\(359\) 31.8770 1.68241 0.841203 0.540720i \(-0.181848\pi\)
0.841203 + 0.540720i \(0.181848\pi\)
\(360\) 0 0
\(361\) −17.2553 −0.908172
\(362\) 0 0
\(363\) −0.0114049 + 0.0476252i −0.000598604 + 0.00249968i
\(364\) 0 0
\(365\) −3.02827 5.24512i −0.158507 0.274542i
\(366\) 0 0
\(367\) −9.17458 + 15.8908i −0.478909 + 0.829495i −0.999708 0.0241848i \(-0.992301\pi\)
0.520798 + 0.853680i \(0.325634\pi\)
\(368\) 0 0
\(369\) −28.5333 + 18.5763i −1.48539 + 0.967044i
\(370\) 0 0
\(371\) 1.29261 2.23887i 0.0671090 0.116236i
\(372\) 0 0
\(373\) 1.09936 + 1.90414i 0.0569226 + 0.0985929i 0.893083 0.449893i \(-0.148538\pi\)
−0.836160 + 0.548486i \(0.815205\pi\)
\(374\) 0 0
\(375\) −1.25707 1.19154i −0.0649147 0.0615311i
\(376\) 0 0
\(377\) 1.83141 0.0943226
\(378\) 0 0
\(379\) −15.4713 −0.794709 −0.397354 0.917665i \(-0.630072\pi\)
−0.397354 + 0.917665i \(0.630072\pi\)
\(380\) 0 0
\(381\) 22.4909 + 21.3186i 1.15225 + 1.09219i
\(382\) 0 0
\(383\) 3.85369 + 6.67479i 0.196915 + 0.341066i 0.947526 0.319677i \(-0.103574\pi\)
−0.750612 + 0.660743i \(0.770241\pi\)
\(384\) 0 0
\(385\) −0.853695 + 1.47864i −0.0435083 + 0.0753586i
\(386\) 0 0
\(387\) 27.6796 + 14.0635i 1.40704 + 0.714890i
\(388\) 0 0
\(389\) 12.3163 21.3325i 0.624464 1.08160i −0.364181 0.931328i \(-0.618651\pi\)
0.988644 0.150274i \(-0.0480157\pi\)
\(390\) 0 0
\(391\) −6.85369 11.8709i −0.346606 0.600340i
\(392\) 0 0
\(393\) −2.42024 + 10.1066i −0.122085 + 0.509808i
\(394\) 0 0
\(395\) 8.05655 0.405369
\(396\) 0 0
\(397\) −6.77301 −0.339928 −0.169964 0.985450i \(-0.554365\pi\)
−0.169964 + 0.985450i \(0.554365\pi\)
\(398\) 0 0
\(399\) 1.12763 0.334723i 0.0564522 0.0167571i
\(400\) 0 0
\(401\) 9.24980 + 16.0211i 0.461913 + 0.800057i 0.999056 0.0434343i \(-0.0138299\pi\)
−0.537143 + 0.843491i \(0.680497\pi\)
\(402\) 0 0
\(403\) −5.76940 + 9.99290i −0.287394 + 0.497782i
\(404\) 0 0
\(405\) 5.30675 + 7.26900i 0.263694 + 0.361200i
\(406\) 0 0
\(407\) −0.485863 + 0.841540i −0.0240833 + 0.0417136i
\(408\) 0 0
\(409\) 6.70739 + 11.6175i 0.331659 + 0.574450i 0.982837 0.184474i \(-0.0590583\pi\)
−0.651178 + 0.758925i \(0.725725\pi\)
\(410\) 0 0
\(411\) 9.41478 2.79466i 0.464397 0.137850i
\(412\) 0 0
\(413\) 2.58522 0.127210
\(414\) 0 0
\(415\) −1.54241 −0.0757140
\(416\) 0 0
\(417\) 3.22699 13.4754i 0.158026 0.659893i
\(418\) 0 0
\(419\) −16.5575 28.6784i −0.808886 1.40103i −0.913636 0.406532i \(-0.866738\pi\)
0.104751 0.994499i \(-0.466596\pi\)
\(420\) 0 0
\(421\) 7.34916 12.7291i 0.358176 0.620379i −0.629480 0.777017i \(-0.716732\pi\)
0.987656 + 0.156637i \(0.0500654\pi\)
\(422\) 0 0
\(423\) −13.0073 6.60876i −0.632435 0.321329i
\(424\) 0 0
\(425\) 1.66044 2.87597i 0.0805433 0.139505i
\(426\) 0 0
\(427\) −1.88924 3.27225i −0.0914266 0.158355i
\(428\) 0 0
\(429\) 5.51414 + 5.22672i 0.266225 + 0.252348i
\(430\) 0 0
\(431\) 32.7549 1.57775 0.788873 0.614556i \(-0.210665\pi\)
0.788873 + 0.614556i \(0.210665\pi\)
\(432\) 0 0
\(433\) −11.8314 −0.568581 −0.284291 0.958738i \(-0.591758\pi\)
−0.284291 + 0.958738i \(0.591758\pi\)
\(434\) 0 0
\(435\) 1.74293 + 1.65208i 0.0835672 + 0.0792113i
\(436\) 0 0
\(437\) 2.72606 + 4.72168i 0.130405 + 0.225869i
\(438\) 0 0
\(439\) 4.15591 7.19824i 0.198351 0.343553i −0.749643 0.661842i \(-0.769775\pi\)
0.947994 + 0.318289i \(0.103108\pi\)
\(440\) 0 0
\(441\) −16.9344 + 11.0249i −0.806399 + 0.524997i
\(442\) 0 0
\(443\) −14.5876 + 25.2664i −0.693076 + 1.20044i 0.277750 + 0.960654i \(0.410411\pi\)
−0.970825 + 0.239789i \(0.922922\pi\)
\(444\) 0 0
\(445\) 1.50000 + 2.59808i 0.0711068 + 0.123161i
\(446\) 0 0
\(447\) −7.12397 + 29.7486i −0.336952 + 1.40706i
\(448\) 0 0
\(449\) 18.9717 0.895331 0.447666 0.894201i \(-0.352256\pi\)
0.447666 + 0.894201i \(0.352256\pi\)
\(450\) 0 0
\(451\) −37.6892 −1.77472
\(452\) 0 0
\(453\) −2.09936 + 0.623167i −0.0986365 + 0.0292790i
\(454\) 0 0
\(455\) 0.339558 + 0.588131i 0.0159187 + 0.0275720i
\(456\) 0 0
\(457\) 11.6176 20.1223i 0.543450 0.941283i −0.455253 0.890362i \(-0.650451\pi\)
0.998703 0.0509206i \(-0.0162155\pi\)
\(458\) 0 0
\(459\) −11.1842 + 13.1407i −0.522033 + 0.613354i
\(460\) 0 0
\(461\) −2.21285 + 3.83277i −0.103063 + 0.178510i −0.912945 0.408082i \(-0.866198\pi\)
0.809882 + 0.586592i \(0.199531\pi\)
\(462\) 0 0
\(463\) −9.75434 16.8950i −0.453322 0.785178i 0.545268 0.838262i \(-0.316428\pi\)
−0.998590 + 0.0530845i \(0.983095\pi\)
\(464\) 0 0
\(465\) −14.5051 + 4.30564i −0.672656 + 0.199669i
\(466\) 0 0
\(467\) 24.5935 1.13805 0.569026 0.822320i \(-0.307321\pi\)
0.569026 + 0.822320i \(0.307321\pi\)
\(468\) 0 0
\(469\) −4.85783 −0.224314
\(470\) 0 0
\(471\) 6.32088 26.3950i 0.291251 1.21622i
\(472\) 0 0
\(473\) 17.1842 + 29.7639i 0.790129 + 1.36854i
\(474\) 0 0
\(475\) −0.660442 + 1.14392i −0.0303032 + 0.0524866i
\(476\) 0 0
\(477\) −0.806748 15.0632i −0.0369384 0.689698i
\(478\) 0 0
\(479\) 16.3774 28.3665i 0.748304 1.29610i −0.200331 0.979728i \(-0.564202\pi\)
0.948635 0.316372i \(-0.102465\pi\)
\(480\) 0 0
\(481\) 0.193252 + 0.334723i 0.00881155 + 0.0152621i
\(482\) 0 0
\(483\) 2.66771 + 2.52866i 0.121385 + 0.115058i
\(484\) 0 0
\(485\) −12.2553 −0.556483
\(486\) 0 0
\(487\) 6.03735 0.273578 0.136789 0.990600i \(-0.456322\pi\)
0.136789 + 0.990600i \(0.456322\pi\)
\(488\) 0 0
\(489\) 19.7453 + 18.7161i 0.892912 + 0.846369i
\(490\) 0 0
\(491\) 7.22153 + 12.5081i 0.325903 + 0.564480i 0.981695 0.190461i \(-0.0609984\pi\)
−0.655792 + 0.754942i \(0.727665\pi\)
\(492\) 0 0
\(493\) −2.30221 + 3.98755i −0.103686 + 0.179590i
\(494\) 0 0
\(495\) 0.532810 + 9.94840i 0.0239480 + 0.447147i
\(496\) 0 0
\(497\) 2.31128 4.00326i 0.103675 0.179571i
\(498\) 0 0
\(499\) 10.4859 + 18.1620i 0.469412 + 0.813045i 0.999388 0.0349673i \(-0.0111327\pi\)
−0.529977 + 0.848012i \(0.677799\pi\)
\(500\) 0 0
\(501\) 2.48679 10.3844i 0.111102 0.463943i
\(502\) 0 0
\(503\) 5.31728 0.237086 0.118543 0.992949i \(-0.462178\pi\)
0.118543 + 0.992949i \(0.462178\pi\)
\(504\) 0 0
\(505\) 11.6700 0.519310
\(506\) 0 0
\(507\) −18.6887 + 5.54750i −0.829995 + 0.246373i
\(508\) 0 0
\(509\) −9.11350 15.7850i −0.403949 0.699659i 0.590250 0.807221i \(-0.299029\pi\)
−0.994198 + 0.107561i \(0.965696\pi\)
\(510\) 0 0
\(511\) −1.55695 + 2.69671i −0.0688753 + 0.119296i
\(512\) 0 0
\(513\) 4.44852 5.22672i 0.196407 0.230765i
\(514\) 0 0
\(515\) 0.146305 0.253408i 0.00644698 0.0111665i
\(516\) 0 0
\(517\) −8.07522 13.9867i −0.355148 0.615134i
\(518\) 0 0
\(519\) 14.2553 4.23149i 0.625737 0.185742i
\(520\) 0 0
\(521\) 40.1232 1.75783 0.878915 0.476978i \(-0.158268\pi\)
0.878915 + 0.476978i \(0.158268\pi\)
\(522\) 0 0
\(523\) −18.9873 −0.830257 −0.415129 0.909763i \(-0.636263\pi\)
−0.415129 + 0.909763i \(0.636263\pi\)
\(524\) 0 0
\(525\) −0.207389 + 0.866025i −0.00905121 + 0.0377964i
\(526\) 0 0
\(527\) −14.5051 25.1235i −0.631851 1.09440i
\(528\) 0 0
\(529\) 2.98133 5.16381i 0.129623 0.224513i
\(530\) 0 0
\(531\) 12.6418 8.23028i 0.548606 0.357164i
\(532\) 0 0
\(533\) −7.49546 + 12.9825i −0.324665 + 0.562336i
\(534\) 0 0
\(535\) 0.936184 + 1.62152i 0.0404748 + 0.0701043i
\(536\) 0 0
\(537\) −1.33956 1.26973i −0.0578062 0.0547931i
\(538\) 0 0
\(539\) −22.3684 −0.963473
\(540\) 0 0
\(541\) 16.5279 0.710589 0.355294 0.934754i \(-0.384381\pi\)
0.355294 + 0.934754i \(0.384381\pi\)
\(542\) 0 0
\(543\) 15.9271 + 15.0969i 0.683498 + 0.647871i
\(544\) 0 0
\(545\) −2.77394 4.80460i −0.118822 0.205806i
\(546\) 0 0
\(547\) 8.83683 15.3058i 0.377835 0.654430i −0.612912 0.790151i \(-0.710002\pi\)
0.990747 + 0.135721i \(0.0433352\pi\)
\(548\) 0 0
\(549\) −19.6559 9.98682i −0.838894 0.426227i
\(550\) 0 0
\(551\) 0.915706 1.58605i 0.0390104 0.0675680i
\(552\) 0 0
\(553\) −2.07108 3.58722i −0.0880715 0.152544i
\(554\) 0 0
\(555\) −0.118031 + 0.492881i −0.00501016 + 0.0209216i
\(556\) 0 0
\(557\) 17.3401 0.734723 0.367362 0.930078i \(-0.380261\pi\)
0.367362 + 0.930078i \(0.380261\pi\)
\(558\) 0 0
\(559\) 13.6700 0.578181
\(560\) 0 0
\(561\) −18.3118 + 5.43563i −0.773125 + 0.229492i
\(562\) 0 0
\(563\) 6.49727 + 11.2536i 0.273827 + 0.474283i 0.969839 0.243748i \(-0.0783770\pi\)
−0.696011 + 0.718031i \(0.745044\pi\)
\(564\) 0 0
\(565\) −3.90064 + 6.75611i −0.164101 + 0.284232i
\(566\) 0 0
\(567\) 1.87237 4.23149i 0.0786321 0.177706i
\(568\) 0 0
\(569\) 8.34009 14.4455i 0.349635 0.605585i −0.636550 0.771236i \(-0.719639\pi\)
0.986184 + 0.165651i \(0.0529724\pi\)
\(570\) 0 0
\(571\) 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i \(-0.0292272\pi\)
−0.577301 + 0.816532i \(0.695894\pi\)
\(572\) 0 0
\(573\) 28.1186 8.34663i 1.17467 0.348686i
\(574\) 0 0
\(575\) −4.12763 −0.172134
\(576\) 0 0
\(577\) −23.5953 −0.982287 −0.491144 0.871079i \(-0.663421\pi\)
−0.491144 + 0.871079i \(0.663421\pi\)
\(578\) 0 0
\(579\) −10.7771 + 45.0037i −0.447883 + 1.87029i
\(580\) 0 0
\(581\) 0.396505 + 0.686767i 0.0164498 + 0.0284919i
\(582\) 0 0
\(583\) 8.34916 14.4612i 0.345787 0.598920i
\(584\) 0 0
\(585\) 3.53281 + 1.79496i 0.146064 + 0.0742124i
\(586\) 0 0
\(587\) 14.0638 24.3592i 0.580476 1.00541i −0.414947 0.909846i \(-0.636200\pi\)
0.995423 0.0955681i \(-0.0304668\pi\)
\(588\) 0 0
\(589\) 5.76940 + 9.99290i 0.237724 + 0.411750i
\(590\) 0 0
\(591\) 17.9198 + 16.9858i 0.737124 + 0.698702i
\(592\) 0 0
\(593\) −9.17872 −0.376925 −0.188462 0.982080i \(-0.560350\pi\)
−0.188462 + 0.982080i \(0.560350\pi\)
\(594\) 0 0
\(595\) −1.70739 −0.0699961
\(596\) 0 0
\(597\) −31.0005 29.3846i −1.26877 1.20263i
\(598\) 0 0
\(599\) −15.7357 27.2550i −0.642942 1.11361i −0.984773 0.173846i \(-0.944380\pi\)
0.341831 0.939761i \(-0.388953\pi\)
\(600\) 0 0
\(601\) 14.6327 25.3446i 0.596880 1.03383i −0.396398 0.918079i \(-0.629740\pi\)
0.993279 0.115748i \(-0.0369265\pi\)
\(602\) 0 0
\(603\) −23.7549 + 15.4653i −0.967373 + 0.629797i
\(604\) 0 0
\(605\) −0.0141369 + 0.0244859i −0.000574748 + 0.000995493i
\(606\) 0 0
\(607\) −22.1017 38.2813i −0.897080 1.55379i −0.831209 0.555960i \(-0.812351\pi\)
−0.0658708 0.997828i \(-0.520983\pi\)
\(608\) 0 0
\(609\) 0.287546 1.20075i 0.0116520 0.0486568i
\(610\) 0 0
\(611\) −6.42385 −0.259881
\(612\) 0 0
\(613\) −35.1715 −1.42056 −0.710282 0.703918i \(-0.751432\pi\)
−0.710282 + 0.703918i \(0.751432\pi\)
\(614\) 0 0
\(615\) −18.8446 + 5.59378i −0.759889 + 0.225563i
\(616\) 0 0
\(617\) 3.71285 + 6.43085i 0.149474 + 0.258896i 0.931033 0.364935i \(-0.118909\pi\)
−0.781559 + 0.623831i \(0.785575\pi\)
\(618\) 0 0
\(619\) 4.27394 7.40268i 0.171784 0.297539i −0.767260 0.641337i \(-0.778380\pi\)
0.939044 + 0.343798i \(0.111714\pi\)
\(620\) 0 0
\(621\) 21.0953 + 3.87228i 0.846527 + 0.155389i
\(622\) 0 0
\(623\) 0.771205 1.33577i 0.0308977 0.0535164i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 7.28354 2.16202i 0.290876 0.0863429i
\(628\) 0 0
\(629\) −0.971726 −0.0387453
\(630\) 0 0
\(631\) 2.36836 0.0942829 0.0471415 0.998888i \(-0.484989\pi\)
0.0471415 + 0.998888i \(0.484989\pi\)
\(632\) 0 0
\(633\) −2.16912 + 9.05788i −0.0862146 + 0.360019i
\(634\) 0 0
\(635\) 8.94578 + 15.4946i 0.355003 + 0.614883i
\(636\) 0 0
\(637\) −4.44852 + 7.70506i −0.176257 + 0.305285i
\(638\) 0 0
\(639\) −1.44252 26.9342i −0.0570654 1.06550i
\(640\) 0 0
\(641\) 0.0665480 0.115265i 0.00262849 0.00455268i −0.864708 0.502275i \(-0.832497\pi\)
0.867337 + 0.497722i \(0.165830\pi\)
\(642\) 0 0
\(643\) −11.3232 19.6124i −0.446544 0.773437i 0.551614 0.834099i \(-0.314012\pi\)
−0.998158 + 0.0606623i \(0.980679\pi\)
\(644\) 0 0
\(645\) 13.0096 + 12.3315i 0.512253 + 0.485552i
\(646\) 0 0
\(647\) −46.3912 −1.82383 −0.911913 0.410385i \(-0.865394\pi\)
−0.911913 + 0.410385i \(0.865394\pi\)
\(648\) 0 0
\(649\) 16.6983 0.655466
\(650\) 0 0
\(651\) 5.64591 + 5.35162i 0.221280 + 0.209746i
\(652\) 0 0
\(653\) −18.2029 31.5283i −0.712333 1.23380i −0.963979 0.265977i \(-0.914305\pi\)
0.251647 0.967819i \(-0.419028\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) 0 0
\(657\) 0.971726 + 18.1436i 0.0379106 + 0.707851i
\(658\) 0 0
\(659\) 9.57068 16.5769i 0.372821 0.645745i −0.617177 0.786824i \(-0.711724\pi\)
0.989998 + 0.141079i \(0.0450572\pi\)
\(660\) 0 0
\(661\) −19.9536 34.5606i −0.776104 1.34425i −0.934172 0.356824i \(-0.883860\pi\)
0.158067 0.987428i \(-0.449474\pi\)
\(662\) 0 0
\(663\) −1.76940 + 7.38874i −0.0687178 + 0.286955i
\(664\) 0 0
\(665\) 0.679116 0.0263350
\(666\) 0 0
\(667\) 5.72298 0.221595
\(668\) 0 0
\(669\) −14.3870 + 4.27061i −0.556235 + 0.165111i
\(670\) 0 0
\(671\) −12.2029 21.1360i −0.471086 0.815945i
\(672\) 0 0
\(673\) −11.8254 + 20.4822i −0.455836 + 0.789532i −0.998736 0.0502658i \(-0.983993\pi\)
0.542899 + 0.839798i \(0.317326\pi\)
\(674\) 0 0
\(675\) 1.74293 + 4.89512i 0.0670855 + 0.188413i
\(676\) 0 0
\(677\) 7.40157 12.8199i 0.284465 0.492709i −0.688014 0.725697i \(-0.741517\pi\)
0.972479 + 0.232989i \(0.0748506\pi\)
\(678\) 0 0
\(679\) 3.15044 + 5.45673i 0.120903 + 0.209410i
\(680\) 0 0
\(681\) −5.51414 + 1.63680i −0.211302 + 0.0627223i
\(682\) 0 0
\(683\) 4.95252 0.189503 0.0947515 0.995501i \(-0.469794\pi\)
0.0947515 + 0.995501i \(0.469794\pi\)
\(684\) 0 0
\(685\) 5.67004 0.216641
\(686\) 0 0
\(687\) 10.2101 42.6359i 0.389540 1.62666i
\(688\) 0 0
\(689\) −3.32088 5.75194i −0.126516 0.219131i
\(690\) 0 0
\(691\) −9.60442 + 16.6353i −0.365369 + 0.632838i −0.988835 0.149012i \(-0.952391\pi\)
0.623466 + 0.781851i \(0.285724\pi\)
\(692\) 0 0
\(693\) 4.29261 2.79466i 0.163063 0.106160i
\(694\) 0 0
\(695\) 4.00000 6.92820i 0.151729 0.262802i
\(696\) 0 0
\(697\) −18.8446 32.6398i −0.713791 1.23632i
\(698\) 0 0
\(699\) −34.7362 32.9256i −1.31384 1.24536i
\(700\) 0 0
\(701\) −29.3492 −1.10850 −0.554251 0.832349i \(-0.686995\pi\)
−0.554251 + 0.832349i \(0.686995\pi\)
\(702\) 0 0
\(703\) 0.386505 0.0145773
\(704\) 0 0
\(705\) −6.11350 5.79483i −0.230248 0.218246i
\(706\) 0 0
\(707\) −3.00000 5.19615i −0.112827 0.195421i
\(708\) 0 0
\(709\) −19.3633 + 33.5382i −0.727204 + 1.25955i 0.230857 + 0.972988i \(0.425847\pi\)
−0.958060 + 0.286566i \(0.907486\pi\)
\(710\) 0 0
\(711\) −21.5479 10.9481i −0.808108 0.410586i
\(712\) 0 0
\(713\) −18.0288 + 31.2268i −0.675184 + 1.16945i
\(714\) 0 0
\(715\) 2.19325 + 3.79882i 0.0820230 + 0.142068i
\(716\) 0 0
\(717\) −1.69365 + 7.07243i −0.0632506 + 0.264125i
\(718\) 0 0
\(719\) 15.0848 0.562569 0.281284 0.959624i \(-0.409240\pi\)
0.281284 + 0.959624i \(0.409240\pi\)
\(720\) 0 0
\(721\) −0.150442 −0.00560275
\(722\) 0 0
\(723\) 5.98494 1.77655i 0.222582 0.0660706i
\(724\) 0 0
\(725\) 0.693252 + 1.20075i 0.0257467 + 0.0445947i
\(726\) 0 0
\(727\) 6.17277 10.6916i 0.228936 0.396528i −0.728557 0.684985i \(-0.759809\pi\)
0.957493 + 0.288457i \(0.0931422\pi\)
\(728\) 0 0
\(729\) −4.31542 26.6529i −0.159830 0.987144i
\(730\) 0 0
\(731\) −17.1842 + 29.7639i −0.635580 + 1.10086i
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) 0 0
\(735\) −11.1842 + 3.31988i −0.412535 + 0.122456i
\(736\) 0 0
\(737\) −31.3774 −1.15580
\(738\) 0 0
\(739\) −29.7266 −1.09351 −0.546755 0.837293i \(-0.684137\pi\)
−0.546755 + 0.837293i \(0.684137\pi\)
\(740\) 0 0
\(741\) 0.703781 2.93888i 0.0258540 0.107962i
\(742\) 0 0
\(743\) 24.1824 + 41.8851i 0.887165 + 1.53662i 0.843212 + 0.537582i \(0.180662\pi\)
0.0439537 + 0.999034i \(0.486005\pi\)
\(744\) 0 0
\(745\) −8.83049 + 15.2948i −0.323524 + 0.560360i
\(746\) 0 0
\(747\) 4.12530 + 2.09599i 0.150937 + 0.0766883i
\(748\) 0 0
\(749\) 0.481327 0.833682i 0.0175873 0.0304621i
\(750\) 0 0
\(751\) −15.9102 27.5573i −0.580573 1.00558i −0.995411 0.0956869i \(-0.969495\pi\)
0.414838 0.909895i \(-0.363838\pi\)
\(752\) 0 0
\(753\) −8.64591 8.19524i −0.315074 0.298651i
\(754\) 0 0
\(755\) −1.26434 −0.0460139
\(756\) 0 0
\(757\) 4.94531 0.179740 0.0898701 0.995953i \(-0.471355\pi\)
0.0898701 + 0.995953i \(0.471355\pi\)
\(758\) 0 0
\(759\) 17.2311 + 16.3330i 0.625450 + 0.592849i
\(760\) 0 0
\(761\) −17.7125 30.6789i −0.642076 1.11211i −0.984969 0.172734i \(-0.944740\pi\)
0.342893 0.939375i \(-0.388593\pi\)
\(762\) 0 0
\(763\) −1.42618 + 2.47022i −0.0516313 + 0.0894281i
\(764\) 0 0
\(765\) −8.34916 + 5.43563i −0.301864 + 0.196525i
\(766\) 0 0
\(767\) 3.32088 5.75194i 0.119910 0.207691i
\(768\) 0 0
\(769\) −24.7125 42.8032i −0.891154 1.54352i −0.838494 0.544911i \(-0.816563\pi\)
−0.0526602 0.998612i \(-0.516770\pi\)
\(770\) 0 0
\(771\) 7.26073 30.3197i 0.261489 1.09194i
\(772\) 0 0
\(773\) 12.6599 0.455345 0.227673 0.973738i \(-0.426888\pi\)
0.227673 + 0.973738i \(0.426888\pi\)
\(774\) 0 0
\(775\) −8.73566 −0.313794
\(776\) 0 0
\(777\) 0.249800 0.0741499i 0.00896153 0.00266011i
\(778\) 0 0
\(779\) 7.49546 + 12.9825i 0.268553 + 0.465147i
\(780\) 0 0
\(781\) 14.9289 25.8576i 0.534199 0.925259i
\(782\) 0 0
\(783\) −2.41658 6.78711i −0.0863616 0.242551i
\(784\) 0 0
\(785\) 7.83502 13.5707i 0.279644 0.484357i
\(786\) 0 0
\(787\) 15.4672 + 26.7900i 0.551346 + 0.954959i 0.998178 + 0.0603410i \(0.0192188\pi\)
−0.446832 + 0.894618i \(0.647448\pi\)
\(788\) 0 0
\(789\) −10.3546 + 3.07364i −0.368634 + 0.109424i
\(790\) 0 0
\(791\) 4.01093 0.142612
\(792\) 0 0
\(793\) −9.70739 −0.344720
\(794\) 0