Properties

Label 1152.2.i.k.769.2
Level $1152$
Weight $2$
Character 1152.769
Analytic conductor $9.199$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 769.2
Root \(1.19051 + 1.25805i\) of defining polynomial
Character \(\chi\) \(=\) 1152.769
Dual form 1152.2.i.k.385.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.494250 - 1.66004i) q^{3} +(0.268104 - 0.464369i) q^{5} +(2.35014 + 4.07056i) q^{7} +(-2.51143 + 1.64095i) q^{9} +O(q^{10})\) \(q+(-0.494250 - 1.66004i) q^{3} +(0.268104 - 0.464369i) q^{5} +(2.35014 + 4.07056i) q^{7} +(-2.51143 + 1.64095i) q^{9} +(-2.59922 - 4.50198i) q^{11} +(-0.778295 + 1.34805i) q^{13} +(-0.903379 - 0.215547i) q^{15} +0.695781 q^{17} +5.80593 q^{19} +(5.59572 - 5.91320i) q^{21} +(4.42809 - 7.66967i) q^{23} +(2.35624 + 4.08113i) q^{25} +(3.96530 + 3.35803i) q^{27} +(1.92199 + 3.32898i) q^{29} +(2.77035 - 4.79840i) q^{31} +(-6.18878 + 6.53990i) q^{33} +2.52033 q^{35} +4.09280 q^{37} +(2.62248 + 0.625725i) q^{39} +(1.01019 - 1.74970i) q^{41} +(-3.71522 - 6.43494i) q^{43} +(0.0886801 + 1.60618i) q^{45} +(-0.186066 - 0.322275i) q^{47} +(-7.54633 + 13.0706i) q^{49} +(-0.343890 - 1.15502i) q^{51} +5.30777 q^{53} -2.78744 q^{55} +(-2.86958 - 9.63804i) q^{57} +(-2.57152 + 4.45401i) q^{59} +(-0.921988 - 1.59693i) q^{61} +(-12.5818 - 6.36650i) q^{63} +(0.417328 + 0.722833i) q^{65} +(5.79316 - 10.0340i) q^{67} +(-14.9205 - 3.56004i) q^{69} +10.6289 q^{71} +4.40840 q^{73} +(5.61024 - 5.92854i) q^{75} +(12.2171 - 21.1606i) q^{77} +(3.32244 + 5.75464i) q^{79} +(3.61459 - 8.24225i) q^{81} +(5.28055 + 9.14617i) q^{83} +(0.186541 - 0.323099i) q^{85} +(4.57628 - 4.83592i) q^{87} -7.30777 q^{89} -7.31642 q^{91} +(-9.33475 - 2.22728i) q^{93} +(1.55659 - 2.69609i) q^{95} +(-7.81612 - 13.5379i) q^{97} +(13.9153 + 7.04125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + 4 q^{11} + 10 q^{13} + 4 q^{15} + 4 q^{17} + 4 q^{19} + 2 q^{21} + 8 q^{23} - 14 q^{25} - 14 q^{27} - 2 q^{29} + 8 q^{31} - 10 q^{33} + 8 q^{35} + 22 q^{39} - 2 q^{41} - 2 q^{43} + 10 q^{45} - 14 q^{47} - 18 q^{49} - 38 q^{51} + 24 q^{53} - 16 q^{55} - 38 q^{57} + 6 q^{59} + 14 q^{61} - 16 q^{63} - 8 q^{65} + 4 q^{67} - 50 q^{69} - 28 q^{71} + 60 q^{73} + 50 q^{75} + 2 q^{77} + 16 q^{79} + 22 q^{81} + 24 q^{83} + 16 q^{85} - 36 q^{87} - 48 q^{89} - 52 q^{91} + 42 q^{93} - 20 q^{95} - 14 q^{97} + 68 q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.494250 1.66004i −0.285356 0.958422i
\(4\) 0 0
\(5\) 0.268104 0.464369i 0.119900 0.207672i −0.799828 0.600229i \(-0.795076\pi\)
0.919728 + 0.392557i \(0.128409\pi\)
\(6\) 0 0
\(7\) 2.35014 + 4.07056i 0.888270 + 1.53853i 0.841919 + 0.539604i \(0.181426\pi\)
0.0463510 + 0.998925i \(0.485241\pi\)
\(8\) 0 0
\(9\) −2.51143 + 1.64095i −0.837144 + 0.546982i
\(10\) 0 0
\(11\) −2.59922 4.50198i −0.783695 1.35740i −0.929776 0.368126i \(-0.879999\pi\)
0.146081 0.989273i \(-0.453334\pi\)
\(12\) 0 0
\(13\) −0.778295 + 1.34805i −0.215860 + 0.373881i −0.953538 0.301272i \(-0.902589\pi\)
0.737678 + 0.675153i \(0.235922\pi\)
\(14\) 0 0
\(15\) −0.903379 0.215547i −0.233252 0.0556540i
\(16\) 0 0
\(17\) 0.695781 0.168752 0.0843759 0.996434i \(-0.473110\pi\)
0.0843759 + 0.996434i \(0.473110\pi\)
\(18\) 0 0
\(19\) 5.80593 1.33197 0.665986 0.745965i \(-0.268011\pi\)
0.665986 + 0.745965i \(0.268011\pi\)
\(20\) 0 0
\(21\) 5.59572 5.91320i 1.22109 1.29037i
\(22\) 0 0
\(23\) 4.42809 7.66967i 0.923320 1.59924i 0.129079 0.991634i \(-0.458798\pi\)
0.794241 0.607603i \(-0.207869\pi\)
\(24\) 0 0
\(25\) 2.35624 + 4.08113i 0.471248 + 0.816226i
\(26\) 0 0
\(27\) 3.96530 + 3.35803i 0.763123 + 0.646253i
\(28\) 0 0
\(29\) 1.92199 + 3.32898i 0.356904 + 0.618176i 0.987442 0.157982i \(-0.0504989\pi\)
−0.630538 + 0.776159i \(0.717166\pi\)
\(30\) 0 0
\(31\) 2.77035 4.79840i 0.497570 0.861817i −0.502426 0.864620i \(-0.667559\pi\)
0.999996 + 0.00280317i \(0.000892278\pi\)
\(32\) 0 0
\(33\) −6.18878 + 6.53990i −1.07733 + 1.13845i
\(34\) 0 0
\(35\) 2.52033 0.426013
\(36\) 0 0
\(37\) 4.09280 0.672852 0.336426 0.941710i \(-0.390782\pi\)
0.336426 + 0.941710i \(0.390782\pi\)
\(38\) 0 0
\(39\) 2.62248 + 0.625725i 0.419933 + 0.100196i
\(40\) 0 0
\(41\) 1.01019 1.74970i 0.157765 0.273258i −0.776297 0.630367i \(-0.782904\pi\)
0.934063 + 0.357109i \(0.116238\pi\)
\(42\) 0 0
\(43\) −3.71522 6.43494i −0.566565 0.981319i −0.996902 0.0786512i \(-0.974939\pi\)
0.430337 0.902668i \(-0.358395\pi\)
\(44\) 0 0
\(45\) 0.0886801 + 1.60618i 0.0132197 + 0.239435i
\(46\) 0 0
\(47\) −0.186066 0.322275i −0.0271404 0.0470086i 0.852136 0.523320i \(-0.175307\pi\)
−0.879277 + 0.476311i \(0.841973\pi\)
\(48\) 0 0
\(49\) −7.54633 + 13.0706i −1.07805 + 1.86723i
\(50\) 0 0
\(51\) −0.343890 1.15502i −0.0481542 0.161735i
\(52\) 0 0
\(53\) 5.30777 0.729078 0.364539 0.931188i \(-0.381227\pi\)
0.364539 + 0.931188i \(0.381227\pi\)
\(54\) 0 0
\(55\) −2.78744 −0.375859
\(56\) 0 0
\(57\) −2.86958 9.63804i −0.380085 1.27659i
\(58\) 0 0
\(59\) −2.57152 + 4.45401i −0.334784 + 0.579862i −0.983443 0.181216i \(-0.941997\pi\)
0.648660 + 0.761079i \(0.275330\pi\)
\(60\) 0 0
\(61\) −0.921988 1.59693i −0.118049 0.204466i 0.800946 0.598737i \(-0.204330\pi\)
−0.918994 + 0.394271i \(0.870997\pi\)
\(62\) 0 0
\(63\) −12.5818 6.36650i −1.58516 0.802103i
\(64\) 0 0
\(65\) 0.417328 + 0.722833i 0.0517631 + 0.0896564i
\(66\) 0 0
\(67\) 5.79316 10.0340i 0.707747 1.22585i −0.257944 0.966160i \(-0.583045\pi\)
0.965691 0.259694i \(-0.0836218\pi\)
\(68\) 0 0
\(69\) −14.9205 3.56004i −1.79622 0.428579i
\(70\) 0 0
\(71\) 10.6289 1.26142 0.630708 0.776021i \(-0.282765\pi\)
0.630708 + 0.776021i \(0.282765\pi\)
\(72\) 0 0
\(73\) 4.40840 0.515964 0.257982 0.966150i \(-0.416943\pi\)
0.257982 + 0.966150i \(0.416943\pi\)
\(74\) 0 0
\(75\) 5.61024 5.92854i 0.647815 0.684569i
\(76\) 0 0
\(77\) 12.2171 21.1606i 1.39227 2.41147i
\(78\) 0 0
\(79\) 3.32244 + 5.75464i 0.373804 + 0.647448i 0.990147 0.140030i \(-0.0447199\pi\)
−0.616343 + 0.787478i \(0.711387\pi\)
\(80\) 0 0
\(81\) 3.61459 8.24225i 0.401622 0.915806i
\(82\) 0 0
\(83\) 5.28055 + 9.14617i 0.579615 + 1.00392i 0.995523 + 0.0945164i \(0.0301305\pi\)
−0.415908 + 0.909407i \(0.636536\pi\)
\(84\) 0 0
\(85\) 0.186541 0.323099i 0.0202333 0.0350450i
\(86\) 0 0
\(87\) 4.57628 4.83592i 0.490629 0.518465i
\(88\) 0 0
\(89\) −7.30777 −0.774622 −0.387311 0.921949i \(-0.626596\pi\)
−0.387311 + 0.921949i \(0.626596\pi\)
\(90\) 0 0
\(91\) −7.31642 −0.766969
\(92\) 0 0
\(93\) −9.33475 2.22728i −0.967969 0.230958i
\(94\) 0 0
\(95\) 1.55659 2.69609i 0.159703 0.276613i
\(96\) 0 0
\(97\) −7.81612 13.5379i −0.793607 1.37457i −0.923720 0.383068i \(-0.874867\pi\)
0.130113 0.991499i \(-0.458466\pi\)
\(98\) 0 0
\(99\) 13.9153 + 7.04125i 1.39854 + 0.707672i
\(100\) 0 0
\(101\) −4.43218 7.67676i −0.441018 0.763866i 0.556747 0.830682i \(-0.312049\pi\)
−0.997765 + 0.0668159i \(0.978716\pi\)
\(102\) 0 0
\(103\) 1.64986 2.85764i 0.162565 0.281571i −0.773223 0.634135i \(-0.781356\pi\)
0.935788 + 0.352563i \(0.114690\pi\)
\(104\) 0 0
\(105\) −1.24567 4.18383i −0.121565 0.408300i
\(106\) 0 0
\(107\) −7.12139 −0.688451 −0.344226 0.938887i \(-0.611858\pi\)
−0.344226 + 0.938887i \(0.611858\pi\)
\(108\) 0 0
\(109\) 2.98862 0.286258 0.143129 0.989704i \(-0.454284\pi\)
0.143129 + 0.989704i \(0.454284\pi\)
\(110\) 0 0
\(111\) −2.02287 6.79419i −0.192002 0.644876i
\(112\) 0 0
\(113\) 3.40833 5.90340i 0.320629 0.555345i −0.659989 0.751275i \(-0.729439\pi\)
0.980618 + 0.195930i \(0.0627725\pi\)
\(114\) 0 0
\(115\) −2.37437 4.11253i −0.221411 0.383496i
\(116\) 0 0
\(117\) −0.257435 4.66267i −0.0237999 0.431064i
\(118\) 0 0
\(119\) 1.63518 + 2.83222i 0.149897 + 0.259629i
\(120\) 0 0
\(121\) −8.01190 + 13.8770i −0.728355 + 1.26155i
\(122\) 0 0
\(123\) −3.40386 0.812162i −0.306915 0.0732302i
\(124\) 0 0
\(125\) 5.20790 0.465809
\(126\) 0 0
\(127\) −17.7567 −1.57565 −0.787826 0.615899i \(-0.788793\pi\)
−0.787826 + 0.615899i \(0.788793\pi\)
\(128\) 0 0
\(129\) −8.84598 + 9.34786i −0.778845 + 0.823033i
\(130\) 0 0
\(131\) −3.51253 + 6.08389i −0.306892 + 0.531552i −0.977681 0.210096i \(-0.932622\pi\)
0.670789 + 0.741648i \(0.265956\pi\)
\(132\) 0 0
\(133\) 13.6448 + 23.6334i 1.18315 + 2.04928i
\(134\) 0 0
\(135\) 2.62248 0.941065i 0.225707 0.0809940i
\(136\) 0 0
\(137\) 5.71048 + 9.89083i 0.487879 + 0.845031i 0.999903 0.0139402i \(-0.00443746\pi\)
−0.512024 + 0.858971i \(0.671104\pi\)
\(138\) 0 0
\(139\) 3.10659 5.38078i 0.263498 0.456392i −0.703671 0.710526i \(-0.748457\pi\)
0.967169 + 0.254134i \(0.0817905\pi\)
\(140\) 0 0
\(141\) −0.443025 + 0.468160i −0.0373094 + 0.0394262i
\(142\) 0 0
\(143\) 8.09185 0.676674
\(144\) 0 0
\(145\) 2.06117 0.171171
\(146\) 0 0
\(147\) 25.4275 + 6.06701i 2.09722 + 0.500399i
\(148\) 0 0
\(149\) −5.47858 + 9.48918i −0.448823 + 0.777384i −0.998310 0.0581186i \(-0.981490\pi\)
0.549487 + 0.835502i \(0.314823\pi\)
\(150\) 0 0
\(151\) 7.28439 + 12.6169i 0.592796 + 1.02675i 0.993854 + 0.110700i \(0.0353091\pi\)
−0.401058 + 0.916053i \(0.631358\pi\)
\(152\) 0 0
\(153\) −1.74741 + 1.14174i −0.141270 + 0.0923041i
\(154\) 0 0
\(155\) −1.48548 2.57293i −0.119317 0.206663i
\(156\) 0 0
\(157\) −7.66049 + 13.2684i −0.611373 + 1.05893i 0.379636 + 0.925136i \(0.376049\pi\)
−0.991009 + 0.133794i \(0.957284\pi\)
\(158\) 0 0
\(159\) −2.62337 8.81108i −0.208047 0.698764i
\(160\) 0 0
\(161\) 41.6265 3.28063
\(162\) 0 0
\(163\) −11.0724 −0.867258 −0.433629 0.901091i \(-0.642767\pi\)
−0.433629 + 0.901091i \(0.642767\pi\)
\(164\) 0 0
\(165\) 1.37769 + 4.62725i 0.107253 + 0.360231i
\(166\) 0 0
\(167\) −4.15607 + 7.19852i −0.321606 + 0.557039i −0.980820 0.194917i \(-0.937556\pi\)
0.659213 + 0.751956i \(0.270889\pi\)
\(168\) 0 0
\(169\) 5.28851 + 9.15997i 0.406809 + 0.704613i
\(170\) 0 0
\(171\) −14.5812 + 9.52721i −1.11505 + 0.728564i
\(172\) 0 0
\(173\) 0.0396656 + 0.0687029i 0.00301572 + 0.00522338i 0.867529 0.497386i \(-0.165707\pi\)
−0.864514 + 0.502609i \(0.832373\pi\)
\(174\) 0 0
\(175\) −11.0750 + 19.1825i −0.837191 + 1.45006i
\(176\) 0 0
\(177\) 8.66478 + 2.06742i 0.651285 + 0.155397i
\(178\) 0 0
\(179\) −20.8011 −1.55475 −0.777375 0.629038i \(-0.783449\pi\)
−0.777375 + 0.629038i \(0.783449\pi\)
\(180\) 0 0
\(181\) −5.13118 −0.381397 −0.190699 0.981649i \(-0.561075\pi\)
−0.190699 + 0.981649i \(0.561075\pi\)
\(182\) 0 0
\(183\) −2.19527 + 2.31982i −0.162279 + 0.171486i
\(184\) 0 0
\(185\) 1.09729 1.90057i 0.0806747 0.139733i
\(186\) 0 0
\(187\) −1.80849 3.13240i −0.132250 0.229063i
\(188\) 0 0
\(189\) −4.35005 + 24.0329i −0.316420 + 1.74813i
\(190\) 0 0
\(191\) −9.89085 17.1315i −0.715677 1.23959i −0.962698 0.270579i \(-0.912785\pi\)
0.247021 0.969010i \(-0.420548\pi\)
\(192\) 0 0
\(193\) 1.79574 3.11031i 0.129260 0.223885i −0.794130 0.607748i \(-0.792073\pi\)
0.923390 + 0.383863i \(0.125407\pi\)
\(194\) 0 0
\(195\) 0.993663 1.05004i 0.0711577 0.0751948i
\(196\) 0 0
\(197\) 1.71261 0.122019 0.0610093 0.998137i \(-0.480568\pi\)
0.0610093 + 0.998137i \(0.480568\pi\)
\(198\) 0 0
\(199\) 18.1299 1.28520 0.642598 0.766203i \(-0.277856\pi\)
0.642598 + 0.766203i \(0.277856\pi\)
\(200\) 0 0
\(201\) −19.5201 4.65752i −1.37684 0.328516i
\(202\) 0 0
\(203\) −9.03389 + 15.6472i −0.634055 + 1.09822i
\(204\) 0 0
\(205\) −0.541672 0.938204i −0.0378320 0.0655270i
\(206\) 0 0
\(207\) 1.46467 + 26.5281i 0.101802 + 1.84383i
\(208\) 0 0
\(209\) −15.0909 26.1382i −1.04386 1.80802i
\(210\) 0 0
\(211\) 0.734306 1.27186i 0.0505517 0.0875581i −0.839642 0.543140i \(-0.817235\pi\)
0.890194 + 0.455582i \(0.150569\pi\)
\(212\) 0 0
\(213\) −5.25332 17.6443i −0.359952 1.20897i
\(214\) 0 0
\(215\) −3.98425 −0.271724
\(216\) 0 0
\(217\) 26.0429 1.76791
\(218\) 0 0
\(219\) −2.17885 7.31809i −0.147233 0.494511i
\(220\) 0 0
\(221\) −0.541523 + 0.937946i −0.0364268 + 0.0630931i
\(222\) 0 0
\(223\) 9.57845 + 16.5904i 0.641420 + 1.11097i 0.985116 + 0.171891i \(0.0549878\pi\)
−0.343696 + 0.939081i \(0.611679\pi\)
\(224\) 0 0
\(225\) −12.6145 6.38302i −0.840964 0.425535i
\(226\) 0 0
\(227\) −5.92737 10.2665i −0.393414 0.681412i 0.599484 0.800387i \(-0.295373\pi\)
−0.992897 + 0.118975i \(0.962039\pi\)
\(228\) 0 0
\(229\) −1.57219 + 2.72311i −0.103893 + 0.179948i −0.913285 0.407320i \(-0.866463\pi\)
0.809392 + 0.587268i \(0.199797\pi\)
\(230\) 0 0
\(231\) −41.1656 9.82214i −2.70850 0.646250i
\(232\) 0 0
\(233\) −2.82935 −0.185357 −0.0926783 0.995696i \(-0.529543\pi\)
−0.0926783 + 0.995696i \(0.529543\pi\)
\(234\) 0 0
\(235\) −0.199539 −0.0130165
\(236\) 0 0
\(237\) 7.91079 8.35960i 0.513861 0.543015i
\(238\) 0 0
\(239\) 1.58766 2.74991i 0.102697 0.177877i −0.810098 0.586295i \(-0.800586\pi\)
0.912795 + 0.408418i \(0.133919\pi\)
\(240\) 0 0
\(241\) 6.63053 + 11.4844i 0.427110 + 0.739776i 0.996615 0.0822117i \(-0.0261984\pi\)
−0.569505 + 0.821988i \(0.692865\pi\)
\(242\) 0 0
\(243\) −15.4689 1.92662i −0.992333 0.123593i
\(244\) 0 0
\(245\) 4.04640 + 7.00857i 0.258515 + 0.447761i
\(246\) 0 0
\(247\) −4.51873 + 7.82666i −0.287520 + 0.497999i
\(248\) 0 0
\(249\) 12.5731 13.2864i 0.796785 0.841991i
\(250\) 0 0
\(251\) −3.06394 −0.193394 −0.0966970 0.995314i \(-0.530828\pi\)
−0.0966970 + 0.995314i \(0.530828\pi\)
\(252\) 0 0
\(253\) −46.0383 −2.89440
\(254\) 0 0
\(255\) −0.628554 0.149973i −0.0393616 0.00939170i
\(256\) 0 0
\(257\) 8.14120 14.1010i 0.507834 0.879595i −0.492125 0.870525i \(-0.663780\pi\)
0.999959 0.00907003i \(-0.00288712\pi\)
\(258\) 0 0
\(259\) 9.61866 + 16.6600i 0.597674 + 1.03520i
\(260\) 0 0
\(261\) −10.2896 5.20664i −0.636912 0.322283i
\(262\) 0 0
\(263\) 11.0730 + 19.1790i 0.682789 + 1.18262i 0.974126 + 0.226005i \(0.0725664\pi\)
−0.291337 + 0.956620i \(0.594100\pi\)
\(264\) 0 0
\(265\) 1.42303 2.46476i 0.0874162 0.151409i
\(266\) 0 0
\(267\) 3.61187 + 12.1312i 0.221043 + 0.742415i
\(268\) 0 0
\(269\) 31.7805 1.93769 0.968845 0.247667i \(-0.0796639\pi\)
0.968845 + 0.247667i \(0.0796639\pi\)
\(270\) 0 0
\(271\) 0.794033 0.0482341 0.0241170 0.999709i \(-0.492323\pi\)
0.0241170 + 0.999709i \(0.492323\pi\)
\(272\) 0 0
\(273\) 3.61614 + 12.1455i 0.218859 + 0.735080i
\(274\) 0 0
\(275\) 12.2488 21.2155i 0.738629 1.27934i
\(276\) 0 0
\(277\) 12.6085 + 21.8385i 0.757569 + 1.31215i 0.944087 + 0.329696i \(0.106946\pi\)
−0.186519 + 0.982451i \(0.559720\pi\)
\(278\) 0 0
\(279\) 0.916345 + 16.5969i 0.0548601 + 0.993628i
\(280\) 0 0
\(281\) −5.06672 8.77581i −0.302255 0.523521i 0.674391 0.738374i \(-0.264406\pi\)
−0.976646 + 0.214853i \(0.931073\pi\)
\(282\) 0 0
\(283\) 11.6766 20.2245i 0.694102 1.20222i −0.276380 0.961048i \(-0.589135\pi\)
0.970482 0.241172i \(-0.0775319\pi\)
\(284\) 0 0
\(285\) −5.24496 1.25145i −0.310684 0.0741295i
\(286\) 0 0
\(287\) 9.49637 0.560553
\(288\) 0 0
\(289\) −16.5159 −0.971523
\(290\) 0 0
\(291\) −18.6103 + 19.6662i −1.09095 + 1.15285i
\(292\) 0 0
\(293\) −13.1967 + 22.8573i −0.770959 + 1.33534i 0.166079 + 0.986112i \(0.446889\pi\)
−0.937038 + 0.349228i \(0.886444\pi\)
\(294\) 0 0
\(295\) 1.37887 + 2.38827i 0.0802809 + 0.139051i
\(296\) 0 0
\(297\) 4.81109 26.5800i 0.279168 1.54233i
\(298\) 0 0
\(299\) 6.89272 + 11.9385i 0.398616 + 0.690424i
\(300\) 0 0
\(301\) 17.4626 30.2461i 1.00653 1.74335i
\(302\) 0 0
\(303\) −10.5531 + 11.1518i −0.606259 + 0.640655i
\(304\) 0 0
\(305\) −0.988754 −0.0566159
\(306\) 0 0
\(307\) −21.6724 −1.23691 −0.618454 0.785821i \(-0.712241\pi\)
−0.618454 + 0.785821i \(0.712241\pi\)
\(308\) 0 0
\(309\) −5.55922 1.32643i −0.316253 0.0754582i
\(310\) 0 0
\(311\) 14.5448 25.1924i 0.824761 1.42853i −0.0773408 0.997005i \(-0.524643\pi\)
0.902102 0.431523i \(-0.142024\pi\)
\(312\) 0 0
\(313\) 3.52393 + 6.10363i 0.199185 + 0.344998i 0.948264 0.317482i \(-0.102837\pi\)
−0.749080 + 0.662480i \(0.769504\pi\)
\(314\) 0 0
\(315\) −6.32963 + 4.13572i −0.356634 + 0.233021i
\(316\) 0 0
\(317\) 0.444372 + 0.769675i 0.0249584 + 0.0432292i 0.878235 0.478230i \(-0.158721\pi\)
−0.853276 + 0.521459i \(0.825388\pi\)
\(318\) 0 0
\(319\) 9.99135 17.3055i 0.559408 0.968923i
\(320\) 0 0
\(321\) 3.51975 + 11.8218i 0.196453 + 0.659826i
\(322\) 0 0
\(323\) 4.03966 0.224772
\(324\) 0 0
\(325\) −7.33540 −0.406895
\(326\) 0 0
\(327\) −1.47713 4.96122i −0.0816853 0.274356i
\(328\) 0 0
\(329\) 0.874561 1.51478i 0.0482161 0.0835127i
\(330\) 0 0
\(331\) 11.4513 + 19.8342i 0.629420 + 1.09019i 0.987668 + 0.156561i \(0.0500407\pi\)
−0.358249 + 0.933626i \(0.616626\pi\)
\(332\) 0 0
\(333\) −10.2788 + 6.71606i −0.563274 + 0.368038i
\(334\) 0 0
\(335\) −3.10634 5.38033i −0.169717 0.293959i
\(336\) 0 0
\(337\) 0.415255 0.719243i 0.0226204 0.0391796i −0.854494 0.519462i \(-0.826132\pi\)
0.877114 + 0.480282i \(0.159466\pi\)
\(338\) 0 0
\(339\) −11.4844 2.74019i −0.623748 0.148827i
\(340\) 0 0
\(341\) −28.8031 −1.55977
\(342\) 0 0
\(343\) −38.0378 −2.05385
\(344\) 0 0
\(345\) −5.65342 + 5.97416i −0.304370 + 0.321638i
\(346\) 0 0
\(347\) −8.53131 + 14.7767i −0.457985 + 0.793253i −0.998854 0.0478537i \(-0.984762\pi\)
0.540870 + 0.841106i \(0.318095\pi\)
\(348\) 0 0
\(349\) 10.9443 + 18.9561i 0.585836 + 1.01470i 0.994771 + 0.102134i \(0.0325671\pi\)
−0.408935 + 0.912564i \(0.634100\pi\)
\(350\) 0 0
\(351\) −7.61296 + 2.73188i −0.406350 + 0.145817i
\(352\) 0 0
\(353\) 9.53407 + 16.5135i 0.507447 + 0.878924i 0.999963 + 0.00862082i \(0.00274413\pi\)
−0.492516 + 0.870304i \(0.663923\pi\)
\(354\) 0 0
\(355\) 2.84964 4.93572i 0.151243 0.261961i
\(356\) 0 0
\(357\) 3.89340 4.11429i 0.206061 0.217751i
\(358\) 0 0
\(359\) −13.1482 −0.693938 −0.346969 0.937877i \(-0.612789\pi\)
−0.346969 + 0.937877i \(0.612789\pi\)
\(360\) 0 0
\(361\) 14.7088 0.774147
\(362\) 0 0
\(363\) 26.9962 + 6.44132i 1.41693 + 0.338081i
\(364\) 0 0
\(365\) 1.18191 2.04712i 0.0618638 0.107151i
\(366\) 0 0
\(367\) −7.79061 13.4937i −0.406666 0.704367i 0.587848 0.808972i \(-0.299975\pi\)
−0.994514 + 0.104605i \(0.966642\pi\)
\(368\) 0 0
\(369\) 0.334139 + 6.05193i 0.0173946 + 0.315051i
\(370\) 0 0
\(371\) 12.4740 + 21.6056i 0.647618 + 1.12171i
\(372\) 0 0
\(373\) 9.92199 17.1854i 0.513741 0.889826i −0.486132 0.873885i \(-0.661593\pi\)
0.999873 0.0159402i \(-0.00507413\pi\)
\(374\) 0 0
\(375\) −2.57401 8.64530i −0.132921 0.446442i
\(376\) 0 0
\(377\) −5.98350 −0.308166
\(378\) 0 0
\(379\) −15.0470 −0.772914 −0.386457 0.922307i \(-0.626301\pi\)
−0.386457 + 0.922307i \(0.626301\pi\)
\(380\) 0 0
\(381\) 8.77625 + 29.4767i 0.449621 + 1.51014i
\(382\) 0 0
\(383\) −16.4288 + 28.4556i −0.839474 + 1.45401i 0.0508616 + 0.998706i \(0.483803\pi\)
−0.890335 + 0.455305i \(0.849530\pi\)
\(384\) 0 0
\(385\) −6.55089 11.3465i −0.333864 0.578270i
\(386\) 0 0
\(387\) 19.8899 + 10.0645i 1.01106 + 0.511605i
\(388\) 0 0
\(389\) −1.87559 3.24862i −0.0950962 0.164711i 0.814553 0.580090i \(-0.196983\pi\)
−0.909649 + 0.415378i \(0.863649\pi\)
\(390\) 0 0
\(391\) 3.08098 5.33641i 0.155812 0.269874i
\(392\) 0 0
\(393\) 11.8355 + 2.82397i 0.597024 + 0.142450i
\(394\) 0 0
\(395\) 3.56304 0.179276
\(396\) 0 0
\(397\) −23.5495 −1.18192 −0.590958 0.806702i \(-0.701250\pi\)
−0.590958 + 0.806702i \(0.701250\pi\)
\(398\) 0 0
\(399\) 32.4884 34.3316i 1.62645 1.71873i
\(400\) 0 0
\(401\) 7.28105 12.6111i 0.363598 0.629771i −0.624952 0.780663i \(-0.714881\pi\)
0.988550 + 0.150893i \(0.0482148\pi\)
\(402\) 0 0
\(403\) 4.31231 + 7.46914i 0.214811 + 0.372064i
\(404\) 0 0
\(405\) −2.85836 3.88828i −0.142033 0.193210i
\(406\) 0 0
\(407\) −10.6381 18.4257i −0.527310 0.913328i
\(408\) 0 0
\(409\) 3.23655 5.60586i 0.160037 0.277192i −0.774845 0.632152i \(-0.782172\pi\)
0.934882 + 0.354959i \(0.115505\pi\)
\(410\) 0 0
\(411\) 13.5967 14.3681i 0.670677 0.708728i
\(412\) 0 0
\(413\) −24.1738 −1.18951
\(414\) 0 0
\(415\) 5.66294 0.277983
\(416\) 0 0
\(417\) −10.4677 2.49760i −0.512606 0.122308i
\(418\) 0 0
\(419\) −13.4378 + 23.2750i −0.656481 + 1.13706i 0.325040 + 0.945700i \(0.394622\pi\)
−0.981520 + 0.191357i \(0.938711\pi\)
\(420\) 0 0
\(421\) −3.85521 6.67742i −0.187892 0.325438i 0.756656 0.653814i \(-0.226832\pi\)
−0.944547 + 0.328376i \(0.893499\pi\)
\(422\) 0 0
\(423\) 0.996127 + 0.504049i 0.0484333 + 0.0245077i
\(424\) 0 0
\(425\) 1.63943 + 2.83957i 0.0795239 + 0.137740i
\(426\) 0 0
\(427\) 4.33361 7.50603i 0.209718 0.363242i
\(428\) 0 0
\(429\) −3.99940 13.4327i −0.193093 0.648539i
\(430\) 0 0
\(431\) 3.45993 0.166659 0.0833294 0.996522i \(-0.473445\pi\)
0.0833294 + 0.996522i \(0.473445\pi\)
\(432\) 0 0
\(433\) −12.7863 −0.614471 −0.307236 0.951633i \(-0.599404\pi\)
−0.307236 + 0.951633i \(0.599404\pi\)
\(434\) 0 0
\(435\) −1.01873 3.42161i −0.0488445 0.164054i
\(436\) 0 0
\(437\) 25.7092 44.5296i 1.22984 2.13014i
\(438\) 0 0
\(439\) −2.76458 4.78840i −0.131946 0.228538i 0.792480 0.609897i \(-0.208789\pi\)
−0.924427 + 0.381359i \(0.875456\pi\)
\(440\) 0 0
\(441\) −2.49609 45.2091i −0.118861 2.15282i
\(442\) 0 0
\(443\) −13.2718 22.9874i −0.630563 1.09217i −0.987437 0.158014i \(-0.949491\pi\)
0.356874 0.934152i \(-0.383842\pi\)
\(444\) 0 0
\(445\) −1.95924 + 3.39350i −0.0928769 + 0.160867i
\(446\) 0 0
\(447\) 18.4602 + 4.40460i 0.873135 + 0.208331i
\(448\) 0 0
\(449\) −29.9625 −1.41402 −0.707010 0.707204i \(-0.749956\pi\)
−0.707010 + 0.707204i \(0.749956\pi\)
\(450\) 0 0
\(451\) −10.5028 −0.494560
\(452\) 0 0
\(453\) 17.3443 18.3283i 0.814904 0.861138i
\(454\) 0 0
\(455\) −1.96156 + 3.39752i −0.0919593 + 0.159278i
\(456\) 0 0
\(457\) −12.3904 21.4608i −0.579597 1.00389i −0.995525 0.0944945i \(-0.969877\pi\)
0.415928 0.909398i \(-0.363457\pi\)
\(458\) 0 0
\(459\) 2.75898 + 2.33645i 0.128778 + 0.109056i
\(460\) 0 0
\(461\) −5.30632 9.19081i −0.247140 0.428059i 0.715591 0.698519i \(-0.246157\pi\)
−0.962731 + 0.270461i \(0.912824\pi\)
\(462\) 0 0
\(463\) 5.31762 9.21040i 0.247131 0.428043i −0.715598 0.698513i \(-0.753846\pi\)
0.962729 + 0.270469i \(0.0871789\pi\)
\(464\) 0 0
\(465\) −3.53696 + 3.73763i −0.164023 + 0.173328i
\(466\) 0 0
\(467\) −27.3831 −1.26714 −0.633569 0.773686i \(-0.718411\pi\)
−0.633569 + 0.773686i \(0.718411\pi\)
\(468\) 0 0
\(469\) 54.4590 2.51468
\(470\) 0 0
\(471\) 25.8121 + 6.15879i 1.18936 + 0.283782i
\(472\) 0 0
\(473\) −19.3133 + 33.4517i −0.888028 + 1.53811i
\(474\) 0 0
\(475\) 13.6802 + 23.6947i 0.627689 + 1.08719i
\(476\) 0 0
\(477\) −13.3301 + 8.70976i −0.610344 + 0.398793i
\(478\) 0 0
\(479\) 20.3026 + 35.1651i 0.927649 + 1.60674i 0.787245 + 0.616641i \(0.211507\pi\)
0.140404 + 0.990094i \(0.455160\pi\)
\(480\) 0 0
\(481\) −3.18541 + 5.51728i −0.145242 + 0.251566i
\(482\) 0 0
\(483\) −20.5739 69.1015i −0.936146 3.14423i
\(484\) 0 0
\(485\) −8.38212 −0.380613
\(486\) 0 0
\(487\) −4.99658 −0.226417 −0.113208 0.993571i \(-0.536113\pi\)
−0.113208 + 0.993571i \(0.536113\pi\)
\(488\) 0 0
\(489\) 5.47254 + 18.3806i 0.247477 + 0.831199i
\(490\) 0 0
\(491\) 19.2049 33.2639i 0.866705 1.50118i 0.00136059 0.999999i \(-0.499567\pi\)
0.865344 0.501178i \(-0.167100\pi\)
\(492\) 0 0
\(493\) 1.33728 + 2.31624i 0.0602282 + 0.104318i
\(494\) 0 0
\(495\) 7.00048 4.57404i 0.314648 0.205588i
\(496\) 0 0
\(497\) 24.9794 + 43.2655i 1.12048 + 1.94072i
\(498\) 0 0
\(499\) 11.3616 19.6788i 0.508614 0.880945i −0.491337 0.870970i \(-0.663491\pi\)
0.999950 0.00997497i \(-0.00317518\pi\)
\(500\) 0 0
\(501\) 14.0039 + 3.34135i 0.625650 + 0.149280i
\(502\) 0 0
\(503\) −40.2323 −1.79387 −0.896935 0.442161i \(-0.854212\pi\)
−0.896935 + 0.442161i \(0.854212\pi\)
\(504\) 0 0
\(505\) −4.75313 −0.211512
\(506\) 0 0
\(507\) 12.5920 13.3064i 0.559232 0.590960i
\(508\) 0 0
\(509\) 4.30968 7.46459i 0.191023 0.330862i −0.754566 0.656224i \(-0.772153\pi\)
0.945590 + 0.325362i \(0.105486\pi\)
\(510\) 0 0
\(511\) 10.3604 + 17.9447i 0.458315 + 0.793825i
\(512\) 0 0
\(513\) 23.0223 + 19.4965i 1.01646 + 0.860791i
\(514\) 0 0
\(515\) −0.884666 1.53229i −0.0389830 0.0675206i
\(516\) 0 0
\(517\) −0.967251 + 1.67533i −0.0425396 + 0.0736808i
\(518\) 0 0
\(519\) 0.0944444 0.0998027i 0.00414565 0.00438085i
\(520\) 0 0
\(521\) −20.5770 −0.901496 −0.450748 0.892651i \(-0.648843\pi\)
−0.450748 + 0.892651i \(0.648843\pi\)
\(522\) 0 0
\(523\) −15.6990 −0.686470 −0.343235 0.939250i \(-0.611523\pi\)
−0.343235 + 0.939250i \(0.611523\pi\)
\(524\) 0 0
\(525\) 37.3174 + 8.90395i 1.62866 + 0.388600i
\(526\) 0 0
\(527\) 1.92756 3.33863i 0.0839659 0.145433i
\(528\) 0 0
\(529\) −27.7159 48.0054i −1.20504 2.08719i
\(530\) 0 0
\(531\) −0.850578 15.4057i −0.0369119 0.668549i
\(532\) 0 0
\(533\) 1.57245 + 2.72357i 0.0681106 + 0.117971i
\(534\) 0 0
\(535\) −1.90927 + 3.30696i −0.0825450 + 0.142972i
\(536\) 0 0
\(537\) 10.2810 + 34.5306i 0.443656 + 1.49011i
\(538\) 0 0
\(539\) 78.4584 3.37944
\(540\) 0 0
\(541\) 4.79886 0.206319 0.103160 0.994665i \(-0.467105\pi\)
0.103160 + 0.994665i \(0.467105\pi\)
\(542\) 0 0
\(543\) 2.53609 + 8.51794i 0.108834 + 0.365540i
\(544\) 0 0
\(545\) 0.801260 1.38782i 0.0343222 0.0594478i
\(546\) 0 0
\(547\) −8.26596 14.3171i −0.353427 0.612153i 0.633421 0.773808i \(-0.281650\pi\)
−0.986847 + 0.161654i \(0.948317\pi\)
\(548\) 0 0
\(549\) 4.93599 + 2.49765i 0.210663 + 0.106597i
\(550\) 0 0
\(551\) 11.1589 + 19.3278i 0.475386 + 0.823393i
\(552\) 0 0
\(553\) −15.6164 + 27.0484i −0.664078 + 1.15022i
\(554\) 0 0
\(555\) −3.69735 0.882190i −0.156944 0.0374469i
\(556\) 0 0
\(557\) 14.2466 0.603649 0.301825 0.953363i \(-0.402404\pi\)
0.301825 + 0.953363i \(0.402404\pi\)
\(558\) 0 0
\(559\) 11.5661 0.489196
\(560\) 0 0
\(561\) −4.30604 + 4.55034i −0.181801 + 0.192116i
\(562\) 0 0
\(563\) 13.4981 23.3794i 0.568876 0.985322i −0.427801 0.903873i \(-0.640712\pi\)
0.996677 0.0814497i \(-0.0259550\pi\)
\(564\) 0 0
\(565\) −1.82757 3.16545i −0.0768865 0.133171i
\(566\) 0 0
\(567\) 42.0454 4.65702i 1.76574 0.195576i
\(568\) 0 0
\(569\) 4.82124 + 8.35063i 0.202117 + 0.350076i 0.949210 0.314643i \(-0.101885\pi\)
−0.747094 + 0.664719i \(0.768551\pi\)
\(570\) 0 0
\(571\) −15.0536 + 26.0736i −0.629973 + 1.09115i 0.357584 + 0.933881i \(0.383601\pi\)
−0.987557 + 0.157264i \(0.949733\pi\)
\(572\) 0 0
\(573\) −23.5503 + 24.8864i −0.983826 + 1.03964i
\(574\) 0 0
\(575\) 41.7346 1.74045
\(576\) 0 0
\(577\) 14.9642 0.622968 0.311484 0.950251i \(-0.399174\pi\)
0.311484 + 0.950251i \(0.399174\pi\)
\(578\) 0 0
\(579\) −6.05076 1.44372i −0.251461 0.0599988i
\(580\) 0 0
\(581\) −24.8201 + 42.9896i −1.02971 + 1.78351i
\(582\) 0 0
\(583\) −13.7961 23.8955i −0.571375 0.989650i
\(584\) 0 0
\(585\) −2.23422 1.13053i −0.0923736 0.0467418i
\(586\) 0 0
\(587\) −12.0511 20.8731i −0.497401 0.861523i 0.502595 0.864522i \(-0.332379\pi\)
−0.999996 + 0.00299890i \(0.999045\pi\)
\(588\) 0 0
\(589\) 16.0845 27.8591i 0.662749 1.14792i
\(590\) 0 0
\(591\) −0.846460 2.84300i −0.0348187 0.116945i
\(592\) 0 0
\(593\) 5.62882 0.231148 0.115574 0.993299i \(-0.463129\pi\)
0.115574 + 0.993299i \(0.463129\pi\)
\(594\) 0 0
\(595\) 1.75360 0.0718904
\(596\) 0 0
\(597\) −8.96073 30.0963i −0.366738 1.23176i
\(598\) 0 0
\(599\) 9.75087 16.8890i 0.398410 0.690066i −0.595120 0.803637i \(-0.702896\pi\)
0.993530 + 0.113571i \(0.0362289\pi\)
\(600\) 0 0
\(601\) −1.36834 2.37003i −0.0558158 0.0966757i 0.836767 0.547558i \(-0.184443\pi\)
−0.892583 + 0.450883i \(0.851109\pi\)
\(602\) 0 0
\(603\) 1.91619 + 34.7061i 0.0780334 + 1.41334i
\(604\) 0 0
\(605\) 4.29604 + 7.44096i 0.174659 + 0.302518i
\(606\) 0 0
\(607\) 23.6876 41.0282i 0.961452 1.66528i 0.242592 0.970128i \(-0.422002\pi\)
0.718860 0.695155i \(-0.244664\pi\)
\(608\) 0 0
\(609\) 30.4398 + 7.26296i 1.23348 + 0.294310i
\(610\) 0 0
\(611\) 0.579256 0.0234342
\(612\) 0 0
\(613\) −23.1963 −0.936891 −0.468446 0.883492i \(-0.655186\pi\)
−0.468446 + 0.883492i \(0.655186\pi\)
\(614\) 0 0
\(615\) −1.28973 + 1.36290i −0.0520069 + 0.0549575i
\(616\) 0 0
\(617\) −19.8253 + 34.3384i −0.798137 + 1.38241i 0.122691 + 0.992445i \(0.460848\pi\)
−0.920828 + 0.389969i \(0.872486\pi\)
\(618\) 0 0
\(619\) −0.813544 1.40910i −0.0326991 0.0566365i 0.849213 0.528051i \(-0.177077\pi\)
−0.881912 + 0.471414i \(0.843744\pi\)
\(620\) 0 0
\(621\) 43.3137 15.5429i 1.73812 0.623717i
\(622\) 0 0
\(623\) −17.1743 29.7467i −0.688074 1.19178i
\(624\) 0 0
\(625\) −10.3849 + 17.9873i −0.415398 + 0.719490i
\(626\) 0 0
\(627\) −35.9316 + 37.9702i −1.43497 + 1.51638i
\(628\) 0 0
\(629\) 2.84769 0.113545
\(630\) 0 0
\(631\) −30.9685 −1.23283 −0.616417 0.787420i \(-0.711417\pi\)
−0.616417 + 0.787420i \(0.711417\pi\)
\(632\) 0 0
\(633\) −2.47425 0.590359i −0.0983428 0.0234647i
\(634\) 0 0
\(635\) −4.76063 + 8.24566i −0.188920 + 0.327219i
\(636\) 0 0
\(637\) −11.7466 20.3456i −0.465415 0.806123i
\(638\) 0 0
\(639\) −26.6937 + 17.4414i −1.05599 + 0.689971i
\(640\) 0 0
\(641\) −16.1499 27.9725i −0.637883 1.10485i −0.985897 0.167356i \(-0.946477\pi\)
0.348014 0.937489i \(-0.386856\pi\)
\(642\) 0 0
\(643\) 3.28376 5.68763i 0.129499 0.224298i −0.793984 0.607939i \(-0.791997\pi\)
0.923482 + 0.383641i \(0.125330\pi\)
\(644\) 0 0
\(645\) 1.96922 + 6.61400i 0.0775379 + 0.260426i
\(646\) 0 0
\(647\) −40.0823 −1.57580 −0.787899 0.615805i \(-0.788831\pi\)
−0.787899 + 0.615805i \(0.788831\pi\)
\(648\) 0 0
\(649\) 26.7358 1.04947
\(650\) 0 0
\(651\) −12.8717 43.2321i −0.504482 1.69440i
\(652\) 0 0
\(653\) 1.62772 2.81929i 0.0636976 0.110327i −0.832418 0.554148i \(-0.813044\pi\)
0.896116 + 0.443821i \(0.146377\pi\)
\(654\) 0 0
\(655\) 1.88345 + 3.26223i 0.0735924 + 0.127466i
\(656\) 0 0
\(657\) −11.0714 + 7.23394i −0.431936 + 0.282223i
\(658\) 0 0
\(659\) 7.58278 + 13.1338i 0.295383 + 0.511619i 0.975074 0.221880i \(-0.0712193\pi\)
−0.679691 + 0.733499i \(0.737886\pi\)
\(660\) 0 0
\(661\) 10.1447 17.5711i 0.394582 0.683435i −0.598466 0.801148i \(-0.704223\pi\)
0.993048 + 0.117713i \(0.0375562\pi\)
\(662\) 0 0
\(663\) 1.82467 + 0.435368i 0.0708643 + 0.0169083i
\(664\) 0 0
\(665\) 14.6328 0.567437
\(666\) 0 0
\(667\) 34.0429 1.31815
\(668\) 0 0
\(669\) 22.8064 24.1003i 0.881747 0.931773i
\(670\) 0 0
\(671\) −4.79290 + 8.30155i −0.185028 + 0.320478i
\(672\) 0 0
\(673\) 11.6256 + 20.1361i 0.448134 + 0.776191i 0.998265 0.0588875i \(-0.0187553\pi\)
−0.550130 + 0.835079i \(0.685422\pi\)
\(674\) 0 0
\(675\) −4.36134 + 24.0952i −0.167868 + 0.927426i
\(676\) 0 0
\(677\) 15.6380 + 27.0859i 0.601018 + 1.04099i 0.992667 + 0.120879i \(0.0385714\pi\)
−0.391649 + 0.920115i \(0.628095\pi\)
\(678\) 0 0
\(679\) 36.7380 63.6320i 1.40987 2.44197i
\(680\) 0 0
\(681\) −14.1132 + 14.9139i −0.540818 + 0.571501i
\(682\) 0 0
\(683\) 24.1812 0.925269 0.462635 0.886549i \(-0.346904\pi\)
0.462635 + 0.886549i \(0.346904\pi\)
\(684\) 0 0
\(685\) 6.12400 0.233986
\(686\) 0 0
\(687\) 5.29752 + 1.26399i 0.202113 + 0.0482243i
\(688\) 0 0
\(689\) −4.13101 + 7.15512i −0.157379 + 0.272588i
\(690\) 0 0
\(691\) 9.03942 + 15.6567i 0.343876 + 0.595610i 0.985149 0.171702i \(-0.0549268\pi\)
−0.641273 + 0.767313i \(0.721593\pi\)
\(692\) 0 0
\(693\) 4.04102 + 73.1910i 0.153506 + 2.78030i
\(694\) 0 0
\(695\) −1.66578 2.88521i −0.0631866 0.109442i
\(696\) 0 0
\(697\) 0.702872 1.21741i 0.0266232 0.0461127i
\(698\) 0 0
\(699\) 1.39840 + 4.69681i 0.0528925 + 0.177650i
\(700\) 0 0
\(701\) 17.2240 0.650541 0.325271 0.945621i \(-0.394545\pi\)
0.325271 + 0.945621i \(0.394545\pi\)
\(702\) 0 0
\(703\) 23.7625 0.896219
\(704\) 0 0
\(705\) 0.0986224 + 0.331242i 0.00371433 + 0.0124753i
\(706\) 0 0
\(707\) 20.8325 36.0830i 0.783487 1.35704i
\(708\) 0 0
\(709\) −13.3258 23.0809i −0.500459 0.866821i −1.00000 0.000530358i \(-0.999831\pi\)
0.499541 0.866290i \(-0.333502\pi\)
\(710\) 0 0
\(711\) −17.7871 9.00045i −0.667070 0.337543i
\(712\) 0 0
\(713\) −24.5347 42.4954i −0.918833 1.59147i
\(714\) 0 0
\(715\) 2.16945 3.75760i 0.0811330 0.140526i
\(716\) 0 0
\(717\) −5.34965 1.27643i −0.199786 0.0476691i
\(718\) 0 0
\(719\) −10.4273 −0.388875 −0.194437 0.980915i \(-0.562288\pi\)
−0.194437 + 0.980915i \(0.562288\pi\)
\(720\) 0 0
\(721\) 15.5096 0.577608
\(722\) 0 0
\(723\) 15.7874 16.6831i 0.587139 0.620451i
\(724\) 0 0
\(725\) −9.05733 + 15.6878i −0.336381 + 0.582629i
\(726\) 0 0
\(727\) 10.5682 + 18.3047i 0.391954 + 0.678884i 0.992707 0.120550i \(-0.0384659\pi\)
−0.600753 + 0.799434i \(0.705133\pi\)
\(728\) 0 0
\(729\) 4.44727 + 26.6312i 0.164714 + 0.986341i
\(730\) 0 0
\(731\) −2.58498 4.47731i −0.0956088 0.165599i
\(732\) 0 0
\(733\) 15.6473 27.1020i 0.577948 1.00103i −0.417767 0.908554i \(-0.637187\pi\)
0.995714 0.0924806i \(-0.0294796\pi\)
\(734\) 0 0
\(735\) 9.63454 10.1812i 0.355375 0.375537i
\(736\) 0 0
\(737\) −60.2308 −2.21863
\(738\) 0 0
\(739\) 31.0455 1.14203 0.571014 0.820940i \(-0.306550\pi\)
0.571014 + 0.820940i \(0.306550\pi\)
\(740\) 0 0
\(741\) 15.2259 + 3.63291i 0.559338 + 0.133458i
\(742\) 0 0
\(743\) −8.93131 + 15.4695i −0.327658 + 0.567520i −0.982047 0.188638i \(-0.939593\pi\)
0.654389 + 0.756158i \(0.272926\pi\)
\(744\) 0 0
\(745\) 2.93765 + 5.08817i 0.107627 + 0.186416i
\(746\) 0 0
\(747\) −28.2701 14.3049i −1.03435 0.523390i
\(748\) 0 0
\(749\) −16.7363 28.9881i −0.611530 1.05920i
\(750\) 0 0
\(751\) 4.70046 8.14144i 0.171522 0.297085i −0.767430 0.641133i \(-0.778465\pi\)
0.938952 + 0.344047i \(0.111798\pi\)
\(752\) 0 0
\(753\) 1.51435 + 5.08625i 0.0551861 + 0.185353i
\(754\) 0 0
\(755\) 7.81189 0.284304
\(756\) 0 0
\(757\) −49.7959 −1.80986 −0.904931 0.425558i \(-0.860078\pi\)
−0.904931 + 0.425558i \(0.860078\pi\)
\(758\) 0 0
\(759\) 22.7544 + 76.4252i 0.825934 + 2.77406i
\(760\) 0 0
\(761\) 5.42633 9.39868i 0.196704 0.340702i −0.750754 0.660582i \(-0.770309\pi\)
0.947458 + 0.319880i \(0.103643\pi\)
\(762\) 0 0
\(763\) 7.02368 + 12.1654i 0.254274 + 0.440416i
\(764\) 0 0
\(765\) 0.0617020 + 1.11755i 0.00223084 + 0.0404050i
\(766\) 0 0
\(767\) −4.00281 6.93307i −0.144533 0.250338i
\(768\) 0 0
\(769\) 2.93798 5.08873i 0.105946 0.183504i −0.808178 0.588938i \(-0.799546\pi\)
0.914124 + 0.405434i \(0.132880\pi\)
\(770\) 0 0
\(771\) −27.4319 6.54527i −0.987936 0.235722i
\(772\) 0 0
\(773\) −26.2781 −0.945159 −0.472579 0.881288i \(-0.656677\pi\)
−0.472579 + 0.881288i \(0.656677\pi\)
\(774\) 0 0
\(775\) 26.1105 0.937917
\(776\) 0 0
\(777\) 22.9022 24.2015i 0.821610 0.868225i
\(778\) 0 0
\(779\) 5.86510 10.1587i 0.210139 0.363971i
\(780\) 0 0
\(781\) −27.6268 47.8510i −0.988564 1.71224i
\(782\) 0 0
\(783\) −3.55755 + 19.6545i −0.127136 + 0.702395i
\(784\) 0 0
\(785\) 4.10761 + 7.11459i 0.146607 + 0.253930i
\(786\) 0 0
\(787\) −16.3824 + 28.3752i −0.583970 + 1.01146i 0.411034 + 0.911620i \(0.365168\pi\)
−0.995003 + 0.0998447i \(0.968165\pi\)
\(788\) 0 0
\(789\) 26.3649 27.8607i 0.938616 0.991868i
\(790\) 0 0
\(791\) 32.0402 1.13922
\(792\) 0 0
\(793\) 2.87032 0.101928
\(794\) 0 0
\(795\) −4.79493 1.14407i −0.170059 0.0405761i
\(796\) 0 0
\(797\)