Properties

Label 432.2.be.a.47.3
Level $432$
Weight $2$
Character 432.47
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 47.3
Character \(\chi\) \(=\) 432.47
Dual form 432.2.be.a.239.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.340461 - 1.69826i) q^{3} +(1.68195 - 0.296574i) q^{5} +(0.981328 - 1.16950i) q^{7} +(-2.76817 + 1.15638i) q^{9} +O(q^{10})\) \(q+(-0.340461 - 1.69826i) q^{3} +(1.68195 - 0.296574i) q^{5} +(0.981328 - 1.16950i) q^{7} +(-2.76817 + 1.15638i) q^{9} +(0.602821 - 3.41877i) q^{11} +(2.74648 + 0.999638i) q^{13} +(-1.07630 - 2.75542i) q^{15} +(0.812691 - 0.469208i) q^{17} +(-1.51710 - 0.875899i) q^{19} +(-2.32022 - 1.26838i) q^{21} +(-0.0294832 + 0.0247394i) q^{23} +(-1.95745 + 0.712454i) q^{25} +(2.90629 + 4.30738i) q^{27} +(-1.84729 - 5.07538i) q^{29} +(-4.26730 - 5.08557i) q^{31} +(-6.01119 + 0.140209i) q^{33} +(1.30371 - 2.25808i) q^{35} +(3.09995 + 5.36926i) q^{37} +(0.762576 - 5.00458i) q^{39} +(1.60794 - 4.41779i) q^{41} +(8.03174 + 1.41621i) q^{43} +(-4.31299 + 2.76595i) q^{45} +(-6.29137 - 5.27909i) q^{47} +(0.810809 + 4.59833i) q^{49} +(-1.07353 - 1.22041i) q^{51} -12.6923i q^{53} -5.92899i q^{55} +(-0.970991 + 2.87464i) q^{57} +(2.57645 + 14.6118i) q^{59} +(10.6194 + 8.91077i) q^{61} +(-1.36410 + 4.37217i) q^{63} +(4.91592 + 0.866810i) q^{65} +(-4.52189 + 12.4238i) q^{67} +(0.0520517 + 0.0416474i) q^{69} +(1.81864 + 3.14997i) q^{71} +(-2.02246 + 3.50300i) q^{73} +(1.87637 + 3.08170i) q^{75} +(-3.40669 - 4.05993i) q^{77} +(4.29234 + 11.7931i) q^{79} +(6.32557 - 6.40213i) q^{81} +(-3.42314 + 1.24592i) q^{83} +(1.22775 - 1.03021i) q^{85} +(-7.99038 + 4.86514i) q^{87} +(7.61727 + 4.39783i) q^{89} +(3.86428 - 2.23104i) q^{91} +(-7.18377 + 8.97842i) q^{93} +(-2.81146 - 1.02329i) q^{95} +(0.737508 - 4.18262i) q^{97} +(2.28469 + 10.1608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 6 q^{5} - 12 q^{9} + O(q^{10}) \) \( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.340461 1.69826i −0.196565 0.980491i
\(4\) 0 0
\(5\) 1.68195 0.296574i 0.752193 0.132632i 0.215610 0.976480i \(-0.430826\pi\)
0.536583 + 0.843848i \(0.319715\pi\)
\(6\) 0 0
\(7\) 0.981328 1.16950i 0.370907 0.442030i −0.548015 0.836468i \(-0.684616\pi\)
0.918922 + 0.394438i \(0.129061\pi\)
\(8\) 0 0
\(9\) −2.76817 + 1.15638i −0.922724 + 0.385460i
\(10\) 0 0
\(11\) 0.602821 3.41877i 0.181757 1.03080i −0.748294 0.663368i \(-0.769127\pi\)
0.930051 0.367430i \(-0.119762\pi\)
\(12\) 0 0
\(13\) 2.74648 + 0.999638i 0.761737 + 0.277250i 0.693536 0.720422i \(-0.256052\pi\)
0.0682011 + 0.997672i \(0.478274\pi\)
\(14\) 0 0
\(15\) −1.07630 2.75542i −0.277899 0.711447i
\(16\) 0 0
\(17\) 0.812691 0.469208i 0.197107 0.113800i −0.398199 0.917299i \(-0.630365\pi\)
0.595305 + 0.803500i \(0.297031\pi\)
\(18\) 0 0
\(19\) −1.51710 0.875899i −0.348047 0.200945i 0.315778 0.948833i \(-0.397735\pi\)
−0.663825 + 0.747888i \(0.731068\pi\)
\(20\) 0 0
\(21\) −2.32022 1.26838i −0.506314 0.276783i
\(22\) 0 0
\(23\) −0.0294832 + 0.0247394i −0.00614768 + 0.00515851i −0.645856 0.763459i \(-0.723499\pi\)
0.639709 + 0.768618i \(0.279055\pi\)
\(24\) 0 0
\(25\) −1.95745 + 0.712454i −0.391490 + 0.142491i
\(26\) 0 0
\(27\) 2.90629 + 4.30738i 0.559316 + 0.828955i
\(28\) 0 0
\(29\) −1.84729 5.07538i −0.343032 0.942474i −0.984509 0.175331i \(-0.943900\pi\)
0.641477 0.767142i \(-0.278322\pi\)
\(30\) 0 0
\(31\) −4.26730 5.08557i −0.766430 0.913396i 0.231806 0.972762i \(-0.425536\pi\)
−0.998236 + 0.0593663i \(0.981092\pi\)
\(32\) 0 0
\(33\) −6.01119 + 0.140209i −1.04641 + 0.0244072i
\(34\) 0 0
\(35\) 1.30371 2.25808i 0.220366 0.381686i
\(36\) 0 0
\(37\) 3.09995 + 5.36926i 0.509628 + 0.882702i 0.999938 + 0.0111534i \(0.00355030\pi\)
−0.490310 + 0.871548i \(0.663116\pi\)
\(38\) 0 0
\(39\) 0.762576 5.00458i 0.122110 0.801374i
\(40\) 0 0
\(41\) 1.60794 4.41779i 0.251119 0.689943i −0.748521 0.663111i \(-0.769236\pi\)
0.999640 0.0268321i \(-0.00854194\pi\)
\(42\) 0 0
\(43\) 8.03174 + 1.41621i 1.22483 + 0.215970i 0.748403 0.663244i \(-0.230821\pi\)
0.476426 + 0.879215i \(0.341932\pi\)
\(44\) 0 0
\(45\) −4.31299 + 2.76595i −0.642942 + 0.412323i
\(46\) 0 0
\(47\) −6.29137 5.27909i −0.917691 0.770034i 0.0558757 0.998438i \(-0.482205\pi\)
−0.973567 + 0.228404i \(0.926649\pi\)
\(48\) 0 0
\(49\) 0.810809 + 4.59833i 0.115830 + 0.656904i
\(50\) 0 0
\(51\) −1.07353 1.22041i −0.150324 0.170892i
\(52\) 0 0
\(53\) 12.6923i 1.74342i −0.490020 0.871711i \(-0.663011\pi\)
0.490020 0.871711i \(-0.336989\pi\)
\(54\) 0 0
\(55\) 5.92899i 0.799465i
\(56\) 0 0
\(57\) −0.970991 + 2.87464i −0.128611 + 0.380756i
\(58\) 0 0
\(59\) 2.57645 + 14.6118i 0.335425 + 1.90229i 0.422997 + 0.906131i \(0.360978\pi\)
−0.0875717 + 0.996158i \(0.527911\pi\)
\(60\) 0 0
\(61\) 10.6194 + 8.91077i 1.35968 + 1.14091i 0.976081 + 0.217408i \(0.0697602\pi\)
0.383600 + 0.923499i \(0.374684\pi\)
\(62\) 0 0
\(63\) −1.36410 + 4.37217i −0.171860 + 0.550842i
\(64\) 0 0
\(65\) 4.91592 + 0.866810i 0.609745 + 0.107515i
\(66\) 0 0
\(67\) −4.52189 + 12.4238i −0.552437 + 1.51781i 0.277937 + 0.960599i \(0.410349\pi\)
−0.830373 + 0.557208i \(0.811873\pi\)
\(68\) 0 0
\(69\) 0.0520517 + 0.0416474i 0.00626629 + 0.00501376i
\(70\) 0 0
\(71\) 1.81864 + 3.14997i 0.215832 + 0.373833i 0.953530 0.301299i \(-0.0974202\pi\)
−0.737697 + 0.675132i \(0.764087\pi\)
\(72\) 0 0
\(73\) −2.02246 + 3.50300i −0.236711 + 0.409996i −0.959769 0.280792i \(-0.909403\pi\)
0.723058 + 0.690788i \(0.242736\pi\)
\(74\) 0 0
\(75\) 1.87637 + 3.08170i 0.216664 + 0.355844i
\(76\) 0 0
\(77\) −3.40669 4.05993i −0.388228 0.462672i
\(78\) 0 0
\(79\) 4.29234 + 11.7931i 0.482926 + 1.32683i 0.906973 + 0.421188i \(0.138387\pi\)
−0.424047 + 0.905640i \(0.639391\pi\)
\(80\) 0 0
\(81\) 6.32557 6.40213i 0.702841 0.711347i
\(82\) 0 0
\(83\) −3.42314 + 1.24592i −0.375739 + 0.136758i −0.522984 0.852342i \(-0.675181\pi\)
0.147246 + 0.989100i \(0.452959\pi\)
\(84\) 0 0
\(85\) 1.22775 1.03021i 0.133169 0.111742i
\(86\) 0 0
\(87\) −7.99038 + 4.86514i −0.856659 + 0.521597i
\(88\) 0 0
\(89\) 7.61727 + 4.39783i 0.807429 + 0.466169i 0.846062 0.533084i \(-0.178967\pi\)
−0.0386332 + 0.999253i \(0.512300\pi\)
\(90\) 0 0
\(91\) 3.86428 2.23104i 0.405086 0.233877i
\(92\) 0 0
\(93\) −7.18377 + 8.97842i −0.744923 + 0.931019i
\(94\) 0 0
\(95\) −2.81146 1.02329i −0.288450 0.104987i
\(96\) 0 0
\(97\) 0.737508 4.18262i 0.0748826 0.424680i −0.924202 0.381904i \(-0.875269\pi\)
0.999085 0.0427765i \(-0.0136203\pi\)
\(98\) 0 0
\(99\) 2.28469 + 10.1608i 0.229620 + 1.02120i
\(100\) 0 0
\(101\) 4.83655 5.76397i 0.481254 0.573537i −0.469716 0.882817i \(-0.655644\pi\)
0.950971 + 0.309281i \(0.100088\pi\)
\(102\) 0 0
\(103\) −12.3823 + 2.18334i −1.22007 + 0.215131i −0.746355 0.665548i \(-0.768198\pi\)
−0.473713 + 0.880679i \(0.657087\pi\)
\(104\) 0 0
\(105\) −4.27867 1.44524i −0.417556 0.141041i
\(106\) 0 0
\(107\) 19.0430 1.84096 0.920478 0.390794i \(-0.127799\pi\)
0.920478 + 0.390794i \(0.127799\pi\)
\(108\) 0 0
\(109\) 4.46704 0.427865 0.213933 0.976848i \(-0.431373\pi\)
0.213933 + 0.976848i \(0.431373\pi\)
\(110\) 0 0
\(111\) 8.06300 7.09254i 0.765306 0.673194i
\(112\) 0 0
\(113\) −1.78707 + 0.315108i −0.168113 + 0.0296428i −0.257071 0.966393i \(-0.582757\pi\)
0.0889580 + 0.996035i \(0.471646\pi\)
\(114\) 0 0
\(115\) −0.0422524 + 0.0503544i −0.00394005 + 0.00469557i
\(116\) 0 0
\(117\) −8.75870 + 0.408809i −0.809742 + 0.0377944i
\(118\) 0 0
\(119\) 0.248778 1.41089i 0.0228054 0.129336i
\(120\) 0 0
\(121\) −0.987967 0.359591i −0.0898152 0.0326901i
\(122\) 0 0
\(123\) −8.05000 1.22662i −0.725844 0.110601i
\(124\) 0 0
\(125\) −10.4765 + 6.04859i −0.937044 + 0.541003i
\(126\) 0 0
\(127\) −6.27879 3.62506i −0.557153 0.321672i 0.194849 0.980833i \(-0.437578\pi\)
−0.752002 + 0.659161i \(0.770912\pi\)
\(128\) 0 0
\(129\) −0.329394 14.1221i −0.0290015 1.24339i
\(130\) 0 0
\(131\) −13.3886 + 11.2343i −1.16976 + 0.981548i −0.999992 0.00393578i \(-0.998747\pi\)
−0.169771 + 0.985484i \(0.554303\pi\)
\(132\) 0 0
\(133\) −2.51314 + 0.914708i −0.217917 + 0.0793152i
\(134\) 0 0
\(135\) 6.16570 + 6.38288i 0.530659 + 0.549351i
\(136\) 0 0
\(137\) 1.81753 + 4.99361i 0.155282 + 0.426633i 0.992801 0.119774i \(-0.0382172\pi\)
−0.837519 + 0.546408i \(0.815995\pi\)
\(138\) 0 0
\(139\) 7.75657 + 9.24392i 0.657904 + 0.784059i 0.987083 0.160208i \(-0.0512165\pi\)
−0.329179 + 0.944267i \(0.606772\pi\)
\(140\) 0 0
\(141\) −6.82330 + 12.4817i −0.574625 + 1.05115i
\(142\) 0 0
\(143\) 5.07317 8.78699i 0.424240 0.734805i
\(144\) 0 0
\(145\) −4.61227 7.98869i −0.383028 0.663425i
\(146\) 0 0
\(147\) 7.53310 2.94251i 0.621320 0.242694i
\(148\) 0 0
\(149\) 0.380050 1.04418i 0.0311349 0.0855425i −0.923151 0.384437i \(-0.874396\pi\)
0.954286 + 0.298894i \(0.0966179\pi\)
\(150\) 0 0
\(151\) 8.54782 + 1.50721i 0.695612 + 0.122655i 0.510264 0.860018i \(-0.329548\pi\)
0.185348 + 0.982673i \(0.440659\pi\)
\(152\) 0 0
\(153\) −1.70709 + 2.23863i −0.138010 + 0.180982i
\(154\) 0 0
\(155\) −8.68565 7.28813i −0.697648 0.585396i
\(156\) 0 0
\(157\) 0.0313604 + 0.177853i 0.00250283 + 0.0141943i 0.986034 0.166547i \(-0.0532616\pi\)
−0.983531 + 0.180741i \(0.942150\pi\)
\(158\) 0 0
\(159\) −21.5548 + 4.32123i −1.70941 + 0.342696i
\(160\) 0 0
\(161\) 0.0587581i 0.00463079i
\(162\) 0 0
\(163\) 21.6854i 1.69853i −0.527967 0.849265i \(-0.677045\pi\)
0.527967 0.849265i \(-0.322955\pi\)
\(164\) 0 0
\(165\) −10.0690 + 2.01859i −0.783868 + 0.157147i
\(166\) 0 0
\(167\) 0.444010 + 2.51811i 0.0343585 + 0.194857i 0.997156 0.0753678i \(-0.0240131\pi\)
−0.962797 + 0.270225i \(0.912902\pi\)
\(168\) 0 0
\(169\) −3.41469 2.86526i −0.262668 0.220405i
\(170\) 0 0
\(171\) 5.21247 + 0.670293i 0.398608 + 0.0512586i
\(172\) 0 0
\(173\) −11.1824 1.97176i −0.850183 0.149910i −0.268454 0.963293i \(-0.586513\pi\)
−0.581730 + 0.813382i \(0.697624\pi\)
\(174\) 0 0
\(175\) −1.08769 + 2.98839i −0.0822213 + 0.225901i
\(176\) 0 0
\(177\) 23.9374 9.35021i 1.79924 0.702805i
\(178\) 0 0
\(179\) 2.60767 + 4.51662i 0.194907 + 0.337588i 0.946870 0.321617i \(-0.104226\pi\)
−0.751963 + 0.659205i \(0.770893\pi\)
\(180\) 0 0
\(181\) 5.98011 10.3579i 0.444498 0.769893i −0.553519 0.832837i \(-0.686715\pi\)
0.998017 + 0.0629432i \(0.0200487\pi\)
\(182\) 0 0
\(183\) 11.5173 21.0683i 0.851384 1.55742i
\(184\) 0 0
\(185\) 6.80635 + 8.11149i 0.500413 + 0.596369i
\(186\) 0 0
\(187\) −1.11420 3.06125i −0.0814787 0.223861i
\(188\) 0 0
\(189\) 7.88950 + 0.828040i 0.573877 + 0.0602310i
\(190\) 0 0
\(191\) −10.3596 + 3.77059i −0.749595 + 0.272830i −0.688435 0.725298i \(-0.741702\pi\)
−0.0611596 + 0.998128i \(0.519480\pi\)
\(192\) 0 0
\(193\) −6.58102 + 5.52213i −0.473712 + 0.397492i −0.848146 0.529762i \(-0.822281\pi\)
0.374434 + 0.927253i \(0.377837\pi\)
\(194\) 0 0
\(195\) −0.201609 8.64363i −0.0144375 0.618983i
\(196\) 0 0
\(197\) 15.1886 + 8.76915i 1.08214 + 0.624776i 0.931474 0.363808i \(-0.118524\pi\)
0.150670 + 0.988584i \(0.451857\pi\)
\(198\) 0 0
\(199\) 15.6687 9.04633i 1.11073 0.641278i 0.171708 0.985148i \(-0.445071\pi\)
0.939017 + 0.343870i \(0.111738\pi\)
\(200\) 0 0
\(201\) 22.6383 + 3.44953i 1.59679 + 0.243311i
\(202\) 0 0
\(203\) −7.74845 2.82021i −0.543835 0.197940i
\(204\) 0 0
\(205\) 1.39429 7.90739i 0.0973812 0.552276i
\(206\) 0 0
\(207\) 0.0530065 0.102577i 0.00368421 0.00712957i
\(208\) 0 0
\(209\) −3.90904 + 4.65861i −0.270394 + 0.322243i
\(210\) 0 0
\(211\) −15.8844 + 2.80084i −1.09352 + 0.192818i −0.691188 0.722675i \(-0.742913\pi\)
−0.402335 + 0.915492i \(0.631801\pi\)
\(212\) 0 0
\(213\) 4.73029 4.16096i 0.324114 0.285104i
\(214\) 0 0
\(215\) 13.9290 0.949952
\(216\) 0 0
\(217\) −10.1352 −0.688023
\(218\) 0 0
\(219\) 6.63758 + 2.24203i 0.448526 + 0.151502i
\(220\) 0 0
\(221\) 2.70108 0.476273i 0.181694 0.0320376i
\(222\) 0 0
\(223\) 1.67593 1.99730i 0.112229 0.133749i −0.707005 0.707208i \(-0.749954\pi\)
0.819234 + 0.573459i \(0.194399\pi\)
\(224\) 0 0
\(225\) 4.59469 4.23575i 0.306313 0.282384i
\(226\) 0 0
\(227\) 3.97284 22.5311i 0.263686 1.49544i −0.509063 0.860729i \(-0.670008\pi\)
0.772750 0.634711i \(-0.218881\pi\)
\(228\) 0 0
\(229\) 0.564600 + 0.205498i 0.0373098 + 0.0135797i 0.360608 0.932718i \(-0.382569\pi\)
−0.323298 + 0.946297i \(0.604792\pi\)
\(230\) 0 0
\(231\) −5.73498 + 7.16769i −0.377334 + 0.471599i
\(232\) 0 0
\(233\) −25.8951 + 14.9505i −1.69644 + 0.979441i −0.747355 + 0.664425i \(0.768676\pi\)
−0.949086 + 0.315016i \(0.897990\pi\)
\(234\) 0 0
\(235\) −12.1474 7.01332i −0.792411 0.457499i
\(236\) 0 0
\(237\) 18.5664 11.3046i 1.20602 0.734313i
\(238\) 0 0
\(239\) 0.533039 0.447273i 0.0344794 0.0289317i −0.625385 0.780316i \(-0.715058\pi\)
0.659865 + 0.751385i \(0.270614\pi\)
\(240\) 0 0
\(241\) −14.8422 + 5.40211i −0.956069 + 0.347981i −0.772492 0.635024i \(-0.780990\pi\)
−0.183577 + 0.983005i \(0.558768\pi\)
\(242\) 0 0
\(243\) −13.0261 8.56278i −0.835623 0.549303i
\(244\) 0 0
\(245\) 2.72749 + 7.49371i 0.174253 + 0.478755i
\(246\) 0 0
\(247\) −3.29111 3.92219i −0.209408 0.249563i
\(248\) 0 0
\(249\) 3.28134 + 5.38920i 0.207947 + 0.341527i
\(250\) 0 0
\(251\) 11.0929 19.2135i 0.700180 1.21275i −0.268223 0.963357i \(-0.586436\pi\)
0.968403 0.249391i \(-0.0802303\pi\)
\(252\) 0 0
\(253\) 0.0668050 + 0.115710i 0.00420000 + 0.00727461i
\(254\) 0 0
\(255\) −2.16756 1.73430i −0.135738 0.108606i
\(256\) 0 0
\(257\) −7.17758 + 19.7202i −0.447725 + 1.23012i 0.486578 + 0.873637i \(0.338245\pi\)
−0.934304 + 0.356478i \(0.883977\pi\)
\(258\) 0 0
\(259\) 9.32143 + 1.64362i 0.579205 + 0.102130i
\(260\) 0 0
\(261\) 10.9827 + 11.9134i 0.679810 + 0.737418i
\(262\) 0 0
\(263\) −6.15049 5.16087i −0.379256 0.318233i 0.433155 0.901320i \(-0.357400\pi\)
−0.812410 + 0.583086i \(0.801845\pi\)
\(264\) 0 0
\(265\) −3.76421 21.3479i −0.231233 1.31139i
\(266\) 0 0
\(267\) 4.87528 14.4334i 0.298363 0.883309i
\(268\) 0 0
\(269\) 26.1874i 1.59668i −0.602209 0.798338i \(-0.705713\pi\)
0.602209 0.798338i \(-0.294287\pi\)
\(270\) 0 0
\(271\) 14.9170i 0.906140i −0.891475 0.453070i \(-0.850329\pi\)
0.891475 0.453070i \(-0.149671\pi\)
\(272\) 0 0
\(273\) −5.10452 5.80297i −0.308940 0.351212i
\(274\) 0 0
\(275\) 1.25572 + 7.12155i 0.0757229 + 0.429446i
\(276\) 0 0
\(277\) −14.2963 11.9960i −0.858983 0.720772i 0.102766 0.994706i \(-0.467231\pi\)
−0.961749 + 0.273933i \(0.911675\pi\)
\(278\) 0 0
\(279\) 17.6935 + 9.14312i 1.05928 + 0.547384i
\(280\) 0 0
\(281\) −4.14342 0.730597i −0.247176 0.0435838i 0.0486874 0.998814i \(-0.484496\pi\)
−0.295863 + 0.955230i \(0.595607\pi\)
\(282\) 0 0
\(283\) 0.667465 1.83384i 0.0396766 0.109011i −0.918272 0.395950i \(-0.870415\pi\)
0.957949 + 0.286939i \(0.0926377\pi\)
\(284\) 0 0
\(285\) −0.780618 + 5.12298i −0.0462398 + 0.303459i
\(286\) 0 0
\(287\) −3.58869 6.21579i −0.211834 0.366907i
\(288\) 0 0
\(289\) −8.05969 + 13.9598i −0.474099 + 0.821164i
\(290\) 0 0
\(291\) −7.35426 + 0.171535i −0.431114 + 0.0100556i
\(292\) 0 0
\(293\) −5.47915 6.52979i −0.320095 0.381474i 0.581871 0.813281i \(-0.302321\pi\)
−0.901966 + 0.431806i \(0.857876\pi\)
\(294\) 0 0
\(295\) 8.66693 + 23.8122i 0.504608 + 1.38640i
\(296\) 0 0
\(297\) 16.4779 7.33935i 0.956144 0.425872i
\(298\) 0 0
\(299\) −0.105706 + 0.0384737i −0.00611311 + 0.00222499i
\(300\) 0 0
\(301\) 9.53804 8.00336i 0.549763 0.461306i
\(302\) 0 0
\(303\) −11.4354 6.25131i −0.656945 0.359128i
\(304\) 0 0
\(305\) 20.5041 + 11.8381i 1.17406 + 0.677845i
\(306\) 0 0
\(307\) −8.57163 + 4.94883i −0.489209 + 0.282445i −0.724246 0.689542i \(-0.757812\pi\)
0.235037 + 0.971986i \(0.424479\pi\)
\(308\) 0 0
\(309\) 7.92358 + 20.2851i 0.450756 + 1.15398i
\(310\) 0 0
\(311\) 22.5915 + 8.22263i 1.28105 + 0.466262i 0.890778 0.454439i \(-0.150160\pi\)
0.390267 + 0.920702i \(0.372383\pi\)
\(312\) 0 0
\(313\) 0.300476 1.70409i 0.0169839 0.0963207i −0.975137 0.221601i \(-0.928872\pi\)
0.992121 + 0.125280i \(0.0399829\pi\)
\(314\) 0 0
\(315\) −0.997677 + 7.75835i −0.0562127 + 0.437133i
\(316\) 0 0
\(317\) −11.5341 + 13.7458i −0.647819 + 0.772040i −0.985583 0.169190i \(-0.945885\pi\)
0.337765 + 0.941231i \(0.390329\pi\)
\(318\) 0 0
\(319\) −18.4651 + 3.25590i −1.03385 + 0.182295i
\(320\) 0 0
\(321\) −6.48339 32.3400i −0.361868 1.80504i
\(322\) 0 0
\(323\) −1.64391 −0.0914698
\(324\) 0 0
\(325\) −6.08830 −0.337718
\(326\) 0 0
\(327\) −1.52085 7.58620i −0.0841033 0.419518i
\(328\) 0 0
\(329\) −12.3478 + 2.17725i −0.680756 + 0.120036i
\(330\) 0 0
\(331\) 6.23357 7.42888i 0.342628 0.408328i −0.567023 0.823702i \(-0.691905\pi\)
0.909651 + 0.415374i \(0.136349\pi\)
\(332\) 0 0
\(333\) −14.7901 11.2783i −0.810493 0.618049i
\(334\) 0 0
\(335\) −3.92104 + 22.2373i −0.214229 + 1.21495i
\(336\) 0 0
\(337\) −25.7092 9.35737i −1.40047 0.509728i −0.472150 0.881518i \(-0.656522\pi\)
−0.928317 + 0.371790i \(0.878744\pi\)
\(338\) 0 0
\(339\) 1.14356 + 2.92762i 0.0621097 + 0.159006i
\(340\) 0 0
\(341\) −19.9588 + 11.5232i −1.08083 + 0.624018i
\(342\) 0 0
\(343\) 15.4284 + 8.90759i 0.833055 + 0.480965i
\(344\) 0 0
\(345\) 0.0999001 + 0.0546118i 0.00537844 + 0.00294020i
\(346\) 0 0
\(347\) −19.6703 + 16.5053i −1.05596 + 0.886052i −0.993707 0.112008i \(-0.964272\pi\)
−0.0622488 + 0.998061i \(0.519827\pi\)
\(348\) 0 0
\(349\) 20.8555 7.59080i 1.11637 0.406326i 0.283045 0.959107i \(-0.408655\pi\)
0.833327 + 0.552780i \(0.186433\pi\)
\(350\) 0 0
\(351\) 3.67626 + 14.7354i 0.196224 + 0.786516i
\(352\) 0 0
\(353\) 6.49361 + 17.8410i 0.345620 + 0.949583i 0.983732 + 0.179640i \(0.0574932\pi\)
−0.638113 + 0.769943i \(0.720285\pi\)
\(354\) 0 0
\(355\) 3.99306 + 4.75874i 0.211930 + 0.252568i
\(356\) 0 0
\(357\) −2.48076 + 0.0578627i −0.131296 + 0.00306242i
\(358\) 0 0
\(359\) −11.3488 + 19.6567i −0.598968 + 1.03744i 0.394006 + 0.919108i \(0.371089\pi\)
−0.992974 + 0.118335i \(0.962244\pi\)
\(360\) 0 0
\(361\) −7.96560 13.7968i −0.419242 0.726149i
\(362\) 0 0
\(363\) −0.274315 + 1.80025i −0.0143978 + 0.0944887i
\(364\) 0 0
\(365\) −2.36278 + 6.49170i −0.123674 + 0.339791i
\(366\) 0 0
\(367\) 7.82713 + 1.38013i 0.408573 + 0.0720424i 0.374157 0.927365i \(-0.377932\pi\)
0.0344155 + 0.999408i \(0.489043\pi\)
\(368\) 0 0
\(369\) 0.657580 + 14.0886i 0.0342323 + 0.733423i
\(370\) 0 0
\(371\) −14.8437 12.4553i −0.770645 0.646648i
\(372\) 0 0
\(373\) 0.275405 + 1.56190i 0.0142599 + 0.0808721i 0.991107 0.133066i \(-0.0424821\pi\)
−0.976847 + 0.213938i \(0.931371\pi\)
\(374\) 0 0
\(375\) 13.8389 + 15.7325i 0.714638 + 0.812421i
\(376\) 0 0
\(377\) 15.7860i 0.813023i
\(378\) 0 0
\(379\) 24.0092i 1.23327i 0.787249 + 0.616635i \(0.211505\pi\)
−0.787249 + 0.616635i \(0.788495\pi\)
\(380\) 0 0
\(381\) −4.01862 + 11.8972i −0.205880 + 0.609512i
\(382\) 0 0
\(383\) −0.226558 1.28488i −0.0115766 0.0656541i 0.978472 0.206379i \(-0.0661679\pi\)
−0.990049 + 0.140725i \(0.955057\pi\)
\(384\) 0 0
\(385\) −6.93396 5.81829i −0.353388 0.296527i
\(386\) 0 0
\(387\) −23.8709 + 5.36743i −1.21343 + 0.272842i
\(388\) 0 0
\(389\) 15.0139 + 2.64735i 0.761234 + 0.134226i 0.540772 0.841169i \(-0.318132\pi\)
0.220462 + 0.975396i \(0.429243\pi\)
\(390\) 0 0
\(391\) −0.0123529 + 0.0339392i −0.000624711 + 0.00171638i
\(392\) 0 0
\(393\) 23.6371 + 18.9124i 1.19233 + 0.954004i
\(394\) 0 0
\(395\) 10.7170 + 18.5625i 0.539233 + 0.933979i
\(396\) 0 0
\(397\) 7.08632 12.2739i 0.355652 0.616008i −0.631577 0.775313i \(-0.717592\pi\)
0.987229 + 0.159305i \(0.0509254\pi\)
\(398\) 0 0
\(399\) 2.40904 + 3.95654i 0.120603 + 0.198075i
\(400\) 0 0
\(401\) 19.9488 + 23.7741i 0.996197 + 1.18722i 0.982299 + 0.187317i \(0.0599793\pi\)
0.0138970 + 0.999903i \(0.495576\pi\)
\(402\) 0 0
\(403\) −6.63634 18.2332i −0.330580 0.908260i
\(404\) 0 0
\(405\) 8.74061 12.6441i 0.434324 0.628289i
\(406\) 0 0
\(407\) 20.2250 7.36129i 1.00252 0.364886i
\(408\) 0 0
\(409\) 6.87431 5.76823i 0.339913 0.285221i −0.456812 0.889563i \(-0.651009\pi\)
0.796725 + 0.604343i \(0.206564\pi\)
\(410\) 0 0
\(411\) 7.86166 4.78676i 0.387787 0.236114i
\(412\) 0 0
\(413\) 19.6168 + 11.3258i 0.965280 + 0.557305i
\(414\) 0 0
\(415\) −5.38806 + 3.11080i −0.264489 + 0.152703i
\(416\) 0 0
\(417\) 13.0578 16.3199i 0.639442 0.799187i
\(418\) 0 0
\(419\) 8.46849 + 3.08228i 0.413713 + 0.150579i 0.540487 0.841352i \(-0.318240\pi\)
−0.126774 + 0.991932i \(0.540462\pi\)
\(420\) 0 0
\(421\) −2.46690 + 13.9905i −0.120229 + 0.681855i 0.863798 + 0.503838i \(0.168079\pi\)
−0.984027 + 0.178017i \(0.943032\pi\)
\(422\) 0 0
\(423\) 23.5202 + 7.33821i 1.14359 + 0.356796i
\(424\) 0 0
\(425\) −1.25651 + 1.49746i −0.0609499 + 0.0726373i
\(426\) 0 0
\(427\) 20.8423 3.67506i 1.00863 0.177849i
\(428\) 0 0
\(429\) −16.6498 5.62394i −0.803860 0.271526i
\(430\) 0 0
\(431\) −26.9626 −1.29874 −0.649372 0.760471i \(-0.724968\pi\)
−0.649372 + 0.760471i \(0.724968\pi\)
\(432\) 0 0
\(433\) 3.92105 0.188434 0.0942169 0.995552i \(-0.469965\pi\)
0.0942169 + 0.995552i \(0.469965\pi\)
\(434\) 0 0
\(435\) −11.9966 + 10.5527i −0.575192 + 0.505962i
\(436\) 0 0
\(437\) 0.0663982 0.0117078i 0.00317626 0.000560060i
\(438\) 0 0
\(439\) −12.3057 + 14.6654i −0.587320 + 0.699941i −0.975089 0.221816i \(-0.928802\pi\)
0.387769 + 0.921757i \(0.373246\pi\)
\(440\) 0 0
\(441\) −7.56187 11.7914i −0.360089 0.561493i
\(442\) 0 0
\(443\) 3.58423 20.3272i 0.170292 0.965772i −0.773147 0.634226i \(-0.781319\pi\)
0.943439 0.331546i \(-0.107570\pi\)
\(444\) 0 0
\(445\) 14.1162 + 5.13787i 0.669171 + 0.243558i
\(446\) 0 0
\(447\) −1.90268 0.289922i −0.0899936 0.0137128i
\(448\) 0 0
\(449\) −12.2207 + 7.05561i −0.576730 + 0.332975i −0.759833 0.650119i \(-0.774719\pi\)
0.183103 + 0.983094i \(0.441386\pi\)
\(450\) 0 0
\(451\) −14.1341 8.16033i −0.665549 0.384255i
\(452\) 0 0
\(453\) −0.350559 15.0296i −0.0164707 0.706151i
\(454\) 0 0
\(455\) 5.83787 4.89855i 0.273684 0.229648i
\(456\) 0 0
\(457\) 13.0602 4.75353i 0.610932 0.222361i −0.0179791 0.999838i \(-0.505723\pi\)
0.628911 + 0.777477i \(0.283501\pi\)
\(458\) 0 0
\(459\) 4.38297 + 2.13691i 0.204579 + 0.0997426i
\(460\) 0 0
\(461\) −11.4525 31.4654i −0.533394 1.46549i −0.855007 0.518617i \(-0.826447\pi\)
0.321613 0.946871i \(-0.395775\pi\)
\(462\) 0 0
\(463\) −12.5926 15.0072i −0.585226 0.697445i 0.389455 0.921046i \(-0.372663\pi\)
−0.974681 + 0.223600i \(0.928219\pi\)
\(464\) 0 0
\(465\) −9.42001 + 17.2318i −0.436843 + 0.799106i
\(466\) 0 0
\(467\) −6.24674 + 10.8197i −0.289065 + 0.500675i −0.973587 0.228317i \(-0.926678\pi\)
0.684522 + 0.728992i \(0.260011\pi\)
\(468\) 0 0
\(469\) 10.0922 + 17.4802i 0.466013 + 0.807159i
\(470\) 0 0
\(471\) 0.291364 0.113810i 0.0134254 0.00524409i
\(472\) 0 0
\(473\) 9.68341 26.6049i 0.445244 1.22330i
\(474\) 0 0
\(475\) 3.59369 + 0.633664i 0.164890 + 0.0290745i
\(476\) 0 0
\(477\) 14.6771 + 35.1345i 0.672020 + 1.60870i
\(478\) 0 0
\(479\) 29.6447 + 24.8749i 1.35450 + 1.13656i 0.977638 + 0.210294i \(0.0674420\pi\)
0.376864 + 0.926269i \(0.377002\pi\)
\(480\) 0 0
\(481\) 3.14663 + 17.8454i 0.143474 + 0.813681i
\(482\) 0 0
\(483\) 0.0997865 0.0200048i 0.00454044 0.000910250i
\(484\) 0 0
\(485\) 7.25369i 0.329373i
\(486\) 0 0
\(487\) 20.1282i 0.912096i 0.889955 + 0.456048i \(0.150736\pi\)
−0.889955 + 0.456048i \(0.849264\pi\)
\(488\) 0 0
\(489\) −36.8274 + 7.38302i −1.66539 + 0.333872i
\(490\) 0 0
\(491\) −1.32914 7.53795i −0.0599834 0.340183i 0.940016 0.341130i \(-0.110810\pi\)
−1.00000 0.000947128i \(0.999699\pi\)
\(492\) 0 0
\(493\) −3.88268 3.25795i −0.174867 0.146731i
\(494\) 0 0
\(495\) 6.85617 + 16.4125i 0.308162 + 0.737686i
\(496\) 0 0
\(497\) 5.46857 + 0.964257i 0.245299 + 0.0432528i
\(498\) 0 0
\(499\) −4.53447 + 12.4584i −0.202991 + 0.557713i −0.998859 0.0477573i \(-0.984793\pi\)
0.795868 + 0.605470i \(0.207015\pi\)
\(500\) 0 0
\(501\) 4.12523 1.61136i 0.184302 0.0719903i
\(502\) 0 0
\(503\) −6.64136 11.5032i −0.296124 0.512902i 0.679122 0.734026i \(-0.262361\pi\)
−0.975246 + 0.221124i \(0.929027\pi\)
\(504\) 0 0
\(505\) 6.42540 11.1291i 0.285927 0.495240i
\(506\) 0 0
\(507\) −3.70340 + 6.77454i −0.164474 + 0.300868i
\(508\) 0 0
\(509\) −24.3879 29.0644i −1.08097 1.28826i −0.955124 0.296206i \(-0.904278\pi\)
−0.125851 0.992049i \(-0.540166\pi\)
\(510\) 0 0
\(511\) 2.11207 + 5.80287i 0.0934325 + 0.256704i
\(512\) 0 0
\(513\) −0.636310 9.08034i −0.0280938 0.400907i
\(514\) 0 0
\(515\) −20.1790 + 7.34455i −0.889193 + 0.323640i
\(516\) 0 0
\(517\) −21.8405 + 18.3264i −0.960546 + 0.805994i
\(518\) 0 0
\(519\) 0.458608 + 19.6620i 0.0201306 + 0.863064i
\(520\) 0 0
\(521\) 17.1443 + 9.89824i 0.751103 + 0.433650i 0.826092 0.563535i \(-0.190559\pi\)
−0.0749891 + 0.997184i \(0.523892\pi\)
\(522\) 0 0
\(523\) −20.9712 + 12.1077i −0.917007 + 0.529434i −0.882679 0.469976i \(-0.844262\pi\)
−0.0343279 + 0.999411i \(0.510929\pi\)
\(524\) 0 0
\(525\) 5.44538 + 0.829744i 0.237656 + 0.0362130i
\(526\) 0 0
\(527\) −5.85419 2.13075i −0.255012 0.0928169i
\(528\) 0 0
\(529\) −3.99365 + 22.6491i −0.173637 + 0.984744i
\(530\) 0 0
\(531\) −24.0288 37.4685i −1.04276 1.62600i
\(532\) 0 0
\(533\) 8.83238 10.5260i 0.382573 0.455933i
\(534\) 0 0
\(535\) 32.0294 5.64766i 1.38475 0.244169i
\(536\) 0 0
\(537\) 6.78259 5.96624i 0.292690 0.257462i
\(538\) 0 0
\(539\) 16.2094 0.698188
\(540\) 0 0
\(541\) −6.77906 −0.291454 −0.145727 0.989325i \(-0.546552\pi\)
−0.145727 + 0.989325i \(0.546552\pi\)
\(542\) 0 0
\(543\) −19.6263 6.62934i −0.842246 0.284492i
\(544\) 0 0
\(545\) 7.51336 1.32481i 0.321837 0.0567485i
\(546\) 0 0
\(547\) 16.7637 19.9782i 0.716765 0.854207i −0.277548 0.960712i \(-0.589522\pi\)
0.994312 + 0.106505i \(0.0339661\pi\)
\(548\) 0 0
\(549\) −39.7007 12.3864i −1.69439 0.528640i
\(550\) 0 0
\(551\) −1.64300 + 9.31790i −0.0699940 + 0.396956i
\(552\) 0 0
\(553\) 18.0043 + 6.55301i 0.765619 + 0.278662i
\(554\) 0 0
\(555\) 11.4581 14.3206i 0.486370 0.607875i
\(556\) 0 0
\(557\) −24.8803 + 14.3647i −1.05421 + 0.608650i −0.923826 0.382813i \(-0.874955\pi\)
−0.130387 + 0.991463i \(0.541622\pi\)
\(558\) 0 0
\(559\) 20.6433 + 11.9184i 0.873120 + 0.504096i
\(560\) 0 0
\(561\) −4.81946 + 2.93444i −0.203478 + 0.123892i
\(562\) 0 0
\(563\) 16.0134 13.4368i 0.674885 0.566296i −0.239622 0.970866i \(-0.577023\pi\)
0.914507 + 0.404571i \(0.132579\pi\)
\(564\) 0 0
\(565\) −2.91231 + 1.05999i −0.122522 + 0.0445943i
\(566\) 0 0
\(567\) −1.27984 13.6803i −0.0537482 0.574520i
\(568\) 0 0
\(569\) −9.78377 26.8807i −0.410157 1.12690i −0.957108 0.289732i \(-0.906434\pi\)
0.546951 0.837165i \(-0.315788\pi\)
\(570\) 0 0
\(571\) −6.24820 7.44632i −0.261479 0.311619i 0.619292 0.785161i \(-0.287420\pi\)
−0.880771 + 0.473542i \(0.842975\pi\)
\(572\) 0 0
\(573\) 9.93048 + 16.3096i 0.414852 + 0.681342i
\(574\) 0 0
\(575\) 0.0400863 0.0694315i 0.00167171 0.00289549i
\(576\) 0 0
\(577\) −3.09107 5.35388i −0.128683 0.222885i 0.794484 0.607285i \(-0.207742\pi\)
−0.923166 + 0.384400i \(0.874408\pi\)
\(578\) 0 0
\(579\) 11.6186 + 9.29621i 0.482852 + 0.386337i
\(580\) 0 0
\(581\) −1.90212 + 5.22603i −0.0789132 + 0.216812i
\(582\) 0 0
\(583\) −43.3921 7.65119i −1.79712 0.316880i
\(584\) 0 0
\(585\) −14.6105 + 3.28520i −0.604069 + 0.135826i
\(586\) 0 0
\(587\) 4.60609 + 3.86497i 0.190114 + 0.159524i 0.732877 0.680362i \(-0.238177\pi\)
−0.542763 + 0.839886i \(0.682622\pi\)
\(588\) 0 0
\(589\) 2.01948 + 11.4531i 0.0832113 + 0.471915i
\(590\) 0 0
\(591\) 9.72117 28.7798i 0.399875 1.18384i
\(592\) 0 0
\(593\) 45.9763i 1.88802i −0.329915 0.944011i \(-0.607020\pi\)
0.329915 0.944011i \(-0.392980\pi\)
\(594\) 0 0
\(595\) 2.44683i 0.100310i
\(596\) 0 0
\(597\) −20.6976 23.5296i −0.847096 0.963003i
\(598\) 0 0
\(599\) −4.50094 25.5261i −0.183903 1.04297i −0.927356 0.374180i \(-0.877924\pi\)
0.743453 0.668788i \(-0.233187\pi\)
\(600\) 0 0
\(601\) 6.44957 + 5.41183i 0.263084 + 0.220753i 0.764782 0.644289i \(-0.222847\pi\)
−0.501698 + 0.865043i \(0.667291\pi\)
\(602\) 0 0
\(603\) −1.84926 39.6202i −0.0753077 1.61346i
\(604\) 0 0
\(605\) −1.76836 0.311810i −0.0718941 0.0126769i
\(606\) 0 0
\(607\) 5.71034 15.6890i 0.231776 0.636798i −0.768219 0.640188i \(-0.778857\pi\)
0.999994 + 0.00338920i \(0.00107882\pi\)
\(608\) 0 0
\(609\) −2.15140 + 14.1191i −0.0871791 + 0.572133i
\(610\) 0 0
\(611\) −12.0020 20.7880i −0.485548 0.840993i
\(612\) 0 0
\(613\) −12.4645 + 21.5892i −0.503437 + 0.871979i 0.496555 + 0.868005i \(0.334598\pi\)
−0.999992 + 0.00397384i \(0.998735\pi\)
\(614\) 0 0
\(615\) −13.9035 + 0.324294i −0.560643 + 0.0130768i
\(616\) 0 0
\(617\) −5.56720 6.63473i −0.224127 0.267104i 0.642249 0.766496i \(-0.278001\pi\)
−0.866376 + 0.499392i \(0.833557\pi\)
\(618\) 0 0
\(619\) −6.19615 17.0238i −0.249044 0.684244i −0.999722 0.0235754i \(-0.992495\pi\)
0.750678 0.660669i \(-0.229727\pi\)
\(620\) 0 0
\(621\) −0.192248 0.0550956i −0.00771466 0.00221091i
\(622\) 0 0
\(623\) 12.6183 4.59269i 0.505542 0.184002i
\(624\) 0 0
\(625\) −7.84845 + 6.58563i −0.313938 + 0.263425i
\(626\) 0 0
\(627\) 9.24240 + 5.05249i 0.369106 + 0.201777i
\(628\) 0 0
\(629\) 5.03860 + 2.90904i 0.200902 + 0.115991i
\(630\) 0 0
\(631\) 39.2093 22.6375i 1.56090 0.901185i 0.563732 0.825958i \(-0.309365\pi\)
0.997166 0.0752273i \(-0.0239682\pi\)
\(632\) 0 0
\(633\) 10.1645 + 26.0222i 0.404005 + 1.03429i
\(634\) 0 0
\(635\) −11.6357 4.23506i −0.461750 0.168063i
\(636\) 0 0
\(637\) −2.36979 + 13.4397i −0.0938944 + 0.532502i
\(638\) 0 0
\(639\) −8.67687 6.61663i −0.343252 0.261750i
\(640\) 0 0
\(641\) 9.21101 10.9773i 0.363813 0.433576i −0.552823 0.833299i \(-0.686449\pi\)
0.916636 + 0.399723i \(0.130894\pi\)
\(642\) 0 0
\(643\) 24.8469 4.38119i 0.979867 0.172777i 0.339299 0.940678i \(-0.389810\pi\)
0.640568 + 0.767901i \(0.278699\pi\)
\(644\) 0 0
\(645\) −4.74228 23.6551i −0.186727 0.931419i
\(646\) 0 0
\(647\) −36.8495 −1.44870 −0.724352 0.689430i \(-0.757861\pi\)
−0.724352 + 0.689430i \(0.757861\pi\)
\(648\) 0 0
\(649\) 51.5074 2.02184
\(650\) 0 0
\(651\) 3.45064 + 17.2122i 0.135241 + 0.674600i
\(652\) 0 0
\(653\) 31.3576 5.52920i 1.22712 0.216374i 0.477732 0.878506i \(-0.341459\pi\)
0.749387 + 0.662132i \(0.230348\pi\)
\(654\) 0 0
\(655\) −19.1871 + 22.8663i −0.749703 + 0.893461i
\(656\) 0 0
\(657\) 1.54771 12.0357i 0.0603820 0.469556i
\(658\) 0 0
\(659\) −2.52273 + 14.3071i −0.0982717 + 0.557326i 0.895424 + 0.445215i \(0.146873\pi\)
−0.993696 + 0.112112i \(0.964239\pi\)
\(660\) 0 0
\(661\) 6.12471 + 2.22921i 0.238224 + 0.0867063i 0.458373 0.888760i \(-0.348432\pi\)
−0.220150 + 0.975466i \(0.570655\pi\)
\(662\) 0 0
\(663\) −1.72845 4.42498i −0.0671273 0.171852i
\(664\) 0 0
\(665\) −3.95571 + 2.28383i −0.153396 + 0.0885630i
\(666\) 0 0
\(667\) 0.180025 + 0.103938i 0.00697061 + 0.00402449i
\(668\) 0 0
\(669\) −3.96252 2.16617i −0.153200 0.0837489i
\(670\) 0 0
\(671\) 36.8655 30.9338i 1.42318 1.19419i
\(672\) 0 0
\(673\) 17.8218 6.48661i 0.686980 0.250040i 0.0251385 0.999684i \(-0.491997\pi\)
0.661842 + 0.749644i \(0.269775\pi\)
\(674\) 0 0
\(675\) −8.75772 6.36088i −0.337085 0.244830i
\(676\) 0 0
\(677\) 9.86289 + 27.0981i 0.379062 + 1.04146i 0.971746 + 0.236029i \(0.0758459\pi\)
−0.592684 + 0.805435i \(0.701932\pi\)
\(678\) 0 0
\(679\) −4.16784 4.96703i −0.159947 0.190617i
\(680\) 0 0
\(681\) −39.6162 + 0.924033i −1.51810 + 0.0354090i
\(682\) 0 0
\(683\) −0.473868 + 0.820764i −0.0181321 + 0.0314057i −0.874949 0.484215i \(-0.839105\pi\)
0.856817 + 0.515621i \(0.172439\pi\)
\(684\) 0 0
\(685\) 4.53797 + 7.86000i 0.173387 + 0.300315i
\(686\) 0 0
\(687\) 0.156764 1.02880i 0.00598094 0.0392513i
\(688\) 0 0
\(689\) 12.6877 34.8592i 0.483363 1.32803i
\(690\) 0 0
\(691\) −21.8003 3.84398i −0.829321 0.146232i −0.257156 0.966370i \(-0.582785\pi\)
−0.572165 + 0.820138i \(0.693896\pi\)
\(692\) 0 0
\(693\) 14.1251 + 7.29917i 0.536570 + 0.277273i
\(694\) 0 0
\(695\) 15.7877 + 13.2475i 0.598862 + 0.502505i
\(696\) 0 0
\(697\) −0.766098 4.34476i −0.0290180 0.164569i
\(698\) 0 0
\(699\) 34.2061 + 38.8865i 1.29379 + 1.47082i
\(700\) 0 0
\(701\) 37.6486i 1.42197i −0.703209 0.710983i \(-0.748250\pi\)
0.703209 0.710983i \(-0.251750\pi\)
\(702\) 0 0
\(703\) 10.8610i 0.409629i
\(704\) 0 0
\(705\) −7.77473 + 23.0173i −0.292813 + 0.866880i
\(706\) 0 0
\(707\) −1.99473 11.3127i −0.0750197 0.425458i
\(708\) 0 0
\(709\) 24.0912 + 20.2150i 0.904766 + 0.759189i 0.971116 0.238608i \(-0.0766911\pi\)
−0.0663503 + 0.997796i \(0.521135\pi\)
\(710\) 0 0
\(711\) −25.5193 27.6818i −0.957048 1.03815i
\(712\) 0 0
\(713\) 0.251628 + 0.0443687i 0.00942353 + 0.00166162i
\(714\) 0 0
\(715\) 5.92684 16.2839i 0.221651 0.608982i
\(716\) 0 0
\(717\) −0.941064 0.752960i −0.0351447 0.0281198i
\(718\) 0 0
\(719\) −10.2799 17.8053i −0.383375 0.664025i 0.608167 0.793809i \(-0.291905\pi\)
−0.991542 + 0.129784i \(0.958572\pi\)
\(720\) 0 0
\(721\) −9.59772 + 16.6237i −0.357438 + 0.619100i
\(722\) 0 0
\(723\) 14.2274 + 23.3667i 0.529122 + 0.869016i
\(724\) 0 0
\(725\) 7.23194 + 8.61869i 0.268588 + 0.320090i
\(726\) 0 0
\(727\) −16.7919 46.1353i −0.622776 1.71106i −0.700089 0.714056i \(-0.746856\pi\)
0.0773130 0.997007i \(-0.475366\pi\)
\(728\) 0 0
\(729\) −10.1070 + 25.0370i −0.374332 + 0.927295i
\(730\) 0 0
\(731\) 7.19182 2.61761i 0.265999 0.0968158i
\(732\) 0 0
\(733\) 31.2847 26.2510i 1.15553 0.969603i 0.155694 0.987805i \(-0.450239\pi\)
0.999834 + 0.0182021i \(0.00579423\pi\)
\(734\) 0 0
\(735\) 11.7977 7.18329i 0.435163 0.264960i
\(736\) 0 0
\(737\) 39.7482 + 22.9486i 1.46414 + 0.845323i
\(738\) 0 0
\(739\) −34.5124 + 19.9257i −1.26956 + 0.732981i −0.974905 0.222623i \(-0.928538\pi\)
−0.294655 + 0.955604i \(0.595205\pi\)
\(740\) 0 0
\(741\) −5.54041 + 6.92451i −0.203532 + 0.254378i
\(742\) 0 0
\(743\) −24.8926 9.06017i −0.913221 0.332385i −0.157683 0.987490i \(-0.550402\pi\)
−0.755538 + 0.655104i \(0.772625\pi\)
\(744\) 0 0
\(745\) 0.329550 1.86897i 0.0120738 0.0684739i
\(746\) 0 0
\(747\) 8.03509 7.40738i 0.293989 0.271022i
\(748\) 0 0
\(749\) 18.6874 22.2708i 0.682824 0.813758i
\(750\) 0 0
\(751\) −6.30283 + 1.11136i −0.229994 + 0.0405541i −0.287457 0.957794i \(-0.592810\pi\)
0.0574634 + 0.998348i \(0.481699\pi\)
\(752\) 0 0
\(753\) −36.4063 12.2972i −1.32672 0.448136i
\(754\) 0 0
\(755\) 14.8240 0.539502
\(756\) 0 0
\(757\) −23.3500 −0.848671 −0.424336 0.905505i \(-0.639492\pi\)
−0.424336 + 0.905505i \(0.639492\pi\)
\(758\) 0 0
\(759\) 0.173761 0.152847i 0.00630711 0.00554799i
\(760\) 0 0
\(761\) −46.5181 + 8.20240i −1.68628 + 0.297337i −0.932870 0.360213i \(-0.882704\pi\)
−0.753411 + 0.657550i \(0.771593\pi\)
\(762\) 0 0
\(763\) 4.38363 5.22421i 0.158698 0.189129i
\(764\) 0 0
\(765\) −2.20732 + 4.27155i −0.0798060 + 0.154438i
\(766\) 0 0
\(767\) −7.53030 + 42.7065i −0.271903 + 1.54204i
\(768\) 0 0
\(769\) 22.1294 + 8.05443i 0.798006 + 0.290450i 0.708660 0.705550i \(-0.249300\pi\)
0.0893459 + 0.996001i \(0.471522\pi\)
\(770\) 0 0
\(771\) 35.9338 + 5.47543i 1.29412 + 0.197193i
\(772\) 0 0
\(773\) 12.0923 6.98148i 0.434929 0.251106i −0.266515 0.963831i \(-0.585872\pi\)
0.701444 + 0.712724i \(0.252539\pi\)
\(774\) 0 0
\(775\) 11.9763 + 6.91450i 0.430200 + 0.248376i
\(776\) 0 0
\(777\) −0.382286 16.3898i −0.0137144 0.587980i
\(778\) 0 0
\(779\) −6.30895 + 5.29384i −0.226042 + 0.189671i
\(780\) 0 0
\(781\) 11.8653 4.31863i 0.424575 0.154533i
\(782\) 0 0
\(783\) 16.4928 22.7075i 0.589405 0.811498i
\(784\) 0 0
\(785\) 0.105493 + 0.289841i 0.00376522 + 0.0103449i
\(786\) 0 0
\(787\) 33.1852 + 39.5486i 1.18292 + 1.40975i 0.891416 + 0.453186i \(0.149713\pi\)
0.291508 + 0.956568i \(0.405843\pi\)
\(788\) 0 0
\(789\) −6.67051 + 12.2022i −0.237476 + 0.434410i
\(790\) 0 0
\(791\) −1.38518 + 2.39920i −0.0492513 + 0.0853057i
\(792\) 0 0
\(793\) 20.2586 + 35.0889i 0.719403 + 1.24604i
\(794\) 0 0
\(795\) −34.9727 + 13.6607i −1.24035 + 0.484495i
\(796\)