Properties

Label 189.2.e.e.109.3
Level 189
Weight 2
Character 189.109
Analytic conductor 1.509
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 189.e (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(1.5091725982\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.3
Root \(0.500000 - 2.05195i\)
Character \(\chi\) = 189.109
Dual form 189.2.e.e.163.3

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(0.730252 + 1.26483i) q^{2}\) \(+(-0.0665372 + 0.115246i) q^{4}\) \(+(0.296790 + 0.514055i) q^{5}\) \(+(2.32383 - 1.26483i) q^{7}\) \(+2.72665 q^{8}\) \(+O(q^{10})\) \(q\)\(+(0.730252 + 1.26483i) q^{2}\) \(+(-0.0665372 + 0.115246i) q^{4}\) \(+(0.296790 + 0.514055i) q^{5}\) \(+(2.32383 - 1.26483i) q^{7}\) \(+2.72665 q^{8}\) \(+(-0.433463 + 0.750780i) q^{10}\) \(+(-2.23025 + 3.86291i) q^{11}\) \(-4.51459 q^{13}\) \(+(3.29679 + 2.01561i) q^{14}\) \(+(2.12422 + 3.67926i) q^{16}\) \(+(0.136673 - 0.236725i) q^{17}\) \(+(-1.43346 - 2.48283i) q^{19}\) \(-0.0789903 q^{20}\) \(-6.51459 q^{22}\) \(+(-2.52704 - 4.37697i) q^{23}\) \(+(2.32383 - 4.02499i) q^{25}\) \(+(-3.29679 - 5.71021i) q^{26}\) \(+(-0.00885441 + 0.351971i) q^{28}\) \(+0.352336 q^{29}\) \(+(-1.25729 + 2.17770i) q^{31}\) \(+(-0.375780 + 0.650870i) q^{32}\) \(+0.399223 q^{34}\) \(+(1.33988 + 0.819187i) q^{35}\) \(+(3.32383 + 5.75705i) q^{37}\) \(+(2.09358 - 3.62619i) q^{38}\) \(+(0.809243 + 1.40165i) q^{40}\) \(-10.8961 q^{41}\) \(+3.38151 q^{43}\) \(+(-0.296790 - 0.514055i) q^{44}\) \(+(3.69076 - 6.39258i) q^{46}\) \(+(-6.21780 - 10.7695i) q^{47}\) \(+(3.80039 - 5.87852i) q^{49}\) \(+6.78794 q^{50}\) \(+(0.300388 - 0.520288i) q^{52}\) \(+(-5.66372 + 9.80984i) q^{53}\) \(-2.64766 q^{55}\) \(+(6.33628 - 3.44877i) q^{56}\) \(+(0.257295 + 0.445647i) q^{58}\) \(+(4.02704 - 6.97504i) q^{59}\) \(+(1.36693 + 2.36758i) q^{61}\) \(-3.67257 q^{62}\) \(+7.39922 q^{64}\) \(+(-1.33988 - 2.32075i) q^{65}\) \(+(-2.93346 + 5.08091i) q^{67}\) \(+(0.0181877 + 0.0315020i) q^{68}\) \(+(-0.0576828 + 2.29294i) q^{70}\) \(+2.60078 q^{71}\) \(+(-5.55768 + 9.62619i) q^{73}\) \(+(-4.85447 + 8.40819i) q^{74}\) \(+0.381515 q^{76}\) \(+(-0.296790 + 11.7977i) q^{77}\) \(+(-5.58113 - 9.66679i) q^{79}\) \(+(-1.26089 + 2.18393i) q^{80}\) \(+(-7.95691 - 13.7818i) q^{82}\) \(+16.5438 q^{83}\) \(+0.162253 q^{85}\) \(+(2.46936 + 4.27706i) q^{86}\) \(+(-6.08113 + 10.5328i) q^{88}\) \(+(2.68716 + 4.65430i) q^{89}\) \(+(-10.4911 + 5.71021i) q^{91}\) \(+0.672570 q^{92}\) \(+(9.08113 - 15.7290i) q^{94}\) \(+(0.850874 - 1.47376i) q^{95}\) \(-2.26615 q^{97}\) \(+(10.2106 + 0.514055i) q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut -\mathstrut 10q^{16} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 26q^{20} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 17q^{26} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut +\mathstrut 24q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 18q^{43} \) \(\mathstrut +\mathstrut q^{44} \) \(\mathstrut +\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 9q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 9q^{52} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut q^{61} \) \(\mathstrut -\mathstrut 42q^{62} \) \(\mathstrut +\mathstrut 66q^{64} \) \(\mathstrut -\mathstrut 10q^{65} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut -\mathstrut 39q^{68} \) \(\mathstrut +\mathstrut 26q^{70} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 7q^{73} \) \(\mathstrut -\mathstrut 36q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 43q^{82} \) \(\mathstrut +\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 54q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 28q^{97} \) \(\mathstrut +\mathstrut 49q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.730252 + 1.26483i 0.516366 + 0.894373i 0.999819 + 0.0190026i \(0.00604908\pi\)
−0.483453 + 0.875370i \(0.660618\pi\)
\(3\) 0 0
\(4\) −0.0665372 + 0.115246i −0.0332686 + 0.0576229i
\(5\) 0.296790 + 0.514055i 0.132728 + 0.229892i 0.924727 0.380630i \(-0.124293\pi\)
−0.791999 + 0.610522i \(0.790960\pi\)
\(6\) 0 0
\(7\) 2.32383 1.26483i 0.878326 0.478062i
\(8\) 2.72665 0.964018
\(9\) 0 0
\(10\) −0.433463 + 0.750780i −0.137073 + 0.237417i
\(11\) −2.23025 + 3.86291i −0.672446 + 1.16471i 0.304762 + 0.952429i \(0.401423\pi\)
−0.977208 + 0.212283i \(0.931910\pi\)
\(12\) 0 0
\(13\) −4.51459 −1.25212 −0.626061 0.779774i \(-0.715334\pi\)
−0.626061 + 0.779774i \(0.715334\pi\)
\(14\) 3.29679 + 2.01561i 0.881104 + 0.538695i
\(15\) 0 0
\(16\) 2.12422 + 3.67926i 0.531055 + 0.919814i
\(17\) 0.136673 0.236725i 0.0331481 0.0574142i −0.848975 0.528432i \(-0.822780\pi\)
0.882124 + 0.471018i \(0.156113\pi\)
\(18\) 0 0
\(19\) −1.43346 2.48283i −0.328859 0.569600i 0.653427 0.756990i \(-0.273331\pi\)
−0.982286 + 0.187389i \(0.939997\pi\)
\(20\) −0.0789903 −0.0176628
\(21\) 0 0
\(22\) −6.51459 −1.38892
\(23\) −2.52704 4.37697i −0.526925 0.912660i −0.999508 0.0313742i \(-0.990012\pi\)
0.472583 0.881286i \(-0.343322\pi\)
\(24\) 0 0
\(25\) 2.32383 4.02499i 0.464766 0.804999i
\(26\) −3.29679 5.71021i −0.646554 1.11986i
\(27\) 0 0
\(28\) −0.00885441 + 0.351971i −0.00167333 + 0.0665162i
\(29\) 0.352336 0.0654272 0.0327136 0.999465i \(-0.489585\pi\)
0.0327136 + 0.999465i \(0.489585\pi\)
\(30\) 0 0
\(31\) −1.25729 + 2.17770i −0.225817 + 0.391126i −0.956564 0.291522i \(-0.905838\pi\)
0.730747 + 0.682648i \(0.239172\pi\)
\(32\) −0.375780 + 0.650870i −0.0664291 + 0.115059i
\(33\) 0 0
\(34\) 0.399223 0.0684663
\(35\) 1.33988 + 0.819187i 0.226482 + 0.138468i
\(36\) 0 0
\(37\) 3.32383 + 5.75705i 0.546435 + 0.946452i 0.998515 + 0.0544753i \(0.0173486\pi\)
−0.452081 + 0.891977i \(0.649318\pi\)
\(38\) 2.09358 3.62619i 0.339623 0.588245i
\(39\) 0 0
\(40\) 0.809243 + 1.40165i 0.127953 + 0.221620i
\(41\) −10.8961 −1.70169 −0.850843 0.525420i \(-0.823908\pi\)
−0.850843 + 0.525420i \(0.823908\pi\)
\(42\) 0 0
\(43\) 3.38151 0.515676 0.257838 0.966188i \(-0.416990\pi\)
0.257838 + 0.966188i \(0.416990\pi\)
\(44\) −0.296790 0.514055i −0.0447427 0.0774967i
\(45\) 0 0
\(46\) 3.69076 6.39258i 0.544172 0.942534i
\(47\) −6.21780 10.7695i −0.906959 1.57090i −0.818265 0.574841i \(-0.805064\pi\)
−0.0886938 0.996059i \(-0.528269\pi\)
\(48\) 0 0
\(49\) 3.80039 5.87852i 0.542913 0.839789i
\(50\) 6.78794 0.959959
\(51\) 0 0
\(52\) 0.300388 0.520288i 0.0416564 0.0721509i
\(53\) −5.66372 + 9.80984i −0.777971 + 1.34749i 0.155138 + 0.987893i \(0.450418\pi\)
−0.933109 + 0.359593i \(0.882916\pi\)
\(54\) 0 0
\(55\) −2.64766 −0.357011
\(56\) 6.33628 3.44877i 0.846722 0.460861i
\(57\) 0 0
\(58\) 0.257295 + 0.445647i 0.0337844 + 0.0585163i
\(59\) 4.02704 6.97504i 0.524276 0.908073i −0.475324 0.879811i \(-0.657669\pi\)
0.999601 0.0282624i \(-0.00899740\pi\)
\(60\) 0 0
\(61\) 1.36693 + 2.36758i 0.175017 + 0.303138i 0.940167 0.340714i \(-0.110669\pi\)
−0.765150 + 0.643852i \(0.777335\pi\)
\(62\) −3.67257 −0.466417
\(63\) 0 0
\(64\) 7.39922 0.924903
\(65\) −1.33988 2.32075i −0.166192 0.287853i
\(66\) 0 0
\(67\) −2.93346 + 5.08091i −0.358380 + 0.620732i −0.987690 0.156422i \(-0.950004\pi\)
0.629311 + 0.777154i \(0.283337\pi\)
\(68\) 0.0181877 + 0.0315020i 0.00220558 + 0.00382018i
\(69\) 0 0
\(70\) −0.0576828 + 2.29294i −0.00689442 + 0.274059i
\(71\) 2.60078 0.308655 0.154328 0.988020i \(-0.450679\pi\)
0.154328 + 0.988020i \(0.450679\pi\)
\(72\) 0 0
\(73\) −5.55768 + 9.62619i −0.650478 + 1.12666i 0.332530 + 0.943093i \(0.392098\pi\)
−0.983007 + 0.183567i \(0.941235\pi\)
\(74\) −4.85447 + 8.40819i −0.564321 + 0.977433i
\(75\) 0 0
\(76\) 0.381515 0.0437627
\(77\) −0.296790 + 11.7977i −0.0338223 + 1.34447i
\(78\) 0 0
\(79\) −5.58113 9.66679i −0.627926 1.08760i −0.987967 0.154663i \(-0.950571\pi\)
0.360042 0.932936i \(-0.382763\pi\)
\(80\) −1.26089 + 2.18393i −0.140972 + 0.244171i
\(81\) 0 0
\(82\) −7.95691 13.7818i −0.878693 1.52194i
\(83\) 16.5438 1.81591 0.907957 0.419063i \(-0.137641\pi\)
0.907957 + 0.419063i \(0.137641\pi\)
\(84\) 0 0
\(85\) 0.162253 0.0175988
\(86\) 2.46936 + 4.27706i 0.266278 + 0.461207i
\(87\) 0 0
\(88\) −6.08113 + 10.5328i −0.648250 + 1.12280i
\(89\) 2.68716 + 4.65430i 0.284838 + 0.493354i 0.972570 0.232611i \(-0.0747268\pi\)
−0.687732 + 0.725965i \(0.741393\pi\)
\(90\) 0 0
\(91\) −10.4911 + 5.71021i −1.09977 + 0.598592i
\(92\) 0.672570 0.0701202
\(93\) 0 0
\(94\) 9.08113 15.7290i 0.936647 1.62232i
\(95\) 0.850874 1.47376i 0.0872978 0.151204i
\(96\) 0 0
\(97\) −2.26615 −0.230093 −0.115046 0.993360i \(-0.536702\pi\)
−0.115046 + 0.993360i \(0.536702\pi\)
\(98\) 10.2106 + 0.514055i 1.03143 + 0.0519274i
\(99\) 0 0
\(100\) 0.309243 + 0.535624i 0.0309243 + 0.0535624i
\(101\) −4.67830 + 8.10306i −0.465509 + 0.806285i −0.999224 0.0393793i \(-0.987462\pi\)
0.533716 + 0.845664i \(0.320795\pi\)
\(102\) 0 0
\(103\) 7.88151 + 13.6512i 0.776589 + 1.34509i 0.933897 + 0.357542i \(0.116385\pi\)
−0.157309 + 0.987550i \(0.550282\pi\)
\(104\) −12.3097 −1.20707
\(105\) 0 0
\(106\) −16.5438 −1.60687
\(107\) −0.512453 0.887595i −0.0495407 0.0858070i 0.840192 0.542290i \(-0.182442\pi\)
−0.889732 + 0.456483i \(0.849109\pi\)
\(108\) 0 0
\(109\) −0.647664 + 1.12179i −0.0620349 + 0.107448i −0.895375 0.445313i \(-0.853092\pi\)
0.833340 + 0.552761i \(0.186426\pi\)
\(110\) −1.93346 3.34886i −0.184348 0.319301i
\(111\) 0 0
\(112\) 9.58998 + 5.86319i 0.906168 + 0.554019i
\(113\) 14.2953 1.34479 0.672396 0.740192i \(-0.265265\pi\)
0.672396 + 0.740192i \(0.265265\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) −0.0234435 + 0.0406053i −0.00217667 + 0.00377011i
\(117\) 0 0
\(118\) 11.7630 1.08287
\(119\) 0.0181877 0.722977i 0.00166726 0.0662752i
\(120\) 0 0
\(121\) −4.44805 7.70425i −0.404368 0.700387i
\(122\) −1.99640 + 3.45787i −0.180746 + 0.313061i
\(123\) 0 0
\(124\) −0.167314 0.289796i −0.0150252 0.0260245i
\(125\) 5.72665 0.512207
\(126\) 0 0
\(127\) 12.3346 1.09452 0.547261 0.836962i \(-0.315671\pi\)
0.547261 + 0.836962i \(0.315671\pi\)
\(128\) 6.15486 + 10.6605i 0.544018 + 0.942267i
\(129\) 0 0
\(130\) 1.95691 3.38946i 0.171632 0.297275i
\(131\) 1.59718 + 2.76639i 0.139546 + 0.241701i 0.927325 0.374257i \(-0.122102\pi\)
−0.787779 + 0.615958i \(0.788769\pi\)
\(132\) 0 0
\(133\) −6.47150 3.95659i −0.561150 0.343080i
\(134\) −8.56867 −0.740221
\(135\) 0 0
\(136\) 0.372660 0.645466i 0.0319553 0.0553483i
\(137\) −5.05408 + 8.75393i −0.431800 + 0.747899i −0.997028 0.0770354i \(-0.975455\pi\)
0.565229 + 0.824934i \(0.308788\pi\)
\(138\) 0 0
\(139\) 18.0761 1.53319 0.766596 0.642130i \(-0.221949\pi\)
0.766596 + 0.642130i \(0.221949\pi\)
\(140\) −0.183560 + 0.0999096i −0.0155137 + 0.00844390i
\(141\) 0 0
\(142\) 1.89922 + 3.28955i 0.159379 + 0.276053i
\(143\) 10.0687 17.4395i 0.841985 1.45836i
\(144\) 0 0
\(145\) 0.104570 + 0.181120i 0.00868405 + 0.0150412i
\(146\) −16.2340 −1.34354
\(147\) 0 0
\(148\) −0.884634 −0.0727165
\(149\) −7.02704 12.1712i −0.575678 0.997103i −0.995968 0.0897132i \(-0.971405\pi\)
0.420290 0.907390i \(-0.361928\pi\)
\(150\) 0 0
\(151\) −0.190757 + 0.330401i −0.0155236 + 0.0268877i −0.873683 0.486496i \(-0.838275\pi\)
0.858159 + 0.513384i \(0.171608\pi\)
\(152\) −3.90856 6.76982i −0.317026 0.549105i
\(153\) 0 0
\(154\) −15.1388 + 8.23988i −1.21992 + 0.663988i
\(155\) −1.49261 −0.119889
\(156\) 0 0
\(157\) 3.75729 6.50783i 0.299865 0.519381i −0.676240 0.736681i \(-0.736392\pi\)
0.976105 + 0.217300i \(0.0697251\pi\)
\(158\) 8.15126 14.1184i 0.648480 1.12320i
\(159\) 0 0
\(160\) −0.446110 −0.0352681
\(161\) −11.4086 6.97504i −0.899120 0.549710i
\(162\) 0 0
\(163\) −7.59572 13.1562i −0.594942 1.03047i −0.993555 0.113351i \(-0.963842\pi\)
0.398613 0.917119i \(-0.369492\pi\)
\(164\) 0.724997 1.25573i 0.0566127 0.0980561i
\(165\) 0 0
\(166\) 12.0811 + 20.9251i 0.937677 + 1.62410i
\(167\) 8.95311 0.692813 0.346406 0.938085i \(-0.387402\pi\)
0.346406 + 0.938085i \(0.387402\pi\)
\(168\) 0 0
\(169\) 7.38151 0.567809
\(170\) 0.118485 + 0.205223i 0.00908741 + 0.0157399i
\(171\) 0 0
\(172\) −0.224997 + 0.389706i −0.0171558 + 0.0297148i
\(173\) 5.23025 + 9.05906i 0.397649 + 0.688748i 0.993435 0.114395i \(-0.0364929\pi\)
−0.595787 + 0.803143i \(0.703160\pi\)
\(174\) 0 0
\(175\) 0.309243 12.2927i 0.0233766 0.929239i
\(176\) −18.9502 −1.42842
\(177\) 0 0
\(178\) −3.92461 + 6.79762i −0.294162 + 0.509503i
\(179\) 4.48395 7.76643i 0.335146 0.580490i −0.648367 0.761328i \(-0.724548\pi\)
0.983513 + 0.180838i \(0.0578810\pi\)
\(180\) 0 0
\(181\) 5.04689 0.375132 0.187566 0.982252i \(-0.439940\pi\)
0.187566 + 0.982252i \(0.439940\pi\)
\(182\) −14.8837 9.09967i −1.10325 0.674512i
\(183\) 0 0
\(184\) −6.89037 11.9345i −0.507965 0.879821i
\(185\) −1.97296 + 3.41726i −0.145055 + 0.251242i
\(186\) 0 0
\(187\) 0.609631 + 1.05591i 0.0445806 + 0.0772159i
\(188\) 1.65486 0.120693
\(189\) 0 0
\(190\) 2.48541 0.180311
\(191\) −6.06507 10.5050i −0.438853 0.760116i 0.558748 0.829338i \(-0.311282\pi\)
−0.997601 + 0.0692211i \(0.977949\pi\)
\(192\) 0 0
\(193\) −8.58113 + 14.8629i −0.617683 + 1.06986i 0.372224 + 0.928143i \(0.378595\pi\)
−0.989907 + 0.141716i \(0.954738\pi\)
\(194\) −1.65486 2.86630i −0.118812 0.205789i
\(195\) 0 0
\(196\) 0.424608 + 0.829120i 0.0303292 + 0.0592228i
\(197\) 0.751560 0.0535464 0.0267732 0.999642i \(-0.491477\pi\)
0.0267732 + 0.999642i \(0.491477\pi\)
\(198\) 0 0
\(199\) −5.14766 + 8.91601i −0.364908 + 0.632040i −0.988761 0.149502i \(-0.952233\pi\)
0.623853 + 0.781542i \(0.285566\pi\)
\(200\) 6.33628 10.9748i 0.448043 0.776033i
\(201\) 0 0
\(202\) −13.6654 −0.961492
\(203\) 0.818771 0.445647i 0.0574664 0.0312783i
\(204\) 0 0
\(205\) −3.23385 5.60119i −0.225862 0.391204i
\(206\) −11.5110 + 19.9376i −0.802009 + 1.38912i
\(207\) 0 0
\(208\) −9.58998 16.6103i −0.664946 1.15172i
\(209\) 12.7879 0.884560
\(210\) 0 0
\(211\) −16.1154 −1.10943 −0.554714 0.832041i \(-0.687172\pi\)
−0.554714 + 0.832041i \(0.687172\pi\)
\(212\) −0.753696 1.30544i −0.0517640 0.0896580i
\(213\) 0 0
\(214\) 0.748440 1.29634i 0.0511623 0.0886157i
\(215\) 1.00360 + 1.73828i 0.0684449 + 0.118550i
\(216\) 0 0
\(217\) −0.167314 + 6.65087i −0.0113580 + 0.451491i
\(218\) −1.89183 −0.128131
\(219\) 0 0
\(220\) 0.176168 0.305132i 0.0118773 0.0205720i
\(221\) −0.617023 + 1.06871i −0.0415054 + 0.0718895i
\(222\) 0 0
\(223\) −6.95311 −0.465615 −0.232807 0.972523i \(-0.574791\pi\)
−0.232807 + 0.972523i \(0.574791\pi\)
\(224\) −0.0500067 + 1.98781i −0.00334121 + 0.132816i
\(225\) 0 0
\(226\) 10.4392 + 18.0812i 0.694405 + 1.20274i
\(227\) 2.64553 4.58219i 0.175590 0.304131i −0.764775 0.644297i \(-0.777150\pi\)
0.940365 + 0.340166i \(0.110483\pi\)
\(228\) 0 0
\(229\) −5.86186 10.1530i −0.387363 0.670932i 0.604731 0.796430i \(-0.293281\pi\)
−0.992094 + 0.125498i \(0.959947\pi\)
\(230\) 4.38151 0.288909
\(231\) 0 0
\(232\) 0.960699 0.0630730
\(233\) 1.93560 + 3.35256i 0.126805 + 0.219633i 0.922437 0.386147i \(-0.126194\pi\)
−0.795632 + 0.605780i \(0.792861\pi\)
\(234\) 0 0
\(235\) 3.69076 6.39258i 0.240758 0.417006i
\(236\) 0.535897 + 0.928200i 0.0348839 + 0.0604207i
\(237\) 0 0
\(238\) 0.927728 0.504951i 0.0601357 0.0327311i
\(239\) −12.3992 −0.802039 −0.401020 0.916069i \(-0.631344\pi\)
−0.401020 + 0.916069i \(0.631344\pi\)
\(240\) 0 0
\(241\) 8.28074 14.3427i 0.533409 0.923892i −0.465829 0.884875i \(-0.654244\pi\)
0.999239 0.0390173i \(-0.0124227\pi\)
\(242\) 6.49640 11.2521i 0.417604 0.723312i
\(243\) 0 0
\(244\) −0.363806 −0.0232903
\(245\) 4.14980 + 0.208922i 0.265121 + 0.0133476i
\(246\) 0 0
\(247\) 6.47150 + 11.2090i 0.411771 + 0.713209i
\(248\) −3.42821 + 5.93783i −0.217691 + 0.377052i
\(249\) 0 0
\(250\) 4.18190 + 7.24327i 0.264487 + 0.458105i
\(251\) −1.84922 −0.116722 −0.0583608 0.998296i \(-0.518587\pi\)
−0.0583608 + 0.998296i \(0.518587\pi\)
\(252\) 0 0
\(253\) 22.5438 1.41731
\(254\) 9.00739 + 15.6013i 0.565174 + 0.978910i
\(255\) 0 0
\(256\) −1.58998 + 2.75393i −0.0993738 + 0.172120i
\(257\) 13.4210 + 23.2459i 0.837180 + 1.45004i 0.892243 + 0.451555i \(0.149130\pi\)
−0.0550638 + 0.998483i \(0.517536\pi\)
\(258\) 0 0
\(259\) 15.0057 + 9.17431i 0.932411 + 0.570064i
\(260\) 0.356609 0.0221159
\(261\) 0 0
\(262\) −2.33269 + 4.04033i −0.144114 + 0.249612i
\(263\) 10.1424 17.5672i 0.625408 1.08324i −0.363054 0.931768i \(-0.618266\pi\)
0.988462 0.151470i \(-0.0484006\pi\)
\(264\) 0 0
\(265\) −6.72373 −0.413035
\(266\) 0.278602 11.0747i 0.0170822 0.679032i
\(267\) 0 0
\(268\) −0.390369 0.676139i −0.0238456 0.0413018i
\(269\) −4.36333 + 7.55750i −0.266037 + 0.460789i −0.967835 0.251587i \(-0.919048\pi\)
0.701798 + 0.712376i \(0.252381\pi\)
\(270\) 0 0
\(271\) −12.0957 20.9504i −0.734762 1.27265i −0.954828 0.297161i \(-0.903960\pi\)
0.220065 0.975485i \(-0.429373\pi\)
\(272\) 1.16129 0.0704138
\(273\) 0 0
\(274\) −14.7630 −0.891867
\(275\) 10.3655 + 17.9535i 0.625061 + 1.08264i
\(276\) 0 0
\(277\) 3.55768 6.16209i 0.213760 0.370244i −0.739128 0.673565i \(-0.764762\pi\)
0.952888 + 0.303321i \(0.0980955\pi\)
\(278\) 13.2001 + 22.8632i 0.791689 + 1.37125i
\(279\) 0 0
\(280\) 3.65340 + 2.23364i 0.218332 + 0.133485i
\(281\) −7.89610 −0.471042 −0.235521 0.971869i \(-0.575680\pi\)
−0.235521 + 0.971869i \(0.575680\pi\)
\(282\) 0 0
\(283\) −1.10457 + 1.91317i −0.0656599 + 0.113726i −0.896987 0.442058i \(-0.854249\pi\)
0.831327 + 0.555784i \(0.187582\pi\)
\(284\) −0.173048 + 0.299729i −0.0102685 + 0.0177856i
\(285\) 0 0
\(286\) 29.4107 1.73909
\(287\) −25.3207 + 13.7818i −1.49463 + 0.813512i
\(288\) 0 0
\(289\) 8.46264 + 14.6577i 0.497802 + 0.862219i
\(290\) −0.152725 + 0.264527i −0.00896830 + 0.0155336i
\(291\) 0 0
\(292\) −0.739586 1.28100i −0.0432810 0.0749649i
\(293\) 19.1914 1.12118 0.560588 0.828095i \(-0.310575\pi\)
0.560588 + 0.828095i \(0.310575\pi\)
\(294\) 0 0
\(295\) 4.78074 0.278345
\(296\) 9.06294 + 15.6975i 0.526773 + 0.912397i
\(297\) 0 0
\(298\) 10.2630 17.7761i 0.594521 1.02974i
\(299\) 11.4086 + 19.7602i 0.659774 + 1.14276i
\(300\) 0 0
\(301\) 7.85807 4.27706i 0.452932 0.246525i
\(302\) −0.557204 −0.0320635
\(303\) 0 0
\(304\) 6.08998 10.5482i 0.349284 0.604978i
\(305\) −0.811379 + 1.40535i −0.0464594 + 0.0804701i
\(306\) 0 0
\(307\) −13.9138 −0.794103 −0.397052 0.917796i \(-0.629967\pi\)
−0.397052 + 0.917796i \(0.629967\pi\)
\(308\) −1.33988 0.819187i −0.0763469 0.0466775i
\(309\) 0 0
\(310\) −1.08998 1.88790i −0.0619067 0.107226i
\(311\) 5.32743 9.22738i 0.302091 0.523237i −0.674519 0.738258i \(-0.735649\pi\)
0.976609 + 0.215021i \(0.0689821\pi\)
\(312\) 0 0
\(313\) 8.28074 + 14.3427i 0.468055 + 0.810695i 0.999334 0.0365022i \(-0.0116216\pi\)
−0.531279 + 0.847197i \(0.678288\pi\)
\(314\) 10.9751 0.619360
\(315\) 0 0
\(316\) 1.48541 0.0835609
\(317\) −13.3186 23.0685i −0.748046 1.29565i −0.948758 0.316003i \(-0.897659\pi\)
0.200712 0.979650i \(-0.435674\pi\)
\(318\) 0 0
\(319\) −0.785799 + 1.36104i −0.0439963 + 0.0762038i
\(320\) 2.19601 + 3.80361i 0.122761 + 0.212628i
\(321\) 0 0
\(322\) 0.491146 19.5235i 0.0273705 1.08800i
\(323\) −0.783663 −0.0436042
\(324\) 0 0
\(325\) −10.4911 + 18.1712i −0.581944 + 1.00796i
\(326\) 11.0936 19.2146i 0.614417 1.06420i
\(327\) 0 0
\(328\) −29.7099 −1.64045
\(329\) −28.0708 17.1621i −1.54759 0.946179i
\(330\) 0 0
\(331\) 11.6534 + 20.1843i 0.640529 + 1.10943i 0.985315 + 0.170747i \(0.0546181\pi\)
−0.344786 + 0.938681i \(0.612049\pi\)
\(332\) −1.10078 + 1.90660i −0.0604130 + 0.104638i
\(333\) 0 0
\(334\) 6.53803 + 11.3242i 0.357745 + 0.619633i
\(335\) −3.48249 −0.190269
\(336\) 0 0
\(337\) −23.2383 −1.26587 −0.632936 0.774204i \(-0.718150\pi\)
−0.632936 + 0.774204i \(0.718150\pi\)
\(338\) 5.39037 + 9.33639i 0.293197 + 0.507833i
\(339\) 0 0
\(340\) −0.0107958 + 0.0186989i −0.000585487 + 0.00101409i
\(341\) −5.60817 9.71363i −0.303699 0.526023i
\(342\) 0 0
\(343\) 1.39610 18.4676i 0.0753825 0.997155i
\(344\) 9.22022 0.497121
\(345\) 0 0
\(346\) −7.63881 + 13.2308i −0.410665 + 0.711293i
\(347\) −8.56867 + 14.8414i −0.459990 + 0.796727i −0.998960 0.0455985i \(-0.985481\pi\)
0.538969 + 0.842325i \(0.318814\pi\)
\(348\) 0 0
\(349\) −19.5146 −1.04459 −0.522296 0.852764i \(-0.674924\pi\)
−0.522296 + 0.852764i \(0.674924\pi\)
\(350\) 15.7740 8.58561i 0.843157 0.458920i
\(351\) 0 0
\(352\) −1.67617 2.90321i −0.0893401 0.154742i
\(353\) −8.03064 + 13.9095i −0.427428 + 0.740327i −0.996644 0.0818613i \(-0.973914\pi\)
0.569216 + 0.822188i \(0.307247\pi\)
\(354\) 0 0
\(355\) 0.771884 + 1.33694i 0.0409673 + 0.0709575i
\(356\) −0.715184 −0.0379047
\(357\) 0 0
\(358\) 13.0977 0.692233
\(359\) −6.93200 12.0066i −0.365857 0.633683i 0.623056 0.782177i \(-0.285891\pi\)
−0.988913 + 0.148494i \(0.952557\pi\)
\(360\) 0 0
\(361\) 5.39037 9.33639i 0.283704 0.491389i
\(362\) 3.68550 + 6.38348i 0.193706 + 0.335508i
\(363\) 0 0
\(364\) 0.0399740 1.58900i 0.00209521 0.0832864i
\(365\) −6.59785 −0.345347
\(366\) 0 0
\(367\) −12.6477 + 21.9064i −0.660203 + 1.14350i 0.320360 + 0.947296i \(0.396196\pi\)
−0.980562 + 0.196209i \(0.937137\pi\)
\(368\) 10.7360 18.5953i 0.559652 0.969346i
\(369\) 0 0
\(370\) −5.76303 −0.299606
\(371\) −0.753696 + 29.9601i −0.0391299 + 1.55545i
\(372\) 0 0
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) −0.890369 + 1.54216i −0.0460399 + 0.0797434i
\(375\) 0 0
\(376\) −16.9538 29.3648i −0.874325 1.51437i
\(377\) −1.59065 −0.0819229
\(378\) 0 0
\(379\) −18.8099 −0.966200 −0.483100 0.875565i \(-0.660489\pi\)
−0.483100 + 0.875565i \(0.660489\pi\)
\(380\) 0.113230 + 0.196119i 0.00580856 + 0.0100607i
\(381\) 0 0
\(382\) 8.85807 15.3426i 0.453218 0.784997i
\(383\) −17.5708 30.4335i −0.897826 1.55508i −0.830267 0.557366i \(-0.811812\pi\)
−0.0675593 0.997715i \(-0.521521\pi\)
\(384\) 0 0
\(385\) −6.15272 + 3.34886i −0.313572 + 0.170673i
\(386\) −25.0656 −1.27580
\(387\) 0 0
\(388\) 0.150783 0.261164i 0.00765486 0.0132586i
\(389\) 4.18929 7.25607i 0.212406 0.367897i −0.740061 0.672539i \(-0.765204\pi\)
0.952467 + 0.304642i \(0.0985368\pi\)
\(390\) 0 0
\(391\) −1.38151 −0.0698662
\(392\) 10.3623 16.0287i 0.523377 0.809572i
\(393\) 0 0
\(394\) 0.548828 + 0.950599i 0.0276496 + 0.0478905i
\(395\) 3.31284 5.73801i 0.166687 0.288711i
\(396\) 0 0
\(397\) 4.62422 + 8.00938i 0.232083 + 0.401979i 0.958421 0.285358i \(-0.0921126\pi\)
−0.726338 + 0.687338i \(0.758779\pi\)
\(398\) −15.0364 −0.753705
\(399\) 0 0
\(400\) 19.7453 0.987266
\(401\) 0.0737345 + 0.127712i 0.00368212 + 0.00637763i 0.867861 0.496808i \(-0.165495\pi\)
−0.864178 + 0.503185i \(0.832161\pi\)
\(402\) 0 0
\(403\) 5.67617 9.83141i 0.282750 0.489738i
\(404\) −0.622563 1.07831i −0.0309737 0.0536480i
\(405\) 0 0
\(406\) 1.16158 + 0.710174i 0.0576482 + 0.0352454i
\(407\) −29.6519 −1.46979
\(408\) 0 0
\(409\) 1.96264 3.39939i 0.0970463 0.168089i −0.813414 0.581685i \(-0.802394\pi\)
0.910461 + 0.413595i \(0.135727\pi\)
\(410\) 4.72306 8.18057i 0.233255 0.404010i
\(411\) 0 0
\(412\) −2.09766 −0.103344
\(413\) 0.535897 21.3024i 0.0263697 1.04822i
\(414\) 0 0
\(415\) 4.91002 + 8.50440i 0.241023 + 0.417465i
\(416\) 1.69649 2.93841i 0.0831774 0.144067i
\(417\) 0 0
\(418\) 9.33842 + 16.1746i 0.456757 + 0.791126i
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) 0 0
\(421\) −24.6883 −1.20323 −0.601617 0.798784i \(-0.705477\pi\)
−0.601617 + 0.798784i \(0.705477\pi\)
\(422\) −11.7683 20.3833i −0.572871 0.992242i
\(423\) 0 0
\(424\) −15.4430 + 26.7480i −0.749978 + 1.29900i
\(425\) −0.635211 1.10022i −0.0308122 0.0533684i
\(426\) 0 0
\(427\) 6.17111 + 3.77293i 0.298641 + 0.182585i
\(428\) 0.136389 0.00659260
\(429\) 0 0
\(430\) −1.46576 + 2.53877i −0.0706853 + 0.122430i
\(431\) 2.73745 4.74140i 0.131858 0.228385i −0.792535 0.609827i \(-0.791239\pi\)
0.924393 + 0.381442i \(0.124572\pi\)
\(432\) 0 0
\(433\) 23.6300 1.13558 0.567792 0.823172i \(-0.307798\pi\)
0.567792 + 0.823172i \(0.307798\pi\)
\(434\) −8.53443 + 4.64519i −0.409666 + 0.222976i
\(435\) 0 0
\(436\) −0.0861875 0.149281i −0.00412763 0.00714927i
\(437\) −7.24484 + 12.5484i −0.346568 + 0.600273i
\(438\) 0 0
\(439\) 2.63307 + 4.56062i 0.125670 + 0.217666i 0.921995 0.387203i \(-0.126559\pi\)
−0.796325 + 0.604869i \(0.793225\pi\)
\(440\) −7.21926 −0.344165
\(441\) 0 0
\(442\) −1.80233 −0.0857281
\(443\) −3.01819 5.22765i −0.143398 0.248373i 0.785376 0.619019i \(-0.212470\pi\)
−0.928774 + 0.370646i \(0.879136\pi\)
\(444\) 0 0
\(445\) −1.59504 + 2.76269i −0.0756122 + 0.130964i
\(446\) −5.07753 8.79454i −0.240428 0.416433i
\(447\) 0 0
\(448\) 17.1946 9.35879i 0.812366 0.442161i
\(449\) 22.1445 1.04507 0.522533 0.852619i \(-0.324987\pi\)
0.522533 + 0.852619i \(0.324987\pi\)
\(450\) 0 0
\(451\) 24.3011 42.0907i 1.14429 1.98197i
\(452\) −0.951172 + 1.64748i −0.0447393 + 0.0774908i
\(453\) 0 0
\(454\) 7.72761 0.362675
\(455\) −6.04902 3.69829i −0.283583 0.173379i
\(456\) 0 0
\(457\) 2.66731 + 4.61992i 0.124772 + 0.216111i 0.921644 0.388037i \(-0.126847\pi\)
−0.796872 + 0.604148i \(0.793513\pi\)
\(458\) 8.56128 14.8286i 0.400042 0.692894i
\(459\) 0 0
\(460\) 0.199612 + 0.345738i 0.00930694 + 0.0161201i
\(461\) −29.6946 −1.38301 −0.691507 0.722370i \(-0.743053\pi\)
−0.691507 + 0.722370i \(0.743053\pi\)
\(462\) 0 0
\(463\) 18.5907 0.863981 0.431990 0.901878i \(-0.357811\pi\)
0.431990 + 0.901878i \(0.357811\pi\)
\(464\) 0.748440 + 1.29634i 0.0347455 + 0.0601809i
\(465\) 0 0
\(466\) −2.82695 + 4.89642i −0.130956 + 0.226822i
\(467\) 12.3063 + 21.3152i 0.569468 + 0.986348i 0.996619 + 0.0821676i \(0.0261843\pi\)
−0.427150 + 0.904181i \(0.640482\pi\)
\(468\) 0 0
\(469\) −0.390369 + 15.5175i −0.0180256 + 0.716532i
\(470\) 10.7807 0.497278
\(471\) 0 0
\(472\) 10.9803 19.0185i 0.505412 0.875399i
\(473\) −7.54163 + 13.0625i −0.346765 + 0.600614i
\(474\) 0 0
\(475\) −13.3245 −0.611370
\(476\) 0.0821100 + 0.0502010i 0.00376351 + 0.00230096i
\(477\) 0 0
\(478\) −9.05456 15.6830i −0.414146 0.717322i
\(479\) −0.178304 + 0.308832i −0.00814693 + 0.0141109i −0.870070 0.492928i \(-0.835927\pi\)
0.861923 + 0.507039i \(0.169260\pi\)
\(480\) 0 0
\(481\) −15.0057 25.9907i −0.684203 1.18507i
\(482\) 24.1881 1.10174
\(483\) 0 0
\(484\) 1.18384 0.0538111
\(485\) −0.672570 1.16492i −0.0305398 0.0528965i
\(486\) 0 0
\(487\) 6.43920 11.1530i 0.291788 0.505391i −0.682445 0.730937i \(-0.739083\pi\)
0.974233 + 0.225546i \(0.0724165\pi\)
\(488\) 3.72713 + 6.45558i 0.168719 + 0.292231i
\(489\) 0 0
\(490\) 2.76615 + 5.40138i 0.124962 + 0.244009i
\(491\) −5.55389 −0.250644 −0.125322 0.992116i \(-0.539996\pi\)
−0.125322 + 0.992116i \(0.539996\pi\)
\(492\) 0 0
\(493\) 0.0481549 0.0834068i 0.00216879 0.00375645i
\(494\) −9.45165 + 16.3707i −0.425250 + 0.736554i
\(495\) 0 0
\(496\) −10.6831 −0.479685
\(497\) 6.04377 3.28955i 0.271100 0.147557i
\(498\) 0 0
\(499\) 14.0577 + 24.3486i 0.629308 + 1.08999i 0.987691 + 0.156419i \(0.0499951\pi\)
−0.358382 + 0.933575i \(0.616672\pi\)
\(500\) −0.381036 + 0.659973i −0.0170404 + 0.0295149i
\(501\) 0 0
\(502\) −1.35040 2.33895i −0.0602711 0.104393i
\(503\) −16.9430 −0.755451 −0.377725 0.925918i \(-0.623294\pi\)
−0.377725 + 0.925918i \(0.623294\pi\)
\(504\) 0 0
\(505\) −5.55389 −0.247145
\(506\) 16.4626 + 28.5141i 0.731854 + 1.26761i
\(507\) 0 0
\(508\) −0.820712 + 1.42151i −0.0364132 + 0.0630695i
\(509\) −11.1513 19.3146i −0.494271 0.856102i 0.505707 0.862705i \(-0.331232\pi\)
−0.999978 + 0.00660269i \(0.997898\pi\)
\(510\) 0 0
\(511\) −0.739586 + 29.3992i −0.0327173 + 1.30054i
\(512\) 19.9751 0.882783
\(513\) 0 0
\(514\) −19.6015 + 33.9507i −0.864583 + 1.49750i
\(515\) −4.67830 + 8.10306i −0.206151 + 0.357064i
\(516\) 0 0
\(517\) 55.4690 2.43953
\(518\) −0.646006 + 25.6793i −0.0283839 + 1.12828i
\(519\) 0 0
\(520\) −3.65340 6.32787i −0.160212 0.277496i
\(521\) 6.18044 10.7048i 0.270770 0.468987i −0.698289 0.715816i \(-0.746055\pi\)
0.969059 + 0.246828i \(0.0793884\pi\)
\(522\) 0 0
\(523\) −3.09572 5.36194i −0.135366 0.234461i 0.790371 0.612628i \(-0.209888\pi\)
−0.925737 + 0.378167i \(0.876554\pi\)
\(524\) −0.425087 −0.0185700
\(525\) 0 0
\(526\) 29.6261 1.29176
\(527\) 0.343677 + 0.595265i 0.0149708 + 0.0259302i
\(528\) 0 0
\(529\) −1.27188 + 2.20297i −0.0552993 + 0.0957812i
\(530\) −4.91002 8.50440i −0.213278 0.369408i
\(531\) 0 0
\(532\) 0.886576 0.482553i 0.0384379 0.0209213i
\(533\) 49.1914 2.13072
\(534\) 0 0
\(535\) 0.304182 0.526858i 0.0131509 0.0227781i
\(536\) −7.99854 + 13.8539i −0.345484 + 0.598396i
\(537\) 0 0
\(538\) −12.7453 −0.549490
\(539\) 14.2324 + 27.7912i 0.613032 + 1.19705i
\(540\) 0 0
\(541\) −13.4100 23.2268i −0.576542 0.998600i −0.995872 0.0907660i \(-0.971068\pi\)
0.419330 0.907834i \(-0.362265\pi\)
\(542\) 17.6659 30.5982i 0.758813 1.31430i
\(543\) 0 0
\(544\) 0.102718 + 0.177913i 0.00440400 + 0.00762795i
\(545\) −0.768879 −0.0329352
\(546\) 0 0
\(547\) −14.6591 −0.626779 −0.313390 0.949625i \(-0.601465\pi\)
−0.313390 + 0.949625i \(0.601465\pi\)
\(548\) −0.672570 1.16492i −0.0287307 0.0497631i
\(549\) 0 0
\(550\) −15.1388 + 26.2212i −0.645521 + 1.11808i
\(551\) −0.505061 0.874792i −0.0215163 0.0372674i
\(552\) 0 0
\(553\) −25.1965 15.4048i −1.07146 0.655079i
\(554\) 10.3920 0.441515
\(555\) 0 0
\(556\) −1.20273 + 2.08319i −0.0510072 + 0.0883470i
\(557\) −11.8399 + 20.5073i −0.501672 + 0.868921i 0.498326 + 0.866990i \(0.333948\pi\)
−0.999998 + 0.00193169i \(0.999385\pi\)
\(558\) 0 0
\(559\) −15.2661 −0.645689
\(560\) −0.167793 + 6.66991i −0.00709054 + 0.281855i
\(561\) 0 0
\(562\) −5.76615 9.98726i −0.243230 0.421287i
\(563\) −8.19289 + 14.1905i −0.345289 + 0.598059i −0.985406 0.170219i \(-0.945553\pi\)
0.640117 + 0.768277i \(0.278886\pi\)
\(564\) 0 0
\(565\) 4.24271 + 7.34858i 0.178492 + 0.309157i
\(566\) −3.22646 −0.135618
\(567\) 0 0
\(568\) 7.09142 0.297549
\(569\) −7.89397 13.6728i −0.330932 0.573192i 0.651763 0.758423i \(-0.274030\pi\)
−0.982695 + 0.185231i \(0.940697\pi\)
\(570\) 0 0
\(571\) −3.19076 + 5.52655i −0.133529 + 0.231279i −0.925035 0.379883i \(-0.875964\pi\)
0.791506 + 0.611162i \(0.209298\pi\)
\(572\) 1.33988 + 2.32075i 0.0560233 + 0.0970353i
\(573\) 0 0
\(574\) −35.9222 21.9623i −1.49936 0.916690i
\(575\) −23.4897 −0.979587
\(576\) 0 0
\(577\) 18.5203 32.0781i 0.771011 1.33543i −0.165998 0.986126i \(-0.553085\pi\)
0.937009 0.349304i \(-0.113582\pi\)
\(578\) −12.3597 + 21.4077i −0.514097 + 0.890442i
\(579\) 0 0
\(580\) −0.0278311 −0.00115563
\(581\) 38.4449 20.9251i 1.59496 0.868120i
\(582\) 0 0
\(583\) −25.2630 43.7569i −1.04629 1.81222i
\(584\) −15.1539 + 26.2473i −0.627072 + 1.08612i
\(585\) 0 0
\(586\) 14.0146 + 24.2740i 0.578937 + 1.00275i
\(587\) 12.0938 0.499163 0.249582 0.968354i \(-0.419707\pi\)
0.249582 + 0.968354i \(0.419707\pi\)
\(588\) 0 0
\(589\) 7.20914 0.297047
\(590\) 3.49115 + 6.04684i 0.143728 + 0.248945i
\(591\) 0 0
\(592\) −14.1211 + 24.4585i −0.580374 + 1.00524i
\(593\) 8.26449 + 14.3145i 0.339382 + 0.587827i 0.984317 0.176411i \(-0.0564487\pi\)
−0.644935 + 0.764238i \(0.723115\pi\)
\(594\) 0 0
\(595\) 0.377048 0.205223i 0.0154575 0.00841331i
\(596\) 1.87024 0.0766080
\(597\) 0 0
\(598\) −16.6623 + 28.8599i −0.681370 + 1.18017i
\(599\) −4.37412 + 7.57620i −0.178722 + 0.309555i −0.941443 0.337172i \(-0.890530\pi\)
0.762721 + 0.646727i \(0.223863\pi\)
\(600\) 0 0
\(601\) −5.92393 −0.241642 −0.120821 0.992674i \(-0.538553\pi\)
−0.120821 + 0.992674i \(0.538553\pi\)
\(602\) 11.1481 + 6.81583i 0.454364 + 0.277792i
\(603\) 0 0
\(604\) −0.0253849 0.0439680i −0.00103290 0.00178903i
\(605\) 2.64027 4.57308i 0.107342 0.185922i
\(606\) 0 0
\(607\) 0.370719 + 0.642104i 0.0150470 + 0.0260622i 0.873451 0.486912i \(-0.161877\pi\)
−0.858404 + 0.512974i \(0.828544\pi\)
\(608\) 2.15467 0.0873833
\(609\) 0 0
\(610\) −2.37005 −0.0959603
\(611\) 28.0708 + 48.6201i 1.13562 + 1.96696i
\(612\) 0 0
\(613\) −2.25350 + 3.90318i −0.0910181 + 0.157648i −0.907940 0.419101i \(-0.862345\pi\)
0.816922 + 0.576749i \(0.195679\pi\)
\(614\) −10.1606 17.5987i −0.410048 0.710224i
\(615\) 0 0
\(616\) −0.809243 + 32.1681i −0.0326053 + 1.29609i
\(617\) 17.2016 0.692508 0.346254 0.938141i \(-0.387453\pi\)
0.346254 + 0.938141i \(0.387453\pi\)
\(618\) 0 0
\(619\) −2.24271 + 3.88448i −0.0901419 + 0.156130i −0.907571 0.419899i \(-0.862065\pi\)
0.817429 + 0.576030i \(0.195399\pi\)
\(620\) 0.0993140 0.172017i 0.00398855 0.00690837i
\(621\) 0 0
\(622\) 15.5615 0.623958
\(623\) 12.1314 + 7.41699i 0.486035 + 0.297155i
\(624\) 0 0
\(625\) −9.91955 17.1812i −0.396782 0.687246i
\(626\) −12.0941 + 20.9475i −0.483376 + 0.837231i
\(627\) 0 0
\(628\) 0.500000 + 0.866025i 0.0199522 + 0.0345582i
\(629\) 1.81711 0.0724531
\(630\) 0 0
\(631\) −17.3068 −0.688973 −0.344486 0.938791i \(-0.611947\pi\)
−0.344486 + 0.938791i \(0.611947\pi\)
\(632\) −15.2178 26.3580i −0.605332 1.04847i
\(633\) 0 0
\(634\) 19.4518 33.6916i 0.772531 1.33806i
\(635\) 3.66079 + 6.34067i 0.145274 + 0.251622i
\(636\) 0 0
\(637\) −17.1572 + 26.5391i −0.679793 + 1.05152i
\(638\) −2.29533 −0.0908729
\(639\) 0 0
\(640\) −3.65340 + 6.32787i −0.144413 + 0.250131i
\(641\) 21.6608 37.5176i 0.855550 1.48186i −0.0205843 0.999788i \(-0.506553\pi\)
0.876134 0.482068i \(-0.160114\pi\)
\(642\) 0 0
\(643\) 29.9823 1.18239 0.591193 0.806530i \(-0.298657\pi\)
0.591193 + 0.806530i \(0.298657\pi\)
\(644\) 1.56294 0.850689i 0.0615884 0.0335218i
\(645\) 0 0
\(646\) −0.572272 0.991204i −0.0225157 0.0389984i
\(647\) 7.08472 12.2711i 0.278529 0.482427i −0.692490 0.721427i \(-0.743486\pi\)
0.971019 + 0.239000i \(0.0768197\pi\)
\(648\) 0 0
\(649\) 17.9626 + 31.1122i 0.705095 + 1.22126i
\(650\) −30.6447 −1.20199
\(651\) 0 0
\(652\) 2.02159 0.0791716
\(653\) −14.1981 24.5919i −0.555617 0.962356i −0.997855 0.0654587i \(-0.979149\pi\)
0.442239 0.896897i \(-0.354184\pi\)
\(654\) 0 0
\(655\) −0.948052 + 1.64207i −0.0370435 + 0.0641611i
\(656\) −23.1457 40.0896i −0.903689 1.56523i
\(657\) 0 0
\(658\) 1.20847 48.0376i 0.0471109 1.87270i
\(659\) −9.39922 −0.366142 −0.183071 0.983100i \(-0.558604\pi\)
−0.183071 + 0.983100i \(0.558604\pi\)
\(660\) 0 0
\(661\) 6.35807 11.0125i 0.247300 0.428337i −0.715476 0.698638i \(-0.753790\pi\)
0.962776 + 0.270301i \(0.0871232\pi\)
\(662\) −17.0198 + 29.4792i −0.661495 + 1.14574i
\(663\) 0 0
\(664\) 45.1091 1.75057
\(665\) 0.113230 4.50098i 0.00439086 0.174540i
\(666\) 0 0
\(667\) −0.890369 1.54216i −0.0344752 0.0597128i
\(668\) −0.595715 + 1.03181i −0.0230489 + 0.0399219i
\(669\) 0 0
\(670\) −2.54309 4.40477i −0.0982483 0.170171i
\(671\) −12.1944 −0.470758
\(672\) 0 0
\(673\) 35.7922 1.37969 0.689844 0.723958i \(-0.257679\pi\)
0.689844 + 0.723958i \(0.257679\pi\)
\(674\) −16.9698 29.3926i −0.653654 1.13216i
\(675\) 0 0
\(676\) −0.491146 + 0.850689i −0.0188902 + 0.0327188i
\(677\) −5.44592 9.43260i −0.209304 0.362524i 0.742192 0.670188i \(-0.233786\pi\)
−0.951495 + 0.307663i \(0.900453\pi\)
\(678\) 0 0
\(679\) −5.26615 + 2.86630i −0.202096 + 0.109999i
\(680\) 0.442407 0.0169655
\(681\) 0 0
\(682\) 8.19076 14.1868i 0.313640 0.543241i
\(683\) −17.5079 + 30.3245i −0.669920 + 1.16034i 0.308006 + 0.951384i \(0.400338\pi\)
−0.977926 + 0.208951i \(0.932995\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 24.3779 11.7201i 0.930753 0.447477i
\(687\) 0 0
\(688\) 7.18308 + 12.4415i 0.273852 + 0.474326i
\(689\) 25.5693 44.2874i 0.974115 1.68722i
\(690\) 0 0
\(691\) −4.21041 7.29264i −0.160171 0.277425i 0.774759 0.632257i \(-0.217871\pi\)
−0.934930 + 0.354832i \(0.884538\pi\)
\(692\) −1.39203 −0.0529169
\(693\) 0 0
\(694\) −25.0292 −0.950095
\(695\) 5.36479 + 9.29209i 0.203498 + 0.352469i
\(696\) 0 0
\(697\) −1.48920 + 2.57938i −0.0564076 + 0.0977009i
\(698\) −14.2506 24.6827i −0.539392 0.934255i
\(699\) 0 0
\(700\) 1.39610 + 0.853559i 0.0527678 + 0.0322615i
\(701\) 42.7453 1.61447 0.807234 0.590231i \(-0.200963\pi\)
0.807234 + 0.590231i \(0.200963\pi\)
\(702\) 0 0
\(703\) 9.52918 16.5050i 0.359400 0.622499i
\(704\) −16.5021 + 28.5825i −0.621948 + 1.07724i
\(705\) 0 0
\(706\) −23.4576 −0.882838
\(707\) −0.622563 + 24.7474i −0.0234139 + 0.930723i
\(708\) 0 0
\(709\) 12.0431 + 20.8593i 0.452288 + 0.783386i 0.998528 0.0542432i \(-0.0172746\pi\)
−0.546240 + 0.837629i \(0.683941\pi\)
\(710\) −1.12734 + 1.95261i −0.0423083 + 0.0732801i
\(711\) 0 0
\(712\) 7.32695 + 12.6907i 0.274589 + 0.475602i
\(713\) 12.7089 0.475954
\(714\) 0 0
\(715\) 11.9531 0.447021
\(716\) 0.596699 + 1.03351i 0.0222997 + 0.0386242i
\(717\) 0 0
\(718\) 10.1242 17.5357i 0.377833 0.654425i
\(719\) −21.0512 36.4617i −0.785076 1.35979i −0.928954 0.370196i \(-0.879291\pi\)
0.143878 0.989595i \(-0.454043\pi\)
\(720\) 0 0
\(721\) 35.5818 + 21.7542i 1.32514 + 0.810170i
\(722\) 15.7453 0.585980
\(723\) 0 0
\(724\) −0.335806 + 0.581633i −0.0124801 + 0.0216162i
\(725\) 0.818771 1.41815i 0.0304084 0.0526689i
\(726\) 0 0
\(727\) 36.0698 1.33776 0.668878 0.743372i \(-0.266775\pi\)
0.668878 + 0.743372i \(0.266775\pi\)
\(728\) −28.6057 + 15.5698i −1.06020 + 0.577054i
\(729\) 0 0
\(730\) −4.81810 8.34519i −0.178326 0.308869i
\(731\) 0.462162 0.800488i 0.0170937 0.0296071i
\(732\) 0 0
\(733\) −17.0665 29.5601i −0.630367 1.09183i −0.987477 0.157765i \(-0.949571\pi\)
0.357110 0.934062i \(-0.383762\pi\)
\(734\) −36.9439 −1.36363
\(735\) 0 0
\(736\) 3.79845 0.140013
\(737\) −13.0847 22.6634i −0.481982 0.834817i
\(738\) 0 0
\(739\) −10.9481 + 18.9626i −0.402731 + 0.697550i −0.994054 0.108884i \(-0.965272\pi\)
0.591324 + 0.806434i \(0.298606\pi\)
\(740\) −0.262550 0.454751i −0.00965154 0.0167170i
\(741\) 0 0
\(742\) −38.4449 + 20.9251i −1.41136 + 0.768185i
\(743\) −28.2852 −1.03768 −0.518842 0.854870i \(-0.673637\pi\)
−0.518842 + 0.854870i \(0.673637\pi\)
\(744\) 0 0
\(745\) 4.17111 7.22457i 0.152818 0.264688i
\(746\) 1.46050 2.52967i 0.0534729 0.0926177i
\(747\) 0 0
\(748\) −0.162253 −0.00593254
\(749\) −2.31351 1.41445i −0.0845340 0.0516830i
\(750\) 0 0
\(751\) 7.24844 + 12.5547i 0.264499 + 0.458126i 0.967432 0.253130i \(-0.0814600\pi\)
−0.702933 + 0.711256i \(0.748127\pi\)
\(752\) 26.4159 45.7538i 0.963291 1.66847i
\(753\) 0 0
\(754\) −1.16158 2.01191i −0.0423022 0.0732696i
\(755\) −0.226459 −0.00824169
\(756\) 0 0
\(757\) −38.9646 −1.41619 −0.708096 0.706116i \(-0.750446\pi\)
−0.708096 + 0.706116i \(0.750446\pi\)
\(758\) −13.7360 23.7914i −0.498914 0.864144i
\(759\) 0 0
\(760\) 2.32004 4.01842i 0.0841566 0.145764i
\(761\) −0.627819 1.08741i −0.0227584 0.0394187i 0.854422 0.519580i \(-0.173912\pi\)
−0.877180 + 0.480161i \(0.840578\pi\)
\(762\) 0 0
\(763\) −0.0861875 + 3.42603i −0.00312020 + 0.124031i
\(764\) 1.61421 0.0584002
\(765\) 0 0
\(766\) 25.6623 44.4483i 0.927215 1.60598i
\(767\) −18.1804 + 31.4894i −0.656458 + 1.13702i
\(768\) 0 0
\(769\) −27.6883 −0.998466 −0.499233 0.866468i \(-0.666385\pi\)
−0.499233 + 0.866468i \(0.666385\pi\)
\(770\) −8.72879 5.33667i −0.314564 0.192320i
\(771\) 0 0
\(772\) −1.14193 1.97788i −0.0410989 0.0711854i
\(773\) 3.95544 6.85103i 0.142267 0.246414i −0.786083 0.618121i \(-0.787894\pi\)
0.928350 + 0.371707i \(0.121227\pi\)
\(774\) 0 0
\(775\) 5.84348 + 10.1212i 0.209904 + 0.363565i
\(776\) −6.17900 −0.221813
\(777\) 0 0
\(778\) 12.2370 0.438717
\(779\) 15.6192 + 27.0532i 0.559614 + 0.969281i
\(780\) 0 0
\(781\) −5.80039 + 10.0466i −0.207554 + 0.359494i
\(782\) −1.00885 1.74739i −0.0360766 0.0624864i
\(783\) 0 0
\(784\) 29.7015 + 1.49533i 1.06077 + 0.0534045i
\(785\) 4.46050 0.159202
\(786\) 0 0
\(787\) −15.8346 + 27.4264i −0.564444 + 0.977645i 0.432658 + 0.901558i \(0.357576\pi\)
−0.997101 + 0.0760866i \(0.975757\pi\)
\(788\) −0.0500067 + 0.0866142i −0.00178142 + 0.00308550i
\(789\) 0 0
\(790\) 9.67684 0.344287
\(791\) 33.2199