Properties

Label 189.2.e.e.163.3
Level 189
Weight 2
Character 189.163
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 163.3
Root \(0.500000 + 2.05195i\)
Character \(\chi\) = 189.163
Dual form 189.2.e.e.109.3

$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

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

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 −0.483453 0.875370i \(-0.660618\pi\)
0.999819 0.0190026i \(-0.00604908\pi\)
\(3\) 0 0
\(4\) −0.0665372 0.115246i −0.0332686 0.0576229i
\(5\) 0.296790 0.514055i 0.132728 0.229892i −0.791999 0.610522i \(-0.790960\pi\)
0.924727 + 0.380630i \(0.124293\pi\)
\(6\) 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 −0.977208 0.212283i \(-0.931910\pi\)
0.304762 0.952429i \(-0.401423\pi\)
\(12\) 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 0.882124 0.471018i \(-0.156113\pi\)
−0.848975 + 0.528432i \(0.822780\pi\)
\(18\) 0 0
\(19\) −1.43346 + 2.48283i −0.328859 + 0.569600i −0.982286 0.187389i \(-0.939997\pi\)
0.653427 + 0.756990i \(0.273331\pi\)
\(20\) −0.0789903 −0.0176628
\(21\) 0 0
\(22\) −6.51459 −1.38892
\(23\) −2.52704 + 4.37697i −0.526925 + 0.912660i 0.472583 + 0.881286i \(0.343322\pi\)
−0.999508 + 0.0313742i \(0.990012\pi\)
\(24\) 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 0.730747 0.682648i \(-0.239172\pi\)
−0.956564 + 0.291522i \(0.905838\pi\)
\(32\) −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 −0.452081 0.891977i \(-0.649318\pi\)
0.998515 0.0544753i \(-0.0173486\pi\)
\(38\) 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 −0.0886938 + 0.996059i \(0.528269\pi\)
−0.818265 + 0.574841i \(0.805064\pi\)
\(48\) 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 −0.933109 0.359593i \(-0.882916\pi\)
0.155138 0.987893i \(-0.450418\pi\)
\(54\) 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 0.999601 + 0.0282624i \(0.00899740\pi\)
−0.475324 + 0.879811i \(0.657669\pi\)
\(60\) 0 0
\(61\) 1.36693 2.36758i 0.175017 0.303138i −0.765150 0.643852i \(-0.777335\pi\)
0.940167 + 0.340714i \(0.110669\pi\)
\(62\) −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 0.629311 0.777154i \(-0.283337\pi\)
−0.987690 + 0.156422i \(0.950004\pi\)
\(68\) 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 −0.983007 0.183567i \(-0.941235\pi\)
0.332530 0.943093i \(-0.392098\pi\)
\(74\) −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 0.360042 + 0.932936i \(0.382763\pi\)
−0.987967 + 0.154663i \(0.950571\pi\)
\(80\) −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 −0.687732 0.725965i \(-0.741393\pi\)
0.972570 + 0.232611i \(0.0747268\pi\)
\(90\) 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 0.533716 0.845664i \(-0.320795\pi\)
−0.999224 + 0.0393793i \(0.987462\pi\)
\(102\) 0 0
\(103\) 7.88151 13.6512i 0.776589 1.34509i −0.157309 0.987550i \(-0.550282\pi\)
0.933897 0.357542i \(-0.116385\pi\)
\(104\) −12.3097 −1.20707
\(105\) 0 0
\(106\) −16.5438 −1.60687
\(107\) −0.512453 + 0.887595i −0.0495407 + 0.0858070i −0.889732 0.456483i \(-0.849109\pi\)
0.840192 + 0.542290i \(0.182442\pi\)
\(108\) 0 0
\(109\) −0.647664 1.12179i −0.0620349 0.107448i 0.833340 0.552761i \(-0.186426\pi\)
−0.895375 + 0.445313i \(0.853092\pi\)
\(110\) −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 −0.787779 0.615958i \(-0.788769\pi\)
0.927325 + 0.374257i \(0.122102\pi\)
\(132\) 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 0.565229 0.824934i \(-0.308788\pi\)
−0.997028 + 0.0770354i \(0.975455\pi\)
\(138\) 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 0.420290 + 0.907390i \(0.361928\pi\)
−0.995968 + 0.0897132i \(0.971405\pi\)
\(150\) 0 0
\(151\) −0.190757 0.330401i −0.0155236 0.0268877i 0.858159 0.513384i \(-0.171608\pi\)
−0.873683 + 0.486496i \(0.838275\pi\)
\(152\) −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 0.976105 0.217300i \(-0.0697251\pi\)
−0.676240 + 0.736681i \(0.736392\pi\)
\(158\) 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 0.398613 + 0.917119i \(0.369492\pi\)
−0.993555 + 0.113351i \(0.963842\pi\)
\(164\) 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 −0.595787 0.803143i \(-0.703160\pi\)
0.993435 + 0.114395i \(0.0364929\pi\)
\(174\) 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 0.983513 0.180838i \(-0.0578810\pi\)
−0.648367 + 0.761328i \(0.724548\pi\)
\(180\) 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 −0.997601 0.0692211i \(-0.977949\pi\)
0.558748 + 0.829338i \(0.311282\pi\)
\(192\) 0 0
\(193\) −8.58113 14.8629i −0.617683 1.06986i −0.989907 0.141716i \(-0.954738\pi\)
0.372224 0.928143i \(-0.378595\pi\)
\(194\) −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 0.623853 0.781542i \(-0.285566\pi\)
−0.988761 + 0.149502i \(0.952233\pi\)
\(200\) 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 0.940365 0.340166i \(-0.110483\pi\)
−0.764775 + 0.644297i \(0.777150\pi\)
\(228\) 0 0
\(229\) −5.86186 + 10.1530i −0.387363 + 0.670932i −0.992094 0.125498i \(-0.959947\pi\)
0.604731 + 0.796430i \(0.293281\pi\)
\(230\) 4.38151 0.288909
\(231\) 0 0
\(232\) 0.960699 0.0630730
\(233\) 1.93560 3.35256i 0.126805 0.219633i −0.795632 0.605780i \(-0.792861\pi\)
0.922437 + 0.386147i \(0.126194\pi\)
\(234\) 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 0.999239 + 0.0390173i \(0.0124227\pi\)
−0.465829 + 0.884875i \(0.654244\pi\)
\(242\) 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 −0.0550638 0.998483i \(-0.517536\pi\)
0.892243 0.451555i \(-0.149130\pi\)
\(258\) 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 0.988462 + 0.151470i \(0.0484006\pi\)
−0.363054 + 0.931768i \(0.618266\pi\)
\(264\) 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 0.701798 0.712376i \(-0.252381\pi\)
−0.967835 + 0.251587i \(0.919048\pi\)
\(270\) 0 0
\(271\) −12.0957 + 20.9504i −0.734762 + 1.27265i 0.220065 + 0.975485i \(0.429373\pi\)
−0.954828 + 0.297161i \(0.903960\pi\)
\(272\) 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 0.952888 0.303321i \(-0.0980955\pi\)
−0.739128 + 0.673565i \(0.764762\pi\)
\(278\) 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 0.831327 0.555784i \(-0.187582\pi\)
−0.896987 + 0.442058i \(0.854249\pi\)
\(284\) −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 0.976609 0.215021i \(-0.0689821\pi\)
−0.674519 + 0.738258i \(0.735649\pi\)
\(312\) 0 0
\(313\) 8.28074 14.3427i 0.468055 0.810695i −0.531279 0.847197i \(-0.678288\pi\)
0.999334 + 0.0365022i \(0.0116216\pi\)
\(314\) 10.9751 0.619360
\(315\) 0 0
\(316\) 1.48541 0.0835609
\(317\) −13.3186 + 23.0685i −0.748046 + 1.29565i 0.200712 + 0.979650i \(0.435674\pi\)
−0.948758 + 0.316003i \(0.897659\pi\)
\(318\) 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 −0.344786 0.938681i \(-0.612049\pi\)
0.985315 0.170747i \(-0.0546181\pi\)
\(332\) −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 0.538969 0.842325i \(-0.318814\pi\)
−0.998960 + 0.0455985i \(0.985481\pi\)
\(348\) 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 0.569216 0.822188i \(-0.307247\pi\)
−0.996644 + 0.0818613i \(0.973914\pi\)
\(354\) 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 −0.988913 0.148494i \(-0.952557\pi\)
0.623056 + 0.782177i \(0.285891\pi\)
\(360\) 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 −0.980562 0.196209i \(-0.937137\pi\)
0.320360 0.947296i \(-0.396196\pi\)
\(368\) 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 −0.890753 0.454488i \(-0.849822\pi\)
0.838975 + 0.544170i \(0.183156\pi\)
\(374\) −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 −0.0675593 + 0.997715i \(0.521521\pi\)
−0.830267 + 0.557366i \(0.811812\pi\)
\(384\) 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 0.952467 0.304642i \(-0.0985368\pi\)
−0.740061 + 0.672539i \(0.765204\pi\)
\(390\) 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 −0.726338 0.687338i \(-0.758779\pi\)
0.958421 + 0.285358i \(0.0921126\pi\)
\(398\) −15.0364 −0.753705
\(399\) 0 0
\(400\) 19.7453 0.987266
\(401\) 0.0737345 0.127712i 0.00368212 0.00637763i −0.864178 0.503185i \(-0.832161\pi\)
0.867861 + 0.496808i \(0.165495\pi\)
\(402\) 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 0.910461 0.413595i \(-0.135727\pi\)
−0.813414 + 0.581685i \(0.802394\pi\)
\(410\) 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 0.924393 0.381442i \(-0.124572\pi\)
−0.792535 + 0.609827i \(0.791239\pi\)
\(432\) 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 −0.796325 0.604869i \(-0.793225\pi\)
0.921995 + 0.387203i \(0.126559\pi\)
\(440\) −7.21926 −0.344165
\(441\) 0 0
\(442\) −1.80233 −0.0857281
\(443\) −3.01819 + 5.22765i −0.143398 + 0.248373i −0.928774 0.370646i \(-0.879136\pi\)
0.785376 + 0.619019i \(0.212470\pi\)
\(444\) 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 −0.796872 0.604148i \(-0.793513\pi\)
0.921644 + 0.388037i \(0.126847\pi\)
\(458\) 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 −0.427150 0.904181i \(-0.640482\pi\)
0.996619 0.0821676i \(-0.0261843\pi\)
\(468\) 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 0.861923 0.507039i \(-0.169260\pi\)
−0.870070 + 0.492928i \(0.835927\pi\)
\(480\) 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 0.974233 0.225546i \(-0.0724165\pi\)
−0.682445 + 0.730937i \(0.739083\pi\)
\(488\) 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 −0.358382 0.933575i \(-0.616672\pi\)
0.987691 0.156419i \(-0.0499951\pi\)
\(500\) −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 −0.999978 0.00660269i \(-0.997898\pi\)
0.505707 + 0.862705i \(0.331232\pi\)
\(510\) 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 0.969059 0.246828i \(-0.0793884\pi\)
−0.698289 + 0.715816i \(0.746055\pi\)
\(522\) 0 0
\(523\) −3.09572 + 5.36194i −0.135366 + 0.234461i −0.925737 0.378167i \(-0.876554\pi\)
0.790371 + 0.612628i \(0.209888\pi\)
\(524\) −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 0.419330 + 0.907834i \(0.362265\pi\)
−0.995872 + 0.0907660i \(0.971068\pi\)
\(542\) 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 −0.999998 0.00193169i \(-0.999385\pi\)
0.498326 0.866990i \(-0.333948\pi\)
\(558\) 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 0.640117 0.768277i \(-0.278886\pi\)
−0.985406 + 0.170219i \(0.945553\pi\)
\(564\) 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 −0.982695 0.185231i \(-0.940697\pi\)
0.651763 + 0.758423i \(0.274030\pi\)
\(570\) 0 0
\(571\) −3.19076 5.52655i −0.133529 0.231279i 0.791506 0.611162i \(-0.209298\pi\)
−0.925035 + 0.379883i \(0.875964\pi\)
\(572\) 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 0.937009 + 0.349304i \(0.113582\pi\)
−0.165998 + 0.986126i \(0.553085\pi\)
\(578\) −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 −0.644935 0.764238i \(-0.723115\pi\)
0.984317 + 0.176411i \(0.0564487\pi\)
\(594\) 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 0.762721 0.646727i \(-0.223863\pi\)
−0.941443 + 0.337172i \(0.890530\pi\)
\(600\) 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 −0.858404 0.512974i \(-0.828544\pi\)
0.873451 + 0.486912i \(0.161877\pi\)
\(608\) 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 0.816922 0.576749i \(-0.195679\pi\)
−0.907940 + 0.419101i \(0.862345\pi\)
\(614\) −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 0.817429 0.576030i \(-0.195399\pi\)
−0.907571 + 0.419899i \(0.862065\pi\)
\(620\) 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 0.876134 + 0.482068i \(0.160114\pi\)
−0.0205843 + 0.999788i \(0.506553\pi\)
\(642\) 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 0.971019 0.239000i \(-0.0768197\pi\)
−0.692490 + 0.721427i \(0.743486\pi\)
\(648\) 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 0.442239 + 0.896897i \(0.354184\pi\)
−0.997855 + 0.0654587i \(0.979149\pi\)
\(654\) 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 0.962776 0.270301i \(-0.0871232\pi\)
−0.715476 + 0.698638i \(0.753790\pi\)
\(662\) −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 −0.951495 0.307663i \(-0.900453\pi\)
0.742192 + 0.670188i \(0.233786\pi\)
\(678\) 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 −0.977926 0.208951i \(-0.932995\pi\)
0.308006 0.951384i \(-0.400338\pi\)
\(684\) 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 −0.934930 0.354832i \(-0.884538\pi\)
0.774759 + 0.632257i \(0.217871\pi\)
\(692\) −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 −0.546240 0.837629i \(-0.683941\pi\)
0.998528 + 0.0542432i \(0.0172746\pi\)
\(710\) −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 0.143878 + 0.989595i \(0.454043\pi\)
−0.928954 + 0.370196i \(0.879291\pi\)
\(720\) 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 0.357110 + 0.934062i \(0.383762\pi\)
−0.987477 + 0.157765i \(0.949571\pi\)
\(734\) −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 0.591324 0.806434i \(-0.298606\pi\)
−0.994054 + 0.108884i \(0.965272\pi\)
\(740\) −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 −0.702933 0.711256i \(-0.748127\pi\)
0.967432 + 0.253130i \(0.0814600\pi\)
\(752\) 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 −0.877180 0.480161i \(-0.840578\pi\)
0.854422 + 0.519580i \(0.173912\pi\)
\(762\) 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 0.928350 0.371707i \(-0.121227\pi\)
−0.786083 + 0.618121i \(0.787894\pi\)
\(774\) 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 −0.997101 0.0760866i \(-0.975757\pi\)
0.432658 0.901558i \(-0.357576\pi\)
\(788\) −0.0500067 0.0866142i −0.00178142 0.00308550i
\(789\) 0 0
\(790\) 9.67684 0.344287