Properties

Label 144.2.l.a.107.4
Level $144$
Weight $2$
Character 144.107
Analytic conductor $1.150$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.4
Root \(0.517174 - 1.31626i\) of defining polynomial
Character \(\chi\) \(=\) 144.107
Dual form 144.2.l.a.35.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.263185 - 1.38951i) q^{2} +(-1.86147 + 0.731395i) q^{4} +(2.63251 - 2.63251i) q^{5} -0.207188 q^{7} +(1.50619 + 2.39403i) q^{8} +O(q^{10})\) \(q+(-0.263185 - 1.38951i) q^{2} +(-1.86147 + 0.731395i) q^{4} +(2.63251 - 2.63251i) q^{5} -0.207188 q^{7} +(1.50619 + 2.39403i) q^{8} +(-4.35074 - 2.96506i) q^{10} +(-3.66686 - 3.66686i) q^{11} +(0.255601 - 0.255601i) q^{13} +(0.0545288 + 0.287890i) q^{14} +(2.93012 - 2.72294i) q^{16} +0.654483i q^{17} +(4.46733 + 4.46733i) q^{19} +(-2.97493 + 6.82574i) q^{20} +(-4.13007 + 6.06020i) q^{22} +3.48934i q^{23} -8.86025i q^{25} +(-0.422430 - 0.287890i) q^{26} +(0.385674 - 0.151536i) q^{28} +(4.33973 + 4.33973i) q^{29} +6.16426i q^{31} +(-4.55471 - 3.35480i) q^{32} +(0.909410 - 0.172250i) q^{34} +(-0.545426 + 0.545426i) q^{35} +(4.39291 + 4.39291i) q^{37} +(5.03166 - 7.38313i) q^{38} +(10.2674 + 2.33726i) q^{40} +0.0684664 q^{41} +(5.65306 - 5.65306i) q^{43} +(9.50767 + 4.14382i) q^{44} +(4.84846 - 0.918340i) q^{46} -9.14619 q^{47} -6.95707 q^{49} +(-12.3114 + 2.33188i) q^{50} +(-0.288848 + 0.662739i) q^{52} +(1.51131 - 1.51131i) q^{53} -19.3061 q^{55} +(-0.312065 - 0.496015i) q^{56} +(4.88795 - 7.17225i) q^{58} +(2.53542 + 2.53542i) q^{59} +(-5.46733 + 5.46733i) q^{61} +(8.56529 - 1.62234i) q^{62} +(-3.46279 + 7.21173i) q^{64} -1.34575i q^{65} +(-4.77135 - 4.77135i) q^{67} +(-0.478686 - 1.21830i) q^{68} +(0.901421 + 0.614326i) q^{70} +5.94986i q^{71} -6.93467i q^{73} +(4.94784 - 7.26014i) q^{74} +(-11.5832 - 5.04841i) q^{76} +(0.759730 + 0.759730i) q^{77} -4.72748i q^{79} +(0.545426 - 14.8817i) q^{80} +(-0.0180193 - 0.0951346i) q^{82} +(4.32777 - 4.32777i) q^{83} +(1.72294 + 1.72294i) q^{85} +(-9.34277 - 6.36717i) q^{86} +(3.25560 - 14.3016i) q^{88} -11.9443 q^{89} +(-0.0529576 + 0.0529576i) q^{91} +(-2.55208 - 6.49529i) q^{92} +(2.40714 + 12.7087i) q^{94} +23.5206 q^{95} -0.925579 q^{97} +(1.83100 + 9.66691i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{10} - 16q^{16} + 16q^{19} - 40q^{22} - 24q^{28} + 24q^{34} + 72q^{40} - 32q^{43} + 40q^{46} + 16q^{49} + 24q^{52} - 64q^{55} + 24q^{58} - 32q^{61} - 48q^{64} - 16q^{67} - 72q^{70} + 80q^{82} - 32q^{85} + 48q^{88} + 48q^{91} + 72q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.263185 1.38951i −0.186100 0.982531i
\(3\) 0 0
\(4\) −1.86147 + 0.731395i −0.930734 + 0.365697i
\(5\) 2.63251 2.63251i 1.17730 1.17730i 0.196865 0.980431i \(-0.436924\pi\)
0.980431 0.196865i \(-0.0630760\pi\)
\(6\) 0 0
\(7\) −0.207188 −0.0783098 −0.0391549 0.999233i \(-0.512467\pi\)
−0.0391549 + 0.999233i \(0.512467\pi\)
\(8\) 1.50619 + 2.39403i 0.532518 + 0.846419i
\(9\) 0 0
\(10\) −4.35074 2.96506i −1.37582 0.937635i
\(11\) −3.66686 3.66686i −1.10560 1.10560i −0.993722 0.111878i \(-0.964313\pi\)
−0.111878 0.993722i \(1.46431\pi\)
\(12\) 0 0
\(13\) 0.255601 0.255601i 0.0708910 0.0708910i −0.670772 0.741663i \(-0.734037\pi\)
0.741663 + 0.670772i \(0.234037\pi\)
\(14\) 0.0545288 + 0.287890i 0.0145734 + 0.0769418i
\(15\) 0 0
\(16\) 2.93012 2.72294i 0.732531 0.680734i
\(17\) 0.654483i 0.158735i 0.996845 + 0.0793677i \(0.0252901\pi\)
−0.996845 + 0.0793677i \(0.974710\pi\)
\(18\) 0 0
\(19\) 4.46733 + 4.46733i 1.02488 + 1.02488i 0.999683 + 0.0251941i \(0.00802039\pi\)
0.0251941 + 0.999683i \(0.491980\pi\)
\(20\) −2.97493 + 6.82574i −0.665215 + 1.52628i
\(21\) 0 0
\(22\) −4.13007 + 6.06020i −0.880534 + 1.29204i
\(23\) 3.48934i 0.727577i 0.931482 + 0.363789i \(0.118517\pi\)
−0.931482 + 0.363789i \(0.881483\pi\)
\(24\) 0 0
\(25\) 8.86025i 1.77205i
\(26\) −0.422430 0.287890i −0.0828454 0.0564598i
\(27\) 0 0
\(28\) 0.385674 0.151536i 0.0728856 0.0286377i
\(29\) 4.33973 + 4.33973i 0.805869 + 0.805869i 0.984006 0.178137i \(-0.0570071\pi\)
−0.178137 + 0.984006i \(0.557007\pi\)
\(30\) 0 0
\(31\) 6.16426i 1.10713i 0.832805 + 0.553567i \(0.186734\pi\)
−0.832805 + 0.553567i \(0.813266\pi\)
\(32\) −4.55471 3.35480i −0.805166 0.593050i
\(33\) 0 0
\(34\) 0.909410 0.172250i 0.155963 0.0295406i
\(35\) −0.545426 + 0.545426i −0.0921938 + 0.0921938i
\(36\) 0 0
\(37\) 4.39291 + 4.39291i 0.722190 + 0.722190i 0.969051 0.246861i \(-0.0793990\pi\)
−0.246861 + 0.969051i \(0.579399\pi\)
\(38\) 5.03166 7.38313i 0.816244 1.19770i
\(39\) 0 0
\(40\) 10.2674 + 2.33726i 1.62342 + 0.369553i
\(41\) 0.0684664 0.0106927 0.00534633 0.999986i \(-0.498298\pi\)
0.00534633 + 0.999986i \(0.498298\pi\)
\(42\) 0 0
\(43\) 5.65306 5.65306i 0.862083 0.862083i −0.129497 0.991580i \(-0.541336\pi\)
0.991580 + 0.129497i \(0.0413361\pi\)
\(44\) 9.50767 + 4.14382i 1.43333 + 0.624704i
\(45\) 0 0
\(46\) 4.84846 0.918340i 0.714867 0.135402i
\(47\) −9.14619 −1.33411 −0.667055 0.745009i \(-0.732445\pi\)
−0.667055 + 0.745009i \(0.732445\pi\)
\(48\) 0 0
\(49\) −6.95707 −0.993868
\(50\) −12.3114 + 2.33188i −1.74109 + 0.329778i
\(51\) 0 0
\(52\) −0.288848 + 0.662739i −0.0400560 + 0.0919053i
\(53\) 1.51131 1.51131i 0.207594 0.207594i −0.595650 0.803244i \(-0.703105\pi\)
0.803244 + 0.595650i \(0.203105\pi\)
\(54\) 0 0
\(55\) −19.3061 −2.60324
\(56\) −0.312065 0.496015i −0.0417014 0.0662829i
\(57\) 0 0
\(58\) 4.88795 7.17225i 0.641819 0.941763i
\(59\) 2.53542 + 2.53542i 0.330083 + 0.330083i 0.852618 0.522535i \(-0.175013\pi\)
−0.522535 + 0.852618i \(0.675013\pi\)
\(60\) 0 0
\(61\) −5.46733 + 5.46733i −0.700020 + 0.700020i −0.964415 0.264394i \(-0.914828\pi\)
0.264394 + 0.964415i \(0.414828\pi\)
\(62\) 8.56529 1.62234i 1.08779 0.206037i
\(63\) 0 0
\(64\) −3.46279 + 7.21173i −0.432849 + 0.901467i
\(65\) 1.34575i 0.166919i
\(66\) 0 0
\(67\) −4.77135 4.77135i −0.582913 0.582913i 0.352790 0.935703i \(-0.385233\pi\)
−0.935703 + 0.352790i \(0.885233\pi\)
\(68\) −0.478686 1.21830i −0.0580491 0.147740i
\(69\) 0 0
\(70\) 0.901421 + 0.614326i 0.107740 + 0.0734260i
\(71\) 5.94986i 0.706119i 0.935601 + 0.353059i \(0.114859\pi\)
−0.935601 + 0.353059i \(0.885141\pi\)
\(72\) 0 0
\(73\) 6.93467i 0.811641i −0.913953 0.405821i \(-0.866986\pi\)
0.913953 0.405821i \(-0.133014\pi\)
\(74\) 4.94784 7.26014i 0.575175 0.843974i
\(75\) 0 0
\(76\) −11.5832 5.04841i −1.32868 0.579093i
\(77\) 0.759730 + 0.759730i 0.0865793 + 0.0865793i
\(78\) 0 0
\(79\) 4.72748i 0.531883i −0.963989 0.265942i \(-0.914317\pi\)
0.963989 0.265942i \(-0.0856828\pi\)
\(80\) 0.545426 14.8817i 0.0609804 1.66383i
\(81\) 0 0
\(82\) −0.0180193 0.0951346i −0.00198990 0.0105059i
\(83\) 4.32777 4.32777i 0.475035 0.475035i −0.428505 0.903539i \(-0.640960\pi\)
0.903539 + 0.428505i \(0.140960\pi\)
\(84\) 0 0
\(85\) 1.72294 + 1.72294i 0.186879 + 0.186879i
\(86\) −9.34277 6.36717i −1.00746 0.686590i
\(87\) 0 0
\(88\) 3.25560 14.3016i 0.347048 1.52455i
\(89\) −11.9443 −1.26609 −0.633045 0.774115i \(-0.718195\pi\)
−0.633045 + 0.774115i \(0.718195\pi\)
\(90\) 0 0
\(91\) −0.0529576 + 0.0529576i −0.00555146 + 0.00555146i
\(92\) −2.55208 6.49529i −0.266073 0.677181i
\(93\) 0 0
\(94\) 2.40714 + 12.7087i 0.248277 + 1.31080i
\(95\) 23.5206 2.41317
\(96\) 0 0
\(97\) −0.925579 −0.0939783 −0.0469892 0.998895i \(-0.514963\pi\)
−0.0469892 + 0.998895i \(0.514963\pi\)
\(98\) 1.83100 + 9.66691i 0.184958 + 0.976506i
\(99\) 0 0
\(100\) 6.48034 + 16.4931i 0.648034 + 1.64931i
\(101\) −2.27104 + 2.27104i −0.225977 + 0.225977i −0.811010 0.585033i \(-0.801082\pi\)
0.585033 + 0.811010i \(0.301082\pi\)
\(102\) 0 0
\(103\) 14.1643 1.39565 0.697823 0.716270i \(-0.254152\pi\)
0.697823 + 0.716270i \(0.254152\pi\)
\(104\) 0.996902 + 0.226934i 0.0977543 + 0.0222527i
\(105\) 0 0
\(106\) −2.49773 1.70222i −0.242601 0.165334i
\(107\) −8.85318 8.85318i −0.855870 0.855870i 0.134979 0.990848i \(-0.456903\pi\)
−0.990848 + 0.134979i \(0.956903\pi\)
\(108\) 0 0
\(109\) −2.66998 + 2.66998i −0.255737 + 0.255737i −0.823318 0.567580i \(-0.807880\pi\)
0.567580 + 0.823318i \(0.307880\pi\)
\(110\) 5.08107 + 26.8260i 0.484461 + 2.55776i
\(111\) 0 0
\(112\) −0.607087 + 0.564160i −0.0573643 + 0.0533081i
\(113\) 8.39289i 0.789536i 0.918781 + 0.394768i \(0.129175\pi\)
−0.918781 + 0.394768i \(0.870825\pi\)
\(114\) 0 0
\(115\) 9.18572 + 9.18572i 0.856573 + 0.856573i
\(116\) −11.2523 4.90422i −1.04475 0.455345i
\(117\) 0 0
\(118\) 2.85570 4.19027i 0.262889 0.385746i
\(119\) 0.135601i 0.0124305i
\(120\) 0 0
\(121\) 15.8917i 1.44470i
\(122\) 9.03583 + 6.15799i 0.818065 + 0.557518i
\(123\) 0 0
\(124\) −4.50851 11.4746i −0.404876 1.03045i
\(125\) −10.1621 10.1621i −0.908930 0.908930i
\(126\) 0 0
\(127\) 9.64397i 0.855764i −0.903835 0.427882i \(-0.859260\pi\)
0.903835 0.427882i \(-0.140740\pi\)
\(128\) 10.9321 + 2.91356i 0.966272 + 0.257525i
\(129\) 0 0
\(130\) −1.86993 + 0.354180i −0.164003 + 0.0310636i
\(131\) 5.07084 5.07084i 0.443041 0.443041i −0.449992 0.893033i \(-0.648573\pi\)
0.893033 + 0.449992i \(0.148573\pi\)
\(132\) 0 0
\(133\) −0.925579 0.925579i −0.0802579 0.0802579i
\(134\) −5.37408 + 7.88557i −0.464250 + 0.681210i
\(135\) 0 0
\(136\) −1.56685 + 0.985775i −0.134357 + 0.0845295i
\(137\) −11.9075 −1.01732 −0.508662 0.860966i \(-0.669860\pi\)
−0.508662 + 0.860966i \(0.669860\pi\)
\(138\) 0 0
\(139\) 0.771348 0.771348i 0.0654249 0.0654249i −0.673637 0.739062i \(-0.735269\pi\)
0.739062 + 0.673637i \(0.235269\pi\)
\(140\) 0.616371 1.41421i 0.0520928 0.119523i
\(141\) 0 0
\(142\) 8.26738 1.56591i 0.693784 0.131408i
\(143\) −1.87451 −0.156754
\(144\) 0 0
\(145\) 22.8488 1.89749
\(146\) −9.63578 + 1.82510i −0.797463 + 0.151046i
\(147\) 0 0
\(148\) −11.3902 4.96431i −0.936270 0.408064i
\(149\) 3.02434 3.02434i 0.247764 0.247764i −0.572289 0.820052i \(-0.693944\pi\)
0.820052 + 0.572289i \(0.193944\pi\)
\(150\) 0 0
\(151\) 6.57864 0.535362 0.267681 0.963508i \(-0.413743\pi\)
0.267681 + 0.963508i \(0.413743\pi\)
\(152\) −3.96630 + 17.4236i −0.321709 + 1.41324i
\(153\) 0 0
\(154\) 0.855702 1.25560i 0.0689545 0.101179i
\(155\) 16.2275 + 16.2275i 1.30342 + 1.30342i
\(156\) 0 0
\(157\) 7.46733 7.46733i 0.595958 0.595958i −0.343276 0.939234i \(-0.611537\pi\)
0.939234 + 0.343276i \(0.111537\pi\)
\(158\) −6.56887 + 1.24420i −0.522591 + 0.0989833i
\(159\) 0 0
\(160\) −20.8219 + 3.15878i −1.64611 + 0.249723i
\(161\) 0.722950i 0.0569764i
\(162\) 0 0
\(163\) −14.0674 14.0674i −1.10185 1.10185i −0.994188 0.107659i \(-0.965665\pi\)
−0.107659 0.994188i \(-0.534335\pi\)
\(164\) −0.127448 + 0.0500760i −0.00995201 + 0.00391028i
\(165\) 0 0
\(166\) −7.15248 4.87447i −0.555140 0.378332i
\(167\) 6.55006i 0.506859i −0.967354 0.253430i \(-0.918441\pi\)
0.967354 0.253430i \(-0.0815586\pi\)
\(168\) 0 0
\(169\) 12.8693i 0.989949i
\(170\) 1.94058 2.84748i 0.148836 0.218392i
\(171\) 0 0
\(172\) −6.38837 + 14.6576i −0.487109 + 1.11763i
\(173\) −0.955645 0.955645i −0.0726563 0.0726563i 0.669845 0.742501i \(-0.266361\pi\)
−0.742501 + 0.669845i \(0.766361\pi\)
\(174\) 0 0
\(175\) 1.83574i 0.138769i
\(176\) −20.7290 0.759730i −1.56251 0.0572668i
\(177\) 0 0
\(178\) 3.14355 + 16.5967i 0.235619 + 1.24397i
\(179\) −8.77829 + 8.77829i −0.656120 + 0.656120i −0.954460 0.298340i \(-0.903567\pi\)
0.298340 + 0.954460i \(0.403567\pi\)
\(180\) 0 0
\(181\) 6.25560 + 6.25560i 0.464975 + 0.464975i 0.900282 0.435307i \(-0.143360\pi\)
−0.435307 + 0.900282i \(0.643360\pi\)
\(182\) 0.0875226 + 0.0596474i 0.00648761 + 0.00442136i
\(183\) 0 0
\(184\) −8.35359 + 5.25560i −0.615835 + 0.387448i
\(185\) 23.1288 1.70046
\(186\) 0 0
\(187\) 2.39990 2.39990i 0.175498 0.175498i
\(188\) 17.0253 6.68948i 1.24170 0.487880i
\(189\) 0 0
\(190\) −6.19027 32.6821i −0.449089 2.37101i
\(191\) −7.13608 −0.516349 −0.258174 0.966098i \(-0.583121\pi\)
−0.258174 + 0.966098i \(0.583121\pi\)
\(192\) 0 0
\(193\) −10.9347 −0.787095 −0.393547 0.919304i \(-0.628752\pi\)
−0.393547 + 0.919304i \(0.628752\pi\)
\(194\) 0.243598 + 1.28610i 0.0174893 + 0.0923366i
\(195\) 0 0
\(196\) 12.9504 5.08837i 0.925026 0.363455i
\(197\) −10.3277 + 10.3277i −0.735819 + 0.735819i −0.971766 0.235947i \(-0.924181\pi\)
0.235947 + 0.971766i \(0.424181\pi\)
\(198\) 0 0
\(199\) 7.18478 0.509316 0.254658 0.967031i \(-0.418037\pi\)
0.254658 + 0.967031i \(0.418037\pi\)
\(200\) 21.2117 13.3452i 1.49990 0.943649i
\(201\) 0 0
\(202\) 3.75333 + 2.55792i 0.264083 + 0.179975i
\(203\) −0.899142 0.899142i −0.0631074 0.0631074i
\(204\) 0 0
\(205\) 0.180239 0.180239i 0.0125884 0.0125884i
\(206\) −3.72782 19.6814i −0.259729 1.37127i
\(207\) 0 0
\(208\) 0.0529576 1.44493i 0.00367195 0.100188i
\(209\) 32.7622i 2.26621i
\(210\) 0 0
\(211\) −0.163320 0.163320i −0.0112434 0.0112434i 0.701463 0.712706i \(-0.252531\pi\)
−0.712706 + 0.701463i \(0.752531\pi\)
\(212\) −1.70789 + 3.91861i −0.117298 + 0.269131i
\(213\) 0 0
\(214\) −9.97155 + 14.6316i −0.681641 + 1.00020i
\(215\) 29.7635i 2.02985i
\(216\) 0 0
\(217\) 1.27716i 0.0866994i
\(218\) 4.41265 + 3.00726i 0.298863 + 0.203677i
\(219\) 0 0
\(220\) 35.9377 14.1204i 2.42292 0.951997i
\(221\) 0.167287 + 0.167287i 0.0112529 + 0.0112529i
\(222\) 0 0
\(223\) 0.621565i 0.0416230i 0.999783 + 0.0208115i \(0.00662499\pi\)
−0.999783 + 0.0208115i \(0.993375\pi\)
\(224\) 0.943681 + 0.695074i 0.0630524 + 0.0464416i
\(225\) 0 0
\(226\) 11.6620 2.20888i 0.775744 0.146932i
\(227\) 10.9257 10.9257i 0.725164 0.725164i −0.244489 0.969652i \(-0.578620\pi\)
0.969652 + 0.244489i \(0.0786201\pi\)
\(228\) 0 0
\(229\) −17.9761 17.9761i −1.18789 1.18789i −0.977649 0.210245i \(-0.932574\pi\)
−0.210245 0.977649i \(-0.567426\pi\)
\(230\) 10.3461 15.1812i 0.682202 1.00102i
\(231\) 0 0
\(232\) −3.85301 + 16.9259i −0.252962 + 1.11124i
\(233\) 21.5409 1.41119 0.705595 0.708616i \(-0.250680\pi\)
0.705595 + 0.708616i \(0.250680\pi\)
\(234\) 0 0
\(235\) −24.0775 + 24.0775i −1.57064 + 1.57064i
\(236\) −6.57399 2.86521i −0.427930 0.186509i
\(237\) 0 0
\(238\) −0.188419 + 0.0356882i −0.0122134 + 0.00231332i
\(239\) −16.5420 −1.07001 −0.535005 0.844849i \(-0.679690\pi\)
−0.535005 + 0.844849i \(0.679690\pi\)
\(240\) 0 0
\(241\) −24.9008 −1.60400 −0.802002 0.597322i \(-0.796232\pi\)
−0.802002 + 0.597322i \(0.796232\pi\)
\(242\) 22.0817 4.18246i 1.41947 0.268859i
\(243\) 0 0
\(244\) 6.17849 14.1760i 0.395537 0.907528i
\(245\) −18.3146 + 18.3146i −1.17008 + 1.17008i
\(246\) 0 0
\(247\) 2.28371 0.145309
\(248\) −14.7574 + 9.28454i −0.937099 + 0.589569i
\(249\) 0 0
\(250\) −11.4459 + 16.7949i −0.723900 + 1.06220i
\(251\) 8.73770 + 8.73770i 0.551519 + 0.551519i 0.926879 0.375360i \(-0.122481\pi\)
−0.375360 + 0.926879i \(0.622481\pi\)
\(252\) 0 0
\(253\) 12.7949 12.7949i 0.804409 0.804409i
\(254\) −13.4004 + 2.53815i −0.840814 + 0.159257i
\(255\) 0 0
\(256\) 1.17125 15.9571i 0.0732029 0.997317i
\(257\) 18.7732i 1.17104i 0.810659 + 0.585519i \(0.199109\pi\)
−0.810659 + 0.585519i \(0.800891\pi\)
\(258\) 0 0
\(259\) −0.910160 0.910160i −0.0565546 0.0565546i
\(260\) 0.984272 + 2.50506i 0.0610420 + 0.155358i
\(261\) 0 0
\(262\) −8.38054 5.71140i −0.517751 0.352852i
\(263\) 19.1523i 1.18098i 0.807045 + 0.590490i \(0.201065\pi\)
−0.807045 + 0.590490i \(0.798935\pi\)
\(264\) 0 0
\(265\) 7.95707i 0.488799i
\(266\) −1.04250 + 1.52970i −0.0639199 + 0.0937918i
\(267\) 0 0
\(268\) 12.3714 + 5.39197i 0.755707 + 0.329367i
\(269\) 4.69478 + 4.69478i 0.286246 + 0.286246i 0.835594 0.549348i \(-0.185124\pi\)
−0.549348 + 0.835594i \(0.685124\pi\)
\(270\) 0 0
\(271\) 25.2478i 1.53369i 0.641831 + 0.766846i \(0.278175\pi\)
−0.641831 + 0.766846i \(0.721825\pi\)
\(272\) 1.78212 + 1.91772i 0.108057 + 0.116279i
\(273\) 0 0
\(274\) 3.13387 + 16.5455i 0.189324 + 0.999553i
\(275\) −32.4893 + 32.4893i −1.95918 + 1.95918i
\(276\) 0 0
\(277\) −21.1473 21.1473i −1.27062 1.27062i −0.945763 0.324858i \(-0.894684\pi\)
−0.324858 0.945763i \(-0.605316\pi\)
\(278\) −1.27480 0.868788i −0.0764575 0.0521064i
\(279\) 0 0
\(280\) −2.12728 0.484253i −0.127129 0.0289396i
\(281\) 6.34812 0.378697 0.189348 0.981910i \(-0.439362\pi\)
0.189348 + 0.981910i \(0.439362\pi\)
\(282\) 0 0
\(283\) 2.56322 2.56322i 0.152368 0.152368i −0.626807 0.779175i \(-0.715639\pi\)
0.779175 + 0.626807i \(0.215639\pi\)
\(284\) −4.35170 11.0755i −0.258226 0.657209i
\(285\) 0 0
\(286\) 0.493342 + 2.60465i 0.0291719 + 0.154016i
\(287\) −0.0141854 −0.000837339
\(288\) 0 0
\(289\) 16.5717 0.974803
\(290\) −6.01346 31.7486i −0.353122 1.86434i
\(291\) 0 0
\(292\) 5.07198 + 12.9087i 0.296815 + 0.755422i
\(293\) 11.7102 11.7102i 0.684119 0.684119i −0.276806 0.960926i \(-0.589276\pi\)
0.960926 + 0.276806i \(0.0892760\pi\)
\(294\) 0 0
\(295\) 13.3490 0.777211
\(296\) −3.90022 + 17.1333i −0.226696 + 0.995855i
\(297\) 0 0
\(298\) −4.99831 3.40639i −0.289544 0.197327i
\(299\) 0.891879 + 0.891879i 0.0515787 + 0.0515787i
\(300\) 0 0
\(301\) −1.17125 + 1.17125i −0.0675096 + 0.0675096i
\(302\) −1.73140 9.14107i −0.0996307 0.526010i
\(303\) 0 0
\(304\) 25.2541 + 0.925579i 1.44842 + 0.0530856i
\(305\) 28.7857i 1.64826i
\(306\) 0 0
\(307\) −11.5572 11.5572i −0.659603 0.659603i 0.295683 0.955286i \(-0.404453\pi\)
−0.955286 + 0.295683i \(0.904453\pi\)
\(308\) −1.96988 0.858551i −0.112244 0.0489205i
\(309\) 0 0
\(310\) 18.2774 26.8191i 1.03809 1.52322i
\(311\) 13.9316i 0.789991i −0.918683 0.394995i \(-0.870746\pi\)
0.918683 0.394995i \(-0.129254\pi\)
\(312\) 0 0
\(313\) 17.8264i 1.00761i 0.863818 + 0.503804i \(0.168067\pi\)
−0.863818 + 0.503804i \(0.831933\pi\)
\(314\) −12.3412 8.41064i −0.696455 0.474640i
\(315\) 0 0
\(316\) 3.45765 + 8.80005i 0.194508 + 0.495042i
\(317\) 11.6127 + 11.6127i 0.652237 + 0.652237i 0.953531 0.301294i \(-0.0974186\pi\)
−0.301294 + 0.953531i \(0.597419\pi\)
\(318\) 0 0
\(319\) 31.8264i 1.78194i
\(320\) 9.86914 + 28.1008i 0.551702 + 1.57088i
\(321\) 0 0
\(322\) −1.00454 + 0.190269i −0.0559811 + 0.0106033i
\(323\) −2.92379 + 2.92379i −0.162684 + 0.162684i
\(324\) 0 0
\(325\) −2.26469 2.26469i −0.125622 0.125622i
\(326\) −15.8445 + 23.2492i −0.877545 + 1.28765i
\(327\) 0 0
\(328\) 0.103123 + 0.163911i 0.00569403 + 0.00905046i
\(329\) 1.89498 0.104474
\(330\) 0 0
\(331\) −23.5572 + 23.5572i −1.29482 + 1.29482i −0.363050 + 0.931770i \(0.618264\pi\)
−0.931770 + 0.363050i \(0.881736\pi\)
\(332\) −4.89070 + 11.2213i −0.268412 + 0.615850i
\(333\) 0 0
\(334\) −9.10137 + 1.72388i −0.498005 + 0.0943263i
\(335\) −25.1213 −1.37252
\(336\) 0 0
\(337\) 22.8488 1.24465 0.622327 0.782757i \(-0.286187\pi\)
0.622327 + 0.782757i \(0.286187\pi\)
\(338\) 17.8821 3.38701i 0.972655 0.184229i
\(339\) 0 0
\(340\) −4.46733 1.94704i −0.242275 0.105593i
\(341\) 22.6035 22.6035i 1.22405 1.22405i
\(342\) 0 0
\(343\) 2.89174 0.156139
\(344\) 22.0482 + 5.01904i 1.18876 + 0.270608i
\(345\) 0 0
\(346\) −1.07637 + 1.57939i −0.0578658 + 0.0849084i
\(347\) −18.0542 18.0542i −0.969198 0.969198i 0.0303420 0.999540i \(-0.490340\pi\)
−0.999540 + 0.0303420i \(0.990340\pi\)
\(348\) 0 0
\(349\) −3.32758 + 3.32758i −0.178121 + 0.178121i −0.790536 0.612415i \(-0.790198\pi\)
0.612415 + 0.790536i \(0.290198\pi\)
\(350\) 2.55077 0.483138i 0.136345 0.0258248i
\(351\) 0 0
\(352\) 4.39990 + 29.0030i 0.234515 + 1.54587i
\(353\) 18.9229i 1.00717i −0.863947 0.503583i \(-0.832015\pi\)
0.863947 0.503583i \(-0.167985\pi\)
\(354\) 0 0
\(355\) 15.6631 + 15.6631i 0.831310 + 0.831310i
\(356\) 22.2339 8.73597i 1.17839 0.463006i
\(357\) 0 0
\(358\) 14.5078 + 9.88720i 0.766762 + 0.522555i
\(359\) 32.0808i 1.69316i 0.532262 + 0.846580i \(0.321342\pi\)
−0.532262 + 0.846580i \(0.678658\pi\)
\(360\) 0 0
\(361\) 20.9141i 1.10074i
\(362\) 7.04583 10.3386i 0.370321 0.543384i
\(363\) 0 0
\(364\) 0.0598459 0.137312i 0.00313678 0.00719709i
\(365\) −18.2556 18.2556i −0.955542 0.955542i
\(366\) 0 0
\(367\) 19.0989i 0.996956i 0.866902 + 0.498478i \(0.166108\pi\)
−0.866902 + 0.498478i \(0.833892\pi\)
\(368\) 9.50124 + 10.2242i 0.495286 + 0.532973i
\(369\) 0 0
\(370\) −6.08715 32.1377i −0.316456 1.67076i
\(371\) −0.313125 + 0.313125i −0.0162566 + 0.0162566i
\(372\) 0 0
\(373\) 3.51026 + 3.51026i 0.181754 + 0.181754i 0.792120 0.610365i \(-0.208977\pi\)
−0.610365 + 0.792120i \(0.708977\pi\)
\(374\) −3.96630 2.70306i −0.205092 0.139772i
\(375\) 0 0
\(376\) −13.7759 21.8963i −0.710437 1.12921i
\(377\) 2.21848 0.114258
\(378\) 0 0
\(379\) 9.07536 9.07536i 0.466170 0.466170i −0.434501 0.900671i \(-0.643075\pi\)
0.900671 + 0.434501i \(0.143075\pi\)
\(380\) −43.7829 + 17.2029i −2.24601 + 0.882488i
\(381\) 0 0
\(382\) 1.87811 + 9.91565i 0.0960923 + 0.507329i
\(383\) 28.3176 1.44696 0.723481 0.690344i \(-0.242541\pi\)
0.723481 + 0.690344i \(0.242541\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) 2.87784 + 15.1938i 0.146478 + 0.773345i
\(387\) 0 0
\(388\) 1.72294 0.676964i 0.0874688 0.0343676i
\(389\) 0.490254 0.490254i 0.0248569 0.0248569i −0.694569 0.719426i \(-0.744405\pi\)
0.719426 + 0.694569i \(0.244405\pi\)
\(390\) 0 0
\(391\) −2.28371 −0.115492
\(392\) −10.4787 16.6555i −0.529253 0.841228i
\(393\) 0 0
\(394\) 17.0685 + 11.6323i 0.859900 + 0.586029i
\(395\) −12.4452 12.4452i −0.626183 0.626183i
\(396\) 0 0
\(397\) 24.4559 24.4559i 1.22741 1.22741i 0.262465 0.964942i \(-0.415465\pi\)
0.964942 0.262465i \(-0.0845354\pi\)
\(398\) −1.89092 9.98332i −0.0947835 0.500418i
\(399\) 0 0
\(400\) −24.1259 25.9616i −1.20629 1.29808i
\(401\) 0.517550i 0.0258452i 0.999916 + 0.0129226i \(0.00411351\pi\)
−0.999916 + 0.0129226i \(0.995886\pi\)
\(402\) 0 0
\(403\) 1.57559 + 1.57559i 0.0784859 + 0.0784859i
\(404\) 2.56644 5.88849i 0.127685 0.292963i
\(405\) 0 0
\(406\) −1.01272 + 1.48601i −0.0502607 + 0.0737492i
\(407\) 32.2164i 1.59691i
\(408\) 0 0
\(409\) 36.5602i 1.80779i −0.427758 0.903893i \(-0.640696\pi\)
0.427758 0.903893i \(-0.359304\pi\)
\(410\) −0.297879 0.203007i −0.0147112 0.0100258i
\(411\) 0 0
\(412\) −26.3663 + 10.3597i −1.29898 + 0.510384i
\(413\) −0.525309 0.525309i −0.0258488 0.0258488i
\(414\) 0 0
\(415\) 22.7858i 1.11851i
\(416\) −2.02168 + 0.306698i −0.0991210 + 0.0150371i
\(417\) 0 0
\(418\) −45.5233 + 8.62251i −2.22662 + 0.421741i
\(419\) 20.9433 20.9433i 1.02315 1.02315i 0.0234208 0.999726i \(-0.492544\pi\)
0.999726 0.0234208i \(-0.00745575\pi\)
\(420\) 0 0
\(421\) 14.2218 + 14.2218i 0.693126 + 0.693126i 0.962919 0.269792i \(-0.0869550\pi\)
−0.269792 + 0.962919i \(0.586955\pi\)
\(422\) −0.183951 + 0.269917i −0.00895459 + 0.0131394i
\(423\) 0 0
\(424\) 5.89444 + 1.34181i 0.286259 + 0.0651638i
\(425\) 5.79888 0.281287
\(426\) 0 0
\(427\) 1.13277 1.13277i 0.0548184 0.0548184i
\(428\) 22.9551 + 10.0047i 1.10958 + 0.483597i
\(429\) 0 0
\(430\) −41.3566 + 7.83330i −1.99439 + 0.377755i
\(431\) 27.9032 1.34405 0.672024 0.740529i \(-0.265425\pi\)
0.672024 + 0.740529i \(0.265425\pi\)
\(432\) 0 0
\(433\) −28.4634 −1.36786 −0.683932 0.729546i \(-0.739731\pi\)
−0.683932 + 0.729546i \(0.739731\pi\)
\(434\) −1.77463 + 0.336130i −0.0851849 + 0.0161347i
\(435\) 0 0
\(436\) 3.01727 6.92288i 0.144501 0.331546i
\(437\) −15.5880 + 15.5880i −0.745677 + 0.745677i
\(438\) 0 0
\(439\) 18.2702 0.871988 0.435994 0.899950i \(-0.356397\pi\)
0.435994 + 0.899950i \(0.356397\pi\)
\(440\) −29.0787 46.2195i −1.38627 2.20343i
\(441\) 0 0
\(442\) 0.188419 0.276474i 0.00896218 0.0131505i
\(443\) 13.9646 + 13.9646i 0.663479 + 0.663479i 0.956198 0.292720i \(-0.0945602\pi\)
−0.292720 + 0.956198i \(0.594560\pi\)
\(444\) 0 0
\(445\) −31.4434 + 31.4434i −1.49056 + 1.49056i
\(446\) 0.863669 0.163586i 0.0408959 0.00774604i
\(447\) 0 0
\(448\) 0.717449 1.49419i 0.0338963 0.0705937i
\(449\) 23.8072i 1.12353i −0.827296 0.561766i \(-0.810122\pi\)
0.827296 0.561766i \(-0.189878\pi\)
\(450\) 0 0
\(451\) −0.251057 0.251057i −0.0118218 0.0118218i
\(452\) −6.13851 15.6231i −0.288731 0.734848i
\(453\) 0 0
\(454\) −18.0568 12.3059i −0.847448 0.577543i
\(455\) 0.278823i 0.0130714i
\(456\) 0 0
\(457\) 13.9662i 0.653310i −0.945144 0.326655i \(-0.894079\pi\)
0.945144 0.326655i \(-0.105921\pi\)
\(458\) −20.2469 + 29.7090i −0.946076 + 1.38821i
\(459\) 0 0
\(460\) −23.8173 10.3805i −1.11049 0.483995i
\(461\) 19.4422 + 19.4422i 0.905514 + 0.905514i 0.995906 0.0903920i \(-0.0288120\pi\)
−0.0903920 + 0.995906i \(0.528812\pi\)
\(462\) 0 0
\(463\) 27.9277i 1.29791i 0.760827 + 0.648955i \(0.224794\pi\)
−0.760827 + 0.648955i \(0.775206\pi\)
\(464\) 24.5328 + 0.899142i 1.13891 + 0.0417416i
\(465\) 0 0
\(466\) −5.66923 29.9312i −0.262622 1.38654i
\(467\) 4.32777 4.32777i 0.200265 0.200265i −0.599848 0.800114i \(-0.704772\pi\)
0.800114 + 0.599848i \(0.204772\pi\)
\(468\) 0 0
\(469\) 0.988567 + 0.988567i 0.0456478 + 0.0456478i
\(470\) 39.7927 + 27.1190i 1.83550 + 1.25091i
\(471\) 0 0
\(472\) −2.25106 + 9.88870i −0.103613 + 0.455164i
\(473\) −41.4580 −1.90624
\(474\) 0 0
\(475\) 39.5817 39.5817i 1.81613 1.81613i
\(476\) 0.0991780 + 0.252417i 0.00454582 + 0.0115695i
\(477\) 0 0
\(478\) 4.35359 + 22.9852i 0.199129 + 1.05132i
\(479\) −30.0898 −1.37484 −0.687420 0.726260i \(-0.741257\pi\)
−0.687420 + 0.726260i \(0.741257\pi\)
\(480\) 0 0
\(481\) 2.24567 0.102394
\(482\) 6.55352 + 34.5999i 0.298505 + 1.57598i
\(483\) 0 0
\(484\) −11.6231 29.5820i −0.528324 1.34463i
\(485\) −2.43660 + 2.43660i −0.110640 + 0.110640i
\(486\) 0 0
\(487\) −27.3397 −1.23888 −0.619440 0.785044i \(-0.712640\pi\)
−0.619440 + 0.785044i \(0.712640\pi\)
\(488\) −21.3238 4.85414i −0.965284 0.219737i
\(489\) 0 0
\(490\) 30.2684 + 20.6282i 1.36739 + 0.931885i
\(491\) 3.78368 + 3.78368i 0.170755 + 0.170755i 0.787311 0.616556i \(-0.211473\pi\)
−0.616556 + 0.787311i \(0.711473\pi\)
\(492\) 0 0
\(493\) −2.84028 + 2.84028i −0.127920 + 0.127920i
\(494\) −0.601038 3.17324i −0.0270420 0.142771i
\(495\) 0 0
\(496\) 16.7849 + 18.0620i 0.753664 + 0.811010i
\(497\) 1.23274i 0.0552960i
\(498\) 0 0
\(499\) 15.2002 + 15.2002i 0.680455 + 0.680455i 0.960103 0.279648i \(-0.0902178\pi\)
−0.279648 + 0.960103i \(0.590218\pi\)
\(500\) 26.3491 + 11.4840i 1.17837 + 0.513579i
\(501\) 0 0
\(502\) 9.84148 14.4407i 0.439247 0.644522i
\(503\) 12.6164i 0.562537i −0.959629 0.281268i \(-0.909245\pi\)
0.959629 0.281268i \(-0.0907551\pi\)
\(504\) 0 0
\(505\) 11.9571i 0.532083i
\(506\) −21.1461 14.4112i −0.940057 0.640657i
\(507\) 0 0
\(508\) 7.05355 + 17.9519i 0.312951 + 0.796488i
\(509\) −26.3204 26.3204i −1.16663 1.16663i −0.982994 0.183639i \(-0.941212\pi\)
−0.183639 0.982994i \(1.44121\pi\)
\(510\) 0 0
\(511\) 1.43678i 0.0635595i
\(512\) −22.4807 + 2.57220i −0.993518 + 0.113676i
\(513\) 0 0
\(514\) 26.0855 4.94081i 1.15058 0.217930i
\(515\) 37.2876 37.2876i 1.64309 1.64309i
\(516\) 0 0
\(517\) 33.5378 + 33.5378i 1.47499 + 1.47499i
\(518\) −1.02513 + 1.50421i −0.0450418 + 0.0660914i
\(519\) 0 0
\(520\) 3.22176 2.02695i 0.141284 0.0888876i
\(521\) −9.60170 −0.420658 −0.210329 0.977631i \(-0.567454\pi\)
−0.210329 + 0.977631i \(0.567454\pi\)
\(522\) 0 0
\(523\) 11.2532 11.2532i 0.492066 0.492066i −0.416890 0.908957i \(-0.636880\pi\)
0.908957 + 0.416890i \(0.136880\pi\)
\(524\) −5.73042 + 13.1480i −0.250334 + 0.574372i
\(525\) 0 0
\(526\) 26.6122 5.04058i 1.16035 0.219780i
\(527\) −4.03441 −0.175741
\(528\) 0 0
\(529\) 10.8245 0.470632
\(530\) −11.0564 + 2.09418i −0.480260 + 0.0909654i
\(531\) 0 0
\(532\) 2.39990 + 1.04597i 0.104049 + 0.0453486i
\(533\) 0.0175001 0.0175001i 0.000758013 0.000758013i
\(534\) 0 0
\(535\) −46.6122 −2.01522
\(536\) 4.23621 18.6093i 0.182977 0.803800i
\(537\) 0 0
\(538\) 5.28785 7.75904i 0.227975 0.334516i
\(539\) 25.5106 + 25.5106i 1.09882 + 1.09882i
\(540\) 0 0
\(541\) 4.66998 4.66998i 0.200778 0.200778i −0.599555 0.800333i \(-0.704656\pi\)
0.800333 + 0.599555i \(0.204656\pi\)
\(542\) 35.0820 6.64483i 1.50690 0.285420i
\(543\) 0 0
\(544\) 2.19566 2.98098i 0.0941381 0.127808i
\(545\) 14.0575i 0.602157i
\(546\) 0 0
\(547\) −18.6755 18.6755i −0.798505 0.798505i 0.184355 0.982860i \(-0.440981\pi\)
−0.982860 + 0.184355i \(0.940981\pi\)
\(548\) 22.1654 8.70907i 0.946859 0.372033i
\(549\) 0 0
\(550\) 53.6948 + 36.5935i 2.28956 + 1.56035i
\(551\) 38.7741i 1.65183i
\(552\) 0 0
\(553\) 0.979478i 0.0416516i
\(554\) −23.8188 + 34.9501i −1.01196 + 1.48489i
\(555\) 0 0
\(556\) −0.871680 + 2.00000i −0.0369675 + 0.0848189i
\(557\) −3.20568 3.20568i −0.135829 0.135829i 0.635923 0.771752i \(-0.280619\pi\)
−0.771752 + 0.635923i \(0.780619\pi\)
\(558\) 0 0
\(559\) 2.88986i 0.122228i
\(560\) −0.113006 + 3.08332i −0.00477536 + 0.130294i
\(561\) 0 0
\(562\) −1.67073 8.82076i −0.0704754 0.372081i
\(563\) −32.4157 + 32.4157i −1.36616 + 1.36616i −0.500319 + 0.865841i \(0.666784\pi\)
−0.865841 + 0.500319i \(0.833216\pi\)
\(564\) 0 0
\(565\) 22.0944 + 22.0944i 0.929518 + 0.929518i
\(566\) −4.23621 2.88701i −0.178061 0.121350i
\(567\) 0 0
\(568\) −14.2442 + 8.96162i −0.597672 + 0.376021i
\(569\) −11.1238 −0.466335 −0.233168 0.972437i \(-0.574909\pi\)
−0.233168 + 0.972437i \(0.574909\pi\)
\(570\) 0 0
\(571\) 16.1349 16.1349i 0.675223 0.675223i −0.283692 0.958915i \(-0.591559\pi\)
0.958915 + 0.283692i \(0.0915594\pi\)
\(572\) 3.48934 1.37101i 0.145897 0.0573246i
\(573\) 0 0
\(574\) 0.00373339 + 0.0197108i 0.000155829 + 0.000822712i
\(575\) 30.9164 1.28930
\(576\) 0 0
\(577\) −10.9795 −0.457082 −0.228541 0.973534i \(-0.573395\pi\)
−0.228541 + 0.973534i \(0.573395\pi\)
\(578\) −4.36141 23.0265i −0.181411 0.957774i
\(579\) 0 0
\(580\) −42.5323 + 16.7115i −1.76606 + 0.693907i
\(581\) −0.896663 + 0.896663i −0.0371999 + 0.0371999i
\(582\) 0 0
\(583\) −11.0835 −0.459032
\(584\) 16.6018 10.4449i 0.686988 0.432214i
\(585\) 0 0
\(586\) −19.3534 13.1895i −0.799483 0.544854i
\(587\) −7.40862 7.40862i −0.305786 0.305786i 0.537486 0.843273i \(-0.319374\pi\)
−0.843273 + 0.537486i \(0.819374\pi\)
\(588\) 0 0
\(589\) −27.5378 + 27.5378i −1.13468 + 1.13468i
\(590\) −3.51326 18.5486i −0.144639 0.763634i
\(591\) 0 0
\(592\) 24.8334 + 0.910160i 1.02065 + 0.0374073i
\(593\) 12.3933i 0.508934i 0.967081 + 0.254467i \(0.0819000\pi\)
−0.967081 + 0.254467i \(0.918100\pi\)
\(594\) 0 0
\(595\) −0.356972 0.356972i −0.0146344 0.0146344i
\(596\) −3.41773 + 7.84170i −0.139996 + 0.321209i
\(597\) 0 0
\(598\) 1.00454 1.47400i 0.0410789 0.0602764i
\(599\) 41.2488i 1.68538i 0.538399 + 0.842690i \(0.319029\pi\)
−0.538399 + 0.842690i \(0.680971\pi\)
\(600\) 0 0
\(601\) 20.4615i 0.834642i −0.908759 0.417321i \(-0.862969\pi\)
0.908759 0.417321i \(-0.137031\pi\)
\(602\) 1.93571 + 1.31920i 0.0788937 + 0.0537667i
\(603\) 0 0
\(604\) −12.2459 + 4.81158i −0.498279 + 0.195780i
\(605\) 41.8352 + 41.8352i 1.70084 + 1.70084i
\(606\) 0 0
\(607\) 30.1643i 1.22433i −0.790730 0.612165i \(-0.790299\pi\)
0.790730 0.612165i \(-0.209701\pi\)
\(608\) −5.36039 35.3344i −0.217393 1.43300i
\(609\) 0 0
\(610\) 39.9979 7.57594i 1.61947 0.306741i
\(611\) −2.33778 + 2.33778i −0.0945764 + 0.0945764i
\(612\) 0 0
\(613\) −1.80074 1.80074i −0.0727312 0.0727312i 0.669805 0.742537i \(-0.266377\pi\)
−0.742537 + 0.669805i \(0.766377\pi\)
\(614\) −13.0171 + 19.1005i −0.525328 + 0.770832i
\(615\) 0 0
\(616\) −0.674522 + 2.96312i −0.0271773 + 0.119387i
\(617\) −30.8098 −1.24036 −0.620178 0.784461i \(-0.712940\pi\)
−0.620178 + 0.784461i \(0.712940\pi\)
\(618\) 0 0
\(619\) −10.0429 + 10.0429i −0.403659 + 0.403659i −0.879520 0.475861i \(-0.842136\pi\)
0.475861 + 0.879520i \(0.342136\pi\)
\(620\) −42.0757 18.3383i −1.68980 0.736482i
\(621\) 0 0
\(622\) −19.3581 + 3.66659i −0.776190 + 0.147017i
\(623\) 2.47471 0.0991472
\(624\) 0 0
\(625\) −9.20274 −0.368110
\(626\) 24.7699 4.69164i 0.990006 0.187516i
\(627\) 0 0
\(628\) −8.43863 + 19.3618i −0.336738 + 0.772619i
\(629\) −2.87509 + 2.87509i −0.114637 + 0.114637i
\(630\) 0 0
\(631\) −4.91925 −0.195832 −0.0979161 0.995195i \(-0.531218\pi\)
−0.0979161 + 0.995195i \(0.531218\pi\)
\(632\) 11.3177 7.12048i 0.450196 0.283237i
\(633\) 0 0
\(634\) 13.0797 19.1923i 0.519462 0.762224i
\(635\) −25.3879 25.3879i −1.00749 1.00749i
\(636\) 0 0
\(637\) −1.77824 + 1.77824i −0.0704563 + 0.0704563i
\(638\) −44.2231 + 8.37622i −1.75081 + 0.331618i
\(639\) 0 0
\(640\) 36.4489 21.1090i 1.44077 0.834405i
\(641\) 15.0833i 0.595756i 0.954604 + 0.297878i \(0.0962789\pi\)
−0.954604 + 0.297878i \(0.903721\pi\)
\(642\) 0 0
\(643\) −2.26109 2.26109i −0.0891686 0.0891686i 0.661116 0.750284i \(-0.270083\pi\)
−0.750284 + 0.661116i \(0.770083\pi\)
\(644\) 0.528761 + 1.34575i 0.0208361 + 0.0530299i
\(645\) 0 0
\(646\) 4.83214 + 3.29314i 0.190118 + 0.129567i
\(647\) 12.1851i 0.479046i 0.970891 + 0.239523i \(0.0769911\pi\)
−0.970891 + 0.239523i \(0.923009\pi\)
\(648\) 0 0
\(649\) 18.5941i 0.729881i
\(650\) −2.55077 + 3.74284i −0.100050 + 0.146806i
\(651\) 0 0
\(652\) 36.4749 + 15.8972i 1.42847 + 0.622583i
\(653\) −11.4822 11.4822i −0.449335 0.449335i 0.445798 0.895133i \(-0.352920\pi\)
−0.895133 + 0.445798i \(0.852920\pi\)
\(654\) 0 0
\(655\) 26.6981i 1.04318i
\(656\) 0.200615 0.186430i 0.00783270 0.00727885i
\(657\) 0 0
\(658\) −0.498731 2.63310i −0.0194425 0.102649i
\(659\) 16.6502 16.6502i 0.648599 0.648599i −0.304056 0.952654i \(-0.598341\pi\)
0.952654 + 0.304056i \(0.0983409\pi\)
\(660\) 0 0
\(661\) −14.6386 14.6386i −0.569375 0.569375i 0.362578 0.931953i \(-0.381896\pi\)
−0.931953 + 0.362578i \(0.881896\pi\)
\(662\) 38.9328 + 26.5330i 1.51317 + 1.03123i
\(663\) 0 0
\(664\) 16.8793 + 3.84239i 0.655043 + 0.149114i
\(665\) −4.87320 −0.188974
\(666\) 0 0
\(667\) −15.1428 + 15.1428i −0.586331 + 0.586331i
\(668\) 4.79068 + 12.1927i 0.185357 + 0.471751i
\(669\) 0 0
\(670\) 6.61153 + 34.9062i 0.255426 + 1.34854i
\(671\) 40.0959 1.54789
\(672\) 0 0
\(673\) −20.5492 −0.792115 −0.396058 0.918226i \(-0.629622\pi\)
−0.396058 + 0.918226i \(0.629622\pi\)
\(674\) −6.01346 31.7486i −0.231630 1.22291i
\(675\) 0 0
\(676\) −9.41256 23.9559i −0.362022 0.921379i
\(677\) 6.72550 6.72550i 0.258482 0.258482i −0.565954 0.824437i \(-0.691492\pi\)
0.824437 + 0.565954i \(0.191492\pi\)
\(678\) 0 0
\(679\) 0.191769 0.00735942
\(680\) −1.52970 + 6.71983i −0.0586612 + 0.257694i
\(681\) 0 0
\(682\) −37.3566 25.4588i −1.43046 0.974870i
\(683\) −30.5399 30.5399i −1.16858 1.16858i −0.982543 0.186033i \(-0.940437\pi\)
−0.186033 0.982543i \(1.44044\pi\)
\(684\) 0 0
\(685\) −31.3466 + 31.3466i −1.19769 + 1.19769i
\(686\) −0.761062 4.01810i −0.0290575 0.153412i
\(687\) 0 0
\(688\) 1.17125 31.9571i 0.0446534 1.21835i
\(689\) 0.772584i 0.0294331i
\(690\) 0 0
\(691\) 10.8672 + 10.8672i 0.413409 + 0.413409i 0.882924 0.469515i \(-0.155571\pi\)
−0.469515 + 0.882924i \(0.655571\pi\)
\(692\) 2.47786 + 1.07995i 0.0941939 + 0.0410535i
\(693\) 0 0
\(694\) −20.3348 + 29.8380i −0.771899 + 1.13263i
\(695\) 4.06117i 0.154049i
\(696\) 0 0
\(697\) 0.0448101i 0.00169730i
\(698\) 5.49947 + 3.74793i 0.208158 + 0.141861i
\(699\) 0 0
\(700\) −1.34265 3.41717i −0.0507474 0.129157i
\(701\) −20.5506 20.5506i −0.776184 0.776184i 0.202995 0.979180i \(-0.434932\pi\)
−0.979180 + 0.202995i \(0.934932\pi\)
\(702\) 0 0
\(703\) 39.2492i 1.48031i
\(704\) 39.1420 13.7469i 1.47522 0.518104i
\(705\) 0 0
\(706\) −26.2936 + 4.98023i −0.989572 + 0.187433i
\(707\) 0.470532 0.470532i 0.0176962 0.0176962i
\(708\) 0 0
\(709\) −33.4311 33.4311i −1.25553 1.25553i −0.953205 0.302325i \(-0.902237\pi\)
−0.302325 0.953205i \(-0.597763\pi\)
\(710\) 17.6417 25.8863i 0.662082 0.971495i
\(711\) 0 0
\(712\) −17.9903 28.5950i −0.674216 1.07164i
\(713\) −21.5092 −0.805525
\(714\) 0 0
\(715\) −4.93467 + 4.93467i −0.184546 + 0.184546i
\(716\) 9.92011 22.7609i 0.370732 0.850615i
\(717\) 0 0
\(718\) 44.5765 8.44318i 1.66358 0.315097i
\(719\) −9.15381 −0.341380 −0.170690 0.985325i \(-0.554600\pi\)
−0.170690 + 0.985325i \(0.554600\pi\)
\(720\) 0 0
\(721\) −2.93467 −0.109293
\(722\) 29.0604 5.50428i 1.08152 0.204848i
\(723\) 0 0
\(724\) −16.2199 7.06929i −0.602808 0.262728i
\(725\) 38.4511 38.4511i 1.42804 1.42804i
\(726\) 0 0
\(727\) −37.6052 −1.39470 −0.697351 0.716730i \(-0.745638\pi\)
−0.697351 + 0.716730i \(0.745638\pi\)
\(728\) −0.206546 0.0470181i −0.00765511 0.00174261i
\(729\) 0 0
\(730\) −20.5617 + 30.1709i −0.761023 + 1.11668i
\(731\) 3.69983 + 3.69983i 0.136843 + 0.136843i
\(732\) 0 0
\(733\) 33.4129 33.4129i 1.23413 1.23413i 0.271771 0.962362i \(-0.412391\pi\)
0.962362 0.271771i \(-0.0876092\pi\)
\(734\) 26.5381 5.02655i 0.979540 0.185533i
\(735\) 0 0
\(736\) 11.7060 15.8929i 0.431489 0.585820i
\(737\) 34.9917i 1.28894i
\(738\) 0 0
\(739\) 21.9860 + 21.9860i 0.808769 + 0.808769i 0.984448 0.175678i \(-0.0562119\pi\)
−0.175678 + 0.984448i \(0.556212\pi\)
\(740\) −43.0535 + 16.9163i −1.58268 + 0.621855i
\(741\) 0 0
\(742\) 0.517500 + 0.352680i 0.0189980 + 0.0129473i
\(743\) 20.6315i 0.756896i −0.925623 0.378448i \(-0.876458\pi\)
0.925623 0.378448i \(-0.123542\pi\)
\(744\) 0 0
\(745\) 15.9232i 0.583382i
\(746\) 3.95369 5.80138i 0.144755 0.212404i
\(747\) 0 0
\(748\) −2.71206 + 6.22261i −0.0991628 + 0.227521i
\(749\) 1.83428 + 1.83428i 0.0670230 + 0.0670230i
\(750\) 0 0
\(751\) 21.1419i 0.771477i 0.922608 + 0.385739i \(0.126053\pi\)
−0.922608 + 0.385739i \(0.873947\pi\)
\(752\) −26.7995 + 24.9045i −0.977276 + 0.908173i
\(753\) 0 0
\(754\) −0.583871 3.08260i −0.0212633 0.112262i
\(755\) 17.3183 17.3183i 0.630279 0.630279i
\(756\) 0 0
\(757\) 16.9156 + 16.9156i 0.614810 + 0.614810i 0.944195 0.329386i \(-0.106842\pi\)
−0.329386 + 0.944195i \(0.606842\pi\)
\(758\) −14.9988 10.2218i −0.544781 0.371272i
\(759\) 0 0
\(760\) 35.4265 + 56.3092i 1.28505 + 2.04255i
\(761\) 29.0688 1.05374 0.526871 0.849945i \(-0.323365\pi\)
0.526871 + 0.849945i \(0.323365\pi\)
\(762\) 0 0
\(763\) 0.553188 0.553188i 0.0200267 0.0200267i
\(764\) 13.2836 5.21929i 0.480583 0.188827i
\(765\) 0 0
\(766\) −7.45276 39.3475i −0.269279 1.42168i
\(767\) 1.29611 0.0467999
\(768\) 0 0
\(769\) 17.9123 0.645933 0.322966 0.946410i \(-0.395320\pi\)
0.322966 + 0.946410i \(0.395320\pi\)
\(770\) −1.05274 5.55803i −0.0379381 0.200298i
\(771\) 0 0
\(772\) 20.3545 7.99756i 0.732576 0.287838i
\(773\) 19.1937 19.1937i 0.690351 0.690351i −0.271958 0.962309i \(-0.587671\pi\)
0.962309 + 0.271958i \(0.0876712\pi\)
\(774\) 0 0
\(775\) 54.6169 1.96190
\(776\) −1.39410 2.21587i −0.0500452 0.0795450i
\(777\) 0 0
\(778\) −0.810240 0.552185i −0.0290485 0.0197968i
\(779\) 0.305862 + 0.305862i 0.0109587 + 0.0109587i
\(780\) 0 0
\(781\) 21.8173 21.8173i 0.780685 0.780685i
\(782\) 0.601038 + 3.17324i 0.0214931 + 0.113475i
\(783\) 0 0
\(784\) −20.3851 + 18.9437i −0.728039 + 0.676559i
\(785\) 39.3157i 1.40324i
\(786\) 0 0
\(787\) 5.09354 + 5.09354i 0.181565 + 0.181565i 0.792038 0.610472i \(-0.209020\pi\)
−0.610472 + 0.792038i \(0.709020\pi\)
\(788\) 11.6711 26.7783i 0.415764 0.953939i
\(789\) 0 0