Properties

Label 144.2.l.a.35.5
Level $144$
Weight $2$
Character 144.35
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 35.5
Root \(-0.517174 - 1.31626i\) of defining polynomial
Character \(\chi\) \(=\) 144.35
Dual form 144.2.l.a.107.5

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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 −0.980431 0.196865i \(-0.936924\pi\)
−0.196865 0.980431i \(1.43692\pi\)
\(6\) 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 0.111878 0.993722i \(-0.464313\pi\)
0.993722 0.111878i \(-0.0356867\pi\)
\(12\) 0 0
\(13\) 0.255601 + 0.255601i 0.0708910 + 0.0708910i 0.741663 0.670772i \(-0.234037\pi\)
−0.670772 + 0.741663i \(0.734037\pi\)
\(14\) −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 0.0251941 0.999683i \(-0.491980\pi\)
0.999683 0.0251941i \(-0.00802039\pi\)
\(20\) 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 \(-0.942993\pi\)
0.178137 + 0.984006i \(0.442993\pi\)
\(30\) 0 0
\(31\) 6.16426i 1.10713i −0.832805 0.553567i \(-0.813266\pi\)
0.832805 0.553567i \(-0.186734\pi\)
\(32\) 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 −0.246861 0.969051i \(-0.579399\pi\)
0.969051 + 0.246861i \(0.0793990\pi\)
\(38\) −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 \(-0.501702\pi\)
−0.00534633 + 0.999986i \(0.501702\pi\)
\(42\) 0 0
\(43\) 5.65306 + 5.65306i 0.862083 + 0.862083i 0.991580 0.129497i \(-0.0413361\pi\)
−0.129497 + 0.991580i \(0.541336\pi\)
\(44\) −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 \(-0.267555\pi\)
0.667055 + 0.745009i \(0.267555\pi\)
\(48\) 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 \(-0.296895\pi\)
−0.803244 + 0.595650i \(0.796895\pi\)
\(54\) 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 \(-0.824987\pi\)
0.522535 + 0.852618i \(0.324987\pi\)
\(60\) 0 0
\(61\) −5.46733 5.46733i −0.700020 0.700020i 0.264394 0.964415i \(-0.414828\pi\)
−0.964415 + 0.264394i \(0.914828\pi\)
\(62\) −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 −0.935703 0.352790i \(-0.885233\pi\)
0.352790 + 0.935703i \(0.385233\pi\)
\(68\) 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 \(0.133014\pi\)
−0.913953 + 0.405821i \(0.866986\pi\)
\(74\) −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 \(0.0856828\pi\)
−0.963989 + 0.265942i \(0.914317\pi\)
\(80\) −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 \(-0.359040\pi\)
−0.903539 + 0.428505i \(0.859040\pi\)
\(84\) 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 \(-0.281805\pi\)
0.633045 + 0.774115i \(0.281805\pi\)
\(90\) 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 \(-0.198918\pi\)
−0.585033 + 0.811010i \(0.698918\pi\)
\(102\) 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 \(-0.543097\pi\)
0.990848 + 0.134979i \(0.0430967\pi\)
\(108\) 0 0
\(109\) −2.66998 2.66998i −0.255737 0.255737i 0.567580 0.823318i \(-0.307880\pi\)
−0.823318 + 0.567580i \(0.807880\pi\)
\(110\) −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 \(0.140740\pi\)
−0.903835 + 0.427882i \(0.859260\pi\)
\(128\) −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 \(-0.351427\pi\)
−0.893033 + 0.449992i \(0.851427\pi\)
\(132\) 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 \(-0.330140\pi\)
0.508662 + 0.860966i \(0.330140\pi\)
\(138\) 0 0
\(139\) 0.771348 + 0.771348i 0.0654249 + 0.0654249i 0.739062 0.673637i \(-0.235269\pi\)
−0.673637 + 0.739062i \(0.735269\pi\)
\(140\) −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 \(-0.306056\pi\)
−0.820052 + 0.572289i \(0.806056\pi\)
\(150\) 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 0.939234 0.343276i \(-0.111537\pi\)
−0.343276 + 0.939234i \(0.611537\pi\)
\(158\) 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 −0.107659 + 0.994188i \(0.534335\pi\)
−0.994188 + 0.107659i \(0.965665\pi\)
\(164\) 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 \(-0.733639\pi\)
0.742501 + 0.669845i \(0.233639\pi\)
\(174\) 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 \(-0.0964328\pi\)
−0.298340 + 0.954460i \(0.596433\pi\)
\(180\) 0 0
\(181\) 6.25560 6.25560i 0.464975 0.464975i −0.435307 0.900282i \(-0.643360\pi\)
0.900282 + 0.435307i \(0.143360\pi\)
\(182\) −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 \(-0.416879\pi\)
0.258174 + 0.966098i \(0.416879\pi\)
\(192\) 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 \(-0.0758192\pi\)
−0.235947 + 0.971766i \(0.575819\pi\)
\(198\) 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 −0.712706 0.701463i \(-0.752531\pi\)
0.701463 + 0.712706i \(0.252531\pi\)
\(212\) 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 \(-0.993375\pi\)
0.999783 0.0208115i \(-0.00662499\pi\)
\(224\) −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 \(-0.421380\pi\)
−0.969652 + 0.244489i \(0.921380\pi\)
\(228\) 0 0
\(229\) −17.9761 + 17.9761i −1.18789 + 1.18789i −0.210245 + 0.977649i \(0.567426\pi\)
−0.977649 + 0.210245i \(0.932574\pi\)
\(230\) −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 \(-0.749320\pi\)
−0.705595 + 0.708616i \(0.749320\pi\)
\(234\) 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 \(-0.320310\pi\)
0.535005 + 0.844849i \(0.320310\pi\)
\(240\) 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 \(-0.877519\pi\)
0.375360 + 0.926879i \(0.377519\pi\)
\(252\) 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 \(-0.814876\pi\)
0.549348 + 0.835594i \(0.314876\pi\)
\(270\) 0 0
\(271\) 25.2478i 1.53369i −0.641831 0.766846i \(-0.721825\pi\)
0.641831 0.766846i \(-0.278175\pi\)
\(272\) −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 −0.324858 + 0.945763i \(0.605316\pi\)
−0.945763 + 0.324858i \(0.894684\pi\)
\(278\) 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 \(-0.560638\pi\)
−0.189348 + 0.981910i \(0.560638\pi\)
\(282\) 0 0
\(283\) 2.56322 + 2.56322i 0.152368 + 0.152368i 0.779175 0.626807i \(-0.215639\pi\)
−0.626807 + 0.779175i \(0.715639\pi\)
\(284\) 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 \(-0.410724\pi\)
−0.960926 + 0.276806i \(0.910724\pi\)
\(294\) 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 −0.955286 0.295683i \(-0.904453\pi\)
0.295683 + 0.955286i \(0.404453\pi\)
\(308\) 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 \(-0.831933\pi\)
0.863818 0.503804i \(-0.168067\pi\)
\(314\) 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 \(-0.902581\pi\)
0.301294 + 0.953531i \(0.402581\pi\)
\(318\) 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 −0.931770 0.363050i \(-0.881736\pi\)
−0.363050 0.931770i \(-0.618264\pi\)
\(332\) 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 \(-0.509660\pi\)
0.999540 + 0.0303420i \(0.00965963\pi\)
\(348\) 0 0
\(349\) −3.32758 3.32758i −0.178121 0.178121i 0.612415 0.790536i \(-0.290198\pi\)
−0.790536 + 0.612415i \(0.790198\pi\)
\(350\) −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 \(-0.833892\pi\)
0.866902 0.498478i \(-0.166108\pi\)
\(368\) −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 −0.610365 0.792120i \(-0.708977\pi\)
0.792120 + 0.610365i \(0.208977\pi\)
\(374\) 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 0.900671 0.434501i \(-0.143075\pi\)
−0.434501 + 0.900671i \(0.643075\pi\)
\(380\) 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 \(-0.757459\pi\)
−0.723481 + 0.690344i \(0.757459\pi\)
\(384\) 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 \(-0.255595\pi\)
−0.719426 + 0.694569i \(0.755595\pi\)
\(390\) 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 0.964942 + 0.262465i \(0.0845354\pi\)
0.262465 + 0.964942i \(0.415465\pi\)
\(398\) 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 \(0.359304\pi\)
−0.427758 + 0.903893i \(0.640696\pi\)
\(410\) 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 −0.999726 0.0234208i \(-0.992544\pi\)
−0.0234208 0.999726i \(1.49254\pi\)
\(420\) 0 0
\(421\) 14.2218 14.2218i 0.693126 0.693126i −0.269792 0.962919i \(-0.586955\pi\)
0.962919 + 0.269792i \(0.0869550\pi\)
\(422\) 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 \(-0.734575\pi\)
−0.672024 + 0.740529i \(0.734575\pi\)
\(432\) 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 \(-0.905440\pi\)
0.292720 + 0.956198i \(0.405440\pi\)
\(444\) 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 \(0.105921\pi\)
−0.945144 + 0.326655i \(0.894079\pi\)
\(458\) 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 \(-0.971188\pi\)
0.0903920 + 0.995906i \(0.471188\pi\)
\(462\) 0 0
\(463\) 27.9277i 1.29791i −0.760827 0.648955i \(-0.775206\pi\)
0.760827 0.648955i \(-0.224794\pi\)
\(464\) −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 \(-0.295228\pi\)
−0.800114 + 0.599848i \(0.795228\pi\)
\(468\) 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 \(-0.258743\pi\)
0.687420 + 0.726260i \(0.258743\pi\)
\(480\) 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 \(-0.788527\pi\)
0.616556 + 0.787311i \(0.288527\pi\)
\(492\) 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 −0.279648 0.960103i \(-0.590218\pi\)
0.960103 + 0.279648i \(0.0902178\pi\)
\(500\) −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 0.183639 0.982994i \(-0.441212\pi\)
0.982994 0.183639i \(-0.0587876\pi\)
\(510\) 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 \(-0.432546\pi\)
0.210329 + 0.977631i \(0.432546\pi\)
\(522\) 0 0
\(523\) 11.2532 + 11.2532i 0.492066 + 0.492066i 0.908957 0.416890i \(-0.136880\pi\)
−0.416890 + 0.908957i \(0.636880\pi\)
\(524\) 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 0.800333 0.599555i \(-0.204656\pi\)
−0.599555 + 0.800333i \(0.704656\pi\)
\(542\) −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 −0.982860 0.184355i \(-0.940981\pi\)
0.184355 + 0.982860i \(0.440981\pi\)
\(548\) −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 \(-0.719381\pi\)
0.771752 + 0.635923i \(0.219381\pi\)
\(558\) 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 0.865841 + 0.500319i \(0.166784\pi\)
0.500319 + 0.865841i \(0.333216\pi\)
\(564\) 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 \(-0.425091\pi\)
0.233168 + 0.972437i \(0.425091\pi\)
\(570\) 0 0
\(571\) 16.1349 + 16.1349i 0.675223 + 0.675223i 0.958915 0.283692i \(-0.0915594\pi\)
−0.283692 + 0.958915i \(0.591559\pi\)
\(572\) −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 \(-0.680626\pi\)
0.843273 + 0.537486i \(0.180626\pi\)
\(588\) 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 \(0.137031\pi\)
−0.908759 + 0.417321i \(0.862969\pi\)
\(602\) −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 \(0.209701\pi\)
−0.790730 + 0.612165i \(0.790299\pi\)
\(608\) 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 −0.742537 0.669805i \(-0.766377\pi\)
0.669805 + 0.742537i \(0.266377\pi\)
\(614\) 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 \(-0.287060\pi\)
0.620178 + 0.784461i \(0.287060\pi\)
\(618\) 0 0
\(619\) −10.0429 10.0429i −0.403659 0.403659i 0.475861 0.879520i \(-0.342136\pi\)
−0.879520 + 0.475861i \(0.842136\pi\)
\(620\) 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 −0.750284 0.661116i \(-0.770083\pi\)
0.661116 + 0.750284i \(0.270083\pi\)
\(644\) −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 \(-0.647080\pi\)
0.895133 + 0.445798i \(0.147080\pi\)
\(654\) 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 \(-0.401659\pi\)
−0.952654 + 0.304056i \(0.901659\pi\)
\(660\) 0 0
\(661\) −14.6386 + 14.6386i −0.569375 + 0.569375i −0.931953 0.362578i \(-0.881896\pi\)
0.362578 + 0.931953i \(0.381896\pi\)
\(662\) −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 \(-0.308508\pi\)
−0.824437 + 0.565954i \(0.808508\pi\)
\(678\) 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 0.186033 0.982543i \(-0.440437\pi\)
0.982543 0.186033i \(-0.0595632\pi\)
\(684\) 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 −0.469515 0.882924i \(-0.655571\pi\)
0.882924 + 0.469515i \(0.155571\pi\)
\(692\) −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 \(-0.565068\pi\)
0.979180 + 0.202995i \(0.0650677\pi\)
\(702\) 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 −0.302325 + 0.953205i \(0.597763\pi\)
−0.953205 + 0.302325i \(0.902237\pi\)
\(710\) −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 \(-0.445400\pi\)
0.170690 + 0.985325i \(0.445400\pi\)
\(720\) 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 0.962362 + 0.271771i \(0.0876092\pi\)
0.271771 + 0.962362i \(0.412391\pi\)
\(734\) −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 −0.175678 0.984448i \(-0.556212\pi\)
0.984448 + 0.175678i \(0.0562119\pi\)
\(740\) 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 \(-0.873947\pi\)
0.922608 0.385739i \(-0.126053\pi\)
\(752\) 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 −0.329386 0.944195i \(-0.606842\pi\)
0.944195 + 0.329386i \(0.106842\pi\)
\(758\) 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 \(-0.676635\pi\)
−0.526871 + 0.849945i \(0.676635\pi\)
\(762\) 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 \(-0.412329\pi\)
−0.962309 + 0.271958i \(0.912329\pi\)
\(774\) 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 −0.610472 0.792038i \(-0.709020\pi\)
0.792038 + 0.610472i \(0.209020\pi\)
\(788\) −11.6711 26.7783i −0.415764 0.953939i
\(789\) 0 0