Properties

Label 140.2.g.a.111.3
Level $140$
Weight $2$
Character 140.111
Analytic conductor $1.118$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 111.3
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 140.111
Dual form 140.2.g.a.111.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} -1.00000i q^{5} +(-0.633975 + 2.36603i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} -1.00000i q^{5} +(-0.633975 + 2.36603i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.36603 - 0.366025i) q^{10} -0.267949i q^{11} +(3.00000 + 1.73205i) q^{12} -0.464102i q^{13} +(-3.36603 + 1.63397i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} -6.46410i q^{17} +6.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(3.00000 + 3.46410i) q^{21} +(-0.366025 - 0.0980762i) q^{22} -1.46410i q^{23} +(3.46410 - 3.46410i) q^{24} -1.00000 q^{25} +(-0.633975 - 0.169873i) q^{26} +5.19615 q^{27} +(1.00000 + 5.19615i) q^{28} +7.92820 q^{29} +(2.36603 + 0.633975i) q^{30} -6.00000 q^{31} +(5.46410 - 1.46410i) q^{32} +0.464102i q^{33} +(-8.83013 - 2.36603i) q^{34} +(-2.00000 + 1.73205i) q^{35} -9.46410 q^{37} +(2.19615 - 8.19615i) q^{38} +0.803848i q^{39} +(2.00000 + 2.00000i) q^{40} -3.46410i q^{41} +(5.83013 - 2.83013i) q^{42} -2.00000i q^{43} +(-0.267949 + 0.464102i) q^{44} +(-2.00000 - 0.535898i) q^{46} +1.73205 q^{47} +(-3.46410 - 6.00000i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(-0.366025 + 1.36603i) q^{50} +11.1962i q^{51} +(-0.464102 + 0.803848i) q^{52} +2.00000 q^{53} +(1.90192 - 7.09808i) q^{54} -0.267949 q^{55} +(7.46410 + 0.535898i) q^{56} -10.3923 q^{57} +(2.90192 - 10.8301i) q^{58} -3.46410 q^{59} +(1.73205 - 3.00000i) q^{60} +9.46410i q^{61} +(-2.19615 + 8.19615i) q^{62} -8.00000i q^{64} -0.464102 q^{65} +(0.633975 + 0.169873i) q^{66} +3.46410i q^{67} +(-6.46410 + 11.1962i) q^{68} +2.53590i q^{69} +(1.63397 + 3.36603i) q^{70} -7.46410i q^{71} +12.9282i q^{73} +(-3.46410 + 12.9282i) q^{74} +1.73205 q^{75} +(-10.3923 - 6.00000i) q^{76} +(-0.535898 + 0.464102i) q^{77} +(1.09808 + 0.294229i) q^{78} -14.6603i q^{79} +(3.46410 - 2.00000i) q^{80} -9.00000 q^{81} +(-4.73205 - 1.26795i) q^{82} +15.4641 q^{83} +(-1.73205 - 9.00000i) q^{84} -6.46410 q^{85} +(-2.73205 - 0.732051i) q^{86} -13.7321 q^{87} +(0.535898 + 0.535898i) q^{88} +2.53590i q^{89} +(-0.928203 + 0.803848i) q^{91} +(-1.46410 + 2.53590i) q^{92} +10.3923 q^{93} +(0.633975 - 2.36603i) q^{94} -6.00000i q^{95} +(-9.46410 + 2.53590i) q^{96} -13.3923i q^{97} +(9.09808 + 3.90192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{8} + O(q^{10}) \) \( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{8} - 2 q^{10} + 12 q^{12} - 10 q^{14} + 8 q^{16} + 24 q^{19} - 4 q^{20} + 12 q^{21} + 2 q^{22} - 4 q^{25} - 6 q^{26} + 4 q^{28} + 4 q^{29} + 6 q^{30} - 24 q^{31} + 8 q^{32} - 18 q^{34} - 8 q^{35} - 24 q^{37} - 12 q^{38} + 8 q^{40} + 6 q^{42} - 8 q^{44} - 8 q^{46} - 4 q^{49} + 2 q^{50} + 12 q^{52} + 8 q^{53} + 18 q^{54} - 8 q^{55} + 16 q^{56} + 22 q^{58} + 12 q^{62} + 12 q^{65} + 6 q^{66} - 12 q^{68} + 10 q^{70} - 16 q^{77} - 6 q^{78} - 36 q^{81} - 12 q^{82} + 48 q^{83} - 12 q^{85} - 4 q^{86} - 48 q^{87} + 16 q^{88} + 24 q^{91} + 8 q^{92} + 6 q^{94} - 24 q^{96} + 26 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.258819 0.965926i
\(3\) −1.73205 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 1.00000i 0.447214i
\(6\) −0.633975 + 2.36603i −0.258819 + 0.965926i
\(7\) −1.73205 2.00000i −0.654654 0.755929i
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) −1.36603 0.366025i −0.431975 0.115747i
\(11\) 0.267949i 0.0807897i −0.999184 0.0403949i \(-0.987138\pi\)
0.999184 0.0403949i \(-0.0128616\pi\)
\(12\) 3.00000 + 1.73205i 0.866025 + 0.500000i
\(13\) 0.464102i 0.128719i −0.997927 0.0643593i \(-0.979500\pi\)
0.997927 0.0643593i \(-0.0205004\pi\)
\(14\) −3.36603 + 1.63397i −0.899608 + 0.436698i
\(15\) 1.73205i 0.447214i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 6.46410i 1.56777i −0.620903 0.783887i \(-0.713234\pi\)
0.620903 0.783887i \(-0.286766\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) 3.00000 + 3.46410i 0.654654 + 0.755929i
\(22\) −0.366025 0.0980762i −0.0780369 0.0209099i
\(23\) 1.46410i 0.305286i −0.988281 0.152643i \(-0.951221\pi\)
0.988281 0.152643i \(-0.0487785\pi\)
\(24\) 3.46410 3.46410i 0.707107 0.707107i
\(25\) −1.00000 −0.200000
\(26\) −0.633975 0.169873i −0.124333 0.0333148i
\(27\) 5.19615 1.00000
\(28\) 1.00000 + 5.19615i 0.188982 + 0.981981i
\(29\) 7.92820 1.47223 0.736115 0.676856i \(-0.236658\pi\)
0.736115 + 0.676856i \(0.236658\pi\)
\(30\) 2.36603 + 0.633975i 0.431975 + 0.115747i
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) 5.46410 1.46410i 0.965926 0.258819i
\(33\) 0.464102i 0.0807897i
\(34\) −8.83013 2.36603i −1.51435 0.405770i
\(35\) −2.00000 + 1.73205i −0.338062 + 0.292770i
\(36\) 0 0
\(37\) −9.46410 −1.55589 −0.777944 0.628333i \(-0.783737\pi\)
−0.777944 + 0.628333i \(0.783737\pi\)
\(38\) 2.19615 8.19615i 0.356263 1.32959i
\(39\) 0.803848i 0.128719i
\(40\) 2.00000 + 2.00000i 0.316228 + 0.316228i
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) 5.83013 2.83013i 0.899608 0.436698i
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) −0.267949 + 0.464102i −0.0403949 + 0.0699660i
\(45\) 0 0
\(46\) −2.00000 0.535898i −0.294884 0.0790139i
\(47\) 1.73205 0.252646 0.126323 0.991989i \(-0.459682\pi\)
0.126323 + 0.991989i \(0.459682\pi\)
\(48\) −3.46410 6.00000i −0.500000 0.866025i
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) −0.366025 + 1.36603i −0.0517638 + 0.193185i
\(51\) 11.1962i 1.56777i
\(52\) −0.464102 + 0.803848i −0.0643593 + 0.111474i
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 1.90192 7.09808i 0.258819 0.965926i
\(55\) −0.267949 −0.0361303
\(56\) 7.46410 + 0.535898i 0.997433 + 0.0716124i
\(57\) −10.3923 −1.37649
\(58\) 2.90192 10.8301i 0.381041 1.42207i
\(59\) −3.46410 −0.450988 −0.225494 0.974245i \(-0.572400\pi\)
−0.225494 + 0.974245i \(0.572400\pi\)
\(60\) 1.73205 3.00000i 0.223607 0.387298i
\(61\) 9.46410i 1.21175i 0.795558 + 0.605877i \(0.207178\pi\)
−0.795558 + 0.605877i \(0.792822\pi\)
\(62\) −2.19615 + 8.19615i −0.278912 + 1.04091i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −0.464102 −0.0575647
\(66\) 0.633975 + 0.169873i 0.0780369 + 0.0209099i
\(67\) 3.46410i 0.423207i 0.977356 + 0.211604i \(0.0678686\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −6.46410 + 11.1962i −0.783887 + 1.35773i
\(69\) 2.53590i 0.305286i
\(70\) 1.63397 + 3.36603i 0.195297 + 0.402317i
\(71\) 7.46410i 0.885826i −0.896565 0.442913i \(-0.853945\pi\)
0.896565 0.442913i \(-0.146055\pi\)
\(72\) 0 0
\(73\) 12.9282i 1.51313i 0.653917 + 0.756566i \(0.273124\pi\)
−0.653917 + 0.756566i \(0.726876\pi\)
\(74\) −3.46410 + 12.9282i −0.402694 + 1.50287i
\(75\) 1.73205 0.200000
\(76\) −10.3923 6.00000i −1.19208 0.688247i
\(77\) −0.535898 + 0.464102i −0.0610713 + 0.0528893i
\(78\) 1.09808 + 0.294229i 0.124333 + 0.0333148i
\(79\) 14.6603i 1.64941i −0.565565 0.824704i \(-0.691342\pi\)
0.565565 0.824704i \(-0.308658\pi\)
\(80\) 3.46410 2.00000i 0.387298 0.223607i
\(81\) −9.00000 −1.00000
\(82\) −4.73205 1.26795i −0.522568 0.140022i
\(83\) 15.4641 1.69741 0.848703 0.528870i \(-0.177384\pi\)
0.848703 + 0.528870i \(0.177384\pi\)
\(84\) −1.73205 9.00000i −0.188982 0.981981i
\(85\) −6.46410 −0.701130
\(86\) −2.73205 0.732051i −0.294605 0.0789391i
\(87\) −13.7321 −1.47223
\(88\) 0.535898 + 0.535898i 0.0571270 + 0.0571270i
\(89\) 2.53590i 0.268805i 0.990927 + 0.134402i \(0.0429115\pi\)
−0.990927 + 0.134402i \(0.957089\pi\)
\(90\) 0 0
\(91\) −0.928203 + 0.803848i −0.0973021 + 0.0842661i
\(92\) −1.46410 + 2.53590i −0.152643 + 0.264386i
\(93\) 10.3923 1.07763
\(94\) 0.633975 2.36603i 0.0653895 0.244037i
\(95\) 6.00000i 0.615587i
\(96\) −9.46410 + 2.53590i −0.965926 + 0.258819i
\(97\) 13.3923i 1.35978i −0.733313 0.679891i \(-0.762027\pi\)
0.733313 0.679891i \(-0.237973\pi\)
\(98\) 9.09808 + 3.90192i 0.919044 + 0.394154i
\(99\) 0 0
\(100\) 1.73205 + 1.00000i 0.173205 + 0.100000i
\(101\) 15.4641i 1.53874i −0.638806 0.769368i \(-0.720571\pi\)
0.638806 0.769368i \(-0.279429\pi\)
\(102\) 15.2942 + 4.09808i 1.51435 + 0.405770i
\(103\) −6.80385 −0.670403 −0.335202 0.942146i \(-0.608804\pi\)
−0.335202 + 0.942146i \(0.608804\pi\)
\(104\) 0.928203 + 0.928203i 0.0910178 + 0.0910178i
\(105\) 3.46410 3.00000i 0.338062 0.292770i
\(106\) 0.732051 2.73205i 0.0711031 0.265360i
\(107\) 2.39230i 0.231273i 0.993292 + 0.115636i \(0.0368907\pi\)
−0.993292 + 0.115636i \(0.963109\pi\)
\(108\) −9.00000 5.19615i −0.866025 0.500000i
\(109\) 2.07180 0.198442 0.0992211 0.995065i \(-0.468365\pi\)
0.0992211 + 0.995065i \(0.468365\pi\)
\(110\) −0.0980762 + 0.366025i −0.00935120 + 0.0348992i
\(111\) 16.3923 1.55589
\(112\) 3.46410 10.0000i 0.327327 0.944911i
\(113\) 5.46410 0.514019 0.257010 0.966409i \(-0.417263\pi\)
0.257010 + 0.966409i \(0.417263\pi\)
\(114\) −3.80385 + 14.1962i −0.356263 + 1.32959i
\(115\) −1.46410 −0.136528
\(116\) −13.7321 7.92820i −1.27499 0.736115i
\(117\) 0 0
\(118\) −1.26795 + 4.73205i −0.116724 + 0.435621i
\(119\) −12.9282 + 11.1962i −1.18513 + 1.02635i
\(120\) −3.46410 3.46410i −0.316228 0.316228i
\(121\) 10.9282 0.993473
\(122\) 12.9282 + 3.46410i 1.17046 + 0.313625i
\(123\) 6.00000i 0.541002i
\(124\) 10.3923 + 6.00000i 0.933257 + 0.538816i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 15.4641i 1.37222i 0.727499 + 0.686109i \(0.240683\pi\)
−0.727499 + 0.686109i \(0.759317\pi\)
\(128\) −10.9282 2.92820i −0.965926 0.258819i
\(129\) 3.46410i 0.304997i
\(130\) −0.169873 + 0.633975i −0.0148988 + 0.0556033i
\(131\) 2.53590 0.221562 0.110781 0.993845i \(-0.464665\pi\)
0.110781 + 0.993845i \(0.464665\pi\)
\(132\) 0.464102 0.803848i 0.0403949 0.0699660i
\(133\) −10.3923 12.0000i −0.901127 1.04053i
\(134\) 4.73205 + 1.26795i 0.408787 + 0.109534i
\(135\) 5.19615i 0.447214i
\(136\) 12.9282 + 12.9282i 1.10858 + 1.10858i
\(137\) 20.3923 1.74223 0.871116 0.491077i \(-0.163397\pi\)
0.871116 + 0.491077i \(0.163397\pi\)
\(138\) 3.46410 + 0.928203i 0.294884 + 0.0790139i
\(139\) 6.92820 0.587643 0.293821 0.955860i \(-0.405073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(140\) 5.19615 1.00000i 0.439155 0.0845154i
\(141\) −3.00000 −0.252646
\(142\) −10.1962 2.73205i −0.855642 0.229269i
\(143\) −0.124356 −0.0103991
\(144\) 0 0
\(145\) 7.92820i 0.658401i
\(146\) 17.6603 + 4.73205i 1.46157 + 0.391627i
\(147\) 1.73205 12.0000i 0.142857 0.989743i
\(148\) 16.3923 + 9.46410i 1.34744 + 0.777944i
\(149\) 3.07180 0.251651 0.125826 0.992052i \(-0.459842\pi\)
0.125826 + 0.992052i \(0.459842\pi\)
\(150\) 0.633975 2.36603i 0.0517638 0.193185i
\(151\) 15.1962i 1.23665i −0.785924 0.618323i \(-0.787812\pi\)
0.785924 0.618323i \(-0.212188\pi\)
\(152\) −12.0000 + 12.0000i −0.973329 + 0.973329i
\(153\) 0 0
\(154\) 0.437822 + 0.901924i 0.0352807 + 0.0726791i
\(155\) 6.00000i 0.481932i
\(156\) 0.803848 1.39230i 0.0643593 0.111474i
\(157\) 7.85641i 0.627009i 0.949587 + 0.313505i \(0.101503\pi\)
−0.949587 + 0.313505i \(0.898497\pi\)
\(158\) −20.0263 5.36603i −1.59321 0.426898i
\(159\) −3.46410 −0.274721
\(160\) −1.46410 5.46410i −0.115747 0.431975i
\(161\) −2.92820 + 2.53590i −0.230775 + 0.199857i
\(162\) −3.29423 + 12.2942i −0.258819 + 0.965926i
\(163\) 20.7846i 1.62798i 0.580881 + 0.813988i \(0.302708\pi\)
−0.580881 + 0.813988i \(0.697292\pi\)
\(164\) −3.46410 + 6.00000i −0.270501 + 0.468521i
\(165\) 0.464102 0.0361303
\(166\) 5.66025 21.1244i 0.439321 1.63957i
\(167\) −5.19615 −0.402090 −0.201045 0.979582i \(-0.564434\pi\)
−0.201045 + 0.979582i \(0.564434\pi\)
\(168\) −12.9282 0.928203i −0.997433 0.0716124i
\(169\) 12.7846 0.983432
\(170\) −2.36603 + 8.83013i −0.181466 + 0.677240i
\(171\) 0 0
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 14.3205i 1.08877i −0.838836 0.544384i \(-0.816763\pi\)
0.838836 0.544384i \(-0.183237\pi\)
\(174\) −5.02628 + 18.7583i −0.381041 + 1.42207i
\(175\) 1.73205 + 2.00000i 0.130931 + 0.151186i
\(176\) 0.928203 0.535898i 0.0699660 0.0403949i
\(177\) 6.00000 0.450988
\(178\) 3.46410 + 0.928203i 0.259645 + 0.0695718i
\(179\) 6.39230i 0.477783i 0.971046 + 0.238892i \(0.0767841\pi\)
−0.971046 + 0.238892i \(0.923216\pi\)
\(180\) 0 0
\(181\) 0.928203i 0.0689928i −0.999405 0.0344964i \(-0.989017\pi\)
0.999405 0.0344964i \(-0.0109827\pi\)
\(182\) 0.758330 + 1.56218i 0.0562112 + 0.115796i
\(183\) 16.3923i 1.21175i
\(184\) 2.92820 + 2.92820i 0.215870 + 0.215870i
\(185\) 9.46410i 0.695815i
\(186\) 3.80385 14.1962i 0.278912 1.04091i
\(187\) −1.73205 −0.126660
\(188\) −3.00000 1.73205i −0.218797 0.126323i
\(189\) −9.00000 10.3923i −0.654654 0.755929i
\(190\) −8.19615 2.19615i −0.594611 0.159326i
\(191\) 7.19615i 0.520695i −0.965515 0.260348i \(-0.916163\pi\)
0.965515 0.260348i \(-0.0838372\pi\)
\(192\) 13.8564i 1.00000i
\(193\) −9.46410 −0.681241 −0.340620 0.940201i \(-0.610637\pi\)
−0.340620 + 0.940201i \(0.610637\pi\)
\(194\) −18.2942 4.90192i −1.31345 0.351938i
\(195\) 0.803848 0.0575647
\(196\) 8.66025 11.0000i 0.618590 0.785714i
\(197\) −13.3205 −0.949047 −0.474523 0.880243i \(-0.657380\pi\)
−0.474523 + 0.880243i \(0.657380\pi\)
\(198\) 0 0
\(199\) 3.46410 0.245564 0.122782 0.992434i \(-0.460818\pi\)
0.122782 + 0.992434i \(0.460818\pi\)
\(200\) 2.00000 2.00000i 0.141421 0.141421i
\(201\) 6.00000i 0.423207i
\(202\) −21.1244 5.66025i −1.48630 0.398254i
\(203\) −13.7321 15.8564i −0.963801 1.11290i
\(204\) 11.1962 19.3923i 0.783887 1.35773i
\(205\) −3.46410 −0.241943
\(206\) −2.49038 + 9.29423i −0.173513 + 0.647560i
\(207\) 0 0
\(208\) 1.60770 0.928203i 0.111474 0.0643593i
\(209\) 1.60770i 0.111207i
\(210\) −2.83013 5.83013i −0.195297 0.402317i
\(211\) 3.19615i 0.220032i −0.993930 0.110016i \(-0.964910\pi\)
0.993930 0.110016i \(-0.0350902\pi\)
\(212\) −3.46410 2.00000i −0.237915 0.137361i
\(213\) 12.9282i 0.885826i
\(214\) 3.26795 + 0.875644i 0.223392 + 0.0598578i
\(215\) −2.00000 −0.136399
\(216\) −10.3923 + 10.3923i −0.707107 + 0.707107i
\(217\) 10.3923 + 12.0000i 0.705476 + 0.814613i
\(218\) 0.758330 2.83013i 0.0513606 0.191680i
\(219\) 22.3923i 1.51313i
\(220\) 0.464102 + 0.267949i 0.0312897 + 0.0180651i
\(221\) −3.00000 −0.201802
\(222\) 6.00000 22.3923i 0.402694 1.50287i
\(223\) −13.7321 −0.919566 −0.459783 0.888031i \(-0.652073\pi\)
−0.459783 + 0.888031i \(0.652073\pi\)
\(224\) −12.3923 8.39230i −0.827996 0.560734i
\(225\) 0 0
\(226\) 2.00000 7.46410i 0.133038 0.496505i
\(227\) 20.6603 1.37127 0.685635 0.727946i \(-0.259525\pi\)
0.685635 + 0.727946i \(0.259525\pi\)
\(228\) 18.0000 + 10.3923i 1.19208 + 0.688247i
\(229\) 8.53590i 0.564068i −0.959404 0.282034i \(-0.908991\pi\)
0.959404 0.282034i \(-0.0910091\pi\)
\(230\) −0.535898 + 2.00000i −0.0353361 + 0.131876i
\(231\) 0.928203 0.803848i 0.0610713 0.0528893i
\(232\) −15.8564 + 15.8564i −1.04102 + 1.04102i
\(233\) −9.07180 −0.594313 −0.297157 0.954829i \(-0.596038\pi\)
−0.297157 + 0.954829i \(0.596038\pi\)
\(234\) 0 0
\(235\) 1.73205i 0.112987i
\(236\) 6.00000 + 3.46410i 0.390567 + 0.225494i
\(237\) 25.3923i 1.64941i
\(238\) 10.5622 + 21.7583i 0.684644 + 1.41038i
\(239\) 23.9808i 1.55119i 0.631233 + 0.775593i \(0.282549\pi\)
−0.631233 + 0.775593i \(0.717451\pi\)
\(240\) −6.00000 + 3.46410i −0.387298 + 0.223607i
\(241\) 16.3923i 1.05592i 0.849269 + 0.527961i \(0.177043\pi\)
−0.849269 + 0.527961i \(0.822957\pi\)
\(242\) 4.00000 14.9282i 0.257130 0.959621i
\(243\) 0 0
\(244\) 9.46410 16.3923i 0.605877 1.04941i
\(245\) 6.92820 + 1.00000i 0.442627 + 0.0638877i
\(246\) 8.19615 + 2.19615i 0.522568 + 0.140022i
\(247\) 2.78461i 0.177180i
\(248\) 12.0000 12.0000i 0.762001 0.762001i
\(249\) −26.7846 −1.69741
\(250\) 1.36603 + 0.366025i 0.0863950 + 0.0231495i
\(251\) −25.8564 −1.63204 −0.816021 0.578022i \(-0.803825\pi\)
−0.816021 + 0.578022i \(0.803825\pi\)
\(252\) 0 0
\(253\) −0.392305 −0.0246640
\(254\) 21.1244 + 5.66025i 1.32546 + 0.355156i
\(255\) 11.1962 0.701130
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 6.00000i 0.374270i 0.982334 + 0.187135i \(0.0599201\pi\)
−0.982334 + 0.187135i \(0.940080\pi\)
\(258\) 4.73205 + 1.26795i 0.294605 + 0.0789391i
\(259\) 16.3923 + 18.9282i 1.01857 + 1.17614i
\(260\) 0.803848 + 0.464102i 0.0498525 + 0.0287824i
\(261\) 0 0
\(262\) 0.928203 3.46410i 0.0573446 0.214013i
\(263\) 11.4641i 0.706907i 0.935452 + 0.353453i \(0.114993\pi\)
−0.935452 + 0.353453i \(0.885007\pi\)
\(264\) −0.928203 0.928203i −0.0571270 0.0571270i
\(265\) 2.00000i 0.122859i
\(266\) −20.1962 + 9.80385i −1.23831 + 0.601112i
\(267\) 4.39230i 0.268805i
\(268\) 3.46410 6.00000i 0.211604 0.366508i
\(269\) 12.0000i 0.731653i −0.930683 0.365826i \(-0.880786\pi\)
0.930683 0.365826i \(-0.119214\pi\)
\(270\) −7.09808 1.90192i −0.431975 0.115747i
\(271\) 9.46410 0.574903 0.287452 0.957795i \(-0.407192\pi\)
0.287452 + 0.957795i \(0.407192\pi\)
\(272\) 22.3923 12.9282i 1.35773 0.783887i
\(273\) 1.60770 1.39230i 0.0973021 0.0842661i
\(274\) 7.46410 27.8564i 0.450923 1.68287i
\(275\) 0.267949i 0.0161579i
\(276\) 2.53590 4.39230i 0.152643 0.264386i
\(277\) 16.7846 1.00849 0.504245 0.863561i \(-0.331771\pi\)
0.504245 + 0.863561i \(0.331771\pi\)
\(278\) 2.53590 9.46410i 0.152093 0.567619i
\(279\) 0 0
\(280\) 0.535898 7.46410i 0.0320261 0.446065i
\(281\) −7.92820 −0.472957 −0.236478 0.971637i \(-0.575993\pi\)
−0.236478 + 0.971637i \(0.575993\pi\)
\(282\) −1.09808 + 4.09808i −0.0653895 + 0.244037i
\(283\) 12.1244 0.720718 0.360359 0.932814i \(-0.382654\pi\)
0.360359 + 0.932814i \(0.382654\pi\)
\(284\) −7.46410 + 12.9282i −0.442913 + 0.767148i
\(285\) 10.3923i 0.615587i
\(286\) −0.0455173 + 0.169873i −0.00269150 + 0.0100448i
\(287\) −6.92820 + 6.00000i −0.408959 + 0.354169i
\(288\) 0 0
\(289\) −24.7846 −1.45792
\(290\) −10.8301 2.90192i −0.635967 0.170407i
\(291\) 23.1962i 1.35978i
\(292\) 12.9282 22.3923i 0.756566 1.31041i
\(293\) 20.3205i 1.18714i 0.804784 + 0.593568i \(0.202281\pi\)
−0.804784 + 0.593568i \(0.797719\pi\)
\(294\) −15.7583 6.75833i −0.919044 0.394154i
\(295\) 3.46410i 0.201688i
\(296\) 18.9282 18.9282i 1.10018 1.10018i
\(297\) 1.39230i 0.0807897i
\(298\) 1.12436 4.19615i 0.0651322 0.243077i
\(299\) −0.679492 −0.0392960
\(300\) −3.00000 1.73205i −0.173205 0.100000i
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) −20.7583 5.56218i −1.19451 0.320067i
\(303\) 26.7846i 1.53874i
\(304\) 12.0000 + 20.7846i 0.688247 + 1.19208i
\(305\) 9.46410 0.541913
\(306\) 0 0
\(307\) 1.73205 0.0988534 0.0494267 0.998778i \(-0.484261\pi\)
0.0494267 + 0.998778i \(0.484261\pi\)
\(308\) 1.39230 0.267949i 0.0793339 0.0152678i
\(309\) 11.7846 0.670403
\(310\) 8.19615 + 2.19615i 0.465510 + 0.124733i
\(311\) 7.85641 0.445496 0.222748 0.974876i \(-0.428497\pi\)
0.222748 + 0.974876i \(0.428497\pi\)
\(312\) −1.60770 1.60770i −0.0910178 0.0910178i
\(313\) 17.5359i 0.991188i −0.868554 0.495594i \(-0.834950\pi\)
0.868554 0.495594i \(-0.165050\pi\)
\(314\) 10.7321 + 2.87564i 0.605645 + 0.162282i
\(315\) 0 0
\(316\) −14.6603 + 25.3923i −0.824704 + 1.42843i
\(317\) −3.07180 −0.172529 −0.0862646 0.996272i \(-0.527493\pi\)
−0.0862646 + 0.996272i \(0.527493\pi\)
\(318\) −1.26795 + 4.73205i −0.0711031 + 0.265360i
\(319\) 2.12436i 0.118941i
\(320\) −8.00000 −0.447214
\(321\) 4.14359i 0.231273i
\(322\) 2.39230 + 4.92820i 0.133318 + 0.274638i
\(323\) 38.7846i 2.15803i
\(324\) 15.5885 + 9.00000i 0.866025 + 0.500000i
\(325\) 0.464102i 0.0257437i
\(326\) 28.3923 + 7.60770i 1.57250 + 0.421351i
\(327\) −3.58846 −0.198442
\(328\) 6.92820 + 6.92820i 0.382546 + 0.382546i
\(329\) −3.00000 3.46410i −0.165395 0.190982i
\(330\) 0.169873 0.633975i 0.00935120 0.0348992i
\(331\) 26.3923i 1.45065i 0.688405 + 0.725326i \(0.258311\pi\)
−0.688405 + 0.725326i \(0.741689\pi\)
\(332\) −26.7846 15.4641i −1.47000 0.848703i
\(333\) 0 0
\(334\) −1.90192 + 7.09808i −0.104069 + 0.388389i
\(335\) 3.46410 0.189264
\(336\) −6.00000 + 17.3205i −0.327327 + 0.944911i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 4.67949 17.4641i 0.254531 0.949922i
\(339\) −9.46410 −0.514019
\(340\) 11.1962 + 6.46410i 0.607197 + 0.350565i
\(341\) 1.60770i 0.0870616i
\(342\) 0 0
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 4.00000 + 4.00000i 0.215666 + 0.215666i
\(345\) 2.53590 0.136528
\(346\) −19.5622 5.24167i −1.05167 0.281794i
\(347\) 34.2487i 1.83857i −0.393596 0.919284i \(-0.628769\pi\)
0.393596 0.919284i \(-0.371231\pi\)
\(348\) 23.7846 + 13.7321i 1.27499 + 0.736115i
\(349\) 5.32051i 0.284800i −0.989809 0.142400i \(-0.954518\pi\)
0.989809 0.142400i \(-0.0454820\pi\)
\(350\) 3.36603 1.63397i 0.179922 0.0873396i
\(351\) 2.41154i 0.128719i
\(352\) −0.392305 1.46410i −0.0209099 0.0780369i
\(353\) 7.39230i 0.393453i −0.980458 0.196726i \(-0.936969\pi\)
0.980458 0.196726i \(-0.0630311\pi\)
\(354\) 2.19615 8.19615i 0.116724 0.435621i
\(355\) −7.46410 −0.396153
\(356\) 2.53590 4.39230i 0.134402 0.232792i
\(357\) 22.3923 19.3923i 1.18513 1.02635i
\(358\) 8.73205 + 2.33975i 0.461503 + 0.123659i
\(359\) 25.3205i 1.33637i −0.743997 0.668183i \(-0.767072\pi\)
0.743997 0.668183i \(-0.232928\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) −1.26795 0.339746i −0.0666419 0.0178567i
\(363\) −18.9282 −0.993473
\(364\) 2.41154 0.464102i 0.126399 0.0243255i
\(365\) 12.9282 0.676693
\(366\) −22.3923 6.00000i −1.17046 0.313625i
\(367\) 11.8756 0.619904 0.309952 0.950752i \(-0.399687\pi\)
0.309952 + 0.950752i \(0.399687\pi\)
\(368\) 5.07180 2.92820i 0.264386 0.152643i
\(369\) 0 0
\(370\) 12.9282 + 3.46410i 0.672105 + 0.180090i
\(371\) −3.46410 4.00000i −0.179847 0.207670i
\(372\) −18.0000 10.3923i −0.933257 0.538816i
\(373\) −3.60770 −0.186799 −0.0933997 0.995629i \(-0.529773\pi\)
−0.0933997 + 0.995629i \(0.529773\pi\)
\(374\) −0.633975 + 2.36603i −0.0327820 + 0.122344i
\(375\) 1.73205i 0.0894427i
\(376\) −3.46410 + 3.46410i −0.178647 + 0.178647i
\(377\) 3.67949i 0.189503i
\(378\) −17.4904 + 8.49038i −0.899608 + 0.436698i
\(379\) 5.60770i 0.288048i −0.989574 0.144024i \(-0.953996\pi\)
0.989574 0.144024i \(-0.0460042\pi\)
\(380\) −6.00000 + 10.3923i −0.307794 + 0.533114i
\(381\) 26.7846i 1.37222i
\(382\) −9.83013 2.63397i −0.502953 0.134766i
\(383\) 27.4641 1.40335 0.701675 0.712497i \(-0.252436\pi\)
0.701675 + 0.712497i \(0.252436\pi\)
\(384\) 18.9282 + 5.07180i 0.965926 + 0.258819i
\(385\) 0.464102 + 0.535898i 0.0236528 + 0.0273119i
\(386\) −3.46410 + 12.9282i −0.176318 + 0.658028i
\(387\) 0 0
\(388\) −13.3923 + 23.1962i −0.679891 + 1.17761i
\(389\) −20.8564 −1.05746 −0.528731 0.848790i \(-0.677332\pi\)
−0.528731 + 0.848790i \(0.677332\pi\)
\(390\) 0.294229 1.09808i 0.0148988 0.0556033i
\(391\) −9.46410 −0.478620
\(392\) −11.8564 15.8564i −0.598839 0.800869i
\(393\) −4.39230 −0.221562
\(394\) −4.87564 + 18.1962i −0.245631 + 0.916709i
\(395\) −14.6603 −0.737637
\(396\) 0 0
\(397\) 12.4641i 0.625555i 0.949826 + 0.312778i \(0.101259\pi\)
−0.949826 + 0.312778i \(0.898741\pi\)
\(398\) 1.26795 4.73205i 0.0635566 0.237196i
\(399\) 18.0000 + 20.7846i 0.901127 + 1.04053i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −10.0718 −0.502962 −0.251481 0.967862i \(-0.580918\pi\)
−0.251481 + 0.967862i \(0.580918\pi\)
\(402\) −8.19615 2.19615i −0.408787 0.109534i
\(403\) 2.78461i 0.138711i
\(404\) −15.4641 + 26.7846i −0.769368 + 1.33258i
\(405\) 9.00000i 0.447214i
\(406\) −26.6865 + 12.9545i −1.32443 + 0.642920i
\(407\) 2.53590i 0.125700i
\(408\) −22.3923 22.3923i −1.10858 1.10858i
\(409\) 4.14359i 0.204888i 0.994739 + 0.102444i \(0.0326662\pi\)
−0.994739 + 0.102444i \(0.967334\pi\)
\(410\) −1.26795 + 4.73205i −0.0626195 + 0.233699i
\(411\) −35.3205 −1.74223
\(412\) 11.7846 + 6.80385i 0.580586 + 0.335202i
\(413\) 6.00000 + 6.92820i 0.295241 + 0.340915i
\(414\) 0 0
\(415\) 15.4641i 0.759103i
\(416\) −0.679492 2.53590i −0.0333148 0.124333i
\(417\) −12.0000 −0.587643
\(418\) −2.19615 0.588457i −0.107417 0.0287824i
\(419\) −24.2487 −1.18463 −0.592314 0.805708i \(-0.701785\pi\)
−0.592314 + 0.805708i \(0.701785\pi\)
\(420\) −9.00000 + 1.73205i −0.439155 + 0.0845154i
\(421\) 19.0000 0.926003 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(422\) −4.36603 1.16987i −0.212535 0.0569485i
\(423\) 0 0
\(424\) −4.00000 + 4.00000i −0.194257 + 0.194257i
\(425\) 6.46410i 0.313555i
\(426\) 17.6603 + 4.73205i 0.855642 + 0.229269i
\(427\) 18.9282 16.3923i 0.916000 0.793279i
\(428\) 2.39230 4.14359i 0.115636 0.200288i
\(429\) 0.215390 0.0103991
\(430\) −0.732051 + 2.73205i −0.0353026 + 0.131751i
\(431\) 13.5885i 0.654533i 0.944932 + 0.327266i \(0.106127\pi\)
−0.944932 + 0.327266i \(0.893873\pi\)
\(432\) 10.3923 + 18.0000i 0.500000 + 0.866025i
\(433\) 31.8564i 1.53092i −0.643483 0.765461i \(-0.722511\pi\)
0.643483 0.765461i \(-0.277489\pi\)
\(434\) 20.1962 9.80385i 0.969446 0.470600i
\(435\) 13.7321i 0.658401i
\(436\) −3.58846 2.07180i −0.171856 0.0992211i
\(437\) 8.78461i 0.420225i
\(438\) −30.5885 8.19615i −1.46157 0.391627i
\(439\) −39.7128 −1.89539 −0.947695 0.319179i \(-0.896593\pi\)
−0.947695 + 0.319179i \(0.896593\pi\)
\(440\) 0.535898 0.535898i 0.0255480 0.0255480i
\(441\) 0 0
\(442\) −1.09808 + 4.09808i −0.0522302 + 0.194926i
\(443\) 26.0000i 1.23530i 0.786454 + 0.617649i \(0.211915\pi\)
−0.786454 + 0.617649i \(0.788085\pi\)
\(444\) −28.3923 16.3923i −1.34744 0.777944i
\(445\) 2.53590 0.120213
\(446\) −5.02628 + 18.7583i −0.238001 + 0.888233i
\(447\) −5.32051 −0.251651
\(448\) −16.0000 + 13.8564i −0.755929 + 0.654654i
\(449\) 11.9282 0.562927 0.281463 0.959572i \(-0.409180\pi\)
0.281463 + 0.959572i \(0.409180\pi\)
\(450\) 0 0
\(451\) −0.928203 −0.0437074
\(452\) −9.46410 5.46410i −0.445154 0.257010i
\(453\) 26.3205i 1.23665i
\(454\) 7.56218 28.2224i 0.354911 1.32454i
\(455\) 0.803848 + 0.928203i 0.0376850 + 0.0435148i
\(456\) 20.7846 20.7846i 0.973329 0.973329i
\(457\) 20.5359 0.960629 0.480314 0.877096i \(-0.340523\pi\)
0.480314 + 0.877096i \(0.340523\pi\)
\(458\) −11.6603 3.12436i −0.544848 0.145992i
\(459\) 33.5885i 1.56777i
\(460\) 2.53590 + 1.46410i 0.118237 + 0.0682641i
\(461\) 27.7128i 1.29071i 0.763881 + 0.645357i \(0.223291\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(462\) −0.758330 1.56218i −0.0352807 0.0726791i
\(463\) 16.3923i 0.761815i 0.924613 + 0.380908i \(0.124388\pi\)
−0.924613 + 0.380908i \(0.875612\pi\)
\(464\) 15.8564 + 27.4641i 0.736115 + 1.27499i
\(465\) 10.3923i 0.481932i
\(466\) −3.32051 + 12.3923i −0.153820 + 0.574062i
\(467\) 22.5167 1.04195 0.520973 0.853573i \(-0.325569\pi\)
0.520973 + 0.853573i \(0.325569\pi\)
\(468\) 0 0
\(469\) 6.92820 6.00000i 0.319915 0.277054i
\(470\) −2.36603 0.633975i −0.109137 0.0292431i
\(471\) 13.6077i 0.627009i
\(472\) 6.92820 6.92820i 0.318896 0.318896i
\(473\) −0.535898 −0.0246406
\(474\) 34.6865 + 9.29423i 1.59321 + 0.426898i
\(475\) −6.00000 −0.275299
\(476\) 33.5885 6.46410i 1.53952 0.296282i
\(477\) 0 0
\(478\) 32.7583 + 8.77757i 1.49833 + 0.401477i
\(479\) 25.1769 1.15036 0.575181 0.818026i \(-0.304932\pi\)
0.575181 + 0.818026i \(0.304932\pi\)
\(480\) 2.53590 + 9.46410i 0.115747 + 0.431975i
\(481\) 4.39230i 0.200272i
\(482\) 22.3923 + 6.00000i 1.01994 + 0.273293i
\(483\) 5.07180 4.39230i 0.230775 0.199857i
\(484\) −18.9282 10.9282i −0.860373 0.496737i
\(485\) −13.3923 −0.608113
\(486\) 0 0
\(487\) 12.7846i 0.579326i 0.957129 + 0.289663i \(0.0935432\pi\)
−0.957129 + 0.289663i \(0.906457\pi\)
\(488\) −18.9282 18.9282i −0.856840 0.856840i
\(489\) 36.0000i 1.62798i
\(490\) 3.90192 9.09808i 0.176271 0.411009i
\(491\) 9.87564i 0.445682i 0.974855 + 0.222841i \(0.0715330\pi\)
−0.974855 + 0.222841i \(0.928467\pi\)
\(492\) 6.00000 10.3923i 0.270501 0.468521i
\(493\) 51.2487i 2.30813i
\(494\) −3.80385 1.01924i −0.171143 0.0458577i
\(495\) 0 0
\(496\) −12.0000 20.7846i −0.538816 0.933257i
\(497\) −14.9282 + 12.9282i −0.669621 + 0.579909i
\(498\) −9.80385 + 36.5885i −0.439321 + 1.63957i
\(499\) 25.5885i 1.14550i −0.819731 0.572748i \(-0.805877\pi\)
0.819731 0.572748i \(-0.194123\pi\)
\(500\) 1.00000 1.73205i 0.0447214 0.0774597i
\(501\) 9.00000 0.402090
\(502\) −9.46410 + 35.3205i −0.422404 + 1.57643i
\(503\) −15.5885 −0.695055 −0.347527 0.937670i \(-0.612979\pi\)
−0.347527 + 0.937670i \(0.612979\pi\)
\(504\) 0 0
\(505\) −15.4641 −0.688143
\(506\) −0.143594 + 0.535898i −0.00638351 + 0.0238236i
\(507\) −22.1436 −0.983432
\(508\) 15.4641 26.7846i 0.686109 1.18837i
\(509\) 25.8564i 1.14607i 0.819533 + 0.573033i \(0.194233\pi\)
−0.819533 + 0.573033i \(0.805767\pi\)
\(510\) 4.09808 15.2942i 0.181466 0.677240i
\(511\) 25.8564 22.3923i 1.14382 0.990577i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 31.1769 1.37649
\(514\) 8.19615 + 2.19615i 0.361517 + 0.0968681i
\(515\) 6.80385i 0.299813i
\(516\) 3.46410 6.00000i 0.152499 0.264135i
\(517\) 0.464102i 0.0204112i
\(518\) 31.8564 15.4641i 1.39969 0.679454i
\(519\) 24.8038i 1.08877i
\(520\) 0.928203 0.928203i 0.0407044 0.0407044i
\(521\) 13.6077i 0.596164i 0.954540 + 0.298082i \(0.0963469\pi\)
−0.954540 + 0.298082i \(0.903653\pi\)
\(522\) 0 0
\(523\) −24.2487 −1.06032 −0.530161 0.847897i \(-0.677869\pi\)
−0.530161 + 0.847897i \(0.677869\pi\)
\(524\) −4.39230 2.53590i −0.191879 0.110781i
\(525\) −3.00000 3.46410i −0.130931 0.151186i
\(526\) 15.6603 + 4.19615i 0.682820 + 0.182961i
\(527\) 38.7846i 1.68948i
\(528\) −1.60770 + 0.928203i −0.0699660 + 0.0403949i
\(529\) 20.8564 0.906800
\(530\) −2.73205 0.732051i −0.118673 0.0317983i
\(531\) 0 0
\(532\) 6.00000 + 31.1769i 0.260133 + 1.35169i
\(533\) −1.60770 −0.0696370
\(534\) −6.00000 1.60770i −0.259645 0.0695718i
\(535\) 2.39230 0.103428
\(536\) −6.92820 6.92820i −0.299253 0.299253i
\(537\) 11.0718i 0.477783i
\(538\) −16.3923 4.39230i −0.706722 0.189366i
\(539\) 1.85641 + 0.267949i 0.0799611 + 0.0115414i
\(540\) −5.19615 + 9.00000i −0.223607 + 0.387298i
\(541\) 7.78461 0.334687 0.167343 0.985899i \(-0.446481\pi\)
0.167343 + 0.985899i \(0.446481\pi\)
\(542\) 3.46410 12.9282i 0.148796 0.555314i
\(543\) 1.60770i 0.0689928i
\(544\) −9.46410 35.3205i −0.405770 1.51435i
\(545\) 2.07180i 0.0887460i
\(546\) −1.31347 2.70577i −0.0562112 0.115796i
\(547\) 21.4641i 0.917739i −0.888504 0.458869i \(-0.848255\pi\)
0.888504 0.458869i \(-0.151745\pi\)
\(548\) −35.3205 20.3923i −1.50882 0.871116i
\(549\) 0 0
\(550\) 0.366025 + 0.0980762i 0.0156074 + 0.00418198i
\(551\) 47.5692 2.02652
\(552\) −5.07180 5.07180i −0.215870 0.215870i
\(553\) −29.3205 + 25.3923i −1.24683 + 1.07979i
\(554\) 6.14359 22.9282i 0.261016 0.974126i
\(555\) 16.3923i 0.695815i
\(556\) −12.0000 6.92820i −0.508913 0.293821i
\(557\) −21.8564 −0.926086 −0.463043 0.886336i \(-0.653242\pi\)
−0.463043 + 0.886336i \(0.653242\pi\)
\(558\) 0 0
\(559\) −0.928203 −0.0392588
\(560\) −10.0000 3.46410i −0.422577 0.146385i
\(561\) 3.00000 0.126660
\(562\) −2.90192 + 10.8301i −0.122410 + 0.456841i
\(563\) 19.1769 0.808211 0.404105 0.914712i \(-0.367583\pi\)
0.404105 + 0.914712i \(0.367583\pi\)
\(564\) 5.19615 + 3.00000i 0.218797 + 0.126323i
\(565\) 5.46410i 0.229876i
\(566\) 4.43782 16.5622i 0.186536 0.696160i
\(567\) 15.5885 + 18.0000i 0.654654 + 0.755929i
\(568\) 14.9282 + 14.9282i 0.626373 + 0.626373i
\(569\) 7.07180 0.296465 0.148233 0.988953i \(-0.452642\pi\)
0.148233 + 0.988953i \(0.452642\pi\)
\(570\) 14.1962 + 3.80385i 0.594611 + 0.159326i
\(571\) 6.67949i 0.279528i 0.990185 + 0.139764i \(0.0446344\pi\)
−0.990185 + 0.139764i \(0.955366\pi\)
\(572\) 0.215390 + 0.124356i 0.00900592 + 0.00519957i
\(573\) 12.4641i 0.520695i
\(574\) 5.66025 + 11.6603i 0.236254 + 0.486690i
\(575\) 1.46410i 0.0610573i
\(576\) 0 0
\(577\) 19.3923i 0.807312i 0.914911 + 0.403656i \(0.132261\pi\)
−0.914911 + 0.403656i \(0.867739\pi\)
\(578\) −9.07180 + 33.8564i −0.377337 + 1.40824i
\(579\) 16.3923 0.681241
\(580\) −7.92820 + 13.7321i −0.329201 + 0.570192i
\(581\) −26.7846 30.9282i −1.11121 1.28312i
\(582\) 31.6865 + 8.49038i 1.31345 + 0.351938i
\(583\) 0.535898i 0.0221946i
\(584\) −25.8564 25.8564i −1.06995 1.06995i
\(585\) 0 0
\(586\) 27.7583 + 7.43782i 1.14669 + 0.307254i
\(587\) −20.5359 −0.847607 −0.423804 0.905754i \(-0.639305\pi\)
−0.423804 + 0.905754i \(0.639305\pi\)
\(588\) −15.0000 + 19.0526i −0.618590 + 0.785714i
\(589\) −36.0000 −1.48335
\(590\) 4.73205 + 1.26795i 0.194815 + 0.0522006i
\(591\) 23.0718 0.949047
\(592\) −18.9282 32.7846i −0.777944 1.34744i
\(593\) 30.4641i 1.25101i 0.780220 + 0.625505i \(0.215107\pi\)
−0.780220 + 0.625505i \(0.784893\pi\)
\(594\) −1.90192 0.509619i −0.0780369 0.0209099i
\(595\) 11.1962 + 12.9282i 0.458997 + 0.530005i
\(596\) −5.32051 3.07180i −0.217937 0.125826i
\(597\) −6.00000 −0.245564
\(598\) −0.248711 + 0.928203i −0.0101706 + 0.0379571i
\(599\) 10.1244i 0.413670i 0.978376 + 0.206835i \(0.0663163\pi\)
−0.978376 + 0.206835i \(0.933684\pi\)
\(600\) −3.46410 + 3.46410i −0.141421 + 0.141421i
\(601\) 14.7846i 0.603077i −0.953454 0.301538i \(-0.902500\pi\)
0.953454 0.301538i \(-0.0975001\pi\)
\(602\) 3.26795 + 6.73205i 0.133192 + 0.274378i
\(603\) 0 0
\(604\) −15.1962 + 26.3205i −0.618323 + 1.07097i
\(605\) 10.9282i 0.444295i
\(606\) 36.5885 + 9.80385i 1.48630 + 0.398254i
\(607\) −29.1962 −1.18504 −0.592518 0.805557i \(-0.701866\pi\)
−0.592518 + 0.805557i \(0.701866\pi\)
\(608\) 32.7846 8.78461i 1.32959 0.356263i
\(609\) 23.7846 + 27.4641i 0.963801 + 1.11290i
\(610\) 3.46410 12.9282i 0.140257 0.523448i
\(611\) 0.803848i 0.0325202i
\(612\) 0 0
\(613\) −10.0000 −0.403896 −0.201948 0.979396i \(-0.564727\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(614\) 0.633975 2.36603i 0.0255851 0.0954850i
\(615\) 6.00000 0.241943
\(616\) 0.143594 2.00000i 0.00578555 0.0805823i
\(617\) −22.9282 −0.923055 −0.461527 0.887126i \(-0.652698\pi\)
−0.461527 + 0.887126i \(0.652698\pi\)
\(618\) 4.31347 16.0981i 0.173513 0.647560i
\(619\) 0.679492 0.0273111 0.0136555 0.999907i \(-0.495653\pi\)
0.0136555 + 0.999907i \(0.495653\pi\)
\(620\) 6.00000 10.3923i 0.240966 0.417365i
\(621\) 7.60770i 0.305286i
\(622\) 2.87564 10.7321i 0.115303 0.430316i
\(623\) 5.07180 4.39230i 0.203197 0.175974i
\(624\) −2.78461 + 1.60770i −0.111474 + 0.0643593i
\(625\) 1.00000 0.0400000
\(626\) −23.9545 6.41858i −0.957414 0.256538i
\(627\) 2.78461i 0.111207i
\(628\) 7.85641 13.6077i 0.313505 0.543006i
\(629\) 61.1769i 2.43928i
\(630\) 0 0
\(631\) 38.9090i 1.54894i −0.632610 0.774471i \(-0.718016\pi\)
0.632610 0.774471i \(-0.281984\pi\)
\(632\) 29.3205 + 29.3205i 1.16631 + 1.16631i
\(633\) 5.53590i 0.220032i
\(634\) −1.12436 + 4.19615i −0.0446539 + 0.166651i
\(635\) 15.4641 0.613674
\(636\) 6.00000 + 3.46410i 0.237915 + 0.137361i
\(637\) 3.21539 + 0.464102i 0.127398 + 0.0183884i
\(638\) −2.90192 0.777568i −0.114888 0.0307842i
\(639\) 0 0
\(640\) −2.92820 + 10.9282i −0.115747 + 0.431975i
\(641\) 8.92820 0.352643 0.176321 0.984333i \(-0.443580\pi\)
0.176321 + 0.984333i \(0.443580\pi\)
\(642\) −5.66025 1.51666i −0.223392 0.0598578i
\(643\) 7.05256 0.278126 0.139063 0.990284i \(-0.455591\pi\)
0.139063 + 0.990284i \(0.455591\pi\)
\(644\) 7.60770 1.46410i 0.299785 0.0576937i
\(645\) 3.46410 0.136399
\(646\) −52.9808 14.1962i −2.08450 0.558540i
\(647\) −10.3923 −0.408564 −0.204282 0.978912i \(-0.565486\pi\)
−0.204282 + 0.978912i \(0.565486\pi\)
\(648\) 18.0000 18.0000i 0.707107 0.707107i
\(649\) 0.928203i 0.0364352i
\(650\) 0.633975 + 0.169873i 0.0248665 + 0.00666297i
\(651\) −18.0000 20.7846i −0.705476 0.814613i
\(652\) 20.7846 36.0000i 0.813988 1.40987i
\(653\) 17.6077 0.689042 0.344521 0.938779i \(-0.388041\pi\)
0.344521 + 0.938779i \(0.388041\pi\)
\(654\) −1.31347 + 4.90192i −0.0513606 + 0.191680i
\(655\) 2.53590i 0.0990857i
\(656\) 12.0000 6.92820i 0.468521 0.270501i
\(657\) 0 0
\(658\) −5.83013 + 2.83013i −0.227282 + 0.110330i
\(659\) 31.1962i 1.21523i 0.794232 + 0.607615i \(0.207874\pi\)
−0.794232 + 0.607615i \(0.792126\pi\)
\(660\) −0.803848 0.464102i −0.0312897 0.0180651i
\(661\) 39.7128i 1.54465i 0.635228 + 0.772325i \(0.280906\pi\)
−0.635228 + 0.772325i \(0.719094\pi\)
\(662\) 36.0526 + 9.66025i 1.40122 + 0.375456i
\(663\) 5.19615 0.201802
\(664\) −30.9282 + 30.9282i −1.20025 + 1.20025i
\(665\) −12.0000 + 10.3923i −0.465340 + 0.402996i
\(666\) 0 0
\(667\) 11.6077i 0.449452i
\(668\) 9.00000 + 5.19615i 0.348220 + 0.201045i
\(669\) 23.7846 0.919566
\(670\) 1.26795 4.73205i 0.0489852 0.182815i
\(671\) 2.53590 0.0978973
\(672\) 21.4641 + 14.5359i 0.827996 + 0.560734i
\(673\) −13.1769 −0.507933 −0.253966 0.967213i \(-0.581735\pi\)
−0.253966 + 0.967213i \(0.581735\pi\)
\(674\) 0 0
\(675\) −5.19615 −0.200000
\(676\) −22.1436 12.7846i −0.851677 0.491716i
\(677\) 25.3923i 0.975906i −0.872870 0.487953i \(-0.837744\pi\)
0.872870 0.487953i \(-0.162256\pi\)
\(678\) −3.46410 + 12.9282i −0.133038 + 0.496505i
\(679\) −26.7846 + 23.1962i −1.02790 + 0.890187i
\(680\) 12.9282 12.9282i 0.495774 0.495774i
\(681\) −35.7846 −1.37127
\(682\) 2.19615 + 0.588457i 0.0840950 + 0.0225332i
\(683\) 7.32051i 0.280111i −0.990144 0.140056i \(-0.955272\pi\)
0.990144 0.140056i \(-0.0447282\pi\)
\(684\) 0 0
\(685\) 20.3923i 0.779150i
\(686\) −7.95448 24.9545i −0.303704 0.952767i
\(687\) 14.7846i 0.564068i
\(688\) 6.92820 4.00000i 0.264135 0.152499i
\(689\) 0.928203i 0.0353617i
\(690\) 0.928203 3.46410i 0.0353361 0.131876i
\(691\) −22.6410 −0.861305 −0.430652 0.902518i \(-0.641717\pi\)
−0.430652 + 0.902518i \(0.641717\pi\)
\(692\) −14.3205 + 24.8038i −0.544384 + 0.942901i
\(693\) 0 0
\(694\) −46.7846 12.5359i −1.77592 0.475856i
\(695\) 6.92820i 0.262802i
\(696\) 27.4641 27.4641i 1.04102 1.04102i
\(697\) −22.3923 −0.848169
\(698\) −7.26795 1.94744i −0.275096 0.0737117i
\(699\) 15.7128 0.594313
\(700\) −1.00000 5.19615i −0.0377964 0.196396i
\(701\) −37.7846 −1.42711 −0.713553 0.700602i \(-0.752915\pi\)
−0.713553 + 0.700602i \(0.752915\pi\)
\(702\) −3.29423 0.882686i −0.124333 0.0333148i
\(703\) −56.7846 −2.14167
\(704\) −2.14359 −0.0807897
\(705\) 3.00000i 0.112987i
\(706\) −10.0981 2.70577i −0.380046 0.101833i
\(707\) −30.9282 + 26.7846i −1.16317 + 1.00734i
\(708\) −10.3923 6.00000i −0.390567 0.225494i
\(709\) 21.0000 0.788672 0.394336 0.918966i \(-0.370975\pi\)
0.394336 + 0.918966i \(0.370975\pi\)
\(710\) −2.73205 + 10.1962i −0.102532 + 0.382655i
\(711\) 0 0
\(712\) −5.07180 5.07180i −0.190074 0.190074i
\(713\) 8.78461i 0.328986i
\(714\) −18.2942 37.6865i −0.684644 1.41038i
\(715\) 0.124356i 0.00465064i
\(716\) 6.39230 11.0718i 0.238892 0.413772i
\(717\) 41.5359i 1.55119i
\(718\) −34.5885 9.26795i −1.29083 0.345877i
\(719\) 38.5359 1.43715 0.718573 0.695451i \(-0.244795\pi\)
0.718573 + 0.695451i \(0.244795\pi\)
\(720\) 0 0
\(721\) 11.7846 + 13.6077i 0.438882 + 0.506777i
\(722\) 6.22243 23.2224i 0.231575 0.864249i
\(723\) 28.3923i 1.05592i
\(724\) −0.928203 + 1.60770i −0.0344964 + 0.0597495i
\(725\) −7.92820 −0.294446
\(726\) −6.92820 + 25.8564i −0.257130 + 0.959621i
\(727\) −13.6077 −0.504681 −0.252341 0.967638i \(-0.581200\pi\)
−0.252341 + 0.967638i \(0.581200\pi\)
\(728\) 0.248711 3.46410i 0.00921785 0.128388i
\(729\) 27.0000 1.00000
\(730\) 4.73205 17.6603i 0.175141 0.653635i
\(731\) −12.9282 −0.478167
\(732\) −16.3923 + 28.3923i −0.605877 + 1.04941i
\(733\) 11.5359i 0.426088i 0.977043 + 0.213044i \(0.0683378\pi\)
−0.977043 + 0.213044i \(0.931662\pi\)
\(734\) 4.34679 16.2224i 0.160443 0.598781i
\(735\) −12.0000 1.73205i −0.442627 0.0638877i
\(736\) −2.14359 8.00000i −0.0790139 0.294884i
\(737\) 0.928203 0.0341908
\(738\) 0 0
\(739\) 4.26795i 0.156999i 0.996914 + 0.0784995i \(0.0250129\pi\)
−0.996914 + 0.0784995i \(0.974987\pi\)
\(740\) 9.46410 16.3923i 0.347907 0.602593i
\(741\) 4.82309i 0.177180i
\(742\) −6.73205 + 3.26795i −0.247141 + 0.119970i
\(743\) 30.3923i 1.11499i −0.830182 0.557493i \(-0.811763\pi\)
0.830182 0.557493i \(-0.188237\pi\)
\(744\) −20.7846 + 20.7846i −0.762001 + 0.762001i
\(745\) 3.07180i 0.112542i
\(746\) −1.32051 + 4.92820i −0.0483472 + 0.180434i
\(747\) 0 0
\(748\) 3.00000 + 1.73205i 0.109691 + 0.0633300i
\(749\) 4.78461 4.14359i 0.174826 0.151404i
\(750\) −2.36603 0.633975i −0.0863950 0.0231495i
\(751\) 25.5885i 0.933736i 0.884327 + 0.466868i \(0.154618\pi\)
−0.884327 + 0.466868i \(0.845382\pi\)
\(752\) 3.46410 + 6.00000i 0.126323 + 0.218797i
\(753\) 44.7846 1.63204
\(754\) −5.02628 1.34679i −0.183046 0.0490471i
\(755\) −15.1962 −0.553045
\(756\) 5.19615 + 27.0000i 0.188982 + 0.981981i
\(757\) 37.8564 1.37591 0.687957 0.725751i \(-0.258508\pi\)
0.687957 + 0.725751i \(0.258508\pi\)
\(758\) −7.66025 2.05256i −0.278233 0.0745523i
\(759\) 0.679492 0.0246640
\(760\) 12.0000 + 12.0000i 0.435286 + 0.435286i
\(761\) 42.2487i 1.53151i −0.643130 0.765757i \(-0.722364\pi\)
0.643130 0.765757i \(-0.277636\pi\)
\(762\) −36.5885 9.80385i −1.32546 0.355156i
\(763\) −3.58846 4.14359i −0.129911 0.150008i
\(764\) −7.19615 + 12.4641i −0.260348 + 0.450935i
\(765\) 0 0
\(766\) 10.0526 37.5167i 0.363214 1.35553i
\(767\) 1.60770i 0.0580505i
\(768\) 13.8564 24.0000i 0.500000 0.866025i
\(769\) 18.0000i 0.649097i 0.945869 + 0.324548i \(0.105212\pi\)
−0.945869 + 0.324548i \(0.894788\pi\)
\(770\) 0.901924 0.437822i 0.0325031 0.0157780i
\(771\) 10.3923i 0.374270i
\(772\) 16.3923 + 9.46410i 0.589972 + 0.340620i
\(773\) 5.53590i 0.199112i −0.995032 0.0995562i \(-0.968258\pi\)
0.995032 0.0995562i \(-0.0317423\pi\)
\(774\) 0 0
\(775\) 6.00000 0.215526
\(776\) 26.7846 + 26.7846i 0.961511 + 0.961511i
\(777\) −28.3923 32.7846i −1.01857 1.17614i
\(778\) −7.63397 + 28.4904i −0.273691 + 1.02143i
\(779\) 20.7846i 0.744686i
\(780\) −1.39230 0.803848i −0.0498525 0.0287824i
\(781\) −2.00000