Properties

Label 546.2.e.g.545.6
Level $546$
Weight $2$
Character 546.545
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.303595776.1
Defining polynomial: \(x^{8} + 5 x^{6} + 16 x^{4} + 45 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 545.6
Root \(0.396143 + 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 546.545
Dual form 546.2.e.g.545.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.396143 + 1.68614i) q^{3} +1.00000 q^{4} -2.37228i q^{5} +(0.396143 + 1.68614i) q^{6} +(0.792287 + 2.52434i) q^{7} +1.00000 q^{8} +(-2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.396143 + 1.68614i) q^{3} +1.00000 q^{4} -2.37228i q^{5} +(0.396143 + 1.68614i) q^{6} +(0.792287 + 2.52434i) q^{7} +1.00000 q^{8} +(-2.68614 + 1.33591i) q^{9} -2.37228i q^{10} +5.74456 q^{11} +(0.396143 + 1.68614i) q^{12} +(-3.46410 + 1.00000i) q^{13} +(0.792287 + 2.52434i) q^{14} +(4.00000 - 0.939764i) q^{15} +1.00000 q^{16} -2.52434 q^{17} +(-2.68614 + 1.33591i) q^{18} +7.57301 q^{19} -2.37228i q^{20} +(-3.94253 + 2.33591i) q^{21} +5.74456 q^{22} +6.78073i q^{23} +(0.396143 + 1.68614i) q^{24} -0.627719 q^{25} +(-3.46410 + 1.00000i) q^{26} +(-3.31662 - 4.00000i) q^{27} +(0.792287 + 2.52434i) q^{28} -7.57301i q^{29} +(4.00000 - 0.939764i) q^{30} -5.84096 q^{31} +1.00000 q^{32} +(2.27567 + 9.68614i) q^{33} -2.52434 q^{34} +(5.98844 - 1.87953i) q^{35} +(-2.68614 + 1.33591i) q^{36} -4.90120i q^{37} +7.57301 q^{38} +(-3.05842 - 5.44482i) q^{39} -2.37228i q^{40} -2.62772i q^{41} +(-3.94253 + 2.33591i) q^{42} -8.37228 q^{43} +5.74456 q^{44} +(3.16915 + 6.37228i) q^{45} +6.78073i q^{46} +4.62772i q^{47} +(0.396143 + 1.68614i) q^{48} +(-5.74456 + 4.00000i) q^{49} -0.627719 q^{50} +(-1.00000 - 4.25639i) q^{51} +(-3.46410 + 1.00000i) q^{52} -3.16915i q^{53} +(-3.31662 - 4.00000i) q^{54} -13.6277i q^{55} +(0.792287 + 2.52434i) q^{56} +(3.00000 + 12.7692i) q^{57} -7.57301i q^{58} -8.74456i q^{59} +(4.00000 - 0.939764i) q^{60} +3.74456i q^{61} -5.84096 q^{62} +(-5.50048 - 5.72230i) q^{63} +1.00000 q^{64} +(2.37228 + 8.21782i) q^{65} +(2.27567 + 9.68614i) q^{66} -2.67181i q^{67} -2.52434 q^{68} +(-11.4333 + 2.68614i) q^{69} +(5.98844 - 1.87953i) q^{70} -2.00000 q^{71} +(-2.68614 + 1.33591i) q^{72} +3.61158 q^{73} -4.90120i q^{74} +(-0.248667 - 1.05842i) q^{75} +7.57301 q^{76} +(4.55134 + 14.5012i) q^{77} +(-3.05842 - 5.44482i) q^{78} -9.37228 q^{79} -2.37228i q^{80} +(5.43070 - 7.17687i) q^{81} -2.62772i q^{82} -4.74456i q^{83} +(-3.94253 + 2.33591i) q^{84} +5.98844i q^{85} -8.37228 q^{86} +(12.7692 - 3.00000i) q^{87} +5.74456 q^{88} -10.0000i q^{89} +(3.16915 + 6.37228i) q^{90} +(-5.26890 - 7.95228i) q^{91} +6.78073i q^{92} +(-2.31386 - 9.84868i) q^{93} +4.62772i q^{94} -17.9653i q^{95} +(0.396143 + 1.68614i) q^{96} -7.42554 q^{97} +(-5.74456 + 4.00000i) q^{98} +(-15.4307 + 7.67420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} + 8q^{4} + 8q^{8} - 10q^{9} + O(q^{10}) \) \( 8q + 8q^{2} + 8q^{4} + 8q^{8} - 10q^{9} + 32q^{15} + 8q^{16} - 10q^{18} + 14q^{21} - 28q^{25} + 32q^{30} + 8q^{32} - 10q^{36} + 10q^{39} + 14q^{42} - 44q^{43} - 28q^{50} - 8q^{51} + 24q^{57} + 32q^{60} - 4q^{63} + 8q^{64} - 4q^{65} - 16q^{71} - 10q^{72} + 10q^{78} - 52q^{79} - 14q^{81} + 14q^{84} - 44q^{86} + 24q^{91} - 30q^{93} - 66q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.396143 + 1.68614i 0.228714 + 0.973494i
\(4\) 1.00000 0.500000
\(5\) 2.37228i 1.06092i −0.847711 0.530458i \(-0.822020\pi\)
0.847711 0.530458i \(-0.177980\pi\)
\(6\) 0.396143 + 1.68614i 0.161725 + 0.688364i
\(7\) 0.792287 + 2.52434i 0.299456 + 0.954110i
\(8\) 1.00000 0.353553
\(9\) −2.68614 + 1.33591i −0.895380 + 0.445302i
\(10\) 2.37228i 0.750181i
\(11\) 5.74456 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0.396143 + 1.68614i 0.114357 + 0.486747i
\(13\) −3.46410 + 1.00000i −0.960769 + 0.277350i
\(14\) 0.792287 + 2.52434i 0.211748 + 0.674658i
\(15\) 4.00000 0.939764i 1.03280 0.242646i
\(16\) 1.00000 0.250000
\(17\) −2.52434 −0.612242 −0.306121 0.951993i \(-0.599031\pi\)
−0.306121 + 0.951993i \(0.599031\pi\)
\(18\) −2.68614 + 1.33591i −0.633129 + 0.314876i
\(19\) 7.57301 1.73737 0.868684 0.495366i \(-0.164966\pi\)
0.868684 + 0.495366i \(0.164966\pi\)
\(20\) 2.37228i 0.530458i
\(21\) −3.94253 + 2.33591i −0.860330 + 0.509737i
\(22\) 5.74456 1.22474
\(23\) 6.78073i 1.41388i 0.707274 + 0.706940i \(0.249925\pi\)
−0.707274 + 0.706940i \(0.750075\pi\)
\(24\) 0.396143 + 1.68614i 0.0808625 + 0.344182i
\(25\) −0.627719 −0.125544
\(26\) −3.46410 + 1.00000i −0.679366 + 0.196116i
\(27\) −3.31662 4.00000i −0.638285 0.769800i
\(28\) 0.792287 + 2.52434i 0.149728 + 0.477055i
\(29\) 7.57301i 1.40627i −0.711055 0.703137i \(-0.751782\pi\)
0.711055 0.703137i \(-0.248218\pi\)
\(30\) 4.00000 0.939764i 0.730297 0.171577i
\(31\) −5.84096 −1.04907 −0.524534 0.851390i \(-0.675760\pi\)
−0.524534 + 0.851390i \(0.675760\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.27567 + 9.68614i 0.396143 + 1.68614i
\(34\) −2.52434 −0.432920
\(35\) 5.98844 1.87953i 1.01223 0.317698i
\(36\) −2.68614 + 1.33591i −0.447690 + 0.222651i
\(37\) 4.90120i 0.805752i −0.915255 0.402876i \(-0.868011\pi\)
0.915255 0.402876i \(-0.131989\pi\)
\(38\) 7.57301 1.22850
\(39\) −3.05842 5.44482i −0.489739 0.871869i
\(40\) 2.37228i 0.375091i
\(41\) 2.62772i 0.410381i −0.978722 0.205190i \(-0.934219\pi\)
0.978722 0.205190i \(-0.0657813\pi\)
\(42\) −3.94253 + 2.33591i −0.608345 + 0.360438i
\(43\) −8.37228 −1.27676 −0.638380 0.769721i \(-0.720395\pi\)
−0.638380 + 0.769721i \(0.720395\pi\)
\(44\) 5.74456 0.866025
\(45\) 3.16915 + 6.37228i 0.472429 + 0.949924i
\(46\) 6.78073i 0.999764i
\(47\) 4.62772i 0.675022i 0.941322 + 0.337511i \(0.109585\pi\)
−0.941322 + 0.337511i \(0.890415\pi\)
\(48\) 0.396143 + 1.68614i 0.0571784 + 0.243373i
\(49\) −5.74456 + 4.00000i −0.820652 + 0.571429i
\(50\) −0.627719 −0.0887728
\(51\) −1.00000 4.25639i −0.140028 0.596014i
\(52\) −3.46410 + 1.00000i −0.480384 + 0.138675i
\(53\) 3.16915i 0.435316i −0.976025 0.217658i \(-0.930158\pi\)
0.976025 0.217658i \(-0.0698417\pi\)
\(54\) −3.31662 4.00000i −0.451335 0.544331i
\(55\) 13.6277i 1.83756i
\(56\) 0.792287 + 2.52434i 0.105874 + 0.337329i
\(57\) 3.00000 + 12.7692i 0.397360 + 1.69132i
\(58\) 7.57301i 0.994385i
\(59\) 8.74456i 1.13845i −0.822183 0.569223i \(-0.807244\pi\)
0.822183 0.569223i \(-0.192756\pi\)
\(60\) 4.00000 0.939764i 0.516398 0.121323i
\(61\) 3.74456i 0.479442i 0.970842 + 0.239721i \(0.0770560\pi\)
−0.970842 + 0.239721i \(0.922944\pi\)
\(62\) −5.84096 −0.741803
\(63\) −5.50048 5.72230i −0.692995 0.720943i
\(64\) 1.00000 0.125000
\(65\) 2.37228 + 8.21782i 0.294245 + 1.01930i
\(66\) 2.27567 + 9.68614i 0.280116 + 1.19228i
\(67\) 2.67181i 0.326414i −0.986592 0.163207i \(-0.947816\pi\)
0.986592 0.163207i \(-0.0521839\pi\)
\(68\) −2.52434 −0.306121
\(69\) −11.4333 + 2.68614i −1.37640 + 0.323373i
\(70\) 5.98844 1.87953i 0.715755 0.224647i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) −2.68614 + 1.33591i −0.316565 + 0.157438i
\(73\) 3.61158 0.422703 0.211352 0.977410i \(-0.432213\pi\)
0.211352 + 0.977410i \(0.432213\pi\)
\(74\) 4.90120i 0.569753i
\(75\) −0.248667 1.05842i −0.0287136 0.122216i
\(76\) 7.57301 0.868684
\(77\) 4.55134 + 14.5012i 0.518674 + 1.65257i
\(78\) −3.05842 5.44482i −0.346298 0.616504i
\(79\) −9.37228 −1.05446 −0.527232 0.849721i \(-0.676770\pi\)
−0.527232 + 0.849721i \(0.676770\pi\)
\(80\) 2.37228i 0.265229i
\(81\) 5.43070 7.17687i 0.603411 0.797430i
\(82\) 2.62772i 0.290183i
\(83\) 4.74456i 0.520783i −0.965503 0.260392i \(-0.916148\pi\)
0.965503 0.260392i \(-0.0838517\pi\)
\(84\) −3.94253 + 2.33591i −0.430165 + 0.254868i
\(85\) 5.98844i 0.649537i
\(86\) −8.37228 −0.902806
\(87\) 12.7692 3.00000i 1.36900 0.321634i
\(88\) 5.74456 0.612372
\(89\) 10.0000i 1.06000i −0.847998 0.529999i \(-0.822192\pi\)
0.847998 0.529999i \(-0.177808\pi\)
\(90\) 3.16915 + 6.37228i 0.334058 + 0.671697i
\(91\) −5.26890 7.95228i −0.552331 0.833625i
\(92\) 6.78073i 0.706940i
\(93\) −2.31386 9.84868i −0.239936 1.02126i
\(94\) 4.62772i 0.477313i
\(95\) 17.9653i 1.84320i
\(96\) 0.396143 + 1.68614i 0.0404312 + 0.172091i
\(97\) −7.42554 −0.753949 −0.376975 0.926224i \(-0.623036\pi\)
−0.376975 + 0.926224i \(0.623036\pi\)
\(98\) −5.74456 + 4.00000i −0.580288 + 0.404061i
\(99\) −15.4307 + 7.67420i −1.55084 + 0.771286i
\(100\) −0.627719 −0.0627719
\(101\) 5.54601 0.551849 0.275924 0.961179i \(-0.411016\pi\)
0.275924 + 0.961179i \(0.411016\pi\)
\(102\) −1.00000 4.25639i −0.0990148 0.421445i
\(103\) 1.62772i 0.160384i 0.996779 + 0.0801919i \(0.0255533\pi\)
−0.996779 + 0.0801919i \(0.974447\pi\)
\(104\) −3.46410 + 1.00000i −0.339683 + 0.0980581i
\(105\) 5.54143 + 9.35279i 0.540788 + 0.912739i
\(106\) 3.16915i 0.307815i
\(107\) 3.75906i 0.363402i −0.983354 0.181701i \(-0.941840\pi\)
0.983354 0.181701i \(-0.0581602\pi\)
\(108\) −3.31662 4.00000i −0.319142 0.384900i
\(109\) 9.74749i 0.933641i −0.884352 0.466820i \(-0.845399\pi\)
0.884352 0.466820i \(-0.154601\pi\)
\(110\) 13.6277i 1.29935i
\(111\) 8.26411 1.94158i 0.784395 0.184286i
\(112\) 0.792287 + 2.52434i 0.0748641 + 0.238528i
\(113\) 10.8896i 1.02441i −0.858863 0.512205i \(-0.828829\pi\)
0.858863 0.512205i \(-0.171171\pi\)
\(114\) 3.00000 + 12.7692i 0.280976 + 1.19594i
\(115\) 16.0858 1.50001
\(116\) 7.57301i 0.703137i
\(117\) 7.96916 7.31386i 0.736749 0.676167i
\(118\) 8.74456i 0.805002i
\(119\) −2.00000 6.37228i −0.183340 0.584146i
\(120\) 4.00000 0.939764i 0.365148 0.0857883i
\(121\) 22.0000 2.00000
\(122\) 3.74456i 0.339017i
\(123\) 4.43070 1.04095i 0.399503 0.0938596i
\(124\) −5.84096 −0.524534
\(125\) 10.3723i 0.927725i
\(126\) −5.50048 5.72230i −0.490021 0.509783i
\(127\) −4.62772 −0.410644 −0.205322 0.978695i \(-0.565824\pi\)
−0.205322 + 0.978695i \(0.565824\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.31662 14.1168i −0.292013 1.24292i
\(130\) 2.37228 + 8.21782i 0.208063 + 0.720751i
\(131\) 12.6217 1.10276 0.551381 0.834254i \(-0.314101\pi\)
0.551381 + 0.834254i \(0.314101\pi\)
\(132\) 2.27567 + 9.68614i 0.198072 + 0.843070i
\(133\) 6.00000 + 19.1168i 0.520266 + 1.65764i
\(134\) 2.67181i 0.230810i
\(135\) −9.48913 + 7.86797i −0.816694 + 0.677167i
\(136\) −2.52434 −0.216460
\(137\) −0.883156 −0.0754531 −0.0377266 0.999288i \(-0.512012\pi\)
−0.0377266 + 0.999288i \(0.512012\pi\)
\(138\) −11.4333 + 2.68614i −0.973264 + 0.228659i
\(139\) 16.7446i 1.42026i 0.704073 + 0.710128i \(0.251363\pi\)
−0.704073 + 0.710128i \(0.748637\pi\)
\(140\) 5.98844 1.87953i 0.506116 0.158849i
\(141\) −7.80298 + 1.83324i −0.657130 + 0.154387i
\(142\) −2.00000 −0.167836
\(143\) −19.8997 + 5.74456i −1.66410 + 0.480384i
\(144\) −2.68614 + 1.33591i −0.223845 + 0.111326i
\(145\) −17.9653 −1.49194
\(146\) 3.61158 0.298896
\(147\) −9.02023 8.10157i −0.743976 0.668206i
\(148\) 4.90120i 0.402876i
\(149\) −13.3723 −1.09550 −0.547750 0.836642i \(-0.684515\pi\)
−0.547750 + 0.836642i \(0.684515\pi\)
\(150\) −0.248667 1.05842i −0.0203035 0.0864198i
\(151\) 1.23472i 0.100480i 0.998737 + 0.0502399i \(0.0159986\pi\)
−0.998737 + 0.0502399i \(0.984001\pi\)
\(152\) 7.57301 0.614252
\(153\) 6.78073 3.37228i 0.548189 0.272633i
\(154\) 4.55134 + 14.5012i 0.366758 + 1.16854i
\(155\) 13.8564i 1.11297i
\(156\) −3.05842 5.44482i −0.244870 0.435934i
\(157\) 19.7446i 1.57579i 0.615811 + 0.787894i \(0.288828\pi\)
−0.615811 + 0.787894i \(0.711172\pi\)
\(158\) −9.37228 −0.745619
\(159\) 5.34363 1.25544i 0.423777 0.0995627i
\(160\) 2.37228i 0.187545i
\(161\) −17.1168 + 5.37228i −1.34900 + 0.423395i
\(162\) 5.43070 7.17687i 0.426676 0.563868i
\(163\) 11.6819i 0.914999i −0.889210 0.457499i \(-0.848745\pi\)
0.889210 0.457499i \(-0.151255\pi\)
\(164\) 2.62772i 0.205190i
\(165\) 22.9783 5.39853i 1.78885 0.420275i
\(166\) 4.74456i 0.368249i
\(167\) 18.3723i 1.42169i 0.703349 + 0.710845i \(0.251687\pi\)
−0.703349 + 0.710845i \(0.748313\pi\)
\(168\) −3.94253 + 2.33591i −0.304173 + 0.180219i
\(169\) 11.0000 6.92820i 0.846154 0.532939i
\(170\) 5.98844i 0.459292i
\(171\) −20.3422 + 10.1168i −1.55561 + 0.773654i
\(172\) −8.37228 −0.638380
\(173\) −23.9538 −1.82117 −0.910585 0.413321i \(-0.864369\pi\)
−0.910585 + 0.413321i \(0.864369\pi\)
\(174\) 12.7692 3.00000i 0.968028 0.227429i
\(175\) −0.497333 1.58457i −0.0375949 0.119783i
\(176\) 5.74456 0.433013
\(177\) 14.7446 3.46410i 1.10827 0.260378i
\(178\) 10.0000i 0.749532i
\(179\) 6.33830i 0.473746i −0.971541 0.236873i \(-0.923877\pi\)
0.971541 0.236873i \(-0.0761226\pi\)
\(180\) 3.16915 + 6.37228i 0.236214 + 0.474962i
\(181\) 14.6277i 1.08727i 0.839322 + 0.543635i \(0.182952\pi\)
−0.839322 + 0.543635i \(0.817048\pi\)
\(182\) −5.26890 7.95228i −0.390557 0.589462i
\(183\) −6.31386 + 1.48338i −0.466734 + 0.109655i
\(184\) 6.78073i 0.499882i
\(185\) −11.6270 −0.854836
\(186\) −2.31386 9.84868i −0.169660 0.722141i
\(187\) −14.5012 −1.06043
\(188\) 4.62772i 0.337511i
\(189\) 7.46963 11.5414i 0.543336 0.839515i
\(190\) 17.9653i 1.30334i
\(191\) 19.5499i 1.41458i 0.706923 + 0.707290i \(0.250083\pi\)
−0.706923 + 0.707290i \(0.749917\pi\)
\(192\) 0.396143 + 1.68614i 0.0285892 + 0.121687i
\(193\) 20.7846i 1.49611i 0.663637 + 0.748054i \(0.269012\pi\)
−0.663637 + 0.748054i \(0.730988\pi\)
\(194\) −7.42554 −0.533122
\(195\) −12.9166 + 7.25544i −0.924980 + 0.519573i
\(196\) −5.74456 + 4.00000i −0.410326 + 0.285714i
\(197\) 3.88316 0.276663 0.138332 0.990386i \(-0.455826\pi\)
0.138332 + 0.990386i \(0.455826\pi\)
\(198\) −15.4307 + 7.67420i −1.09661 + 0.545382i
\(199\) 5.11684i 0.362723i 0.983416 + 0.181362i \(0.0580505\pi\)
−0.983416 + 0.181362i \(0.941950\pi\)
\(200\) −0.627719 −0.0443864
\(201\) 4.50506 1.05842i 0.317762 0.0746553i
\(202\) 5.54601 0.390216
\(203\) 19.1168 6.00000i 1.34174 0.421117i
\(204\) −1.00000 4.25639i −0.0700140 0.298007i
\(205\) −6.23369 −0.435380
\(206\) 1.62772i 0.113409i
\(207\) −9.05842 18.2140i −0.629604 1.26596i
\(208\) −3.46410 + 1.00000i −0.240192 + 0.0693375i
\(209\) 43.5036 3.00921
\(210\) 5.54143 + 9.35279i 0.382395 + 0.645404i
\(211\) 11.6277 0.800485 0.400243 0.916409i \(-0.368926\pi\)
0.400243 + 0.916409i \(0.368926\pi\)
\(212\) 3.16915i 0.217658i
\(213\) −0.792287 3.37228i −0.0542866 0.231065i
\(214\) 3.75906i 0.256964i
\(215\) 19.8614i 1.35454i
\(216\) −3.31662 4.00000i −0.225668 0.272166i
\(217\) −4.62772 14.7446i −0.314150 1.00093i
\(218\) 9.74749i 0.660184i
\(219\) 1.43070 + 6.08963i 0.0966780 + 0.411499i
\(220\) 13.6277i 0.918781i
\(221\) 8.74456 2.52434i 0.588223 0.169805i
\(222\) 8.26411 1.94158i 0.554651 0.130310i
\(223\) −9.30506 −0.623113 −0.311557 0.950228i \(-0.600850\pi\)
−0.311557 + 0.950228i \(0.600850\pi\)
\(224\) 0.792287 + 2.52434i 0.0529369 + 0.168664i
\(225\) 1.68614 0.838574i 0.112409 0.0559049i
\(226\) 10.8896i 0.724368i
\(227\) 11.4891i 0.762560i −0.924460 0.381280i \(-0.875483\pi\)
0.924460 0.381280i \(-0.124517\pi\)
\(228\) 3.00000 + 12.7692i 0.198680 + 0.845659i
\(229\) 1.58457 0.104712 0.0523558 0.998628i \(-0.483327\pi\)
0.0523558 + 0.998628i \(0.483327\pi\)
\(230\) 16.0858 1.06067
\(231\) −22.6481 + 13.4188i −1.49014 + 0.882890i
\(232\) 7.57301i 0.497193i
\(233\) 12.4742i 0.817213i 0.912711 + 0.408606i \(0.133985\pi\)
−0.912711 + 0.408606i \(0.866015\pi\)
\(234\) 7.96916 7.31386i 0.520960 0.478122i
\(235\) 10.9783 0.716142
\(236\) 8.74456i 0.569223i
\(237\) −3.71277 15.8030i −0.241170 1.02651i
\(238\) −2.00000 6.37228i −0.129641 0.413054i
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 4.00000 0.939764i 0.258199 0.0606615i
\(241\) 23.3639 1.50500 0.752499 0.658593i \(-0.228848\pi\)
0.752499 + 0.658593i \(0.228848\pi\)
\(242\) 22.0000 1.41421
\(243\) 14.2525 + 6.31386i 0.914302 + 0.405034i
\(244\) 3.74456i 0.239721i
\(245\) 9.48913 + 13.6277i 0.606238 + 0.870643i
\(246\) 4.43070 1.04095i 0.282491 0.0663688i
\(247\) −26.2337 + 7.57301i −1.66921 + 0.481859i
\(248\) −5.84096 −0.370901
\(249\) 8.00000 1.87953i 0.506979 0.119110i
\(250\) 10.3723i 0.656001i
\(251\) −0.147477 −0.00930865 −0.00465433 0.999989i \(-0.501482\pi\)
−0.00465433 + 0.999989i \(0.501482\pi\)
\(252\) −5.50048 5.72230i −0.346497 0.360471i
\(253\) 38.9523i 2.44891i
\(254\) −4.62772 −0.290369
\(255\) −10.0974 + 2.37228i −0.632321 + 0.148558i
\(256\) 1.00000 0.0625000
\(257\) −12.2718 −0.765496 −0.382748 0.923853i \(-0.625022\pi\)
−0.382748 + 0.923853i \(0.625022\pi\)
\(258\) −3.31662 14.1168i −0.206484 0.878876i
\(259\) 12.3723 3.88316i 0.768776 0.241288i
\(260\) 2.37228 + 8.21782i 0.147123 + 0.509648i
\(261\) 10.1168 + 20.3422i 0.626217 + 1.25915i
\(262\) 12.6217 0.779771
\(263\) 20.4897i 1.26345i −0.775194 0.631723i \(-0.782348\pi\)
0.775194 0.631723i \(-0.217652\pi\)
\(264\) 2.27567 + 9.68614i 0.140058 + 0.596141i
\(265\) −7.51811 −0.461834
\(266\) 6.00000 + 19.1168i 0.367884 + 1.17213i
\(267\) 16.8614 3.96143i 1.03190 0.242436i
\(268\) 2.67181i 0.163207i
\(269\) 4.55134 0.277500 0.138750 0.990327i \(-0.455692\pi\)
0.138750 + 0.990327i \(0.455692\pi\)
\(270\) −9.48913 + 7.86797i −0.577490 + 0.478829i
\(271\) 14.6487 0.889845 0.444922 0.895569i \(-0.353231\pi\)
0.444922 + 0.895569i \(0.353231\pi\)
\(272\) −2.52434 −0.153060
\(273\) 11.3214 12.0343i 0.685203 0.728352i
\(274\) −0.883156 −0.0533534
\(275\) −3.60597 −0.217448
\(276\) −11.4333 + 2.68614i −0.688201 + 0.161687i
\(277\) −5.48913 −0.329810 −0.164905 0.986309i \(-0.552732\pi\)
−0.164905 + 0.986309i \(0.552732\pi\)
\(278\) 16.7446i 1.00427i
\(279\) 15.6896 7.80298i 0.939315 0.467152i
\(280\) 5.98844 1.87953i 0.357878 0.112323i
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) −7.80298 + 1.83324i −0.464661 + 0.109168i
\(283\) 5.37228i 0.319349i −0.987170 0.159674i \(-0.948956\pi\)
0.987170 0.159674i \(-0.0510445\pi\)
\(284\) −2.00000 −0.118678
\(285\) 30.2921 7.11684i 1.79435 0.421565i
\(286\) −19.8997 + 5.74456i −1.17670 + 0.339683i
\(287\) 6.63325 2.08191i 0.391548 0.122891i
\(288\) −2.68614 + 1.33591i −0.158282 + 0.0787191i
\(289\) −10.6277 −0.625160
\(290\) −17.9653 −1.05496
\(291\) −2.94158 12.5205i −0.172438 0.733965i
\(292\) 3.61158 0.211352
\(293\) 11.4891i 0.671202i 0.942004 + 0.335601i \(0.108939\pi\)
−0.942004 + 0.335601i \(0.891061\pi\)
\(294\) −9.02023 8.10157i −0.526071 0.472493i
\(295\) −20.7446 −1.20780
\(296\) 4.90120i 0.284876i
\(297\) −19.0526 22.9783i −1.10554 1.33333i
\(298\) −13.3723 −0.774635
\(299\) −6.78073 23.4891i −0.392140 1.35841i
\(300\) −0.248667 1.05842i −0.0143568 0.0611080i
\(301\) −6.63325 21.1345i −0.382334 1.21817i
\(302\) 1.23472i 0.0710500i
\(303\) 2.19702 + 9.35135i 0.126215 + 0.537221i
\(304\) 7.57301 0.434342
\(305\) 8.88316 0.508648
\(306\) 6.78073 3.37228i 0.387628 0.192780i
\(307\) 14.5561 0.830762 0.415381 0.909648i \(-0.363648\pi\)
0.415381 + 0.909648i \(0.363648\pi\)
\(308\) 4.55134 + 14.5012i 0.259337 + 0.826284i
\(309\) −2.74456 + 0.644810i −0.156133 + 0.0366820i
\(310\) 13.8564i 0.786991i
\(311\) 10.3923 0.589294 0.294647 0.955606i \(-0.404798\pi\)
0.294647 + 0.955606i \(0.404798\pi\)
\(312\) −3.05842 5.44482i −0.173149 0.308252i
\(313\) 8.74456i 0.494272i 0.968981 + 0.247136i \(0.0794894\pi\)
−0.968981 + 0.247136i \(0.920511\pi\)
\(314\) 19.7446i 1.11425i
\(315\) −13.5749 + 13.0487i −0.764860 + 0.735210i
\(316\) −9.37228 −0.527232
\(317\) 24.8614 1.39636 0.698178 0.715924i \(-0.253994\pi\)
0.698178 + 0.715924i \(0.253994\pi\)
\(318\) 5.34363 1.25544i 0.299656 0.0704014i
\(319\) 43.5036i 2.43574i
\(320\) 2.37228i 0.132615i
\(321\) 6.33830 1.48913i 0.353769 0.0831149i
\(322\) −17.1168 + 5.37228i −0.953884 + 0.299386i
\(323\) −19.1168 −1.06369
\(324\) 5.43070 7.17687i 0.301706 0.398715i
\(325\) 2.17448 0.627719i 0.120619 0.0348196i
\(326\) 11.6819i 0.647002i
\(327\) 16.4356 3.86141i 0.908893 0.213536i
\(328\) 2.62772i 0.145091i
\(329\) −11.6819 + 3.66648i −0.644045 + 0.202140i
\(330\) 22.9783 5.39853i 1.26491 0.297179i
\(331\) 32.6689i 1.79565i 0.440357 + 0.897823i \(0.354852\pi\)
−0.440357 + 0.897823i \(0.645148\pi\)
\(332\) 4.74456i 0.260392i
\(333\) 6.54755 + 13.1653i 0.358803 + 0.721455i
\(334\) 18.3723i 1.00529i
\(335\) −6.33830 −0.346298
\(336\) −3.94253 + 2.33591i −0.215083 + 0.127434i
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) 11.0000 6.92820i 0.598321 0.376845i
\(339\) 18.3615 4.31386i 0.997258 0.234297i
\(340\) 5.98844i 0.324769i
\(341\) −33.5538 −1.81704
\(342\) −20.3422 + 10.1168i −1.09998 + 0.547056i
\(343\) −14.6487 11.3321i −0.790955 0.611874i
\(344\) −8.37228 −0.451403
\(345\) 6.37228 + 27.1229i 0.343072 + 1.46025i
\(346\) −23.9538 −1.28776
\(347\) 25.8333i 1.38680i 0.720551 + 0.693402i \(0.243889\pi\)
−0.720551 + 0.693402i \(0.756111\pi\)
\(348\) 12.7692 3.00000i 0.684499 0.160817i
\(349\) −23.3639 −1.25064 −0.625319 0.780369i \(-0.715031\pi\)
−0.625319 + 0.780369i \(0.715031\pi\)
\(350\) −0.497333 1.58457i −0.0265836 0.0846990i
\(351\) 15.4891 + 10.5398i 0.826748 + 0.562572i
\(352\) 5.74456 0.306186
\(353\) 6.11684i 0.325567i 0.986662 + 0.162783i \(0.0520472\pi\)
−0.986662 + 0.162783i \(0.947953\pi\)
\(354\) 14.7446 3.46410i 0.783665 0.184115i
\(355\) 4.74456i 0.251815i
\(356\) 10.0000i 0.529999i
\(357\) 9.95228 5.89662i 0.526730 0.312082i
\(358\) 6.33830i 0.334989i
\(359\) −28.2337 −1.49012 −0.745059 0.666999i \(-0.767578\pi\)
−0.745059 + 0.666999i \(0.767578\pi\)
\(360\) 3.16915 + 6.37228i 0.167029 + 0.335849i
\(361\) 38.3505 2.01845
\(362\) 14.6277i 0.768816i
\(363\) 8.71516 + 37.0951i 0.457427 + 1.94699i
\(364\) −5.26890 7.95228i −0.276165 0.416812i
\(365\) 8.56768i 0.448453i
\(366\) −6.31386 + 1.48338i −0.330031 + 0.0775377i
\(367\) 6.74456i 0.352063i −0.984385 0.176032i \(-0.943674\pi\)
0.984385 0.176032i \(-0.0563261\pi\)
\(368\) 6.78073i 0.353470i
\(369\) 3.51039 + 7.05842i 0.182744 + 0.367447i
\(370\) −11.6270 −0.604460
\(371\) 8.00000 2.51087i 0.415339 0.130358i
\(372\) −2.31386 9.84868i −0.119968 0.510631i
\(373\) 22.2337 1.15122 0.575608 0.817726i \(-0.304765\pi\)
0.575608 + 0.817726i \(0.304765\pi\)
\(374\) −14.5012 −0.749840
\(375\) 17.4891 4.10891i 0.903135 0.212183i
\(376\) 4.62772i 0.238656i
\(377\) 7.57301 + 26.2337i 0.390030 + 1.35110i
\(378\) 7.46963 11.5414i 0.384196 0.593627i
\(379\) 14.8511i 0.762848i 0.924400 + 0.381424i \(0.124566\pi\)
−0.924400 + 0.381424i \(0.875434\pi\)
\(380\) 17.9653i 0.921601i
\(381\) −1.83324 7.80298i −0.0939198 0.399759i
\(382\) 19.5499i 1.00026i
\(383\) 26.4891i 1.35353i 0.736199 + 0.676766i \(0.236619\pi\)
−0.736199 + 0.676766i \(0.763381\pi\)
\(384\) 0.396143 + 1.68614i 0.0202156 + 0.0860455i
\(385\) 34.4010 10.7971i 1.75324 0.550269i
\(386\) 20.7846i 1.05791i
\(387\) 22.4891 11.1846i 1.14319 0.568545i
\(388\) −7.42554 −0.376975
\(389\) 7.92287i 0.401705i 0.979621 + 0.200853i \(0.0643713\pi\)
−0.979621 + 0.200853i \(0.935629\pi\)
\(390\) −12.9166 + 7.25544i −0.654060 + 0.367393i
\(391\) 17.1168i 0.865636i
\(392\) −5.74456 + 4.00000i −0.290144 + 0.202031i
\(393\) 5.00000 + 21.2819i 0.252217 + 1.07353i
\(394\) 3.88316 0.195631
\(395\) 22.2337i 1.11870i
\(396\) −15.4307 + 7.67420i −0.775422 + 0.385643i
\(397\) −6.63325 −0.332913 −0.166457 0.986049i \(-0.553233\pi\)
−0.166457 + 0.986049i \(0.553233\pi\)
\(398\) 5.11684i 0.256484i
\(399\) −29.8568 + 17.6899i −1.49471 + 0.885601i
\(400\) −0.627719 −0.0313859
\(401\) −16.9783 −0.847853 −0.423927 0.905697i \(-0.639349\pi\)
−0.423927 + 0.905697i \(0.639349\pi\)
\(402\) 4.50506 1.05842i 0.224692 0.0527893i
\(403\) 20.2337 5.84096i 1.00791 0.290959i
\(404\) 5.54601 0.275924
\(405\) −17.0256 12.8832i −0.846007 0.640169i
\(406\) 19.1168 6.00000i 0.948753 0.297775i
\(407\) 28.1552i 1.39560i
\(408\) −1.00000 4.25639i −0.0495074 0.210723i
\(409\) 6.57835 0.325278 0.162639 0.986686i \(-0.447999\pi\)
0.162639 + 0.986686i \(0.447999\pi\)
\(410\) −6.23369 −0.307860
\(411\) −0.349857 1.48913i −0.0172571 0.0734531i
\(412\) 1.62772i 0.0801919i
\(413\) 22.0742 6.92820i 1.08620 0.340915i
\(414\) −9.05842 18.2140i −0.445197 0.895169i
\(415\) −11.2554 −0.552508
\(416\) −3.46410 + 1.00000i −0.169842 + 0.0490290i
\(417\) −28.2337 + 6.63325i −1.38261 + 0.324832i
\(418\) 43.5036 2.12783
\(419\) −8.36530 −0.408672 −0.204336 0.978901i \(-0.565503\pi\)
−0.204336 + 0.978901i \(0.565503\pi\)
\(420\) 5.54143 + 9.35279i 0.270394 + 0.456369i
\(421\) 6.43087i 0.313421i 0.987645 + 0.156711i \(0.0500890\pi\)
−0.987645 + 0.156711i \(0.949911\pi\)
\(422\) 11.6277 0.566028
\(423\) −6.18220 12.4307i −0.300589 0.604401i
\(424\) 3.16915i 0.153907i
\(425\) 1.58457 0.0768631
\(426\) −0.792287 3.37228i −0.0383864 0.163388i
\(427\) −9.45254 + 2.96677i −0.457441 + 0.143572i
\(428\) 3.75906i 0.181701i
\(429\) −17.5693 31.2781i −0.848254 1.51012i
\(430\) 19.8614i 0.957802i
\(431\) 6.23369 0.300266 0.150133 0.988666i \(-0.452030\pi\)
0.150133 + 0.988666i \(0.452030\pi\)
\(432\) −3.31662 4.00000i −0.159571 0.192450i
\(433\) 38.4674i 1.84862i −0.381638 0.924312i \(-0.624640\pi\)
0.381638 0.924312i \(-0.375360\pi\)
\(434\) −4.62772 14.7446i −0.222138 0.707762i
\(435\) −7.11684 30.2921i −0.341227 1.45239i
\(436\) 9.74749i 0.466820i
\(437\) 51.3505i 2.45643i
\(438\) 1.43070 + 6.08963i 0.0683616 + 0.290974i
\(439\) 34.6060i 1.65165i −0.563924 0.825826i \(-0.690709\pi\)
0.563924 0.825826i \(-0.309291\pi\)
\(440\) 13.6277i 0.649676i
\(441\) 10.0871 18.4188i 0.480337 0.877084i
\(442\) 8.74456 2.52434i 0.415936 0.120071i
\(443\) 9.80240i 0.465726i −0.972510 0.232863i \(-0.925191\pi\)
0.972510 0.232863i \(-0.0748094\pi\)
\(444\) 8.26411 1.94158i 0.392197 0.0921432i
\(445\) −23.7228 −1.12457
\(446\) −9.30506 −0.440608
\(447\) −5.29734 22.5475i −0.250556 1.06646i
\(448\) 0.792287 + 2.52434i 0.0374320 + 0.119264i
\(449\) −3.11684 −0.147093 −0.0735465 0.997292i \(-0.523432\pi\)
−0.0735465 + 0.997292i \(0.523432\pi\)
\(450\) 1.68614 0.838574i 0.0794854 0.0395308i
\(451\) 15.0951i 0.710800i
\(452\) 10.8896i 0.512205i
\(453\) −2.08191 + 0.489125i −0.0978165 + 0.0229811i
\(454\) 11.4891i 0.539211i
\(455\) −18.8650 + 12.4993i −0.884406 + 0.585977i
\(456\) 3.00000 + 12.7692i 0.140488 + 0.597971i
\(457\) 2.87419i 0.134449i 0.997738 + 0.0672246i \(0.0214144\pi\)
−0.997738 + 0.0672246i \(0.978586\pi\)
\(458\) 1.58457 0.0740423
\(459\) 8.37228 + 10.0974i 0.390785 + 0.471304i
\(460\) 16.0858 0.750004
\(461\) 18.6060i 0.866566i −0.901258 0.433283i \(-0.857355\pi\)
0.901258 0.433283i \(-0.142645\pi\)
\(462\) −22.6481 + 13.4188i −1.05369 + 0.624297i
\(463\) 15.0911i 0.701344i −0.936498 0.350672i \(-0.885953\pi\)
0.936498 0.350672i \(-0.114047\pi\)
\(464\) 7.57301i 0.351568i
\(465\) −23.3639 + 5.48913i −1.08347 + 0.254552i
\(466\) 12.4742i 0.577857i
\(467\) −18.2603 −0.844985 −0.422492 0.906367i \(-0.638845\pi\)
−0.422492 + 0.906367i \(0.638845\pi\)
\(468\) 7.96916 7.31386i 0.368374 0.338083i
\(469\) 6.74456 2.11684i 0.311435 0.0977468i
\(470\) 10.9783 0.506389
\(471\) −33.2921 + 7.82168i −1.53402 + 0.360404i
\(472\) 8.74456i 0.402501i
\(473\) −48.0951 −2.21141
\(474\) −3.71277 15.8030i −0.170533 0.725855i
\(475\) −4.75372 −0.218116
\(476\) −2.00000 6.37228i −0.0916698 0.292073i
\(477\) 4.23369 + 8.51278i 0.193847 + 0.389773i
\(478\) 18.0000 0.823301
\(479\) 34.3723i 1.57051i −0.619173 0.785255i \(-0.712532\pi\)
0.619173 0.785255i \(-0.287468\pi\)
\(480\) 4.00000 0.939764i 0.182574 0.0428942i
\(481\) 4.90120 + 16.9783i 0.223475 + 0.774142i
\(482\) 23.3639 1.06419
\(483\) −15.8391 26.7332i −0.720706 1.21640i
\(484\) 22.0000 1.00000
\(485\) 17.6155i 0.799877i
\(486\) 14.2525 + 6.31386i 0.646509 + 0.286402i
\(487\) 10.9822i 0.497652i 0.968548 + 0.248826i \(0.0800447\pi\)
−0.968548 + 0.248826i \(0.919955\pi\)
\(488\) 3.74456i 0.169508i
\(489\) 19.6974 4.62772i 0.890746 0.209273i
\(490\) 9.48913 + 13.6277i 0.428675 + 0.615638i
\(491\) 8.21782i 0.370865i −0.982657 0.185433i \(-0.940631\pi\)
0.982657 0.185433i \(-0.0593686\pi\)
\(492\) 4.43070 1.04095i 0.199752 0.0469298i
\(493\) 19.1168i 0.860979i
\(494\) −26.2337 + 7.57301i −1.18031 + 0.340726i
\(495\) 18.2054 + 36.6060i 0.818270 + 1.64532i
\(496\) −5.84096 −0.262267
\(497\) −1.58457 5.04868i −0.0710779 0.226464i
\(498\) 8.00000 1.87953i 0.358489 0.0842236i
\(499\) 26.0357i 1.16552i 0.812646 + 0.582758i \(0.198027\pi\)
−0.812646 + 0.582758i \(0.801973\pi\)
\(500\) 10.3723i 0.463863i
\(501\) −30.9783 + 7.27806i −1.38401 + 0.325160i
\(502\) −0.147477 −0.00658221
\(503\) 14.1514 0.630978 0.315489 0.948929i \(-0.397831\pi\)
0.315489 + 0.948929i \(0.397831\pi\)
\(504\) −5.50048 5.72230i −0.245011 0.254892i
\(505\) 13.1567i 0.585465i
\(506\) 38.9523i 1.73164i
\(507\) 16.0395 + 15.8030i 0.712339 + 0.701835i
\(508\) −4.62772 −0.205322
\(509\) 4.88316i 0.216442i −0.994127 0.108221i \(-0.965485\pi\)
0.994127 0.108221i \(-0.0345154\pi\)
\(510\) −10.0974 + 2.37228i −0.447118 + 0.105046i
\(511\) 2.86141 + 9.11684i 0.126581 + 0.403305i
\(512\) 1.00000 0.0441942
\(513\) −25.1168 30.2921i −1.10894 1.33743i
\(514\) −12.2718 −0.541287
\(515\) 3.86141 0.170154
\(516\) −3.31662 14.1168i −0.146006 0.621459i
\(517\) 26.5842i 1.16917i
\(518\) 12.3723 3.88316i 0.543607 0.170616i
\(519\) −9.48913 40.3894i −0.416526 1.77290i
\(520\) 2.37228 + 8.21782i 0.104031 + 0.360375i
\(521\) 35.9855 1.57656 0.788278 0.615320i \(-0.210973\pi\)
0.788278 + 0.615320i \(0.210973\pi\)
\(522\) 10.1168 + 20.3422i 0.442802 + 0.890353i
\(523\) 14.3505i 0.627505i −0.949505 0.313752i \(-0.898414\pi\)
0.949505 0.313752i \(-0.101586\pi\)
\(524\) 12.6217 0.551381
\(525\) 2.47480 1.46629i 0.108009 0.0639943i
\(526\) 20.4897i 0.893391i
\(527\) 14.7446 0.642283
\(528\) 2.27567 + 9.68614i 0.0990359 + 0.421535i
\(529\) −22.9783 −0.999054
\(530\) −7.51811 −0.326566
\(531\) 11.6819 + 23.4891i 0.506952 + 1.01934i
\(532\) 6.00000 + 19.1168i 0.260133 + 0.828820i
\(533\) 2.62772 + 9.10268i 0.113819 + 0.394281i
\(534\) 16.8614 3.96143i 0.729664 0.171428i
\(535\) −8.91754 −0.385539
\(536\) 2.67181i 0.115405i
\(537\) 10.6873 2.51087i 0.461189 0.108352i
\(538\) 4.55134 0.196222
\(539\) −33.0000 + 22.9783i −1.42141 + 0.989743i
\(540\) −9.48913 + 7.86797i −0.408347 + 0.338583i
\(541\) 5.39853i 0.232101i −0.993243 0.116051i \(-0.962977\pi\)
0.993243 0.116051i \(-0.0370234\pi\)
\(542\) 14.6487 0.629215
\(543\) −24.6644 + 5.79468i −1.05845 + 0.248673i
\(544\) −2.52434 −0.108230
\(545\) −23.1238 −0.990515
\(546\) 11.3214 12.0343i 0.484512 0.515023i
\(547\) 17.4891 0.747781 0.373890 0.927473i \(-0.378024\pi\)
0.373890 + 0.927473i \(0.378024\pi\)
\(548\) −0.883156 −0.0377266
\(549\) −5.00239 10.0584i −0.213497 0.429283i
\(550\) −3.60597 −0.153759
\(551\) 57.3505i 2.44321i
\(552\) −11.4333 + 2.68614i −0.486632 + 0.114330i
\(553\) −7.42554 23.6588i −0.315766 1.00607i
\(554\) −5.48913 −0.233211
\(555\) −4.60597 19.6048i −0.195513 0.832177i
\(556\) 16.7446i 0.710128i
\(557\) 24.6277 1.04351 0.521755 0.853095i \(-0.325278\pi\)
0.521755 + 0.853095i \(0.325278\pi\)
\(558\) 15.6896 7.80298i 0.664196 0.330327i
\(559\) 29.0024 8.37228i 1.22667 0.354110i
\(560\) 5.98844 1.87953i 0.253058 0.0794245i
\(561\) −5.74456 24.4511i −0.242536 1.03233i
\(562\) −14.0000 −0.590554
\(563\) −35.7832 −1.50808 −0.754040 0.656828i \(-0.771898\pi\)
−0.754040 + 0.656828i \(0.771898\pi\)
\(564\) −7.80298 + 1.83324i −0.328565 + 0.0771934i
\(565\) −25.8333 −1.08681
\(566\) 5.37228i 0.225814i
\(567\) 22.4195 + 8.02279i 0.941531 + 0.336925i
\(568\) −2.00000 −0.0839181
\(569\) 39.5971i 1.66000i −0.557765 0.829999i \(-0.688341\pi\)
0.557765 0.829999i \(-0.311659\pi\)
\(570\) 30.2921 7.11684i 1.26879 0.298092i
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) −19.8997 + 5.74456i −0.832050 + 0.240192i
\(573\) −32.9639 + 7.74456i −1.37709 + 0.323534i
\(574\) 6.63325 2.08191i 0.276866 0.0868971i
\(575\) 4.25639i 0.177504i
\(576\) −2.68614 + 1.33591i −0.111923 + 0.0556628i
\(577\) 6.92820 0.288425 0.144212 0.989547i \(-0.453935\pi\)
0.144212 + 0.989547i \(0.453935\pi\)
\(578\) −10.6277 −0.442055
\(579\) −35.0458 + 8.23369i −1.45645 + 0.342180i
\(580\) −17.9653 −0.745969
\(581\) 11.9769 3.75906i 0.496885 0.155952i
\(582\) −2.94158 12.5205i −0.121932 0.518991i
\(583\) 18.2054i 0.753989i
\(584\) 3.61158 0.149448
\(585\) −17.3505 18.9051i −0.717356 0.781629i
\(586\) 11.4891i 0.474611i
\(587\) 5.25544i 0.216915i 0.994101 + 0.108458i \(0.0345912\pi\)
−0.994101 + 0.108458i \(0.965409\pi\)
\(588\) −9.02023 8.10157i −0.371988 0.334103i
\(589\) −44.2337 −1.82262
\(590\) −20.7446 −0.854040
\(591\) 1.53829 + 6.54755i 0.0632767 + 0.269330i
\(592\) 4.90120i 0.201438i
\(593\) 30.7446i 1.26253i −0.775568 0.631264i \(-0.782536\pi\)
0.775568 0.631264i \(-0.217464\pi\)
\(594\) −19.0526 22.9783i −0.781736 0.942809i
\(595\) −15.1168 + 4.74456i −0.619730 + 0.194508i
\(596\) −13.3723 −0.547750
\(597\) −8.62772 + 2.02700i −0.353109 + 0.0829598i
\(598\) −6.78073 23.4891i −0.277285 0.960542i
\(599\) 1.43710i 0.0587182i 0.999569 + 0.0293591i \(0.00934663\pi\)
−0.999569 + 0.0293591i \(0.990653\pi\)
\(600\) −0.248667 1.05842i −0.0101518 0.0432099i
\(601\) 26.0000i 1.06056i 0.847822 + 0.530281i \(0.177914\pi\)
−0.847822 + 0.530281i \(0.822086\pi\)
\(602\) −6.63325 21.1345i −0.270351 0.861377i
\(603\) 3.56930 + 7.17687i 0.145353 + 0.292265i
\(604\) 1.23472i 0.0502399i
\(605\) 52.1902i 2.12183i
\(606\) 2.19702 + 9.35135i 0.0892476 + 0.379873i
\(607\) 0.883156i 0.0358462i −0.999839 0.0179231i \(-0.994295\pi\)
0.999839 0.0179231i \(-0.00570541\pi\)
\(608\) 7.57301 0.307126
\(609\) 17.6899 + 29.8568i 0.716829 + 1.20986i
\(610\) 8.88316 0.359668
\(611\) −4.62772 16.0309i −0.187217 0.648540i
\(612\) 6.78073 3.37228i 0.274095 0.136316i
\(613\) 3.02167i 0.122044i −0.998136 0.0610221i \(-0.980564\pi\)
0.998136 0.0610221i \(-0.0194360\pi\)
\(614\) 14.5561 0.587437
\(615\) −2.46943 10.5109i −0.0995772 0.423839i
\(616\) 4.55134 + 14.5012i 0.183379 + 0.584271i
\(617\) 22.6060 0.910082 0.455041 0.890470i \(-0.349625\pi\)
0.455041 + 0.890470i \(0.349625\pi\)
\(618\) −2.74456 + 0.644810i −0.110403 + 0.0259381i
\(619\) 16.3807 0.658398 0.329199 0.944261i \(-0.393221\pi\)
0.329199 + 0.944261i \(0.393221\pi\)
\(620\) 13.8564i 0.556487i
\(621\) 27.1229 22.4891i 1.08840 0.902458i
\(622\) 10.3923 0.416693
\(623\) 25.2434 7.92287i 1.01135 0.317423i
\(624\) −3.05842 5.44482i −0.122435 0.217967i
\(625\) −27.7446 −1.10978
\(626\) 8.74456i 0.349503i
\(627\) 17.2337 + 73.3533i 0.688247 + 2.92945i
\(628\) 19.7446i 0.787894i
\(629\) 12.3723i 0.493315i
\(630\) −13.5749 + 13.0487i −0.540838 + 0.519872i
\(631\) 24.3036i 0.967512i 0.875203 + 0.483756i \(0.160728\pi\)
−0.875203 + 0.483756i \(0.839272\pi\)
\(632\) −9.37228 −0.372809
\(633\) 4.60625 + 19.6060i 0.183082 + 0.779267i
\(634\) 24.8614 0.987373
\(635\) 10.9783i 0.435659i
\(636\) 5.34363 1.25544i 0.211889 0.0497813i
\(637\) 15.8997 19.6010i 0.629971 0.776619i
\(638\) 43.5036i 1.72233i
\(639\) 5.37228 2.67181i 0.212524 0.105695i
\(640\) 2.37228i 0.0937727i
\(641\) 20.9870i 0.828936i 0.910064 + 0.414468i \(0.136032\pi\)
−0.910064 + 0.414468i \(0.863968\pi\)
\(642\) 6.33830 1.48913i 0.250153 0.0587711i
\(643\) 28.3576 1.11832 0.559158 0.829061i \(-0.311125\pi\)
0.559158 + 0.829061i \(0.311125\pi\)
\(644\) −17.1168 + 5.37228i −0.674498 + 0.211698i
\(645\) −33.4891 + 7.86797i −1.31863 + 0.309801i
\(646\) −19.1168 −0.752142
\(647\) 32.7615 1.28799 0.643994 0.765031i \(-0.277276\pi\)
0.643994 + 0.765031i \(0.277276\pi\)
\(648\) 5.43070 7.17687i 0.213338 0.281934i
\(649\) 50.2337i 1.97184i
\(650\) 2.17448 0.627719i 0.0852902 0.0246212i
\(651\) 23.0282 13.6439i 0.902545 0.534748i
\(652\) 11.6819i 0.457499i
\(653\) 11.3321i 0.443458i −0.975108 0.221729i \(-0.928830\pi\)
0.975108 0.221729i \(-0.0711701\pi\)
\(654\) 16.4356 3.86141i 0.642685 0.150993i
\(655\) 29.9422i 1.16994i
\(656\) 2.62772i 0.102595i
\(657\) −9.70121 + 4.82473i −0.378480 + 0.188231i
\(658\) −11.6819 + 3.66648i −0.455409 + 0.142934i
\(659\) 48.3123i 1.88198i 0.338436 + 0.940990i \(0.390102\pi\)
−0.338436 + 0.940990i \(0.609898\pi\)
\(660\) 22.9783 5.39853i 0.894427 0.210138i
\(661\) 4.16381 0.161954 0.0809768 0.996716i \(-0.474196\pi\)
0.0809768 + 0.996716i \(0.474196\pi\)
\(662\) 32.6689i 1.26971i
\(663\) 7.72049 + 13.7446i 0.299839 + 0.533795i
\(664\) 4.74456i 0.184125i
\(665\) 45.3505 14.2337i 1.75862 0.551959i
\(666\) 6.54755 + 13.1653i 0.253712 + 0.510145i
\(667\) 51.3505 1.98830
\(668\) 18.3723i 0.710845i
\(669\) −3.68614 15.6896i −0.142514 0.606597i
\(670\) −6.33830 −0.244870
\(671\) 21.5109i 0.830418i
\(672\) −3.94253 + 2.33591i −0.152086 + 0.0901096i
\(673\) −10.7663 −0.415011 −0.207505 0.978234i \(-0.566534\pi\)
−0.207505 + 0.978234i \(0.566534\pi\)
\(674\) 5.00000 0.192593
\(675\) 2.08191 + 2.51087i 0.0801327 + 0.0966436i
\(676\) 11.0000 6.92820i 0.423077 0.266469i
\(677\) −29.2048 −1.12243 −0.561216 0.827669i \(-0.689666\pi\)
−0.561216 + 0.827669i \(0.689666\pi\)
\(678\) 18.3615 4.31386i 0.705168 0.165673i
\(679\) −5.88316 18.7446i −0.225775 0.719350i
\(680\) 5.98844i 0.229646i
\(681\) 19.3723 4.55134i 0.742347 0.174408i
\(682\) −33.5538 −1.28484
\(683\) −19.0000 −0.727015 −0.363507 0.931591i \(-0.618421\pi\)
−0.363507 + 0.931591i \(0.618421\pi\)
\(684\) −20.3422 + 10.1168i −0.777803 + 0.386827i
\(685\) 2.09509i 0.0800494i
\(686\) −14.6487 11.3321i −0.559290 0.432660i
\(687\) 0.627719 + 2.67181i 0.0239490 + 0.101936i
\(688\) −8.37228 −0.319190
\(689\) 3.16915 + 10.9783i 0.120735 + 0.418238i
\(690\) 6.37228 + 27.1229i 0.242589 + 1.03255i
\(691\) −31.1769 −1.18603 −0.593013 0.805193i \(-0.702062\pi\)
−0.593013 + 0.805193i \(0.702062\pi\)
\(692\) −23.9538 −0.910585
\(693\) −31.5978 32.8721i −1.20030 1.24871i
\(694\) 25.8333i 0.980618i
\(695\) 39.7228 1.50677
\(696\) 12.7692 3.00000i 0.484014 0.113715i
\(697\) 6.63325i 0.251252i
\(698\) −23.3639 −0.884335
\(699\) −21.0333 + 4.94158i −0.795552 + 0.186908i
\(700\) −0.497333 1.58457i −0.0187974 0.0598913i
\(701\) 13.2665i 0.501069i 0.968108 + 0.250534i \(0.0806063\pi\)
−0.968108 + 0.250534i \(0.919394\pi\)
\(702\) 15.4891 + 10.5398i 0.584599 + 0.397798i
\(703\) 37.1168i 1.39989i
\(704\) 5.74456 0.216506
\(705\) 4.34896 + 18.5109i 0.163791 + 0.697160i
\(706\) 6.11684i 0.230210i
\(707\) 4.39403 + 14.0000i 0.165255 + 0.526524i
\(708\) 14.7446 3.46410i 0.554135 0.130189i
\(709\) 30.3846i 1.14112i 0.821256 + 0.570559i \(0.193274\pi\)
−0.821256 + 0.570559i \(0.806726\pi\)
\(710\) 4.74456i 0.178060i
\(711\) 25.1753 12.5205i 0.944146 0.469555i
\(712\) 10.0000i 0.374766i
\(713\) 39.6060i 1.48326i
\(714\) 9.95228 5.89662i 0.372455 0.220675i
\(715\) 13.6277 + 47.2078i 0.509648 + 1.76547i
\(716\) 6.33830i 0.236873i
\(717\) 7.13058 + 30.3505i 0.266296 + 1.13346i
\(718\) −28.2337 −1.05367
\(719\) −23.3639 −0.871325 −0.435662 0.900110i \(-0.643486\pi\)
−0.435662 + 0.900110i \(0.643486\pi\)
\(720\) 3.16915 + 6.37228i 0.118107 + 0.237481i
\(721\) −4.10891 + 1.28962i −0.153024 + 0.0480280i
\(722\) 38.3505 1.42726
\(723\) 9.25544 + 39.3947i 0.344213 + 1.46511i
\(724\) 14.6277i 0.543635i
\(725\) 4.75372i 0.176549i
\(726\) 8.71516 + 37.0951i 0.323450 + 1.37673i
\(727\) 29.8614i 1.10750i −0.832684 0.553749i \(-0.813197\pi\)
0.832684 0.553749i \(-0.186803\pi\)
\(728\) −5.26890 7.95228i −0.195278 0.294731i
\(729\) −5.00000 + 26.5330i −0.185185 + 0.982704i
\(730\) 8.56768i 0.317104i
\(731\) 21.1345 0.781686
\(732\) −6.31386 + 1.48338i −0.233367 + 0.0548275i
\(733\) 1.28962 0.0476332 0.0238166 0.999716i \(-0.492418\pi\)
0.0238166 + 0.999716i \(0.492418\pi\)
\(734\) 6.74456i 0.248946i
\(735\) −19.2192 + 21.3985i −0.708911 + 0.789297i
\(736\) 6.78073i 0.249941i
\(737\) 15.3484i 0.565366i
\(738\) 3.51039 + 7.05842i 0.129219 + 0.259824i
\(739\) 41.3841i 1.52234i −0.648554 0.761169i \(-0.724626\pi\)
0.648554 0.761169i \(-0.275374\pi\)
\(740\) −11.6270 −0.427418
\(741\) −23.1615 41.2337i −0.850858 1.51476i
\(742\) 8.00000 2.51087i 0.293689 0.0921771i
\(743\) −44.9783 −1.65009 −0.825046 0.565066i \(-0.808851\pi\)
−0.825046 + 0.565066i \(0.808851\pi\)
\(744\) −2.31386 9.84868i −0.0848302 0.361070i
\(745\) 31.7228i 1.16223i
\(746\) 22.2337 0.814033
\(747\) 6.33830 + 12.7446i 0.231906 + 0.466299i
\(748\) −14.5012 −0.530217
\(749\) 9.48913 2.97825i 0.346725 0.108823i
\(750\) 17.4891 4.10891i 0.638613 0.150036i
\(751\) −21.6060 −0.788413 −0.394207 0.919022i \(-0.628981\pi\)
−0.394207 + 0.919022i \(0.628981\pi\)
\(752\) 4.62772i 0.168756i
\(753\) −0.0584220 0.248667i −0.00212902 0.00906192i
\(754\) 7.57301 + 26.2337i 0.275793 + 0.955375i
\(755\) 2.92910 0.106601
\(756\) 7.46963 11.5414i 0.271668 0.419758i
\(757\) −18.4674 −0.671208 −0.335604 0.942003i \(-0.608940\pi\)
−0.335604 + 0.942003i \(0.608940\pi\)
\(758\) 14.8511i 0.539415i
\(759\) −65.6791 + 15.4307i −2.38400 + 0.560099i
\(760\) 17.9653i 0.651671i
\(761\) 30.8614i 1.11873i 0.828923 + 0.559363i \(0.188954\pi\)
−0.828923 + 0.559363i \(0.811046\pi\)
\(762\) −1.83324 7.80298i −0.0664113 0.282672i
\(763\) 24.6060 7.72281i 0.890796 0.279585i
\(764\) 19.5499i 0.707290i
\(765\) −8.00000 16.0858i −0.289241 0.581583i
\(766\) 26.4891i 0.957091i
\(767\) 8.74456 + 30.2921i 0.315748 + 1.09378i
\(768\) 0.396143 + 1.68614i 0.0142946 + 0.0608434i
\(769\) 14.2988 0.515629 0.257815 0.966194i \(-0.416998\pi\)
0.257815 + 0.966194i \(0.416998\pi\)
\(770\) 34.4010 10.7971i 1.23972 0.389099i
\(771\) −4.86141 20.6920i −0.175079 0.745205i
\(772\) 20.7846i 0.748054i
\(773\) 9.86141i 0.354690i −0.984149 0.177345i \(-0.943249\pi\)
0.984149 0.177345i \(-0.0567509\pi\)
\(774\) 22.4891 11.1846i 0.808355 0.402022i
\(775\) 3.66648 0.131704
\(776\) −7.42554 −0.266561
\(777\) 11.4487 + 19.3231i 0.410721 + 0.693213i
\(778\) 7.92287i 0.284049i
\(779\) 19.8997i 0.712982i
\(780\) −12.9166 + 7.25544i −0.462490 + 0.259786i
\(781\) −11.4891 −0.411113
\(782\)