Properties

Label 1050.2.bc.g.607.1
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.1
Root \(0.339278 + 0.0446668i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.g.493.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.781940 - 2.52756i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.781940 - 2.52756i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.31272 - 2.27370i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(1.21865 + 1.21865i) q^{13} +(-0.101115 + 2.64382i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-7.31238 - 1.95935i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.32616 - 4.02903i) q^{19} +(-2.23906 - 1.40948i) q^{21} +(1.85647 + 1.85647i) q^{22} +(1.32840 + 4.95766i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-1.49254 - 0.861717i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.586601 - 2.57990i) q^{28} -5.99410i q^{29} +(-8.66177 + 5.00088i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.53598 + 0.679515i) q^{33} +7.57033 q^{34} -1.00000 q^{36} +(3.82271 - 1.02429i) q^{37} +(-1.20411 + 4.49380i) q^{38} +(1.49254 - 0.861717i) q^{39} -5.59423i q^{41} +(2.52756 + 0.781940i) q^{42} +(0.545731 - 0.545731i) q^{43} +(-2.27370 - 1.31272i) q^{44} +(-2.56627 - 4.44492i) q^{46} +(1.64085 + 6.12372i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-5.77714 - 3.95280i) q^{49} +(-3.78517 + 6.55610i) q^{51} +(1.66471 + 0.446058i) q^{52} +(-8.28728 - 2.22057i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.23434 + 2.34017i) q^{56} +(-3.28969 - 3.28969i) q^{57} +(1.55139 + 5.78985i) q^{58} +(3.86022 + 6.68609i) q^{59} +(4.16543 + 2.40491i) q^{61} +(7.07231 - 7.07231i) q^{62} +(-1.94096 + 1.79796i) q^{63} -1.00000i q^{64} +(2.27370 - 1.31272i) q^{66} +(0.663456 - 2.47605i) q^{67} +(-7.31238 + 1.95935i) q^{68} +5.13255 q^{69} -8.36973 q^{71} +(0.965926 - 0.258819i) q^{72} +(3.53363 - 13.1877i) q^{73} +(-3.42734 + 1.97878i) q^{74} -4.65232i q^{76} +(-6.77339 + 1.54009i) q^{77} +(-1.21865 + 1.21865i) q^{78} +(-7.78980 - 4.49744i) q^{79} +(0.500000 + 0.866025i) q^{81} +(1.44789 + 5.40361i) q^{82} +(-7.99504 - 7.99504i) q^{83} +(-2.64382 - 0.101115i) q^{84} +(-0.385890 + 0.668382i) q^{86} +(-5.78985 - 1.55139i) q^{87} +(2.53598 + 0.679515i) q^{88} +(0.0812661 - 0.140757i) q^{89} +(4.03313 - 2.12731i) q^{91} +(3.62926 + 3.62926i) q^{92} +(2.58864 + 9.66095i) q^{93} +(-3.16987 - 5.49038i) q^{94} +(0.866025 + 0.500000i) q^{96} +(-4.35278 + 4.35278i) q^{97} +(6.60335 + 2.32288i) q^{98} +2.62544i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + O(q^{10}) \) \( 16q + 4q^{7} + 4q^{11} - 16q^{13} - 16q^{14} + 8q^{16} - 12q^{17} + 8q^{19} + 8q^{21} - 4q^{22} + 40q^{23} + 8q^{24} - 12q^{26} + 4q^{28} - 24q^{31} - 4q^{33} - 16q^{34} - 16q^{36} + 8q^{37} + 20q^{38} + 12q^{39} - 8q^{42} + 24q^{43} - 4q^{46} - 52q^{49} + 8q^{51} - 8q^{52} + 28q^{53} + 8q^{54} + 8q^{56} + 8q^{57} + 12q^{58} - 8q^{59} + 24q^{61} + 8q^{62} + 4q^{63} + 84q^{67} - 12q^{68} + 8q^{69} - 32q^{71} - 16q^{73} + 24q^{74} - 44q^{77} + 16q^{78} - 12q^{79} + 8q^{81} - 36q^{82} - 16q^{83} - 4q^{84} - 8q^{86} - 48q^{87} + 4q^{88} + 16q^{89} + 8q^{91} - 8q^{92} + 32q^{93} - 8q^{94} + 44q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) 0.258819 0.965926i 0.149429 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 0.781940 2.52756i 0.295546 0.955329i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) −1.31272 2.27370i −0.395800 0.685546i 0.597403 0.801942i \(-0.296199\pi\)
−0.993203 + 0.116395i \(0.962866\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) 1.21865 + 1.21865i 0.337993 + 0.337993i 0.855612 0.517618i \(-0.173181\pi\)
−0.517618 + 0.855612i \(0.673181\pi\)
\(14\) −0.101115 + 2.64382i −0.0270242 + 0.706590i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −7.31238 1.95935i −1.77351 0.475211i −0.784136 0.620589i \(-0.786894\pi\)
−0.989376 + 0.145377i \(0.953560\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) 2.32616 4.02903i 0.533658 0.924322i −0.465569 0.885011i \(-0.654150\pi\)
0.999227 0.0393108i \(-0.0125162\pi\)
\(20\) 0 0
\(21\) −2.23906 1.40948i −0.488602 0.307573i
\(22\) 1.85647 + 1.85647i 0.395800 + 0.395800i
\(23\) 1.32840 + 4.95766i 0.276991 + 1.03374i 0.954496 + 0.298225i \(0.0963946\pi\)
−0.677505 + 0.735518i \(0.736939\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −1.49254 0.861717i −0.292711 0.168997i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −0.586601 2.57990i −0.110857 0.487556i
\(29\) 5.99410i 1.11308i −0.830822 0.556538i \(-0.812129\pi\)
0.830822 0.556538i \(-0.187871\pi\)
\(30\) 0 0
\(31\) −8.66177 + 5.00088i −1.55570 + 0.898184i −0.558040 + 0.829814i \(0.688447\pi\)
−0.997660 + 0.0683700i \(0.978220\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) −2.53598 + 0.679515i −0.441458 + 0.118288i
\(34\) 7.57033 1.29830
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 3.82271 1.02429i 0.628449 0.168392i 0.0694832 0.997583i \(-0.477865\pi\)
0.558966 + 0.829191i \(0.311198\pi\)
\(38\) −1.20411 + 4.49380i −0.195332 + 0.728990i
\(39\) 1.49254 0.861717i 0.238997 0.137985i
\(40\) 0 0
\(41\) 5.59423i 0.873671i −0.899541 0.436836i \(-0.856099\pi\)
0.899541 0.436836i \(-0.143901\pi\)
\(42\) 2.52756 + 0.781940i 0.390011 + 0.120656i
\(43\) 0.545731 0.545731i 0.0832233 0.0832233i −0.664270 0.747493i \(-0.731257\pi\)
0.747493 + 0.664270i \(0.231257\pi\)
\(44\) −2.27370 1.31272i −0.342773 0.197900i
\(45\) 0 0
\(46\) −2.56627 4.44492i −0.378376 0.655367i
\(47\) 1.64085 + 6.12372i 0.239342 + 0.893237i 0.976143 + 0.217127i \(0.0696687\pi\)
−0.736801 + 0.676109i \(0.763665\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) −5.77714 3.95280i −0.825306 0.564686i
\(50\) 0 0
\(51\) −3.78517 + 6.55610i −0.530029 + 0.918038i
\(52\) 1.66471 + 0.446058i 0.230854 + 0.0618571i
\(53\) −8.28728 2.22057i −1.13835 0.305019i −0.360060 0.932929i \(-0.617244\pi\)
−0.778286 + 0.627910i \(0.783911\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 1.23434 + 2.34017i 0.164946 + 0.312719i
\(57\) −3.28969 3.28969i −0.435730 0.435730i
\(58\) 1.55139 + 5.78985i 0.203707 + 0.760245i
\(59\) 3.86022 + 6.68609i 0.502557 + 0.870455i 0.999996 + 0.00295539i \(0.000940731\pi\)
−0.497438 + 0.867499i \(0.665726\pi\)
\(60\) 0 0
\(61\) 4.16543 + 2.40491i 0.533328 + 0.307917i 0.742371 0.669989i \(-0.233701\pi\)
−0.209042 + 0.977907i \(0.567035\pi\)
\(62\) 7.07231 7.07231i 0.898184 0.898184i
\(63\) −1.94096 + 1.79796i −0.244538 + 0.226522i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 2.27370 1.31272i 0.279873 0.161585i
\(67\) 0.663456 2.47605i 0.0810541 0.302498i −0.913484 0.406875i \(-0.866618\pi\)
0.994538 + 0.104377i \(0.0332850\pi\)
\(68\) −7.31238 + 1.95935i −0.886756 + 0.237606i
\(69\) 5.13255 0.617886
\(70\) 0 0
\(71\) −8.36973 −0.993304 −0.496652 0.867950i \(-0.665437\pi\)
−0.496652 + 0.867950i \(0.665437\pi\)
\(72\) 0.965926 0.258819i 0.113835 0.0305021i
\(73\) 3.53363 13.1877i 0.413581 1.54350i −0.374081 0.927396i \(-0.622042\pi\)
0.787662 0.616108i \(-0.211291\pi\)
\(74\) −3.42734 + 1.97878i −0.398421 + 0.230028i
\(75\) 0 0
\(76\) 4.65232i 0.533658i
\(77\) −6.77339 + 1.54009i −0.771899 + 0.175509i
\(78\) −1.21865 + 1.21865i −0.137985 + 0.137985i
\(79\) −7.78980 4.49744i −0.876421 0.506002i −0.00694408 0.999976i \(-0.502210\pi\)
−0.869477 + 0.493974i \(0.835544\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 1.44789 + 5.40361i 0.159893 + 0.596729i
\(83\) −7.99504 7.99504i −0.877570 0.877570i 0.115713 0.993283i \(-0.463085\pi\)
−0.993283 + 0.115713i \(0.963085\pi\)
\(84\) −2.64382 0.101115i −0.288464 0.0110326i
\(85\) 0 0
\(86\) −0.385890 + 0.668382i −0.0416116 + 0.0720734i
\(87\) −5.78985 1.55139i −0.620738 0.166326i
\(88\) 2.53598 + 0.679515i 0.270337 + 0.0724365i
\(89\) 0.0812661 0.140757i 0.00861419 0.0149202i −0.861686 0.507442i \(-0.830591\pi\)
0.870300 + 0.492521i \(0.163925\pi\)
\(90\) 0 0
\(91\) 4.03313 2.12731i 0.422787 0.223002i
\(92\) 3.62926 + 3.62926i 0.378376 + 0.378376i
\(93\) 2.58864 + 9.66095i 0.268430 + 1.00179i
\(94\) −3.16987 5.49038i −0.326947 0.566289i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) −4.35278 + 4.35278i −0.441958 + 0.441958i −0.892670 0.450711i \(-0.851170\pi\)
0.450711 + 0.892670i \(0.351170\pi\)
\(98\) 6.60335 + 2.32288i 0.667039 + 0.234647i
\(99\) 2.62544i 0.263867i
\(100\) 0 0
\(101\) −6.64586 + 3.83699i −0.661287 + 0.381795i −0.792767 0.609524i \(-0.791360\pi\)
0.131480 + 0.991319i \(0.458027\pi\)
\(102\) 1.95935 7.31238i 0.194004 0.724033i
\(103\) 3.92931 1.05286i 0.387167 0.103741i −0.0599847 0.998199i \(-0.519105\pi\)
0.447151 + 0.894458i \(0.352439\pi\)
\(104\) −1.72343 −0.168997
\(105\) 0 0
\(106\) 8.57963 0.833327
\(107\) −2.72108 + 0.729112i −0.263057 + 0.0704859i −0.387937 0.921686i \(-0.626812\pi\)
0.124880 + 0.992172i \(0.460145\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) 10.5314 6.08031i 1.00872 0.582388i 0.0979069 0.995196i \(-0.468785\pi\)
0.910818 + 0.412808i \(0.135452\pi\)
\(110\) 0 0
\(111\) 3.95756i 0.375635i
\(112\) −1.79796 1.94096i −0.169892 0.183404i
\(113\) −1.63875 + 1.63875i −0.154161 + 0.154161i −0.779973 0.625813i \(-0.784767\pi\)
0.625813 + 0.779973i \(0.284767\pi\)
\(114\) 4.02903 + 2.32616i 0.377353 + 0.217865i
\(115\) 0 0
\(116\) −2.99705 5.19104i −0.278269 0.481976i
\(117\) −0.446058 1.66471i −0.0412380 0.153902i
\(118\) −5.45917 5.45917i −0.502557 0.502557i
\(119\) −10.6702 + 16.9504i −0.978137 + 1.55384i
\(120\) 0 0
\(121\) 2.05352 3.55681i 0.186684 0.323346i
\(122\) −4.64593 1.24487i −0.420623 0.112706i
\(123\) −5.40361 1.44789i −0.487227 0.130552i
\(124\) −5.00088 + 8.66177i −0.449092 + 0.777850i
\(125\) 0 0
\(126\) 1.40948 2.23906i 0.125566 0.199471i
\(127\) −6.79622 6.79622i −0.603067 0.603067i 0.338058 0.941125i \(-0.390230\pi\)
−0.941125 + 0.338058i \(0.890230\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) −0.385890 0.668382i −0.0339757 0.0588477i
\(130\) 0 0
\(131\) −3.66846 2.11799i −0.320515 0.185050i 0.331107 0.943593i \(-0.392578\pi\)
−0.651622 + 0.758544i \(0.725911\pi\)
\(132\) −1.85647 + 1.85647i −0.161585 + 0.161585i
\(133\) −8.36470 9.02997i −0.725311 0.782998i
\(134\) 2.56340i 0.221444i
\(135\) 0 0
\(136\) 6.55610 3.78517i 0.562181 0.324575i
\(137\) 2.13852 7.98108i 0.182706 0.681870i −0.812403 0.583096i \(-0.801841\pi\)
0.995110 0.0987740i \(-0.0314921\pi\)
\(138\) −4.95766 + 1.32840i −0.422024 + 0.113081i
\(139\) −9.35059 −0.793106 −0.396553 0.918012i \(-0.629794\pi\)
−0.396553 + 0.918012i \(0.629794\pi\)
\(140\) 0 0
\(141\) 6.33974 0.533903
\(142\) 8.08453 2.16624i 0.678439 0.181787i
\(143\) 1.17110 4.37060i 0.0979322 0.365488i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 13.6529i 1.12992i
\(147\) −5.31335 + 4.55723i −0.438238 + 0.375874i
\(148\) 2.79841 2.79841i 0.230028 0.230028i
\(149\) 4.12068 + 2.37908i 0.337579 + 0.194902i 0.659201 0.751967i \(-0.270895\pi\)
−0.321622 + 0.946868i \(0.604228\pi\)
\(150\) 0 0
\(151\) −1.07557 1.86294i −0.0875286 0.151604i 0.818937 0.573883i \(-0.194564\pi\)
−0.906466 + 0.422279i \(0.861230\pi\)
\(152\) 1.20411 + 4.49380i 0.0976661 + 0.364495i
\(153\) 5.35303 + 5.35303i 0.432767 + 0.432767i
\(154\) 6.14399 3.24069i 0.495097 0.261142i
\(155\) 0 0
\(156\) 0.861717 1.49254i 0.0689926 0.119499i
\(157\) −3.67471 0.984635i −0.293274 0.0785824i 0.109182 0.994022i \(-0.465177\pi\)
−0.402456 + 0.915439i \(0.631843\pi\)
\(158\) 8.68839 + 2.32805i 0.691211 + 0.185209i
\(159\) −4.28981 + 7.43018i −0.340204 + 0.589251i
\(160\) 0 0
\(161\) 13.5695 + 0.518978i 1.06943 + 0.0409012i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) −1.15466 4.30925i −0.0904399 0.337526i 0.905849 0.423601i \(-0.139234\pi\)
−0.996289 + 0.0860750i \(0.972568\pi\)
\(164\) −2.79711 4.84474i −0.218418 0.378311i
\(165\) 0 0
\(166\) 9.79189 + 5.65335i 0.759998 + 0.438785i
\(167\) 16.1327 16.1327i 1.24839 1.24839i 0.291956 0.956432i \(-0.405694\pi\)
0.956432 0.291956i \(-0.0943062\pi\)
\(168\) 2.57990 0.586601i 0.199044 0.0452572i
\(169\) 10.0298i 0.771521i
\(170\) 0 0
\(171\) −4.02903 + 2.32616i −0.308107 + 0.177886i
\(172\) 0.199752 0.745483i 0.0152309 0.0568425i
\(173\) 11.9603 3.20476i 0.909327 0.243653i 0.226309 0.974055i \(-0.427334\pi\)
0.683017 + 0.730402i \(0.260667\pi\)
\(174\) 5.99410 0.454411
\(175\) 0 0
\(176\) −2.62544 −0.197900
\(177\) 7.45736 1.99819i 0.560530 0.150194i
\(178\) −0.0420664 + 0.156994i −0.00315301 + 0.0117672i
\(179\) 17.5544 10.1350i 1.31208 0.757528i 0.329637 0.944108i \(-0.393074\pi\)
0.982440 + 0.186580i \(0.0597403\pi\)
\(180\) 0 0
\(181\) 7.52637i 0.559431i 0.960083 + 0.279715i \(0.0902401\pi\)
−0.960083 + 0.279715i \(0.909760\pi\)
\(182\) −3.34512 + 3.09867i −0.247957 + 0.229689i
\(183\) 3.40106 3.40106i 0.251413 0.251413i
\(184\) −4.44492 2.56627i −0.327684 0.189188i
\(185\) 0 0
\(186\) −5.00088 8.66177i −0.366682 0.635112i
\(187\) 5.14415 + 19.1982i 0.376178 + 1.40391i
\(188\) 4.48288 + 4.48288i 0.326947 + 0.326947i
\(189\) 1.23434 + 2.34017i 0.0897851 + 0.170222i
\(190\) 0 0
\(191\) −2.16395 + 3.74807i −0.156578 + 0.271201i −0.933632 0.358233i \(-0.883379\pi\)
0.777055 + 0.629433i \(0.216713\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) 20.5434 + 5.50458i 1.47874 + 0.396228i 0.905920 0.423449i \(-0.139181\pi\)
0.572825 + 0.819678i \(0.305847\pi\)
\(194\) 3.07788 5.33105i 0.220979 0.382747i
\(195\) 0 0
\(196\) −6.97955 0.534660i −0.498539 0.0381900i
\(197\) 14.1314 + 14.1314i 1.00682 + 1.00682i 0.999977 + 0.00684089i \(0.00217754\pi\)
0.00684089 + 0.999977i \(0.497822\pi\)
\(198\) −0.679515 2.53598i −0.0482910 0.180224i
\(199\) −0.422034 0.730985i −0.0299172 0.0518182i 0.850679 0.525685i \(-0.176191\pi\)
−0.880596 + 0.473867i \(0.842858\pi\)
\(200\) 0 0
\(201\) −2.21997 1.28170i −0.156584 0.0904041i
\(202\) 5.42632 5.42632i 0.381795 0.381795i
\(203\) −15.1505 4.68703i −1.06335 0.328965i
\(204\) 7.57033i 0.530029i
\(205\) 0 0
\(206\) −3.52293 + 2.03396i −0.245454 + 0.141713i
\(207\) 1.32840 4.95766i 0.0923302 0.344581i
\(208\) 1.66471 0.446058i 0.115427 0.0309285i
\(209\) −12.2144 −0.844888
\(210\) 0 0
\(211\) 22.1844 1.52724 0.763619 0.645667i \(-0.223421\pi\)
0.763619 + 0.645667i \(0.223421\pi\)
\(212\) −8.28728 + 2.22057i −0.569173 + 0.152509i
\(213\) −2.16624 + 8.08453i −0.148429 + 0.553943i
\(214\) 2.43966 1.40854i 0.166771 0.0962855i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 5.86704 + 25.8036i 0.398280 + 1.75166i
\(218\) −8.59885 + 8.59885i −0.582388 + 0.582388i
\(219\) −11.8238 6.82646i −0.798976 0.461289i
\(220\) 0 0
\(221\) −6.52348 11.2990i −0.438817 0.760053i
\(222\) 1.02429 + 3.82271i 0.0687459 + 0.256563i
\(223\) 10.7632 + 10.7632i 0.720757 + 0.720757i 0.968759 0.248002i \(-0.0797741\pi\)
−0.248002 + 0.968759i \(0.579774\pi\)
\(224\) 2.23906 + 1.40948i 0.149603 + 0.0941747i
\(225\) 0 0
\(226\) 1.15877 2.00705i 0.0770804 0.133507i
\(227\) −3.61119 0.967615i −0.239683 0.0642229i 0.136978 0.990574i \(-0.456261\pi\)
−0.376661 + 0.926351i \(0.622928\pi\)
\(228\) −4.49380 1.20411i −0.297609 0.0797441i
\(229\) −7.59088 + 13.1478i −0.501619 + 0.868830i 0.498379 + 0.866959i \(0.333929\pi\)
−0.999998 + 0.00187073i \(0.999405\pi\)
\(230\) 0 0
\(231\) −0.265472 + 6.94119i −0.0174668 + 0.456697i
\(232\) 4.23847 + 4.23847i 0.278269 + 0.278269i
\(233\) 0.313957 + 1.17170i 0.0205680 + 0.0767607i 0.975447 0.220234i \(-0.0706822\pi\)
−0.954879 + 0.296995i \(0.904016\pi\)
\(234\) 0.861717 + 1.49254i 0.0563322 + 0.0975702i
\(235\) 0 0
\(236\) 6.68609 + 3.86022i 0.435227 + 0.251279i
\(237\) −6.36034 + 6.36034i −0.413149 + 0.413149i
\(238\) 5.91955 19.1345i 0.383707 1.24030i
\(239\) 16.1593i 1.04526i 0.852560 + 0.522630i \(0.175049\pi\)
−0.852560 + 0.522630i \(0.824951\pi\)
\(240\) 0 0
\(241\) −21.8384 + 12.6084i −1.40674 + 0.812180i −0.995072 0.0991549i \(-0.968386\pi\)
−0.411665 + 0.911335i \(0.635053\pi\)
\(242\) −1.06298 + 3.96710i −0.0683311 + 0.255015i
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) 4.80982 0.307917
\(245\) 0 0
\(246\) 5.59423 0.356675
\(247\) 7.74476 2.07520i 0.492787 0.132042i
\(248\) 2.58864 9.66095i 0.164379 0.613471i
\(249\) −9.79189 + 5.65335i −0.620536 + 0.358266i
\(250\) 0 0
\(251\) 2.07559i 0.131010i −0.997852 0.0655051i \(-0.979134\pi\)
0.997852 0.0655051i \(-0.0208659\pi\)
\(252\) −0.781940 + 2.52756i −0.0492576 + 0.159221i
\(253\) 9.52841 9.52841i 0.599046 0.599046i
\(254\) 8.32363 + 4.80565i 0.522271 + 0.301533i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.16526 4.34881i −0.0726869 0.271271i 0.920012 0.391890i \(-0.128179\pi\)
−0.992699 + 0.120619i \(0.961512\pi\)
\(258\) 0.545731 + 0.545731i 0.0339757 + 0.0339757i
\(259\) 0.400169 10.4631i 0.0248653 0.650143i
\(260\) 0 0
\(261\) −2.99705 + 5.19104i −0.185513 + 0.321317i
\(262\) 4.09164 + 1.09635i 0.252782 + 0.0677328i
\(263\) 21.6364 + 5.79744i 1.33415 + 0.357486i 0.854263 0.519842i \(-0.174009\pi\)
0.479892 + 0.877327i \(0.340676\pi\)
\(264\) 1.31272 2.27370i 0.0807924 0.139937i
\(265\) 0 0
\(266\) 10.4168 + 6.55734i 0.638695 + 0.402056i
\(267\) −0.114928 0.114928i −0.00703346 0.00703346i
\(268\) −0.663456 2.47605i −0.0405270 0.151249i
\(269\) −5.86211 10.1535i −0.357419 0.619068i 0.630110 0.776506i \(-0.283010\pi\)
−0.987529 + 0.157438i \(0.949677\pi\)
\(270\) 0 0
\(271\) 20.8254 + 12.0235i 1.26505 + 0.730377i 0.974047 0.226344i \(-0.0726775\pi\)
0.291004 + 0.956722i \(0.406011\pi\)
\(272\) −5.35303 + 5.35303i −0.324575 + 0.324575i
\(273\) −1.01097 4.44629i −0.0611866 0.269102i
\(274\) 8.26262i 0.499163i
\(275\) 0 0
\(276\) 4.44492 2.56627i 0.267552 0.154471i
\(277\) 7.03917 26.2705i 0.422943 1.57844i −0.345433 0.938444i \(-0.612268\pi\)
0.768375 0.640000i \(-0.221066\pi\)
\(278\) 9.03197 2.42011i 0.541702 0.145149i
\(279\) 10.0018 0.598789
\(280\) 0 0
\(281\) 22.1913 1.32382 0.661910 0.749583i \(-0.269746\pi\)
0.661910 + 0.749583i \(0.269746\pi\)
\(282\) −6.12372 + 1.64085i −0.364662 + 0.0977110i
\(283\) −2.87361 + 10.7244i −0.170818 + 0.637502i 0.826408 + 0.563072i \(0.190380\pi\)
−0.997226 + 0.0744302i \(0.976286\pi\)
\(284\) −7.24840 + 4.18486i −0.430113 + 0.248326i
\(285\) 0 0
\(286\) 4.52478i 0.267556i
\(287\) −14.1398 4.37435i −0.834643 0.258210i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 34.9094 + 20.1550i 2.05350 + 1.18559i
\(290\) 0 0
\(291\) 3.07788 + 5.33105i 0.180429 + 0.312512i
\(292\) −3.53363 13.1877i −0.206790 0.771752i
\(293\) 6.51580 + 6.51580i 0.380657 + 0.380657i 0.871339 0.490682i \(-0.163252\pi\)
−0.490682 + 0.871339i \(0.663252\pi\)
\(294\) 3.95280 5.77714i 0.230532 0.336930i
\(295\) 0 0
\(296\) −1.97878 + 3.42734i −0.115014 + 0.199210i
\(297\) 2.53598 + 0.679515i 0.147153 + 0.0394294i
\(298\) −4.59602 1.23150i −0.266240 0.0713389i
\(299\) −4.42280 + 7.66052i −0.255777 + 0.443019i
\(300\) 0 0
\(301\) −0.952640 1.80610i −0.0549093 0.104102i
\(302\) 1.52108 + 1.52108i 0.0875286 + 0.0875286i
\(303\) 1.98617 + 7.41249i 0.114103 + 0.425836i
\(304\) −2.32616 4.02903i −0.133414 0.231081i
\(305\) 0 0
\(306\) −6.55610 3.78517i −0.374787 0.216384i
\(307\) −20.6010 + 20.6010i −1.17576 + 1.17576i −0.194947 + 0.980814i \(0.562454\pi\)
−0.980814 + 0.194947i \(0.937546\pi\)
\(308\) −5.09588 + 4.72045i −0.290365 + 0.268973i
\(309\) 4.06792i 0.231416i
\(310\) 0 0
\(311\) 28.4631 16.4332i 1.61399 0.931840i 0.625562 0.780175i \(-0.284870\pi\)
0.988432 0.151665i \(-0.0484634\pi\)
\(312\) −0.446058 + 1.66471i −0.0252530 + 0.0942456i
\(313\) 21.4272 5.74141i 1.21114 0.324523i 0.403930 0.914790i \(-0.367644\pi\)
0.807208 + 0.590267i \(0.200977\pi\)
\(314\) 3.80434 0.214691
\(315\) 0 0
\(316\) −8.99488 −0.506002
\(317\) −13.8751 + 3.71781i −0.779301 + 0.208813i −0.626476 0.779440i \(-0.715504\pi\)
−0.152824 + 0.988253i \(0.548837\pi\)
\(318\) 2.22057 8.28728i 0.124523 0.464728i
\(319\) −13.6288 + 7.86858i −0.763065 + 0.440556i
\(320\) 0 0
\(321\) 2.81707i 0.157234i
\(322\) −13.2415 + 3.01076i −0.737918 + 0.167783i
\(323\) −24.9040 + 24.9040i −1.38570 + 1.38570i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) 2.23063 + 3.86356i 0.123543 + 0.213983i
\(327\) −3.14740 11.7462i −0.174051 0.649569i
\(328\) 3.95571 + 3.95571i 0.218418 + 0.218418i
\(329\) 16.7611 + 0.641044i 0.924071 + 0.0353419i
\(330\) 0 0
\(331\) 1.44533 2.50339i 0.0794427 0.137599i −0.823567 0.567219i \(-0.808019\pi\)
0.903010 + 0.429620i \(0.141353\pi\)
\(332\) −10.9214 2.92639i −0.599391 0.160606i
\(333\) −3.82271 1.02429i −0.209483 0.0561308i
\(334\) −11.4076 + 19.7585i −0.624194 + 1.08114i
\(335\) 0 0
\(336\) −2.34017 + 1.23434i −0.127667 + 0.0673388i
\(337\) 23.4453 + 23.4453i 1.27715 + 1.27715i 0.942257 + 0.334891i \(0.108699\pi\)
0.334891 + 0.942257i \(0.391301\pi\)
\(338\) 2.59590 + 9.68802i 0.141198 + 0.526959i
\(339\) 1.15877 + 2.00705i 0.0629359 + 0.109008i
\(340\) 0 0
\(341\) 22.7410 + 13.1295i 1.23149 + 0.711003i
\(342\) 3.28969 3.28969i 0.177886 0.177886i
\(343\) −14.5083 + 11.5112i −0.783377 + 0.621547i
\(344\) 0.771781i 0.0416116i
\(345\) 0 0
\(346\) −10.7233 + 6.19112i −0.576490 + 0.332837i
\(347\) 2.93447 10.9516i 0.157531 0.587912i −0.841345 0.540499i \(-0.818235\pi\)
0.998875 0.0474135i \(-0.0150978\pi\)
\(348\) −5.78985 + 1.55139i −0.310369 + 0.0831631i
\(349\) −6.80786 −0.364417 −0.182208 0.983260i \(-0.558325\pi\)
−0.182208 + 0.983260i \(0.558325\pi\)
\(350\) 0 0
\(351\) −1.72343 −0.0919901
\(352\) 2.53598 0.679515i 0.135168 0.0362183i
\(353\) 7.20154 26.8765i 0.383299 1.43049i −0.457531 0.889194i \(-0.651266\pi\)
0.840830 0.541299i \(-0.182067\pi\)
\(354\) −6.68609 + 3.86022i −0.355362 + 0.205168i
\(355\) 0 0
\(356\) 0.162532i 0.00861419i
\(357\) 13.6112 + 14.6937i 0.720380 + 0.777674i
\(358\) −14.3331 + 14.3331i −0.757528 + 0.757528i
\(359\) 11.8979 + 6.86927i 0.627948 + 0.362546i 0.779957 0.625833i \(-0.215241\pi\)
−0.152009 + 0.988379i \(0.548574\pi\)
\(360\) 0 0
\(361\) −1.32204 2.28984i −0.0695809 0.120518i
\(362\) −1.94797 7.26992i −0.102383 0.382098i
\(363\) −2.90412 2.90412i −0.152427 0.152427i
\(364\) 2.42914 3.85887i 0.127322 0.202260i
\(365\) 0 0
\(366\) −2.40491 + 4.16543i −0.125707 + 0.217730i
\(367\) −24.3587 6.52689i −1.27151 0.340701i −0.440903 0.897555i \(-0.645342\pi\)
−0.830610 + 0.556854i \(0.812008\pi\)
\(368\) 4.95766 + 1.32840i 0.258436 + 0.0692477i
\(369\) −2.79711 + 4.84474i −0.145612 + 0.252207i
\(370\) 0 0
\(371\) −12.0928 + 19.2103i −0.627827 + 0.997348i
\(372\) 7.07231 + 7.07231i 0.366682 + 0.366682i
\(373\) −6.95037 25.9391i −0.359876 1.34308i −0.874235 0.485502i \(-0.838637\pi\)
0.514359 0.857575i \(-0.328030\pi\)
\(374\) −9.93774 17.2127i −0.513868 0.890046i
\(375\) 0 0
\(376\) −5.49038 3.16987i −0.283145 0.163474i
\(377\) 7.30472 7.30472i 0.376212 0.376212i
\(378\) −1.79796 1.94096i −0.0924772 0.0998323i
\(379\) 3.51982i 0.180801i −0.995905 0.0904005i \(-0.971185\pi\)
0.995905 0.0904005i \(-0.0288147\pi\)
\(380\) 0 0
\(381\) −8.32363 + 4.80565i −0.426433 + 0.246201i
\(382\) 1.12014 4.18042i 0.0573114 0.213889i
\(383\) −8.65762 + 2.31980i −0.442384 + 0.118536i −0.473133 0.880991i \(-0.656877\pi\)
0.0307499 + 0.999527i \(0.490210\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −21.2681 −1.08252
\(387\) −0.745483 + 0.199752i −0.0378950 + 0.0101539i
\(388\) −1.59323 + 5.94601i −0.0808840 + 0.301863i
\(389\) 27.3119 15.7685i 1.38477 0.799497i 0.392049 0.919944i \(-0.371766\pi\)
0.992720 + 0.120447i \(0.0384329\pi\)
\(390\) 0 0
\(391\) 38.8551i 1.96499i
\(392\) 6.88011 1.29000i 0.347498 0.0651548i
\(393\) −2.99529 + 2.99529i −0.151092 + 0.151092i
\(394\) −17.3073 9.99238i −0.871930 0.503409i
\(395\) 0 0
\(396\) 1.31272 + 2.27370i 0.0659667 + 0.114258i
\(397\) 1.60945 + 6.00656i 0.0807762 + 0.301461i 0.994481 0.104918i \(-0.0334580\pi\)
−0.913705 + 0.406379i \(0.866791\pi\)
\(398\) 0.596847 + 0.596847i 0.0299172 + 0.0299172i
\(399\) −10.8872 + 5.74255i −0.545043 + 0.287487i
\(400\) 0 0
\(401\) 10.2570 17.7657i 0.512211 0.887176i −0.487688 0.873018i \(-0.662160\pi\)
0.999900 0.0141584i \(-0.00450691\pi\)
\(402\) 2.47605 + 0.663456i 0.123494 + 0.0330902i
\(403\) −16.6500 4.46136i −0.829396 0.222236i
\(404\) −3.83699 + 6.64586i −0.190897 + 0.330644i
\(405\) 0 0
\(406\) 15.8473 + 0.606094i 0.786489 + 0.0300799i
\(407\) −7.34708 7.34708i −0.364181 0.364181i
\(408\) −1.95935 7.31238i −0.0970021 0.362017i
\(409\) −12.8256 22.2145i −0.634184 1.09844i −0.986687 0.162628i \(-0.948003\pi\)
0.352504 0.935810i \(-0.385330\pi\)
\(410\) 0 0
\(411\) −7.15564 4.13131i −0.352962 0.203783i
\(412\) 2.87646 2.87646i 0.141713 0.141713i
\(413\) 19.9180 4.52881i 0.980099 0.222848i
\(414\) 5.13255i 0.252251i
\(415\) 0 0
\(416\) −1.49254 + 0.861717i −0.0731777 + 0.0422492i
\(417\) −2.42011 + 9.03197i −0.118513 + 0.442298i
\(418\) 11.7982 3.16132i 0.577069 0.154625i
\(419\) −1.54146 −0.0753054 −0.0376527 0.999291i \(-0.511988\pi\)
−0.0376527 + 0.999291i \(0.511988\pi\)
\(420\) 0 0
\(421\) −20.0850 −0.978884 −0.489442 0.872036i \(-0.662800\pi\)
−0.489442 + 0.872036i \(0.662800\pi\)
\(422\) −21.4285 + 5.74175i −1.04312 + 0.279504i
\(423\) 1.64085 6.12372i 0.0797807 0.297746i
\(424\) 7.43018 4.28981i 0.360841 0.208332i
\(425\) 0 0
\(426\) 8.36973i 0.405515i
\(427\) 9.33568 8.64788i 0.451785 0.418500i
\(428\) −1.99197 + 1.99197i −0.0962855 + 0.0962855i
\(429\) −3.91857 2.26239i −0.189190 0.109229i
\(430\) 0 0
\(431\) −10.9503 18.9665i −0.527457 0.913583i −0.999488 0.0320007i \(-0.989812\pi\)
0.472030 0.881582i \(-0.343521\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) −5.51584 5.51584i −0.265074 0.265074i 0.562038 0.827112i \(-0.310018\pi\)
−0.827112 + 0.562038i \(0.810018\pi\)
\(434\) −12.3456 23.4058i −0.592606 1.12352i
\(435\) 0 0
\(436\) 6.08031 10.5314i 0.291194 0.504362i
\(437\) 23.0646 + 6.18014i 1.10333 + 0.295636i
\(438\) 13.1877 + 3.53363i 0.630133 + 0.168844i
\(439\) −2.62203 + 4.54150i −0.125143 + 0.216754i −0.921789 0.387692i \(-0.873272\pi\)
0.796646 + 0.604446i \(0.206606\pi\)
\(440\) 0 0
\(441\) 3.02675 + 6.31180i 0.144131 + 0.300562i
\(442\) 9.22560 + 9.22560i 0.438817 + 0.438817i
\(443\) −0.336567 1.25609i −0.0159908 0.0596784i 0.957469 0.288535i \(-0.0931681\pi\)
−0.973460 + 0.228856i \(0.926501\pi\)
\(444\) −1.97878 3.42734i −0.0939087 0.162655i
\(445\) 0 0
\(446\) −13.1822 7.61073i −0.624194 0.360378i
\(447\) 3.36452 3.36452i 0.159136 0.159136i
\(448\) −2.52756 0.781940i −0.119416 0.0369432i
\(449\) 22.3625i 1.05535i −0.849445 0.527676i \(-0.823063\pi\)
0.849445 0.527676i \(-0.176937\pi\)
\(450\) 0 0
\(451\) −12.7196 + 7.34366i −0.598942 + 0.345799i
\(452\) −0.599825 + 2.23858i −0.0282134 + 0.105294i
\(453\) −2.07784 + 0.556756i −0.0976255 + 0.0261587i
\(454\) 3.73858 0.175460
\(455\) 0 0
\(456\) 4.65232 0.217865
\(457\) 3.18706 0.853971i 0.149085 0.0399471i −0.183505 0.983019i \(-0.558744\pi\)
0.332589 + 0.943072i \(0.392078\pi\)
\(458\) 3.92933 14.6644i 0.183605 0.685225i
\(459\) 6.55610 3.78517i 0.306013 0.176676i
\(460\) 0 0
\(461\) 6.97417i 0.324819i −0.986723 0.162410i \(-0.948073\pi\)
0.986723 0.162410i \(-0.0519266\pi\)
\(462\) −1.54009 6.77339i −0.0716513 0.315127i
\(463\) −16.6658 + 16.6658i −0.774527 + 0.774527i −0.978894 0.204367i \(-0.934486\pi\)
0.204367 + 0.978894i \(0.434486\pi\)
\(464\) −5.19104 2.99705i −0.240988 0.139135i
\(465\) 0 0
\(466\) −0.606518 1.05052i −0.0280964 0.0486644i
\(467\) 2.96609 + 11.0696i 0.137254 + 0.512240i 0.999978 + 0.00656516i \(0.00208977\pi\)
−0.862724 + 0.505675i \(0.831244\pi\)
\(468\) −1.21865 1.21865i −0.0563322 0.0563322i
\(469\) −5.73959 3.61305i −0.265030 0.166835i
\(470\) 0 0
\(471\) −1.90217 + 3.29465i −0.0876473 + 0.151810i
\(472\) −7.45736 1.99819i −0.343253 0.0919744i
\(473\) −1.95722 0.524436i −0.0899932 0.0241136i
\(474\) 4.49744 7.78980i 0.206574 0.357797i
\(475\) 0 0
\(476\) −0.765475 + 20.0146i −0.0350855 + 0.917367i
\(477\) 6.06671 + 6.06671i 0.277776 + 0.277776i
\(478\) −4.18234 15.6087i −0.191296 0.713926i
\(479\) 5.05860 + 8.76174i 0.231133 + 0.400334i 0.958142 0.286294i \(-0.0924234\pi\)
−0.727009 + 0.686628i \(0.759090\pi\)
\(480\) 0 0
\(481\) 5.90680 + 3.41029i 0.269327 + 0.155496i
\(482\) 17.8310 17.8310i 0.812180 0.812180i
\(483\) 4.01334 12.9728i 0.182614 0.590284i
\(484\) 4.10705i 0.186684i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) 9.56331 35.6908i 0.433355 1.61730i −0.311617 0.950208i \(-0.600871\pi\)
0.744972 0.667095i \(-0.232463\pi\)
\(488\) −4.64593 + 1.24487i −0.210311 + 0.0563528i
\(489\) −4.46126 −0.201745
\(490\) 0 0
\(491\) −8.00737 −0.361368 −0.180684 0.983541i \(-0.557831\pi\)
−0.180684 + 0.983541i \(0.557831\pi\)
\(492\) −5.40361 + 1.44789i −0.243613 + 0.0652760i
\(493\) −11.7445 + 43.8311i −0.528946 + 1.97405i
\(494\) −6.94376 + 4.00898i −0.312415 + 0.180373i
\(495\) 0 0
\(496\) 10.0018i 0.449092i
\(497\) −6.54463 + 21.1550i −0.293567 + 0.948932i
\(498\) 7.99504 7.99504i 0.358266 0.358266i
\(499\) 10.3636 + 5.98341i 0.463937 + 0.267854i 0.713698 0.700453i \(-0.247019\pi\)
−0.249761 + 0.968307i \(0.580352\pi\)
\(500\) 0 0
\(501\) −11.4076 19.7585i −0.509652 0.882744i
\(502\) 0.537203 + 2.00487i 0.0239765 + 0.0894816i
\(503\) −20.3121 20.3121i −0.905670 0.905670i 0.0902493 0.995919i \(-0.471234\pi\)
−0.995919 + 0.0902493i \(0.971234\pi\)
\(504\) 0.101115 2.64382i 0.00450403 0.117765i
\(505\) 0 0
\(506\) −6.73760 + 11.6699i −0.299523 + 0.518789i
\(507\) −9.68802 2.59590i −0.430260 0.115288i
\(508\) −9.28381 2.48759i −0.411902 0.110369i
\(509\) 14.7797 25.5992i 0.655098 1.13466i −0.326771 0.945103i \(-0.605961\pi\)
0.981869 0.189559i \(-0.0607060\pi\)
\(510\) 0 0
\(511\) −30.5696 19.2435i −1.35232 0.851281i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 1.20411 + 4.49380i 0.0531627 + 0.198406i
\(514\) 2.25111 + 3.89904i 0.0992922 + 0.171979i
\(515\) 0 0
\(516\) −0.668382 0.385890i −0.0294239 0.0169879i
\(517\) 11.7695 11.7695i 0.517624 0.517624i
\(518\) 2.32151 + 10.2101i 0.102001 + 0.448607i
\(519\) 12.3822i 0.543520i
\(520\) 0 0
\(521\) −7.64664 + 4.41479i −0.335005 + 0.193415i −0.658061 0.752964i \(-0.728623\pi\)
0.323056 + 0.946380i \(0.395290\pi\)
\(522\) 1.55139 5.78985i 0.0679024 0.253415i
\(523\) −39.8792 + 10.6856i −1.74380 + 0.467249i −0.983284 0.182076i \(-0.941718\pi\)
−0.760511 + 0.649325i \(0.775052\pi\)
\(524\) −4.23598 −0.185050
\(525\) 0 0
\(526\) −22.3996 −0.976669
\(527\) 73.1366 19.5969i 3.18588 0.853654i
\(528\) −0.679515 + 2.53598i −0.0295721 + 0.110365i
\(529\) −2.89515 + 1.67152i −0.125876 + 0.0726746i
\(530\) 0 0
\(531\) 7.72043i 0.335038i
\(532\) −11.7590 3.63784i −0.509818 0.157720i
\(533\) 6.81741 6.81741i 0.295295 0.295295i
\(534\) 0.140757 + 0.0812661i 0.00609115 + 0.00351673i
\(535\) 0 0
\(536\) 1.28170 + 2.21997i 0.0553610 + 0.0958880i
\(537\) −5.24628 19.5794i −0.226394 0.844913i
\(538\) 8.29027 + 8.29027i 0.357419 + 0.357419i
\(539\) −1.40372 + 18.3244i −0.0604625 + 0.789288i
\(540\) 0 0
\(541\) 12.7674 22.1137i 0.548911 0.950742i −0.449438 0.893311i \(-0.648376\pi\)
0.998349 0.0574309i \(-0.0182909\pi\)
\(542\) −23.2277 6.22384i −0.997714 0.267337i
\(543\) 7.26992 + 1.94797i 0.311982 + 0.0835953i
\(544\) 3.78517 6.55610i 0.162288 0.281090i
\(545\) 0 0
\(546\) 2.12731 + 4.03313i 0.0910403 + 0.172602i
\(547\) −22.6183 22.6183i −0.967087 0.967087i 0.0323883 0.999475i \(-0.489689\pi\)
−0.999475 + 0.0323883i \(0.989689\pi\)
\(548\) −2.13852 7.98108i −0.0913532 0.340935i
\(549\) −2.40491 4.16543i −0.102639 0.177776i
\(550\) 0 0
\(551\) −24.1504 13.9432i −1.02884 0.594002i
\(552\) −3.62926 + 3.62926i −0.154471 + 0.154471i
\(553\) −17.4587 + 16.1725i −0.742420 + 0.687723i
\(554\) 27.1973i 1.15550i
\(555\) 0 0
\(556\) −8.09784 + 4.67529i −0.343425 + 0.198277i
\(557\) 4.53960 16.9420i 0.192349 0.717856i −0.800588 0.599215i \(-0.795480\pi\)
0.992937 0.118641i \(-0.0378538\pi\)
\(558\) −9.66095 + 2.58864i −0.408981 + 0.109586i
\(559\) 1.33011 0.0562578
\(560\) 0 0
\(561\) 19.8755 0.839143
\(562\) −21.4351 + 5.74352i −0.904186 + 0.242276i
\(563\) −4.04211 + 15.0854i −0.170355 + 0.635772i 0.826942 + 0.562288i \(0.190079\pi\)
−0.997296 + 0.0734847i \(0.976588\pi\)
\(564\) 5.49038 3.16987i 0.231187 0.133476i
\(565\) 0 0
\(566\) 11.1028i 0.466684i
\(567\) 2.57990 0.586601i 0.108346 0.0246349i
\(568\) 5.91829 5.91829i 0.248326 0.248326i
\(569\) −15.5107 8.95511i −0.650243 0.375418i 0.138307 0.990389i \(-0.455834\pi\)
−0.788549 + 0.614972i \(0.789167\pi\)
\(570\) 0 0
\(571\) 10.2340 + 17.7258i 0.428278 + 0.741800i 0.996720 0.0809234i \(-0.0257869\pi\)
−0.568442 + 0.822723i \(0.692454\pi\)
\(572\) −1.17110 4.37060i −0.0489661 0.182744i
\(573\) 3.06028 + 3.06028i 0.127845 + 0.127845i
\(574\) 14.7901 + 0.565661i 0.617327 + 0.0236102i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −24.7298 6.62634i −1.02952 0.275858i −0.295754 0.955264i \(-0.595571\pi\)
−0.733763 + 0.679406i \(0.762238\pi\)
\(578\) −38.9364 10.4330i −1.61954 0.433955i
\(579\) 10.6340 18.4187i 0.441935 0.765455i
\(580\) 0 0
\(581\) −26.4596 + 13.9563i −1.09773 + 0.579006i
\(582\) −4.35278 4.35278i −0.180429 0.180429i
\(583\) 5.82998 + 21.7578i 0.241453 + 0.901116i
\(584\) 6.82646 + 11.8238i 0.282481 + 0.489271i
\(585\) 0 0
\(586\) −7.98019 4.60737i −0.329659 0.190329i
\(587\) −26.2627 + 26.2627i −1.08398 + 1.08398i −0.0878438 + 0.996134i \(0.527998\pi\)
−0.996134 + 0.0878438i \(0.972002\pi\)
\(588\) −2.32288 + 6.60335i −0.0957941 + 0.272318i
\(589\) 46.5313i 1.91729i
\(590\) 0 0
\(591\) 17.3073 9.99238i 0.711927 0.411032i
\(592\) 1.02429 3.82271i 0.0420981 0.157112i
\(593\) 9.29705 2.49114i 0.381784 0.102299i −0.0628225 0.998025i \(-0.520010\pi\)
0.444606 + 0.895726i \(0.353344\pi\)
\(594\) −2.62544 −0.107723
\(595\) 0 0
\(596\) 4.75815 0.194902
\(597\) −0.815308 + 0.218461i −0.0333683 + 0.00894102i
\(598\) 2.28941 8.54420i 0.0936210 0.349398i
\(599\) −3.36700 + 1.94394i −0.137572 + 0.0794273i −0.567206 0.823576i \(-0.691976\pi\)
0.429634 + 0.903003i \(0.358642\pi\)
\(600\) 0 0
\(601\) 36.4068i 1.48506i 0.669811 + 0.742531i \(0.266375\pi\)
−0.669811 + 0.742531i \(0.733625\pi\)
\(602\) 1.38763 + 1.49800i 0.0565557 + 0.0610538i
\(603\) −1.81260 + 1.81260i −0.0738146 + 0.0738146i
\(604\) −1.86294 1.07557i −0.0758020 0.0437643i
\(605\) 0 0
\(606\) −3.83699 6.64586i −0.155867 0.269969i
\(607\) −1.79097 6.68399i −0.0726932 0.271295i 0.920007 0.391902i \(-0.128183\pi\)
−0.992700 + 0.120607i \(0.961516\pi\)
\(608\) 3.28969 + 3.28969i 0.133414 + 0.133414i
\(609\) −8.44855 + 13.4211i −0.342352 + 0.543851i
\(610\) 0 0
\(611\) −5.46307 + 9.46231i −0.221012 + 0.382804i
\(612\) 7.31238 + 1.95935i 0.295585 + 0.0792019i
\(613\) 43.0478 + 11.5346i 1.73869 + 0.465880i 0.982154 0.188077i \(-0.0602255\pi\)
0.756532 + 0.653957i \(0.226892\pi\)
\(614\) 14.5671 25.2310i 0.587881 1.01824i
\(615\) 0 0
\(616\) 3.70050 5.87851i 0.149098 0.236852i
\(617\) −8.27627 8.27627i −0.333190 0.333190i 0.520607 0.853797i \(-0.325706\pi\)
−0.853797 + 0.520607i \(0.825706\pi\)
\(618\) 1.05286 + 3.92931i 0.0423521 + 0.158060i
\(619\) 5.79761 + 10.0418i 0.233026 + 0.403612i 0.958697 0.284429i \(-0.0918040\pi\)
−0.725671 + 0.688042i \(0.758471\pi\)
\(620\) 0 0
\(621\) −4.44492 2.56627i −0.178368 0.102981i
\(622\) −23.2400 + 23.2400i −0.931840 + 0.931840i
\(623\) −0.292227 0.315469i −0.0117078 0.0126390i
\(624\) 1.72343i 0.0689926i
\(625\) 0 0
\(626\) −19.2111 + 11.0915i −0.767831 + 0.443307i
\(627\) −3.16132 + 11.7982i −0.126251 + 0.471175i
\(628\) −3.67471 + 0.984635i −0.146637 + 0.0392912i
\(629\) −29.9600 −1.19458
\(630\) 0 0
\(631\) 2.25813 0.0898949 0.0449474 0.998989i \(-0.485688\pi\)
0.0449474 + 0.998989i \(0.485688\pi\)
\(632\) 8.68839 2.32805i 0.345606 0.0926047i
\(633\) 5.74175 21.4285i 0.228214 0.851706i
\(634\) 12.4400 7.18226i 0.494057 0.285244i
\(635\) 0 0
\(636\) 8.57963i 0.340204i
\(637\) −2.22323 11.8574i −0.0880875 0.469808i
\(638\) 11.1279 11.1279i 0.440556 0.440556i
\(639\) 7.24840 + 4.18486i 0.286742 + 0.165551i
\(640\) 0 0
\(641\) −9.61246 16.6493i −0.379669 0.657607i 0.611345 0.791364i \(-0.290629\pi\)
−0.991014 + 0.133758i \(0.957296\pi\)
\(642\) −0.729112 2.72108i −0.0287757 0.107393i
\(643\) 15.5634 + 15.5634i 0.613760 + 0.613760i 0.943924 0.330163i \(-0.107104\pi\)
−0.330163 + 0.943924i \(0.607104\pi\)
\(644\) 12.0110 6.33531i 0.473301 0.249646i
\(645\) 0 0
\(646\) 17.6098 30.5011i 0.692848 1.20005i
\(647\) 9.54764 + 2.55828i 0.375357 + 0.100577i 0.441565 0.897229i \(-0.354423\pi\)
−0.0662082 + 0.997806i \(0.521090\pi\)
\(648\) −0.965926 0.258819i −0.0379452 0.0101674i
\(649\) 10.1348 17.5539i 0.397825 0.689053i
\(650\) 0 0
\(651\) 26.4428 + 1.01133i 1.03638 + 0.0396371i
\(652\) −3.15459 3.15459i −0.123543 0.123543i
\(653\) 2.57589 + 9.61337i 0.100803 + 0.376200i 0.997835 0.0657640i \(-0.0209485\pi\)
−0.897033 + 0.441964i \(0.854282\pi\)
\(654\) 6.08031 + 10.5314i 0.237759 + 0.411810i
\(655\) 0 0
\(656\) −4.84474 2.79711i −0.189155 0.109209i
\(657\) −9.65407 + 9.65407i −0.376641 + 0.376641i
\(658\) −16.3559 + 3.71890i −0.637620 + 0.144978i
\(659\) 16.2333i 0.632360i 0.948699 + 0.316180i \(0.102400\pi\)
−0.948699 + 0.316180i \(0.897600\pi\)
\(660\) 0 0
\(661\) −8.77097 + 5.06392i −0.341151 + 0.196964i −0.660781 0.750579i \(-0.729775\pi\)
0.319630 + 0.947543i \(0.396441\pi\)
\(662\) −0.748160 + 2.79217i −0.0290780 + 0.108521i
\(663\) −12.6024 + 3.37680i −0.489437 + 0.131144i
\(664\) 11.3067 0.438785
\(665\) 0 0
\(666\) 3.95756 0.153352
\(667\) 29.7167 7.96256i 1.15064 0.308312i
\(668\) 5.90499 22.0377i 0.228471 0.852665i
\(669\) 13.1822 7.61073i 0.509652 0.294248i
\(670\) 0 0
\(671\) 12.6279i 0.487495i
\(672\) 1.94096 1.79796i 0.0748742 0.0693579i
\(673\) −15.2038 + 15.2038i −0.586062 + 0.586062i −0.936563 0.350501i \(-0.886011\pi\)
0.350501 + 0.936563i \(0.386011\pi\)
\(674\) −28.7145 16.5783i −1.10604 0.638574i
\(675\) 0 0
\(676\) −5.01489 8.68604i −0.192880 0.334078i
\(677\) −3.12140 11.6492i −0.119965 0.447716i 0.879645 0.475630i \(-0.157780\pi\)
−0.999610 + 0.0279145i \(0.991113\pi\)
\(678\) −1.63875 1.63875i −0.0629359 0.0629359i
\(679\) 7.59832 + 14.4056i 0.291597 + 0.552834i
\(680\) 0 0
\(681\) −1.86929 + 3.23770i −0.0716313 + 0.124069i
\(682\) −25.3643 6.79634i −0.971248 0.260245i
\(683\) 11.3177 + 3.03256i 0.433058 + 0.116038i 0.468761 0.883325i \(-0.344700\pi\)
−0.0357033 + 0.999362i \(0.511367\pi\)
\(684\) −2.32616 + 4.02903i −0.0889429 + 0.154054i
\(685\) 0 0
\(686\) 11.0347 14.8740i 0.421305 0.567893i
\(687\) 10.7351 + 10.7351i 0.409570 + 0.409570i
\(688\) −0.199752 0.745483i −0.00761546 0.0284213i
\(689\) −7.39321 12.8054i −0.281659 0.487848i
\(690\) 0 0
\(691\) −24.8579 14.3517i −0.945639 0.545965i −0.0539153 0.998546i \(-0.517170\pi\)
−0.891723 + 0.452581i \(0.850503\pi\)
\(692\) 8.75557 8.75557i 0.332837 0.332837i
\(693\) 6.63597 + 2.05294i 0.252080 + 0.0779847i
\(694\) 11.3379i 0.430382i
\(695\) 0 0
\(696\) 5.19104 2.99705i 0.196766 0.113603i
\(697\) −10.9610 + 40.9071i −0.415178 + 1.54947i
\(698\) 6.57589 1.76200i 0.248901 0.0666929i
\(699\) 1.21304 0.0458812
\(700\) 0 0
\(701\) 47.8761 1.80825 0.904127 0.427264i \(-0.140523\pi\)
0.904127 + 0.427264i \(0.140523\pi\)
\(702\) 1.66471 0.446058i 0.0628304 0.0168354i
\(703\) 4.76533 17.7844i 0.179728 0.670753i
\(704\) −2.27370 + 1.31272i −0.0856933 + 0.0494751i
\(705\) 0 0
\(706\) 27.8246i 1.04719i
\(707\) 4.50156 + 19.7981i 0.169299 + 0.744585i
\(708\) 5.45917 5.45917i 0.205168 0.205168i
\(709\) 22.0830 + 12.7496i 0.829343 + 0.478822i 0.853628 0.520883i \(-0.174397\pi\)
−0.0242844 + 0.999705i \(0.507731\pi\)
\(710\) 0 0
\(711\) 4.49744 + 7.78980i 0.168667 + 0.292140i
\(712\) 0.0420664 + 0.156994i 0.00157651 + 0.00588360i
\(713\) −36.2989 36.2989i −1.35941 1.35941i
\(714\) −16.9504 10.6702i −0.634353 0.399323i
\(715\) 0 0
\(716\) 10.1350 17.5544i 0.378764 0.656038i
\(717\) 15.6087 + 4.18234i 0.582918 + 0.156192i
\(718\) −13.2704 3.55579i −0.495247 0.132701i
\(719\) 16.0438 27.7887i 0.598333 1.03634i −0.394734 0.918795i \(-0.629163\pi\)
0.993067 0.117548i \(-0.0375033\pi\)
\(720\) 0 0
\(721\) 0.411329 10.7549i 0.0153187 0.400532i
\(722\) 1.86964 + 1.86964i 0.0695809 + 0.0695809i
\(723\) 6.52660 + 24.3576i 0.242727 + 0.905869i
\(724\) 3.76319 + 6.51803i 0.139858 + 0.242241i
\(725\) 0 0
\(726\) 3.55681 + 2.05352i 0.132006 + 0.0762134i
\(727\) 11.3772 11.3772i 0.421956 0.421956i −0.463921 0.885877i \(-0.653558\pi\)
0.885877 + 0.463921i \(0.153558\pi\)
\(728\) −1.34762 + 4.35609i −0.0499462 + 0.161447i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −5.05987 + 2.92132i −0.187146 + 0.108049i
\(732\) 1.24487 4.64593i 0.0460119 0.171719i
\(733\) −20.2877 + 5.43607i −0.749343 + 0.200786i −0.613226 0.789907i \(-0.710129\pi\)
−0.136116 + 0.990693i \(0.543462\pi\)
\(734\) 25.2180 0.930812
\(735\) 0 0
\(736\) −5.13255 −0.189188
\(737\) −6.50073 + 1.74187i −0.239458 + 0.0641625i
\(738\) 1.44789 5.40361i 0.0532976 0.198910i
\(739\) −31.8347 + 18.3797i −1.17106 + 0.676110i −0.953929 0.300033i \(-0.903002\pi\)
−0.217128 + 0.976143i \(0.569669\pi\)
\(740\) 0 0
\(741\) 8.01797i 0.294547i
\(742\) 6.70876 21.6855i 0.246286 0.796101i
\(743\) 17.1637 17.1637i 0.629676 0.629676i −0.318310 0.947987i \(-0.603115\pi\)
0.947987 + 0.318310i \(0.103115\pi\)
\(744\) −8.66177 5.00088i −0.317556 0.183341i
\(745\) 0 0
\(746\) 13.4271 + 23.2564i 0.491600 + 0.851477i
\(747\) 2.92639 + 10.9214i 0.107071 + 0.399594i
\(748\) 14.0541 + 14.0541i 0.513868 + 0.513868i
\(749\) −0.284849 + 7.44782i −0.0104081 + 0.272138i
\(750\) 0 0
\(751\) −15.1318 + 26.2091i −0.552168 + 0.956384i 0.445949 + 0.895058i \(0.352866\pi\)
−0.998118 + 0.0613255i \(0.980467\pi\)
\(752\) 6.12372 + 1.64085i 0.223309 + 0.0598355i
\(753\) −2.00487 0.537203i −0.0730615 0.0195768i
\(754\) −5.16522 + 8.94642i −0.188106 + 0.325809i
\(755\) 0 0
\(756\) 2.23906 + 1.40948i 0.0814337 + 0.0512622i
\(757\) 1.48321 + 1.48321i 0.0539082 + 0.0539082i 0.733547 0.679639i \(-0.237863\pi\)
−0.679639 + 0.733547i \(0.737863\pi\)
\(758\) 0.910996 + 3.39988i 0.0330889 + 0.123489i
\(759\) −6.73760 11.6699i −0.244560 0.423590i
\(760\) 0 0
\(761\) 5.99246 + 3.45975i 0.217226 + 0.125416i 0.604665 0.796480i \(-0.293307\pi\)
−0.387439 + 0.921895i \(0.626640\pi\)
\(762\) 6.79622 6.79622i 0.246201 0.246201i
\(763\) −7.13342 31.3732i −0.258247 1.13579i
\(764\) 4.32789i 0.156578i
\(765\) 0 0
\(766\) 7.76221 4.48151i 0.280460 0.161924i
\(767\) −3.44376 + 12.8523i −0.124347 + 0.464069i
\(768\) −0.965926 + 0.258819i −0.0348548 + 0.00933933i
\(769\) −16.5757 −0.597736 −0.298868 0.954294i \(-0.596609\pi\)
−0.298868 + 0.954294i \(0.596609\pi\)
\(770\) 0 0
\(771\) −4.50222 −0.162143
\(772\) 20.5434 5.50458i 0.739372 0.198114i
\(773\) 1.73720 6.48331i 0.0624827 0.233189i −0.927622 0.373521i \(-0.878150\pi\)
0.990104 + 0.140332i \(0.0448171\pi\)
\(774\) 0.668382 0.385890i 0.0240245 0.0138705i
\(775\) 0 0
\(776\) 6.15577i 0.220979i
\(777\) −10.0030 3.09457i −0.358854 0.111017i
\(778\) −22.3001 + 22.3001i −0.799497 + 0.799497i
\(779\) −22.5393 13.0131i −0.807554 0.466241i
\(780\) 0 0
\(781\) 10.9871 + 19.0303i 0.393150 + 0.680956i