Properties

Label 105.3.l.a.22.4
Level 105
Weight 3
Character 105.22
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.4
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.01289 - 1.01289i) q^{2} +(1.22474 - 1.22474i) q^{3} -1.94811i q^{4} +(3.97454 - 3.03365i) q^{5} -2.48106 q^{6} +(1.87083 + 1.87083i) q^{7} +(-6.02478 + 6.02478i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.01289 - 1.01289i) q^{2} +(1.22474 - 1.22474i) q^{3} -1.94811i q^{4} +(3.97454 - 3.03365i) q^{5} -2.48106 q^{6} +(1.87083 + 1.87083i) q^{7} +(-6.02478 + 6.02478i) q^{8} -3.00000i q^{9} +(-7.09851 - 0.953024i) q^{10} -10.7111 q^{11} +(-2.38594 - 2.38594i) q^{12} +(15.5836 - 15.5836i) q^{13} -3.78988i q^{14} +(1.15236 - 8.58324i) q^{15} +4.41239 q^{16} +(-13.8771 - 13.8771i) q^{17} +(-3.03866 + 3.03866i) q^{18} +33.1159i q^{19} +(-5.90989 - 7.74287i) q^{20} +4.58258 q^{21} +(10.8491 + 10.8491i) q^{22} +(8.39058 - 8.39058i) q^{23} +14.7576i q^{24} +(6.59399 - 24.1147i) q^{25} -31.5688 q^{26} +(-3.67423 - 3.67423i) q^{27} +(3.64459 - 3.64459i) q^{28} +42.0711i q^{29} +(-9.86108 + 7.52666i) q^{30} +44.7239 q^{31} +(19.6298 + 19.6298i) q^{32} +(-13.1183 + 13.1183i) q^{33} +28.1118i q^{34} +(13.1111 + 1.76026i) q^{35} -5.84434 q^{36} +(21.6841 + 21.6841i) q^{37} +(33.5427 - 33.5427i) q^{38} -38.1718i q^{39} +(-5.66870 + 42.2228i) q^{40} -22.6096 q^{41} +(-4.64164 - 4.64164i) q^{42} +(9.41107 - 9.41107i) q^{43} +20.8664i q^{44} +(-9.10094 - 11.9236i) q^{45} -16.9974 q^{46} +(46.0043 + 46.0043i) q^{47} +(5.40405 - 5.40405i) q^{48} +7.00000i q^{49} +(-31.1045 + 17.7465i) q^{50} -33.9917 q^{51} +(-30.3586 - 30.3586i) q^{52} +(51.4312 - 51.4312i) q^{53} +7.44318i q^{54} +(-42.5716 + 32.4936i) q^{55} -22.5426 q^{56} +(40.5586 + 40.5586i) q^{57} +(42.6133 - 42.6133i) q^{58} -5.55721i q^{59} +(-16.7211 - 2.24493i) q^{60} -49.2291 q^{61} +(-45.3003 - 45.3003i) q^{62} +(5.61249 - 5.61249i) q^{63} -57.4152i q^{64} +(14.6625 - 109.213i) q^{65} +26.5748 q^{66} +(-38.8463 - 38.8463i) q^{67} +(-27.0341 + 27.0341i) q^{68} -20.5526i q^{69} +(-11.4972 - 15.0630i) q^{70} +23.5507 q^{71} +(18.0743 + 18.0743i) q^{72} +(-60.1053 + 60.1053i) q^{73} -43.9271i q^{74} +(-21.4584 - 37.6103i) q^{75} +64.5136 q^{76} +(-20.0386 - 20.0386i) q^{77} +(-38.6638 + 38.6638i) q^{78} -8.04945i q^{79} +(17.5372 - 13.3856i) q^{80} -9.00000 q^{81} +(22.9010 + 22.9010i) q^{82} +(-5.76487 + 5.76487i) q^{83} -8.92738i q^{84} +(-97.2531 - 13.0569i) q^{85} -19.0647 q^{86} +(51.5264 + 51.5264i) q^{87} +(64.5318 - 64.5318i) q^{88} +62.2564i q^{89} +(-2.85907 + 21.2955i) q^{90} +58.3084 q^{91} +(-16.3458 - 16.3458i) q^{92} +(54.7753 - 54.7753i) q^{93} -93.1945i q^{94} +(100.462 + 131.621i) q^{95} +48.0831 q^{96} +(21.9918 + 21.9918i) q^{97} +(7.09022 - 7.09022i) q^{98} +32.1332i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.01289 1.01289i −0.506444 0.506444i 0.406989 0.913433i \(-0.366579\pi\)
−0.913433 + 0.406989i \(0.866579\pi\)
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 1.94811i 0.487029i
\(5\) 3.97454 3.03365i 0.794909 0.606729i
\(6\) −2.48106 −0.413510
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) −6.02478 + 6.02478i −0.753097 + 0.753097i
\(9\) 3.00000i 0.333333i
\(10\) −7.09851 0.953024i −0.709851 0.0953024i
\(11\) −10.7111 −0.973734 −0.486867 0.873476i \(-0.661860\pi\)
−0.486867 + 0.873476i \(0.661860\pi\)
\(12\) −2.38594 2.38594i −0.198829 0.198829i
\(13\) 15.5836 15.5836i 1.19874 1.19874i 0.224192 0.974545i \(-0.428026\pi\)
0.974545 0.224192i \(-0.0719741\pi\)
\(14\) 3.78988i 0.270706i
\(15\) 1.15236 8.58324i 0.0768239 0.572216i
\(16\) 4.41239 0.275774
\(17\) −13.8771 13.8771i −0.816298 0.816298i 0.169271 0.985569i \(-0.445859\pi\)
−0.985569 + 0.169271i \(0.945859\pi\)
\(18\) −3.03866 + 3.03866i −0.168815 + 0.168815i
\(19\) 33.1159i 1.74294i 0.490446 + 0.871472i \(0.336834\pi\)
−0.490446 + 0.871472i \(0.663166\pi\)
\(20\) −5.90989 7.74287i −0.295494 0.387143i
\(21\) 4.58258 0.218218
\(22\) 10.8491 + 10.8491i 0.493142 + 0.493142i
\(23\) 8.39058 8.39058i 0.364808 0.364808i −0.500772 0.865579i \(-0.666950\pi\)
0.865579 + 0.500772i \(0.166950\pi\)
\(24\) 14.7576i 0.614901i
\(25\) 6.59399 24.1147i 0.263759 0.964588i
\(26\) −31.5688 −1.21419
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 3.64459 3.64459i 0.130164 0.130164i
\(29\) 42.0711i 1.45073i 0.688366 + 0.725364i \(0.258328\pi\)
−0.688366 + 0.725364i \(0.741672\pi\)
\(30\) −9.86108 + 7.52666i −0.328703 + 0.250889i
\(31\) 44.7239 1.44270 0.721352 0.692568i \(-0.243521\pi\)
0.721352 + 0.692568i \(0.243521\pi\)
\(32\) 19.6298 + 19.6298i 0.613433 + 0.613433i
\(33\) −13.1183 + 13.1183i −0.397525 + 0.397525i
\(34\) 28.1118i 0.826819i
\(35\) 13.1111 + 1.76026i 0.374603 + 0.0502931i
\(36\) −5.84434 −0.162343
\(37\) 21.6841 + 21.6841i 0.586056 + 0.586056i 0.936561 0.350505i \(-0.113990\pi\)
−0.350505 + 0.936561i \(0.613990\pi\)
\(38\) 33.5427 33.5427i 0.882703 0.882703i
\(39\) 38.1718i 0.978764i
\(40\) −5.66870 + 42.2228i −0.141717 + 1.05557i
\(41\) −22.6096 −0.551454 −0.275727 0.961236i \(-0.588919\pi\)
−0.275727 + 0.961236i \(0.588919\pi\)
\(42\) −4.64164 4.64164i −0.110515 0.110515i
\(43\) 9.41107 9.41107i 0.218862 0.218862i −0.589157 0.808019i \(-0.700540\pi\)
0.808019 + 0.589157i \(0.200540\pi\)
\(44\) 20.8664i 0.474237i
\(45\) −9.10094 11.9236i −0.202243 0.264970i
\(46\) −16.9974 −0.369510
\(47\) 46.0043 + 46.0043i 0.978816 + 0.978816i 0.999780 0.0209647i \(-0.00667376\pi\)
−0.0209647 + 0.999780i \(0.506674\pi\)
\(48\) 5.40405 5.40405i 0.112584 0.112584i
\(49\) 7.00000i 0.142857i
\(50\) −31.1045 + 17.7465i −0.622090 + 0.354931i
\(51\) −33.9917 −0.666505
\(52\) −30.3586 30.3586i −0.583819 0.583819i
\(53\) 51.4312 51.4312i 0.970400 0.970400i −0.0291746 0.999574i \(-0.509288\pi\)
0.999574 + 0.0291746i \(0.00928789\pi\)
\(54\) 7.44318i 0.137837i
\(55\) −42.5716 + 32.4936i −0.774030 + 0.590793i
\(56\) −22.5426 −0.402547
\(57\) 40.5586 + 40.5586i 0.711554 + 0.711554i
\(58\) 42.6133 42.6133i 0.734712 0.734712i
\(59\) 5.55721i 0.0941900i −0.998890 0.0470950i \(-0.985004\pi\)
0.998890 0.0470950i \(-0.0149964\pi\)
\(60\) −16.7211 2.24493i −0.278686 0.0374155i
\(61\) −49.2291 −0.807034 −0.403517 0.914972i \(-0.632212\pi\)
−0.403517 + 0.914972i \(0.632212\pi\)
\(62\) −45.3003 45.3003i −0.730649 0.730649i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 57.4152i 0.897113i
\(65\) 14.6625 109.213i 0.225578 1.68019i
\(66\) 26.5748 0.402649
\(67\) −38.8463 38.8463i −0.579796 0.579796i 0.355051 0.934847i \(-0.384463\pi\)
−0.934847 + 0.355051i \(0.884463\pi\)
\(68\) −27.0341 + 27.0341i −0.397561 + 0.397561i
\(69\) 20.5526i 0.297864i
\(70\) −11.4972 15.0630i −0.164245 0.215186i
\(71\) 23.5507 0.331699 0.165850 0.986151i \(-0.446963\pi\)
0.165850 + 0.986151i \(0.446963\pi\)
\(72\) 18.0743 + 18.0743i 0.251032 + 0.251032i
\(73\) −60.1053 + 60.1053i −0.823360 + 0.823360i −0.986588 0.163228i \(-0.947809\pi\)
0.163228 + 0.986588i \(0.447809\pi\)
\(74\) 43.9271i 0.593609i
\(75\) −21.4584 37.6103i −0.286112 0.501471i
\(76\) 64.5136 0.848863
\(77\) −20.0386 20.0386i −0.260241 0.260241i
\(78\) −38.6638 + 38.6638i −0.495689 + 0.495689i
\(79\) 8.04945i 0.101892i −0.998701 0.0509459i \(-0.983776\pi\)
0.998701 0.0509459i \(-0.0162236\pi\)
\(80\) 17.5372 13.3856i 0.219215 0.167320i
\(81\) −9.00000 −0.111111
\(82\) 22.9010 + 22.9010i 0.279280 + 0.279280i
\(83\) −5.76487 + 5.76487i −0.0694562 + 0.0694562i −0.740982 0.671525i \(-0.765639\pi\)
0.671525 + 0.740982i \(0.265639\pi\)
\(84\) 8.92738i 0.106278i
\(85\) −97.2531 13.0569i −1.14415 0.153611i
\(86\) −19.0647 −0.221683
\(87\) 51.5264 + 51.5264i 0.592257 + 0.592257i
\(88\) 64.5318 64.5318i 0.733316 0.733316i
\(89\) 62.2564i 0.699510i 0.936841 + 0.349755i \(0.113735\pi\)
−0.936841 + 0.349755i \(0.886265\pi\)
\(90\) −2.85907 + 21.2955i −0.0317675 + 0.236617i
\(91\) 58.3084 0.640752
\(92\) −16.3458 16.3458i −0.177672 0.177672i
\(93\) 54.7753 54.7753i 0.588982 0.588982i
\(94\) 93.1945i 0.991431i
\(95\) 100.462 + 131.621i 1.05749 + 1.38548i
\(96\) 48.0831 0.500866
\(97\) 21.9918 + 21.9918i 0.226719 + 0.226719i 0.811321 0.584601i \(-0.198749\pi\)
−0.584601 + 0.811321i \(0.698749\pi\)
\(98\) 7.09022 7.09022i 0.0723492 0.0723492i
\(99\) 32.1332i 0.324578i
\(100\) −46.9782 12.8458i −0.469782 0.128458i
\(101\) −85.1311 −0.842882 −0.421441 0.906856i \(-0.638476\pi\)
−0.421441 + 0.906856i \(0.638476\pi\)
\(102\) 34.4298 + 34.4298i 0.337547 + 0.337547i
\(103\) −80.6390 + 80.6390i −0.782903 + 0.782903i −0.980320 0.197417i \(-0.936745\pi\)
0.197417 + 0.980320i \(0.436745\pi\)
\(104\) 187.775i 1.80553i
\(105\) 18.2136 13.9019i 0.173463 0.132399i
\(106\) −104.188 −0.982906
\(107\) 32.1195 + 32.1195i 0.300183 + 0.300183i 0.841085 0.540903i \(-0.181917\pi\)
−0.540903 + 0.841085i \(0.681917\pi\)
\(108\) −7.15783 + 7.15783i −0.0662762 + 0.0662762i
\(109\) 59.1909i 0.543036i −0.962433 0.271518i \(-0.912474\pi\)
0.962433 0.271518i \(-0.0875257\pi\)
\(110\) 76.0327 + 10.2079i 0.691207 + 0.0927992i
\(111\) 53.1149 0.478512
\(112\) 8.25483 + 8.25483i 0.0737038 + 0.0737038i
\(113\) −23.2737 + 23.2737i −0.205962 + 0.205962i −0.802549 0.596587i \(-0.796523\pi\)
0.596587 + 0.802549i \(0.296523\pi\)
\(114\) 82.1626i 0.720724i
\(115\) 7.89467 58.8028i 0.0686493 0.511328i
\(116\) 81.9593 0.706546
\(117\) −46.7507 46.7507i −0.399579 0.399579i
\(118\) −5.62883 + 5.62883i −0.0477020 + 0.0477020i
\(119\) 51.9232i 0.436330i
\(120\) 44.7694 + 58.6548i 0.373078 + 0.488790i
\(121\) −6.27280 −0.0518413
\(122\) 49.8635 + 49.8635i 0.408718 + 0.408718i
\(123\) −27.6910 + 27.6910i −0.225130 + 0.225130i
\(124\) 87.1272i 0.702639i
\(125\) −46.9474 115.849i −0.375579 0.926790i
\(126\) −11.3696 −0.0902353
\(127\) 4.63998 + 4.63998i 0.0365353 + 0.0365353i 0.725138 0.688603i \(-0.241776\pi\)
−0.688603 + 0.725138i \(0.741776\pi\)
\(128\) 20.3642 20.3642i 0.159095 0.159095i
\(129\) 23.0523i 0.178700i
\(130\) −125.472 + 95.7687i −0.965167 + 0.736682i
\(131\) −51.2674 −0.391354 −0.195677 0.980668i \(-0.562690\pi\)
−0.195677 + 0.980668i \(0.562690\pi\)
\(132\) 25.5560 + 25.5560i 0.193606 + 0.193606i
\(133\) −61.9542 + 61.9542i −0.465821 + 0.465821i
\(134\) 78.6939i 0.587268i
\(135\) −25.7497 3.45708i −0.190739 0.0256080i
\(136\) 167.212 1.22950
\(137\) −34.4467 34.4467i −0.251436 0.251436i 0.570123 0.821559i \(-0.306895\pi\)
−0.821559 + 0.570123i \(0.806895\pi\)
\(138\) −20.8175 + 20.8175i −0.150852 + 0.150852i
\(139\) 207.019i 1.48935i 0.667430 + 0.744673i \(0.267394\pi\)
−0.667430 + 0.744673i \(0.732606\pi\)
\(140\) 3.42918 25.5420i 0.0244942 0.182443i
\(141\) 112.687 0.799200
\(142\) −23.8542 23.8542i −0.167987 0.167987i
\(143\) −166.917 + 166.917i −1.16725 + 1.16725i
\(144\) 13.2372i 0.0919248i
\(145\) 127.629 + 167.213i 0.880199 + 1.15320i
\(146\) 121.760 0.833972
\(147\) 8.57321 + 8.57321i 0.0583212 + 0.0583212i
\(148\) 42.2430 42.2430i 0.285426 0.285426i
\(149\) 63.0323i 0.423036i 0.977374 + 0.211518i \(0.0678406\pi\)
−0.977374 + 0.211518i \(0.932159\pi\)
\(150\) −16.3601 + 59.8300i −0.109067 + 0.398867i
\(151\) −31.5113 −0.208684 −0.104342 0.994541i \(-0.533274\pi\)
−0.104342 + 0.994541i \(0.533274\pi\)
\(152\) −199.516 199.516i −1.31261 1.31261i
\(153\) −41.6312 + 41.6312i −0.272099 + 0.272099i
\(154\) 40.5937i 0.263596i
\(155\) 177.757 135.676i 1.14682 0.875331i
\(156\) −74.3631 −0.476686
\(157\) −163.580 163.580i −1.04191 1.04191i −0.999082 0.0428304i \(-0.986363\pi\)
−0.0428304 0.999082i \(-0.513637\pi\)
\(158\) −8.15319 + 8.15319i −0.0516025 + 0.0516025i
\(159\) 125.980i 0.792328i
\(160\) 137.570 + 18.4697i 0.859810 + 0.115435i
\(161\) 31.3947 0.194998
\(162\) 9.11599 + 9.11599i 0.0562716 + 0.0562716i
\(163\) −80.5107 + 80.5107i −0.493931 + 0.493931i −0.909542 0.415612i \(-0.863568\pi\)
0.415612 + 0.909542i \(0.363568\pi\)
\(164\) 44.0461i 0.268574i
\(165\) −12.3430 + 91.9358i −0.0748061 + 0.557187i
\(166\) 11.6783 0.0703514
\(167\) −124.516 124.516i −0.745606 0.745606i 0.228044 0.973651i \(-0.426767\pi\)
−0.973651 + 0.228044i \(0.926767\pi\)
\(168\) −27.6090 + 27.6090i −0.164339 + 0.164339i
\(169\) 316.696i 1.87394i
\(170\) 85.2814 + 111.732i 0.501655 + 0.657245i
\(171\) 99.3478 0.580981
\(172\) −18.3338 18.3338i −0.106592 0.106592i
\(173\) 161.634 161.634i 0.934299 0.934299i −0.0636715 0.997971i \(-0.520281\pi\)
0.997971 + 0.0636715i \(0.0202810\pi\)
\(174\) 104.381i 0.599890i
\(175\) 57.4507 32.7783i 0.328290 0.187304i
\(176\) −47.2615 −0.268531
\(177\) −6.80616 6.80616i −0.0384529 0.0384529i
\(178\) 63.0587 63.0587i 0.354263 0.354263i
\(179\) 2.98679i 0.0166860i 0.999965 + 0.00834298i \(0.00265568\pi\)
−0.999965 + 0.00834298i \(0.997344\pi\)
\(180\) −23.2286 + 17.7297i −0.129048 + 0.0984982i
\(181\) −91.6182 −0.506178 −0.253089 0.967443i \(-0.581447\pi\)
−0.253089 + 0.967443i \(0.581447\pi\)
\(182\) −59.0599 59.0599i −0.324505 0.324505i
\(183\) −60.2930 + 60.2930i −0.329470 + 0.329470i
\(184\) 101.103i 0.549471i
\(185\) 151.966 + 20.4025i 0.821438 + 0.110284i
\(186\) −110.963 −0.596573
\(187\) 148.638 + 148.638i 0.794858 + 0.794858i
\(188\) 89.6217 89.6217i 0.476711 0.476711i
\(189\) 13.7477i 0.0727393i
\(190\) 31.5603 235.074i 0.166107 1.23723i
\(191\) −238.486 −1.24862 −0.624308 0.781178i \(-0.714619\pi\)
−0.624308 + 0.781178i \(0.714619\pi\)
\(192\) −70.3190 70.3190i −0.366245 0.366245i
\(193\) −69.3305 + 69.3305i −0.359226 + 0.359226i −0.863527 0.504302i \(-0.831750\pi\)
0.504302 + 0.863527i \(0.331750\pi\)
\(194\) 44.5504i 0.229641i
\(195\) −115.800 151.716i −0.593845 0.778028i
\(196\) 13.6368 0.0695755
\(197\) 63.9728 + 63.9728i 0.324735 + 0.324735i 0.850580 0.525845i \(-0.176251\pi\)
−0.525845 + 0.850580i \(0.676251\pi\)
\(198\) 32.5474 32.5474i 0.164381 0.164381i
\(199\) 50.4616i 0.253576i 0.991930 + 0.126788i \(0.0404668\pi\)
−0.991930 + 0.126788i \(0.959533\pi\)
\(200\) 105.558 + 185.013i 0.527792 + 0.925065i
\(201\) −95.1536 −0.473401
\(202\) 86.2283 + 86.2283i 0.426873 + 0.426873i
\(203\) −78.7078 + 78.7078i −0.387723 + 0.387723i
\(204\) 66.2198i 0.324607i
\(205\) −89.8628 + 68.5895i −0.438355 + 0.334583i
\(206\) 163.357 0.792993
\(207\) −25.1717 25.1717i −0.121603 0.121603i
\(208\) 68.7608 68.7608i 0.330581 0.330581i
\(209\) 354.707i 1.69716i
\(210\) −32.5295 4.36730i −0.154902 0.0207967i
\(211\) 213.312 1.01096 0.505478 0.862840i \(-0.331316\pi\)
0.505478 + 0.862840i \(0.331316\pi\)
\(212\) −100.194 100.194i −0.472612 0.472612i
\(213\) 28.8436 28.8436i 0.135416 0.135416i
\(214\) 65.0670i 0.304051i
\(215\) 8.85485 65.9545i 0.0411853 0.306765i
\(216\) 44.2729 0.204967
\(217\) 83.6707 + 83.6707i 0.385579 + 0.385579i
\(218\) −59.9538 + 59.9538i −0.275017 + 0.275017i
\(219\) 147.227i 0.672271i
\(220\) 63.3013 + 82.9344i 0.287733 + 0.376975i
\(221\) −432.509 −1.95705
\(222\) −53.7994 53.7994i −0.242340 0.242340i
\(223\) −120.538 + 120.538i −0.540530 + 0.540530i −0.923684 0.383154i \(-0.874838\pi\)
0.383154 + 0.923684i \(0.374838\pi\)
\(224\) 73.4482i 0.327894i
\(225\) −72.3441 19.7820i −0.321529 0.0879198i
\(226\) 47.1473 0.208616
\(227\) −106.933 106.933i −0.471069 0.471069i 0.431191 0.902260i \(-0.358093\pi\)
−0.902260 + 0.431191i \(0.858093\pi\)
\(228\) 79.0127 79.0127i 0.346547 0.346547i
\(229\) 409.120i 1.78655i −0.449508 0.893276i \(-0.648401\pi\)
0.449508 0.893276i \(-0.351599\pi\)
\(230\) −67.5571 + 51.5642i −0.293726 + 0.224192i
\(231\) −49.0843 −0.212486
\(232\) −253.469 253.469i −1.09254 1.09254i
\(233\) 248.686 248.686i 1.06732 1.06732i 0.0697560 0.997564i \(-0.477778\pi\)
0.997564 0.0697560i \(-0.0222221\pi\)
\(234\) 94.7065i 0.404729i
\(235\) 322.407 + 43.2854i 1.37194 + 0.184193i
\(236\) −10.8261 −0.0458732
\(237\) −9.85852 9.85852i −0.0415971 0.0415971i
\(238\) −52.5924 + 52.5924i −0.220977 + 0.220977i
\(239\) 375.543i 1.57131i 0.618665 + 0.785655i \(0.287674\pi\)
−0.618665 + 0.785655i \(0.712326\pi\)
\(240\) 5.08466 37.8726i 0.0211861 0.157803i
\(241\) −109.153 −0.452919 −0.226459 0.974021i \(-0.572715\pi\)
−0.226459 + 0.974021i \(0.572715\pi\)
\(242\) 6.35364 + 6.35364i 0.0262547 + 0.0262547i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 95.9039i 0.393049i
\(245\) 21.2355 + 27.8218i 0.0866756 + 0.113558i
\(246\) 56.0958 0.228032
\(247\) 516.065 + 516.065i 2.08933 + 2.08933i
\(248\) −269.451 + 269.451i −1.08650 + 1.08650i
\(249\) 14.1210i 0.0567108i
\(250\) −69.7894 + 164.894i −0.279158 + 0.659577i
\(251\) 93.2026 0.371325 0.185663 0.982614i \(-0.440557\pi\)
0.185663 + 0.982614i \(0.440557\pi\)
\(252\) −10.9338 10.9338i −0.0433880 0.0433880i
\(253\) −89.8722 + 89.8722i −0.355226 + 0.355226i
\(254\) 9.39956i 0.0370061i
\(255\) −135.102 + 103.119i −0.529810 + 0.404388i
\(256\) −270.914 −1.05826
\(257\) 136.298 + 136.298i 0.530344 + 0.530344i 0.920675 0.390331i \(-0.127639\pi\)
−0.390331 + 0.920675i \(0.627639\pi\)
\(258\) −23.3494 + 23.3494i −0.0905016 + 0.0905016i
\(259\) 81.1343i 0.313260i
\(260\) −212.759 28.5643i −0.818303 0.109863i
\(261\) 126.213 0.483576
\(262\) 51.9282 + 51.9282i 0.198199 + 0.198199i
\(263\) −32.1577 + 32.1577i −0.122272 + 0.122272i −0.765595 0.643323i \(-0.777555\pi\)
0.643323 + 0.765595i \(0.277555\pi\)
\(264\) 158.070i 0.598750i
\(265\) 48.3915 360.439i 0.182609 1.36015i
\(266\) 125.505 0.471825
\(267\) 76.2482 + 76.2482i 0.285574 + 0.285574i
\(268\) −75.6770 + 75.6770i −0.282377 + 0.282377i
\(269\) 148.213i 0.550979i 0.961304 + 0.275489i \(0.0888399\pi\)
−0.961304 + 0.275489i \(0.911160\pi\)
\(270\) 22.5800 + 29.5832i 0.0836295 + 0.109568i
\(271\) 287.937 1.06250 0.531250 0.847215i \(-0.321723\pi\)
0.531250 + 0.847215i \(0.321723\pi\)
\(272\) −61.2311 61.2311i −0.225114 0.225114i
\(273\) 71.4129 71.4129i 0.261586 0.261586i
\(274\) 69.7814i 0.254677i
\(275\) −70.6287 + 258.295i −0.256832 + 0.939253i
\(276\) −40.0389 −0.145068
\(277\) 230.005 + 230.005i 0.830342 + 0.830342i 0.987563 0.157222i \(-0.0502537\pi\)
−0.157222 + 0.987563i \(0.550254\pi\)
\(278\) 209.687 209.687i 0.754270 0.754270i
\(279\) 134.172i 0.480902i
\(280\) −89.5967 + 68.3864i −0.319988 + 0.244237i
\(281\) 204.481 0.727689 0.363845 0.931460i \(-0.381464\pi\)
0.363845 + 0.931460i \(0.381464\pi\)
\(282\) −114.139 114.139i −0.404750 0.404750i
\(283\) −81.5319 + 81.5319i −0.288099 + 0.288099i −0.836328 0.548229i \(-0.815302\pi\)
0.548229 + 0.836328i \(0.315302\pi\)
\(284\) 45.8794i 0.161547i
\(285\) 284.242 + 38.1614i 0.997340 + 0.133900i
\(286\) 338.136 1.18229
\(287\) −42.2987 42.2987i −0.147382 0.147382i
\(288\) 58.8895 58.8895i 0.204478 0.204478i
\(289\) 96.1461i 0.332686i
\(290\) 40.0948 298.642i 0.138258 1.02980i
\(291\) 53.8686 0.185115
\(292\) 117.092 + 117.092i 0.401000 + 0.401000i
\(293\) −92.3268 + 92.3268i −0.315108 + 0.315108i −0.846885 0.531776i \(-0.821525\pi\)
0.531776 + 0.846885i \(0.321525\pi\)
\(294\) 17.3674i 0.0590728i
\(295\) −16.8586 22.0874i −0.0571478 0.0748724i
\(296\) −261.283 −0.882713
\(297\) 39.3550 + 39.3550i 0.132508 + 0.132508i
\(298\) 63.8447 63.8447i 0.214244 0.214244i
\(299\) 261.510i 0.874617i
\(300\) −73.2692 + 41.8035i −0.244231 + 0.139345i
\(301\) 35.2130 0.116987
\(302\) 31.9174 + 31.9174i 0.105687 + 0.105687i
\(303\) −104.264 + 104.264i −0.344105 + 0.344105i
\(304\) 146.120i 0.480659i
\(305\) −195.663 + 149.344i −0.641518 + 0.489651i
\(306\) 84.3355 0.275606
\(307\) −323.348 323.348i −1.05325 1.05325i −0.998500 0.0547502i \(-0.982564\pi\)
−0.0547502 0.998500i \(-0.517436\pi\)
\(308\) −39.0375 + 39.0375i −0.126745 + 0.126745i
\(309\) 197.524i 0.639238i
\(310\) −317.473 42.6229i −1.02411 0.137493i
\(311\) 237.025 0.762138 0.381069 0.924547i \(-0.375556\pi\)
0.381069 + 0.924547i \(0.375556\pi\)
\(312\) 229.977 + 229.977i 0.737104 + 0.737104i
\(313\) 92.0773 92.0773i 0.294177 0.294177i −0.544551 0.838728i \(-0.683300\pi\)
0.838728 + 0.544551i \(0.183300\pi\)
\(314\) 331.377i 1.05534i
\(315\) 5.28077 39.3334i 0.0167644 0.124868i
\(316\) −15.6812 −0.0496242
\(317\) 211.432 + 211.432i 0.666979 + 0.666979i 0.957016 0.290036i \(-0.0936674\pi\)
−0.290036 + 0.957016i \(0.593667\pi\)
\(318\) −127.604 + 127.604i −0.401270 + 0.401270i
\(319\) 450.627i 1.41262i
\(320\) −174.178 228.199i −0.544305 0.713123i
\(321\) 78.6765 0.245098
\(322\) −31.7993 31.7993i −0.0987556 0.0987556i
\(323\) 459.552 459.552i 1.42276 1.42276i
\(324\) 17.5330i 0.0541143i
\(325\) −273.036 478.551i −0.840109 1.47247i
\(326\) 163.097 0.500296
\(327\) −72.4938 72.4938i −0.221694 0.221694i
\(328\) 136.218 136.218i 0.415298 0.415298i
\(329\) 172.132i 0.523199i
\(330\) 105.623 80.6186i 0.320069 0.244299i
\(331\) −31.3695 −0.0947718 −0.0473859 0.998877i \(-0.515089\pi\)
−0.0473859 + 0.998877i \(0.515089\pi\)
\(332\) 11.2306 + 11.2306i 0.0338272 + 0.0338272i
\(333\) 65.0522 65.0522i 0.195352 0.195352i
\(334\) 252.242i 0.755216i
\(335\) −272.242 36.5504i −0.812663 0.109106i
\(336\) 20.2201 0.0601789
\(337\) −236.725 236.725i −0.702449 0.702449i 0.262486 0.964936i \(-0.415458\pi\)
−0.964936 + 0.262486i \(0.915458\pi\)
\(338\) −320.777 + 320.777i −0.949046 + 0.949046i
\(339\) 57.0086i 0.168167i
\(340\) −25.4363 + 189.460i −0.0748127 + 0.557236i
\(341\) −479.041 −1.40481
\(342\) −100.628 100.628i −0.294234 0.294234i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 113.399i 0.329649i
\(345\) −62.3494 81.6874i −0.180723 0.236775i
\(346\) −327.434 −0.946341
\(347\) −11.7481 11.7481i −0.0338562 0.0338562i 0.689976 0.723832i \(-0.257621\pi\)
−0.723832 + 0.689976i \(0.757621\pi\)
\(348\) 100.379 100.379i 0.288446 0.288446i
\(349\) 384.239i 1.10097i 0.834845 + 0.550486i \(0.185557\pi\)
−0.834845 + 0.550486i \(0.814443\pi\)
\(350\) −91.3919 24.9904i −0.261120 0.0714012i
\(351\) −114.515 −0.326255
\(352\) −210.257 210.257i −0.597320 0.597320i
\(353\) 244.010 244.010i 0.691247 0.691247i −0.271259 0.962506i \(-0.587440\pi\)
0.962506 + 0.271259i \(0.0874400\pi\)
\(354\) 13.7878i 0.0389485i
\(355\) 93.6031 71.4444i 0.263671 0.201252i
\(356\) 121.283 0.340681
\(357\) −63.5927 63.5927i −0.178131 0.178131i
\(358\) 3.02528 3.02528i 0.00845050 0.00845050i
\(359\) 545.782i 1.52029i −0.649756 0.760143i \(-0.725129\pi\)
0.649756 0.760143i \(-0.274871\pi\)
\(360\) 126.668 + 17.0061i 0.351856 + 0.0472391i
\(361\) −735.664 −2.03785
\(362\) 92.7990 + 92.7990i 0.256351 + 0.256351i
\(363\) −7.68258 + 7.68258i −0.0211641 + 0.0211641i
\(364\) 113.591i 0.312064i
\(365\) −56.5529 + 421.229i −0.154939 + 1.15405i
\(366\) 122.140 0.333716
\(367\) −88.6633 88.6633i −0.241589 0.241589i 0.575918 0.817507i \(-0.304645\pi\)
−0.817507 + 0.575918i \(0.804645\pi\)
\(368\) 37.0225 37.0225i 0.100605 0.100605i
\(369\) 67.8288i 0.183818i
\(370\) −133.259 174.590i −0.360160 0.471865i
\(371\) 192.438 0.518700
\(372\) −106.709 106.709i −0.286851 0.286851i
\(373\) 397.173 397.173i 1.06481 1.06481i 0.0670567 0.997749i \(-0.478639\pi\)
0.997749 0.0670567i \(-0.0213608\pi\)
\(374\) 301.108i 0.805102i
\(375\) −199.384 84.3866i −0.531690 0.225031i
\(376\) −554.332 −1.47429
\(377\) 655.618 + 655.618i 1.73904 + 1.73904i
\(378\) −13.9249 + 13.9249i −0.0368384 + 0.0368384i
\(379\) 371.866i 0.981177i −0.871391 0.490589i \(-0.836782\pi\)
0.871391 0.490589i \(-0.163218\pi\)
\(380\) 256.412 195.711i 0.674769 0.515030i
\(381\) 11.3656 0.0298309
\(382\) 241.559 + 241.559i 0.632355 + 0.632355i
\(383\) −40.1675 + 40.1675i −0.104876 + 0.104876i −0.757598 0.652722i \(-0.773627\pi\)
0.652722 + 0.757598i \(0.273627\pi\)
\(384\) 49.8818i 0.129900i
\(385\) −140.434 18.8543i −0.364764 0.0489721i
\(386\) 140.448 0.363855
\(387\) −28.2332 28.2332i −0.0729540 0.0729540i
\(388\) 42.8425 42.8425i 0.110419 0.110419i
\(389\) 344.589i 0.885833i −0.896563 0.442917i \(-0.853944\pi\)
0.896563 0.442917i \(-0.146056\pi\)
\(390\) −36.3786 + 270.963i −0.0932786 + 0.694777i
\(391\) −232.873 −0.595584
\(392\) −42.1734 42.1734i −0.107585 0.107585i
\(393\) −62.7895 + 62.7895i −0.159770 + 0.159770i
\(394\) 129.595i 0.328920i
\(395\) −24.4192 31.9929i −0.0618207 0.0809946i
\(396\) 62.5992 0.158079
\(397\) −215.178 215.178i −0.542009 0.542009i 0.382108 0.924117i \(-0.375198\pi\)
−0.924117 + 0.382108i \(0.875198\pi\)
\(398\) 51.1120 51.1120i 0.128422 0.128422i
\(399\) 151.756i 0.380341i
\(400\) 29.0952 106.404i 0.0727381 0.266009i
\(401\) 280.987 0.700716 0.350358 0.936616i \(-0.386060\pi\)
0.350358 + 0.936616i \(0.386060\pi\)
\(402\) 96.3800 + 96.3800i 0.239751 + 0.239751i
\(403\) 696.958 696.958i 1.72942 1.72942i
\(404\) 165.845i 0.410508i
\(405\) −35.7709 + 27.3028i −0.0883232 + 0.0674144i
\(406\) 159.444 0.392720
\(407\) −232.260 232.260i −0.570663 0.570663i
\(408\) 204.793 204.793i 0.501943 0.501943i
\(409\) 497.992i 1.21758i 0.793330 + 0.608792i \(0.208346\pi\)
−0.793330 + 0.608792i \(0.791654\pi\)
\(410\) 160.495 + 21.5475i 0.391450 + 0.0525548i
\(411\) −84.3770 −0.205297
\(412\) 157.094 + 157.094i 0.381296 + 0.381296i
\(413\) 10.3966 10.3966i 0.0251733 0.0251733i
\(414\) 50.9923i 0.123170i
\(415\) −5.42415 + 40.4013i −0.0130702 + 0.0973525i
\(416\) 611.806 1.47069
\(417\) 253.545 + 253.545i 0.608023 + 0.608023i
\(418\) −359.279 + 359.279i −0.859519 + 0.859519i
\(419\) 151.915i 0.362565i −0.983431 0.181283i \(-0.941975\pi\)
0.983431 0.181283i \(-0.0580249\pi\)
\(420\) −27.0825 35.4823i −0.0644822 0.0844816i
\(421\) 157.507 0.374126 0.187063 0.982348i \(-0.440103\pi\)
0.187063 + 0.982348i \(0.440103\pi\)
\(422\) −216.061 216.061i −0.511993 0.511993i
\(423\) 138.013 138.013i 0.326272 0.326272i
\(424\) 619.723i 1.46161i
\(425\) −426.147 + 243.136i −1.00270 + 0.572085i
\(426\) −58.4306 −0.137161
\(427\) −92.0991 92.0991i −0.215689 0.215689i
\(428\) 62.5725 62.5725i 0.146198 0.146198i
\(429\) 408.861i 0.953057i
\(430\) −75.7735 + 57.8356i −0.176218 + 0.134501i
\(431\) −608.684 −1.41226 −0.706130 0.708083i \(-0.749560\pi\)
−0.706130 + 0.708083i \(0.749560\pi\)
\(432\) −16.2122 16.2122i −0.0375281 0.0375281i
\(433\) −556.887 + 556.887i −1.28611 + 1.28611i −0.348985 + 0.937128i \(0.613474\pi\)
−0.937128 + 0.348985i \(0.886526\pi\)
\(434\) 169.498i 0.390549i
\(435\) 361.106 + 48.4810i 0.830130 + 0.111451i
\(436\) −115.311 −0.264474
\(437\) 277.862 + 277.862i 0.635839 + 0.635839i
\(438\) 149.125 149.125i 0.340468 0.340468i
\(439\) 450.053i 1.02518i 0.858634 + 0.512588i \(0.171313\pi\)
−0.858634 + 0.512588i \(0.828687\pi\)
\(440\) 60.7178 452.251i 0.137995 1.02784i
\(441\) 21.0000 0.0476190
\(442\) 438.083 + 438.083i 0.991138 + 0.991138i
\(443\) −191.060 + 191.060i −0.431287 + 0.431287i −0.889066 0.457779i \(-0.848645\pi\)
0.457779 + 0.889066i \(0.348645\pi\)
\(444\) 103.474i 0.233049i
\(445\) 188.864 + 247.441i 0.424413 + 0.556046i
\(446\) 244.183 0.547497
\(447\) 77.1985 + 77.1985i 0.172704 + 0.172704i
\(448\) 107.414 107.414i 0.239764 0.239764i
\(449\) 400.837i 0.892733i 0.894850 + 0.446367i \(0.147282\pi\)
−0.894850 + 0.446367i \(0.852718\pi\)
\(450\) 53.2396 + 93.3134i 0.118310 + 0.207363i
\(451\) 242.173 0.536969
\(452\) 45.3398 + 45.3398i 0.100309 + 0.100309i
\(453\) −38.5933 + 38.5933i −0.0851950 + 0.0851950i
\(454\) 216.622i 0.477140i
\(455\) 231.749 176.887i 0.509339 0.388763i
\(456\) −488.712 −1.07174
\(457\) −209.145 209.145i −0.457647 0.457647i 0.440235 0.897882i \(-0.354895\pi\)
−0.897882 + 0.440235i \(0.854895\pi\)
\(458\) −414.393 + 414.393i −0.904789 + 0.904789i
\(459\) 101.975i 0.222168i
\(460\) −114.555 15.3797i −0.249032 0.0334342i
\(461\) 167.687 0.363747 0.181873 0.983322i \(-0.441784\pi\)
0.181873 + 0.983322i \(0.441784\pi\)
\(462\) 49.7169 + 49.7169i 0.107612 + 0.107612i
\(463\) −462.257 + 462.257i −0.998395 + 0.998395i −0.999999 0.00160374i \(-0.999490\pi\)
0.00160374 + 0.999999i \(0.499490\pi\)
\(464\) 185.634i 0.400073i
\(465\) 51.5379 383.876i 0.110834 0.825539i
\(466\) −503.781 −1.08108
\(467\) 453.333 + 453.333i 0.970734 + 0.970734i 0.999584 0.0288502i \(-0.00918458\pi\)
−0.0288502 + 0.999584i \(0.509185\pi\)
\(468\) −91.0758 + 91.0758i −0.194606 + 0.194606i
\(469\) 145.350i 0.309914i
\(470\) −282.719 370.406i −0.601530 0.788097i
\(471\) −400.688 −0.850718
\(472\) 33.4809 + 33.4809i 0.0709342 + 0.0709342i
\(473\) −100.803 + 100.803i −0.213113 + 0.213113i
\(474\) 19.9712i 0.0421332i
\(475\) 798.581 + 218.366i 1.68122 + 0.459718i
\(476\) −101.152 −0.212505
\(477\) −154.294 154.294i −0.323467 0.323467i
\(478\) 380.383 380.383i 0.795781 0.795781i
\(479\) 508.689i 1.06198i 0.847378 + 0.530991i \(0.178180\pi\)
−0.847378 + 0.530991i \(0.821820\pi\)
\(480\) 191.108 145.867i 0.398142 0.303890i
\(481\) 675.830 1.40505
\(482\) 110.560 + 110.560i 0.229378 + 0.229378i
\(483\) 38.4505 38.4505i 0.0796076 0.0796076i
\(484\) 12.2201i 0.0252482i
\(485\) 154.122 + 20.6920i 0.317778 + 0.0426639i
\(486\) 22.3295 0.0459455
\(487\) −417.605 417.605i −0.857505 0.857505i 0.133538 0.991044i \(-0.457366\pi\)
−0.991044 + 0.133538i \(0.957366\pi\)
\(488\) 296.594 296.594i 0.607775 0.607775i
\(489\) 197.210i 0.403293i
\(490\) 6.67117 49.6896i 0.0136146 0.101407i
\(491\) −269.127 −0.548120 −0.274060 0.961713i \(-0.588367\pi\)
−0.274060 + 0.961713i \(0.588367\pi\)
\(492\) 53.9452 + 53.9452i 0.109645 + 0.109645i
\(493\) 583.824 583.824i 1.18423 1.18423i
\(494\) 1045.43i 2.11626i
\(495\) 97.4809 + 127.715i 0.196931 + 0.258010i
\(496\) 197.339 0.397861
\(497\) 44.0593 + 44.0593i 0.0886504 + 0.0886504i
\(498\) 14.3030 14.3030i 0.0287208 0.0287208i
\(499\) 605.561i 1.21355i −0.794874 0.606774i \(-0.792463\pi\)
0.794874 0.606774i \(-0.207537\pi\)
\(500\) −225.687 + 91.4589i −0.451373 + 0.182918i
\(501\) −305.001 −0.608785
\(502\) −94.4038 94.4038i −0.188055 0.188055i
\(503\) −279.566 + 279.566i −0.555798 + 0.555798i −0.928108 0.372310i \(-0.878566\pi\)
0.372310 + 0.928108i \(0.378566\pi\)
\(504\) 67.6279i 0.134182i
\(505\) −338.357 + 258.258i −0.670014 + 0.511401i
\(506\) 182.061 0.359804
\(507\) −387.871 387.871i −0.765032 0.765032i
\(508\) 9.03921 9.03921i 0.0177937 0.0177937i
\(509\) 476.825i 0.936788i 0.883520 + 0.468394i \(0.155167\pi\)
−0.883520 + 0.468394i \(0.844833\pi\)
\(510\) 241.291 + 32.3949i 0.473119 + 0.0635195i
\(511\) −224.893 −0.440104
\(512\) 192.949 + 192.949i 0.376854 + 0.376854i
\(513\) 121.676 121.676i 0.237185 0.237185i
\(514\) 276.110i 0.537179i
\(515\) −75.8730 + 565.133i −0.147326 + 1.09735i
\(516\) −44.9085 −0.0870321
\(517\) −492.756 492.756i −0.953106 0.953106i
\(518\) 82.1800 82.1800i 0.158649 0.158649i
\(519\) 395.920i 0.762852i
\(520\) 569.643 + 746.320i 1.09547 + 1.43523i
\(521\) −331.427 −0.636137 −0.318068 0.948068i \(-0.603034\pi\)
−0.318068 + 0.948068i \(0.603034\pi\)
\(522\) −127.840 127.840i −0.244904 0.244904i
\(523\) −103.667 + 103.667i −0.198216 + 0.198216i −0.799235 0.601019i \(-0.794762\pi\)
0.601019 + 0.799235i \(0.294762\pi\)
\(524\) 99.8748i 0.190601i
\(525\) 30.2174 110.507i 0.0575570 0.210490i
\(526\) 65.1442 0.123848
\(527\) −620.636 620.636i −1.17768 1.17768i
\(528\) −57.8832 + 57.8832i −0.109627 + 0.109627i
\(529\) 388.196i 0.733831i
\(530\) −414.100 + 316.070i −0.781321 + 0.596358i
\(531\) −16.6716 −0.0313967
\(532\) 120.694 + 120.694i 0.226868 + 0.226868i
\(533\) −352.338 + 352.338i −0.661048 + 0.661048i
\(534\) 154.462i 0.289254i
\(535\) 225.100 + 30.2212i 0.420747 + 0.0564882i
\(536\) 468.080 0.873284
\(537\) 3.65805 + 3.65805i 0.00681201 + 0.00681201i
\(538\) 150.123 150.123i 0.279040 0.279040i
\(539\) 74.9775i 0.139105i
\(540\) −6.73478 + 50.1634i −0.0124718 + 0.0928952i
\(541\) 533.708 0.986521 0.493260 0.869882i \(-0.335805\pi\)
0.493260 + 0.869882i \(0.335805\pi\)
\(542\) −291.648 291.648i −0.538096 0.538096i
\(543\) −112.209 + 112.209i −0.206646 + 0.206646i
\(544\) 544.809i 1.00149i
\(545\) −179.564 235.257i −0.329476 0.431664i
\(546\) −144.667 −0.264957
\(547\) 160.272 + 160.272i 0.293001 + 0.293001i 0.838265 0.545263i \(-0.183570\pi\)
−0.545263 + 0.838265i \(0.683570\pi\)
\(548\) −67.1062 + 67.1062i −0.122457 + 0.122457i
\(549\) 147.687i 0.269011i
\(550\) 333.163 190.085i 0.605750 0.345608i
\(551\) −1393.22 −2.52854
\(552\) 123.825 + 123.825i 0.224321 + 0.224321i
\(553\) 15.0591 15.0591i 0.0272317 0.0272317i
\(554\) 465.938i 0.841044i
\(555\) 211.107 161.132i 0.380374 0.290327i
\(556\) 403.297 0.725354
\(557\) 47.4479 + 47.4479i 0.0851847 + 0.0851847i 0.748415 0.663231i \(-0.230815\pi\)
−0.663231 + 0.748415i \(0.730815\pi\)
\(558\) −135.901 + 135.901i −0.243550 + 0.243550i
\(559\) 293.316i 0.524716i
\(560\) 57.8514 + 7.76694i 0.103306 + 0.0138695i
\(561\) 364.088 0.648999
\(562\) −207.116 207.116i −0.368534 0.368534i
\(563\) −13.3672 + 13.3672i −0.0237428 + 0.0237428i −0.718879 0.695136i \(-0.755344\pi\)
0.695136 + 0.718879i \(0.255344\pi\)
\(564\) 219.527i 0.389233i
\(565\) −21.8981 + 163.106i −0.0387578 + 0.288684i
\(566\) 165.165 0.291812
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) −141.887 + 141.887i −0.249802 + 0.249802i
\(569\) 510.404i 0.897020i −0.893778 0.448510i \(-0.851955\pi\)
0.893778 0.448510i \(-0.148045\pi\)
\(570\) −249.252 326.559i −0.437284 0.572910i
\(571\) 957.728 1.67728 0.838641 0.544685i \(-0.183351\pi\)
0.838641 + 0.544685i \(0.183351\pi\)
\(572\) 325.173 + 325.173i 0.568485 + 0.568485i
\(573\) −292.084 + 292.084i −0.509746 + 0.509746i
\(574\) 85.6877i 0.149282i
\(575\) −147.009 257.664i −0.255668 0.448111i
\(576\) −172.246 −0.299038
\(577\) −53.6149 53.6149i −0.0929202 0.0929202i 0.659119 0.752039i \(-0.270929\pi\)
−0.752039 + 0.659119i \(0.770929\pi\)
\(578\) 97.3853 97.3853i 0.168487 0.168487i
\(579\) 169.824i 0.293306i
\(580\) 325.751 248.636i 0.561639 0.428682i
\(581\) −21.5702 −0.0371259
\(582\) −54.5629 54.5629i −0.0937506 0.0937506i
\(583\) −550.883 + 550.883i −0.944912 + 0.944912i
\(584\) 724.242i 1.24014i
\(585\) −327.638 43.9876i −0.560065 0.0751925i
\(586\) 187.033 0.319170
\(587\) −263.340 263.340i −0.448620 0.448620i 0.446275 0.894896i \(-0.352750\pi\)
−0.894896 + 0.446275i \(0.852750\pi\)
\(588\) 16.7016 16.7016i 0.0284041 0.0284041i
\(589\) 1481.07i 2.51455i
\(590\) −5.29615 + 39.4479i −0.00897653 + 0.0668609i
\(591\) 156.701 0.265145
\(592\) 95.6785 + 95.6785i 0.161619 + 0.161619i
\(593\) 530.088 530.088i 0.893908 0.893908i −0.100980 0.994888i \(-0.532198\pi\)
0.994888 + 0.100980i \(0.0321978\pi\)
\(594\) 79.7245i 0.134216i
\(595\) −157.517 206.371i −0.264734 0.346842i
\(596\) 122.794 0.206030
\(597\) 61.8026 + 61.8026i 0.103522 + 0.103522i
\(598\) −264.881 + 264.881i −0.442945 + 0.442945i
\(599\) 837.821i 1.39870i −0.714780 0.699349i \(-0.753473\pi\)
0.714780 0.699349i \(-0.246527\pi\)
\(600\) 355.876 + 97.3116i 0.593127 + 0.162186i
\(601\) −744.532 −1.23882 −0.619411 0.785067i \(-0.712629\pi\)
−0.619411 + 0.785067i \(0.712629\pi\)
\(602\) −35.6668 35.6668i −0.0592472 0.0592472i
\(603\) −116.539 + 116.539i −0.193265 + 0.193265i
\(604\) 61.3877i 0.101635i
\(605\) −24.9315 + 19.0294i −0.0412091 + 0.0314536i
\(606\) 211.215 0.348540
\(607\) −394.249 394.249i −0.649504 0.649504i 0.303369 0.952873i \(-0.401888\pi\)
−0.952873 + 0.303369i \(0.901888\pi\)
\(608\) −650.060 + 650.060i −1.06918 + 1.06918i
\(609\) 192.794i 0.316575i
\(610\) 349.453 + 46.9165i 0.572874 + 0.0769123i
\(611\) 1433.82 2.34668
\(612\) 81.1024 + 81.1024i 0.132520 + 0.132520i
\(613\) 679.539 679.539i 1.10855 1.10855i 0.115204 0.993342i \(-0.463248\pi\)
0.993342 0.115204i \(-0.0367522\pi\)
\(614\) 655.030i 1.06682i
\(615\) −26.0544 + 194.064i −0.0423648 + 0.315551i
\(616\) 241.456 0.391974
\(617\) −215.402 215.402i −0.349111 0.349111i 0.510667 0.859778i \(-0.329398\pi\)
−0.859778 + 0.510667i \(0.829398\pi\)
\(618\) 200.070 200.070i 0.323738 0.323738i
\(619\) 407.617i 0.658508i 0.944241 + 0.329254i \(0.106797\pi\)
−0.944241 + 0.329254i \(0.893203\pi\)
\(620\) −264.313 346.291i −0.426311 0.558533i
\(621\) −61.6579 −0.0992881
\(622\) −240.080 240.080i −0.385980 0.385980i
\(623\) −116.471 + 116.471i −0.186952 + 0.186952i
\(624\) 168.429i 0.269918i
\(625\) −538.039 318.024i −0.860862 0.508839i
\(626\) −186.528 −0.297968
\(627\) −434.426 434.426i −0.692864 0.692864i
\(628\) −318.673 + 318.673i −0.507441 + 0.507441i
\(629\) 601.822i 0.956792i
\(630\) −45.1891 + 34.4915i −0.0717288 + 0.0547484i
\(631\) 1160.78 1.83959 0.919795 0.392399i \(-0.128355\pi\)
0.919795 + 0.392399i \(0.128355\pi\)
\(632\) 48.4961 + 48.4961i 0.0767344 + 0.0767344i
\(633\) 261.252 261.252i 0.412721 0.412721i
\(634\) 428.315i 0.675576i
\(635\) 32.5178 + 4.36574i 0.0512092 + 0.00687518i
\(636\) −245.424 −0.385886
\(637\) 109.085 + 109.085i 0.171248 + 0.171248i
\(638\) −456.435 + 456.435i −0.715415 + 0.715415i
\(639\) 70.6520i 0.110566i
\(640\) 19.1606 142.716i 0.0299384 0.222993i
\(641\) 1053.98 1.64428 0.822139 0.569288i \(-0.192781\pi\)
0.822139 + 0.569288i \(0.192781\pi\)
\(642\) −79.6905 79.6905i −0.124128 0.124128i
\(643\) 391.465 391.465i 0.608810 0.608810i −0.333825 0.942635i \(-0.608340\pi\)
0.942635 + 0.333825i \(0.108340\pi\)
\(644\) 61.1604i 0.0949696i
\(645\) −69.9325 91.6224i −0.108423 0.142050i
\(646\) −930.950 −1.44110
\(647\) 93.4553 + 93.4553i 0.144444 + 0.144444i 0.775631 0.631187i \(-0.217432\pi\)
−0.631187 + 0.775631i \(0.717432\pi\)
\(648\) 54.2230 54.2230i 0.0836774 0.0836774i
\(649\) 59.5237i 0.0917160i
\(650\) −208.165 + 761.274i −0.320253 + 1.17119i
\(651\) 204.950 0.314824
\(652\) 156.844 + 156.844i 0.240558 + 0.240558i
\(653\) −774.653 + 774.653i −1.18630 + 1.18630i −0.208217 + 0.978083i \(0.566766\pi\)
−0.978083 + 0.208217i \(0.933234\pi\)
\(654\) 146.856i 0.224551i
\(655\) −203.765 + 155.527i −0.311091 + 0.237446i
\(656\) −99.7624 −0.152077
\(657\) 180.316 + 180.316i 0.274453 + 0.274453i
\(658\) 174.351 174.351i 0.264971 0.264971i
\(659\) 1143.20i 1.73476i −0.497650 0.867378i \(-0.665804\pi\)
0.497650 0.867378i \(-0.334196\pi\)
\(660\) 179.101 + 24.0456i 0.271366 + 0.0364327i
\(661\) −27.1447 −0.0410661 −0.0205330 0.999789i \(-0.506536\pi\)
−0.0205330 + 0.999789i \(0.506536\pi\)
\(662\) 31.7738 + 31.7738i 0.0479966 + 0.0479966i
\(663\) −529.713 + 529.713i −0.798964 + 0.798964i
\(664\) 69.4641i 0.104615i
\(665\) −58.2926 + 434.187i −0.0876580 + 0.652913i
\(666\) −131.781 −0.197870
\(667\) 353.001 + 353.001i 0.529237 + 0.529237i
\(668\) −242.572 + 242.572i −0.363132 + 0.363132i
\(669\) 295.257i 0.441341i
\(670\) 238.729 + 312.772i 0.356313 + 0.466824i
\(671\) 527.296 0.785837
\(672\) 89.9552 + 89.9552i 0.133862 + 0.133862i
\(673\) −121.151 + 121.151i −0.180016 + 0.180016i −0.791363 0.611347i \(-0.790628\pi\)
0.611347 + 0.791363i \(0.290628\pi\)
\(674\) 479.553i 0.711503i
\(675\) −112.831 + 64.3753i −0.167157 + 0.0953708i
\(676\) −616.960 −0.912662
\(677\) 344.602 + 344.602i 0.509013 + 0.509013i 0.914224 0.405210i \(-0.132802\pi\)
−0.405210 + 0.914224i \(0.632802\pi\)
\(678\) 57.7434 57.7434i 0.0851672 0.0851672i
\(679\) 82.2857i 0.121187i
\(680\) 664.593 507.263i 0.977343 0.745976i
\(681\) −261.931 −0.384626
\(682\) 485.215 + 485.215i 0.711458 + 0.711458i
\(683\) −436.309 + 436.309i −0.638813 + 0.638813i −0.950263 0.311449i \(-0.899186\pi\)
0.311449 + 0.950263i \(0.399186\pi\)
\(684\) 193.541i 0.282954i
\(685\) −241.409 32.4109i −0.352422 0.0473151i
\(686\) 26.5292 0.0386723
\(687\) −501.068 501.068i −0.729357 0.729357i
\(688\) 41.5253 41.5253i 0.0603565 0.0603565i
\(689\) 1602.96i 2.32651i
\(690\) −19.5872 + 145.893i −0.0283872 + 0.211439i
\(691\) −250.866 −0.363048 −0.181524 0.983387i \(-0.558103\pi\)
−0.181524 + 0.983387i \(0.558103\pi\)
\(692\) −314.881 314.881i −0.455031 0.455031i
\(693\) −60.1158 + 60.1158i −0.0867472 + 0.0867472i
\(694\) 23.7990i 0.0342926i
\(695\) 628.022 + 822.806i 0.903629 + 1.18389i
\(696\) −620.869 −0.892054
\(697\) 313.755 + 313.755i 0.450151 + 0.450151i
\(698\) 389.191 389.191i 0.557580 0.557580i
\(699\) 609.153i 0.871463i
\(700\) −63.8558 111.921i −0.0912226 0.159887i
\(701\) 73.4709 0.104809 0.0524044 0.998626i \(-0.483312\pi\)
0.0524044 + 0.998626i \(0.483312\pi\)
\(702\) 115.991 + 115.991i 0.165230 + 0.165230i
\(703\) −718.088 + 718.088i −1.02146 + 1.02146i
\(704\) 614.979i 0.873550i
\(705\) 447.880 341.853i 0.635291 0.484898i
\(706\) −494.310 −0.700156
\(707\) −159.266 159.266i −0.225270 0.225270i
\(708\) −13.2592 + 13.2592i −0.0187277 + 0.0187277i
\(709\) 1378.34i 1.94407i −0.234842 0.972033i \(-0.575457\pi\)
0.234842 0.972033i \(-0.424543\pi\)
\(710\) −167.175 22.4443i −0.235457 0.0316118i
\(711\) −24.1483 −0.0339639
\(712\) −375.081 375.081i −0.526799 0.526799i
\(713\) 375.259 375.259i 0.526310 0.526310i
\(714\) 128.825i 0.180427i
\(715\) −157.052 + 1169.79i −0.219653 + 1.63606i
\(716\) 5.81860 0.00812654
\(717\) 459.945 + 459.945i 0.641485 + 0.641485i
\(718\) −552.817 + 552.817i −0.769940 + 0.769940i
\(719\) 1115.67i 1.55170i 0.630920 + 0.775848i \(0.282677\pi\)
−0.630920 + 0.775848i \(0.717323\pi\)
\(720\) −40.1569 52.6117i −0.0557735 0.0730718i
\(721\) −301.724 −0.418479
\(722\) 745.146 + 745.146i 1.03206 + 1.03206i
\(723\) −133.685 + 133.685i −0.184903 + 0.184903i
\(724\) 178.483i 0.246523i
\(725\) 1014.53 + 277.416i 1.39935 + 0.382643i
\(726\) 15.5632 0.0214369
\(727\) −458.699 458.699i −0.630948 0.630948i 0.317358 0.948306i \(-0.397204\pi\)
−0.948306 + 0.317358i \(0.897204\pi\)
\(728\) −351.295 + 351.295i −0.482548 + 0.482548i
\(729\) 27.0000i 0.0370370i
\(730\) 483.940 369.376i 0.662931 0.505995i
\(731\) −261.196 −0.357313
\(732\) 117.458 + 117.458i 0.160461 + 0.160461i
\(733\) 460.978 460.978i 0.628892 0.628892i −0.318897 0.947789i \(-0.603312\pi\)
0.947789 + 0.318897i \(0.103312\pi\)
\(734\) 179.612i 0.244703i
\(735\) 60.0827 + 8.06651i 0.0817452 + 0.0109748i
\(736\) 329.412 0.447570
\(737\) 416.086 + 416.086i 0.564567 + 0.564567i
\(738\) 68.7030 68.7030i 0.0930935 0.0930935i
\(739\) 999.301i 1.35223i 0.736794 + 0.676117i \(0.236339\pi\)
−0.736794 + 0.676117i \(0.763661\pi\)
\(740\) 39.7464 296.047i 0.0537113 0.400064i
\(741\) 1264.09 1.70593
\(742\) −194.918 194.918i −0.262693 0.262693i
\(743\) 698.589 698.589i 0.940228 0.940228i −0.0580840 0.998312i \(-0.518499\pi\)
0.998312 + 0.0580840i \(0.0184991\pi\)
\(744\) 660.018i 0.887121i
\(745\) 191.218 + 250.525i 0.256668 + 0.336275i
\(746\) −804.583 −1.07853
\(747\) 17.2946 + 17.2946i 0.0231521 + 0.0231521i
\(748\) 289.565 289.565i 0.387118 0.387118i
\(749\) 120.180i 0.160454i
\(750\) 116.479 + 287.428i 0.155306 + 0.383237i
\(751\) 89.3571 0.118984 0.0594921 0.998229i \(-0.481052\pi\)
0.0594921 + 0.998229i \(0.481052\pi\)
\(752\) 202.989 + 202.989i 0.269932 + 0.269932i
\(753\) 114.149 114.149i 0.151593 0.151593i
\(754\) 1328.14i 1.76145i
\(755\) −125.243 + 95.5942i −0.165885 + 0.126615i
\(756\) −26.7821 −0.0354261
\(757\) −171.328 171.328i −0.226325 0.226325i 0.584830 0.811156i \(-0.301161\pi\)
−0.811156 + 0.584830i \(0.801161\pi\)
\(758\) −376.659 + 376.659i −0.496912 + 0.496912i
\(759\) 220.141i 0.290041i
\(760\) −1398.25 187.724i −1.83980 0.247005i
\(761\) 734.145 0.964711 0.482356 0.875975i \(-0.339781\pi\)
0.482356 + 0.875975i \(0.339781\pi\)
\(762\) −11.5121 11.5121i −0.0151077 0.0151077i
\(763\) 110.736 110.736i 0.145133 0.145133i
\(764\) 464.598i 0.608112i
\(765\) −39.1707 + 291.759i −0.0512035 + 0.381385i
\(766\) 81.3703 0.106228
\(767\) −86.6012 86.6012i −0.112909 0.112909i
\(768\) −331.801 + 331.801i −0.432032 + 0.432032i
\(769\) 703.817i 0.915237i 0.889149 + 0.457618i \(0.151297\pi\)
−0.889149 + 0.457618i \(0.848703\pi\)
\(770\) 123.147 + 161.341i 0.159931 + 0.209534i
\(771\) 333.861 0.433024
\(772\) 135.064 + 135.064i 0.174953 + 0.174953i