Properties

Label 690.2.i.f.47.14
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.14
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.31559 - 1.12660i) q^{3} -1.00000i q^{4} +(0.192443 - 2.22777i) q^{5} +(0.133641 - 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.461565 - 2.96428i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.31559 - 1.12660i) q^{3} -1.00000i q^{4} +(0.192443 - 2.22777i) q^{5} +(0.133641 - 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.461565 - 2.96428i) q^{9} +(-1.43919 - 1.71135i) q^{10} -2.97195i q^{11} +(-1.12660 - 1.31559i) q^{12} +(-1.33263 + 1.33263i) q^{13} +2.77200 q^{14} +(-2.25662 - 3.14764i) q^{15} -1.00000 q^{16} +(-0.217329 + 0.217329i) q^{17} +(-1.76969 - 2.42244i) q^{18} +6.42606i q^{19} +(-2.22777 - 0.192443i) q^{20} +(4.78694 + 0.370453i) q^{21} +(-2.10149 - 2.10149i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.72689 - 0.133641i) q^{24} +(-4.92593 - 0.857436i) q^{25} +1.88462i q^{26} +(-2.73231 - 4.41978i) q^{27} +(1.96010 - 1.96010i) q^{28} +1.22002 q^{29} +(-3.82139 - 0.630048i) q^{30} +6.33502 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.34819 - 3.90988i) q^{33} +0.307349i q^{34} +(4.74387 - 3.98945i) q^{35} +(-2.96428 - 0.461565i) q^{36} +(1.43305 + 1.43305i) q^{37} +(4.54391 + 4.54391i) q^{38} +(-0.251863 + 3.25453i) q^{39} +(-1.71135 + 1.43919i) q^{40} +3.04579i q^{41} +(3.64682 - 3.12292i) q^{42} +(-1.80190 + 1.80190i) q^{43} -2.97195 q^{44} +(-6.51491 - 1.59872i) q^{45} +1.00000 q^{46} +(-0.199419 + 0.199419i) q^{47} +(-1.31559 + 1.12660i) q^{48} +0.683996i q^{49} +(-4.08946 + 2.87686i) q^{50} +(-0.0410744 + 0.530758i) q^{51} +(1.33263 + 1.33263i) q^{52} +(-9.17886 - 9.17886i) q^{53} +(-5.05729 - 1.19322i) q^{54} +(-6.62083 - 0.571930i) q^{55} -2.77200i q^{56} +(7.23957 + 8.45408i) q^{57} +(0.862686 - 0.862686i) q^{58} -9.43000 q^{59} +(-3.14764 + 2.25662i) q^{60} +5.57225 q^{61} +(4.47954 - 4.47954i) q^{62} +(6.71501 - 4.90558i) q^{63} +1.00000i q^{64} +(2.71234 + 3.22525i) q^{65} +(-5.13223 - 0.397175i) q^{66} +(9.41060 + 9.41060i) q^{67} +(0.217329 + 0.217329i) q^{68} +(1.72689 + 0.133641i) q^{69} +(0.533451 - 6.17539i) q^{70} +7.64983i q^{71} +(-2.42244 + 1.76969i) q^{72} +(-4.05708 + 4.05708i) q^{73} +2.02664 q^{74} +(-7.44650 + 4.42150i) q^{75} +6.42606 q^{76} +(5.82533 - 5.82533i) q^{77} +(2.12321 + 2.47940i) q^{78} -14.4298i q^{79} +(-0.192443 + 2.22777i) q^{80} +(-8.57391 - 2.73642i) q^{81} +(2.15370 + 2.15370i) q^{82} +(12.1736 + 12.1736i) q^{83} +(0.370453 - 4.78694i) q^{84} +(0.442336 + 0.525982i) q^{85} +2.54827i q^{86} +(1.60505 - 1.37447i) q^{87} +(-2.10149 + 2.10149i) q^{88} +2.45643 q^{89} +(-5.73720 + 3.47628i) q^{90} -5.22418 q^{91} +(0.707107 - 0.707107i) q^{92} +(8.33431 - 7.13701i) q^{93} +0.282021i q^{94} +(14.3158 + 1.23665i) q^{95} +(-0.133641 + 1.72689i) q^{96} +(8.98748 + 8.98748i) q^{97} +(0.483658 + 0.483658i) q^{98} +(-8.80970 - 1.37175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 1.31559 1.12660i 0.759557 0.650440i
\(4\) 1.00000i 0.500000i
\(5\) 0.192443 2.22777i 0.0860629 0.996290i
\(6\) 0.133641 1.72689i 0.0545587 0.704999i
\(7\) 1.96010 + 1.96010i 0.740849 + 0.740849i 0.972741 0.231893i \(-0.0744918\pi\)
−0.231893 + 0.972741i \(0.574492\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.461565 2.96428i 0.153855 0.988093i
\(10\) −1.43919 1.71135i −0.455113 0.541176i
\(11\) 2.97195i 0.896078i −0.894014 0.448039i \(-0.852123\pi\)
0.894014 0.448039i \(-0.147877\pi\)
\(12\) −1.12660 1.31559i −0.325220 0.379779i
\(13\) −1.33263 + 1.33263i −0.369605 + 0.369605i −0.867333 0.497728i \(-0.834168\pi\)
0.497728 + 0.867333i \(0.334168\pi\)
\(14\) 2.77200 0.740849
\(15\) −2.25662 3.14764i −0.582657 0.812718i
\(16\) −1.00000 −0.250000
\(17\) −0.217329 + 0.217329i −0.0527100 + 0.0527100i −0.732970 0.680260i \(-0.761867\pi\)
0.680260 + 0.732970i \(0.261867\pi\)
\(18\) −1.76969 2.42244i −0.417119 0.570974i
\(19\) 6.42606i 1.47424i 0.675762 + 0.737120i \(0.263815\pi\)
−0.675762 + 0.737120i \(0.736185\pi\)
\(20\) −2.22777 0.192443i −0.498145 0.0430315i
\(21\) 4.78694 + 0.370453i 1.04459 + 0.0808394i
\(22\) −2.10149 2.10149i −0.448039 0.448039i
\(23\) 0.707107 + 0.707107i 0.147442 + 0.147442i
\(24\) −1.72689 0.133641i −0.352499 0.0272793i
\(25\) −4.92593 0.857436i −0.985186 0.171487i
\(26\) 1.88462i 0.369605i
\(27\) −2.73231 4.41978i −0.525834 0.850587i
\(28\) 1.96010 1.96010i 0.370424 0.370424i
\(29\) 1.22002 0.226552 0.113276 0.993564i \(-0.463866\pi\)
0.113276 + 0.993564i \(0.463866\pi\)
\(30\) −3.82139 0.630048i −0.697688 0.115030i
\(31\) 6.33502 1.13780 0.568902 0.822405i \(-0.307368\pi\)
0.568902 + 0.822405i \(0.307368\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −3.34819 3.90988i −0.582845 0.680623i
\(34\) 0.307349i 0.0527100i
\(35\) 4.74387 3.98945i 0.801860 0.674340i
\(36\) −2.96428 0.461565i −0.494047 0.0769276i
\(37\) 1.43305 + 1.43305i 0.235592 + 0.235592i 0.815022 0.579430i \(-0.196725\pi\)
−0.579430 + 0.815022i \(0.696725\pi\)
\(38\) 4.54391 + 4.54391i 0.737120 + 0.737120i
\(39\) −0.251863 + 3.25453i −0.0403303 + 0.521142i
\(40\) −1.71135 + 1.43919i −0.270588 + 0.227557i
\(41\) 3.04579i 0.475672i 0.971305 + 0.237836i \(0.0764380\pi\)
−0.971305 + 0.237836i \(0.923562\pi\)
\(42\) 3.64682 3.12292i 0.562717 0.481878i
\(43\) −1.80190 + 1.80190i −0.274786 + 0.274786i −0.831024 0.556237i \(-0.812245\pi\)
0.556237 + 0.831024i \(0.312245\pi\)
\(44\) −2.97195 −0.448039
\(45\) −6.51491 1.59872i −0.971186 0.238323i
\(46\) 1.00000 0.147442
\(47\) −0.199419 + 0.199419i −0.0290883 + 0.0290883i −0.721501 0.692413i \(-0.756548\pi\)
0.692413 + 0.721501i \(0.256548\pi\)
\(48\) −1.31559 + 1.12660i −0.189889 + 0.162610i
\(49\) 0.683996i 0.0977137i
\(50\) −4.08946 + 2.87686i −0.578337 + 0.406850i
\(51\) −0.0410744 + 0.530758i −0.00575157 + 0.0743210i
\(52\) 1.33263 + 1.33263i 0.184803 + 0.184803i
\(53\) −9.17886 9.17886i −1.26081 1.26081i −0.950699 0.310114i \(-0.899633\pi\)
−0.310114 0.950699i \(-0.600367\pi\)
\(54\) −5.05729 1.19322i −0.688211 0.162377i
\(55\) −6.62083 0.571930i −0.892753 0.0771191i
\(56\) 2.77200i 0.370424i
\(57\) 7.23957 + 8.45408i 0.958905 + 1.11977i
\(58\) 0.862686 0.862686i 0.113276 0.113276i
\(59\) −9.43000 −1.22768 −0.613841 0.789430i \(-0.710376\pi\)
−0.613841 + 0.789430i \(0.710376\pi\)
\(60\) −3.14764 + 2.25662i −0.406359 + 0.291329i
\(61\) 5.57225 0.713454 0.356727 0.934209i \(-0.383893\pi\)
0.356727 + 0.934209i \(0.383893\pi\)
\(62\) 4.47954 4.47954i 0.568902 0.568902i
\(63\) 6.71501 4.90558i 0.846011 0.618044i
\(64\) 1.00000i 0.125000i
\(65\) 2.71234 + 3.22525i 0.336425 + 0.400043i
\(66\) −5.13223 0.397175i −0.631734 0.0488888i
\(67\) 9.41060 + 9.41060i 1.14969 + 1.14969i 0.986614 + 0.163074i \(0.0521410\pi\)
0.163074 + 0.986614i \(0.447859\pi\)
\(68\) 0.217329 + 0.217329i 0.0263550 + 0.0263550i
\(69\) 1.72689 + 0.133641i 0.207893 + 0.0160885i
\(70\) 0.533451 6.17539i 0.0637596 0.738100i
\(71\) 7.64983i 0.907868i 0.891035 + 0.453934i \(0.149980\pi\)
−0.891035 + 0.453934i \(0.850020\pi\)
\(72\) −2.42244 + 1.76969i −0.285487 + 0.208560i
\(73\) −4.05708 + 4.05708i −0.474845 + 0.474845i −0.903479 0.428633i \(-0.858995\pi\)
0.428633 + 0.903479i \(0.358995\pi\)
\(74\) 2.02664 0.235592
\(75\) −7.44650 + 4.42150i −0.859848 + 0.510550i
\(76\) 6.42606 0.737120
\(77\) 5.82533 5.82533i 0.663858 0.663858i
\(78\) 2.12321 + 2.47940i 0.240406 + 0.280736i
\(79\) 14.4298i 1.62348i −0.584018 0.811741i \(-0.698520\pi\)
0.584018 0.811741i \(-0.301480\pi\)
\(80\) −0.192443 + 2.22777i −0.0215157 + 0.249072i
\(81\) −8.57391 2.73642i −0.952657 0.304047i
\(82\) 2.15370 + 2.15370i 0.237836 + 0.237836i
\(83\) 12.1736 + 12.1736i 1.33622 + 1.33622i 0.899688 + 0.436533i \(0.143794\pi\)
0.436533 + 0.899688i \(0.356206\pi\)
\(84\) 0.370453 4.78694i 0.0404197 0.522297i
\(85\) 0.442336 + 0.525982i 0.0479780 + 0.0570508i
\(86\) 2.54827i 0.274786i
\(87\) 1.60505 1.37447i 0.172080 0.147359i
\(88\) −2.10149 + 2.10149i −0.224019 + 0.224019i
\(89\) 2.45643 0.260381 0.130191 0.991489i \(-0.458441\pi\)
0.130191 + 0.991489i \(0.458441\pi\)
\(90\) −5.73720 + 3.47628i −0.604754 + 0.366432i
\(91\) −5.22418 −0.547643
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) 8.33431 7.13701i 0.864227 0.740073i
\(94\) 0.282021i 0.0290883i
\(95\) 14.3158 + 1.23665i 1.46877 + 0.126877i
\(96\) −0.133641 + 1.72689i −0.0136397 + 0.176250i
\(97\) 8.98748 + 8.98748i 0.912541 + 0.912541i 0.996472 0.0839309i \(-0.0267475\pi\)
−0.0839309 + 0.996472i \(0.526748\pi\)
\(98\) 0.483658 + 0.483658i 0.0488568 + 0.0488568i
\(99\) −8.80970 1.37175i −0.885409 0.137866i
\(100\) −0.857436 + 4.92593i −0.0857436 + 0.492593i
\(101\) 3.00976i 0.299482i 0.988725 + 0.149741i \(0.0478440\pi\)
−0.988725 + 0.149741i \(0.952156\pi\)
\(102\) 0.346258 + 0.404346i 0.0342847 + 0.0400363i
\(103\) −1.81831 + 1.81831i −0.179163 + 0.179163i −0.790991 0.611828i \(-0.790435\pi\)
0.611828 + 0.790991i \(0.290435\pi\)
\(104\) 1.88462 0.184803
\(105\) 1.74649 10.5929i 0.170440 1.03376i
\(106\) −12.9809 −1.26081
\(107\) 10.1552 10.1552i 0.981744 0.981744i −0.0180921 0.999836i \(-0.505759\pi\)
0.999836 + 0.0180921i \(0.00575922\pi\)
\(108\) −4.41978 + 2.73231i −0.425294 + 0.262917i
\(109\) 3.22282i 0.308690i −0.988017 0.154345i \(-0.950673\pi\)
0.988017 0.154345i \(-0.0493268\pi\)
\(110\) −5.08605 + 4.27722i −0.484936 + 0.407817i
\(111\) 3.49978 + 0.270842i 0.332184 + 0.0257072i
\(112\) −1.96010 1.96010i −0.185212 0.185212i
\(113\) 3.72990 + 3.72990i 0.350880 + 0.350880i 0.860437 0.509557i \(-0.170191\pi\)
−0.509557 + 0.860437i \(0.670191\pi\)
\(114\) 11.0971 + 0.858785i 1.03934 + 0.0804326i
\(115\) 1.71135 1.43919i 0.159584 0.134206i
\(116\) 1.22002i 0.113276i
\(117\) 3.33519 + 4.56539i 0.308339 + 0.422070i
\(118\) −6.66802 + 6.66802i −0.613841 + 0.613841i
\(119\) −0.851973 −0.0781003
\(120\) −0.630048 + 3.82139i −0.0575152 + 0.348844i
\(121\) 2.16749 0.197044
\(122\) 3.94018 3.94018i 0.356727 0.356727i
\(123\) 3.43137 + 4.00701i 0.309396 + 0.361300i
\(124\) 6.33502i 0.568902i
\(125\) −2.85813 + 10.8088i −0.255639 + 0.966772i
\(126\) 1.27946 8.21699i 0.113983 0.732028i
\(127\) −9.95020 9.95020i −0.882938 0.882938i 0.110895 0.993832i \(-0.464628\pi\)
−0.993832 + 0.110895i \(0.964628\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −0.340552 + 4.40057i −0.0299840 + 0.387448i
\(130\) 4.19851 + 0.362682i 0.368234 + 0.0318093i
\(131\) 4.14724i 0.362346i 0.983451 + 0.181173i \(0.0579894\pi\)
−0.983451 + 0.181173i \(0.942011\pi\)
\(132\) −3.90988 + 3.34819i −0.340311 + 0.291423i
\(133\) −12.5957 + 12.5957i −1.09219 + 1.09219i
\(134\) 13.3086 1.14969
\(135\) −10.3721 + 5.23641i −0.892686 + 0.450679i
\(136\) 0.307349 0.0263550
\(137\) −6.71805 + 6.71805i −0.573962 + 0.573962i −0.933233 0.359271i \(-0.883025\pi\)
0.359271 + 0.933233i \(0.383025\pi\)
\(138\) 1.31559 1.12660i 0.111991 0.0959022i
\(139\) 21.3303i 1.80921i −0.426247 0.904607i \(-0.640165\pi\)
0.426247 0.904607i \(-0.359835\pi\)
\(140\) −3.98945 4.74387i −0.337170 0.400930i
\(141\) −0.0376896 + 0.487019i −0.00317404 + 0.0410144i
\(142\) 5.40925 + 5.40925i 0.453934 + 0.453934i
\(143\) 3.96052 + 3.96052i 0.331195 + 0.331195i
\(144\) −0.461565 + 2.96428i −0.0384638 + 0.247023i
\(145\) 0.234784 2.71793i 0.0194978 0.225712i
\(146\) 5.73758i 0.474845i
\(147\) 0.770587 + 0.899860i 0.0635569 + 0.0742192i
\(148\) 1.43305 1.43305i 0.117796 0.117796i
\(149\) −2.04707 −0.167703 −0.0838514 0.996478i \(-0.526722\pi\)
−0.0838514 + 0.996478i \(0.526722\pi\)
\(150\) −2.13900 + 8.39194i −0.174649 + 0.685199i
\(151\) −2.64015 −0.214852 −0.107426 0.994213i \(-0.534261\pi\)
−0.107426 + 0.994213i \(0.534261\pi\)
\(152\) 4.54391 4.54391i 0.368560 0.368560i
\(153\) 0.543912 + 0.744535i 0.0439727 + 0.0601921i
\(154\) 8.23826i 0.663858i
\(155\) 1.21913 14.1130i 0.0979227 1.13358i
\(156\) 3.25453 + 0.251863i 0.260571 + 0.0201652i
\(157\) 0.750993 + 0.750993i 0.0599358 + 0.0599358i 0.736439 0.676504i \(-0.236506\pi\)
−0.676504 + 0.736439i \(0.736506\pi\)
\(158\) −10.2034 10.2034i −0.811741 0.811741i
\(159\) −22.4165 1.73477i −1.77774 0.137577i
\(160\) 1.43919 + 1.71135i 0.113778 + 0.135294i
\(161\) 2.77200i 0.218464i
\(162\) −7.99761 + 4.12773i −0.628352 + 0.324305i
\(163\) 6.60415 6.60415i 0.517277 0.517277i −0.399469 0.916747i \(-0.630806\pi\)
0.916747 + 0.399469i \(0.130806\pi\)
\(164\) 3.04579 0.237836
\(165\) −9.35465 + 6.70657i −0.728259 + 0.522106i
\(166\) 17.2160 1.33622
\(167\) −5.25056 + 5.25056i −0.406300 + 0.406300i −0.880446 0.474146i \(-0.842757\pi\)
0.474146 + 0.880446i \(0.342757\pi\)
\(168\) −3.12292 3.64682i −0.240939 0.281359i
\(169\) 9.44819i 0.726784i
\(170\) 0.684704 + 0.0591471i 0.0525144 + 0.00453638i
\(171\) 19.0487 + 2.96605i 1.45669 + 0.226819i
\(172\) 1.80190 + 1.80190i 0.137393 + 0.137393i
\(173\) 16.1787 + 16.1787i 1.23004 + 1.23004i 0.963947 + 0.266093i \(0.0857329\pi\)
0.266093 + 0.963947i \(0.414267\pi\)
\(174\) 0.163045 2.10684i 0.0123604 0.159719i
\(175\) −7.97466 11.3360i −0.602828 0.856920i
\(176\) 2.97195i 0.224019i
\(177\) −12.4060 + 10.6238i −0.932495 + 0.798533i
\(178\) 1.73696 1.73696i 0.130191 0.130191i
\(179\) −12.6087 −0.942418 −0.471209 0.882022i \(-0.656182\pi\)
−0.471209 + 0.882022i \(0.656182\pi\)
\(180\) −1.59872 + 6.51491i −0.119161 + 0.485593i
\(181\) −1.75381 −0.130360 −0.0651799 0.997874i \(-0.520762\pi\)
−0.0651799 + 0.997874i \(0.520762\pi\)
\(182\) −3.69405 + 3.69405i −0.273822 + 0.273822i
\(183\) 7.33081 6.27767i 0.541909 0.464059i
\(184\) 1.00000i 0.0737210i
\(185\) 3.46829 2.91673i 0.254994 0.214442i
\(186\) 0.846618 10.9399i 0.0620771 0.802150i
\(187\) 0.645891 + 0.645891i 0.0472322 + 0.0472322i
\(188\) 0.199419 + 0.199419i 0.0145441 + 0.0145441i
\(189\) 3.30761 14.0188i 0.240593 1.01972i
\(190\) 10.9972 9.24836i 0.797824 0.670946i
\(191\) 26.9285i 1.94848i 0.225520 + 0.974238i \(0.427592\pi\)
−0.225520 + 0.974238i \(0.572408\pi\)
\(192\) 1.12660 + 1.31559i 0.0813050 + 0.0949447i
\(193\) −10.9317 + 10.9317i −0.786878 + 0.786878i −0.980981 0.194103i \(-0.937820\pi\)
0.194103 + 0.980981i \(0.437820\pi\)
\(194\) 12.7102 0.912541
\(195\) 7.20189 + 1.18740i 0.515738 + 0.0850317i
\(196\) 0.683996 0.0488568
\(197\) 1.97929 1.97929i 0.141019 0.141019i −0.633073 0.774092i \(-0.718207\pi\)
0.774092 + 0.633073i \(0.218207\pi\)
\(198\) −7.19938 + 5.25943i −0.511637 + 0.373771i
\(199\) 15.8892i 1.12636i −0.826336 0.563178i \(-0.809579\pi\)
0.826336 0.563178i \(-0.190421\pi\)
\(200\) 2.87686 + 4.08946i 0.203425 + 0.289168i
\(201\) 22.9825 + 1.77857i 1.62106 + 0.125451i
\(202\) 2.12822 + 2.12822i 0.149741 + 0.149741i
\(203\) 2.39137 + 2.39137i 0.167841 + 0.167841i
\(204\) 0.530758 + 0.0410744i 0.0371605 + 0.00287579i
\(205\) 6.78531 + 0.586139i 0.473907 + 0.0409377i
\(206\) 2.57147i 0.179163i
\(207\) 2.42244 1.76969i 0.168371 0.123002i
\(208\) 1.33263 1.33263i 0.0924013 0.0924013i
\(209\) 19.0980 1.32103
\(210\) −6.25536 8.72527i −0.431661 0.602101i
\(211\) 11.3907 0.784169 0.392085 0.919929i \(-0.371754\pi\)
0.392085 + 0.919929i \(0.371754\pi\)
\(212\) −9.17886 + 9.17886i −0.630407 + 0.630407i
\(213\) 8.61826 + 10.0641i 0.590514 + 0.689578i
\(214\) 14.3617i 0.981744i
\(215\) 3.66745 + 4.36097i 0.250118 + 0.297416i
\(216\) −1.19322 + 5.05729i −0.0811884 + 0.344105i
\(217\) 12.4173 + 12.4173i 0.842941 + 0.842941i
\(218\) −2.27888 2.27888i −0.154345 0.154345i
\(219\) −0.766775 + 9.90815i −0.0518138 + 0.669531i
\(220\) −0.571930 + 6.62083i −0.0385595 + 0.446377i
\(221\) 0.579238i 0.0389638i
\(222\) 2.66623 2.28320i 0.178946 0.153239i
\(223\) −10.4680 + 10.4680i −0.700989 + 0.700989i −0.964623 0.263634i \(-0.915079\pi\)
0.263634 + 0.964623i \(0.415079\pi\)
\(224\) −2.77200 −0.185212
\(225\) −4.81532 + 14.2061i −0.321021 + 0.947072i
\(226\) 5.27488 0.350880
\(227\) 16.1663 16.1663i 1.07299 1.07299i 0.0758747 0.997117i \(-0.475825\pi\)
0.997117 0.0758747i \(-0.0241749\pi\)
\(228\) 8.45408 7.23957i 0.559885 0.479453i
\(229\) 16.0298i 1.05928i −0.848224 0.529638i \(-0.822328\pi\)
0.848224 0.529638i \(-0.177672\pi\)
\(230\) 0.192443 2.22777i 0.0126893 0.146895i
\(231\) 1.10097 14.2266i 0.0724384 0.936038i
\(232\) −0.862686 0.862686i −0.0566381 0.0566381i
\(233\) 4.14654 + 4.14654i 0.271649 + 0.271649i 0.829764 0.558115i \(-0.188475\pi\)
−0.558115 + 0.829764i \(0.688475\pi\)
\(234\) 5.58655 + 0.869877i 0.365204 + 0.0568657i
\(235\) 0.405884 + 0.482637i 0.0264769 + 0.0314838i
\(236\) 9.43000i 0.613841i
\(237\) −16.2566 18.9838i −1.05598 1.23313i
\(238\) −0.602436 + 0.602436i −0.0390501 + 0.0390501i
\(239\) −29.7656 −1.92538 −0.962690 0.270608i \(-0.912775\pi\)
−0.962690 + 0.270608i \(0.912775\pi\)
\(240\) 2.25662 + 3.14764i 0.145664 + 0.203180i
\(241\) −18.1553 −1.16949 −0.584743 0.811219i \(-0.698805\pi\)
−0.584743 + 0.811219i \(0.698805\pi\)
\(242\) 1.53265 1.53265i 0.0985222 0.0985222i
\(243\) −14.3626 + 6.05932i −0.921362 + 0.388706i
\(244\) 5.57225i 0.356727i
\(245\) 1.52379 + 0.131630i 0.0973512 + 0.00840953i
\(246\) 5.25973 + 0.407041i 0.335348 + 0.0259520i
\(247\) −8.56357 8.56357i −0.544887 0.544887i
\(248\) −4.47954 4.47954i −0.284451 0.284451i
\(249\) 29.7301 + 2.30076i 1.88407 + 0.145805i
\(250\) 5.62200 + 9.66401i 0.355567 + 0.611206i
\(251\) 19.1213i 1.20693i −0.797390 0.603464i \(-0.793787\pi\)
0.797390 0.603464i \(-0.206213\pi\)
\(252\) −4.90558 6.71501i −0.309022 0.423006i
\(253\) 2.10149 2.10149i 0.132119 0.132119i
\(254\) −14.0717 −0.882938
\(255\) 1.17450 + 0.193645i 0.0735502 + 0.0121265i
\(256\) 1.00000 0.0625000
\(257\) −17.0084 + 17.0084i −1.06096 + 1.06096i −0.0629387 + 0.998017i \(0.520047\pi\)
−0.998017 + 0.0629387i \(0.979953\pi\)
\(258\) 2.87086 + 3.35248i 0.178732 + 0.208716i
\(259\) 5.61785i 0.349076i
\(260\) 3.22525 2.71234i 0.200022 0.168212i
\(261\) 0.563120 3.61649i 0.0348563 0.223855i
\(262\) 2.93254 + 2.93254i 0.181173 + 0.181173i
\(263\) −12.3574 12.3574i −0.761992 0.761992i 0.214690 0.976682i \(-0.431126\pi\)
−0.976682 + 0.214690i \(0.931126\pi\)
\(264\) −0.397175 + 5.13223i −0.0244444 + 0.315867i
\(265\) −22.2148 + 18.6820i −1.36464 + 1.14763i
\(266\) 17.8131i 1.09219i
\(267\) 3.23166 2.76740i 0.197774 0.169362i
\(268\) 9.41060 9.41060i 0.574844 0.574844i
\(269\) −20.0999 −1.22552 −0.612758 0.790271i \(-0.709940\pi\)
−0.612758 + 0.790271i \(0.709940\pi\)
\(270\) −3.63146 + 11.0369i −0.221004 + 0.671682i
\(271\) −27.8676 −1.69284 −0.846419 0.532518i \(-0.821246\pi\)
−0.846419 + 0.532518i \(0.821246\pi\)
\(272\) 0.217329 0.217329i 0.0131775 0.0131775i
\(273\) −6.87289 + 5.88554i −0.415966 + 0.356209i
\(274\) 9.50076i 0.573962i
\(275\) −2.54826 + 14.6396i −0.153666 + 0.882804i
\(276\) 0.133641 1.72689i 0.00804423 0.103946i
\(277\) 7.04930 + 7.04930i 0.423551 + 0.423551i 0.886424 0.462873i \(-0.153182\pi\)
−0.462873 + 0.886424i \(0.653182\pi\)
\(278\) −15.0828 15.0828i −0.904607 0.904607i
\(279\) 2.92403 18.7788i 0.175057 1.12426i
\(280\) −6.17539 0.533451i −0.369050 0.0318798i
\(281\) 15.7886i 0.941867i −0.882169 0.470934i \(-0.843917\pi\)
0.882169 0.470934i \(-0.156083\pi\)
\(282\) 0.317724 + 0.371025i 0.0189202 + 0.0220942i
\(283\) 13.2043 13.2043i 0.784912 0.784912i −0.195743 0.980655i \(-0.562712\pi\)
0.980655 + 0.195743i \(0.0627118\pi\)
\(284\) 7.64983 0.453934
\(285\) 20.2270 14.5012i 1.19814 0.858977i
\(286\) 5.60102 0.331195
\(287\) −5.97005 + 5.97005i −0.352401 + 0.352401i
\(288\) 1.76969 + 2.42244i 0.104280 + 0.142744i
\(289\) 16.9055i 0.994443i
\(290\) −1.75585 2.08788i −0.103107 0.122605i
\(291\) 21.9491 + 1.69860i 1.28668 + 0.0995740i
\(292\) 4.05708 + 4.05708i 0.237423 + 0.237423i
\(293\) −6.93824 6.93824i −0.405336 0.405336i 0.474772 0.880109i \(-0.342530\pi\)
−0.880109 + 0.474772i \(0.842530\pi\)
\(294\) 1.18118 + 0.0914098i 0.0688880 + 0.00533113i
\(295\) −1.81473 + 21.0079i −0.105658 + 1.22313i
\(296\) 2.02664i 0.117796i
\(297\) −13.1354 + 8.12031i −0.762192 + 0.471188i
\(298\) −1.44750 + 1.44750i −0.0838514 + 0.0838514i
\(299\) −1.88462 −0.108991
\(300\) 4.42150 + 7.44650i 0.255275 + 0.429924i
\(301\) −7.06380 −0.407150
\(302\) −1.86687 + 1.86687i −0.107426 + 0.107426i
\(303\) 3.39078 + 3.95962i 0.194795 + 0.227474i
\(304\) 6.42606i 0.368560i
\(305\) 1.07234 12.4137i 0.0614019 0.710807i
\(306\) 0.911070 + 0.141862i 0.0520824 + 0.00810970i
\(307\) −8.38939 8.38939i −0.478808 0.478808i 0.425943 0.904750i \(-0.359943\pi\)
−0.904750 + 0.425943i \(0.859943\pi\)
\(308\) −5.82533 5.82533i −0.331929 0.331929i
\(309\) −0.343654 + 4.44065i −0.0195498 + 0.252620i
\(310\) −9.11733 10.8414i −0.517830 0.615753i
\(311\) 22.7094i 1.28773i −0.765139 0.643865i \(-0.777330\pi\)
0.765139 0.643865i \(-0.222670\pi\)
\(312\) 2.47940 2.12321i 0.140368 0.120203i
\(313\) −19.0911 + 19.0911i −1.07909 + 1.07909i −0.0825035 + 0.996591i \(0.526292\pi\)
−0.996591 + 0.0825035i \(0.973708\pi\)
\(314\) 1.06206 0.0599358
\(315\) −9.63625 15.9035i −0.542941 0.896063i
\(316\) −14.4298 −0.811741
\(317\) 0.0275450 0.0275450i 0.00154708 0.00154708i −0.706333 0.707880i \(-0.749652\pi\)
0.707880 + 0.706333i \(0.249652\pi\)
\(318\) −17.0775 + 14.6242i −0.957660 + 0.820084i
\(319\) 3.62585i 0.203009i
\(320\) 2.22777 + 0.192443i 0.124536 + 0.0107579i
\(321\) 1.91931 24.8010i 0.107125 1.38426i
\(322\) 1.96010 + 1.96010i 0.109232 + 0.109232i
\(323\) −1.39657 1.39657i −0.0777072 0.0777072i
\(324\) −2.73642 + 8.57391i −0.152023 + 0.476329i
\(325\) 7.70709 5.42180i 0.427513 0.300747i
\(326\) 9.33968i 0.517277i
\(327\) −3.63082 4.23992i −0.200785 0.234468i
\(328\) 2.15370 2.15370i 0.118918 0.118918i
\(329\) −0.781764 −0.0431000
\(330\) −1.87247 + 11.3570i −0.103076 + 0.625182i
\(331\) 1.05162 0.0578024 0.0289012 0.999582i \(-0.490799\pi\)
0.0289012 + 0.999582i \(0.490799\pi\)
\(332\) 12.1736 12.1736i 0.668111 0.668111i
\(333\) 4.90941 3.58652i 0.269034 0.196540i
\(334\) 7.42541i 0.406300i
\(335\) 22.7757 19.1537i 1.24437 1.04648i
\(336\) −4.78694 0.370453i −0.261149 0.0202099i
\(337\) −10.0242 10.0242i −0.546054 0.546054i 0.379243 0.925297i \(-0.376184\pi\)
−0.925297 + 0.379243i \(0.876184\pi\)
\(338\) 6.68088 + 6.68088i 0.363392 + 0.363392i
\(339\) 9.10912 + 0.704939i 0.494740 + 0.0382871i
\(340\) 0.525982 0.442336i 0.0285254 0.0239890i
\(341\) 18.8274i 1.01956i
\(342\) 15.5667 11.3721i 0.841753 0.614934i
\(343\) 12.3800 12.3800i 0.668458 0.668458i
\(344\) 2.54827 0.137393
\(345\) 0.630048 3.82139i 0.0339206 0.205737i
\(346\) 22.8801 1.23004
\(347\) −18.2887 + 18.2887i −0.981790 + 0.981790i −0.999837 0.0180467i \(-0.994255\pi\)
0.0180467 + 0.999837i \(0.494255\pi\)
\(348\) −1.37447 1.60505i −0.0736794 0.0860398i
\(349\) 28.7041i 1.53649i −0.640154 0.768247i \(-0.721129\pi\)
0.640154 0.768247i \(-0.278871\pi\)
\(350\) −13.6547 2.37681i −0.729874 0.127046i
\(351\) 9.53110 + 2.24877i 0.508732 + 0.120031i
\(352\) 2.10149 + 2.10149i 0.112010 + 0.112010i
\(353\) −10.4582 10.4582i −0.556631 0.556631i 0.371715 0.928347i \(-0.378770\pi\)
−0.928347 + 0.371715i \(0.878770\pi\)
\(354\) −1.26023 + 16.2846i −0.0669807 + 0.865514i
\(355\) 17.0421 + 1.47215i 0.904499 + 0.0781337i
\(356\) 2.45643i 0.130191i
\(357\) −1.12085 + 0.959829i −0.0593216 + 0.0507995i
\(358\) −8.91569 + 8.91569i −0.471209 + 0.471209i
\(359\) 10.4419 0.551105 0.275552 0.961286i \(-0.411139\pi\)
0.275552 + 0.961286i \(0.411139\pi\)
\(360\) 3.47628 + 5.73720i 0.183216 + 0.302377i
\(361\) −22.2943 −1.17338
\(362\) −1.24013 + 1.24013i −0.0651799 + 0.0651799i
\(363\) 2.85153 2.44188i 0.149667 0.128166i
\(364\) 5.22418i 0.273822i
\(365\) 8.25749 + 9.81900i 0.432217 + 0.513950i
\(366\) 0.744681 9.62265i 0.0389251 0.502984i
\(367\) 11.3139 + 11.3139i 0.590580 + 0.590580i 0.937788 0.347208i \(-0.112870\pi\)
−0.347208 + 0.937788i \(0.612870\pi\)
\(368\) −0.707107 0.707107i −0.0368605 0.0368605i
\(369\) 9.02856 + 1.40583i 0.470008 + 0.0731846i
\(370\) 0.390012 4.51489i 0.0202758 0.234718i
\(371\) 35.9830i 1.86814i
\(372\) −7.13701 8.33431i −0.370037 0.432114i
\(373\) −20.2494 + 20.2494i −1.04847 + 1.04847i −0.0497082 + 0.998764i \(0.515829\pi\)
−0.998764 + 0.0497082i \(0.984171\pi\)
\(374\) 0.913428 0.0472322
\(375\) 8.41706 + 17.4400i 0.434655 + 0.900597i
\(376\) 0.282021 0.0145441
\(377\) −1.62584 + 1.62584i −0.0837349 + 0.0837349i
\(378\) −7.57398 12.2516i −0.389563 0.630157i
\(379\) 31.4641i 1.61620i −0.589042 0.808102i \(-0.700495\pi\)
0.589042 0.808102i \(-0.299505\pi\)
\(380\) 1.23665 14.3158i 0.0634387 0.734385i
\(381\) −24.3003 1.88056i −1.24494 0.0963438i
\(382\) 19.0413 + 19.0413i 0.974238 + 0.974238i
\(383\) 5.10098 + 5.10098i 0.260648 + 0.260648i 0.825317 0.564669i \(-0.190996\pi\)
−0.564669 + 0.825317i \(0.690996\pi\)
\(384\) 1.72689 + 0.133641i 0.0881249 + 0.00681983i
\(385\) −11.8565 14.0985i −0.604261 0.718529i
\(386\) 15.4597i 0.786878i
\(387\) 4.50963 + 6.17302i 0.229237 + 0.313792i
\(388\) 8.98748 8.98748i 0.456270 0.456270i
\(389\) −18.3647 −0.931129 −0.465565 0.885014i \(-0.654149\pi\)
−0.465565 + 0.885014i \(0.654149\pi\)
\(390\) 5.93212 4.25288i 0.300385 0.215353i
\(391\) −0.307349 −0.0155433
\(392\) 0.483658 0.483658i 0.0244284 0.0244284i
\(393\) 4.67226 + 5.45608i 0.235685 + 0.275223i
\(394\) 2.79914i 0.141019i
\(395\) −32.1463 2.77691i −1.61746 0.139722i
\(396\) −1.37175 + 8.80970i −0.0689331 + 0.442704i
\(397\) −6.90089 6.90089i −0.346346 0.346346i 0.512401 0.858746i \(-0.328756\pi\)
−0.858746 + 0.512401i \(0.828756\pi\)
\(398\) −11.2354 11.2354i −0.563178 0.563178i
\(399\) −2.38055 + 30.7612i −0.119177 + 1.53998i
\(400\) 4.92593 + 0.857436i 0.246297 + 0.0428718i
\(401\) 18.3481i 0.916261i 0.888885 + 0.458131i \(0.151481\pi\)
−0.888885 + 0.458131i \(0.848519\pi\)
\(402\) 17.5087 14.9934i 0.873254 0.747803i
\(403\) −8.44225 + 8.44225i −0.420538 + 0.420538i
\(404\) 3.00976 0.149741
\(405\) −7.74610 + 18.5741i −0.384907 + 0.922955i
\(406\) 3.38190 0.167841
\(407\) 4.25896 4.25896i 0.211109 0.211109i
\(408\) 0.404346 0.346258i 0.0200181 0.0171423i
\(409\) 15.8713i 0.784783i 0.919798 + 0.392392i \(0.128352\pi\)
−0.919798 + 0.392392i \(0.871648\pi\)
\(410\) 5.21240 4.38348i 0.257422 0.216485i
\(411\) −1.26969 + 16.4067i −0.0626292 + 0.809285i
\(412\) 1.81831 + 1.81831i 0.0895816 + 0.0895816i
\(413\) −18.4838 18.4838i −0.909526 0.909526i
\(414\) 0.461565 2.96428i 0.0226847 0.145686i
\(415\) 29.4626 24.7772i 1.44626 1.21626i
\(416\) 1.88462i 0.0924013i
\(417\) −24.0306 28.0620i −1.17679 1.37420i
\(418\) 13.5043 13.5043i 0.660517 0.660517i
\(419\) 19.9035 0.972349 0.486175 0.873862i \(-0.338392\pi\)
0.486175 + 0.873862i \(0.338392\pi\)
\(420\) −10.5929 1.74649i −0.516881 0.0852202i
\(421\) −9.07200 −0.442142 −0.221071 0.975258i \(-0.570955\pi\)
−0.221071 + 0.975258i \(0.570955\pi\)
\(422\) 8.05445 8.05445i 0.392085 0.392085i
\(423\) 0.499089 + 0.683180i 0.0242666 + 0.0332173i
\(424\) 12.9809i 0.630407i
\(425\) 1.25689 0.884201i 0.0609682 0.0428901i
\(426\) 13.2104 + 1.02233i 0.640046 + 0.0495320i
\(427\) 10.9222 + 10.9222i 0.528561 + 0.528561i
\(428\) −10.1552 10.1552i −0.490872 0.490872i
\(429\) 9.67232 + 0.748525i 0.466984 + 0.0361391i
\(430\) 5.67695 + 0.490395i 0.273767 + 0.0236489i
\(431\) 6.60333i 0.318071i −0.987273 0.159036i \(-0.949162\pi\)
0.987273 0.159036i \(-0.0508384\pi\)
\(432\) 2.73231 + 4.41978i 0.131458 + 0.212647i
\(433\) −2.95935 + 2.95935i −0.142217 + 0.142217i −0.774631 0.632414i \(-0.782064\pi\)
0.632414 + 0.774631i \(0.282064\pi\)
\(434\) 17.5607 0.842941
\(435\) −2.75313 3.84019i −0.132002 0.184123i
\(436\) −3.22282 −0.154345
\(437\) −4.54391 + 4.54391i −0.217365 + 0.217365i
\(438\) 6.46393 + 7.54831i 0.308858 + 0.360672i
\(439\) 11.2528i 0.537068i −0.963270 0.268534i \(-0.913461\pi\)
0.963270 0.268534i \(-0.0865392\pi\)
\(440\) 4.27722 + 5.08605i 0.203909 + 0.242468i
\(441\) 2.02756 + 0.315709i 0.0965503 + 0.0150338i
\(442\) −0.409583 0.409583i −0.0194819 0.0194819i
\(443\) −16.2317 16.2317i −0.771194 0.771194i 0.207122 0.978315i \(-0.433590\pi\)
−0.978315 + 0.207122i \(0.933590\pi\)
\(444\) 0.270842 3.49978i 0.0128536 0.166092i
\(445\) 0.472722 5.47236i 0.0224092 0.259415i
\(446\) 14.8040i 0.700989i
\(447\) −2.69311 + 2.30622i −0.127380 + 0.109081i
\(448\) −1.96010 + 1.96010i −0.0926061 + 0.0926061i
\(449\) −3.47861 −0.164166 −0.0820828 0.996626i \(-0.526157\pi\)
−0.0820828 + 0.996626i \(0.526157\pi\)
\(450\) 6.64027 + 13.4502i 0.313025 + 0.634047i
\(451\) 9.05193 0.426239
\(452\) 3.72990 3.72990i 0.175440 0.175440i
\(453\) −3.47336 + 2.97438i −0.163193 + 0.139749i
\(454\) 22.8625i 1.07299i
\(455\) −1.00535 + 11.6383i −0.0471318 + 0.545611i
\(456\) 0.858785 11.0971i 0.0402163 0.519669i
\(457\) 24.5212 + 24.5212i 1.14705 + 1.14705i 0.987129 + 0.159925i \(0.0511251\pi\)
0.159925 + 0.987129i \(0.448875\pi\)
\(458\) −11.3347 11.3347i −0.529638 0.529638i
\(459\) 1.55436 + 0.366736i 0.0725511 + 0.0171178i
\(460\) −1.43919 1.71135i −0.0671028 0.0797921i
\(461\) 7.06441i 0.329022i −0.986375 0.164511i \(-0.947395\pi\)
0.986375 0.164511i \(-0.0526047\pi\)
\(462\) −9.28119 10.8382i −0.431800 0.504238i
\(463\) 4.91698 4.91698i 0.228512 0.228512i −0.583559 0.812071i \(-0.698340\pi\)
0.812071 + 0.583559i \(0.198340\pi\)
\(464\) −1.22002 −0.0566381
\(465\) −14.2957 19.9404i −0.662950 0.924714i
\(466\) 5.86409 0.271649
\(467\) 0.279235 0.279235i 0.0129214 0.0129214i −0.700617 0.713538i \(-0.747092\pi\)
0.713538 + 0.700617i \(0.247092\pi\)
\(468\) 4.56539 3.33519i 0.211035 0.154169i
\(469\) 36.8915i 1.70349i
\(470\) 0.628279 + 0.0542729i 0.0289804 + 0.00250342i
\(471\) 1.83407 + 0.141935i 0.0845093 + 0.00654003i
\(472\) 6.66802 + 6.66802i 0.306920 + 0.306920i
\(473\) 5.35515 + 5.35515i 0.246230 + 0.246230i
\(474\) −24.9187 1.92841i −1.14455 0.0885750i
\(475\) 5.50994 31.6544i 0.252813 1.45240i
\(476\) 0.851973i 0.0390501i
\(477\) −31.4454 + 22.9721i −1.43978 + 1.05182i
\(478\) −21.0475 + 21.0475i −0.962690 + 0.962690i
\(479\) −19.9714 −0.912518 −0.456259 0.889847i \(-0.650811\pi\)
−0.456259 + 0.889847i \(0.650811\pi\)
\(480\) 3.82139 + 0.630048i 0.174422 + 0.0287576i
\(481\) −3.81946 −0.174152
\(482\) −12.8377 + 12.8377i −0.584743 + 0.584743i
\(483\) 3.12292 + 3.64682i 0.142098 + 0.165936i
\(484\) 2.16749i 0.0985222i
\(485\) 21.7516 18.2925i 0.987691 0.830619i
\(486\) −5.87131 + 14.4405i −0.266328 + 0.655034i
\(487\) −1.40410 1.40410i −0.0636258 0.0636258i 0.674578 0.738204i \(-0.264326\pi\)
−0.738204 + 0.674578i \(0.764326\pi\)
\(488\) −3.94018 3.94018i −0.178363 0.178363i
\(489\) 1.24816 16.1286i 0.0564439 0.729360i
\(490\) 1.17056 0.984403i 0.0528803 0.0444708i
\(491\) 6.45884i 0.291483i 0.989323 + 0.145742i \(0.0465568\pi\)
−0.989323 + 0.145742i \(0.953443\pi\)
\(492\) 4.00701 3.43137i 0.180650 0.154698i
\(493\) −0.265146 + 0.265146i −0.0119416 + 0.0119416i
\(494\) −12.1107 −0.544887
\(495\) −4.75131 + 19.3620i −0.213556 + 0.870258i
\(496\) −6.33502 −0.284451
\(497\) −14.9944 + 14.9944i −0.672593 + 0.672593i
\(498\) 22.6492 19.3955i 1.01494 0.869132i
\(499\) 9.53761i 0.426962i 0.976947 + 0.213481i \(0.0684802\pi\)
−0.976947 + 0.213481i \(0.931520\pi\)
\(500\) 10.8088 + 2.85813i 0.483386 + 0.127819i
\(501\) −0.992338 + 12.8228i −0.0443344 + 0.572883i
\(502\) −13.5208 13.5208i −0.603464 0.603464i
\(503\) 15.2096 + 15.2096i 0.678161 + 0.678161i 0.959584 0.281423i \(-0.0908064\pi\)
−0.281423 + 0.959584i \(0.590806\pi\)
\(504\) −8.21699 1.27946i −0.366014 0.0569917i
\(505\) 6.70506 + 0.579206i 0.298371 + 0.0257743i
\(506\) 2.97195i 0.132119i
\(507\) 10.6443 + 12.4300i 0.472730 + 0.552034i
\(508\) −9.95020 + 9.95020i −0.441469 + 0.441469i
\(509\) −27.1370 −1.20282 −0.601412 0.798939i \(-0.705395\pi\)
−0.601412 + 0.798939i \(0.705395\pi\)
\(510\) 0.967426 0.693571i 0.0428384 0.0307118i
\(511\) −15.9046 −0.703577
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 28.4018 17.5580i 1.25397 0.775205i
\(514\) 24.0535i 1.06096i
\(515\) 3.70085 + 4.40069i 0.163079 + 0.193918i
\(516\) 4.40057 + 0.340552i 0.193724 + 0.0149920i
\(517\) 0.592665 + 0.592665i 0.0260654 + 0.0260654i
\(518\) 3.97242 + 3.97242i 0.174538 + 0.174538i
\(519\) 39.5113 + 3.05771i 1.73435 + 0.134219i
\(520\) 0.362682 4.19851i 0.0159047 0.184117i
\(521\) 41.9658i 1.83855i −0.393611 0.919277i \(-0.628774\pi\)
0.393611 0.919277i \(-0.371226\pi\)
\(522\) −2.15906 2.95543i −0.0944994 0.129356i
\(523\) 22.7710 22.7710i 0.995704 0.995704i −0.00428643 0.999991i \(-0.501364\pi\)
0.999991 + 0.00428643i \(0.00136442\pi\)
\(524\) 4.14724 0.181173
\(525\) −23.2625 5.92932i −1.01526 0.258777i
\(526\) −17.4761 −0.761992
\(527\) −1.37678 + 1.37678i −0.0599736 + 0.0599736i
\(528\) 3.34819 + 3.90988i 0.145711 + 0.170156i
\(529\) 1.00000i 0.0434783i
\(530\) −2.49807 + 28.9184i −0.108509 + 1.25614i
\(531\) −4.35256 + 27.9532i −0.188885 + 1.21306i
\(532\) 12.5957 + 12.5957i 0.546094 + 0.546094i
\(533\) −4.05891 4.05891i −0.175811 0.175811i
\(534\) 0.328279 4.24198i 0.0142060 0.183568i
\(535\) −20.6693 24.5779i −0.893610 1.06259i
\(536\) 13.3086i 0.574844i
\(537\) −16.5879 + 14.2049i −0.715820 + 0.612986i
\(538\) −14.2128 + 14.2128i −0.612758 + 0.612758i
\(539\) 2.03280 0.0875591
\(540\) 5.23641 + 10.3721i 0.225339 + 0.446343i
\(541\) 8.43337 0.362579 0.181290 0.983430i \(-0.441973\pi\)
0.181290 + 0.983430i \(0.441973\pi\)
\(542\) −19.7054 + 19.7054i −0.846419 + 0.846419i
\(543\) −2.30730 + 1.97584i −0.0990157 + 0.0847912i
\(544\) 0.307349i 0.0131775i
\(545\) −7.17971 0.620208i −0.307545 0.0265668i
\(546\) −0.698164 + 9.02157i −0.0298787 + 0.386088i
\(547\) −13.9532 13.9532i −0.596597 0.596597i 0.342808 0.939405i \(-0.388622\pi\)
−0.939405 + 0.342808i \(0.888622\pi\)
\(548\) 6.71805 + 6.71805i 0.286981 + 0.286981i
\(549\) 2.57196 16.5177i 0.109769 0.704959i
\(550\) 8.54990 + 12.1537i 0.364569 + 0.518235i
\(551\) 7.83994i 0.333993i
\(552\) −1.12660 1.31559i −0.0479511 0.0559953i
\(553\) 28.2839 28.2839i 1.20275 1.20275i
\(554\) 9.96921 0.423551
\(555\) 1.27688 7.74459i 0.0542006 0.328739i
\(556\) −21.3303 −0.904607
\(557\) 19.9924 19.9924i 0.847106 0.847106i −0.142665 0.989771i \(-0.545567\pi\)
0.989771 + 0.142665i \(0.0455671\pi\)
\(558\) −11.2110 15.3462i −0.474600 0.649657i
\(559\) 4.80252i 0.203125i
\(560\) −4.74387 + 3.98945i −0.200465 + 0.168585i
\(561\) 1.57739 + 0.122071i 0.0665974 + 0.00515386i
\(562\) −11.1642 11.1642i −0.470934 0.470934i
\(563\) 31.0332 + 31.0332i 1.30789 + 1.30789i 0.922935 + 0.384957i \(0.125784\pi\)
0.384957 + 0.922935i \(0.374216\pi\)
\(564\) 0.487019 + 0.0376896i 0.0205072 + 0.00158702i
\(565\) 9.02716 7.59158i 0.379776 0.319380i
\(566\) 18.6737i 0.784912i
\(567\) −11.4421 22.1694i −0.480522 0.931027i
\(568\) 5.40925 5.40925i 0.226967 0.226967i
\(569\) 30.3632 1.27289 0.636447 0.771321i \(-0.280404\pi\)
0.636447 + 0.771321i \(0.280404\pi\)
\(570\) 4.04873 24.5565i 0.169583 1.02856i
\(571\) −13.6437 −0.570973 −0.285486 0.958383i \(-0.592155\pi\)
−0.285486 + 0.958383i \(0.592155\pi\)
\(572\) 3.96052 3.96052i 0.165598 0.165598i
\(573\) 30.3375 + 35.4269i 1.26737 + 1.47998i
\(574\) 8.44292i 0.352401i
\(575\) −2.87686 4.08946i −0.119973 0.170542i
\(576\) 2.96428 + 0.461565i 0.123512 + 0.0192319i
\(577\) 29.2454 + 29.2454i 1.21750 + 1.21750i 0.968503 + 0.249001i \(0.0801021\pi\)
0.249001 + 0.968503i \(0.419898\pi\)
\(578\) 11.9540 + 11.9540i 0.497222 + 0.497222i
\(579\) −2.06605 + 26.6972i −0.0858620 + 1.10950i
\(580\) −2.71793 0.234784i −0.112856 0.00974888i
\(581\) 47.7228i 1.97988i
\(582\) 16.7215 14.3193i 0.693127 0.593553i
\(583\) −27.2791 + 27.2791i −1.12979 + 1.12979i
\(584\) 5.73758 0.237423
\(585\) 10.8125 6.55147i 0.447041 0.270870i
\(586\) −9.81215 −0.405336
\(587\) 30.7364 30.7364i 1.26863 1.26863i 0.321830 0.946798i \(-0.395702\pi\)
0.946798 0.321830i \(-0.104298\pi\)
\(588\) 0.899860 0.770587i 0.0371096 0.0317785i
\(589\) 40.7093i 1.67740i
\(590\) 13.5716 + 16.1380i 0.558734 + 0.664392i
\(591\) 0.374079 4.83380i 0.0153876 0.198836i
\(592\) −1.43305 1.43305i −0.0588980 0.0588980i
\(593\) −24.9741 24.9741i −1.02557 1.02557i −0.999665 0.0259005i \(-0.991755\pi\)
−0.0259005 0.999665i \(-0.508245\pi\)
\(594\) −3.54620 + 15.0300i −0.145502 + 0.616690i
\(595\) −0.163956 + 1.89800i −0.00672154 + 0.0778105i
\(596\) 2.04707i 0.0838514i
\(597\) −17.9007 20.9037i −0.732627 0.855531i
\(598\) −1.33263 + 1.33263i −0.0544953 + 0.0544953i
\(599\) −35.3695 −1.44516 −0.722579 0.691288i \(-0.757044\pi\)
−0.722579 + 0.691288i \(0.757044\pi\)
\(600\) 8.39194 + 2.13900i 0.342600 + 0.0873244i
\(601\) 36.5041 1.48903 0.744517 0.667604i \(-0.232680\pi\)
0.744517 + 0.667604i \(0.232680\pi\)
\(602\) −4.99486 + 4.99486i −0.203575 + 0.203575i
\(603\) 32.2393 23.5521i 1.31288 0.959114i
\(604\) 2.64015i 0.107426i
\(605\) 0.417117 4.82867i 0.0169582 0.196313i
\(606\) 5.19752 + 0.402227i 0.211135 + 0.0163394i
\(607\) 22.0917 + 22.0917i 0.896673 + 0.896673i 0.995140 0.0984669i \(-0.0313939\pi\)
−0.0984669 + 0.995140i \(0.531394\pi\)
\(608\) −4.54391 4.54391i −0.184280 0.184280i
\(609\) 5.84017 + 0.451961i 0.236656 + 0.0183144i
\(610\) −8.01956 9.53607i −0.324702 0.386104i
\(611\) 0.531504i 0.0215024i
\(612\) 0.744535 0.543912i 0.0300960 0.0219863i
\(613\) 16.7926 16.7926i 0.678246 0.678246i −0.281357 0.959603i \(-0.590784\pi\)
0.959603 + 0.281357i \(0.0907845\pi\)
\(614\) −11.8644 −0.478808
\(615\) 9.58705 6.87318i 0.386587 0.277154i
\(616\) −8.23826 −0.331929
\(617\) −26.9980 + 26.9980i −1.08690 + 1.08690i −0.0910505 + 0.995846i \(0.529022\pi\)
−0.995846 + 0.0910505i \(0.970978\pi\)
\(618\) 2.89701 + 3.38301i 0.116535 + 0.136085i
\(619\) 31.5835i 1.26945i 0.772739 + 0.634724i \(0.218886\pi\)
−0.772739 + 0.634724i \(0.781114\pi\)
\(620\) −14.1130 1.21913i −0.566791 0.0489614i
\(621\) 1.19322 5.05729i 0.0478823 0.202942i
\(622\) −16.0579 16.0579i −0.643865 0.643865i
\(623\) 4.81485 + 4.81485i 0.192903 + 0.192903i
\(624\) 0.251863 3.25453i 0.0100826 0.130286i
\(625\) 23.5296 + 8.44734i 0.941184 + 0.337894i
\(626\) 26.9989i 1.07909i
\(627\) 25.1251 21.5157i 1.00340 0.859254i
\(628\) 0.750993 0.750993i 0.0299679 0.0299679i
\(629\) −0.622887 −0.0248361
\(630\) −18.0594 4.43164i −0.719502 0.176561i
\(631\) −27.4404 −1.09239 −0.546193 0.837659i \(-0.683924\pi\)
−0.546193 + 0.837659i \(0.683924\pi\)
\(632\) −10.2034 + 10.2034i −0.405870 + 0.405870i
\(633\) 14.9855 12.8327i 0.595622 0.510055i
\(634\) 0.0389545i 0.00154708i
\(635\) −24.0816 + 20.2519i −0.955650 + 0.803673i
\(636\) −1.73477 + 22.4165i −0.0687883 + 0.888872i
\(637\) −0.911514 0.911514i −0.0361155 0.0361155i
\(638\) −2.56386 2.56386i −0.101504 0.101504i
\(639\) 22.6762 + 3.53090i 0.897058 + 0.139680i
\(640\) 1.71135 1.43919i 0.0676470 0.0568892i
\(641\) 1.78898i 0.0706606i 0.999376 + 0.0353303i \(0.0112483\pi\)
−0.999376 + 0.0353303i \(0.988752\pi\)
\(642\) −16.1798 18.8941i −0.638566 0.745691i
\(643\) 24.6839 24.6839i 0.973437 0.973437i −0.0262188 0.999656i \(-0.508347\pi\)
0.999656 + 0.0262188i \(0.00834667\pi\)
\(644\) 2.77200 0.109232
\(645\) 9.73792 + 1.60553i 0.383430 + 0.0632177i
\(646\) −1.97505 −0.0777072
\(647\) −2.36727 + 2.36727i −0.0930671 + 0.0930671i −0.752108 0.659040i \(-0.770963\pi\)
0.659040 + 0.752108i \(0.270963\pi\)
\(648\) 4.12773 + 7.99761i 0.162153 + 0.314176i
\(649\) 28.0255i 1.10010i
\(650\) 1.61594 9.28353i 0.0633826 0.364130i
\(651\) 30.3254 + 2.34683i 1.18854 + 0.0919794i
\(652\) −6.60415 6.60415i −0.258639 0.258639i
\(653\) −2.10868 2.10868i −0.0825189 0.0825189i 0.664643 0.747161i \(-0.268584\pi\)
−0.747161 + 0.664643i \(0.768584\pi\)
\(654\) −5.56545 0.430701i −0.217626 0.0168417i
\(655\) 9.23911 + 0.798106i 0.361002 + 0.0311846i
\(656\) 3.04579i 0.118918i
\(657\) 10.1537 + 13.8989i 0.396134 + 0.542249i
\(658\) −0.552791 + 0.552791i −0.0215500 + 0.0215500i
\(659\) −40.8784 −1.59240 −0.796199 0.605035i \(-0.793159\pi\)
−0.796199 + 0.605035i \(0.793159\pi\)
\(660\) 6.70657 + 9.35465i 0.261053 + 0.364129i
\(661\) 17.8125 0.692828 0.346414 0.938082i \(-0.387399\pi\)
0.346414 + 0.938082i \(0.387399\pi\)
\(662\) 0.743610 0.743610i 0.0289012 0.0289012i
\(663\) −0.652567 0.762041i −0.0253436 0.0295952i
\(664\) 17.2160i 0.668111i
\(665\) 25.6365 + 30.4844i 0.994140 + 1.18213i
\(666\) 0.935427 6.00753i 0.0362471 0.232787i
\(667\) 0.862686 + 0.862686i 0.0334033 + 0.0334033i
\(668\) 5.25056 + 5.25056i 0.203150 + 0.203150i
\(669\) −1.97842 + 25.5648i −0.0764900 + 0.988392i
\(670\) 2.56114 29.6485i 0.0989455 1.14542i
\(671\) 16.5605i 0.639310i
\(672\) −3.64682 + 3.12292i −0.140679 + 0.120469i
\(673\) 13.7420 13.7420i 0.529714 0.529714i −0.390773 0.920487i \(-0.627792\pi\)
0.920487 + 0.390773i \(0.127792\pi\)
\(674\) −14.1764 −0.546054
\(675\) 9.66951 + 24.1143i 0.372179 + 0.928161i
\(676\) 9.44819 0.363392
\(677\) −1.91031 + 1.91031i −0.0734192 + 0.0734192i −0.742863 0.669444i \(-0.766533\pi\)
0.669444 + 0.742863i \(0.266533\pi\)
\(678\) 6.93959 5.94265i 0.266513 0.228226i
\(679\) 35.2328i 1.35211i
\(680\) 0.0591471 0.684704i 0.00226819 0.0262572i
\(681\) 3.05537 39.4810i 0.117082 1.51292i
\(682\) −13.3130 13.3130i −0.509780 0.509780i
\(683\) 33.5563 + 33.5563i 1.28400 + 1.28400i 0.938374 + 0.345623i \(0.112332\pi\)
0.345623 + 0.938374i \(0.387668\pi\)
\(684\) 2.96605 19.0487i 0.113410 0.728344i
\(685\) 13.6735 + 16.2591i 0.522436 + 0.621229i
\(686\) 17.5080i 0.668458i
\(687\) −18.0590 21.0886i −0.688996 0.804581i
\(688\) 1.80190 1.80190i 0.0686966 0.0686966i
\(689\) 24.4641 0.932006
\(690\) −2.25662 3.14764i −0.0859081 0.119829i
\(691\) −27.4000 −1.04234 −0.521172 0.853451i \(-0.674505\pi\)
−0.521172 + 0.853451i \(0.674505\pi\)
\(692\) 16.1787 16.1787i 0.615020 0.615020i
\(693\) −14.5791 19.9567i −0.553816 0.758092i
\(694\) 25.8642i 0.981790i
\(695\) −47.5191 4.10486i −1.80250 0.155706i
\(696\) −2.10684 0.163045i −0.0798596 0.00618020i
\(697\) −0.661937 0.661937i −0.0250727 0.0250727i
\(698\) −20.2968 20.2968i −0.768247 0.768247i
\(699\) 10.1266 + 0.783682i 0.383024 + 0.0296416i
\(700\) −11.3360 + 7.97466i −0.428460 + 0.301414i
\(701\) 17.7628i 0.670893i 0.942059 + 0.335446i \(0.108887\pi\)
−0.942059 + 0.335446i \(0.891113\pi\)
\(702\) 8.32963 5.14938i 0.314381 0.194351i
\(703\) −9.20888 + 9.20888i −0.347319 + 0.347319i
\(704\) 2.97195 0.112010
\(705\) 1.07771 + 0.177687i 0.0405891 + 0.00669208i
\(706\) −14.7901 −0.556631
\(707\) −5.89944 + 5.89944i −0.221871 + 0.221871i
\(708\) 10.6238 + 12.4060i 0.399267 + 0.466247i
\(709\) 25.1030i 0.942763i 0.881929 + 0.471382i \(0.156245\pi\)
−0.881929 + 0.471382i \(0.843755\pi\)
\(710\) 13.0915 11.0096i 0.491316 0.413183i
\(711\) −42.7740 6.66031i −1.60415 0.249781i
\(712\) −1.73696 1.73696i −0.0650953 0.0650953i
\(713\) 4.47954 + 4.47954i 0.167760 + 0.167760i
\(714\) −0.113858 + 1.47126i −0.00426104 + 0.0550606i
\(715\) 9.58530 8.06095i 0.358470 0.301463i
\(716\) 12.6087i 0.471209i
\(717\) −39.1594 + 33.5338i −1.46244 + 1.25234i
\(718\) 7.38357 7.38357i 0.275552 0.275552i
\(719\) −7.11858 −0.265478 −0.132739 0.991151i \(-0.542377\pi\)
−0.132739 + 0.991151i \(0.542377\pi\)
\(720\) 6.51491 + 1.59872i 0.242797 + 0.0595806i
\(721\) −7.12813 −0.265466
\(722\) −15.7644 + 15.7644i −0.586692 + 0.586692i
\(723\) −23.8850 + 20.4537i −0.888292 + 0.760681i
\(724\) 1.75381i 0.0651799i
\(725\) −6.00975 1.04609i −0.223196 0.0388508i
\(726\) 0.289665 3.74301i 0.0107505 0.138916i
\(727\) −21.0233 21.0233i −0.779711 0.779711i 0.200070 0.979782i \(-0.435883\pi\)
−0.979782 + 0.200070i \(0.935883\pi\)
\(728\) 3.69405 + 3.69405i 0.136911 + 0.136911i
\(729\) −12.0689 + 24.1524i −0.446998 + 0.894535i
\(730\) 12.7820 + 1.10415i 0.473083 + 0.0408666i
\(731\) 0.783208i 0.0289680i
\(732\) −6.27767 7.33081i −0.232030 0.270955i
\(733\) −8.70985 + 8.70985i −0.321706 + 0.321706i −0.849421 0.527715i \(-0.823049\pi\)
0.527715 + 0.849421i \(0.323049\pi\)
\(734\) 16.0003 0.590580
\(735\) 2.15298 1.54352i 0.0794137 0.0569336i
\(736\) −1.00000 −0.0368605
\(737\) 27.9679 27.9679i 1.03021 1.03021i
\(738\) 7.37823 5.39009i 0.271596 0.198412i
\(739\) 13.3134i 0.489743i −0.969556 0.244871i \(-0.921254\pi\)
0.969556 0.244871i \(-0.0787458\pi\)
\(740\) −2.91673 3.46829i −0.107221 0.127497i
\(741\) −20.9138 1.61849i −0.768289 0.0594566i
\(742\) −25.4438 25.4438i −0.934072 0.934072i
\(743\) 31.8345 + 31.8345i 1.16789 + 1.16789i 0.982702 + 0.185193i \(0.0592909\pi\)
0.185193 + 0.982702i \(0.440709\pi\)
\(744\) −10.9399 0.846618i −0.401075 0.0310385i
\(745\) −0.393944 + 4.56041i −0.0144330 + 0.167081i
\(746\) 28.6369i 1.04847i
\(747\) 41.7047 30.4669i 1.52590 1.11473i
\(748\) 0.645891 0.645891i 0.0236161 0.0236161i
\(749\) 39.8106 1.45465
\(750\) 18.2837 + 6.38017i 0.667626 + 0.232971i
\(751\) 1.87068 0.0682622 0.0341311 0.999417i \(-0.489134\pi\)
0.0341311 + 0.999417i \(0.489134\pi\)
\(752\) 0.199419 0.199419i 0.00727207 0.00727207i
\(753\) −21.5420 25.1559i −0.785035 0.916732i
\(754\) 2.29928i 0.0837349i
\(755\) −0.508077 + 5.88165i −0.0184908 + 0.214055i
\(756\) −14.0188 3.30761i −0.509860 0.120297i
\(757\) −4.50446 4.50446i −0.163717 0.163717i 0.620494 0.784211i \(-0.286932\pi\)
−0.784211 + 0.620494i \(0.786932\pi\)
\(758\) −22.2485 22.2485i −0.808102 0.808102i
\(759\) 0.397175 5.13223i 0.0144165 0.186288i
\(760\) −9.24836 10.9972i −0.335473 0.398912i
\(761\) 29.5482i 1.07112i 0.844497 + 0.535561i \(0.179900\pi\)
−0.844497 + 0.535561i \(0.820100\pi\)
\(762\) −18.5126 + 15.8531i −0.670642 + 0.574298i
\(763\) 6.31706 6.31706i 0.228693 0.228693i
\(764\) 26.9285 0.974238
\(765\) 1.76333 1.06843i 0.0637532 0.0386292i
\(766\) 7.21387 0.260648
\(767\) 12.5667 12.5667i 0.453757 0.453757i
\(768\) 1.31559 1.12660i 0.0474723 0.0406525i
\(769\) 14.7558i 0.532107i 0.963958 + 0.266054i \(0.0857199\pi\)
−0.963958 + 0.266054i \(0.914280\pi\)
\(770\) −18.3530 1.58539i −0.661395 0.0571336i
\(771\) −3.21454 + 41.5378i −0.115769 + 1.49595i
\(772\) 10.9317 + 10.9317i 0.393439 + 0.393439i
\(773\) −9.22983 9.22983i −0.331974 0.331974i 0.521362 0.853336i \(-0.325424\pi\)
−0.853336 + 0.521362i \(0.825424\pi\)
\(774\) 7.55377 + 1.17619i 0.271515 + 0.0422773i
\(775\) −31.2059 5.43188i −1.12095 0.195119i
\(776\) 12.7102i 0.456270i
\(777\) 6.32905 + 7.39080i 0.227053 + 0.265144i
\(778\) −12.9858 + 12.9858i −0.465565 + 0.465565i