Properties

Label 690.2.i.f.323.14
Level $690$
Weight $2$
Character 690.323
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

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 323.14
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.f.47.14

$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 −0.231893 0.972741i \(-0.574492\pi\)
0.972741 + 0.231893i \(0.0744918\pi\)
\(8\) −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 \(0.147877\pi\)
−0.894014 + 0.448039i \(0.852123\pi\)
\(12\) −1.12660 + 1.31559i −0.325220 + 0.379779i
\(13\) −1.33263 1.33263i −0.369605 0.369605i 0.497728 0.867333i \(-0.334168\pi\)
−0.867333 + 0.497728i \(0.834168\pi\)
\(14\) 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 0.680260 0.732970i \(-0.261867\pi\)
−0.732970 + 0.680260i \(0.761867\pi\)
\(18\) −1.76969 + 2.42244i −0.417119 + 0.570974i
\(19\) 6.42606i 1.47424i −0.675762 0.737120i \(-0.736185\pi\)
0.675762 0.737120i \(-0.263815\pi\)
\(20\) −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 −0.579430 0.815022i \(-0.696725\pi\)
0.815022 + 0.579430i \(0.196725\pi\)
\(38\) 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 \(-0.923562\pi\)
0.971305 0.237836i \(-0.0764380\pi\)
\(42\) 3.64682 + 3.12292i 0.562717 + 0.481878i
\(43\) −1.80190 1.80190i −0.274786 0.274786i 0.556237 0.831024i \(-0.312245\pi\)
−0.831024 + 0.556237i \(0.812245\pi\)
\(44\) −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 0.692413 0.721501i \(-0.256548\pi\)
−0.721501 + 0.692413i \(0.756548\pi\)
\(48\) −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 −0.310114 + 0.950699i \(0.600367\pi\)
−0.950699 + 0.310114i \(0.899633\pi\)
\(54\) −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 0.163074 0.986614i \(-0.447859\pi\)
0.986614 0.163074i \(-0.0521410\pi\)
\(68\) 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 \(-0.850020\pi\)
0.891035 0.453934i \(-0.149980\pi\)
\(72\) −2.42244 1.76969i −0.285487 0.208560i
\(73\) −4.05708 4.05708i −0.474845 0.474845i 0.428633 0.903479i \(-0.358995\pi\)
−0.903479 + 0.428633i \(0.858995\pi\)
\(74\) 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 \(0.301480\pi\)
−0.584018 + 0.811741i \(0.698520\pi\)
\(80\) −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 0.436533 0.899688i \(-0.356206\pi\)
0.899688 0.436533i \(-0.143794\pi\)
\(84\) 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 −0.0839309 0.996472i \(-0.526748\pi\)
0.996472 + 0.0839309i \(0.0267475\pi\)
\(98\) 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 \(-0.952156\pi\)
0.988725 0.149741i \(-0.0478440\pi\)
\(102\) 0.346258 0.404346i 0.0342847 0.0400363i
\(103\) −1.81831 1.81831i −0.179163 0.179163i 0.611828 0.790991i \(-0.290435\pi\)
−0.790991 + 0.611828i \(0.790435\pi\)
\(104\) 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 0.999836 0.0180921i \(-0.00575922\pi\)
−0.0180921 + 0.999836i \(0.505759\pi\)
\(108\) −4.41978 2.73231i −0.425294 0.262917i
\(109\) 3.22282i 0.308690i 0.988017 + 0.154345i \(0.0493268\pi\)
−0.988017 + 0.154345i \(0.950673\pi\)
\(110\) −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 −0.509557 0.860437i \(-0.670191\pi\)
0.860437 + 0.509557i \(0.170191\pi\)
\(114\) 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 −0.993832 0.110895i \(-0.964628\pi\)
0.110895 + 0.993832i \(0.464628\pi\)
\(128\) 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 \(-0.942011\pi\)
0.983451 0.181173i \(-0.0579894\pi\)
\(132\) −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 0.359271 0.933233i \(-0.383025\pi\)
−0.933233 + 0.359271i \(0.883025\pi\)
\(138\) 1.31559 + 1.12660i 0.111991 + 0.0959022i
\(139\) 21.3303i 1.80921i 0.426247 + 0.904607i \(0.359835\pi\)
−0.426247 + 0.904607i \(0.640165\pi\)
\(140\) −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 −0.676504 0.736439i \(-0.736506\pi\)
0.736439 + 0.676504i \(0.236506\pi\)
\(158\) −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 0.916747 0.399469i \(-0.130806\pi\)
−0.399469 + 0.916747i \(0.630806\pi\)
\(164\) 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 0.474146 0.880446i \(-0.342757\pi\)
−0.880446 + 0.474146i \(0.842757\pi\)
\(168\) −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 0.266093 0.963947i \(-0.414267\pi\)
0.963947 0.266093i \(-0.0857329\pi\)
\(174\) 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 \(-0.572408\pi\)
0.225520 0.974238i \(-0.427592\pi\)
\(192\) 1.12660 1.31559i 0.0813050 0.0949447i
\(193\) −10.9317 10.9317i −0.786878 0.786878i 0.194103 0.980981i \(-0.437820\pi\)
−0.980981 + 0.194103i \(0.937820\pi\)
\(194\) 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 0.774092 0.633073i \(-0.218207\pi\)
−0.633073 + 0.774092i \(0.718207\pi\)
\(198\) −7.19938 5.25943i −0.511637 0.373771i
\(199\) 15.8892i 1.12636i 0.826336 + 0.563178i \(0.190421\pi\)
−0.826336 + 0.563178i \(0.809579\pi\)
\(200\) 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 0.263634 0.964623i \(-0.415079\pi\)
−0.964623 + 0.263634i \(0.915079\pi\)
\(224\) −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 0.997117 + 0.0758747i \(0.0241749\pi\)
0.0758747 + 0.997117i \(0.475825\pi\)
\(228\) 8.45408 + 7.23957i 0.559885 + 0.479453i
\(229\) 16.0298i 1.05928i 0.848224 + 0.529638i \(0.177672\pi\)
−0.848224 + 0.529638i \(0.822328\pi\)
\(230\) 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 −0.558115 0.829764i \(-0.688475\pi\)
0.829764 + 0.558115i \(0.188475\pi\)
\(234\) 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 \(0.206213\pi\)
−0.797390 + 0.603464i \(0.793787\pi\)
\(252\) −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 −0.998017 0.0629387i \(-0.979953\pi\)
−0.0629387 0.998017i \(-0.520047\pi\)
\(258\) 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 −0.976682 0.214690i \(-0.931126\pi\)
0.214690 + 0.976682i \(0.431126\pi\)
\(264\) −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 −0.462873 0.886424i \(-0.653182\pi\)
0.886424 + 0.462873i \(0.153182\pi\)
\(278\) −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 \(0.156083\pi\)
−0.882169 + 0.470934i \(0.843917\pi\)
\(282\) 0.317724 0.371025i 0.0189202 0.0220942i
\(283\) 13.2043 + 13.2043i 0.784912 + 0.784912i 0.980655 0.195743i \(-0.0627118\pi\)
−0.195743 + 0.980655i \(0.562712\pi\)
\(284\) 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 −0.880109 0.474772i \(-0.842530\pi\)
0.474772 + 0.880109i \(0.342530\pi\)
\(294\) 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 −0.904750 0.425943i \(-0.859943\pi\)
0.425943 + 0.904750i \(0.359943\pi\)
\(308\) −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 \(0.222670\pi\)
−0.765139 + 0.643865i \(0.777330\pi\)
\(312\) 2.47940 + 2.12321i 0.140368 + 0.120203i
\(313\) −19.0911 19.0911i −1.07909 1.07909i −0.996591 0.0825035i \(-0.973708\pi\)
−0.0825035 0.996591i \(-0.526292\pi\)
\(314\) 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 0.707880 0.706333i \(-0.249652\pi\)
−0.706333 + 0.707880i \(0.749652\pi\)
\(318\) −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 −0.925297 0.379243i \(-0.876184\pi\)
0.379243 + 0.925297i \(0.376184\pi\)
\(338\) 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 0.0180467 0.999837i \(-0.494255\pi\)
−0.999837 + 0.0180467i \(0.994255\pi\)
\(348\) −1.37447 + 1.60505i −0.0736794 + 0.0860398i
\(349\) 28.7041i 1.53649i 0.640154 + 0.768247i \(0.278871\pi\)
−0.640154 + 0.768247i \(0.721129\pi\)
\(350\) −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 −0.928347 0.371715i \(-0.878770\pi\)
0.371715 + 0.928347i \(0.378770\pi\)
\(354\) −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 −0.347208 0.937788i \(-0.612870\pi\)
0.937788 + 0.347208i \(0.112870\pi\)
\(368\) −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 −0.998764 0.0497082i \(-0.984171\pi\)
−0.0497082 0.998764i \(-0.515829\pi\)
\(374\) 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 \(0.299505\pi\)
−0.589042 + 0.808102i \(0.700495\pi\)
\(380\) 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 −0.564669 0.825317i \(-0.690996\pi\)
0.825317 + 0.564669i \(0.190996\pi\)
\(384\) 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 −0.858746 0.512401i \(-0.828756\pi\)
0.512401 + 0.858746i \(0.328756\pi\)
\(398\) −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 \(-0.848519\pi\)
0.888885 0.458131i \(-0.151481\pi\)
\(402\) 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 \(-0.871648\pi\)
0.919798 0.392392i \(-0.128352\pi\)
\(410\) 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 \(0.0508384\pi\)
−0.987273 + 0.159036i \(0.949162\pi\)
\(432\) 2.73231 4.41978i 0.131458 0.212647i
\(433\) −2.95935 2.95935i −0.142217 0.142217i 0.632414 0.774631i \(-0.282064\pi\)
−0.774631 + 0.632414i \(0.782064\pi\)
\(434\) 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 \(0.0865392\pi\)
−0.963270 + 0.268534i \(0.913461\pi\)
\(440\) 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 −0.978315 0.207122i \(-0.933590\pi\)
0.207122 + 0.978315i \(0.433590\pi\)
\(444\) 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 0.159925 0.987129i \(-0.448875\pi\)
0.987129 0.159925i \(-0.0511251\pi\)
\(458\) −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 \(0.0526047\pi\)
−0.986375 + 0.164511i \(0.947395\pi\)
\(462\) −9.28119 + 10.8382i −0.431800 + 0.504238i
\(463\) 4.91698 + 4.91698i 0.228512 + 0.228512i 0.812071 0.583559i \(-0.198340\pi\)
−0.583559 + 0.812071i \(0.698340\pi\)
\(464\) −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 0.713538 0.700617i \(-0.247092\pi\)
−0.700617 + 0.713538i \(0.747092\pi\)
\(468\) 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 −0.738204 0.674578i \(-0.764326\pi\)
0.674578 + 0.738204i \(0.264326\pi\)
\(488\) −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 \(-0.953443\pi\)
0.989323 0.145742i \(-0.0465568\pi\)
\(492\) 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 \(-0.931520\pi\)
0.976947 0.213481i \(-0.0684802\pi\)
\(500\) 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 −0.281423 0.959584i \(-0.590806\pi\)
0.959584 + 0.281423i \(0.0908064\pi\)
\(504\) −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 \(0.371226\pi\)
−0.393611 + 0.919277i \(0.628774\pi\)
\(522\) −2.15906 + 2.95543i −0.0944994 + 0.129356i
\(523\) 22.7710 + 22.7710i 0.995704 + 0.995704i 0.999991 0.00428643i \(-0.00136442\pi\)
−0.00428643 + 0.999991i \(0.501364\pi\)
\(524\) 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 −0.939405 0.342808i \(-0.888622\pi\)
0.342808 + 0.939405i \(0.388622\pi\)
\(548\) 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 0.989771 0.142665i \(-0.0455671\pi\)
−0.142665 + 0.989771i \(0.545567\pi\)
\(558\) −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 0.384957 0.922935i \(-0.374216\pi\)
0.922935 0.384957i \(-0.125784\pi\)
\(564\) 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 0.249001 0.968503i \(-0.419898\pi\)
0.968503 0.249001i \(-0.0801021\pi\)
\(578\) 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 0.946798 + 0.321830i \(0.104298\pi\)
0.321830 + 0.946798i \(0.395702\pi\)
\(588\) 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 −0.0259005 + 0.999665i \(0.508245\pi\)
−0.999665 + 0.0259005i \(0.991755\pi\)
\(594\) −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 −0.0984669 0.995140i \(-0.531394\pi\)
0.995140 + 0.0984669i \(0.0313939\pi\)
\(608\) −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 0.959603 0.281357i \(-0.0907845\pi\)
−0.281357 + 0.959603i \(0.590784\pi\)
\(614\) −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 −0.995846 0.0910505i \(-0.970978\pi\)
−0.0910505 0.995846i \(-0.529022\pi\)
\(618\) 2.89701 3.38301i 0.116535 0.136085i
\(619\) 31.5835i 1.26945i −0.772739 0.634724i \(-0.781114\pi\)
0.772739 0.634724i \(-0.218886\pi\)
\(620\) −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 \(-0.988752\pi\)
0.999376 0.0353303i \(-0.0112483\pi\)
\(642\) −16.1798 + 18.8941i −0.638566 + 0.745691i
\(643\) 24.6839 + 24.6839i 0.973437 + 0.973437i 0.999656 0.0262188i \(-0.00834667\pi\)
−0.0262188 + 0.999656i \(0.508347\pi\)
\(644\) 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 0.659040 0.752108i \(-0.270963\pi\)
−0.752108 + 0.659040i \(0.770963\pi\)
\(648\) 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 −0.747161 0.664643i \(-0.768584\pi\)
0.664643 + 0.747161i \(0.268584\pi\)
\(654\) −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 0.920487 0.390773i \(-0.127792\pi\)
−0.390773 + 0.920487i \(0.627792\pi\)
\(674\) −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 0.669444 0.742863i \(-0.266533\pi\)
−0.742863 + 0.669444i \(0.766533\pi\)
\(678\) 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 0.345623 0.938374i \(-0.387668\pi\)
0.938374 0.345623i \(-0.112332\pi\)
\(684\) 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 \(-0.891113\pi\)
0.942059 0.335446i \(-0.108887\pi\)
\(702\) 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 \(-0.843755\pi\)
0.881929 0.471382i \(-0.156245\pi\)
\(710\) 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 −0.979782 0.200070i \(-0.935883\pi\)
0.200070 + 0.979782i \(0.435883\pi\)
\(728\) 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 0.527715 0.849421i \(-0.323049\pi\)
−0.849421 + 0.527715i \(0.823049\pi\)
\(734\) 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 \(0.0787458\pi\)
−0.969556 + 0.244871i \(0.921254\pi\)
\(740\) −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 0.185193 0.982702i \(-0.440709\pi\)
0.982702 0.185193i \(-0.0592909\pi\)
\(744\) −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 −0.784211 0.620494i \(-0.786932\pi\)
0.620494 + 0.784211i \(0.286932\pi\)
\(758\) −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 \(-0.820100\pi\)
0.844497 0.535561i \(-0.179900\pi\)
\(762\) −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 \(-0.914280\pi\)
0.963958 0.266054i \(-0.0857199\pi\)
\(770\) −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 −0.853336 0.521362i \(-0.825424\pi\)
0.521362 + 0.853336i \(0.325424\pi\)
\(774\) 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