Properties

Label 105.3.l.a.22.10
Level 105
Weight 3
Character 105.22
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 22.10
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.10

$q$-expansion

\(f(q)\) \(=\) \(q+(2.24469 + 2.24469i) q^{2} +(1.22474 - 1.22474i) q^{3} +6.07726i q^{4} +(-3.05058 + 3.96156i) q^{5} +5.49834 q^{6} +(1.87083 + 1.87083i) q^{7} +(-4.66280 + 4.66280i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(2.24469 + 2.24469i) q^{2} +(1.22474 - 1.22474i) q^{3} +6.07726i q^{4} +(-3.05058 + 3.96156i) q^{5} +5.49834 q^{6} +(1.87083 + 1.87083i) q^{7} +(-4.66280 + 4.66280i) q^{8} -3.00000i q^{9} +(-15.7401 + 2.04487i) q^{10} +3.94671 q^{11} +(7.44309 + 7.44309i) q^{12} +(8.57045 - 8.57045i) q^{13} +8.39886i q^{14} +(1.11572 + 8.58808i) q^{15} +3.37595 q^{16} +(-17.2039 - 17.2039i) q^{17} +(6.73407 - 6.73407i) q^{18} -24.3758i q^{19} +(-24.0754 - 18.5392i) q^{20} +4.58258 q^{21} +(8.85913 + 8.85913i) q^{22} +(-19.6705 + 19.6705i) q^{23} +11.4215i q^{24} +(-6.38793 - 24.1701i) q^{25} +38.4760 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-11.3695 + 11.3695i) q^{28} +17.5580i q^{29} +(-16.7731 + 21.7820i) q^{30} -43.8736 q^{31} +(26.2292 + 26.2292i) q^{32} +(4.83371 - 4.83371i) q^{33} -77.2348i q^{34} +(-13.1185 + 1.70429i) q^{35} +18.2318 q^{36} +(32.9598 + 32.9598i) q^{37} +(54.7160 - 54.7160i) q^{38} -20.9932i q^{39} +(-4.24773 - 32.6962i) q^{40} +22.4582 q^{41} +(10.2865 + 10.2865i) q^{42} +(14.3533 - 14.3533i) q^{43} +23.9852i q^{44} +(11.8847 + 9.15174i) q^{45} -88.3085 q^{46} +(38.7355 + 38.7355i) q^{47} +(4.13468 - 4.13468i) q^{48} +7.00000i q^{49} +(39.9155 - 68.5933i) q^{50} -42.1407 q^{51} +(52.0849 + 52.0849i) q^{52} +(9.01352 - 9.01352i) q^{53} -16.4950i q^{54} +(-12.0397 + 15.6351i) q^{55} -17.4466 q^{56} +(-29.8541 - 29.8541i) q^{57} +(-39.4121 + 39.4121i) q^{58} +58.0335i q^{59} +(-52.1920 + 6.78052i) q^{60} -89.2995 q^{61} +(-98.4827 - 98.4827i) q^{62} +(5.61249 - 5.61249i) q^{63} +104.249i q^{64} +(7.80752 + 60.0972i) q^{65} +21.7004 q^{66} +(-21.2058 - 21.2058i) q^{67} +(104.552 - 104.552i) q^{68} +48.1828i q^{69} +(-33.2726 - 25.6214i) q^{70} -78.8147 q^{71} +(13.9884 + 13.9884i) q^{72} +(-18.2694 + 18.2694i) q^{73} +147.969i q^{74} +(-37.4258 - 21.7786i) q^{75} +148.138 q^{76} +(7.38362 + 7.38362i) q^{77} +(47.1233 - 47.1233i) q^{78} -112.267i q^{79} +(-10.2986 + 13.3740i) q^{80} -9.00000 q^{81} +(50.4118 + 50.4118i) q^{82} +(-12.9380 + 12.9380i) q^{83} +27.8495i q^{84} +(120.636 - 15.6724i) q^{85} +64.4373 q^{86} +(21.5040 + 21.5040i) q^{87} +(-18.4027 + 18.4027i) q^{88} +22.2193i q^{89} +(6.13461 + 47.2202i) q^{90} +32.0677 q^{91} +(-119.543 - 119.543i) q^{92} +(-53.7340 + 53.7340i) q^{93} +173.898i q^{94} +(96.5661 + 74.3602i) q^{95} +64.2481 q^{96} +(90.6427 + 90.6427i) q^{97} +(-15.7128 + 15.7128i) q^{98} -11.8401i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24469 + 2.24469i 1.12234 + 1.12234i 0.991388 + 0.130957i \(0.0418048\pi\)
0.130957 + 0.991388i \(0.458195\pi\)
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 6.07726i 1.51932i
\(5\) −3.05058 + 3.96156i −0.610116 + 0.792312i
\(6\) 5.49834 0.916391
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) −4.66280 + 4.66280i −0.582850 + 0.582850i
\(9\) 3.00000i 0.333333i
\(10\) −15.7401 + 2.04487i −1.57401 + 0.204487i
\(11\) 3.94671 0.358792 0.179396 0.983777i \(-0.442586\pi\)
0.179396 + 0.983777i \(0.442586\pi\)
\(12\) 7.44309 + 7.44309i 0.620258 + 0.620258i
\(13\) 8.57045 8.57045i 0.659265 0.659265i −0.295941 0.955206i \(-0.595633\pi\)
0.955206 + 0.295941i \(0.0956331\pi\)
\(14\) 8.39886i 0.599918i
\(15\) 1.11572 + 8.58808i 0.0743814 + 0.572539i
\(16\) 3.37595 0.210997
\(17\) −17.2039 17.2039i −1.01199 1.01199i −0.999927 0.0120660i \(-0.996159\pi\)
−0.0120660 0.999927i \(-0.503841\pi\)
\(18\) 6.73407 6.73407i 0.374115 0.374115i
\(19\) 24.3758i 1.28294i −0.767150 0.641468i \(-0.778326\pi\)
0.767150 0.641468i \(-0.221674\pi\)
\(20\) −24.0754 18.5392i −1.20377 0.926958i
\(21\) 4.58258 0.218218
\(22\) 8.85913 + 8.85913i 0.402688 + 0.402688i
\(23\) −19.6705 + 19.6705i −0.855240 + 0.855240i −0.990773 0.135533i \(-0.956725\pi\)
0.135533 + 0.990773i \(0.456725\pi\)
\(24\) 11.4215i 0.475895i
\(25\) −6.38793 24.1701i −0.255517 0.966804i
\(26\) 38.4760 1.47985
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −11.3695 + 11.3695i −0.406054 + 0.406054i
\(29\) 17.5580i 0.605447i 0.953078 + 0.302723i \(0.0978958\pi\)
−0.953078 + 0.302723i \(0.902104\pi\)
\(30\) −16.7731 + 21.7820i −0.559104 + 0.726067i
\(31\) −43.8736 −1.41528 −0.707639 0.706574i \(-0.750240\pi\)
−0.707639 + 0.706574i \(0.750240\pi\)
\(32\) 26.2292 + 26.2292i 0.819662 + 0.819662i
\(33\) 4.83371 4.83371i 0.146476 0.146476i
\(34\) 77.2348i 2.27161i
\(35\) −13.1185 + 1.70429i −0.374815 + 0.0486940i
\(36\) 18.2318 0.506438
\(37\) 32.9598 + 32.9598i 0.890805 + 0.890805i 0.994599 0.103794i \(-0.0330981\pi\)
−0.103794 + 0.994599i \(0.533098\pi\)
\(38\) 54.7160 54.7160i 1.43990 1.43990i
\(39\) 20.9932i 0.538288i
\(40\) −4.24773 32.6962i −0.106193 0.817406i
\(41\) 22.4582 0.547762 0.273881 0.961764i \(-0.411693\pi\)
0.273881 + 0.961764i \(0.411693\pi\)
\(42\) 10.2865 + 10.2865i 0.244916 + 0.244916i
\(43\) 14.3533 14.3533i 0.333797 0.333797i −0.520230 0.854026i \(-0.674154\pi\)
0.854026 + 0.520230i \(0.174154\pi\)
\(44\) 23.9852i 0.545118i
\(45\) 11.8847 + 9.15174i 0.264104 + 0.203372i
\(46\) −88.3085 −1.91975
\(47\) 38.7355 + 38.7355i 0.824159 + 0.824159i 0.986702 0.162542i \(-0.0519693\pi\)
−0.162542 + 0.986702i \(0.551969\pi\)
\(48\) 4.13468 4.13468i 0.0861391 0.0861391i
\(49\) 7.00000i 0.142857i
\(50\) 39.9155 68.5933i 0.798309 1.37187i
\(51\) −42.1407 −0.826289
\(52\) 52.0849 + 52.0849i 1.00163 + 1.00163i
\(53\) 9.01352 9.01352i 0.170067 0.170067i −0.616942 0.787009i \(-0.711629\pi\)
0.787009 + 0.616942i \(0.211629\pi\)
\(54\) 16.4950i 0.305464i
\(55\) −12.0397 + 15.6351i −0.218905 + 0.284275i
\(56\) −17.4466 −0.311547
\(57\) −29.8541 29.8541i −0.523756 0.523756i
\(58\) −39.4121 + 39.4121i −0.679520 + 0.679520i
\(59\) 58.0335i 0.983618i 0.870703 + 0.491809i \(0.163664\pi\)
−0.870703 + 0.491809i \(0.836336\pi\)
\(60\) −52.1920 + 6.78052i −0.869867 + 0.113009i
\(61\) −89.2995 −1.46393 −0.731963 0.681344i \(-0.761396\pi\)
−0.731963 + 0.681344i \(0.761396\pi\)
\(62\) −98.4827 98.4827i −1.58843 1.58843i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 104.249i 1.62889i
\(65\) 7.80752 + 60.0972i 0.120116 + 0.924572i
\(66\) 21.7004 0.328793
\(67\) −21.2058 21.2058i −0.316505 0.316505i 0.530918 0.847423i \(-0.321847\pi\)
−0.847423 + 0.530918i \(0.821847\pi\)
\(68\) 104.552 104.552i 1.53754 1.53754i
\(69\) 48.1828i 0.698301i
\(70\) −33.2726 25.6214i −0.475323 0.366020i
\(71\) −78.8147 −1.11007 −0.555033 0.831828i \(-0.687294\pi\)
−0.555033 + 0.831828i \(0.687294\pi\)
\(72\) 13.9884 + 13.9884i 0.194283 + 0.194283i
\(73\) −18.2694 + 18.2694i −0.250266 + 0.250266i −0.821080 0.570814i \(-0.806628\pi\)
0.570814 + 0.821080i \(0.306628\pi\)
\(74\) 147.969i 1.99958i
\(75\) −37.4258 21.7786i −0.499011 0.290382i
\(76\) 148.138 1.94918
\(77\) 7.38362 + 7.38362i 0.0958911 + 0.0958911i
\(78\) 47.1233 47.1233i 0.604145 0.604145i
\(79\) 112.267i 1.42110i −0.703646 0.710551i \(-0.748446\pi\)
0.703646 0.710551i \(-0.251554\pi\)
\(80\) −10.2986 + 13.3740i −0.128732 + 0.167175i
\(81\) −9.00000 −0.111111
\(82\) 50.4118 + 50.4118i 0.614777 + 0.614777i
\(83\) −12.9380 + 12.9380i −0.155879 + 0.155879i −0.780738 0.624859i \(-0.785157\pi\)
0.624859 + 0.780738i \(0.285157\pi\)
\(84\) 27.8495i 0.331542i
\(85\) 120.636 15.6724i 1.41925 0.184382i
\(86\) 64.4373 0.749270
\(87\) 21.5040 + 21.5040i 0.247173 + 0.247173i
\(88\) −18.4027 + 18.4027i −0.209122 + 0.209122i
\(89\) 22.2193i 0.249655i 0.992178 + 0.124827i \(0.0398377\pi\)
−0.992178 + 0.124827i \(0.960162\pi\)
\(90\) 6.13461 + 47.2202i 0.0681624 + 0.524669i
\(91\) 32.0677 0.352392
\(92\) −119.543 119.543i −1.29938 1.29938i
\(93\) −53.7340 + 53.7340i −0.577785 + 0.577785i
\(94\) 173.898i 1.84998i
\(95\) 96.5661 + 74.3602i 1.01649 + 0.782739i
\(96\) 64.2481 0.669251
\(97\) 90.6427 + 90.6427i 0.934461 + 0.934461i 0.997981 0.0635195i \(-0.0202325\pi\)
−0.0635195 + 0.997981i \(0.520233\pi\)
\(98\) −15.7128 + 15.7128i −0.160335 + 0.160335i
\(99\) 11.8401i 0.119597i
\(100\) 146.888 38.8211i 1.46888 0.388211i
\(101\) −180.124 −1.78341 −0.891703 0.452621i \(-0.850489\pi\)
−0.891703 + 0.452621i \(0.850489\pi\)
\(102\) −94.5929 94.5929i −0.927381 0.927381i
\(103\) 137.374 137.374i 1.33373 1.33373i 0.431729 0.902003i \(-0.357904\pi\)
0.902003 0.431729i \(-0.142096\pi\)
\(104\) 79.9247i 0.768506i
\(105\) −13.9795 + 18.1542i −0.133138 + 0.172897i
\(106\) 40.4651 0.381746
\(107\) −102.254 102.254i −0.955648 0.955648i 0.0434091 0.999057i \(-0.486178\pi\)
−0.999057 + 0.0434091i \(0.986178\pi\)
\(108\) 22.3293 22.3293i 0.206753 0.206753i
\(109\) 58.4672i 0.536396i 0.963364 + 0.268198i \(0.0864282\pi\)
−0.963364 + 0.268198i \(0.913572\pi\)
\(110\) −62.1215 + 8.07051i −0.564741 + 0.0733683i
\(111\) 80.7347 0.727340
\(112\) 6.31582 + 6.31582i 0.0563913 + 0.0563913i
\(113\) 39.8190 39.8190i 0.352381 0.352381i −0.508614 0.860995i \(-0.669842\pi\)
0.860995 + 0.508614i \(0.169842\pi\)
\(114\) 134.026i 1.17567i
\(115\) −17.9195 137.933i −0.155822 1.19941i
\(116\) −106.704 −0.919864
\(117\) −25.7113 25.7113i −0.219755 0.219755i
\(118\) −130.267 + 130.267i −1.10396 + 1.10396i
\(119\) 64.3710i 0.540933i
\(120\) −45.2469 34.8422i −0.377058 0.290351i
\(121\) −105.423 −0.871269
\(122\) −200.450 200.450i −1.64303 1.64303i
\(123\) 27.5056 27.5056i 0.223623 0.223623i
\(124\) 266.631i 2.15025i
\(125\) 115.238 + 48.4267i 0.921906 + 0.387413i
\(126\) 25.1966 0.199973
\(127\) 28.1517 + 28.1517i 0.221667 + 0.221667i 0.809200 0.587533i \(-0.199901\pi\)
−0.587533 + 0.809200i \(0.699901\pi\)
\(128\) −129.090 + 129.090i −1.00851 + 1.00851i
\(129\) 35.1582i 0.272544i
\(130\) −117.374 + 152.425i −0.902877 + 1.17250i
\(131\) −32.5463 −0.248445 −0.124223 0.992254i \(-0.539644\pi\)
−0.124223 + 0.992254i \(0.539644\pi\)
\(132\) 29.3757 + 29.3757i 0.222543 + 0.222543i
\(133\) 45.6029 45.6029i 0.342879 0.342879i
\(134\) 95.2009i 0.710454i
\(135\) 25.7642 3.34716i 0.190846 0.0247938i
\(136\) 160.437 1.17968
\(137\) 184.159 + 184.159i 1.34423 + 1.34423i 0.891804 + 0.452422i \(0.149440\pi\)
0.452422 + 0.891804i \(0.350560\pi\)
\(138\) −108.155 + 108.155i −0.783734 + 0.783734i
\(139\) 76.2552i 0.548599i −0.961644 0.274299i \(-0.911554\pi\)
0.961644 0.274299i \(-0.0884459\pi\)
\(140\) −10.3574 79.7246i −0.0739816 0.569462i
\(141\) 94.8822 0.672923
\(142\) −176.914 176.914i −1.24588 1.24588i
\(143\) 33.8251 33.8251i 0.236539 0.236539i
\(144\) 10.1278i 0.0703323i
\(145\) −69.5569 53.5619i −0.479703 0.369393i
\(146\) −82.0184 −0.561770
\(147\) 8.57321 + 8.57321i 0.0583212 + 0.0583212i
\(148\) −200.305 + 200.305i −1.35341 + 1.35341i
\(149\) 232.403i 1.55975i −0.625933 0.779877i \(-0.715282\pi\)
0.625933 0.779877i \(-0.284718\pi\)
\(150\) −35.1231 132.896i −0.234154 0.885971i
\(151\) 170.930 1.13199 0.565994 0.824409i \(-0.308492\pi\)
0.565994 + 0.824409i \(0.308492\pi\)
\(152\) 113.659 + 113.659i 0.747760 + 0.747760i
\(153\) −51.6117 + 51.6117i −0.337331 + 0.337331i
\(154\) 33.1478i 0.215246i
\(155\) 133.840 173.808i 0.863484 1.12134i
\(156\) 127.581 0.817829
\(157\) 199.875 + 199.875i 1.27309 + 1.27309i 0.944457 + 0.328635i \(0.106589\pi\)
0.328635 + 0.944457i \(0.393411\pi\)
\(158\) 252.005 252.005i 1.59497 1.59497i
\(159\) 22.0785i 0.138859i
\(160\) −183.923 + 23.8943i −1.14952 + 0.149339i
\(161\) −73.6004 −0.457145
\(162\) −20.2022 20.2022i −0.124705 0.124705i
\(163\) −147.090 + 147.090i −0.902392 + 0.902392i −0.995643 0.0932506i \(-0.970274\pi\)
0.0932506 + 0.995643i \(0.470274\pi\)
\(164\) 136.485i 0.832223i
\(165\) 4.40342 + 33.8947i 0.0266874 + 0.205422i
\(166\) −58.0834 −0.349900
\(167\) 43.6355 + 43.6355i 0.261290 + 0.261290i 0.825578 0.564288i \(-0.190849\pi\)
−0.564288 + 0.825578i \(0.690849\pi\)
\(168\) −21.3677 + 21.3677i −0.127188 + 0.127188i
\(169\) 22.0948i 0.130738i
\(170\) 305.970 + 235.611i 1.79982 + 1.38595i
\(171\) −73.1273 −0.427645
\(172\) 87.2285 + 87.2285i 0.507143 + 0.507143i
\(173\) −79.6322 + 79.6322i −0.460302 + 0.460302i −0.898754 0.438453i \(-0.855527\pi\)
0.438453 + 0.898754i \(0.355527\pi\)
\(174\) 96.5397i 0.554826i
\(175\) 33.2674 57.1689i 0.190099 0.326679i
\(176\) 13.3239 0.0757039
\(177\) 71.0762 + 71.0762i 0.401560 + 0.401560i
\(178\) −49.8754 + 49.8754i −0.280199 + 0.280199i
\(179\) 189.993i 1.06141i −0.847555 0.530707i \(-0.821926\pi\)
0.847555 0.530707i \(-0.178074\pi\)
\(180\) −55.6175 + 72.2263i −0.308986 + 0.401257i
\(181\) 193.279 1.06784 0.533920 0.845535i \(-0.320718\pi\)
0.533920 + 0.845535i \(0.320718\pi\)
\(182\) 71.9820 + 71.9820i 0.395505 + 0.395505i
\(183\) −109.369 + 109.369i −0.597646 + 0.597646i
\(184\) 183.440i 0.996955i
\(185\) −231.119 + 30.0258i −1.24929 + 0.162302i
\(186\) −241.232 −1.29695
\(187\) −67.8987 67.8987i −0.363095 0.363095i
\(188\) −235.406 + 235.406i −1.25216 + 1.25216i
\(189\) 13.7477i 0.0727393i
\(190\) 49.8453 + 383.677i 0.262344 + 2.01935i
\(191\) 236.062 1.23593 0.617963 0.786207i \(-0.287958\pi\)
0.617963 + 0.786207i \(0.287958\pi\)
\(192\) 127.678 + 127.678i 0.664991 + 0.664991i
\(193\) 126.994 126.994i 0.658001 0.658001i −0.296906 0.954907i \(-0.595955\pi\)
0.954907 + 0.296906i \(0.0959548\pi\)
\(194\) 406.930i 2.09757i
\(195\) 83.1660 + 64.0415i 0.426492 + 0.328418i
\(196\) −42.5408 −0.217045
\(197\) 123.086 + 123.086i 0.624804 + 0.624804i 0.946756 0.321952i \(-0.104339\pi\)
−0.321952 + 0.946756i \(0.604339\pi\)
\(198\) 26.5774 26.5774i 0.134229 0.134229i
\(199\) 27.6913i 0.139152i −0.997577 0.0695761i \(-0.977835\pi\)
0.997577 0.0695761i \(-0.0221647\pi\)
\(200\) 142.486 + 82.9148i 0.712431 + 0.414574i
\(201\) −51.9434 −0.258425
\(202\) −404.322 404.322i −2.00160 2.00160i
\(203\) −32.8479 + 32.8479i −0.161812 + 0.161812i
\(204\) 256.100i 1.25539i
\(205\) −68.5106 + 88.9697i −0.334198 + 0.433998i
\(206\) 616.726 2.99381
\(207\) 59.0116 + 59.0116i 0.285080 + 0.285080i
\(208\) 28.9334 28.9334i 0.139103 0.139103i
\(209\) 96.2041i 0.460307i
\(210\) −72.1301 + 9.37078i −0.343477 + 0.0446228i
\(211\) −171.536 −0.812965 −0.406483 0.913658i \(-0.633245\pi\)
−0.406483 + 0.913658i \(0.633245\pi\)
\(212\) 54.7775 + 54.7775i 0.258385 + 0.258385i
\(213\) −96.5278 + 96.5278i −0.453182 + 0.453182i
\(214\) 459.059i 2.14513i
\(215\) 13.0756 + 100.647i 0.0608166 + 0.468126i
\(216\) 34.2645 0.158632
\(217\) −82.0801 82.0801i −0.378249 0.378249i
\(218\) −131.241 + 131.241i −0.602021 + 0.602021i
\(219\) 44.7508i 0.204341i
\(220\) −95.0187 73.1687i −0.431903 0.332585i
\(221\) −294.890 −1.33434
\(222\) 181.224 + 181.224i 0.816326 + 0.816326i
\(223\) 6.27227 6.27227i 0.0281268 0.0281268i −0.692904 0.721030i \(-0.743669\pi\)
0.721030 + 0.692904i \(0.243669\pi\)
\(224\) 98.1406i 0.438128i
\(225\) −72.5103 + 19.1638i −0.322268 + 0.0851724i
\(226\) 178.763 0.790985
\(227\) −155.382 155.382i −0.684501 0.684501i 0.276510 0.961011i \(-0.410822\pi\)
−0.961011 + 0.276510i \(0.910822\pi\)
\(228\) 181.431 181.431i 0.795751 0.795751i
\(229\) 283.171i 1.23656i 0.785960 + 0.618278i \(0.212169\pi\)
−0.785960 + 0.618278i \(0.787831\pi\)
\(230\) 269.392 349.839i 1.17127 1.52104i
\(231\) 18.0861 0.0782948
\(232\) −81.8693 81.8693i −0.352885 0.352885i
\(233\) 18.5950 18.5950i 0.0798069 0.0798069i −0.666077 0.745883i \(-0.732028\pi\)
0.745883 + 0.666077i \(0.232028\pi\)
\(234\) 115.428i 0.493282i
\(235\) −271.619 + 35.2873i −1.15582 + 0.150159i
\(236\) −352.684 −1.49443
\(237\) −137.499 137.499i −0.580162 0.580162i
\(238\) 144.493 144.493i 0.607113 0.607113i
\(239\) 265.031i 1.10892i −0.832211 0.554459i \(-0.812925\pi\)
0.832211 0.554459i \(-0.187075\pi\)
\(240\) 3.76662 + 28.9929i 0.0156942 + 0.120804i
\(241\) 127.492 0.529011 0.264506 0.964384i \(-0.414791\pi\)
0.264506 + 0.964384i \(0.414791\pi\)
\(242\) −236.643 236.643i −0.977864 0.977864i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 542.696i 2.22417i
\(245\) −27.7309 21.3541i −0.113187 0.0871594i
\(246\) 123.483 0.501964
\(247\) −208.911 208.911i −0.845795 0.845795i
\(248\) 204.574 204.574i 0.824896 0.824896i
\(249\) 31.6914i 0.127275i
\(250\) 149.971 + 367.377i 0.599885 + 1.46951i
\(251\) 31.9519 0.127298 0.0636492 0.997972i \(-0.479726\pi\)
0.0636492 + 0.997972i \(0.479726\pi\)
\(252\) 34.1085 + 34.1085i 0.135351 + 0.135351i
\(253\) −77.6338 + 77.6338i −0.306853 + 0.306853i
\(254\) 126.383i 0.497573i
\(255\) 128.554 166.943i 0.504132 0.654679i
\(256\) −162.537 −0.634910
\(257\) −138.387 138.387i −0.538470 0.538470i 0.384610 0.923079i \(-0.374336\pi\)
−0.923079 + 0.384610i \(0.874336\pi\)
\(258\) 78.9192 78.9192i 0.305888 0.305888i
\(259\) 123.324i 0.476155i
\(260\) −365.226 + 47.4484i −1.40472 + 0.182494i
\(261\) 52.6739 0.201816
\(262\) −73.0564 73.0564i −0.278841 0.278841i
\(263\) −230.486 + 230.486i −0.876373 + 0.876373i −0.993157 0.116785i \(-0.962741\pi\)
0.116785 + 0.993157i \(0.462741\pi\)
\(264\) 45.0773i 0.170747i
\(265\) 8.21116 + 63.2041i 0.0309855 + 0.238506i
\(266\) 204.729 0.769657
\(267\) 27.2129 + 27.2129i 0.101921 + 0.101921i
\(268\) 128.873 128.873i 0.480870 0.480870i
\(269\) 332.673i 1.23670i 0.785901 + 0.618352i \(0.212199\pi\)
−0.785901 + 0.618352i \(0.787801\pi\)
\(270\) 65.3461 + 50.3194i 0.242022 + 0.186368i
\(271\) −253.724 −0.936251 −0.468126 0.883662i \(-0.655071\pi\)
−0.468126 + 0.883662i \(0.655071\pi\)
\(272\) −58.0794 58.0794i −0.213527 0.213527i
\(273\) 39.2747 39.2747i 0.143863 0.143863i
\(274\) 826.759i 3.01737i
\(275\) −25.2113 95.3924i −0.0916775 0.346881i
\(276\) −292.819 −1.06094
\(277\) 252.491 + 252.491i 0.911521 + 0.911521i 0.996392 0.0848711i \(-0.0270479\pi\)
−0.0848711 + 0.996392i \(0.527048\pi\)
\(278\) 171.169 171.169i 0.615717 0.615717i
\(279\) 131.621i 0.471759i
\(280\) 53.2223 69.1158i 0.190080 0.246842i
\(281\) −3.26524 −0.0116201 −0.00581004 0.999983i \(-0.501849\pi\)
−0.00581004 + 0.999983i \(0.501849\pi\)
\(282\) 212.981 + 212.981i 0.755252 + 0.755252i
\(283\) 61.6256 61.6256i 0.217758 0.217758i −0.589795 0.807553i \(-0.700791\pi\)
0.807553 + 0.589795i \(0.200791\pi\)
\(284\) 478.977i 1.68654i
\(285\) 209.341 27.1966i 0.734531 0.0954265i
\(286\) 151.854 0.530956
\(287\) 42.0155 + 42.0155i 0.146395 + 0.146395i
\(288\) 78.6875 78.6875i 0.273221 0.273221i
\(289\) 302.947i 1.04826i
\(290\) −35.9038 276.364i −0.123806 0.952978i
\(291\) 222.028 0.762984
\(292\) −111.028 111.028i −0.380233 0.380233i
\(293\) 150.796 150.796i 0.514663 0.514663i −0.401289 0.915952i \(-0.631438\pi\)
0.915952 + 0.401289i \(0.131438\pi\)
\(294\) 38.4884i 0.130913i
\(295\) −229.903 177.036i −0.779332 0.600121i
\(296\) −307.370 −1.03841
\(297\) −14.5011 14.5011i −0.0488254 0.0488254i
\(298\) 521.673 521.673i 1.75058 1.75058i
\(299\) 337.171i 1.12766i
\(300\) 132.354 227.446i 0.441181 0.758155i
\(301\) 53.7050 0.178422
\(302\) 383.685 + 383.685i 1.27048 + 1.27048i
\(303\) −220.606 + 220.606i −0.728072 + 0.728072i
\(304\) 82.2914i 0.270695i
\(305\) 272.415 353.766i 0.893165 1.15989i
\(306\) −231.704 −0.757203
\(307\) 37.6731 + 37.6731i 0.122714 + 0.122714i 0.765797 0.643083i \(-0.222345\pi\)
−0.643083 + 0.765797i \(0.722345\pi\)
\(308\) −44.8722 + 44.8722i −0.145689 + 0.145689i
\(309\) 336.497i 1.08899i
\(310\) 690.574 89.7159i 2.22766 0.289406i
\(311\) 208.646 0.670888 0.335444 0.942060i \(-0.391114\pi\)
0.335444 + 0.942060i \(0.391114\pi\)
\(312\) 97.8873 + 97.8873i 0.313741 + 0.313741i
\(313\) −25.0439 + 25.0439i −0.0800125 + 0.0800125i −0.745980 0.665968i \(-0.768019\pi\)
0.665968 + 0.745980i \(0.268019\pi\)
\(314\) 897.316i 2.85770i
\(315\) 5.11287 + 39.3555i 0.0162313 + 0.124938i
\(316\) 682.276 2.15910
\(317\) −164.900 164.900i −0.520188 0.520188i 0.397440 0.917628i \(-0.369899\pi\)
−0.917628 + 0.397440i \(0.869899\pi\)
\(318\) 49.5595 49.5595i 0.155847 0.155847i
\(319\) 69.2961i 0.217229i
\(320\) −412.988 318.019i −1.29059 0.993811i
\(321\) −250.471 −0.780284
\(322\) −165.210 165.210i −0.513074 0.513074i
\(323\) −419.358 + 419.358i −1.29832 + 1.29832i
\(324\) 54.6953i 0.168813i
\(325\) −261.896 152.401i −0.805834 0.468927i
\(326\) −660.342 −2.02559
\(327\) 71.6074 + 71.6074i 0.218983 + 0.218983i
\(328\) −104.718 + 104.718i −0.319263 + 0.319263i
\(329\) 144.935i 0.440532i
\(330\) −66.1987 + 85.9673i −0.200602 + 0.260507i
\(331\) −324.395 −0.980045 −0.490023 0.871710i \(-0.663011\pi\)
−0.490023 + 0.871710i \(0.663011\pi\)
\(332\) −78.6273 78.6273i −0.236829 0.236829i
\(333\) 98.8794 98.8794i 0.296935 0.296935i
\(334\) 195.896i 0.586516i
\(335\) 148.698 19.3181i 0.443875 0.0576660i
\(336\) 15.4705 0.0460433
\(337\) −27.1490 27.1490i −0.0805607 0.0805607i 0.665678 0.746239i \(-0.268142\pi\)
−0.746239 + 0.665678i \(0.768142\pi\)
\(338\) −49.5959 + 49.5959i −0.146734 + 0.146734i
\(339\) 97.5362i 0.287718i
\(340\) 95.2454 + 733.137i 0.280134 + 2.15628i
\(341\) −173.156 −0.507790
\(342\) −164.148 164.148i −0.479965 0.479965i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 133.853i 0.389107i
\(345\) −190.879 146.985i −0.553272 0.426044i
\(346\) −357.499 −1.03323
\(347\) −0.188420 0.188420i −0.000542997 0.000542997i 0.706835 0.707378i \(-0.250122\pi\)
−0.707378 + 0.706835i \(0.750122\pi\)
\(348\) −130.685 + 130.685i −0.375533 + 0.375533i
\(349\) 222.903i 0.638690i 0.947638 + 0.319345i \(0.103463\pi\)
−0.947638 + 0.319345i \(0.896537\pi\)
\(350\) 203.001 53.6513i 0.580004 0.153290i
\(351\) −62.9797 −0.179429
\(352\) 103.519 + 103.519i 0.294088 + 0.294088i
\(353\) 10.0036 10.0036i 0.0283387 0.0283387i −0.692795 0.721134i \(-0.743621\pi\)
0.721134 + 0.692795i \(0.243621\pi\)
\(354\) 319.088i 0.901378i
\(355\) 240.430 312.229i 0.677269 0.879519i
\(356\) −135.032 −0.379304
\(357\) −78.8381 78.8381i −0.220835 0.220835i
\(358\) 426.476 426.476i 1.19127 1.19127i
\(359\) 605.191i 1.68577i −0.538096 0.842884i \(-0.680856\pi\)
0.538096 0.842884i \(-0.319144\pi\)
\(360\) −98.0887 + 12.7432i −0.272469 + 0.0353978i
\(361\) −233.179 −0.645924
\(362\) 433.851 + 433.851i 1.19848 + 1.19848i
\(363\) −129.117 + 129.117i −0.355694 + 0.355694i
\(364\) 194.884i 0.535395i
\(365\) −16.6431 128.108i −0.0455976 0.350980i
\(366\) −490.999 −1.34153
\(367\) 259.533 + 259.533i 0.707174 + 0.707174i 0.965940 0.258766i \(-0.0833157\pi\)
−0.258766 + 0.965940i \(0.583316\pi\)
\(368\) −66.4067 + 66.4067i −0.180453 + 0.180453i
\(369\) 67.3747i 0.182587i
\(370\) −586.188 451.391i −1.58429 1.21998i
\(371\) 33.7255 0.0909044
\(372\) −326.556 326.556i −0.877837 0.877837i
\(373\) 446.882 446.882i 1.19807 1.19807i 0.223332 0.974742i \(-0.428307\pi\)
0.974742 0.223332i \(-0.0716934\pi\)
\(374\) 304.823i 0.815035i
\(375\) 200.448 81.8272i 0.534527 0.218206i
\(376\) −361.232 −0.960724
\(377\) 150.480 + 150.480i 0.399150 + 0.399150i
\(378\) 30.8594 30.8594i 0.0816386 0.0816386i
\(379\) 51.1198i 0.134881i −0.997723 0.0674404i \(-0.978517\pi\)
0.997723 0.0674404i \(-0.0214832\pi\)
\(380\) −451.907 + 586.858i −1.18923 + 1.54436i
\(381\) 68.9572 0.180990
\(382\) 529.886 + 529.886i 1.38714 + 1.38714i
\(383\) 405.345 405.345i 1.05834 1.05834i 0.0601525 0.998189i \(-0.480841\pi\)
0.998189 0.0601525i \(-0.0191587\pi\)
\(384\) 316.204i 0.823448i
\(385\) −51.7750 + 6.72634i −0.134480 + 0.0174710i
\(386\) 570.125 1.47701
\(387\) −43.0598 43.0598i −0.111266 0.111266i
\(388\) −550.859 + 550.859i −1.41974 + 1.41974i
\(389\) 47.3061i 0.121609i −0.998150 0.0608047i \(-0.980633\pi\)
0.998150 0.0608047i \(-0.0193667\pi\)
\(390\) 42.9285 + 330.435i 0.110073 + 0.847269i
\(391\) 676.819 1.73099
\(392\) −32.6396 32.6396i −0.0832644 0.0832644i
\(393\) −39.8610 + 39.8610i −0.101427 + 0.101427i
\(394\) 552.581i 1.40249i
\(395\) 444.753 + 342.480i 1.12596 + 0.867037i
\(396\) 71.9555 0.181706
\(397\) −338.755 338.755i −0.853287 0.853287i 0.137249 0.990537i \(-0.456174\pi\)
−0.990537 + 0.137249i \(0.956174\pi\)
\(398\) 62.1583 62.1583i 0.156177 0.156177i
\(399\) 111.704i 0.279960i
\(400\) −21.5653 81.5971i −0.0539133 0.203993i
\(401\) 351.967 0.877723 0.438861 0.898555i \(-0.355382\pi\)
0.438861 + 0.898555i \(0.355382\pi\)
\(402\) −116.597 116.597i −0.290042 0.290042i
\(403\) −376.017 + 376.017i −0.933044 + 0.933044i
\(404\) 1094.66i 2.70955i
\(405\) 27.4552 35.6541i 0.0677906 0.0880347i
\(406\) −147.467 −0.363219
\(407\) 130.083 + 130.083i 0.319614 + 0.319614i
\(408\) 196.494 196.494i 0.481603 0.481603i
\(409\) 34.7110i 0.0848681i 0.999099 + 0.0424340i \(0.0135112\pi\)
−0.999099 + 0.0424340i \(0.986489\pi\)
\(410\) −353.494 + 45.9242i −0.862181 + 0.112010i
\(411\) 451.096 1.09756
\(412\) 834.860 + 834.860i 2.02636 + 2.02636i
\(413\) −108.571 + 108.571i −0.262883 + 0.262883i
\(414\) 264.925i 0.639916i
\(415\) −11.7862 90.7228i −0.0284006 0.218609i
\(416\) 449.592 1.08075
\(417\) −93.3932 93.3932i −0.223964 0.223964i
\(418\) 215.948 215.948i 0.516623 0.516623i
\(419\) 522.337i 1.24663i 0.781972 + 0.623313i \(0.214214\pi\)
−0.781972 + 0.623313i \(0.785786\pi\)
\(420\) −110.328 84.9571i −0.262685 0.202279i
\(421\) 150.337 0.357096 0.178548 0.983931i \(-0.442860\pi\)
0.178548 + 0.983931i \(0.442860\pi\)
\(422\) −385.044 385.044i −0.912427 0.912427i
\(423\) 116.206 116.206i 0.274720 0.274720i
\(424\) 84.0566i 0.198247i
\(425\) −305.923 + 525.717i −0.719818 + 1.23698i
\(426\) −433.350 −1.01725
\(427\) −167.064 167.064i −0.391251 0.391251i
\(428\) 621.426 621.426i 1.45193 1.45193i
\(429\) 82.8542i 0.193133i
\(430\) −196.571 + 255.272i −0.457142 + 0.593656i
\(431\) −165.122 −0.383113 −0.191557 0.981482i \(-0.561354\pi\)
−0.191557 + 0.981482i \(0.561354\pi\)
\(432\) −12.4040 12.4040i −0.0287130 0.0287130i
\(433\) −173.796 + 173.796i −0.401377 + 0.401377i −0.878718 0.477341i \(-0.841601\pi\)
0.477341 + 0.878718i \(0.341601\pi\)
\(434\) 368.488i 0.849052i
\(435\) −150.789 + 19.5898i −0.346642 + 0.0450339i
\(436\) −355.320 −0.814955
\(437\) 479.484 + 479.484i 1.09722 + 1.09722i
\(438\) −100.452 + 100.452i −0.229342 + 0.229342i
\(439\) 140.286i 0.319558i 0.987153 + 0.159779i \(0.0510782\pi\)
−0.987153 + 0.159779i \(0.948922\pi\)
\(440\) −16.7646 129.043i −0.0381013 0.293278i
\(441\) 21.0000 0.0476190
\(442\) −661.937 661.937i −1.49759 1.49759i
\(443\) 548.196 548.196i 1.23746 1.23746i 0.276429 0.961034i \(-0.410849\pi\)
0.961034 0.276429i \(-0.0891511\pi\)
\(444\) 490.646i 1.10506i
\(445\) −88.0230 67.7817i −0.197805 0.152318i
\(446\) 28.1586 0.0631359
\(447\) −284.635 284.635i −0.636767 0.636767i
\(448\) −195.032 + 195.032i −0.435339 + 0.435339i
\(449\) 693.773i 1.54515i −0.634923 0.772576i \(-0.718968\pi\)
0.634923 0.772576i \(-0.281032\pi\)
\(450\) −205.780 119.746i −0.457289 0.266103i
\(451\) 88.6361 0.196532
\(452\) 241.990 + 241.990i 0.535377 + 0.535377i
\(453\) 209.346 209.346i 0.462132 0.462132i
\(454\) 697.568i 1.53649i
\(455\) −97.8250 + 127.038i −0.215000 + 0.279205i
\(456\) 278.408 0.610543
\(457\) 327.671 + 327.671i 0.717004 + 0.717004i 0.967990 0.250987i \(-0.0807551\pi\)
−0.250987 + 0.967990i \(0.580755\pi\)
\(458\) −635.632 + 635.632i −1.38784 + 1.38784i
\(459\) 126.422i 0.275430i
\(460\) 838.252 108.901i 1.82229 0.236742i
\(461\) 93.1493 0.202059 0.101030 0.994883i \(-0.467786\pi\)
0.101030 + 0.994883i \(0.467786\pi\)
\(462\) 40.5977 + 40.5977i 0.0878737 + 0.0878737i
\(463\) −498.598 + 498.598i −1.07689 + 1.07689i −0.0800990 + 0.996787i \(0.525524\pi\)
−0.996787 + 0.0800990i \(0.974476\pi\)
\(464\) 59.2747i 0.127747i
\(465\) −48.9507 376.790i −0.105270 0.810302i
\(466\) 83.4800 0.179142
\(467\) −308.256 308.256i −0.660078 0.660078i 0.295320 0.955398i \(-0.404574\pi\)
−0.955398 + 0.295320i \(0.904574\pi\)
\(468\) 156.255 156.255i 0.333877 0.333877i
\(469\) 79.3449i 0.169179i
\(470\) −688.909 530.491i −1.46576 1.12870i
\(471\) 489.593 1.03948
\(472\) −270.599 270.599i −0.573302 0.573302i
\(473\) 56.6482 56.6482i 0.119764 0.119764i
\(474\) 617.283i 1.30228i
\(475\) −589.165 + 155.711i −1.24035 + 0.327812i
\(476\) 391.200 0.821848
\(477\) −27.0406 27.0406i −0.0566888 0.0566888i
\(478\) 594.913 594.913i 1.24459 1.24459i
\(479\) 178.073i 0.371760i 0.982572 + 0.185880i \(0.0595136\pi\)
−0.982572 + 0.185880i \(0.940486\pi\)
\(480\) −195.994 + 254.523i −0.408321 + 0.530256i
\(481\) 564.961 1.17455
\(482\) 286.179 + 286.179i 0.593733 + 0.593733i
\(483\) −90.1417 + 90.1417i −0.186629 + 0.186629i
\(484\) 640.686i 1.32373i
\(485\) −635.600 + 82.5739i −1.31051 + 0.170255i
\(486\) −49.4851 −0.101821
\(487\) −330.361 330.361i −0.678359 0.678359i 0.281270 0.959629i \(-0.409244\pi\)
−0.959629 + 0.281270i \(0.909244\pi\)
\(488\) 416.386 416.386i 0.853250 0.853250i
\(489\) 360.295i 0.736800i
\(490\) −14.3141 110.181i −0.0292124 0.224858i
\(491\) −729.372 −1.48548 −0.742741 0.669578i \(-0.766475\pi\)
−0.742741 + 0.669578i \(0.766475\pi\)
\(492\) 167.159 + 167.159i 0.339753 + 0.339753i
\(493\) 302.065 302.065i 0.612708 0.612708i
\(494\) 937.882i 1.89855i
\(495\) 46.9054 + 36.1192i 0.0947584 + 0.0729682i
\(496\) −148.115 −0.298619
\(497\) −147.449 147.449i −0.296678 0.296678i
\(498\) −71.1373 + 71.1373i −0.142846 + 0.142846i
\(499\) 385.715i 0.772976i 0.922294 + 0.386488i \(0.126312\pi\)
−0.922294 + 0.386488i \(0.873688\pi\)
\(500\) −294.301 + 700.333i −0.588603 + 1.40067i
\(501\) 106.885 0.213343
\(502\) 71.7220 + 71.7220i 0.142873 + 0.142873i
\(503\) −139.070 + 139.070i −0.276482 + 0.276482i −0.831703 0.555221i \(-0.812634\pi\)
0.555221 + 0.831703i \(0.312634\pi\)
\(504\) 52.3398i 0.103849i
\(505\) 549.482 713.572i 1.08808 1.41301i
\(506\) −348.528 −0.688790
\(507\) 27.0605 + 27.0605i 0.0533737 + 0.0533737i
\(508\) −171.085 + 171.085i −0.336781 + 0.336781i
\(509\) 337.164i 0.662404i −0.943560 0.331202i \(-0.892546\pi\)
0.943560 0.331202i \(-0.107454\pi\)
\(510\) 663.298 86.1724i 1.30059 0.168965i
\(511\) −68.3579 −0.133773
\(512\) 151.514 + 151.514i 0.295926 + 0.295926i
\(513\) −89.5623 + 89.5623i −0.174585 + 0.174585i
\(514\) 621.270i 1.20870i
\(515\) 125.146 + 963.289i 0.243001 + 1.87046i
\(516\) 213.665 0.414080
\(517\) 152.878 + 152.878i 0.295702 + 0.295702i
\(518\) −276.825 + 276.825i −0.534411 + 0.534411i
\(519\) 195.058i 0.375835i
\(520\) −316.626 243.816i −0.608897 0.468878i
\(521\) −346.121 −0.664340 −0.332170 0.943220i \(-0.607781\pi\)
−0.332170 + 0.943220i \(0.607781\pi\)
\(522\) 118.236 + 118.236i 0.226507 + 0.226507i
\(523\) −295.339 + 295.339i −0.564702 + 0.564702i −0.930639 0.365938i \(-0.880748\pi\)
0.365938 + 0.930639i \(0.380748\pi\)
\(524\) 197.793i 0.377467i
\(525\) −29.2732 110.761i −0.0557585 0.210974i
\(526\) −1034.74 −1.96718
\(527\) 754.797 + 754.797i 1.43225 + 1.43225i
\(528\) 16.3184 16.3184i 0.0309060 0.0309060i
\(529\) 244.859i 0.462872i
\(530\) −123.442 + 160.305i −0.232910 + 0.302462i
\(531\) 174.100 0.327873
\(532\) 277.141 + 277.141i 0.520941 + 0.520941i
\(533\) 192.477 192.477i 0.361120 0.361120i
\(534\) 122.169i 0.228781i
\(535\) 717.022 93.1519i 1.34023 0.174116i
\(536\) 197.757 0.368950
\(537\) −232.693 232.693i −0.433321 0.433321i
\(538\) −746.748 + 746.748i −1.38801 + 1.38801i
\(539\) 27.6270i 0.0512560i
\(540\) 20.3416 + 156.576i 0.0376696 + 0.289956i
\(541\) −734.168 −1.35706 −0.678529 0.734574i \(-0.737382\pi\)
−0.678529 + 0.734574i \(0.737382\pi\)
\(542\) −569.532 569.532i −1.05080 1.05080i
\(543\) 236.718 236.718i 0.435944 0.435944i
\(544\) 902.487i 1.65898i
\(545\) −231.621 178.359i −0.424993 0.327264i
\(546\) 176.319 0.322929
\(547\) 124.027 + 124.027i 0.226740 + 0.226740i 0.811329 0.584589i \(-0.198744\pi\)
−0.584589 + 0.811329i \(0.698744\pi\)
\(548\) −1119.18 + 1119.18i −2.04230 + 2.04230i
\(549\) 267.899i 0.487976i
\(550\) 157.535 270.718i 0.286427 0.492214i
\(551\) 427.989 0.776749
\(552\) −224.667 224.667i −0.407005 0.407005i
\(553\) 210.032 210.032i 0.379805 0.379805i
\(554\) 1133.53i 2.04608i
\(555\) −246.288 + 319.835i −0.443761 + 0.576280i
\(556\) 463.423 0.833494
\(557\) −436.412 436.412i −0.783504 0.783504i 0.196916 0.980420i \(-0.436907\pi\)
−0.980420 + 0.196916i \(0.936907\pi\)
\(558\) −295.448 + 295.448i −0.529477 + 0.529477i
\(559\) 246.028i 0.440121i
\(560\) −44.2874 + 5.75360i −0.0790847 + 0.0102743i
\(561\) −166.317 −0.296466
\(562\) −7.32946 7.32946i −0.0130417 0.0130417i
\(563\) −259.609 + 259.609i −0.461117 + 0.461117i −0.899021 0.437905i \(-0.855721\pi\)
0.437905 + 0.899021i \(0.355721\pi\)
\(564\) 576.624i 1.02238i
\(565\) 36.2744 + 279.216i 0.0642025 + 0.494188i
\(566\) 276.661 0.488800
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) 367.497 367.497i 0.647002 0.647002i
\(569\) 151.092i 0.265539i 0.991147 + 0.132770i \(0.0423870\pi\)
−0.991147 + 0.132770i \(0.957613\pi\)
\(570\) 530.954 + 408.858i 0.931498 + 0.717295i
\(571\) −502.406 −0.879871 −0.439935 0.898029i \(-0.644999\pi\)
−0.439935 + 0.898029i \(0.644999\pi\)
\(572\) 205.564 + 205.564i 0.359377 + 0.359377i
\(573\) 289.116 289.116i 0.504565 0.504565i
\(574\) 188.624i 0.328612i
\(575\) 601.093 + 349.785i 1.04538 + 0.608321i
\(576\) 312.747 0.542963
\(577\) 81.3805 + 81.3805i 0.141041 + 0.141041i 0.774102 0.633061i \(-0.218202\pi\)
−0.633061 + 0.774102i \(0.718202\pi\)
\(578\) −680.023 + 680.023i −1.17651 + 1.17651i
\(579\) 311.071i 0.537255i
\(580\) 325.510 422.715i 0.561224 0.728820i
\(581\) −48.4094 −0.0833208
\(582\) 498.385 + 498.385i 0.856331 + 0.856331i
\(583\) 35.5738 35.5738i 0.0610185 0.0610185i
\(584\) 170.374i 0.291736i
\(585\) 180.292 23.4226i 0.308191 0.0400386i
\(586\) 676.981 1.15526
\(587\) −283.065 283.065i −0.482224 0.482224i 0.423617 0.905841i \(-0.360760\pi\)
−0.905841 + 0.423617i \(0.860760\pi\)
\(588\) −52.1017 + 52.1017i −0.0886083 + 0.0886083i
\(589\) 1069.45i 1.81571i
\(590\) −118.671 913.451i −0.201137 1.54822i
\(591\) 301.499 0.510150
\(592\) 111.271 + 111.271i 0.187957 + 0.187957i
\(593\) 5.75309 5.75309i 0.00970167 0.00970167i −0.702239 0.711941i \(-0.747816\pi\)
0.711941 + 0.702239i \(0.247816\pi\)
\(594\) 65.1011i 0.109598i
\(595\) 255.010 + 196.369i 0.428588 + 0.330032i
\(596\) 1412.38 2.36976
\(597\) −33.9148 33.9148i −0.0568086 0.0568086i
\(598\) −756.843 + 756.843i −1.26562 + 1.26562i
\(599\) 619.287i 1.03387i 0.856025 + 0.516934i \(0.172927\pi\)
−0.856025 + 0.516934i \(0.827073\pi\)
\(600\) 276.059 72.9597i 0.460098 0.121600i
\(601\) 457.367 0.761011 0.380505 0.924779i \(-0.375750\pi\)
0.380505 + 0.924779i \(0.375750\pi\)
\(602\) 120.551 + 120.551i 0.200251 + 0.200251i
\(603\) −63.6174 + 63.6174i −0.105502 + 0.105502i
\(604\) 1038.79i 1.71985i
\(605\) 321.603 417.642i 0.531575 0.690317i
\(606\) −990.383 −1.63430
\(607\) −25.5979 25.5979i −0.0421713 0.0421713i 0.685707 0.727878i \(-0.259493\pi\)
−0.727878 + 0.685707i \(0.759493\pi\)
\(608\) 639.356 639.356i 1.05157 1.05157i
\(609\) 80.4606i 0.132119i
\(610\) 1405.58 182.606i 2.30423 0.299354i
\(611\) 663.961 1.08668
\(612\) −313.657 313.657i −0.512512 0.512512i
\(613\) −308.221 + 308.221i −0.502808 + 0.502808i −0.912309 0.409501i \(-0.865703\pi\)
0.409501 + 0.912309i \(0.365703\pi\)
\(614\) 169.129i 0.275454i
\(615\) 25.0571 + 192.873i 0.0407433 + 0.313615i
\(616\) −68.8567 −0.111780
\(617\) 21.2194 + 21.2194i 0.0343913 + 0.0343913i 0.724093 0.689702i \(-0.242258\pi\)
−0.689702 + 0.724093i \(0.742258\pi\)
\(618\) 755.332 755.332i 1.22222 1.22222i
\(619\) 794.043i 1.28278i −0.767213 0.641392i \(-0.778357\pi\)
0.767213 0.641392i \(-0.221643\pi\)
\(620\) 1056.28 + 813.380i 1.70367 + 1.31190i
\(621\) 144.548 0.232767
\(622\) 468.346 + 468.346i 0.752968 + 0.752968i
\(623\) −41.5685 + 41.5685i −0.0667230 + 0.0667230i
\(624\) 70.8721i 0.113577i
\(625\) −543.389 + 308.794i −0.869422 + 0.494071i
\(626\) −112.432 −0.179603
\(627\) −117.825 117.825i −0.187919 0.187919i
\(628\) −1214.69 + 1214.69i −1.93423 + 1.93423i
\(629\) 1134.07i 1.80298i
\(630\) −76.8641 + 99.8178i −0.122007 + 0.158441i
\(631\) −365.937 −0.579932 −0.289966 0.957037i \(-0.593644\pi\)
−0.289966 + 0.957037i \(0.593644\pi\)
\(632\) 523.479 + 523.479i 0.828290 + 0.828290i
\(633\) −210.087 + 210.087i −0.331892 + 0.331892i
\(634\) 740.297i 1.16766i
\(635\) −197.403 + 25.6457i −0.310871 + 0.0403869i
\(636\) 134.177 0.210970
\(637\) 59.9931 + 59.9931i 0.0941808 + 0.0941808i
\(638\) −155.548 + 155.548i −0.243806 + 0.243806i
\(639\) 236.444i 0.370022i
\(640\) −117.598 905.195i −0.183747 1.41437i
\(641\) 610.251 0.952029 0.476014 0.879437i \(-0.342081\pi\)
0.476014 + 0.879437i \(0.342081\pi\)
\(642\) −562.230 562.230i −0.875747 0.875747i
\(643\) −18.4704 + 18.4704i −0.0287253 + 0.0287253i −0.721324 0.692598i \(-0.756466\pi\)
0.692598 + 0.721324i \(0.256466\pi\)
\(644\) 447.289i 0.694548i
\(645\) 139.281 + 107.253i 0.215940 + 0.166283i
\(646\) −1882.66 −2.91433
\(647\) −633.369 633.369i −0.978931 0.978931i 0.0208512 0.999783i \(-0.493362\pi\)
−0.999783 + 0.0208512i \(0.993362\pi\)
\(648\) 41.9652 41.9652i 0.0647612 0.0647612i
\(649\) 229.041i 0.352914i
\(650\) −245.782 929.969i −0.378126 1.43072i
\(651\) −201.054 −0.308839
\(652\) −893.904 893.904i −1.37102 1.37102i
\(653\) 345.393 345.393i 0.528933 0.528933i −0.391321 0.920254i \(-0.627982\pi\)
0.920254 + 0.391321i \(0.127982\pi\)
\(654\) 321.473i 0.491548i
\(655\) 99.2852 128.934i 0.151580 0.196846i
\(656\) 75.8178 0.115576
\(657\) 54.8083 + 54.8083i 0.0834221 + 0.0834221i
\(658\) −325.334 + 325.334i −0.494428 + 0.494428i
\(659\) 347.238i 0.526917i 0.964671 + 0.263458i \(0.0848632\pi\)
−0.964671 + 0.263458i \(0.915137\pi\)
\(660\) −205.987 + 26.7608i −0.312101 + 0.0405466i
\(661\) −482.959 −0.730649 −0.365324 0.930880i \(-0.619042\pi\)
−0.365324 + 0.930880i \(0.619042\pi\)
\(662\) −728.166 728.166i −1.09995 1.09995i
\(663\) −361.165 + 361.165i −0.544744 + 0.544744i
\(664\) 120.654i 0.181708i
\(665\) 41.5434 + 319.774i 0.0624713 + 0.480863i
\(666\) 443.907 0.666527
\(667\) −345.374 345.374i −0.517802 0.517802i
\(668\) −265.184 + 265.184i −0.396982 + 0.396982i
\(669\) 15.3639i 0.0229654i
\(670\) 377.144 + 290.418i 0.562902 + 0.433459i
\(671\) −352.439 −0.525245
\(672\) 120.197 + 120.197i 0.178865 + 0.178865i
\(673\) 769.503 769.503i 1.14339 1.14339i 0.155566 0.987825i \(-0.450280\pi\)
0.987825 0.155566i \(-0.0497202\pi\)
\(674\) 121.882i 0.180834i
\(675\) −65.3359 + 112.277i −0.0967939 + 0.166337i
\(676\) −134.276 −0.198633
\(677\) 265.615 + 265.615i 0.392341 + 0.392341i 0.875521 0.483180i \(-0.160518\pi\)
−0.483180 + 0.875521i \(0.660518\pi\)
\(678\) 218.939 218.939i 0.322918 0.322918i
\(679\) 339.154i 0.499490i
\(680\) −489.425 + 635.580i −0.719742 + 0.934676i
\(681\) −380.606 −0.558893
\(682\) −388.682 388.682i −0.569916 0.569916i
\(683\) 346.533 346.533i 0.507369 0.507369i −0.406349 0.913718i \(-0.633198\pi\)
0.913718 + 0.406349i \(0.133198\pi\)
\(684\) 444.414i 0.649728i
\(685\) −1291.35 + 167.766i −1.88518 + 0.244913i
\(686\) −58.7920 −0.0857026
\(687\) 346.813 + 346.813i 0.504822 + 0.504822i
\(688\) 48.4559 48.4559i 0.0704301 0.0704301i
\(689\) 154.500i 0.224238i
\(690\) −98.5275 758.400i −0.142794 1.09913i
\(691\) −330.788 −0.478709 −0.239355 0.970932i \(-0.576936\pi\)
−0.239355 + 0.970932i \(0.576936\pi\)
\(692\) −483.946 483.946i −0.699343 0.699343i
\(693\) 22.1508 22.1508i 0.0319637 0.0319637i
\(694\) 0.845888i 0.00121886i
\(695\) 302.090 + 232.623i 0.434661 + 0.334709i
\(696\) −200.538 −0.288129
\(697\) −386.369 386.369i −0.554331 0.554331i
\(698\) −500.348 + 500.348i −0.716830 + 0.716830i
\(699\) 45.5483i 0.0651620i
\(700\) 347.430 + 202.175i 0.496329 + 0.288821i
\(701\) −595.747 −0.849853 −0.424926 0.905228i \(-0.639700\pi\)
−0.424926 + 0.905228i \(0.639700\pi\)
\(702\) −141.370 141.370i −0.201382 0.201382i
\(703\) 803.421 803.421i 1.14285 1.14285i
\(704\) 411.440i 0.584432i
\(705\) −289.446 + 375.882i −0.410561 + 0.533165i
\(706\) 44.9098 0.0636116
\(707\) −336.981 336.981i −0.476635 0.476635i
\(708\) −431.948 + 431.948i −0.610097 + 0.610097i
\(709\) 546.791i 0.771215i 0.922663 + 0.385608i \(0.126008\pi\)
−0.922663 + 0.385608i \(0.873992\pi\)
\(710\) 1240.55 161.166i 1.74725 0.226994i
\(711\) −336.801 −0.473701
\(712\) −103.604 103.604i −0.145511 0.145511i
\(713\) 863.018 863.018i 1.21040 1.21040i
\(714\) 353.934i 0.495706i
\(715\) 30.8140 + 237.186i 0.0430965 + 0.331729i
\(716\) 1154.64 1.61262
\(717\) −324.596 324.596i −0.452714 0.452714i
\(718\) 1358.46 1358.46i 1.89201 1.89201i
\(719\) 383.796i 0.533791i −0.963725 0.266896i \(-0.914002\pi\)
0.963725 0.266896i \(-0.0859979\pi\)
\(720\) 40.1221 + 30.8958i 0.0557251 + 0.0429108i
\(721\) 514.008 0.712910
\(722\) −523.413 523.413i −0.724949 0.724949i
\(723\) 156.145 156.145i 0.215968 0.215968i
\(724\) 1174.61i 1.62239i
\(725\) 424.378 112.159i 0.585349 0.154702i
\(726\) −579.655 −0.798422
\(727\) −331.503 331.503i −0.455988 0.455988i 0.441348 0.897336i \(-0.354500\pi\)
−0.897336 + 0.441348i \(0.854500\pi\)
\(728\) −149.525 + 149.525i −0.205392 + 0.205392i
\(729\) 27.0000i 0.0370370i
\(730\) 250.204 324.921i 0.342745 0.445097i
\(731\) −493.864 −0.675600
\(732\) −664.665 664.665i −0.908012 0.908012i
\(733\) 771.577 771.577i 1.05263 1.05263i 0.0540934 0.998536i \(-0.482773\pi\)
0.998536 0.0540934i \(-0.0172269\pi\)
\(734\) 1165.14i 1.58739i
\(735\) −60.1166 + 7.81004i −0.0817913 + 0.0106259i
\(736\) −1031.88 −1.40202
\(737\) −83.6931 83.6931i −0.113559 0.113559i
\(738\) 151.235 151.235i 0.204926 0.204926i
\(739\) 644.895i 0.872658i −0.899787 0.436329i \(-0.856278\pi\)
0.899787 0.436329i \(-0.143722\pi\)
\(740\) −182.474 1404.57i −0.246587 1.89807i
\(741\) −511.726 −0.690589
\(742\) 75.7033 + 75.7033i 0.102026 + 0.102026i
\(743\) 351.711 351.711i 0.473366 0.473366i −0.429636 0.903002i \(-0.641358\pi\)
0.903002 + 0.429636i \(0.141358\pi\)
\(744\) 501.102i 0.673525i
\(745\) 920.680 + 708.965i 1.23581 + 0.951631i
\(746\) 2006.22 2.68930
\(747\) 38.8139 + 38.8139i 0.0519597 + 0.0519597i
\(748\) 412.638 412.638i 0.551655 0.551655i
\(749\) 382.601i 0.510815i
\(750\) 633.620 + 266.266i 0.844826 + 0.355022i
\(751\) 1346.30 1.79268 0.896339 0.443369i \(-0.146217\pi\)
0.896339 + 0.443369i \(0.146217\pi\)
\(752\) 130.769 + 130.769i 0.173895 + 0.173895i
\(753\) 39.1329 39.1329i 0.0519693 0.0519693i
\(754\) 675.560i 0.895968i
\(755\) −521.436 + 677.151i −0.690644 + 0.896888i
\(756\) 83.5485 0.110514
\(757\) 391.030 + 391.030i 0.516553 + 0.516553i 0.916527 0.399974i \(-0.130981\pi\)
−0.399974 + 0.916527i \(0.630981\pi\)
\(758\) 114.748 114.748i 0.151383 0.151383i
\(759\) 190.163i 0.250545i
\(760\) −796.996 + 103.542i −1.04868 + 0.136239i
\(761\) −385.783 −0.506943 −0.253471 0.967343i \(-0.581572\pi\)
−0.253471 + 0.967343i \(0.581572\pi\)
\(762\) 154.788 + 154.788i 0.203133 + 0.203133i
\(763\) −109.382 + 109.382i −0.143358 + 0.143358i
\(764\) 1434.61i 1.87776i
\(765\) −47.0173 361.908i −0.0614605 0.473083i
\(766\) 1819.75 2.37565
\(767\) 497.373 + 497.373i 0.648465 + 0.648465i
\(768\) −199.066 + 199.066i −0.259201 + 0.259201i
\(769\) 1014.63i 1.31941i −0.751525 0.659705i \(-0.770681\pi\)
0.751525 0.659705i \(-0.229319\pi\)
\(770\) −131.317 101.120i −0.170542 0.131325i
\(771\) −338.977 −0.439659
\(772\) 771.776 + 771.776i 0.999710 + 0.999710i
\(773\)