Properties

Label 690.2.i.f.47.16
Level $690$
Weight $2$
Character 690.47
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 47.16
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.73145 + 0.0456124i) q^{3} -1.00000i q^{4} +(-1.54063 + 1.62063i) q^{5} +(1.25657 - 1.19207i) q^{6} +(0.528026 + 0.528026i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99584 + 0.157951i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.73145 + 0.0456124i) q^{3} -1.00000i q^{4} +(-1.54063 + 1.62063i) q^{5} +(1.25657 - 1.19207i) q^{6} +(0.528026 + 0.528026i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99584 + 0.157951i) q^{9} +(0.0565714 + 2.23535i) q^{10} +4.60712i q^{11} +(0.0456124 - 1.73145i) q^{12} +(4.73992 - 4.73992i) q^{13} +0.746742 q^{14} +(-2.74145 + 2.73578i) q^{15} -1.00000 q^{16} +(3.32957 - 3.32957i) q^{17} +(2.23007 - 2.00669i) q^{18} +5.21085i q^{19} +(1.62063 + 1.54063i) q^{20} +(0.890166 + 0.938335i) q^{21} +(3.25773 + 3.25773i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-1.19207 - 1.25657i) q^{24} +(-0.252914 - 4.99360i) q^{25} -6.70326i q^{26} +(5.17994 + 0.410132i) q^{27} +(0.528026 - 0.528026i) q^{28} -2.50593 q^{29} +(-0.00400919 + 3.87298i) q^{30} +3.91972 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.210142 + 7.97700i) q^{33} -4.70873i q^{34} +(-1.66923 + 0.0422442i) q^{35} +(0.157951 - 2.99584i) q^{36} +(-7.08238 - 7.08238i) q^{37} +(3.68463 + 3.68463i) q^{38} +(8.42313 - 7.99073i) q^{39} +(2.23535 - 0.0565714i) q^{40} +4.23059i q^{41} +(1.29295 + 0.0340607i) q^{42} +(-7.82352 + 7.82352i) q^{43} +4.60712 q^{44} +(-4.87146 + 4.61182i) q^{45} +1.00000 q^{46} +(2.42130 - 2.42130i) q^{47} +(-1.73145 - 0.0456124i) q^{48} -6.44238i q^{49} +(-3.70985 - 3.35217i) q^{50} +(5.91686 - 5.61312i) q^{51} +(-4.73992 - 4.73992i) q^{52} +(1.66113 + 1.66113i) q^{53} +(3.95278 - 3.37276i) q^{54} +(-7.46646 - 7.09787i) q^{55} -0.746742i q^{56} +(-0.237680 + 9.02233i) q^{57} +(-1.77196 + 1.77196i) q^{58} -12.7399 q^{59} +(2.73578 + 2.74145i) q^{60} -1.51016 q^{61} +(2.77166 - 2.77166i) q^{62} +(1.49848 + 1.66528i) q^{63} +1.00000i q^{64} +(0.379213 + 14.9841i) q^{65} +(5.49200 + 5.78918i) q^{66} +(-5.25010 - 5.25010i) q^{67} +(-3.32957 - 3.32957i) q^{68} +(1.19207 + 1.25657i) q^{69} +(-1.15045 + 1.21020i) q^{70} +10.9186i q^{71} +(-2.00669 - 2.23007i) q^{72} +(-5.55728 + 5.55728i) q^{73} -10.0160 q^{74} +(-0.210138 - 8.65770i) q^{75} +5.21085 q^{76} +(-2.43268 + 2.43268i) q^{77} +(0.305752 - 11.6064i) q^{78} -6.67082i q^{79} +(1.54063 - 1.62063i) q^{80} +(8.95010 + 0.946393i) q^{81} +(2.99148 + 2.99148i) q^{82} +(-9.68331 - 9.68331i) q^{83} +(0.938335 - 0.890166i) q^{84} +(0.266380 + 10.5257i) q^{85} +11.0641i q^{86} +(-4.33889 - 0.114301i) q^{87} +(3.25773 - 3.25773i) q^{88} -9.07840 q^{89} +(-0.183598 + 6.70569i) q^{90} +5.00560 q^{91} +(0.707107 - 0.707107i) q^{92} +(6.78680 + 0.178788i) q^{93} -3.42424i q^{94} +(-8.44489 - 8.02800i) q^{95} +(-1.25657 + 1.19207i) q^{96} +(5.69526 + 5.69526i) q^{97} +(-4.55545 - 4.55545i) q^{98} +(-0.727700 + 13.8022i) 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
\(3\) 1.73145 + 0.0456124i 0.999653 + 0.0263343i
\(4\) 1.00000i 0.500000i
\(5\) −1.54063 + 1.62063i −0.688991 + 0.724770i
\(6\) 1.25657 1.19207i 0.512994 0.486659i
\(7\) 0.528026 + 0.528026i 0.199575 + 0.199575i 0.799818 0.600243i \(-0.204929\pi\)
−0.600243 + 0.799818i \(0.704929\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 2.99584 + 0.157951i 0.998613 + 0.0526504i
\(10\) 0.0565714 + 2.23535i 0.0178895 + 0.706880i
\(11\) 4.60712i 1.38910i 0.719445 + 0.694549i \(0.244396\pi\)
−0.719445 + 0.694549i \(0.755604\pi\)
\(12\) 0.0456124 1.73145i 0.0131672 0.499827i
\(13\) 4.73992 4.73992i 1.31462 1.31462i 0.396645 0.917972i \(-0.370174\pi\)
0.917972 0.396645i \(-0.129826\pi\)
\(14\) 0.746742 0.199575
\(15\) −2.74145 + 2.73578i −0.707838 + 0.706374i
\(16\) −1.00000 −0.250000
\(17\) 3.32957 3.32957i 0.807541 0.807541i −0.176721 0.984261i \(-0.556549\pi\)
0.984261 + 0.176721i \(0.0565489\pi\)
\(18\) 2.23007 2.00669i 0.525632 0.472981i
\(19\) 5.21085i 1.19545i 0.801700 + 0.597726i \(0.203929\pi\)
−0.801700 + 0.597726i \(0.796071\pi\)
\(20\) 1.62063 + 1.54063i 0.362385 + 0.344495i
\(21\) 0.890166 + 0.938335i 0.194250 + 0.204762i
\(22\) 3.25773 + 3.25773i 0.694549 + 0.694549i
\(23\) 0.707107 + 0.707107i 0.147442 + 0.147442i
\(24\) −1.19207 1.25657i −0.243330 0.256497i
\(25\) −0.252914 4.99360i −0.0505828 0.998720i
\(26\) 6.70326i 1.31462i
\(27\) 5.17994 + 0.410132i 0.996880 + 0.0789300i
\(28\) 0.528026 0.528026i 0.0997876 0.0997876i
\(29\) −2.50593 −0.465339 −0.232669 0.972556i \(-0.574746\pi\)
−0.232669 + 0.972556i \(0.574746\pi\)
\(30\) −0.00400919 + 3.87298i −0.000731975 + 0.707106i
\(31\) 3.91972 0.704003 0.352001 0.935999i \(-0.385501\pi\)
0.352001 + 0.935999i \(0.385501\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −0.210142 + 7.97700i −0.0365810 + 1.38862i
\(34\) 4.70873i 0.807541i
\(35\) −1.66923 + 0.0422442i −0.282151 + 0.00714058i
\(36\) 0.157951 2.99584i 0.0263252 0.499307i
\(37\) −7.08238 7.08238i −1.16434 1.16434i −0.983516 0.180820i \(-0.942125\pi\)
−0.180820 0.983516i \(-0.557875\pi\)
\(38\) 3.68463 + 3.68463i 0.597726 + 0.597726i
\(39\) 8.42313 7.99073i 1.34878 1.27954i
\(40\) 2.23535 0.0565714i 0.353440 0.00894473i
\(41\) 4.23059i 0.660707i 0.943857 + 0.330353i \(0.107168\pi\)
−0.943857 + 0.330353i \(0.892832\pi\)
\(42\) 1.29295 + 0.0340607i 0.199506 + 0.00525568i
\(43\) −7.82352 + 7.82352i −1.19308 + 1.19308i −0.216877 + 0.976199i \(0.569587\pi\)
−0.976199 + 0.216877i \(0.930413\pi\)
\(44\) 4.60712 0.694549
\(45\) −4.87146 + 4.61182i −0.726195 + 0.687489i
\(46\) 1.00000 0.147442
\(47\) 2.42130 2.42130i 0.353184 0.353184i −0.508109 0.861293i \(-0.669655\pi\)
0.861293 + 0.508109i \(0.169655\pi\)
\(48\) −1.73145 0.0456124i −0.249913 0.00658358i
\(49\) 6.44238i 0.920340i
\(50\) −3.70985 3.35217i −0.524651 0.474069i
\(51\) 5.91686 5.61312i 0.828527 0.785994i
\(52\) −4.73992 4.73992i −0.657308 0.657308i
\(53\) 1.66113 + 1.66113i 0.228173 + 0.228173i 0.811929 0.583756i \(-0.198418\pi\)
−0.583756 + 0.811929i \(0.698418\pi\)
\(54\) 3.95278 3.37276i 0.537905 0.458975i
\(55\) −7.46646 7.09787i −1.00678 0.957077i
\(56\) 0.746742i 0.0997876i
\(57\) −0.237680 + 9.02233i −0.0314814 + 1.19504i
\(58\) −1.77196 + 1.77196i −0.232669 + 0.232669i
\(59\) −12.7399 −1.65860 −0.829299 0.558806i \(-0.811260\pi\)
−0.829299 + 0.558806i \(0.811260\pi\)
\(60\) 2.73578 + 2.74145i 0.353187 + 0.353919i
\(61\) −1.51016 −0.193356 −0.0966778 0.995316i \(-0.530822\pi\)
−0.0966778 + 0.995316i \(0.530822\pi\)
\(62\) 2.77166 2.77166i 0.352001 0.352001i
\(63\) 1.49848 + 1.66528i 0.188791 + 0.209806i
\(64\) 1.00000i 0.125000i
\(65\) 0.379213 + 14.9841i 0.0470356 + 1.85855i
\(66\) 5.49200 + 5.78918i 0.676018 + 0.712599i
\(67\) −5.25010 5.25010i −0.641402 0.641402i 0.309498 0.950900i \(-0.399839\pi\)
−0.950900 + 0.309498i \(0.899839\pi\)
\(68\) −3.32957 3.32957i −0.403770 0.403770i
\(69\) 1.19207 + 1.25657i 0.143508 + 0.151274i
\(70\) −1.15045 + 1.21020i −0.137505 + 0.144646i
\(71\) 10.9186i 1.29580i 0.761727 + 0.647898i \(0.224352\pi\)
−0.761727 + 0.647898i \(0.775648\pi\)
\(72\) −2.00669 2.23007i −0.236491 0.262816i
\(73\) −5.55728 + 5.55728i −0.650430 + 0.650430i −0.953097 0.302667i \(-0.902123\pi\)
0.302667 + 0.953097i \(0.402123\pi\)
\(74\) −10.0160 −1.16434
\(75\) −0.210138 8.65770i −0.0242647 0.999706i
\(76\) 5.21085 0.597726
\(77\) −2.43268 + 2.43268i −0.277230 + 0.277230i
\(78\) 0.305752 11.6064i 0.0346196 1.31416i
\(79\) 6.67082i 0.750526i −0.926918 0.375263i \(-0.877552\pi\)
0.926918 0.375263i \(-0.122448\pi\)
\(80\) 1.54063 1.62063i 0.172248 0.181192i
\(81\) 8.95010 + 0.946393i 0.994456 + 0.105155i
\(82\) 2.99148 + 2.99148i 0.330353 + 0.330353i
\(83\) −9.68331 9.68331i −1.06288 1.06288i −0.997886 0.0649958i \(-0.979297\pi\)
−0.0649958 0.997886i \(-0.520703\pi\)
\(84\) 0.938335 0.890166i 0.102381 0.0971251i
\(85\) 0.266380 + 10.5257i 0.0288929 + 1.14167i
\(86\) 11.0641i 1.19308i
\(87\) −4.33889 0.114301i −0.465178 0.0122544i
\(88\) 3.25773 3.25773i 0.347275 0.347275i
\(89\) −9.07840 −0.962309 −0.481154 0.876636i \(-0.659782\pi\)
−0.481154 + 0.876636i \(0.659782\pi\)
\(90\) −0.183598 + 6.70569i −0.0193529 + 0.706842i
\(91\) 5.00560 0.524730
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) 6.78680 + 0.178788i 0.703759 + 0.0185394i
\(94\) 3.42424i 0.353184i
\(95\) −8.44489 8.02800i −0.866428 0.823656i
\(96\) −1.25657 + 1.19207i −0.128248 + 0.121665i
\(97\) 5.69526 + 5.69526i 0.578266 + 0.578266i 0.934425 0.356159i \(-0.115914\pi\)
−0.356159 + 0.934425i \(0.615914\pi\)
\(98\) −4.55545 4.55545i −0.460170 0.460170i
\(99\) −0.727700 + 13.8022i −0.0731366 + 1.38717i
\(100\) −4.99360 + 0.252914i −0.499360 + 0.0252914i
\(101\) 7.99014i 0.795049i −0.917592 0.397524i \(-0.869869\pi\)
0.917592 0.397524i \(-0.130131\pi\)
\(102\) 0.214777 8.15293i 0.0212660 0.807260i
\(103\) 8.37328 8.37328i 0.825044 0.825044i −0.161783 0.986826i \(-0.551724\pi\)
0.986826 + 0.161783i \(0.0517244\pi\)
\(104\) −6.70326 −0.657308
\(105\) −2.89212 0.00299383i −0.282242 0.000292168i
\(106\) 2.34919 0.228173
\(107\) 10.8290 10.8290i 1.04688 1.04688i 0.0480314 0.998846i \(-0.484705\pi\)
0.998846 0.0480314i \(-0.0152948\pi\)
\(108\) 0.410132 5.17994i 0.0394650 0.498440i
\(109\) 5.81042i 0.556538i −0.960503 0.278269i \(-0.910239\pi\)
0.960503 0.278269i \(-0.0897606\pi\)
\(110\) −10.2985 + 0.260631i −0.981927 + 0.0248502i
\(111\) −11.9397 12.5858i −1.13327 1.19459i
\(112\) −0.528026 0.528026i −0.0498938 0.0498938i
\(113\) −0.624299 0.624299i −0.0587291 0.0587291i 0.677132 0.735861i \(-0.263222\pi\)
−0.735861 + 0.677132i \(0.763222\pi\)
\(114\) 6.21169 + 6.54782i 0.581778 + 0.613259i
\(115\) −2.23535 + 0.0565714i −0.208448 + 0.00527531i
\(116\) 2.50593i 0.232669i
\(117\) 14.9487 13.4514i 1.38201 1.24358i
\(118\) −9.00849 + 9.00849i −0.829299 + 0.829299i
\(119\) 3.51621 0.322330
\(120\) 3.87298 + 0.00400919i 0.353553 + 0.000365988i
\(121\) −10.2255 −0.929595
\(122\) −1.06784 + 1.06784i −0.0966778 + 0.0966778i
\(123\) −0.192967 + 7.32505i −0.0173993 + 0.660478i
\(124\) 3.91972i 0.352001i
\(125\) 8.48245 + 7.28341i 0.758693 + 0.651448i
\(126\) 2.23712 + 0.117949i 0.199298 + 0.0105077i
\(127\) 11.0353 + 11.0353i 0.979224 + 0.979224i 0.999789 0.0205641i \(-0.00654623\pi\)
−0.0205641 + 0.999789i \(0.506546\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −13.9029 + 13.1892i −1.22408 + 1.16124i
\(130\) 10.8635 + 10.3272i 0.952795 + 0.905759i
\(131\) 9.85239i 0.860807i −0.902637 0.430404i \(-0.858371\pi\)
0.902637 0.430404i \(-0.141629\pi\)
\(132\) 7.97700 + 0.210142i 0.694309 + 0.0182905i
\(133\) −2.75147 + 2.75147i −0.238582 + 0.238582i
\(134\) −7.42476 −0.641402
\(135\) −8.64505 + 7.76293i −0.744048 + 0.668127i
\(136\) −4.70873 −0.403770
\(137\) −7.59469 + 7.59469i −0.648858 + 0.648858i −0.952717 0.303859i \(-0.901725\pi\)
0.303859 + 0.952717i \(0.401725\pi\)
\(138\) 1.73145 + 0.0456124i 0.147391 + 0.00388279i
\(139\) 14.6607i 1.24350i 0.783214 + 0.621752i \(0.213579\pi\)
−0.783214 + 0.621752i \(0.786421\pi\)
\(140\) 0.0422442 + 1.66923i 0.00357029 + 0.141076i
\(141\) 4.30281 4.08193i 0.362362 0.343760i
\(142\) 7.72060 + 7.72060i 0.647898 + 0.647898i
\(143\) 21.8374 + 21.8374i 1.82613 + 1.82613i
\(144\) −2.99584 0.157951i −0.249653 0.0131626i
\(145\) 3.86071 4.06119i 0.320614 0.337264i
\(146\) 7.85918i 0.650430i
\(147\) 0.293852 11.1547i 0.0242365 0.920020i
\(148\) −7.08238 + 7.08238i −0.582168 + 0.582168i
\(149\) −5.81897 −0.476708 −0.238354 0.971178i \(-0.576608\pi\)
−0.238354 + 0.971178i \(0.576608\pi\)
\(150\) −6.27051 5.97333i −0.511985 0.487720i
\(151\) 2.78052 0.226276 0.113138 0.993579i \(-0.463910\pi\)
0.113138 + 0.993579i \(0.463910\pi\)
\(152\) 3.68463 3.68463i 0.298863 0.298863i
\(153\) 10.5008 9.44896i 0.848938 0.763903i
\(154\) 3.44033i 0.277230i
\(155\) −6.03884 + 6.35244i −0.485052 + 0.510240i
\(156\) −7.99073 8.42313i −0.639771 0.674390i
\(157\) −6.33516 6.33516i −0.505601 0.505601i 0.407572 0.913173i \(-0.366375\pi\)
−0.913173 + 0.407572i \(0.866375\pi\)
\(158\) −4.71698 4.71698i −0.375263 0.375263i
\(159\) 2.80039 + 2.95192i 0.222085 + 0.234103i
\(160\) −0.0565714 2.23535i −0.00447236 0.176720i
\(161\) 0.746742i 0.0588515i
\(162\) 6.99788 5.65948i 0.549805 0.444651i
\(163\) −3.13303 + 3.13303i −0.245398 + 0.245398i −0.819079 0.573681i \(-0.805515\pi\)
0.573681 + 0.819079i \(0.305515\pi\)
\(164\) 4.23059 0.330353
\(165\) −12.6040 12.6302i −0.981224 0.983257i
\(166\) −13.6943 −1.06288
\(167\) 5.90660 5.90660i 0.457067 0.457067i −0.440625 0.897691i \(-0.645243\pi\)
0.897691 + 0.440625i \(0.145243\pi\)
\(168\) 0.0340607 1.29295i 0.00262784 0.0997529i
\(169\) 31.9337i 2.45644i
\(170\) 7.63113 + 7.25441i 0.585281 + 0.556388i
\(171\) −0.823061 + 15.6109i −0.0629410 + 1.19379i
\(172\) 7.82352 + 7.82352i 0.596538 + 0.596538i
\(173\) −10.1099 10.1099i −0.768643 0.768643i 0.209225 0.977868i \(-0.432906\pi\)
−0.977868 + 0.209225i \(0.932906\pi\)
\(174\) −3.14888 + 2.98723i −0.238716 + 0.226462i
\(175\) 2.50321 2.77030i 0.189225 0.209415i
\(176\) 4.60712i 0.347275i
\(177\) −22.0585 0.581099i −1.65802 0.0436781i
\(178\) −6.41940 + 6.41940i −0.481154 + 0.481154i
\(179\) −10.7084 −0.800386 −0.400193 0.916431i \(-0.631057\pi\)
−0.400193 + 0.916431i \(0.631057\pi\)
\(180\) 4.61182 + 4.87146i 0.343744 + 0.363097i
\(181\) 19.3288 1.43670 0.718349 0.695683i \(-0.244898\pi\)
0.718349 + 0.695683i \(0.244898\pi\)
\(182\) 3.53949 3.53949i 0.262365 0.262365i
\(183\) −2.61476 0.0688818i −0.193288 0.00509189i
\(184\) 1.00000i 0.0737210i
\(185\) 22.3893 0.566619i 1.64609 0.0416587i
\(186\) 4.92542 4.67257i 0.361149 0.342610i
\(187\) 15.3397 + 15.3397i 1.12175 + 1.12175i
\(188\) −2.42130 2.42130i −0.176592 0.176592i
\(189\) 2.51858 + 2.95170i 0.183200 + 0.214705i
\(190\) −11.6481 + 0.294785i −0.845042 + 0.0213860i
\(191\) 16.3310i 1.18167i −0.806792 0.590835i \(-0.798798\pi\)
0.806792 0.590835i \(-0.201202\pi\)
\(192\) −0.0456124 + 1.73145i −0.00329179 + 0.124957i
\(193\) −4.44978 + 4.44978i −0.320302 + 0.320302i −0.848883 0.528581i \(-0.822724\pi\)
0.528581 + 0.848883i \(0.322724\pi\)
\(194\) 8.05432 0.578266
\(195\) −0.0268747 + 25.9616i −0.00192453 + 1.85915i
\(196\) −6.44238 −0.460170
\(197\) −19.0107 + 19.0107i −1.35446 + 1.35446i −0.473858 + 0.880601i \(0.657139\pi\)
−0.880601 + 0.473858i \(0.842861\pi\)
\(198\) 9.24506 + 10.2742i 0.657018 + 0.730154i
\(199\) 19.6455i 1.39263i 0.717737 + 0.696315i \(0.245178\pi\)
−0.717737 + 0.696315i \(0.754822\pi\)
\(200\) −3.35217 + 3.70985i −0.237034 + 0.262326i
\(201\) −8.85081 9.32975i −0.624288 0.658070i
\(202\) −5.64988 5.64988i −0.397524 0.397524i
\(203\) −1.32319 1.32319i −0.0928701 0.0928701i
\(204\) −5.61312 5.91686i −0.392997 0.414263i
\(205\) −6.85624 6.51777i −0.478860 0.455221i
\(206\) 11.8416i 0.825044i
\(207\) 2.00669 + 2.23007i 0.139475 + 0.155000i
\(208\) −4.73992 + 4.73992i −0.328654 + 0.328654i
\(209\) −24.0070 −1.66060
\(210\) −2.04715 + 2.04292i −0.141267 + 0.140975i
\(211\) −4.38087 −0.301592 −0.150796 0.988565i \(-0.548184\pi\)
−0.150796 + 0.988565i \(0.548184\pi\)
\(212\) 1.66113 1.66113i 0.114087 0.114087i
\(213\) −0.498023 + 18.9050i −0.0341239 + 1.29535i
\(214\) 15.3145i 1.04688i
\(215\) −0.625914 24.7322i −0.0426870 1.68672i
\(216\) −3.37276 3.95278i −0.229488 0.268953i
\(217\) 2.06972 + 2.06972i 0.140501 + 0.140501i
\(218\) −4.10859 4.10859i −0.278269 0.278269i
\(219\) −9.87563 + 9.36867i −0.667333 + 0.633076i
\(220\) −7.09787 + 7.46646i −0.478538 + 0.503388i
\(221\) 31.5638i 2.12321i
\(222\) −17.3422 0.456854i −1.16393 0.0306620i
\(223\) 8.23185 8.23185i 0.551245 0.551245i −0.375555 0.926800i \(-0.622548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(224\) −0.746742 −0.0498938
\(225\) 0.0310551 15.0000i 0.00207034 0.999998i
\(226\) −0.882892 −0.0587291
\(227\) −4.42457 + 4.42457i −0.293669 + 0.293669i −0.838528 0.544859i \(-0.816583\pi\)
0.544859 + 0.838528i \(0.316583\pi\)
\(228\) 9.02233 + 0.237680i 0.597519 + 0.0157407i
\(229\) 0.539521i 0.0356526i 0.999841 + 0.0178263i \(0.00567458\pi\)
−0.999841 + 0.0178263i \(0.994325\pi\)
\(230\) −1.54063 + 1.62063i −0.101586 + 0.106861i
\(231\) −4.32302 + 4.10110i −0.284434 + 0.269833i
\(232\) 1.77196 + 1.77196i 0.116335 + 0.116335i
\(233\) 5.01691 + 5.01691i 0.328669 + 0.328669i 0.852080 0.523411i \(-0.175341\pi\)
−0.523411 + 0.852080i \(0.675341\pi\)
\(234\) 1.05879 20.0819i 0.0692151 1.31279i
\(235\) 0.193714 + 7.65439i 0.0126365 + 0.499317i
\(236\) 12.7399i 0.829299i
\(237\) 0.304272 11.5502i 0.0197646 0.750265i
\(238\) 2.48633 2.48633i 0.161165 0.161165i
\(239\) −3.23606 −0.209324 −0.104662 0.994508i \(-0.533376\pi\)
−0.104662 + 0.994508i \(0.533376\pi\)
\(240\) 2.74145 2.73578i 0.176960 0.176594i
\(241\) 2.49371 0.160634 0.0803171 0.996769i \(-0.474407\pi\)
0.0803171 + 0.996769i \(0.474407\pi\)
\(242\) −7.23056 + 7.23056i −0.464798 + 0.464798i
\(243\) 15.4535 + 2.04687i 0.991342 + 0.131307i
\(244\) 1.51016i 0.0966778i
\(245\) 10.4407 + 9.92532i 0.667034 + 0.634106i
\(246\) 5.04315 + 5.31604i 0.321539 + 0.338939i
\(247\) 24.6990 + 24.6990i 1.57156 + 1.57156i
\(248\) −2.77166 2.77166i −0.176001 0.176001i
\(249\) −16.3245 17.2078i −1.03452 1.09050i
\(250\) 11.1481 0.847847i 0.705071 0.0536226i
\(251\) 5.39309i 0.340409i 0.985409 + 0.170205i \(0.0544428\pi\)
−0.985409 + 0.170205i \(0.945557\pi\)
\(252\) 1.66528 1.49848i 0.104903 0.0943953i
\(253\) −3.25773 + 3.25773i −0.204811 + 0.204811i
\(254\) 15.6063 0.979224
\(255\) −0.0188782 + 18.2368i −0.00118220 + 1.14203i
\(256\) 1.00000 0.0625000
\(257\) 0.454641 0.454641i 0.0283597 0.0283597i −0.692785 0.721144i \(-0.743616\pi\)
0.721144 + 0.692785i \(0.243616\pi\)
\(258\) −0.504662 + 19.1570i −0.0314189 + 1.19266i
\(259\) 7.47937i 0.464745i
\(260\) 14.9841 0.379213i 0.929277 0.0235178i
\(261\) −7.50735 0.395814i −0.464693 0.0245003i
\(262\) −6.96669 6.96669i −0.430404 0.430404i
\(263\) −10.1010 10.1010i −0.622853 0.622853i 0.323407 0.946260i \(-0.395172\pi\)
−0.946260 + 0.323407i \(0.895172\pi\)
\(264\) 5.78918 5.49200i 0.356300 0.338009i
\(265\) −5.25126 + 0.132897i −0.322582 + 0.00816379i
\(266\) 3.89116i 0.238582i
\(267\) −15.7188 0.414088i −0.961975 0.0253418i
\(268\) −5.25010 + 5.25010i −0.320701 + 0.320701i
\(269\) −23.4948 −1.43250 −0.716252 0.697842i \(-0.754144\pi\)
−0.716252 + 0.697842i \(0.754144\pi\)
\(270\) −0.623753 + 11.6022i −0.0379604 + 0.706087i
\(271\) −6.16572 −0.374541 −0.187270 0.982308i \(-0.559964\pi\)
−0.187270 + 0.982308i \(0.559964\pi\)
\(272\) −3.32957 + 3.32957i −0.201885 + 0.201885i
\(273\) 8.66695 + 0.228318i 0.524548 + 0.0138184i
\(274\) 10.7405i 0.648858i
\(275\) 23.0061 1.16521i 1.38732 0.0702645i
\(276\) 1.25657 1.19207i 0.0756368 0.0717540i
\(277\) 16.3851 + 16.3851i 0.984482 + 0.984482i 0.999881 0.0153991i \(-0.00490187\pi\)
−0.0153991 + 0.999881i \(0.504902\pi\)
\(278\) 10.3667 + 10.3667i 0.621752 + 0.621752i
\(279\) 11.7429 + 0.619125i 0.703026 + 0.0370660i
\(280\) 1.21020 + 1.15045i 0.0723230 + 0.0687527i
\(281\) 0.344451i 0.0205482i −0.999947 0.0102741i \(-0.996730\pi\)
0.999947 0.0102741i \(-0.00327041\pi\)
\(282\) 0.156188 5.92890i 0.00930086 0.353061i
\(283\) −1.89935 + 1.89935i −0.112905 + 0.112905i −0.761302 0.648397i \(-0.775440\pi\)
0.648397 + 0.761302i \(0.275440\pi\)
\(284\) 10.9186 0.647898
\(285\) −14.2557 14.2853i −0.844437 0.846187i
\(286\) 30.8827 1.82613
\(287\) −2.23386 + 2.23386i −0.131861 + 0.131861i
\(288\) −2.23007 + 2.00669i −0.131408 + 0.118245i
\(289\) 5.17214i 0.304243i
\(290\) −0.141764 5.60163i −0.00832466 0.328939i
\(291\) 9.60129 + 10.1208i 0.562838 + 0.593294i
\(292\) 5.55728 + 5.55728i 0.325215 + 0.325215i
\(293\) −0.184488 0.184488i −0.0107779 0.0107779i 0.701697 0.712475i \(-0.252426\pi\)
−0.712475 + 0.701697i \(0.752426\pi\)
\(294\) −7.67975 8.09532i −0.447892 0.472128i
\(295\) 19.6275 20.6468i 1.14276 1.20210i
\(296\) 10.0160i 0.582168i
\(297\) −1.88953 + 23.8646i −0.109642 + 1.38477i
\(298\) −4.11463 + 4.11463i −0.238354 + 0.238354i
\(299\) 6.70326 0.387659
\(300\) −8.65770 + 0.210138i −0.499853 + 0.0121323i
\(301\) −8.26205 −0.476217
\(302\) 1.96613 1.96613i 0.113138 0.113138i
\(303\) 0.364450 13.8345i 0.0209371 0.794773i
\(304\) 5.21085i 0.298863i
\(305\) 2.32659 2.44741i 0.133220 0.140138i
\(306\) 0.743750 14.1066i 0.0425173 0.806420i
\(307\) −5.11094 5.11094i −0.291697 0.291697i 0.546054 0.837750i \(-0.316130\pi\)
−0.837750 + 0.546054i \(0.816130\pi\)
\(308\) 2.43268 + 2.43268i 0.138615 + 0.138615i
\(309\) 14.8798 14.1160i 0.846484 0.803031i
\(310\) 0.221744 + 8.76196i 0.0125942 + 0.497646i
\(311\) 13.3425i 0.756584i 0.925686 + 0.378292i \(0.123489\pi\)
−0.925686 + 0.378292i \(0.876511\pi\)
\(312\) −11.6064 0.305752i −0.657081 0.0173098i
\(313\) 5.87924 5.87924i 0.332314 0.332314i −0.521151 0.853465i \(-0.674497\pi\)
0.853465 + 0.521151i \(0.174497\pi\)
\(314\) −8.95927 −0.505601
\(315\) −5.00742 0.137100i −0.282136 0.00772471i
\(316\) −6.67082 −0.375263
\(317\) 15.0768 15.0768i 0.846797 0.846797i −0.142935 0.989732i \(-0.545654\pi\)
0.989732 + 0.142935i \(0.0456540\pi\)
\(318\) 4.06750 + 0.107152i 0.228094 + 0.00600879i
\(319\) 11.5451i 0.646402i
\(320\) −1.62063 1.54063i −0.0905962 0.0861239i
\(321\) 19.2438 18.2559i 1.07408 1.01895i
\(322\) 0.528026 + 0.528026i 0.0294257 + 0.0294257i
\(323\) 17.3499 + 17.3499i 0.965376 + 0.965376i
\(324\) 0.946393 8.95010i 0.0525774 0.497228i
\(325\) −24.8680 22.4705i −1.37943 1.24644i
\(326\) 4.43077i 0.245398i
\(327\) 0.265027 10.0605i 0.0146561 0.556345i
\(328\) 2.99148 2.99148i 0.165177 0.165177i
\(329\) 2.55702 0.140973
\(330\) −17.8433 0.0184708i −0.982241 0.00101679i
\(331\) 18.7391 1.02999 0.514996 0.857192i \(-0.327793\pi\)
0.514996 + 0.857192i \(0.327793\pi\)
\(332\) −9.68331 + 9.68331i −0.531441 + 0.531441i
\(333\) −20.0990 22.3363i −1.10142 1.22402i
\(334\) 8.35320i 0.457067i
\(335\) 16.5970 0.420029i 0.906788 0.0229487i
\(336\) −0.890166 0.938335i −0.0485626 0.0511904i
\(337\) 11.5783 + 11.5783i 0.630712 + 0.630712i 0.948247 0.317535i \(-0.102855\pi\)
−0.317535 + 0.948247i \(0.602855\pi\)
\(338\) −22.5805 22.5805i −1.22822 1.22822i
\(339\) −1.05247 1.10942i −0.0571621 0.0602553i
\(340\) 10.5257 0.266380i 0.570835 0.0144465i
\(341\) 18.0586i 0.977929i
\(342\) 10.4566 + 11.6206i 0.565426 + 0.628367i
\(343\) 7.09793 7.09793i 0.383252 0.383252i
\(344\) 11.0641 0.596538
\(345\) −3.87298 0.00400919i −0.208514 0.000215848i
\(346\) −14.2976 −0.768643
\(347\) 9.53609 9.53609i 0.511924 0.511924i −0.403191 0.915116i \(-0.632099\pi\)
0.915116 + 0.403191i \(0.132099\pi\)
\(348\) −0.114301 + 4.33889i −0.00612720 + 0.232589i
\(349\) 22.7071i 1.21549i −0.794134 0.607743i \(-0.792075\pi\)
0.794134 0.607743i \(-0.207925\pi\)
\(350\) −0.188862 3.72893i −0.0100951 0.199320i
\(351\) 26.4965 22.6085i 1.41428 1.20675i
\(352\) −3.25773 3.25773i −0.173637 0.173637i
\(353\) 20.2080 + 20.2080i 1.07556 + 1.07556i 0.996902 + 0.0786597i \(0.0250641\pi\)
0.0786597 + 0.996902i \(0.474936\pi\)
\(354\) −16.0086 + 15.1868i −0.850850 + 0.807172i
\(355\) −17.6950 16.8215i −0.939155 0.892792i
\(356\) 9.07840i 0.481154i
\(357\) 6.08813 + 0.160383i 0.322218 + 0.00848835i
\(358\) −7.57201 + 7.57201i −0.400193 + 0.400193i
\(359\) 9.55317 0.504197 0.252098 0.967702i \(-0.418879\pi\)
0.252098 + 0.967702i \(0.418879\pi\)
\(360\) 6.70569 + 0.183598i 0.353421 + 0.00967645i
\(361\) −8.15300 −0.429105
\(362\) 13.6675 13.6675i 0.718349 0.718349i
\(363\) −17.7050 0.466412i −0.929273 0.0244803i
\(364\) 5.00560i 0.262365i
\(365\) −0.444605 17.5680i −0.0232717 0.919552i
\(366\) −1.89762 + 1.80021i −0.0991902 + 0.0940983i
\(367\) −15.8937 15.8937i −0.829645 0.829645i 0.157823 0.987467i \(-0.449553\pi\)
−0.987467 + 0.157823i \(0.949553\pi\)
\(368\) −0.707107 0.707107i −0.0368605 0.0368605i
\(369\) −0.668227 + 12.6742i −0.0347865 + 0.659790i
\(370\) 15.4310 16.2323i 0.802217 0.843876i
\(371\) 1.75424i 0.0910754i
\(372\) 0.178788 6.78680i 0.00926972 0.351879i
\(373\) 21.9117 21.9117i 1.13455 1.13455i 0.145135 0.989412i \(-0.453638\pi\)
0.989412 0.145135i \(-0.0463617\pi\)
\(374\) 21.6937 1.12175
\(375\) 14.3547 + 12.9978i 0.741275 + 0.671202i
\(376\) −3.42424 −0.176592
\(377\) −11.8779 + 11.8779i −0.611742 + 0.611742i
\(378\) 3.86808 + 0.306263i 0.198952 + 0.0157525i
\(379\) 3.01254i 0.154744i 0.997002 + 0.0773719i \(0.0246529\pi\)
−0.997002 + 0.0773719i \(0.975347\pi\)
\(380\) −8.02800 + 8.44489i −0.411828 + 0.433214i
\(381\) 18.6037 + 19.6104i 0.953098 + 1.00467i
\(382\) −11.5478 11.5478i −0.590835 0.590835i
\(383\) 17.7386 + 17.7386i 0.906400 + 0.906400i 0.995980 0.0895800i \(-0.0285525\pi\)
−0.0895800 + 0.995980i \(0.528552\pi\)
\(384\) 1.19207 + 1.25657i 0.0608324 + 0.0641242i
\(385\) −0.194624 7.69035i −0.00991897 0.391936i
\(386\) 6.29293i 0.320302i
\(387\) −24.6738 + 22.2023i −1.25424 + 1.12861i
\(388\) 5.69526 5.69526i 0.289133 0.289133i
\(389\) 20.0679 1.01748 0.508742 0.860919i \(-0.330111\pi\)
0.508742 + 0.860919i \(0.330111\pi\)
\(390\) 18.3386 + 18.3766i 0.928612 + 0.930536i
\(391\) 4.70873 0.238131
\(392\) −4.55545 + 4.55545i −0.230085 + 0.230085i
\(393\) 0.449391 17.0589i 0.0226688 0.860509i
\(394\) 26.8853i 1.35446i
\(395\) 10.8110 + 10.2773i 0.543958 + 0.517105i
\(396\) 13.8022 + 0.727700i 0.693586 + 0.0365683i
\(397\) 26.1076 + 26.1076i 1.31030 + 1.31030i 0.921190 + 0.389114i \(0.127219\pi\)
0.389114 + 0.921190i \(0.372781\pi\)
\(398\) 13.8914 + 13.8914i 0.696315 + 0.696315i
\(399\) −4.88953 + 4.63853i −0.244783 + 0.232217i
\(400\) 0.252914 + 4.99360i 0.0126457 + 0.249680i
\(401\) 21.9907i 1.09816i −0.835769 0.549082i \(-0.814978\pi\)
0.835769 0.549082i \(-0.185022\pi\)
\(402\) −12.8556 0.338661i −0.641179 0.0168909i
\(403\) 18.5792 18.5792i 0.925494 0.925494i
\(404\) −7.99014 −0.397524
\(405\) −15.3226 + 13.0468i −0.761384 + 0.648301i
\(406\) −1.87128 −0.0928701
\(407\) 32.6294 32.6294i 1.61738 1.61738i
\(408\) −8.15293 0.214777i −0.403630 0.0106330i
\(409\) 38.2076i 1.88924i −0.328159 0.944622i \(-0.606428\pi\)
0.328159 0.944622i \(-0.393572\pi\)
\(410\) −9.45685 + 0.239330i −0.467041 + 0.0118197i
\(411\) −13.4962 + 12.8034i −0.665721 + 0.631546i
\(412\) −8.37328 8.37328i −0.412522 0.412522i
\(413\) −6.72701 6.72701i −0.331015 0.331015i
\(414\) 2.99584 + 0.157951i 0.147237 + 0.00776288i
\(415\) 30.6115 0.774704i 1.50266 0.0380287i
\(416\) 6.70326i 0.328654i
\(417\) −0.668710 + 25.3843i −0.0327469 + 1.24307i
\(418\) −16.9755 + 16.9755i −0.830300 + 0.830300i
\(419\) −9.14872 −0.446944 −0.223472 0.974710i \(-0.571739\pi\)
−0.223472 + 0.974710i \(0.571739\pi\)
\(420\) −0.00299383 + 2.89212i −0.000146084 + 0.141121i
\(421\) −28.4290 −1.38554 −0.692772 0.721157i \(-0.743611\pi\)
−0.692772 + 0.721157i \(0.743611\pi\)
\(422\) −3.09774 + 3.09774i −0.150796 + 0.150796i
\(423\) 7.63629 6.87139i 0.371289 0.334099i
\(424\) 2.34919i 0.114087i
\(425\) −17.4687 15.7845i −0.847354 0.765659i
\(426\) 13.0157 + 13.7200i 0.630612 + 0.664736i
\(427\) −0.797401 0.797401i −0.0385890 0.0385890i
\(428\) −10.8290 10.8290i −0.523439 0.523439i
\(429\) 36.8143 + 38.8064i 1.77741 + 1.87359i
\(430\) −17.9309 17.0457i −0.864706 0.822019i
\(431\) 11.1238i 0.535814i −0.963445 0.267907i \(-0.913668\pi\)
0.963445 0.267907i \(-0.0863321\pi\)
\(432\) −5.17994 0.410132i −0.249220 0.0197325i
\(433\) −20.0373 + 20.0373i −0.962929 + 0.962929i −0.999337 0.0364075i \(-0.988409\pi\)
0.0364075 + 0.999337i \(0.488409\pi\)
\(434\) 2.92702 0.140501
\(435\) 6.86986 6.85565i 0.329385 0.328703i
\(436\) −5.81042 −0.278269
\(437\) −3.68463 + 3.68463i −0.176260 + 0.176260i
\(438\) −0.358476 + 13.6078i −0.0171286 + 0.650204i
\(439\) 13.8002i 0.658647i 0.944217 + 0.329324i \(0.106821\pi\)
−0.944217 + 0.329324i \(0.893179\pi\)
\(440\) 0.260631 + 10.2985i 0.0124251 + 0.490963i
\(441\) 1.01758 19.3003i 0.0484563 0.919063i
\(442\) −22.3190 22.3190i −1.06161 1.06161i
\(443\) −4.08292 4.08292i −0.193986 0.193986i 0.603430 0.797416i \(-0.293800\pi\)
−0.797416 + 0.603430i \(0.793800\pi\)
\(444\) −12.5858 + 11.9397i −0.597297 + 0.566635i
\(445\) 13.9865 14.7128i 0.663022 0.697452i
\(446\) 11.6416i 0.551245i
\(447\) −10.0753 0.265417i −0.476543 0.0125538i
\(448\) −0.528026 + 0.528026i −0.0249469 + 0.0249469i
\(449\) 5.80447 0.273930 0.136965 0.990576i \(-0.456265\pi\)
0.136965 + 0.990576i \(0.456265\pi\)
\(450\) −10.5846 10.6285i −0.498964 0.501034i
\(451\) −19.4908 −0.917787
\(452\) −0.624299 + 0.624299i −0.0293645 + 0.0293645i
\(453\) 4.81433 + 0.126826i 0.226197 + 0.00595882i
\(454\) 6.25729i 0.293669i
\(455\) −7.71178 + 8.11225i −0.361534 + 0.380308i
\(456\) 6.54782 6.21169i 0.306630 0.290889i
\(457\) −3.04689 3.04689i −0.142528 0.142528i 0.632243 0.774770i \(-0.282135\pi\)
−0.774770 + 0.632243i \(0.782135\pi\)
\(458\) 0.381499 + 0.381499i 0.0178263 + 0.0178263i
\(459\) 18.6126 15.8814i 0.868760 0.741282i
\(460\) 0.0565714 + 2.23535i 0.00263766 + 0.104224i
\(461\) 10.8450i 0.505103i 0.967583 + 0.252551i \(0.0812697\pi\)
−0.967583 + 0.252551i \(0.918730\pi\)
\(462\) −0.156922 + 5.95676i −0.00730066 + 0.277133i
\(463\) −0.966000 + 0.966000i −0.0448939 + 0.0448939i −0.729197 0.684303i \(-0.760106\pi\)
0.684303 + 0.729197i \(0.260106\pi\)
\(464\) 2.50593 0.116335
\(465\) −10.7457 + 10.7235i −0.498320 + 0.497290i
\(466\) 7.09498 0.328669
\(467\) 4.97855 4.97855i 0.230380 0.230380i −0.582471 0.812851i \(-0.697914\pi\)
0.812851 + 0.582471i \(0.197914\pi\)
\(468\) −13.4514 14.9487i −0.621789 0.691004i
\(469\) 5.54438i 0.256016i
\(470\) 5.54945 + 5.27549i 0.255977 + 0.243340i
\(471\) −10.6800 11.2580i −0.492111 0.518740i
\(472\) 9.00849 + 9.00849i 0.414649 + 0.414649i
\(473\) −36.0439 36.0439i −1.65730 1.65730i
\(474\) −7.95206 8.38237i −0.365250 0.385015i
\(475\) 26.0209 1.31790i 1.19392 0.0604693i
\(476\) 3.51621i 0.161165i
\(477\) 4.71409 + 5.23884i 0.215843 + 0.239870i
\(478\) −2.28824 + 2.28824i −0.104662 + 0.104662i
\(479\) −19.7275 −0.901373 −0.450686 0.892682i \(-0.648821\pi\)
−0.450686 + 0.892682i \(0.648821\pi\)
\(480\) 0.00400919 3.87298i 0.000182994 0.176777i
\(481\) −67.1398 −3.06131
\(482\) 1.76332 1.76332i 0.0803171 0.0803171i
\(483\) −0.0340607 + 1.29295i −0.00154981 + 0.0588311i
\(484\) 10.2255i 0.464798i
\(485\) −18.0042 + 0.455644i −0.817530 + 0.0206897i
\(486\) 12.3746 9.47991i 0.561324 0.430018i
\(487\) 5.32308 + 5.32308i 0.241212 + 0.241212i 0.817351 0.576140i \(-0.195442\pi\)
−0.576140 + 0.817351i \(0.695442\pi\)
\(488\) 1.06784 + 1.06784i 0.0483389 + 0.0483389i
\(489\) −5.56758 + 5.28177i −0.251775 + 0.238850i
\(490\) 14.4010 0.364454i 0.650570 0.0164644i
\(491\) 6.35205i 0.286664i 0.989675 + 0.143332i \(0.0457817\pi\)
−0.989675 + 0.143332i \(0.954218\pi\)
\(492\) 7.32505 + 0.192967i 0.330239 + 0.00869964i
\(493\) −8.34367 + 8.34367i −0.375780 + 0.375780i
\(494\) 34.9297 1.57156
\(495\) −21.2472 22.4434i −0.954990 1.00876i
\(496\) −3.91972 −0.176001
\(497\) −5.76529 + 5.76529i −0.258609 + 0.258609i
\(498\) −23.7109 0.624629i −1.06251 0.0279903i
\(499\) 26.5555i 1.18879i 0.804174 + 0.594394i \(0.202608\pi\)
−0.804174 + 0.594394i \(0.797392\pi\)
\(500\) 7.28341 8.48245i 0.325724 0.379347i
\(501\) 10.4964 9.95758i 0.468945 0.444872i
\(502\) 3.81349 + 3.81349i 0.170205 + 0.170205i
\(503\) 20.7736 + 20.7736i 0.926248 + 0.926248i 0.997461 0.0712128i \(-0.0226869\pi\)
−0.0712128 + 0.997461i \(0.522687\pi\)
\(504\) 0.117949 2.23712i 0.00525386 0.0996492i
\(505\) 12.9491 + 12.3099i 0.576227 + 0.547781i
\(506\) 4.60712i 0.204811i
\(507\) 1.45657 55.2915i 0.0646886 2.45558i
\(508\) 11.0353 11.0353i 0.489612 0.489612i
\(509\) 3.09578 0.137218 0.0686090 0.997644i \(-0.478144\pi\)
0.0686090 + 0.997644i \(0.478144\pi\)
\(510\) 12.8820 + 12.9087i 0.570426 + 0.571608i
\(511\) −5.86877 −0.259619
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −2.13714 + 26.9919i −0.0943570 + 1.19172i
\(514\) 0.642960i 0.0283597i
\(515\) 0.669896 + 26.4702i 0.0295192 + 1.16641i
\(516\) 13.1892 + 13.9029i 0.580622 + 0.612041i
\(517\) 11.1552 + 11.1552i 0.490607 + 0.490607i
\(518\) −5.28871 5.28871i −0.232373 0.232373i
\(519\) −17.0437 17.9660i −0.748134 0.788618i
\(520\) 10.3272 10.8635i 0.452880 0.476397i
\(521\) 7.99544i 0.350287i 0.984543 + 0.175143i \(0.0560389\pi\)
−0.984543 + 0.175143i \(0.943961\pi\)
\(522\) −5.58838 + 5.02862i −0.244597 + 0.220097i
\(523\) −16.4846 + 16.4846i −0.720823 + 0.720823i −0.968773 0.247950i \(-0.920243\pi\)
0.247950 + 0.968773i \(0.420243\pi\)
\(524\) −9.85239 −0.430404
\(525\) 4.46054 4.68245i 0.194674 0.204359i
\(526\) −14.2850 −0.622853
\(527\) 13.0510 13.0510i 0.568511 0.568511i
\(528\) 0.210142 7.97700i 0.00914525 0.347154i
\(529\) 1.00000i 0.0434783i
\(530\) −3.61923 + 3.80717i −0.157209 + 0.165373i
\(531\) −38.1668 2.01229i −1.65630 0.0873258i
\(532\) 2.75147 + 2.75147i 0.119291 + 0.119291i
\(533\) 20.0526 + 20.0526i 0.868576 + 0.868576i
\(534\) −11.4077 + 10.8221i −0.493658 + 0.468317i
\(535\) 0.866363 + 34.2333i 0.0374561 + 1.48003i
\(536\) 7.42476i 0.320701i
\(537\) −18.5411 0.488437i −0.800108 0.0210776i
\(538\) −16.6133 + 16.6133i −0.716252 + 0.716252i
\(539\) 29.6808 1.27844
\(540\) 7.76293 + 8.64505i 0.334063 + 0.372024i
\(541\) −19.2338 −0.826927 −0.413463 0.910521i \(-0.635681\pi\)
−0.413463 + 0.910521i \(0.635681\pi\)
\(542\) −4.35982 + 4.35982i −0.187270 + 0.187270i
\(543\) 33.4668 + 0.881633i 1.43620 + 0.0378345i
\(544\) 4.70873i 0.201885i
\(545\) 9.41658 + 8.95172i 0.403362 + 0.383450i
\(546\) 6.28990 5.96701i 0.269183 0.255365i
\(547\) −18.7883 18.7883i −0.803330 0.803330i 0.180284 0.983615i \(-0.442298\pi\)
−0.983615 + 0.180284i \(0.942298\pi\)
\(548\) 7.59469 + 7.59469i 0.324429 + 0.324429i
\(549\) −4.52418 0.238531i −0.193087 0.0101802i
\(550\) 15.4439 17.0917i 0.658528 0.728793i
\(551\) 13.0580i 0.556290i
\(552\) 0.0456124 1.73145i 0.00194139 0.0736954i
\(553\) 3.52237 3.52237i 0.149786 0.149786i
\(554\) 23.1720 0.984482
\(555\) 38.7918 + 0.0401561i 1.64662 + 0.00170453i
\(556\) 14.6607 0.621752
\(557\) 17.0441 17.0441i 0.722182 0.722182i −0.246867 0.969049i \(-0.579401\pi\)
0.969049 + 0.246867i \(0.0794012\pi\)
\(558\) 8.74124 7.86566i 0.370046 0.332980i
\(559\) 74.1657i 3.13688i
\(560\) 1.66923 0.0422442i 0.0705379 0.00178515i
\(561\) 25.8603 + 27.2597i 1.09182 + 1.15091i
\(562\) −0.243563 0.243563i −0.0102741 0.0102741i
\(563\) 3.36582 + 3.36582i 0.141852 + 0.141852i 0.774467 0.632614i \(-0.218018\pi\)
−0.632614 + 0.774467i \(0.718018\pi\)
\(564\) −4.08193 4.30281i −0.171880 0.181181i
\(565\) 1.97357 0.0499465i 0.0830289 0.00210126i
\(566\) 2.68608i 0.112905i
\(567\) 4.22617 + 5.22561i 0.177482 + 0.219455i
\(568\) 7.72060 7.72060i 0.323949 0.323949i
\(569\) 34.6119 1.45100 0.725502 0.688220i \(-0.241607\pi\)
0.725502 + 0.688220i \(0.241607\pi\)
\(570\) −20.1815 0.0208913i −0.845312 0.000875042i
\(571\) 10.0717 0.421486 0.210743 0.977541i \(-0.432412\pi\)
0.210743 + 0.977541i \(0.432412\pi\)
\(572\) 21.8374 21.8374i 0.913066 0.913066i
\(573\) 0.744897 28.2763i 0.0311185 1.18126i
\(574\) 3.15916i 0.131861i
\(575\) 3.35217 3.70985i 0.139795 0.154711i
\(576\) −0.157951 + 2.99584i −0.00658130 + 0.124827i
\(577\) 22.9930 + 22.9930i 0.957209 + 0.957209i 0.999121 0.0419120i \(-0.0133449\pi\)
−0.0419120 + 0.999121i \(0.513345\pi\)
\(578\) −3.65725 3.65725i −0.152122 0.152122i
\(579\) −7.90753 + 7.50160i −0.328626 + 0.311756i
\(580\) −4.06119 3.86071i −0.168632 0.160307i
\(581\) 10.2261i 0.424249i
\(582\) 13.9457 + 0.367377i 0.578066 + 0.0152283i
\(583\) −7.65301 + 7.65301i −0.316955 + 0.316955i
\(584\) 7.85918 0.325215
\(585\) −1.23070 + 44.9500i −0.0508833 + 1.85845i
\(586\) −0.260905 −0.0107779
\(587\) −27.0582 + 27.0582i −1.11681 + 1.11681i −0.124605 + 0.992206i \(0.539766\pi\)
−0.992206 + 0.124605i \(0.960234\pi\)
\(588\) −11.1547 0.293852i −0.460010 0.0121183i
\(589\) 20.4251i 0.841601i
\(590\) −0.720716 28.4782i −0.0296714 1.17243i
\(591\) −33.7833 + 32.0490i −1.38966 + 1.31832i
\(592\) 7.08238 + 7.08238i 0.291084 + 0.291084i
\(593\) −4.06419 4.06419i −0.166896 0.166896i 0.618717 0.785614i \(-0.287653\pi\)
−0.785614 + 0.618717i \(0.787653\pi\)
\(594\) 15.5387 + 18.2109i 0.637562 + 0.747203i
\(595\) −5.41717 + 5.69848i −0.222082 + 0.233615i
\(596\) 5.81897i 0.238354i
\(597\) −0.896076 + 34.0151i −0.0366740 + 1.39215i
\(598\) 4.73992 4.73992i 0.193830 0.193830i
\(599\) 3.30686 0.135115 0.0675574 0.997715i \(-0.478479\pi\)
0.0675574 + 0.997715i \(0.478479\pi\)
\(600\) −5.97333 + 6.27051i −0.243860 + 0.255993i
\(601\) 9.16480 0.373840 0.186920 0.982375i \(-0.440149\pi\)
0.186920 + 0.982375i \(0.440149\pi\)
\(602\) −5.84215 + 5.84215i −0.238108 + 0.238108i
\(603\) −14.8992 16.5577i −0.606742 0.674282i
\(604\) 2.78052i 0.113138i
\(605\) 15.7538 16.5719i 0.640483 0.673743i
\(606\) −9.52479 10.0402i −0.386918 0.407855i
\(607\) −22.2691 22.2691i −0.903875 0.903875i 0.0918938 0.995769i \(-0.470708\pi\)
−0.995769 + 0.0918938i \(0.970708\pi\)
\(608\) −3.68463 3.68463i −0.149431 0.149431i
\(609\) −2.23069 2.35140i −0.0903922 0.0952835i
\(610\) −0.0854316 3.37573i −0.00345903 0.136679i
\(611\) 22.9536i 0.928602i
\(612\) −9.44896 10.5008i −0.381952 0.424469i
\(613\) 5.89129 5.89129i 0.237947 0.237947i −0.578053 0.816000i \(-0.696187\pi\)
0.816000 + 0.578053i \(0.196187\pi\)
\(614\) −7.22796 −0.291697
\(615\) −11.5739 11.5979i −0.466706 0.467674i
\(616\) 3.44033 0.138615
\(617\) −21.2085 + 21.2085i −0.853823 + 0.853823i −0.990602 0.136778i \(-0.956325\pi\)
0.136778 + 0.990602i \(0.456325\pi\)
\(618\) 0.540124 20.5031i 0.0217270 0.824758i
\(619\) 6.49659i 0.261120i −0.991440 0.130560i \(-0.958322\pi\)
0.991440 0.130560i \(-0.0416775\pi\)
\(620\) 6.35244 + 6.03884i 0.255120 + 0.242526i
\(621\) 3.37276 + 3.95278i 0.135344 + 0.158620i
\(622\) 9.43458 + 9.43458i 0.378292 + 0.378292i
\(623\) −4.79363 4.79363i −0.192053 0.192053i
\(624\) −8.42313 + 7.99073i −0.337195 + 0.319885i
\(625\) −24.8721 + 2.52590i −0.994883 + 0.101036i
\(626\) 8.31450i 0.332314i
\(627\) −41.5670 1.09502i −1.66002 0.0437308i
\(628\) −6.33516 + 6.33516i −0.252800 + 0.252800i
\(629\) −47.1626 −1.88050
\(630\) −3.63772 + 3.44384i −0.144930 + 0.137206i
\(631\) −18.5689 −0.739217 −0.369609 0.929188i \(-0.620508\pi\)
−0.369609 + 0.929188i \(0.620508\pi\)
\(632\) −4.71698 + 4.71698i −0.187631 + 0.187631i
\(633\) −7.58526 0.199822i −0.301487 0.00794222i
\(634\) 21.3218i 0.846797i
\(635\) −34.8855 + 0.882869i −1.38439 + 0.0350356i
\(636\) 2.95192 2.80039i 0.117051 0.111043i
\(637\) −30.5363 30.5363i −1.20989 1.20989i
\(638\) −8.16362 8.16362i −0.323201 0.323201i
\(639\) −1.72460 + 32.7103i −0.0682242 + 1.29400i
\(640\) −2.23535 + 0.0565714i −0.0883601 + 0.00223618i
\(641\) 21.0110i 0.829884i 0.909848 + 0.414942i \(0.136198\pi\)
−0.909848 + 0.414942i \(0.863802\pi\)
\(642\) 0.698531 26.5163i 0.0275688 1.04651i
\(643\) −23.8932 + 23.8932i −0.942254 + 0.942254i −0.998421 0.0561671i \(-0.982112\pi\)
0.0561671 + 0.998421i \(0.482112\pi\)
\(644\) 0.746742 0.0294257
\(645\) 0.0443583 42.8512i 0.00174661 1.68726i
\(646\) 24.5365 0.965376
\(647\) 1.33655 1.33655i 0.0525450 0.0525450i −0.680346 0.732891i \(-0.738170\pi\)
0.732891 + 0.680346i \(0.238170\pi\)
\(648\) −5.65948 6.99788i −0.222325 0.274903i
\(649\) 58.6944i 2.30396i
\(650\) −33.4734 + 1.69535i −1.31293 + 0.0664970i
\(651\) 3.48920 + 3.67801i 0.136753 + 0.144153i
\(652\) 3.13303 + 3.13303i 0.122699 + 0.122699i
\(653\) −27.6886 27.6886i −1.08354 1.08354i −0.996177 0.0873627i \(-0.972156\pi\)
−0.0873627 0.996177i \(-0.527844\pi\)
\(654\) −6.92642 7.30122i −0.270844 0.285500i
\(655\) 15.9671 + 15.1789i 0.623887 + 0.593088i
\(656\) 4.23059i 0.165177i
\(657\) −17.5265 + 15.7709i −0.683773 + 0.615282i
\(658\) 1.80809 1.80809i 0.0704867 0.0704867i
\(659\) 26.7954 1.04380 0.521901 0.853006i \(-0.325223\pi\)
0.521901 + 0.853006i \(0.325223\pi\)
\(660\) −12.6302 + 12.6040i −0.491629 + 0.490612i
\(661\) 19.6886 0.765797 0.382899 0.923790i \(-0.374926\pi\)
0.382899 + 0.923790i \(0.374926\pi\)
\(662\) 13.2505 13.2505i 0.514996 0.514996i
\(663\) 1.43970 54.6512i 0.0559134 2.12248i
\(664\) 13.6943i 0.531441i
\(665\) −0.220129 8.69812i −0.00853622 0.337299i
\(666\) −30.0063 1.58204i −1.16272 0.0613028i
\(667\) −1.77196 1.77196i −0.0686105 0.0686105i
\(668\) −5.90660 5.90660i −0.228533 0.228533i
\(669\) 14.6285 13.8776i 0.565571 0.536537i
\(670\) 11.4388 12.0328i 0.441920 0.464869i
\(671\) 6.95746i 0.268590i
\(672\) −1.29295 0.0340607i −0.0498765 0.00131392i
\(673\) −10.7591 + 10.7591i −0.414733 + 0.414733i −0.883384 0.468651i \(-0.844740\pi\)
0.468651 + 0.883384i \(0.344740\pi\)
\(674\) 16.3742 0.630712
\(675\) 0.737955 25.9703i 0.0284039 0.999597i
\(676\) −31.9337 −1.22822
\(677\) −21.0042 + 21.0042i −0.807257 + 0.807257i −0.984218 0.176961i \(-0.943373\pi\)
0.176961 + 0.984218i \(0.443373\pi\)
\(678\) −1.52868 0.0402708i −0.0587087 0.00154659i
\(679\) 6.01450i 0.230815i
\(680\) 7.25441 7.63113i 0.278194 0.292641i
\(681\) −7.86275 + 7.45912i −0.301301 + 0.285834i
\(682\) 12.7694 + 12.7694i 0.488965 + 0.488965i
\(683\) 21.6555 + 21.6555i 0.828624 + 0.828624i 0.987326 0.158702i \(-0.0507310\pi\)
−0.158702 + 0.987326i \(0.550731\pi\)
\(684\) 15.6109 + 0.823061i 0.596897 + 0.0314705i
\(685\) −0.607606 24.0088i −0.0232154 0.917330i
\(686\) 10.0380i 0.383252i
\(687\) −0.0246089 + 0.934154i −0.000938886 + 0.0356402i
\(688\) 7.82352 7.82352i 0.298269 0.298269i
\(689\) 15.7472 0.599921
\(690\) −2.74145 + 2.73578i −0.104365 + 0.104149i
\(691\) −10.1870 −0.387532 −0.193766 0.981048i \(-0.562070\pi\)
−0.193766 + 0.981048i \(0.562070\pi\)
\(692\) −10.1099 + 10.1099i −0.384321 + 0.384321i
\(693\) −7.67216 + 6.90367i −0.291441 + 0.262249i
\(694\) 13.4861i 0.511924i
\(695\) −23.7596 22.5867i −0.901255 0.856763i
\(696\) 2.98723 + 3.14888i 0.113231 + 0.119358i
\(697\) 14.0861 + 14.0861i 0.533548 + 0.533548i
\(698\) −16.0564 16.0564i −0.607743 0.607743i
\(699\) 8.45769 + 8.91536i 0.319899 + 0.337210i
\(700\) −2.77030 2.50321i −0.104707 0.0946123i
\(701\) 8.07940i 0.305155i 0.988292 + 0.152577i \(0.0487573\pi\)
−0.988292 + 0.152577i \(0.951243\pi\)
\(702\) 2.74922 34.7225i 0.103763 1.31052i
\(703\) 36.9053 36.9053i 1.39191 1.39191i
\(704\) −4.60712 −0.173637
\(705\) −0.0137285 + 13.2620i −0.000517044 + 0.499477i
\(706\) 28.5784 1.07556
\(707\) 4.21900 4.21900i 0.158672 0.158672i
\(708\) −0.581099 + 22.0585i −0.0218390 + 0.829011i
\(709\) 3.66459i 0.137627i 0.997630 + 0.0688133i \(0.0219213\pi\)
−0.997630 + 0.0688133i \(0.978079\pi\)
\(710\) −24.4069 + 0.617680i −0.915973 + 0.0231811i
\(711\) 1.05366 19.9847i 0.0395155 0.749485i
\(712\) 6.41940 + 6.41940i 0.240577 + 0.240577i
\(713\) 2.77166 + 2.77166i 0.103800 + 0.103800i
\(714\) 4.41837 4.19155i 0.165353 0.156865i
\(715\) −69.0337 + 1.74708i −2.58172 + 0.0653370i
\(716\) 10.7084i 0.400193i
\(717\) −5.60308 0.147605i −0.209251 0.00551240i
\(718\) 6.75511 6.75511i 0.252098 0.252098i
\(719\) 2.43829 0.0909327 0.0454664 0.998966i \(-0.485523\pi\)
0.0454664 + 0.998966i \(0.485523\pi\)
\(720\) 4.87146 4.61182i 0.181549 0.171872i
\(721\) 8.84262 0.329316
\(722\) −5.76504 + 5.76504i −0.214553 + 0.214553i
\(723\) 4.31774 + 0.113744i 0.160579 + 0.00423020i
\(724\) 19.3288i 0.718349i
\(725\) 0.633784 + 12.5136i 0.0235382 + 0.464743i
\(726\) −12.8491 + 12.1895i −0.476877 + 0.452396i
\(727\) 20.2113 + 20.2113i 0.749597 + 0.749597i 0.974403 0.224807i \(-0.0721751\pi\)
−0.224807 + 0.974403i \(0.572175\pi\)
\(728\) −3.53949 3.53949i −0.131182 0.131182i
\(729\) 26.6636 + 4.24892i 0.987540 + 0.157367i
\(730\) −12.7369 12.1081i −0.471412 0.448140i
\(731\) 52.0980i 1.92691i
\(732\) −0.0688818 + 2.61476i −0.00254594 + 0.0966442i
\(733\) −27.8025 + 27.8025i −1.02691 + 1.02691i −0.0272828 + 0.999628i \(0.508685\pi\)
−0.999628 + 0.0272828i \(0.991315\pi\)
\(734\) −22.4771 −0.829645
\(735\) 17.6249 + 17.6614i 0.650104 + 0.651452i
\(736\) −1.00000 −0.0368605
\(737\) 24.1878 24.1878i 0.890970 0.890970i
\(738\) 8.48948 + 9.43449i 0.312502 + 0.347288i
\(739\) 4.34293i 0.159757i 0.996805 + 0.0798786i \(0.0254533\pi\)
−0.996805 + 0.0798786i \(0.974547\pi\)
\(740\) −0.566619 22.3893i −0.0208293 0.823047i
\(741\) 41.6385 + 43.8917i 1.52963 + 1.61240i
\(742\) 1.24043 + 1.24043i 0.0455377 + 0.0455377i
\(743\) −23.1858 23.1858i −0.850606 0.850606i 0.139601 0.990208i \(-0.455418\pi\)
−0.990208 + 0.139601i \(0.955418\pi\)
\(744\) −4.67257 4.92542i −0.171305 0.180575i
\(745\) 8.96488 9.43042i 0.328448 0.345504i
\(746\) 30.9879i 1.13455i
\(747\) −27.4801 30.5391i −1.00545 1.11737i
\(748\) 15.3397 15.3397i 0.560877 0.560877i
\(749\) 11.4360 0.417861
\(750\) 19.3411 0.959511i 0.706238 0.0350364i
\(751\) 4.73251 0.172692 0.0863459 0.996265i \(-0.472481\pi\)
0.0863459 + 0.996265i \(0.472481\pi\)
\(752\) −2.42130 + 2.42130i −0.0882959 + 0.0882959i
\(753\) −0.245992 + 9.33787i −0.00896445 + 0.340291i
\(754\) 16.7979i 0.611742i
\(755\) −4.28376 + 4.50621i −0.155902 + 0.163998i
\(756\) 2.95170 2.51858i 0.107352 0.0916000i
\(757\) 5.16180 + 5.16180i 0.187609 + 0.187609i 0.794662 0.607053i \(-0.207648\pi\)
−0.607053 + 0.794662i \(0.707648\pi\)
\(758\) 2.13019 + 2.13019i 0.0773719 + 0.0773719i
\(759\) −5.78918 + 5.49200i −0.210134 + 0.199347i
\(760\) 0.294785 + 11.6481i 0.0106930 + 0.422521i
\(761\) 17.2128i 0.623963i 0.950088 + 0.311982i \(0.100993\pi\)
−0.950088 + 0.311982i \(0.899007\pi\)
\(762\) 27.0215 + 0.711839i 0.978885 + 0.0257872i
\(763\) 3.06806 3.06806i 0.111071 0.111071i
\(764\) −16.3310 −0.590835
\(765\) −0.864512 + 31.5753i −0.0312565 + 1.14161i
\(766\) 25.0862 0.906400
\(767\) −60.3862 + 60.3862i −2.18042 + 2.18042i
\(768\) 1.73145 + 0.0456124i 0.0624783 + 0.00164590i
\(769\) 41.6311i 1.50126i 0.660725 + 0.750628i \(0.270249\pi\)
−0.660725 + 0.750628i \(0.729751\pi\)
\(770\) −5.57552 5.30028i −0.200928 0.191009i
\(771\) 0.807926 0.766451i 0.0290967 0.0276031i
\(772\) 4.44978 + 4.44978i 0.160151 + 0.160151i
\(773\) −19.8333 19.8333i −0.713355 0.713355i 0.253881 0.967235i \(-0.418293\pi\)
−0.967235 + 0.253881i \(0.918293\pi\)
\(774\) −1.74759 + 33.1464i −0.0628159 + 1.19142i
\(775\) −0.991353 19.5735i −0.0356104 0.703102i
\(776\) 8.05432i 0.289133i
\(777\) 0.341152 12.9501i 0.0122388 0.464584i