Properties

Label 690.2.i.f.323.16
Level $690$
Weight $2$
Character 690.323
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 323.16
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.f.47.16

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

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

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
\(3\) 1.73145 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 −0.600243 0.799818i \(-0.704929\pi\)
0.799818 + 0.600243i \(0.204929\pi\)
\(8\) −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 \(-0.755604\pi\)
0.719445 0.694549i \(-0.244396\pi\)
\(12\) 0.0456124 + 1.73145i 0.0131672 + 0.499827i
\(13\) 4.73992 + 4.73992i 1.31462 + 1.31462i 0.917972 + 0.396645i \(0.129826\pi\)
0.396645 + 0.917972i \(0.370174\pi\)
\(14\) 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 0.984261 0.176721i \(-0.0565489\pi\)
−0.176721 + 0.984261i \(0.556549\pi\)
\(18\) 2.23007 + 2.00669i 0.525632 + 0.472981i
\(19\) 5.21085i 1.19545i −0.801700 0.597726i \(-0.796071\pi\)
0.801700 0.597726i \(-0.203929\pi\)
\(20\) 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 −0.180820 + 0.983516i \(0.557875\pi\)
−0.983516 + 0.180820i \(0.942125\pi\)
\(38\) 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 \(-0.892832\pi\)
0.943857 0.330353i \(-0.107168\pi\)
\(42\) 1.29295 0.0340607i 0.199506 0.00525568i
\(43\) −7.82352 7.82352i −1.19308 1.19308i −0.976199 0.216877i \(-0.930413\pi\)
−0.216877 0.976199i \(-0.569587\pi\)
\(44\) 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 0.861293 0.508109i \(-0.169655\pi\)
−0.508109 + 0.861293i \(0.669655\pi\)
\(48\) −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 −0.583756 0.811929i \(-0.698418\pi\)
0.811929 + 0.583756i \(0.198418\pi\)
\(54\) 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 −0.950900 0.309498i \(-0.899839\pi\)
0.309498 + 0.950900i \(0.399839\pi\)
\(68\) −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 \(-0.775648\pi\)
0.761727 0.647898i \(-0.224352\pi\)
\(72\) −2.00669 + 2.23007i −0.236491 + 0.262816i
\(73\) −5.55728 5.55728i −0.650430 0.650430i 0.302667 0.953097i \(-0.402123\pi\)
−0.953097 + 0.302667i \(0.902123\pi\)
\(74\) −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 \(0.122448\pi\)
−0.926918 + 0.375263i \(0.877552\pi\)
\(80\) 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 −0.0649958 + 0.997886i \(0.520703\pi\)
−0.997886 + 0.0649958i \(0.979297\pi\)
\(84\) 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 −0.356159 0.934425i \(-0.615914\pi\)
0.934425 + 0.356159i \(0.115914\pi\)
\(98\) −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 \(0.130131\pi\)
−0.917592 + 0.397524i \(0.869869\pi\)
\(102\) 0.214777 + 8.15293i 0.0212660 + 0.807260i
\(103\) 8.37328 + 8.37328i 0.825044 + 0.825044i 0.986826 0.161783i \(-0.0517244\pi\)
−0.161783 + 0.986826i \(0.551724\pi\)
\(104\) −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 0.998846 + 0.0480314i \(0.0152948\pi\)
0.0480314 + 0.998846i \(0.484705\pi\)
\(108\) 0.410132 + 5.17994i 0.0394650 + 0.498440i
\(109\) 5.81042i 0.556538i 0.960503 + 0.278269i \(0.0897606\pi\)
−0.960503 + 0.278269i \(0.910239\pi\)
\(110\) −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 −0.735861 0.677132i \(-0.763222\pi\)
0.677132 + 0.735861i \(0.263222\pi\)
\(114\) 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 −0.0205641 0.999789i \(-0.506546\pi\)
0.999789 + 0.0205641i \(0.00654623\pi\)
\(128\) 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 \(0.141629\pi\)
−0.902637 + 0.430404i \(0.858371\pi\)
\(132\) 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 0.303859 0.952717i \(-0.401725\pi\)
−0.952717 + 0.303859i \(0.901725\pi\)
\(138\) 1.73145 0.0456124i 0.147391 0.00388279i
\(139\) 14.6607i 1.24350i −0.783214 0.621752i \(-0.786421\pi\)
0.783214 0.621752i \(-0.213579\pi\)
\(140\) 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 −0.913173 0.407572i \(-0.866375\pi\)
0.407572 + 0.913173i \(0.366375\pi\)
\(158\) −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 0.573681 0.819079i \(-0.305515\pi\)
−0.819079 + 0.573681i \(0.805515\pi\)
\(164\) 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 0.897691 0.440625i \(-0.145243\pi\)
−0.440625 + 0.897691i \(0.645243\pi\)
\(168\) 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 −0.977868 0.209225i \(-0.932906\pi\)
0.209225 + 0.977868i \(0.432906\pi\)
\(174\) −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 \(0.201202\pi\)
−0.806792 + 0.590835i \(0.798798\pi\)
\(192\) −0.0456124 1.73145i −0.00329179 0.124957i
\(193\) −4.44978 4.44978i −0.320302 0.320302i 0.528581 0.848883i \(-0.322724\pi\)
−0.848883 + 0.528581i \(0.822724\pi\)
\(194\) 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 −0.880601 0.473858i \(-0.842861\pi\)
−0.473858 0.880601i \(-0.657139\pi\)
\(198\) 9.24506 10.2742i 0.657018 0.730154i
\(199\) 19.6455i 1.39263i −0.717737 0.696315i \(-0.754822\pi\)
0.717737 0.696315i \(-0.245178\pi\)
\(200\) −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 0.926800 0.375555i \(-0.122548\pi\)
−0.375555 + 0.926800i \(0.622548\pi\)
\(224\) −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 0.544859 0.838528i \(-0.316583\pi\)
−0.838528 + 0.544859i \(0.816583\pi\)
\(228\) 9.02233 0.237680i 0.597519 0.0157407i
\(229\) 0.539521i 0.0356526i −0.999841 0.0178263i \(-0.994325\pi\)
0.999841 0.0178263i \(-0.00567458\pi\)
\(230\) −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 −0.523411 0.852080i \(-0.675341\pi\)
0.852080 + 0.523411i \(0.175341\pi\)
\(234\) 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 \(-0.945557\pi\)
0.985409 0.170205i \(-0.0544428\pi\)
\(252\) 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 0.721144 0.692785i \(-0.243616\pi\)
−0.692785 + 0.721144i \(0.743616\pi\)
\(258\) −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 −0.946260 0.323407i \(-0.895172\pi\)
0.323407 + 0.946260i \(0.395172\pi\)
\(264\) 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 −0.0153991 0.999881i \(-0.504902\pi\)
0.999881 + 0.0153991i \(0.00490187\pi\)
\(278\) 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 \(0.00327041\pi\)
−0.999947 + 0.0102741i \(0.996730\pi\)
\(282\) 0.156188 + 5.92890i 0.00930086 + 0.353061i
\(283\) −1.89935 1.89935i −0.112905 0.112905i 0.648397 0.761302i \(-0.275440\pi\)
−0.761302 + 0.648397i \(0.775440\pi\)
\(284\) 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 −0.712475 0.701697i \(-0.752426\pi\)
0.701697 + 0.712475i \(0.252426\pi\)
\(294\) −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 −0.837750 0.546054i \(-0.816130\pi\)
0.546054 + 0.837750i \(0.316130\pi\)
\(308\) 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 \(-0.876511\pi\)
0.925686 0.378292i \(-0.123489\pi\)
\(312\) −11.6064 + 0.305752i −0.657081 + 0.0173098i
\(313\) 5.87924 + 5.87924i 0.332314 + 0.332314i 0.853465 0.521151i \(-0.174497\pi\)
−0.521151 + 0.853465i \(0.674497\pi\)
\(314\) −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 0.989732 0.142935i \(-0.0456540\pi\)
−0.142935 + 0.989732i \(0.545654\pi\)
\(318\) 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 −0.317535 0.948247i \(-0.602855\pi\)
0.948247 + 0.317535i \(0.102855\pi\)
\(338\) −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 0.915116 0.403191i \(-0.132099\pi\)
−0.403191 + 0.915116i \(0.632099\pi\)
\(348\) −0.114301 4.33889i −0.00612720 0.232589i
\(349\) 22.7071i 1.21549i 0.794134 + 0.607743i \(0.207925\pi\)
−0.794134 + 0.607743i \(0.792075\pi\)
\(350\) −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 0.0786597 0.996902i \(-0.474936\pi\)
0.996902 0.0786597i \(-0.0250641\pi\)
\(354\) −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 −0.987467 0.157823i \(-0.949553\pi\)
0.157823 + 0.987467i \(0.449553\pi\)
\(368\) −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 0.989412 + 0.145135i \(0.0463617\pi\)
0.145135 + 0.989412i \(0.453638\pi\)
\(374\) 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 \(-0.975347\pi\)
0.997002 0.0773719i \(-0.0246529\pi\)
\(380\) −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 −0.0895800 0.995980i \(-0.528552\pi\)
0.995980 + 0.0895800i \(0.0285525\pi\)
\(384\) 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 0.389114 0.921190i \(-0.372781\pi\)
0.921190 0.389114i \(-0.127219\pi\)
\(398\) 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 \(0.185022\pi\)
−0.835769 + 0.549082i \(0.814978\pi\)
\(402\) −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 \(0.393572\pi\)
−0.328159 + 0.944622i \(0.606428\pi\)
\(410\) −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 \(0.0863321\pi\)
−0.963445 + 0.267907i \(0.913668\pi\)
\(432\) −5.17994 + 0.410132i −0.249220 + 0.0197325i
\(433\) −20.0373 20.0373i −0.962929 0.962929i 0.0364075 0.999337i \(-0.488409\pi\)
−0.999337 + 0.0364075i \(0.988409\pi\)
\(434\) 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 \(-0.893179\pi\)
0.944217 0.329324i \(-0.106821\pi\)
\(440\) 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 −0.797416 0.603430i \(-0.793800\pi\)
0.603430 + 0.797416i \(0.293800\pi\)
\(444\) −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 −0.774770 0.632243i \(-0.782135\pi\)
0.632243 + 0.774770i \(0.282135\pi\)
\(458\) 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 \(-0.918730\pi\)
0.967583 0.252551i \(-0.0812697\pi\)
\(462\) −0.156922 5.95676i −0.00730066 0.277133i
\(463\) −0.966000 0.966000i −0.0448939 0.0448939i 0.684303 0.729197i \(-0.260106\pi\)
−0.729197 + 0.684303i \(0.760106\pi\)
\(464\) 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 0.812851 0.582471i \(-0.197914\pi\)
−0.582471 + 0.812851i \(0.697914\pi\)
\(468\) −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 −0.576140 0.817351i \(-0.695442\pi\)
0.817351 + 0.576140i \(0.195442\pi\)
\(488\) 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 \(-0.954218\pi\)
0.989675 0.143332i \(-0.0457817\pi\)
\(492\) 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 \(-0.797392\pi\)
0.804174 0.594394i \(-0.202608\pi\)
\(500\) 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 −0.0712128 0.997461i \(-0.522687\pi\)
0.997461 + 0.0712128i \(0.0226869\pi\)
\(504\) 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 \(-0.943961\pi\)
0.984543 0.175143i \(-0.0560389\pi\)
\(522\) −5.58838 5.02862i −0.244597 0.220097i
\(523\) −16.4846 16.4846i −0.720823 0.720823i 0.247950 0.968773i \(-0.420243\pi\)
−0.968773 + 0.247950i \(0.920243\pi\)
\(524\) −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 −0.983615 0.180284i \(-0.942298\pi\)
0.180284 + 0.983615i \(0.442298\pi\)
\(548\) 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 0.969049 0.246867i \(-0.0794012\pi\)
−0.246867 + 0.969049i \(0.579401\pi\)
\(558\) 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 −0.632614 0.774467i \(-0.718018\pi\)
0.774467 + 0.632614i \(0.218018\pi\)
\(564\) −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 −0.0419120 0.999121i \(-0.513345\pi\)
0.999121 + 0.0419120i \(0.0133449\pi\)
\(578\) −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 −0.992206 0.124605i \(-0.960234\pi\)
−0.124605 0.992206i \(-0.539766\pi\)
\(588\) −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 −0.785614 0.618717i \(-0.787653\pi\)
0.618717 + 0.785614i \(0.287653\pi\)
\(594\) 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 −0.995769 0.0918938i \(-0.970708\pi\)
0.0918938 + 0.995769i \(0.470708\pi\)
\(608\) −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 0.816000 0.578053i \(-0.196187\pi\)
−0.578053 + 0.816000i \(0.696187\pi\)
\(614\) −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 0.136778 0.990602i \(-0.456325\pi\)
−0.990602 + 0.136778i \(0.956325\pi\)
\(618\) 0.540124 + 20.5031i 0.0217270 + 0.824758i
\(619\) 6.49659i 0.261120i 0.991440 + 0.130560i \(0.0416775\pi\)
−0.991440 + 0.130560i \(0.958322\pi\)
\(620\) 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 \(-0.863802\pi\)
0.909848 0.414942i \(-0.136198\pi\)
\(642\) 0.698531 + 26.5163i 0.0275688 + 1.04651i
\(643\) −23.8932 23.8932i −0.942254 0.942254i 0.0561671 0.998421i \(-0.482112\pi\)
−0.998421 + 0.0561671i \(0.982112\pi\)
\(644\) 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 0.732891 0.680346i \(-0.238170\pi\)
−0.680346 + 0.732891i \(0.738170\pi\)
\(648\) −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 −0.0873627 + 0.996177i \(0.527844\pi\)
−0.996177 + 0.0873627i \(0.972156\pi\)
\(654\) −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 0.468651 0.883384i \(-0.344740\pi\)
−0.883384 + 0.468651i \(0.844740\pi\)
\(674\) 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 0.176961 0.984218i \(-0.443373\pi\)
−0.984218 + 0.176961i \(0.943373\pi\)
\(678\) −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 −0.158702 0.987326i \(-0.550731\pi\)
0.987326 + 0.158702i \(0.0507310\pi\)
\(684\) 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 \(-0.951243\pi\)
0.988292 0.152577i \(-0.0487573\pi\)
\(702\) 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 \(-0.978079\pi\)
0.997630 0.0688133i \(-0.0219213\pi\)
\(710\) −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 −0.224807 0.974403i \(-0.572175\pi\)
0.974403 + 0.224807i \(0.0721751\pi\)
\(728\) −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 −0.999628 0.0272828i \(-0.991315\pi\)
−0.0272828 0.999628i \(-0.508685\pi\)
\(734\) −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 \(-0.974547\pi\)
0.996805 0.0798786i \(-0.0254533\pi\)
\(740\) −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 −0.990208 0.139601i \(-0.955418\pi\)
0.139601 + 0.990208i \(0.455418\pi\)
\(744\) −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 −0.607053 0.794662i \(-0.707648\pi\)
0.794662 + 0.607053i \(0.207648\pi\)
\(758\) 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 \(-0.899007\pi\)
0.950088 0.311982i \(-0.100993\pi\)
\(762\) 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 \(-0.729751\pi\)
0.660725 0.750628i \(-0.270249\pi\)
\(770\) −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 −0.967235 0.253881i \(-0.918293\pi\)
0.253881 + 0.967235i \(0.418293\pi\)
\(774\) −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