Properties

Label 690.2.i.f.47.5
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 47.5
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.0456124 - 1.73145i) q^{3} -1.00000i q^{4} +(1.54063 - 1.62063i) q^{5} +(1.25657 + 1.19207i) q^{6} +(0.528026 + 0.528026i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.99584 + 0.157951i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.0456124 - 1.73145i) 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} +(-1.73145 + 0.0456124i) q^{12} +(4.73992 - 4.73992i) q^{13} -0.746742 q^{14} +(-2.87632 - 2.59360i) q^{15} -1.00000 q^{16} +(-3.32957 + 3.32957i) q^{17} +(2.00669 - 2.23007i) 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} +(0.410132 + 5.17994i) q^{27} +(0.528026 - 0.528026i) q^{28} +2.50593 q^{29} +(3.86782 - 0.199910i) q^{30} +3.91972 q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.97700 + 0.210142i) 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} +(0.0340607 + 1.29295i) q^{42} +(-7.82352 + 7.82352i) q^{43} -4.60712 q^{44} +(-4.35950 + 5.09851i) q^{45} +1.00000 q^{46} +(-2.42130 + 2.42130i) q^{47} +(0.0456124 + 1.73145i) 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} +(9.02233 - 0.237680i) q^{57} +(-1.77196 + 1.77196i) q^{58} +12.7399 q^{59} +(-2.59360 + 2.87632i) q^{60} -1.51016 q^{61} +(-2.77166 + 2.77166i) q^{62} +(-1.66528 - 1.49848i) 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} +(-2.23007 - 2.00669i) q^{72} +(-5.55728 + 5.55728i) q^{73} +10.0160 q^{74} +(-8.63463 + 0.665678i) q^{75} +5.21085 q^{76} +(2.43268 - 2.43268i) q^{77} +(11.6064 - 0.305752i) 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} +(-0.114301 - 4.33889i) q^{87} +(3.25773 - 3.25773i) q^{88} +9.07840 q^{89} +(-0.522555 - 6.68782i) q^{90} +5.00560 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-0.178788 - 6.78680i) 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
\(3\) −0.0456124 1.73145i −0.0263343 0.999653i
\(4\) 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 \(-0.755604\pi\)
0.719445 0.694549i \(-0.244396\pi\)
\(12\) −1.73145 + 0.0456124i −0.499827 + 0.0131672i
\(13\) 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
\(15\) −2.87632 2.59360i −0.742663 0.669666i
\(16\) −1.00000 −0.250000
\(17\) −3.32957 + 3.32957i −0.807541 + 0.807541i −0.984261 0.176721i \(-0.943451\pi\)
0.176721 + 0.984261i \(0.443451\pi\)
\(18\) 2.00669 2.23007i 0.472981 0.525632i
\(19\) 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
\(27\) 0.410132 + 5.17994i 0.0789300 + 0.996880i
\(28\) 0.528026 0.528026i 0.0997876 0.0997876i
\(29\) 2.50593 0.465339 0.232669 0.972556i \(-0.425254\pi\)
0.232669 + 0.972556i \(0.425254\pi\)
\(30\) 3.86782 0.199910i 0.706164 0.0364985i
\(31\) 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
\(33\) −7.97700 + 0.210142i −1.38862 + 0.0365810i
\(34\) 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 \(-0.892832\pi\)
0.943857 0.330353i \(-0.107168\pi\)
\(42\) 0.0340607 + 1.29295i 0.00525568 + 0.199506i
\(43\) −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
\(45\) −4.35950 + 5.09851i −0.649876 + 0.760040i
\(46\) 1.00000 0.147442
\(47\) −2.42130 + 2.42130i −0.353184 + 0.353184i −0.861293 0.508109i \(-0.830345\pi\)
0.508109 + 0.861293i \(0.330345\pi\)
\(48\) 0.0456124 + 1.73145i 0.00658358 + 0.249913i
\(49\) 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 \(-0.301582\pi\)
−0.811929 + 0.583756i \(0.801582\pi\)
\(54\) −3.95278 3.37276i −0.537905 0.458975i
\(55\) −7.46646 7.09787i −1.00678 0.957077i
\(56\) 0.746742i 0.0997876i
\(57\) 9.02233 0.237680i 1.19504 0.0314814i
\(58\) −1.77196 + 1.77196i −0.232669 + 0.232669i
\(59\) 12.7399 1.65860 0.829299 0.558806i \(-0.188740\pi\)
0.829299 + 0.558806i \(0.188740\pi\)
\(60\) −2.59360 + 2.87632i −0.334833 + 0.371331i
\(61\) −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
\(63\) −1.66528 1.49848i −0.209806 0.188791i
\(64\) 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 \(-0.775648\pi\)
0.761727 0.647898i \(-0.224352\pi\)
\(72\) −2.23007 2.00669i −0.262816 0.236491i
\(73\) −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
\(75\) −8.63463 + 0.665678i −0.997041 + 0.0768659i
\(76\) 5.21085 0.597726
\(77\) 2.43268 2.43268i 0.277230 0.277230i
\(78\) 11.6064 0.305752i 1.31416 0.0346196i
\(79\) 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 \(0.0207034\pi\)
0.0649958 + 0.997886i \(0.479297\pi\)
\(84\) −0.938335 0.890166i −0.102381 0.0971251i
\(85\) 0.266380 + 10.5257i 0.0288929 + 1.14167i
\(86\) 11.0641i 1.19308i
\(87\) −0.114301 4.33889i −0.0122544 0.465178i
\(88\) 3.25773 3.25773i 0.347275 0.347275i
\(89\) 9.07840 0.962309 0.481154 0.876636i \(-0.340218\pi\)
0.481154 + 0.876636i \(0.340218\pi\)
\(90\) −0.522555 6.68782i −0.0550822 0.704958i
\(91\) 5.00560 0.524730
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) −0.178788 6.78680i −0.0185394 0.703759i
\(94\) 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 \(0.130131\pi\)
−0.917592 + 0.397524i \(0.869869\pi\)
\(102\) −8.15293 + 0.214777i −0.807260 + 0.0212660i
\(103\) 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
\(105\) −0.149281 2.88826i −0.0145684 0.281866i
\(106\) 2.34919 0.228173
\(107\) −10.8290 + 10.8290i −1.04688 + 1.04688i −0.0480314 + 0.998846i \(0.515295\pi\)
−0.998846 + 0.0480314i \(0.984705\pi\)
\(108\) 5.17994 0.410132i 0.498440 0.0394650i
\(109\) 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 0.735861 0.677132i \(-0.236778\pi\)
−0.677132 + 0.735861i \(0.736778\pi\)
\(114\) −6.21169 + 6.54782i −0.581778 + 0.613259i
\(115\) −2.23535 + 0.0565714i −0.208448 + 0.00527531i
\(116\) 2.50593i 0.232669i
\(117\) −13.4514 + 14.9487i −1.24358 + 1.38201i
\(118\) −9.00849 + 9.00849i −0.829299 + 0.829299i
\(119\) −3.51621 −0.322330
\(120\) −0.199910 3.86782i −0.0182492 0.353082i
\(121\) −10.2255 −0.929595
\(122\) 1.06784 1.06784i 0.0966778 0.0966778i
\(123\) −7.32505 + 0.192967i −0.660478 + 0.0173993i
\(124\) 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 \(0.141629\pi\)
−0.902637 + 0.430404i \(0.858371\pi\)
\(132\) 0.210142 + 7.97700i 0.0182905 + 0.694309i
\(133\) −2.75147 + 2.75147i −0.238582 + 0.238582i
\(134\) 7.42476 0.641402
\(135\) 9.02666 + 7.31570i 0.776891 + 0.629635i
\(136\) −4.70873 −0.403770
\(137\) 7.59469 7.59469i 0.648858 0.648858i −0.303859 0.952717i \(-0.598275\pi\)
0.952717 + 0.303859i \(0.0982751\pi\)
\(138\) −0.0456124 1.73145i −0.00388279 0.147391i
\(139\) 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
\(147\) −11.1547 + 0.293852i −0.920020 + 0.0242365i
\(148\) −7.08238 + 7.08238i −0.582168 + 0.582168i
\(149\) 5.81897 0.476708 0.238354 0.971178i \(-0.423392\pi\)
0.238354 + 0.971178i \(0.423392\pi\)
\(150\) 5.63490 6.57631i 0.460088 0.536954i
\(151\) 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
\(153\) 9.44896 10.5008i 0.763903 0.848938i
\(154\) 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
\(162\) −5.65948 + 6.99788i −0.444651 + 0.549805i
\(163\) −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
\(165\) −11.9490 + 13.2516i −0.930232 + 1.03163i
\(166\) −13.6943 −1.06288
\(167\) −5.90660 + 5.90660i −0.457067 + 0.457067i −0.897691 0.440625i \(-0.854757\pi\)
0.440625 + 0.897691i \(0.354757\pi\)
\(168\) 1.29295 0.0340607i 0.0997529 0.00262784i
\(169\) 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 \(-0.0670941\pi\)
−0.209225 + 0.977868i \(0.567094\pi\)
\(174\) 3.14888 + 2.98723i 0.238716 + 0.226462i
\(175\) 2.50321 2.77030i 0.189225 0.209415i
\(176\) 4.60712i 0.347275i
\(177\) −0.581099 22.0585i −0.0436781 1.65802i
\(178\) −6.41940 + 6.41940i −0.481154 + 0.481154i
\(179\) 10.7084 0.800386 0.400193 0.916431i \(-0.368943\pi\)
0.400193 + 0.916431i \(0.368943\pi\)
\(180\) 5.09851 + 4.35950i 0.380020 + 0.324938i
\(181\) 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
\(183\) 0.0688818 + 2.61476i 0.00509189 + 0.193288i
\(184\) 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 \(0.798798\pi\)
\(192\) 1.73145 0.0456124i 0.124957 0.00329179i
\(193\) −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
\(195\) −25.9270 + 1.34005i −1.85667 + 0.0959630i
\(196\) −6.44238 −0.460170
\(197\) 19.0107 19.0107i 1.35446 1.35446i 0.473858 0.880601i \(-0.342861\pi\)
0.880601 0.473858i \(-0.157139\pi\)
\(198\) −10.2742 9.24506i −0.730154 0.657018i
\(199\) 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
\(207\) 2.23007 + 2.00669i 0.155000 + 0.139475i
\(208\) −4.73992 + 4.73992i −0.328654 + 0.328654i
\(209\) 24.0070 1.66060
\(210\) 2.14787 + 1.93675i 0.148217 + 0.133649i
\(211\) −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
\(213\) −18.9050 + 0.498023i −1.29535 + 0.0341239i
\(214\) 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
\(222\) −0.456854 17.3422i −0.0306620 1.16393i
\(223\) 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
\(225\) 1.54644 + 14.9201i 0.103096 + 0.994671i
\(226\) −0.882892 −0.0587291
\(227\) 4.42457 4.42457i 0.293669 0.293669i −0.544859 0.838528i \(-0.683417\pi\)
0.838528 + 0.544859i \(0.183417\pi\)
\(228\) −0.237680 9.02233i −0.0157407 0.597519i
\(229\) 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 0.523411 0.852080i \(-0.324659\pi\)
−0.852080 + 0.523411i \(0.824659\pi\)
\(234\) −1.05879 20.0819i −0.0692151 1.31279i
\(235\) 0.193714 + 7.65439i 0.0126365 + 0.499317i
\(236\) 12.7399i 0.829299i
\(237\) −11.5502 + 0.304272i −0.750265 + 0.0197646i
\(238\) 2.48633 2.48633i 0.161165 0.161165i
\(239\) 3.23606 0.209324 0.104662 0.994508i \(-0.466624\pi\)
0.104662 + 0.994508i \(0.466624\pi\)
\(240\) 2.87632 + 2.59360i 0.185666 + 0.167416i
\(241\) 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
\(243\) −2.04687 15.4535i −0.131307 0.991342i
\(244\) 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 \(-0.0544428\pi\)
\(252\) −1.49848 + 1.66528i −0.0943953 + 0.104903i
\(253\) −3.25773 + 3.25773i −0.204811 + 0.204811i
\(254\) −15.6063 −0.979224
\(255\) 18.2125 0.941324i 1.14051 0.0589480i
\(256\) 1.00000 0.0625000
\(257\) −0.454641 + 0.454641i −0.0283597 + 0.0283597i −0.721144 0.692785i \(-0.756384\pi\)
0.692785 + 0.721144i \(0.256384\pi\)
\(258\) −19.1570 + 0.504662i −1.19266 + 0.0314189i
\(259\) 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 \(-0.104828\pi\)
−0.323407 + 0.946260i \(0.604828\pi\)
\(264\) −5.78918 5.49200i −0.356300 0.338009i
\(265\) −5.25126 + 0.132897i −0.322582 + 0.00816379i
\(266\) 3.89116i 0.238582i
\(267\) −0.414088 15.7188i −0.0253418 0.961975i
\(268\) −5.25010 + 5.25010i −0.320701 + 0.320701i
\(269\) 23.4948 1.43250 0.716252 0.697842i \(-0.245856\pi\)
0.716252 + 0.697842i \(0.245856\pi\)
\(270\) −11.5558 + 1.20983i −0.703263 + 0.0736277i
\(271\) −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
\(273\) −0.228318 8.66695i −0.0138184 0.524548i
\(274\) 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 \(0.00327041\pi\)
−0.999947 + 0.0102741i \(0.996730\pi\)
\(282\) −5.92890 + 0.156188i −0.353061 + 0.00930086i
\(283\) −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
\(285\) 13.5149 14.9881i 0.800553 0.887818i
\(286\) 30.8827 1.82613
\(287\) 2.23386 2.23386i 0.131861 0.131861i
\(288\) −2.00669 + 2.23007i −0.118245 + 0.131408i
\(289\) 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 \(-0.247574\pi\)
−0.701697 + 0.712475i \(0.747574\pi\)
\(294\) 7.67975 8.09532i 0.447892 0.472128i
\(295\) 19.6275 20.6468i 1.14276 1.20210i
\(296\) 10.0160i 0.582168i
\(297\) 23.8646 1.88953i 1.38477 0.109642i
\(298\) −4.11463 + 4.11463i −0.238354 + 0.238354i
\(299\) −6.70326 −0.387659
\(300\) 0.665678 + 8.63463i 0.0384330 + 0.498521i
\(301\) −8.26205 −0.476217
\(302\) −1.96613 + 1.96613i −0.113138 + 0.113138i
\(303\) 13.8345 0.364450i 0.794773 0.0209371i
\(304\) 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 \(-0.876511\pi\)
0.925686 0.378292i \(-0.123489\pi\)
\(312\) −0.305752 11.6064i −0.0173098 0.657081i
\(313\) 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
\(315\) −4.99407 + 0.390214i −0.281384 + 0.0219861i
\(316\) −6.67082 −0.375263
\(317\) −15.0768 + 15.0768i −0.846797 + 0.846797i −0.989732 0.142935i \(-0.954346\pi\)
0.142935 + 0.989732i \(0.454346\pi\)
\(318\) −0.107152 4.06750i −0.00600879 0.228094i
\(319\) 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
\(327\) −10.0605 + 0.265027i −0.556345 + 0.0146561i
\(328\) 2.99148 2.99148i 0.165177 0.165177i
\(329\) −2.55702 −0.140973
\(330\) −0.921011 17.8195i −0.0507000 0.980932i
\(331\) 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
\(333\) 22.3363 + 20.0990i 1.22402 + 1.10142i
\(334\) 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
\(342\) 11.6206 + 10.4566i 0.628367 + 0.565426i
\(343\) 7.09793 7.09793i 0.383252 0.383252i
\(344\) −11.0641 −0.596538
\(345\) 0.199910 + 3.86782i 0.0107628 + 0.208236i
\(346\) −14.2976 −0.768643
\(347\) −9.53609 + 9.53609i −0.511924 + 0.511924i −0.915116 0.403191i \(-0.867901\pi\)
0.403191 + 0.915116i \(0.367901\pi\)
\(348\) −4.33889 + 0.114301i −0.232589 + 0.00612720i
\(349\) 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 \(-0.974936\pi\)
−0.0786597 0.996902i \(-0.525064\pi\)
\(354\) 16.0086 + 15.1868i 0.850850 + 0.807172i
\(355\) −17.6950 16.8215i −0.939155 0.892792i
\(356\) 9.07840i 0.481154i
\(357\) 0.160383 + 6.08813i 0.00848835 + 0.322218i
\(358\) −7.57201 + 7.57201i −0.400193 + 0.400193i
\(359\) −9.55317 −0.504197 −0.252098 0.967702i \(-0.581121\pi\)
−0.252098 + 0.967702i \(0.581121\pi\)
\(360\) −6.68782 + 0.522555i −0.352479 + 0.0275411i
\(361\) −8.15300 −0.429105
\(362\) −13.6675 + 13.6675i −0.718349 + 0.718349i
\(363\) 0.466412 + 17.7050i 0.0244803 + 0.929273i
\(364\) 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
\(372\) −6.78680 + 0.178788i −0.351879 + 0.00926972i
\(373\) 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
\(375\) −12.2240 + 15.0191i −0.631242 + 0.775586i
\(376\) −3.42424 −0.176592
\(377\) 11.8779 11.8779i 0.611742 0.611742i
\(378\) −0.306263 3.86808i −0.0157525 0.198952i
\(379\) 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 0.0895800 0.995980i \(-0.471448\pi\)
−0.995980 + 0.0895800i \(0.971448\pi\)
\(384\) −1.19207 + 1.25657i −0.0608324 + 0.0641242i
\(385\) −0.194624 7.69035i −0.00991897 0.391936i
\(386\) 6.29293i 0.320302i
\(387\) 22.2023 24.6738i 1.12861 1.25424i
\(388\) 5.69526 5.69526i 0.289133 0.289133i
\(389\) −20.0679 −1.01748 −0.508742 0.860919i \(-0.669889\pi\)
−0.508742 + 0.860919i \(0.669889\pi\)
\(390\) 17.3856 19.2807i 0.880354 0.976317i
\(391\) 4.70873 0.238131
\(392\) 4.55545 4.55545i 0.230085 0.230085i
\(393\) 17.0589 0.449391i 0.860509 0.0226688i
\(394\) 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 \(0.185022\pi\)
−0.835769 + 0.549082i \(0.814978\pi\)
\(402\) −0.338661 12.8556i −0.0168909 0.641179i
\(403\) 18.5792 18.5792i 0.925494 0.925494i
\(404\) 7.99014 0.397524
\(405\) 12.2550 15.9629i 0.608958 0.793202i
\(406\) −1.87128 −0.0928701
\(407\) −32.6294 + 32.6294i −1.61738 + 1.61738i
\(408\) 0.214777 + 8.15293i 0.0106330 + 0.403630i
\(409\) 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
\(417\) 25.3843 0.668710i 1.24307 0.0327469i
\(418\) −16.9755 + 16.9755i −0.830300 + 0.830300i
\(419\) 9.14872 0.446944 0.223472 0.974710i \(-0.428261\pi\)
0.223472 + 0.974710i \(0.428261\pi\)
\(420\) −2.88826 + 0.149281i −0.140933 + 0.00728419i
\(421\) −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
\(423\) 6.87139 7.63629i 0.334099 0.371289i
\(424\) 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 \(0.913668\pi\)
\(432\) −0.410132 5.17994i −0.0197325 0.249220i
\(433\) −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
\(435\) −7.20785 6.49938i −0.345590 0.311622i
\(436\) −5.81042 −0.278269
\(437\) 3.68463 3.68463i 0.176260 0.176260i
\(438\) −13.6078 + 0.358476i −0.650204 + 0.0171286i
\(439\) 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 0.797416 0.603430i \(-0.206200\pi\)
−0.603430 + 0.797416i \(0.706200\pi\)
\(444\) 12.5858 + 11.9397i 0.597297 + 0.566635i
\(445\) 13.9865 14.7128i 0.663022 0.697452i
\(446\) 11.6416i 0.551245i
\(447\) −0.265417 10.0753i −0.0125538 0.476543i
\(448\) −0.528026 + 0.528026i −0.0249469 + 0.0249469i
\(449\) −5.80447 −0.273930 −0.136965 0.990576i \(-0.543735\pi\)
−0.136965 + 0.990576i \(0.543735\pi\)
\(450\) −11.6436 9.45659i −0.548884 0.445788i
\(451\) −19.4908 −0.917787
\(452\) 0.624299 0.624299i 0.0293645 0.0293645i
\(453\) −0.126826 4.81433i −0.00595882 0.226197i
\(454\) 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 \(-0.918730\pi\)
0.967583 0.252551i \(-0.0812697\pi\)
\(462\) 5.95676 0.156922i 0.277133 0.00730066i
\(463\) −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
\(465\) −11.2744 10.1662i −0.522837 0.471446i
\(466\) 7.09498 0.328669
\(467\) −4.97855 + 4.97855i −0.230380 + 0.230380i −0.812851 0.582471i \(-0.802086\pi\)
0.582471 + 0.812851i \(0.302086\pi\)
\(468\) 14.9487 + 13.4514i 0.691004 + 0.621789i
\(469\) 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
\(477\) 5.23884 + 4.71409i 0.239870 + 0.215843i
\(478\) −2.28824 + 2.28824i −0.104662 + 0.104662i
\(479\) 19.7275 0.901373 0.450686 0.892682i \(-0.351179\pi\)
0.450686 + 0.892682i \(0.351179\pi\)
\(480\) −3.86782 + 0.199910i −0.176541 + 0.00912462i
\(481\) −67.1398 −3.06131
\(482\) −1.76332 + 1.76332i −0.0803171 + 0.0803171i
\(483\) −1.29295 + 0.0340607i −0.0588311 + 0.00154981i
\(484\) 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 \(-0.954218\pi\)
0.989675 0.143332i \(-0.0457817\pi\)
\(492\) 0.192967 + 7.32505i 0.00869964 + 0.330239i
\(493\) −8.34367 + 8.34367i −0.375780 + 0.375780i
\(494\) −34.9297 −1.57156
\(495\) 23.4894 + 20.0847i 1.05577 + 0.902742i
\(496\) −3.91972 −0.176001
\(497\) 5.76529 5.76529i 0.258609 0.258609i
\(498\) 0.624629 + 23.7109i 0.0279903 + 1.06251i
\(499\) 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 0.0712128 0.997461i \(-0.477313\pi\)
−0.997461 + 0.0712128i \(0.977313\pi\)
\(504\) −0.117949 2.23712i −0.00525386 0.0996492i
\(505\) 12.9491 + 12.3099i 0.576227 + 0.547781i
\(506\) 4.60712i 0.204811i
\(507\) −55.2915 + 1.45657i −2.45558 + 0.0646886i
\(508\) 11.0353 11.0353i 0.489612 0.489612i
\(509\) −3.09578 −0.137218 −0.0686090 0.997644i \(-0.521856\pi\)
−0.0686090 + 0.997644i \(0.521856\pi\)
\(510\) −12.2126 + 13.5438i −0.540782 + 0.599730i
\(511\) −5.86877 −0.259619
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −26.9919 + 2.13714i −1.19172 + 0.0943570i
\(514\) 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 \(-0.0560389\pi\)
\(522\) 5.02862 5.58838i 0.220097 0.244597i
\(523\) −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
\(525\) −4.91081 4.20782i −0.214325 0.183644i
\(526\) −14.2850 −0.622853
\(527\) −13.0510 + 13.0510i −0.568511 + 0.568511i
\(528\) 7.97700 0.210142i 0.347154 0.00914525i
\(529\) 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
\(537\) −0.488437 18.5411i −0.0210776 0.800108i
\(538\) −16.6133 + 16.6133i −0.716252 + 0.716252i
\(539\) −29.6808 −1.27844
\(540\) 7.31570 9.02666i 0.314818 0.388445i
\(541\) −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
\(543\) −0.881633 33.4668i −0.0378345 1.43620i
\(544\) 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
\(552\) −1.73145 + 0.0456124i −0.0736954 + 0.00194139i
\(553\) 3.52237 3.52237i 0.149786 0.149786i
\(554\) −23.1720 −0.984482
\(555\) 2.00230 + 38.7401i 0.0849930 + 1.64443i
\(556\) 14.6607 0.621752
\(557\) −17.0441 + 17.0441i −0.722182 + 0.722182i −0.969049 0.246867i \(-0.920599\pi\)
0.246867 + 0.969049i \(0.420599\pi\)
\(558\) 7.86566 8.74124i 0.332980 0.370046i
\(559\) 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 \(-0.281982\pi\)
−0.774467 + 0.632614i \(0.781982\pi\)
\(564\) 4.08193 4.30281i 0.171880 0.181181i
\(565\) 1.97357 0.0499465i 0.0830289 0.00210126i
\(566\) 2.68608i 0.112905i
\(567\) 5.22561 + 4.22617i 0.219455 + 0.177482i
\(568\) 7.72060 7.72060i 0.323949 0.323949i
\(569\) −34.6119 −1.45100 −0.725502 0.688220i \(-0.758393\pi\)
−0.725502 + 0.688220i \(0.758393\pi\)
\(570\) 1.04170 + 20.1546i 0.0436322 + 0.844185i
\(571\) 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
\(573\) 28.2763 0.744897i 1.18126 0.0311185i
\(574\) 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
\(582\) 0.367377 + 13.9457i 0.0152283 + 0.578066i
\(583\) −7.65301 + 7.65301i −0.316955 + 0.316955i
\(584\) −7.85918 −0.325215
\(585\) 3.50282 + 44.8302i 0.144824 + 1.85350i
\(586\) −0.260905 −0.0107779
\(587\) 27.0582 27.0582i 1.11681 1.11681i 0.124605 0.992206i \(-0.460234\pi\)
0.992206 0.124605i \(-0.0397665\pi\)
\(588\) 0.293852 + 11.1547i 0.0121183 + 0.460010i
\(589\) 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 \(-0.212347\pi\)
−0.618717 + 0.785614i \(0.712347\pi\)
\(594\) −15.5387 + 18.2109i −0.637562 + 0.747203i
\(595\) −5.41717 + 5.69848i −0.222082 + 0.233615i
\(596\) 5.81897i 0.238354i
\(597\) 34.0151 0.896076i 1.39215 0.0366740i
\(598\) 4.73992 4.73992i 0.193830 0.193830i
\(599\) −3.30686 −0.135115 −0.0675574 0.997715i \(-0.521521\pi\)
−0.0675574 + 0.997715i \(0.521521\pi\)
\(600\) −6.57631 5.63490i −0.268477 0.230044i
\(601\) 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
\(603\) 16.5577 + 14.8992i 0.674282 + 0.606742i
\(604\) 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
\(612\) −10.5008 9.44896i −0.424469 0.381952i
\(613\) 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
\(615\) −10.9725 + 12.1685i −0.442453 + 0.490682i
\(616\) 3.44033 0.138615
\(617\) 21.2085 21.2085i 0.853823 0.853823i −0.136778 0.990602i \(-0.543675\pi\)
0.990602 + 0.136778i \(0.0436748\pi\)
\(618\) 20.5031 0.540124i 0.824758 0.0217270i
\(619\) 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
\(627\) −1.09502 41.5670i −0.0437308 1.66002i
\(628\) −6.33516 + 6.33516i −0.252800 + 0.252800i
\(629\) 47.1626 1.88050
\(630\) 3.25542 3.80727i 0.129699 0.151685i
\(631\) −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
\(633\) 0.199822 + 7.58526i 0.00794222 + 0.301487i
\(634\) 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 \(-0.136198\pi\)
\(642\) −26.5163 + 0.698531i −1.04651 + 0.0275688i
\(643\) −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
\(645\) 42.7941 2.21184i 1.68502 0.0870909i
\(646\) 24.5365 0.965376
\(647\) −1.33655 + 1.33655i −0.0525450 + 0.0525450i −0.732891 0.680346i \(-0.761830\pi\)
0.680346 + 0.732891i \(0.261830\pi\)
\(648\) 6.99788 + 5.65948i 0.274903 + 0.222325i
\(649\) 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 \(0.0278439\pi\)
0.0873627 + 0.996177i \(0.472156\pi\)
\(654\) 6.92642 7.30122i 0.270844 0.285500i
\(655\) 15.9671 + 15.1789i 0.623887 + 0.593088i
\(656\) 4.23059i 0.165177i
\(657\) 15.7709 17.5265i 0.615282 0.683773i
\(658\) 1.80809 1.80809i 0.0704867 0.0704867i
\(659\) −26.7954 −1.04380 −0.521901 0.853006i \(-0.674777\pi\)
−0.521901 + 0.853006i \(0.674777\pi\)
\(660\) 13.2516 + 11.9490i 0.515816 + 0.465116i
\(661\) 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
\(663\) 54.6512 1.43970i 2.12248 0.0559134i
\(664\) 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
\(672\) −0.0340607 1.29295i −0.00131392 0.0498765i
\(673\) −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
\(675\) 25.7628 3.35812i 0.991612 0.129254i
\(676\) −31.9337 −1.22822
\(677\) 21.0042 21.0042i 0.807257 0.807257i −0.176961 0.984218i \(-0.556627\pi\)
0.984218 + 0.176961i \(0.0566266\pi\)
\(678\) 0.0402708 + 1.52868i 0.00154659 + 0.0587087i
\(679\) 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 \(-0.449269\pi\)
−0.987326 + 0.158702i \(0.949269\pi\)
\(684\) −15.6109 + 0.823061i −0.596897 + 0.0314705i
\(685\) −0.607606 24.0088i −0.0232154 0.917330i
\(686\) 10.0380i 0.383252i
\(687\) 0.934154 0.0246089i 0.0356402 0.000938886i
\(688\) 7.82352 7.82352i 0.298269 0.298269i
\(689\) −15.7472 −0.599921
\(690\) −2.87632 2.59360i −0.109500 0.0987368i
\(691\) −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
\(693\) −6.90367 + 7.67216i −0.262249 + 0.291441i
\(694\) 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 \(-0.0487573\pi\)
\(702\) −34.7225 + 2.74922i −1.31052 + 0.103763i
\(703\) 36.9053 36.9053i 1.39191 1.39191i
\(704\) 4.60712 0.173637
\(705\) 13.2444 0.684542i 0.498811 0.0257813i
\(706\) 28.5784 1.07556
\(707\) −4.21900 + 4.21900i −0.158672 + 0.158672i
\(708\) −22.0585 + 0.581099i −0.829011 + 0.0218390i
\(709\) 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
\(717\) −0.147605 5.60308i −0.00551240 0.209251i
\(718\) 6.75511 6.75511i 0.252098 0.252098i
\(719\) −2.43829 −0.0909327 −0.0454664 0.998966i \(-0.514477\pi\)
−0.0454664 + 0.998966i \(0.514477\pi\)
\(720\) 4.35950 5.09851i 0.162469 0.190010i
\(721\) 8.84262 0.329316
\(722\) 5.76504 5.76504i 0.214553 0.214553i
\(723\) −0.113744 4.31774i −0.00423020 0.160579i
\(724\) 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
\(732\) 2.61476 0.0688818i 0.0966442 0.00254594i
\(733\) −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
\(735\) −16.7090 + 18.5303i −0.616320 + 0.683502i
\(736\) −1.00000 −0.0368605
\(737\) −24.1878 + 24.1878i −0.890970 + 0.890970i
\(738\) −9.43449 8.48948i −0.347288 0.312502i
\(739\) 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 0.990208 0.139601i \(-0.0445821\pi\)
−0.139601 + 0.990208i \(0.544582\pi\)
\(744\) 4.67257 4.92542i 0.171305 0.180575i
\(745\) 8.96488 9.43042i 0.328448 0.345504i
\(746\) 30.9879i 1.13455i
\(747\) −30.5391 27.4801i −1.11737 1.00545i
\(748\) 15.3397 15.3397i 0.560877 0.560877i
\(749\) −11.4360 −0.417861
\(750\) −1.97650 19.2638i −0.0721715 0.703414i
\(751\) 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
\(753\) −9.33787 + 0.245992i −0.340291 + 0.00896445i
\(754\) 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 \(-0.899007\pi\)
0.950088 0.311982i \(-0.100993\pi\)
\(762\) 0.711839 + 27.0215i 0.0257872 + 0.978885i
\(763\) 3.06806 3.06806i 0.111071 0.111071i
\(764\) 16.3310 0.590835
\(765\) −2.46057 31.4911i −0.0889622 1.13856i
\(766\) 25.0862 0.906400
\(767\) 60.3862 60.3862i 2.18042 2.18042i
\(768\) −0.0456124 1.73145i −0.00164590 0.0624783i
\(769\) 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 0.967235 0.253881i \(-0.0817071\pi\)
−0.253881 + 0.967235i \(0.581707\pi\)
\(774\) 1.74759 + 33.1464i 0.0628159 + 1.19142i
\(775\) −0.991353 19.5735i −0.0356104 0.703102i
\(776\) 8.05432i 0.289133i
\(777\) −12.9501 + 0.341152i −0.464584 + 0.0122388i