Properties

Label 370.2.h.e.253.3
Level $370$
Weight $2$
Character 370.253
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.3
Root \(-1.23675 - 1.23675i\) of defining polynomial
Character \(\chi\) \(=\) 370.253
Dual form 370.2.h.e.117.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.23675 + 1.23675i) q^{3} +1.00000 q^{4} +(-1.26849 + 1.84145i) q^{5} +(1.23675 - 1.23675i) q^{6} +(1.28708 - 1.28708i) q^{7} -1.00000 q^{8} -0.0591090i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.23675 + 1.23675i) q^{3} +1.00000 q^{4} +(-1.26849 + 1.84145i) q^{5} +(1.23675 - 1.23675i) q^{6} +(1.28708 - 1.28708i) q^{7} -1.00000 q^{8} -0.0591090i q^{9} +(1.26849 - 1.84145i) q^{10} +4.27563i q^{11} +(-1.23675 + 1.23675i) q^{12} -1.50964 q^{13} +(-1.28708 + 1.28708i) q^{14} +(-0.708613 - 3.84622i) q^{15} +1.00000 q^{16} -2.12121i q^{17} +0.0591090i q^{18} +(-0.381960 - 0.381960i) q^{19} +(-1.26849 + 1.84145i) q^{20} +3.18360i q^{21} -4.27563i q^{22} -8.90184 q^{23} +(1.23675 - 1.23675i) q^{24} +(-1.78188 - 4.67171i) q^{25} +1.50964 q^{26} +(-3.63715 - 3.63715i) q^{27} +(1.28708 - 1.28708i) q^{28} +(0.279903 - 0.279903i) q^{29} +(0.708613 + 3.84622i) q^{30} +(-1.59328 - 1.59328i) q^{31} -1.00000 q^{32} +(-5.28790 - 5.28790i) q^{33} +2.12121i q^{34} +(0.737449 + 4.00274i) q^{35} -0.0591090i q^{36} +(-5.63727 + 2.28498i) q^{37} +(0.381960 + 0.381960i) q^{38} +(1.86705 - 1.86705i) q^{39} +(1.26849 - 1.84145i) q^{40} -0.270882i q^{41} -3.18360i q^{42} +0.302660 q^{43} +4.27563i q^{44} +(0.108846 + 0.0749790i) q^{45} +8.90184 q^{46} +(-3.17973 + 3.17973i) q^{47} +(-1.23675 + 1.23675i) q^{48} +3.68685i q^{49} +(1.78188 + 4.67171i) q^{50} +(2.62341 + 2.62341i) q^{51} -1.50964 q^{52} +(9.71066 + 9.71066i) q^{53} +(3.63715 + 3.63715i) q^{54} +(-7.87337 - 5.42359i) q^{55} +(-1.28708 + 1.28708i) q^{56} +0.944780 q^{57} +(-0.279903 + 0.279903i) q^{58} +(-4.06655 - 4.06655i) q^{59} +(-0.708613 - 3.84622i) q^{60} +(4.47102 + 4.47102i) q^{61} +(1.59328 + 1.59328i) q^{62} +(-0.0760780 - 0.0760780i) q^{63} +1.00000 q^{64} +(1.91496 - 2.77993i) q^{65} +(5.28790 + 5.28790i) q^{66} +(-6.17649 - 6.17649i) q^{67} -2.12121i q^{68} +(11.0094 - 11.0094i) q^{69} +(-0.737449 - 4.00274i) q^{70} -7.90805 q^{71} +0.0591090i q^{72} +(8.32545 - 8.32545i) q^{73} +(5.63727 - 2.28498i) q^{74} +(7.98149 + 3.57401i) q^{75} +(-0.381960 - 0.381960i) q^{76} +(5.50309 + 5.50309i) q^{77} +(-1.86705 + 1.86705i) q^{78} +(-2.20061 - 2.20061i) q^{79} +(-1.26849 + 1.84145i) q^{80} +9.17383 q^{81} +0.270882i q^{82} +(10.1305 + 10.1305i) q^{83} +3.18360i q^{84} +(3.90611 + 2.69073i) q^{85} -0.302660 q^{86} +0.692342i q^{87} -4.27563i q^{88} +(5.24983 - 5.24983i) q^{89} +(-0.108846 - 0.0749790i) q^{90} +(-1.94303 + 1.94303i) q^{91} -8.90184 q^{92} +3.94099 q^{93} +(3.17973 - 3.17973i) q^{94} +(1.18787 - 0.218849i) q^{95} +(1.23675 - 1.23675i) q^{96} +12.2566i q^{97} -3.68685i q^{98} +0.252728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + O(q^{10}) \) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + 4q^{10} + 4q^{12} + 2q^{14} - 4q^{15} + 20q^{16} + 6q^{19} - 4q^{20} - 4q^{23} - 4q^{24} + 10q^{25} - 20q^{27} - 2q^{28} + 18q^{29} + 4q^{30} + 12q^{31} - 20q^{32} + 4q^{33} - 12q^{35} - 32q^{37} - 6q^{38} + 6q^{39} + 4q^{40} + 16q^{43} + 22q^{45} + 4q^{46} - 22q^{47} + 4q^{48} - 10q^{50} + 8q^{51} - 4q^{53} + 20q^{54} + 16q^{55} + 2q^{56} + 24q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{61} - 12q^{62} - 2q^{63} + 20q^{64} + 20q^{65} - 4q^{66} + 8q^{67} - 34q^{69} + 12q^{70} + 16q^{71} - 6q^{73} + 32q^{74} - 26q^{75} + 6q^{76} - 4q^{77} - 6q^{78} + 12q^{79} - 4q^{80} - 28q^{81} + 6q^{83} + 10q^{85} - 16q^{86} - 44q^{89} - 22q^{90} - 40q^{91} - 4q^{92} - 40q^{93} + 22q^{94} + 50q^{95} - 4q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.23675 + 1.23675i −0.714039 + 0.714039i −0.967378 0.253339i \(-0.918471\pi\)
0.253339 + 0.967378i \(0.418471\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.26849 + 1.84145i −0.567285 + 0.823522i
\(6\) 1.23675 1.23675i 0.504902 0.504902i
\(7\) 1.28708 1.28708i 0.486471 0.486471i −0.420720 0.907191i \(-0.638222\pi\)
0.907191 + 0.420720i \(0.138222\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.0591090i 0.0197030i
\(10\) 1.26849 1.84145i 0.401131 0.582318i
\(11\) 4.27563i 1.28915i 0.764540 + 0.644576i \(0.222966\pi\)
−0.764540 + 0.644576i \(0.777034\pi\)
\(12\) −1.23675 + 1.23675i −0.357019 + 0.357019i
\(13\) −1.50964 −0.418700 −0.209350 0.977841i \(-0.567135\pi\)
−0.209350 + 0.977841i \(0.567135\pi\)
\(14\) −1.28708 + 1.28708i −0.343987 + 0.343987i
\(15\) −0.708613 3.84622i −0.182963 0.993090i
\(16\) 1.00000 0.250000
\(17\) 2.12121i 0.514470i −0.966349 0.257235i \(-0.917189\pi\)
0.966349 0.257235i \(-0.0828114\pi\)
\(18\) 0.0591090i 0.0139321i
\(19\) −0.381960 0.381960i −0.0876277 0.0876277i 0.661934 0.749562i \(-0.269736\pi\)
−0.749562 + 0.661934i \(0.769736\pi\)
\(20\) −1.26849 + 1.84145i −0.283642 + 0.411761i
\(21\) 3.18360i 0.694718i
\(22\) 4.27563i 0.911568i
\(23\) −8.90184 −1.85616 −0.928081 0.372379i \(-0.878542\pi\)
−0.928081 + 0.372379i \(0.878542\pi\)
\(24\) 1.23675 1.23675i 0.252451 0.252451i
\(25\) −1.78188 4.67171i −0.356376 0.934343i
\(26\) 1.50964 0.296066
\(27\) −3.63715 3.63715i −0.699970 0.699970i
\(28\) 1.28708 1.28708i 0.243235 0.243235i
\(29\) 0.279903 0.279903i 0.0519767 0.0519767i −0.680641 0.732617i \(-0.738298\pi\)
0.732617 + 0.680641i \(0.238298\pi\)
\(30\) 0.708613 + 3.84622i 0.129374 + 0.702221i
\(31\) −1.59328 1.59328i −0.286162 0.286162i 0.549398 0.835561i \(-0.314857\pi\)
−0.835561 + 0.549398i \(0.814857\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.28790 5.28790i −0.920505 0.920505i
\(34\) 2.12121i 0.363785i
\(35\) 0.737449 + 4.00274i 0.124652 + 0.676587i
\(36\) 0.0591090i 0.00985149i
\(37\) −5.63727 + 2.28498i −0.926762 + 0.375649i
\(38\) 0.381960 + 0.381960i 0.0619621 + 0.0619621i
\(39\) 1.86705 1.86705i 0.298968 0.298968i
\(40\) 1.26849 1.84145i 0.200565 0.291159i
\(41\) 0.270882i 0.0423047i −0.999776 0.0211524i \(-0.993266\pi\)
0.999776 0.0211524i \(-0.00673350\pi\)
\(42\) 3.18360i 0.491240i
\(43\) 0.302660 0.0461552 0.0230776 0.999734i \(-0.492654\pi\)
0.0230776 + 0.999734i \(0.492654\pi\)
\(44\) 4.27563i 0.644576i
\(45\) 0.108846 + 0.0749790i 0.0162258 + 0.0111772i
\(46\) 8.90184 1.31250
\(47\) −3.17973 + 3.17973i −0.463811 + 0.463811i −0.899902 0.436091i \(-0.856362\pi\)
0.436091 + 0.899902i \(0.356362\pi\)
\(48\) −1.23675 + 1.23675i −0.178510 + 0.178510i
\(49\) 3.68685i 0.526692i
\(50\) 1.78188 + 4.67171i 0.251996 + 0.660680i
\(51\) 2.62341 + 2.62341i 0.367351 + 0.367351i
\(52\) −1.50964 −0.209350
\(53\) 9.71066 + 9.71066i 1.33386 + 1.33386i 0.901884 + 0.431978i \(0.142184\pi\)
0.431978 + 0.901884i \(0.357816\pi\)
\(54\) 3.63715 + 3.63715i 0.494954 + 0.494954i
\(55\) −7.87337 5.42359i −1.06164 0.731316i
\(56\) −1.28708 + 1.28708i −0.171993 + 0.171993i
\(57\) 0.944780 0.125139
\(58\) −0.279903 + 0.279903i −0.0367531 + 0.0367531i
\(59\) −4.06655 4.06655i −0.529420 0.529420i 0.390979 0.920399i \(-0.372136\pi\)
−0.920399 + 0.390979i \(0.872136\pi\)
\(60\) −0.708613 3.84622i −0.0914815 0.496545i
\(61\) 4.47102 + 4.47102i 0.572455 + 0.572455i 0.932814 0.360359i \(-0.117346\pi\)
−0.360359 + 0.932814i \(0.617346\pi\)
\(62\) 1.59328 + 1.59328i 0.202347 + 0.202347i
\(63\) −0.0760780 0.0760780i −0.00958493 0.00958493i
\(64\) 1.00000 0.125000
\(65\) 1.91496 2.77993i 0.237522 0.344808i
\(66\) 5.28790 + 5.28790i 0.650895 + 0.650895i
\(67\) −6.17649 6.17649i −0.754578 0.754578i 0.220752 0.975330i \(-0.429149\pi\)
−0.975330 + 0.220752i \(0.929149\pi\)
\(68\) 2.12121i 0.257235i
\(69\) 11.0094 11.0094i 1.32537 1.32537i
\(70\) −0.737449 4.00274i −0.0881420 0.478419i
\(71\) −7.90805 −0.938513 −0.469256 0.883062i \(-0.655478\pi\)
−0.469256 + 0.883062i \(0.655478\pi\)
\(72\) 0.0591090i 0.00696606i
\(73\) 8.32545 8.32545i 0.974420 0.974420i −0.0252606 0.999681i \(-0.508042\pi\)
0.999681 + 0.0252606i \(0.00804156\pi\)
\(74\) 5.63727 2.28498i 0.655320 0.265624i
\(75\) 7.98149 + 3.57401i 0.921623 + 0.412691i
\(76\) −0.381960 0.381960i −0.0438138 0.0438138i
\(77\) 5.50309 + 5.50309i 0.627135 + 0.627135i
\(78\) −1.86705 + 1.86705i −0.211402 + 0.211402i
\(79\) −2.20061 2.20061i −0.247588 0.247588i 0.572392 0.819980i \(-0.306016\pi\)
−0.819980 + 0.572392i \(0.806016\pi\)
\(80\) −1.26849 + 1.84145i −0.141821 + 0.205880i
\(81\) 9.17383 1.01931
\(82\) 0.270882i 0.0299139i
\(83\) 10.1305 + 10.1305i 1.11197 + 1.11197i 0.992884 + 0.119087i \(0.0379968\pi\)
0.119087 + 0.992884i \(0.462003\pi\)
\(84\) 3.18360i 0.347359i
\(85\) 3.90611 + 2.69073i 0.423677 + 0.291851i
\(86\) −0.302660 −0.0326367
\(87\) 0.692342i 0.0742268i
\(88\) 4.27563i 0.455784i
\(89\) 5.24983 5.24983i 0.556481 0.556481i −0.371823 0.928304i \(-0.621267\pi\)
0.928304 + 0.371823i \(0.121267\pi\)
\(90\) −0.108846 0.0749790i −0.0114734 0.00790348i
\(91\) −1.94303 + 1.94303i −0.203685 + 0.203685i
\(92\) −8.90184 −0.928081
\(93\) 3.94099 0.408662
\(94\) 3.17973 3.17973i 0.327964 0.327964i
\(95\) 1.18787 0.218849i 0.121873 0.0224534i
\(96\) 1.23675 1.23675i 0.126225 0.126225i
\(97\) 12.2566i 1.24447i 0.782829 + 0.622237i \(0.213776\pi\)
−0.782829 + 0.622237i \(0.786224\pi\)
\(98\) 3.68685i 0.372428i
\(99\) 0.252728 0.0254001
\(100\) −1.78188 4.67171i −0.178188 0.467171i
\(101\) 19.3052i 1.92094i 0.278383 + 0.960470i \(0.410202\pi\)
−0.278383 + 0.960470i \(0.589798\pi\)
\(102\) −2.62341 2.62341i −0.259757 0.259757i
\(103\) 10.5846i 1.04293i 0.853272 + 0.521466i \(0.174615\pi\)
−0.853272 + 0.521466i \(0.825385\pi\)
\(104\) 1.50964 0.148033
\(105\) −5.86244 4.03835i −0.572115 0.394103i
\(106\) −9.71066 9.71066i −0.943183 0.943183i
\(107\) 2.77915 2.77915i 0.268670 0.268670i −0.559894 0.828564i \(-0.689158\pi\)
0.828564 + 0.559894i \(0.189158\pi\)
\(108\) −3.63715 3.63715i −0.349985 0.349985i
\(109\) 4.14598 + 4.14598i 0.397113 + 0.397113i 0.877213 0.480101i \(-0.159400\pi\)
−0.480101 + 0.877213i \(0.659400\pi\)
\(110\) 7.87337 + 5.42359i 0.750696 + 0.517119i
\(111\) 4.14595 9.79786i 0.393516 0.929972i
\(112\) 1.28708 1.28708i 0.121618 0.121618i
\(113\) 2.26739i 0.213298i −0.994297 0.106649i \(-0.965988\pi\)
0.994297 0.106649i \(-0.0340122\pi\)
\(114\) −0.944780 −0.0884867
\(115\) 11.2919 16.3923i 1.05297 1.52859i
\(116\) 0.279903 0.279903i 0.0259884 0.0259884i
\(117\) 0.0892335i 0.00824964i
\(118\) 4.06655 + 4.06655i 0.374356 + 0.374356i
\(119\) −2.73017 2.73017i −0.250275 0.250275i
\(120\) 0.708613 + 3.84622i 0.0646872 + 0.351110i
\(121\) −7.28104 −0.661913
\(122\) −4.47102 4.47102i −0.404787 0.404787i
\(123\) 0.335014 + 0.335014i 0.0302072 + 0.0302072i
\(124\) −1.59328 1.59328i −0.143081 0.143081i
\(125\) 10.8630 + 2.64477i 0.971618 + 0.236555i
\(126\) 0.0760780 + 0.0760780i 0.00677757 + 0.00677757i
\(127\) −7.95386 + 7.95386i −0.705791 + 0.705791i −0.965647 0.259857i \(-0.916325\pi\)
0.259857 + 0.965647i \(0.416325\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.374315 + 0.374315i −0.0329566 + 0.0329566i
\(130\) −1.91496 + 2.77993i −0.167954 + 0.243816i
\(131\) −6.31669 6.31669i −0.551892 0.551892i 0.375095 0.926987i \(-0.377610\pi\)
−0.926987 + 0.375095i \(0.877610\pi\)
\(132\) −5.28790 5.28790i −0.460252 0.460252i
\(133\) −0.983227 −0.0852566
\(134\) 6.17649 + 6.17649i 0.533567 + 0.533567i
\(135\) 11.3113 2.08395i 0.973523 0.179358i
\(136\) 2.12121i 0.181893i
\(137\) −3.53660 + 3.53660i −0.302152 + 0.302152i −0.841855 0.539703i \(-0.818536\pi\)
0.539703 + 0.841855i \(0.318536\pi\)
\(138\) −11.0094 + 11.0094i −0.937179 + 0.937179i
\(139\) −5.70896 −0.484228 −0.242114 0.970248i \(-0.577841\pi\)
−0.242114 + 0.970248i \(0.577841\pi\)
\(140\) 0.737449 + 4.00274i 0.0623258 + 0.338293i
\(141\) 7.86507i 0.662358i
\(142\) 7.90805 0.663629
\(143\) 6.45468i 0.539768i
\(144\) 0.0591090i 0.00492575i
\(145\) 0.160374 + 0.870482i 0.0133184 + 0.0722896i
\(146\) −8.32545 + 8.32545i −0.689019 + 0.689019i
\(147\) −4.55971 4.55971i −0.376079 0.376079i
\(148\) −5.63727 + 2.28498i −0.463381 + 0.187824i
\(149\) 7.36973i 0.603752i −0.953347 0.301876i \(-0.902387\pi\)
0.953347 0.301876i \(-0.0976129\pi\)
\(150\) −7.98149 3.57401i −0.651686 0.291817i
\(151\) 4.96769i 0.404265i 0.979358 + 0.202132i \(0.0647871\pi\)
−0.979358 + 0.202132i \(0.935213\pi\)
\(152\) 0.381960 + 0.381960i 0.0309811 + 0.0309811i
\(153\) −0.125383 −0.0101366
\(154\) −5.50309 5.50309i −0.443451 0.443451i
\(155\) 4.95501 0.912892i 0.397996 0.0733252i
\(156\) 1.86705 1.86705i 0.149484 0.149484i
\(157\) 8.28379 8.28379i 0.661119 0.661119i −0.294525 0.955644i \(-0.595161\pi\)
0.955644 + 0.294525i \(0.0951615\pi\)
\(158\) 2.20061 + 2.20061i 0.175071 + 0.175071i
\(159\) −24.0194 −1.90486
\(160\) 1.26849 1.84145i 0.100283 0.145579i
\(161\) −11.4574 + 11.4574i −0.902968 + 0.902968i
\(162\) −9.17383 −0.720764
\(163\) 19.2629i 1.50879i 0.656422 + 0.754394i \(0.272069\pi\)
−0.656422 + 0.754394i \(0.727931\pi\)
\(164\) 0.270882i 0.0211524i
\(165\) 16.4450 3.02977i 1.28024 0.235867i
\(166\) −10.1305 10.1305i −0.786282 0.786282i
\(167\) 22.3611i 1.73036i −0.501466 0.865178i \(-0.667206\pi\)
0.501466 0.865178i \(-0.332794\pi\)
\(168\) 3.18360i 0.245620i
\(169\) −10.7210 −0.824690
\(170\) −3.90611 2.69073i −0.299585 0.206370i
\(171\) −0.0225773 + 0.0225773i −0.00172653 + 0.00172653i
\(172\) 0.302660 0.0230776
\(173\) −6.44977 + 6.44977i −0.490367 + 0.490367i −0.908422 0.418055i \(-0.862712\pi\)
0.418055 + 0.908422i \(0.362712\pi\)
\(174\) 0.692342i 0.0524863i
\(175\) −8.30629 3.71945i −0.627897 0.281164i
\(176\) 4.27563i 0.322288i
\(177\) 10.0586 0.756053
\(178\) −5.24983 + 5.24983i −0.393492 + 0.393492i
\(179\) −8.44973 + 8.44973i −0.631562 + 0.631562i −0.948460 0.316897i \(-0.897359\pi\)
0.316897 + 0.948460i \(0.397359\pi\)
\(180\) 0.108846 + 0.0749790i 0.00811292 + 0.00558860i
\(181\) 1.63147 0.121266 0.0606330 0.998160i \(-0.480688\pi\)
0.0606330 + 0.998160i \(0.480688\pi\)
\(182\) 1.94303 1.94303i 0.144027 0.144027i
\(183\) −11.0591 −0.817511
\(184\) 8.90184 0.656252
\(185\) 2.94313 13.2792i 0.216383 0.976309i
\(186\) −3.94099 −0.288967
\(187\) 9.06953 0.663230
\(188\) −3.17973 + 3.17973i −0.231905 + 0.231905i
\(189\) −9.36262 −0.681030
\(190\) −1.18787 + 0.218849i −0.0861773 + 0.0158770i
\(191\) −14.3915 + 14.3915i −1.04133 + 1.04133i −0.0422206 + 0.999108i \(0.513443\pi\)
−0.999108 + 0.0422206i \(0.986557\pi\)
\(192\) −1.23675 + 1.23675i −0.0892549 + 0.0892549i
\(193\) −1.88527 −0.135705 −0.0678525 0.997695i \(-0.521615\pi\)
−0.0678525 + 0.997695i \(0.521615\pi\)
\(194\) 12.2566i 0.879976i
\(195\) 1.06975 + 5.80642i 0.0766066 + 0.415807i
\(196\) 3.68685i 0.263346i
\(197\) −16.9005 + 16.9005i −1.20411 + 1.20411i −0.231210 + 0.972904i \(0.574268\pi\)
−0.972904 + 0.231210i \(0.925732\pi\)
\(198\) −0.252728 −0.0179606
\(199\) 6.68597 6.68597i 0.473956 0.473956i −0.429236 0.903192i \(-0.641217\pi\)
0.903192 + 0.429236i \(0.141217\pi\)
\(200\) 1.78188 + 4.67171i 0.125998 + 0.330340i
\(201\) 15.2776 1.07760
\(202\) 19.3052i 1.35831i
\(203\) 0.720516i 0.0505703i
\(204\) 2.62341 + 2.62341i 0.183676 + 0.183676i
\(205\) 0.498816 + 0.343611i 0.0348388 + 0.0239988i
\(206\) 10.5846i 0.737464i
\(207\) 0.526178i 0.0365719i
\(208\) −1.50964 −0.104675
\(209\) 1.63312 1.63312i 0.112965 0.112965i
\(210\) 5.86244 + 4.03835i 0.404547 + 0.278673i
\(211\) 16.4186 1.13030 0.565151 0.824987i \(-0.308818\pi\)
0.565151 + 0.824987i \(0.308818\pi\)
\(212\) 9.71066 + 9.71066i 0.666931 + 0.666931i
\(213\) 9.78029 9.78029i 0.670135 0.670135i
\(214\) −2.77915 + 2.77915i −0.189978 + 0.189978i
\(215\) −0.383920 + 0.557333i −0.0261832 + 0.0380098i
\(216\) 3.63715 + 3.63715i 0.247477 + 0.247477i
\(217\) −4.10137 −0.278419
\(218\) −4.14598 4.14598i −0.280801 0.280801i
\(219\) 20.5930i 1.39155i
\(220\) −7.87337 5.42359i −0.530822 0.365658i
\(221\) 3.20228i 0.215408i
\(222\) −4.14595 + 9.79786i −0.278258 + 0.657590i
\(223\) 13.7600 + 13.7600i 0.921436 + 0.921436i 0.997131 0.0756947i \(-0.0241175\pi\)
−0.0756947 + 0.997131i \(0.524117\pi\)
\(224\) −1.28708 + 1.28708i −0.0859967 + 0.0859967i
\(225\) −0.276140 + 0.105325i −0.0184093 + 0.00702167i
\(226\) 2.26739i 0.150825i
\(227\) 5.23067i 0.347172i −0.984819 0.173586i \(-0.944465\pi\)
0.984819 0.173586i \(-0.0555355\pi\)
\(228\) 0.944780 0.0625696
\(229\) 3.12544i 0.206535i −0.994654 0.103267i \(-0.967070\pi\)
0.994654 0.103267i \(-0.0329298\pi\)
\(230\) −11.2919 + 16.3923i −0.744564 + 1.08088i
\(231\) −13.6119 −0.895597
\(232\) −0.279903 + 0.279903i −0.0183766 + 0.0183766i
\(233\) −7.43576 + 7.43576i −0.487133 + 0.487133i −0.907400 0.420268i \(-0.861936\pi\)
0.420268 + 0.907400i \(0.361936\pi\)
\(234\) 0.0892335i 0.00583338i
\(235\) −1.82187 9.88875i −0.118845 0.645071i
\(236\) −4.06655 4.06655i −0.264710 0.264710i
\(237\) 5.44322 0.353575
\(238\) 2.73017 + 2.73017i 0.176971 + 0.176971i
\(239\) 19.2129 + 19.2129i 1.24278 + 1.24278i 0.958842 + 0.283939i \(0.0916414\pi\)
0.283939 + 0.958842i \(0.408359\pi\)
\(240\) −0.708613 3.84622i −0.0457407 0.248272i
\(241\) 19.0019 19.0019i 1.22402 1.22402i 0.257830 0.966190i \(-0.416993\pi\)
0.966190 0.257830i \(-0.0830073\pi\)
\(242\) 7.28104 0.468043
\(243\) −0.434298 + 0.434298i −0.0278602 + 0.0278602i
\(244\) 4.47102 + 4.47102i 0.286228 + 0.286228i
\(245\) −6.78914 4.67672i −0.433743 0.298785i
\(246\) −0.335014 0.335014i −0.0213597 0.0213597i
\(247\) 0.576624 + 0.576624i 0.0366897 + 0.0366897i
\(248\) 1.59328 + 1.59328i 0.101174 + 0.101174i
\(249\) −25.0579 −1.58798
\(250\) −10.8630 2.64477i −0.687038 0.167270i
\(251\) −2.56669 2.56669i −0.162008 0.162008i 0.621448 0.783456i \(-0.286545\pi\)
−0.783456 + 0.621448i \(0.786545\pi\)
\(252\) −0.0760780 0.0760780i −0.00479246 0.00479246i
\(253\) 38.0610i 2.39287i
\(254\) 7.95386 7.95386i 0.499069 0.499069i
\(255\) −8.15865 + 1.50312i −0.510915 + 0.0941289i
\(256\) 1.00000 0.0625000
\(257\) 13.8993i 0.867015i 0.901150 + 0.433507i \(0.142724\pi\)
−0.901150 + 0.433507i \(0.857276\pi\)
\(258\) 0.374315 0.374315i 0.0233038 0.0233038i
\(259\) −4.31467 + 10.1966i −0.268100 + 0.633585i
\(260\) 1.91496 2.77993i 0.118761 0.172404i
\(261\) −0.0165448 0.0165448i −0.00102410 0.00102410i
\(262\) 6.31669 + 6.31669i 0.390246 + 0.390246i
\(263\) 14.2273 14.2273i 0.877290 0.877290i −0.115964 0.993253i \(-0.536996\pi\)
0.993253 + 0.115964i \(0.0369956\pi\)
\(264\) 5.28790 + 5.28790i 0.325448 + 0.325448i
\(265\) −30.1996 + 5.56385i −1.85514 + 0.341784i
\(266\) 0.983227 0.0602855
\(267\) 12.9855i 0.794699i
\(268\) −6.17649 6.17649i −0.377289 0.377289i
\(269\) 21.4303i 1.30663i −0.757086 0.653315i \(-0.773378\pi\)
0.757086 0.653315i \(-0.226622\pi\)
\(270\) −11.3113 + 2.08395i −0.688385 + 0.126825i
\(271\) −17.5063 −1.06343 −0.531717 0.846922i \(-0.678453\pi\)
−0.531717 + 0.846922i \(0.678453\pi\)
\(272\) 2.12121i 0.128617i
\(273\) 4.80610i 0.290878i
\(274\) 3.53660 3.53660i 0.213654 0.213654i
\(275\) 19.9745 7.61866i 1.20451 0.459422i
\(276\) 11.0094 11.0094i 0.662686 0.662686i
\(277\) −9.92772 −0.596499 −0.298249 0.954488i \(-0.596403\pi\)
−0.298249 + 0.954488i \(0.596403\pi\)
\(278\) 5.70896 0.342401
\(279\) −0.0941773 + 0.0941773i −0.00563825 + 0.00563825i
\(280\) −0.737449 4.00274i −0.0440710 0.239210i
\(281\) 9.25821 9.25821i 0.552299 0.552299i −0.374805 0.927104i \(-0.622290\pi\)
0.927104 + 0.374805i \(0.122290\pi\)
\(282\) 7.86507i 0.468358i
\(283\) 7.32826i 0.435620i 0.975991 + 0.217810i \(0.0698912\pi\)
−0.975991 + 0.217810i \(0.930109\pi\)
\(284\) −7.90805 −0.469256
\(285\) −1.19844 + 1.73976i −0.0709895 + 0.103055i
\(286\) 6.45468i 0.381673i
\(287\) −0.348647 0.348647i −0.0205800 0.0205800i
\(288\) 0.0591090i 0.00348303i
\(289\) 12.5005 0.735321
\(290\) −0.160374 0.870482i −0.00941750 0.0511165i
\(291\) −15.1584 15.1584i −0.888603 0.888603i
\(292\) 8.32545 8.32545i 0.487210 0.487210i
\(293\) −12.6098 12.6098i −0.736675 0.736675i 0.235258 0.971933i \(-0.424406\pi\)
−0.971933 + 0.235258i \(0.924406\pi\)
\(294\) 4.55971 + 4.55971i 0.265928 + 0.265928i
\(295\) 12.6467 2.32998i 0.736321 0.135657i
\(296\) 5.63727 2.28498i 0.327660 0.132812i
\(297\) 15.5511 15.5511i 0.902368 0.902368i
\(298\) 7.36973i 0.426917i
\(299\) 13.4386 0.777175
\(300\) 7.98149 + 3.57401i 0.460812 + 0.206345i
\(301\) 0.389548 0.389548i 0.0224532 0.0224532i
\(302\) 4.96769i 0.285858i
\(303\) −23.8758 23.8758i −1.37163 1.37163i
\(304\) −0.381960 0.381960i −0.0219069 0.0219069i
\(305\) −13.9046 + 2.56173i −0.796174 + 0.146684i
\(306\) 0.125383 0.00716765
\(307\) 17.0291 + 17.0291i 0.971903 + 0.971903i 0.999616 0.0277133i \(-0.00882256\pi\)
−0.0277133 + 0.999616i \(0.508823\pi\)
\(308\) 5.50309 + 5.50309i 0.313567 + 0.313567i
\(309\) −13.0905 13.0905i −0.744694 0.744694i
\(310\) −4.95501 + 0.912892i −0.281426 + 0.0518488i
\(311\) 3.74670 + 3.74670i 0.212456 + 0.212456i 0.805310 0.592854i \(-0.201999\pi\)
−0.592854 + 0.805310i \(0.701999\pi\)
\(312\) −1.86705 + 1.86705i −0.105701 + 0.105701i
\(313\) 14.7056 0.831208 0.415604 0.909546i \(-0.363570\pi\)
0.415604 + 0.909546i \(0.363570\pi\)
\(314\) −8.28379 + 8.28379i −0.467481 + 0.467481i
\(315\) 0.236598 0.0435899i 0.0133308 0.00245601i
\(316\) −2.20061 2.20061i −0.123794 0.123794i
\(317\) 13.6458 + 13.6458i 0.766423 + 0.766423i 0.977475 0.211052i \(-0.0676890\pi\)
−0.211052 + 0.977475i \(0.567689\pi\)
\(318\) 24.0194 1.34694
\(319\) 1.19676 + 1.19676i 0.0670059 + 0.0670059i
\(320\) −1.26849 + 1.84145i −0.0709106 + 0.102940i
\(321\) 6.87423i 0.383682i
\(322\) 11.4574 11.4574i 0.638495 0.638495i
\(323\) −0.810219 + 0.810219i −0.0450818 + 0.0450818i
\(324\) 9.17383 0.509657
\(325\) 2.69000 + 7.05262i 0.149214 + 0.391209i
\(326\) 19.2629i 1.06687i
\(327\) −10.2551 −0.567108
\(328\) 0.270882i 0.0149570i
\(329\) 8.18513i 0.451261i
\(330\) −16.4450 + 3.02977i −0.905269 + 0.166783i
\(331\) −15.5423 + 15.5423i −0.854280 + 0.854280i −0.990657 0.136377i \(-0.956454\pi\)
0.136377 + 0.990657i \(0.456454\pi\)
\(332\) 10.1305 + 10.1305i 0.555985 + 0.555985i
\(333\) 0.135063 + 0.333213i 0.00740141 + 0.0182600i
\(334\) 22.3611i 1.22355i
\(335\) 19.2085 3.53890i 1.04947 0.193351i
\(336\) 3.18360i 0.173680i
\(337\) 14.8294 + 14.8294i 0.807811 + 0.807811i 0.984302 0.176491i \(-0.0564747\pi\)
−0.176491 + 0.984302i \(0.556475\pi\)
\(338\) 10.7210 0.583144
\(339\) 2.80420 + 2.80420i 0.152303 + 0.152303i
\(340\) 3.90611 + 2.69073i 0.211838 + 0.145925i
\(341\) 6.81229 6.81229i 0.368906 0.368906i
\(342\) 0.0225773 0.0225773i 0.00122084 0.00122084i
\(343\) 13.7548 + 13.7548i 0.742691 + 0.742691i
\(344\) −0.302660 −0.0163183
\(345\) 6.30795 + 34.2384i 0.339609 + 1.84334i
\(346\) 6.44977 6.44977i 0.346742 0.346742i
\(347\) −8.24738 −0.442742 −0.221371 0.975190i \(-0.571053\pi\)
−0.221371 + 0.975190i \(0.571053\pi\)
\(348\) 0.692342i 0.0371134i
\(349\) 16.1967i 0.866991i 0.901156 + 0.433496i \(0.142720\pi\)
−0.901156 + 0.433496i \(0.857280\pi\)
\(350\) 8.30629 + 3.71945i 0.443990 + 0.198813i
\(351\) 5.49080 + 5.49080i 0.293077 + 0.293077i
\(352\) 4.27563i 0.227892i
\(353\) 20.3765i 1.08453i −0.840207 0.542266i \(-0.817567\pi\)
0.840207 0.542266i \(-0.182433\pi\)
\(354\) −10.0586 −0.534610
\(355\) 10.0313 14.5623i 0.532404 0.772885i
\(356\) 5.24983 5.24983i 0.278241 0.278241i
\(357\) 6.75309 0.357411
\(358\) 8.44973 8.44973i 0.446582 0.446582i
\(359\) 30.2708i 1.59763i 0.601575 + 0.798816i \(0.294540\pi\)
−0.601575 + 0.798816i \(0.705460\pi\)
\(360\) −0.108846 0.0749790i −0.00573670 0.00395174i
\(361\) 18.7082i 0.984643i
\(362\) −1.63147 −0.0857480
\(363\) 9.00484 9.00484i 0.472632 0.472632i
\(364\) −1.94303 + 1.94303i −0.101843 + 0.101843i
\(365\) 4.77017 + 25.8916i 0.249682 + 1.35523i
\(366\) 11.0591 0.578067
\(367\) 13.0615 13.0615i 0.681804 0.681804i −0.278603 0.960406i \(-0.589871\pi\)
0.960406 + 0.278603i \(0.0898713\pi\)
\(368\) −8.90184 −0.464040
\(369\) −0.0160116 −0.000833529
\(370\) −2.94313 + 13.2792i −0.153006 + 0.690354i
\(371\) 24.9968 1.29777
\(372\) 3.94099 0.204331
\(373\) −16.1154 + 16.1154i −0.834423 + 0.834423i −0.988118 0.153695i \(-0.950883\pi\)
0.153695 + 0.988118i \(0.450883\pi\)
\(374\) −9.06953 −0.468974
\(375\) −16.7058 + 10.1639i −0.862683 + 0.524863i
\(376\) 3.17973 3.17973i 0.163982 0.163982i
\(377\) −0.422554 + 0.422554i −0.0217627 + 0.0217627i
\(378\) 9.36262 0.481561
\(379\) 7.07736i 0.363539i −0.983341 0.181770i \(-0.941817\pi\)
0.983341 0.181770i \(-0.0581825\pi\)
\(380\) 1.18787 0.218849i 0.0609366 0.0112267i
\(381\) 19.6739i 1.00792i
\(382\) 14.3915 14.3915i 0.736331 0.736331i
\(383\) −17.6507 −0.901911 −0.450955 0.892546i \(-0.648917\pi\)
−0.450955 + 0.892546i \(0.648917\pi\)
\(384\) 1.23675 1.23675i 0.0631127 0.0631127i
\(385\) −17.1143 + 3.15306i −0.872223 + 0.160695i
\(386\) 1.88527 0.0959579
\(387\) 0.0178899i 0.000909395i
\(388\) 12.2566i 0.622237i
\(389\) 14.9010 + 14.9010i 0.755508 + 0.755508i 0.975501 0.219993i \(-0.0706035\pi\)
−0.219993 + 0.975501i \(0.570603\pi\)
\(390\) −1.06975 5.80642i −0.0541690 0.294020i
\(391\) 18.8827i 0.954939i
\(392\) 3.68685i 0.186214i
\(393\) 15.6244 0.788144
\(394\) 16.9005 16.9005i 0.851437 0.851437i
\(395\) 6.84376 1.26087i 0.344347 0.0634412i
\(396\) 0.252728 0.0127001
\(397\) −3.61759 3.61759i −0.181562 0.181562i 0.610474 0.792036i \(-0.290979\pi\)
−0.792036 + 0.610474i \(0.790979\pi\)
\(398\) −6.68597 + 6.68597i −0.335137 + 0.335137i
\(399\) 1.21601 1.21601i 0.0608765 0.0608765i
\(400\) −1.78188 4.67171i −0.0890939 0.233586i
\(401\) −12.9977 12.9977i −0.649075 0.649075i 0.303694 0.952770i \(-0.401780\pi\)
−0.952770 + 0.303694i \(0.901780\pi\)
\(402\) −15.2776 −0.761976
\(403\) 2.40529 + 2.40529i 0.119816 + 0.119816i
\(404\) 19.3052i 0.960470i
\(405\) −11.6369 + 16.8932i −0.578242 + 0.839428i
\(406\) 0.720516i 0.0357586i
\(407\) −9.76975 24.1029i −0.484269 1.19474i
\(408\) −2.62341 2.62341i −0.129878 0.129878i
\(409\) 1.73592 1.73592i 0.0858355 0.0858355i −0.662885 0.748721i \(-0.730668\pi\)
0.748721 + 0.662885i \(0.230668\pi\)
\(410\) −0.498816 0.343611i −0.0246348 0.0169697i
\(411\) 8.74779i 0.431497i
\(412\) 10.5846i 0.521466i
\(413\) −10.4680 −0.515095
\(414\) 0.526178i 0.0258603i
\(415\) −31.5053 + 5.80442i −1.54654 + 0.284928i
\(416\) 1.50964 0.0740164
\(417\) 7.06057 7.06057i 0.345758 0.345758i
\(418\) −1.63312 + 1.63312i −0.0798786 + 0.0798786i
\(419\) 16.7428i 0.817941i −0.912548 0.408970i \(-0.865888\pi\)
0.912548 0.408970i \(-0.134112\pi\)
\(420\) −5.86244 4.03835i −0.286058 0.197052i
\(421\) −0.463240 0.463240i −0.0225770 0.0225770i 0.695728 0.718305i \(-0.255082\pi\)
−0.718305 + 0.695728i \(0.755082\pi\)
\(422\) −16.4186 −0.799245
\(423\) 0.187950 + 0.187950i 0.00913846 + 0.00913846i
\(424\) −9.71066 9.71066i −0.471592 0.471592i
\(425\) −9.90970 + 3.77974i −0.480691 + 0.183345i
\(426\) −9.78029 + 9.78029i −0.473857 + 0.473857i
\(427\) 11.5091 0.556965
\(428\) 2.77915 2.77915i 0.134335 0.134335i
\(429\) 7.98284 + 7.98284i 0.385415 + 0.385415i
\(430\) 0.383920 0.557333i 0.0185143 0.0268770i
\(431\) −27.2475 27.2475i −1.31247 1.31247i −0.919591 0.392877i \(-0.871480\pi\)
−0.392877 0.919591i \(-0.628520\pi\)
\(432\) −3.63715 3.63715i −0.174993 0.174993i
\(433\) 17.1809 + 17.1809i 0.825660 + 0.825660i 0.986913 0.161253i \(-0.0515536\pi\)
−0.161253 + 0.986913i \(0.551554\pi\)
\(434\) 4.10137 0.196872
\(435\) −1.27491 0.878227i −0.0611274 0.0421078i
\(436\) 4.14598 + 4.14598i 0.198556 + 0.198556i
\(437\) 3.40015 + 3.40015i 0.162651 + 0.162651i
\(438\) 20.5930i 0.983973i
\(439\) 13.3023 13.3023i 0.634886 0.634886i −0.314404 0.949289i \(-0.601805\pi\)
0.949289 + 0.314404i \(0.101805\pi\)
\(440\) 7.87337 + 5.42359i 0.375348 + 0.258559i
\(441\) 0.217926 0.0103774
\(442\) 3.20228i 0.152317i
\(443\) 24.4725 24.4725i 1.16272 1.16272i 0.178845 0.983877i \(-0.442764\pi\)
0.983877 0.178845i \(-0.0572360\pi\)
\(444\) 4.14595 9.79786i 0.196758 0.464986i
\(445\) 3.00796 + 16.3267i 0.142591 + 0.773958i
\(446\) −13.7600 13.7600i −0.651554 0.651554i
\(447\) 9.11453 + 9.11453i 0.431102 + 0.431102i
\(448\) 1.28708 1.28708i 0.0608088 0.0608088i
\(449\) −20.4966 20.4966i −0.967296 0.967296i 0.0321863 0.999482i \(-0.489753\pi\)
−0.999482 + 0.0321863i \(0.989753\pi\)
\(450\) 0.276140 0.105325i 0.0130174 0.00496507i
\(451\) 1.15819 0.0545372
\(452\) 2.26739i 0.106649i
\(453\) −6.14380 6.14380i −0.288661 0.288661i
\(454\) 5.23067i 0.245488i
\(455\) −1.11329 6.04271i −0.0521916 0.283287i
\(456\) −0.944780 −0.0442434
\(457\) 25.3795i 1.18720i 0.804759 + 0.593601i \(0.202294\pi\)
−0.804759 + 0.593601i \(0.797706\pi\)
\(458\) 3.12544i 0.146042i
\(459\) −7.71517 + 7.71517i −0.360113 + 0.360113i
\(460\) 11.2919 16.3923i 0.526486 0.764295i
\(461\) −19.5684 + 19.5684i −0.911392 + 0.911392i −0.996382 0.0849894i \(-0.972914\pi\)
0.0849894 + 0.996382i \(0.472914\pi\)
\(462\) 13.6119 0.633283
\(463\) −40.3494 −1.87520 −0.937599 0.347720i \(-0.886956\pi\)
−0.937599 + 0.347720i \(0.886956\pi\)
\(464\) 0.279903 0.279903i 0.0129942 0.0129942i
\(465\) −4.99910 + 7.25714i −0.231828 + 0.336542i
\(466\) 7.43576 7.43576i 0.344455 0.344455i
\(467\) 6.84915i 0.316941i −0.987364 0.158471i \(-0.949344\pi\)
0.987364 0.158471i \(-0.0506563\pi\)
\(468\) 0.0892335i 0.00412482i
\(469\) −15.8993 −0.734161
\(470\) 1.82187 + 9.88875i 0.0840364 + 0.456134i
\(471\) 20.4900i 0.944129i
\(472\) 4.06655 + 4.06655i 0.187178 + 0.187178i
\(473\) 1.29406i 0.0595011i
\(474\) −5.44322 −0.250015
\(475\) −1.10380 + 2.46501i −0.0506459 + 0.113103i
\(476\) −2.73017 2.73017i −0.125137 0.125137i
\(477\) 0.573987 0.573987i 0.0262811 0.0262811i
\(478\) −19.2129 19.2129i −0.878779 0.878779i
\(479\) −30.4703 30.4703i −1.39222 1.39222i −0.820327 0.571895i \(-0.806208\pi\)
−0.571895 0.820327i \(-0.693792\pi\)
\(480\) 0.708613 + 3.84622i 0.0323436 + 0.175555i
\(481\) 8.51028 3.44951i 0.388035 0.157284i
\(482\) −19.0019 + 19.0019i −0.865513 + 0.865513i
\(483\) 28.3399i 1.28951i
\(484\) −7.28104 −0.330956
\(485\) −22.5700 15.5474i −1.02485 0.705971i
\(486\) 0.434298 0.434298i 0.0197001 0.0197001i
\(487\) 38.9294i 1.76406i 0.471194 + 0.882029i \(0.343823\pi\)
−0.471194 + 0.882029i \(0.656177\pi\)
\(488\) −4.47102 4.47102i −0.202393 0.202393i
\(489\) −23.8234 23.8234i −1.07733 1.07733i
\(490\) 6.78914 + 4.67672i 0.306702 + 0.211273i
\(491\) 8.64964 0.390353 0.195176 0.980768i \(-0.437472\pi\)
0.195176 + 0.980768i \(0.437472\pi\)
\(492\) 0.335014 + 0.335014i 0.0151036 + 0.0151036i
\(493\) −0.593735 0.593735i −0.0267405 0.0267405i
\(494\) −0.576624 0.576624i −0.0259435 0.0259435i
\(495\) −0.320583 + 0.465387i −0.0144091 + 0.0209176i
\(496\) −1.59328 1.59328i −0.0715405 0.0715405i
\(497\) −10.1783 + 10.1783i −0.456559 + 0.456559i
\(498\) 25.0579 1.12287
\(499\) −10.9240 + 10.9240i −0.489024 + 0.489024i −0.907998 0.418974i \(-0.862390\pi\)
0.418974 + 0.907998i \(0.362390\pi\)
\(500\) 10.8630 + 2.64477i 0.485809 + 0.118278i
\(501\) 27.6551 + 27.6551i 1.23554 + 1.23554i
\(502\) 2.56669 + 2.56669i 0.114557 + 0.114557i
\(503\) 37.0071 1.65007 0.825033 0.565085i \(-0.191157\pi\)
0.825033 + 0.565085i \(0.191157\pi\)
\(504\) 0.0760780 + 0.0760780i 0.00338878 + 0.00338878i
\(505\) −35.5496 24.4884i −1.58194 1.08972i
\(506\) 38.0610i 1.69202i
\(507\) 13.2592 13.2592i 0.588861 0.588861i
\(508\) −7.95386 + 7.95386i −0.352895 + 0.352895i
\(509\) 1.39333 0.0617583 0.0308791 0.999523i \(-0.490169\pi\)
0.0308791 + 0.999523i \(0.490169\pi\)
\(510\) 8.15865 1.50312i 0.361271 0.0665592i
\(511\) 21.4311i 0.948054i
\(512\) −1.00000 −0.0441942
\(513\) 2.77849i 0.122673i
\(514\) 13.8993i 0.613072i
\(515\) −19.4910 13.4264i −0.858877 0.591640i
\(516\) −0.374315 + 0.374315i −0.0164783 + 0.0164783i
\(517\) −13.5953 13.5953i −0.597923 0.597923i
\(518\) 4.31467 10.1966i 0.189576 0.448012i
\(519\) 15.9535i 0.700282i
\(520\) −1.91496 + 2.77993i −0.0839768 + 0.121908i
\(521\) 3.37437i 0.147834i 0.997264 + 0.0739169i \(0.0235500\pi\)
−0.997264 + 0.0739169i \(0.976450\pi\)
\(522\) 0.0165448 + 0.0165448i 0.000724146 + 0.000724146i
\(523\) −6.99302 −0.305783 −0.152892 0.988243i \(-0.548859\pi\)
−0.152892 + 0.988243i \(0.548859\pi\)
\(524\) −6.31669 6.31669i −0.275946 0.275946i
\(525\) 14.8729 5.67279i 0.649105 0.247581i
\(526\) −14.2273 + 14.2273i −0.620338 + 0.620338i
\(527\) −3.37969 + 3.37969i −0.147222 + 0.147222i
\(528\) −5.28790 5.28790i −0.230126 0.230126i
\(529\) 56.2427 2.44534
\(530\) 30.1996 5.56385i 1.31179 0.241678i
\(531\) −0.240370 + 0.240370i −0.0104312 + 0.0104312i
\(532\) −0.983227 −0.0426283
\(533\) 0.408936i 0.0177130i
\(534\) 12.9855i 0.561937i
\(535\) 1.59235 + 8.64297i 0.0688432 + 0.373668i
\(536\) 6.17649 + 6.17649i 0.266784 + 0.266784i
\(537\) 20.9004i 0.901920i
\(538\) 21.4303i 0.923927i
\(539\) −15.7636 −0.678986
\(540\) 11.3113 2.08395i 0.486762 0.0896790i
\(541\) 3.85792 3.85792i 0.165865 0.165865i −0.619294 0.785159i \(-0.712581\pi\)
0.785159 + 0.619294i \(0.212581\pi\)
\(542\) 17.5063 0.751962
\(543\) −2.01772 + 2.01772i −0.0865886 + 0.0865886i
\(544\) 2.12121i 0.0909463i
\(545\) −12.8937 + 2.37549i −0.552307 + 0.101755i
\(546\) 4.80610i 0.205682i
\(547\) −5.76769 −0.246609 −0.123304 0.992369i \(-0.539349\pi\)
−0.123304 + 0.992369i \(0.539349\pi\)
\(548\) −3.53660 + 3.53660i −0.151076 + 0.151076i
\(549\) 0.264277 0.264277i 0.0112791 0.0112791i
\(550\) −19.9745 + 7.61866i −0.851717 + 0.324861i
\(551\) −0.213824 −0.00910920
\(552\) −11.0094 + 11.0094i −0.468590 + 0.468590i
\(553\) −5.66473 −0.240889
\(554\) 9.92772 0.421788
\(555\) 12.7832 + 20.0630i 0.542616 + 0.851628i
\(556\) −5.70896 −0.242114
\(557\) −33.4435 −1.41705 −0.708524 0.705687i \(-0.750639\pi\)
−0.708524 + 0.705687i \(0.750639\pi\)
\(558\) 0.0941773 0.0941773i 0.00398684 0.00398684i
\(559\) −0.456909 −0.0193252
\(560\) 0.737449 + 4.00274i 0.0311629 + 0.169147i
\(561\) −11.2168 + 11.2168i −0.473572 + 0.473572i
\(562\) −9.25821 + 9.25821i −0.390534 + 0.390534i
\(563\) 14.9840 0.631500 0.315750 0.948842i \(-0.397744\pi\)
0.315750 + 0.948842i \(0.397744\pi\)
\(564\) 7.86507i 0.331179i
\(565\) 4.17529 + 2.87616i 0.175656 + 0.121001i
\(566\) 7.32826i 0.308030i
\(567\) 11.8075 11.8075i 0.495867 0.495867i
\(568\) 7.90805 0.331814
\(569\) 8.42505 8.42505i 0.353197 0.353197i −0.508101 0.861298i \(-0.669652\pi\)
0.861298 + 0.508101i \(0.169652\pi\)
\(570\) 1.19844 1.73976i 0.0501972 0.0728707i
\(571\) −22.3944 −0.937176 −0.468588 0.883417i \(-0.655237\pi\)
−0.468588 + 0.883417i \(0.655237\pi\)
\(572\) 6.45468i 0.269884i
\(573\) 35.5973i 1.48710i
\(574\) 0.348647 + 0.348647i 0.0145523 + 0.0145523i
\(575\) 15.8620 + 41.5868i 0.661491 + 1.73429i
\(576\) 0.0591090i 0.00246287i
\(577\) 15.1857i 0.632189i 0.948728 + 0.316094i \(0.102372\pi\)
−0.948728 + 0.316094i \(0.897628\pi\)
\(578\) −12.5005 −0.519950
\(579\) 2.33162 2.33162i 0.0968986 0.0968986i
\(580\) 0.160374 + 0.870482i 0.00665918 + 0.0361448i
\(581\) 26.0776 1.08188
\(582\) 15.1584 + 15.1584i 0.628337 + 0.628337i
\(583\) −41.5192 + 41.5192i −1.71955 + 1.71955i
\(584\) −8.32545 + 8.32545i −0.344510 + 0.344510i
\(585\) −0.164319 0.113192i −0.00679376 0.00467990i
\(586\) 12.6098 + 12.6098i 0.520908 + 0.520908i
\(587\) 36.1936 1.49387 0.746934 0.664898i \(-0.231525\pi\)
0.746934 + 0.664898i \(0.231525\pi\)
\(588\) −4.55971 4.55971i −0.188039 0.188039i
\(589\) 1.21714i 0.0501514i
\(590\) −12.6467 + 2.32998i −0.520657 + 0.0959239i
\(591\) 41.8036i 1.71957i
\(592\) −5.63727 + 2.28498i −0.231691 + 0.0939122i
\(593\) 28.1253 + 28.1253i 1.15497 + 1.15497i 0.985543 + 0.169424i \(0.0541906\pi\)
0.169424 + 0.985543i \(0.445809\pi\)
\(594\) −15.5511 + 15.5511i −0.638070 + 0.638070i
\(595\) 8.49067 1.56429i 0.348083 0.0641295i
\(596\) 7.36973i 0.301876i
\(597\) 16.5378i 0.676846i
\(598\) −13.4386 −0.549545
\(599\) 8.68551i 0.354880i 0.984132 + 0.177440i \(0.0567816\pi\)
−0.984132 + 0.177440i \(0.943218\pi\)
\(600\) −7.98149 3.57401i −0.325843 0.145908i
\(601\) −17.1654 −0.700191 −0.350095 0.936714i \(-0.613851\pi\)
−0.350095 + 0.936714i \(0.613851\pi\)
\(602\) −0.389548 + 0.389548i −0.0158768 + 0.0158768i
\(603\) −0.365086 + 0.365086i −0.0148674 + 0.0148674i
\(604\) 4.96769i 0.202132i
\(605\) 9.23591 13.4077i 0.375493 0.545100i
\(606\) 23.8758 + 23.8758i 0.969886 + 0.969886i
\(607\) 40.1612 1.63009 0.815047 0.579395i \(-0.196711\pi\)
0.815047 + 0.579395i \(0.196711\pi\)
\(608\) 0.381960 + 0.381960i 0.0154905 + 0.0154905i
\(609\) 0.891100 + 0.891100i 0.0361092 + 0.0361092i
\(610\) 13.9046 2.56173i 0.562980 0.103721i
\(611\) 4.80026 4.80026i 0.194198 0.194198i
\(612\) −0.125383 −0.00506830
\(613\) −12.5774 + 12.5774i −0.507997 + 0.507997i −0.913911 0.405914i \(-0.866953\pi\)
0.405914 + 0.913911i \(0.366953\pi\)
\(614\) −17.0291 17.0291i −0.687239 0.687239i
\(615\) −1.04187 + 0.191951i −0.0420124 + 0.00774019i
\(616\) −5.50309 5.50309i −0.221726 0.221726i
\(617\) −33.9984 33.9984i −1.36872 1.36872i −0.862264 0.506459i \(-0.830954\pi\)
−0.506459 0.862264i \(-0.669046\pi\)
\(618\) 13.0905 + 13.0905i 0.526578 + 0.526578i
\(619\) −5.28421 −0.212390 −0.106195 0.994345i \(-0.533867\pi\)
−0.106195 + 0.994345i \(0.533867\pi\)
\(620\) 4.95501 0.912892i 0.198998 0.0366626i
\(621\) 32.3773 + 32.3773i 1.29926 + 1.29926i
\(622\) −3.74670 3.74670i −0.150229 0.150229i
\(623\) 13.5139i 0.541424i
\(624\) 1.86705 1.86705i 0.0747420 0.0747420i
\(625\) −18.6498 + 16.6489i −0.745993 + 0.665954i
\(626\) −14.7056 −0.587753
\(627\) 4.03953i 0.161323i
\(628\) 8.28379 8.28379i 0.330559 0.330559i
\(629\) 4.84694 + 11.9579i 0.193260 + 0.476791i
\(630\) −0.236598 + 0.0435899i −0.00942628 + 0.00173666i
\(631\) −5.35861 5.35861i −0.213323 0.213323i 0.592355 0.805677i \(-0.298198\pi\)
−0.805677 + 0.592355i \(0.798198\pi\)
\(632\) 2.20061 + 2.20061i 0.0875356 + 0.0875356i
\(633\) −20.3057 + 20.3057i −0.807080 + 0.807080i
\(634\) −13.6458 13.6458i −0.541943 0.541943i
\(635\) −4.55726 24.7360i −0.180849 0.981618i
\(636\) −24.0194 −0.952430
\(637\) 5.56582i 0.220526i
\(638\) −1.19676 1.19676i −0.0473803 0.0473803i
\(639\) 0.467437i 0.0184915i
\(640\) 1.26849 1.84145i 0.0501414 0.0727897i
\(641\) 24.0958 0.951727 0.475864 0.879519i \(-0.342136\pi\)
0.475864 + 0.879519i \(0.342136\pi\)
\(642\) 6.87423i 0.271304i
\(643\) 6.55586i 0.258538i 0.991610 + 0.129269i \(0.0412631\pi\)
−0.991610 + 0.129269i \(0.958737\pi\)
\(644\) −11.4574 + 11.4574i −0.451484 + 0.451484i
\(645\) −0.214469 1.16410i −0.00844469 0.0458363i
\(646\) 0.810219 0.810219i 0.0318776 0.0318776i
\(647\) −6.75259 −0.265472 −0.132736 0.991151i \(-0.542376\pi\)
−0.132736 + 0.991151i \(0.542376\pi\)
\(648\) −9.17383 −0.360382
\(649\) 17.3871 17.3871i 0.682503 0.682503i
\(650\) −2.69000 7.05262i −0.105511 0.276627i
\(651\) 5.07237 5.07237i 0.198802 0.198802i
\(652\) 19.2629i 0.754394i
\(653\) 18.5694i 0.726675i −0.931658 0.363338i \(-0.881637\pi\)
0.931658 0.363338i \(-0.118363\pi\)
\(654\) 10.2551 0.401006
\(655\) 19.6445 3.61923i 0.767575 0.141415i
\(656\) 0.270882i 0.0105762i
\(657\) −0.492109 0.492109i −0.0191990 0.0191990i
\(658\) 8.18513i 0.319090i
\(659\) 29.5588 1.15145 0.575724 0.817644i \(-0.304720\pi\)
0.575724 + 0.817644i \(0.304720\pi\)
\(660\) 16.4450 3.02977i 0.640122 0.117934i
\(661\) −35.1268 35.1268i −1.36627 1.36627i −0.865686 0.500587i \(-0.833118\pi\)
−0.500587 0.865686i \(-0.666882\pi\)
\(662\) 15.5423 15.5423i 0.604067 0.604067i
\(663\) −3.96042 3.96042i −0.153810 0.153810i
\(664\) −10.1305 10.1305i −0.393141 0.393141i
\(665\) 1.24721 1.81056i 0.0483648 0.0702106i
\(666\) −0.135063 0.333213i −0.00523358 0.0129118i
\(667\) −2.49165 + 2.49165i −0.0964772 + 0.0964772i
\(668\) 22.3611i 0.865178i
\(669\) −34.0353 −1.31588
\(670\) −19.2085 + 3.53890i −0.742089 + 0.136720i
\(671\) −19.1164 + 19.1164i −0.737982 + 0.737982i
\(672\) 3.18360i 0.122810i
\(673\) −1.64758 1.64758i −0.0635097 0.0635097i 0.674639 0.738148i \(-0.264300\pi\)
−0.738148 + 0.674639i \(0.764300\pi\)
\(674\) −14.8294 14.8294i −0.571209 0.571209i
\(675\) −10.5108 + 23.4727i −0.404560 + 0.903464i
\(676\) −10.7210 −0.412345
\(677\) −18.6418 18.6418i −0.716461 0.716461i 0.251417 0.967879i \(-0.419103\pi\)
−0.967879 + 0.251417i \(0.919103\pi\)
\(678\) −2.80420 2.80420i −0.107695 0.107695i
\(679\) 15.7753 + 15.7753i 0.605400 + 0.605400i
\(680\) −3.90611 2.69073i −0.149792 0.103185i
\(681\) 6.46904 + 6.46904i 0.247894 + 0.247894i
\(682\) −6.81229 + 6.81229i −0.260856 + 0.260856i
\(683\) 21.7547 0.832421 0.416210 0.909268i \(-0.363358\pi\)
0.416210 + 0.909268i \(0.363358\pi\)
\(684\) −0.0225773 + 0.0225773i −0.000863263 + 0.000863263i
\(685\) −2.02634 10.9986i −0.0774225 0.420235i
\(686\) −13.7548 13.7548i −0.525162 0.525162i
\(687\) 3.86539 + 3.86539i 0.147474 + 0.147474i
\(688\) 0.302660 0.0115388
\(689\) −14.6596 14.6596i −0.558488 0.558488i
\(690\) −6.30795 34.2384i −0.240140 1.30343i
\(691\) 10.1836i 0.387401i −0.981061 0.193700i \(-0.937951\pi\)
0.981061 0.193700i \(-0.0620490\pi\)
\(692\) −6.44977 + 6.44977i −0.245183 + 0.245183i
\(693\) 0.325282 0.325282i 0.0123564 0.0123564i
\(694\) 8.24738 0.313066
\(695\) 7.24175 10.5128i 0.274695 0.398772i
\(696\) 0.692342i 0.0262431i
\(697\) −0.574599 −0.0217645
\(698\) 16.1967i 0.613056i
\(699\) 18.3924i 0.695663i
\(700\) −8.30629 3.71945i −0.313948 0.140582i
\(701\) 10.1893 10.1893i 0.384844 0.384844i −0.488000 0.872844i \(-0.662273\pi\)
0.872844 + 0.488000i \(0.162273\pi\)
\(702\) −5.49080 5.49080i −0.207237 0.207237i
\(703\) 3.02599 + 1.28044i 0.114127 + 0.0482927i
\(704\) 4.27563i 0.161144i
\(705\) 14.4831 + 9.97674i 0.545466 + 0.375746i
\(706\) 20.3765i 0.766880i
\(707\) 24.8474 + 24.8474i 0.934481 + 0.934481i
\(708\) 10.0586 0.378026
\(709\) 35.9766 + 35.9766i 1.35113 + 1.35113i 0.884402 + 0.466725i \(0.154566\pi\)
0.466725 + 0.884402i \(0.345434\pi\)
\(710\) −10.0313 + 14.5623i −0.376467 + 0.546513i
\(711\) −0.130076 + 0.130076i −0.00487822 + 0.00487822i
\(712\) −5.24983 + 5.24983i −0.196746 + 0.196746i
\(713\) 14.1831 + 14.1831i 0.531163 + 0.531163i
\(714\) −6.75309 −0.252728
\(715\) 11.8860 + 8.18769i 0.444510 + 0.306202i
\(716\) −8.44973 + 8.44973i −0.315781 + 0.315781i
\(717\) −47.5233 −1.77479
\(718\) 30.2708i 1.12970i
\(719\) 10.7340i 0.400310i −0.979764 0.200155i \(-0.935855\pi\)
0.979764 0.200155i \(-0.0641446\pi\)
\(720\) 0.108846 + 0.0749790i 0.00405646 + 0.00279430i
\(721\) 13.6232 + 13.6232i 0.507356 + 0.507356i
\(722\) 18.7082i 0.696248i
\(723\) 47.0013i 1.74800i
\(724\) 1.63147 0.0606330
\(725\) −1.80638 0.808875i −0.0670873 0.0300408i
\(726\) −9.00484 + 9.00484i −0.334201 + 0.334201i
\(727\) −14.6699 −0.544078 −0.272039 0.962286i \(-0.587698\pi\)
−0.272039 + 0.962286i \(0.587698\pi\)
\(728\) 1.94303 1.94303i 0.0720136 0.0720136i
\(729\) 26.4473i 0.979528i
\(730\) −4.77017 25.8916i −0.176552 0.958292i
\(731\) 0.642006i 0.0237455i
\(732\) −11.0591 −0.408755
\(733\) −22.2345 + 22.2345i −0.821249 + 0.821249i −0.986287 0.165039i \(-0.947225\pi\)
0.165039 + 0.986287i \(0.447225\pi\)
\(734\) −13.0615 + 13.0615i −0.482108 + 0.482108i
\(735\) 14.1804 2.61255i 0.523053 0.0963652i
\(736\) 8.90184 0.328126
\(737\) 26.4084 26.4084i 0.972766 0.972766i
\(738\) 0.0160116 0.000589394
\(739\) −4.21587 −0.155083 −0.0775416 0.996989i \(-0.524707\pi\)
−0.0775416 + 0.996989i \(0.524707\pi\)
\(740\) 2.94313 13.2792i 0.108192 0.488154i
\(741\) −1.42628 −0.0523957
\(742\) −24.9968 −0.917662
\(743\) 0.649329 0.649329i 0.0238216 0.0238216i −0.695096 0.718917i \(-0.744638\pi\)
0.718917 + 0.695096i \(0.244638\pi\)
\(744\) −3.94099 −0.144484
\(745\) 13.5710 + 9.34842i 0.497203 + 0.342499i
\(746\) 16.1154 16.1154i 0.590026 0.590026i
\(747\) 0.598806 0.598806i 0.0219091 0.0219091i
\(748\) 9.06953 0.331615
\(749\) 7.15397i 0.261400i
\(750\) 16.7058 10.1639i 0.610009 0.371134i
\(751\) 25.7790i 0.940688i −0.882483 0.470344i \(-0.844130\pi\)
0.882483 0.470344i \(-0.155870\pi\)
\(752\) −3.17973 + 3.17973i −0.115953 + 0.115953i
\(753\) 6.34872 0.231360
\(754\) 0.422554 0.422554i 0.0153885 0.0153885i
\(755\) −9.14775 6.30145i −0.332921 0.229333i
\(756\) −9.36262 −0.340515
\(757\) 15.9640i 0.580222i −0.956993 0.290111i \(-0.906308\pi\)
0.956993 0.290111i \(-0.0936923\pi\)
\(758\) 7.07736i 0.257061i
\(759\) 47.0720 + 47.0720i 1.70861 + 1.70861i
\(760\) −1.18787 + 0.218849i −0.0430887 + 0.00793848i
\(761\) 28.4393i 1.03092i 0.856912 + 0.515462i \(0.172380\pi\)
−0.856912 + 0.515462i \(0.827620\pi\)
\(762\) 19.6739i 0.712710i
\(763\) 10.6724 0.386368
\(764\) −14.3915 + 14.3915i −0.520664 + 0.520664i
\(765\) 0.159046 0.230886i 0.00575033 0.00834770i
\(766\) 17.6507 0.637747
\(767\) 6.13905 + 6.13905i 0.221668 + 0.221668i
\(768\) −1.23675 + 1.23675i −0.0446274 + 0.0446274i
\(769\) 21.9651 21.9651i 0.792083 0.792083i −0.189749 0.981833i \(-0.560768\pi\)
0.981833 + 0.189749i \(0.0607675\pi\)
\(770\) 17.1143 3.15306i 0.616755 0.113629i
\(771\) −17.1900 17.1900i −0.619082 0.619082i
\(772\) −1.88527 −0.0678525
\(773\) 2.60816 + 2.60816i 0.0938089 + 0.0938089i 0.752454 0.658645i \(-0.228870\pi\)
−0.658645 + 0.752454i \(0.728870\pi\)
\(774\) 0.0178899i 0.000643040i
\(775\) −4.60433 + 10.2824i −0.165392 + 0.369355i
\(776\) 12.2566i 0.439988i
\(777\) −7.27447 17.9468i −0.260970 0.643838i