Properties

Label 462.2.g.a.419.4
Level $462$
Weight $2$
Character 462.419
Analytic conductor $3.689$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 419.4
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 462.419
Dual form 462.2.g.a.419.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +1.23607 q^{5} +(-1.61803 + 0.618034i) q^{6} +(2.61803 - 0.381966i) q^{7} -1.00000i q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +1.23607 q^{5} +(-1.61803 + 0.618034i) q^{6} +(2.61803 - 0.381966i) q^{7} -1.00000i q^{8} +(-2.23607 + 2.00000i) q^{9} +1.23607i q^{10} -1.00000i q^{11} +(-0.618034 - 1.61803i) q^{12} +6.00000i q^{13} +(0.381966 + 2.61803i) q^{14} +(0.763932 + 2.00000i) q^{15} +1.00000 q^{16} +2.76393 q^{17} +(-2.00000 - 2.23607i) q^{18} +2.00000i q^{19} -1.23607 q^{20} +(2.23607 + 4.00000i) q^{21} +1.00000 q^{22} -3.23607i q^{23} +(1.61803 - 0.618034i) q^{24} -3.47214 q^{25} -6.00000 q^{26} +(-4.61803 - 2.38197i) q^{27} +(-2.61803 + 0.381966i) q^{28} -8.47214i q^{29} +(-2.00000 + 0.763932i) q^{30} +5.23607i q^{31} +1.00000i q^{32} +(1.61803 - 0.618034i) q^{33} +2.76393i q^{34} +(3.23607 - 0.472136i) q^{35} +(2.23607 - 2.00000i) q^{36} +4.47214 q^{37} -2.00000 q^{38} +(-9.70820 + 3.70820i) q^{39} -1.23607i q^{40} -10.1803 q^{41} +(-4.00000 + 2.23607i) q^{42} -6.94427 q^{43} +1.00000i q^{44} +(-2.76393 + 2.47214i) q^{45} +3.23607 q^{46} +10.4721 q^{47} +(0.618034 + 1.61803i) q^{48} +(6.70820 - 2.00000i) q^{49} -3.47214i q^{50} +(1.70820 + 4.47214i) q^{51} -6.00000i q^{52} -5.70820i q^{53} +(2.38197 - 4.61803i) q^{54} -1.23607i q^{55} +(-0.381966 - 2.61803i) q^{56} +(-3.23607 + 1.23607i) q^{57} +8.47214 q^{58} -1.23607 q^{59} +(-0.763932 - 2.00000i) q^{60} -12.4721i q^{61} -5.23607 q^{62} +(-5.09017 + 6.09017i) q^{63} -1.00000 q^{64} +7.41641i q^{65} +(0.618034 + 1.61803i) q^{66} +10.4721 q^{67} -2.76393 q^{68} +(5.23607 - 2.00000i) q^{69} +(0.472136 + 3.23607i) q^{70} +16.1803i q^{71} +(2.00000 + 2.23607i) q^{72} -8.18034i q^{73} +4.47214i q^{74} +(-2.14590 - 5.61803i) q^{75} -2.00000i q^{76} +(-0.381966 - 2.61803i) q^{77} +(-3.70820 - 9.70820i) q^{78} +2.76393 q^{79} +1.23607 q^{80} +(1.00000 - 8.94427i) q^{81} -10.1803i q^{82} +6.00000 q^{83} +(-2.23607 - 4.00000i) q^{84} +3.41641 q^{85} -6.94427i q^{86} +(13.7082 - 5.23607i) q^{87} -1.00000 q^{88} +4.94427 q^{89} +(-2.47214 - 2.76393i) q^{90} +(2.29180 + 15.7082i) q^{91} +3.23607i q^{92} +(-8.47214 + 3.23607i) q^{93} +10.4721i q^{94} +2.47214i q^{95} +(-1.61803 + 0.618034i) q^{96} +6.47214i q^{97} +(2.00000 + 6.70820i) q^{98} +(2.00000 + 2.23607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 4q^{4} - 4q^{5} - 2q^{6} + 6q^{7} + O(q^{10}) \) \( 4q - 2q^{3} - 4q^{4} - 4q^{5} - 2q^{6} + 6q^{7} + 2q^{12} + 6q^{14} + 12q^{15} + 4q^{16} + 20q^{17} - 8q^{18} + 4q^{20} + 4q^{22} + 2q^{24} + 4q^{25} - 24q^{26} - 14q^{27} - 6q^{28} - 8q^{30} + 2q^{33} + 4q^{35} - 8q^{38} - 12q^{39} + 4q^{41} - 16q^{42} + 8q^{43} - 20q^{45} + 4q^{46} + 24q^{47} - 2q^{48} - 20q^{51} + 14q^{54} - 6q^{56} - 4q^{57} + 16q^{58} + 4q^{59} - 12q^{60} - 12q^{62} + 2q^{63} - 4q^{64} - 2q^{66} + 24q^{67} - 20q^{68} + 12q^{69} - 16q^{70} + 8q^{72} - 22q^{75} - 6q^{77} + 12q^{78} + 20q^{79} - 4q^{80} + 4q^{81} + 24q^{83} - 40q^{85} + 28q^{87} - 4q^{88} - 16q^{89} + 8q^{90} + 36q^{91} - 16q^{93} - 2q^{96} + 8q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.618034 + 1.61803i 0.356822 + 0.934172i
\(4\) −1.00000 −0.500000
\(5\) 1.23607 0.552786 0.276393 0.961045i \(-0.410861\pi\)
0.276393 + 0.961045i \(0.410861\pi\)
\(6\) −1.61803 + 0.618034i −0.660560 + 0.252311i
\(7\) 2.61803 0.381966i 0.989524 0.144370i
\(8\) 1.00000i 0.353553i
\(9\) −2.23607 + 2.00000i −0.745356 + 0.666667i
\(10\) 1.23607i 0.390879i
\(11\) 1.00000i 0.301511i
\(12\) −0.618034 1.61803i −0.178411 0.467086i
\(13\) 6.00000i 1.66410i 0.554700 + 0.832050i \(0.312833\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0.381966 + 2.61803i 0.102085 + 0.699699i
\(15\) 0.763932 + 2.00000i 0.197246 + 0.516398i
\(16\) 1.00000 0.250000
\(17\) 2.76393 0.670352 0.335176 0.942156i \(-0.391204\pi\)
0.335176 + 0.942156i \(0.391204\pi\)
\(18\) −2.00000 2.23607i −0.471405 0.527046i
\(19\) 2.00000i 0.458831i 0.973329 + 0.229416i \(0.0736815\pi\)
−0.973329 + 0.229416i \(0.926318\pi\)
\(20\) −1.23607 −0.276393
\(21\) 2.23607 + 4.00000i 0.487950 + 0.872872i
\(22\) 1.00000 0.213201
\(23\) 3.23607i 0.674767i −0.941367 0.337383i \(-0.890458\pi\)
0.941367 0.337383i \(-0.109542\pi\)
\(24\) 1.61803 0.618034i 0.330280 0.126156i
\(25\) −3.47214 −0.694427
\(26\) −6.00000 −1.17670
\(27\) −4.61803 2.38197i −0.888741 0.458410i
\(28\) −2.61803 + 0.381966i −0.494762 + 0.0721848i
\(29\) 8.47214i 1.57324i −0.617440 0.786618i \(-0.711830\pi\)
0.617440 0.786618i \(-0.288170\pi\)
\(30\) −2.00000 + 0.763932i −0.365148 + 0.139474i
\(31\) 5.23607i 0.940426i 0.882553 + 0.470213i \(0.155823\pi\)
−0.882553 + 0.470213i \(0.844177\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.61803 0.618034i 0.281664 0.107586i
\(34\) 2.76393i 0.474010i
\(35\) 3.23607 0.472136i 0.546995 0.0798055i
\(36\) 2.23607 2.00000i 0.372678 0.333333i
\(37\) 4.47214 0.735215 0.367607 0.929981i \(-0.380177\pi\)
0.367607 + 0.929981i \(0.380177\pi\)
\(38\) −2.00000 −0.324443
\(39\) −9.70820 + 3.70820i −1.55456 + 0.593788i
\(40\) 1.23607i 0.195440i
\(41\) −10.1803 −1.58990 −0.794951 0.606674i \(-0.792503\pi\)
−0.794951 + 0.606674i \(0.792503\pi\)
\(42\) −4.00000 + 2.23607i −0.617213 + 0.345033i
\(43\) −6.94427 −1.05899 −0.529496 0.848313i \(-0.677619\pi\)
−0.529496 + 0.848313i \(0.677619\pi\)
\(44\) 1.00000i 0.150756i
\(45\) −2.76393 + 2.47214i −0.412023 + 0.368524i
\(46\) 3.23607 0.477132
\(47\) 10.4721 1.52752 0.763759 0.645501i \(-0.223352\pi\)
0.763759 + 0.645501i \(0.223352\pi\)
\(48\) 0.618034 + 1.61803i 0.0892055 + 0.233543i
\(49\) 6.70820 2.00000i 0.958315 0.285714i
\(50\) 3.47214i 0.491034i
\(51\) 1.70820 + 4.47214i 0.239196 + 0.626224i
\(52\) 6.00000i 0.832050i
\(53\) 5.70820i 0.784082i −0.919948 0.392041i \(-0.871769\pi\)
0.919948 0.392041i \(-0.128231\pi\)
\(54\) 2.38197 4.61803i 0.324145 0.628435i
\(55\) 1.23607i 0.166671i
\(56\) −0.381966 2.61803i −0.0510424 0.349850i
\(57\) −3.23607 + 1.23607i −0.428628 + 0.163721i
\(58\) 8.47214 1.11245
\(59\) −1.23607 −0.160922 −0.0804612 0.996758i \(-0.525639\pi\)
−0.0804612 + 0.996758i \(0.525639\pi\)
\(60\) −0.763932 2.00000i −0.0986232 0.258199i
\(61\) 12.4721i 1.59689i −0.602066 0.798447i \(-0.705655\pi\)
0.602066 0.798447i \(-0.294345\pi\)
\(62\) −5.23607 −0.664981
\(63\) −5.09017 + 6.09017i −0.641301 + 0.767289i
\(64\) −1.00000 −0.125000
\(65\) 7.41641i 0.919892i
\(66\) 0.618034 + 1.61803i 0.0760747 + 0.199166i
\(67\) 10.4721 1.27938 0.639688 0.768635i \(-0.279064\pi\)
0.639688 + 0.768635i \(0.279064\pi\)
\(68\) −2.76393 −0.335176
\(69\) 5.23607 2.00000i 0.630349 0.240772i
\(70\) 0.472136 + 3.23607i 0.0564310 + 0.386784i
\(71\) 16.1803i 1.92025i 0.279566 + 0.960127i \(0.409809\pi\)
−0.279566 + 0.960127i \(0.590191\pi\)
\(72\) 2.00000 + 2.23607i 0.235702 + 0.263523i
\(73\) 8.18034i 0.957436i −0.877969 0.478718i \(-0.841102\pi\)
0.877969 0.478718i \(-0.158898\pi\)
\(74\) 4.47214i 0.519875i
\(75\) −2.14590 5.61803i −0.247787 0.648715i
\(76\) 2.00000i 0.229416i
\(77\) −0.381966 2.61803i −0.0435291 0.298353i
\(78\) −3.70820 9.70820i −0.419871 1.09924i
\(79\) 2.76393 0.310967 0.155483 0.987839i \(-0.450307\pi\)
0.155483 + 0.987839i \(0.450307\pi\)
\(80\) 1.23607 0.138197
\(81\) 1.00000 8.94427i 0.111111 0.993808i
\(82\) 10.1803i 1.12423i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −2.23607 4.00000i −0.243975 0.436436i
\(85\) 3.41641 0.370561
\(86\) 6.94427i 0.748820i
\(87\) 13.7082 5.23607i 1.46967 0.561365i
\(88\) −1.00000 −0.106600
\(89\) 4.94427 0.524092 0.262046 0.965055i \(-0.415603\pi\)
0.262046 + 0.965055i \(0.415603\pi\)
\(90\) −2.47214 2.76393i −0.260586 0.291344i
\(91\) 2.29180 + 15.7082i 0.240246 + 1.64667i
\(92\) 3.23607i 0.337383i
\(93\) −8.47214 + 3.23607i −0.878520 + 0.335565i
\(94\) 10.4721i 1.08012i
\(95\) 2.47214i 0.253636i
\(96\) −1.61803 + 0.618034i −0.165140 + 0.0630778i
\(97\) 6.47214i 0.657146i 0.944479 + 0.328573i \(0.106568\pi\)
−0.944479 + 0.328573i \(0.893432\pi\)
\(98\) 2.00000 + 6.70820i 0.202031 + 0.677631i
\(99\) 2.00000 + 2.23607i 0.201008 + 0.224733i
\(100\) 3.47214 0.347214
\(101\) −11.2361 −1.11803 −0.559015 0.829157i \(-0.688821\pi\)
−0.559015 + 0.829157i \(0.688821\pi\)
\(102\) −4.47214 + 1.70820i −0.442807 + 0.169137i
\(103\) 3.70820i 0.365380i −0.983171 0.182690i \(-0.941520\pi\)
0.983171 0.182690i \(-0.0584805\pi\)
\(104\) 6.00000 0.588348
\(105\) 2.76393 + 4.94427i 0.269732 + 0.482512i
\(106\) 5.70820 0.554430
\(107\) 8.94427i 0.864675i −0.901712 0.432338i \(-0.857689\pi\)
0.901712 0.432338i \(-0.142311\pi\)
\(108\) 4.61803 + 2.38197i 0.444371 + 0.229205i
\(109\) 13.2361 1.26779 0.633893 0.773421i \(-0.281456\pi\)
0.633893 + 0.773421i \(0.281456\pi\)
\(110\) 1.23607 0.117854
\(111\) 2.76393 + 7.23607i 0.262341 + 0.686817i
\(112\) 2.61803 0.381966i 0.247381 0.0360924i
\(113\) 8.00000i 0.752577i −0.926503 0.376288i \(-0.877200\pi\)
0.926503 0.376288i \(-0.122800\pi\)
\(114\) −1.23607 3.23607i −0.115768 0.303086i
\(115\) 4.00000i 0.373002i
\(116\) 8.47214i 0.786618i
\(117\) −12.0000 13.4164i −1.10940 1.24035i
\(118\) 1.23607i 0.113789i
\(119\) 7.23607 1.05573i 0.663329 0.0967784i
\(120\) 2.00000 0.763932i 0.182574 0.0697371i
\(121\) −1.00000 −0.0909091
\(122\) 12.4721 1.12917
\(123\) −6.29180 16.4721i −0.567312 1.48524i
\(124\) 5.23607i 0.470213i
\(125\) −10.4721 −0.936656
\(126\) −6.09017 5.09017i −0.542555 0.453468i
\(127\) −4.29180 −0.380835 −0.190418 0.981703i \(-0.560984\pi\)
−0.190418 + 0.981703i \(0.560984\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.29180 11.2361i −0.377872 0.989281i
\(130\) −7.41641 −0.650462
\(131\) 17.4164 1.52168 0.760839 0.648940i \(-0.224788\pi\)
0.760839 + 0.648940i \(0.224788\pi\)
\(132\) −1.61803 + 0.618034i −0.140832 + 0.0537930i
\(133\) 0.763932 + 5.23607i 0.0662413 + 0.454025i
\(134\) 10.4721i 0.904655i
\(135\) −5.70820 2.94427i −0.491284 0.253403i
\(136\) 2.76393i 0.237005i
\(137\) 2.47214i 0.211209i −0.994408 0.105604i \(-0.966322\pi\)
0.994408 0.105604i \(-0.0336777\pi\)
\(138\) 2.00000 + 5.23607i 0.170251 + 0.445724i
\(139\) 10.0000i 0.848189i −0.905618 0.424094i \(-0.860592\pi\)
0.905618 0.424094i \(-0.139408\pi\)
\(140\) −3.23607 + 0.472136i −0.273498 + 0.0399028i
\(141\) 6.47214 + 16.9443i 0.545052 + 1.42697i
\(142\) −16.1803 −1.35782
\(143\) 6.00000 0.501745
\(144\) −2.23607 + 2.00000i −0.186339 + 0.166667i
\(145\) 10.4721i 0.869664i
\(146\) 8.18034 0.677010
\(147\) 7.38197 + 9.61803i 0.608854 + 0.793282i
\(148\) −4.47214 −0.367607
\(149\) 2.00000i 0.163846i −0.996639 0.0819232i \(-0.973894\pi\)
0.996639 0.0819232i \(-0.0261062\pi\)
\(150\) 5.61803 2.14590i 0.458711 0.175212i
\(151\) −10.1803 −0.828464 −0.414232 0.910171i \(-0.635950\pi\)
−0.414232 + 0.910171i \(0.635950\pi\)
\(152\) 2.00000 0.162221
\(153\) −6.18034 + 5.52786i −0.499651 + 0.446901i
\(154\) 2.61803 0.381966i 0.210967 0.0307797i
\(155\) 6.47214i 0.519854i
\(156\) 9.70820 3.70820i 0.777278 0.296894i
\(157\) 13.4164i 1.07075i −0.844616 0.535373i \(-0.820171\pi\)
0.844616 0.535373i \(-0.179829\pi\)
\(158\) 2.76393i 0.219887i
\(159\) 9.23607 3.52786i 0.732468 0.279778i
\(160\) 1.23607i 0.0977198i
\(161\) −1.23607 8.47214i −0.0974158 0.667698i
\(162\) 8.94427 + 1.00000i 0.702728 + 0.0785674i
\(163\) 9.52786 0.746280 0.373140 0.927775i \(-0.378281\pi\)
0.373140 + 0.927775i \(0.378281\pi\)
\(164\) 10.1803 0.794951
\(165\) 2.00000 0.763932i 0.155700 0.0594720i
\(166\) 6.00000i 0.465690i
\(167\) −21.8885 −1.69379 −0.846893 0.531763i \(-0.821530\pi\)
−0.846893 + 0.531763i \(0.821530\pi\)
\(168\) 4.00000 2.23607i 0.308607 0.172516i
\(169\) −23.0000 −1.76923
\(170\) 3.41641i 0.262027i
\(171\) −4.00000 4.47214i −0.305888 0.341993i
\(172\) 6.94427 0.529496
\(173\) −5.70820 −0.433987 −0.216993 0.976173i \(-0.569625\pi\)
−0.216993 + 0.976173i \(0.569625\pi\)
\(174\) 5.23607 + 13.7082i 0.396945 + 1.03922i
\(175\) −9.09017 + 1.32624i −0.687152 + 0.100254i
\(176\) 1.00000i 0.0753778i
\(177\) −0.763932 2.00000i −0.0574206 0.150329i
\(178\) 4.94427i 0.370589i
\(179\) 4.94427i 0.369552i 0.982781 + 0.184776i \(0.0591560\pi\)
−0.982781 + 0.184776i \(0.940844\pi\)
\(180\) 2.76393 2.47214i 0.206011 0.184262i
\(181\) 12.4721i 0.927047i 0.886085 + 0.463523i \(0.153415\pi\)
−0.886085 + 0.463523i \(0.846585\pi\)
\(182\) −15.7082 + 2.29180i −1.16437 + 0.169879i
\(183\) 20.1803 7.70820i 1.49177 0.569807i
\(184\) −3.23607 −0.238566
\(185\) 5.52786 0.406417
\(186\) −3.23607 8.47214i −0.237280 0.621207i
\(187\) 2.76393i 0.202119i
\(188\) −10.4721 −0.763759
\(189\) −13.0000 4.47214i −0.945611 0.325300i
\(190\) −2.47214 −0.179348
\(191\) 1.70820i 0.123601i −0.998089 0.0618006i \(-0.980316\pi\)
0.998089 0.0618006i \(-0.0196843\pi\)
\(192\) −0.618034 1.61803i −0.0446028 0.116772i
\(193\) 14.9443 1.07571 0.537856 0.843037i \(-0.319234\pi\)
0.537856 + 0.843037i \(0.319234\pi\)
\(194\) −6.47214 −0.464672
\(195\) −12.0000 + 4.58359i −0.859338 + 0.328238i
\(196\) −6.70820 + 2.00000i −0.479157 + 0.142857i
\(197\) 2.94427i 0.209771i −0.994484 0.104885i \(-0.966552\pi\)
0.994484 0.104885i \(-0.0334476\pi\)
\(198\) −2.23607 + 2.00000i −0.158910 + 0.142134i
\(199\) 2.18034i 0.154560i −0.997009 0.0772801i \(-0.975376\pi\)
0.997009 0.0772801i \(-0.0246236\pi\)
\(200\) 3.47214i 0.245517i
\(201\) 6.47214 + 16.9443i 0.456509 + 1.19516i
\(202\) 11.2361i 0.790567i
\(203\) −3.23607 22.1803i −0.227127 1.55675i
\(204\) −1.70820 4.47214i −0.119598 0.313112i
\(205\) −12.5836 −0.878876
\(206\) 3.70820 0.258363
\(207\) 6.47214 + 7.23607i 0.449845 + 0.502941i
\(208\) 6.00000i 0.416025i
\(209\) 2.00000 0.138343
\(210\) −4.94427 + 2.76393i −0.341187 + 0.190729i
\(211\) −17.4164 −1.19899 −0.599497 0.800377i \(-0.704633\pi\)
−0.599497 + 0.800377i \(0.704633\pi\)
\(212\) 5.70820i 0.392041i
\(213\) −26.1803 + 10.0000i −1.79385 + 0.685189i
\(214\) 8.94427 0.611418
\(215\) −8.58359 −0.585396
\(216\) −2.38197 + 4.61803i −0.162072 + 0.314217i
\(217\) 2.00000 + 13.7082i 0.135769 + 0.930574i
\(218\) 13.2361i 0.896460i
\(219\) 13.2361 5.05573i 0.894411 0.341634i
\(220\) 1.23607i 0.0833357i
\(221\) 16.5836i 1.11553i
\(222\) −7.23607 + 2.76393i −0.485653 + 0.185503i
\(223\) 25.5967i 1.71409i 0.515246 + 0.857043i \(0.327701\pi\)
−0.515246 + 0.857043i \(0.672299\pi\)
\(224\) 0.381966 + 2.61803i 0.0255212 + 0.174925i
\(225\) 7.76393 6.94427i 0.517595 0.462951i
\(226\) 8.00000 0.532152
\(227\) −22.0000 −1.46019 −0.730096 0.683345i \(-0.760525\pi\)
−0.730096 + 0.683345i \(0.760525\pi\)
\(228\) 3.23607 1.23607i 0.214314 0.0818606i
\(229\) 2.00000i 0.132164i −0.997814 0.0660819i \(-0.978950\pi\)
0.997814 0.0660819i \(-0.0210498\pi\)
\(230\) 4.00000 0.263752
\(231\) 4.00000 2.23607i 0.263181 0.147122i
\(232\) −8.47214 −0.556223
\(233\) 1.41641i 0.0927920i −0.998923 0.0463960i \(-0.985226\pi\)
0.998923 0.0463960i \(-0.0147736\pi\)
\(234\) 13.4164 12.0000i 0.877058 0.784465i
\(235\) 12.9443 0.844391
\(236\) 1.23607 0.0804612
\(237\) 1.70820 + 4.47214i 0.110960 + 0.290496i
\(238\) 1.05573 + 7.23607i 0.0684327 + 0.469045i
\(239\) 13.8885i 0.898375i −0.893437 0.449188i \(-0.851713\pi\)
0.893437 0.449188i \(-0.148287\pi\)
\(240\) 0.763932 + 2.00000i 0.0493116 + 0.129099i
\(241\) 4.18034i 0.269279i 0.990895 + 0.134640i \(0.0429877\pi\)
−0.990895 + 0.134640i \(0.957012\pi\)
\(242\) 1.00000i 0.0642824i
\(243\) 15.0902 3.90983i 0.968035 0.250816i
\(244\) 12.4721i 0.798447i
\(245\) 8.29180 2.47214i 0.529743 0.157939i
\(246\) 16.4721 6.29180i 1.05023 0.401150i
\(247\) −12.0000 −0.763542
\(248\) 5.23607 0.332491
\(249\) 3.70820 + 9.70820i 0.234998 + 0.615232i
\(250\) 10.4721i 0.662316i
\(251\) 11.7082 0.739015 0.369508 0.929228i \(-0.379526\pi\)
0.369508 + 0.929228i \(0.379526\pi\)
\(252\) 5.09017 6.09017i 0.320651 0.383645i
\(253\) −3.23607 −0.203450
\(254\) 4.29180i 0.269291i
\(255\) 2.11146 + 5.52786i 0.132225 + 0.346168i
\(256\) 1.00000 0.0625000
\(257\) −16.9443 −1.05695 −0.528477 0.848947i \(-0.677237\pi\)
−0.528477 + 0.848947i \(0.677237\pi\)
\(258\) 11.2361 4.29180i 0.699527 0.267196i
\(259\) 11.7082 1.70820i 0.727512 0.106143i
\(260\) 7.41641i 0.459946i
\(261\) 16.9443 + 18.9443i 1.04882 + 1.17262i
\(262\) 17.4164i 1.07599i
\(263\) 30.4721i 1.87899i 0.342559 + 0.939496i \(0.388706\pi\)
−0.342559 + 0.939496i \(0.611294\pi\)
\(264\) −0.618034 1.61803i −0.0380374 0.0995831i
\(265\) 7.05573i 0.433430i
\(266\) −5.23607 + 0.763932i −0.321044 + 0.0468397i
\(267\) 3.05573 + 8.00000i 0.187008 + 0.489592i
\(268\) −10.4721 −0.639688
\(269\) −25.5967 −1.56066 −0.780331 0.625367i \(-0.784949\pi\)
−0.780331 + 0.625367i \(0.784949\pi\)
\(270\) 2.94427 5.70820i 0.179183 0.347390i
\(271\) 10.2918i 0.625182i −0.949888 0.312591i \(-0.898803\pi\)
0.949888 0.312591i \(-0.101197\pi\)
\(272\) 2.76393 0.167588
\(273\) −24.0000 + 13.4164i −1.45255 + 0.811998i
\(274\) 2.47214 0.149347
\(275\) 3.47214i 0.209378i
\(276\) −5.23607 + 2.00000i −0.315174 + 0.120386i
\(277\) −1.81966 −0.109333 −0.0546664 0.998505i \(-0.517410\pi\)
−0.0546664 + 0.998505i \(0.517410\pi\)
\(278\) 10.0000 0.599760
\(279\) −10.4721 11.7082i −0.626950 0.700952i
\(280\) −0.472136 3.23607i −0.0282155 0.193392i
\(281\) 1.41641i 0.0844958i 0.999107 + 0.0422479i \(0.0134519\pi\)
−0.999107 + 0.0422479i \(0.986548\pi\)
\(282\) −16.9443 + 6.47214i −1.00902 + 0.385410i
\(283\) 2.94427i 0.175019i −0.996164 0.0875094i \(-0.972109\pi\)
0.996164 0.0875094i \(-0.0278908\pi\)
\(284\) 16.1803i 0.960127i
\(285\) −4.00000 + 1.52786i −0.236940 + 0.0905029i
\(286\) 6.00000i 0.354787i
\(287\) −26.6525 + 3.88854i −1.57325 + 0.229533i
\(288\) −2.00000 2.23607i −0.117851 0.131762i
\(289\) −9.36068 −0.550628
\(290\) 10.4721 0.614945
\(291\) −10.4721 + 4.00000i −0.613887 + 0.234484i
\(292\) 8.18034i 0.478718i
\(293\) −4.18034 −0.244218 −0.122109 0.992517i \(-0.538966\pi\)
−0.122109 + 0.992517i \(0.538966\pi\)
\(294\) −9.61803 + 7.38197i −0.560935 + 0.430525i
\(295\) −1.52786 −0.0889557
\(296\) 4.47214i 0.259938i
\(297\) −2.38197 + 4.61803i −0.138216 + 0.267966i
\(298\) 2.00000 0.115857
\(299\) 19.4164 1.12288
\(300\) 2.14590 + 5.61803i 0.123893 + 0.324357i
\(301\) −18.1803 + 2.65248i −1.04790 + 0.152886i
\(302\) 10.1803i 0.585813i
\(303\) −6.94427 18.1803i −0.398938 1.04443i
\(304\) 2.00000i 0.114708i
\(305\) 15.4164i 0.882741i
\(306\) −5.52786 6.18034i −0.316007 0.353307i
\(307\) 12.4721i 0.711822i 0.934520 + 0.355911i \(0.115829\pi\)
−0.934520 + 0.355911i \(0.884171\pi\)
\(308\) 0.381966 + 2.61803i 0.0217645 + 0.149176i
\(309\) 6.00000 2.29180i 0.341328 0.130376i
\(310\) −6.47214 −0.367593
\(311\) −1.52786 −0.0866372 −0.0433186 0.999061i \(-0.513793\pi\)
−0.0433186 + 0.999061i \(0.513793\pi\)
\(312\) 3.70820 + 9.70820i 0.209936 + 0.549619i
\(313\) 8.00000i 0.452187i 0.974106 + 0.226093i \(0.0725954\pi\)
−0.974106 + 0.226093i \(0.927405\pi\)
\(314\) 13.4164 0.757132
\(315\) −6.29180 + 7.52786i −0.354503 + 0.424147i
\(316\) −2.76393 −0.155483
\(317\) 25.7082i 1.44392i −0.691937 0.721958i \(-0.743242\pi\)
0.691937 0.721958i \(-0.256758\pi\)
\(318\) 3.52786 + 9.23607i 0.197833 + 0.517933i
\(319\) −8.47214 −0.474349
\(320\) −1.23607 −0.0690983
\(321\) 14.4721 5.52786i 0.807756 0.308535i
\(322\) 8.47214 1.23607i 0.472134 0.0688834i
\(323\) 5.52786i 0.307579i
\(324\) −1.00000 + 8.94427i −0.0555556 + 0.496904i
\(325\) 20.8328i 1.15560i
\(326\) 9.52786i 0.527700i
\(327\) 8.18034 + 21.4164i 0.452374 + 1.18433i
\(328\) 10.1803i 0.562115i
\(329\) 27.4164 4.00000i 1.51152 0.220527i
\(330\) 0.763932 + 2.00000i 0.0420531 + 0.110096i
\(331\) −8.94427 −0.491622 −0.245811 0.969318i \(-0.579054\pi\)
−0.245811 + 0.969318i \(0.579054\pi\)
\(332\) −6.00000 −0.329293
\(333\) −10.0000 + 8.94427i −0.547997 + 0.490143i
\(334\) 21.8885i 1.19769i
\(335\) 12.9443 0.707221
\(336\) 2.23607 + 4.00000i 0.121988 + 0.218218i
\(337\) −13.4164 −0.730838 −0.365419 0.930843i \(-0.619074\pi\)
−0.365419 + 0.930843i \(0.619074\pi\)
\(338\) 23.0000i 1.25104i
\(339\) 12.9443 4.94427i 0.703036 0.268536i
\(340\) −3.41641 −0.185281
\(341\) 5.23607 0.283549
\(342\) 4.47214 4.00000i 0.241825 0.216295i
\(343\) 16.7984 7.79837i 0.907027 0.421073i
\(344\) 6.94427i 0.374410i
\(345\) 6.47214 2.47214i 0.348448 0.133095i
\(346\) 5.70820i 0.306875i
\(347\) 0.944272i 0.0506912i 0.999679 + 0.0253456i \(0.00806861\pi\)
−0.999679 + 0.0253456i \(0.991931\pi\)
\(348\) −13.7082 + 5.23607i −0.734837 + 0.280683i
\(349\) 22.0000i 1.17763i −0.808267 0.588817i \(-0.799594\pi\)
0.808267 0.588817i \(-0.200406\pi\)
\(350\) −1.32624 9.09017i −0.0708904 0.485890i
\(351\) 14.2918 27.7082i 0.762840 1.47895i
\(352\) 1.00000 0.0533002
\(353\) −16.9443 −0.901853 −0.450926 0.892561i \(-0.648906\pi\)
−0.450926 + 0.892561i \(0.648906\pi\)
\(354\) 2.00000 0.763932i 0.106299 0.0406025i
\(355\) 20.0000i 1.06149i
\(356\) −4.94427 −0.262046
\(357\) 6.18034 + 11.0557i 0.327098 + 0.585131i
\(358\) −4.94427 −0.261313
\(359\) 34.8328i 1.83841i 0.393784 + 0.919203i \(0.371166\pi\)
−0.393784 + 0.919203i \(0.628834\pi\)
\(360\) 2.47214 + 2.76393i 0.130293 + 0.145672i
\(361\) 15.0000 0.789474
\(362\) −12.4721 −0.655521
\(363\) −0.618034 1.61803i −0.0324384 0.0849248i
\(364\) −2.29180 15.7082i −0.120123 0.823334i
\(365\) 10.1115i 0.529258i
\(366\) 7.70820 + 20.1803i 0.402914 + 1.05484i
\(367\) 4.65248i 0.242857i 0.992600 + 0.121429i \(0.0387476\pi\)
−0.992600 + 0.121429i \(0.961252\pi\)
\(368\) 3.23607i 0.168692i
\(369\) 22.7639 20.3607i 1.18504 1.05993i
\(370\) 5.52786i 0.287380i
\(371\) −2.18034 14.9443i −0.113198 0.775868i
\(372\) 8.47214 3.23607i 0.439260 0.167782i
\(373\) −30.1803 −1.56268 −0.781339 0.624106i \(-0.785463\pi\)
−0.781339 + 0.624106i \(0.785463\pi\)
\(374\) 2.76393 0.142920
\(375\) −6.47214 16.9443i −0.334220 0.874998i
\(376\) 10.4721i 0.540059i
\(377\) 50.8328 2.61802
\(378\) 4.47214 13.0000i 0.230022 0.668648i
\(379\) 32.3607 1.66226 0.831128 0.556081i \(-0.187696\pi\)
0.831128 + 0.556081i \(0.187696\pi\)
\(380\) 2.47214i 0.126818i
\(381\) −2.65248 6.94427i −0.135890 0.355766i
\(382\) 1.70820 0.0873993
\(383\) 20.0000 1.02195 0.510976 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(384\) 1.61803 0.618034i 0.0825700 0.0315389i
\(385\) −0.472136 3.23607i −0.0240623 0.164925i
\(386\) 14.9443i 0.760643i
\(387\) 15.5279 13.8885i 0.789326 0.705994i
\(388\) 6.47214i 0.328573i
\(389\) 12.7639i 0.647157i −0.946201 0.323579i \(-0.895114\pi\)
0.946201 0.323579i \(-0.104886\pi\)
\(390\) −4.58359 12.0000i −0.232099 0.607644i
\(391\) 8.94427i 0.452331i
\(392\) −2.00000 6.70820i −0.101015 0.338815i
\(393\) 10.7639 + 28.1803i 0.542969 + 1.42151i
\(394\) 2.94427 0.148330
\(395\) 3.41641 0.171898
\(396\) −2.00000 2.23607i −0.100504 0.112367i
\(397\) 2.94427i 0.147769i 0.997267 + 0.0738844i \(0.0235396\pi\)
−0.997267 + 0.0738844i \(0.976460\pi\)
\(398\) 2.18034 0.109291
\(399\) −8.00000 + 4.47214i −0.400501 + 0.223887i
\(400\) −3.47214 −0.173607
\(401\) 6.47214i 0.323203i 0.986856 + 0.161602i \(0.0516659\pi\)
−0.986856 + 0.161602i \(0.948334\pi\)
\(402\) −16.9443 + 6.47214i −0.845103 + 0.322801i
\(403\) −31.4164 −1.56496
\(404\) 11.2361 0.559015
\(405\) 1.23607 11.0557i 0.0614207 0.549364i
\(406\) 22.1803 3.23607i 1.10079 0.160603i
\(407\) 4.47214i 0.221676i
\(408\) 4.47214 1.70820i 0.221404 0.0845687i
\(409\) 0.763932i 0.0377740i −0.999822 0.0188870i \(-0.993988\pi\)
0.999822 0.0188870i \(-0.00601228\pi\)
\(410\) 12.5836i 0.621459i
\(411\) 4.00000 1.52786i 0.197305 0.0753640i
\(412\) 3.70820i 0.182690i
\(413\) −3.23607 + 0.472136i −0.159236 + 0.0232323i
\(414\) −7.23607 + 6.47214i −0.355633 + 0.318088i
\(415\) 7.41641 0.364057
\(416\) −6.00000 −0.294174
\(417\) 16.1803 6.18034i 0.792355 0.302653i
\(418\) 2.00000i 0.0978232i
\(419\) 31.1246 1.52054 0.760268 0.649609i \(-0.225067\pi\)
0.760268 + 0.649609i \(0.225067\pi\)
\(420\) −2.76393 4.94427i −0.134866 0.241256i
\(421\) −4.47214 −0.217959 −0.108979 0.994044i \(-0.534758\pi\)
−0.108979 + 0.994044i \(0.534758\pi\)
\(422\) 17.4164i 0.847817i
\(423\) −23.4164 + 20.9443i −1.13854 + 1.01835i
\(424\) −5.70820 −0.277215
\(425\) −9.59675 −0.465511
\(426\) −10.0000 26.1803i −0.484502 1.26844i
\(427\) −4.76393 32.6525i −0.230543 1.58016i
\(428\) 8.94427i 0.432338i
\(429\) 3.70820 + 9.70820i 0.179034 + 0.468717i
\(430\) 8.58359i 0.413938i
\(431\) 29.8885i 1.43968i 0.694140 + 0.719840i \(0.255785\pi\)
−0.694140 + 0.719840i \(0.744215\pi\)
\(432\) −4.61803 2.38197i −0.222185 0.114602i
\(433\) 17.5279i 0.842335i 0.906983 + 0.421168i \(0.138380\pi\)
−0.906983 + 0.421168i \(0.861620\pi\)
\(434\) −13.7082 + 2.00000i −0.658015 + 0.0960031i
\(435\) 16.9443 6.47214i 0.812416 0.310315i
\(436\) −13.2361 −0.633893
\(437\) 6.47214 0.309604
\(438\) 5.05573 + 13.2361i 0.241572 + 0.632444i
\(439\) 12.7639i 0.609189i −0.952482 0.304595i \(-0.901479\pi\)
0.952482 0.304595i \(-0.0985210\pi\)
\(440\) −1.23607 −0.0589272
\(441\) −11.0000 + 17.8885i −0.523810 + 0.851835i
\(442\) −16.5836 −0.788801
\(443\) 5.88854i 0.279773i −0.990168 0.139887i \(-0.955326\pi\)
0.990168 0.139887i \(-0.0446738\pi\)
\(444\) −2.76393 7.23607i −0.131170 0.343409i
\(445\) 6.11146 0.289711
\(446\) −25.5967 −1.21204
\(447\) 3.23607 1.23607i 0.153061 0.0584640i
\(448\) −2.61803 + 0.381966i −0.123690 + 0.0180462i
\(449\) 4.58359i 0.216313i −0.994134 0.108157i \(-0.965505\pi\)
0.994134 0.108157i \(-0.0344948\pi\)
\(450\) 6.94427 + 7.76393i 0.327356 + 0.365995i
\(451\) 10.1803i 0.479373i
\(452\) 8.00000i 0.376288i
\(453\) −6.29180 16.4721i −0.295614 0.773928i
\(454\) 22.0000i 1.03251i
\(455\) 2.83282 + 19.4164i 0.132804 + 0.910255i
\(456\) 1.23607 + 3.23607i 0.0578842 + 0.151543i
\(457\) −2.00000 −0.0935561 −0.0467780 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) 2.00000 0.0934539
\(459\) −12.7639 6.58359i −0.595769 0.307296i
\(460\) 4.00000i 0.186501i
\(461\) −36.7639 −1.71227 −0.856134 0.516755i \(-0.827140\pi\)
−0.856134 + 0.516755i \(0.827140\pi\)
\(462\) 2.23607 + 4.00000i 0.104031 + 0.186097i
\(463\) −17.5279 −0.814589 −0.407294 0.913297i \(-0.633528\pi\)
−0.407294 + 0.913297i \(0.633528\pi\)
\(464\) 8.47214i 0.393309i
\(465\) −10.4721 + 4.00000i −0.485634 + 0.185496i
\(466\) 1.41641 0.0656138
\(467\) 8.65248 0.400389 0.200194 0.979756i \(-0.435843\pi\)
0.200194 + 0.979756i \(0.435843\pi\)
\(468\) 12.0000 + 13.4164i 0.554700 + 0.620174i
\(469\) 27.4164 4.00000i 1.26597 0.184703i
\(470\) 12.9443i 0.597075i
\(471\) 21.7082 8.29180i 1.00026 0.382066i
\(472\) 1.23607i 0.0568946i
\(473\) 6.94427i 0.319298i
\(474\) −4.47214 + 1.70820i −0.205412 + 0.0784604i
\(475\) 6.94427i 0.318625i
\(476\) −7.23607 + 1.05573i −0.331665 + 0.0483892i
\(477\) 11.4164 + 12.7639i 0.522721 + 0.584420i
\(478\) 13.8885 0.635247
\(479\) 16.9443 0.774204 0.387102 0.922037i \(-0.373476\pi\)
0.387102 + 0.922037i \(0.373476\pi\)
\(480\) −2.00000 + 0.763932i −0.0912871 + 0.0348686i
\(481\) 26.8328i 1.22347i
\(482\) −4.18034 −0.190409
\(483\) 12.9443 7.23607i 0.588985 0.329252i
\(484\) 1.00000 0.0454545
\(485\) 8.00000i 0.363261i
\(486\) 3.90983 + 15.0902i 0.177353 + 0.684504i
\(487\) 10.4721 0.474538 0.237269 0.971444i \(-0.423748\pi\)
0.237269 + 0.971444i \(0.423748\pi\)
\(488\) −12.4721 −0.564587
\(489\) 5.88854 + 15.4164i 0.266289 + 0.697154i
\(490\) 2.47214 + 8.29180i 0.111680 + 0.374585i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 6.29180 + 16.4721i 0.283656 + 0.742621i
\(493\) 23.4164i 1.05462i
\(494\) 12.0000i 0.539906i
\(495\) 2.47214 + 2.76393i 0.111114 + 0.124230i
\(496\) 5.23607i 0.235106i
\(497\) 6.18034 + 42.3607i 0.277226 + 1.90014i
\(498\) −9.70820 + 3.70820i −0.435035 + 0.166169i
\(499\) 36.9443 1.65385 0.826926 0.562310i \(-0.190087\pi\)
0.826926 + 0.562310i \(0.190087\pi\)
\(500\) 10.4721 0.468328
\(501\) −13.5279 35.4164i −0.604380 1.58229i
\(502\) 11.7082i 0.522563i
\(503\) −31.4164 −1.40079 −0.700394 0.713756i \(-0.746992\pi\)
−0.700394 + 0.713756i \(0.746992\pi\)
\(504\) 6.09017 + 5.09017i 0.271278 + 0.226734i
\(505\) −13.8885 −0.618032
\(506\) 3.23607i 0.143861i
\(507\) −14.2148 37.2148i −0.631301 1.65277i
\(508\) 4.29180 0.190418
\(509\) −23.1246 −1.02498 −0.512490 0.858693i \(-0.671277\pi\)
−0.512490 + 0.858693i \(0.671277\pi\)
\(510\) −5.52786 + 2.11146i −0.244778 + 0.0934969i
\(511\) −3.12461 21.4164i −0.138225 0.947406i
\(512\) 1.00000i 0.0441942i
\(513\) 4.76393 9.23607i 0.210333 0.407782i
\(514\) 16.9443i 0.747380i
\(515\) 4.58359i 0.201977i
\(516\) 4.29180 + 11.2361i 0.188936 + 0.494640i
\(517\) 10.4721i 0.460564i
\(518\) 1.70820 + 11.7082i 0.0750542 + 0.514429i
\(519\) −3.52786 9.23607i −0.154856 0.405418i
\(520\) 7.41641 0.325231
\(521\) 36.9443 1.61856 0.809279 0.587425i \(-0.199858\pi\)
0.809279 + 0.587425i \(0.199858\pi\)
\(522\) −18.9443 + 16.9443i −0.829168 + 0.741631i
\(523\) 41.7771i 1.82678i 0.407081 + 0.913392i \(0.366547\pi\)
−0.407081 + 0.913392i \(0.633453\pi\)
\(524\) −17.4164 −0.760839
\(525\) −7.76393 13.8885i −0.338846 0.606146i
\(526\) −30.4721 −1.32865
\(527\) 14.4721i 0.630416i
\(528\) 1.61803 0.618034i 0.0704159 0.0268965i
\(529\) 12.5279 0.544690
\(530\) 7.05573 0.306481
\(531\) 2.76393 2.47214i 0.119944 0.107282i
\(532\) −0.763932 5.23607i −0.0331207 0.227012i
\(533\) 61.0820i 2.64576i
\(534\) −8.00000 + 3.05573i −0.346194 + 0.132234i
\(535\) 11.0557i 0.477981i
\(536\) 10.4721i 0.452327i
\(537\) −8.00000 + 3.05573i −0.345225 + 0.131864i
\(538\) 25.5967i 1.10355i
\(539\) −2.00000 6.70820i −0.0861461 0.288943i
\(540\) 5.70820 + 2.94427i 0.245642 + 0.126701i
\(541\) 25.5967 1.10049 0.550245 0.835003i \(-0.314534\pi\)
0.550245 + 0.835003i \(0.314534\pi\)
\(542\) 10.2918 0.442070
\(543\) −20.1803 + 7.70820i −0.866021 + 0.330791i
\(544\) 2.76393i 0.118503i
\(545\) 16.3607 0.700815
\(546\) −13.4164 24.0000i −0.574169 1.02711i
\(547\) −28.8328 −1.23280 −0.616401 0.787432i \(-0.711410\pi\)
−0.616401 + 0.787432i \(0.711410\pi\)
\(548\) 2.47214i 0.105604i
\(549\) 24.9443 + 27.8885i 1.06460 + 1.19025i
\(550\) −3.47214 −0.148052
\(551\) 16.9443 0.721850
\(552\) −2.00000 5.23607i −0.0851257 0.222862i
\(553\) 7.23607 1.05573i 0.307709 0.0448941i
\(554\) 1.81966i 0.0773100i
\(555\) 3.41641 + 8.94427i 0.145018 + 0.379663i
\(556\) 10.0000i 0.424094i
\(557\) 26.9443i 1.14167i −0.821066 0.570833i \(-0.806620\pi\)
0.821066 0.570833i \(-0.193380\pi\)
\(558\) 11.7082 10.4721i 0.495648 0.443321i
\(559\) 41.6656i 1.76227i
\(560\) 3.23607 0.472136i 0.136749 0.0199514i
\(561\) 4.47214 1.70820i 0.188814 0.0721204i
\(562\) −1.41641 −0.0597476
\(563\) −32.4721 −1.36854 −0.684269 0.729230i \(-0.739878\pi\)
−0.684269 + 0.729230i \(0.739878\pi\)
\(564\) −6.47214 16.9443i −0.272526 0.713483i
\(565\) 9.88854i 0.416014i
\(566\) 2.94427 0.123757
\(567\) −0.798374 23.7984i −0.0335286 0.999438i
\(568\) 16.1803 0.678912
\(569\) 6.00000i 0.251533i −0.992060 0.125767i \(-0.959861\pi\)
0.992060 0.125767i \(-0.0401390\pi\)
\(570\) −1.52786 4.00000i −0.0639952 0.167542i
\(571\) −9.05573 −0.378970 −0.189485 0.981884i \(-0.560682\pi\)
−0.189485 + 0.981884i \(0.560682\pi\)
\(572\) −6.00000 −0.250873
\(573\) 2.76393 1.05573i 0.115465 0.0441037i
\(574\) −3.88854 26.6525i −0.162305 1.11245i
\(575\) 11.2361i 0.468576i
\(576\) 2.23607 2.00000i 0.0931695 0.0833333i
\(577\) 46.4721i 1.93466i 0.253520 + 0.967330i \(0.418412\pi\)
−0.253520 + 0.967330i \(0.581588\pi\)
\(578\) 9.36068i 0.389353i
\(579\) 9.23607 + 24.1803i 0.383838 + 1.00490i
\(580\) 10.4721i 0.434832i
\(581\) 15.7082 2.29180i 0.651686 0.0950797i
\(582\) −4.00000 10.4721i −0.165805 0.434084i
\(583\) −5.70820 −0.236410
\(584\) −8.18034 −0.338505
\(585\) −14.8328 16.5836i −0.613261 0.685647i
\(586\) 4.18034i 0.172688i
\(587\) −21.5967 −0.891393 −0.445697 0.895184i \(-0.647044\pi\)
−0.445697 + 0.895184i \(0.647044\pi\)
\(588\) −7.38197 9.61803i −0.304427 0.396641i
\(589\) −10.4721 −0.431497
\(590\) 1.52786i 0.0629012i
\(591\) 4.76393 1.81966i 0.195962 0.0748508i
\(592\) 4.47214 0.183804
\(593\) −11.7082 −0.480798 −0.240399 0.970674i \(-0.577278\pi\)
−0.240399 + 0.970674i \(0.577278\pi\)
\(594\) −4.61803 2.38197i −0.189480 0.0977332i
\(595\) 8.94427 1.30495i 0.366679 0.0534978i
\(596\) 2.00000i 0.0819232i
\(597\) 3.52786 1.34752i 0.144386 0.0551505i
\(598\) 19.4164i 0.793996i
\(599\) 2.29180i 0.0936402i 0.998903 + 0.0468201i \(0.0149088\pi\)
−0.998903 + 0.0468201i \(0.985091\pi\)
\(600\) −5.61803 + 2.14590i −0.229355 + 0.0876059i
\(601\) 4.76393i 0.194325i 0.995269 + 0.0971624i \(0.0309766\pi\)
−0.995269 + 0.0971624i \(0.969023\pi\)
\(602\) −2.65248 18.1803i −0.108107 0.740975i
\(603\) −23.4164 + 20.9443i −0.953590 + 0.852917i
\(604\) 10.1803 0.414232
\(605\) −1.23607 −0.0502533
\(606\) 18.1803 6.94427i 0.738526 0.282092i
\(607\) 3.23607i 0.131348i 0.997841 + 0.0656740i \(0.0209197\pi\)
−0.997841 + 0.0656740i \(0.979080\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 33.8885 18.9443i 1.37323 0.767661i
\(610\) 15.4164 0.624192
\(611\) 62.8328i 2.54194i
\(612\) 6.18034 5.52786i 0.249825 0.223451i
\(613\) 18.1803 0.734297 0.367149 0.930162i \(-0.380334\pi\)
0.367149 + 0.930162i \(0.380334\pi\)
\(614\) −12.4721 −0.503334
\(615\) −7.77709 20.3607i −0.313602 0.821022i
\(616\) −2.61803 + 0.381966i −0.105484 + 0.0153898i
\(617\) 28.9443i 1.16525i 0.812740 + 0.582626i \(0.197975\pi\)
−0.812740 + 0.582626i \(0.802025\pi\)
\(618\) 2.29180 + 6.00000i 0.0921896 + 0.241355i
\(619\) 16.7639i 0.673799i 0.941541 + 0.336900i \(0.109378\pi\)
−0.941541 + 0.336900i \(0.890622\pi\)
\(620\) 6.47214i 0.259927i
\(621\) −7.70820 + 14.9443i −0.309320 + 0.599693i
\(622\) 1.52786i 0.0612618i
\(623\) 12.9443 1.88854i 0.518601 0.0756629i
\(624\) −9.70820 + 3.70820i −0.388639 + 0.148447i
\(625\) 4.41641 0.176656
\(626\) −8.00000 −0.319744
\(627\) 1.23607 + 3.23607i 0.0493638 + 0.129236i
\(628\) 13.4164i 0.535373i
\(629\) 12.3607 0.492853
\(630\) −7.52786 6.29180i −0.299917 0.250671i
\(631\) −15.0557 −0.599359 −0.299680 0.954040i \(-0.596880\pi\)
−0.299680 + 0.954040i \(0.596880\pi\)
\(632\) 2.76393i 0.109943i
\(633\) −10.7639 28.1803i −0.427828 1.12007i
\(634\) 25.7082 1.02100
\(635\) −5.30495 −0.210521
\(636\) −9.23607 + 3.52786i −0.366234 + 0.139889i
\(637\) 12.0000 + 40.2492i 0.475457 + 1.59473i
\(638\) 8.47214i 0.335415i
\(639\) −32.3607 36.1803i −1.28017 1.43127i
\(640\) 1.23607i 0.0488599i
\(641\) 12.3607i 0.488217i −0.969748 0.244109i \(-0.921505\pi\)
0.969748 0.244109i \(-0.0784954\pi\)
\(642\) 5.52786 + 14.4721i 0.218167 + 0.571170i
\(643\) 26.0689i 1.02806i 0.857773 + 0.514028i \(0.171847\pi\)
−0.857773 + 0.514028i \(0.828153\pi\)
\(644\) 1.23607 + 8.47214i 0.0487079 + 0.333849i
\(645\) −5.30495 13.8885i −0.208882 0.546861i
\(646\) −5.52786 −0.217491
\(647\) −29.8885 −1.17504 −0.587520 0.809210i \(-0.699896\pi\)
−0.587520 + 0.809210i \(0.699896\pi\)
\(648\) −8.94427 1.00000i −0.351364 0.0392837i
\(649\) 1.23607i 0.0485199i
\(650\) 20.8328 0.817130
\(651\) −20.9443 + 11.7082i −0.820871 + 0.458881i
\(652\) −9.52786 −0.373140
\(653\) 16.7639i 0.656023i 0.944674 + 0.328012i \(0.106379\pi\)
−0.944674 + 0.328012i \(0.893621\pi\)
\(654\) −21.4164 + 8.18034i −0.837448 + 0.319877i
\(655\) 21.5279 0.841163
\(656\) −10.1803 −0.397475
\(657\) 16.3607 + 18.2918i 0.638291 + 0.713631i
\(658\) 4.00000 + 27.4164i 0.155936 + 1.06880i
\(659\) 25.8885i 1.00847i 0.863565 + 0.504237i \(0.168226\pi\)
−0.863565 + 0.504237i \(0.831774\pi\)
\(660\) −2.00000 + 0.763932i −0.0778499 + 0.0297360i
\(661\) 35.5279i 1.38187i 0.722915 + 0.690937i \(0.242802\pi\)
−0.722915 + 0.690937i \(0.757198\pi\)
\(662\) 8.94427i 0.347629i
\(663\) −26.8328 + 10.2492i −1.04210 + 0.398047i
\(664\) 6.00000i 0.232845i
\(665\) 0.944272 + 6.47214i 0.0366173 + 0.250979i
\(666\) −8.94427 10.0000i −0.346583 0.387492i
\(667\) −27.4164 −1.06157
\(668\) 21.8885 0.846893
\(669\) −41.4164 + 15.8197i −1.60125 + 0.611623i
\(670\) 12.9443i 0.500081i
\(671\) −12.4721 −0.481481
\(672\) −4.00000 + 2.23607i −0.154303 + 0.0862582i
\(673\) 51.3050 1.97766 0.988830 0.149046i \(-0.0476202\pi\)
0.988830 + 0.149046i \(0.0476202\pi\)
\(674\) 13.4164i 0.516781i
\(675\) 16.0344 + 8.27051i 0.617166 + 0.318332i
\(676\) 23.0000 0.884615
\(677\) 7.23607 0.278105 0.139052 0.990285i \(-0.455594\pi\)
0.139052 + 0.990285i \(0.455594\pi\)
\(678\) 4.94427 + 12.9443i 0.189884 + 0.497122i
\(679\) 2.47214 + 16.9443i 0.0948719 + 0.650261i
\(680\) 3.41641i 0.131013i
\(681\) −13.5967 35.5967i −0.521029 1.36407i
\(682\) 5.23607i 0.200499i
\(683\) 1.88854i 0.0722631i 0.999347 + 0.0361316i \(0.0115035\pi\)
−0.999347 + 0.0361316i \(0.988496\pi\)
\(684\) 4.00000 + 4.47214i 0.152944 + 0.170996i
\(685\) 3.05573i 0.116753i
\(686\) 7.79837 + 16.7984i 0.297743 + 0.641365i
\(687\) 3.23607 1.23607i 0.123464 0.0471589i
\(688\) −6.94427 −0.264748
\(689\) 34.2492 1.30479
\(690\) 2.47214 + 6.47214i 0.0941126 + 0.246390i
\(691\) 19.5967i 0.745495i 0.927933 + 0.372748i \(0.121584\pi\)
−0.927933 + 0.372748i \(0.878416\pi\)
\(692\) 5.70820 0.216993
\(693\) 6.09017 + 5.09017i 0.231346 + 0.193360i
\(694\) −0.944272 −0.0358441
\(695\) 12.3607i 0.468867i
\(696\) −5.23607 13.7082i −0.198473 0.519608i
\(697\) −28.1378 −1.06579
\(698\) 22.0000 0.832712
\(699\) 2.29180 0.875388i 0.0866837 0.0331102i
\(700\) 9.09017 1.32624i 0.343576 0.0501271i
\(701\) 9.41641i 0.355653i 0.984062 + 0.177826i \(0.0569066\pi\)
−0.984062 + 0.177826i \(0.943093\pi\)
\(702\) 27.7082 + 14.2918i 1.04578 + 0.539409i
\(703\) 8.94427i 0.337340i
\(704\) 1.00000i 0.0376889i
\(705\) 8.00000 + 20.9443i 0.301297 + 0.788807i
\(706\) 16.9443i 0.637706i
\(707\) −29.4164 + 4.29180i −1.10632 + 0.161410i
\(708\) 0.763932 + 2.00000i 0.0287103 + 0.0751646i
\(709\) −49.4164 −1.85587 −0.927936 0.372739i \(-0.878419\pi\)
−0.927936 + 0.372739i \(0.878419\pi\)
\(710\) −20.0000 −0.750587
\(711\) −6.18034 + 5.52786i −0.231781 + 0.207311i
\(712\) 4.94427i 0.185294i
\(713\) 16.9443 0.634568
\(714\) −11.0557 + 6.18034i −0.413750 + 0.231293i
\(715\) 7.41641 0.277358
\(716\) 4.94427i 0.184776i
\(717\) 22.4721 8.58359i 0.839237 0.320560i
\(718\) −34.8328 −1.29995
\(719\) −26.4721 −0.987244 −0.493622 0.869677i \(-0.664327\pi\)
−0.493622 + 0.869677i \(0.664327\pi\)
\(720\) −2.76393 + 2.47214i −0.103006 + 0.0921311i
\(721\) −1.41641 9.70820i −0.0527498 0.361552i
\(722\) 15.0000i 0.558242i
\(723\) −6.76393 + 2.58359i −0.251553 + 0.0960848i
\(724\) 12.4721i 0.463523i
\(725\) 29.4164i 1.09250i
\(726\) 1.61803 0.618034i 0.0600509 0.0229374i
\(727\) 15.7082i 0.582585i −0.956634 0.291293i \(-0.905915\pi\)
0.956634 0.291293i \(-0.0940853\pi\)
\(728\) 15.7082 2.29180i 0.582185 0.0849396i
\(729\) 15.6525 + 22.0000i 0.579721 + 0.814815i
\(730\) 10.1115 0.374242
\(731\) −19.1935 −0.709897
\(732\) −20.1803 + 7.70820i −0.745887 + 0.284903i
\(733\) 53.4164i 1.97298i 0.163821 + 0.986490i \(0.447618\pi\)
−0.163821 + 0.986490i \(0.552382\pi\)
\(734\) −4.65248 −0.171726
\(735\) 9.12461 + 11.8885i 0.336566 + 0.438516i
\(736\) 3.23607 0.119283
\(737\) 10.4721i 0.385746i
\(738\) 20.3607 + 22.7639i 0.749487 + 0.837952i
\(739\) −17.4164 −0.640673 −0.320336 0.947304i \(-0.603796\pi\)
−0.320336 + 0.947304i \(0.603796\pi\)
\(740\) −5.52786 −0.203208
\(741\) −7.41641 19.4164i −0.272449 0.713280i
\(742\) 14.9443 2.18034i 0.548621 0.0800428i
\(743\) 10.4721i 0.384185i 0.981377 + 0.192093i \(0.0615274\pi\)
−0.981377 + 0.192093i \(0.938473\pi\)
\(744\) 3.23607 + 8.47214i 0.118640 + 0.310604i
\(745\) 2.47214i 0.0905721i
\(746\) 30.1803i 1.10498i
\(747\) −13.4164 + 12.0000i −0.490881 + 0.439057i
\(748\) 2.76393i 0.101059i
\(749\) −3.41641 23.4164i −0.124833 0.855617i
\(750\) 16.9443 6.47214i 0.618717 0.236329i
\(751\) 12.3607 0.451048 0.225524 0.974238i \(-0.427591\pi\)
0.225524 + 0.974238i \(0.427591\pi\)
\(752\) 10.4721 0.381880
\(753\) 7.23607 + 18.9443i 0.263697 + 0.690368i
\(754\) 50.8328i 1.85122i
\(755\) −12.5836 −0.457964
\(756\) 13.0000 + 4.47214i 0.472805 + 0.162650i
\(757\) 25.4164 0.923775 0.461888 0.886939i \(-0.347172\pi\)
0.461888 + 0.886939i \(0.347172\pi\)
\(758\) 32.3607i 1.17539i
\(759\) −2.00000 5.23607i −0.0725954 0.190057i
\(760\) 2.47214 0.0896738
\(761\) 7.12461 0.258267 0.129133 0.991627i \(-0.458780\pi\)
0.129133 + 0.991627i \(0.458780\pi\)
\(762\) 6.94427 2.65248i 0.251564 0.0960891i
\(763\) 34.6525 5.05573i 1.25450 0.183030i
\(764\) 1.70820i 0.0618006i
\(765\) −7.63932 + 6.83282i −0.276200 + 0.247041i
\(766\) 20.0000i 0.722629i
\(767\) 7.41641i 0.267791i
\(768\) 0.618034 + 1.61803i 0.0223014 + 0.0583858i
\(769\) 33.4853i 1.20751i −0.797170 0.603755i \(-0.793670\pi\)
0.797170 0.603755i \(-0.206330\pi\)
\(770\) 3.23607 0.472136i 0.116620 0.0170146i
\(771\) −10.4721 27.4164i −0.377145 0.987378i
\(772\) −14.9443 −0.537856
\(773\) −39.1246 −1.40721 −0.703607 0.710589i \(-0.748429\pi\)
−0.703607 + 0.710589i \(0.748429\pi\)
\(774\) 13.8885 + 15.5279i 0.499213 + 0.558138i
\(775\) 18.1803i 0.653057i
\(776\) 6.47214 0.232336
\(777\) 10.0000 + 17.8885i 0.358748 + 0.641748i
\(778\) 12.7639 0.457609
\(779\) 20.3607i 0.729497i
\(780\) 12.0000 4.58359i 0.429669 0.164119i
\(781\) 16.1803 0.578978
\(782\) 8.94427 0.319847