Properties

Label 126.2.e.a.25.1
Level $126$
Weight $2$
Character 126.25
Analytic conductor $1.006$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00611506547\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 126.25
Dual form 126.2.e.a.121.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} -1.73205i q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.73205i q^{12} +(0.500000 + 0.866025i) q^{13} +(2.00000 + 1.73205i) q^{14} +(-4.50000 - 2.59808i) q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +3.00000 q^{18} +(3.50000 + 6.06218i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(3.00000 - 3.46410i) q^{21} +(-1.50000 - 2.59808i) q^{22} +(4.50000 - 7.79423i) q^{23} -1.73205i q^{24} +(-2.00000 - 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{26} -5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(4.50000 + 2.59808i) q^{30} +8.00000 q^{31} -1.00000 q^{32} +(-4.50000 + 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +(7.50000 - 2.59808i) q^{35} -3.00000 q^{36} +(0.500000 + 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-1.50000 + 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(-3.00000 + 3.46410i) q^{42} +(0.500000 - 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} +(4.50000 - 7.79423i) q^{45} +(-4.50000 + 7.79423i) q^{46} +1.73205i q^{48} +(1.00000 + 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-1.50000 + 2.59808i) q^{53} +5.19615i q^{54} -9.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(-10.5000 + 6.06218i) q^{57} +(1.50000 - 2.59808i) q^{58} +(-4.50000 - 2.59808i) q^{60} +2.00000 q^{61} -8.00000 q^{62} +(6.00000 + 5.19615i) q^{63} +1.00000 q^{64} -3.00000 q^{65} +(4.50000 - 2.59808i) q^{66} -4.00000 q^{67} +(-1.50000 + 2.59808i) q^{68} +(13.5000 + 7.79423i) q^{69} +(-7.50000 + 2.59808i) q^{70} +12.0000 q^{71} +3.00000 q^{72} +(-5.50000 + 9.52628i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(6.00000 - 3.46410i) q^{75} +(3.50000 + 6.06218i) q^{76} +(1.50000 - 7.79423i) q^{77} +(1.50000 - 0.866025i) q^{78} -16.0000 q^{79} +(-1.50000 + 2.59808i) q^{80} +9.00000 q^{81} +(1.50000 + 2.59808i) q^{82} +(4.50000 - 7.79423i) q^{83} +(3.00000 - 3.46410i) q^{84} +(-4.50000 - 7.79423i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-4.50000 - 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(-4.50000 + 7.79423i) q^{90} +(0.500000 - 2.59808i) q^{91} +(4.50000 - 7.79423i) q^{92} +13.8564i q^{93} -21.0000 q^{95} -1.73205i q^{96} +(0.500000 - 0.866025i) q^{97} +(-1.00000 - 6.92820i) q^{98} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} + q^{13} + 4 q^{14} - 9 q^{15} + 2 q^{16} - 3 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20} + 6 q^{21} - 3 q^{22} + 9 q^{23} - 4 q^{25} - q^{26} - 4 q^{28} - 3 q^{29} + 9 q^{30} + 16 q^{31} - 2 q^{32} - 9 q^{33} + 3 q^{34} + 15 q^{35} - 6 q^{36} + q^{37} - 7 q^{38} - 3 q^{39} + 3 q^{40} - 3 q^{41} - 6 q^{42} + q^{43} + 3 q^{44} + 9 q^{45} - 9 q^{46} + 2 q^{49} + 4 q^{50} - 9 q^{51} + q^{52} - 3 q^{53} - 18 q^{55} + 4 q^{56} - 21 q^{57} + 3 q^{58} - 9 q^{60} + 4 q^{61} - 16 q^{62} + 12 q^{63} + 2 q^{64} - 6 q^{65} + 9 q^{66} - 8 q^{67} - 3 q^{68} + 27 q^{69} - 15 q^{70} + 24 q^{71} + 6 q^{72} - 11 q^{73} - q^{74} + 12 q^{75} + 7 q^{76} + 3 q^{77} + 3 q^{78} - 32 q^{79} - 3 q^{80} + 18 q^{81} + 3 q^{82} + 9 q^{83} + 6 q^{84} - 9 q^{85} - q^{86} - 9 q^{87} - 3 q^{88} - 3 q^{89} - 9 q^{90} + q^{91} + 9 q^{92} - 42 q^{95} + q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.73205i 1.00000i
\(4\) 1.00000 0.500000
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 1.73205i 0.707107i
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 1.73205i 0.500000i
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) −4.50000 2.59808i −1.16190 0.670820i
\(16\) 1.00000 0.250000
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 3.00000 0.707107
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 3.00000 3.46410i 0.654654 0.755929i
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 4.50000 7.79423i 0.938315 1.62521i 0.169701 0.985496i \(-0.445720\pi\)
0.768613 0.639713i \(-0.220947\pi\)
\(24\) 1.73205i 0.353553i
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −0.500000 0.866025i −0.0980581 0.169842i
\(27\) 5.19615i 1.00000i
\(28\) −2.00000 1.73205i −0.377964 0.327327i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 4.50000 + 2.59808i 0.821584 + 0.474342i
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) 1.50000 2.59808i 0.257248 0.445566i
\(35\) 7.50000 2.59808i 1.26773 0.439155i
\(36\) −3.00000 −0.500000
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −3.50000 6.06218i −0.567775 0.983415i
\(39\) −1.50000 + 0.866025i −0.240192 + 0.138675i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) −3.00000 + 3.46410i −0.462910 + 0.534522i
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 4.50000 7.79423i 0.670820 1.16190i
\(46\) −4.50000 + 7.79423i −0.663489 + 1.14920i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) −4.50000 2.59808i −0.630126 0.363803i
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) 5.19615i 0.707107i
\(55\) −9.00000 −1.21356
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) −10.5000 + 6.06218i −1.39076 + 0.802955i
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −4.50000 2.59808i −0.580948 0.335410i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −8.00000 −1.01600
\(63\) 6.00000 + 5.19615i 0.755929 + 0.654654i
\(64\) 1.00000 0.125000
\(65\) −3.00000 −0.372104
\(66\) 4.50000 2.59808i 0.553912 0.319801i
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 13.5000 + 7.79423i 1.62521 + 0.938315i
\(70\) −7.50000 + 2.59808i −0.896421 + 0.310530i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 3.00000 0.353553
\(73\) −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i \(0.389279\pi\)
−0.984594 + 0.174855i \(0.944054\pi\)
\(74\) −0.500000 0.866025i −0.0581238 0.100673i
\(75\) 6.00000 3.46410i 0.692820 0.400000i
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) 1.50000 7.79423i 0.170941 0.888235i
\(78\) 1.50000 0.866025i 0.169842 0.0980581i
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) 9.00000 1.00000
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i \(-0.668890\pi\)
0.999976 + 0.00698436i \(0.00222321\pi\)
\(84\) 3.00000 3.46410i 0.327327 0.377964i
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) −0.500000 + 0.866025i −0.0539164 + 0.0933859i
\(87\) −4.50000 2.59808i −0.482451 0.278543i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i \(-0.217494\pi\)
−0.934508 + 0.355942i \(0.884160\pi\)
\(90\) −4.50000 + 7.79423i −0.474342 + 0.821584i
\(91\) 0.500000 2.59808i 0.0524142 0.272352i
\(92\) 4.50000 7.79423i 0.469157 0.812605i
\(93\) 13.8564i 1.43684i
\(94\) 0 0
\(95\) −21.0000 −2.15455
\(96\) 1.73205i 0.176777i
\(97\) 0.500000 0.866025i 0.0507673 0.0879316i −0.839525 0.543321i \(-0.817167\pi\)
0.890292 + 0.455389i \(0.150500\pi\)
\(98\) −1.00000 6.92820i −0.101015 0.699854i
\(99\) −4.50000 7.79423i −0.452267 0.783349i
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 4.50000 + 2.59808i 0.445566 + 0.257248i
\(103\) 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i \(-0.612075\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) −0.500000 0.866025i −0.0490290 0.0849208i
\(105\) 4.50000 + 12.9904i 0.439155 + 1.26773i
\(106\) 1.50000 2.59808i 0.145693 0.252347i
\(107\) −4.50000 7.79423i −0.435031 0.753497i 0.562267 0.826956i \(-0.309929\pi\)
−0.997298 + 0.0734594i \(0.976596\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 6.50000 11.2583i 0.622587 1.07835i −0.366415 0.930451i \(-0.619415\pi\)
0.989002 0.147901i \(-0.0472517\pi\)
\(110\) 9.00000 0.858116
\(111\) −1.50000 + 0.866025i −0.142374 + 0.0821995i
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) 4.50000 + 7.79423i 0.423324 + 0.733219i 0.996262 0.0863794i \(-0.0275297\pi\)
−0.572938 + 0.819599i \(0.694196\pi\)
\(114\) 10.5000 6.06218i 0.983415 0.567775i
\(115\) 13.5000 + 23.3827i 1.25888 + 2.18045i
\(116\) −1.50000 + 2.59808i −0.139272 + 0.241225i
\(117\) −1.50000 2.59808i −0.138675 0.240192i
\(118\) 0 0
\(119\) 7.50000 2.59808i 0.687524 0.238165i
\(120\) 4.50000 + 2.59808i 0.410792 + 0.237171i
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −2.00000 −0.181071
\(123\) 4.50000 2.59808i 0.405751 0.234261i
\(124\) 8.00000 0.718421
\(125\) −3.00000 −0.268328
\(126\) −6.00000 5.19615i −0.534522 0.462910i
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.50000 + 0.866025i 0.132068 + 0.0762493i
\(130\) 3.00000 0.263117
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) −4.50000 + 2.59808i −0.391675 + 0.226134i
\(133\) 3.50000 18.1865i 0.303488 1.57697i
\(134\) 4.00000 0.345547
\(135\) 13.5000 + 7.79423i 1.16190 + 0.670820i
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) −13.5000 7.79423i −1.14920 0.663489i
\(139\) 3.50000 + 6.06218i 0.296866 + 0.514187i 0.975417 0.220366i \(-0.0707252\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 7.50000 2.59808i 0.633866 0.219578i
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) −1.50000 + 2.59808i −0.125436 + 0.217262i
\(144\) −3.00000 −0.250000
\(145\) −4.50000 7.79423i −0.373705 0.647275i
\(146\) 5.50000 9.52628i 0.455183 0.788400i
\(147\) −12.0000 + 1.73205i −0.989743 + 0.142857i
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) −6.00000 + 3.46410i −0.489898 + 0.282843i
\(151\) 3.50000 + 6.06218i 0.284826 + 0.493333i 0.972567 0.232623i \(-0.0747309\pi\)
−0.687741 + 0.725956i \(0.741398\pi\)
\(152\) −3.50000 6.06218i −0.283887 0.491708i
\(153\) 4.50000 7.79423i 0.363803 0.630126i
\(154\) −1.50000 + 7.79423i −0.120873 + 0.628077i
\(155\) −12.0000 + 20.7846i −0.963863 + 1.66946i
\(156\) −1.50000 + 0.866025i −0.120096 + 0.0693375i
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 16.0000 1.27289
\(159\) −4.50000 2.59808i −0.356873 0.206041i
\(160\) 1.50000 2.59808i 0.118585 0.205396i
\(161\) −22.5000 + 7.79423i −1.77325 + 0.614271i
\(162\) −9.00000 −0.707107
\(163\) 9.50000 + 16.4545i 0.744097 + 1.28881i 0.950615 + 0.310372i \(0.100454\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) 15.5885i 1.21356i
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) 7.50000 + 12.9904i 0.580367 + 1.00523i 0.995436 + 0.0954356i \(0.0304244\pi\)
−0.415068 + 0.909790i \(0.636242\pi\)
\(168\) −3.00000 + 3.46410i −0.231455 + 0.267261i
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 4.50000 + 7.79423i 0.345134 + 0.597790i
\(171\) −10.5000 18.1865i −0.802955 1.39076i
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 4.50000 + 2.59808i 0.341144 + 0.196960i
\(175\) −2.00000 + 10.3923i −0.151186 + 0.785584i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 0 0
\(178\) 1.50000 + 2.59808i 0.112430 + 0.194734i
\(179\) 10.5000 18.1865i 0.784807 1.35933i −0.144308 0.989533i \(-0.546095\pi\)
0.929114 0.369792i \(-0.120571\pi\)
\(180\) 4.50000 7.79423i 0.335410 0.580948i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −0.500000 + 2.59808i −0.0370625 + 0.192582i
\(183\) 3.46410i 0.256074i
\(184\) −4.50000 + 7.79423i −0.331744 + 0.574598i
\(185\) −3.00000 −0.220564
\(186\) 13.8564i 1.01600i
\(187\) −9.00000 −0.658145
\(188\) 0 0
\(189\) −9.00000 + 10.3923i −0.654654 + 0.755929i
\(190\) 21.0000 1.52350
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.73205i 0.125000i
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −0.500000 + 0.866025i −0.0358979 + 0.0621770i
\(195\) 5.19615i 0.372104i
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 4.50000 + 7.79423i 0.319801 + 0.553912i
\(199\) 12.5000 21.6506i 0.886102 1.53477i 0.0416556 0.999132i \(-0.486737\pi\)
0.844446 0.535641i \(-0.179930\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 6.92820i 0.488678i
\(202\) 1.50000 + 2.59808i 0.105540 + 0.182800i
\(203\) 7.50000 2.59808i 0.526397 0.182349i
\(204\) −4.50000 2.59808i −0.315063 0.181902i
\(205\) 9.00000 0.628587
\(206\) −6.50000 + 11.2583i −0.452876 + 0.784405i
\(207\) −13.5000 + 23.3827i −0.938315 + 1.62521i
\(208\) 0.500000 + 0.866025i 0.0346688 + 0.0600481i
\(209\) −10.5000 + 18.1865i −0.726300 + 1.25799i
\(210\) −4.50000 12.9904i −0.310530 0.896421i
\(211\) −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i \(-0.221724\pi\)
−0.939156 + 0.343490i \(0.888391\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 20.7846i 1.42414i
\(214\) 4.50000 + 7.79423i 0.307614 + 0.532803i
\(215\) 1.50000 + 2.59808i 0.102299 + 0.177187i
\(216\) 5.19615i 0.353553i
\(217\) −16.0000 13.8564i −1.08615 0.940634i
\(218\) −6.50000 + 11.2583i −0.440236 + 0.762510i
\(219\) −16.5000 9.52628i −1.11497 0.643726i
\(220\) −9.00000 −0.606780
\(221\) −3.00000 −0.201802
\(222\) 1.50000 0.866025i 0.100673 0.0581238i
\(223\) 0.500000 0.866025i 0.0334825 0.0579934i −0.848799 0.528716i \(-0.822674\pi\)
0.882281 + 0.470723i \(0.156007\pi\)
\(224\) 2.00000 + 1.73205i 0.133631 + 0.115728i
\(225\) 6.00000 + 10.3923i 0.400000 + 0.692820i
\(226\) −4.50000 7.79423i −0.299336 0.518464i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) −10.5000 + 6.06218i −0.695379 + 0.401478i
\(229\) 6.50000 11.2583i 0.429532 0.743971i −0.567300 0.823511i \(-0.692012\pi\)
0.996832 + 0.0795401i \(0.0253452\pi\)
\(230\) −13.5000 23.3827i −0.890164 1.54181i
\(231\) 13.5000 + 2.59808i 0.888235 + 0.170941i
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i \(-0.197997\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(234\) 1.50000 + 2.59808i 0.0980581 + 0.169842i
\(235\) 0 0
\(236\) 0 0
\(237\) 27.7128i 1.80014i
\(238\) −7.50000 + 2.59808i −0.486153 + 0.168408i
\(239\) 1.50000 + 2.59808i 0.0970269 + 0.168056i 0.910453 0.413613i \(-0.135733\pi\)
−0.813426 + 0.581669i \(0.802400\pi\)
\(240\) −4.50000 2.59808i −0.290474 0.167705i
\(241\) 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i \(-0.0291519\pi\)
−0.577107 + 0.816668i \(0.695819\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) 15.5885i 1.00000i
\(244\) 2.00000 0.128037
\(245\) −19.5000 7.79423i −1.24581 0.497955i
\(246\) −4.50000 + 2.59808i −0.286910 + 0.165647i
\(247\) −3.50000 + 6.06218i −0.222700 + 0.385727i
\(248\) −8.00000 −0.508001
\(249\) 13.5000 + 7.79423i 0.855528 + 0.493939i
\(250\) 3.00000 0.189737
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 6.00000 + 5.19615i 0.377964 + 0.327327i
\(253\) 27.0000 1.69748
\(254\) 4.00000 0.250982
\(255\) 13.5000 7.79423i 0.845403 0.488094i
\(256\) 1.00000 0.0625000
\(257\) 10.5000 18.1865i 0.654972 1.13444i −0.326929 0.945049i \(-0.606014\pi\)
0.981901 0.189396i \(-0.0606529\pi\)
\(258\) −1.50000 0.866025i −0.0933859 0.0539164i
\(259\) 0.500000 2.59808i 0.0310685 0.161437i
\(260\) −3.00000 −0.186052
\(261\) 4.50000 7.79423i 0.278543 0.482451i
\(262\) 7.50000 12.9904i 0.463352 0.802548i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) 4.50000 2.59808i 0.276956 0.159901i
\(265\) −4.50000 7.79423i −0.276433 0.478796i
\(266\) −3.50000 + 18.1865i −0.214599 + 1.11509i
\(267\) 4.50000 2.59808i 0.275396 0.159000i
\(268\) −4.00000 −0.244339
\(269\) −7.50000 + 12.9904i −0.457283 + 0.792038i −0.998816 0.0486418i \(-0.984511\pi\)
0.541533 + 0.840679i \(0.317844\pi\)
\(270\) −13.5000 7.79423i −0.821584 0.474342i
\(271\) −2.50000 4.33013i −0.151864 0.263036i 0.780049 0.625719i \(-0.215194\pi\)
−0.931913 + 0.362682i \(0.881861\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 4.50000 + 0.866025i 0.272352 + 0.0524142i
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) 6.00000 10.3923i 0.361814 0.626680i
\(276\) 13.5000 + 7.79423i 0.812605 + 0.469157i
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) −3.50000 6.06218i −0.209916 0.363585i
\(279\) −24.0000 −1.43684
\(280\) −7.50000 + 2.59808i −0.448211 + 0.155265i
\(281\) 10.5000 18.1865i 0.626377 1.08492i −0.361895 0.932219i \(-0.617870\pi\)
0.988273 0.152699i \(-0.0487965\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 12.0000 0.712069
\(285\) 36.3731i 2.15455i
\(286\) 1.50000 2.59808i 0.0886969 0.153627i
\(287\) −1.50000 + 7.79423i −0.0885422 + 0.460079i
\(288\) 3.00000 0.176777
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 4.50000 + 7.79423i 0.264249 + 0.457693i
\(291\) 1.50000 + 0.866025i 0.0879316 + 0.0507673i
\(292\) −5.50000 + 9.52628i −0.321863 + 0.557483i
\(293\) 4.50000 + 7.79423i 0.262893 + 0.455344i 0.967009 0.254741i \(-0.0819901\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(294\) 12.0000 1.73205i 0.699854 0.101015i
\(295\) 0 0
\(296\) −0.500000 0.866025i −0.0290619 0.0503367i
\(297\) 13.5000 7.79423i 0.783349 0.452267i
\(298\) −4.50000 + 7.79423i −0.260678 + 0.451508i
\(299\) 9.00000 0.520483
\(300\) 6.00000 3.46410i 0.346410 0.200000i
\(301\) −2.50000 + 0.866025i −0.144098 + 0.0499169i
\(302\) −3.50000 6.06218i −0.201402 0.348839i
\(303\) 4.50000 2.59808i 0.258518 0.149256i
\(304\) 3.50000 + 6.06218i 0.200739 + 0.347690i
\(305\) −3.00000 + 5.19615i −0.171780 + 0.297531i
\(306\) −4.50000 + 7.79423i −0.257248 + 0.445566i
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 1.50000 7.79423i 0.0854704 0.444117i
\(309\) 19.5000 + 11.2583i 1.10932 + 0.640464i
\(310\) 12.0000 20.7846i 0.681554 1.18049i
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 1.50000 0.866025i 0.0849208 0.0490290i
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 22.0000 1.24153
\(315\) −22.5000 + 7.79423i −1.26773 + 0.439155i
\(316\) −16.0000 −0.900070
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 4.50000 + 2.59808i 0.252347 + 0.145693i
\(319\) −9.00000 −0.503903
\(320\) −1.50000 + 2.59808i −0.0838525 + 0.145237i
\(321\) 13.5000 7.79423i 0.753497 0.435031i
\(322\) 22.5000 7.79423i 1.25388 0.434355i
\(323\) −21.0000 −1.16847
\(324\) 9.00000 0.500000
\(325\) 2.00000 3.46410i 0.110940 0.192154i
\(326\) −9.50000 16.4545i −0.526156 0.911330i
\(327\) 19.5000 + 11.2583i 1.07835 + 0.622587i
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) 0 0
\(330\) 15.5885i 0.858116i
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 4.50000 7.79423i 0.246970 0.427764i
\(333\) −1.50000 2.59808i −0.0821995 0.142374i
\(334\) −7.50000 12.9904i −0.410382 0.710802i
\(335\) 6.00000 10.3923i 0.327815 0.567792i
\(336\) 3.00000 3.46410i 0.163663 0.188982i
\(337\) 6.50000 + 11.2583i 0.354078 + 0.613280i 0.986960 0.160968i \(-0.0514616\pi\)
−0.632882 + 0.774248i \(0.718128\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) −13.5000 + 7.79423i −0.733219 + 0.423324i
\(340\) −4.50000 7.79423i −0.244047 0.422701i
\(341\) 12.0000 + 20.7846i 0.649836 + 1.12555i
\(342\) 10.5000 + 18.1865i 0.567775 + 0.983415i
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) −40.5000 + 23.3827i −2.18045 + 1.25888i
\(346\) 6.00000 0.322562
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) −4.50000 2.59808i −0.241225 0.139272i
\(349\) −11.5000 + 19.9186i −0.615581 + 1.06622i 0.374701 + 0.927146i \(0.377745\pi\)
−0.990282 + 0.139072i \(0.955588\pi\)
\(350\) 2.00000 10.3923i 0.106904 0.555492i
\(351\) 4.50000 2.59808i 0.240192 0.138675i
\(352\) −1.50000 2.59808i −0.0799503 0.138478i
\(353\) −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i \(-0.192107\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(354\) 0 0
\(355\) −18.0000 + 31.1769i −0.955341 + 1.65470i
\(356\) −1.50000 2.59808i −0.0794998 0.137698i
\(357\) 4.50000 + 12.9904i 0.238165 + 0.687524i
\(358\) −10.5000 + 18.1865i −0.554942 + 0.961188i
\(359\) −4.50000 7.79423i −0.237501 0.411364i 0.722496 0.691375i \(-0.242995\pi\)
−0.959997 + 0.280012i \(0.909662\pi\)
\(360\) −4.50000 + 7.79423i −0.237171 + 0.410792i
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −2.00000 −0.105118
\(363\) 3.00000 + 1.73205i 0.157459 + 0.0909091i
\(364\) 0.500000 2.59808i 0.0262071 0.136176i
\(365\) −16.5000 28.5788i −0.863649 1.49588i
\(366\) 3.46410i 0.181071i
\(367\) −8.50000 14.7224i −0.443696 0.768505i 0.554264 0.832341i \(-0.313000\pi\)
−0.997960 + 0.0638362i \(0.979666\pi\)
\(368\) 4.50000 7.79423i 0.234579 0.406302i
\(369\) 4.50000 + 7.79423i 0.234261 + 0.405751i
\(370\) 3.00000 0.155963
\(371\) 7.50000 2.59808i 0.389381 0.134885i
\(372\) 13.8564i 0.718421i
\(373\) 6.50000 11.2583i 0.336557 0.582934i −0.647225 0.762299i \(-0.724071\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) 9.00000 0.465379
\(375\) 5.19615i 0.268328i
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) 9.00000 10.3923i 0.462910 0.534522i
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) −21.0000 −1.07728
\(381\) 6.92820i 0.354943i
\(382\) 0 0
\(383\) −7.50000 + 12.9904i −0.383232 + 0.663777i −0.991522 0.129937i \(-0.958522\pi\)
0.608290 + 0.793715i \(0.291856\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 18.0000 + 15.5885i 0.917365 + 0.794461i
\(386\) −14.0000 −0.712581
\(387\) −1.50000 + 2.59808i −0.0762493 + 0.132068i
\(388\) 0.500000 0.866025i 0.0253837 0.0439658i
\(389\) −13.5000 23.3827i −0.684477 1.18555i −0.973601 0.228257i \(-0.926697\pi\)
0.289124 0.957292i \(-0.406636\pi\)
\(390\) 5.19615i 0.263117i
\(391\) 13.5000 + 23.3827i 0.682724 + 1.18251i
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) −22.5000 12.9904i −1.13497 0.655278i
\(394\) −18.0000 −0.906827
\(395\) 24.0000 41.5692i 1.20757 2.09157i
\(396\) −4.50000 7.79423i −0.226134 0.391675i
\(397\) 6.50000 + 11.2583i 0.326226 + 0.565039i 0.981760 0.190126i \(-0.0608897\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(398\) −12.5000 + 21.6506i −0.626568 + 1.08525i
\(399\) 31.5000 + 6.06218i 1.57697 + 0.303488i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −13.5000 + 23.3827i −0.674158 + 1.16768i 0.302556 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214544i \(0.931173\pi\)
\(402\) 6.92820i 0.345547i
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) −1.50000 2.59808i −0.0746278 0.129259i
\(405\) −13.5000 + 23.3827i −0.670820 + 1.16190i
\(406\) −7.50000 + 2.59808i −0.372219 + 0.128940i
\(407\) −1.50000 + 2.59808i −0.0743522 + 0.128782i
\(408\) 4.50000 + 2.59808i 0.222783 + 0.128624i
\(409\) −34.0000 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(410\) −9.00000 −0.444478
\(411\) −13.5000 + 7.79423i −0.665906 + 0.384461i
\(412\) 6.50000 11.2583i 0.320232 0.554658i
\(413\) 0 0
\(414\) 13.5000 23.3827i 0.663489 1.14920i
\(415\) 13.5000 + 23.3827i 0.662689 + 1.14781i
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) −10.5000 + 6.06218i −0.514187 + 0.296866i
\(418\) 10.5000 18.1865i 0.513572 0.889532i
\(419\) −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i \(-0.237220\pi\)
−0.954759 + 0.297382i \(0.903887\pi\)
\(420\) 4.50000 + 12.9904i 0.219578 + 0.633866i
\(421\) −17.5000 + 30.3109i −0.852898 + 1.47726i 0.0256838 + 0.999670i \(0.491824\pi\)
−0.878582 + 0.477592i \(0.841510\pi\)
\(422\) 2.50000 + 4.33013i 0.121698 + 0.210787i
\(423\) 0 0
\(424\) 1.50000 2.59808i 0.0728464 0.126174i
\(425\) 12.0000 0.582086
\(426\) 20.7846i 1.00702i
\(427\) −4.00000 3.46410i −0.193574 0.167640i
\(428\) −4.50000 7.79423i −0.217516 0.376748i
\(429\) −4.50000 2.59808i −0.217262 0.125436i
\(430\) −1.50000 2.59808i −0.0723364 0.125290i
\(431\) −13.5000 + 23.3827i −0.650272 + 1.12630i 0.332785 + 0.943003i \(0.392012\pi\)
−0.983057 + 0.183301i \(0.941322\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 16.0000 + 13.8564i 0.768025 + 0.665129i
\(435\) 13.5000 7.79423i 0.647275 0.373705i
\(436\) 6.50000 11.2583i 0.311294 0.539176i
\(437\) 63.0000 3.01370
\(438\) 16.5000 + 9.52628i 0.788400 + 0.455183i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 9.00000 0.429058
\(441\) −3.00000 20.7846i −0.142857 0.989743i
\(442\) 3.00000 0.142695
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) −1.50000 + 0.866025i −0.0711868 + 0.0410997i
\(445\) 9.00000 0.426641
\(446\) −0.500000 + 0.866025i −0.0236757 + 0.0410075i
\(447\) 13.5000 + 7.79423i 0.638528 + 0.368654i
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −6.00000 10.3923i −0.282843 0.489898i
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) 4.50000 + 7.79423i 0.211662 + 0.366610i
\(453\) −10.5000 + 6.06218i −0.493333 + 0.284826i
\(454\) −1.50000 2.59808i −0.0703985 0.121934i
\(455\) 6.00000 + 5.19615i 0.281284 + 0.243599i
\(456\) 10.5000 6.06218i 0.491708 0.283887i
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −6.50000 + 11.2583i −0.303725 + 0.526067i
\(459\) 13.5000 + 7.79423i 0.630126 + 0.363803i
\(460\) 13.5000 + 23.3827i 0.629441 + 1.09022i
\(461\) 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i \(-0.766122\pi\)
0.951584 + 0.307388i \(0.0994551\pi\)
\(462\) −13.5000 2.59808i −0.628077 0.120873i
\(463\) −20.5000 35.5070i −0.952716 1.65015i −0.739511 0.673145i \(-0.764943\pi\)
−0.213205 0.977007i \(-0.568390\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) −36.0000 20.7846i −1.66946 0.963863i
\(466\) 1.50000 + 2.59808i 0.0694862 + 0.120354i
\(467\) 1.50000 + 2.59808i 0.0694117 + 0.120225i 0.898642 0.438682i \(-0.144554\pi\)
−0.829231 + 0.558906i \(0.811221\pi\)
\(468\) −1.50000 2.59808i −0.0693375 0.120096i
\(469\) 8.00000 + 6.92820i 0.369406 + 0.319915i
\(470\) 0 0
\(471\) 38.1051i 1.75579i
\(472\) 0 0
\(473\) 3.00000 0.137940
\(474\) 27.7128i 1.27289i
\(475\) 14.0000 24.2487i 0.642364 1.11261i
\(476\) 7.50000 2.59808i 0.343762 0.119083i
\(477\) 4.50000 7.79423i 0.206041 0.356873i
\(478\) −1.50000 2.59808i −0.0686084 0.118833i
\(479\) 1.50000 + 2.59808i 0.0685367 + 0.118709i 0.898257 0.439470i \(-0.144834\pi\)
−0.829721 + 0.558179i \(0.811500\pi\)
\(480\) 4.50000 + 2.59808i 0.205396 + 0.118585i
\(481\) −0.500000 + 0.866025i −0.0227980 + 0.0394874i
\(482\) −6.50000 11.2583i −0.296067 0.512803i
\(483\) −13.5000 38.9711i −0.614271 1.77325i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 1.50000 + 2.59808i 0.0681115 + 0.117973i
\(486\) 15.5885i 0.707107i
\(487\) 12.5000 21.6506i 0.566429 0.981084i −0.430486 0.902597i \(-0.641658\pi\)
0.996915 0.0784867i \(-0.0250088\pi\)
\(488\) −2.00000 −0.0905357
\(489\) −28.5000 + 16.4545i −1.28881 + 0.744097i
\(490\) 19.5000 + 7.79423i 0.880920 + 0.352107i
\(491\) −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i \(-0.323806\pi\)
−0.999552 + 0.0299272i \(0.990472\pi\)
\(492\) 4.50000 2.59808i 0.202876 0.117130i
\(493\) −4.50000 7.79423i −0.202670 0.351034i
\(494\) 3.50000 6.06218i 0.157472 0.272750i
\(495\) 27.0000 1.21356
\(496\) 8.00000 0.359211
\(497\) −24.0000 20.7846i −1.07655 0.932317i
\(498\) −13.5000 7.79423i −0.604949 0.349268i
\(499\) 12.5000 21.6506i 0.559577 0.969216i −0.437955 0.898997i \(-0.644297\pi\)
0.997532 0.0702185i \(-0.0223697\pi\)
\(500\) −3.00000 −0.134164
\(501\) −22.5000 + 12.9904i −1.00523 + 0.580367i
\(502\) −12.0000 −0.535586
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) −6.00000 5.19615i −0.267261 0.231455i
\(505\) 9.00000 0.400495
\(506\) −27.0000 −1.20030
\(507\) 18.0000 + 10.3923i 0.799408 + 0.461538i
\(508\) −4.00000 −0.177471
\(509\) 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i \(-0.769415\pi\)
0.948353 + 0.317217i \(0.102748\pi\)
\(510\) −13.5000 + 7.79423i −0.597790 + 0.345134i
\(511\) 27.5000 9.52628i 1.21653 0.421418i
\(512\) −1.00000 −0.0441942
\(513\) 31.5000 18.1865i 1.39076 0.802955i
\(514\) −10.5000 + 18.1865i −0.463135 + 0.802174i
\(515\) 19.5000 + 33.7750i 0.859273 + 1.48830i
\(516\) 1.50000 + 0.866025i 0.0660338 + 0.0381246i
\(517\) 0 0
\(518\) −0.500000 + 2.59808i −0.0219687 + 0.114153i
\(519\) 10.3923i 0.456172i
\(520\) 3.00000 0.131559
\(521\) −1.50000 + 2.59808i −0.0657162 + 0.113824i −0.897011 0.442007i \(-0.854267\pi\)
0.831295 + 0.555831i \(0.187600\pi\)
\(522\) −4.50000 + 7.79423i −0.196960 + 0.341144i
\(523\) 3.50000 + 6.06218i 0.153044 + 0.265081i 0.932345 0.361569i \(-0.117759\pi\)
−0.779301 + 0.626650i \(0.784426\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) −18.0000 3.46410i −0.785584 0.151186i
\(526\) 4.50000 + 7.79423i 0.196209 + 0.339845i
\(527\) −12.0000 + 20.7846i −0.522728 + 0.905392i
\(528\) −4.50000 + 2.59808i −0.195837 + 0.113067i
\(529\) −29.0000 50.2295i −1.26087 2.18389i
\(530\) 4.50000 + 7.79423i 0.195468 + 0.338560i
\(531\) 0 0
\(532\) 3.50000 18.1865i 0.151744 0.788486i
\(533\) 1.50000 2.59808i 0.0649722 0.112535i
\(534\) −4.50000 + 2.59808i −0.194734 + 0.112430i
\(535\) 27.0000 1.16731
\(536\) 4.00000 0.172774
\(537\) 31.5000 + 18.1865i 1.35933 + 0.784807i
\(538\) 7.50000 12.9904i 0.323348 0.560055i
\(539\) −16.5000 + 12.9904i −0.710705 + 0.559535i
\(540\) 13.5000 + 7.79423i 0.580948 + 0.335410i
\(541\) −5.50000 9.52628i −0.236463 0.409567i 0.723234 0.690604i \(-0.242655\pi\)
−0.959697 + 0.281037i \(0.909322\pi\)
\(542\) 2.50000 + 4.33013i 0.107384 + 0.185995i
\(543\) 3.46410i 0.148659i
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) 19.5000 + 33.7750i 0.835288 + 1.44676i
\(546\) −4.50000 0.866025i −0.192582 0.0370625i
\(547\) −5.50000 + 9.52628i −0.235163 + 0.407314i −0.959320 0.282321i \(-0.908896\pi\)
0.724157 + 0.689635i \(0.242229\pi\)
\(548\) 4.50000 + 7.79423i 0.192230 + 0.332953i
\(549\) −6.00000 −0.256074
\(550\) −6.00000 + 10.3923i −0.255841 + 0.443129i
\(551\) −21.0000 −0.894630
\(552\) −13.5000 7.79423i −0.574598 0.331744i
\(553\) 32.0000 + 27.7128i 1.36078 + 1.17847i
\(554\) −0.500000 0.866025i −0.0212430 0.0367939i
\(555\) 5.19615i 0.220564i
\(556\) 3.50000 + 6.06218i 0.148433 + 0.257094i
\(557\) 4.50000 7.79423i 0.190671 0.330252i −0.754802 0.655953i \(-0.772267\pi\)
0.945473 + 0.325701i \(0.105600\pi\)
\(558\) 24.0000 1.01600
\(559\) 1.00000 0.0422955
\(560\) 7.50000 2.59808i 0.316933 0.109789i
\(561\) 15.5885i 0.658145i
\(562\) −10.5000 + 18.1865i −0.442916 + 0.767153i
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) −27.0000 −1.13590
\(566\) 4.00000 0.168133
\(567\) −18.0000 15.5885i −0.755929 0.654654i
\(568\) −12.0000 −0.503509
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 36.3731i 1.52350i
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) −1.50000 + 2.59808i −0.0627182 + 0.108631i
\(573\) 0 0
\(574\) 1.50000 7.79423i 0.0626088 0.325325i
\(575\) −36.0000 −1.50130
\(576\) −3.00000 −0.125000
\(577\) 12.5000 21.6506i 0.520382 0.901328i −0.479337 0.877631i \(-0.659123\pi\)
0.999719 0.0236970i \(-0.00754370\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) 24.2487i 1.00774i
\(580\) −4.50000 7.79423i −0.186852 0.323638i
\(581\) −22.5000 + 7.79423i −0.933457 + 0.323359i
\(582\) −1.50000 0.866025i −0.0621770 0.0358979i
\(583\) −9.00000 −0.372742
\(584\) 5.50000 9.52628i 0.227592 0.394200i
\(585\) 9.00000 0.372104
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i \(-0.853053\pi\)
0.833408 + 0.552658i \(0.186386\pi\)
\(588\) −12.0000 + 1.73205i −0.494872 + 0.0714286i
\(589\) 28.0000 + 48.4974i 1.15372 + 1.99830i
\(590\) 0 0
\(591\) 31.1769i 1.28245i
\(592\) 0.500000 + 0.866025i 0.0205499 + 0.0355934i
\(593\) −19.5000 33.7750i −0.800769 1.38697i −0.919111 0.394000i \(-0.871091\pi\)
0.118342 0.992973i \(-0.462242\pi\)
\(594\) −13.5000 + 7.79423i −0.553912 + 0.319801i
\(595\) −4.50000 + 23.3827i −0.184482 + 0.958597i
\(596\) 4.50000 7.79423i 0.184327 0.319264i
\(597\) 37.5000 + 21.6506i 1.53477 + 0.886102i
\(598\) −9.00000 −0.368037
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −6.00000 + 3.46410i −0.244949 + 0.141421i
\(601\) 12.5000 21.6506i 0.509886 0.883148i −0.490049 0.871695i \(-0.663021\pi\)
0.999934 0.0114528i \(-0.00364562\pi\)
\(602\) 2.50000 0.866025i 0.101892 0.0352966i
\(603\) 12.0000 0.488678
\(604\) 3.50000 + 6.06218i 0.142413 + 0.246667i
\(605\) 3.00000 + 5.19615i 0.121967 + 0.211254i
\(606\) −4.50000 + 2.59808i −0.182800 + 0.105540i
\(607\) 6.50000 11.2583i 0.263827 0.456962i −0.703429 0.710766i \(-0.748349\pi\)
0.967256 + 0.253804i \(0.0816819\pi\)
\(608\) −3.50000 6.06218i −0.141944 0.245854i
\(609\) 4.50000 + 12.9904i 0.182349 + 0.526397i
\(610\) 3.00000 5.19615i 0.121466 0.210386i
\(611\) 0 0
\(612\) 4.50000 7.79423i 0.181902 0.315063i
\(613\) −11.5000 + 19.9186i −0.464481 + 0.804504i −0.999178 0.0405396i \(-0.987092\pi\)
0.534697 + 0.845044i \(0.320426\pi\)
\(614\) 28.0000 1.12999
\(615\) 15.5885i 0.628587i
\(616\) −1.50000 + 7.79423i −0.0604367 + 0.314038i
\(617\) 22.5000 + 38.9711i 0.905816 + 1.56892i 0.819818 + 0.572624i \(0.194074\pi\)
0.0859976 + 0.996295i \(0.472592\pi\)
\(618\) −19.5000 11.2583i −0.784405 0.452876i
\(619\) −8.50000 14.7224i −0.341644 0.591744i 0.643094 0.765787i \(-0.277650\pi\)
−0.984738 + 0.174042i \(0.944317\pi\)
\(620\) −12.0000 + 20.7846i −0.481932 + 0.834730i
\(621\) −40.5000 23.3827i −1.62521 0.938315i
\(622\) 24.0000 0.962312
\(623\) −1.50000 + 7.79423i −0.0600962 + 0.312269i
\(624\) −1.50000 + 0.866025i −0.0600481 + 0.0346688i
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 10.0000 0.399680
\(627\) −31.5000 18.1865i −1.25799 0.726300i
\(628\) −22.0000 −0.877896
\(629\) −3.00000 −0.119618
\(630\) 22.5000 7.79423i 0.896421 0.310530i
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 16.0000 0.636446
\(633\) 7.50000 4.33013i 0.298098 0.172107i
\(634\) −18.0000 −0.714871
\(635\) 6.00000 10.3923i 0.238103 0.412406i
\(636\) −4.50000 2.59808i −0.178437 0.103020i
\(637\) −5.50000 + 4.33013i −0.217918 + 0.171566i
\(638\) 9.00000 0.356313
\(639\) −36.0000 −1.42414
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.330997 + 0.943632i \(0.607385\pi\)
\(642\) −13.5000 + 7.79423i −0.532803 + 0.307614i
\(643\) −14.5000 25.1147i −0.571824 0.990429i −0.996379 0.0850262i \(-0.972903\pi\)
0.424555 0.905402i \(-0.360431\pi\)
\(644\) −22.5000 + 7.79423i −0.886624 + 0.307136i
\(645\) −4.50000 + 2.59808i −0.177187 + 0.102299i
\(646\) 21.0000 0.826234
\(647\) 10.5000 18.1865i 0.412798 0.714986i −0.582397 0.812905i \(-0.697885\pi\)
0.995194 + 0.0979182i \(0.0312184\pi\)
\(648\) −9.00000 −0.353553
\(649\) 0 0
\(650\) −2.00000 + 3.46410i −0.0784465 + 0.135873i
\(651\) 24.0000 27.7128i 0.940634 1.08615i
\(652\) 9.50000 + 16.4545i 0.372049 + 0.644407i
\(653\) −7.50000 + 12.9904i −0.293498 + 0.508353i −0.974634 0.223803i \(-0.928153\pi\)
0.681137 + 0.732156i \(0.261486\pi\)
\(654\) −19.5000 11.2583i −0.762510 0.440236i
\(655\) −22.5000 38.9711i −0.879148 1.52273i
\(656\) −1.50000 2.59808i −0.0585652 0.101438i
\(657\) 16.5000 28.5788i 0.643726 1.11497i
\(658\) 0 0
\(659\) −1.50000 + 2.59808i −0.0584317 + 0.101207i −0.893762 0.448542i \(-0.851943\pi\)
0.835330 + 0.549749i \(0.185277\pi\)
\(660\) 15.5885i 0.606780i
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) −8.00000 −0.310929
\(663\) 5.19615i 0.201802i
\(664\) −4.50000 + 7.79423i −0.174634 + 0.302475i
\(665\) 42.0000 + 36.3731i 1.62869 + 1.41049i
\(666\) 1.50000 + 2.59808i 0.0581238 + 0.100673i
\(667\) 13.5000 + 23.3827i 0.522722 + 0.905381i
\(668\) 7.50000 + 12.9904i 0.290184 + 0.502613i
\(669\) 1.50000 + 0.866025i 0.0579934 + 0.0334825i
\(670\) −6.00000 + 10.3923i −0.231800 + 0.401490i
\(671\) 3.00000 + 5.19615i 0.115814 + 0.200595i
\(672\) −3.00000 + 3.46410i −0.115728 + 0.133631i
\(673\) −17.5000 + 30.3109i −0.674575 + 1.16840i 0.302017 + 0.953302i \(0.402340\pi\)
−0.976593 + 0.215096i \(0.930993\pi\)
\(674\) −6.50000 11.2583i −0.250371 0.433655i
\(675\) −18.0000 + 10.3923i −0.692820 + 0.400000i
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 13.5000 7.79423i 0.518464 0.299336i
\(679\) −2.50000 + 0.866025i −0.0959412 + 0.0332350i
\(680\) 4.50000 + 7.79423i 0.172567 + 0.298895i
\(681\) −4.50000 + 2.59808i −0.172440 + 0.0995585i
\(682\) −12.0000 20.7846i −0.459504 0.795884i
\(683\) 4.50000 7.79423i 0.172188 0.298238i −0.766997 0.641651i \(-0.778250\pi\)
0.939184 + 0.343413i \(0.111583\pi\)
\(684\) −10.5000 18.1865i −0.401478 0.695379i
\(685\) −27.0000 −1.03162
\(686\) −10.0000 + 15.5885i −0.381802 + 0.595170i
\(687\) 19.5000 + 11.2583i 0.743971 + 0.429532i
\(688\) 0.500000 0.866025i 0.0190623 0.0330169i
\(689\) −3.00000 −0.114291
\(690\) 40.5000 23.3827i 1.54181 0.890164i
\(691\) 44.0000 1.67384 0.836919 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) −6.00000 −0.228086
\(693\) −4.50000 + 23.3827i −0.170941 + 0.888235i
\(694\) −12.0000 −0.455514
\(695\) −21.0000 −0.796575
\(696\) 4.50000 + 2.59808i 0.170572 + 0.0984798i
\(697\) 9.00000 0.340899
\(698\) 11.5000 19.9186i 0.435281 0.753930i
\(699\) 4.50000 2.59808i 0.170206 0.0982683i
\(700\) −2.00000 + 10.3923i −0.0755929 + 0.392792i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) −4.50000 + 2.59808i −0.169842 + 0.0980581i
\(703\) −3.50000 + 6.06218i −0.132005 + 0.228639i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 1.50000 + 2.59808i 0.0564532 + 0.0977799i
\(707\) −1.50000 + 7.79423i −0.0564133 + 0.293132i
\(708\) 0 0
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 18.0000 31.1769i 0.675528 1.17005i
\(711\) 48.0000 1.80014
\(712\) 1.50000 + 2.59808i 0.0562149 + 0.0973670i
\(713\) 36.0000 62.3538i 1.34821 2.33517i
\(714\) −4.50000 12.9904i −0.168408 0.486153i
\(715\) −4.50000 7.79423i −0.168290 0.291488i
\(716\) 10.5000 18.1865i 0.392403 0.679663i
\(717\) −4.50000 + 2.59808i −0.168056 + 0.0970269i
\(718\) 4.50000 + 7.79423i 0.167939 + 0.290878i
\(719\) 7.50000 + 12.9904i 0.279703 + 0.484459i 0.971311 0.237814i \(-0.0764307\pi\)
−0.691608 + 0.722273i \(0.743097\pi\)
\(720\) 4.50000 7.79423i 0.167705 0.290474i
\(721\) −32.5000 + 11.2583i −1.21036 + 0.419282i
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) −19.5000 + 11.2583i −0.725213 + 0.418702i
\(724\) 2.00000 0.0743294
\(725\) 12.0000 0.445669
\(726\) −3.00000 1.73205i −0.111340 0.0642824i
\(727\) 6.50000 11.2583i 0.241072 0.417548i −0.719948 0.694028i \(-0.755834\pi\)
0.961020 + 0.276479i \(0.0891678\pi\)
\(728\) −0.500000 + 2.59808i −0.0185312 + 0.0962911i
\(729\) −27.0000 −1.00000
\(730\) 16.5000 + 28.5788i 0.610692 + 1.05775i
\(731\) 1.50000 + 2.59808i 0.0554795 + 0.0960933i
\(732\) 3.46410i 0.128037i
\(733\) 0.500000 0.866025i 0.0184679 0.0319874i −0.856644 0.515908i \(-0.827454\pi\)
0.875112 + 0.483921i \(0.160788\pi\)
\(734\) 8.50000 + 14.7224i 0.313741 + 0.543415i
\(735\) 13.5000 33.7750i 0.497955 1.24581i
\(736\) −4.50000 + 7.79423i −0.165872 + 0.287299i
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) −4.50000 7.79423i −0.165647 0.286910i
\(739\) −11.5000 + 19.9186i −0.423034 + 0.732717i −0.996235 0.0866983i \(-0.972368\pi\)
0.573200 + 0.819415i \(0.305702\pi\)
\(740\) −3.00000 −0.110282
\(741\) −10.5000 6.06218i −0.385727 0.222700i
\(742\) −7.50000 + 2.59808i −0.275334 + 0.0953784i
\(743\) −10.5000 18.1865i −0.385208 0.667199i 0.606590 0.795015i \(-0.292537\pi\)
−0.991798 + 0.127815i \(0.959204\pi\)
\(744\) 13.8564i 0.508001i
\(745\) 13.5000 + 23.3827i 0.494602 + 0.856675i
\(746\) −6.50000 + 11.2583i −0.237982 + 0.412197i
\(747\) −13.5000 + 23.3827i −0.493939 + 0.855528i
\(748\) −9.00000 −0.329073
\(749\) −4.50000 + 23.3827i −0.164426 + 0.854385i
\(750\) 5.19615i 0.189737i
\(751\) 6.50000 11.2583i 0.237188 0.410822i −0.722718 0.691143i \(-0.757107\pi\)
0.959906 + 0.280321i \(0.0904408\pi\)
\(752\) 0 0
\(753\) 20.7846i 0.757433i
\(754\) 3.00000 0.109254
\(755\) −21.0000 −0.764268
\(756\) −9.00000 + 10.3923i −0.327327 + 0.377964i
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 28.0000 1.01701
\(759\) 46.7654i 1.69748i
\(760\) 21.0000 0.761750
\(761\) 22.5000 38.9711i 0.815624 1.41270i −0.0932544 0.995642i \(-0.529727\pi\)
0.908879 0.417061i \(-0.136940\pi\)
\(762\) 6.92820i 0.250982i
\(763\) −32.5000 + 11.2583i −1.17658 + 0.407579i
\(764\) 0 0
\(765\) 13.5000 + 23.3827i 0.488094 + 0.845403i
\(766\) 7.50000 12.9904i 0.270986 0.469362i
\(767\) 0 0
\(768\) 1.73205i 0.0625000i
\(769\) −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i \(-0.302780\pi\)
−0.995397 + 0.0958377i \(0.969447\pi\)
\(770\) −18.0000 15.5885i −0.648675 0.561769i
\(771\) 31.5000 + 18.1865i 1.13444 + 0.654972i
\(772\) 14.0000 0.503871
\(773\) −13.5000 + 23.3827i −0.485561 + 0.841017i −0.999862 0.0165929i \(-0.994718\pi\)
0.514301 + 0.857610i \(0.328051\pi\)
\(774\) 1.50000 2.59808i 0.0539164 0.0933859