Properties

Label 126.2.e.a.121.1
Level $126$
Weight $2$
Character 126.121
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 121.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 126.121
Dual form 126.2.e.a.25.1

$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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 −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 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 −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 1.73205i 0.500000i
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 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 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 3.00000 0.707107
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) −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 0.768613 + 0.639713i \(0.220947\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 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 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 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 −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −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 −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) −3.00000 3.46410i −0.462910 0.534522i
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 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 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 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 −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) −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 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 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 −0.934508 0.355942i \(-0.884160\pi\)
0.775509 + 0.631337i \(0.217494\pi\)
\(90\) −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 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) −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 −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 4.50000 2.59808i 0.445566 0.257248i
\(103\) 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) −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 −0.997298 0.0734594i \(-0.976596\pi\)
0.562267 + 0.826956i \(0.309929\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 6.50000 + 11.2583i 0.622587 + 1.07835i 0.989002 + 0.147901i \(0.0472517\pi\)
−0.366415 + 0.930451i \(0.619415\pi\)
\(110\) 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 −0.572938 0.819599i \(-0.694196\pi\)
0.996262 + 0.0863794i \(0.0275297\pi\)
\(114\) 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 −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) −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 −0.607233 0.794524i \(-0.707721\pi\)
0.991694 + 0.128618i \(0.0410540\pi\)
\(138\) −13.5000 + 7.79423i −1.14920 + 0.663489i
\(139\) 3.50000 6.06218i 0.296866 0.514187i −0.678551 0.734553i \(-0.737392\pi\)
0.975417 + 0.220366i \(0.0707252\pi\)
\(140\) 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 0.989355 0.145519i \(-0.0464853\pi\)
−0.620701 + 0.784047i \(0.713152\pi\)
\(150\) −6.00000 3.46410i −0.489898 0.282843i
\(151\) 3.50000 6.06218i 0.284826 0.493333i −0.687741 0.725956i \(-0.741398\pi\)
0.972567 + 0.232623i \(0.0747309\pi\)
\(152\) −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 −0.206518 0.978443i \(-0.566213\pi\)
0.950615 0.310372i \(-0.100454\pi\)
\(164\) −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 −0.415068 0.909790i \(-0.636242\pi\)
0.995436 0.0954356i \(-0.0304244\pi\)
\(168\) −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 0.929114 + 0.369792i \(0.120571\pi\)
−0.144308 + 0.989533i \(0.546095\pi\)
\(180\) 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 0.844446 + 0.535641i \(0.179930\pi\)
0.0416556 + 0.999132i \(0.486737\pi\)
\(200\) 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 −0.939156 0.343490i \(-0.888391\pi\)
0.767049 + 0.641588i \(0.221724\pi\)
\(212\) −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 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) 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 −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) −10.5000 6.06218i −0.695379 0.401478i
\(229\) 6.50000 + 11.2583i 0.429532 + 0.743971i 0.996832 0.0795401i \(-0.0253452\pi\)
−0.567300 + 0.823511i \(0.692012\pi\)
\(230\) −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 −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) 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 −0.813426 0.581669i \(-0.802400\pi\)
0.910453 + 0.413613i \(0.135733\pi\)
\(240\) −4.50000 + 2.59808i −0.290474 + 0.167705i
\(241\) 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i \(-0.695819\pi\)
0.995809 + 0.0914555i \(0.0291519\pi\)
\(242\) −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 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) −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 −0.970758 0.240059i \(-0.922833\pi\)
0.693276 + 0.720672i \(0.256167\pi\)
\(264\) 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 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) −13.5000 + 7.79423i −0.821584 + 0.474342i
\(271\) −2.50000 + 4.33013i −0.151864 + 0.263036i −0.931913 0.362682i \(-0.881861\pi\)
0.780049 + 0.625719i \(0.215194\pi\)
\(272\) −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 −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) −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 0.988273 + 0.152699i \(0.0487965\pi\)
−0.361895 + 0.932219i \(0.617870\pi\)
\(282\) 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 −0.704117 0.710084i \(-0.748657\pi\)
0.967009 + 0.254741i \(0.0819901\pi\)
\(294\) 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 −0.632882 0.774248i \(-0.718128\pi\)
0.986960 + 0.160968i \(0.0514616\pi\)
\(338\) −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 −0.990282 0.139072i \(-0.955588\pi\)
0.374701 0.927146i \(-0.377745\pi\)
\(350\) 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 −0.903179 0.429263i \(-0.858773\pi\)
0.823343 + 0.567545i \(0.192107\pi\)
\(354\) 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 −0.959997 0.280012i \(-0.909662\pi\)
0.722496 + 0.691375i \(0.242995\pi\)
\(360\) −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 −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 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 0.983783 0.179364i \(-0.0574041\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 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 0.608290 0.793715i \(-0.291856\pi\)
−0.991522 + 0.129937i \(0.958522\pi\)
\(384\) 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 0.289124 + 0.957292i \(0.406636\pi\)
−0.973601 + 0.228257i \(0.926697\pi\)
\(390\) 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 −0.655534 0.755166i \(-0.727556\pi\)
0.981760 + 0.190126i \(0.0608897\pi\)
\(398\) −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 −0.976714 0.214544i \(-0.931173\pi\)
0.302556 0.953131i \(-0.402160\pi\)
\(402\) 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 −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 4.50000 12.9904i 0.219578 0.633866i
\(421\) −17.5000 30.3109i −0.852898 1.47726i −0.878582 0.477592i \(-0.841510\pi\)
0.0256838 0.999670i \(-0.491824\pi\)
\(422\) 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 −0.983057 0.183301i \(-0.941322\pi\)
0.332785 0.943003i \(-0.392012\pi\)
\(432\) 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 0.951584 0.307388i \(-0.0994551\pi\)
−0.741998 + 0.670402i \(0.766122\pi\)
\(462\) −13.5000 + 2.59808i −0.628077 + 0.120873i
\(463\) −20.5000 + 35.5070i −0.952716 + 1.65015i −0.213205 + 0.977007i \(0.568390\pi\)
−0.739511 + 0.673145i \(0.764943\pi\)
\(464\) −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 −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) −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 −0.829721 0.558179i \(-0.811500\pi\)
0.898257 + 0.439470i \(0.144834\pi\)
\(480\) 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 0.996915 + 0.0784867i \(0.0250088\pi\)
−0.430486 + 0.902597i \(0.641658\pi\)
\(488\) −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 −0.999552 0.0299272i \(-0.990472\pi\)
0.525694 + 0.850674i \(0.323806\pi\)
\(492\) 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 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) −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 0.948353 0.317217i \(-0.102748\pi\)
−0.748894 + 0.662690i \(0.769415\pi\)
\(510\) −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 0.831295 0.555831i \(-0.187600\pi\)
−0.897011 + 0.442007i \(0.854267\pi\)
\(522\) −4.50000 7.79423i −0.196960 0.341144i
\(523\) 3.50000 6.06218i 0.153044 0.265081i −0.779301 0.626650i \(-0.784426\pi\)
0.932345 + 0.361569i \(0.117759\pi\)
\(524\) −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 −0.959697 0.281037i \(-0.909322\pi\)
0.723234 + 0.690604i \(0.242655\pi\)
\(542\) 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 0.724157 0.689635i \(-0.242229\pi\)
−0.959320 + 0.282321i \(0.908896\pi\)
\(548\) 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 0.945473 0.325701i \(-0.105600\pi\)
−0.754802 + 0.655953i \(0.772267\pi\)
\(558\) 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 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) −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 0.833408 0.552658i \(-0.186386\pi\)
−0.895320 + 0.445424i \(0.853053\pi\)
\(588\) −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 0.118342 + 0.992973i \(0.462242\pi\)
−0.919111 + 0.394000i \(0.871091\pi\)
\(594\) −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 0.999934 + 0.0114528i \(0.00364562\pi\)
−0.490049 + 0.871695i \(0.663021\pi\)
\(602\) 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 0.967256 0.253804i \(-0.0816819\pi\)
−0.703429 + 0.710766i \(0.748349\pi\)
\(608\) −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 0.534697 0.845044i \(-0.320426\pi\)
−0.999178 + 0.0405396i \(0.987092\pi\)
\(614\) 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 0.0859976 0.996295i \(-0.472592\pi\)
0.819818 0.572624i \(-0.194074\pi\)
\(618\) −19.5000 + 11.2583i −0.784405 + 0.452876i
\(619\) −8.50000 + 14.7224i −0.341644 + 0.591744i −0.984738 0.174042i \(-0.944317\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) −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 −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) −13.5000 7.79423i −0.532803 0.307614i
\(643\) −14.5000 + 25.1147i −0.571824 + 0.990429i 0.424555 + 0.905402i \(0.360431\pi\)
−0.996379 + 0.0850262i \(0.972903\pi\)
\(644\) −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 0.995194 0.0979182i \(-0.0312184\pi\)
−0.582397 + 0.812905i \(0.697885\pi\)
\(648\) −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 0.681137 0.732156i \(-0.261486\pi\)
−0.974634 + 0.223803i \(0.928153\pi\)
\(654\) −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 0.835330 0.549749i \(-0.185277\pi\)
−0.893762 + 0.448542i \(0.851943\pi\)
\(660\) 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 −0.976593 0.215096i \(-0.930993\pi\)
0.302017 0.953302i \(-0.402340\pi\)
\(674\) −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 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) −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 −0.691608 0.722273i \(-0.743097\pi\)
0.971311 + 0.237814i \(0.0764307\pi\)
\(720\) 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 0.961020 0.276479i \(-0.0891678\pi\)
−0.719948 + 0.694028i \(0.755834\pi\)
\(728\) −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 0.875112 0.483921i \(-0.160788\pi\)
−0.856644 + 0.515908i \(0.827454\pi\)
\(734\) 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 0.573200 0.819415i \(-0.305702\pi\)
−0.996235 + 0.0866983i \(0.972368\pi\)
\(740\) −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 −0.991798 0.127815i \(-0.959204\pi\)
0.606590 + 0.795015i \(0.292537\pi\)
\(744\) 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 0.959906 0.280321i \(-0.0904408\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(752\) 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 0.908879 + 0.417061i \(0.136940\pi\)
−0.0932544 + 0.995642i \(0.529727\pi\)
\(762\) 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 −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) −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 0.514301 0.857610i \(-0.328051\pi\)
−0.999862 + 0.0165929i \(0.994718\pi\)
\(774\) 1.50000 + 2.59808i