Properties

Label 42.2.e.b.37.1
Level $42$
Weight $2$
Character 42.37
Analytic conductor $0.335$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 42.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.335371688489\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 42.37
Dual form 42.2.e.b.25.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} -4.00000 q^{13} +(2.00000 - 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} +3.00000 q^{20} +(-0.500000 - 2.59808i) q^{21} -3.00000 q^{22} +(0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(-2.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 - 2.59808i) q^{28} +9.00000 q^{29} +(1.50000 - 2.59808i) q^{30} +(0.500000 + 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(-6.00000 + 5.19615i) q^{35} +1.00000 q^{36} +(-4.00000 + 6.92820i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(2.00000 + 3.46410i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-2.50000 - 0.866025i) q^{42} -10.0000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(3.00000 - 5.19615i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(1.50000 + 2.59808i) q^{53} +(0.500000 - 0.866025i) q^{54} +9.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} -4.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(5.00000 - 8.66025i) q^{61} +1.00000 q^{62} +(-2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(1.50000 + 2.59808i) q^{66} +(5.00000 + 8.66025i) q^{67} +(1.50000 + 7.79423i) q^{70} -6.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(4.00000 + 6.92820i) q^{74} +(-2.00000 + 3.46410i) q^{75} -4.00000 q^{76} +(-1.50000 - 7.79423i) q^{77} +4.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} -9.00000 q^{83} +(-2.00000 + 1.73205i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(-4.50000 - 7.79423i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-3.00000 + 5.19615i) q^{89} -3.00000 q^{90} +(-10.0000 - 3.46410i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(0.500000 - 0.866025i) q^{96} -1.00000 q^{97} +(6.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} - 3q^{5} - 2q^{6} + 5q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} - 3q^{5} - 2q^{6} + 5q^{7} - 2q^{8} - q^{9} + 3q^{10} - 3q^{11} - q^{12} - 8q^{13} + 4q^{14} + 6q^{15} - q^{16} + q^{18} + 4q^{19} + 6q^{20} - q^{21} - 6q^{22} + q^{24} - 4q^{25} - 4q^{26} + 2q^{27} - q^{28} + 18q^{29} + 3q^{30} + q^{31} + q^{32} - 3q^{33} - 12q^{35} + 2q^{36} - 8q^{37} - 4q^{38} + 4q^{39} + 3q^{40} - 5q^{42} - 20q^{43} - 3q^{44} - 3q^{45} + 6q^{47} + 2q^{48} + 11q^{49} - 8q^{50} + 4q^{52} + 3q^{53} + q^{54} + 18q^{55} - 5q^{56} - 8q^{57} + 9q^{58} - 3q^{59} - 3q^{60} + 10q^{61} + 2q^{62} - 4q^{63} + 2q^{64} + 12q^{65} + 3q^{66} + 10q^{67} + 3q^{70} - 12q^{71} + q^{72} - 2q^{73} + 8q^{74} - 4q^{75} - 8q^{76} - 3q^{77} + 8q^{78} + q^{79} - 3q^{80} - q^{81} - 18q^{83} - 4q^{84} - 10q^{86} - 9q^{87} + 3q^{88} - 6q^{89} - 6q^{90} - 20q^{91} + q^{93} - 6q^{94} + 12q^{95} + q^{96} - 2q^{97} + 13q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) −1.00000 −0.408248
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 2.00000 1.73205i 0.534522 0.462910i
\(15\) 3.00000 0.774597
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) 3.00000 0.670820
\(21\) −0.500000 2.59808i −0.109109 0.566947i
\(22\) −3.00000 −0.639602
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −2.00000 + 3.46410i −0.392232 + 0.679366i
\(27\) 1.00000 0.192450
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 0 0
\(35\) −6.00000 + 5.19615i −1.01419 + 0.878310i
\(36\) 1.00000 0.166667
\(37\) −4.00000 + 6.92820i −0.657596 + 1.13899i 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) −2.00000 3.46410i −0.324443 0.561951i
\(39\) 2.00000 + 3.46410i 0.320256 + 0.554700i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −2.50000 0.866025i −0.385758 0.133631i
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) −1.50000 2.59808i −0.223607 0.387298i
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 1.00000 0.144338
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 9.00000 1.21356
\(56\) −2.50000 0.866025i −0.334077 0.115728i
\(57\) −4.00000 −0.529813
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) −1.50000 2.59808i −0.193649 0.335410i
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 1.00000 0.127000
\(63\) −2.00000 + 1.73205i −0.251976 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 1.50000 + 2.59808i 0.184637 + 0.319801i
\(67\) 5.00000 + 8.66025i 0.610847 + 1.05802i 0.991098 + 0.133135i \(0.0425044\pi\)
−0.380251 + 0.924883i \(0.624162\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.50000 + 7.79423i 0.179284 + 0.931589i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) −4.00000 −0.458831
\(77\) −1.50000 7.79423i −0.170941 0.888235i
\(78\) 4.00000 0.452911
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) −2.00000 + 1.73205i −0.218218 + 0.188982i
\(85\) 0 0
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) −3.00000 −0.316228
\(91\) −10.0000 3.46410i −1.04828 0.363137i
\(92\) 0 0
\(93\) 0.500000 0.866025i 0.0518476 0.0898027i
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 6.00000 + 10.3923i 0.615587 + 1.06623i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 6.50000 2.59808i 0.656599 0.262445i
\(99\) 3.00000 0.301511
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 4.00000 0.392232
\(105\) 7.50000 + 2.59808i 0.731925 + 0.253546i
\(106\) 3.00000 0.291386
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 4.50000 7.79423i 0.429058 0.743151i
\(111\) 8.00000 0.759326
\(112\) −2.00000 + 1.73205i −0.188982 + 0.163663i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) −2.00000 + 3.46410i −0.187317 + 0.324443i
\(115\) 0 0
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) 2.00000 3.46410i 0.184900 0.320256i
\(118\) −3.00000 −0.276172
\(119\) 0 0
\(120\) −3.00000 −0.273861
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −5.00000 8.66025i −0.452679 0.784063i
\(123\) 0 0
\(124\) 0.500000 0.866025i 0.0449013 0.0777714i
\(125\) −3.00000 −0.268328
\(126\) 0.500000 + 2.59808i 0.0445435 + 0.231455i
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 5.00000 + 8.66025i 0.440225 + 0.762493i
\(130\) −6.00000 10.3923i −0.526235 0.911465i
\(131\) 4.50000 7.79423i 0.393167 0.680985i −0.599699 0.800226i \(-0.704713\pi\)
0.992865 + 0.119241i \(0.0380462\pi\)
\(132\) 3.00000 0.261116
\(133\) 8.00000 6.92820i 0.693688 0.600751i
\(134\) 10.0000 0.863868
\(135\) −1.50000 + 2.59808i −0.129099 + 0.223607i
\(136\) 0 0
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 7.50000 + 2.59808i 0.633866 + 0.219578i
\(141\) −6.00000 −0.505291
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) 6.00000 + 10.3923i 0.501745 + 0.869048i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −13.5000 + 23.3827i −1.12111 + 1.94183i
\(146\) −2.00000 −0.165521
\(147\) 1.00000 6.92820i 0.0824786 0.571429i
\(148\) 8.00000 0.657596
\(149\) −9.00000 + 15.5885i −0.737309 + 1.27706i 0.216394 + 0.976306i \(0.430570\pi\)
−0.953703 + 0.300750i \(0.902763\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) 0.500000 + 0.866025i 0.0406894 + 0.0704761i 0.885653 0.464348i \(-0.153711\pi\)
−0.844963 + 0.534824i \(0.820378\pi\)
\(152\) −2.00000 + 3.46410i −0.162221 + 0.280976i
\(153\) 0 0
\(154\) −7.50000 2.59808i −0.604367 0.209359i
\(155\) −3.00000 −0.240966
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −0.500000 0.866025i −0.0397779 0.0688973i
\(159\) 1.50000 2.59808i 0.118958 0.206041i
\(160\) −3.00000 −0.237171
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 0 0
\(165\) −4.50000 7.79423i −0.350325 0.606780i
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0.500000 + 2.59808i 0.0385758 + 0.200446i
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 2.00000 + 3.46410i 0.152944 + 0.264906i
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) −9.00000 −0.682288
\(175\) −2.00000 10.3923i −0.151186 0.785584i
\(176\) 3.00000 0.226134
\(177\) −1.50000 + 2.59808i −0.112747 + 0.195283i
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) −1.50000 + 2.59808i −0.111803 + 0.193649i
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −8.00000 + 6.92820i −0.592999 + 0.513553i
\(183\) −10.0000 −0.739221
\(184\) 0 0
\(185\) −12.0000 20.7846i −0.882258 1.52811i
\(186\) −0.500000 0.866025i −0.0366618 0.0635001i
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 2.50000 + 0.866025i 0.181848 + 0.0629941i
\(190\) 12.0000 0.870572
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i \(0.0730182\pi\)
−0.289980 + 0.957033i \(0.593649\pi\)
\(194\) −0.500000 + 0.866025i −0.0358979 + 0.0621770i
\(195\) −12.0000 −0.859338
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 1.50000 2.59808i 0.106600 0.184637i
\(199\) −10.0000 17.3205i −0.708881 1.22782i −0.965272 0.261245i \(-0.915867\pi\)
0.256391 0.966573i \(-0.417466\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 5.00000 8.66025i 0.352673 0.610847i
\(202\) 18.0000 1.26648
\(203\) 22.5000 + 7.79423i 1.57919 + 0.547048i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 0 0
\(208\) 2.00000 3.46410i 0.138675 0.240192i
\(209\) −12.0000 −0.830057
\(210\) 6.00000 5.19615i 0.414039 0.358569i
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) 15.0000 25.9808i 1.02299 1.77187i
\(216\) −1.00000 −0.0680414
\(217\) 0.500000 + 2.59808i 0.0339422 + 0.176369i
\(218\) −14.0000 −0.948200
\(219\) −1.00000 + 1.73205i −0.0675737 + 0.117041i
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) 0 0
\(222\) 4.00000 6.92820i 0.268462 0.464991i
\(223\) −19.0000 −1.27233 −0.636167 0.771551i \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) 0.500000 + 2.59808i 0.0334077 + 0.173591i
\(225\) 4.00000 0.266667
\(226\) 0 0
\(227\) 13.5000 + 23.3827i 0.896026 + 1.55196i 0.832529 + 0.553981i \(0.186892\pi\)
0.0634974 + 0.997982i \(0.479775\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) 0 0
\(231\) −6.00000 + 5.19615i −0.394771 + 0.341882i
\(232\) −9.00000 −0.590879
\(233\) 12.0000 20.7846i 0.786146 1.36165i −0.142166 0.989843i \(-0.545407\pi\)
0.928312 0.371802i \(-0.121260\pi\)
\(234\) −2.00000 3.46410i −0.130744 0.226455i
\(235\) 9.00000 + 15.5885i 0.587095 + 1.01688i
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) −1.50000 + 2.59808i −0.0968246 + 0.167705i
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −10.0000 −0.640184
\(245\) −19.5000 + 7.79423i −1.24581 + 0.497955i
\(246\) 0 0
\(247\) −8.00000 + 13.8564i −0.509028 + 0.881662i
\(248\) −0.500000 0.866025i −0.0317500 0.0549927i
\(249\) 4.50000 + 7.79423i 0.285176 + 0.493939i
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) 2.50000 + 0.866025i 0.157485 + 0.0545545i
\(253\) 0 0
\(254\) 2.50000 4.33013i 0.156864 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 10.0000 0.622573
\(259\) −16.0000 + 13.8564i −0.994192 + 0.860995i
\(260\) −12.0000 −0.744208
\(261\) −4.50000 + 7.79423i −0.278543 + 0.482451i
\(262\) −4.50000 7.79423i −0.278011 0.481529i
\(263\) 3.00000 + 5.19615i 0.184988 + 0.320408i 0.943572 0.331166i \(-0.107442\pi\)
−0.758585 + 0.651575i \(0.774109\pi\)
\(264\) 1.50000 2.59808i 0.0923186 0.159901i
\(265\) −9.00000 −0.552866
\(266\) −2.00000 10.3923i −0.122628 0.637193i
\(267\) 6.00000 0.367194
\(268\) 5.00000 8.66025i 0.305424 0.529009i
\(269\) −10.5000 18.1865i −0.640196 1.10885i −0.985389 0.170321i \(-0.945520\pi\)
0.345192 0.938532i \(-0.387814\pi\)
\(270\) 1.50000 + 2.59808i 0.0912871 + 0.158114i
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) 0 0
\(273\) 2.00000 + 10.3923i 0.121046 + 0.628971i
\(274\) −18.0000 −1.08742
\(275\) −6.00000 + 10.3923i −0.361814 + 0.626680i
\(276\) 0 0
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) 1.00000 1.73205i 0.0599760 0.103882i
\(279\) −1.00000 −0.0598684
\(280\) 6.00000 5.19615i 0.358569 0.310530i
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 6.00000 10.3923i 0.355409 0.615587i
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 13.5000 + 23.3827i 0.792747 + 1.37308i
\(291\) 0.500000 + 0.866025i 0.0293105 + 0.0507673i
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) 33.0000 1.92788 0.963940 0.266119i \(-0.0857413\pi\)
0.963940 + 0.266119i \(0.0857413\pi\)
\(294\) −5.50000 4.33013i −0.320767 0.252538i
\(295\) 9.00000 0.524000
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) −1.50000 2.59808i −0.0870388 0.150756i
\(298\) 9.00000 + 15.5885i 0.521356 + 0.903015i
\(299\) 0 0
\(300\) 4.00000 0.230940
\(301\) −25.0000 8.66025i −1.44098 0.499169i
\(302\) 1.00000 0.0575435
\(303\) 9.00000 15.5885i 0.517036 0.895533i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 15.0000 + 25.9808i 0.858898 + 1.48765i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) −6.00000 + 5.19615i −0.341882 + 0.296078i
\(309\) 8.00000 0.455104
\(310\) −1.50000 + 2.59808i −0.0851943 + 0.147561i
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) −2.00000 3.46410i −0.113228 0.196116i
\(313\) 15.5000 26.8468i 0.876112 1.51747i 0.0205381 0.999789i \(-0.493462\pi\)
0.855574 0.517681i \(-0.173205\pi\)
\(314\) 4.00000 0.225733
\(315\) −1.50000 7.79423i −0.0845154 0.439155i
\(316\) −1.00000 −0.0562544
\(317\) −4.50000 + 7.79423i −0.252745 + 0.437767i −0.964281 0.264883i \(-0.914667\pi\)
0.711535 + 0.702650i \(0.248000\pi\)
\(318\) −1.50000 2.59808i −0.0841158 0.145693i
\(319\) −13.5000 23.3827i −0.755855 1.30918i
\(320\) −1.50000 + 2.59808i −0.0838525 + 0.145237i
\(321\) −3.00000 −0.167444
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 8.00000 + 13.8564i 0.443760 + 0.768615i
\(326\) −8.00000 13.8564i −0.443079 0.767435i
\(327\) −7.00000 + 12.1244i −0.387101 + 0.670478i
\(328\) 0 0
\(329\) 12.0000 10.3923i 0.661581 0.572946i
\(330\) −9.00000 −0.495434
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) 4.50000 + 7.79423i 0.246970 + 0.427764i
\(333\) −4.00000 6.92820i −0.219199 0.379663i
\(334\) 3.00000 5.19615i 0.164153 0.284321i
\(335\) −30.0000 −1.63908
\(336\) 2.50000 + 0.866025i 0.136386 + 0.0472456i
\(337\) −7.00000 −0.381314 −0.190657 0.981657i \(-0.561062\pi\)
−0.190657 + 0.981657i \(0.561062\pi\)
\(338\) 1.50000 2.59808i 0.0815892 0.141317i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.50000 2.59808i 0.0812296 0.140694i
\(342\) 4.00000 0.216295
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 10.0000 0.539164
\(345\) 0 0
\(346\) 9.00000 + 15.5885i 0.483843 + 0.838041i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) −4.50000 + 7.79423i −0.241225 + 0.417815i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) −10.0000 3.46410i −0.534522 0.185164i
\(351\) −4.00000 −0.213504
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 1.50000 + 2.59808i 0.0797241 + 0.138086i
\(355\) 9.00000 15.5885i 0.477670 0.827349i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −15.0000 + 25.9808i −0.791670 + 1.37121i 0.133263 + 0.991081i \(0.457455\pi\)
−0.924932 + 0.380131i \(0.875879\pi\)
\(360\) 1.50000 + 2.59808i 0.0790569 + 0.136931i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 4.00000 6.92820i 0.210235 0.364138i
\(363\) −2.00000 −0.104973
\(364\) 2.00000 + 10.3923i 0.104828 + 0.544705i
\(365\) 6.00000 0.314054
\(366\) −5.00000 + 8.66025i −0.261354 + 0.452679i
\(367\) 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −24.0000 −1.24770
\(371\) 1.50000 + 7.79423i 0.0778761 + 0.404656i
\(372\) −1.00000 −0.0518476
\(373\) −4.00000 + 6.92820i −0.207112 + 0.358729i −0.950804 0.309794i \(-0.899740\pi\)
0.743691 + 0.668523i \(0.233073\pi\)
\(374\) 0 0
\(375\) 1.50000 + 2.59808i 0.0774597 + 0.134164i
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −36.0000 −1.85409
\(378\) 2.00000 1.73205i 0.102869 0.0890871i
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 6.00000 10.3923i 0.307794 0.533114i
\(381\) −2.50000 4.33013i −0.128079 0.221839i
\(382\) 0 0
\(383\) −9.00000 + 15.5885i −0.459879 + 0.796533i −0.998954 0.0457244i \(-0.985440\pi\)
0.539076 + 0.842257i \(0.318774\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 22.5000 + 7.79423i 1.14671 + 0.397231i
\(386\) 19.0000 0.967075
\(387\) 5.00000 8.66025i 0.254164 0.440225i
\(388\) 0.500000 + 0.866025i 0.0253837 + 0.0439658i
\(389\) 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) −6.00000 + 10.3923i −0.303822 + 0.526235i
\(391\) 0 0
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) −9.00000 −0.453990
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 1.50000 + 2.59808i 0.0754732 + 0.130723i
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) 2.00000 3.46410i 0.100377 0.173858i −0.811463 0.584404i \(-0.801328\pi\)
0.911840 + 0.410546i \(0.134662\pi\)
\(398\) −20.0000 −1.00251
\(399\) −10.0000 3.46410i −0.500626 0.173422i
\(400\) 4.00000 0.200000
\(401\) −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i \(0.371202\pi\)
−0.992932 + 0.118686i \(0.962132\pi\)
\(402\) −5.00000 8.66025i −0.249377 0.431934i
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 9.00000 15.5885i 0.447767 0.775555i
\(405\) 3.00000 0.149071
\(406\) 18.0000 15.5885i 0.893325 0.773642i
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i \(0.0454247\pi\)
−0.371750 + 0.928333i \(0.621242\pi\)
\(410\) 0 0
\(411\) −9.00000 + 15.5885i −0.443937 + 0.768922i
\(412\) 8.00000 0.394132
\(413\) −1.50000 7.79423i −0.0738102 0.383529i
\(414\) 0 0
\(415\) 13.5000 23.3827i 0.662689 1.14781i
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) −1.00000 1.73205i −0.0489702 0.0848189i
\(418\) −6.00000 + 10.3923i −0.293470 + 0.508304i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −1.50000 7.79423i −0.0731925 0.380319i
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 7.00000 12.1244i 0.340755 0.590204i
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) −1.50000 2.59808i −0.0728464 0.126174i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) 20.0000 17.3205i 0.967868 0.838198i
\(428\) −3.00000 −0.145010
\(429\) 6.00000 10.3923i 0.289683 0.501745i
\(430\) −15.0000 25.9808i −0.723364 1.25290i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 2.50000 + 0.866025i 0.120004 + 0.0415705i
\(435\) 27.0000 1.29455
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 0 0
\(438\) 1.00000 + 1.73205i 0.0477818 + 0.0827606i
\(439\) −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i \(0.481332\pi\)
−0.893843 + 0.448379i \(0.852001\pi\)
\(440\) −9.00000 −0.429058
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) 0 0
\(443\) 16.5000 28.5788i 0.783939 1.35782i −0.145692 0.989330i \(-0.546541\pi\)
0.929631 0.368492i \(-0.120126\pi\)
\(444\) −4.00000 6.92820i −0.189832 0.328798i
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) −9.50000 + 16.4545i −0.449838 + 0.779142i
\(447\) 18.0000 0.851371
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 2.00000 3.46410i 0.0942809 0.163299i
\(451\) 0 0
\(452\) 0 0
\(453\) 0.500000 0.866025i 0.0234920 0.0406894i
\(454\) 27.0000 1.26717
\(455\) 24.0000 20.7846i 1.12514 0.974398i
\(456\) 4.00000 0.187317
\(457\) 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) −2.00000 3.46410i −0.0934539 0.161867i
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 1.50000 + 7.79423i 0.0697863 + 0.362620i
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −4.50000 + 7.79423i −0.208907 + 0.361838i
\(465\) 1.50000 + 2.59808i 0.0695608 + 0.120483i
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) −18.0000 + 31.1769i −0.832941 + 1.44270i 0.0627555 + 0.998029i \(0.480011\pi\)
−0.895696 + 0.444667i \(0.853322\pi\)
\(468\) −4.00000 −0.184900
\(469\) 5.00000 + 25.9808i 0.230879 + 1.19968i
\(470\) 18.0000 0.830278
\(471\) 2.00000 3.46410i 0.0921551 0.159617i
\(472\) 1.50000 + 2.59808i 0.0690431 + 0.119586i
\(473\) 15.0000 + 25.9808i 0.689701 + 1.19460i
\(474\) −0.500000 + 0.866025i −0.0229658 + 0.0397779i
\(475\) −16.0000 −0.734130
\(476\) 0 0
\(477\) −3.00000 −0.137361
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 1.50000 + 2.59808i 0.0684653 + 0.118585i
\(481\) 16.0000 27.7128i 0.729537 1.26360i
\(482\) 1.00000 0.0455488
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 1.50000 2.59808i 0.0681115 0.117973i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −20.5000 35.5070i −0.928944 1.60898i −0.785093 0.619378i \(-0.787385\pi\)
−0.143851 0.989599i \(-0.545949\pi\)
\(488\) −5.00000 + 8.66025i −0.226339 + 0.392031i
\(489\) −16.0000 −0.723545
\(490\) −3.00000 + 20.7846i −0.135526 + 0.938953i
\(491\) −33.0000 −1.48927 −0.744635 0.667472i \(-0.767376\pi\)
−0.744635 + 0.667472i \(0.767376\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 8.00000 + 13.8564i 0.359937 + 0.623429i
\(495\) −4.50000 + 7.79423i −0.202260 + 0.350325i
\(496\) −1.00000 −0.0449013
\(497\) −15.0000 5.19615i −0.672842 0.233079i
\(498\) 9.00000 0.403300
\(499\) −1.00000 + 1.73205i −0.0447661 + 0.0775372i −0.887540 0.460730i \(-0.847588\pi\)
0.842774 + 0.538267i \(0.180921\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) −3.00000 5.19615i −0.134030 0.232147i
\(502\) 13.5000 23.3827i 0.602534 1.04362i
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 2.00000 1.73205i 0.0890871 0.0771517i
\(505\) −54.0000 −2.40297
\(506\) 0 0
\(507\) −1.50000 2.59808i −0.0666173 0.115385i
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) 1.50000 2.59808i 0.0664863 0.115158i −0.830866 0.556473i \(-0.812154\pi\)
0.897352 + 0.441315i \(0.145488\pi\)
\(510\) 0 0
\(511\) −1.00000 5.19615i −0.0442374 0.229864i
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 3.46410i 0.0883022 0.152944i
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) −12.0000 20.7846i −0.528783 0.915879i
\(516\) 5.00000 8.66025i 0.220113 0.381246i
\(517\) −18.0000 −0.791639
\(518\) 4.00000 + 20.7846i 0.175750 + 0.913223i
\(519\) 18.0000 0.790112
\(520\) −6.00000 + 10.3923i −0.263117 + 0.455733i
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) −9.00000 −0.393167
\(525\) −8.00000 + 6.92820i −0.349149 + 0.302372i
\(526\) 6.00000 0.261612
\(527\) 0 0
\(528\) −1.50000 2.59808i −0.0652791 0.113067i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) −4.50000 + 7.79423i −0.195468 + 0.338560i
\(531\) 3.00000 0.130189
\(532\) −10.0000 3.46410i −0.433555 0.150188i
\(533\) 0 0
\(534\) 3.00000 5.19615i 0.129823 0.224860i
\(535\) 4.50000 + 7.79423i 0.194552 + 0.336974i
\(536\) −5.00000 8.66025i −0.215967 0.374066i
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) −21.0000 −0.905374
\(539\) 3.00000 20.7846i 0.129219 0.895257i
\(540\) 3.00000 0.129099
\(541\) −13.0000 + 22.5167i −0.558914 + 0.968067i 0.438674 + 0.898646i \(0.355448\pi\)
−0.997587 + 0.0694205i \(0.977885\pi\)
\(542\) 5.50000 + 9.52628i 0.236245 + 0.409189i
\(543\) −4.00000 6.92820i −0.171656 0.297318i
\(544\) 0 0
\(545\) 42.0000 1.79908
\(546\) 10.0000 + 3.46410i 0.427960 + 0.148250i
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −9.00000 + 15.5885i −0.384461 + 0.665906i
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) 6.00000 + 10.3923i 0.255841 + 0.443129i
\(551\) 18.0000 31.1769i 0.766826 1.32818i
\(552\) 0 0
\(553\) 2.00000 1.73205i 0.0850487 0.0736543i
\(554\) −8.00000 −0.339887
\(555\) −12.0000 + 20.7846i −0.509372 + 0.882258i
\(556\) −1.00000 1.73205i −0.0424094 0.0734553i
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) −0.500000 + 0.866025i −0.0211667 + 0.0366618i
\(559\) 40.0000 1.69182
\(560\) −1.50000 7.79423i −0.0633866 0.329366i
\(561\) 0 0
\(562\) 3.00000 5.19615i 0.126547 0.219186i
\(563\) −19.5000 33.7750i −0.821827 1.42345i −0.904320 0.426855i \(-0.859622\pi\)
0.0824933 0.996592i \(-0.473712\pi\)
\(564\) 3.00000 + 5.19615i 0.126323 + 0.218797i
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) −0.500000 2.59808i −0.0209980 0.109109i
\(568\) 6.00000 0.251754
\(569\) 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i \(-0.561165\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(570\) −6.00000 10.3923i −0.251312 0.435286i
\(571\) 17.0000 + 29.4449i 0.711428 + 1.23223i 0.964321 + 0.264735i \(0.0852845\pi\)
−0.252893 + 0.967494i \(0.581382\pi\)
\(572\) 6.00000 10.3923i 0.250873 0.434524i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −11.5000 19.9186i −0.478751 0.829222i 0.520952 0.853586i \(-0.325577\pi\)
−0.999703 + 0.0243645i \(0.992244\pi\)
\(578\) −8.50000 14.7224i −0.353553 0.612372i
\(579\) 9.50000 16.4545i 0.394807 0.683825i
\(580\) 27.0000 1.12111
\(581\) −22.5000 7.79423i −0.933457 0.323359i
\(582\) 1.00000 0.0414513
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 1.00000 + 1.73205i 0.0413803 + 0.0716728i
\(585\) 6.00000 + 10.3923i 0.248069 + 0.429669i
\(586\) 16.5000 28.5788i 0.681609 1.18058i
\(587\) 21.0000 0.866763 0.433381 0.901211i \(-0.357320\pi\)
0.433381 + 0.901211i \(0.357320\pi\)
\(588\) −6.50000 + 2.59808i −0.268055 + 0.107143i
\(589\) 4.00000 0.164817
\(590\) 4.50000 7.79423i 0.185262 0.320883i
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) −12.0000 + 20.7846i −0.492781 + 0.853522i −0.999965 0.00831589i \(-0.997353\pi\)
0.507184 + 0.861838i \(0.330686\pi\)
\(594\) −3.00000 −0.123091
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) −10.0000 + 17.3205i −0.409273 + 0.708881i
\(598\) 0 0
\(599\) 9.00000 + 15.5885i 0.367730 + 0.636927i 0.989210 0.146503i \(-0.0468017\pi\)
−0.621480 + 0.783430i \(0.713468\pi\)
\(600\) 2.00000 3.46410i 0.0816497 0.141421i
\(601\) 11.0000 0.448699 0.224350 0.974509i \(-0.427974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(602\) −20.0000 + 17.3205i −0.815139 + 0.705931i
\(603\) −10.0000 −0.407231
\(604\) 0.500000 0.866025i 0.0203447 0.0352381i
\(605\) 3.00000 + 5.19615i 0.121967 + 0.211254i
\(606\) −9.00000 15.5885i −0.365600 0.633238i
\(607\) 3.50000 6.06218i 0.142061 0.246056i −0.786212 0.617957i \(-0.787961\pi\)
0.928272 + 0.371901i \(0.121294\pi\)
\(608\) 4.00000 0.162221
\(609\) −4.50000 23.3827i −0.182349 0.947514i
\(610\) 30.0000 1.21466
\(611\) −12.0000 + 20.7846i −0.485468 + 0.840855i
\(612\) 0 0
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) 0 0
\(616\) 1.50000 + 7.79423i 0.0604367 + 0.314038i
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 4.00000 6.92820i 0.160904 0.278693i
\(619\) 17.0000 + 29.4449i 0.683288 + 1.18349i 0.973972 + 0.226670i \(0.0727838\pi\)
−0.290684 + 0.956819i \(0.593883\pi\)
\(620\) 1.50000 + 2.59808i 0.0602414 + 0.104341i
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) −12.0000 + 10.3923i −0.480770 + 0.416359i
\(624\) −4.00000 −0.160128
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) −15.5000 26.8468i −0.619505 1.07301i
\(627\) 6.00000 + 10.3923i 0.239617 + 0.415029i
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 0 0
\(630\) −7.50000 2.59808i −0.298807 0.103510i
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) −0.500000 + 0.866025i −0.0198889 + 0.0344486i
\(633\) −7.00000 12.1244i −0.278225 0.481900i
\(634\) 4.50000 + 7.79423i 0.178718 + 0.309548i
\(635\) −7.50000 + 12.9904i −0.297628 + 0.515508i
\(636\) −3.00000 −0.118958
\(637\) −22.0000 17.3205i −0.871672 0.686264i
\(638\) −27.0000 −1.06894
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) 15.0000 + 25.9808i 0.592464 + 1.02618i 0.993899 + 0.110291i \(0.0351782\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(642\) −1.50000 + 2.59808i −0.0592003 + 0.102538i
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 0 0
\(645\) −30.0000 −1.18125
\(646\) 0 0
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −4.50000 + 7.79423i −0.176640 + 0.305950i
\(650\) 16.0000 0.627572
\(651\) 2.00000 1.73205i 0.0783862 0.0678844i
\(652\) −16.0000 −0.626608
\(653\) −1.50000 + 2.59808i −0.0586995 + 0.101671i −0.893882 0.448303i \(-0.852029\pi\)
0.835182 + 0.549973i \(0.185362\pi\)
\(654\) 7.00000 + 12.1244i 0.273722 + 0.474100i
\(655\) 13.5000 + 23.3827i 0.527489 + 0.913637i
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) −3.00000 15.5885i −0.116952 0.607701i
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) −4.50000 + 7.79423i −0.175162 + 0.303390i
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 10.0000 + 17.3205i 0.388661 + 0.673181i
\(663\) 0 0
\(664\) 9.00000 0.349268
\(665\) 6.00000 + 31.1769i 0.232670 + 1.20899i
\(666\) −8.00000 −0.309994
\(667\) 0 0
\(668\) −3.00000 5.19615i −0.116073 0.201045i
\(669\) 9.50000 + 16.4545i 0.367291 + 0.636167i
\(670\) −15.0000 + 25.9808i −0.579501 + 1.00372i
\(671\) −30.0000 −1.15814
\(672\) 2.00000 1.73205i 0.0771517 0.0668153i
\(673\) 29.0000 1.11787 0.558934 0.829212i \(-0.311211\pi\)
0.558934 + 0.829212i \(0.311211\pi\)
\(674\) −3.50000 + 6.06218i −0.134815 + 0.233506i
\(675\) −2.00000 3.46410i −0.0769800 0.133333i
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) 16.5000 28.5788i 0.634147 1.09837i −0.352549 0.935793i \(-0.614685\pi\)
0.986695 0.162581i \(-0.0519817\pi\)
\(678\) 0 0
\(679\) −2.50000 0.866025i −0.0959412 0.0332350i
\(680\) 0 0
\(681\) 13.5000 23.3827i 0.517321 0.896026i
\(682\) −1.50000 2.59808i −0.0574380 0.0994855i
\(683\) −16.5000 28.5788i −0.631355 1.09354i −0.987275 0.159022i \(-0.949166\pi\)
0.355920 0.934516i \(-0.384168\pi\)
\(684\) 2.00000 3.46410i 0.0764719 0.132453i
\(685\) 54.0000 2.06323
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) −4.00000 −0.152610
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 18.0000 0.684257
\(693\) 7.50000 + 2.59808i 0.284901 + 0.0986928i
\(694\) −12.0000 −0.455514
\(695\) −3.00000 + 5.19615i −0.113796 + 0.197101i
\(696\) 4.50000 + 7.79423i 0.170572 + 0.295439i
\(697\) 0 0
\(698\) 13.0000 22.5167i 0.492057 0.852268i
\(699\) −24.0000 −0.907763
\(700\) −8.00000 + 6.92820i −0.302372 + 0.261861i
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) −2.00000 + 3.46410i −0.0754851 + 0.130744i
\(703\) 16.0000 + 27.7128i 0.603451 + 1.04521i
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) 9.00000 15.5885i 0.338960 0.587095i
\(706\) −24.0000 −0.903252
\(707\) 9.00000 + 46.7654i 0.338480 + 1.75879i
\(708\) 3.00000 0.112747
\(709\) 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) −9.00000 15.5885i −0.337764 0.585024i
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) −36.0000 −1.34632
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 12.0000 + 20.7846i 0.448148 + 0.776215i
\(718\) 15.0000 + 25.9808i 0.559795 + 0.969593i
\(719\) 9.00000 15.5885i 0.335643 0.581351i −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 3.00000 0.111803
\(721\) −16.0000 + 13.8564i −0.595871 + 0.516040i
\(722\) 3.00000 0.111648
\(723\) 0.500000 0.866025i 0.0185952 0.0322078i
\(724\) −4.00000 6.92820i −0.148659 0.257485i
\(725\) −18.0000 31.1769i −0.668503 1.15788i
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) −13.0000 −0.482143 −0.241072 0.970507i \(-0.577499\pi\)
−0.241072 + 0.970507i \(0.577499\pi\)
\(728\) 10.0000 + 3.46410i 0.370625 + 0.128388i
\(729\) 1.00000 0.0370370
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 0 0
\(732\) 5.00000 + 8.66025i 0.184805 + 0.320092i
\(733\) 5.00000 8.66025i 0.184679 0.319874i −0.758789 0.651336i \(-0.774209\pi\)
0.943468 + 0.331463i \(0.107542\pi\)
\(734\) 19.0000 0.701303
\(735\) 16.5000 + 12.9904i 0.608612 + 0.479157i
\(736\) 0 0
\(737\) 15.0000 25.9808i 0.552532 0.957014i
\(738\) 0 0
\(739\) −25.0000 43.3013i −0.919640 1.59286i −0.799962 0.600050i \(-0.795147\pi\)
−0.119677 0.992813i \(-0.538186\pi\)
\(740\) −12.0000 + 20.7846i −0.441129 + 0.764057i
\(741\) 16.0000 0.587775
\(742\) 7.50000 + 2.59808i 0.275334 + 0.0953784i
\(743\) 42.0000 1.54083 0.770415 0.637542i \(-0.220049\pi\)
0.770415 + 0.637542i \(0.220049\pi\)
\(744\) −0.500000 + 0.866025i −0.0183309 + 0.0317500i
\(745\) −27.0000 46.7654i −0.989203 1.71335i
\(746\) 4.00000 + 6.92820i 0.146450 + 0.253660i
\(747\) 4.50000 7.79423i 0.164646 0.285176i
\(748\) 0 0
\(749\) 6.00000 5.19615i 0.219235 0.189863i
\(750\) 3.00000 0.109545
\(751\) 3.50000 6.06218i 0.127717 0.221212i −0.795075 0.606511i \(-0.792568\pi\)
0.922792 + 0.385299i \(0.125902\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) −13.5000 23.3827i −0.491967 0.852112i
\(754\) −18.0000 + 31.1769i −0.655521 + 1.13540i
\(755\) −3.00000 −0.109181
\(756\) −0.500000 2.59808i −0.0181848 0.0944911i
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 4.00000 6.92820i 0.145287 0.251644i
\(759\) 0 0
\(760\) −6.00000 10.3923i −0.217643 0.376969i
\(761\) −6.00000 + 10.3923i −0.217500 + 0.376721i −0.954043 0.299670i \(-0.903123\pi\)
0.736543 + 0.676391i \(0.236457\pi\)
\(762\) −5.00000 −0.181131
\(763\) −7.00000 36.3731i −0.253417 1.31679i
\(764\) 0 0
\(765\) 0 0
\(766\) 9.00000 + 15.5885i 0.325183 + 0.563234i
\(767\) 6.00000 + 10.3923i 0.216647 + 0.375244i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −19.0000 −0.685158 −0.342579 0.939489i \(-0.611300\pi\)
−0.342579 + 0.939489i \(0.611300\pi\)
\(770\) 18.0000 15.5885i 0.648675 0.561769i
\(771\) 6.00000 0.216085
\(772\) 9.50000 16.4545i 0.341912 0.592210i
\(773\) −3.00000 5.19615i −0.107903 0.186893i 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) −5.00000 8.66025i −0.179721 0.311286i
\(775\) 2.00000 3.46410i 0.0718421 0.124434i
\(776\) 1.00000 0.0358979
\(777\) 20.0000 + 6.92820i 0.717496 + 0.248548i
\(778\) 6.00000 0.215110
\(779\) 0 0
\(780\) 6.00000 + 10.3923i 0.214834 + 0.372104i
\(781\) 9.00000 +