Properties

Label 74.2.c.a.47.1
Level $74$
Weight $2$
Character 74.47
Analytic conductor $0.591$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 47.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 74.47
Dual form 74.2.c.a.63.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(-1.00000 + 1.73205i) q^{12} +(3.00000 + 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} -6.00000 q^{23} +(1.00000 + 1.73205i) q^{24} +(2.00000 - 3.46410i) q^{25} +6.00000 q^{26} -4.00000 q^{27} -9.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +10.0000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.00000 - 3.46410i) q^{33} +(1.50000 + 2.59808i) q^{34} +1.00000 q^{36} +(-0.500000 + 6.06218i) q^{37} -2.00000 q^{38} +(6.00000 - 10.3923i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.50000 - 2.59808i) q^{41} -8.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} -1.00000 q^{45} +(-3.00000 + 5.19615i) q^{46} +2.00000 q^{47} +2.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(-2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(3.00000 - 5.19615i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-2.00000 + 3.46410i) q^{57} +(-4.50000 + 7.79423i) q^{58} +(-4.00000 + 6.92820i) q^{59} -2.00000 q^{60} +(2.50000 + 4.33013i) q^{61} +(5.00000 - 8.66025i) q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} -4.00000 q^{66} +(3.00000 + 5.19615i) q^{67} +3.00000 q^{68} +(6.00000 + 10.3923i) q^{69} +(0.500000 - 0.866025i) q^{72} -2.00000 q^{73} +(5.00000 + 3.46410i) q^{74} -8.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(-6.00000 - 10.3923i) q^{78} +(-3.00000 - 5.19615i) q^{79} -1.00000 q^{80} +(5.50000 + 9.52628i) q^{81} -3.00000 q^{82} +(-1.00000 + 1.73205i) q^{83} -3.00000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(9.00000 + 15.5885i) q^{87} -2.00000 q^{88} +(6.50000 - 11.2583i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(3.00000 + 5.19615i) q^{92} +(-10.0000 - 17.3205i) q^{93} +(1.00000 - 1.73205i) q^{94} +(1.00000 - 1.73205i) q^{95} +(1.00000 - 1.73205i) q^{96} +3.00000 q^{97} +(-3.50000 - 6.06218i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} + q^{20} + 2 q^{22} - 12 q^{23} + 2 q^{24} + 4 q^{25} + 12 q^{26} - 8 q^{27} - 18 q^{29} - 2 q^{30} + 20 q^{31} + q^{32} - 4 q^{33} + 3 q^{34} + 2 q^{36} - q^{37} - 4 q^{38} + 12 q^{39} - q^{40} - 3 q^{41} - 16 q^{43} - 2 q^{44} - 2 q^{45} - 6 q^{46} + 4 q^{47} + 4 q^{48} + 7 q^{49} - 4 q^{50} + 12 q^{51} + 6 q^{52} + 6 q^{53} - 4 q^{54} + 2 q^{55} - 4 q^{57} - 9 q^{58} - 8 q^{59} - 4 q^{60} + 5 q^{61} + 10 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{66} + 6 q^{67} + 6 q^{68} + 12 q^{69} + q^{72} - 4 q^{73} + 10 q^{74} - 16 q^{75} - 2 q^{76} - 12 q^{78} - 6 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 2 q^{83} - 6 q^{85} - 8 q^{86} + 18 q^{87} - 4 q^{88} + 13 q^{89} - q^{90} + 6 q^{92} - 20 q^{93} + 2 q^{94} + 2 q^{95} + 2 q^{96} + 6 q^{97} - 7 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) −2.00000 −0.816497
\(7\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.00000 0.316228
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −1.00000 + 1.73205i −0.288675 + 0.500000i
\(13\) 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i \(0.146166\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 0 0
\(15\) 1.00000 1.73205i 0.258199 0.447214i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 0 0
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 1.00000 + 1.73205i 0.204124 + 0.353553i
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 6.00000 1.17670
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −2.00000 3.46410i −0.348155 0.603023i
\(34\) 1.50000 + 2.59808i 0.257248 + 0.445566i
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −0.500000 + 6.06218i −0.0821995 + 0.996616i
\(38\) −2.00000 −0.324443
\(39\) 6.00000 10.3923i 0.960769 1.66410i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) −1.00000 −0.149071
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 2.00000 0.288675
\(49\) 3.50000 6.06218i 0.500000 0.866025i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 6.00000 0.840168
\(52\) 3.00000 5.19615i 0.416025 0.720577i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) −2.00000 + 3.46410i −0.272166 + 0.471405i
\(55\) 1.00000 + 1.73205i 0.134840 + 0.233550i
\(56\) 0 0
\(57\) −2.00000 + 3.46410i −0.264906 + 0.458831i
\(58\) −4.50000 + 7.79423i −0.590879 + 1.02343i
\(59\) −4.00000 + 6.92820i −0.520756 + 0.901975i 0.478953 + 0.877841i \(0.341016\pi\)
−0.999709 + 0.0241347i \(0.992317\pi\)
\(60\) −2.00000 −0.258199
\(61\) 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i \(-0.0629528\pi\)
−0.660415 + 0.750901i \(0.729619\pi\)
\(62\) 5.00000 8.66025i 0.635001 1.09985i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) −4.00000 −0.492366
\(67\) 3.00000 + 5.19615i 0.366508 + 0.634811i 0.989017 0.147802i \(-0.0472198\pi\)
−0.622509 + 0.782613i \(0.713886\pi\)
\(68\) 3.00000 0.363803
\(69\) 6.00000 + 10.3923i 0.722315 + 1.25109i
\(70\) 0 0
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 5.00000 + 3.46410i 0.581238 + 0.402694i
\(75\) −8.00000 −0.923760
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) 0 0
\(78\) −6.00000 10.3923i −0.679366 1.17670i
\(79\) −3.00000 5.19615i −0.337526 0.584613i 0.646440 0.762964i \(-0.276257\pi\)
−0.983967 + 0.178352i \(0.942924\pi\)
\(80\) −1.00000 −0.111803
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) −3.00000 −0.331295
\(83\) −1.00000 + 1.73205i −0.109764 + 0.190117i −0.915675 0.401920i \(-0.868343\pi\)
0.805910 + 0.592037i \(0.201676\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) 9.00000 + 15.5885i 0.964901 + 1.67126i
\(88\) −2.00000 −0.213201
\(89\) 6.50000 11.2583i 0.688999 1.19338i −0.283164 0.959072i \(-0.591384\pi\)
0.972162 0.234309i \(-0.0752827\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) 0 0
\(92\) 3.00000 + 5.19615i 0.312772 + 0.541736i
\(93\) −10.0000 17.3205i −1.03695 1.79605i
\(94\) 1.00000 1.73205i 0.103142 0.178647i
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 1.00000 1.73205i 0.102062 0.176777i
\(97\) 3.00000 0.304604 0.152302 0.988334i \(-0.451331\pi\)
0.152302 + 0.988334i \(0.451331\pi\)
\(98\) −3.50000 6.06218i −0.353553 0.612372i
\(99\) −1.00000 + 1.73205i −0.100504 + 0.174078i
\(100\) −4.00000 −0.400000
\(101\) 7.00000 0.696526 0.348263 0.937397i \(-0.386772\pi\)
0.348263 + 0.937397i \(0.386772\pi\)
\(102\) 3.00000 5.19615i 0.297044 0.514496i
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) 2.00000 + 3.46410i 0.192450 + 0.333333i
\(109\) 6.50000 11.2583i 0.622587 1.07835i −0.366415 0.930451i \(-0.619415\pi\)
0.989002 0.147901i \(-0.0472517\pi\)
\(110\) 2.00000 0.190693
\(111\) 11.0000 5.19615i 1.04407 0.493197i
\(112\) 0 0
\(113\) 5.00000 8.66025i 0.470360 0.814688i −0.529065 0.848581i \(-0.677457\pi\)
0.999425 + 0.0338931i \(0.0107906\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) −3.00000 5.19615i −0.279751 0.484544i
\(116\) 4.50000 + 7.79423i 0.417815 + 0.723676i
\(117\) −6.00000 −0.554700
\(118\) 4.00000 + 6.92820i 0.368230 + 0.637793i
\(119\) 0 0
\(120\) −1.00000 + 1.73205i −0.0912871 + 0.158114i
\(121\) −7.00000 −0.636364
\(122\) 5.00000 0.452679
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) −5.00000 8.66025i −0.449013 0.777714i
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 7.00000 12.1244i 0.621150 1.07586i −0.368122 0.929777i \(-0.619999\pi\)
0.989272 0.146085i \(-0.0466674\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 8.00000 + 13.8564i 0.704361 + 1.21999i
\(130\) 3.00000 + 5.19615i 0.263117 + 0.455733i
\(131\) −7.00000 + 12.1244i −0.611593 + 1.05931i 0.379379 + 0.925241i \(0.376138\pi\)
−0.990972 + 0.134069i \(0.957196\pi\)
\(132\) −2.00000 + 3.46410i −0.174078 + 0.301511i
\(133\) 0 0
\(134\) 6.00000 0.518321
\(135\) −2.00000 3.46410i −0.172133 0.298142i
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) −21.0000 −1.79415 −0.897076 0.441877i \(-0.854313\pi\)
−0.897076 + 0.441877i \(0.854313\pi\)
\(138\) 12.0000 1.02151
\(139\) −7.00000 + 12.1244i −0.593732 + 1.02837i 0.399992 + 0.916519i \(0.369013\pi\)
−0.993724 + 0.111856i \(0.964321\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) 0 0
\(143\) 6.00000 + 10.3923i 0.501745 + 0.869048i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −4.50000 7.79423i −0.373705 0.647275i
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) −14.0000 −1.15470
\(148\) 5.50000 2.59808i 0.452097 0.213561i
\(149\) −9.00000 −0.737309 −0.368654 0.929567i \(-0.620181\pi\)
−0.368654 + 0.929567i \(0.620181\pi\)
\(150\) −4.00000 + 6.92820i −0.326599 + 0.565685i
\(151\) −3.00000 5.19615i −0.244137 0.422857i 0.717752 0.696299i \(-0.245171\pi\)
−0.961888 + 0.273442i \(0.911838\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) −1.50000 2.59808i −0.121268 0.210042i
\(154\) 0 0
\(155\) 5.00000 + 8.66025i 0.401610 + 0.695608i
\(156\) −12.0000 −0.960769
\(157\) 8.50000 14.7224i 0.678374 1.17498i −0.297097 0.954847i \(-0.596018\pi\)
0.975470 0.220131i \(-0.0706483\pi\)
\(158\) −6.00000 −0.477334
\(159\) −12.0000 −0.951662
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 0 0
\(162\) 11.0000 0.864242
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 2.00000 3.46410i 0.155700 0.269680i
\(166\) 1.00000 + 1.73205i 0.0776151 + 0.134433i
\(167\) 10.0000 + 17.3205i 0.773823 + 1.34030i 0.935454 + 0.353450i \(0.114991\pi\)
−0.161630 + 0.986851i \(0.551675\pi\)
\(168\) 0 0
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) −1.50000 + 2.59808i −0.115045 + 0.199263i
\(171\) 2.00000 0.152944
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) −3.50000 + 6.06218i −0.266100 + 0.460899i −0.967851 0.251523i \(-0.919068\pi\)
0.701751 + 0.712422i \(0.252402\pi\)
\(174\) 18.0000 1.36458
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 16.0000 1.20263
\(178\) −6.50000 11.2583i −0.487196 0.843848i
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −5.50000 9.52628i −0.408812 0.708083i 0.585945 0.810351i \(-0.300723\pi\)
−0.994757 + 0.102268i \(0.967390\pi\)
\(182\) 0 0
\(183\) 5.00000 8.66025i 0.369611 0.640184i
\(184\) 6.00000 0.442326
\(185\) −5.50000 + 2.59808i −0.404368 + 0.191014i
\(186\) −20.0000 −1.46647
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) −1.00000 1.73205i −0.0729325 0.126323i
\(189\) 0 0
\(190\) −1.00000 1.73205i −0.0725476 0.125656i
\(191\) 22.0000 1.59186 0.795932 0.605386i \(-0.206981\pi\)
0.795932 + 0.605386i \(0.206981\pi\)
\(192\) −1.00000 1.73205i −0.0721688 0.125000i
\(193\) 11.0000 0.791797 0.395899 0.918294i \(-0.370433\pi\)
0.395899 + 0.918294i \(0.370433\pi\)
\(194\) 1.50000 2.59808i 0.107694 0.186531i
\(195\) 12.0000 0.859338
\(196\) −7.00000 −0.500000
\(197\) 4.50000 7.79423i 0.320612 0.555316i −0.660003 0.751263i \(-0.729445\pi\)
0.980614 + 0.195947i \(0.0627782\pi\)
\(198\) 1.00000 + 1.73205i 0.0710669 + 0.123091i
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 6.00000 10.3923i 0.423207 0.733017i
\(202\) 3.50000 6.06218i 0.246259 0.426533i
\(203\) 0 0
\(204\) −3.00000 5.19615i −0.210042 0.363803i
\(205\) 1.50000 2.59808i 0.104765 0.181458i
\(206\) −4.00000 + 6.92820i −0.278693 + 0.482711i
\(207\) 3.00000 5.19615i 0.208514 0.361158i
\(208\) −6.00000 −0.416025
\(209\) −2.00000 3.46410i −0.138343 0.239617i
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) −8.00000 −0.546869
\(215\) −4.00000 6.92820i −0.272798 0.472500i
\(216\) 4.00000 0.272166
\(217\) 0 0
\(218\) −6.50000 11.2583i −0.440236 0.762510i
\(219\) 2.00000 + 3.46410i 0.135147 + 0.234082i
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) −18.0000 −1.21081
\(222\) 1.00000 12.1244i 0.0671156 0.813733i
\(223\) 2.00000 0.133930 0.0669650 0.997755i \(-0.478668\pi\)
0.0669650 + 0.997755i \(0.478668\pi\)
\(224\) 0 0
\(225\) 2.00000 + 3.46410i 0.133333 + 0.230940i
\(226\) −5.00000 8.66025i −0.332595 0.576072i
\(227\) −15.0000 25.9808i −0.995585 1.72440i −0.579082 0.815270i \(-0.696589\pi\)
−0.416503 0.909134i \(-0.636745\pi\)
\(228\) 4.00000 0.264906
\(229\) 8.50000 + 14.7224i 0.561696 + 0.972886i 0.997349 + 0.0727709i \(0.0231842\pi\)
−0.435653 + 0.900115i \(0.643482\pi\)
\(230\) −6.00000 −0.395628
\(231\) 0 0
\(232\) 9.00000 0.590879
\(233\) −1.00000 −0.0655122 −0.0327561 0.999463i \(-0.510428\pi\)
−0.0327561 + 0.999463i \(0.510428\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) 1.00000 + 1.73205i 0.0652328 + 0.112987i
\(236\) 8.00000 0.520756
\(237\) −6.00000 + 10.3923i −0.389742 + 0.675053i
\(238\) 0 0
\(239\) −2.00000 + 3.46410i −0.129369 + 0.224074i −0.923432 0.383761i \(-0.874629\pi\)
0.794063 + 0.607835i \(0.207962\pi\)
\(240\) 1.00000 + 1.73205i 0.0645497 + 0.111803i
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) −3.50000 + 6.06218i −0.224989 + 0.389692i
\(243\) 5.00000 8.66025i 0.320750 0.555556i
\(244\) 2.50000 4.33013i 0.160046 0.277208i
\(245\) 7.00000 0.447214
\(246\) 3.00000 + 5.19615i 0.191273 + 0.331295i
\(247\) 6.00000 10.3923i 0.381771 0.661247i
\(248\) −10.0000 −0.635001
\(249\) 4.00000 0.253490
\(250\) 4.50000 7.79423i 0.284605 0.492950i
\(251\) 20.0000 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) −7.00000 12.1244i −0.439219 0.760750i
\(255\) 3.00000 + 5.19615i 0.187867 + 0.325396i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.50000 + 16.4545i −0.592594 + 1.02640i 0.401288 + 0.915952i \(0.368563\pi\)
−0.993882 + 0.110450i \(0.964771\pi\)
\(258\) 16.0000 0.996116
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 4.50000 7.79423i 0.278543 0.482451i
\(262\) 7.00000 + 12.1244i 0.432461 + 0.749045i
\(263\) 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) 2.00000 + 3.46410i 0.123091 + 0.213201i
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) −26.0000 −1.59117
\(268\) 3.00000 5.19615i 0.183254 0.317406i
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) −4.00000 −0.243432
\(271\) −3.00000 + 5.19615i −0.182237 + 0.315644i −0.942642 0.333805i \(-0.891667\pi\)
0.760405 + 0.649449i \(0.225000\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) 0 0
\(274\) −10.5000 + 18.1865i −0.634328 + 1.09869i
\(275\) 4.00000 6.92820i 0.241209 0.417786i
\(276\) 6.00000 10.3923i 0.361158 0.625543i
\(277\) 10.5000 + 18.1865i 0.630884 + 1.09272i 0.987371 + 0.158423i \(0.0506409\pi\)
−0.356488 + 0.934300i \(0.616026\pi\)
\(278\) 7.00000 + 12.1244i 0.419832 + 0.727171i
\(279\) −5.00000 + 8.66025i −0.299342 + 0.518476i
\(280\) 0 0
\(281\) 4.50000 7.79423i 0.268447 0.464965i −0.700014 0.714130i \(-0.746823\pi\)
0.968461 + 0.249165i \(0.0801561\pi\)
\(282\) −4.00000 −0.238197
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) 0 0
\(285\) −4.00000 −0.236940
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) −9.00000 −0.528498
\(291\) −3.00000 5.19615i −0.175863 0.304604i
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) −3.50000 6.06218i −0.204472 0.354156i 0.745492 0.666514i \(-0.232214\pi\)
−0.949964 + 0.312358i \(0.898881\pi\)
\(294\) −7.00000 + 12.1244i −0.408248 + 0.707107i
\(295\) −8.00000 −0.465778
\(296\) 0.500000 6.06218i 0.0290619 0.352357i
\(297\) −8.00000 −0.464207
\(298\) −4.50000 + 7.79423i −0.260678 + 0.451508i
\(299\) −18.0000 31.1769i −1.04097 1.80301i
\(300\) 4.00000 + 6.92820i 0.230940 + 0.400000i
\(301\) 0 0
\(302\) −6.00000 −0.345261
\(303\) −7.00000 12.1244i −0.402139 0.696526i
\(304\) 2.00000 0.114708
\(305\) −2.50000 + 4.33013i −0.143150 + 0.247942i
\(306\) −3.00000 −0.171499
\(307\) 32.0000 1.82634 0.913168 0.407583i \(-0.133628\pi\)
0.913168 + 0.407583i \(0.133628\pi\)
\(308\) 0 0
\(309\) 8.00000 + 13.8564i 0.455104 + 0.788263i
\(310\) 10.0000 0.567962
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) −6.00000 + 10.3923i −0.339683 + 0.588348i
\(313\) −9.50000 + 16.4545i −0.536972 + 0.930062i 0.462093 + 0.886831i \(0.347098\pi\)
−0.999065 + 0.0432311i \(0.986235\pi\)
\(314\) −8.50000 14.7224i −0.479683 0.830835i
\(315\) 0 0
\(316\) −3.00000 + 5.19615i −0.168763 + 0.292306i
\(317\) −3.50000 + 6.06218i −0.196580 + 0.340486i −0.947417 0.320001i \(-0.896317\pi\)
0.750838 + 0.660487i \(0.229650\pi\)
\(318\) −6.00000 + 10.3923i −0.336463 + 0.582772i
\(319\) −18.0000 −1.00781
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) −8.00000 + 13.8564i −0.446516 + 0.773389i
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 5.50000 9.52628i 0.305556 0.529238i
\(325\) 24.0000 1.33128
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) −26.0000 −1.43780
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) 0 0
\(330\) −2.00000 3.46410i −0.110096 0.190693i
\(331\) 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) 2.00000 0.109764
\(333\) −5.00000 3.46410i −0.273998 0.189832i
\(334\) 20.0000 1.09435
\(335\) −3.00000 + 5.19615i −0.163908 + 0.283896i
\(336\) 0 0
\(337\) −7.50000 12.9904i −0.408551 0.707631i 0.586177 0.810183i \(-0.300632\pi\)
−0.994728 + 0.102552i \(0.967299\pi\)
\(338\) 11.5000 + 19.9186i 0.625518 + 1.08343i
\(339\) −20.0000 −1.08625
\(340\) 1.50000 + 2.59808i 0.0813489 + 0.140900i
\(341\) 20.0000 1.08306
\(342\) 1.00000 1.73205i 0.0540738 0.0936586i
\(343\) 0 0
\(344\) 8.00000 0.431331
\(345\) −6.00000 + 10.3923i −0.323029 + 0.559503i
\(346\) 3.50000 + 6.06218i 0.188161 + 0.325905i
\(347\) −6.00000 −0.322097 −0.161048 0.986947i \(-0.551488\pi\)
−0.161048 + 0.986947i \(0.551488\pi\)
\(348\) 9.00000 15.5885i 0.482451 0.835629i
\(349\) −9.50000 + 16.4545i −0.508523 + 0.880788i 0.491428 + 0.870918i \(0.336475\pi\)
−0.999951 + 0.00987003i \(0.996858\pi\)
\(350\) 0 0
\(351\) −12.0000 20.7846i −0.640513 1.10940i
\(352\) 1.00000 + 1.73205i 0.0533002 + 0.0923186i
\(353\) 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i \(-0.644573\pi\)
0.997592 0.0693543i \(-0.0220939\pi\)
\(354\) 8.00000 13.8564i 0.425195 0.736460i
\(355\) 0 0
\(356\) −13.0000 −0.688999
\(357\) 0 0
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) 1.00000 0.0527046
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −11.0000 −0.578147
\(363\) 7.00000 + 12.1244i 0.367405 + 0.636364i
\(364\) 0 0
\(365\) −1.00000 1.73205i −0.0523424 0.0906597i
\(366\) −5.00000 8.66025i −0.261354 0.452679i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) 3.00000 0.156174
\(370\) −0.500000 + 6.06218i −0.0259938 + 0.315158i
\(371\) 0 0
\(372\) −10.0000 + 17.3205i −0.518476 + 0.898027i
\(373\) 18.5000 + 32.0429i 0.957894 + 1.65912i 0.727603 + 0.685999i \(0.240634\pi\)
0.230291 + 0.973122i \(0.426032\pi\)
\(374\) 3.00000 + 5.19615i 0.155126 + 0.268687i
\(375\) −9.00000 15.5885i −0.464758 0.804984i
\(376\) −2.00000 −0.103142
\(377\) −27.0000 46.7654i −1.39057 2.40854i
\(378\) 0 0
\(379\) 10.0000 17.3205i 0.513665 0.889695i −0.486209 0.873843i \(-0.661621\pi\)
0.999874 0.0158521i \(-0.00504609\pi\)
\(380\) −2.00000 −0.102598
\(381\) −28.0000 −1.43448
\(382\) 11.0000 19.0526i 0.562809 0.974814i
\(383\) −4.00000 6.92820i −0.204390 0.354015i 0.745548 0.666452i \(-0.232188\pi\)
−0.949938 + 0.312437i \(0.898855\pi\)
\(384\) −2.00000 −0.102062
\(385\) 0 0
\(386\) 5.50000 9.52628i 0.279943 0.484875i
\(387\) 4.00000 6.92820i 0.203331 0.352180i
\(388\) −1.50000 2.59808i −0.0761510 0.131897i
\(389\) −5.50000 9.52628i −0.278861 0.483002i 0.692241 0.721666i \(-0.256624\pi\)
−0.971102 + 0.238665i \(0.923290\pi\)
\(390\) 6.00000 10.3923i 0.303822 0.526235i
\(391\) 9.00000 15.5885i 0.455150 0.788342i
\(392\) −3.50000 + 6.06218i −0.176777 + 0.306186i
\(393\) 28.0000 1.41241
\(394\) −4.50000 7.79423i −0.226707 0.392668i
\(395\) 3.00000 5.19615i 0.150946 0.261447i
\(396\) 2.00000 0.100504
\(397\) −25.0000 −1.25471 −0.627357 0.778732i \(-0.715863\pi\)
−0.627357 + 0.778732i \(0.715863\pi\)
\(398\) −10.0000 + 17.3205i −0.501255 + 0.868199i
\(399\) 0 0
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) −6.00000 10.3923i −0.299253 0.518321i
\(403\) 30.0000 + 51.9615i 1.49441 + 2.58839i
\(404\) −3.50000 6.06218i −0.174132 0.301605i
\(405\) −5.50000 + 9.52628i −0.273297 + 0.473365i
\(406\) 0 0
\(407\) −1.00000 + 12.1244i −0.0495682 + 0.600982i
\(408\) −6.00000 −0.297044
\(409\) 10.5000 18.1865i 0.519192 0.899266i −0.480560 0.876962i \(-0.659566\pi\)
0.999751 0.0223042i \(-0.00710022\pi\)
\(410\) −1.50000 2.59808i −0.0740797 0.128310i
\(411\) 21.0000 + 36.3731i 1.03585 + 1.79415i
\(412\) 4.00000 + 6.92820i 0.197066 + 0.341328i
\(413\) 0 0
\(414\) −3.00000 5.19615i −0.147442 0.255377i
\(415\) −2.00000 −0.0981761
\(416\) −3.00000 + 5.19615i −0.147087 + 0.254762i
\(417\) 28.0000 1.37117
\(418\) −4.00000 −0.195646
\(419\) 2.00000 3.46410i 0.0977064 0.169232i −0.813029 0.582224i \(-0.802183\pi\)
0.910735 + 0.412991i \(0.135516\pi\)
\(420\) 0 0
\(421\) −25.0000 −1.21843 −0.609213 0.793007i \(-0.708514\pi\)
−0.609213 + 0.793007i \(0.708514\pi\)
\(422\) −6.00000 + 10.3923i −0.292075 + 0.505889i
\(423\) −1.00000 + 1.73205i −0.0486217 + 0.0842152i
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 0 0
\(427\) 0 0
\(428\) −4.00000 + 6.92820i −0.193347 + 0.334887i
\(429\) 12.0000 20.7846i 0.579365 1.00349i
\(430\) −8.00000 −0.385794
\(431\) 1.00000 + 1.73205i 0.0481683 + 0.0834300i 0.889104 0.457705i \(-0.151328\pi\)
−0.840936 + 0.541135i \(0.817995\pi\)
\(432\) 2.00000 3.46410i 0.0962250 0.166667i
\(433\) −9.00000 −0.432512 −0.216256 0.976337i \(-0.569385\pi\)
−0.216256 + 0.976337i \(0.569385\pi\)
\(434\) 0 0
\(435\) −9.00000 + 15.5885i −0.431517 + 0.747409i
\(436\) −13.0000 −0.622587
\(437\) 6.00000 + 10.3923i 0.287019 + 0.497131i
\(438\) 4.00000 0.191127
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) −1.00000 1.73205i −0.0476731 0.0825723i
\(441\) 3.50000 + 6.06218i 0.166667 + 0.288675i
\(442\) −9.00000 + 15.5885i −0.428086 + 0.741467i
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) −10.0000 6.92820i −0.474579 0.328798i
\(445\) 13.0000 0.616259
\(446\) 1.00000 1.73205i 0.0473514 0.0820150i
\(447\) 9.00000 + 15.5885i 0.425685 + 0.737309i
\(448\) 0 0
\(449\) 17.0000 + 29.4449i 0.802280 + 1.38959i 0.918112 + 0.396320i \(0.129713\pi\)
−0.115833 + 0.993269i \(0.536954\pi\)
\(450\) 4.00000 0.188562
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) −10.0000 −0.470360
\(453\) −6.00000 + 10.3923i −0.281905 + 0.488273i
\(454\) −30.0000 −1.40797
\(455\) 0 0
\(456\) 2.00000 3.46410i 0.0936586 0.162221i
\(457\) −13.5000 23.3827i −0.631503 1.09380i −0.987245 0.159211i \(-0.949105\pi\)
0.355741 0.934585i \(-0.384228\pi\)
\(458\) 17.0000 0.794358
\(459\) 6.00000 10.3923i 0.280056 0.485071i
\(460\) −3.00000 + 5.19615i −0.139876 + 0.242272i
\(461\) −13.0000 + 22.5167i −0.605470 + 1.04871i 0.386507 + 0.922287i \(0.373682\pi\)
−0.991977 + 0.126419i \(0.959652\pi\)
\(462\) 0 0
\(463\) 10.0000 + 17.3205i 0.464739 + 0.804952i 0.999190 0.0402476i \(-0.0128147\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 10.0000 17.3205i 0.463739 0.803219i
\(466\) −0.500000 + 0.866025i −0.0231621 + 0.0401179i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 3.00000 + 5.19615i 0.138675 + 0.240192i
\(469\) 0 0
\(470\) 2.00000 0.0922531
\(471\) −34.0000 −1.56664
\(472\) 4.00000 6.92820i 0.184115 0.318896i
\(473\) −16.0000 −0.735681
\(474\) 6.00000 + 10.3923i 0.275589 + 0.477334i
\(475\) −8.00000 −0.367065
\(476\) 0 0
\(477\) 3.00000 + 5.19615i 0.137361 + 0.237915i
\(478\) 2.00000 + 3.46410i 0.0914779 + 0.158444i
\(479\) −16.0000 + 27.7128i −0.731059 + 1.26623i 0.225372 + 0.974273i \(0.427640\pi\)
−0.956431 + 0.291958i \(0.905693\pi\)
\(480\) 2.00000 0.0912871
\(481\) −33.0000 + 15.5885i −1.50467 + 0.710772i
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 1.50000 + 2.59808i 0.0681115 + 0.117973i
\(486\) −5.00000 8.66025i −0.226805 0.392837i
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) −2.50000 4.33013i −0.113170 0.196016i
\(489\) 8.00000 0.361773
\(490\) 3.50000 6.06218i 0.158114 0.273861i
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 6.00000 0.270501
\(493\) 13.5000 23.3827i 0.608009 1.05310i
\(494\) −6.00000 10.3923i −0.269953 0.467572i
\(495\) −2.00000 −0.0898933
\(496\) −5.00000 + 8.66025i −0.224507 + 0.388857i
\(497\) 0 0
\(498\) 2.00000 3.46410i 0.0896221 0.155230i
\(499\) −15.0000 25.9808i −0.671492 1.16306i −0.977481 0.211024i \(-0.932320\pi\)
0.305989 0.952035i \(-0.401013\pi\)
\(500\) −4.50000 7.79423i −0.201246 0.348569i
\(501\) 20.0000 34.6410i 0.893534 1.54765i
\(502\) 10.0000 17.3205i 0.446322 0.773052i
\(503\) −7.00000 + 12.1244i −0.312115 + 0.540598i −0.978820 0.204723i \(-0.934371\pi\)
0.666705 + 0.745321i \(0.267704\pi\)
\(504\) 0 0
\(505\) 3.50000 + 6.06218i 0.155748 + 0.269763i
\(506\) −6.00000 + 10.3923i −0.266733 + 0.461994i
\(507\) 46.0000 2.04293
\(508\) −14.0000 −0.621150
\(509\) 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i \(-0.769415\pi\)
0.948353 + 0.317217i \(0.102748\pi\)
\(510\) 6.00000 0.265684
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 4.00000 + 6.92820i 0.176604 + 0.305888i
\(514\) 9.50000 + 16.4545i 0.419027 + 0.725776i
\(515\) −4.00000 6.92820i −0.176261 0.305293i
\(516\) 8.00000 13.8564i 0.352180 0.609994i
\(517\) 4.00000 0.175920
\(518\) 0 0
\(519\) 14.0000 0.614532
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) −15.0000 25.9808i −0.657162 1.13824i −0.981347 0.192244i \(-0.938423\pi\)
0.324185 0.945994i \(-0.394910\pi\)
\(522\) −4.50000 7.79423i −0.196960 0.341144i
\(523\) −3.00000 5.19615i −0.131181 0.227212i 0.792951 0.609285i \(-0.208544\pi\)
−0.924132 + 0.382073i \(0.875210\pi\)
\(524\) 14.0000 0.611593
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) −15.0000 + 25.9808i −0.653410 + 1.13174i
\(528\) 4.00000 0.174078
\(529\) 13.0000 0.565217
\(530\) 3.00000 5.19615i 0.130312 0.225706i
\(531\) −4.00000 6.92820i −0.173585 0.300658i
\(532\) 0 0
\(533\) 9.00000 15.5885i 0.389833 0.675211i
\(534\) −13.0000 + 22.5167i −0.562565 + 0.974391i
\(535\) 4.00000 6.92820i 0.172935 0.299532i
\(536\) −3.00000 5.19615i −0.129580 0.224440i
\(537\) −24.0000 41.5692i −1.03568 1.79384i
\(538\) 1.00000 1.73205i 0.0431131 0.0746740i
\(539\) 7.00000 12.1244i 0.301511 0.522233i
\(540\) −2.00000 + 3.46410i −0.0860663 + 0.149071i
\(541\) −9.00000 −0.386940 −0.193470 0.981106i \(-0.561974\pi\)
−0.193470 + 0.981106i \(0.561974\pi\)
\(542\) 3.00000 + 5.19615i 0.128861 + 0.223194i
\(543\) −11.0000 + 19.0526i −0.472055 + 0.817624i
\(544\) −3.00000 −0.128624
\(545\) 13.0000 0.556859
\(546\) 0 0
\(547\) −6.00000 −0.256541 −0.128271 0.991739i \(-0.540943\pi\)
−0.128271 + 0.991739i \(0.540943\pi\)
\(548\) 10.5000 + 18.1865i 0.448538 + 0.776890i
\(549\) −5.00000 −0.213395
\(550\) −4.00000 6.92820i −0.170561 0.295420i
\(551\) 9.00000 + 15.5885i 0.383413 + 0.664091i
\(552\) −6.00000 10.3923i −0.255377 0.442326i
\(553\) 0 0
\(554\) 21.0000 0.892205
\(555\) 10.0000 + 6.92820i 0.424476 + 0.294086i
\(556\) 14.0000 0.593732
\(557\) −17.5000 + 30.3109i −0.741499 + 1.28431i 0.210314 + 0.977634i \(0.432551\pi\)
−0.951813 + 0.306680i \(0.900782\pi\)
\(558\) 5.00000 + 8.66025i 0.211667 + 0.366618i
\(559\) −24.0000 41.5692i −1.01509 1.75819i
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) −4.50000 7.79423i −0.189821 0.328780i
\(563\) 10.0000 0.421450 0.210725 0.977545i \(-0.432418\pi\)
0.210725 + 0.977545i \(0.432418\pi\)
\(564\) −2.00000 + 3.46410i −0.0842152 + 0.145865i
\(565\) 10.0000 0.420703
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 0 0
\(569\) 11.0000 0.461144 0.230572 0.973055i \(-0.425940\pi\)
0.230572 + 0.973055i \(0.425940\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) −9.00000 + 15.5885i −0.376638 + 0.652357i −0.990571 0.137002i \(-0.956253\pi\)
0.613933 + 0.789359i \(0.289587\pi\)
\(572\) 6.00000 10.3923i 0.250873 0.434524i
\(573\) −22.0000 38.1051i −0.919063 1.59186i
\(574\) 0 0
\(575\) −12.0000 + 20.7846i −0.500435 + 0.866778i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 1.00000 1.73205i 0.0416305 0.0721062i −0.844459 0.535620i \(-0.820078\pi\)
0.886090 + 0.463513i \(0.153411\pi\)
\(578\) 8.00000 0.332756
\(579\) −11.0000 19.0526i −0.457144 0.791797i
\(580\) −4.50000 + 7.79423i −0.186852 + 0.323638i
\(581\) 0 0
\(582\) −6.00000 −0.248708
\(583\) 6.00000 10.3923i 0.248495 0.430405i
\(584\) 2.00000 0.0827606
\(585\) −3.00000 5.19615i −0.124035 0.214834i
\(586\) −7.00000 −0.289167
\(587\) −15.0000 25.9808i −0.619116 1.07234i −0.989647 0.143521i \(-0.954158\pi\)
0.370531 0.928820i \(-0.379176\pi\)
\(588\) 7.00000 + 12.1244i 0.288675 + 0.500000i
\(589\) −10.0000 17.3205i −0.412043 0.713679i
\(590\) −4.00000 + 6.92820i −0.164677 + 0.285230i
\(591\) −18.0000 −0.740421
\(592\) −5.00000 3.46410i −0.205499 0.142374i
\(593\) 19.0000 0.780236 0.390118 0.920765i \(-0.372434\pi\)
0.390118 + 0.920765i \(0.372434\pi\)
\(594\) −4.00000 + 6.92820i −0.164122 + 0.284268i
\(595\) 0 0
\(596\) 4.50000 + 7.79423i 0.184327 + 0.319264i
\(597\) 20.0000 + 34.6410i 0.818546 + 1.41776i
\(598\) −36.0000 −1.47215
\(599\) −5.00000 8.66025i −0.204294 0.353848i 0.745613 0.666379i \(-0.232157\pi\)
−0.949908 + 0.312531i \(0.898823\pi\)
\(600\) 8.00000 0.326599
\(601\) 2.50000 4.33013i 0.101977 0.176630i −0.810522 0.585708i \(-0.800816\pi\)
0.912499 + 0.409079i \(0.134150\pi\)
\(602\) 0 0
\(603\) −6.00000 −0.244339
\(604\) −3.00000 + 5.19615i −0.122068 + 0.211428i
\(605\) −3.50000 6.06218i −0.142295 0.246463i
\(606\) −14.0000 −0.568711
\(607\) −5.00000 + 8.66025i −0.202944 + 0.351509i −0.949476 0.313841i \(-0.898384\pi\)
0.746532 + 0.665350i \(0.231718\pi\)
\(608\) 1.00000 1.73205i 0.0405554 0.0702439i
\(609\) 0 0
\(610\) 2.50000 + 4.33013i 0.101222 + 0.175322i
\(611\) 6.00000 + 10.3923i 0.242734 + 0.420428i
\(612\) −1.50000 + 2.59808i −0.0606339 + 0.105021i
\(613\) −5.50000 + 9.52628i −0.222143 + 0.384763i −0.955458 0.295126i \(-0.904638\pi\)
0.733316 + 0.679888i \(0.237972\pi\)
\(614\) 16.0000 27.7128i 0.645707 1.11840i
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) −7.00000 + 12.1244i −0.281809 + 0.488108i −0.971830 0.235681i \(-0.924268\pi\)
0.690021 + 0.723789i \(0.257601\pi\)
\(618\) 16.0000 0.643614
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 5.00000 8.66025i 0.200805 0.347804i
\(621\) 24.0000 0.963087
\(622\) −6.00000 10.3923i −0.240578 0.416693i
\(623\) 0 0
\(624\) 6.00000 + 10.3923i 0.240192 + 0.416025i
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 9.50000 + 16.4545i 0.379696 + 0.657653i
\(627\) −4.00000 + 6.92820i −0.159745 + 0.276686i
\(628\) −17.0000 −0.678374
\(629\) −15.0000 10.3923i −0.598089 0.414368i
\(630\) 0 0
\(631\) −5.00000 + 8.66025i −0.199047 + 0.344759i −0.948220 0.317615i \(-0.897118\pi\)
0.749173 + 0.662375i \(0.230451\pi\)
\(632\) 3.00000 + 5.19615i 0.119334 + 0.206692i
\(633\) 12.0000 + 20.7846i 0.476957 + 0.826114i
\(634\) 3.50000 + 6.06218i 0.139003 + 0.240760i
\(635\) 14.0000 0.555573
\(636\) 6.00000 + 10.3923i 0.237915 + 0.412082i
\(637\) 42.0000 1.66410
\(638\) −9.00000 + 15.5885i −0.356313 + 0.617153i
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) −9.50000 + 16.4545i −0.375227 + 0.649913i −0.990361 0.138510i \(-0.955769\pi\)
0.615134 + 0.788423i \(0.289102\pi\)
\(642\) 8.00000 + 13.8564i 0.315735 + 0.546869i
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 0 0
\(645\) −8.00000 + 13.8564i −0.315000 + 0.545595i
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) −2.00000 3.46410i −0.0786281 0.136188i 0.824030 0.566546i \(-0.191721\pi\)
−0.902658 + 0.430358i \(0.858387\pi\)
\(648\) −5.50000 9.52628i −0.216060 0.374228i
\(649\) −8.00000 + 13.8564i −0.314027 + 0.543912i
\(650\) 12.0000 20.7846i 0.470679 0.815239i
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −7.50000 12.9904i −0.293498 0.508353i 0.681137 0.732156i \(-0.261486\pi\)
−0.974634 + 0.223803i \(0.928153\pi\)
\(654\) −13.0000 + 22.5167i −0.508340 + 0.880471i
\(655\) −14.0000 −0.547025
\(656\) 3.00000 0.117130
\(657\) 1.00000 1.73205i 0.0390137 0.0675737i
\(658\) 0 0
\(659\) 10.0000 + 17.3205i 0.389545 + 0.674711i 0.992388 0.123148i \(-0.0392990\pi\)
−0.602844 + 0.797859i \(0.705966\pi\)
\(660\) −4.00000 −0.155700
\(661\) −13.5000 23.3827i −0.525089 0.909481i −0.999573 0.0292169i \(-0.990699\pi\)
0.474484 0.880264i \(-0.342635\pi\)
\(662\) −10.0000 17.3205i −0.388661 0.673181i
\(663\) 18.0000 + 31.1769i 0.699062 + 1.21081i
\(664\) 1.00000 1.73205i 0.0388075 0.0672166i
\(665\) 0 0
\(666\) −5.50000 + 2.59808i −0.213121 + 0.100673i
\(667\) 54.0000 2.09089
\(668\) 10.0000 17.3205i 0.386912 0.670151i
\(669\) −2.00000 3.46410i −0.0773245 0.133930i
\(670\) 3.00000 + 5.19615i 0.115900 + 0.200745i
\(671\) 5.00000 + 8.66025i 0.193023 + 0.334325i
\(672\) 0 0
\(673\) 1.00000 + 1.73205i 0.0385472 + 0.0667657i 0.884655 0.466246i \(-0.154394\pi\)
−0.846108 + 0.533011i \(0.821060\pi\)
\(674\) −15.0000 −0.577778
\(675\) −8.00000 + 13.8564i −0.307920 + 0.533333i
\(676\) 23.0000 0.884615
\(677\) 47.0000 1.80636 0.903178 0.429265i \(-0.141228\pi\)
0.903178 + 0.429265i \(0.141228\pi\)
\(678\) −10.0000 + 17.3205i −0.384048 + 0.665190i
\(679\) 0 0
\(680\) 3.00000 0.115045
\(681\) −30.0000 + 51.9615i −1.14960 + 1.99117i
\(682\) 10.0000 17.3205i 0.382920 0.663237i
\(683\) 12.0000 20.7846i 0.459167 0.795301i −0.539750 0.841825i \(-0.681481\pi\)
0.998917 + 0.0465244i \(0.0148145\pi\)
\(684\) −1.00000 1.73205i −0.0382360 0.0662266i
\(685\) −10.5000 18.1865i −0.401184 0.694872i
\(686\) 0 0
\(687\) 17.0000 29.4449i 0.648590 1.12339i
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) 36.0000 1.37149
\(690\) 6.00000 + 10.3923i 0.228416 + 0.395628i
\(691\) −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i \(0.566655\pi\)
−0.743170 + 0.669102i \(0.766679\pi\)
\(692\) 7.00000 0.266100
\(693\) 0 0
\(694\) −3.00000 + 5.19615i −0.113878 + 0.197243i
\(695\) −14.0000 −0.531050
\(696\) −9.00000 15.5885i −0.341144 0.590879i
\(697\) 9.00000 0.340899
\(698\) 9.50000 + 16.4545i 0.359580 + 0.622811i
\(699\) 1.00000 + 1.73205i 0.0378235 + 0.0655122i
\(700\) 0 0
\(701\) 1.00000 1.73205i 0.0377695 0.0654187i −0.846523 0.532353i \(-0.821308\pi\)
0.884292 + 0.466934i \(0.154641\pi\)
\(702\) −24.0000 −0.905822
\(703\) 11.0000 5.19615i 0.414873 0.195977i
\(704\) 2.00000 0.0753778
\(705\) 2.00000 3.46410i 0.0753244 0.130466i
\(706\) −10.5000 18.1865i −0.395173 0.684459i
\(707\) 0 0
\(708\) −8.00000 13.8564i −0.300658 0.520756i
\(709\) −6.00000 −0.225335 −0.112667 0.993633i \(-0.535939\pi\)
−0.112667 + 0.993633i \(0.535939\pi\)
\(710\) 0 0
\(711\) 6.00000 0.225018
\(712\) −6.50000 + 11.2583i −0.243598 + 0.421924i
\(713\) −60.0000 −2.24702
\(714\) 0 0
\(715\) −6.00000 + 10.3923i −0.224387 + 0.388650i
\(716\) −12.0000 20.7846i −0.448461 0.776757i
\(717\) 8.00000 0.298765
\(718\) 8.00000 13.8564i 0.298557 0.517116i
\(719\) −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i \(-0.942287\pi\)
0.647965 + 0.761670i \(0.275620\pi\)
\(720\) 0.500000 0.866025i 0.0186339 0.0322749i
\(721\) 0 0
\(722\) −7.50000 12.9904i −0.279121 0.483452i
\(723\) 10.0000 17.3205i 0.371904 0.644157i
\(724\) −5.50000 + 9.52628i −0.204406 + 0.354041i
\(725\) −18.0000 + 31.1769i −0.668503 + 1.15788i
\(726\) 14.0000 0.519589
\(727\) 14.0000 + 24.2487i 0.519231 + 0.899335i 0.999750 + 0.0223506i \(0.00711500\pi\)
−0.480519 + 0.876984i \(0.659552\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −2.00000 −0.0740233
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) −10.0000 −0.369611
\(733\) −13.0000 22.5167i −0.480166 0.831672i 0.519575 0.854425i \(-0.326090\pi\)
−0.999741 + 0.0227529i \(0.992757\pi\)
\(734\) 4.00000 0.147643
\(735\) −7.00000 12.1244i −0.258199 0.447214i
\(736\) −3.00000 5.19615i −0.110581 0.191533i
\(737\) 6.00000 + 10.3923i 0.221013 + 0.382805i
\(738\) 1.50000 2.59808i 0.0552158 0.0956365i
\(739\) 34.0000 1.25071 0.625355 0.780340i \(-0.284954\pi\)
0.625355 + 0.780340i \(0.284954\pi\)
\(740\) 5.00000 + 3.46410i 0.183804 + 0.127343i
\(741\) −24.0000 −0.881662
\(742\) 0 0
\(743\) −9.00000 15.5885i −0.330178 0.571885i 0.652369 0.757902i \(-0.273775\pi\)
−0.982547 + 0.186017i \(0.940442\pi\)
\(744\) 10.0000 + 17.3205i 0.366618 + 0.635001i
\(745\) −4.50000 7.79423i −0.164867 0.285558i
\(746\) 37.0000 1.35467
\(747\) −1.00000 1.73205i −0.0365881 0.0633724i
\(748\) 6.00000 0.219382
\(749\) 0 0
\(750\) −18.0000 −0.657267
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) −1.00000 + 1.73205i −0.0364662 + 0.0631614i
\(753\) −20.0000 34.6410i −0.728841 1.26239i
\(754\) −54.0000 −1.96656
\(755\) 3.00000 5.19615i 0.109181 0.189107i
\(756\) 0 0
\(757\) 8.50000 14.7224i 0.308938 0.535096i −0.669193 0.743089i \(-0.733360\pi\)
0.978130 + 0.207993i \(0.0666932\pi\)
\(758\) −10.0000 17.3205i −0.363216 0.629109i
\(759\) 12.0000 + 20.7846i 0.435572 + 0.754434i
\(760\) −1.00000 + 1.73205i −0.0362738 + 0.0628281i
\(761\) 6.50000 11.2583i 0.235625 0.408114i −0.723829 0.689979i \(-0.757620\pi\)
0.959454 + 0.281865i \(0.0909530\pi\)
\(762\) −14.0000 + 24.2487i −0.507166 + 0.878438i
\(763\) 0 0
\(764\) −11.0000 19.0526i −0.397966 0.689297i
\(765\) 1.50000 2.59808i 0.0542326 0.0939336i
\(766\) −8.00000 −0.289052
\(767\) −48.0000 −1.73318
\(768\) −1.00000 + 1.73205i −0.0360844 + 0.0625000i
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 38.0000 1.36854
\(772\) −5.50000 9.52628i −0.197949 0.342858i
\(773\) −11.5000 19.9186i −0.413626 0.716422i 0.581657 0.813434i \(-0.302405\pi\)
−0.995283 + 0.0970125i \(0.969071\pi\)
\(774\) −4.00000 6.92820i −0.143777 0.249029i
\(775\) 20.0000 34.6410i 0.718421 1.24434i
\(776\) −3.00000 −0.107694
\(777\) 0 0
\(778\) −11.0000 −0.394369
\(779\) −3.00000 + 5.19615i −0.107486 + 0.186171i
\(780\) −6.00000