Properties

Label 1014.2.e.n.991.2
Level $1014$
Weight $2$
Character 1014.991
Analytic conductor $8.097$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.2
Root \(0.222521 - 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 1014.991
Dual form 1014.2.e.n.529.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.13706 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.0244587 + 0.0423637i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.13706 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.0244587 + 0.0423637i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.06853 - 1.85075i) q^{10} +(3.14795 + 5.45241i) q^{11} -1.00000 q^{12} -0.0489173 q^{14} +(-1.06853 - 1.85075i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.44504 - 2.50289i) q^{17} -1.00000 q^{18} +(-3.60388 + 6.24210i) q^{19} +(1.06853 - 1.85075i) q^{20} -0.0489173 q^{21} +(-3.14795 + 5.45241i) q^{22} +(-1.35690 - 2.35021i) q^{23} +(-0.500000 - 0.866025i) q^{24} -0.432960 q^{25} -1.00000 q^{27} +(-0.0244587 - 0.0423637i) q^{28} +(-2.45593 - 4.25379i) q^{29} +(1.06853 - 1.85075i) q^{30} -9.00969 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.14795 + 5.45241i) q^{33} +2.89008 q^{34} +(0.0522697 - 0.0905338i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.0881460 - 0.152673i) q^{37} -7.20775 q^{38} +2.13706 q^{40} +(-4.29590 - 7.44071i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(-3.35690 + 5.81431i) q^{43} -6.29590 q^{44} +(1.06853 - 1.85075i) q^{45} +(1.35690 - 2.35021i) q^{46} -7.20775 q^{47} +(0.500000 - 0.866025i) q^{48} +(3.49880 + 6.06011i) q^{49} +(-0.216480 - 0.374955i) q^{50} +2.89008 q^{51} +9.34481 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-6.72737 - 11.6521i) q^{55} +(0.0244587 - 0.0423637i) q^{56} -7.20775 q^{57} +(2.45593 - 4.25379i) q^{58} +(-2.13437 + 3.69685i) q^{59} +2.13706 q^{60} +(-3.55496 + 6.15737i) q^{61} +(-4.50484 - 7.80262i) q^{62} +(-0.0244587 - 0.0423637i) q^{63} +1.00000 q^{64} -6.29590 q^{66} +(2.69202 + 4.66272i) q^{67} +(1.44504 + 2.50289i) q^{68} +(1.35690 - 2.35021i) q^{69} +0.104539 q^{70} +(-4.35690 + 7.54637i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.9487 q^{73} +(0.0881460 - 0.152673i) q^{74} +(-0.216480 - 0.374955i) q^{75} +(-3.60388 - 6.24210i) q^{76} -0.307979 q^{77} +13.8291 q^{79} +(1.06853 + 1.85075i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.29590 - 7.44071i) q^{82} +11.1347 q^{83} +(0.0244587 - 0.0423637i) q^{84} +(-3.08815 + 5.34883i) q^{85} -6.71379 q^{86} +(2.45593 - 4.25379i) q^{87} +(-3.14795 - 5.45241i) q^{88} +(1.96077 + 3.39616i) q^{89} +2.13706 q^{90} +2.71379 q^{92} +(-4.50484 - 7.80262i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(7.70171 - 13.3398i) q^{95} +1.00000 q^{96} +(-1.23945 + 2.14678i) q^{97} +(-3.49880 + 6.06011i) q^{98} -6.29590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 5 q^{11} - 6 q^{12} + 18 q^{14} - q^{15} - 3 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + q^{20} + 18 q^{21} - 5 q^{22} - 3 q^{24} + 36 q^{25} - 6 q^{27} + 9 q^{28} - 11 q^{29} + q^{30} - 10 q^{31} + 3 q^{32} - 5 q^{33} + 16 q^{34} + 4 q^{35} - 3 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 2 q^{41} + 9 q^{42} - 12 q^{43} - 10 q^{44} + q^{45} - 8 q^{47} + 3 q^{48} - 20 q^{49} + 18 q^{50} + 16 q^{51} + 10 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 8 q^{57} + 11 q^{58} - 5 q^{59} + 2 q^{60} - 22 q^{61} - 5 q^{62} + 9 q^{63} + 6 q^{64} - 10 q^{66} + 6 q^{67} + 8 q^{68} + 8 q^{70} - 18 q^{71} + 3 q^{72} + 26 q^{73} + 8 q^{74} + 18 q^{75} - 4 q^{76} - 12 q^{77} + 62 q^{79} + q^{80} - 3 q^{81} - 2 q^{82} - 26 q^{83} - 9 q^{84} - 26 q^{85} - 24 q^{86} + 11 q^{87} - 5 q^{88} - 14 q^{89} + 2 q^{90} - 5 q^{93} - 4 q^{94} - 8 q^{95} + 6 q^{96} - 23 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −2.13706 −0.955724 −0.477862 0.878435i \(-0.658588\pi\)
−0.477862 + 0.878435i \(0.658588\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −0.0244587 + 0.0423637i −0.00924451 + 0.0160120i −0.870611 0.491973i \(-0.836276\pi\)
0.861366 + 0.507985i \(0.169609\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.06853 1.85075i −0.337899 0.585259i
\(11\) 3.14795 + 5.45241i 0.949142 + 1.64396i 0.747237 + 0.664557i \(0.231380\pi\)
0.201905 + 0.979405i \(0.435287\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −0.0489173 −0.0130737
\(15\) −1.06853 1.85075i −0.275894 0.477862i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.44504 2.50289i 0.350474 0.607039i −0.635858 0.771806i \(-0.719354\pi\)
0.986333 + 0.164767i \(0.0526871\pi\)
\(18\) −1.00000 −0.235702
\(19\) −3.60388 + 6.24210i −0.826786 + 1.43203i 0.0737611 + 0.997276i \(0.476500\pi\)
−0.900547 + 0.434759i \(0.856834\pi\)
\(20\) 1.06853 1.85075i 0.238931 0.413841i
\(21\) −0.0489173 −0.0106746
\(22\) −3.14795 + 5.45241i −0.671145 + 1.16246i
\(23\) −1.35690 2.35021i −0.282932 0.490053i 0.689173 0.724597i \(-0.257974\pi\)
−0.972106 + 0.234543i \(0.924641\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.432960 −0.0865921
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −0.0244587 0.0423637i −0.00462225 0.00800598i
\(29\) −2.45593 4.25379i −0.456054 0.789909i 0.542694 0.839931i \(-0.317404\pi\)
−0.998748 + 0.0500215i \(0.984071\pi\)
\(30\) 1.06853 1.85075i 0.195086 0.337899i
\(31\) −9.00969 −1.61819 −0.809094 0.587679i \(-0.800042\pi\)
−0.809094 + 0.587679i \(0.800042\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −3.14795 + 5.45241i −0.547987 + 0.949142i
\(34\) 2.89008 0.495645
\(35\) 0.0522697 0.0905338i 0.00883520 0.0153030i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −0.0881460 0.152673i −0.0144911 0.0250993i 0.858689 0.512497i \(-0.171279\pi\)
−0.873180 + 0.487398i \(0.837946\pi\)
\(38\) −7.20775 −1.16925
\(39\) 0 0
\(40\) 2.13706 0.337899
\(41\) −4.29590 7.44071i −0.670906 1.16204i −0.977647 0.210251i \(-0.932572\pi\)
0.306741 0.951793i \(-0.400761\pi\)
\(42\) −0.0244587 0.0423637i −0.00377405 0.00653685i
\(43\) −3.35690 + 5.81431i −0.511922 + 0.886675i 0.487983 + 0.872853i \(0.337733\pi\)
−0.999904 + 0.0138213i \(0.995600\pi\)
\(44\) −6.29590 −0.949142
\(45\) 1.06853 1.85075i 0.159287 0.275894i
\(46\) 1.35690 2.35021i 0.200063 0.346520i
\(47\) −7.20775 −1.05136 −0.525679 0.850683i \(-0.676189\pi\)
−0.525679 + 0.850683i \(0.676189\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 3.49880 + 6.06011i 0.499829 + 0.865729i
\(50\) −0.216480 0.374955i −0.0306149 0.0530266i
\(51\) 2.89008 0.404693
\(52\) 0 0
\(53\) 9.34481 1.28361 0.641804 0.766868i \(-0.278186\pi\)
0.641804 + 0.766868i \(0.278186\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −6.72737 11.6521i −0.907118 1.57117i
\(56\) 0.0244587 0.0423637i 0.00326843 0.00566108i
\(57\) −7.20775 −0.954690
\(58\) 2.45593 4.25379i 0.322479 0.558550i
\(59\) −2.13437 + 3.69685i −0.277872 + 0.481288i −0.970856 0.239665i \(-0.922962\pi\)
0.692984 + 0.720953i \(0.256296\pi\)
\(60\) 2.13706 0.275894
\(61\) −3.55496 + 6.15737i −0.455166 + 0.788370i −0.998698 0.0510183i \(-0.983753\pi\)
0.543532 + 0.839388i \(0.317087\pi\)
\(62\) −4.50484 7.80262i −0.572116 0.990934i
\(63\) −0.0244587 0.0423637i −0.00308150 0.00533732i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.29590 −0.774971
\(67\) 2.69202 + 4.66272i 0.328883 + 0.569642i 0.982290 0.187365i \(-0.0599946\pi\)
−0.653408 + 0.757006i \(0.726661\pi\)
\(68\) 1.44504 + 2.50289i 0.175237 + 0.303520i
\(69\) 1.35690 2.35021i 0.163351 0.282932i
\(70\) 0.104539 0.0124949
\(71\) −4.35690 + 7.54637i −0.517068 + 0.895589i 0.482735 + 0.875766i \(0.339643\pi\)
−0.999804 + 0.0198223i \(0.993690\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 14.9487 1.74961 0.874806 0.484474i \(-0.160989\pi\)
0.874806 + 0.484474i \(0.160989\pi\)
\(74\) 0.0881460 0.152673i 0.0102468 0.0177479i
\(75\) −0.216480 0.374955i −0.0249970 0.0432960i
\(76\) −3.60388 6.24210i −0.413393 0.716017i
\(77\) −0.307979 −0.0350974
\(78\) 0 0
\(79\) 13.8291 1.55589 0.777947 0.628330i \(-0.216261\pi\)
0.777947 + 0.628330i \(0.216261\pi\)
\(80\) 1.06853 + 1.85075i 0.119465 + 0.206920i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.29590 7.44071i 0.474402 0.821689i
\(83\) 11.1347 1.22219 0.611094 0.791558i \(-0.290730\pi\)
0.611094 + 0.791558i \(0.290730\pi\)
\(84\) 0.0244587 0.0423637i 0.00266866 0.00462225i
\(85\) −3.08815 + 5.34883i −0.334956 + 0.580162i
\(86\) −6.71379 −0.723967
\(87\) 2.45593 4.25379i 0.263303 0.456054i
\(88\) −3.14795 5.45241i −0.335572 0.581229i
\(89\) 1.96077 + 3.39616i 0.207841 + 0.359992i 0.951034 0.309085i \(-0.100023\pi\)
−0.743193 + 0.669077i \(0.766690\pi\)
\(90\) 2.13706 0.225266
\(91\) 0 0
\(92\) 2.71379 0.282932
\(93\) −4.50484 7.80262i −0.467131 0.809094i
\(94\) −3.60388 6.24210i −0.371711 0.643823i
\(95\) 7.70171 13.3398i 0.790179 1.36863i
\(96\) 1.00000 0.102062
\(97\) −1.23945 + 2.14678i −0.125847 + 0.217973i −0.922064 0.387038i \(-0.873498\pi\)
0.796217 + 0.605011i \(0.206831\pi\)
\(98\) −3.49880 + 6.06011i −0.353433 + 0.612163i
\(99\) −6.29590 −0.632761
\(100\) 0.216480 0.374955i 0.0216480 0.0374955i
\(101\) −0.826396 1.43136i −0.0822295 0.142426i 0.821978 0.569520i \(-0.192871\pi\)
−0.904207 + 0.427094i \(0.859537\pi\)
\(102\) 1.44504 + 2.50289i 0.143080 + 0.247823i
\(103\) −8.23490 −0.811409 −0.405704 0.914004i \(-0.632974\pi\)
−0.405704 + 0.914004i \(0.632974\pi\)
\(104\) 0 0
\(105\) 0.104539 0.0102020
\(106\) 4.67241 + 8.09285i 0.453824 + 0.786047i
\(107\) 4.18329 + 7.24567i 0.404414 + 0.700466i 0.994253 0.107055i \(-0.0341421\pi\)
−0.589839 + 0.807521i \(0.700809\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 17.4276 1.66926 0.834630 0.550811i \(-0.185682\pi\)
0.834630 + 0.550811i \(0.185682\pi\)
\(110\) 6.72737 11.6521i 0.641429 1.11099i
\(111\) 0.0881460 0.152673i 0.00836645 0.0144911i
\(112\) 0.0489173 0.00462225
\(113\) 6.98792 12.1034i 0.657368 1.13859i −0.323926 0.946082i \(-0.605003\pi\)
0.981294 0.192513i \(-0.0616636\pi\)
\(114\) −3.60388 6.24210i −0.337534 0.584626i
\(115\) 2.89977 + 5.02255i 0.270405 + 0.468355i
\(116\) 4.91185 0.456054
\(117\) 0 0
\(118\) −4.26875 −0.392970
\(119\) 0.0706876 + 0.122435i 0.00647992 + 0.0112236i
\(120\) 1.06853 + 1.85075i 0.0975431 + 0.168950i
\(121\) −14.3192 + 24.8015i −1.30174 + 2.25468i
\(122\) −7.10992 −0.643702
\(123\) 4.29590 7.44071i 0.387348 0.670906i
\(124\) 4.50484 7.80262i 0.404547 0.700696i
\(125\) 11.6106 1.03848
\(126\) 0.0244587 0.0423637i 0.00217895 0.00377405i
\(127\) 3.76055 + 6.51347i 0.333695 + 0.577977i 0.983233 0.182352i \(-0.0583711\pi\)
−0.649538 + 0.760329i \(0.725038\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −6.71379 −0.591116
\(130\) 0 0
\(131\) 5.12498 0.447772 0.223886 0.974615i \(-0.428126\pi\)
0.223886 + 0.974615i \(0.428126\pi\)
\(132\) −3.14795 5.45241i −0.273994 0.474571i
\(133\) −0.176292 0.305347i −0.0152865 0.0264769i
\(134\) −2.69202 + 4.66272i −0.232555 + 0.402797i
\(135\) 2.13706 0.183929
\(136\) −1.44504 + 2.50289i −0.123911 + 0.214621i
\(137\) −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i \(-0.887992\pi\)
0.767853 + 0.640626i \(0.221325\pi\)
\(138\) 2.71379 0.231013
\(139\) −4.34481 + 7.52544i −0.368522 + 0.638299i −0.989335 0.145660i \(-0.953470\pi\)
0.620812 + 0.783959i \(0.286803\pi\)
\(140\) 0.0522697 + 0.0905338i 0.00441760 + 0.00765150i
\(141\) −3.60388 6.24210i −0.303501 0.525679i
\(142\) −8.71379 −0.731245
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 5.24847 + 9.09062i 0.435862 + 0.754935i
\(146\) 7.47434 + 12.9459i 0.618581 + 1.07141i
\(147\) −3.49880 + 6.06011i −0.288576 + 0.499829i
\(148\) 0.176292 0.0144911
\(149\) −2.43416 + 4.21608i −0.199414 + 0.345395i −0.948339 0.317260i \(-0.897237\pi\)
0.748925 + 0.662655i \(0.230570\pi\)
\(150\) 0.216480 0.374955i 0.0176755 0.0306149i
\(151\) −14.7463 −1.20004 −0.600019 0.799986i \(-0.704840\pi\)
−0.600019 + 0.799986i \(0.704840\pi\)
\(152\) 3.60388 6.24210i 0.292313 0.506301i
\(153\) 1.44504 + 2.50289i 0.116825 + 0.202346i
\(154\) −0.153989 0.266717i −0.0124088 0.0214927i
\(155\) 19.2543 1.54654
\(156\) 0 0
\(157\) −16.7138 −1.33391 −0.666953 0.745100i \(-0.732402\pi\)
−0.666953 + 0.745100i \(0.732402\pi\)
\(158\) 6.91454 + 11.9763i 0.550091 + 0.952786i
\(159\) 4.67241 + 8.09285i 0.370546 + 0.641804i
\(160\) −1.06853 + 1.85075i −0.0844748 + 0.146315i
\(161\) 0.132751 0.0104623
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 2.77479 4.80608i 0.217338 0.376441i −0.736655 0.676269i \(-0.763596\pi\)
0.953993 + 0.299828i \(0.0969292\pi\)
\(164\) 8.59179 0.670906
\(165\) 6.72737 11.6521i 0.523725 0.907118i
\(166\) 5.56734 + 9.64291i 0.432109 + 0.748435i
\(167\) −1.96077 3.39616i −0.151729 0.262802i 0.780134 0.625612i \(-0.215151\pi\)
−0.931863 + 0.362810i \(0.881817\pi\)
\(168\) 0.0489173 0.00377405
\(169\) 0 0
\(170\) −6.17629 −0.473700
\(171\) −3.60388 6.24210i −0.275595 0.477345i
\(172\) −3.35690 5.81431i −0.255961 0.443337i
\(173\) 1.74214 3.01747i 0.132452 0.229414i −0.792169 0.610302i \(-0.791048\pi\)
0.924621 + 0.380888i \(0.124382\pi\)
\(174\) 4.91185 0.372367
\(175\) 0.0105896 0.0183418i 0.000800501 0.00138651i
\(176\) 3.14795 5.45241i 0.237286 0.410991i
\(177\) −4.26875 −0.320859
\(178\) −1.96077 + 3.39616i −0.146966 + 0.254553i
\(179\) −1.79440 3.10800i −0.134120 0.232303i 0.791141 0.611634i \(-0.209487\pi\)
−0.925261 + 0.379331i \(0.876154\pi\)
\(180\) 1.06853 + 1.85075i 0.0796436 + 0.137947i
\(181\) 5.50604 0.409261 0.204630 0.978839i \(-0.434401\pi\)
0.204630 + 0.978839i \(0.434401\pi\)
\(182\) 0 0
\(183\) −7.10992 −0.525580
\(184\) 1.35690 + 2.35021i 0.100032 + 0.173260i
\(185\) 0.188374 + 0.326273i 0.0138495 + 0.0239880i
\(186\) 4.50484 7.80262i 0.330311 0.572116i
\(187\) 18.1957 1.33060
\(188\) 3.60388 6.24210i 0.262840 0.455252i
\(189\) 0.0244587 0.0423637i 0.00177911 0.00308150i
\(190\) 15.4034 1.11748
\(191\) 2.82908 4.90012i 0.204705 0.354560i −0.745333 0.666692i \(-0.767710\pi\)
0.950039 + 0.312132i \(0.101043\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −6.70171 11.6077i −0.482400 0.835541i 0.517396 0.855746i \(-0.326901\pi\)
−0.999796 + 0.0202053i \(0.993568\pi\)
\(194\) −2.47889 −0.177974
\(195\) 0 0
\(196\) −6.99761 −0.499829
\(197\) −9.99061 17.3042i −0.711801 1.23288i −0.964180 0.265248i \(-0.914546\pi\)
0.252379 0.967628i \(-0.418787\pi\)
\(198\) −3.14795 5.45241i −0.223715 0.387486i
\(199\) 3.12080 5.40539i 0.221228 0.383178i −0.733953 0.679200i \(-0.762327\pi\)
0.955181 + 0.296022i \(0.0956603\pi\)
\(200\) 0.432960 0.0306149
\(201\) −2.69202 + 4.66272i −0.189881 + 0.328883i
\(202\) 0.826396 1.43136i 0.0581450 0.100710i
\(203\) 0.240275 0.0168640
\(204\) −1.44504 + 2.50289i −0.101173 + 0.175237i
\(205\) 9.18060 + 15.9013i 0.641201 + 1.11059i
\(206\) −4.11745 7.13163i −0.286876 0.496884i
\(207\) 2.71379 0.188622
\(208\) 0 0
\(209\) −45.3793 −3.13895
\(210\) 0.0522697 + 0.0905338i 0.00360695 + 0.00624743i
\(211\) 2.54288 + 4.40439i 0.175059 + 0.303211i 0.940182 0.340674i \(-0.110655\pi\)
−0.765123 + 0.643884i \(0.777322\pi\)
\(212\) −4.67241 + 8.09285i −0.320902 + 0.555819i
\(213\) −8.71379 −0.597059
\(214\) −4.18329 + 7.24567i −0.285964 + 0.495304i
\(215\) 7.17390 12.4256i 0.489256 0.847416i
\(216\) 1.00000 0.0680414
\(217\) 0.220365 0.381683i 0.0149594 0.0259104i
\(218\) 8.71379 + 15.0927i 0.590172 + 1.02221i
\(219\) 7.47434 + 12.9459i 0.505069 + 0.874806i
\(220\) 13.4547 0.907118
\(221\) 0 0
\(222\) 0.176292 0.0118319
\(223\) 10.2741 + 17.7953i 0.688006 + 1.19166i 0.972482 + 0.232979i \(0.0748473\pi\)
−0.284475 + 0.958683i \(0.591819\pi\)
\(224\) 0.0244587 + 0.0423637i 0.00163421 + 0.00283054i
\(225\) 0.216480 0.374955i 0.0144320 0.0249970i
\(226\) 13.9758 0.929659
\(227\) −2.20560 + 3.82020i −0.146390 + 0.253556i −0.929891 0.367836i \(-0.880099\pi\)
0.783500 + 0.621391i \(0.213432\pi\)
\(228\) 3.60388 6.24210i 0.238672 0.413393i
\(229\) 0.230586 0.0152376 0.00761878 0.999971i \(-0.497575\pi\)
0.00761878 + 0.999971i \(0.497575\pi\)
\(230\) −2.89977 + 5.02255i −0.191205 + 0.331177i
\(231\) −0.153989 0.266717i −0.0101317 0.0175487i
\(232\) 2.45593 + 4.25379i 0.161240 + 0.279275i
\(233\) −7.82371 −0.512548 −0.256274 0.966604i \(-0.582495\pi\)
−0.256274 + 0.966604i \(0.582495\pi\)
\(234\) 0 0
\(235\) 15.4034 1.00481
\(236\) −2.13437 3.69685i −0.138936 0.240644i
\(237\) 6.91454 + 11.9763i 0.449148 + 0.777947i
\(238\) −0.0706876 + 0.122435i −0.00458200 + 0.00793625i
\(239\) 11.1535 0.721457 0.360729 0.932671i \(-0.382528\pi\)
0.360729 + 0.932671i \(0.382528\pi\)
\(240\) −1.06853 + 1.85075i −0.0689734 + 0.119465i
\(241\) 1.77263 3.07029i 0.114185 0.197775i −0.803268 0.595617i \(-0.796908\pi\)
0.917454 + 0.397842i \(0.130241\pi\)
\(242\) −28.6383 −1.84094
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −3.55496 6.15737i −0.227583 0.394185i
\(245\) −7.47716 12.9508i −0.477699 0.827398i
\(246\) 8.59179 0.547793
\(247\) 0 0
\(248\) 9.00969 0.572116
\(249\) 5.56734 + 9.64291i 0.352816 + 0.611094i
\(250\) 5.80529 + 10.0551i 0.367159 + 0.635938i
\(251\) 2.08546 3.61212i 0.131633 0.227995i −0.792673 0.609647i \(-0.791311\pi\)
0.924306 + 0.381652i \(0.124645\pi\)
\(252\) 0.0489173 0.00308150
\(253\) 8.54288 14.7967i 0.537086 0.930260i
\(254\) −3.76055 + 6.51347i −0.235958 + 0.408691i
\(255\) −6.17629 −0.386774
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.44504 + 9.43109i 0.339652 + 0.588295i 0.984367 0.176128i \(-0.0563572\pi\)
−0.644715 + 0.764423i \(0.723024\pi\)
\(258\) −3.35690 5.81431i −0.208991 0.361983i
\(259\) 0.00862374 0.000535853
\(260\) 0 0
\(261\) 4.91185 0.304036
\(262\) 2.56249 + 4.43836i 0.158311 + 0.274203i
\(263\) 15.6136 + 27.0435i 0.962774 + 1.66757i 0.715481 + 0.698632i \(0.246207\pi\)
0.247292 + 0.968941i \(0.420459\pi\)
\(264\) 3.14795 5.45241i 0.193743 0.335572i
\(265\) −19.9705 −1.22678
\(266\) 0.176292 0.305347i 0.0108092 0.0187220i
\(267\) −1.96077 + 3.39616i −0.119997 + 0.207841i
\(268\) −5.38404 −0.328883
\(269\) −7.95862 + 13.7847i −0.485245 + 0.840470i −0.999856 0.0169542i \(-0.994603\pi\)
0.514611 + 0.857424i \(0.327936\pi\)
\(270\) 1.06853 + 1.85075i 0.0650288 + 0.112633i
\(271\) −1.76055 3.04937i −0.106946 0.185236i 0.807586 0.589750i \(-0.200774\pi\)
−0.914532 + 0.404514i \(0.867441\pi\)
\(272\) −2.89008 −0.175237
\(273\) 0 0
\(274\) −4.00000 −0.241649
\(275\) −1.36294 2.36068i −0.0821882 0.142354i
\(276\) 1.35690 + 2.35021i 0.0816755 + 0.141466i
\(277\) 4.29052 7.43140i 0.257792 0.446509i −0.707858 0.706355i \(-0.750338\pi\)
0.965650 + 0.259845i \(0.0836716\pi\)
\(278\) −8.68963 −0.521169
\(279\) 4.50484 7.80262i 0.269698 0.467131i
\(280\) −0.0522697 + 0.0905338i −0.00312371 + 0.00541043i
\(281\) −8.07846 −0.481920 −0.240960 0.970535i \(-0.577462\pi\)
−0.240960 + 0.970535i \(0.577462\pi\)
\(282\) 3.60388 6.24210i 0.214608 0.371711i
\(283\) 8.70171 + 15.0718i 0.517263 + 0.895926i 0.999799 + 0.0200496i \(0.00638242\pi\)
−0.482536 + 0.875876i \(0.660284\pi\)
\(284\) −4.35690 7.54637i −0.258534 0.447794i
\(285\) 15.4034 0.912420
\(286\) 0 0
\(287\) 0.420288 0.0248088
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 4.32371 + 7.48888i 0.254336 + 0.440522i
\(290\) −5.24847 + 9.09062i −0.308201 + 0.533820i
\(291\) −2.47889 −0.145315
\(292\) −7.47434 + 12.9459i −0.437403 + 0.757604i
\(293\) 9.68545 16.7757i 0.565830 0.980046i −0.431142 0.902284i \(-0.641889\pi\)
0.996972 0.0777621i \(-0.0247775\pi\)
\(294\) −6.99761 −0.408109
\(295\) 4.56129 7.90039i 0.265569 0.459979i
\(296\) 0.0881460 + 0.152673i 0.00512338 + 0.00887396i
\(297\) −3.14795 5.45241i −0.182662 0.316381i
\(298\) −4.86831 −0.282014
\(299\) 0 0
\(300\) 0.432960 0.0249970
\(301\) −0.164210 0.284421i −0.00946493 0.0163937i
\(302\) −7.37316 12.7707i −0.424278 0.734870i
\(303\) 0.826396 1.43136i 0.0474752 0.0822295i
\(304\) 7.20775 0.413393
\(305\) 7.59717 13.1587i 0.435013 0.753464i
\(306\) −1.44504 + 2.50289i −0.0826075 + 0.143080i
\(307\) −12.4263 −0.709204 −0.354602 0.935017i \(-0.615384\pi\)
−0.354602 + 0.935017i \(0.615384\pi\)
\(308\) 0.153989 0.266717i 0.00877435 0.0151976i
\(309\) −4.11745 7.13163i −0.234233 0.405704i
\(310\) 9.62714 + 16.6747i 0.546785 + 0.947059i
\(311\) 2.71379 0.153885 0.0769425 0.997036i \(-0.475484\pi\)
0.0769425 + 0.997036i \(0.475484\pi\)
\(312\) 0 0
\(313\) 15.3884 0.869801 0.434901 0.900478i \(-0.356783\pi\)
0.434901 + 0.900478i \(0.356783\pi\)
\(314\) −8.35690 14.4746i −0.471607 0.816847i
\(315\) 0.0522697 + 0.0905338i 0.00294507 + 0.00510100i
\(316\) −6.91454 + 11.9763i −0.388973 + 0.673722i
\(317\) 25.6528 1.44080 0.720402 0.693557i \(-0.243957\pi\)
0.720402 + 0.693557i \(0.243957\pi\)
\(318\) −4.67241 + 8.09285i −0.262016 + 0.453824i
\(319\) 15.4623 26.7814i 0.865721 1.49947i
\(320\) −2.13706 −0.119465
\(321\) −4.18329 + 7.24567i −0.233489 + 0.404414i
\(322\) 0.0663757 + 0.114966i 0.00369898 + 0.00640681i
\(323\) 10.4155 + 18.0402i 0.579534 + 1.00378i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 5.54958 0.307363
\(327\) 8.71379 + 15.0927i 0.481874 + 0.834630i
\(328\) 4.29590 + 7.44071i 0.237201 + 0.410845i
\(329\) 0.176292 0.305347i 0.00971929 0.0168343i
\(330\) 13.4547 0.740659
\(331\) 1.91185 3.31143i 0.105085 0.182013i −0.808688 0.588238i \(-0.799822\pi\)
0.913773 + 0.406225i \(0.133155\pi\)
\(332\) −5.56734 + 9.64291i −0.305547 + 0.529223i
\(333\) 0.176292 0.00966074
\(334\) 1.96077 3.39616i 0.107289 0.185829i
\(335\) −5.75302 9.96452i −0.314321 0.544420i
\(336\) 0.0244587 + 0.0423637i 0.00133433 + 0.00231113i
\(337\) 20.1304 1.09657 0.548285 0.836291i \(-0.315281\pi\)
0.548285 + 0.836291i \(0.315281\pi\)
\(338\) 0 0
\(339\) 13.9758 0.759063
\(340\) −3.08815 5.34883i −0.167478 0.290081i
\(341\) −28.3620 49.1245i −1.53589 2.66024i
\(342\) 3.60388 6.24210i 0.194875 0.337534i
\(343\) −0.684726 −0.0369717
\(344\) 3.35690 5.81431i 0.180992 0.313487i
\(345\) −2.89977 + 5.02255i −0.156118 + 0.270405i
\(346\) 3.48427 0.187316
\(347\) −1.46950 + 2.54525i −0.0788869 + 0.136636i −0.902770 0.430124i \(-0.858470\pi\)
0.823883 + 0.566760i \(0.191803\pi\)
\(348\) 2.45593 + 4.25379i 0.131652 + 0.228027i
\(349\) −3.68664 6.38546i −0.197342 0.341806i 0.750324 0.661070i \(-0.229897\pi\)
−0.947666 + 0.319265i \(0.896564\pi\)
\(350\) 0.0211793 0.00113208
\(351\) 0 0
\(352\) 6.29590 0.335572
\(353\) 1.00538 + 1.74136i 0.0535108 + 0.0926834i 0.891540 0.452942i \(-0.149626\pi\)
−0.838029 + 0.545625i \(0.816292\pi\)
\(354\) −2.13437 3.69685i −0.113441 0.196485i
\(355\) 9.31096 16.1271i 0.494175 0.855935i
\(356\) −3.92154 −0.207841
\(357\) −0.0706876 + 0.122435i −0.00374118 + 0.00647992i
\(358\) 1.79440 3.10800i 0.0948373 0.164263i
\(359\) 31.4577 1.66027 0.830137 0.557559i \(-0.188262\pi\)
0.830137 + 0.557559i \(0.188262\pi\)
\(360\) −1.06853 + 1.85075i −0.0563166 + 0.0975431i
\(361\) −16.4758 28.5370i −0.867149 1.50195i
\(362\) 2.75302 + 4.76837i 0.144696 + 0.250620i
\(363\) −28.6383 −1.50312
\(364\) 0 0
\(365\) −31.9463 −1.67215
\(366\) −3.55496 6.15737i −0.185821 0.321851i
\(367\) 2.24967 + 3.89654i 0.117432 + 0.203398i 0.918749 0.394842i \(-0.129201\pi\)
−0.801317 + 0.598239i \(0.795867\pi\)
\(368\) −1.35690 + 2.35021i −0.0707331 + 0.122513i
\(369\) 8.59179 0.447271
\(370\) −0.188374 + 0.326273i −0.00979308 + 0.0169621i
\(371\) −0.228562 + 0.395881i −0.0118663 + 0.0205531i
\(372\) 9.00969 0.467131
\(373\) −18.9148 + 32.7615i −0.979373 + 1.69632i −0.314698 + 0.949192i \(0.601903\pi\)
−0.664676 + 0.747132i \(0.731430\pi\)
\(374\) 9.09783 + 15.7579i 0.470438 + 0.814822i
\(375\) 5.80529 + 10.0551i 0.299784 + 0.519241i
\(376\) 7.20775 0.371711
\(377\) 0 0
\(378\) 0.0489173 0.00251604
\(379\) 4.21983 + 7.30896i 0.216758 + 0.375436i 0.953815 0.300395i \(-0.0971183\pi\)
−0.737057 + 0.675831i \(0.763785\pi\)
\(380\) 7.70171 + 13.3398i 0.395089 + 0.684315i
\(381\) −3.76055 + 6.51347i −0.192659 + 0.333695i
\(382\) 5.65817 0.289497
\(383\) −0.643104 + 1.11389i −0.0328611 + 0.0569171i −0.881988 0.471271i \(-0.843795\pi\)
0.849127 + 0.528188i \(0.177129\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0.658170 0.0335434
\(386\) 6.70171 11.6077i 0.341108 0.590817i
\(387\) −3.35690 5.81431i −0.170641 0.295558i
\(388\) −1.23945 2.14678i −0.0629234 0.108986i
\(389\) 23.3924 1.18604 0.593021 0.805187i \(-0.297935\pi\)
0.593021 + 0.805187i \(0.297935\pi\)
\(390\) 0 0
\(391\) −7.84309 −0.396642
\(392\) −3.49880 6.06011i −0.176716 0.306082i
\(393\) 2.56249 + 4.43836i 0.129261 + 0.223886i
\(394\) 9.99061 17.3042i 0.503320 0.871775i
\(395\) −29.5536 −1.48700
\(396\) 3.14795 5.45241i 0.158190 0.273994i
\(397\) −18.5429 + 32.1172i −0.930640 + 1.61192i −0.148411 + 0.988926i \(0.547416\pi\)
−0.782229 + 0.622990i \(0.785918\pi\)
\(398\) 6.24160 0.312863
\(399\) 0.176292 0.305347i 0.00882564 0.0152865i
\(400\) 0.216480 + 0.374955i 0.0108240 + 0.0187477i
\(401\) −2.43296 4.21401i −0.121496 0.210438i 0.798862 0.601515i \(-0.205436\pi\)
−0.920358 + 0.391077i \(0.872103\pi\)
\(402\) −5.38404 −0.268532
\(403\) 0 0
\(404\) 1.65279 0.0822295
\(405\) 1.06853 + 1.85075i 0.0530958 + 0.0919646i
\(406\) 0.120137 + 0.208084i 0.00596232 + 0.0103270i
\(407\) 0.554958 0.961216i 0.0275083 0.0476457i
\(408\) −2.89008 −0.143080
\(409\) 0.222521 0.385418i 0.0110030 0.0190577i −0.860472 0.509499i \(-0.829831\pi\)
0.871474 + 0.490441i \(0.163164\pi\)
\(410\) −9.18060 + 15.9013i −0.453398 + 0.785308i
\(411\) −4.00000 −0.197305
\(412\) 4.11745 7.13163i 0.202852 0.351350i
\(413\) −0.104408 0.180840i −0.00513758 0.00889855i
\(414\) 1.35690 + 2.35021i 0.0666878 + 0.115507i
\(415\) −23.7955 −1.16807
\(416\) 0 0
\(417\) −8.68963 −0.425533
\(418\) −22.6896 39.2996i −1.10979 1.92221i
\(419\) −8.99343 15.5771i −0.439358 0.760990i 0.558282 0.829651i \(-0.311461\pi\)
−0.997640 + 0.0686612i \(0.978127\pi\)
\(420\) −0.0522697 + 0.0905338i −0.00255050 + 0.00441760i
\(421\) −21.2814 −1.03719 −0.518597 0.855019i \(-0.673545\pi\)
−0.518597 + 0.855019i \(0.673545\pi\)
\(422\) −2.54288 + 4.40439i −0.123785 + 0.214402i
\(423\) 3.60388 6.24210i 0.175226 0.303501i
\(424\) −9.34481 −0.453824
\(425\) −0.625646 + 1.08365i −0.0303483 + 0.0525648i
\(426\) −4.35690 7.54637i −0.211092 0.365623i
\(427\) −0.173899 0.301202i −0.00841557 0.0145762i
\(428\) −8.36658 −0.404414
\(429\) 0 0
\(430\) 14.3478 0.691912
\(431\) 12.3569 + 21.4028i 0.595211 + 1.03094i 0.993517 + 0.113683i \(0.0362648\pi\)
−0.398306 + 0.917252i \(0.630402\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −16.1087 + 27.9011i −0.774136 + 1.34084i 0.161143 + 0.986931i \(0.448482\pi\)
−0.935279 + 0.353911i \(0.884851\pi\)
\(434\) 0.440730 0.0211557
\(435\) −5.24847 + 9.09062i −0.251645 + 0.435862i
\(436\) −8.71379 + 15.0927i −0.417315 + 0.722811i
\(437\) 19.5603 0.935698
\(438\) −7.47434 + 12.9459i −0.357138 + 0.618581i
\(439\) −16.0438 27.7887i −0.765731 1.32628i −0.939859 0.341561i \(-0.889044\pi\)
0.174129 0.984723i \(-0.444289\pi\)
\(440\) 6.72737 + 11.6521i 0.320715 + 0.555494i
\(441\) −6.99761 −0.333219
\(442\) 0 0
\(443\) 20.5109 0.974504 0.487252 0.873261i \(-0.337999\pi\)
0.487252 + 0.873261i \(0.337999\pi\)
\(444\) 0.0881460 + 0.152673i 0.00418322 + 0.00724556i
\(445\) −4.19029 7.25780i −0.198639 0.344053i
\(446\) −10.2741 + 17.7953i −0.486494 + 0.842632i
\(447\) −4.86831 −0.230263
\(448\) −0.0244587 + 0.0423637i −0.00115556 + 0.00200149i
\(449\) −7.65817 + 13.2643i −0.361411 + 0.625983i −0.988193 0.153212i \(-0.951038\pi\)
0.626782 + 0.779195i \(0.284372\pi\)
\(450\) 0.432960 0.0204099
\(451\) 27.0465 46.8460i 1.27357 2.20589i
\(452\) 6.98792 + 12.1034i 0.328684 + 0.569297i
\(453\) −7.37316 12.7707i −0.346421 0.600019i
\(454\) −4.41119 −0.207027
\(455\) 0 0
\(456\) 7.20775 0.337534
\(457\) −9.59299 16.6155i −0.448741 0.777242i 0.549563 0.835452i \(-0.314794\pi\)
−0.998304 + 0.0582096i \(0.981461\pi\)
\(458\) 0.115293 + 0.199693i 0.00538729 + 0.00933106i
\(459\) −1.44504 + 2.50289i −0.0674488 + 0.116825i
\(460\) −5.79954 −0.270405
\(461\) 4.15615 7.19865i 0.193571 0.335275i −0.752860 0.658181i \(-0.771326\pi\)
0.946431 + 0.322906i \(0.104660\pi\)
\(462\) 0.153989 0.266717i 0.00716423 0.0124088i
\(463\) 6.32842 0.294107 0.147053 0.989129i \(-0.453021\pi\)
0.147053 + 0.989129i \(0.453021\pi\)
\(464\) −2.45593 + 4.25379i −0.114014 + 0.197477i
\(465\) 9.62714 + 16.6747i 0.446448 + 0.773270i
\(466\) −3.91185 6.77553i −0.181213 0.313870i
\(467\) −31.1879 −1.44320 −0.721602 0.692308i \(-0.756594\pi\)
−0.721602 + 0.692308i \(0.756594\pi\)
\(468\) 0 0
\(469\) −0.263373 −0.0121614
\(470\) 7.70171 + 13.3398i 0.355253 + 0.615317i
\(471\) −8.35690 14.4746i −0.385065 0.666953i
\(472\) 2.13437 3.69685i 0.0982426 0.170161i
\(473\) −42.2693 −1.94355
\(474\) −6.91454 + 11.9763i −0.317595 + 0.550091i
\(475\) 1.56033 2.70258i 0.0715931 0.124003i
\(476\) −0.141375 −0.00647992
\(477\) −4.67241 + 8.09285i −0.213935 + 0.370546i
\(478\) 5.57673 + 9.65918i 0.255074 + 0.441800i
\(479\) −8.96615 15.5298i −0.409674 0.709576i 0.585179 0.810904i \(-0.301024\pi\)
−0.994853 + 0.101328i \(0.967691\pi\)
\(480\) −2.13706 −0.0975431
\(481\) 0 0
\(482\) 3.54527 0.161483
\(483\) 0.0663757 + 0.114966i 0.00302020 + 0.00523114i
\(484\) −14.3192 24.8015i −0.650871 1.12734i
\(485\) 2.64878 4.58782i 0.120275 0.208322i
\(486\) 1.00000 0.0453609
\(487\) 15.1640 26.2648i 0.687145 1.19017i −0.285612 0.958345i \(-0.592197\pi\)
0.972757 0.231825i \(-0.0744697\pi\)
\(488\) 3.55496 6.15737i 0.160925 0.278731i
\(489\) 5.54958 0.250961
\(490\) 7.47716 12.9508i 0.337784 0.585059i
\(491\) −15.0477 26.0634i −0.679094 1.17623i −0.975254 0.221087i \(-0.929039\pi\)
0.296160 0.955138i \(-0.404294\pi\)
\(492\) 4.29590 + 7.44071i 0.193674 + 0.335453i
\(493\) −14.1957 −0.639341
\(494\) 0 0
\(495\) 13.4547 0.604745
\(496\) 4.50484 + 7.80262i 0.202273 + 0.350348i
\(497\) −0.213128 0.369148i −0.00956009 0.0165586i
\(498\) −5.56734 + 9.64291i −0.249478 + 0.432109i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −5.80529 + 10.0551i −0.259620 + 0.449676i
\(501\) 1.96077 3.39616i 0.0876008 0.151729i
\(502\) 4.17092 0.186157
\(503\) −16.8756 + 29.2294i −0.752446 + 1.30328i 0.194188 + 0.980964i \(0.437793\pi\)
−0.946634 + 0.322311i \(0.895540\pi\)
\(504\) 0.0244587 + 0.0423637i 0.00108948 + 0.00188703i
\(505\) 1.76606 + 3.05891i 0.0785887 + 0.136120i
\(506\) 17.0858 0.759554
\(507\) 0 0
\(508\) −7.52111 −0.333695
\(509\) −7.37196 12.7686i −0.326756 0.565959i 0.655110 0.755534i \(-0.272622\pi\)
−0.981866 + 0.189575i \(0.939289\pi\)
\(510\) −3.08815 5.34883i −0.136745 0.236850i
\(511\) −0.365625 + 0.633281i −0.0161743 + 0.0280147i
\(512\) −1.00000 −0.0441942
\(513\) 3.60388 6.24210i 0.159115 0.275595i
\(514\) −5.44504 + 9.43109i −0.240171 + 0.415988i
\(515\) 17.5985 0.775483
\(516\) 3.35690 5.81431i 0.147779 0.255961i
\(517\) −22.6896 39.2996i −0.997889 1.72839i
\(518\) 0.00431187 + 0.00746837i 0.000189453 + 0.000328142i
\(519\) 3.48427 0.152943
\(520\) 0 0
\(521\) 22.1086 0.968595 0.484297 0.874903i \(-0.339075\pi\)
0.484297 + 0.874903i \(0.339075\pi\)
\(522\) 2.45593 + 4.25379i 0.107493 + 0.186183i
\(523\) 8.67994 + 15.0341i 0.379547 + 0.657395i 0.990996 0.133889i \(-0.0427464\pi\)
−0.611449 + 0.791284i \(0.709413\pi\)
\(524\) −2.56249 + 4.43836i −0.111943 + 0.193891i
\(525\) 0.0211793 0.000924339
\(526\) −15.6136 + 27.0435i −0.680784 + 1.17915i
\(527\) −13.0194 + 22.5502i −0.567133 + 0.982303i
\(528\) 6.29590 0.273994
\(529\) 7.81767 13.5406i 0.339899 0.588722i
\(530\) −9.98523 17.2949i −0.433731 0.751244i
\(531\) −2.13437 3.69685i −0.0926240 0.160429i
\(532\) 0.352584 0.0152865
\(533\) 0 0
\(534\) −3.92154 −0.169702
\(535\) −8.93996 15.4845i −0.386508 0.669452i
\(536\) −2.69202 4.66272i −0.116278 0.201399i
\(537\) 1.79440 3.10800i 0.0774343 0.134120i
\(538\) −15.9172 −0.686241
\(539\) −22.0281 + 38.1538i −0.948818 + 1.64340i
\(540\) −1.06853 + 1.85075i −0.0459823 + 0.0796436i
\(541\) 8.83579 0.379880 0.189940 0.981796i \(-0.439171\pi\)
0.189940 + 0.981796i \(0.439171\pi\)
\(542\) 1.76055 3.04937i 0.0756222 0.130982i
\(543\) 2.75302 + 4.76837i 0.118143 + 0.204630i
\(544\) −1.44504 2.50289i −0.0619557 0.107310i
\(545\) −37.2438 −1.59535
\(546\) 0 0
\(547\) −8.10859 −0.346698 −0.173349 0.984860i \(-0.555459\pi\)
−0.173349 + 0.984860i \(0.555459\pi\)
\(548\) −2.00000 3.46410i −0.0854358 0.147979i
\(549\) −3.55496 6.15737i −0.151722 0.262790i
\(550\) 1.36294 2.36068i 0.0581158 0.100660i
\(551\) 35.4034 1.50824
\(552\) −1.35690 + 2.35021i −0.0577533 + 0.100032i
\(553\) −0.338241 + 0.585851i −0.0143835 + 0.0249129i
\(554\) 8.58104 0.364573
\(555\) −0.188374 + 0.326273i −0.00799601 + 0.0138495i
\(556\) −4.34481 7.52544i −0.184261 0.319150i
\(557\) −4.78017 8.27949i −0.202542 0.350813i 0.746805 0.665043i \(-0.231587\pi\)
−0.949347 + 0.314230i \(0.898254\pi\)
\(558\) 9.00969 0.381411
\(559\) 0 0
\(560\) −0.104539 −0.00441760
\(561\) 9.09783 + 15.7579i 0.384111 + 0.665300i
\(562\) −4.03923 6.99615i −0.170385 0.295115i
\(563\) 22.5819 39.1129i 0.951712 1.64841i 0.209994 0.977703i \(-0.432656\pi\)
0.741719 0.670711i \(-0.234011\pi\)
\(564\) 7.20775 0.303501
\(565\) −14.9336 + 25.8658i −0.628262 + 1.08818i
\(566\) −8.70171 + 15.0718i −0.365760 + 0.633515i
\(567\) 0.0489173 0.00205434
\(568\) 4.35690 7.54637i 0.182811 0.316638i
\(569\) 1.60388 + 2.77799i 0.0672380 + 0.116460i 0.897685 0.440639i \(-0.145248\pi\)
−0.830447 + 0.557098i \(0.811915\pi\)
\(570\) 7.70171 + 13.3398i 0.322589 + 0.558741i
\(571\) 0.0241632 0.00101120 0.000505599 1.00000i \(-0.499839\pi\)
0.000505599 1.00000i \(0.499839\pi\)
\(572\) 0 0
\(573\) 5.65817 0.236373
\(574\) 0.210144 + 0.363980i 0.00877123 + 0.0151922i
\(575\) 0.587482 + 1.01755i 0.0244997 + 0.0424347i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −46.0200 −1.91584 −0.957918 0.287041i \(-0.907328\pi\)
−0.957918 + 0.287041i \(0.907328\pi\)
\(578\) −4.32371 + 7.48888i −0.179843 + 0.311496i
\(579\) 6.70171 11.6077i 0.278514 0.482400i
\(580\) −10.4969 −0.435862
\(581\) −0.272339 + 0.471705i −0.0112985 + 0.0195696i
\(582\) −1.23945 2.14678i −0.0513767 0.0889871i
\(583\) 29.4170 + 50.9517i 1.21833 + 2.11020i
\(584\) −14.9487 −0.618581
\(585\) 0 0
\(586\) 19.3709 0.800204
\(587\) 12.9693 + 22.4634i 0.535299 + 0.927165i 0.999149 + 0.0412510i \(0.0131343\pi\)
−0.463850 + 0.885914i \(0.653532\pi\)
\(588\) −3.49880 6.06011i −0.144288 0.249915i
\(589\) 32.4698 56.2393i 1.33789 2.31730i
\(590\) 9.12259 0.375571
\(591\) 9.99061 17.3042i 0.410959 0.711801i
\(592\) −0.0881460 + 0.152673i −0.00362278 + 0.00627484i
\(593\) −8.30691 −0.341124 −0.170562 0.985347i \(-0.554558\pi\)
−0.170562 + 0.985347i \(0.554558\pi\)
\(594\) 3.14795 5.45241i 0.129162 0.223715i
\(595\) −0.151064 0.261650i −0.00619302 0.0107266i
\(596\) −2.43416 4.21608i −0.0997069 0.172697i
\(597\) 6.24160 0.255452
\(598\) 0 0
\(599\) 37.1702 1.51873 0.759366 0.650664i \(-0.225509\pi\)
0.759366 + 0.650664i \(0.225509\pi\)
\(600\) 0.216480 + 0.374955i 0.00883776 + 0.0153075i
\(601\) 6.28501 + 10.8860i 0.256371 + 0.444048i 0.965267 0.261265i \(-0.0841398\pi\)
−0.708896 + 0.705313i \(0.750806\pi\)
\(602\) 0.164210 0.284421i 0.00669272 0.0115921i
\(603\) −5.38404 −0.219255
\(604\) 7.37316 12.7707i 0.300010 0.519632i
\(605\) 30.6010 53.0024i 1.24411 2.15485i
\(606\) 1.65279 0.0671401
\(607\) −4.02446 + 6.97057i −0.163348 + 0.282927i −0.936067 0.351821i \(-0.885563\pi\)
0.772720 + 0.634748i \(0.218896\pi\)
\(608\) 3.60388 + 6.24210i 0.146156 + 0.253150i
\(609\) 0.120137 + 0.208084i 0.00486821 + 0.00843199i
\(610\) 15.1943 0.615201
\(611\) 0 0
\(612\) −2.89008 −0.116825
\(613\) −15.2295 26.3783i −0.615115 1.06541i −0.990364 0.138486i \(-0.955776\pi\)
0.375250 0.926924i \(-0.377557\pi\)
\(614\) −6.21313 10.7615i −0.250741 0.434297i
\(615\) −9.18060 + 15.9013i −0.370198 + 0.641201i
\(616\) 0.307979 0.0124088
\(617\) −2.36658 + 4.09904i −0.0952751 + 0.165021i −0.909723 0.415215i \(-0.863706\pi\)
0.814448 + 0.580236i \(0.197040\pi\)
\(618\) 4.11745 7.13163i 0.165628 0.286876i
\(619\) −24.9095 −1.00120 −0.500598 0.865680i \(-0.666886\pi\)
−0.500598 + 0.865680i \(0.666886\pi\)
\(620\) −9.62714 + 16.6747i −0.386635 + 0.669672i
\(621\) 1.35690 + 2.35021i 0.0544504 + 0.0943108i
\(622\) 1.35690 + 2.35021i 0.0544066 + 0.0942349i
\(623\) −0.191831 −0.00768556
\(624\) 0 0
\(625\) −22.6477 −0.905910
\(626\) 7.69418 + 13.3267i 0.307521 + 0.532642i
\(627\) −22.6896 39.2996i −0.906136 1.56947i
\(628\) 8.35690 14.4746i 0.333476 0.577598i
\(629\) −0.509499 −0.0203150
\(630\) −0.0522697 + 0.0905338i −0.00208248 + 0.00360695i
\(631\) −12.2148 + 21.1566i −0.486262 + 0.842230i −0.999875 0.0157918i \(-0.994973\pi\)
0.513614 + 0.858022i \(0.328306\pi\)
\(632\) −13.8291 −0.550091
\(633\) −2.54288 + 4.40439i −0.101070 + 0.175059i
\(634\) 12.8264 + 22.2160i 0.509401 + 0.882309i
\(635\) −8.03654 13.9197i −0.318920 0.552386i
\(636\) −9.34481 −0.370546
\(637\) 0 0
\(638\) 30.9245 1.22431
\(639\) −4.35690 7.54637i −0.172356 0.298530i
\(640\) −1.06853 1.85075i −0.0422374 0.0731574i
\(641\) −24.3991 + 42.2605i −0.963707 + 1.66919i −0.250657 + 0.968076i \(0.580647\pi\)
−0.713050 + 0.701113i \(0.752687\pi\)
\(642\) −8.36658 −0.330203
\(643\) 14.1347 24.4820i 0.557417 0.965475i −0.440294 0.897854i \(-0.645126\pi\)
0.997711 0.0676209i \(-0.0215408\pi\)
\(644\) −0.0663757 + 0.114966i −0.00261557 + 0.00453030i
\(645\) 14.3478 0.564944
\(646\) −10.4155 + 18.0402i −0.409792 + 0.709781i
\(647\) −17.4480 30.2209i −0.685953 1.18810i −0.973136 0.230229i \(-0.926052\pi\)
0.287184 0.957876i \(-0.407281\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −26.8756 −1.05496
\(650\) 0 0
\(651\) 0.440730 0.0172736
\(652\) 2.77479 + 4.80608i 0.108669 + 0.188221i
\(653\) 5.85786 + 10.1461i 0.229236 + 0.397048i 0.957582 0.288162i \(-0.0930440\pi\)
−0.728346 + 0.685209i \(0.759711\pi\)
\(654\) −8.71379 + 15.0927i −0.340736 + 0.590172i
\(655\) −10.9524 −0.427946
\(656\) −4.29590 + 7.44071i −0.167727 + 0.290511i
\(657\) −7.47434 + 12.9459i −0.291602 + 0.505069i
\(658\) 0.352584 0.0137452
\(659\) 3.56734 6.17881i 0.138964 0.240692i −0.788141 0.615495i \(-0.788956\pi\)
0.927105 + 0.374803i \(0.122290\pi\)
\(660\) 6.72737 + 11.6521i 0.261862 + 0.453559i
\(661\) 4.26444 + 7.38622i 0.165867 + 0.287291i 0.936963 0.349429i \(-0.113624\pi\)
−0.771096 + 0.636719i \(0.780291\pi\)
\(662\) 3.82371 0.148613
\(663\) 0 0
\(664\) −11.1347 −0.432109
\(665\) 0.376747 + 0.652545i 0.0146096 + 0.0253046i
\(666\) 0.0881460 + 0.152673i 0.00341559 + 0.00591597i
\(667\) −6.66487 + 11.5439i −0.258065 + 0.446982i
\(668\) 3.92154 0.151729
\(669\) −10.2741 + 17.7953i −0.397221 + 0.688006i
\(670\) 5.75302 9.96452i 0.222259 0.384963i
\(671\) −44.7633 −1.72807
\(672\) −0.0244587 + 0.0423637i −0.000943514 + 0.00163421i
\(673\) 15.7969 + 27.3610i 0.608924 + 1.05469i 0.991418 + 0.130729i \(0.0417319\pi\)
−0.382494 + 0.923958i \(0.624935\pi\)
\(674\) 10.0652 + 17.4334i 0.387696 + 0.671510i
\(675\) 0.432960 0.0166646
\(676\) 0 0
\(677\) −17.3002 −0.664901 −0.332451 0.943121i \(-0.607875\pi\)
−0.332451 + 0.943121i \(0.607875\pi\)
\(678\) 6.98792 + 12.1034i 0.268369 + 0.464829i
\(679\) −0.0606304 0.105015i −0.00232678 0.00403011i
\(680\) 3.08815 5.34883i 0.118425 0.205118i
\(681\) −4.41119 −0.169037
\(682\) 28.3620 49.1245i 1.08604 1.88107i
\(683\) −15.1978 + 26.3234i −0.581529 + 1.00724i 0.413770 + 0.910382i \(0.364212\pi\)
−0.995298 + 0.0968556i \(0.969122\pi\)
\(684\) 7.20775 0.275595
\(685\) 4.27413 7.40300i 0.163306 0.282854i
\(686\) −0.342363 0.592990i −0.0130715 0.0226405i
\(687\) 0.115293 + 0.199693i 0.00439871 + 0.00761878i
\(688\) 6.71379 0.255961
\(689\) 0 0
\(690\) −5.79954 −0.220785
\(691\) −17.8659 30.9447i −0.679652 1.17719i −0.975086 0.221828i \(-0.928798\pi\)
0.295434 0.955363i \(-0.404536\pi\)
\(692\) 1.74214 + 3.01747i 0.0662260 + 0.114707i
\(693\) 0.153989 0.266717i 0.00584957 0.0101317i
\(694\) −2.93900 −0.111563
\(695\) 9.28514 16.0823i 0.352206 0.610038i
\(696\) −2.45593 + 4.25379i −0.0930917 + 0.161240i
\(697\) −24.8310 −0.940541
\(698\) 3.68664 6.38546i 0.139542 0.241693i
\(699\) −3.91185 6.77553i −0.147960 0.256274i
\(700\) 0.0105896 + 0.0183418i 0.000400250 + 0.000693254i
\(701\) 20.1328 0.760404 0.380202 0.924904i \(-0.375855\pi\)
0.380202 + 0.924904i \(0.375855\pi\)
\(702\) 0 0
\(703\) 1.27067 0.0479242
\(704\) 3.14795 + 5.45241i 0.118643 + 0.205495i
\(705\) 7.70171 + 13.3398i 0.290063 + 0.502404i
\(706\) −1.00538 + 1.74136i −0.0378379 + 0.0655371i
\(707\) 0.0808502 0.00304069
\(708\) 2.13437 3.69685i 0.0802147 0.138936i
\(709\) −8.30798 + 14.3898i −0.312013 + 0.540422i −0.978798 0.204828i \(-0.934336\pi\)
0.666785 + 0.745250i \(0.267670\pi\)
\(710\) 18.6219 0.698868
\(711\) −6.91454 + 11.9763i −0.259316 + 0.449148i
\(712\) −1.96077 3.39616i −0.0734830 0.127276i
\(713\) 12.2252 + 21.1747i 0.457838 + 0.792998i
\(714\) −0.141375 −0.00529083
\(715\) 0 0
\(716\) 3.58881 0.134120
\(717\) 5.57673 + 9.65918i 0.208267 + 0.360729i
\(718\) 15.7289 + 27.2432i 0.586996 + 1.01671i
\(719\) −1.02416 + 1.77390i −0.0381948 + 0.0661554i −0.884491 0.466557i \(-0.845494\pi\)
0.846296 + 0.532713i \(0.178827\pi\)
\(720\) −2.13706 −0.0796436
\(721\) 0.201415 0.348860i 0.00750107 0.0129922i
\(722\) 16.4758 28.5370i 0.613167 1.06204i
\(723\) 3.54527 0.131850
\(724\) −2.75302 + 4.76837i −0.102315 + 0.177215i
\(725\) 1.06332 + 1.84172i 0.0394907 + 0.0683998i
\(726\) −14.3192 24.8015i −0.531434 0.920470i
\(727\) 29.9377 1.11033 0.555163 0.831741i \(-0.312656\pi\)
0.555163 + 0.831741i \(0.312656\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −15.9731 27.6663i −0.591193 1.02398i
\(731\) 9.70171 + 16.8039i 0.358831 + 0.621513i
\(732\) 3.55496 6.15737i 0.131395 0.227583i
\(733\) −1.46250 −0.0540187 −0.0270093 0.999635i \(-0.508598\pi\)
−0.0270093 + 0.999635i \(0.508598\pi\)
\(734\) −2.24967 + 3.89654i −0.0830368 + 0.143824i
\(735\) 7.47716 12.9508i 0.275799 0.477699i
\(736\) −2.71379 −0.100032
\(737\) −16.9487 + 29.3560i −0.624313 + 1.08134i
\(738\) 4.29590 + 7.44071i 0.158134 + 0.273896i
\(739\) −20.1933 34.9758i −0.742822 1.28660i −0.951206 0.308558i \(-0.900154\pi\)
0.208384 0.978047i \(-0.433180\pi\)
\(740\) −0.376747 −0.0138495
\(741\) 0 0
\(742\) −0.457123 −0.0167815
\(743\) 4.88769 + 8.46573i 0.179312 + 0.310577i 0.941645 0.336607i \(-0.109280\pi\)
−0.762333 + 0.647185i \(0.775946\pi\)
\(744\) 4.50484 + 7.80262i 0.165156 + 0.286058i
\(745\) 5.20195 9.01004i 0.190585 0.330102i
\(746\) −37.8297 −1.38504
\(747\) −5.56734 + 9.64291i −0.203698 + 0.352816i
\(748\) −9.09783 + 15.7579i −0.332650 + 0.576166i
\(749\) −0.409271 −0.0149544
\(750\) −5.80529 + 10.0551i −0.211979 + 0.367159i
\(751\) −17.2729 29.9176i −0.630298 1.09171i −0.987491 0.157678i \(-0.949599\pi\)
0.357192 0.934031i \(-0.383734\pi\)
\(752\) 3.60388 + 6.24210i 0.131420 + 0.227626i
\(753\) 4.17092 0.151997
\(754\) 0 0
\(755\) 31.5138 1.14690
\(756\) 0.0244587 + 0.0423637i 0.000889553 + 0.00154075i
\(757\) 2.57242 + 4.45556i 0.0934961 + 0.161940i 0.908980 0.416840i \(-0.136862\pi\)
−0.815484 + 0.578780i \(0.803529\pi\)
\(758\) −4.21983 + 7.30896i −0.153271 + 0.265474i
\(759\) 17.0858 0.620174
\(760\) −7.70171 + 13.3398i −0.279370 + 0.483884i
\(761\) 9.75600 16.8979i 0.353655 0.612548i −0.633232 0.773962i \(-0.718272\pi\)
0.986887 + 0.161414i \(0.0516054\pi\)
\(762\) −7.52111 −0.272461
\(763\) −0.426256 + 0.738296i −0.0154315 + 0.0267281i
\(764\) 2.82908 + 4.90012i 0.102353 + 0.177280i
\(765\) −3.08815 5.34883i −0.111652 0.193387i
\(766\) −1.28621 −0.0464726
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −2.87800 4.98485i −0.103783 0.179758i 0.809457 0.587179i \(-0.199762\pi\)
−0.913241 + 0.407421i \(0.866428\pi\)
\(770\) 0.329085 + 0.569992i 0.0118594 + 0.0205411i
\(771\) −5.44504 + 9.43109i −0.196098 + 0.339652i
\(772\) 13.4034 0.482400
\(773\) 2.06369 3.57441i 0.0742257 0.128563i −0.826524 0.562902i \(-0.809685\pi\)
0.900749 + 0.434339i \(0.143018\pi\)
\(774\) 3.35690 5.81431i 0.120661 0.208991i
\(775\) 3.90084 0.140122
\(776\) 1.23945 2.14678i 0.0444935 0.0770651i
\(777\) 0.00431187 + 0.00746837i 0.000154687 + 0.000267926i
\(778\) 11.6962 + 20.2584i 0.419329 + 0.726299i
\(779\) 61.9275