Properties

Label 1014.2.e.k.991.1
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.900969 + 1.56052i\) of defining polynomial
Character \(\chi\) \(=\) 1014.991
Dual form 1014.2.e.k.529.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -4.04892 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.346011 - 0.599308i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -4.04892 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.346011 - 0.599308i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.02446 + 3.50647i) q^{10} +(-2.42543 - 4.20096i) q^{11} +1.00000 q^{12} -0.692021 q^{14} +(2.02446 + 3.50647i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.69202 + 6.39477i) q^{17} +1.00000 q^{18} +(-0.890084 + 1.54167i) q^{19} +(2.02446 - 3.50647i) q^{20} -0.692021 q^{21} +(-2.42543 + 4.20096i) q^{22} +(-2.55496 - 4.42532i) q^{23} +(-0.500000 - 0.866025i) q^{24} +11.3937 q^{25} +1.00000 q^{27} +(0.346011 + 0.599308i) q^{28} +(1.67241 + 2.89669i) q^{29} +(2.02446 - 3.50647i) q^{30} -0.972853 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.42543 + 4.20096i) q^{33} +7.38404 q^{34} +(-1.40097 + 2.42655i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.643104 + 1.11389i) q^{37} +1.78017 q^{38} -4.04892 q^{40} +(0.753020 + 1.30427i) q^{41} +(0.346011 + 0.599308i) q^{42} +(4.15883 - 7.20331i) q^{43} +4.85086 q^{44} +(2.02446 - 3.50647i) q^{45} +(-2.55496 + 4.42532i) q^{46} +7.20775 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.26055 + 5.64744i) q^{49} +(-5.69687 - 9.86726i) q^{50} +7.38404 q^{51} +13.4765 q^{53} +(-0.500000 - 0.866025i) q^{54} +(9.82036 + 17.0094i) q^{55} +(0.346011 - 0.599308i) q^{56} +1.78017 q^{57} +(1.67241 - 2.89669i) q^{58} +(0.653989 - 1.13274i) q^{59} -4.04892 q^{60} +(0.198062 - 0.343054i) q^{61} +(0.486426 + 0.842515i) q^{62} +(0.346011 + 0.599308i) q^{63} +1.00000 q^{64} +4.85086 q^{66} +(3.02715 + 5.24317i) q^{67} +(-3.69202 - 6.39477i) q^{68} +(-2.55496 + 4.42532i) q^{69} +2.80194 q^{70} +(-0.664874 + 1.15160i) q^{71} +(-0.500000 + 0.866025i) q^{72} +7.65279 q^{73} +(0.643104 - 1.11389i) q^{74} +(-5.69687 - 9.86726i) q^{75} +(-0.890084 - 1.54167i) q^{76} -3.35690 q^{77} -8.33944 q^{79} +(2.02446 + 3.50647i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.753020 - 1.30427i) q^{82} -15.3274 q^{83} +(0.346011 - 0.599308i) q^{84} +(14.9487 - 25.8919i) q^{85} -8.31767 q^{86} +(1.67241 - 2.89669i) q^{87} +(-2.42543 - 4.20096i) q^{88} +(1.55496 + 2.69327i) q^{89} -4.04892 q^{90} +5.10992 q^{92} +(0.486426 + 0.842515i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(3.60388 - 6.24210i) q^{95} +1.00000 q^{96} +(-4.27144 + 7.39835i) q^{97} +(3.26055 - 5.64744i) q^{98} +4.85086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} - q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} - 3 q^{16} - 12 q^{17} + 6 q^{18} - 4 q^{19} + 3 q^{20} + 6 q^{21} - q^{22} - 16 q^{23} - 3 q^{24} + 4 q^{25} + 6 q^{27} - 3 q^{28} - 13 q^{29} + 3 q^{30} - 18 q^{31} - 3 q^{32} - q^{33} + 24 q^{34} - 4 q^{35} - 3 q^{36} + 12 q^{37} + 8 q^{38} - 6 q^{40} + 14 q^{41} - 3 q^{42} + 8 q^{43} + 2 q^{44} + 3 q^{45} - 16 q^{46} + 8 q^{47} - 3 q^{48} + 4 q^{49} - 2 q^{50} + 24 q^{51} + 30 q^{53} - 3 q^{54} + 22 q^{55} - 3 q^{56} + 8 q^{57} - 13 q^{58} + 9 q^{59} - 6 q^{60} + 10 q^{61} + 9 q^{62} - 3 q^{63} + 6 q^{64} + 2 q^{66} + 6 q^{67} - 12 q^{68} - 16 q^{69} + 8 q^{70} - 6 q^{71} - 3 q^{72} + 10 q^{73} + 12 q^{74} - 2 q^{75} - 4 q^{76} - 12 q^{77} - 10 q^{79} + 3 q^{80} - 3 q^{81} + 14 q^{82} - 14 q^{83} - 3 q^{84} + 26 q^{85} - 16 q^{86} - 13 q^{87} - q^{88} + 10 q^{89} - 6 q^{90} + 32 q^{92} + 9 q^{93} - 4 q^{94} + 4 q^{95} + 6 q^{96} - 7 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −4.04892 −1.81073 −0.905365 0.424633i \(-0.860403\pi\)
−0.905365 + 0.424633i \(0.860403\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 0.346011 0.599308i 0.130780 0.226517i −0.793198 0.608964i \(-0.791585\pi\)
0.923977 + 0.382447i \(0.124919\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 2.02446 + 3.50647i 0.640190 + 1.10884i
\(11\) −2.42543 4.20096i −0.731294 1.26664i −0.956330 0.292288i \(-0.905583\pi\)
0.225036 0.974350i \(-0.427750\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) −0.692021 −0.184951
\(15\) 2.02446 + 3.50647i 0.522713 + 0.905365i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.69202 + 6.39477i −0.895447 + 1.55096i −0.0621960 + 0.998064i \(0.519810\pi\)
−0.833251 + 0.552895i \(0.813523\pi\)
\(18\) 1.00000 0.235702
\(19\) −0.890084 + 1.54167i −0.204199 + 0.353683i −0.949877 0.312623i \(-0.898792\pi\)
0.745678 + 0.666306i \(0.232126\pi\)
\(20\) 2.02446 3.50647i 0.452683 0.784069i
\(21\) −0.692021 −0.151011
\(22\) −2.42543 + 4.20096i −0.517103 + 0.895648i
\(23\) −2.55496 4.42532i −0.532746 0.922742i −0.999269 0.0382335i \(-0.987827\pi\)
0.466523 0.884509i \(-0.345506\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 11.3937 2.27875
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0.346011 + 0.599308i 0.0653899 + 0.113259i
\(29\) 1.67241 + 2.89669i 0.310558 + 0.537903i 0.978483 0.206326i \(-0.0661507\pi\)
−0.667925 + 0.744228i \(0.732817\pi\)
\(30\) 2.02446 3.50647i 0.369614 0.640190i
\(31\) −0.972853 −0.174730 −0.0873648 0.996176i \(-0.527845\pi\)
−0.0873648 + 0.996176i \(0.527845\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.42543 + 4.20096i −0.422213 + 0.731294i
\(34\) 7.38404 1.26635
\(35\) −1.40097 + 2.42655i −0.236807 + 0.410162i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 0.643104 + 1.11389i 0.105726 + 0.183122i 0.914034 0.405637i \(-0.132950\pi\)
−0.808309 + 0.588759i \(0.799617\pi\)
\(38\) 1.78017 0.288781
\(39\) 0 0
\(40\) −4.04892 −0.640190
\(41\) 0.753020 + 1.30427i 0.117602 + 0.203693i 0.918817 0.394684i \(-0.129146\pi\)
−0.801215 + 0.598377i \(0.795813\pi\)
\(42\) 0.346011 + 0.599308i 0.0533906 + 0.0924753i
\(43\) 4.15883 7.20331i 0.634216 1.09849i −0.352464 0.935825i \(-0.614656\pi\)
0.986681 0.162669i \(-0.0520104\pi\)
\(44\) 4.85086 0.731294
\(45\) 2.02446 3.50647i 0.301788 0.522713i
\(46\) −2.55496 + 4.42532i −0.376708 + 0.652477i
\(47\) 7.20775 1.05136 0.525679 0.850683i \(-0.323811\pi\)
0.525679 + 0.850683i \(0.323811\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 3.26055 + 5.64744i 0.465793 + 0.806778i
\(50\) −5.69687 9.86726i −0.805658 1.39544i
\(51\) 7.38404 1.03397
\(52\) 0 0
\(53\) 13.4765 1.85114 0.925570 0.378577i \(-0.123586\pi\)
0.925570 + 0.378577i \(0.123586\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 9.82036 + 17.0094i 1.32418 + 2.29354i
\(56\) 0.346011 0.599308i 0.0462376 0.0800859i
\(57\) 1.78017 0.235789
\(58\) 1.67241 2.89669i 0.219598 0.380355i
\(59\) 0.653989 1.13274i 0.0851422 0.147471i −0.820310 0.571920i \(-0.806199\pi\)
0.905452 + 0.424449i \(0.139532\pi\)
\(60\) −4.04892 −0.522713
\(61\) 0.198062 0.343054i 0.0253593 0.0439236i −0.853067 0.521801i \(-0.825260\pi\)
0.878427 + 0.477877i \(0.158594\pi\)
\(62\) 0.486426 + 0.842515i 0.0617762 + 0.107000i
\(63\) 0.346011 + 0.599308i 0.0435933 + 0.0755057i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.85086 0.597099
\(67\) 3.02715 + 5.24317i 0.369825 + 0.640555i 0.989538 0.144273i \(-0.0460843\pi\)
−0.619713 + 0.784828i \(0.712751\pi\)
\(68\) −3.69202 6.39477i −0.447723 0.775480i
\(69\) −2.55496 + 4.42532i −0.307581 + 0.532746i
\(70\) 2.80194 0.334896
\(71\) −0.664874 + 1.15160i −0.0789061 + 0.136669i −0.902778 0.430106i \(-0.858476\pi\)
0.823872 + 0.566776i \(0.191809\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 7.65279 0.895692 0.447846 0.894111i \(-0.352191\pi\)
0.447846 + 0.894111i \(0.352191\pi\)
\(74\) 0.643104 1.11389i 0.0747593 0.129487i
\(75\) −5.69687 9.86726i −0.657817 1.13937i
\(76\) −0.890084 1.54167i −0.102100 0.176842i
\(77\) −3.35690 −0.382554
\(78\) 0 0
\(79\) −8.33944 −0.938260 −0.469130 0.883129i \(-0.655432\pi\)
−0.469130 + 0.883129i \(0.655432\pi\)
\(80\) 2.02446 + 3.50647i 0.226341 + 0.392035i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0.753020 1.30427i 0.0831572 0.144032i
\(83\) −15.3274 −1.68240 −0.841198 0.540727i \(-0.818149\pi\)
−0.841198 + 0.540727i \(0.818149\pi\)
\(84\) 0.346011 0.599308i 0.0377529 0.0653899i
\(85\) 14.9487 25.8919i 1.62141 2.80837i
\(86\) −8.31767 −0.896917
\(87\) 1.67241 2.89669i 0.179301 0.310558i
\(88\) −2.42543 4.20096i −0.258551 0.447824i
\(89\) 1.55496 + 2.69327i 0.164825 + 0.285486i 0.936593 0.350419i \(-0.113961\pi\)
−0.771768 + 0.635904i \(0.780627\pi\)
\(90\) −4.04892 −0.426793
\(91\) 0 0
\(92\) 5.10992 0.532746
\(93\) 0.486426 + 0.842515i 0.0504401 + 0.0873648i
\(94\) −3.60388 6.24210i −0.371711 0.643823i
\(95\) 3.60388 6.24210i 0.369750 0.640425i
\(96\) 1.00000 0.102062
\(97\) −4.27144 + 7.39835i −0.433699 + 0.751188i −0.997188 0.0749347i \(-0.976125\pi\)
0.563490 + 0.826123i \(0.309458\pi\)
\(98\) 3.26055 5.64744i 0.329366 0.570478i
\(99\) 4.85086 0.487529
\(100\) −5.69687 + 9.86726i −0.569687 + 0.986726i
\(101\) 5.99880 + 10.3902i 0.596903 + 1.03387i 0.993275 + 0.115777i \(0.0369357\pi\)
−0.396372 + 0.918090i \(0.629731\pi\)
\(102\) −3.69202 6.39477i −0.365565 0.633176i
\(103\) −12.3230 −1.21423 −0.607113 0.794616i \(-0.707672\pi\)
−0.607113 + 0.794616i \(0.707672\pi\)
\(104\) 0 0
\(105\) 2.80194 0.273441
\(106\) −6.73825 11.6710i −0.654477 1.13359i
\(107\) −2.94989 5.10935i −0.285176 0.493940i 0.687476 0.726207i \(-0.258719\pi\)
−0.972652 + 0.232268i \(0.925385\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −0.792249 −0.0758837 −0.0379418 0.999280i \(-0.512080\pi\)
−0.0379418 + 0.999280i \(0.512080\pi\)
\(110\) 9.82036 17.0094i 0.936334 1.62178i
\(111\) 0.643104 1.11389i 0.0610407 0.105726i
\(112\) −0.692021 −0.0653899
\(113\) −3.10992 + 5.38653i −0.292556 + 0.506722i −0.974413 0.224763i \(-0.927839\pi\)
0.681857 + 0.731485i \(0.261173\pi\)
\(114\) −0.890084 1.54167i −0.0833640 0.144391i
\(115\) 10.3448 + 17.9177i 0.964659 + 1.67084i
\(116\) −3.34481 −0.310558
\(117\) 0 0
\(118\) −1.30798 −0.120409
\(119\) 2.55496 + 4.42532i 0.234213 + 0.405668i
\(120\) 2.02446 + 3.50647i 0.184807 + 0.320095i
\(121\) −6.26540 + 10.8520i −0.569582 + 0.986544i
\(122\) −0.396125 −0.0358634
\(123\) 0.753020 1.30427i 0.0678976 0.117602i
\(124\) 0.486426 0.842515i 0.0436824 0.0756601i
\(125\) −25.8877 −2.31547
\(126\) 0.346011 0.599308i 0.0308251 0.0533906i
\(127\) 3.00269 + 5.20081i 0.266446 + 0.461497i 0.967941 0.251176i \(-0.0808174\pi\)
−0.701496 + 0.712674i \(0.747484\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −8.31767 −0.732330
\(130\) 0 0
\(131\) 8.81700 0.770345 0.385173 0.922845i \(-0.374142\pi\)
0.385173 + 0.922845i \(0.374142\pi\)
\(132\) −2.42543 4.20096i −0.211106 0.365647i
\(133\) 0.615957 + 1.06687i 0.0534103 + 0.0925093i
\(134\) 3.02715 5.24317i 0.261506 0.452941i
\(135\) −4.04892 −0.348475
\(136\) −3.69202 + 6.39477i −0.316588 + 0.548347i
\(137\) −7.87800 + 13.6451i −0.673063 + 1.16578i 0.303968 + 0.952682i \(0.401688\pi\)
−0.977031 + 0.213097i \(0.931645\pi\)
\(138\) 5.10992 0.434985
\(139\) 3.04892 5.28088i 0.258606 0.447918i −0.707263 0.706951i \(-0.750070\pi\)
0.965869 + 0.259032i \(0.0834036\pi\)
\(140\) −1.40097 2.42655i −0.118403 0.205081i
\(141\) −3.60388 6.24210i −0.303501 0.525679i
\(142\) 1.32975 0.111590
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −6.77144 11.7285i −0.562337 0.973997i
\(146\) −3.82640 6.62751i −0.316675 0.548497i
\(147\) 3.26055 5.64744i 0.268926 0.465793i
\(148\) −1.28621 −0.105726
\(149\) −1.27628 + 2.21059i −0.104557 + 0.181098i −0.913557 0.406710i \(-0.866676\pi\)
0.809000 + 0.587809i \(0.200009\pi\)
\(150\) −5.69687 + 9.86726i −0.465147 + 0.805658i
\(151\) 17.7168 1.44177 0.720885 0.693054i \(-0.243735\pi\)
0.720885 + 0.693054i \(0.243735\pi\)
\(152\) −0.890084 + 1.54167i −0.0721953 + 0.125046i
\(153\) −3.69202 6.39477i −0.298482 0.516986i
\(154\) 1.67845 + 2.90716i 0.135253 + 0.234265i
\(155\) 3.93900 0.316388
\(156\) 0 0
\(157\) −6.31767 −0.504205 −0.252102 0.967701i \(-0.581122\pi\)
−0.252102 + 0.967701i \(0.581122\pi\)
\(158\) 4.16972 + 7.22216i 0.331725 + 0.574565i
\(159\) −6.73825 11.6710i −0.534378 0.925570i
\(160\) 2.02446 3.50647i 0.160048 0.277210i
\(161\) −3.53617 −0.278689
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −7.29590 + 12.6369i −0.571459 + 0.989796i 0.424958 + 0.905213i \(0.360289\pi\)
−0.996416 + 0.0845824i \(0.973044\pi\)
\(164\) −1.50604 −0.117602
\(165\) 9.82036 17.0094i 0.764514 1.32418i
\(166\) 7.66368 + 13.2739i 0.594817 + 1.03025i
\(167\) 9.75063 + 16.8886i 0.754526 + 1.30688i 0.945610 + 0.325304i \(0.105467\pi\)
−0.191083 + 0.981574i \(0.561200\pi\)
\(168\) −0.692021 −0.0533906
\(169\) 0 0
\(170\) −29.8974 −2.29302
\(171\) −0.890084 1.54167i −0.0680664 0.117894i
\(172\) 4.15883 + 7.20331i 0.317108 + 0.549247i
\(173\) 4.64526 8.04583i 0.353173 0.611713i −0.633631 0.773636i \(-0.718436\pi\)
0.986803 + 0.161923i \(0.0517695\pi\)
\(174\) −3.34481 −0.253570
\(175\) 3.94235 6.82836i 0.298014 0.516175i
\(176\) −2.42543 + 4.20096i −0.182823 + 0.316660i
\(177\) −1.30798 −0.0983137
\(178\) 1.55496 2.69327i 0.116549 0.201869i
\(179\) −11.3964 19.7392i −0.851808 1.47538i −0.879575 0.475761i \(-0.842173\pi\)
0.0277662 0.999614i \(-0.491161\pi\)
\(180\) 2.02446 + 3.50647i 0.150894 + 0.261356i
\(181\) 0.537500 0.0399520 0.0199760 0.999800i \(-0.493641\pi\)
0.0199760 + 0.999800i \(0.493641\pi\)
\(182\) 0 0
\(183\) −0.396125 −0.0292824
\(184\) −2.55496 4.42532i −0.188354 0.326239i
\(185\) −2.60388 4.51004i −0.191441 0.331585i
\(186\) 0.486426 0.842515i 0.0356665 0.0617762i
\(187\) 35.8189 2.61934
\(188\) −3.60388 + 6.24210i −0.262840 + 0.455252i
\(189\) 0.346011 0.599308i 0.0251686 0.0435933i
\(190\) −7.20775 −0.522905
\(191\) 4.89977 8.48665i 0.354535 0.614073i −0.632503 0.774558i \(-0.717972\pi\)
0.987038 + 0.160485i \(0.0513058\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 7.09783 + 12.2938i 0.510913 + 0.884928i 0.999920 + 0.0126478i \(0.00402603\pi\)
−0.489007 + 0.872280i \(0.662641\pi\)
\(194\) 8.54288 0.613343
\(195\) 0 0
\(196\) −6.52111 −0.465793
\(197\) 1.50484 + 2.60647i 0.107216 + 0.185703i 0.914641 0.404266i \(-0.132473\pi\)
−0.807426 + 0.589969i \(0.799140\pi\)
\(198\) −2.42543 4.20096i −0.172368 0.298549i
\(199\) −6.44720 + 11.1669i −0.457030 + 0.791599i −0.998802 0.0489263i \(-0.984420\pi\)
0.541773 + 0.840525i \(0.317753\pi\)
\(200\) 11.3937 0.805658
\(201\) 3.02715 5.24317i 0.213518 0.369825i
\(202\) 5.99880 10.3902i 0.422074 0.731054i
\(203\) 2.31468 0.162459
\(204\) −3.69202 + 6.39477i −0.258493 + 0.447723i
\(205\) −3.04892 5.28088i −0.212946 0.368833i
\(206\) 6.16152 + 10.6721i 0.429294 + 0.743558i
\(207\) 5.10992 0.355164
\(208\) 0 0
\(209\) 8.63533 0.597319
\(210\) −1.40097 2.42655i −0.0966760 0.167448i
\(211\) −3.89977 6.75460i −0.268471 0.465006i 0.699996 0.714147i \(-0.253185\pi\)
−0.968467 + 0.249141i \(0.919852\pi\)
\(212\) −6.73825 + 11.6710i −0.462785 + 0.801567i
\(213\) 1.32975 0.0911129
\(214\) −2.94989 + 5.10935i −0.201650 + 0.349268i
\(215\) −16.8388 + 29.1656i −1.14839 + 1.98908i
\(216\) 1.00000 0.0680414
\(217\) −0.336618 + 0.583039i −0.0228511 + 0.0395792i
\(218\) 0.396125 + 0.686108i 0.0268289 + 0.0464691i
\(219\) −3.82640 6.62751i −0.258564 0.447846i
\(220\) −19.6407 −1.32418
\(221\) 0 0
\(222\) −1.28621 −0.0863246
\(223\) 6.09783 + 10.5618i 0.408341 + 0.707268i 0.994704 0.102781i \(-0.0327740\pi\)
−0.586363 + 0.810049i \(0.699441\pi\)
\(224\) 0.346011 + 0.599308i 0.0231188 + 0.0400430i
\(225\) −5.69687 + 9.86726i −0.379791 + 0.657817i
\(226\) 6.21983 0.413737
\(227\) −3.37167 + 5.83990i −0.223785 + 0.387608i −0.955954 0.293515i \(-0.905175\pi\)
0.732169 + 0.681123i \(0.238508\pi\)
\(228\) −0.890084 + 1.54167i −0.0589472 + 0.102100i
\(229\) −19.8237 −1.30999 −0.654994 0.755634i \(-0.727329\pi\)
−0.654994 + 0.755634i \(0.727329\pi\)
\(230\) 10.3448 17.9177i 0.682117 1.18146i
\(231\) 1.67845 + 2.90716i 0.110434 + 0.191277i
\(232\) 1.67241 + 2.89669i 0.109799 + 0.190177i
\(233\) −30.0301 −1.96734 −0.983670 0.179983i \(-0.942396\pi\)
−0.983670 + 0.179983i \(0.942396\pi\)
\(234\) 0 0
\(235\) −29.1836 −1.90373
\(236\) 0.653989 + 1.13274i 0.0425711 + 0.0737353i
\(237\) 4.16972 + 7.22216i 0.270852 + 0.469130i
\(238\) 2.55496 4.42532i 0.165613 0.286851i
\(239\) 22.0978 1.42939 0.714695 0.699436i \(-0.246565\pi\)
0.714695 + 0.699436i \(0.246565\pi\)
\(240\) 2.02446 3.50647i 0.130678 0.226341i
\(241\) −5.06369 + 8.77056i −0.326181 + 0.564962i −0.981751 0.190173i \(-0.939095\pi\)
0.655570 + 0.755135i \(0.272428\pi\)
\(242\) 12.5308 0.805510
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0.198062 + 0.343054i 0.0126796 + 0.0219618i
\(245\) −13.2017 22.8660i −0.843426 1.46086i
\(246\) −1.50604 −0.0960217
\(247\) 0 0
\(248\) −0.972853 −0.0617762
\(249\) 7.66368 + 13.2739i 0.485666 + 0.841198i
\(250\) 12.9438 + 22.4194i 0.818641 + 1.41793i
\(251\) −2.77359 + 4.80401i −0.175068 + 0.303226i −0.940185 0.340665i \(-0.889348\pi\)
0.765117 + 0.643891i \(0.222681\pi\)
\(252\) −0.692021 −0.0435933
\(253\) −12.3937 + 21.4666i −0.779187 + 1.34959i
\(254\) 3.00269 5.20081i 0.188405 0.326328i
\(255\) −29.8974 −1.87225
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.89977 + 11.9508i 0.430396 + 0.745468i 0.996907 0.0785862i \(-0.0250406\pi\)
−0.566511 + 0.824054i \(0.691707\pi\)
\(258\) 4.15883 + 7.20331i 0.258918 + 0.448459i
\(259\) 0.890084 0.0553071
\(260\) 0 0
\(261\) −3.34481 −0.207039
\(262\) −4.40850 7.63575i −0.272358 0.471738i
\(263\) 11.2349 + 19.4594i 0.692773 + 1.19992i 0.970926 + 0.239382i \(0.0769448\pi\)
−0.278152 + 0.960537i \(0.589722\pi\)
\(264\) −2.42543 + 4.20096i −0.149275 + 0.258551i
\(265\) −54.5652 −3.35192
\(266\) 0.615957 1.06687i 0.0377668 0.0654139i
\(267\) 1.55496 2.69327i 0.0951619 0.164825i
\(268\) −6.05429 −0.369825
\(269\) 13.0070 22.5288i 0.793051 1.37360i −0.131019 0.991380i \(-0.541825\pi\)
0.924070 0.382224i \(-0.124842\pi\)
\(270\) 2.02446 + 3.50647i 0.123205 + 0.213397i
\(271\) −1.44235 2.49823i −0.0876167 0.151757i 0.818887 0.573955i \(-0.194592\pi\)
−0.906503 + 0.422199i \(0.861258\pi\)
\(272\) 7.38404 0.447723
\(273\) 0 0
\(274\) 15.7560 0.951855
\(275\) −27.6347 47.8647i −1.66643 2.88635i
\(276\) −2.55496 4.42532i −0.153790 0.266373i
\(277\) 0.731250 1.26656i 0.0439366 0.0761004i −0.843221 0.537567i \(-0.819343\pi\)
0.887157 + 0.461467i \(0.152677\pi\)
\(278\) −6.09783 −0.365724
\(279\) 0.486426 0.842515i 0.0291216 0.0504401i
\(280\) −1.40097 + 2.42655i −0.0837239 + 0.145014i
\(281\) 5.68233 0.338980 0.169490 0.985532i \(-0.445788\pi\)
0.169490 + 0.985532i \(0.445788\pi\)
\(282\) −3.60388 + 6.24210i −0.214608 + 0.371711i
\(283\) 12.6039 + 21.8306i 0.749223 + 1.29769i 0.948196 + 0.317687i \(0.102906\pi\)
−0.198973 + 0.980005i \(0.563761\pi\)
\(284\) −0.664874 1.15160i −0.0394530 0.0683347i
\(285\) −7.20775 −0.426950
\(286\) 0 0
\(287\) 1.04221 0.0615199
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −18.7620 32.4968i −1.10365 1.91158i
\(290\) −6.77144 + 11.7285i −0.397633 + 0.688720i
\(291\) 8.54288 0.500792
\(292\) −3.82640 + 6.62751i −0.223923 + 0.387846i
\(293\) 3.57457 6.19134i 0.208829 0.361702i −0.742517 0.669827i \(-0.766368\pi\)
0.951346 + 0.308125i \(0.0997015\pi\)
\(294\) −6.52111 −0.380319
\(295\) −2.64795 + 4.58638i −0.154170 + 0.267029i
\(296\) 0.643104 + 1.11389i 0.0373797 + 0.0647435i
\(297\) −2.42543 4.20096i −0.140738 0.243765i
\(298\) 2.55257 0.147866
\(299\) 0 0
\(300\) 11.3937 0.657817
\(301\) −2.87800 4.98485i −0.165885 0.287322i
\(302\) −8.85839 15.3432i −0.509743 0.882901i
\(303\) 5.99880 10.3902i 0.344622 0.596903i
\(304\) 1.78017 0.102100
\(305\) −0.801938 + 1.38900i −0.0459188 + 0.0795337i
\(306\) −3.69202 + 6.39477i −0.211059 + 0.365565i
\(307\) −17.9952 −1.02704 −0.513521 0.858077i \(-0.671659\pi\)
−0.513521 + 0.858077i \(0.671659\pi\)
\(308\) 1.67845 2.90716i 0.0956384 0.165651i
\(309\) 6.16152 + 10.6721i 0.350517 + 0.607113i
\(310\) −1.96950 3.41127i −0.111860 0.193747i
\(311\) 3.32975 0.188813 0.0944064 0.995534i \(-0.469905\pi\)
0.0944064 + 0.995534i \(0.469905\pi\)
\(312\) 0 0
\(313\) −17.8834 −1.01083 −0.505414 0.862877i \(-0.668660\pi\)
−0.505414 + 0.862877i \(0.668660\pi\)
\(314\) 3.15883 + 5.47126i 0.178263 + 0.308761i
\(315\) −1.40097 2.42655i −0.0789357 0.136721i
\(316\) 4.16972 7.22216i 0.234565 0.406279i
\(317\) 4.39373 0.246777 0.123388 0.992358i \(-0.460624\pi\)
0.123388 + 0.992358i \(0.460624\pi\)
\(318\) −6.73825 + 11.6710i −0.377862 + 0.654477i
\(319\) 8.11260 14.0514i 0.454219 0.786730i
\(320\) −4.04892 −0.226341
\(321\) −2.94989 + 5.10935i −0.164647 + 0.285176i
\(322\) 1.76809 + 3.06241i 0.0985316 + 0.170662i
\(323\) −6.57242 11.3838i −0.365699 0.633409i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 14.5918 0.808165
\(327\) 0.396125 + 0.686108i 0.0219057 + 0.0379418i
\(328\) 0.753020 + 1.30427i 0.0415786 + 0.0720162i
\(329\) 2.49396 4.31966i 0.137496 0.238151i
\(330\) −19.6407 −1.08119
\(331\) 12.8388 22.2374i 0.705683 1.22228i −0.260762 0.965403i \(-0.583974\pi\)
0.966445 0.256875i \(-0.0826930\pi\)
\(332\) 7.66368 13.2739i 0.420599 0.728499i
\(333\) −1.28621 −0.0704838
\(334\) 9.75063 16.8886i 0.533531 0.924102i
\(335\) −12.2567 21.2292i −0.669653 1.15987i
\(336\) 0.346011 + 0.599308i 0.0188764 + 0.0326949i
\(337\) −24.6504 −1.34279 −0.671396 0.741098i \(-0.734305\pi\)
−0.671396 + 0.741098i \(0.734305\pi\)
\(338\) 0 0
\(339\) 6.21983 0.337815
\(340\) 14.9487 + 25.8919i 0.810707 + 1.40418i
\(341\) 2.35958 + 4.08692i 0.127779 + 0.221319i
\(342\) −0.890084 + 1.54167i −0.0481302 + 0.0833640i
\(343\) 9.35690 0.505225
\(344\) 4.15883 7.20331i 0.224229 0.388377i
\(345\) 10.3448 17.9177i 0.556946 0.964659i
\(346\) −9.29052 −0.499461
\(347\) −7.14795 + 12.3806i −0.383722 + 0.664626i −0.991591 0.129411i \(-0.958691\pi\)
0.607869 + 0.794037i \(0.292025\pi\)
\(348\) 1.67241 + 2.89669i 0.0896504 + 0.155279i
\(349\) −5.53079 9.57962i −0.296057 0.512785i 0.679173 0.733978i \(-0.262338\pi\)
−0.975230 + 0.221193i \(0.929005\pi\)
\(350\) −7.88471 −0.421455
\(351\) 0 0
\(352\) 4.85086 0.258551
\(353\) 5.25236 + 9.09735i 0.279555 + 0.484203i 0.971274 0.237963i \(-0.0764798\pi\)
−0.691719 + 0.722166i \(0.743146\pi\)
\(354\) 0.653989 + 1.13274i 0.0347591 + 0.0602046i
\(355\) 2.69202 4.66272i 0.142878 0.247471i
\(356\) −3.10992 −0.164825
\(357\) 2.55496 4.42532i 0.135223 0.234213i
\(358\) −11.3964 + 19.7392i −0.602320 + 1.04325i
\(359\) 5.10992 0.269691 0.134846 0.990867i \(-0.456946\pi\)
0.134846 + 0.990867i \(0.456946\pi\)
\(360\) 2.02446 3.50647i 0.106698 0.184807i
\(361\) 7.91550 + 13.7101i 0.416605 + 0.721582i
\(362\) −0.268750 0.465488i −0.0141252 0.0244655i
\(363\) 12.5308 0.657696
\(364\) 0 0
\(365\) −30.9855 −1.62186
\(366\) 0.198062 + 0.343054i 0.0103529 + 0.0179317i
\(367\) 4.22401 + 7.31620i 0.220492 + 0.381903i 0.954957 0.296743i \(-0.0959005\pi\)
−0.734466 + 0.678646i \(0.762567\pi\)
\(368\) −2.55496 + 4.42532i −0.133186 + 0.230686i
\(369\) −1.50604 −0.0784014
\(370\) −2.60388 + 4.51004i −0.135369 + 0.234466i
\(371\) 4.66301 8.07658i 0.242092 0.419315i
\(372\) −0.972853 −0.0504401
\(373\) −3.84548 + 6.66056i −0.199111 + 0.344871i −0.948241 0.317553i \(-0.897139\pi\)
0.749129 + 0.662424i \(0.230472\pi\)
\(374\) −17.9095 31.0201i −0.926076 1.60401i
\(375\) 12.9438 + 22.4194i 0.668417 + 1.15773i
\(376\) 7.20775 0.371711
\(377\) 0 0
\(378\) −0.692021 −0.0355937
\(379\) 5.70171 + 9.87565i 0.292877 + 0.507278i 0.974489 0.224436i \(-0.0720540\pi\)
−0.681612 + 0.731714i \(0.738721\pi\)
\(380\) 3.60388 + 6.24210i 0.184875 + 0.320213i
\(381\) 3.00269 5.20081i 0.153832 0.266446i
\(382\) −9.79954 −0.501388
\(383\) −10.3351 + 17.9010i −0.528100 + 0.914696i 0.471363 + 0.881939i \(0.343762\pi\)
−0.999463 + 0.0327572i \(0.989571\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 13.5918 0.692702
\(386\) 7.09783 12.2938i 0.361270 0.625738i
\(387\) 4.15883 + 7.20331i 0.211405 + 0.366165i
\(388\) −4.27144 7.39835i −0.216849 0.375594i
\(389\) 17.4776 0.886148 0.443074 0.896485i \(-0.353888\pi\)
0.443074 + 0.896485i \(0.353888\pi\)
\(390\) 0 0
\(391\) 37.7318 1.90818
\(392\) 3.26055 + 5.64744i 0.164683 + 0.285239i
\(393\) −4.40850 7.63575i −0.222379 0.385173i
\(394\) 1.50484 2.60647i 0.0758130 0.131312i
\(395\) 33.7657 1.69894
\(396\) −2.42543 + 4.20096i −0.121882 + 0.211106i
\(397\) 9.67994 16.7661i 0.485822 0.841469i −0.514045 0.857763i \(-0.671854\pi\)
0.999867 + 0.0162944i \(0.00518690\pi\)
\(398\) 12.8944 0.646338
\(399\) 0.615957 1.06687i 0.0308364 0.0534103i
\(400\) −5.69687 9.86726i −0.284843 0.493363i
\(401\) 7.24160 + 12.5428i 0.361628 + 0.626359i 0.988229 0.152982i \(-0.0488876\pi\)
−0.626601 + 0.779341i \(0.715554\pi\)
\(402\) −6.05429 −0.301961
\(403\) 0 0
\(404\) −11.9976 −0.596903
\(405\) 2.02446 + 3.50647i 0.100596 + 0.174238i
\(406\) −1.15734 2.00457i −0.0574379 0.0994854i
\(407\) 3.11960 5.40331i 0.154633 0.267832i
\(408\) 7.38404 0.365565
\(409\) 9.44922 16.3665i 0.467234 0.809273i −0.532065 0.846703i \(-0.678584\pi\)
0.999299 + 0.0374304i \(0.0119172\pi\)
\(410\) −3.04892 + 5.28088i −0.150575 + 0.260804i
\(411\) 15.7560 0.777186
\(412\) 6.16152 10.6721i 0.303556 0.525775i
\(413\) −0.452575 0.783882i −0.0222697 0.0385723i
\(414\) −2.55496 4.42532i −0.125569 0.217492i
\(415\) 62.0592 3.04637
\(416\) 0 0
\(417\) −6.09783 −0.298612
\(418\) −4.31767 7.47842i −0.211184 0.365781i
\(419\) 10.8802 + 18.8450i 0.531531 + 0.920638i 0.999323 + 0.0367993i \(0.0117162\pi\)
−0.467792 + 0.883838i \(0.654950\pi\)
\(420\) −1.40097 + 2.42655i −0.0683603 + 0.118403i
\(421\) 20.5918 1.00358 0.501791 0.864989i \(-0.332675\pi\)
0.501791 + 0.864989i \(0.332675\pi\)
\(422\) −3.89977 + 6.75460i −0.189838 + 0.328809i
\(423\) −3.60388 + 6.24210i −0.175226 + 0.303501i
\(424\) 13.4765 0.654477
\(425\) −42.0659 + 72.8603i −2.04050 + 3.53424i
\(426\) −0.664874 1.15160i −0.0322133 0.0557950i
\(427\) −0.137063 0.237401i −0.00663296 0.0114886i
\(428\) 5.89977 0.285176
\(429\) 0 0
\(430\) 33.6775 1.62408
\(431\) −17.2567 29.8894i −0.831224 1.43972i −0.897068 0.441893i \(-0.854307\pi\)
0.0658433 0.997830i \(-0.479026\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 1.06315 1.84144i 0.0510920 0.0884939i −0.839348 0.543594i \(-0.817063\pi\)
0.890440 + 0.455100i \(0.150397\pi\)
\(434\) 0.673235 0.0323163
\(435\) −6.77144 + 11.7285i −0.324666 + 0.562337i
\(436\) 0.396125 0.686108i 0.0189709 0.0328586i
\(437\) 9.09651 0.435145
\(438\) −3.82640 + 6.62751i −0.182832 + 0.316675i
\(439\) −10.9160 18.9071i −0.520994 0.902388i −0.999702 0.0244137i \(-0.992228\pi\)
0.478708 0.877974i \(-0.341105\pi\)
\(440\) 9.82036 + 17.0094i 0.468167 + 0.810889i
\(441\) −6.52111 −0.310529
\(442\) 0 0
\(443\) −7.54048 −0.358259 −0.179130 0.983825i \(-0.557328\pi\)
−0.179130 + 0.983825i \(0.557328\pi\)
\(444\) 0.643104 + 1.11389i 0.0305204 + 0.0528628i
\(445\) −6.29590 10.9048i −0.298454 0.516938i
\(446\) 6.09783 10.5618i 0.288741 0.500114i
\(447\) 2.55257 0.120732
\(448\) 0.346011 0.599308i 0.0163475 0.0283146i
\(449\) −9.87800 + 17.1092i −0.466172 + 0.807433i −0.999254 0.0386305i \(-0.987700\pi\)
0.533082 + 0.846064i \(0.321034\pi\)
\(450\) 11.3937 0.537106
\(451\) 3.65279 6.32682i 0.172003 0.297918i
\(452\) −3.10992 5.38653i −0.146278 0.253361i
\(453\) −8.85839 15.3432i −0.416203 0.720885i
\(454\) 6.74333 0.316480
\(455\) 0 0
\(456\) 1.78017 0.0833640
\(457\) −11.9291 20.6618i −0.558019 0.966517i −0.997662 0.0683441i \(-0.978228\pi\)
0.439643 0.898173i \(-0.355105\pi\)
\(458\) 9.91185 + 17.1678i 0.463151 + 0.802200i
\(459\) −3.69202 + 6.39477i −0.172329 + 0.298482i
\(460\) −20.6896 −0.964659
\(461\) 8.78866 15.2224i 0.409329 0.708978i −0.585486 0.810683i \(-0.699096\pi\)
0.994815 + 0.101704i \(0.0324296\pi\)
\(462\) 1.67845 2.90716i 0.0780885 0.135253i
\(463\) 23.8431 1.10808 0.554041 0.832489i \(-0.313085\pi\)
0.554041 + 0.832489i \(0.313085\pi\)
\(464\) 1.67241 2.89669i 0.0776396 0.134476i
\(465\) −1.96950 3.41127i −0.0913334 0.158194i
\(466\) 15.0151 + 26.0069i 0.695559 + 1.20474i
\(467\) 8.61058 0.398450 0.199225 0.979954i \(-0.436158\pi\)
0.199225 + 0.979954i \(0.436158\pi\)
\(468\) 0 0
\(469\) 4.18970 0.193462
\(470\) 14.5918 + 25.2737i 0.673069 + 1.16579i
\(471\) 3.15883 + 5.47126i 0.145551 + 0.252102i
\(472\) 0.653989 1.13274i 0.0301023 0.0521387i
\(473\) −40.3478 −1.85519
\(474\) 4.16972 7.22216i 0.191522 0.331725i
\(475\) −10.1414 + 17.5654i −0.465318 + 0.805955i
\(476\) −5.10992 −0.234213
\(477\) −6.73825 + 11.6710i −0.308523 + 0.534378i
\(478\) −11.0489 19.1373i −0.505366 0.875319i
\(479\) −3.29052 5.69935i −0.150348 0.260410i 0.781008 0.624522i \(-0.214706\pi\)
−0.931355 + 0.364112i \(0.881373\pi\)
\(480\) −4.04892 −0.184807
\(481\) 0 0
\(482\) 10.1274 0.461289
\(483\) 1.76809 + 3.06241i 0.0804507 + 0.139345i
\(484\) −6.26540 10.8520i −0.284791 0.493272i
\(485\) 17.2947 29.9553i 0.785312 1.36020i
\(486\) 1.00000 0.0453609
\(487\) 11.6380 20.1576i 0.527369 0.913430i −0.472122 0.881533i \(-0.656512\pi\)
0.999491 0.0318970i \(-0.0101548\pi\)
\(488\) 0.198062 0.343054i 0.00896586 0.0155293i
\(489\) 14.5918 0.659864
\(490\) −13.2017 + 22.8660i −0.596392 + 1.03298i
\(491\) 7.77024 + 13.4585i 0.350666 + 0.607372i 0.986366 0.164565i \(-0.0526219\pi\)
−0.635700 + 0.771936i \(0.719289\pi\)
\(492\) 0.753020 + 1.30427i 0.0339488 + 0.0588010i
\(493\) −24.6983 −1.11235
\(494\) 0 0
\(495\) −19.6407 −0.882784
\(496\) 0.486426 + 0.842515i 0.0218412 + 0.0378301i
\(497\) 0.460107 + 0.796929i 0.0206386 + 0.0357472i
\(498\) 7.66368 13.2739i 0.343418 0.594817i
\(499\) 9.53617 0.426898 0.213449 0.976954i \(-0.431530\pi\)
0.213449 + 0.976954i \(0.431530\pi\)
\(500\) 12.9438 22.4194i 0.578866 1.00263i
\(501\) 9.75063 16.8886i 0.435626 0.754526i
\(502\) 5.54719 0.247583
\(503\) 6.91723 11.9810i 0.308424 0.534206i −0.669594 0.742728i \(-0.733532\pi\)
0.978018 + 0.208521i \(0.0668651\pi\)
\(504\) 0.346011 + 0.599308i 0.0154125 + 0.0266953i
\(505\) −24.2887 42.0692i −1.08083 1.87205i
\(506\) 24.7875 1.10194
\(507\) 0 0
\(508\) −6.00538 −0.266446
\(509\) 20.4819 + 35.4757i 0.907843 + 1.57243i 0.817054 + 0.576560i \(0.195605\pi\)
0.0907888 + 0.995870i \(0.471061\pi\)
\(510\) 14.9487 + 25.8919i 0.661939 + 1.14651i
\(511\) 2.64795 4.58638i 0.117138 0.202890i
\(512\) 1.00000 0.0441942
\(513\) −0.890084 + 1.54167i −0.0392982 + 0.0680664i
\(514\) 6.89977 11.9508i 0.304336 0.527125i
\(515\) 49.8950 2.19864
\(516\) 4.15883 7.20331i 0.183082 0.317108i
\(517\) −17.4819 30.2795i −0.768852 1.33169i
\(518\) −0.445042 0.770835i −0.0195540 0.0338686i
\(519\) −9.29052 −0.407809
\(520\) 0 0
\(521\) 36.3672 1.59327 0.796637 0.604457i \(-0.206610\pi\)
0.796637 + 0.604457i \(0.206610\pi\)
\(522\) 1.67241 + 2.89669i 0.0731993 + 0.126785i
\(523\) 3.01507 + 5.22225i 0.131840 + 0.228353i 0.924386 0.381459i \(-0.124578\pi\)
−0.792546 + 0.609812i \(0.791245\pi\)
\(524\) −4.40850 + 7.63575i −0.192586 + 0.333569i
\(525\) −7.88471 −0.344117
\(526\) 11.2349 19.4594i 0.489865 0.848471i
\(527\) 3.59179 6.22117i 0.156461 0.270998i
\(528\) 4.85086 0.211106
\(529\) −1.55562 + 2.69442i −0.0676357 + 0.117149i
\(530\) 27.2826 + 47.2549i 1.18508 + 2.05262i
\(531\) 0.653989 + 1.13274i 0.0283807 + 0.0491568i
\(532\) −1.23191 −0.0534103
\(533\) 0 0
\(534\) −3.10992 −0.134579
\(535\) 11.9438 + 20.6873i 0.516377 + 0.894392i
\(536\) 3.02715 + 5.24317i 0.130753 + 0.226471i
\(537\) −11.3964 + 19.7392i −0.491792 + 0.851808i
\(538\) −26.0140 −1.12154
\(539\) 15.8165 27.3949i 0.681264 1.17998i
\(540\) 2.02446 3.50647i 0.0871188 0.150894i
\(541\) −7.92154 −0.340574 −0.170287 0.985395i \(-0.554469\pi\)
−0.170287 + 0.985395i \(0.554469\pi\)
\(542\) −1.44235 + 2.49823i −0.0619544 + 0.107308i
\(543\) −0.268750 0.465488i −0.0115332 0.0199760i
\(544\) −3.69202 6.39477i −0.158294 0.274173i
\(545\) 3.20775 0.137405
\(546\) 0 0
\(547\) 18.4155 0.787390 0.393695 0.919241i \(-0.371197\pi\)
0.393695 + 0.919241i \(0.371197\pi\)
\(548\) −7.87800 13.6451i −0.336532 0.582890i
\(549\) 0.198062 + 0.343054i 0.00845309 + 0.0146412i
\(550\) −27.6347 + 47.8647i −1.17835 + 2.04096i
\(551\) −5.95433 −0.253663
\(552\) −2.55496 + 4.42532i −0.108746 + 0.188354i
\(553\) −2.88553 + 4.99789i −0.122705 + 0.212532i
\(554\) −1.46250 −0.0621357
\(555\) −2.60388 + 4.51004i −0.110528 + 0.191441i
\(556\) 3.04892 + 5.28088i 0.129303 + 0.223959i
\(557\) 11.9879 + 20.7637i 0.507944 + 0.879786i 0.999958 + 0.00919783i \(0.00292780\pi\)
−0.492013 + 0.870588i \(0.663739\pi\)
\(558\) −0.972853 −0.0411841
\(559\) 0 0
\(560\) 2.80194 0.118403
\(561\) −17.9095 31.0201i −0.756138 1.30967i
\(562\) −2.84117 4.92104i −0.119847 0.207582i
\(563\) 1.14646 1.98572i 0.0483174 0.0836882i −0.840855 0.541260i \(-0.817947\pi\)
0.889173 + 0.457572i \(0.151281\pi\)
\(564\) 7.20775 0.303501
\(565\) 12.5918 21.8096i 0.529741 0.917538i
\(566\) 12.6039 21.8306i 0.529780 0.917607i
\(567\) −0.692021 −0.0290622
\(568\) −0.664874 + 1.15160i −0.0278975 + 0.0483199i
\(569\) 22.1715 + 38.4022i 0.929478 + 1.60990i 0.784197 + 0.620513i \(0.213075\pi\)
0.145281 + 0.989390i \(0.453591\pi\)
\(570\) 3.60388 + 6.24210i 0.150950 + 0.261453i
\(571\) −15.2707 −0.639058 −0.319529 0.947577i \(-0.603525\pi\)
−0.319529 + 0.947577i \(0.603525\pi\)
\(572\) 0 0
\(573\) −9.79954 −0.409382
\(574\) −0.521106 0.902583i −0.0217506 0.0376731i
\(575\) −29.1105 50.4209i −1.21399 2.10270i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 8.77048 0.365120 0.182560 0.983195i \(-0.441562\pi\)
0.182560 + 0.983195i \(0.441562\pi\)
\(578\) −18.7620 + 32.4968i −0.780398 + 1.35169i
\(579\) 7.09783 12.2938i 0.294976 0.510913i
\(580\) 13.5429 0.562337
\(581\) −5.30343 + 9.18581i −0.220023 + 0.381092i
\(582\) −4.27144 7.39835i −0.177057 0.306671i
\(583\) −32.6863 56.6143i −1.35373 2.34472i
\(584\) 7.65279 0.316675
\(585\) 0 0
\(586\) −7.14914 −0.295328
\(587\) 19.0715 + 33.0328i 0.787166 + 1.36341i 0.927697 + 0.373335i \(0.121786\pi\)
−0.140531 + 0.990076i \(0.544881\pi\)
\(588\) 3.26055 + 5.64744i 0.134463 + 0.232897i
\(589\) 0.865921 1.49982i 0.0356796 0.0617989i
\(590\) 5.29590 0.218029
\(591\) 1.50484 2.60647i 0.0619010 0.107216i
\(592\) 0.643104 1.11389i 0.0264314 0.0457806i
\(593\) −37.9517 −1.55849 −0.779244 0.626720i \(-0.784397\pi\)
−0.779244 + 0.626720i \(0.784397\pi\)
\(594\) −2.42543 + 4.20096i −0.0995165 + 0.172368i
\(595\) −10.3448 17.9177i −0.424096 0.734556i
\(596\) −1.27628 2.21059i −0.0522786 0.0905491i
\(597\) 12.8944 0.527732
\(598\) 0 0
\(599\) −3.57971 −0.146263 −0.0731315 0.997322i \(-0.523299\pi\)
−0.0731315 + 0.997322i \(0.523299\pi\)
\(600\) −5.69687 9.86726i −0.232574 0.402829i
\(601\) 2.85839 + 4.95087i 0.116596 + 0.201950i 0.918417 0.395615i \(-0.129468\pi\)
−0.801821 + 0.597565i \(0.796135\pi\)
\(602\) −2.87800 + 4.98485i −0.117299 + 0.203167i
\(603\) −6.05429 −0.246550
\(604\) −8.85839 + 15.3432i −0.360443 + 0.624305i
\(605\) 25.3681 43.9388i 1.03136 1.78637i
\(606\) −11.9976 −0.487369
\(607\) −11.2143 + 19.4238i −0.455175 + 0.788387i −0.998698 0.0510075i \(-0.983757\pi\)
0.543523 + 0.839394i \(0.317090\pi\)
\(608\) −0.890084 1.54167i −0.0360977 0.0625230i
\(609\) −1.15734 2.00457i −0.0468979 0.0812295i
\(610\) 1.60388 0.0649390
\(611\) 0 0
\(612\) 7.38404 0.298482
\(613\) 19.9801 + 34.6066i 0.806991 + 1.39775i 0.914939 + 0.403592i \(0.132239\pi\)
−0.107948 + 0.994157i \(0.534428\pi\)
\(614\) 8.99761 + 15.5843i 0.363114 + 0.628932i
\(615\) −3.04892 + 5.28088i −0.122944 + 0.212946i
\(616\) −3.35690 −0.135253
\(617\) −15.7235 + 27.2339i −0.633003 + 1.09639i 0.353931 + 0.935272i \(0.384845\pi\)
−0.986934 + 0.161123i \(0.948489\pi\)
\(618\) 6.16152 10.6721i 0.247853 0.429294i
\(619\) −29.3685 −1.18042 −0.590210 0.807250i \(-0.700955\pi\)
−0.590210 + 0.807250i \(0.700955\pi\)
\(620\) −1.96950 + 3.41127i −0.0790970 + 0.137000i
\(621\) −2.55496 4.42532i −0.102527 0.177582i
\(622\) −1.66487 2.88365i −0.0667554 0.115624i
\(623\) 2.15213 0.0862232
\(624\) 0 0
\(625\) 47.8485 1.91394
\(626\) 8.94169 + 15.4875i 0.357382 + 0.619003i
\(627\) −4.31767 7.47842i −0.172431 0.298659i
\(628\) 3.15883 5.47126i 0.126051 0.218327i
\(629\) −9.49742 −0.378687
\(630\) −1.40097 + 2.42655i −0.0558159 + 0.0966760i
\(631\) −10.8400 + 18.7754i −0.431532 + 0.747436i −0.997005 0.0773307i \(-0.975360\pi\)
0.565473 + 0.824767i \(0.308694\pi\)
\(632\) −8.33944 −0.331725
\(633\) −3.89977 + 6.75460i −0.155002 + 0.268471i
\(634\) −2.19687 3.80508i −0.0872487 0.151119i
\(635\) −12.1576 21.0576i −0.482461 0.835647i
\(636\) 13.4765 0.534378
\(637\) 0 0
\(638\) −16.2252 −0.642362
\(639\) −0.664874 1.15160i −0.0263020 0.0455564i
\(640\) 2.02446 + 3.50647i 0.0800238 + 0.138605i
\(641\) −7.00538 + 12.1337i −0.276696 + 0.479251i −0.970562 0.240853i \(-0.922573\pi\)
0.693866 + 0.720104i \(0.255906\pi\)
\(642\) 5.89977 0.232845
\(643\) −15.3937 + 26.6627i −0.607070 + 1.05148i 0.384651 + 0.923062i \(0.374322\pi\)
−0.991721 + 0.128413i \(0.959012\pi\)
\(644\) 1.76809 3.06241i 0.0696723 0.120676i
\(645\) 33.6775 1.32605
\(646\) −6.57242 + 11.3838i −0.258588 + 0.447888i
\(647\) 8.30127 + 14.3782i 0.326357 + 0.565266i 0.981786 0.189990i \(-0.0608456\pi\)
−0.655429 + 0.755257i \(0.727512\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −6.34481 −0.249056
\(650\) 0 0
\(651\) 0.673235 0.0263862
\(652\) −7.29590 12.6369i −0.285729 0.494898i
\(653\) −14.2729 24.7214i −0.558543 0.967425i −0.997618 0.0689745i \(-0.978027\pi\)
0.439075 0.898450i \(-0.355306\pi\)
\(654\) 0.396125 0.686108i 0.0154897 0.0268289i
\(655\) −35.6993 −1.39489
\(656\) 0.753020 1.30427i 0.0294005 0.0509232i
\(657\) −3.82640 + 6.62751i −0.149282 + 0.258564i
\(658\) −4.98792 −0.194449
\(659\) −13.8593 + 24.0051i −0.539884 + 0.935106i 0.459026 + 0.888423i \(0.348198\pi\)
−0.998910 + 0.0466830i \(0.985135\pi\)
\(660\) 9.82036 + 17.0094i 0.382257 + 0.662088i
\(661\) −5.40044 9.35383i −0.210053 0.363822i 0.741678 0.670756i \(-0.234030\pi\)
−0.951731 + 0.306934i \(0.900697\pi\)
\(662\) −25.6775 −0.997986
\(663\) 0 0
\(664\) −15.3274 −0.594817
\(665\) −2.49396 4.31966i −0.0967116 0.167509i
\(666\) 0.643104 + 1.11389i 0.0249198 + 0.0431623i
\(667\) 8.54586 14.8019i 0.330897 0.573130i
\(668\) −19.5013 −0.754526
\(669\) 6.09783 10.5618i 0.235756 0.408341i
\(670\) −12.2567 + 21.2292i −0.473516 + 0.820154i
\(671\) −1.92154 −0.0741803
\(672\) 0.346011 0.599308i 0.0133477 0.0231188i
\(673\) −8.16301 14.1388i −0.314661 0.545009i 0.664704 0.747107i \(-0.268558\pi\)
−0.979365 + 0.202098i \(0.935224\pi\)
\(674\) 12.3252 + 21.3479i 0.474749 + 0.822289i
\(675\) 11.3937 0.438545
\(676\) 0 0
\(677\) 41.4252 1.59210 0.796050 0.605231i \(-0.206919\pi\)
0.796050 + 0.605231i \(0.206919\pi\)
\(678\) −3.10992 5.38653i −0.119436 0.206869i
\(679\) 2.95593 + 5.11982i 0.113438 + 0.196480i
\(680\) 14.9487 25.8919i 0.573256 0.992909i
\(681\) 6.74333 0.258405
\(682\) 2.35958 4.08692i 0.0903532 0.156496i
\(683\) −15.6163 + 27.0481i −0.597539 + 1.03497i 0.395644 + 0.918404i \(0.370521\pi\)
−0.993183 + 0.116564i \(0.962812\pi\)
\(684\) 1.78017 0.0680664
\(685\) 31.8974 55.2479i 1.21874 2.11091i
\(686\) −4.67845 8.10331i −0.178624 0.309386i
\(687\) 9.91185 + 17.1678i 0.378161 + 0.654994i
\(688\) −8.31767 −0.317108
\(689\) 0 0
\(690\) −20.6896 −0.787641
\(691\) −12.4819 21.6192i −0.474833 0.822435i 0.524752 0.851255i \(-0.324158\pi\)
−0.999585 + 0.0288205i \(0.990825\pi\)
\(692\) 4.64526 + 8.04583i 0.176586 + 0.305856i
\(693\) 1.67845 2.90716i 0.0637590 0.110434i
\(694\) 14.2959 0.542665
\(695\) −12.3448 + 21.3818i −0.468265 + 0.811060i
\(696\) 1.67241 2.89669i 0.0633924 0.109799i
\(697\) −11.1207 −0.421225
\(698\) −5.53079 + 9.57962i −0.209344 + 0.362594i
\(699\) 15.0151 + 26.0069i 0.567922 + 0.983670i
\(700\) 3.94235 + 6.82836i 0.149007 + 0.258088i
\(701\) 8.17151 0.308634 0.154317 0.988021i \(-0.450682\pi\)
0.154317 + 0.988021i \(0.450682\pi\)
\(702\) 0 0
\(703\) −2.28967 −0.0863564
\(704\) −2.42543 4.20096i −0.0914117 0.158330i
\(705\) 14.5918 + 25.2737i 0.549559 + 0.951864i
\(706\) 5.25236 9.09735i 0.197675 0.342383i
\(707\) 8.30260 0.312251
\(708\) 0.653989 1.13274i 0.0245784 0.0425711i
\(709\) 18.3991 31.8682i 0.690993 1.19684i −0.280520 0.959848i \(-0.590507\pi\)
0.971513 0.236987i \(-0.0761598\pi\)
\(710\) −5.38404 −0.202060
\(711\) 4.16972 7.22216i 0.156377 0.270852i
\(712\) 1.55496 + 2.69327i 0.0582745 + 0.100934i
\(713\) 2.48560 + 4.30518i 0.0930864 + 0.161230i
\(714\) −5.10992 −0.191234
\(715\) 0 0
\(716\) 22.7928 0.851808
\(717\) −11.0489 19.1373i −0.412629 0.714695i
\(718\) −2.55496 4.42532i −0.0953502 0.165151i
\(719\) −17.6112 + 30.5034i −0.656786 + 1.13759i 0.324657 + 0.945832i \(0.394751\pi\)
−0.981443 + 0.191755i \(0.938582\pi\)
\(720\) −4.04892 −0.150894
\(721\) −4.26391 + 7.38530i −0.158796 + 0.275043i
\(722\) 7.91550 13.7101i 0.294584 0.510235i
\(723\) 10.1274 0.376641
\(724\) −0.268750 + 0.465488i −0.00998801 + 0.0172997i
\(725\) 19.0550 + 33.0042i 0.707683 + 1.22574i
\(726\) −6.26540 10.8520i −0.232531 0.402755i
\(727\) 40.6872 1.50901 0.754503 0.656297i \(-0.227878\pi\)
0.754503 + 0.656297i \(0.227878\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 15.4928 + 26.8343i 0.573413 + 0.993180i
\(731\) 30.7090 + 53.1896i 1.13581 + 1.96729i
\(732\) 0.198062 0.343054i 0.00732059 0.0126796i
\(733\) 27.1400 1.00244 0.501220 0.865320i \(-0.332885\pi\)
0.501220 + 0.865320i \(0.332885\pi\)
\(734\) 4.22401 7.31620i 0.155911 0.270046i
\(735\) −13.2017 + 22.8660i −0.486952 + 0.843426i
\(736\) 5.10992 0.188354
\(737\) 14.6843 25.4339i 0.540901 0.936869i
\(738\) 0.753020 + 1.30427i 0.0277191 + 0.0480108i
\(739\) −1.86294 3.22670i −0.0685292 0.118696i 0.829725 0.558173i \(-0.188497\pi\)
−0.898254 + 0.439476i \(0.855164\pi\)
\(740\) 5.20775 0.191441
\(741\) 0 0
\(742\) −9.32603 −0.342369
\(743\) −10.9293 18.9301i −0.400958 0.694479i 0.592884 0.805288i \(-0.297989\pi\)
−0.993842 + 0.110809i \(0.964656\pi\)
\(744\) 0.486426 + 0.842515i 0.0178333 + 0.0308881i
\(745\) 5.16756 8.95048i 0.189325 0.327920i
\(746\) 7.69096 0.281586
\(747\) 7.66368 13.2739i 0.280399 0.485666i
\(748\) −17.9095 + 31.0201i −0.654835 + 1.13421i
\(749\) −4.08277 −0.149181
\(750\) 12.9438 22.4194i 0.472642 0.818641i
\(751\) −26.6821 46.2147i −0.973644 1.68640i −0.684341 0.729162i \(-0.739910\pi\)
−0.289303 0.957238i \(-0.593423\pi\)
\(752\) −3.60388 6.24210i −0.131420 0.227626i
\(753\) 5.54719 0.202151
\(754\) 0 0
\(755\) −71.7338 −2.61066
\(756\) 0.346011 + 0.599308i 0.0125843 + 0.0217966i
\(757\) 2.31767 + 4.01432i 0.0842370 + 0.145903i 0.905066 0.425271i \(-0.139821\pi\)
−0.820829 + 0.571174i \(0.806488\pi\)
\(758\) 5.70171 9.87565i 0.207095 0.358700i
\(759\) 24.7875 0.899728
\(760\) 3.60388 6.24210i 0.130726 0.226425i
\(761\) −5.78017 + 10.0115i −0.209531 + 0.362918i −0.951567 0.307442i \(-0.900527\pi\)
0.742036 + 0.670360i \(0.233860\pi\)
\(762\) −6.00538 −0.217552
\(763\) −0.274127 + 0.474801i −0.00992405 + 0.0171890i
\(764\) 4.89977 + 8.48665i 0.177268 + 0.307036i
\(765\) 14.9487 + 25.8919i 0.540471 + 0.936123i
\(766\) 20.6703 0.746847
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −7.37196 12.7686i −0.265840 0.460448i 0.701944 0.712233i \(-0.252316\pi\)
−0.967783 + 0.251785i \(0.918983\pi\)
\(770\) −6.79590 11.7708i −0.244907 0.424192i
\(771\) 6.89977 11.9508i 0.248489 0.430396i
\(772\) −14.1957 −0.510913
\(773\) 3.21134 5.56220i 0.115504 0.200059i −0.802477 0.596683i \(-0.796485\pi\)
0.917981 + 0.396624i \(0.129818\pi\)
\(774\) 4.15883 7.20331i 0.149486 0.258918i
\(775\) −11.0844 −0.398164
\(776\) −4.27144 + 7.39835i −0.153336 + 0.265585i
\(777\) −0.445042 0.770835i −0.0159658 0.0276536i
\(778\) −8.73878 15.1360i −0.313301 0.542652i