Properties

Label 637.2.g.d.373.2
Level $637$
Weight $2$
Character 637.373
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 637.373
Dual form 637.2.g.d.263.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 + 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} +O(q^{10})\) \(q+(0.866025 + 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 + 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} -3.00000 q^{10} +4.73205 q^{11} +(-0.366025 + 0.633975i) q^{12} +(1.59808 + 3.23205i) q^{13} +(-0.633975 + 1.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-2.13397 + 3.69615i) q^{17} +(-2.13397 - 3.69615i) q^{18} -2.00000 q^{19} +(-0.866025 - 1.50000i) q^{20} +(4.09808 + 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +1.26795 q^{24} +(1.00000 + 1.73205i) q^{25} +(-3.46410 + 5.19615i) q^{26} -4.00000 q^{27} +(1.50000 - 2.59808i) q^{29} -2.19615 q^{30} +(-3.09808 - 5.36603i) q^{31} +(-2.59808 + 4.50000i) q^{32} +3.46410 q^{33} -7.39230 q^{34} +(1.23205 - 2.13397i) q^{36} +(3.50000 + 6.06218i) q^{37} +(-1.73205 - 3.00000i) q^{38} +(1.16987 + 2.36603i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(2.59808 - 4.50000i) q^{41} +(-5.09808 - 8.83013i) q^{43} +(-2.36603 + 4.09808i) q^{44} +(2.13397 - 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} +(-0.464102 + 0.803848i) q^{47} +(1.83013 + 3.16987i) q^{48} +(-1.73205 + 3.00000i) q^{50} +(-1.56218 + 2.70577i) q^{51} +(-3.59808 - 0.232051i) q^{52} +(-1.96410 - 3.40192i) q^{53} +(-3.46410 - 6.00000i) q^{54} +(-4.09808 + 7.09808i) q^{55} -1.46410 q^{57} +5.19615 q^{58} +(5.36603 - 9.29423i) q^{59} +(-0.633975 - 1.09808i) q^{60} +15.1962 q^{61} +(5.36603 - 9.29423i) q^{62} +1.00000 q^{64} +(-6.23205 - 0.401924i) q^{65} +(3.00000 + 5.19615i) q^{66} +4.19615 q^{67} +(-2.13397 - 3.69615i) q^{68} +(-0.464102 - 0.803848i) q^{69} +(-3.00000 - 5.19615i) q^{71} -4.26795 q^{72} +(3.59808 + 6.23205i) q^{73} +(-6.06218 + 10.5000i) q^{74} +(0.732051 + 1.26795i) q^{75} +(1.00000 - 1.73205i) q^{76} +(-2.53590 + 3.80385i) q^{78} +(-2.90192 + 5.02628i) q^{79} -8.66025 q^{80} +4.46410 q^{81} +9.00000 q^{82} -8.19615 q^{83} +(-3.69615 - 6.40192i) q^{85} +(8.83013 - 15.2942i) q^{86} +(1.09808 - 1.90192i) q^{87} +8.19615 q^{88} +(-0.464102 - 0.803848i) q^{89} +7.39230 q^{90} +1.26795 q^{92} +(-2.26795 - 3.92820i) q^{93} -1.60770 q^{94} +(1.73205 - 3.00000i) q^{95} +(-1.90192 + 3.29423i) q^{96} +(-7.19615 - 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{19} + 6 q^{22} - 6 q^{23} + 12 q^{24} + 4 q^{25} - 16 q^{27} + 6 q^{29} + 12 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} - 6 q^{60} + 40 q^{61} + 18 q^{62} + 4 q^{64} - 18 q^{65} + 12 q^{66} - 4 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} - 24 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} - 6 q^{87} + 12 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} - 48 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 1.50000i 0.612372 + 1.06066i 0.990839 + 0.135045i \(0.0431180\pi\)
−0.378467 + 0.925615i \(0.623549\pi\)
\(3\) 0.732051 0.422650 0.211325 0.977416i \(-0.432222\pi\)
0.211325 + 0.977416i \(0.432222\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.866025 + 1.50000i −0.387298 + 0.670820i −0.992085 0.125567i \(-0.959925\pi\)
0.604787 + 0.796387i \(0.293258\pi\)
\(6\) 0.633975 + 1.09808i 0.258819 + 0.448288i
\(7\) 0 0
\(8\) 1.73205 0.612372
\(9\) −2.46410 −0.821367
\(10\) −3.00000 −0.948683
\(11\) 4.73205 1.42677 0.713384 0.700774i \(-0.247162\pi\)
0.713384 + 0.700774i \(0.247162\pi\)
\(12\) −0.366025 + 0.633975i −0.105662 + 0.183013i
\(13\) 1.59808 + 3.23205i 0.443227 + 0.896410i
\(14\) 0 0
\(15\) −0.633975 + 1.09808i −0.163692 + 0.283522i
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) −2.13397 + 3.69615i −0.517565 + 0.896449i 0.482227 + 0.876046i \(0.339828\pi\)
−0.999792 + 0.0204023i \(0.993505\pi\)
\(18\) −2.13397 3.69615i −0.502983 0.871191i
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −0.866025 1.50000i −0.193649 0.335410i
\(21\) 0 0
\(22\) 4.09808 + 7.09808i 0.873713 + 1.51331i
\(23\) −0.633975 1.09808i −0.132193 0.228965i 0.792329 0.610094i \(-0.208868\pi\)
−0.924522 + 0.381130i \(0.875535\pi\)
\(24\) 1.26795 0.258819
\(25\) 1.00000 + 1.73205i 0.200000 + 0.346410i
\(26\) −3.46410 + 5.19615i −0.679366 + 1.01905i
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) −2.19615 −0.400961
\(31\) −3.09808 5.36603i −0.556431 0.963767i −0.997791 0.0664364i \(-0.978837\pi\)
0.441360 0.897330i \(-0.354496\pi\)
\(32\) −2.59808 + 4.50000i −0.459279 + 0.795495i
\(33\) 3.46410 0.603023
\(34\) −7.39230 −1.26777
\(35\) 0 0
\(36\) 1.23205 2.13397i 0.205342 0.355662i
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) −1.73205 3.00000i −0.280976 0.486664i
\(39\) 1.16987 + 2.36603i 0.187330 + 0.378867i
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) 2.59808 4.50000i 0.405751 0.702782i −0.588657 0.808383i \(-0.700343\pi\)
0.994409 + 0.105601i \(0.0336766\pi\)
\(42\) 0 0
\(43\) −5.09808 8.83013i −0.777449 1.34658i −0.933408 0.358818i \(-0.883180\pi\)
0.155958 0.987764i \(-0.450153\pi\)
\(44\) −2.36603 + 4.09808i −0.356692 + 0.617808i
\(45\) 2.13397 3.69615i 0.318114 0.550990i
\(46\) 1.09808 1.90192i 0.161903 0.280423i
\(47\) −0.464102 + 0.803848i −0.0676962 + 0.117253i −0.897887 0.440226i \(-0.854898\pi\)
0.830191 + 0.557480i \(0.188232\pi\)
\(48\) 1.83013 + 3.16987i 0.264156 + 0.457532i
\(49\) 0 0
\(50\) −1.73205 + 3.00000i −0.244949 + 0.424264i
\(51\) −1.56218 + 2.70577i −0.218749 + 0.378884i
\(52\) −3.59808 0.232051i −0.498963 0.0321797i
\(53\) −1.96410 3.40192i −0.269790 0.467290i 0.699017 0.715105i \(-0.253621\pi\)
−0.968808 + 0.247814i \(0.920288\pi\)
\(54\) −3.46410 6.00000i −0.471405 0.816497i
\(55\) −4.09808 + 7.09808i −0.552584 + 0.957104i
\(56\) 0 0
\(57\) −1.46410 −0.193925
\(58\) 5.19615 0.682288
\(59\) 5.36603 9.29423i 0.698597 1.21001i −0.270356 0.962760i \(-0.587141\pi\)
0.968953 0.247245i \(-0.0795253\pi\)
\(60\) −0.633975 1.09808i −0.0818458 0.141761i
\(61\) 15.1962 1.94567 0.972834 0.231504i \(-0.0743646\pi\)
0.972834 + 0.231504i \(0.0743646\pi\)
\(62\) 5.36603 9.29423i 0.681486 1.18037i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.23205 0.401924i −0.772991 0.0498525i
\(66\) 3.00000 + 5.19615i 0.369274 + 0.639602i
\(67\) 4.19615 0.512642 0.256321 0.966592i \(-0.417490\pi\)
0.256321 + 0.966592i \(0.417490\pi\)
\(68\) −2.13397 3.69615i −0.258782 0.448224i
\(69\) −0.464102 0.803848i −0.0558713 0.0967719i
\(70\) 0 0
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) −4.26795 −0.502983
\(73\) 3.59808 + 6.23205i 0.421123 + 0.729406i 0.996050 0.0887986i \(-0.0283027\pi\)
−0.574927 + 0.818205i \(0.694969\pi\)
\(74\) −6.06218 + 10.5000i −0.704714 + 1.22060i
\(75\) 0.732051 + 1.26795i 0.0845299 + 0.146410i
\(76\) 1.00000 1.73205i 0.114708 0.198680i
\(77\) 0 0
\(78\) −2.53590 + 3.80385i −0.287134 + 0.430701i
\(79\) −2.90192 + 5.02628i −0.326492 + 0.565501i −0.981813 0.189850i \(-0.939200\pi\)
0.655321 + 0.755350i \(0.272533\pi\)
\(80\) −8.66025 −0.968246
\(81\) 4.46410 0.496011
\(82\) 9.00000 0.993884
\(83\) −8.19615 −0.899645 −0.449822 0.893118i \(-0.648513\pi\)
−0.449822 + 0.893118i \(0.648513\pi\)
\(84\) 0 0
\(85\) −3.69615 6.40192i −0.400904 0.694386i
\(86\) 8.83013 15.2942i 0.952177 1.64922i
\(87\) 1.09808 1.90192i 0.117726 0.203908i
\(88\) 8.19615 0.873713
\(89\) −0.464102 0.803848i −0.0491947 0.0852077i 0.840379 0.541998i \(-0.182332\pi\)
−0.889574 + 0.456791i \(0.848999\pi\)
\(90\) 7.39230 0.779217
\(91\) 0 0
\(92\) 1.26795 0.132193
\(93\) −2.26795 3.92820i −0.235175 0.407336i
\(94\) −1.60770 −0.165821
\(95\) 1.73205 3.00000i 0.177705 0.307794i
\(96\) −1.90192 + 3.29423i −0.194114 + 0.336216i
\(97\) −7.19615 12.4641i −0.730659 1.26554i −0.956602 0.291397i \(-0.905880\pi\)
0.225944 0.974140i \(-0.427454\pi\)
\(98\) 0 0
\(99\) −11.6603 −1.17190
\(100\) −2.00000 −0.200000
\(101\) 4.26795 0.424677 0.212338 0.977196i \(-0.431892\pi\)
0.212338 + 0.977196i \(0.431892\pi\)
\(102\) −5.41154 −0.535823
\(103\) 3.19615 5.53590i 0.314926 0.545468i −0.664496 0.747292i \(-0.731354\pi\)
0.979422 + 0.201824i \(0.0646869\pi\)
\(104\) 2.76795 + 5.59808i 0.271420 + 0.548937i
\(105\) 0 0
\(106\) 3.40192 5.89230i 0.330424 0.572311i
\(107\) −9.92820 17.1962i −0.959796 1.66241i −0.722991 0.690858i \(-0.757233\pi\)
−0.236805 0.971557i \(-0.576100\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) −6.19615 10.7321i −0.593484 1.02794i −0.993759 0.111549i \(-0.964419\pi\)
0.400275 0.916395i \(-0.368915\pi\)
\(110\) −14.1962 −1.35355
\(111\) 2.56218 + 4.43782i 0.243191 + 0.421219i
\(112\) 0 0
\(113\) 3.69615 + 6.40192i 0.347705 + 0.602242i 0.985841 0.167681i \(-0.0536278\pi\)
−0.638137 + 0.769923i \(0.720294\pi\)
\(114\) −1.26795 2.19615i −0.118754 0.205689i
\(115\) 2.19615 0.204792
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) −3.93782 7.96410i −0.364052 0.736281i
\(118\) 18.5885 1.71121
\(119\) 0 0
\(120\) −1.09808 + 1.90192i −0.100240 + 0.173621i
\(121\) 11.3923 1.03566
\(122\) 13.1603 + 22.7942i 1.19147 + 2.06369i
\(123\) 1.90192 3.29423i 0.171491 0.297031i
\(124\) 6.19615 0.556431
\(125\) −12.1244 −1.08444
\(126\) 0 0
\(127\) 1.19615 2.07180i 0.106141 0.183842i −0.808063 0.589097i \(-0.799484\pi\)
0.914204 + 0.405254i \(0.132817\pi\)
\(128\) 6.06218 + 10.5000i 0.535826 + 0.928078i
\(129\) −3.73205 6.46410i −0.328589 0.569132i
\(130\) −4.79423 9.69615i −0.420482 0.850409i
\(131\) 1.73205 3.00000i 0.151330 0.262111i −0.780387 0.625297i \(-0.784978\pi\)
0.931717 + 0.363186i \(0.118311\pi\)
\(132\) −1.73205 + 3.00000i −0.150756 + 0.261116i
\(133\) 0 0
\(134\) 3.63397 + 6.29423i 0.313928 + 0.543739i
\(135\) 3.46410 6.00000i 0.298142 0.516398i
\(136\) −3.69615 + 6.40192i −0.316942 + 0.548960i
\(137\) −10.9641 + 18.9904i −0.936726 + 1.62246i −0.165200 + 0.986260i \(0.552827\pi\)
−0.771526 + 0.636198i \(0.780506\pi\)
\(138\) 0.803848 1.39230i 0.0684280 0.118521i
\(139\) 10.2942 + 17.8301i 0.873145 + 1.51233i 0.858726 + 0.512436i \(0.171257\pi\)
0.0144194 + 0.999896i \(0.495410\pi\)
\(140\) 0 0
\(141\) −0.339746 + 0.588457i −0.0286118 + 0.0495570i
\(142\) 5.19615 9.00000i 0.436051 0.755263i
\(143\) 7.56218 + 15.2942i 0.632381 + 1.27897i
\(144\) −6.16025 10.6699i −0.513355 0.889156i
\(145\) 2.59808 + 4.50000i 0.215758 + 0.373705i
\(146\) −6.23205 + 10.7942i −0.515768 + 0.893337i
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) 0.464102 0.0380207 0.0190103 0.999819i \(-0.493948\pi\)
0.0190103 + 0.999819i \(0.493948\pi\)
\(150\) −1.26795 + 2.19615i −0.103528 + 0.179315i
\(151\) −1.00000 1.73205i −0.0813788 0.140952i 0.822464 0.568818i \(-0.192599\pi\)
−0.903842 + 0.427865i \(0.859266\pi\)
\(152\) −3.46410 −0.280976
\(153\) 5.25833 9.10770i 0.425111 0.736314i
\(154\) 0 0
\(155\) 10.7321 0.862019
\(156\) −2.63397 0.169873i −0.210887 0.0136007i
\(157\) −4.59808 7.96410i −0.366966 0.635605i 0.622123 0.782919i \(-0.286270\pi\)
−0.989090 + 0.147315i \(0.952937\pi\)
\(158\) −10.0526 −0.799739
\(159\) −1.43782 2.49038i −0.114027 0.197500i
\(160\) −4.50000 7.79423i −0.355756 0.616188i
\(161\) 0 0
\(162\) 3.86603 + 6.69615i 0.303744 + 0.526099i
\(163\) 5.80385 0.454592 0.227296 0.973826i \(-0.427011\pi\)
0.227296 + 0.973826i \(0.427011\pi\)
\(164\) 2.59808 + 4.50000i 0.202876 + 0.351391i
\(165\) −3.00000 + 5.19615i −0.233550 + 0.404520i
\(166\) −7.09808 12.2942i −0.550918 0.954217i
\(167\) 12.2942 21.2942i 0.951356 1.64780i 0.208861 0.977945i \(-0.433024\pi\)
0.742495 0.669852i \(-0.233642\pi\)
\(168\) 0 0
\(169\) −7.89230 + 10.3301i −0.607100 + 0.794625i
\(170\) 6.40192 11.0885i 0.491005 0.850446i
\(171\) 4.92820 0.376869
\(172\) 10.1962 0.777449
\(173\) −15.4641 −1.17571 −0.587857 0.808965i \(-0.700028\pi\)
−0.587857 + 0.808965i \(0.700028\pi\)
\(174\) 3.80385 0.288369
\(175\) 0 0
\(176\) 11.8301 + 20.4904i 0.891729 + 1.54452i
\(177\) 3.92820 6.80385i 0.295262 0.511409i
\(178\) 0.803848 1.39230i 0.0602509 0.104358i
\(179\) 6.92820 0.517838 0.258919 0.965899i \(-0.416634\pi\)
0.258919 + 0.965899i \(0.416634\pi\)
\(180\) 2.13397 + 3.69615i 0.159057 + 0.275495i
\(181\) 25.5885 1.90198 0.950988 0.309229i \(-0.100071\pi\)
0.950988 + 0.309229i \(0.100071\pi\)
\(182\) 0 0
\(183\) 11.1244 0.822336
\(184\) −1.09808 1.90192i −0.0809513 0.140212i
\(185\) −12.1244 −0.891400
\(186\) 3.92820 6.80385i 0.288030 0.498882i
\(187\) −10.0981 + 17.4904i −0.738444 + 1.27902i
\(188\) −0.464102 0.803848i −0.0338481 0.0586266i
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 1.26795 0.0917456 0.0458728 0.998947i \(-0.485393\pi\)
0.0458728 + 0.998947i \(0.485393\pi\)
\(192\) 0.732051 0.0528312
\(193\) 5.00000 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) 12.4641 21.5885i 0.894870 1.54996i
\(195\) −4.56218 0.294229i −0.326704 0.0210702i
\(196\) 0 0
\(197\) −6.00000 + 10.3923i −0.427482 + 0.740421i −0.996649 0.0818013i \(-0.973933\pi\)
0.569166 + 0.822222i \(0.307266\pi\)
\(198\) −10.0981 17.4904i −0.717639 1.24299i
\(199\) 1.00000 1.73205i 0.0708881 0.122782i −0.828403 0.560133i \(-0.810750\pi\)
0.899291 + 0.437351i \(0.144083\pi\)
\(200\) 1.73205 + 3.00000i 0.122474 + 0.212132i
\(201\) 3.07180 0.216668
\(202\) 3.69615 + 6.40192i 0.260060 + 0.450438i
\(203\) 0 0
\(204\) −1.56218 2.70577i −0.109374 0.189442i
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) 11.0718 0.771409
\(207\) 1.56218 + 2.70577i 0.108579 + 0.188064i
\(208\) −10.0000 + 15.0000i −0.693375 + 1.04006i
\(209\) −9.46410 −0.654646
\(210\) 0 0
\(211\) 6.09808 10.5622i 0.419809 0.727130i −0.576111 0.817371i \(-0.695430\pi\)
0.995920 + 0.0902411i \(0.0287638\pi\)
\(212\) 3.92820 0.269790
\(213\) −2.19615 3.80385i −0.150478 0.260635i
\(214\) 17.1962 29.7846i 1.17550 2.03603i
\(215\) 17.6603 1.20442
\(216\) −6.92820 −0.471405
\(217\) 0 0
\(218\) 10.7321 18.5885i 0.726866 1.25897i
\(219\) 2.63397 + 4.56218i 0.177988 + 0.308283i
\(220\) −4.09808 7.09808i −0.276292 0.478552i
\(221\) −15.3564 0.990381i −1.03298 0.0666202i
\(222\) −4.43782 + 7.68653i −0.297847 + 0.515886i
\(223\) −5.00000 + 8.66025i −0.334825 + 0.579934i −0.983451 0.181173i \(-0.942010\pi\)
0.648626 + 0.761107i \(0.275344\pi\)
\(224\) 0 0
\(225\) −2.46410 4.26795i −0.164273 0.284530i
\(226\) −6.40192 + 11.0885i −0.425850 + 0.737593i
\(227\) −5.83013 + 10.0981i −0.386959 + 0.670233i −0.992039 0.125932i \(-0.959808\pi\)
0.605080 + 0.796165i \(0.293141\pi\)
\(228\) 0.732051 1.26795i 0.0484812 0.0839720i
\(229\) 3.19615 5.53590i 0.211208 0.365822i −0.740885 0.671632i \(-0.765594\pi\)
0.952093 + 0.305809i \(0.0989270\pi\)
\(230\) 1.90192 + 3.29423i 0.125409 + 0.217215i
\(231\) 0 0
\(232\) 2.59808 4.50000i 0.170572 0.295439i
\(233\) −12.9282 + 22.3923i −0.846955 + 1.46697i 0.0369580 + 0.999317i \(0.488233\pi\)
−0.883913 + 0.467652i \(0.845100\pi\)
\(234\) 8.53590 12.8038i 0.558009 0.837014i
\(235\) −0.803848 1.39230i −0.0524372 0.0908240i
\(236\) 5.36603 + 9.29423i 0.349299 + 0.605003i
\(237\) −2.12436 + 3.67949i −0.137992 + 0.239009i
\(238\) 0 0
\(239\) −26.1962 −1.69449 −0.847244 0.531204i \(-0.821740\pi\)
−0.847244 + 0.531204i \(0.821740\pi\)
\(240\) −6.33975 −0.409229
\(241\) −5.40192 + 9.35641i −0.347969 + 0.602699i −0.985888 0.167404i \(-0.946462\pi\)
0.637920 + 0.770103i \(0.279795\pi\)
\(242\) 9.86603 + 17.0885i 0.634212 + 1.09849i
\(243\) 15.2679 0.979439
\(244\) −7.59808 + 13.1603i −0.486417 + 0.842499i
\(245\) 0 0
\(246\) 6.58846 0.420065
\(247\) −3.19615 6.46410i −0.203366 0.411301i
\(248\) −5.36603 9.29423i −0.340743 0.590184i
\(249\) −6.00000 −0.380235
\(250\) −10.5000 18.1865i −0.664078 1.15022i
\(251\) −11.1962 19.3923i −0.706695 1.22403i −0.966076 0.258256i \(-0.916852\pi\)
0.259382 0.965775i \(-0.416481\pi\)
\(252\) 0 0
\(253\) −3.00000 5.19615i −0.188608 0.326679i
\(254\) 4.14359 0.259992
\(255\) −2.70577 4.68653i −0.169442 0.293482i
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) −9.06218 15.6962i −0.565283 0.979099i −0.997023 0.0771011i \(-0.975434\pi\)
0.431740 0.901998i \(-0.357900\pi\)
\(258\) 6.46410 11.1962i 0.402437 0.697042i
\(259\) 0 0
\(260\) 3.46410 5.19615i 0.214834 0.322252i
\(261\) −3.69615 + 6.40192i −0.228786 + 0.396269i
\(262\) 6.00000 0.370681
\(263\) 4.73205 0.291791 0.145895 0.989300i \(-0.453394\pi\)
0.145895 + 0.989300i \(0.453394\pi\)
\(264\) 6.00000 0.369274
\(265\) 6.80385 0.417957
\(266\) 0 0
\(267\) −0.339746 0.588457i −0.0207921 0.0360130i
\(268\) −2.09808 + 3.63397i −0.128160 + 0.221980i
\(269\) 9.46410 16.3923i 0.577036 0.999456i −0.418781 0.908087i \(-0.637542\pi\)
0.995817 0.0913690i \(-0.0291243\pi\)
\(270\) 12.0000 0.730297
\(271\) 8.09808 + 14.0263i 0.491923 + 0.852036i 0.999957 0.00930143i \(-0.00296078\pi\)
−0.508034 + 0.861337i \(0.669627\pi\)
\(272\) −21.3397 −1.29391
\(273\) 0 0
\(274\) −37.9808 −2.29450
\(275\) 4.73205 + 8.19615i 0.285353 + 0.494247i
\(276\) 0.928203 0.0558713
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) −17.8301 + 30.8827i −1.06938 + 1.85222i
\(279\) 7.63397 + 13.2224i 0.457034 + 0.791606i
\(280\) 0 0
\(281\) −7.39230 −0.440988 −0.220494 0.975388i \(-0.570767\pi\)
−0.220494 + 0.975388i \(0.570767\pi\)
\(282\) −1.17691 −0.0700842
\(283\) 0.196152 0.0116601 0.00583003 0.999983i \(-0.498144\pi\)
0.00583003 + 0.999983i \(0.498144\pi\)
\(284\) 6.00000 0.356034
\(285\) 1.26795 2.19615i 0.0751068 0.130089i
\(286\) −16.3923 + 24.5885i −0.969297 + 1.45395i
\(287\) 0 0
\(288\) 6.40192 11.0885i 0.377237 0.653394i
\(289\) −0.607695 1.05256i −0.0357468 0.0619152i
\(290\) −4.50000 + 7.79423i −0.264249 + 0.457693i
\(291\) −5.26795 9.12436i −0.308813 0.534879i
\(292\) −7.19615 −0.421123
\(293\) −5.59808 9.69615i −0.327043 0.566455i 0.654881 0.755732i \(-0.272719\pi\)
−0.981924 + 0.189277i \(0.939386\pi\)
\(294\) 0 0
\(295\) 9.29423 + 16.0981i 0.541131 + 0.937266i
\(296\) 6.06218 + 10.5000i 0.352357 + 0.610300i
\(297\) −18.9282 −1.09833
\(298\) 0.401924 + 0.696152i 0.0232828 + 0.0403270i
\(299\) 2.53590 3.80385i 0.146655 0.219982i
\(300\) −1.46410 −0.0845299
\(301\) 0 0
\(302\) 1.73205 3.00000i 0.0996683 0.172631i
\(303\) 3.12436 0.179490
\(304\) −5.00000 8.66025i −0.286770 0.496700i
\(305\) −13.1603 + 22.7942i −0.753554 + 1.30519i
\(306\) 18.2154 1.04130
\(307\) −26.5885 −1.51748 −0.758742 0.651392i \(-0.774186\pi\)
−0.758742 + 0.651392i \(0.774186\pi\)
\(308\) 0 0
\(309\) 2.33975 4.05256i 0.133103 0.230542i
\(310\) 9.29423 + 16.0981i 0.527877 + 0.914309i
\(311\) 2.36603 + 4.09808i 0.134165 + 0.232381i 0.925278 0.379289i \(-0.123831\pi\)
−0.791113 + 0.611670i \(0.790498\pi\)
\(312\) 2.02628 + 4.09808i 0.114715 + 0.232008i
\(313\) −6.39230 + 11.0718i −0.361314 + 0.625815i −0.988177 0.153315i \(-0.951005\pi\)
0.626863 + 0.779129i \(0.284339\pi\)
\(314\) 7.96410 13.7942i 0.449440 0.778453i
\(315\) 0 0
\(316\) −2.90192 5.02628i −0.163246 0.282750i
\(317\) −0.232051 + 0.401924i −0.0130333 + 0.0225743i −0.872468 0.488670i \(-0.837482\pi\)
0.859435 + 0.511245i \(0.170815\pi\)
\(318\) 2.49038 4.31347i 0.139654 0.241887i
\(319\) 7.09808 12.2942i 0.397416 0.688345i
\(320\) −0.866025 + 1.50000i −0.0484123 + 0.0838525i
\(321\) −7.26795 12.5885i −0.405657 0.702619i
\(322\) 0 0
\(323\) 4.26795 7.39230i 0.237475 0.411319i
\(324\) −2.23205 + 3.86603i −0.124003 + 0.214779i
\(325\) −4.00000 + 6.00000i −0.221880 + 0.332820i
\(326\) 5.02628 + 8.70577i 0.278380 + 0.482168i
\(327\) −4.53590 7.85641i −0.250836 0.434460i
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) 0 0
\(330\) −10.3923 −0.572078
\(331\) −26.9808 −1.48300 −0.741498 0.670955i \(-0.765885\pi\)
−0.741498 + 0.670955i \(0.765885\pi\)
\(332\) 4.09808 7.09808i 0.224911 0.389558i
\(333\) −8.62436 14.9378i −0.472612 0.818588i
\(334\) 42.5885 2.33034
\(335\) −3.63397 + 6.29423i −0.198545 + 0.343890i
\(336\) 0 0
\(337\) 11.0000 0.599208 0.299604 0.954064i \(-0.403145\pi\)
0.299604 + 0.954064i \(0.403145\pi\)
\(338\) −22.3301 2.89230i −1.21460 0.157321i
\(339\) 2.70577 + 4.68653i 0.146957 + 0.254538i
\(340\) 7.39230 0.400904
\(341\) −14.6603 25.3923i −0.793897 1.37507i
\(342\) 4.26795 + 7.39230i 0.230784 + 0.399730i
\(343\) 0 0
\(344\) −8.83013 15.2942i −0.476089 0.824610i
\(345\) 1.60770 0.0865554
\(346\) −13.3923 23.1962i −0.719975 1.24703i
\(347\) −5.36603 + 9.29423i −0.288063 + 0.498940i −0.973347 0.229336i \(-0.926345\pi\)
0.685284 + 0.728276i \(0.259678\pi\)
\(348\) 1.09808 + 1.90192i 0.0588631 + 0.101954i
\(349\) 8.39230 14.5359i 0.449230 0.778089i −0.549106 0.835753i \(-0.685032\pi\)
0.998336 + 0.0576637i \(0.0183651\pi\)
\(350\) 0 0
\(351\) −6.39230 12.9282i −0.341196 0.690056i
\(352\) −12.2942 + 21.2942i −0.655285 + 1.13499i
\(353\) −3.33975 −0.177757 −0.0888784 0.996042i \(-0.528328\pi\)
−0.0888784 + 0.996042i \(0.528328\pi\)
\(354\) 13.6077 0.723241
\(355\) 10.3923 0.551566
\(356\) 0.928203 0.0491947
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) −2.53590 + 4.39230i −0.133840 + 0.231817i −0.925154 0.379593i \(-0.876064\pi\)
0.791314 + 0.611410i \(0.209397\pi\)
\(360\) 3.69615 6.40192i 0.194804 0.337411i
\(361\) −15.0000 −0.789474
\(362\) 22.1603 + 38.3827i 1.16472 + 2.01735i
\(363\) 8.33975 0.437723
\(364\) 0 0
\(365\) −12.4641 −0.652401
\(366\) 9.63397 + 16.6865i 0.503576 + 0.872219i
\(367\) 6.19615 0.323437 0.161718 0.986837i \(-0.448296\pi\)
0.161718 + 0.986837i \(0.448296\pi\)
\(368\) 3.16987 5.49038i 0.165241 0.286206i
\(369\) −6.40192 + 11.0885i −0.333271 + 0.577242i
\(370\) −10.5000 18.1865i −0.545869 0.945473i
\(371\) 0 0
\(372\) 4.53590 0.235175
\(373\) 9.39230 0.486315 0.243158 0.969987i \(-0.421817\pi\)
0.243158 + 0.969987i \(0.421817\pi\)
\(374\) −34.9808 −1.80881
\(375\) −8.87564 −0.458336
\(376\) −0.803848 + 1.39230i −0.0414553 + 0.0718026i
\(377\) 10.7942 + 0.696152i 0.555931 + 0.0358537i
\(378\) 0 0
\(379\) 2.29423 3.97372i 0.117847 0.204116i −0.801067 0.598574i \(-0.795734\pi\)
0.918914 + 0.394458i \(0.129068\pi\)
\(380\) 1.73205 + 3.00000i 0.0888523 + 0.153897i
\(381\) 0.875644 1.51666i 0.0448606 0.0777009i
\(382\) 1.09808 + 1.90192i 0.0561825 + 0.0973109i
\(383\) −5.66025 −0.289225 −0.144613 0.989488i \(-0.546194\pi\)
−0.144613 + 0.989488i \(0.546194\pi\)
\(384\) 4.43782 + 7.68653i 0.226467 + 0.392252i
\(385\) 0 0
\(386\) 4.33013 + 7.50000i 0.220398 + 0.381740i
\(387\) 12.5622 + 21.7583i 0.638571 + 1.10604i
\(388\) 14.3923 0.730659
\(389\) 15.2321 + 26.3827i 0.772296 + 1.33766i 0.936302 + 0.351196i \(0.114225\pi\)
−0.164006 + 0.986459i \(0.552442\pi\)
\(390\) −3.50962 7.09808i −0.177716 0.359425i
\(391\) 5.41154 0.273673
\(392\) 0 0
\(393\) 1.26795 2.19615i 0.0639596 0.110781i
\(394\) −20.7846 −1.04711
\(395\) −5.02628 8.70577i −0.252900 0.438035i
\(396\) 5.83013 10.0981i 0.292975 0.507447i
\(397\) −22.7846 −1.14353 −0.571763 0.820419i \(-0.693740\pi\)
−0.571763 + 0.820419i \(0.693740\pi\)
\(398\) 3.46410 0.173640
\(399\) 0 0
\(400\) −5.00000 + 8.66025i −0.250000 + 0.433013i
\(401\) −8.42820 14.5981i −0.420884 0.728993i 0.575142 0.818054i \(-0.304947\pi\)
−0.996026 + 0.0890606i \(0.971614\pi\)
\(402\) 2.66025 + 4.60770i 0.132681 + 0.229811i
\(403\) 12.3923 18.5885i 0.617305 0.925957i
\(404\) −2.13397 + 3.69615i −0.106169 + 0.183890i
\(405\) −3.86603 + 6.69615i −0.192104 + 0.332734i
\(406\) 0 0
\(407\) 16.5622 + 28.6865i 0.820957 + 1.42194i
\(408\) −2.70577 + 4.68653i −0.133956 + 0.232018i
\(409\) −13.5981 + 23.5526i −0.672382 + 1.16460i 0.304845 + 0.952402i \(0.401395\pi\)
−0.977227 + 0.212197i \(0.931938\pi\)
\(410\) −7.79423 + 13.5000i −0.384930 + 0.666717i
\(411\) −8.02628 + 13.9019i −0.395907 + 0.685731i
\(412\) 3.19615 + 5.53590i 0.157463 + 0.272734i
\(413\) 0 0
\(414\) −2.70577 + 4.68653i −0.132981 + 0.230331i
\(415\) 7.09808 12.2942i 0.348431 0.603500i
\(416\) −18.6962 1.20577i −0.916654 0.0591178i
\(417\) 7.53590 + 13.0526i 0.369035 + 0.639187i
\(418\) −8.19615 14.1962i −0.400887 0.694357i
\(419\) −10.9019 + 18.8827i −0.532594 + 0.922480i 0.466682 + 0.884425i \(0.345449\pi\)
−0.999276 + 0.0380543i \(0.987884\pi\)
\(420\) 0 0
\(421\) 30.1769 1.47073 0.735366 0.677670i \(-0.237010\pi\)
0.735366 + 0.677670i \(0.237010\pi\)
\(422\) 21.1244 1.02832
\(423\) 1.14359 1.98076i 0.0556034 0.0963079i
\(424\) −3.40192 5.89230i −0.165212 0.286156i
\(425\) −8.53590 −0.414052
\(426\) 3.80385 6.58846i 0.184297 0.319212i
\(427\) 0 0
\(428\) 19.8564 0.959796
\(429\) 5.53590 + 11.1962i 0.267276 + 0.540555i
\(430\) 15.2942 + 26.4904i 0.737553 + 1.27748i
\(431\) 35.3205 1.70133 0.850665 0.525709i \(-0.176200\pi\)
0.850665 + 0.525709i \(0.176200\pi\)
\(432\) −10.0000 17.3205i −0.481125 0.833333i
\(433\) 8.79423 + 15.2321i 0.422624 + 0.732006i 0.996195 0.0871498i \(-0.0277759\pi\)
−0.573572 + 0.819155i \(0.694443\pi\)
\(434\) 0 0
\(435\) 1.90192 + 3.29423i 0.0911903 + 0.157946i
\(436\) 12.3923 0.593484
\(437\) 1.26795 + 2.19615i 0.0606542 + 0.105056i
\(438\) −4.56218 + 7.90192i −0.217989 + 0.377569i
\(439\) −8.29423 14.3660i −0.395862 0.685653i 0.597349 0.801982i \(-0.296221\pi\)
−0.993211 + 0.116329i \(0.962887\pi\)
\(440\) −7.09808 + 12.2942i −0.338388 + 0.586104i
\(441\) 0 0
\(442\) −11.8135 23.8923i −0.561909 1.13644i
\(443\) 5.66025 9.80385i 0.268927 0.465795i −0.699658 0.714478i \(-0.746664\pi\)
0.968585 + 0.248683i \(0.0799977\pi\)
\(444\) −5.12436 −0.243191
\(445\) 1.60770 0.0762121
\(446\) −17.3205 −0.820150
\(447\) 0.339746 0.0160694
\(448\) 0 0
\(449\) 6.00000 + 10.3923i 0.283158 + 0.490443i 0.972161 0.234315i \(-0.0752847\pi\)
−0.689003 + 0.724758i \(0.741951\pi\)
\(450\) 4.26795 7.39230i 0.201193 0.348477i
\(451\) 12.2942 21.2942i 0.578913 1.00271i
\(452\) −7.39230 −0.347705
\(453\) −0.732051 1.26795i −0.0343947 0.0595734i
\(454\) −20.1962 −0.947852
\(455\) 0 0
\(456\) −2.53590 −0.118754
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) 11.0718 0.517351
\(459\) 8.53590 14.7846i 0.398422 0.690086i
\(460\) −1.09808 + 1.90192i −0.0511981 + 0.0886777i
\(461\) 7.79423 + 13.5000i 0.363013 + 0.628758i 0.988455 0.151513i \(-0.0484146\pi\)
−0.625442 + 0.780271i \(0.715081\pi\)
\(462\) 0 0
\(463\) 26.5885 1.23567 0.617835 0.786308i \(-0.288010\pi\)
0.617835 + 0.786308i \(0.288010\pi\)
\(464\) 15.0000 0.696358
\(465\) 7.85641 0.364332
\(466\) −44.7846 −2.07461
\(467\) −9.75833 + 16.9019i −0.451562 + 0.782128i −0.998483 0.0550561i \(-0.982466\pi\)
0.546922 + 0.837184i \(0.315800\pi\)
\(468\) 8.86603 + 0.571797i 0.409832 + 0.0264313i
\(469\) 0 0
\(470\) 1.39230 2.41154i 0.0642222 0.111236i
\(471\) −3.36603 5.83013i −0.155098 0.268638i
\(472\) 9.29423 16.0981i 0.427802 0.740974i
\(473\) −24.1244 41.7846i −1.10924 1.92126i
\(474\) −7.35898 −0.338009
\(475\) −2.00000 3.46410i −0.0917663 0.158944i
\(476\) 0 0
\(477\) 4.83975 + 8.38269i 0.221597 + 0.383817i
\(478\) −22.6865 39.2942i −1.03766 1.79728i
\(479\) −4.73205 −0.216213 −0.108106 0.994139i \(-0.534479\pi\)
−0.108106 + 0.994139i \(0.534479\pi\)
\(480\) −3.29423 5.70577i −0.150360 0.260432i
\(481\) −14.0000 + 21.0000i −0.638345 + 0.957518i
\(482\) −18.7128 −0.852345
\(483\) 0 0
\(484\) −5.69615 + 9.86603i −0.258916 + 0.448456i
\(485\) 24.9282 1.13193
\(486\) 13.2224 + 22.9019i 0.599782 + 1.03885i
\(487\) 0.392305 0.679492i 0.0177770 0.0307907i −0.857000 0.515316i \(-0.827674\pi\)
0.874777 + 0.484526i \(0.161008\pi\)
\(488\) 26.3205 1.19147
\(489\) 4.24871 0.192133
\(490\) 0 0
\(491\) −14.1962 + 24.5885i −0.640663 + 1.10966i 0.344622 + 0.938742i \(0.388007\pi\)
−0.985285 + 0.170920i \(0.945326\pi\)
\(492\) 1.90192 + 3.29423i 0.0857453 + 0.148515i
\(493\) 6.40192 + 11.0885i 0.288328 + 0.499399i
\(494\) 6.92820 10.3923i 0.311715 0.467572i
\(495\) 10.0981 17.4904i 0.453875 0.786134i
\(496\) 15.4904 26.8301i 0.695539 1.20471i
\(497\) 0 0
\(498\) −5.19615 9.00000i −0.232845 0.403300i
\(499\) −6.49038 + 11.2417i −0.290549 + 0.503246i −0.973940 0.226807i \(-0.927171\pi\)
0.683390 + 0.730053i \(0.260505\pi\)
\(500\) 6.06218 10.5000i 0.271109 0.469574i
\(501\) 9.00000 15.5885i 0.402090 0.696441i
\(502\) 19.3923 33.5885i 0.865521 1.49913i
\(503\) 6.29423 + 10.9019i 0.280646 + 0.486093i 0.971544 0.236859i \(-0.0761181\pi\)
−0.690898 + 0.722952i \(0.742785\pi\)
\(504\) 0 0
\(505\) −3.69615 + 6.40192i −0.164477 + 0.284882i
\(506\) 5.19615 9.00000i 0.230997 0.400099i
\(507\) −5.77757 + 7.56218i −0.256591 + 0.335848i
\(508\) 1.19615 + 2.07180i 0.0530707 + 0.0919211i
\(509\) 5.13397 + 8.89230i 0.227559 + 0.394144i 0.957084 0.289810i \(-0.0935921\pi\)
−0.729525 + 0.683954i \(0.760259\pi\)
\(510\) 4.68653 8.11731i 0.207523 0.359441i
\(511\) 0 0
\(512\) −8.66025 −0.382733
\(513\) 8.00000 0.353209
\(514\) 15.6962 27.1865i 0.692328 1.19915i
\(515\) 5.53590 + 9.58846i 0.243941 + 0.422518i
\(516\) 7.46410 0.328589
\(517\) −2.19615 + 3.80385i −0.0965867 + 0.167293i
\(518\) 0 0
\(519\) −11.3205 −0.496915
\(520\) −10.7942 0.696152i −0.473358 0.0305283i
\(521\) 0.0621778 + 0.107695i 0.00272406 + 0.00471821i 0.867384 0.497639i \(-0.165800\pi\)
−0.864660 + 0.502357i \(0.832466\pi\)
\(522\) −12.8038 −0.560409
\(523\) 16.5885 + 28.7321i 0.725363 + 1.25636i 0.958825 + 0.283999i \(0.0916612\pi\)
−0.233462 + 0.972366i \(0.575005\pi\)
\(524\) 1.73205 + 3.00000i 0.0756650 + 0.131056i
\(525\) 0 0
\(526\) 4.09808 + 7.09808i 0.178685 + 0.309491i
\(527\) 26.4449 1.15196
\(528\) 8.66025 + 15.0000i 0.376889 + 0.652791i
\(529\) 10.6962 18.5263i 0.465050 0.805490i
\(530\) 5.89230 + 10.2058i 0.255945 + 0.443310i
\(531\) −13.2224 + 22.9019i −0.573805 + 0.993859i
\(532\) 0 0
\(533\) 18.6962 + 1.20577i 0.809820 + 0.0522278i
\(534\) 0.588457 1.01924i 0.0254650 0.0441067i
\(535\) 34.3923 1.48691
\(536\) 7.26795 0.313928
\(537\) 5.07180 0.218864
\(538\) 32.7846 1.41344
\(539\) 0 0
\(540\) 3.46410 + 6.00000i 0.149071 + 0.258199i
\(541\) 17.6962 30.6506i 0.760817 1.31777i −0.181613 0.983370i \(-0.558132\pi\)
0.942430 0.334404i \(-0.108535\pi\)
\(542\) −14.0263 + 24.2942i −0.602480 + 1.04353i
\(543\) 18.7321 0.803869
\(544\) −11.0885 19.2058i −0.475414 0.823441i
\(545\) 21.4641 0.919421
\(546\) 0 0
\(547\) 28.1962 1.20558 0.602790 0.797900i \(-0.294056\pi\)
0.602790 + 0.797900i \(0.294056\pi\)
\(548\) −10.9641 18.9904i −0.468363 0.811229i
\(549\) −37.4449 −1.59811
\(550\) −8.19615 + 14.1962i −0.349485 + 0.605326i
\(551\) −3.00000 + 5.19615i −0.127804 + 0.221364i
\(552\) −0.803848 1.39230i −0.0342140 0.0592604i
\(553\) 0 0
\(554\) −29.4449 −1.25099
\(555\) −8.87564 −0.376750
\(556\) −20.5885 −0.873145
\(557\) −25.6410 −1.08644 −0.543222 0.839589i \(-0.682796\pi\)
−0.543222 + 0.839589i \(0.682796\pi\)
\(558\) −13.2224 + 22.9019i −0.559750 + 0.969516i
\(559\) 20.3923 30.5885i 0.862503 1.29375i
\(560\) 0 0
\(561\) −7.39230 + 12.8038i −0.312103 + 0.540579i
\(562\) −6.40192 11.0885i −0.270049 0.467738i
\(563\) −5.02628 + 8.70577i −0.211832 + 0.366905i −0.952288 0.305201i \(-0.901276\pi\)
0.740456 + 0.672105i \(0.234610\pi\)
\(564\) −0.339746 0.588457i −0.0143059 0.0247785i
\(565\) −12.8038 −0.538662
\(566\) 0.169873 + 0.294229i 0.00714029 + 0.0123674i
\(567\) 0 0
\(568\) −5.19615 9.00000i −0.218026 0.377632i
\(569\) −14.5359 25.1769i −0.609377 1.05547i −0.991343 0.131295i \(-0.958086\pi\)
0.381967 0.924176i \(-0.375247\pi\)
\(570\) 4.39230 0.183973
\(571\) 12.3923 + 21.4641i 0.518602 + 0.898245i 0.999766 + 0.0216144i \(0.00688062\pi\)
−0.481165 + 0.876630i \(0.659786\pi\)
\(572\) −17.0263 1.09808i −0.711905 0.0459129i
\(573\) 0.928203 0.0387762
\(574\) 0 0
\(575\) 1.26795 2.19615i 0.0528771 0.0915859i
\(576\) −2.46410 −0.102671
\(577\) 16.4019 + 28.4090i 0.682821 + 1.18268i 0.974116 + 0.226048i \(0.0725805\pi\)
−0.291295 + 0.956633i \(0.594086\pi\)
\(578\) 1.05256 1.82309i 0.0437807 0.0758304i
\(579\) 3.66025 0.152115
\(580\) −5.19615 −0.215758
\(581\) 0 0
\(582\) 9.12436 15.8038i 0.378217 0.655091i
\(583\) −9.29423 16.0981i −0.384928 0.666714i
\(584\) 6.23205 + 10.7942i 0.257884 + 0.446668i
\(585\) 15.3564 + 0.990381i 0.634909 + 0.0409472i
\(586\) 9.69615 16.7942i 0.400544 0.693763i
\(587\) −2.19615 + 3.80385i −0.0906449 + 0.157002i −0.907783 0.419441i \(-0.862226\pi\)
0.817138 + 0.576442i \(0.195559\pi\)
\(588\) 0 0
\(589\) 6.19615 + 10.7321i 0.255308 + 0.442206i
\(590\) −16.0981 + 27.8827i −0.662747 + 1.14791i
\(591\) −4.39230 + 7.60770i −0.180675 + 0.312939i
\(592\) −17.5000 + 30.3109i −0.719246 + 1.24577i
\(593\) 20.7224 35.8923i 0.850968 1.47392i −0.0293672 0.999569i \(-0.509349\pi\)
0.880335 0.474352i \(-0.157317\pi\)
\(594\) −16.3923 28.3923i −0.672584 1.16495i
\(595\) 0 0
\(596\) −0.232051 + 0.401924i −0.00950517 + 0.0164634i
\(597\) 0.732051 1.26795i 0.0299608 0.0518937i
\(598\) 7.90192 + 0.509619i 0.323134 + 0.0208399i
\(599\) −8.07180 13.9808i −0.329805 0.571238i 0.652668 0.757644i \(-0.273650\pi\)
−0.982473 + 0.186405i \(0.940316\pi\)
\(600\) 1.26795 + 2.19615i 0.0517638 + 0.0896575i
\(601\) 10.9904 19.0359i 0.448307 0.776490i −0.549969 0.835185i \(-0.685360\pi\)
0.998276 + 0.0586946i \(0.0186938\pi\)
\(602\) 0 0
\(603\) −10.3397 −0.421067
\(604\) 2.00000 0.0813788
\(605\) −9.86603 + 17.0885i −0.401111 + 0.694745i
\(606\) 2.70577 + 4.68653i 0.109914 + 0.190377i
\(607\) −6.39230 −0.259456 −0.129728 0.991550i \(-0.541410\pi\)
−0.129728 + 0.991550i \(0.541410\pi\)
\(608\) 5.19615 9.00000i 0.210732 0.364998i
\(609\) 0 0
\(610\) −45.5885 −1.84582
\(611\) −3.33975 0.215390i −0.135112 0.00871376i
\(612\) 5.25833 + 9.10770i 0.212555 + 0.368157i
\(613\) −17.3923 −0.702469 −0.351234 0.936288i \(-0.614238\pi\)
−0.351234 + 0.936288i \(0.614238\pi\)
\(614\) −23.0263 39.8827i −0.929265 1.60953i
\(615\) 3.29423 + 5.70577i 0.132836 + 0.230079i
\(616\) 0 0
\(617\) −14.3038 24.7750i −0.575851 0.997404i −0.995949 0.0899245i \(-0.971337\pi\)
0.420097 0.907479i \(-0.361996\pi\)
\(618\) 8.10512 0.326036
\(619\) −18.6865 32.3660i −0.751075 1.30090i −0.947302 0.320342i \(-0.896202\pi\)
0.196227 0.980559i \(-0.437131\pi\)
\(620\) −5.36603 + 9.29423i −0.215505 + 0.373265i
\(621\) 2.53590 + 4.39230i 0.101762 + 0.176257i
\(622\) −4.09808 + 7.09808i −0.164318 + 0.284607i
\(623\) 0 0
\(624\) −7.32051 + 10.9808i −0.293055 + 0.439582i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −22.1436 −0.885036
\(627\) −6.92820 −0.276686
\(628\) 9.19615 0.366966
\(629\) −29.8756 −1.19122
\(630\) 0 0
\(631\) −14.3923 24.9282i −0.572949 0.992376i −0.996261 0.0863924i \(-0.972466\pi\)
0.423313 0.905984i \(-0.360867\pi\)
\(632\) −5.02628 + 8.70577i −0.199935 + 0.346297i
\(633\) 4.46410 7.73205i 0.177432 0.307321i
\(634\) −0.803848 −0.0319249
\(635\) 2.07180 + 3.58846i 0.0822167 + 0.142404i
\(636\) 2.87564 0.114027
\(637\) 0 0
\(638\) 24.5885 0.973466
\(639\) 7.39230 + 12.8038i 0.292435 + 0.506512i
\(640\) −21.0000 −0.830098
\(641\) −0.571797 + 0.990381i −0.0225846 + 0.0391177i −0.877097 0.480314i \(-0.840523\pi\)
0.854512 + 0.519431i \(0.173856\pi\)
\(642\) 12.5885 21.8038i 0.496827 0.860529i
\(643\) 20.3923 + 35.3205i 0.804194 + 1.39290i 0.916834 + 0.399269i \(0.130736\pi\)
−0.112640 + 0.993636i \(0.535931\pi\)
\(644\) 0 0
\(645\) 12.9282 0.509048
\(646\) 14.7846 0.581693
\(647\) 45.0333 1.77044 0.885221 0.465170i \(-0.154007\pi\)
0.885221 + 0.465170i \(0.154007\pi\)
\(648\) 7.73205 0.303744
\(649\) 25.3923 43.9808i 0.996735 1.72640i
\(650\) −12.4641 0.803848i −0.488882 0.0315295i
\(651\) 0 0
\(652\) −2.90192 + 5.02628i −0.113648 + 0.196844i
\(653\) 5.07180 + 8.78461i 0.198475 + 0.343768i 0.948034 0.318169i \(-0.103068\pi\)
−0.749559 + 0.661937i \(0.769735\pi\)
\(654\) 7.85641 13.6077i 0.307210 0.532103i
\(655\) 3.00000 + 5.19615i 0.117220 + 0.203030i
\(656\) 25.9808 1.01438
\(657\) −8.86603 15.3564i −0.345897 0.599110i
\(658\) 0 0
\(659\) −3.80385 6.58846i −0.148177 0.256650i 0.782377 0.622805i \(-0.214007\pi\)
−0.930554 + 0.366156i \(0.880674\pi\)
\(660\) −3.00000 5.19615i −0.116775 0.202260i
\(661\) 22.8038 0.886967 0.443483 0.896283i \(-0.353742\pi\)
0.443483 + 0.896283i \(0.353742\pi\)
\(662\) −23.3660 40.4711i −0.908146 1.57296i
\(663\) −11.2417 0.725009i −0.436590 0.0281570i
\(664\) −14.1962 −0.550918
\(665\) 0 0
\(666\) 14.9378 25.8731i 0.578829 1.00256i
\(667\) −3.80385 −0.147286
\(668\) 12.2942 + 21.2942i 0.475678 + 0.823898i
\(669\) −3.66025 + 6.33975i −0.141514 + 0.245109i
\(670\) −12.5885 −0.486335
\(671\) 71.9090 2.77601
\(672\) 0 0
\(673\) −9.08846 + 15.7417i −0.350334 + 0.606797i −0.986308 0.164914i \(-0.947265\pi\)
0.635974 + 0.771711i \(0.280599\pi\)
\(674\) 9.52628 + 16.5000i 0.366939 + 0.635556i
\(675\) −4.00000 6.92820i −0.153960 0.266667i
\(676\) −5.00000 12.0000i −0.192308 0.461538i
\(677\) −18.4641 + 31.9808i −0.709633 + 1.22912i 0.255360 + 0.966846i \(0.417806\pi\)
−0.964993 + 0.262275i \(0.915527\pi\)
\(678\) −4.68653 + 8.11731i −0.179985 + 0.311744i
\(679\) 0 0
\(680\) −6.40192 11.0885i −0.245503 0.425223i
\(681\) −4.26795 + 7.39230i −0.163548 + 0.283274i
\(682\) 25.3923 43.9808i 0.972322 1.68411i
\(683\) −4.26795 + 7.39230i −0.163309 + 0.282859i −0.936053 0.351858i \(-0.885550\pi\)
0.772745 + 0.634717i \(0.218883\pi\)
\(684\) −2.46410 + 4.26795i −0.0942173 + 0.163189i
\(685\) −18.9904 32.8923i −0.725585 1.25675i
\(686\) 0 0
\(687\) 2.33975 4.05256i 0.0892669 0.154615i
\(688\) 25.4904 44.1506i 0.971812 1.68323i
\(689\) 7.85641 11.7846i 0.299305 0.448958i
\(690\) 1.39230 + 2.41154i 0.0530041 + 0.0918059i
\(691\) −10.1962 17.6603i −0.387880 0.671828i 0.604284 0.796769i \(-0.293459\pi\)
−0.992164 + 0.124941i \(0.960126\pi\)
\(692\) 7.73205 13.3923i 0.293928 0.509099i
\(693\) 0 0
\(694\) −18.5885 −0.705608
\(695\) −35.6603 −1.35267
\(696\) 1.90192 3.29423i 0.0720922 0.124867i
\(697\) 11.0885 + 19.2058i 0.420005 + 0.727470i
\(698\) 29.0718 1.10038
\(699\) −9.46410 + 16.3923i −0.357965 + 0.620014i
\(700\) 0 0
\(701\) −20.7846 −0.785024 −0.392512 0.919747i \(-0.628394\pi\)
−0.392512 + 0.919747i \(0.628394\pi\)
\(702\) 13.8564 20.7846i 0.522976 0.784465i
\(703\) −7.00000 12.1244i −0.264010 0.457279i
\(704\) 4.73205 0.178346
\(705\) −0.588457 1.01924i −0.0221626 0.0383867i
\(706\) −2.89230 5.00962i −0.108853 0.188539i
\(707\) 0 0
\(708\) 3.92820 + 6.80385i 0.147631 + 0.255704i
\(709\) −32.1769 −1.20843 −0.604215 0.796822i \(-0.706513\pi\)
−0.604215 + 0.796822i \(0.706513\pi\)
\(710\) 9.00000 + 15.5885i 0.337764 + 0.585024i
\(711\) 7.15064 12.3853i 0.268170 0.464484i
\(712\) −0.803848 1.39230i −0.0301255 0.0521788i
\(713\) −3.92820 + 6.80385i −0.147112 + 0.254806i
\(714\) 0 0
\(715\) −29.4904 1.90192i −1.10288 0.0711279i
\(716\) −3.46410 + 6.00000i −0.129460 + 0.224231i
\(717\) −19.1769 −0.716175
\(718\) −8.78461 −0.327839
\(719\) 10.7321 0.400238 0.200119 0.979772i \(-0.435867\pi\)
0.200119 + 0.979772i \(0.435867\pi\)
\(720\) 21.3397 0.795285
\(721\) 0 0
\(722\) −12.9904 22.5000i −0.483452 0.837363i
\(723\) −3.95448 + 6.84936i −0.147069 + 0.254731i
\(724\) −12.7942 + 22.1603i −0.475494 + 0.823579i
\(725\) 6.00000 0.222834
\(726\) 7.22243 + 12.5096i 0.268050 + 0.464276i
\(727\) −21.1769 −0.785408 −0.392704 0.919665i \(-0.628460\pi\)
−0.392704 + 0.919665i \(0.628460\pi\)
\(728\) 0 0
\(729\) −2.21539 −0.0820515
\(730\) −10.7942 18.6962i −0.399512 0.691976i
\(731\) 43.5167 1.60952
\(732\) −5.56218 + 9.63397i −0.205584 + 0.356082i
\(733\) −3.79423 + 6.57180i −0.140143 + 0.242735i −0.927550 0.373698i \(-0.878090\pi\)
0.787407 + 0.616433i \(0.211423\pi\)
\(734\) 5.36603 + 9.29423i 0.198064 + 0.343056i
\(735\) 0 0
\(736\) 6.58846 0.242854
\(737\) 19.8564 0.731420
\(738\) −22.1769 −0.816344
\(739\) −0.784610 −0.0288623 −0.0144312 0.999896i \(-0.504594\pi\)
−0.0144312 + 0.999896i \(0.504594\pi\)
\(740\) 6.06218 10.5000i 0.222850 0.385988i
\(741\) −2.33975 4.73205i −0.0859527 0.173836i
\(742\) 0 0
\(743\) 14.1962 24.5885i 0.520806 0.902063i −0.478901 0.877869i \(-0.658965\pi\)
0.999707 0.0241941i \(-0.00770196\pi\)
\(744\) −3.92820 6.80385i −0.144015 0.249441i
\(745\) −0.401924 + 0.696152i −0.0147253 + 0.0255051i
\(746\) 8.13397 + 14.0885i 0.297806 + 0.515815i
\(747\) 20.1962 0.738939
\(748\) −10.0981 17.4904i −0.369222 0.639512i
\(749\) 0 0
\(750\) −7.68653 13.3135i −0.280673 0.486139i
\(751\) −23.0981 40.0070i −0.842861 1.45988i −0.887466 0.460873i \(-0.847536\pi\)
0.0446053 0.999005i \(-0.485797\pi\)
\(752\) −4.64102 −0.169240
\(753\) −8.19615 14.1962i −0.298684 0.517337i
\(754\) 8.30385 + 16.7942i 0.302408 + 0.611610i
\(755\) 3.46410 0.126072
\(756\) 0 0
\(757\) 8.00000 13.8564i 0.290765 0.503620i −0.683226 0.730207i \(-0.739424\pi\)
0.973991 + 0.226587i \(0.0727569\pi\)
\(758\) 7.94744 0.288664
\(759\) −2.19615 3.80385i −0.0797153 0.138071i
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) −6.67949 −0.242131 −0.121066 0.992644i \(-0.538631\pi\)
−0.121066 + 0.992644i \(0.538631\pi\)
\(762\) 3.03332 0.109886
\(763\) 0 0
\(764\) −0.633975 + 1.09808i −0.0229364 + 0.0397270i
\(765\) 9.10770 + 15.7750i 0.329289 + 0.570346i
\(766\) −4.90192 8.49038i −0.177114 0.306770i
\(767\) 38.6147 + 2.49038i 1.39430 + 0.0899224i
\(768\) −6.95448 + 12.0455i −0.250948 + 0.434655i
\(769\) −23.5885 + 40.8564i −0.850622 + 1.47332i 0.0300268 + 0.999549i \(0.490441\pi\)
−0.880648 + 0.473771i \(0.842893\pi\)
\(770\) 0 0
\(771\) −6.63397 11.4904i −0.238917 0.413816i
\(772\) −2.50000 + 4.33013i −0.0899770 + 0.155845i
\(773\) 0.464102 0.803848i 0.0166926 0.0289124i −0.857558 0.514387i \(-0.828020\pi\)
0.874251 + 0.485474i \(0.161353\pi\)
\(774\) −21.7583 + 37.6865i −0.782087 + 1.35461i
\(775\) 6.19615 10.7321i 0.222572 0.385507i
\(776\) −12.4641 21.5885i −0.447435 0.774980i
\(777\) 0 0
\(778\) −26.3827 + 45.6962i −0.945865 + 1.63829i
\(779\) −5.19615 + 9.00000i −0.186171 + 0.322458i
\(780\)