Properties

Label 210.3.l.b.127.3
Level 210
Weight 3
Character 210.127
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.3
Root \(3.76660 + 3.76660i\) of \(x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + 86081152 x^{5} + 178889856 x^{4} + 70149120 x^{3} + 10035200 x^{2} - 7168000 x + 2560000\)
Character \(\chi\) \(=\) 210.127
Dual form 210.3.l.b.43.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.294013 + 4.99135i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.294013 + 4.99135i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(4.69734 - 5.28536i) q^{10} -3.32459 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.80162 + 7.80162i) q^{13} +3.74166i q^{14} +(-6.47322 - 5.75304i) q^{15} -4.00000 q^{16} +(-13.6628 - 13.6628i) q^{17} +(-3.00000 + 3.00000i) q^{18} -37.1623i q^{19} +(-9.98270 + 0.588026i) q^{20} +4.58258 q^{21} +(3.32459 + 3.32459i) q^{22} +(-31.5017 + 31.5017i) q^{23} +4.89898i q^{24} +(-24.8271 + 2.93504i) q^{25} +15.6032 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +55.3464i q^{29} +(0.720182 + 12.2263i) q^{30} -4.54280 q^{31} +(4.00000 + 4.00000i) q^{32} +(4.07177 - 4.07177i) q^{33} +27.3257i q^{34} +(8.78791 - 9.88801i) q^{35} +6.00000 q^{36} +(-46.8661 - 46.8661i) q^{37} +(-37.1623 + 37.1623i) q^{38} -19.1100i q^{39} +(10.5707 + 9.39467i) q^{40} +9.94537 q^{41} +(-4.58258 - 4.58258i) q^{42} +(23.0431 - 23.0431i) q^{43} -6.64917i q^{44} +(14.9740 - 0.882039i) q^{45} +63.0035 q^{46} +(-6.38149 - 6.38149i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(27.7622 + 21.8921i) q^{50} +33.4670 q^{51} +(-15.6032 - 15.6032i) q^{52} +(-42.9239 + 42.9239i) q^{53} -7.34847i q^{54} +(-0.977472 - 16.5942i) q^{55} -7.48331 q^{56} +(45.5143 + 45.5143i) q^{57} +(55.3464 - 55.3464i) q^{58} -59.2884i q^{59} +(11.5061 - 12.9464i) q^{60} +47.1648 q^{61} +(4.54280 + 4.54280i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(-41.2344 - 36.6468i) q^{65} -8.14354 q^{66} +(8.48975 + 8.48975i) q^{67} +(27.3257 - 27.3257i) q^{68} -77.1632i q^{69} +(-18.6759 + 1.10010i) q^{70} +85.6769 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-34.7848 + 34.7848i) q^{73} +93.7322i q^{74} +(26.8122 - 34.0016i) q^{75} +74.3246 q^{76} +(6.21973 + 6.21973i) q^{77} +(-19.1100 + 19.1100i) q^{78} +96.4868i q^{79} +(-1.17605 - 19.9654i) q^{80} -9.00000 q^{81} +(-9.94537 - 9.94537i) q^{82} +(19.6272 - 19.6272i) q^{83} +9.16515i q^{84} +(64.1789 - 72.2131i) q^{85} -46.0863 q^{86} +(-67.7852 - 67.7852i) q^{87} +(-6.64917 + 6.64917i) q^{88} +43.0279i q^{89} +(-15.8561 - 14.0920i) q^{90} +29.1910 q^{91} +(-63.0035 - 63.0035i) q^{92} +(5.56377 - 5.56377i) q^{93} +12.7630i q^{94} +(185.490 - 10.9262i) q^{95} -9.79796 q^{96} +(88.5610 + 88.5610i) q^{97} +(7.00000 - 7.00000i) q^{98} +9.97376i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + O(q^{10}) \) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + 24q^{10} + 8q^{11} - 32q^{13} - 12q^{15} - 64q^{16} + 56q^{17} - 48q^{18} - 16q^{20} - 8q^{22} + 24q^{23} + 40q^{25} + 64q^{26} - 112q^{31} + 64q^{32} + 24q^{33} + 28q^{35} + 96q^{36} - 152q^{37} - 16q^{40} + 24q^{45} - 48q^{46} + 80q^{47} - 72q^{50} - 72q^{51} - 64q^{52} + 48q^{53} - 24q^{55} + 24q^{57} + 96q^{58} + 24q^{60} + 96q^{61} + 112q^{62} + 16q^{65} - 48q^{66} - 80q^{67} - 112q^{68} + 536q^{71} - 96q^{72} - 288q^{75} - 168q^{77} - 48q^{78} + 64q^{80} - 144q^{81} - 256q^{83} + 40q^{85} - 144q^{87} + 16q^{88} + 24q^{90} + 48q^{92} + 192q^{93} + 360q^{95} + 688q^{97} + 112q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 0.294013 + 4.99135i 0.0588026 + 0.998270i
\(6\) 2.44949 0.408248
\(7\) −1.87083 1.87083i −0.267261 0.267261i
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 4.69734 5.28536i 0.469734 0.528536i
\(11\) −3.32459 −0.302235 −0.151118 0.988516i \(-0.548287\pi\)
−0.151118 + 0.988516i \(0.548287\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −7.80162 + 7.80162i −0.600124 + 0.600124i −0.940345 0.340221i \(-0.889498\pi\)
0.340221 + 0.940345i \(0.389498\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −6.47322 5.75304i −0.431548 0.383536i
\(16\) −4.00000 −0.250000
\(17\) −13.6628 13.6628i −0.803697 0.803697i 0.179975 0.983671i \(-0.442398\pi\)
−0.983671 + 0.179975i \(0.942398\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 37.1623i 1.95591i −0.208817 0.977955i \(-0.566961\pi\)
0.208817 0.977955i \(-0.433039\pi\)
\(20\) −9.98270 + 0.588026i −0.499135 + 0.0294013i
\(21\) 4.58258 0.218218
\(22\) 3.32459 + 3.32459i 0.151118 + 0.151118i
\(23\) −31.5017 + 31.5017i −1.36964 + 1.36964i −0.508693 + 0.860948i \(0.669871\pi\)
−0.860948 + 0.508693i \(0.830129\pi\)
\(24\) 4.89898i 0.204124i
\(25\) −24.8271 + 2.93504i −0.993085 + 0.117402i
\(26\) 15.6032 0.600124
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 3.74166 3.74166i 0.133631 0.133631i
\(29\) 55.3464i 1.90850i 0.299016 + 0.954248i \(0.403342\pi\)
−0.299016 + 0.954248i \(0.596658\pi\)
\(30\) 0.720182 + 12.2263i 0.0240061 + 0.407542i
\(31\) −4.54280 −0.146542 −0.0732710 0.997312i \(-0.523344\pi\)
−0.0732710 + 0.997312i \(0.523344\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 4.07177 4.07177i 0.123387 0.123387i
\(34\) 27.3257i 0.803697i
\(35\) 8.78791 9.88801i 0.251083 0.282514i
\(36\) 6.00000 0.166667
\(37\) −46.8661 46.8661i −1.26665 1.26665i −0.947807 0.318843i \(-0.896706\pi\)
−0.318843 0.947807i \(-0.603294\pi\)
\(38\) −37.1623 + 37.1623i −0.977955 + 0.977955i
\(39\) 19.1100i 0.489999i
\(40\) 10.5707 + 9.39467i 0.264268 + 0.234867i
\(41\) 9.94537 0.242570 0.121285 0.992618i \(-0.461298\pi\)
0.121285 + 0.992618i \(0.461298\pi\)
\(42\) −4.58258 4.58258i −0.109109 0.109109i
\(43\) 23.0431 23.0431i 0.535887 0.535887i −0.386431 0.922318i \(-0.626292\pi\)
0.922318 + 0.386431i \(0.126292\pi\)
\(44\) 6.64917i 0.151118i
\(45\) 14.9740 0.882039i 0.332757 0.0196009i
\(46\) 63.0035 1.36964
\(47\) −6.38149 6.38149i −0.135776 0.135776i 0.635952 0.771728i \(-0.280608\pi\)
−0.771728 + 0.635952i \(0.780608\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) 27.7622 + 21.8921i 0.555243 + 0.437841i
\(51\) 33.4670 0.656216
\(52\) −15.6032 15.6032i −0.300062 0.300062i
\(53\) −42.9239 + 42.9239i −0.809885 + 0.809885i −0.984616 0.174731i \(-0.944094\pi\)
0.174731 + 0.984616i \(0.444094\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −0.977472 16.5942i −0.0177722 0.301712i
\(56\) −7.48331 −0.133631
\(57\) 45.5143 + 45.5143i 0.798497 + 0.798497i
\(58\) 55.3464 55.3464i 0.954248 0.954248i
\(59\) 59.2884i 1.00489i −0.864610 0.502444i \(-0.832434\pi\)
0.864610 0.502444i \(-0.167566\pi\)
\(60\) 11.5061 12.9464i 0.191768 0.215774i
\(61\) 47.1648 0.773193 0.386596 0.922249i \(-0.373651\pi\)
0.386596 + 0.922249i \(0.373651\pi\)
\(62\) 4.54280 + 4.54280i 0.0732710 + 0.0732710i
\(63\) −5.61249 + 5.61249i −0.0890871 + 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) −41.2344 36.6468i −0.634375 0.563797i
\(66\) −8.14354 −0.123387
\(67\) 8.48975 + 8.48975i 0.126713 + 0.126713i 0.767619 0.640906i \(-0.221441\pi\)
−0.640906 + 0.767619i \(0.721441\pi\)
\(68\) 27.3257 27.3257i 0.401848 0.401848i
\(69\) 77.1632i 1.11831i
\(70\) −18.6759 + 1.10010i −0.266799 + 0.0157157i
\(71\) 85.6769 1.20672 0.603358 0.797470i \(-0.293829\pi\)
0.603358 + 0.797470i \(0.293829\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −34.7848 + 34.7848i −0.476505 + 0.476505i −0.904012 0.427507i \(-0.859392\pi\)
0.427507 + 0.904012i \(0.359392\pi\)
\(74\) 93.7322i 1.26665i
\(75\) 26.8122 34.0016i 0.357496 0.453354i
\(76\) 74.3246 0.977955
\(77\) 6.21973 + 6.21973i 0.0807757 + 0.0807757i
\(78\) −19.1100 + 19.1100i −0.245000 + 0.245000i
\(79\) 96.4868i 1.22135i 0.791880 + 0.610676i \(0.209102\pi\)
−0.791880 + 0.610676i \(0.790898\pi\)
\(80\) −1.17605 19.9654i −0.0147006 0.249567i
\(81\) −9.00000 −0.111111
\(82\) −9.94537 9.94537i −0.121285 0.121285i
\(83\) 19.6272 19.6272i 0.236472 0.236472i −0.578915 0.815388i \(-0.696524\pi\)
0.815388 + 0.578915i \(0.196524\pi\)
\(84\) 9.16515i 0.109109i
\(85\) 64.1789 72.2131i 0.755046 0.849565i
\(86\) −46.0863 −0.535887
\(87\) −67.7852 67.7852i −0.779140 0.779140i
\(88\) −6.64917 + 6.64917i −0.0755588 + 0.0755588i
\(89\) 43.0279i 0.483460i 0.970344 + 0.241730i \(0.0777148\pi\)
−0.970344 + 0.241730i \(0.922285\pi\)
\(90\) −15.8561 14.0920i −0.176179 0.156578i
\(91\) 29.1910 0.320780
\(92\) −63.0035 63.0035i −0.684820 0.684820i
\(93\) 5.56377 5.56377i 0.0598255 0.0598255i
\(94\) 12.7630i 0.135776i
\(95\) 185.490 10.9262i 1.95252 0.115013i
\(96\) −9.79796 −0.102062
\(97\) 88.5610 + 88.5610i 0.913000 + 0.913000i 0.996507 0.0835068i \(-0.0266120\pi\)
−0.0835068 + 0.996507i \(0.526612\pi\)
\(98\) 7.00000 7.00000i 0.0714286 0.0714286i
\(99\) 9.97376i 0.100745i
\(100\) −5.87008 49.6542i −0.0587008 0.496542i
\(101\) −101.113 −1.00112 −0.500558 0.865703i \(-0.666872\pi\)
−0.500558 + 0.865703i \(0.666872\pi\)
\(102\) −33.4670 33.4670i −0.328108 0.328108i
\(103\) −48.7475 + 48.7475i −0.473276 + 0.473276i −0.902973 0.429697i \(-0.858620\pi\)
0.429697 + 0.902973i \(0.358620\pi\)
\(104\) 31.2065i 0.300062i
\(105\) 1.34734 + 22.8732i 0.0128318 + 0.217840i
\(106\) 85.8479 0.809885
\(107\) −11.0826 11.0826i −0.103576 0.103576i 0.653420 0.756996i \(-0.273334\pi\)
−0.756996 + 0.653420i \(0.773334\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 1.00349i 0.00920630i −0.999989 0.00460315i \(-0.998535\pi\)
0.999989 0.00460315i \(-0.00146523\pi\)
\(110\) −15.6167 + 17.5716i −0.141970 + 0.159742i
\(111\) 114.798 1.03422
\(112\) 7.48331 + 7.48331i 0.0668153 + 0.0668153i
\(113\) −129.405 + 129.405i −1.14517 + 1.14517i −0.157683 + 0.987490i \(0.550402\pi\)
−0.987490 + 0.157683i \(0.949598\pi\)
\(114\) 91.0286i 0.798497i
\(115\) −166.498 147.974i −1.44781 1.28673i
\(116\) −110.693 −0.954248
\(117\) 23.4048 + 23.4048i 0.200041 + 0.200041i
\(118\) −59.2884 + 59.2884i −0.502444 + 0.502444i
\(119\) 51.1217i 0.429594i
\(120\) −24.4525 + 1.44036i −0.203771 + 0.0120030i
\(121\) −109.947 −0.908654
\(122\) −47.1648 47.1648i −0.386596 0.386596i
\(123\) −12.1805 + 12.1805i −0.0990288 + 0.0990288i
\(124\) 9.08560i 0.0732710i
\(125\) −21.9493 123.058i −0.175594 0.984463i
\(126\) 11.2250 0.0890871
\(127\) 124.878 + 124.878i 0.983289 + 0.983289i 0.999863 0.0165736i \(-0.00527577\pi\)
−0.0165736 + 0.999863i \(0.505276\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 56.4439i 0.437550i
\(130\) 4.58755 + 77.8812i 0.0352889 + 0.599086i
\(131\) 137.486 1.04951 0.524754 0.851254i \(-0.324157\pi\)
0.524754 + 0.851254i \(0.324157\pi\)
\(132\) 8.14354 + 8.14354i 0.0616935 + 0.0616935i
\(133\) −69.5243 + 69.5243i −0.522739 + 0.522739i
\(134\) 16.9795i 0.126713i
\(135\) −17.2591 + 19.4197i −0.127845 + 0.143849i
\(136\) −54.6514 −0.401848
\(137\) 69.9065 + 69.9065i 0.510267 + 0.510267i 0.914608 0.404341i \(-0.132499\pi\)
−0.404341 + 0.914608i \(0.632499\pi\)
\(138\) −77.1632 + 77.1632i −0.559154 + 0.559154i
\(139\) 121.192i 0.871888i 0.899974 + 0.435944i \(0.143585\pi\)
−0.899974 + 0.435944i \(0.856415\pi\)
\(140\) 19.7760 + 17.5758i 0.141257 + 0.125542i
\(141\) 15.6314 0.110861
\(142\) −85.6769 85.6769i −0.603358 0.603358i
\(143\) 25.9372 25.9372i 0.181379 0.181379i
\(144\) 12.0000i 0.0833333i
\(145\) −276.253 + 16.2726i −1.90519 + 0.112225i
\(146\) 69.5697 0.476505
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) 93.7322 93.7322i 0.633325 0.633325i
\(149\) 131.094i 0.879823i 0.898041 + 0.439911i \(0.144990\pi\)
−0.898041 + 0.439911i \(0.855010\pi\)
\(150\) −60.8138 + 7.18936i −0.405425 + 0.0479290i
\(151\) −105.336 −0.697586 −0.348793 0.937200i \(-0.613408\pi\)
−0.348793 + 0.937200i \(0.613408\pi\)
\(152\) −74.3246 74.3246i −0.488977 0.488977i
\(153\) −40.9885 + 40.9885i −0.267899 + 0.267899i
\(154\) 12.4395i 0.0807757i
\(155\) −1.33564 22.6747i −0.00861705 0.146288i
\(156\) 38.2200 0.245000
\(157\) −34.7788 34.7788i −0.221521 0.221521i 0.587618 0.809139i \(-0.300066\pi\)
−0.809139 + 0.587618i \(0.800066\pi\)
\(158\) 96.4868 96.4868i 0.610676 0.610676i
\(159\) 105.142i 0.661269i
\(160\) −18.7893 + 21.1414i −0.117433 + 0.132134i
\(161\) 117.869 0.732104
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 71.0414 71.0414i 0.435837 0.435837i −0.454771 0.890608i \(-0.650279\pi\)
0.890608 + 0.454771i \(0.150279\pi\)
\(164\) 19.8907i 0.121285i
\(165\) 21.5208 + 19.1265i 0.130429 + 0.115918i
\(166\) −39.2544 −0.236472
\(167\) −155.443 155.443i −0.930797 0.930797i 0.0669588 0.997756i \(-0.478670\pi\)
−0.997756 + 0.0669588i \(0.978670\pi\)
\(168\) 9.16515 9.16515i 0.0545545 0.0545545i
\(169\) 47.2696i 0.279702i
\(170\) −136.392 + 8.03411i −0.802306 + 0.0472594i
\(171\) −111.487 −0.651970
\(172\) 46.0863 + 46.0863i 0.267944 + 0.267944i
\(173\) −16.5518 + 16.5518i −0.0956751 + 0.0956751i −0.753324 0.657649i \(-0.771551\pi\)
0.657649 + 0.753324i \(0.271551\pi\)
\(174\) 135.570i 0.779140i
\(175\) 51.9382 + 40.9563i 0.296790 + 0.234036i
\(176\) 13.2983 0.0755588
\(177\) 72.6131 + 72.6131i 0.410244 + 0.410244i
\(178\) 43.0279 43.0279i 0.241730 0.241730i
\(179\) 184.541i 1.03096i −0.856903 0.515478i \(-0.827614\pi\)
0.856903 0.515478i \(-0.172386\pi\)
\(180\) 1.76408 + 29.9481i 0.00980043 + 0.166378i
\(181\) −73.9362 −0.408488 −0.204244 0.978920i \(-0.565474\pi\)
−0.204244 + 0.978920i \(0.565474\pi\)
\(182\) −29.1910 29.1910i −0.160390 0.160390i
\(183\) −57.7648 + 57.7648i −0.315655 + 0.315655i
\(184\) 126.007i 0.684820i
\(185\) 220.146 247.704i 1.18998 1.33894i
\(186\) −11.1275 −0.0598255
\(187\) 45.4233 + 45.4233i 0.242905 + 0.242905i
\(188\) 12.7630 12.7630i 0.0678882 0.0678882i
\(189\) 13.7477i 0.0727393i
\(190\) −196.416 174.564i −1.03377 0.918756i
\(191\) −255.605 −1.33825 −0.669123 0.743152i \(-0.733330\pi\)
−0.669123 + 0.743152i \(0.733330\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 153.794 153.794i 0.796858 0.796858i −0.185741 0.982599i \(-0.559468\pi\)
0.982599 + 0.185741i \(0.0594684\pi\)
\(194\) 177.122i 0.913000i
\(195\) 95.3846 5.61858i 0.489152 0.0288132i
\(196\) −14.0000 −0.0714286
\(197\) 132.071 + 132.071i 0.670411 + 0.670411i 0.957811 0.287400i \(-0.0927908\pi\)
−0.287400 + 0.957811i \(0.592791\pi\)
\(198\) 9.97376 9.97376i 0.0503725 0.0503725i
\(199\) 223.530i 1.12327i −0.827387 0.561633i \(-0.810173\pi\)
0.827387 0.561633i \(-0.189827\pi\)
\(200\) −43.7841 + 55.5243i −0.218921 + 0.277622i
\(201\) −20.7956 −0.103460
\(202\) 101.113 + 101.113i 0.500558 + 0.500558i
\(203\) 103.544 103.544i 0.510067 0.510067i
\(204\) 66.9340i 0.328108i
\(205\) 2.92407 + 49.6408i 0.0142638 + 0.242150i
\(206\) 97.4950 0.473276
\(207\) 94.5052 + 94.5052i 0.456547 + 0.456547i
\(208\) 31.2065 31.2065i 0.150031 0.150031i
\(209\) 123.549i 0.591145i
\(210\) 21.5259 24.2206i 0.102504 0.115336i
\(211\) −122.409 −0.580137 −0.290069 0.957006i \(-0.593678\pi\)
−0.290069 + 0.957006i \(0.593678\pi\)
\(212\) −85.8479 85.8479i −0.404943 0.404943i
\(213\) −104.932 + 104.932i −0.492640 + 0.492640i
\(214\) 22.1652i 0.103576i
\(215\) 121.791 + 108.241i 0.566471 + 0.503448i
\(216\) 14.6969 0.0680414
\(217\) 8.49880 + 8.49880i 0.0391650 + 0.0391650i
\(218\) −1.00349 + 1.00349i −0.00460315 + 0.00460315i
\(219\) 85.2051i 0.389064i
\(220\) 33.1883 1.95494i 0.150856 0.00888611i
\(221\) 213.185 0.964636
\(222\) −114.798 114.798i −0.517108 0.517108i
\(223\) 139.840 139.840i 0.627083 0.627083i −0.320250 0.947333i \(-0.603767\pi\)
0.947333 + 0.320250i \(0.103767\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 8.80513 + 74.4813i 0.0391339 + 0.331028i
\(226\) 258.809 1.14517
\(227\) −61.8255 61.8255i −0.272359 0.272359i 0.557690 0.830049i \(-0.311688\pi\)
−0.830049 + 0.557690i \(0.811688\pi\)
\(228\) −91.0286 + 91.0286i −0.399248 + 0.399248i
\(229\) 145.539i 0.635540i 0.948168 + 0.317770i \(0.102934\pi\)
−0.948168 + 0.317770i \(0.897066\pi\)
\(230\) 18.5238 + 314.472i 0.0805384 + 1.36727i
\(231\) −15.2352 −0.0659531
\(232\) 110.693 + 110.693i 0.477124 + 0.477124i
\(233\) 78.2015 78.2015i 0.335629 0.335629i −0.519090 0.854719i \(-0.673729\pi\)
0.854719 + 0.519090i \(0.173729\pi\)
\(234\) 46.8097i 0.200041i
\(235\) 29.9760 33.7285i 0.127557 0.143525i
\(236\) 118.577 0.502444
\(237\) −118.172 118.172i −0.498615 0.498615i
\(238\) 51.1217 51.1217i 0.214797 0.214797i
\(239\) 183.007i 0.765720i −0.923806 0.382860i \(-0.874939\pi\)
0.923806 0.382860i \(-0.125061\pi\)
\(240\) 25.8929 + 23.0121i 0.107887 + 0.0958840i
\(241\) 39.6298 0.164439 0.0822194 0.996614i \(-0.473799\pi\)
0.0822194 + 0.996614i \(0.473799\pi\)
\(242\) 109.947 + 109.947i 0.454327 + 0.454327i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 94.3295i 0.386596i
\(245\) −34.9394 + 2.05809i −0.142610 + 0.00840037i
\(246\) 24.3611 0.0990288
\(247\) 289.926 + 289.926i 1.17379 + 1.17379i
\(248\) −9.08560 + 9.08560i −0.0366355 + 0.0366355i
\(249\) 48.0766i 0.193079i
\(250\) −101.109 + 145.007i −0.404434 + 0.580029i
\(251\) −15.9671 −0.0636141 −0.0318070 0.999494i \(-0.510126\pi\)
−0.0318070 + 0.999494i \(0.510126\pi\)
\(252\) −11.2250 11.2250i −0.0445435 0.0445435i
\(253\) 104.730 104.730i 0.413954 0.413954i
\(254\) 249.755i 0.983289i
\(255\) 9.83973 + 167.045i 0.0385872 + 0.655080i
\(256\) 16.0000 0.0625000
\(257\) 59.0712 + 59.0712i 0.229849 + 0.229849i 0.812630 0.582781i \(-0.198035\pi\)
−0.582781 + 0.812630i \(0.698035\pi\)
\(258\) 56.4439 56.4439i 0.218775 0.218775i
\(259\) 175.357i 0.677053i
\(260\) 73.2936 82.4687i 0.281899 0.317187i
\(261\) 166.039 0.636165
\(262\) −137.486 137.486i −0.524754 0.524754i
\(263\) 186.291 186.291i 0.708330 0.708330i −0.257854 0.966184i \(-0.583015\pi\)
0.966184 + 0.257854i \(0.0830153\pi\)
\(264\) 16.2871i 0.0616935i
\(265\) −226.868 201.628i −0.856107 0.760861i
\(266\) 139.049 0.522739
\(267\) −52.6982 52.6982i −0.197372 0.197372i
\(268\) −16.9795 + 16.9795i −0.0633563 + 0.0633563i
\(269\) 120.015i 0.446153i 0.974801 + 0.223077i \(0.0716100\pi\)
−0.974801 + 0.223077i \(0.928390\pi\)
\(270\) 36.6788 2.16055i 0.135847 0.00800202i
\(271\) −457.758 −1.68914 −0.844571 0.535444i \(-0.820144\pi\)
−0.844571 + 0.535444i \(0.820144\pi\)
\(272\) 54.6514 + 54.6514i 0.200924 + 0.200924i
\(273\) −35.7515 + 35.7515i −0.130958 + 0.130958i
\(274\) 139.813i 0.510267i
\(275\) 82.5399 9.75780i 0.300145 0.0354829i
\(276\) 154.326 0.559154
\(277\) 2.98510 + 2.98510i 0.0107766 + 0.0107766i 0.712475 0.701698i \(-0.247574\pi\)
−0.701698 + 0.712475i \(0.747574\pi\)
\(278\) 121.192 121.192i 0.435944 0.435944i
\(279\) 13.6284i 0.0488473i
\(280\) −2.20019 37.3518i −0.00785783 0.133399i
\(281\) −196.044 −0.697666 −0.348833 0.937185i \(-0.613422\pi\)
−0.348833 + 0.937185i \(0.613422\pi\)
\(282\) −15.6314 15.6314i −0.0554305 0.0554305i
\(283\) −226.011 + 226.011i −0.798627 + 0.798627i −0.982879 0.184252i \(-0.941014\pi\)
0.184252 + 0.982879i \(0.441014\pi\)
\(284\) 171.354i 0.603358i
\(285\) −213.796 + 240.560i −0.750161 + 0.844069i
\(286\) −51.8743 −0.181379
\(287\) −18.6061 18.6061i −0.0648296 0.0648296i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 84.3465i 0.291856i
\(290\) 292.526 + 259.981i 1.00871 + 0.896485i
\(291\) −216.929 −0.745462
\(292\) −69.5697 69.5697i −0.238252 0.238252i
\(293\) −106.875 + 106.875i −0.364762 + 0.364762i −0.865563 0.500801i \(-0.833039\pi\)
0.500801 + 0.865563i \(0.333039\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 295.929 17.4316i 1.00315 0.0590900i
\(296\) −187.464 −0.633325
\(297\) −12.2153 12.2153i −0.0411290 0.0411290i
\(298\) 131.094 131.094i 0.439911 0.439911i
\(299\) 491.529i 1.64391i
\(300\) 68.0031 + 53.6244i 0.226677 + 0.178748i
\(301\) −86.2196 −0.286444
\(302\) 105.336 + 105.336i 0.348793 + 0.348793i
\(303\) 123.837 123.837i 0.408704 0.408704i
\(304\) 148.649i 0.488977i
\(305\) 13.8671 + 235.416i 0.0454658 + 0.771855i
\(306\) 81.9771 0.267899
\(307\) −169.042 169.042i −0.550624 0.550624i 0.375997 0.926621i \(-0.377300\pi\)
−0.926621 + 0.375997i \(0.877300\pi\)
\(308\) −12.4395 + 12.4395i −0.0403879 + 0.0403879i
\(309\) 119.406i 0.386429i
\(310\) −21.3391 + 24.0103i −0.0688357 + 0.0774527i
\(311\) 184.053 0.591810 0.295905 0.955217i \(-0.404379\pi\)
0.295905 + 0.955217i \(0.404379\pi\)
\(312\) −38.2200 38.2200i −0.122500 0.122500i
\(313\) 208.497 208.497i 0.666124 0.666124i −0.290692 0.956817i \(-0.593886\pi\)
0.956817 + 0.290692i \(0.0938856\pi\)
\(314\) 69.5576i 0.221521i
\(315\) −29.6640 26.3637i −0.0941715 0.0836944i
\(316\) −192.974 −0.610676
\(317\) −403.707 403.707i −1.27352 1.27352i −0.944227 0.329296i \(-0.893189\pi\)
−0.329296 0.944227i \(-0.606811\pi\)
\(318\) −105.142 + 105.142i −0.330634 + 0.330634i
\(319\) 184.004i 0.576815i
\(320\) 39.9308 2.35210i 0.124784 0.00735032i
\(321\) 27.1467 0.0845691
\(322\) −117.869 117.869i −0.366052 0.366052i
\(323\) −507.742 + 507.742i −1.57196 + 1.57196i
\(324\) 18.0000i 0.0555556i
\(325\) 170.794 216.590i 0.525519 0.666430i
\(326\) −142.083 −0.435837
\(327\) 1.22901 + 1.22901i 0.00375846 + 0.00375846i
\(328\) 19.8907 19.8907i 0.0606425 0.0606425i
\(329\) 23.8773i 0.0725755i
\(330\) −2.39431 40.6473i −0.00725548 0.123173i
\(331\) −26.7859 −0.0809241 −0.0404620 0.999181i \(-0.512883\pi\)
−0.0404620 + 0.999181i \(0.512883\pi\)
\(332\) 39.2544 + 39.2544i 0.118236 + 0.118236i
\(333\) −140.598 + 140.598i −0.422217 + 0.422217i
\(334\) 310.886i 0.930797i
\(335\) −39.8792 + 44.8714i −0.119042 + 0.133944i
\(336\) −18.3303 −0.0545545
\(337\) 325.031 + 325.031i 0.964485 + 0.964485i 0.999391 0.0349056i \(-0.0111130\pi\)
−0.0349056 + 0.999391i \(0.511113\pi\)
\(338\) 47.2696 47.2696i 0.139851 0.139851i
\(339\) 316.975i 0.935030i
\(340\) 144.426 + 128.358i 0.424783 + 0.377523i
\(341\) 15.1029 0.0442901
\(342\) 111.487 + 111.487i 0.325985 + 0.325985i
\(343\) 13.0958 13.0958i 0.0381802 0.0381802i
\(344\) 92.1726i 0.267944i
\(345\) 385.148 22.6870i 1.11637 0.0657594i
\(346\) 33.1036 0.0956751
\(347\) −119.676 119.676i −0.344887 0.344887i 0.513314 0.858201i \(-0.328418\pi\)
−0.858201 + 0.513314i \(0.828418\pi\)
\(348\) 135.570 135.570i 0.389570 0.389570i
\(349\) 592.030i 1.69636i −0.529708 0.848180i \(-0.677698\pi\)
0.529708 0.848180i \(-0.322302\pi\)
\(350\) −10.9819 92.8945i −0.0313769 0.265413i
\(351\) −57.3299 −0.163333
\(352\) −13.2983 13.2983i −0.0377794 0.0377794i
\(353\) 92.2147 92.2147i 0.261231 0.261231i −0.564323 0.825554i \(-0.690863\pi\)
0.825554 + 0.564323i \(0.190863\pi\)
\(354\) 145.226i 0.410244i
\(355\) 25.1901 + 427.643i 0.0709581 + 1.20463i
\(356\) −86.0558 −0.241730
\(357\) −62.6110 62.6110i −0.175381 0.175381i
\(358\) −184.541 + 184.541i −0.515478 + 0.515478i
\(359\) 464.557i 1.29403i 0.762477 + 0.647016i \(0.223983\pi\)
−0.762477 + 0.647016i \(0.776017\pi\)
\(360\) 28.1840 31.7122i 0.0782889 0.0880894i
\(361\) −1020.03 −2.82558
\(362\) 73.9362 + 73.9362i 0.204244 + 0.204244i
\(363\) 134.657 134.657i 0.370956 0.370956i
\(364\) 58.3820i 0.160390i
\(365\) −183.850 163.396i −0.503700 0.447660i
\(366\) 115.530 0.315655
\(367\) 450.255 + 450.255i 1.22685 + 1.22685i 0.965148 + 0.261705i \(0.0842847\pi\)
0.261705 + 0.965148i \(0.415715\pi\)
\(368\) 126.007 126.007i 0.342410 0.342410i
\(369\) 29.8361i 0.0808567i
\(370\) −467.850 + 27.5585i −1.26446 + 0.0744824i
\(371\) 160.607 0.432902
\(372\) 11.1275 + 11.1275i 0.0299128 + 0.0299128i
\(373\) 447.933 447.933i 1.20089 1.20089i 0.226997 0.973895i \(-0.427109\pi\)
0.973895 0.226997i \(-0.0728907\pi\)
\(374\) 90.8466i 0.242905i
\(375\) 177.597 + 123.832i 0.473591 + 0.330219i
\(376\) −25.5259 −0.0678882
\(377\) −431.791 431.791i −1.14534 1.14534i
\(378\) −13.7477 + 13.7477i −0.0363696 + 0.0363696i
\(379\) 200.204i 0.528242i −0.964490 0.264121i \(-0.914918\pi\)
0.964490 0.264121i \(-0.0850818\pi\)
\(380\) 21.8524 + 370.980i 0.0575063 + 0.976262i
\(381\) −305.887 −0.802852
\(382\) 255.605 + 255.605i 0.669123 + 0.669123i
\(383\) −260.633 + 260.633i −0.680503 + 0.680503i −0.960114 0.279610i \(-0.909795\pi\)
0.279610 + 0.960114i \(0.409795\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −29.2162 + 32.8735i −0.0758862 + 0.0853858i
\(386\) −307.587 −0.796858
\(387\) −69.1294 69.1294i −0.178629 0.178629i
\(388\) −177.122 + 177.122i −0.456500 + 0.456500i
\(389\) 192.566i 0.495028i −0.968884 0.247514i \(-0.920386\pi\)
0.968884 0.247514i \(-0.0796136\pi\)
\(390\) −101.003 89.7660i −0.258982 0.230169i
\(391\) 860.807 2.20155
\(392\) 14.0000 + 14.0000i 0.0357143 + 0.0357143i
\(393\) −168.385 + 168.385i −0.428460 + 0.428460i
\(394\) 264.142i 0.670411i
\(395\) −481.599 + 28.3684i −1.21924 + 0.0718187i
\(396\) −19.9475 −0.0503725
\(397\) −183.256 183.256i −0.461602 0.461602i 0.437578 0.899180i \(-0.355836\pi\)
−0.899180 + 0.437578i \(0.855836\pi\)
\(398\) −223.530 + 223.530i −0.561633 + 0.561633i
\(399\) 170.299i 0.426814i
\(400\) 99.3085 11.7402i 0.248271 0.0293504i
\(401\) −327.614 −0.816992 −0.408496 0.912760i \(-0.633947\pi\)
−0.408496 + 0.912760i \(0.633947\pi\)
\(402\) 20.7956 + 20.7956i 0.0517302 + 0.0517302i
\(403\) 35.4412 35.4412i 0.0879434 0.0879434i
\(404\) 202.225i 0.500558i
\(405\) −2.64612 44.9221i −0.00653362 0.110919i
\(406\) −207.087 −0.510067
\(407\) 155.810 + 155.810i 0.382826 + 0.382826i
\(408\) 66.9340 66.9340i 0.164054 0.164054i
\(409\) 637.257i 1.55809i 0.626971 + 0.779043i \(0.284295\pi\)
−0.626971 + 0.779043i \(0.715705\pi\)
\(410\) 46.7168 52.5649i 0.113943 0.128207i
\(411\) −171.235 −0.416631
\(412\) −97.4950 97.4950i −0.236638 0.236638i
\(413\) −110.918 + 110.918i −0.268568 + 0.268568i
\(414\) 189.010i 0.456547i
\(415\) 103.737 + 92.1955i 0.249968 + 0.222158i
\(416\) −62.4129 −0.150031
\(417\) −148.430 148.430i −0.355947 0.355947i
\(418\) 123.549 123.549i 0.295572 0.295572i
\(419\) 332.788i 0.794244i −0.917766 0.397122i \(-0.870009\pi\)
0.917766 0.397122i \(-0.129991\pi\)
\(420\) −45.7465 + 2.69467i −0.108920 + 0.00641589i
\(421\) −287.551 −0.683018 −0.341509 0.939879i \(-0.610938\pi\)
−0.341509 + 0.939879i \(0.610938\pi\)
\(422\) 122.409 + 122.409i 0.290069 + 0.290069i
\(423\) −19.1445 + 19.1445i −0.0452588 + 0.0452588i
\(424\) 171.696i 0.404943i
\(425\) 379.310 + 299.108i 0.892494 + 0.703783i
\(426\) 209.865 0.492640
\(427\) −88.2372 88.2372i −0.206645 0.206645i
\(428\) 22.1652 22.1652i 0.0517878 0.0517878i
\(429\) 63.5328i 0.148095i
\(430\) −13.5500 230.033i −0.0315116 0.534960i
\(431\) −321.978 −0.747049 −0.373524 0.927620i \(-0.621851\pi\)
−0.373524 + 0.927620i \(0.621851\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 285.044 285.044i 0.658300 0.658300i −0.296678 0.954978i \(-0.595879\pi\)
0.954978 + 0.296678i \(0.0958788\pi\)
\(434\) 16.9976i 0.0391650i
\(435\) 318.410 358.269i 0.731977 0.823608i
\(436\) 2.00697 0.00460315
\(437\) 1170.68 + 1170.68i 2.67889 + 2.67889i
\(438\) −85.2051 + 85.2051i −0.194532 + 0.194532i
\(439\) 342.297i 0.779721i 0.920874 + 0.389860i \(0.127477\pi\)
−0.920874 + 0.389860i \(0.872523\pi\)
\(440\) −35.1433 31.2334i −0.0798711 0.0709850i
\(441\) 21.0000 0.0476190
\(442\) −213.185 213.185i −0.482318 0.482318i
\(443\) −545.221 + 545.221i −1.23075 + 1.23075i −0.267070 + 0.963677i \(0.586055\pi\)
−0.963677 + 0.267070i \(0.913945\pi\)
\(444\) 229.596i 0.517108i
\(445\) −214.767 + 12.6508i −0.482623 + 0.0284287i
\(446\) −279.679 −0.627083
\(447\) −160.556 160.556i −0.359186 0.359186i
\(448\) −14.9666 + 14.9666i −0.0334077 + 0.0334077i
\(449\) 65.3316i 0.145505i −0.997350 0.0727523i \(-0.976822\pi\)
0.997350 0.0727523i \(-0.0231783\pi\)
\(450\) 65.6762 83.2865i 0.145947 0.185081i
\(451\) −33.0643 −0.0733132
\(452\) −258.809 258.809i −0.572586 0.572586i
\(453\) 129.009 129.009i 0.284788 0.284788i
\(454\) 123.651i 0.272359i
\(455\) 8.58253 + 145.702i 0.0188627 + 0.320225i
\(456\) 182.057 0.399248
\(457\) 147.331 + 147.331i 0.322387 + 0.322387i 0.849682 0.527295i \(-0.176794\pi\)
−0.527295 + 0.849682i \(0.676794\pi\)
\(458\) 145.539 145.539i 0.317770 0.317770i
\(459\) 100.401i 0.218739i
\(460\) 295.948 332.996i 0.643366 0.723905i
\(461\) −52.5087 −0.113902 −0.0569509 0.998377i \(-0.518138\pi\)
−0.0569509 + 0.998377i \(0.518138\pi\)
\(462\) 15.2352 + 15.2352i 0.0329766 + 0.0329766i
\(463\) −76.6237 + 76.6237i −0.165494 + 0.165494i −0.784995 0.619502i \(-0.787335\pi\)
0.619502 + 0.784995i \(0.287335\pi\)
\(464\) 221.386i 0.477124i
\(465\) 29.4066 + 26.1349i 0.0632399 + 0.0562041i
\(466\) −156.403 −0.335629
\(467\) 54.4091 + 54.4091i 0.116508 + 0.116508i 0.762957 0.646449i \(-0.223747\pi\)
−0.646449 + 0.762957i \(0.723747\pi\)
\(468\) −46.8097 + 46.8097i −0.100021 + 0.100021i
\(469\) 31.7657i 0.0677308i
\(470\) −63.7045 + 3.75248i −0.135541 + 0.00798400i
\(471\) 85.1904 0.180871
\(472\) −118.577 118.577i −0.251222 0.251222i
\(473\) −76.6089 + 76.6089i −0.161964 + 0.161964i
\(474\) 236.343i 0.498615i
\(475\) 109.073 + 922.632i 0.229627 + 1.94238i
\(476\) −102.243 −0.214797
\(477\) 128.772 + 128.772i 0.269962 + 0.269962i
\(478\) −183.007 + 183.007i −0.382860 + 0.382860i
\(479\) 165.940i 0.346430i −0.984884 0.173215i \(-0.944584\pi\)
0.984884 0.173215i \(-0.0554156\pi\)
\(480\) −2.88073 48.9050i −0.00600152 0.101885i
\(481\) 731.262 1.52030
\(482\) −39.6298 39.6298i −0.0822194 0.0822194i
\(483\) −144.359 + 144.359i −0.298880 + 0.298880i
\(484\) 219.894i 0.454327i
\(485\) −416.001 + 468.077i −0.857734 + 0.965107i
\(486\) −22.0454 −0.0453609
\(487\) −49.2440 49.2440i −0.101117 0.101117i 0.654738 0.755856i \(-0.272779\pi\)
−0.755856 + 0.654738i \(0.772779\pi\)
\(488\) 94.3295 94.3295i 0.193298 0.193298i
\(489\) 174.015i 0.355859i
\(490\) 36.9975 + 32.8813i 0.0755052 + 0.0671048i
\(491\) −207.513 −0.422633 −0.211316 0.977418i \(-0.567775\pi\)
−0.211316 + 0.977418i \(0.567775\pi\)
\(492\) −24.3611 24.3611i −0.0495144 0.0495144i
\(493\) 756.189 756.189i 1.53385 1.53385i
\(494\) 579.852i 1.17379i
\(495\) −49.7825 + 2.93242i −0.100571 + 0.00592407i
\(496\) 18.1712 0.0366355
\(497\) −160.287 160.287i −0.322509 0.322509i
\(498\) 48.0766 48.0766i 0.0965393 0.0965393i
\(499\) 299.711i 0.600624i 0.953841 + 0.300312i \(0.0970908\pi\)
−0.953841 + 0.300312i \(0.902909\pi\)
\(500\) 246.116 43.8986i 0.492231 0.0877972i
\(501\) 380.756 0.759993
\(502\) 15.9671 + 15.9671i 0.0318070 + 0.0318070i
\(503\) −354.819 + 354.819i −0.705406 + 0.705406i −0.965566 0.260160i \(-0.916225\pi\)
0.260160 + 0.965566i \(0.416225\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) −29.7284 504.688i −0.0588682 0.999383i
\(506\) −209.461 −0.413954
\(507\) −57.8932 57.8932i −0.114188 0.114188i
\(508\) −249.755 + 249.755i −0.491645 + 0.491645i
\(509\) 46.3713i 0.0911027i 0.998962 + 0.0455514i \(0.0145045\pi\)
−0.998962 + 0.0455514i \(0.985496\pi\)
\(510\) 157.206 176.885i 0.308246 0.346834i
\(511\) 130.153 0.254702
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 136.543 136.543i 0.266166 0.266166i
\(514\) 118.142i 0.229849i
\(515\) −257.648 228.983i −0.500287 0.444628i
\(516\) −112.888 −0.218775
\(517\) 21.2158 + 21.2158i 0.0410364 + 0.0410364i
\(518\) 175.357 175.357i 0.338527 0.338527i
\(519\) 40.5435i 0.0781184i
\(520\) −155.762 + 9.17511i −0.299543 + 0.0176444i
\(521\) 784.619 1.50599 0.752993 0.658028i \(-0.228609\pi\)
0.752993 + 0.658028i \(0.228609\pi\)
\(522\) −166.039 166.039i −0.318083 0.318083i
\(523\) 271.744 271.744i 0.519587 0.519587i −0.397859 0.917446i \(-0.630247\pi\)
0.917446 + 0.397859i \(0.130247\pi\)
\(524\) 274.971i 0.524754i
\(525\) −113.772 + 13.4501i −0.216709 + 0.0256192i
\(526\) −372.582 −0.708330
\(527\) 62.0676 + 62.0676i 0.117775 + 0.117775i
\(528\) −16.2871 + 16.2871i −0.0308467 + 0.0308467i
\(529\) 1455.72i 2.75183i
\(530\) 25.2404 + 428.497i 0.0476234 + 0.808484i
\(531\) −177.865 −0.334963
\(532\) −139.049 139.049i −0.261369 0.261369i
\(533\) −77.5900 + 77.5900i −0.145572 + 0.145572i
\(534\) 105.396i 0.197372i
\(535\) 52.0586 58.5755i 0.0973058 0.109487i
\(536\) 33.9590 0.0633563
\(537\) 226.016 + 226.016i 0.420886 + 0.420886i
\(538\) 120.015 120.015i 0.223077 0.223077i
\(539\) 23.2721i 0.0431765i
\(540\) −38.8393 34.5182i −0.0719247 0.0639226i
\(541\) 545.359 1.00806 0.504029 0.863687i \(-0.331851\pi\)
0.504029 + 0.863687i \(0.331851\pi\)
\(542\) 457.758 + 457.758i 0.844571 + 0.844571i
\(543\) 90.5530 90.5530i 0.166764 0.166764i
\(544\) 109.303i 0.200924i
\(545\) 5.00875 0.295038i 0.00919037 0.000541354i
\(546\) 71.5030 0.130958
\(547\) 93.2739 + 93.2739i 0.170519 + 0.170519i 0.787207 0.616688i \(-0.211526\pi\)
−0.616688 + 0.787207i \(0.711526\pi\)
\(548\) −139.813 + 139.813i −0.255133 + 0.255133i
\(549\) 141.494i 0.257731i
\(550\) −92.2977 72.7821i −0.167814 0.132331i
\(551\) 2056.80 3.73285
\(552\) −154.326 154.326i −0.279577 0.279577i
\(553\) 180.510 180.510i 0.326420 0.326420i
\(554\) 5.97021i 0.0107766i
\(555\) 33.7521 + 572.997i 0.0608146 + 1.03243i
\(556\) −242.385 −0.435944
\(557\) 549.179 + 549.179i 0.985958 + 0.985958i 0.999903 0.0139446i \(-0.00443886\pi\)
−0.0139446 + 0.999903i \(0.504439\pi\)
\(558\) 13.6284 13.6284i 0.0244237 0.0244237i
\(559\) 359.548i 0.643198i
\(560\) −35.1516 + 39.5520i −0.0627708 + 0.0706286i
\(561\) −111.264 −0.198331
\(562\) 196.044 + 196.044i 0.348833 + 0.348833i
\(563\) −45.1575 + 45.1575i −0.0802088 + 0.0802088i −0.746073 0.665864i \(-0.768063\pi\)
0.665864 + 0.746073i \(0.268063\pi\)
\(564\) 31.2628i 0.0554305i
\(565\) −683.950 607.856i −1.21053 1.07585i
\(566\) 452.023 0.798627
\(567\) 16.8375 + 16.8375i 0.0296957 + 0.0296957i
\(568\) 171.354 171.354i 0.301679 0.301679i
\(569\) 392.758i 0.690260i 0.938555 + 0.345130i \(0.112165\pi\)
−0.938555 + 0.345130i \(0.887835\pi\)
\(570\) 454.356 26.7636i 0.797115 0.0469537i
\(571\) −0.726963 −0.00127314 −0.000636570 1.00000i \(-0.500203\pi\)
−0.000636570 1.00000i \(0.500203\pi\)
\(572\) 51.8743 + 51.8743i 0.0906893 + 0.0906893i
\(573\) 313.051 313.051i 0.546337 0.546337i
\(574\) 37.2122i 0.0648296i
\(575\) 689.638 874.556i 1.19937 1.52097i
\(576\) −24.0000 −0.0416667
\(577\) −184.973 184.973i −0.320577 0.320577i 0.528411 0.848988i \(-0.322788\pi\)
−0.848988 + 0.528411i \(0.822788\pi\)
\(578\) 84.3465 84.3465i 0.145928 0.145928i
\(579\) 376.716i 0.650632i
\(580\) −32.5451 552.506i −0.0561123 0.952597i
\(581\) −73.4382 −0.126400
\(582\) 216.929 + 216.929i 0.372731 + 0.372731i
\(583\) 142.704 142.704i 0.244776 0.244776i
\(584\) 139.139i 0.238252i
\(585\) −109.940 + 123.703i −0.187932 + 0.211458i
\(586\) 213.751 0.364762
\(587\) −703.941 703.941i −1.19922 1.19922i −0.974401 0.224817i \(-0.927822\pi\)
−0.224817 0.974401i \(-0.572178\pi\)
\(588\) 17.1464 17.1464i 0.0291606 0.0291606i
\(589\) 168.821i 0.286623i
\(590\) −313.361 278.497i −0.531120 0.472030i
\(591\) −323.506 −0.547388
\(592\) 187.464 + 187.464i 0.316663 + 0.316663i
\(593\) 730.917 730.917i 1.23257 1.23257i 0.269603 0.962972i \(-0.413107\pi\)
0.962972 0.269603i \(-0.0868925\pi\)
\(594\) 24.4306i 0.0411290i
\(595\) −255.166 + 15.0304i −0.428851 + 0.0252612i
\(596\) −262.187 −0.439911
\(597\) 273.767 + 273.767i 0.458571 + 0.458571i
\(598\) −491.529 + 491.529i −0.821955 + 0.821955i
\(599\) 646.505i 1.07931i 0.841887 + 0.539654i \(0.181445\pi\)
−0.841887 + 0.539654i \(0.818555\pi\)
\(600\) −14.3787 121.628i −0.0239645 0.202713i
\(601\) −133.146 −0.221541 −0.110771 0.993846i \(-0.535332\pi\)
−0.110771 + 0.993846i \(0.535332\pi\)
\(602\) 86.2196 + 86.2196i 0.143222 + 0.143222i
\(603\) 25.4692 25.4692i 0.0422376 0.0422376i
\(604\) 210.671i 0.348793i
\(605\) −32.3259 548.784i −0.0534312 0.907082i
\(606\) −247.674 −0.408704
\(607\) −1.17531 1.17531i −0.00193627 0.00193627i 0.706138 0.708074i \(-0.250436\pi\)
−0.708074 + 0.706138i \(0.750436\pi\)
\(608\) 148.649 148.649i 0.244489 0.244489i
\(609\) 253.629i 0.416468i
\(610\) 221.549 249.283i 0.363195 0.408660i
\(611\) 99.5718 0.162965
\(612\) −81.9771 81.9771i −0.133949 0.133949i
\(613\) −464.748 + 464.748i −0.758153 + 0.758153i −0.975986 0.217833i \(-0.930101\pi\)
0.217833 + 0.975986i \(0.430101\pi\)
\(614\) 338.083i 0.550624i
\(615\) −64.3786 57.2161i −0.104681 0.0930343i
\(616\) 24.8789 0.0403879
\(617\) −591.643 591.643i −0.958903 0.958903i 0.0402851 0.999188i \(-0.487173\pi\)
−0.999188 + 0.0402851i \(0.987173\pi\)
\(618\) −119.406 + 119.406i −0.193214 + 0.193214i
\(619\) 1133.85i 1.83175i 0.401466 + 0.915874i \(0.368501\pi\)
−0.401466 + 0.915874i \(0.631499\pi\)
\(620\) 45.3494 2.67129i 0.0731442 0.00430853i
\(621\) −231.490 −0.372769
\(622\) −184.053 184.053i −0.295905 0.295905i
\(623\) 80.4978 80.4978i 0.129210 0.129210i
\(624\) 76.4399i 0.122500i
\(625\) 607.771 145.737i 0.972434 0.233180i
\(626\) −416.994 −0.666124
\(627\) −151.316 151.316i −0.241334 0.241334i
\(628\) 69.5576 69.5576i 0.110761 0.110761i
\(629\) 1280.65i 2.03601i
\(630\) 3.30029 + 56.0277i 0.00523855 + 0.0889329i
\(631\) −383.255 −0.607377 −0.303689 0.952771i \(-0.598218\pi\)
−0.303689 + 0.952771i \(0.598218\pi\)
\(632\) 192.974 + 192.974i 0.305338 + 0.305338i
\(633\) 149.920 149.920i 0.236840 0.236840i
\(634\) 807.414i 1.27352i
\(635\) −586.592 + 660.024i −0.923768 + 1.03941i
\(636\) 210.283 0.330634
\(637\) −54.6113 54.6113i −0.0857320 0.0857320i
\(638\) −184.004 + 184.004i −0.288407 + 0.288407i
\(639\) 257.031i 0.402239i
\(640\) −42.2829 37.5787i −0.0660670 0.0587167i
\(641\) −129.610 −0.202199 −0.101100 0.994876i \(-0.532236\pi\)
−0.101100 + 0.994876i \(0.532236\pi\)
\(642\) −27.1467 27.1467i −0.0422845 0.0422845i
\(643\) 233.464 233.464i 0.363085 0.363085i −0.501862 0.864948i \(-0.667352\pi\)
0.864948 + 0.501862i \(0.167352\pi\)
\(644\) 235.737i 0.366052i
\(645\) −281.731 + 16.5953i −0.436793 + 0.0257291i
\(646\) 1015.48 1.57196
\(647\) −430.823 430.823i −0.665878 0.665878i 0.290881 0.956759i \(-0.406052\pi\)
−0.956759 + 0.290881i \(0.906052\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 197.109i 0.303712i
\(650\) −387.383 + 45.7962i −0.595974 + 0.0704556i
\(651\) −20.8177 −0.0319781
\(652\) 142.083 + 142.083i 0.217918 + 0.217918i
\(653\) 170.000 170.000i 0.260337 0.260337i −0.564854 0.825191i \(-0.691068\pi\)
0.825191 + 0.564854i \(0.191068\pi\)
\(654\) 2.45803i 0.00375846i
\(655\) 40.4225 + 686.238i 0.0617138 + 1.04769i
\(656\) −39.7815 −0.0606425
\(657\) 104.355 + 104.355i 0.158835 + 0.158835i
\(658\) 23.8773 23.8773i 0.0362878 0.0362878i
\(659\) 532.095i 0.807429i −0.914885 0.403714i \(-0.867719\pi\)
0.914885 0.403714i \(-0.132281\pi\)
\(660\) −38.2529 + 43.0416i −0.0579590 + 0.0652145i
\(661\) 1235.23 1.86872 0.934362 0.356325i \(-0.115971\pi\)
0.934362 + 0.356325i \(0.115971\pi\)
\(662\) 26.7859 + 26.7859i 0.0404620 + 0.0404620i
\(663\) −261.097 + 261.097i −0.393811 + 0.393811i
\(664\) 78.5087i 0.118236i
\(665\) −367.461 326.579i −0.552573 0.491096i
\(666\) 281.196 0.422217
\(667\) −1743.51 1743.51i −2.61395 2.61395i
\(668\) 310.886 310.886i 0.465398 0.465398i
\(669\) 342.536i 0.512011i
\(670\) 84.7506 4.99219i 0.126493 0.00745103i
\(671\) −156.803 −0.233686
\(672\) 18.3303 + 18.3303i 0.0272772 + 0.0272772i
\(673\) −350.867 + 350.867i −0.521347 + 0.521347i −0.917978 0.396631i \(-0.870179\pi\)
0.396631 + 0.917978i \(0.370179\pi\)
\(674\) 650.063i 0.964485i
\(675\) −102.005 80.4366i −0.151118 0.119165i
\(676\) −94.5391 −0.139851
\(677\) −721.673 721.673i −1.06599 1.06599i −0.997663 0.0683230i \(-0.978235\pi\)
−0.0683230 0.997663i \(-0.521765\pi\)
\(678\) −316.975 + 316.975i −0.467515 + 0.467515i
\(679\) 331.365i 0.488019i
\(680\) −16.0682 272.784i −0.0236297 0.401153i
\(681\) 151.441 0.222380
\(682\) −15.1029 15.1029i −0.0221451 0.0221451i
\(683\) 314.116 314.116i 0.459906 0.459906i −0.438719 0.898624i \(-0.644568\pi\)
0.898624 + 0.438719i \(0.144568\pi\)
\(684\) 222.974i 0.325985i
\(685\) −328.374 + 369.481i −0.479379 + 0.539389i
\(686\) −26.1916 −0.0381802
\(687\) −178.248 178.248i −0.259458 0.259458i
\(688\) −92.1726 + 92.1726i −0.133972 + 0.133972i
\(689\) 669.752i 0.972064i
\(690\) −407.835 362.461i −0.591066 0.525306i
\(691\) −1255.23 −1.81654 −0.908269 0.418387i \(-0.862595\pi\)
−0.908269 + 0.418387i \(0.862595\pi\)
\(692\) −33.1036 33.1036i −0.0478376 0.0478376i
\(693\) 18.6592 18.6592i 0.0269252 0.0269252i
\(694\) 239.351i 0.344887i
\(695\) −604.914 + 35.6322i −0.870380 + 0.0512693i
\(696\) −271.141 −0.389570
\(697\) −135.882 135.882i −0.194953 0.194953i
\(698\) −592.030 + 592.030i −0.848180 + 0.848180i
\(699\) 191.554i 0.274040i
\(700\) −81.9126 + 103.876i −0.117018 + 0.148395i
\(701\) 275.772 0.393398 0.196699 0.980464i \(-0.436978\pi\)
0.196699 + 0.980464i \(0.436978\pi\)
\(702\) 57.3299 + 57.3299i 0.0816666 + 0.0816666i
\(703\) −1741.65 + 1741.65i −2.47745 + 2.47745i
\(704\) 26.5967i 0.0377794i
\(705\) 4.59583 + 78.0217i 0.00651891 + 0.110669i
\(706\) −184.429 −0.261231
\(707\) 189.164 + 189.164i 0.267559 + 0.267559i
\(708\) −145.226 + 145.226i −0.205122 + 0.205122i
\(709\) 533.450i 0.752398i 0.926539 + 0.376199i \(0.122769\pi\)
−0.926539 + 0.376199i \(0.877231\pi\)
\(710\) 402.453 452.833i 0.566835 0.637793i
\(711\) 289.460 0.407117
\(712\) 86.0558 + 86.0558i 0.120865 + 0.120865i
\(713\) 143.106 143.106i 0.200710 0.200710i
\(714\) 125.222i 0.175381i
\(715\) 137.087 + 121.835i 0.191730 + 0.170399i
\(716\) 369.082 0.515478
\(717\) 224.137 + 224.137i 0.312604 + 0.312604i
\(718\) 464.557 464.557i 0.647016 0.647016i
\(719\) 260.982i 0.362979i 0.983393 + 0.181490i \(0.0580919\pi\)
−0.983393 + 0.181490i \(0.941908\pi\)
\(720\) −59.8962 + 3.52816i −0.0831891 + 0.00490022i
\(721\) 182.396 0.252977
\(722\) 1020.03 + 1020.03i 1.41279 + 1.41279i
\(723\) −48.5363 + 48.5363i −0.0671319 + 0.0671319i
\(724\) 147.872i 0.204244i
\(725\) −162.444 1374.09i −0.224061 1.89530i
\(726\) −269.314 −0.370956
\(727\) 293.600 + 293.600i 0.403852 + 0.403852i 0.879588 0.475736i \(-0.157818\pi\)
−0.475736 + 0.879588i \(0.657818\pi\)
\(728\) 58.3820 58.3820i 0.0801950 0.0801950i
\(729\) 27.0000i 0.0370370i
\(730\) 20.4544 + 347.246i 0.0280197 + 0.475680i
\(731\) −629.670 −0.861381
\(732\) −115.530 115.530i −0.157827 0.157827i
\(733\) 416.677 416.677i 0.568455 0.568455i −0.363241 0.931695i \(-0.618330\pi\)
0.931695 + 0.363241i \(0.118330\pi\)
\(734\) 900.510i 1.22685i
\(735\) 40.2713 45.3125i 0.0547908 0.0616497i
\(736\) −252.014 −0.342410
\(737\) −28.2249 28.2249i −0.0382970 0.0382970i
\(738\) −29.8361 + 29.8361i −0.0404283 + 0.0404283i
\(739\) 96.5954i 0.130711i −0.997862 0.0653555i \(-0.979182\pi\)
0.997862 0.0653555i \(-0.0208181\pi\)
\(740\) 495.408 + 440.291i 0.669471 + 0.594988i
\(741\) −710.170 −0.958395
\(742\) −160.607 160.607i −0.216451 0.216451i
\(743\) −517.336 + 517.336i −0.696280 + 0.696280i −0.963606 0.267326i \(-0.913860\pi\)
0.267326 + 0.963606i \(0.413860\pi\)
\(744\) 22.2551i 0.0299128i
\(745\) −654.334 + 38.5432i −0.878300 + 0.0517359i
\(746\) −895.866 −1.20089
\(747\) −58.8816 58.8816i −0.0788240 0.0788240i
\(748\) −90.8466 + 90.8466i −0.121453 + 0.121453i
\(749\) 41.4672i 0.0553635i
\(750\) −53.7646 301.429i −0.0716862 0.401905i
\(751\) 429.736 0.572218 0.286109 0.958197i \(-0.407638\pi\)
0.286109 + 0.958197i \(0.407638\pi\)
\(752\) 25.5259 + 25.5259i 0.0339441 + 0.0339441i
\(753\) 19.5557 19.5557i 0.0259703 0.0259703i
\(754\) 863.583i 1.14534i
\(755\) −30.9700 525.766i −0.0410199 0.696379i
\(756\) 27.4955 0.0363696
\(757\) 400.880 + 400.880i 0.529565 + 0.529565i 0.920443 0.390878i \(-0.127829\pi\)
−0.390878 + 0.920443i \(0.627829\pi\)
\(758\) −200.204 + 200.204i −0.264121 + 0.264121i
\(759\) 256.536i 0.337992i
\(760\) 349.127 392.832i 0.459378 0.516884i
\(761\) −45.5634 −0.0598730 −0.0299365 0.999552i \(-0.509531\pi\)
−0.0299365 + 0.999552i \(0.509531\pi\)
\(762\) 305.887 + 305.887i 0.401426 + 0.401426i
\(763\) −1.87735 + 1.87735i −0.00246049 + 0.00246049i
\(764\) 511.210i 0.669123i
\(765\) −216.639 192.537i −0.283188 0.251682i
\(766\) 521.265 0.680503
\(767\) 462.545 + 462.545i 0.603058 + 0.603058i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 1217.00i 1.58257i 0.611445 + 0.791287i \(0.290588\pi\)
−0.611445 + 0.791287i \(0.709412\pi\)
\(770\) 62.0897 3.65736i 0.0806360 0.00474982i
\(771\) −144.694 −0.187671
\(772\) 307.587 + 307.587i 0.398429 + 0.398429i