Properties

Label 1950.2.i.z.451.2
Level $1950$
Weight $2$
Character 1950.451
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.2
Root \(1.28078 + 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 1950.451
Dual form 1950.2.i.z.601.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(1.78078 + 3.08440i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(1.78078 + 3.08440i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.280776 - 0.486319i) q^{11} +1.00000 q^{12} +(2.84233 + 2.21837i) q^{13} -3.56155 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.56155 + 2.70469i) q^{17} +1.00000 q^{18} +(1.21922 + 2.11176i) q^{19} -3.56155 q^{21} +(0.280776 + 0.486319i) q^{22} +(3.84233 - 6.65511i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.34233 + 1.35234i) q^{26} +1.00000 q^{27} +(1.78078 - 3.08440i) q^{28} +(-0.561553 + 0.972638i) q^{29} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.280776 + 0.486319i) q^{33} -3.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.280776 + 0.486319i) q^{37} -2.43845 q^{38} +(-3.34233 + 1.35234i) q^{39} +(1.56155 - 2.70469i) q^{41} +(1.78078 - 3.08440i) q^{42} +(-0.219224 - 0.379706i) q^{43} -0.561553 q^{44} +(3.84233 + 6.65511i) q^{46} +4.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.84233 + 4.92306i) q^{49} -3.12311 q^{51} +(0.500000 - 3.57071i) q^{52} +4.24621 q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.78078 + 3.08440i) q^{56} -2.43845 q^{57} +(-0.561553 - 0.972638i) q^{58} +(5.12311 + 8.87348i) q^{59} +(0.842329 + 1.45896i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.78078 - 3.08440i) q^{63} +1.00000 q^{64} -0.561553 q^{66} +(-5.90388 + 10.2258i) q^{67} +(1.56155 - 2.70469i) q^{68} +(3.84233 + 6.65511i) q^{69} +(-6.28078 - 10.8786i) q^{71} +(-0.500000 - 0.866025i) q^{72} +9.00000 q^{73} +(-0.280776 - 0.486319i) q^{74} +(1.21922 - 2.11176i) q^{76} +2.00000 q^{77} +(0.500000 - 3.57071i) q^{78} -15.8078 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.56155 + 2.70469i) q^{82} +6.56155 q^{83} +(1.78078 + 3.08440i) q^{84} +0.438447 q^{86} +(-0.561553 - 0.972638i) q^{87} +(0.280776 - 0.486319i) q^{88} +(-5.12311 + 8.87348i) q^{89} +(-1.78078 + 12.7173i) q^{91} -7.68466 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-2.00000 + 3.46410i) q^{94} +1.00000 q^{96} +(1.40388 + 2.43160i) q^{97} +(-2.84233 - 4.92306i) q^{98} -0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9} - 3 q^{11} + 4 q^{12} - q^{13} - 6 q^{14} - 2 q^{16} - 2 q^{17} + 4 q^{18} + 9 q^{19} - 6 q^{21} - 3 q^{22} + 3 q^{23} - 2 q^{24} - q^{26} + 4 q^{27} + 3 q^{28} + 6 q^{29} + 16 q^{31} - 2 q^{32} - 3 q^{33} + 4 q^{34} - 2 q^{36} + 3 q^{37} - 18 q^{38} - q^{39} - 2 q^{41} + 3 q^{42} - 5 q^{43} + 6 q^{44} + 3 q^{46} + 16 q^{47} - 2 q^{48} + q^{49} + 4 q^{51} + 2 q^{52} - 16 q^{53} - 2 q^{54} + 3 q^{56} - 18 q^{57} + 6 q^{58} + 4 q^{59} - 9 q^{61} - 8 q^{62} + 3 q^{63} + 4 q^{64} + 6 q^{66} - 3 q^{67} - 2 q^{68} + 3 q^{69} - 21 q^{71} - 2 q^{72} + 36 q^{73} + 3 q^{74} + 9 q^{76} + 8 q^{77} + 2 q^{78} - 22 q^{79} - 2 q^{81} - 2 q^{82} + 18 q^{83} + 3 q^{84} + 10 q^{86} + 6 q^{87} - 3 q^{88} - 4 q^{89} - 3 q^{91} - 6 q^{92} - 8 q^{93} - 8 q^{94} + 4 q^{96} - 15 q^{97} + q^{98} + 6 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 1.78078 + 3.08440i 0.673070 + 1.16579i 0.977029 + 0.213107i \(0.0683582\pi\)
−0.303959 + 0.952685i \(0.598308\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.280776 0.486319i 0.0846573 0.146631i −0.820588 0.571520i \(-0.806354\pi\)
0.905245 + 0.424890i \(0.139687\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.84233 + 2.21837i 0.788320 + 0.615265i
\(14\) −3.56155 −0.951865
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.56155 + 2.70469i 0.378732 + 0.655983i 0.990878 0.134761i \(-0.0430268\pi\)
−0.612146 + 0.790745i \(0.709693\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.21922 + 2.11176i 0.279709 + 0.484470i 0.971312 0.237807i \(-0.0764287\pi\)
−0.691603 + 0.722278i \(0.743095\pi\)
\(20\) 0 0
\(21\) −3.56155 −0.777195
\(22\) 0.280776 + 0.486319i 0.0598617 + 0.103684i
\(23\) 3.84233 6.65511i 0.801181 1.38769i −0.117658 0.993054i \(-0.537539\pi\)
0.918839 0.394632i \(-0.129128\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) −3.34233 + 1.35234i −0.655485 + 0.265217i
\(27\) 1.00000 0.192450
\(28\) 1.78078 3.08440i 0.336535 0.582896i
\(29\) −0.561553 + 0.972638i −0.104278 + 0.180614i −0.913443 0.406967i \(-0.866586\pi\)
0.809165 + 0.587581i \(0.199920\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.280776 + 0.486319i 0.0488769 + 0.0846573i
\(34\) −3.12311 −0.535608
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −0.280776 + 0.486319i −0.0461594 + 0.0799504i −0.888182 0.459492i \(-0.848032\pi\)
0.842023 + 0.539442i \(0.181365\pi\)
\(38\) −2.43845 −0.395568
\(39\) −3.34233 + 1.35234i −0.535201 + 0.216548i
\(40\) 0 0
\(41\) 1.56155 2.70469i 0.243874 0.422401i −0.717941 0.696104i \(-0.754915\pi\)
0.961814 + 0.273703i \(0.0882485\pi\)
\(42\) 1.78078 3.08440i 0.274780 0.475933i
\(43\) −0.219224 0.379706i −0.0334313 0.0579047i 0.848826 0.528673i \(-0.177310\pi\)
−0.882257 + 0.470768i \(0.843977\pi\)
\(44\) −0.561553 −0.0846573
\(45\) 0 0
\(46\) 3.84233 + 6.65511i 0.566521 + 0.981242i
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −2.84233 + 4.92306i −0.406047 + 0.703294i
\(50\) 0 0
\(51\) −3.12311 −0.437322
\(52\) 0.500000 3.57071i 0.0693375 0.495169i
\(53\) 4.24621 0.583262 0.291631 0.956531i \(-0.405802\pi\)
0.291631 + 0.956531i \(0.405802\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 1.78078 + 3.08440i 0.237966 + 0.412170i
\(57\) −2.43845 −0.322980
\(58\) −0.561553 0.972638i −0.0737355 0.127714i
\(59\) 5.12311 + 8.87348i 0.666972 + 1.15523i 0.978747 + 0.205073i \(0.0657431\pi\)
−0.311775 + 0.950156i \(0.600924\pi\)
\(60\) 0 0
\(61\) 0.842329 + 1.45896i 0.107849 + 0.186800i 0.914899 0.403683i \(-0.132270\pi\)
−0.807050 + 0.590484i \(0.798937\pi\)
\(62\) −2.00000 + 3.46410i −0.254000 + 0.439941i
\(63\) 1.78078 3.08440i 0.224357 0.388597i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.561553 −0.0691224
\(67\) −5.90388 + 10.2258i −0.721274 + 1.24928i 0.239215 + 0.970967i \(0.423110\pi\)
−0.960489 + 0.278317i \(0.910224\pi\)
\(68\) 1.56155 2.70469i 0.189366 0.327992i
\(69\) 3.84233 + 6.65511i 0.462562 + 0.801181i
\(70\) 0 0
\(71\) −6.28078 10.8786i −0.745391 1.29106i −0.950012 0.312214i \(-0.898929\pi\)
0.204621 0.978841i \(-0.434404\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 9.00000 1.05337 0.526685 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) −0.280776 0.486319i −0.0326396 0.0565334i
\(75\) 0 0
\(76\) 1.21922 2.11176i 0.139855 0.242235i
\(77\) 2.00000 0.227921
\(78\) 0.500000 3.57071i 0.0566139 0.404304i
\(79\) −15.8078 −1.77851 −0.889256 0.457409i \(-0.848777\pi\)
−0.889256 + 0.457409i \(0.848777\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.56155 + 2.70469i 0.172445 + 0.298683i
\(83\) 6.56155 0.720224 0.360112 0.932909i \(-0.382738\pi\)
0.360112 + 0.932909i \(0.382738\pi\)
\(84\) 1.78078 + 3.08440i 0.194299 + 0.336535i
\(85\) 0 0
\(86\) 0.438447 0.0472790
\(87\) −0.561553 0.972638i −0.0602048 0.104278i
\(88\) 0.280776 0.486319i 0.0299309 0.0518418i
\(89\) −5.12311 + 8.87348i −0.543048 + 0.940587i 0.455679 + 0.890144i \(0.349397\pi\)
−0.998727 + 0.0504427i \(0.983937\pi\)
\(90\) 0 0
\(91\) −1.78078 + 12.7173i −0.186676 + 1.33313i
\(92\) −7.68466 −0.801181
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) −2.00000 + 3.46410i −0.206284 + 0.357295i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 1.40388 + 2.43160i 0.142543 + 0.246891i 0.928453 0.371449i \(-0.121139\pi\)
−0.785911 + 0.618340i \(0.787806\pi\)
\(98\) −2.84233 4.92306i −0.287119 0.497304i
\(99\) −0.561553 −0.0564382
\(100\) 0 0
\(101\) 3.12311 5.40938i 0.310761 0.538253i −0.667767 0.744371i \(-0.732750\pi\)
0.978527 + 0.206118i \(0.0660829\pi\)
\(102\) 1.56155 2.70469i 0.154617 0.267804i
\(103\) −4.43845 −0.437333 −0.218667 0.975800i \(-0.570171\pi\)
−0.218667 + 0.975800i \(0.570171\pi\)
\(104\) 2.84233 + 2.21837i 0.278713 + 0.217529i
\(105\) 0 0
\(106\) −2.12311 + 3.67733i −0.206214 + 0.357174i
\(107\) −2.68466 + 4.64996i −0.259536 + 0.449529i −0.966118 0.258102i \(-0.916903\pi\)
0.706582 + 0.707631i \(0.250236\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −2.80776 −0.268935 −0.134468 0.990918i \(-0.542932\pi\)
−0.134468 + 0.990918i \(0.542932\pi\)
\(110\) 0 0
\(111\) −0.280776 0.486319i −0.0266501 0.0461594i
\(112\) −3.56155 −0.336535
\(113\) −2.00000 3.46410i −0.188144 0.325875i 0.756487 0.654008i \(-0.226914\pi\)
−0.944632 + 0.328133i \(0.893581\pi\)
\(114\) 1.21922 2.11176i 0.114191 0.197784i
\(115\) 0 0
\(116\) 1.12311 0.104278
\(117\) 0.500000 3.57071i 0.0462250 0.330113i
\(118\) −10.2462 −0.943240
\(119\) −5.56155 + 9.63289i −0.509827 + 0.883046i
\(120\) 0 0
\(121\) 5.34233 + 9.25319i 0.485666 + 0.841199i
\(122\) −1.68466 −0.152522
\(123\) 1.56155 + 2.70469i 0.140800 + 0.243874i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 0 0
\(126\) 1.78078 + 3.08440i 0.158644 + 0.274780i
\(127\) −10.9039 + 18.8861i −0.967563 + 1.67587i −0.264998 + 0.964249i \(0.585371\pi\)
−0.702565 + 0.711619i \(0.747962\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0.438447 0.0386031
\(130\) 0 0
\(131\) 0.876894 0.0766146 0.0383073 0.999266i \(-0.487803\pi\)
0.0383073 + 0.999266i \(0.487803\pi\)
\(132\) 0.280776 0.486319i 0.0244384 0.0423286i
\(133\) −4.34233 + 7.52113i −0.376528 + 0.652165i
\(134\) −5.90388 10.2258i −0.510018 0.883377i
\(135\) 0 0
\(136\) 1.56155 + 2.70469i 0.133902 + 0.231925i
\(137\) −8.24621 14.2829i −0.704521 1.22027i −0.966864 0.255292i \(-0.917828\pi\)
0.262343 0.964975i \(-0.415505\pi\)
\(138\) −7.68466 −0.654162
\(139\) −10.7808 18.6729i −0.914414 1.58381i −0.807758 0.589515i \(-0.799319\pi\)
−0.106656 0.994296i \(-0.534014\pi\)
\(140\) 0 0
\(141\) −2.00000 + 3.46410i −0.168430 + 0.291730i
\(142\) 12.5616 1.05414
\(143\) 1.87689 0.759413i 0.156954 0.0635053i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −4.50000 + 7.79423i −0.372423 + 0.645055i
\(147\) −2.84233 4.92306i −0.234431 0.406047i
\(148\) 0.561553 0.0461594
\(149\) 5.12311 + 8.87348i 0.419701 + 0.726944i 0.995909 0.0903593i \(-0.0288015\pi\)
−0.576208 + 0.817303i \(0.695468\pi\)
\(150\) 0 0
\(151\) −16.6847 −1.35778 −0.678889 0.734241i \(-0.737538\pi\)
−0.678889 + 0.734241i \(0.737538\pi\)
\(152\) 1.21922 + 2.11176i 0.0988921 + 0.171286i
\(153\) 1.56155 2.70469i 0.126244 0.218661i
\(154\) −1.00000 + 1.73205i −0.0805823 + 0.139573i
\(155\) 0 0
\(156\) 2.84233 + 2.21837i 0.227568 + 0.177612i
\(157\) 17.2462 1.37640 0.688199 0.725522i \(-0.258402\pi\)
0.688199 + 0.725522i \(0.258402\pi\)
\(158\) 7.90388 13.6899i 0.628799 1.08911i
\(159\) −2.12311 + 3.67733i −0.168373 + 0.291631i
\(160\) 0 0
\(161\) 27.3693 2.15700
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 8.24621 + 14.2829i 0.645893 + 1.11872i 0.984094 + 0.177646i \(0.0568482\pi\)
−0.338201 + 0.941074i \(0.609818\pi\)
\(164\) −3.12311 −0.243874
\(165\) 0 0
\(166\) −3.28078 + 5.68247i −0.254638 + 0.441045i
\(167\) −11.8423 + 20.5115i −0.916387 + 1.58723i −0.111529 + 0.993761i \(0.535575\pi\)
−0.804858 + 0.593468i \(0.797759\pi\)
\(168\) −3.56155 −0.274780
\(169\) 3.15767 + 12.6107i 0.242898 + 0.970052i
\(170\) 0 0
\(171\) 1.21922 2.11176i 0.0932364 0.161490i
\(172\) −0.219224 + 0.379706i −0.0167156 + 0.0289523i
\(173\) 4.43845 + 7.68762i 0.337449 + 0.584479i 0.983952 0.178433i \(-0.0571027\pi\)
−0.646503 + 0.762911i \(0.723769\pi\)
\(174\) 1.12311 0.0851424
\(175\) 0 0
\(176\) 0.280776 + 0.486319i 0.0211643 + 0.0366577i
\(177\) −10.2462 −0.770152
\(178\) −5.12311 8.87348i −0.383993 0.665095i
\(179\) 7.84233 13.5833i 0.586163 1.01526i −0.408566 0.912729i \(-0.633971\pi\)
0.994729 0.102536i \(-0.0326956\pi\)
\(180\) 0 0
\(181\) −15.4924 −1.15154 −0.575771 0.817611i \(-0.695298\pi\)
−0.575771 + 0.817611i \(0.695298\pi\)
\(182\) −10.1231 7.90084i −0.750375 0.585649i
\(183\) −1.68466 −0.124534
\(184\) 3.84233 6.65511i 0.283260 0.490621i
\(185\) 0 0
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 1.75379 0.128250
\(188\) −2.00000 3.46410i −0.145865 0.252646i
\(189\) 1.78078 + 3.08440i 0.129532 + 0.224357i
\(190\) 0 0
\(191\) −7.96543 13.7965i −0.576359 0.998282i −0.995893 0.0905428i \(-0.971140\pi\)
0.419534 0.907740i \(-0.362194\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.50000 + 2.59808i −0.107972 + 0.187014i −0.914949 0.403570i \(-0.867769\pi\)
0.806976 + 0.590584i \(0.201102\pi\)
\(194\) −2.80776 −0.201586
\(195\) 0 0
\(196\) 5.68466 0.406047
\(197\) −2.56155 + 4.43674i −0.182503 + 0.316105i −0.942732 0.333550i \(-0.891753\pi\)
0.760229 + 0.649655i \(0.225087\pi\)
\(198\) 0.280776 0.486319i 0.0199539 0.0345612i
\(199\) 2.21922 + 3.84381i 0.157317 + 0.272480i 0.933900 0.357534i \(-0.116382\pi\)
−0.776584 + 0.630014i \(0.783049\pi\)
\(200\) 0 0
\(201\) −5.90388 10.2258i −0.416428 0.721274i
\(202\) 3.12311 + 5.40938i 0.219741 + 0.380602i
\(203\) −4.00000 −0.280745
\(204\) 1.56155 + 2.70469i 0.109331 + 0.189366i
\(205\) 0 0
\(206\) 2.21922 3.84381i 0.154621 0.267811i
\(207\) −7.68466 −0.534121
\(208\) −3.34233 + 1.35234i −0.231749 + 0.0937682i
\(209\) 1.36932 0.0947176
\(210\) 0 0
\(211\) −0.561553 + 0.972638i −0.0386589 + 0.0669592i −0.884707 0.466147i \(-0.845642\pi\)
0.846049 + 0.533106i \(0.178975\pi\)
\(212\) −2.12311 3.67733i −0.145815 0.252560i
\(213\) 12.5616 0.860703
\(214\) −2.68466 4.64996i −0.183519 0.317865i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 7.12311 + 12.3376i 0.483548 + 0.837530i
\(218\) 1.40388 2.43160i 0.0950829 0.164688i
\(219\) −4.50000 + 7.79423i −0.304082 + 0.526685i
\(220\) 0 0
\(221\) −1.56155 + 11.1517i −0.105041 + 0.750146i
\(222\) 0.561553 0.0376890
\(223\) 0.219224 0.379706i 0.0146803 0.0254270i −0.858592 0.512660i \(-0.828660\pi\)
0.873272 + 0.487233i \(0.161994\pi\)
\(224\) 1.78078 3.08440i 0.118983 0.206085i
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) −14.8423 25.7077i −0.985120 1.70628i −0.641402 0.767205i \(-0.721647\pi\)
−0.343718 0.939073i \(-0.611686\pi\)
\(228\) 1.21922 + 2.11176i 0.0807451 + 0.139855i
\(229\) 9.49242 0.627277 0.313638 0.949542i \(-0.398452\pi\)
0.313638 + 0.949542i \(0.398452\pi\)
\(230\) 0 0
\(231\) −1.00000 + 1.73205i −0.0657952 + 0.113961i
\(232\) −0.561553 + 0.972638i −0.0368677 + 0.0638568i
\(233\) −25.3693 −1.66200 −0.831000 0.556273i \(-0.812231\pi\)
−0.831000 + 0.556273i \(0.812231\pi\)
\(234\) 2.84233 + 2.21837i 0.185809 + 0.145019i
\(235\) 0 0
\(236\) 5.12311 8.87348i 0.333486 0.577614i
\(237\) 7.90388 13.6899i 0.513412 0.889256i
\(238\) −5.56155 9.63289i −0.360502 0.624408i
\(239\) 27.0540 1.74998 0.874988 0.484144i \(-0.160869\pi\)
0.874988 + 0.484144i \(0.160869\pi\)
\(240\) 0 0
\(241\) −7.78078 13.4767i −0.501204 0.868111i −0.999999 0.00139067i \(-0.999557\pi\)
0.498795 0.866720i \(-0.333776\pi\)
\(242\) −10.6847 −0.686836
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0.842329 1.45896i 0.0539246 0.0934002i
\(245\) 0 0
\(246\) −3.12311 −0.199122
\(247\) −1.21922 + 8.70700i −0.0775773 + 0.554013i
\(248\) 4.00000 0.254000
\(249\) −3.28078 + 5.68247i −0.207911 + 0.360112i
\(250\) 0 0
\(251\) −11.9654 20.7247i −0.755252 1.30813i −0.945249 0.326350i \(-0.894181\pi\)
0.189998 0.981785i \(-0.439152\pi\)
\(252\) −3.56155 −0.224357
\(253\) −2.15767 3.73720i −0.135652 0.234955i
\(254\) −10.9039 18.8861i −0.684170 1.18502i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.80776 11.7914i 0.424657 0.735527i −0.571732 0.820441i \(-0.693728\pi\)
0.996388 + 0.0849138i \(0.0270615\pi\)
\(258\) −0.219224 + 0.379706i −0.0136483 + 0.0236395i
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) 1.12311 0.0695185
\(262\) −0.438447 + 0.759413i −0.0270874 + 0.0469167i
\(263\) −3.15767 + 5.46925i −0.194710 + 0.337248i −0.946806 0.321806i \(-0.895710\pi\)
0.752095 + 0.659054i \(0.229043\pi\)
\(264\) 0.280776 + 0.486319i 0.0172806 + 0.0299309i
\(265\) 0 0
\(266\) −4.34233 7.52113i −0.266245 0.461150i
\(267\) −5.12311 8.87348i −0.313529 0.543048i
\(268\) 11.8078 0.721274
\(269\) 1.68466 + 2.91791i 0.102715 + 0.177908i 0.912803 0.408401i \(-0.133914\pi\)
−0.810087 + 0.586310i \(0.800580\pi\)
\(270\) 0 0
\(271\) −4.46543 + 7.73436i −0.271256 + 0.469829i −0.969184 0.246339i \(-0.920772\pi\)
0.697928 + 0.716168i \(0.254106\pi\)
\(272\) −3.12311 −0.189366
\(273\) −10.1231 7.90084i −0.612678 0.478181i
\(274\) 16.4924 0.996344
\(275\) 0 0
\(276\) 3.84233 6.65511i 0.231281 0.400591i
\(277\) −2.50000 4.33013i −0.150210 0.260172i 0.781094 0.624413i \(-0.214662\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 21.5616 1.29318
\(279\) −2.00000 3.46410i −0.119737 0.207390i
\(280\) 0 0
\(281\) −1.75379 −0.104622 −0.0523111 0.998631i \(-0.516659\pi\)
−0.0523111 + 0.998631i \(0.516659\pi\)
\(282\) −2.00000 3.46410i −0.119098 0.206284i
\(283\) −14.8078 + 25.6478i −0.880230 + 1.52460i −0.0291454 + 0.999575i \(0.509279\pi\)
−0.851085 + 0.525028i \(0.824055\pi\)
\(284\) −6.28078 + 10.8786i −0.372696 + 0.645528i
\(285\) 0 0
\(286\) −0.280776 + 2.00514i −0.0166027 + 0.118567i
\(287\) 11.1231 0.656576
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 3.62311 6.27540i 0.213124 0.369141i
\(290\) 0 0
\(291\) −2.80776 −0.164594
\(292\) −4.50000 7.79423i −0.263343 0.456123i
\(293\) −10.1231 17.5337i −0.591398 1.02433i −0.994044 0.108976i \(-0.965243\pi\)
0.402646 0.915356i \(-0.368090\pi\)
\(294\) 5.68466 0.331536
\(295\) 0 0
\(296\) −0.280776 + 0.486319i −0.0163198 + 0.0282667i
\(297\) 0.280776 0.486319i 0.0162923 0.0282191i
\(298\) −10.2462 −0.593547
\(299\) 25.6847 10.3923i 1.48538 0.601003i
\(300\) 0 0
\(301\) 0.780776 1.35234i 0.0450032 0.0779478i
\(302\) 8.34233 14.4493i 0.480047 0.831466i
\(303\) 3.12311 + 5.40938i 0.179418 + 0.310761i
\(304\) −2.43845 −0.139855
\(305\) 0 0
\(306\) 1.56155 + 2.70469i 0.0892680 + 0.154617i
\(307\) 22.2462 1.26966 0.634829 0.772653i \(-0.281070\pi\)
0.634829 + 0.772653i \(0.281070\pi\)
\(308\) −1.00000 1.73205i −0.0569803 0.0986928i
\(309\) 2.21922 3.84381i 0.126247 0.218667i
\(310\) 0 0
\(311\) −10.3153 −0.584929 −0.292465 0.956276i \(-0.594475\pi\)
−0.292465 + 0.956276i \(0.594475\pi\)
\(312\) −3.34233 + 1.35234i −0.189222 + 0.0765614i
\(313\) 31.0000 1.75222 0.876112 0.482108i \(-0.160129\pi\)
0.876112 + 0.482108i \(0.160129\pi\)
\(314\) −8.62311 + 14.9357i −0.486630 + 0.842868i
\(315\) 0 0
\(316\) 7.90388 + 13.6899i 0.444628 + 0.770118i
\(317\) 16.2462 0.912478 0.456239 0.889857i \(-0.349196\pi\)
0.456239 + 0.889857i \(0.349196\pi\)
\(318\) −2.12311 3.67733i −0.119058 0.206214i
\(319\) 0.315342 + 0.546188i 0.0176557 + 0.0305806i
\(320\) 0 0
\(321\) −2.68466 4.64996i −0.149843 0.259536i
\(322\) −13.6847 + 23.7025i −0.762616 + 1.32089i
\(323\) −3.80776 + 6.59524i −0.211870 + 0.366969i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −16.4924 −0.913431
\(327\) 1.40388 2.43160i 0.0776349 0.134468i
\(328\) 1.56155 2.70469i 0.0862223 0.149341i
\(329\) 7.12311 + 12.3376i 0.392710 + 0.680193i
\(330\) 0 0
\(331\) 8.34233 + 14.4493i 0.458536 + 0.794207i 0.998884 0.0472342i \(-0.0150407\pi\)
−0.540348 + 0.841442i \(0.681707\pi\)
\(332\) −3.28078 5.68247i −0.180056 0.311866i
\(333\) 0.561553 0.0307729
\(334\) −11.8423 20.5115i −0.647983 1.12234i
\(335\) 0 0
\(336\) 1.78078 3.08440i 0.0971493 0.168268i
\(337\) 8.05398 0.438728 0.219364 0.975643i \(-0.429602\pi\)
0.219364 + 0.975643i \(0.429602\pi\)
\(338\) −12.5000 3.57071i −0.679910 0.194221i
\(339\) 4.00000 0.217250
\(340\) 0 0
\(341\) 1.12311 1.94528i 0.0608196 0.105343i
\(342\) 1.21922 + 2.11176i 0.0659281 + 0.114191i
\(343\) 4.68466 0.252948
\(344\) −0.219224 0.379706i −0.0118197 0.0204724i
\(345\) 0 0
\(346\) −8.87689 −0.477225
\(347\) 12.4039 + 21.4842i 0.665875 + 1.15333i 0.979047 + 0.203633i \(0.0652751\pi\)
−0.313172 + 0.949696i \(0.601392\pi\)
\(348\) −0.561553 + 0.972638i −0.0301024 + 0.0521389i
\(349\) 9.62311 16.6677i 0.515113 0.892202i −0.484733 0.874662i \(-0.661083\pi\)
0.999846 0.0175398i \(-0.00558339\pi\)
\(350\) 0 0
\(351\) 2.84233 + 2.21837i 0.151712 + 0.118408i
\(352\) −0.561553 −0.0299309
\(353\) −1.12311 + 1.94528i −0.0597769 + 0.103537i −0.894365 0.447338i \(-0.852372\pi\)
0.834588 + 0.550874i \(0.185706\pi\)
\(354\) 5.12311 8.87348i 0.272290 0.471620i
\(355\) 0 0
\(356\) 10.2462 0.543048
\(357\) −5.56155 9.63289i −0.294349 0.509827i
\(358\) 7.84233 + 13.5833i 0.414480 + 0.717900i
\(359\) −4.87689 −0.257393 −0.128696 0.991684i \(-0.541079\pi\)
−0.128696 + 0.991684i \(0.541079\pi\)
\(360\) 0 0
\(361\) 6.52699 11.3051i 0.343526 0.595004i
\(362\) 7.74621 13.4168i 0.407132 0.705173i
\(363\) −10.6847 −0.560799
\(364\) 11.9039 4.81645i 0.623933 0.252450i
\(365\) 0 0
\(366\) 0.842329 1.45896i 0.0440293 0.0762609i
\(367\) 5.09612 8.82674i 0.266015 0.460752i −0.701814 0.712360i \(-0.747626\pi\)
0.967829 + 0.251609i \(0.0809595\pi\)
\(368\) 3.84233 + 6.65511i 0.200295 + 0.346922i
\(369\) −3.12311 −0.162582
\(370\) 0 0
\(371\) 7.56155 + 13.0970i 0.392576 + 0.679962i
\(372\) 4.00000 0.207390
\(373\) 4.74621 + 8.22068i 0.245750 + 0.425651i 0.962342 0.271841i \(-0.0876326\pi\)
−0.716593 + 0.697492i \(0.754299\pi\)
\(374\) −0.876894 + 1.51883i −0.0453431 + 0.0785366i
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) −3.75379 + 1.51883i −0.193330 + 0.0782235i
\(378\) −3.56155 −0.183187
\(379\) 12.0270 20.8314i 0.617785 1.07003i −0.372104 0.928191i \(-0.621364\pi\)
0.989889 0.141844i \(-0.0453031\pi\)
\(380\) 0 0
\(381\) −10.9039 18.8861i −0.558623 0.967563i
\(382\) 15.9309 0.815094
\(383\) 2.71922 + 4.70983i 0.138946 + 0.240661i 0.927098 0.374819i \(-0.122295\pi\)
−0.788152 + 0.615481i \(0.788962\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) −1.50000 2.59808i −0.0763480 0.132239i
\(387\) −0.219224 + 0.379706i −0.0111438 + 0.0193016i
\(388\) 1.40388 2.43160i 0.0712713 0.123446i
\(389\) 11.3693 0.576447 0.288224 0.957563i \(-0.406935\pi\)
0.288224 + 0.957563i \(0.406935\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) −2.84233 + 4.92306i −0.143559 + 0.248652i
\(393\) −0.438447 + 0.759413i −0.0221167 + 0.0383073i
\(394\) −2.56155 4.43674i −0.129049 0.223520i
\(395\) 0 0
\(396\) 0.280776 + 0.486319i 0.0141095 + 0.0244384i
\(397\) 4.90388 + 8.49377i 0.246119 + 0.426290i 0.962446 0.271475i \(-0.0875113\pi\)
−0.716327 + 0.697765i \(0.754178\pi\)
\(398\) −4.43845 −0.222479
\(399\) −4.34233 7.52113i −0.217388 0.376528i
\(400\) 0 0
\(401\) 6.31534 10.9385i 0.315373 0.546242i −0.664144 0.747605i \(-0.731204\pi\)
0.979517 + 0.201363i \(0.0645370\pi\)
\(402\) 11.8078 0.588918
\(403\) 11.3693 + 8.87348i 0.566346 + 0.442019i
\(404\) −6.24621 −0.310761
\(405\) 0 0
\(406\) 2.00000 3.46410i 0.0992583 0.171920i
\(407\) 0.157671 + 0.273094i 0.00781545 + 0.0135368i
\(408\) −3.12311 −0.154617
\(409\) −8.12311 14.0696i −0.401662 0.695699i 0.592265 0.805743i \(-0.298234\pi\)
−0.993927 + 0.110045i \(0.964901\pi\)
\(410\) 0 0
\(411\) 16.4924 0.813511
\(412\) 2.21922 + 3.84381i 0.109333 + 0.189371i
\(413\) −18.2462 + 31.6034i −0.897837 + 1.55510i
\(414\) 3.84233 6.65511i 0.188840 0.327081i
\(415\) 0 0
\(416\) 0.500000 3.57071i 0.0245145 0.175069i
\(417\) 21.5616 1.05587
\(418\) −0.684658 + 1.18586i −0.0334877 + 0.0580025i
\(419\) 5.96543 10.3324i 0.291431 0.504773i −0.682718 0.730682i \(-0.739202\pi\)
0.974148 + 0.225910i \(0.0725354\pi\)
\(420\) 0 0
\(421\) 31.2462 1.52285 0.761424 0.648255i \(-0.224501\pi\)
0.761424 + 0.648255i \(0.224501\pi\)
\(422\) −0.561553 0.972638i −0.0273360 0.0473473i
\(423\) −2.00000 3.46410i −0.0972433 0.168430i
\(424\) 4.24621 0.206214
\(425\) 0 0
\(426\) −6.28078 + 10.8786i −0.304305 + 0.527071i
\(427\) −3.00000 + 5.19615i −0.145180 + 0.251459i
\(428\) 5.36932 0.259536
\(429\) −0.280776 + 2.00514i −0.0135560 + 0.0968093i
\(430\) 0 0
\(431\) −9.15767 + 15.8616i −0.441109 + 0.764024i −0.997772 0.0667146i \(-0.978748\pi\)
0.556663 + 0.830739i \(0.312082\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 6.84233 + 11.8513i 0.328821 + 0.569535i 0.982278 0.187428i \(-0.0600153\pi\)
−0.653457 + 0.756964i \(0.726682\pi\)
\(434\) −14.2462 −0.683840
\(435\) 0 0
\(436\) 1.40388 + 2.43160i 0.0672338 + 0.116452i
\(437\) 18.7386 0.896390
\(438\) −4.50000 7.79423i −0.215018 0.372423i
\(439\) 3.46543 6.00231i 0.165396 0.286475i −0.771400 0.636351i \(-0.780443\pi\)
0.936796 + 0.349876i \(0.113776\pi\)
\(440\) 0 0
\(441\) 5.68466 0.270698
\(442\) −8.87689 6.92820i −0.422231 0.329541i
\(443\) −2.80776 −0.133401 −0.0667004 0.997773i \(-0.521247\pi\)
−0.0667004 + 0.997773i \(0.521247\pi\)
\(444\) −0.280776 + 0.486319i −0.0133251 + 0.0230797i
\(445\) 0 0
\(446\) 0.219224 + 0.379706i 0.0103805 + 0.0179796i
\(447\) −10.2462 −0.484629
\(448\) 1.78078 + 3.08440i 0.0841338 + 0.145724i
\(449\) 1.56155 + 2.70469i 0.0736942 + 0.127642i 0.900518 0.434819i \(-0.143188\pi\)
−0.826823 + 0.562462i \(0.809854\pi\)
\(450\) 0 0
\(451\) −0.876894 1.51883i −0.0412913 0.0715187i
\(452\) −2.00000 + 3.46410i −0.0940721 + 0.162938i
\(453\) 8.34233 14.4493i 0.391957 0.678889i
\(454\) 29.6847 1.39317
\(455\) 0 0
\(456\) −2.43845 −0.114191
\(457\) −2.25379 + 3.90368i −0.105428 + 0.182606i −0.913913 0.405910i \(-0.866955\pi\)
0.808485 + 0.588517i \(0.200288\pi\)
\(458\) −4.74621 + 8.22068i −0.221776 + 0.384127i
\(459\) 1.56155 + 2.70469i 0.0728870 + 0.126244i
\(460\) 0 0
\(461\) −5.31534 9.20644i −0.247560 0.428787i 0.715288 0.698830i \(-0.246295\pi\)
−0.962848 + 0.270043i \(0.912962\pi\)
\(462\) −1.00000 1.73205i −0.0465242 0.0805823i
\(463\) 27.8078 1.29234 0.646168 0.763195i \(-0.276370\pi\)
0.646168 + 0.763195i \(0.276370\pi\)
\(464\) −0.561553 0.972638i −0.0260694 0.0451536i
\(465\) 0 0
\(466\) 12.6847 21.9705i 0.587605 1.01776i
\(467\) −3.43845 −0.159112 −0.0795562 0.996830i \(-0.525350\pi\)
−0.0795562 + 0.996830i \(0.525350\pi\)
\(468\) −3.34233 + 1.35234i −0.154499 + 0.0625121i
\(469\) −42.0540 −1.94187
\(470\) 0 0
\(471\) −8.62311 + 14.9357i −0.397332 + 0.688199i
\(472\) 5.12311 + 8.87348i 0.235810 + 0.408435i
\(473\) −0.246211 −0.0113208
\(474\) 7.90388 + 13.6899i 0.363037 + 0.628799i
\(475\) 0 0
\(476\) 11.1231 0.509827
\(477\) −2.12311 3.67733i −0.0972103 0.168373i
\(478\) −13.5270 + 23.4294i −0.618710 + 1.07164i
\(479\) 5.80776 10.0593i 0.265364 0.459623i −0.702295 0.711886i \(-0.747841\pi\)
0.967659 + 0.252263i \(0.0811747\pi\)
\(480\) 0 0
\(481\) −1.87689 + 0.759413i −0.0855790 + 0.0346262i
\(482\) 15.5616 0.708809
\(483\) −13.6847 + 23.7025i −0.622674 + 1.07850i
\(484\) 5.34233 9.25319i 0.242833 0.420599i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −21.3423 36.9660i −0.967113 1.67509i −0.703827 0.710372i \(-0.748527\pi\)
−0.263286 0.964718i \(-0.584806\pi\)
\(488\) 0.842329 + 1.45896i 0.0381305 + 0.0660439i
\(489\) −16.4924 −0.745813
\(490\) 0 0
\(491\) −15.6501 + 27.1068i −0.706279 + 1.22331i 0.259949 + 0.965622i \(0.416294\pi\)
−0.966228 + 0.257689i \(0.917039\pi\)
\(492\) 1.56155 2.70469i 0.0704002 0.121937i
\(493\) −3.50758 −0.157973
\(494\) −6.93087 5.40938i −0.311835 0.243379i
\(495\) 0 0
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) 22.3693 38.7448i 1.00340 1.73794i
\(498\) −3.28078 5.68247i −0.147015 0.254638i
\(499\) 6.05398 0.271013 0.135507 0.990776i \(-0.456734\pi\)
0.135507 + 0.990776i \(0.456734\pi\)
\(500\) 0 0
\(501\) −11.8423 20.5115i −0.529076 0.916387i
\(502\) 23.9309 1.06809
\(503\) 12.1577 + 21.0577i 0.542084 + 0.938917i 0.998784 + 0.0492961i \(0.0156978\pi\)
−0.456700 + 0.889621i \(0.650969\pi\)
\(504\) 1.78078 3.08440i 0.0793221 0.137390i
\(505\) 0 0
\(506\) 4.31534 0.191840
\(507\) −12.5000 3.57071i −0.555144 0.158581i
\(508\) 21.8078 0.967563
\(509\) 8.12311 14.0696i 0.360050 0.623625i −0.627918 0.778279i \(-0.716093\pi\)
0.987969 + 0.154654i \(0.0494262\pi\)
\(510\) 0 0
\(511\) 16.0270 + 27.7596i 0.708992 + 1.22801i
\(512\) 1.00000 0.0441942
\(513\) 1.21922 + 2.11176i 0.0538300 + 0.0932364i
\(514\) 6.80776 + 11.7914i 0.300278 + 0.520096i
\(515\) 0 0
\(516\) −0.219224 0.379706i −0.00965078 0.0167156i
\(517\) 1.12311 1.94528i 0.0493941 0.0855531i
\(518\) 1.00000 1.73205i 0.0439375 0.0761019i
\(519\) −8.87689 −0.389652
\(520\) 0 0
\(521\) 34.7386 1.52193 0.760964 0.648795i \(-0.224727\pi\)
0.760964 + 0.648795i \(0.224727\pi\)
\(522\) −0.561553 + 0.972638i −0.0245785 + 0.0425712i
\(523\) −12.4654 + 21.5908i −0.545075 + 0.944098i 0.453527 + 0.891243i \(0.350166\pi\)
−0.998602 + 0.0528556i \(0.983168\pi\)
\(524\) −0.438447 0.759413i −0.0191537 0.0331751i
\(525\) 0 0
\(526\) −3.15767 5.46925i −0.137681 0.238470i
\(527\) 6.24621 + 10.8188i 0.272089 + 0.471272i
\(528\) −0.561553 −0.0244384
\(529\) −18.0270 31.2237i −0.783782 1.35755i
\(530\) 0 0
\(531\) 5.12311 8.87348i 0.222324 0.385076i
\(532\) 8.68466 0.376528
\(533\) 10.4384 4.22351i 0.452139 0.182941i
\(534\) 10.2462 0.443397
\(535\) 0 0
\(536\) −5.90388 + 10.2258i −0.255009 + 0.441688i
\(537\) 7.84233 + 13.5833i 0.338421 + 0.586163i
\(538\) −3.36932 −0.145262
\(539\) 1.59612 + 2.76456i 0.0687497 + 0.119078i
\(540\) 0 0
\(541\) −22.3153 −0.959411 −0.479706 0.877429i \(-0.659257\pi\)
−0.479706 + 0.877429i \(0.659257\pi\)
\(542\) −4.46543 7.73436i −0.191807 0.332219i
\(543\) 7.74621 13.4168i 0.332422 0.575771i
\(544\) 1.56155 2.70469i 0.0669510 0.115963i
\(545\) 0 0
\(546\) 11.9039 4.81645i 0.509439 0.206125i
\(547\) −30.9309 −1.32251 −0.661254 0.750162i \(-0.729976\pi\)
−0.661254 + 0.750162i \(0.729976\pi\)
\(548\) −8.24621 + 14.2829i −0.352261 + 0.610133i
\(549\) 0.842329 1.45896i 0.0359497 0.0622668i
\(550\) 0 0
\(551\) −2.73863 −0.116670
\(552\) 3.84233 + 6.65511i 0.163540 + 0.283260i
\(553\) −28.1501 48.7574i −1.19706 2.07338i
\(554\) 5.00000 0.212430
\(555\) 0 0
\(556\) −10.7808 + 18.6729i −0.457207 + 0.791905i
\(557\) 15.8078 27.3799i 0.669796 1.16012i −0.308164 0.951333i \(-0.599715\pi\)
0.977961 0.208788i \(-0.0669520\pi\)
\(558\) 4.00000 0.169334
\(559\) 0.219224 1.56557i 0.00927217 0.0662165i
\(560\) 0 0
\(561\) −0.876894 + 1.51883i −0.0370225 + 0.0641249i
\(562\) 0.876894 1.51883i 0.0369896 0.0640678i
\(563\) −10.4039 18.0201i −0.438471 0.759455i 0.559100 0.829100i \(-0.311147\pi\)
−0.997572 + 0.0696453i \(0.977813\pi\)
\(564\) 4.00000 0.168430
\(565\) 0 0
\(566\) −14.8078 25.6478i −0.622417 1.07806i
\(567\) −3.56155 −0.149571
\(568\) −6.28078 10.8786i −0.263536 0.456457i
\(569\) 5.75379 9.96585i 0.241211 0.417790i −0.719848 0.694131i \(-0.755789\pi\)
0.961060 + 0.276341i \(0.0891220\pi\)
\(570\) 0 0
\(571\) 21.4233 0.896537 0.448268 0.893899i \(-0.352041\pi\)
0.448268 + 0.893899i \(0.352041\pi\)
\(572\) −1.59612 1.24573i −0.0667370 0.0520867i
\(573\) 15.9309 0.665522
\(574\) −5.56155 + 9.63289i −0.232135 + 0.402069i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 23.0000 0.957503 0.478751 0.877951i \(-0.341090\pi\)
0.478751 + 0.877951i \(0.341090\pi\)
\(578\) 3.62311 + 6.27540i 0.150701 + 0.261022i
\(579\) −1.50000 2.59808i −0.0623379 0.107972i
\(580\) 0 0
\(581\) 11.6847 + 20.2384i 0.484761 + 0.839631i
\(582\) 1.40388 2.43160i 0.0581928 0.100793i
\(583\) 1.19224 2.06501i 0.0493774 0.0855241i
\(584\) 9.00000 0.372423
\(585\) 0 0
\(586\) 20.2462 0.836363
\(587\) 8.96543 15.5286i 0.370043 0.640933i −0.619529 0.784974i \(-0.712676\pi\)
0.989572 + 0.144041i \(0.0460096\pi\)
\(588\) −2.84233 + 4.92306i −0.117216 + 0.203024i
\(589\) 4.87689 + 8.44703i 0.200949 + 0.348054i
\(590\) 0 0
\(591\) −2.56155 4.43674i −0.105368 0.182503i
\(592\) −0.280776 0.486319i −0.0115398 0.0199876i
\(593\) −38.9848 −1.60092 −0.800458 0.599389i \(-0.795410\pi\)
−0.800458 + 0.599389i \(0.795410\pi\)
\(594\) 0.280776 + 0.486319i 0.0115204 + 0.0199539i
\(595\) 0 0
\(596\) 5.12311 8.87348i 0.209851 0.363472i
\(597\) −4.43845 −0.181654
\(598\) −3.84233 + 27.4397i −0.157125 + 1.12209i
\(599\) −18.3153 −0.748345 −0.374172 0.927359i \(-0.622073\pi\)
−0.374172 + 0.927359i \(0.622073\pi\)
\(600\) 0 0
\(601\) 2.90388 5.02967i 0.118452 0.205165i −0.800703 0.599062i \(-0.795540\pi\)
0.919154 + 0.393898i \(0.128874\pi\)
\(602\) 0.780776 + 1.35234i 0.0318221 + 0.0551174i
\(603\) 11.8078 0.480849
\(604\) 8.34233 + 14.4493i 0.339445 + 0.587935i
\(605\) 0 0
\(606\) −6.24621 −0.253735
\(607\) 19.6847 + 34.0948i 0.798976 + 1.38387i 0.920284 + 0.391252i \(0.127958\pi\)
−0.121308 + 0.992615i \(0.538709\pi\)
\(608\) 1.21922 2.11176i 0.0494460 0.0856431i
\(609\) 2.00000 3.46410i 0.0810441 0.140372i
\(610\) 0 0
\(611\) 11.3693 + 8.87348i 0.459953 + 0.358983i
\(612\) −3.12311 −0.126244
\(613\) 18.2732 31.6501i 0.738048 1.27834i −0.215326 0.976542i \(-0.569081\pi\)
0.953373 0.301794i \(-0.0975853\pi\)
\(614\) −11.1231 + 19.2658i −0.448892 + 0.777504i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −23.6847 41.0230i −0.953508 1.65153i −0.737745 0.675079i \(-0.764109\pi\)
−0.215763 0.976446i \(-0.569224\pi\)
\(618\) 2.21922 + 3.84381i 0.0892703 + 0.154621i
\(619\) −12.3002 −0.494386 −0.247193 0.968966i \(-0.579508\pi\)
−0.247193 + 0.968966i \(0.579508\pi\)
\(620\) 0 0
\(621\) 3.84233 6.65511i 0.154187 0.267060i
\(622\) 5.15767 8.93335i 0.206804 0.358195i
\(623\) −36.4924 −1.46204
\(624\) 0.500000 3.57071i 0.0200160 0.142943i
\(625\) 0 0
\(626\) −15.5000 + 26.8468i −0.619505 + 1.07301i
\(627\) −0.684658 + 1.18586i −0.0273426 + 0.0473588i
\(628\) −8.62311 14.9357i −0.344099 0.595998i
\(629\) −1.75379 −0.0699281
\(630\) 0 0
\(631\) −16.4654 28.5190i −0.655479 1.13532i −0.981774 0.190054i \(-0.939134\pi\)
0.326295 0.945268i \(-0.394200\pi\)
\(632\) −15.8078 −0.628799
\(633\) −0.561553 0.972638i −0.0223197 0.0386589i
\(634\) −8.12311 + 14.0696i −0.322610 + 0.558776i
\(635\) 0 0
\(636\) 4.24621 0.168373
\(637\) −19.0000 + 7.68762i −0.752807 + 0.304594i
\(638\) −0.630683 −0.0249690
\(639\) −6.28078 + 10.8786i −0.248464 + 0.430352i
\(640\) 0 0
\(641\) −19.1231 33.1222i −0.755317 1.30825i −0.945216 0.326444i \(-0.894149\pi\)
0.189899 0.981804i \(-0.439184\pi\)
\(642\) 5.36932 0.211910
\(643\) −12.2732 21.2578i −0.484008 0.838326i 0.515824 0.856695i \(-0.327486\pi\)
−0.999831 + 0.0183689i \(0.994153\pi\)
\(644\) −13.6847 23.7025i −0.539251 0.934010i
\(645\) 0 0
\(646\) −3.80776 6.59524i −0.149814 0.259486i
\(647\) −16.2116 + 28.0794i −0.637346 + 1.10391i 0.348667 + 0.937247i \(0.386634\pi\)
−0.986013 + 0.166668i \(0.946699\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 5.75379 0.225856
\(650\) 0 0
\(651\) −14.2462 −0.558353
\(652\) 8.24621 14.2829i 0.322947 0.559360i
\(653\) 18.8078 32.5760i 0.736005 1.27480i −0.218276 0.975887i \(-0.570043\pi\)
0.954281 0.298911i \(-0.0966232\pi\)
\(654\) 1.40388 + 2.43160i 0.0548961 + 0.0950829i
\(655\) 0 0
\(656\) 1.56155 + 2.70469i 0.0609684 + 0.105600i
\(657\) −4.50000 7.79423i −0.175562 0.304082i
\(658\) −14.2462 −0.555375
\(659\) −9.15767 15.8616i −0.356732 0.617878i 0.630681 0.776042i \(-0.282776\pi\)
−0.987413 + 0.158164i \(0.949442\pi\)
\(660\) 0 0
\(661\) 24.2732 42.0424i 0.944118 1.63526i 0.186610 0.982434i \(-0.440250\pi\)
0.757508 0.652826i \(-0.226417\pi\)
\(662\) −16.6847 −0.648468
\(663\) −8.87689 6.92820i −0.344750 0.269069i
\(664\) 6.56155 0.254638
\(665\) 0 0
\(666\) −0.280776 + 0.486319i −0.0108799 + 0.0188445i
\(667\) 4.31534 + 7.47439i 0.167091 + 0.289410i
\(668\) 23.6847 0.916387
\(669\) 0.219224 + 0.379706i 0.00847567 + 0.0146803i
\(670\) 0 0
\(671\) 0.946025 0.0365209
\(672\) 1.78078 + 3.08440i 0.0686949 + 0.118983i
\(673\) −14.3769 + 24.9015i −0.554189 + 0.959883i 0.443778 + 0.896137i \(0.353638\pi\)
−0.997966 + 0.0637458i \(0.979695\pi\)
\(674\) −4.02699 + 6.97495i −0.155114 + 0.268665i
\(675\) 0 0
\(676\) 9.34233 9.03996i 0.359320 0.347691i
\(677\) 11.6155 0.446421 0.223211 0.974770i \(-0.428346\pi\)
0.223211 + 0.974770i \(0.428346\pi\)
\(678\) −2.00000 + 3.46410i −0.0768095 + 0.133038i
\(679\) −5.00000 + 8.66025i −0.191882 + 0.332350i
\(680\) 0 0
\(681\) 29.6847 1.13752
\(682\) 1.12311 + 1.94528i 0.0430059 + 0.0744885i
\(683\) −7.71922 13.3701i −0.295368 0.511592i 0.679703 0.733488i \(-0.262109\pi\)
−0.975070 + 0.221896i \(0.928776\pi\)
\(684\) −2.43845 −0.0932364
\(685\) 0 0
\(686\) −2.34233 + 4.05703i −0.0894305 + 0.154898i
\(687\) −4.74621 + 8.22068i −0.181079 + 0.313638i
\(688\) 0.438447 0.0167156
\(689\) 12.0691 + 9.41967i 0.459797 + 0.358861i
\(690\) 0 0
\(691\) 2.41146 4.17677i 0.0917362 0.158892i −0.816506 0.577338i \(-0.804092\pi\)
0.908242 + 0.418446i \(0.137425\pi\)
\(692\) 4.43845 7.68762i 0.168724 0.292239i
\(693\) −1.00000 1.73205i −0.0379869 0.0657952i
\(694\) −24.8078 −0.941690
\(695\) 0 0
\(696\) −0.561553 0.972638i −0.0212856 0.0368677i
\(697\) 9.75379 0.369451
\(698\) 9.62311 + 16.6677i 0.364240 + 0.630882i
\(699\) 12.6847 21.9705i 0.479778 0.831000i
\(700\) 0 0
\(701\) −0.876894 −0.0331198 −0.0165599 0.999863i \(-0.505271\pi\)
−0.0165599 + 0.999863i \(0.505271\pi\)
\(702\) −3.34233 + 1.35234i −0.126148 + 0.0510410i
\(703\) −1.36932 −0.0516448
\(704\) 0.280776 0.486319i 0.0105822 0.0183288i
\(705\) 0 0
\(706\) −1.12311 1.94528i −0.0422686 0.0732114i
\(707\) 22.2462 0.836655
\(708\) 5.12311 + 8.87348i 0.192538 + 0.333486i
\(709\) 14.3769 + 24.9015i 0.539936 + 0.935196i 0.998907 + 0.0467448i \(0.0148848\pi\)
−0.458971 + 0.888451i \(0.651782\pi\)
\(710\) 0 0
\(711\) 7.90388 + 13.6899i 0.296419 + 0.513412i
\(712\) −5.12311 + 8.87348i −0.191997 + 0.332548i
\(713\) 15.3693 26.6204i 0.575585 0.996943i
\(714\) 11.1231 0.416272
\(715\) 0 0
\(716\) −15.6847 −0.586163
\(717\) −13.5270 + 23.4294i −0.505175 + 0.874988i
\(718\) 2.43845 4.22351i 0.0910020 0.157620i
\(719\) 8.71922 + 15.1021i 0.325172 + 0.563215i 0.981547 0.191220i \(-0.0612444\pi\)
−0.656375 + 0.754435i \(0.727911\pi\)
\(720\) 0 0
\(721\) −7.90388 13.6899i −0.294356 0.509839i
\(722\) 6.52699 + 11.3051i 0.242909 + 0.420731i
\(723\) 15.5616 0.578740
\(724\) 7.74621 + 13.4168i 0.287886 + 0.498633i
\(725\) 0 0
\(726\) 5.34233 9.25319i 0.198272 0.343418i
\(727\) −50.7926 −1.88379 −0.941897 0.335902i \(-0.890959\pi\)
−0.941897 + 0.335902i \(0.890959\pi\)
\(728\) −1.78078 + 12.7173i −0.0660000 + 0.471334i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.684658 1.18586i 0.0253230 0.0438607i
\(732\) 0.842329 + 1.45896i 0.0311334 + 0.0539246i
\(733\) −47.9848 −1.77236 −0.886180 0.463340i \(-0.846651\pi\)
−0.886180 + 0.463340i \(0.846651\pi\)
\(734\) 5.09612 + 8.82674i 0.188101 + 0.325801i
\(735\) 0 0
\(736\) −7.68466 −0.283260
\(737\) 3.31534 + 5.74234i 0.122122 + 0.211522i
\(738\) 1.56155 2.70469i 0.0574816 0.0995610i
\(739\) 6.56155 11.3649i 0.241371 0.418066i −0.719734 0.694250i \(-0.755736\pi\)
0.961105 + 0.276183i \(0.0890697\pi\)
\(740\) 0 0
\(741\) −6.93087 5.40938i −0.254612 0.198718i
\(742\) −15.1231 −0.555187
\(743\) −5.56155 + 9.63289i −0.204034 + 0.353397i −0.949824 0.312784i \(-0.898739\pi\)
0.745791 + 0.666180i \(0.232072\pi\)
\(744\) −2.00000 + 3.46410i −0.0733236 + 0.127000i
\(745\) 0 0
\(746\) −9.49242 −0.347542
\(747\) −3.28078 5.68247i −0.120037 0.207911i
\(748\) −0.876894 1.51883i −0.0320624 0.0555338i
\(749\) −19.1231 −0.698743
\(750\) 0 0
\(751\) −25.1231 + 43.5145i −0.916755 + 1.58787i −0.112444 + 0.993658i \(0.535868\pi\)
−0.804311 + 0.594208i \(0.797465\pi\)
\(752\) −2.00000 + 3.46410i −0.0729325 + 0.126323i
\(753\) 23.9309 0.872089
\(754\) 0.561553 4.01029i 0.0204505 0.146046i
\(755\) 0 0
\(756\) 1.78078 3.08440i 0.0647662 0.112178i
\(757\) 15.3423 26.5737i 0.557626 0.965837i −0.440068 0.897965i \(-0.645046\pi\)
0.997694 0.0678727i \(-0.0216212\pi\)
\(758\) 12.0270 + 20.8314i 0.436840 + 0.756629i
\(759\) 4.31534 0.156637
\(760\) 0 0
\(761\) 11.4924 + 19.9055i 0.416600 + 0.721572i 0.995595 0.0937588i \(-0.0298882\pi\)
−0.578995 + 0.815331i \(0.696555\pi\)
\(762\) 21.8078 0.790012
\(763\) −5.00000 8.66025i −0.181012 0.313522i
\(764\) −7.96543 + 13.7965i −0.288179 + 0.499141i
\(765\) 0 0
\(766\) −5.43845 −0.196499
\(767\) −5.12311 + 36.5863i −0.184985 + 1.32105i
\(768\) 1.00000 0.0360844
\(769\) 4.65767 8.06732i 0.167960 0.290915i −0.769743 0.638354i \(-0.779615\pi\)
0.937702 + 0.347439i \(0.112949\pi\)
\(770\) 0 0
\(771\) 6.80776 + 11.7914i 0.245176 + 0.424657i
\(772\) 3.00000 0.107972
\(773\) 14.8078 + 25.6478i 0.532598 + 0.922487i 0.999275 + 0.0380595i \(0.0121177\pi\)
−0.466677 + 0.884428i \(0.654549\pi\)
\(774\) −0.219224 0.379706i −0.00787983 0.0136483i
\(775\) 0 0
\(776\) 1.40388 + 2.43160i 0.0503964 + 0.0872892i
\(777\) 1.00000 1.73205i 0.0358748 0.0621370i
\(778\) −5.68466 + 9.84612i −0.203805 + 0.353000i
\(779\) 7.61553 0.272855
\(780\) 0 0
\(781\) −7.05398 −0.252411
\(782\) −12.0000 + 20.7846i −0.429119 + 0.743256i
\(783\) −0.561553 + 0.972638i −0.0200683 + 0.0347592i
\(784\) −2.84233 4.92306i −0.101512 0.175824i