Properties

Label 1950.2.z.m.1849.1
Level $1950$
Weight $2$
Character 1950.1849
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
Defining polynomial: \(x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1849.1
Root \(-2.21837 - 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1849
Dual form 1950.2.z.m.1699.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-3.08440 - 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-3.08440 - 1.78078i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.280776 + 0.486319i) q^{11} -1.00000i q^{12} +(2.21837 + 2.84233i) q^{13} +3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.70469 - 1.56155i) q^{17} +1.00000i q^{18} +(-1.21922 + 2.11176i) q^{19} -3.56155 q^{21} +(-0.486319 - 0.280776i) q^{22} +(-6.65511 + 3.84233i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.34233 - 1.35234i) q^{26} -1.00000i q^{27} +(-3.08440 + 1.78078i) q^{28} +(0.561553 + 0.972638i) q^{29} +4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(0.486319 + 0.280776i) q^{33} +3.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-0.486319 + 0.280776i) q^{37} -2.43845i q^{38} +(3.34233 + 1.35234i) q^{39} +(1.56155 + 2.70469i) q^{41} +(3.08440 - 1.78078i) q^{42} +(-0.379706 - 0.219224i) q^{43} +0.561553 q^{44} +(3.84233 - 6.65511i) q^{46} -4.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.84233 + 4.92306i) q^{49} -3.12311 q^{51} +(3.57071 - 0.500000i) q^{52} +4.24621i q^{53} +(0.500000 + 0.866025i) q^{54} +(1.78078 - 3.08440i) q^{56} +2.43845i q^{57} +(-0.972638 - 0.561553i) q^{58} +(-5.12311 + 8.87348i) q^{59} +(0.842329 - 1.45896i) q^{61} +(-3.46410 + 2.00000i) q^{62} +(-3.08440 + 1.78078i) q^{63} -1.00000 q^{64} -0.561553 q^{66} +(-10.2258 + 5.90388i) q^{67} +(-2.70469 + 1.56155i) q^{68} +(-3.84233 + 6.65511i) q^{69} +(-6.28078 + 10.8786i) q^{71} +(0.866025 + 0.500000i) q^{72} +9.00000i q^{73} +(0.280776 - 0.486319i) q^{74} +(1.21922 + 2.11176i) q^{76} -2.00000i q^{77} +(-3.57071 + 0.500000i) q^{78} +15.8078 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.70469 - 1.56155i) q^{82} +6.56155i q^{83} +(-1.78078 + 3.08440i) q^{84} +0.438447 q^{86} +(0.972638 + 0.561553i) q^{87} +(-0.486319 + 0.280776i) q^{88} +(5.12311 + 8.87348i) q^{89} +(-1.78078 - 12.7173i) q^{91} +7.68466i q^{92} +(3.46410 - 2.00000i) q^{93} +(2.00000 + 3.46410i) q^{94} +1.00000 q^{96} +(-2.43160 - 1.40388i) q^{97} +(-4.92306 - 2.84233i) q^{98} +0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} - 6q^{11} + 12q^{14} - 4q^{16} - 18q^{19} - 12q^{21} + 4q^{24} - 2q^{26} - 12q^{29} + 32q^{31} - 8q^{34} - 4q^{36} + 2q^{39} - 4q^{41} - 12q^{44} + 6q^{46} - 2q^{49} + 8q^{51} + 4q^{54} + 6q^{56} - 8q^{59} - 18q^{61} - 8q^{64} + 12q^{66} - 6q^{69} - 42q^{71} - 6q^{74} + 18q^{76} + 44q^{79} - 4q^{81} - 6q^{84} + 20q^{86} + 8q^{89} - 6q^{91} + 16q^{94} + 8q^{96} - 12q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −3.08440 1.78078i −1.16579 0.673070i −0.213107 0.977029i \(-0.568358\pi\)
−0.952685 + 0.303959i \(0.901692\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 0.280776 + 0.486319i 0.0846573 + 0.146631i 0.905245 0.424890i \(-0.139687\pi\)
−0.820588 + 0.571520i \(0.806354\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.21837 + 2.84233i 0.615265 + 0.788320i
\(14\) 3.56155 0.951865
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.70469 1.56155i −0.655983 0.378732i 0.134761 0.990878i \(-0.456973\pi\)
−0.790745 + 0.612146i \(0.790307\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.21922 + 2.11176i −0.279709 + 0.484470i −0.971312 0.237807i \(-0.923571\pi\)
0.691603 + 0.722278i \(0.256905\pi\)
\(20\) 0 0
\(21\) −3.56155 −0.777195
\(22\) −0.486319 0.280776i −0.103684 0.0598617i
\(23\) −6.65511 + 3.84233i −1.38769 + 0.801181i −0.993054 0.117658i \(-0.962461\pi\)
−0.394632 + 0.918839i \(0.629128\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −3.34233 1.35234i −0.655485 0.265217i
\(27\) 1.00000i 0.192450i
\(28\) −3.08440 + 1.78078i −0.582896 + 0.336535i
\(29\) 0.561553 + 0.972638i 0.104278 + 0.180614i 0.913443 0.406967i \(-0.133414\pi\)
−0.809165 + 0.587581i \(0.800080\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0.486319 + 0.280776i 0.0846573 + 0.0488769i
\(34\) 3.12311 0.535608
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −0.486319 + 0.280776i −0.0799504 + 0.0461594i −0.539442 0.842023i \(-0.681365\pi\)
0.459492 + 0.888182i \(0.348032\pi\)
\(38\) 2.43845i 0.395568i
\(39\) 3.34233 + 1.35234i 0.535201 + 0.216548i
\(40\) 0 0
\(41\) 1.56155 + 2.70469i 0.243874 + 0.422401i 0.961814 0.273703i \(-0.0882485\pi\)
−0.717941 + 0.696104i \(0.754915\pi\)
\(42\) 3.08440 1.78078i 0.475933 0.274780i
\(43\) −0.379706 0.219224i −0.0579047 0.0334313i 0.470768 0.882257i \(-0.343977\pi\)
−0.528673 + 0.848826i \(0.677310\pi\)
\(44\) 0.561553 0.0846573
\(45\) 0 0
\(46\) 3.84233 6.65511i 0.566521 0.981242i
\(47\) 4.00000i 0.583460i −0.956501 0.291730i \(-0.905769\pi\)
0.956501 0.291730i \(-0.0942309\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) 2.84233 + 4.92306i 0.406047 + 0.703294i
\(50\) 0 0
\(51\) −3.12311 −0.437322
\(52\) 3.57071 0.500000i 0.495169 0.0693375i
\(53\) 4.24621i 0.583262i 0.956531 + 0.291631i \(0.0941979\pi\)
−0.956531 + 0.291631i \(0.905802\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 1.78078 3.08440i 0.237966 0.412170i
\(57\) 2.43845i 0.322980i
\(58\) −0.972638 0.561553i −0.127714 0.0737355i
\(59\) −5.12311 + 8.87348i −0.666972 + 1.15523i 0.311775 + 0.950156i \(0.399076\pi\)
−0.978747 + 0.205073i \(0.934257\pi\)
\(60\) 0 0
\(61\) 0.842329 1.45896i 0.107849 0.186800i −0.807050 0.590484i \(-0.798937\pi\)
0.914899 + 0.403683i \(0.132270\pi\)
\(62\) −3.46410 + 2.00000i −0.439941 + 0.254000i
\(63\) −3.08440 + 1.78078i −0.388597 + 0.224357i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −0.561553 −0.0691224
\(67\) −10.2258 + 5.90388i −1.24928 + 0.721274i −0.970967 0.239215i \(-0.923110\pi\)
−0.278317 + 0.960489i \(0.589776\pi\)
\(68\) −2.70469 + 1.56155i −0.327992 + 0.189366i
\(69\) −3.84233 + 6.65511i −0.462562 + 0.801181i
\(70\) 0 0
\(71\) −6.28078 + 10.8786i −0.745391 + 1.29106i 0.204621 + 0.978841i \(0.434404\pi\)
−0.950012 + 0.312214i \(0.898929\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 9.00000i 1.05337i 0.850060 + 0.526685i \(0.176565\pi\)
−0.850060 + 0.526685i \(0.823435\pi\)
\(74\) 0.280776 0.486319i 0.0326396 0.0565334i
\(75\) 0 0
\(76\) 1.21922 + 2.11176i 0.139855 + 0.242235i
\(77\) 2.00000i 0.227921i
\(78\) −3.57071 + 0.500000i −0.404304 + 0.0566139i
\(79\) 15.8078 1.77851 0.889256 0.457409i \(-0.151223\pi\)
0.889256 + 0.457409i \(0.151223\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.70469 1.56155i −0.298683 0.172445i
\(83\) 6.56155i 0.720224i 0.932909 + 0.360112i \(0.117262\pi\)
−0.932909 + 0.360112i \(0.882738\pi\)
\(84\) −1.78078 + 3.08440i −0.194299 + 0.336535i
\(85\) 0 0
\(86\) 0.438447 0.0472790
\(87\) 0.972638 + 0.561553i 0.104278 + 0.0602048i
\(88\) −0.486319 + 0.280776i −0.0518418 + 0.0299309i
\(89\) 5.12311 + 8.87348i 0.543048 + 0.940587i 0.998727 + 0.0504427i \(0.0160632\pi\)
−0.455679 + 0.890144i \(0.650603\pi\)
\(90\) 0 0
\(91\) −1.78078 12.7173i −0.186676 1.33313i
\(92\) 7.68466i 0.801181i
\(93\) 3.46410 2.00000i 0.359211 0.207390i
\(94\) 2.00000 + 3.46410i 0.206284 + 0.357295i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −2.43160 1.40388i −0.246891 0.142543i 0.371449 0.928453i \(-0.378861\pi\)
−0.618340 + 0.785911i \(0.712194\pi\)
\(98\) −4.92306 2.84233i −0.497304 0.287119i
\(99\) 0.561553 0.0564382
\(100\) 0 0
\(101\) 3.12311 + 5.40938i 0.310761 + 0.538253i 0.978527 0.206118i \(-0.0660829\pi\)
−0.667767 + 0.744371i \(0.732750\pi\)
\(102\) 2.70469 1.56155i 0.267804 0.154617i
\(103\) 4.43845i 0.437333i −0.975800 0.218667i \(-0.929829\pi\)
0.975800 0.218667i \(-0.0701707\pi\)
\(104\) −2.84233 + 2.21837i −0.278713 + 0.217529i
\(105\) 0 0
\(106\) −2.12311 3.67733i −0.206214 0.357174i
\(107\) −4.64996 + 2.68466i −0.449529 + 0.259536i −0.707631 0.706582i \(-0.750236\pi\)
0.258102 + 0.966118i \(0.416903\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 2.80776 0.268935 0.134468 0.990918i \(-0.457068\pi\)
0.134468 + 0.990918i \(0.457068\pi\)
\(110\) 0 0
\(111\) −0.280776 + 0.486319i −0.0266501 + 0.0461594i
\(112\) 3.56155i 0.336535i
\(113\) −3.46410 2.00000i −0.325875 0.188144i 0.328133 0.944632i \(-0.393581\pi\)
−0.654008 + 0.756487i \(0.726914\pi\)
\(114\) −1.21922 2.11176i −0.114191 0.197784i
\(115\) 0 0
\(116\) 1.12311 0.104278
\(117\) 3.57071 0.500000i 0.330113 0.0462250i
\(118\) 10.2462i 0.943240i
\(119\) 5.56155 + 9.63289i 0.509827 + 0.883046i
\(120\) 0 0
\(121\) 5.34233 9.25319i 0.485666 0.841199i
\(122\) 1.68466i 0.152522i
\(123\) 2.70469 + 1.56155i 0.243874 + 0.140800i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 0 0
\(126\) 1.78078 3.08440i 0.158644 0.274780i
\(127\) −18.8861 + 10.9039i −1.67587 + 0.967563i −0.711619 + 0.702565i \(0.752038\pi\)
−0.964249 + 0.264998i \(0.914629\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −0.438447 −0.0386031
\(130\) 0 0
\(131\) 0.876894 0.0766146 0.0383073 0.999266i \(-0.487803\pi\)
0.0383073 + 0.999266i \(0.487803\pi\)
\(132\) 0.486319 0.280776i 0.0423286 0.0244384i
\(133\) 7.52113 4.34233i 0.652165 0.376528i
\(134\) 5.90388 10.2258i 0.510018 0.883377i
\(135\) 0 0
\(136\) 1.56155 2.70469i 0.133902 0.231925i
\(137\) 14.2829 + 8.24621i 1.22027 + 0.704521i 0.964975 0.262343i \(-0.0844951\pi\)
0.255292 + 0.966864i \(0.417828\pi\)
\(138\) 7.68466i 0.654162i
\(139\) 10.7808 18.6729i 0.914414 1.58381i 0.106656 0.994296i \(-0.465986\pi\)
0.807758 0.589515i \(-0.200681\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) 12.5616i 1.05414i
\(143\) −0.759413 + 1.87689i −0.0635053 + 0.156954i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −4.50000 7.79423i −0.372423 0.645055i
\(147\) 4.92306 + 2.84233i 0.406047 + 0.234431i
\(148\) 0.561553i 0.0461594i
\(149\) −5.12311 + 8.87348i −0.419701 + 0.726944i −0.995909 0.0903593i \(-0.971198\pi\)
0.576208 + 0.817303i \(0.304532\pi\)
\(150\) 0 0
\(151\) −16.6847 −1.35778 −0.678889 0.734241i \(-0.737538\pi\)
−0.678889 + 0.734241i \(0.737538\pi\)
\(152\) −2.11176 1.21922i −0.171286 0.0988921i
\(153\) −2.70469 + 1.56155i −0.218661 + 0.126244i
\(154\) 1.00000 + 1.73205i 0.0805823 + 0.139573i
\(155\) 0 0
\(156\) 2.84233 2.21837i 0.227568 0.177612i
\(157\) 17.2462i 1.37640i −0.725522 0.688199i \(-0.758402\pi\)
0.725522 0.688199i \(-0.241598\pi\)
\(158\) −13.6899 + 7.90388i −1.08911 + 0.628799i
\(159\) 2.12311 + 3.67733i 0.168373 + 0.291631i
\(160\) 0 0
\(161\) 27.3693 2.15700
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 14.2829 + 8.24621i 1.11872 + 0.645893i 0.941074 0.338201i \(-0.109818\pi\)
0.177646 + 0.984094i \(0.443152\pi\)
\(164\) 3.12311 0.243874
\(165\) 0 0
\(166\) −3.28078 5.68247i −0.254638 0.441045i
\(167\) −20.5115 + 11.8423i −1.58723 + 0.916387i −0.593468 + 0.804858i \(0.702241\pi\)
−0.993761 + 0.111529i \(0.964425\pi\)
\(168\) 3.56155i 0.274780i
\(169\) −3.15767 + 12.6107i −0.242898 + 0.970052i
\(170\) 0 0
\(171\) 1.21922 + 2.11176i 0.0932364 + 0.161490i
\(172\) −0.379706 + 0.219224i −0.0289523 + 0.0167156i
\(173\) 7.68762 + 4.43845i 0.584479 + 0.337449i 0.762911 0.646503i \(-0.223769\pi\)
−0.178433 + 0.983952i \(0.557103\pi\)
\(174\) −1.12311 −0.0851424
\(175\) 0 0
\(176\) 0.280776 0.486319i 0.0211643 0.0366577i
\(177\) 10.2462i 0.770152i
\(178\) −8.87348 5.12311i −0.665095 0.383993i
\(179\) −7.84233 13.5833i −0.586163 1.01526i −0.994729 0.102536i \(-0.967304\pi\)
0.408566 0.912729i \(-0.366029\pi\)
\(180\) 0 0
\(181\) −15.4924 −1.15154 −0.575771 0.817611i \(-0.695298\pi\)
−0.575771 + 0.817611i \(0.695298\pi\)
\(182\) 7.90084 + 10.1231i 0.585649 + 0.750375i
\(183\) 1.68466i 0.124534i
\(184\) −3.84233 6.65511i −0.283260 0.490621i
\(185\) 0 0
\(186\) −2.00000 + 3.46410i −0.146647 + 0.254000i
\(187\) 1.75379i 0.128250i
\(188\) −3.46410 2.00000i −0.252646 0.145865i
\(189\) −1.78078 + 3.08440i −0.129532 + 0.224357i
\(190\) 0 0
\(191\) −7.96543 + 13.7965i −0.576359 + 0.998282i 0.419534 + 0.907740i \(0.362194\pi\)
−0.995893 + 0.0905428i \(0.971140\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 2.59808 1.50000i 0.187014 0.107972i −0.403570 0.914949i \(-0.632231\pi\)
0.590584 + 0.806976i \(0.298898\pi\)
\(194\) 2.80776 0.201586
\(195\) 0 0
\(196\) 5.68466 0.406047
\(197\) −4.43674 + 2.56155i −0.316105 + 0.182503i −0.649655 0.760229i \(-0.725087\pi\)
0.333550 + 0.942732i \(0.391753\pi\)
\(198\) −0.486319 + 0.280776i −0.0345612 + 0.0199539i
\(199\) −2.21922 + 3.84381i −0.157317 + 0.272480i −0.933900 0.357534i \(-0.883618\pi\)
0.776584 + 0.630014i \(0.216951\pi\)
\(200\) 0 0
\(201\) −5.90388 + 10.2258i −0.416428 + 0.721274i
\(202\) −5.40938 3.12311i −0.380602 0.219741i
\(203\) 4.00000i 0.280745i
\(204\) −1.56155 + 2.70469i −0.109331 + 0.189366i
\(205\) 0 0
\(206\) 2.21922 + 3.84381i 0.154621 + 0.267811i
\(207\) 7.68466i 0.534121i
\(208\) 1.35234 3.34233i 0.0937682 0.231749i
\(209\) −1.36932 −0.0947176
\(210\) 0 0
\(211\) −0.561553 0.972638i −0.0386589 0.0669592i 0.846049 0.533106i \(-0.178975\pi\)
−0.884707 + 0.466147i \(0.845642\pi\)
\(212\) 3.67733 + 2.12311i 0.252560 + 0.145815i
\(213\) 12.5616i 0.860703i
\(214\) 2.68466 4.64996i 0.183519 0.317865i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −12.3376 7.12311i −0.837530 0.483548i
\(218\) −2.43160 + 1.40388i −0.164688 + 0.0950829i
\(219\) 4.50000 + 7.79423i 0.304082 + 0.526685i
\(220\) 0 0
\(221\) −1.56155 11.1517i −0.105041 0.750146i
\(222\) 0.561553i 0.0376890i
\(223\) −0.379706 + 0.219224i −0.0254270 + 0.0146803i −0.512660 0.858592i \(-0.671340\pi\)
0.487233 + 0.873272i \(0.338006\pi\)
\(224\) −1.78078 3.08440i −0.118983 0.206085i
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) 25.7077 + 14.8423i 1.70628 + 0.985120i 0.939073 + 0.343718i \(0.111686\pi\)
0.767205 + 0.641402i \(0.221647\pi\)
\(228\) 2.11176 + 1.21922i 0.139855 + 0.0807451i
\(229\) −9.49242 −0.627277 −0.313638 0.949542i \(-0.601548\pi\)
−0.313638 + 0.949542i \(0.601548\pi\)
\(230\) 0 0
\(231\) −1.00000 1.73205i −0.0657952 0.113961i
\(232\) −0.972638 + 0.561553i −0.0638568 + 0.0368677i
\(233\) 25.3693i 1.66200i −0.556273 0.831000i \(-0.687769\pi\)
0.556273 0.831000i \(-0.312231\pi\)
\(234\) −2.84233 + 2.21837i −0.185809 + 0.145019i
\(235\) 0 0
\(236\) 5.12311 + 8.87348i 0.333486 + 0.577614i
\(237\) 13.6899 7.90388i 0.889256 0.513412i
\(238\) −9.63289 5.56155i −0.624408 0.360502i
\(239\) −27.0540 −1.74998 −0.874988 0.484144i \(-0.839131\pi\)
−0.874988 + 0.484144i \(0.839131\pi\)
\(240\) 0 0
\(241\) −7.78078 + 13.4767i −0.501204 + 0.868111i 0.498795 + 0.866720i \(0.333776\pi\)
−0.999999 + 0.00139067i \(0.999557\pi\)
\(242\) 10.6847i 0.686836i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −0.842329 1.45896i −0.0539246 0.0934002i
\(245\) 0 0
\(246\) −3.12311 −0.199122
\(247\) −8.70700 + 1.21922i −0.554013 + 0.0775773i
\(248\) 4.00000i 0.254000i
\(249\) 3.28078 + 5.68247i 0.207911 + 0.360112i
\(250\) 0 0
\(251\) −11.9654 + 20.7247i −0.755252 + 1.30813i 0.189998 + 0.981785i \(0.439152\pi\)
−0.945249 + 0.326350i \(0.894181\pi\)
\(252\) 3.56155i 0.224357i
\(253\) −3.73720 2.15767i −0.234955 0.135652i
\(254\) 10.9039 18.8861i 0.684170 1.18502i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 11.7914 6.80776i 0.735527 0.424657i −0.0849138 0.996388i \(-0.527061\pi\)
0.820441 + 0.571732i \(0.193728\pi\)
\(258\) 0.379706 0.219224i 0.0236395 0.0136483i
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) 1.12311 0.0695185
\(262\) −0.759413 + 0.438447i −0.0469167 + 0.0270874i
\(263\) 5.46925 3.15767i 0.337248 0.194710i −0.321806 0.946806i \(-0.604290\pi\)
0.659054 + 0.752095i \(0.270957\pi\)
\(264\) −0.280776 + 0.486319i −0.0172806 + 0.0299309i
\(265\) 0 0
\(266\) −4.34233 + 7.52113i −0.266245 + 0.461150i
\(267\) 8.87348 + 5.12311i 0.543048 + 0.313529i
\(268\) 11.8078i 0.721274i
\(269\) −1.68466 + 2.91791i −0.102715 + 0.177908i −0.912803 0.408401i \(-0.866086\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(270\) 0 0
\(271\) −4.46543 7.73436i −0.271256 0.469829i 0.697928 0.716168i \(-0.254106\pi\)
−0.969184 + 0.246339i \(0.920772\pi\)
\(272\) 3.12311i 0.189366i
\(273\) −7.90084 10.1231i −0.478181 0.612678i
\(274\) −16.4924 −0.996344
\(275\) 0 0
\(276\) 3.84233 + 6.65511i 0.231281 + 0.400591i
\(277\) 4.33013 + 2.50000i 0.260172 + 0.150210i 0.624413 0.781094i \(-0.285338\pi\)
−0.364241 + 0.931305i \(0.618672\pi\)
\(278\) 21.5616i 1.29318i
\(279\) 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 \(0.516659\pi\)
\(282\) 3.46410 + 2.00000i 0.206284 + 0.119098i
\(283\) 25.6478 14.8078i 1.52460 0.880230i 0.525028 0.851085i \(-0.324055\pi\)
0.999575 0.0291454i \(-0.00927859\pi\)
\(284\) 6.28078 + 10.8786i 0.372696 + 0.645528i
\(285\) 0 0
\(286\) −0.280776 2.00514i −0.0166027 0.118567i
\(287\) 11.1231i 0.656576i
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) −3.62311 6.27540i −0.213124 0.369141i
\(290\) 0 0
\(291\) −2.80776 −0.164594
\(292\) 7.79423 + 4.50000i 0.456123 + 0.263343i
\(293\) −17.5337 10.1231i −1.02433 0.591398i −0.108976 0.994044i \(-0.534757\pi\)
−0.915356 + 0.402646i \(0.868090\pi\)
\(294\) −5.68466 −0.331536
\(295\) 0 0
\(296\) −0.280776 0.486319i −0.0163198 0.0282667i
\(297\) 0.486319 0.280776i 0.0282191 0.0162923i
\(298\) 10.2462i 0.593547i
\(299\) −25.6847 10.3923i −1.48538 0.601003i
\(300\) 0 0
\(301\) 0.780776 + 1.35234i 0.0450032 + 0.0779478i
\(302\) 14.4493 8.34233i 0.831466 0.480047i
\(303\) 5.40938 + 3.12311i 0.310761 + 0.179418i
\(304\) 2.43845 0.139855
\(305\) 0 0
\(306\) 1.56155 2.70469i 0.0892680 0.154617i
\(307\) 22.2462i 1.26966i −0.772653 0.634829i \(-0.781070\pi\)
0.772653 0.634829i \(-0.218930\pi\)
\(308\) −1.73205 1.00000i −0.0986928 0.0569803i
\(309\) −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 \(0.594475\pi\)
\(312\) −1.35234 + 3.34233i −0.0765614 + 0.189222i
\(313\) 31.0000i 1.75222i 0.482108 + 0.876112i \(0.339871\pi\)
−0.482108 + 0.876112i \(0.660129\pi\)
\(314\) 8.62311 + 14.9357i 0.486630 + 0.842868i
\(315\) 0 0
\(316\) 7.90388 13.6899i 0.444628 0.770118i
\(317\) 16.2462i 0.912478i −0.889857 0.456239i \(-0.849196\pi\)
0.889857 0.456239i \(-0.150804\pi\)
\(318\) −3.67733 2.12311i −0.206214 0.119058i
\(319\) −0.315342 + 0.546188i −0.0176557 + 0.0305806i
\(320\) 0 0
\(321\) −2.68466 + 4.64996i −0.149843 + 0.259536i
\(322\) −23.7025 + 13.6847i −1.32089 + 0.762616i
\(323\) 6.59524 3.80776i 0.366969 0.211870i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −16.4924 −0.913431
\(327\) 2.43160 1.40388i 0.134468 0.0776349i
\(328\) −2.70469 + 1.56155i −0.149341 + 0.0862223i
\(329\) −7.12311 + 12.3376i −0.392710 + 0.680193i
\(330\) 0 0
\(331\) 8.34233 14.4493i 0.458536 0.794207i −0.540348 0.841442i \(-0.681707\pi\)
0.998884 + 0.0472342i \(0.0150407\pi\)
\(332\) 5.68247 + 3.28078i 0.311866 + 0.180056i
\(333\) 0.561553i 0.0307729i
\(334\) 11.8423 20.5115i 0.647983 1.12234i
\(335\) 0 0
\(336\) 1.78078 + 3.08440i 0.0971493 + 0.168268i
\(337\) 8.05398i 0.438728i −0.975643 0.219364i \(-0.929602\pi\)
0.975643 0.219364i \(-0.0703982\pi\)
\(338\) −3.57071 12.5000i −0.194221 0.679910i
\(339\) −4.00000 −0.217250
\(340\) 0 0
\(341\) 1.12311 + 1.94528i 0.0608196 + 0.105343i
\(342\) −2.11176 1.21922i −0.114191 0.0659281i
\(343\) 4.68466i 0.252948i
\(344\) 0.219224 0.379706i 0.0118197 0.0204724i
\(345\) 0 0
\(346\) −8.87689 −0.477225
\(347\) −21.4842 12.4039i −1.15333 0.665875i −0.203633 0.979047i \(-0.565275\pi\)
−0.949696 + 0.313172i \(0.898608\pi\)
\(348\) 0.972638 0.561553i 0.0521389 0.0301024i
\(349\) −9.62311 16.6677i −0.515113 0.892202i −0.999846 0.0175398i \(-0.994417\pi\)
0.484733 0.874662i \(-0.338917\pi\)
\(350\) 0 0
\(351\) 2.84233 2.21837i 0.151712 0.118408i
\(352\) 0.561553i 0.0299309i
\(353\) 1.94528 1.12311i 0.103537 0.0597769i −0.447338 0.894365i \(-0.647628\pi\)
0.550874 + 0.834588i \(0.314294\pi\)
\(354\) −5.12311 8.87348i −0.272290 0.471620i
\(355\) 0 0
\(356\) 10.2462 0.543048
\(357\) 9.63289 + 5.56155i 0.509827 + 0.294349i
\(358\) 13.5833 + 7.84233i 0.717900 + 0.414480i
\(359\) 4.87689 0.257393 0.128696 0.991684i \(-0.458921\pi\)
0.128696 + 0.991684i \(0.458921\pi\)
\(360\) 0 0
\(361\) 6.52699 + 11.3051i 0.343526 + 0.595004i
\(362\) 13.4168 7.74621i 0.705173 0.407132i
\(363\) 10.6847i 0.560799i
\(364\) −11.9039 4.81645i −0.623933 0.252450i
\(365\) 0 0
\(366\) 0.842329 + 1.45896i 0.0440293 + 0.0762609i
\(367\) 8.82674 5.09612i 0.460752 0.266015i −0.251609 0.967829i \(-0.580960\pi\)
0.712360 + 0.701814i \(0.247626\pi\)
\(368\) 6.65511 + 3.84233i 0.346922 + 0.200295i
\(369\) 3.12311 0.162582
\(370\) 0 0
\(371\) 7.56155 13.0970i 0.392576 0.679962i
\(372\) 4.00000i 0.207390i
\(373\) 8.22068 + 4.74621i 0.425651 + 0.245750i 0.697492 0.716593i \(-0.254299\pi\)
−0.271841 + 0.962342i \(0.587633\pi\)
\(374\) 0.876894 + 1.51883i 0.0453431 + 0.0785366i
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) −1.51883 + 3.75379i −0.0782235 + 0.193330i
\(378\) 3.56155i 0.183187i
\(379\) −12.0270 20.8314i −0.617785 1.07003i −0.989889 0.141844i \(-0.954697\pi\)
0.372104 0.928191i \(-0.378636\pi\)
\(380\) 0 0
\(381\) −10.9039 + 18.8861i −0.558623 + 0.967563i
\(382\) 15.9309i 0.815094i
\(383\) 4.70983 + 2.71922i 0.240661 + 0.138946i 0.615481 0.788152i \(-0.288962\pi\)
−0.374819 + 0.927098i \(0.622295\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) −1.50000 + 2.59808i −0.0763480 + 0.132239i
\(387\) −0.379706 + 0.219224i −0.0193016 + 0.0111438i
\(388\) −2.43160 + 1.40388i −0.123446 + 0.0712713i
\(389\) −11.3693 −0.576447 −0.288224 0.957563i \(-0.593065\pi\)
−0.288224 + 0.957563i \(0.593065\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) −4.92306 + 2.84233i −0.248652 + 0.143559i
\(393\) 0.759413 0.438447i 0.0383073 0.0221167i
\(394\) 2.56155 4.43674i 0.129049 0.223520i
\(395\) 0 0
\(396\) 0.280776 0.486319i 0.0141095 0.0244384i
\(397\) −8.49377 4.90388i −0.426290 0.246119i 0.271475 0.962446i \(-0.412489\pi\)
−0.697765 + 0.716327i \(0.745822\pi\)
\(398\) 4.43845i 0.222479i
\(399\) 4.34233 7.52113i 0.217388 0.376528i
\(400\) 0 0
\(401\) 6.31534 + 10.9385i 0.315373 + 0.546242i 0.979517 0.201363i \(-0.0645370\pi\)
−0.664144 + 0.747605i \(0.731204\pi\)
\(402\) 11.8078i 0.588918i
\(403\) 8.87348 + 11.3693i 0.442019 + 0.566346i
\(404\) 6.24621 0.310761
\(405\) 0 0
\(406\) 2.00000 + 3.46410i 0.0992583 + 0.171920i
\(407\) −0.273094 0.157671i −0.0135368 0.00781545i
\(408\) 3.12311i 0.154617i
\(409\) 8.12311 14.0696i 0.401662 0.695699i −0.592265 0.805743i \(-0.701766\pi\)
0.993927 + 0.110045i \(0.0350994\pi\)
\(410\) 0 0
\(411\) 16.4924 0.813511
\(412\) −3.84381 2.21922i −0.189371 0.109333i
\(413\) 31.6034 18.2462i 1.55510 0.897837i
\(414\) −3.84233 6.65511i −0.188840 0.327081i
\(415\) 0 0
\(416\) 0.500000 + 3.57071i 0.0245145 + 0.175069i
\(417\) 21.5616i 1.05587i
\(418\) 1.18586 0.684658i 0.0580025 0.0334877i
\(419\) −5.96543 10.3324i −0.291431 0.504773i 0.682718 0.730682i \(-0.260798\pi\)
−0.974148 + 0.225910i \(0.927465\pi\)
\(420\) 0 0
\(421\) 31.2462 1.52285 0.761424 0.648255i \(-0.224501\pi\)
0.761424 + 0.648255i \(0.224501\pi\)
\(422\) 0.972638 + 0.561553i 0.0473473 + 0.0273360i
\(423\) −3.46410 2.00000i −0.168430 0.0972433i
\(424\) −4.24621 −0.206214
\(425\) 0 0
\(426\) −6.28078 10.8786i −0.304305 0.527071i
\(427\) −5.19615 + 3.00000i −0.251459 + 0.145180i
\(428\) 5.36932i 0.259536i
\(429\) 0.280776 + 2.00514i 0.0135560 + 0.0968093i
\(430\) 0 0
\(431\) −9.15767 15.8616i −0.441109 0.764024i 0.556663 0.830739i \(-0.312082\pi\)
−0.997772 + 0.0667146i \(0.978748\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 11.8513 + 6.84233i 0.569535 + 0.328821i 0.756964 0.653457i \(-0.226682\pi\)
−0.187428 + 0.982278i \(0.560015\pi\)
\(434\) 14.2462 0.683840
\(435\) 0 0
\(436\) 1.40388 2.43160i 0.0672338 0.116452i
\(437\) 18.7386i 0.896390i
\(438\) −7.79423 4.50000i −0.372423 0.215018i
\(439\) −3.46543 6.00231i −0.165396 0.286475i 0.771400 0.636351i \(-0.219557\pi\)
−0.936796 + 0.349876i \(0.886224\pi\)
\(440\) 0 0
\(441\) 5.68466 0.270698
\(442\) 6.92820 + 8.87689i 0.329541 + 0.422231i
\(443\) 2.80776i 0.133401i −0.997773 0.0667004i \(-0.978753\pi\)
0.997773 0.0667004i \(-0.0212472\pi\)
\(444\) 0.280776 + 0.486319i 0.0133251 + 0.0230797i
\(445\) 0 0
\(446\) 0.219224 0.379706i 0.0103805 0.0179796i
\(447\) 10.2462i 0.484629i
\(448\) 3.08440 + 1.78078i 0.145724 + 0.0841338i
\(449\) −1.56155 + 2.70469i −0.0736942 + 0.127642i −0.900518 0.434819i \(-0.856812\pi\)
0.826823 + 0.562462i \(0.190146\pi\)
\(450\) 0 0
\(451\) −0.876894 + 1.51883i −0.0412913 + 0.0715187i
\(452\) −3.46410 + 2.00000i −0.162938 + 0.0940721i
\(453\) −14.4493 + 8.34233i −0.678889 + 0.391957i
\(454\) −29.6847 −1.39317
\(455\) 0 0
\(456\) −2.43845 −0.114191
\(457\) −3.90368 + 2.25379i −0.182606 + 0.105428i −0.588517 0.808485i \(-0.700288\pi\)
0.405910 + 0.913913i \(0.366955\pi\)
\(458\) 8.22068 4.74621i 0.384127 0.221776i
\(459\) −1.56155 + 2.70469i −0.0728870 + 0.126244i
\(460\) 0 0
\(461\) −5.31534 + 9.20644i −0.247560 + 0.428787i −0.962848 0.270043i \(-0.912962\pi\)
0.715288 + 0.698830i \(0.246295\pi\)
\(462\) 1.73205 + 1.00000i 0.0805823 + 0.0465242i
\(463\) 27.8078i 1.29234i 0.763195 + 0.646168i \(0.223630\pi\)
−0.763195 + 0.646168i \(0.776370\pi\)
\(464\) 0.561553 0.972638i 0.0260694 0.0451536i
\(465\) 0 0
\(466\) 12.6847 + 21.9705i 0.587605 + 1.01776i
\(467\) 3.43845i 0.159112i 0.996830 + 0.0795562i \(0.0253503\pi\)
−0.996830 + 0.0795562i \(0.974650\pi\)
\(468\) 1.35234 3.34233i 0.0625121 0.154499i
\(469\) 42.0540 1.94187
\(470\) 0 0
\(471\) −8.62311 14.9357i −0.397332 0.688199i
\(472\) −8.87348 5.12311i −0.408435 0.235810i
\(473\) 0.246211i 0.0113208i
\(474\) −7.90388 + 13.6899i −0.363037 + 0.628799i
\(475\) 0 0
\(476\) 11.1231 0.509827
\(477\) 3.67733 + 2.12311i 0.168373 + 0.0972103i
\(478\) 23.4294 13.5270i 1.07164 0.618710i
\(479\) −5.80776 10.0593i −0.265364 0.459623i 0.702295 0.711886i \(-0.252159\pi\)
−0.967659 + 0.252263i \(0.918825\pi\)
\(480\) 0 0
\(481\) −1.87689 0.759413i −0.0855790 0.0346262i
\(482\) 15.5616i 0.708809i
\(483\) 23.7025 13.6847i 1.07850 0.622674i
\(484\) −5.34233 9.25319i −0.242833 0.420599i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 36.9660 + 21.3423i 1.67509 + 0.967113i 0.964718 + 0.263286i \(0.0848064\pi\)
0.710372 + 0.703827i \(0.248527\pi\)
\(488\) 1.45896 + 0.842329i 0.0660439 + 0.0381305i
\(489\) 16.4924 0.745813
\(490\) 0 0
\(491\) −15.6501 27.1068i −0.706279 1.22331i −0.966228 0.257689i \(-0.917039\pi\)
0.259949 0.965622i \(-0.416294\pi\)
\(492\) 2.70469 1.56155i 0.121937 0.0704002i
\(493\) 3.50758i 0.157973i
\(494\) 6.93087 5.40938i 0.311835 0.243379i
\(495\) 0 0
\(496\) −2.00000 3.46410i −0.0898027 0.155543i
\(497\) 38.7448 22.3693i 1.73794 1.00340i
\(498\) −5.68247 3.28078i −0.254638 0.147015i
\(499\) −6.05398 −0.271013 −0.135507 0.990776i \(-0.543266\pi\)
−0.135507 + 0.990776i \(0.543266\pi\)
\(500\) 0 0
\(501\) −11.8423 + 20.5115i −0.529076 + 0.916387i
\(502\) 23.9309i 1.06809i
\(503\) 21.0577 + 12.1577i 0.938917 + 0.542084i 0.889621 0.456700i \(-0.150969\pi\)
0.0492961 + 0.998784i \(0.484302\pi\)
\(504\) −1.78078 3.08440i −0.0793221 0.137390i
\(505\) 0 0
\(506\) 4.31534 0.191840
\(507\) 3.57071 + 12.5000i 0.158581 + 0.555144i
\(508\) 21.8078i 0.967563i
\(509\) −8.12311 14.0696i −0.360050 0.623625i 0.627918 0.778279i \(-0.283907\pi\)
−0.987969 + 0.154654i \(0.950574\pi\)
\(510\) 0 0
\(511\) 16.0270 27.7596i 0.708992 1.22801i
\(512\) 1.00000i 0.0441942i
\(513\) 2.11176 + 1.21922i 0.0932364 + 0.0538300i
\(514\) −6.80776 + 11.7914i −0.300278 + 0.520096i
\(515\) 0 0
\(516\) −0.219224 + 0.379706i −0.00965078 + 0.0167156i
\(517\) 1.94528 1.12311i 0.0855531 0.0493941i
\(518\) −1.73205 + 1.00000i −0.0761019 + 0.0439375i
\(519\) 8.87689 0.389652
\(520\) 0 0
\(521\) 34.7386 1.52193 0.760964 0.648795i \(-0.224727\pi\)
0.760964 + 0.648795i \(0.224727\pi\)
\(522\) −0.972638 + 0.561553i −0.0425712 + 0.0245785i
\(523\) 21.5908 12.4654i 0.944098 0.545075i 0.0528556 0.998602i \(-0.483168\pi\)
0.891243 + 0.453527i \(0.149834\pi\)
\(524\) 0.438447 0.759413i 0.0191537 0.0331751i
\(525\) 0 0
\(526\) −3.15767 + 5.46925i −0.137681 + 0.238470i
\(527\) −10.8188 6.24621i −0.471272 0.272089i
\(528\) 0.561553i 0.0244384i
\(529\) 18.0270 31.2237i 0.783782 1.35755i
\(530\) 0 0
\(531\) 5.12311 + 8.87348i 0.222324 + 0.385076i
\(532\) 8.68466i 0.376528i
\(533\) −4.22351 + 10.4384i −0.182941 + 0.452139i
\(534\) −10.2462 −0.443397
\(535\) 0 0
\(536\) −5.90388 10.2258i −0.255009 0.441688i
\(537\) −13.5833 7.84233i −0.586163 0.338421i
\(538\) 3.36932i 0.145262i
\(539\) −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 \(0.659257\pi\)
\(542\) 7.73436 + 4.46543i 0.332219 + 0.191807i
\(543\) −13.4168 + 7.74621i −0.575771 + 0.332422i
\(544\) −1.56155 2.70469i −0.0669510 0.115963i
\(545\) 0 0
\(546\) 11.9039 + 4.81645i 0.509439 + 0.206125i
\(547\) 30.9309i 1.32251i 0.750162 + 0.661254i \(0.229976\pi\)
−0.750162 + 0.661254i \(0.770024\pi\)
\(548\) 14.2829 8.24621i 0.610133 0.352261i
\(549\) −0.842329 1.45896i −0.0359497 0.0622668i
\(550\) 0 0
\(551\) −2.73863 −0.116670
\(552\) −6.65511 3.84233i −0.283260 0.163540i
\(553\) −48.7574 28.1501i −2.07338 1.19706i
\(554\) −5.00000 −0.212430
\(555\) 0 0
\(556\) −10.7808 18.6729i −0.457207 0.791905i
\(557\) 27.3799 15.8078i 1.16012 0.669796i 0.208788 0.977961i \(-0.433048\pi\)
0.951333 + 0.308164i \(0.0997147\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −0.219224 1.56557i −0.00927217 0.0662165i
\(560\) 0 0
\(561\) −0.876894 1.51883i −0.0370225 0.0641249i
\(562\) 1.51883 0.876894i 0.0640678 0.0369896i
\(563\) −18.0201 10.4039i −0.759455 0.438471i 0.0696453 0.997572i \(-0.477813\pi\)
−0.829100 + 0.559100i \(0.811147\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) −14.8078 + 25.6478i −0.622417 + 1.07806i
\(567\) 3.56155i 0.149571i
\(568\) −10.8786 6.28078i −0.456457 0.263536i
\(569\) −5.75379 9.96585i −0.241211 0.417790i 0.719848 0.694131i \(-0.244211\pi\)
−0.961060 + 0.276341i \(0.910878\pi\)
\(570\) 0 0
\(571\) 21.4233 0.896537 0.448268 0.893899i \(-0.352041\pi\)
0.448268 + 0.893899i \(0.352041\pi\)
\(572\) 1.24573 + 1.59612i 0.0520867 + 0.0667370i
\(573\) 15.9309i 0.665522i
\(574\) 5.56155 + 9.63289i 0.232135 + 0.402069i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 23.0000i 0.957503i −0.877951 0.478751i \(-0.841090\pi\)
0.877951 0.478751i \(-0.158910\pi\)
\(578\) 6.27540 + 3.62311i 0.261022 + 0.150701i
\(579\) 1.50000 2.59808i 0.0623379 0.107972i
\(580\) 0 0
\(581\) 11.6847 20.2384i 0.484761 0.839631i
\(582\) 2.43160 1.40388i 0.100793 0.0581928i
\(583\) −2.06501 + 1.19224i −0.0855241 + 0.0493774i
\(584\) −9.00000 −0.372423
\(585\) 0 0
\(586\) 20.2462 0.836363
\(587\) 15.5286 8.96543i 0.640933 0.370043i −0.144041 0.989572i \(-0.546010\pi\)
0.784974 + 0.619529i \(0.212676\pi\)
\(588\) 4.92306 2.84233i 0.203024 0.117216i
\(589\) −4.87689 + 8.44703i −0.200949 + 0.348054i
\(590\) 0 0
\(591\) −2.56155 + 4.43674i −0.105368 + 0.182503i
\(592\) 0.486319 + 0.280776i 0.0199876 + 0.0115398i
\(593\) 38.9848i 1.60092i −0.599389 0.800458i \(-0.704590\pi\)
0.599389 0.800458i \(-0.295410\pi\)
\(594\) −0.280776 + 0.486319i −0.0115204 + 0.0199539i
\(595\) 0 0
\(596\) 5.12311 + 8.87348i 0.209851 + 0.363472i
\(597\) 4.43845i 0.181654i
\(598\) 27.4397 3.84233i 1.12209 0.157125i
\(599\) 18.3153 0.748345 0.374172 0.927359i \(-0.377927\pi\)
0.374172 + 0.927359i \(0.377927\pi\)
\(600\) 0 0
\(601\) 2.90388 + 5.02967i 0.118452 + 0.205165i 0.919154 0.393898i \(-0.128874\pi\)
−0.800703 + 0.599062i \(0.795540\pi\)
\(602\) −1.35234 0.780776i −0.0551174 0.0318221i
\(603\) 11.8078i 0.480849i
\(604\) −8.34233 + 14.4493i −0.339445 + 0.587935i
\(605\) 0 0
\(606\) −6.24621 −0.253735
\(607\) −34.0948 19.6847i −1.38387 0.798976i −0.391252 0.920284i \(-0.627958\pi\)
−0.992615 + 0.121308i \(0.961291\pi\)
\(608\) −2.11176 + 1.21922i −0.0856431 + 0.0494460i
\(609\) −2.00000 3.46410i −0.0810441 0.140372i
\(610\) 0 0
\(611\) 11.3693 8.87348i 0.459953 0.358983i
\(612\) 3.12311i 0.126244i
\(613\) −31.6501 + 18.2732i −1.27834 + 0.738048i −0.976542 0.215326i \(-0.930919\pi\)
−0.301794 + 0.953373i \(0.597585\pi\)
\(614\) 11.1231 + 19.2658i 0.448892 + 0.777504i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) 41.0230 + 23.6847i 1.65153 + 0.953508i 0.976446 + 0.215763i \(0.0692240\pi\)
0.675079 + 0.737745i \(0.264109\pi\)
\(618\) 3.84381 + 2.21922i 0.154621 + 0.0892703i
\(619\) 12.3002 0.494386 0.247193 0.968966i \(-0.420492\pi\)
0.247193 + 0.968966i \(0.420492\pi\)
\(620\) 0 0
\(621\) 3.84233 + 6.65511i 0.154187 + 0.267060i
\(622\) 8.93335 5.15767i 0.358195 0.206804i
\(623\) 36.4924i 1.46204i
\(624\) −0.500000 3.57071i −0.0200160 0.142943i
\(625\) 0 0
\(626\) −15.5000 26.8468i −0.619505 1.07301i
\(627\) −1.18586 + 0.684658i −0.0473588 + 0.0273426i
\(628\) −14.9357 8.62311i −0.595998 0.344099i
\(629\) 1.75379 0.0699281
\(630\) 0 0
\(631\) −16.4654 + 28.5190i −0.655479 + 1.13532i 0.326295 + 0.945268i \(0.394200\pi\)
−0.981774 + 0.190054i \(0.939134\pi\)
\(632\) 15.8078i 0.628799i
\(633\) −0.972638 0.561553i −0.0386589 0.0223197i
\(634\) 8.12311 + 14.0696i 0.322610 + 0.558776i
\(635\) 0 0
\(636\) 4.24621 0.168373
\(637\) −7.68762 + 19.0000i −0.304594 + 0.752807i
\(638\) 0.630683i 0.0249690i
\(639\) 6.28078 + 10.8786i 0.248464 + 0.430352i
\(640\) 0 0
\(641\) −19.1231 + 33.1222i −0.755317 + 1.30825i 0.189899 + 0.981804i \(0.439184\pi\)
−0.945216 + 0.326444i \(0.894149\pi\)
\(642\) 5.36932i 0.211910i
\(643\) −21.2578 12.2732i −0.838326 0.484008i 0.0183689 0.999831i \(-0.494153\pi\)
−0.856695 + 0.515824i \(0.827486\pi\)
\(644\) 13.6847 23.7025i 0.539251 0.934010i
\(645\) 0 0
\(646\) −3.80776 + 6.59524i −0.149814 + 0.259486i
\(647\) −28.0794 + 16.2116i −1.10391 + 0.637346i −0.937247 0.348667i \(-0.886634\pi\)
−0.166668 + 0.986013i \(0.553301\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −5.75379 −0.225856
\(650\) 0 0
\(651\) −14.2462 −0.558353
\(652\) 14.2829 8.24621i 0.559360 0.322947i
\(653\) −32.5760 + 18.8078i −1.27480 + 0.736005i −0.975887 0.218276i \(-0.929957\pi\)
−0.298911 + 0.954281i \(0.596623\pi\)
\(654\) −1.40388 + 2.43160i −0.0548961 + 0.0950829i
\(655\) 0 0
\(656\) 1.56155 2.70469i 0.0609684 0.105600i
\(657\) 7.79423 + 4.50000i 0.304082 + 0.175562i
\(658\) 14.2462i 0.555375i
\(659\) 9.15767 15.8616i 0.356732 0.617878i −0.630681 0.776042i \(-0.717224\pi\)
0.987413 + 0.158164i \(0.0505575\pi\)
\(660\) 0 0
\(661\) 24.2732 + 42.0424i 0.944118 + 1.63526i 0.757508 + 0.652826i \(0.226417\pi\)
0.186610 + 0.982434i \(0.440250\pi\)
\(662\) 16.6847i 0.648468i
\(663\) −6.92820 8.87689i −0.269069 0.344750i
\(664\) −6.56155 −0.254638
\(665\) 0 0
\(666\) −0.280776 0.486319i −0.0108799 0.0188445i
\(667\) −7.47439 4.31534i −0.289410 0.167091i
\(668\) 23.6847i 0.916387i
\(669\) −0.219224 + 0.379706i −0.00847567 + 0.0146803i
\(670\) 0 0
\(671\) 0.946025 0.0365209
\(672\) −3.08440 1.78078i −0.118983 0.0686949i
\(673\) 24.9015 14.3769i 0.959883 0.554189i 0.0637458 0.997966i \(-0.479695\pi\)
0.896137 + 0.443778i \(0.146362\pi\)
\(674\) 4.02699 + 6.97495i 0.155114 + 0.268665i
\(675\) 0 0
\(676\) 9.34233 + 9.03996i 0.359320 + 0.347691i
\(677\) 11.6155i 0.446421i −0.974770 0.223211i \(-0.928346\pi\)
0.974770 0.223211i \(-0.0716537\pi\)
\(678\) 3.46410 2.00000i 0.133038 0.0768095i
\(679\) 5.00000 + 8.66025i 0.191882 + 0.332350i
\(680\) 0 0
\(681\) 29.6847 1.13752
\(682\) −1.94528 1.12311i −0.0744885 0.0430059i
\(683\) −13.3701 7.71922i −0.511592 0.295368i 0.221896 0.975070i \(-0.428776\pi\)
−0.733488 + 0.679703i \(0.762109\pi\)
\(684\) 2.43845 0.0932364
\(685\) 0 0
\(686\) −2.34233 4.05703i −0.0894305 0.154898i
\(687\) −8.22068 + 4.74621i −0.313638 + 0.181079i
\(688\) 0.438447i 0.0167156i
\(689\) −12.0691 + 9.41967i −0.459797 + 0.358861i
\(690\) 0 0
\(691\) 2.41146 + 4.17677i 0.0917362 + 0.158892i 0.908242 0.418446i \(-0.137425\pi\)
−0.816506 + 0.577338i \(0.804092\pi\)
\(692\) 7.68762 4.43845i 0.292239 0.168724i
\(693\) −1.73205 1.00000i −0.0657952 0.0379869i
\(694\) 24.8078 0.941690
\(695\) 0 0
\(696\) −0.561553 + 0.972638i −0.0212856 + 0.0368677i
\(697\) 9.75379i 0.369451i
\(698\) 16.6677 + 9.62311i 0.630882 + 0.364240i
\(699\) −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 \(0.505271\pi\)
\(702\) −1.35234 + 3.34233i −0.0510410 + 0.126148i
\(703\) 1.36932i 0.0516448i
\(704\) −0.280776 0.486319i −0.0105822 0.0183288i
\(705\) 0 0
\(706\) −1.12311 + 1.94528i −0.0422686 + 0.0732114i
\(707\) 22.2462i 0.836655i
\(708\) 8.87348 + 5.12311i 0.333486 + 0.192538i
\(709\) −14.3769 + 24.9015i −0.539936 + 0.935196i 0.458971 + 0.888451i \(0.348218\pi\)
−0.998907 + 0.0467448i \(0.985115\pi\)
\(710\) 0 0
\(711\) 7.90388 13.6899i 0.296419 0.513412i
\(712\) −8.87348 + 5.12311i −0.332548 + 0.191997i
\(713\) −26.6204 + 15.3693i −0.996943 + 0.575585i
\(714\) −11.1231 −0.416272
\(715\) 0 0
\(716\) −15.6847 −0.586163
\(717\) −23.4294 + 13.5270i −0.874988 + 0.505175i
\(718\) −4.22351 + 2.43845i −0.157620 + 0.0910020i
\(719\) −8.71922 + 15.1021i −0.325172 + 0.563215i −0.981547 0.191220i \(-0.938756\pi\)
0.656375 + 0.754435i \(0.272089\pi\)
\(720\) 0 0
\(721\) −7.90388 + 13.6899i −0.294356 + 0.509839i
\(722\) −11.3051 6.52699i −0.420731 0.242909i
\(723\) 15.5616i 0.578740i
\(724\) −7.74621 + 13.4168i −0.287886 + 0.498633i
\(725\) 0 0
\(726\) 5.34233 + 9.25319i 0.198272 + 0.343418i
\(727\) 50.7926i 1.88379i 0.335902 + 0.941897i \(0.390959\pi\)
−0.335902 + 0.941897i \(0.609041\pi\)
\(728\) 12.7173 1.78078i 0.471334 0.0660000i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0.684658 + 1.18586i 0.0253230 + 0.0438607i
\(732\) −1.45896 0.842329i −0.0539246 0.0311334i
\(733\) 47.9848i 1.77236i −0.463340 0.886180i \(-0.653349\pi\)
0.463340 0.886180i \(-0.346651\pi\)
\(734\) −5.09612 + 8.82674i −0.188101 + 0.325801i
\(735\) 0 0
\(736\) −7.68466 −0.283260
\(737\) −5.74234 3.31534i −0.211522 0.122122i
\(738\) −2.70469 + 1.56155i −0.0995610 + 0.0574816i
\(739\) −6.56155 11.3649i −0.241371 0.418066i 0.719734 0.694250i \(-0.244264\pi\)
−0.961105 + 0.276183i \(0.910930\pi\)
\(740\) 0 0
\(741\) −6.93087 + 5.40938i −0.254612 + 0.198718i
\(742\) 15.1231i 0.555187i
\(743\) 9.63289 5.56155i 0.353397 0.204034i −0.312784 0.949824i \(-0.601261\pi\)
0.666180 + 0.745791i \(0.267928\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) 0 0
\(746\) −9.49242 −0.347542
\(747\) 5.68247 + 3.28078i 0.207911 + 0.120037i
\(748\) −1.51883 0.876894i −0.0555338 0.0320624i
\(749\) 19.1231 0.698743
\(750\) 0 0
\(751\) −25.1231 43.5145i −0.916755 1.58787i −0.804311 0.594208i \(-0.797465\pi\)
−0.112444 0.993658i \(-0.535868\pi\)
\(752\) −3.46410 + 2.00000i −0.126323 + 0.0729325i
\(753\) 23.9309i 0.872089i
\(754\) −0.561553 4.01029i −0.0204505 0.146046i
\(755\) 0 0
\(756\) 1.78078 + 3.08440i 0.0647662 + 0.112178i
\(757\) 26.5737 15.3423i 0.965837 0.557626i 0.0678727 0.997694i \(-0.478379\pi\)
0.897965 + 0.440068i \(0.145046\pi\)
\(758\) 20.8314 + 12.0270i 0.756629 + 0.436840i
\(759\) −4.31534 −0.156637
\(760\) 0 0
\(761\) 11.4924 19.9055i 0.416600 0.721572i −0.578995 0.815331i \(-0.696555\pi\)
0.995595 + 0.0937588i \(0.0298882\pi\)
\(762\) 21.8078i 0.790012i
\(763\) −8.66025 5.00000i −0.313522 0.181012i
\(764\) 7.96543 + 13.7965i 0.288179 + 0.499141i
\(765\) 0 0
\(766\) −5.43845 −0.196499
\(767\) −36.5863 + 5.12311i −1.32105 + 0.184985i
\(768\) 1.00000i 0.0360844i
\(769\) −4.65767 8.06732i −0.167960 0.290915i 0.769743 0.638354i \(-0.220385\pi\)
−0.937702 + 0.347439i \(0.887051\pi\)
\(770\) 0 0
\(771\) 6.80776 11.7914i 0.245176 0.424657i
\(772\) 3.00000i 0.107972i
\(773\) 25.6478 + 14.8078i 0.922487 + 0.532598i 0.884428 0.466677i \(-0.154549\pi\)
0.0380595 + 0.999275i \(0.487882\pi\)
\(774\) 0.219224 0.379706i 0.00787983 0.0136483i
\(775\) 0 0
\(776\) 1.40388 2.43160i 0.0503964 0.0872892i
\(777\) 1.73205 1.00000i 0.0621370 0.0358748i
\(778\) 9.84612 5.68466i 0.353000 0.203805i
\(779\) −7.61553 −0.272855
\(780\) 0 0
\(781\) −7.05398 −0.252411
\(782\) −20.7846 + 12.0000i −0.743256 + 0.429119i
\(783\) 0.972638 0.561553i 0.0347592 0.0200683i
\(784\) 2.84233 4.92306i 0.101512 0.175824i