Properties

Label 567.2.g.a.109.1
Level $567$
Weight $2$
Character 567.109
Analytic conductor $4.528$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 567.109
Dual form 567.2.g.a.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} -2.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} -2.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +(2.00000 - 3.46410i) q^{10} -2.00000 q^{11} +(-0.500000 + 0.866025i) q^{13} +(-5.00000 - 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-0.500000 - 0.866025i) q^{19} +(2.00000 + 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} -1.00000 q^{25} +(-1.00000 - 1.73205i) q^{26} +(4.00000 - 3.46410i) q^{28} +(-2.00000 - 3.46410i) q^{29} +(-4.50000 - 7.79423i) q^{31} +(4.00000 + 6.92820i) q^{32} +(-1.00000 - 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +2.00000 q^{38} +(5.00000 - 8.66025i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(2.00000 + 3.46410i) q^{44} +(3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{50} +2.00000 q^{52} +(-6.00000 + 10.3923i) q^{53} +4.00000 q^{55} +8.00000 q^{58} +(6.00000 + 10.3923i) q^{59} +(-5.00000 + 8.66025i) q^{61} +18.0000 q^{62} -8.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(2.50000 + 4.33013i) q^{67} +(10.0000 + 3.46410i) q^{70} -6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} +6.00000 q^{74} +(-1.00000 + 1.73205i) q^{76} +(-1.00000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-4.00000 + 6.92820i) q^{80} +(10.0000 + 17.3205i) q^{82} +(-3.00000 - 5.19615i) q^{83} +10.0000 q^{86} +(-8.00000 - 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 + 10.3923i) q^{94} +(1.00000 + 1.73205i) q^{95} +(3.00000 + 5.19615i) q^{97} +(2.00000 - 13.8564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 2q^{4} - 4q^{5} + q^{7} + O(q^{10}) \) \( 2q - 2q^{2} - 2q^{4} - 4q^{5} + q^{7} + 4q^{10} - 4q^{11} - q^{13} - 10q^{14} + 4q^{16} - q^{19} + 4q^{20} + 4q^{22} - 2q^{25} - 2q^{26} + 8q^{28} - 4q^{29} - 9q^{31} + 8q^{32} - 2q^{35} - 3q^{37} + 4q^{38} + 10q^{41} - 5q^{43} + 4q^{44} + 6q^{47} - 13q^{49} + 2q^{50} + 4q^{52} - 12q^{53} + 8q^{55} + 16q^{58} + 12q^{59} - 10q^{61} + 36q^{62} - 16q^{64} + 2q^{65} + 5q^{67} + 20q^{70} - 12q^{71} + 3q^{73} + 12q^{74} - 2q^{76} - 2q^{77} + q^{79} - 8q^{80} + 20q^{82} - 6q^{83} + 20q^{86} - 16q^{89} - 5q^{91} + 12q^{94} + 2q^{95} + 6q^{97} + 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 0 0
\(9\) 0 0
\(10\) 2.00000 3.46410i 0.632456 1.09545i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) −5.00000 1.73205i −1.33631 0.462910i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 2.00000 + 3.46410i 0.447214 + 0.774597i
\(21\) 0 0
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 0 0
\(28\) 4.00000 3.46410i 0.755929 0.654654i
\(29\) −2.00000 3.46410i −0.371391 0.643268i 0.618389 0.785872i \(-0.287786\pi\)
−0.989780 + 0.142605i \(0.954452\pi\)
\(30\) 0 0
\(31\) −4.50000 7.79423i −0.808224 1.39988i −0.914093 0.405505i \(-0.867096\pi\)
0.105869 0.994380i \(-0.466238\pi\)
\(32\) 4.00000 + 6.92820i 0.707107 + 1.22474i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 5.19615i −0.169031 0.878310i
\(36\) 0 0
\(37\) −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) 2.00000 0.324443
\(39\) 0 0
\(40\) 0 0
\(41\) 5.00000 8.66025i 0.780869 1.35250i −0.150567 0.988600i \(-0.548110\pi\)
0.931436 0.363905i \(-0.118557\pi\)
\(42\) 0 0
\(43\) −2.50000 4.33013i −0.381246 0.660338i 0.609994 0.792406i \(-0.291172\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 1.00000 1.73205i 0.141421 0.244949i
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 8.00000 1.05045
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 18.0000 2.28600
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 0 0
\(67\) 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i \(-0.0678686\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 10.0000 + 3.46410i 1.19523 + 0.414039i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 1.50000 2.59808i 0.175562 0.304082i −0.764794 0.644275i \(-0.777159\pi\)
0.940356 + 0.340193i \(0.110493\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) −1.00000 5.19615i −0.113961 0.592157i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) −4.00000 + 6.92820i −0.447214 + 0.774597i
\(81\) 0 0
\(82\) 10.0000 + 17.3205i 1.10432 + 1.91273i
\(83\) −3.00000 5.19615i −0.329293 0.570352i 0.653079 0.757290i \(-0.273477\pi\)
−0.982372 + 0.186938i \(0.940144\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 10.0000 1.07833
\(87\) 0 0
\(88\) 0 0
\(89\) −8.00000 13.8564i −0.847998 1.46878i −0.882992 0.469389i \(-0.844474\pi\)
0.0349934 0.999388i \(-0.488859\pi\)
\(90\) 0 0
\(91\) −2.50000 0.866025i −0.262071 0.0907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 6.00000 + 10.3923i 0.618853 + 1.07188i
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) 0 0
\(97\) 3.00000 + 5.19615i 0.304604 + 0.527589i 0.977173 0.212445i \(-0.0681426\pi\)
−0.672569 + 0.740034i \(0.734809\pi\)
\(98\) 2.00000 13.8564i 0.202031 1.39971i
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −12.0000 20.7846i −1.16554 2.01878i
\(107\) 4.00000 + 6.92820i 0.386695 + 0.669775i 0.992003 0.126217i \(-0.0402834\pi\)
−0.605308 + 0.795991i \(0.706950\pi\)
\(108\) 0 0
\(109\) −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i \(-0.975180\pi\)
0.565940 + 0.824447i \(0.308513\pi\)
\(110\) −4.00000 + 6.92820i −0.381385 + 0.660578i
\(111\) 0 0
\(112\) 10.0000 + 3.46410i 0.944911 + 0.327327i
\(113\) −5.00000 + 8.66025i −0.470360 + 0.814688i −0.999425 0.0338931i \(-0.989209\pi\)
0.529065 + 0.848581i \(0.322543\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.00000 + 6.92820i −0.371391 + 0.643268i
\(117\) 0 0
\(118\) −24.0000 −2.20938
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −10.0000 17.3205i −0.905357 1.56813i
\(123\) 0 0
\(124\) −9.00000 + 15.5885i −0.808224 + 1.39988i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −15.0000 −1.33103 −0.665517 0.746382i \(-0.731789\pi\)
−0.665517 + 0.746382i \(0.731789\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) −14.0000 −1.22319 −0.611593 0.791173i \(-0.709471\pi\)
−0.611593 + 0.791173i \(0.709471\pi\)
\(132\) 0 0
\(133\) 2.00000 1.73205i 0.173422 0.150188i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 0 0
\(139\) 1.50000 2.59808i 0.127228 0.220366i −0.795373 0.606120i \(-0.792725\pi\)
0.922602 + 0.385754i \(0.126059\pi\)
\(140\) −8.00000 + 6.92820i −0.676123 + 0.585540i
\(141\) 0 0
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) 1.00000 1.73205i 0.0836242 0.144841i
\(144\) 0 0
\(145\) 4.00000 + 6.92820i 0.332182 + 0.575356i
\(146\) 3.00000 + 5.19615i 0.248282 + 0.430037i
\(147\) 0 0
\(148\) −3.00000 + 5.19615i −0.246598 + 0.427121i
\(149\) −12.0000 −0.983078 −0.491539 0.870855i \(-0.663566\pi\)
−0.491539 + 0.870855i \(0.663566\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 10.0000 + 3.46410i 0.805823 + 0.279145i
\(155\) 9.00000 + 15.5885i 0.722897 + 1.25210i
\(156\) 0 0
\(157\) 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i \(0.0220180\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) 1.00000 + 1.73205i 0.0795557 + 0.137795i
\(159\) 0 0
\(160\) −8.00000 13.8564i −0.632456 1.09545i
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) −20.0000 −1.56174
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 7.00000 12.1244i 0.541676 0.938211i −0.457132 0.889399i \(-0.651123\pi\)
0.998808 0.0488118i \(-0.0155435\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) −5.00000 + 8.66025i −0.381246 + 0.660338i
\(173\) −4.00000 + 6.92820i −0.304114 + 0.526742i −0.977064 0.212947i \(-0.931694\pi\)
0.672949 + 0.739689i \(0.265027\pi\)
\(174\) 0 0
\(175\) −0.500000 2.59808i −0.0377964 0.196396i
\(176\) −4.00000 + 6.92820i −0.301511 + 0.522233i
\(177\) 0 0
\(178\) 32.0000 2.39850
\(179\) −1.00000 + 1.73205i −0.0747435 + 0.129460i −0.900975 0.433872i \(-0.857147\pi\)
0.826231 + 0.563331i \(0.190480\pi\)
\(180\) 0 0
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) 4.00000 3.46410i 0.296500 0.256776i
\(183\) 0 0
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) 11.0000 + 8.66025i 0.785714 + 0.618590i
\(197\) 16.0000 1.13995 0.569976 0.821661i \(-0.306952\pi\)
0.569976 + 0.821661i \(0.306952\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −2.00000 + 3.46410i −0.140720 + 0.243733i
\(203\) 8.00000 6.92820i 0.561490 0.486265i
\(204\) 0 0
\(205\) −10.0000 + 17.3205i −0.698430 + 1.20972i
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 0 0
\(208\) 2.00000 + 3.46410i 0.138675 + 0.240192i
\(209\) 1.00000 + 1.73205i 0.0691714 + 0.119808i
\(210\) 0 0
\(211\) −2.00000 + 3.46410i −0.137686 + 0.238479i −0.926620 0.375999i \(-0.877300\pi\)
0.788935 + 0.614477i \(0.210633\pi\)
\(212\) 24.0000 1.64833
\(213\) 0 0
\(214\) −16.0000 −1.09374
\(215\) 5.00000 + 8.66025i 0.340997 + 0.590624i
\(216\) 0 0
\(217\) 18.0000 15.5885i 1.22192 1.05821i
\(218\) −9.00000 15.5885i −0.609557 1.05578i
\(219\) 0 0
\(220\) −4.00000 6.92820i −0.269680 0.467099i
\(221\) 0 0
\(222\) 0 0
\(223\) −8.00000 13.8564i −0.535720 0.927894i −0.999128 0.0417488i \(-0.986707\pi\)
0.463409 0.886145i \(-0.346626\pi\)
\(224\) −16.0000 + 13.8564i −1.06904 + 0.925820i
\(225\) 0 0
\(226\) −10.0000 17.3205i −0.665190 1.15214i
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 0 0
\(229\) −19.0000 −1.25556 −0.627778 0.778393i \(-0.716035\pi\)
−0.627778 + 0.778393i \(0.716035\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 0 0
\(235\) −6.00000 + 10.3923i −0.391397 + 0.677919i
\(236\) 12.0000 20.7846i 0.781133 1.35296i
\(237\) 0 0
\(238\) 0 0
\(239\) −3.00000 + 5.19615i −0.194054 + 0.336111i −0.946590 0.322440i \(-0.895497\pi\)
0.752536 + 0.658551i \(0.228830\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 7.00000 12.1244i 0.449977 0.779383i
\(243\) 0 0
\(244\) 20.0000 1.28037
\(245\) 13.0000 5.19615i 0.830540 0.331970i
\(246\) 0 0
\(247\) 1.00000 0.0636285
\(248\) 0 0
\(249\) 0 0
\(250\) −12.0000 + 20.7846i −0.758947 + 1.31453i
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 15.0000 25.9808i 0.941184 1.63018i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 26.0000 1.62184 0.810918 0.585160i \(-0.198968\pi\)
0.810918 + 0.585160i \(0.198968\pi\)
\(258\) 0 0
\(259\) 6.00000 5.19615i 0.372822 0.322873i
\(260\) −4.00000 −0.248069
\(261\) 0 0
\(262\) 14.0000 24.2487i 0.864923 1.49809i
\(263\) 4.00000 0.246651 0.123325 0.992366i \(-0.460644\pi\)
0.123325 + 0.992366i \(0.460644\pi\)
\(264\) 0 0
\(265\) 12.0000 20.7846i 0.737154 1.27679i
\(266\) 1.00000 + 5.19615i 0.0613139 + 0.318597i
\(267\) 0 0
\(268\) 5.00000 8.66025i 0.305424 0.529009i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 12.0000 20.7846i 0.724947 1.25564i
\(275\) 2.00000 0.120605
\(276\) 0 0
\(277\) 13.0000 0.781094 0.390547 0.920583i \(-0.372286\pi\)
0.390547 + 0.920583i \(0.372286\pi\)
\(278\) 3.00000 + 5.19615i 0.179928 + 0.311645i
\(279\) 0 0
\(280\) 0 0
\(281\) 2.00000 + 3.46410i 0.119310 + 0.206651i 0.919494 0.393103i \(-0.128598\pi\)
−0.800184 + 0.599754i \(0.795265\pi\)
\(282\) 0 0
\(283\) 5.50000 + 9.52628i 0.326941 + 0.566279i 0.981903 0.189383i \(-0.0606488\pi\)
−0.654962 + 0.755662i \(0.727315\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) 2.00000 + 3.46410i 0.118262 + 0.204837i
\(287\) 25.0000 + 8.66025i 1.47570 + 0.511199i
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −16.0000 −0.939552
\(291\) 0 0
\(292\) −6.00000 −0.351123
\(293\) −4.00000 + 6.92820i −0.233682 + 0.404750i −0.958889 0.283782i \(-0.908411\pi\)
0.725206 + 0.688531i \(0.241744\pi\)
\(294\) 0 0
\(295\) −12.0000 20.7846i −0.698667 1.21013i
\(296\) 0 0
\(297\) 0 0
\(298\) 12.0000 20.7846i 0.695141 1.20402i
\(299\) 0 0
\(300\) 0 0
\(301\) 10.0000 8.66025i 0.576390 0.499169i
\(302\) 16.0000 27.7128i 0.920697 1.59469i
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) 10.0000 17.3205i 0.572598 0.991769i
\(306\) 0 0
\(307\) −17.0000 −0.970241 −0.485121 0.874447i \(-0.661224\pi\)
−0.485121 + 0.874447i \(0.661224\pi\)
\(308\) −8.00000 + 6.92820i −0.455842 + 0.394771i
\(309\) 0 0
\(310\) −36.0000 −2.04466
\(311\) 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) −28.0000 −1.58013
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) −12.0000 + 20.7846i −0.673987 + 1.16738i 0.302777 + 0.953062i \(0.402086\pi\)
−0.976764 + 0.214318i \(0.931247\pi\)
\(318\) 0 0
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 16.0000 0.894427
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.500000 0.866025i 0.0277350 0.0480384i
\(326\) 8.00000 0.443079
\(327\) 0 0
\(328\) 0 0
\(329\) 15.0000 + 5.19615i 0.826977 + 0.286473i
\(330\) 0 0
\(331\) 12.5000 21.6506i 0.687062 1.19003i −0.285722 0.958313i \(-0.592233\pi\)
0.972784 0.231714i \(-0.0744333\pi\)
\(332\) −6.00000 + 10.3923i −0.329293 + 0.570352i
\(333\) 0 0
\(334\) 14.0000 + 24.2487i 0.766046 + 1.32683i
\(335\) −5.00000 8.66025i −0.273179 0.473160i
\(336\) 0 0
\(337\) −6.50000 + 11.2583i −0.354078 + 0.613280i −0.986960 0.160968i \(-0.948538\pi\)
0.632882 + 0.774248i \(0.281872\pi\)
\(338\) −24.0000 −1.30543
\(339\) 0 0
\(340\) 0 0
\(341\) 9.00000 + 15.5885i 0.487377 + 0.844162i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) −8.00000 13.8564i −0.430083 0.744925i
\(347\) −16.0000 27.7128i −0.858925 1.48770i −0.872955 0.487800i \(-0.837799\pi\)
0.0140303 0.999902i \(-0.495534\pi\)
\(348\) 0 0
\(349\) 7.00000 + 12.1244i 0.374701 + 0.649002i 0.990282 0.139072i \(-0.0444119\pi\)
−0.615581 + 0.788074i \(0.711079\pi\)
\(350\) 5.00000 + 1.73205i 0.267261 + 0.0925820i
\(351\) 0 0
\(352\) −8.00000 13.8564i −0.426401 0.738549i
\(353\) 34.0000 1.80964 0.904819 0.425797i \(-0.140006\pi\)
0.904819 + 0.425797i \(0.140006\pi\)
\(354\) 0 0
\(355\) 12.0000 0.636894
\(356\) −16.0000 + 27.7128i −0.847998 + 1.46878i
\(357\) 0 0
\(358\) −2.00000 3.46410i −0.105703 0.183083i
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) −13.0000 + 22.5167i −0.683265 + 1.18345i
\(363\) 0 0
\(364\) 1.00000 + 5.19615i 0.0524142 + 0.272352i
\(365\) −3.00000 + 5.19615i −0.157027 + 0.271979i
\(366\) 0 0
\(367\) −9.00000 −0.469796 −0.234898 0.972020i \(-0.575476\pi\)
−0.234898 + 0.972020i \(0.575476\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −12.0000 −0.623850
\(371\) −30.0000 10.3923i −1.55752 0.539542i
\(372\) 0 0
\(373\) 23.0000 1.19089 0.595447 0.803394i \(-0.296975\pi\)
0.595447 + 0.803394i \(0.296975\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 3.00000 0.154100 0.0770498 0.997027i \(-0.475450\pi\)
0.0770498 + 0.997027i \(0.475450\pi\)
\(380\) 2.00000 3.46410i 0.102598 0.177705i
\(381\) 0 0
\(382\) −10.0000 17.3205i −0.511645 0.886194i
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 0 0
\(385\) 2.00000 + 10.3923i 0.101929 + 0.529641i
\(386\) 22.0000 1.11977
\(387\) 0 0
\(388\) 6.00000 10.3923i 0.304604 0.527589i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −16.0000 + 27.7128i −0.806068 + 1.39615i
\(395\) −1.00000 + 1.73205i −0.0503155 + 0.0871489i
\(396\) 0 0
\(397\) 4.50000 + 7.79423i 0.225849 + 0.391181i 0.956574 0.291491i \(-0.0941512\pi\)
−0.730725 + 0.682672i \(0.760818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) −36.0000 −1.79775 −0.898877 0.438201i \(-0.855616\pi\)
−0.898877 + 0.438201i \(0.855616\pi\)
\(402\) 0 0
\(403\) 9.00000 0.448322
\(404\) −2.00000 3.46410i −0.0995037 0.172345i
\(405\) 0 0
\(406\) 4.00000 + 20.7846i 0.198517 + 1.03152i
\(407\) 3.00000 + 5.19615i 0.148704 + 0.257564i
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) −20.0000 34.6410i −0.987730 1.71080i
\(411\) 0 0
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) −24.0000 + 20.7846i −1.18096 + 1.02274i
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) −8.00000 −0.392232
\(417\) 0 0
\(418\) −4.00000 −0.195646
\(419\) −15.0000 + 25.9808i −0.732798 + 1.26924i 0.222885 + 0.974845i \(0.428453\pi\)
−0.955683 + 0.294398i \(0.904881\pi\)
\(420\) 0 0
\(421\) 3.50000 + 6.06218i 0.170580 + 0.295452i 0.938623 0.344946i \(-0.112103\pi\)
−0.768043 + 0.640398i \(0.778769\pi\)
\(422\) −4.00000 6.92820i −0.194717 0.337260i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −25.0000 8.66025i −1.20983 0.419099i
\(428\) 8.00000 13.8564i 0.386695 0.669775i
\(429\) 0 0
\(430\) −20.0000 −0.964486
\(431\) 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) 0 0
\(433\) 31.0000 1.48976 0.744882 0.667196i \(-0.232506\pi\)
0.744882 + 0.667196i \(0.232506\pi\)
\(434\) 9.00000 + 46.7654i 0.432014 + 2.24481i
\(435\) 0 0
\(436\) 18.0000 0.862044
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 0 0
\(445\) 16.0000 + 27.7128i 0.758473 + 1.31371i
\(446\) 32.0000 1.51524
\(447\) 0 0
\(448\) −4.00000 20.7846i −0.188982 0.981981i
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −10.0000 + 17.3205i −0.470882 + 0.815591i
\(452\) 20.0000 0.940721
\(453\) 0 0
\(454\) −18.0000 + 31.1769i −0.844782 + 1.46321i
\(455\) 5.00000 + 1.73205i 0.234404 + 0.0811998i
\(456\) 0 0
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 19.0000 32.9090i 0.887812 1.53773i
\(459\) 0 0
\(460\) 0 0
\(461\) −10.0000 17.3205i −0.465746 0.806696i 0.533488 0.845807i \(-0.320881\pi\)
−0.999235 + 0.0391109i \(0.987547\pi\)
\(462\) 0 0
\(463\) 8.50000 14.7224i 0.395029 0.684209i −0.598076 0.801439i \(-0.704068\pi\)
0.993105 + 0.117230i \(0.0374014\pi\)
\(464\) −16.0000 −0.742781
\(465\) 0 0
\(466\) 12.0000 0.555889
\(467\) −3.00000 5.19615i −0.138823 0.240449i 0.788228 0.615383i \(-0.210999\pi\)
−0.927052 + 0.374934i \(0.877665\pi\)
\(468\) 0 0
\(469\) −10.0000 + 8.66025i −0.461757 + 0.399893i
\(470\) −12.0000 20.7846i −0.553519 0.958723i
\(471\) 0 0
\(472\) 0 0
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) 0 0
\(475\) 0.500000 + 0.866025i 0.0229416 + 0.0397360i
\(476\) 0 0
\(477\) 0 0
\(478\) −6.00000 10.3923i −0.274434 0.475333i
\(479\) −28.0000 −1.27935 −0.639676 0.768644i \(-0.720932\pi\)
−0.639676 + 0.768644i \(0.720932\pi\)
\(480\) 0 0
\(481\) 3.00000 0.136788
\(482\) −14.0000 + 24.2487i −0.637683 + 1.10450i
\(483\) 0 0
\(484\) 7.00000 + 12.1244i 0.318182 + 0.551107i
\(485\) −6.00000 10.3923i −0.272446 0.471890i
\(486\) 0 0
\(487\) −15.5000 + 26.8468i −0.702372 + 1.21654i 0.265260 + 0.964177i \(0.414542\pi\)
−0.967632 + 0.252367i \(0.918791\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −4.00000 + 27.7128i −0.180702 + 1.25194i
\(491\) 14.0000 24.2487i 0.631811 1.09433i −0.355370 0.934726i \(-0.615645\pi\)
0.987181 0.159603i \(-0.0510215\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.00000 + 1.73205i −0.0449921 + 0.0779287i
\(495\) 0 0
\(496\) −36.0000 −1.61645
\(497\) −3.00000 15.5885i −0.134568 0.699238i
\(498\) 0 0
\(499\) 37.0000 1.65635 0.828174 0.560471i \(-0.189380\pi\)
0.828174 + 0.560471i \(0.189380\pi\)
\(500\) −12.0000 20.7846i −0.536656 0.929516i
\(501\) 0 0
\(502\) 8.00000 13.8564i 0.357057 0.618442i
\(503\) −42.0000 −1.87269 −0.936344 0.351085i \(-0.885813\pi\)
−0.936344 + 0.351085i \(0.885813\pi\)
\(504\) 0 0
\(505\) −4.00000 −0.177998
\(506\) 0 0
\(507\) 0 0
\(508\) 15.0000 + 25.9808i 0.665517 + 1.15271i
\(509\) 2.00000 0.0886484 0.0443242 0.999017i \(-0.485887\pi\)
0.0443242 + 0.999017i \(0.485887\pi\)
\(510\) 0 0
\(511\) 7.50000 + 2.59808i 0.331780 + 0.114932i
\(512\) 32.0000 1.41421
\(513\) 0 0
\(514\) −26.0000 + 45.0333i −1.14681 + 1.98633i
\(515\) 14.0000 0.616914
\(516\) 0 0
\(517\) −6.00000 + 10.3923i −0.263880 + 0.457053i
\(518\) 3.00000 + 15.5885i 0.131812 + 0.684917i
\(519\) 0 0
\(520\) 0 0
\(521\) −6.00000 + 10.3923i −0.262865 + 0.455295i −0.967002 0.254769i \(-0.918001\pi\)
0.704137 + 0.710064i \(0.251334\pi\)
\(522\) 0 0
\(523\) −15.5000 26.8468i −0.677768 1.17393i −0.975652 0.219326i \(-0.929614\pi\)
0.297884 0.954602i \(-0.403719\pi\)
\(524\) 14.0000 + 24.2487i 0.611593 + 1.05931i
\(525\) 0 0
\(526\) −4.00000 + 6.92820i −0.174408 + 0.302084i
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 24.0000 + 41.5692i 1.04249 + 1.80565i
\(531\) 0 0
\(532\) −5.00000 1.73205i −0.216777 0.0750939i
\(533\) 5.00000 + 8.66025i 0.216574 + 0.375117i
\(534\) 0 0
\(535\) −8.00000 13.8564i −0.345870 0.599065i
\(536\) 0 0
\(537\) 0 0
\(538\) −6.00000 10.3923i −0.258678 0.448044i
\(539\) 13.0000 5.19615i 0.559950 0.223814i
\(540\) 0 0
\(541\) 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i \(-0.0327407\pi\)
−0.586278 + 0.810110i \(0.699407\pi\)
\(542\) 32.0000 1.37452
\(543\) 0 0
\(544\) 0 0
\(545\) 9.00000 15.5885i 0.385518 0.667736i
\(546\) 0 0
\(547\) −14.0000 24.2487i −0.598597 1.03680i −0.993028 0.117875i \(-0.962392\pi\)
0.394432 0.918925i \(-0.370941\pi\)
\(548\) 12.0000 + 20.7846i 0.512615 + 0.887875i
\(549\) 0 0
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) −2.00000 + 3.46410i −0.0852029 + 0.147576i
\(552\) 0 0
\(553\) 2.50000 + 0.866025i 0.106311 + 0.0368271i
\(554\) −13.0000 + 22.5167i −0.552317 + 0.956641i
\(555\) 0 0
\(556\) −6.00000 −0.254457
\(557\) 1.00000 1.73205i 0.0423714 0.0733893i −0.844062 0.536246i \(-0.819842\pi\)
0.886433 + 0.462856i \(0.153175\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) −20.0000 6.92820i −0.845154 0.292770i
\(561\) 0 0
\(562\) −8.00000 −0.337460
\(563\) 13.0000 + 22.5167i 0.547885 + 0.948964i 0.998419 + 0.0562051i \(0.0179001\pi\)
−0.450535 + 0.892759i \(0.648767\pi\)
\(564\) 0 0
\(565\) 10.0000 17.3205i 0.420703 0.728679i
\(566\) −22.0000 −0.924729
\(567\) 0 0
\(568\) 0 0
\(569\) 13.0000 22.5167i 0.544988 0.943948i −0.453619 0.891196i \(-0.649867\pi\)
0.998608 0.0527519i \(-0.0167993\pi\)
\(570\) 0 0
\(571\) 9.50000 + 16.4545i 0.397563 + 0.688599i 0.993425 0.114488i \(-0.0365228\pi\)
−0.595862 + 0.803087i \(0.703189\pi\)
\(572\) −4.00000 −0.167248
\(573\) 0 0
\(574\) −40.0000 + 34.6410i −1.66957 + 1.44589i
\(575\) 0 0
\(576\) 0 0
\(577\) 8.50000 14.7224i 0.353860 0.612903i −0.633062 0.774101i \(-0.718202\pi\)
0.986922 + 0.161198i \(0.0515357\pi\)
\(578\) −34.0000 −1.41421
\(579\) 0 0
\(580\) 8.00000 13.8564i 0.332182 0.575356i
\(581\) 12.0000 10.3923i 0.497844 0.431145i
\(582\) 0 0
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) −8.00000 13.8564i −0.330477 0.572403i
\(587\) −8.00000 13.8564i −0.330195 0.571915i 0.652355 0.757914i \(-0.273781\pi\)
−0.982550 + 0.185999i \(0.940448\pi\)
\(588\) 0 0
\(589\) −4.50000 + 7.79423i −0.185419 + 0.321156i
\(590\) 48.0000 1.97613
\(591\) 0 0
\(592\) −12.0000 −0.493197
\(593\) 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 + 20.7846i 0.491539 + 0.851371i
\(597\) 0 0
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i \(-0.107905\pi\)
−0.759531 + 0.650471i \(0.774572\pi\)
\(602\) 5.00000 + 25.9808i 0.203785 + 1.05890i
\(603\) 0 0
\(604\) 16.0000 + 27.7128i 0.651031 + 1.12762i
\(605\) 14.0000 0.569181
\(606\) 0 0
\(607\) 23.0000 0.933541 0.466771 0.884378i \(-0.345417\pi\)
0.466771 + 0.884378i \(0.345417\pi\)
\(608\) 4.00000 6.92820i 0.162221 0.280976i
\(609\) 0 0
\(610\) 20.0000 + 34.6410i 0.809776 + 1.40257i
\(611\) 3.00000 + 5.19615i 0.121367 + 0.210214i
\(612\) 0 0
\(613\) −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i \(0.407575\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) 17.0000 29.4449i 0.686064 1.18830i
\(615\) 0 0
\(616\) 0 0
\(617\) 3.00000 5.19615i 0.120775 0.209189i −0.799298 0.600935i \(-0.794795\pi\)
0.920074 + 0.391745i \(0.128129\pi\)
\(618\) 0 0
\(619\) −29.0000 −1.16561 −0.582804 0.812613i \(-0.698045\pi\)
−0.582804 + 0.812613i \(0.698045\pi\)
\(620\) 18.0000 31.1769i 0.722897 1.25210i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 32.0000 27.7128i 1.28205 1.11029i
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 1.00000 + 1.73205i 0.0399680 + 0.0692267i
\(627\) 0 0
\(628\) 14.0000 24.2487i 0.558661 0.967629i
\(629\) 0 0
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −24.0000 41.5692i −0.953162 1.65092i
\(635\) 30.0000 1.19051
\(636\) 0 0
\(637\) 1.00000 6.92820i 0.0396214 0.274505i
\(638\) −16.0000 −0.633446
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 9.50000 16.4545i 0.374643 0.648901i −0.615630 0.788035i \(-0.711098\pi\)
0.990274 + 0.139134i \(0.0444318\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.00000 + 1.73205i −0.0393141 + 0.0680939i −0.885013 0.465566i \(-0.845851\pi\)
0.845699 + 0.533660i \(0.179184\pi\)
\(648\) 0 0
\(649\) −12.0000 20.7846i −0.471041 0.815867i
\(650\) 1.00000 + 1.73205i 0.0392232 + 0.0679366i
\(651\) 0 0
\(652\) −4.00000 + 6.92820i −0.156652 + 0.271329i
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 0 0
\(655\) 28.0000 1.09405
\(656\) −20.0000 34.6410i −0.780869 1.35250i
\(657\) 0 0
\(658\) −24.0000 + 20.7846i −0.935617 + 0.810268i
\(659\) −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 0 0
\(661\) 20.5000 + 35.5070i 0.797358 + 1.38106i 0.921331 + 0.388778i \(0.127103\pi\)
−0.123974 + 0.992286i \(0.539564\pi\)
\(662\) 25.0000 + 43.3013i 0.971653 + 1.68295i
\(663\) 0 0
\(664\) 0 0
\(665\) −4.00000 + 3.46410i −0.155113 + 0.134332i
\(666\) 0 0
\(667\) 0 0
\(668\) −28.0000 −1.08335
\(669\) 0 0
\(670\) 20.0000 0.772667
\(671\) 10.0000 17.3205i 0.386046 0.668651i
\(672\) 0 0
\(673\) 20.5000 + 35.5070i 0.790217 + 1.36870i 0.925832 + 0.377934i \(0.123365\pi\)
−0.135615 + 0.990762i \(0.543301\pi\)
\(674\) −13.0000 22.5167i −0.500741 0.867309i
\(675\) 0 0
\(676\) 12.0000 20.7846i 0.461538 0.799408i
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 0 0
\(679\) −12.0000 + 10.3923i −0.460518 + 0.398820i
\(680\) 0 0
\(681\) 0 0
\(682\) −36.0000 −1.37851
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 0 0
\(685\) 24.0000 0.916993
\(686\) 37.0000 1.73205i 1.41267 0.0661300i
\(687\) 0 0
\(688\) −20.0000 −0.762493
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) 18.5000 32.0429i 0.703773 1.21897i −0.263359 0.964698i \(-0.584830\pi\)
0.967132 0.254273i \(-0.0818362\pi\)
\(692\) 16.0000 0.608229
\(693\) 0 0
\(694\) 64.0000 2.42941
\(695\) −3.00000 + 5.19615i −0.113796 + 0.197101i
\(696\) 0 0
\(697\) 0 0
\(698\) −28.0000 −1.05982
\(699\) 0 0
\(700\) −4.00000 + 3.46410i −0.151186 + 0.130931i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −1.50000 + 2.59808i −0.0565736 + 0.0979883i
\(704\) 16.0000 0.603023
\(705\) 0 0
\(706\) −34.0000 + 58.8897i −1.27961 + 2.21634i
\(707\) 1.00000 + 5.19615i 0.0376089 + 0.195421i
\(708\) 0 0
\(709\) −15.0000 + 25.9808i −0.563337 + 0.975728i 0.433865 + 0.900978i \(0.357149\pi\)
−0.997202 + 0.0747503i \(0.976184\pi\)
\(710\) −12.0000 + 20.7846i −0.450352 + 0.780033i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −2.00000 + 3.46410i −0.0747958 + 0.129550i
\(716\) 4.00000 0.149487
\(717\) 0 0
\(718\) 40.0000 1.49279
\(719\) 9.00000 + 15.5885i 0.335643 + 0.581351i 0.983608 0.180319i \(-0.0577130\pi\)
−0.647965 + 0.761670i \(0.724380\pi\)
\(720\) 0 0
\(721\) −3.50000 18.1865i −0.130347 0.677302i
\(722\) 18.0000 + 31.1769i 0.669891 + 1.16028i
\(723\) 0 0
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) 2.00000 + 3.46410i 0.0742781 + 0.128654i
\(726\) 0 0
\(727\) 6.50000 + 11.2583i 0.241072 + 0.417548i 0.961020 0.276479i \(-0.0891678\pi\)
−0.719948 + 0.694028i \(0.755834\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −6.00000 10.3923i −0.222070 0.384636i
\(731\) 0 0
\(732\) 0 0
\(733\) −15.0000 −0.554038 −0.277019 0.960864i \(-0.589346\pi\)
−0.277019 + 0.960864i \(0.589346\pi\)
\(734\) 9.00000 15.5885i 0.332196 0.575380i
\(735\) 0 0
\(736\) 0 0
\(737\) −5.00000 8.66025i −0.184177 0.319005i
\(738\) 0 0
\(739\) 7.50000 12.9904i 0.275892 0.477859i −0.694468 0.719524i \(-0.744360\pi\)
0.970360 + 0.241665i \(0.0776935\pi\)
\(740\) 6.00000 10.3923i 0.220564 0.382029i
\(741\) 0 0
\(742\) 48.0000 41.5692i 1.76214 1.52605i
\(743\) −21.0000 + 36.3731i −0.770415 + 1.33440i 0.166920 + 0.985970i \(0.446618\pi\)
−0.937336 + 0.348428i \(0.886716\pi\)
\(744\) 0 0
\(745\) 24.0000 0.879292
\(746\) −23.0000 + 39.8372i −0.842090 + 1.45854i
\(747\) 0 0
\(748\) 0 0
\(749\) −16.0000 + 13.8564i −0.584627 + 0.506302i
\(750\) 0 0
\(751\) 13.0000 0.474377 0.237188 0.971464i \(-0.423774\pi\)
0.237188 + 0.971464i \(0.423774\pi\)
\(752\) −12.0000 20.7846i −0.437595 0.757937i
\(753\) 0 0
\(754\) −4.00000 + 6.92820i −0.145671 + 0.252310i
\(755\) 32.0000 1.16460
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −3.00000 + 5.19615i −0.108965 + 0.188733i
\(759\) 0 0
\(760\) 0 0
\(761\) −48.0000 −1.74000 −0.869999 0.493053i \(-0.835881\pi\)
−0.869999 + 0.493053i \(0.835881\pi\)
\(762\) 0 0
\(763\) −22.5000 7.79423i −0.814555 0.282170i
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) 24.5000 42.4352i 0.883493 1.53025i 0.0360609 0.999350i \(-0.488519\pi\)
0.847432 0.530904i \(-0.178148\pi\)
\(770\) −20.0000 6.92820i −0.720750 0.249675i
\(771\) 0 0
\(772\) −11.0000 + 19.0526i −0.395899 + 0.685717i
\(773\) 17.0000 29.4449i 0.611448 1.05906i −0.379549 0.925172i \(-0.623921\pi\)
0.990997 0.133887i \(-0.0427458\pi\)
\(774\) 0 0
\(775\) 4.50000 + 7.79423i 0.161645 + 0.279977i
\(776\) 0 0
\(777\) 0 0
\(778\) 6.00000 10.3923i 0.215110 0.372582i
\(779\) −10.0000 −0.358287
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) 0 0
\(784\) −4.00000 + 27.7128i −0.142857 + 0.989743i
\(785\) −14.0000 24.2487i −0.499681 0.865474i
\(786\) 0 0
\(787\) −20.0000 34.6410i −0.712923 1.23482i −0.963755 0.266788i \(-0.914038\pi\)
0.250832 0.968031i \(-0.419296\pi\)
\(788\) −16.0000 27.7128i −0.569976 0.987228i
\(789\) 0 0
\(790\) −2.00000 3.46410i −0.0711568 0.123247i
\(791\) −25.0000 8.66025i −0.888898 0.307923i
\(792\) 0 0
\(793\) −5.00000 8.66025i −0.177555 0.307535i