Properties

Label 567.2.g.f.109.1
Level $567$
Weight $2$
Character 567.109
Analytic conductor $4.528$
Analytic rank $0$
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: \(0\)
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.f.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 \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 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 \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 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 0.989780 0.142605i \(-0.0455477\pi\)
−0.618389 + 0.785872i \(0.712214\pi\)
\(30\) 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 \(0.451890\pi\)
−0.931436 + 0.363905i \(0.881443\pi\)
\(42\) 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 −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 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 \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) 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 \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) 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 \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 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 0.982372 0.186938i \(-0.0598564\pi\)
−0.653079 + 0.757290i \(0.726523\pi\)
\(84\) 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 \(0.155526\pi\)
−0.0349934 + 0.999388i \(0.511141\pi\)
\(90\) 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 \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 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 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) 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 −0.529065 0.848581i \(-0.677457\pi\)
0.999425 + 0.0338931i \(0.0107906\pi\)
\(114\) 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 \(-0.290529\pi\)
0.611593 + 0.791173i \(0.290529\pi\)
\(132\) 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 \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 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 \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 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 \(0.348877\pi\)
−0.998808 + 0.0488118i \(0.984457\pi\)
\(168\) 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 −0.672949 0.739689i \(-0.734973\pi\)
0.977064 + 0.212947i \(0.0683062\pi\)
\(174\) 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 −0.826231 0.563331i \(-0.809520\pi\)
0.900975 + 0.433872i \(0.142853\pi\)
\(180\) 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 −0.626468 0.779447i \(-0.715500\pi\)
0.988255 + 0.152813i \(0.0488333\pi\)
\(192\) 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 \(-0.693048\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(198\) 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 \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 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 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 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 −0.752536 0.658551i \(-0.771170\pi\)
0.946590 + 0.322440i \(0.104503\pi\)
\(240\) 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 \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 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 \(-0.801032\pi\)
−0.810918 + 0.585160i \(0.801032\pi\)
\(258\) 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 \(-0.539356\pi\)
−0.123325 + 0.992366i \(0.539356\pi\)
\(264\) 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 −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 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 0.800184 0.599754i \(-0.204735\pi\)
−0.919494 + 0.393103i \(0.871402\pi\)
\(282\) 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 −0.725206 0.688531i \(-0.758256\pi\)
0.958889 + 0.283782i \(0.0915890\pi\)
\(294\) 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 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) 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 \(-0.597914\pi\)
0.976764 0.214318i \(-0.0687530\pi\)
\(318\) 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 \(0.162201\pi\)
−0.0140303 + 0.999902i \(0.504466\pi\)
\(348\) 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 \(-0.859994\pi\)
−0.904819 + 0.425797i \(0.859994\pi\)
\(354\) 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 \(0.0103087\pi\)
−0.471696 + 0.881761i \(0.656358\pi\)
\(360\) 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 \(-0.400813\pi\)
0.306586 + 0.951843i \(0.400813\pi\)
\(384\) 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 \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 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 \(-0.144384\pi\)
0.898877 + 0.438201i \(0.144384\pi\)
\(402\) 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 \(-0.571547\pi\)
0.955683 0.294398i \(-0.0951193\pi\)
\(420\) 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 −0.997173 0.0751385i \(-0.976060\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(432\) 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 −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 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 \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 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 0.999235 0.0391109i \(-0.0124526\pi\)
−0.533488 + 0.845807i \(0.679119\pi\)
\(462\) 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 0.927052 0.374934i \(-0.122335\pi\)
−0.788228 + 0.615383i \(0.789001\pi\)
\(468\) 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 \(-0.279068\pi\)
0.639676 + 0.768644i \(0.279068\pi\)
\(480\) 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 \(0.384355\pi\)
−0.987181 + 0.159603i \(0.948978\pi\)
\(492\) 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 \(-0.114187\pi\)
0.936344 + 0.351085i \(0.114187\pi\)
\(504\) 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 \(-0.514113\pi\)
−0.0443242 + 0.999017i \(0.514113\pi\)
\(510\) 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 −0.704137 0.710064i \(-0.748666\pi\)
0.967002 + 0.254769i \(0.0819994\pi\)
\(522\) 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 −0.886433 0.462856i \(-0.846825\pi\)
0.844062 + 0.536246i \(0.180158\pi\)
\(558\) 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 \(-0.982100\pi\)
0.450535 0.892759i \(-0.351233\pi\)
\(564\) 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 \(0.350133\pi\)
−0.998608 + 0.0527519i \(0.983201\pi\)
\(570\) 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 0.982550 0.185999i \(-0.0595520\pi\)
−0.652355 + 0.757914i \(0.726219\pi\)
\(588\) 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 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 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 0.962175 0.272433i \(-0.0878284\pi\)
−0.717021 + 0.697051i \(0.754495\pi\)
\(600\) 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 −0.920074 0.391745i \(-0.871871\pi\)
0.799298 + 0.600935i \(0.205205\pi\)
\(618\) 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 −0.845699 0.533660i \(-0.820816\pi\)
0.885013 + 0.465566i \(0.154149\pi\)
\(648\) 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 \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 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 \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 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 −0.727386 0.686229i \(-0.759265\pi\)
0.957984 + 0.286820i \(0.0925982\pi\)
\(678\) 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 −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 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 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) 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 \(-0.553382\pi\)
0.937336 0.348428i \(-0.113284\pi\)
\(744\) 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 \(-0.164119\pi\)
0.869999 + 0.493053i \(0.164119\pi\)
\(762\) 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 \(0.376079\pi\)
−0.990997 + 0.133887i \(0.957254\pi\)
\(774\) 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
\(794\) 18.0000