Properties

Label 567.2.h.f.352.1
Level $567$
Weight $2$
Character 567.352
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.h (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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 352.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 567.352
Dual form 567.2.h.f.298.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +2.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})\) \(q+2.00000 q^{2} +2.00000 q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(2.00000 + 3.46410i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(4.00000 + 3.46410i) q^{14} -4.00000 q^{16} +(-0.500000 + 0.866025i) q^{19} +(2.00000 + 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(4.00000 + 3.46410i) q^{28} +(-2.00000 - 3.46410i) q^{29} +9.00000 q^{31} -8.00000 q^{32} +(-1.00000 + 5.19615i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(5.00000 - 8.66025i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(2.00000 - 3.46410i) q^{44} -6.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(1.00000 - 1.73205i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(-6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-4.00000 - 6.92820i) q^{58} -12.0000 q^{59} +10.0000 q^{61} +18.0000 q^{62} -8.00000 q^{64} -2.00000 q^{65} -5.00000 q^{67} +(-2.00000 + 10.3923i) q^{70} -6.00000 q^{71} +(1.50000 + 2.59808i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(5.00000 - 1.73205i) q^{77} -1.00000 q^{79} +(-4.00000 - 6.92820i) q^{80} +(10.0000 - 17.3205i) q^{82} +(-3.00000 - 5.19615i) q^{83} +(-5.00000 - 8.66025i) q^{86} +(-8.00000 + 13.8564i) q^{89} +(-2.50000 + 0.866025i) q^{91} -12.0000 q^{94} -2.00000 q^{95} +(3.00000 + 5.19615i) q^{97} +(2.00000 + 13.8564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{2} + 4q^{4} + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 2q + 4q^{2} + 4q^{4} + 2q^{5} + 4q^{7} + 4q^{10} + 2q^{11} - q^{13} + 8q^{14} - 8q^{16} - q^{19} + 4q^{20} + 4q^{22} + q^{25} - 2q^{26} + 8q^{28} - 4q^{29} + 18q^{31} - 16q^{32} - 2q^{35} - 3q^{37} - 2q^{38} + 10q^{41} - 5q^{43} + 4q^{44} - 12q^{47} + 2q^{49} + 2q^{50} - 2q^{52} - 12q^{53} + 8q^{55} - 8q^{58} - 24q^{59} + 20q^{61} + 36q^{62} - 16q^{64} - 4q^{65} - 10q^{67} - 4q^{70} - 12q^{71} + 3q^{73} - 6q^{74} - 2q^{76} + 10q^{77} - 2q^{79} - 8q^{80} + 20q^{82} - 6q^{83} - 10q^{86} - 16q^{89} - 5q^{91} - 24q^{94} - 4q^{95} + 6q^{97} + 4q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) 0 0
\(4\) 2.00000 1.00000
\(5\) 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 2.00000 + 3.46410i 0.632456 + 1.09545i
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 4.00000 + 3.46410i 1.06904 + 0.925820i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 2.00000 + 3.46410i 0.447214 + 0.774597i
\(21\) 0 0
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −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
\(31\) 9.00000 1.61645 0.808224 0.588875i \(-0.200429\pi\)
0.808224 + 0.588875i \(0.200429\pi\)
\(32\) −8.00000 −1.41421
\(33\) 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 −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −1.00000 + 1.73205i −0.162221 + 0.280976i
\(39\) 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
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 1.00000 1.73205i 0.141421 0.244949i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i \(-0.858312\pi\)
0.0783936 0.996922i \(-0.475021\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) −4.00000 6.92820i −0.525226 0.909718i
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 18.0000 2.28600
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) −5.00000 −0.610847 −0.305424 0.952217i \(-0.598798\pi\)
−0.305424 + 0.952217i \(0.598798\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −2.00000 + 10.3923i −0.239046 + 1.24212i
\(71\) −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 0.940356 0.340193i \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) −3.00000 + 5.19615i −0.348743 + 0.604040i
\(75\) 0 0
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) 5.00000 1.73205i 0.569803 0.197386i
\(78\) 0 0
\(79\) −1.00000 −0.112509 −0.0562544 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) −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
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 0 0
\(88\) 0 0
\(89\) −8.00000 + 13.8564i −0.847998 + 1.46878i 0.0349934 + 0.999388i \(0.488859\pi\)
−0.882992 + 0.469389i \(0.844474\pi\)
\(90\) 0 0
\(91\) −2.50000 + 0.866025i −0.262071 + 0.0907841i
\(92\) 0 0
\(93\) 0 0
\(94\) −12.0000 −1.23771
\(95\) −2.00000 −0.205196
\(96\) 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
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 0 0
\(103\) 3.50000 + 6.06218i 0.344865 + 0.597324i 0.985329 0.170664i \(-0.0545913\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 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 \(-0.706950\pi\)
0.992003 + 0.126217i \(0.0402834\pi\)
\(108\) 0 0
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) 8.00000 0.762770
\(111\) 0 0
\(112\) −8.00000 6.92820i −0.755929 0.654654i
\(113\) −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
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 20.0000 1.81071
\(123\) 0 0
\(124\) 18.0000 1.61645
\(125\) 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
\(130\) −4.00000 −0.350823
\(131\) 7.00000 + 12.1244i 0.611593 + 1.05931i 0.990972 + 0.134069i \(0.0428042\pi\)
−0.379379 + 0.925241i \(0.623862\pi\)
\(132\) 0 0
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) 1.50000 2.59808i 0.127228 0.220366i −0.795373 0.606120i \(-0.792725\pi\)
0.922602 + 0.385754i \(0.126059\pi\)
\(140\) −2.00000 + 10.3923i −0.169031 + 0.878310i
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) 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
\(149\) 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 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
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) −2.00000 −0.159111
\(159\) 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 −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 10.0000 17.3205i 0.780869 1.35250i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 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
\(173\) 8.00000 0.608229 0.304114 0.952636i \(-0.401639\pi\)
0.304114 + 0.952636i \(0.401639\pi\)
\(174\) 0 0
\(175\) 2.50000 0.866025i 0.188982 0.0654654i
\(176\) −4.00000 + 6.92820i −0.301511 + 0.522233i
\(177\) 0 0
\(178\) −16.0000 + 27.7128i −1.19925 + 2.07716i
\(179\) −1.00000 1.73205i −0.0747435 0.129460i 0.826231 0.563331i \(-0.190480\pi\)
−0.900975 + 0.433872i \(0.857147\pi\)
\(180\) 0 0
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) −5.00000 + 1.73205i −0.370625 + 0.128388i
\(183\) 0 0
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) 10.0000 0.723575 0.361787 0.932261i \(-0.382167\pi\)
0.361787 + 0.932261i \(0.382167\pi\)
\(192\) 0 0
\(193\) 11.0000 0.791797 0.395899 0.918294i \(-0.370433\pi\)
0.395899 + 0.918294i \(0.370433\pi\)
\(194\) 6.00000 + 10.3923i 0.430775 + 0.746124i
\(195\) 0 0
\(196\) 2.00000 + 13.8564i 0.142857 + 0.989743i
\(197\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −2.00000 + 3.46410i −0.140720 + 0.243733i
\(203\) 2.00000 10.3923i 0.140372 0.729397i
\(204\) 0 0
\(205\) 20.0000 1.39686
\(206\) 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 \(0.210633\pi\)
\(212\) −12.0000 20.7846i −0.824163 1.42749i
\(213\) 0 0
\(214\) 8.00000 13.8564i 0.546869 0.947204i
\(215\) 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
\(220\) 8.00000 0.539360
\(221\) 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
\(227\) −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i \(0.370447\pi\)
−0.993210 + 0.116331i \(0.962887\pi\)
\(228\) 0 0
\(229\) 9.50000 + 16.4545i 0.627778 + 1.08734i 0.987997 + 0.154475i \(0.0493686\pi\)
−0.360219 + 0.932868i \(0.617298\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) −6.00000 10.3923i −0.391397 0.677919i
\(236\) −24.0000 −1.56227
\(237\) 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
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 7.00000 + 12.1244i 0.449977 + 0.779383i
\(243\) 0 0
\(244\) 20.0000 1.28037
\(245\) −11.0000 + 8.66025i −0.702764 + 0.553283i
\(246\) 0 0
\(247\) −0.500000 0.866025i −0.0318142 0.0551039i
\(248\) 0 0
\(249\) 0 0
\(250\) 24.0000 1.51789
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −30.0000 −1.88237
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −13.0000 22.5167i −0.810918 1.40455i −0.912222 0.409695i \(-0.865635\pi\)
0.101305 0.994855i \(-0.467698\pi\)
\(258\) 0 0
\(259\) −7.50000 + 2.59808i −0.466027 + 0.161437i
\(260\) −4.00000 −0.248069
\(261\) 0 0
\(262\) 14.0000 + 24.2487i 0.864923 + 1.49809i
\(263\) −2.00000 + 3.46410i −0.123325 + 0.213606i −0.921077 0.389380i \(-0.872689\pi\)
0.797752 + 0.602986i \(0.206023\pi\)
\(264\) 0 0
\(265\) 12.0000 20.7846i 0.737154 1.27679i
\(266\) −5.00000 + 1.73205i −0.306570 + 0.106199i
\(267\) 0 0
\(268\) −10.0000 −0.610847
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 12.0000 20.7846i 0.724947 1.25564i
\(275\) −1.00000 1.73205i −0.0603023 0.104447i
\(276\) 0 0
\(277\) −6.50000 + 11.2583i −0.390547 + 0.676448i −0.992522 0.122068i \(-0.961047\pi\)
0.601975 + 0.798515i \(0.294381\pi\)
\(278\) 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
\(283\) −11.0000 −0.653882 −0.326941 0.945045i \(-0.606018\pi\)
−0.326941 + 0.945045i \(0.606018\pi\)
\(284\) −12.0000 −0.712069
\(285\) 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
\(290\) 8.00000 13.8564i 0.469776 0.813676i
\(291\) 0 0
\(292\) 3.00000 + 5.19615i 0.175562 + 0.304082i
\(293\) −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
\(301\) 2.50000 12.9904i 0.144098 0.748753i
\(302\) 16.0000 27.7128i 0.920697 1.59469i
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 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 \(0.661224\pi\)
\(308\) 10.0000 3.46410i 0.569803 0.197386i
\(309\) 0 0
\(310\) 18.0000 + 31.1769i 1.02233 + 1.77073i
\(311\) −6.00000 −0.340229 −0.170114 0.985424i \(-0.554414\pi\)
−0.170114 + 0.985424i \(0.554414\pi\)
\(312\) 0 0
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) −28.0000 −1.58013
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) 24.0000 1.34797 0.673987 0.738743i \(-0.264580\pi\)
0.673987 + 0.738743i \(0.264580\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) −8.00000 13.8564i −0.447214 0.774597i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.500000 + 0.866025i 0.0277350 + 0.0480384i
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) 0 0
\(328\) 0 0
\(329\) −12.0000 10.3923i −0.661581 0.572946i
\(330\) 0 0
\(331\) −25.0000 −1.37412 −0.687062 0.726599i \(-0.741100\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(332\) −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 \(0.281872\pi\)
\(338\) 12.0000 + 20.7846i 0.652714 + 1.13053i
\(339\) 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
\(346\) 16.0000 0.860165
\(347\) 32.0000 1.71785 0.858925 0.512101i \(-0.171133\pi\)
0.858925 + 0.512101i \(0.171133\pi\)
\(348\) 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
\(353\) −17.0000 + 29.4449i −0.904819 + 1.56719i −0.0836583 + 0.996495i \(0.526660\pi\)
−0.821160 + 0.570697i \(0.806673\pi\)
\(354\) 0 0
\(355\) −6.00000 10.3923i −0.318447 0.551566i
\(356\) −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 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 26.0000 1.36653
\(363\) 0 0
\(364\) −5.00000 + 1.73205i −0.262071 + 0.0907841i
\(365\) −3.00000 + 5.19615i −0.157027 + 0.271979i
\(366\) 0 0
\(367\) 4.50000 7.79423i 0.234898 0.406855i −0.724345 0.689438i \(-0.757858\pi\)
0.959243 + 0.282582i \(0.0911910\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −12.0000 −0.623850
\(371\) 6.00000 31.1769i 0.311504 1.61862i
\(372\) 0 0
\(373\) −11.5000 19.9186i −0.595447 1.03135i −0.993484 0.113975i \(-0.963641\pi\)
0.398036 0.917370i \(-0.369692\pi\)
\(374\) 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 \(0.475450\pi\)
\(380\) −4.00000 −0.205196
\(381\) 0 0
\(382\) 20.0000 1.02329
\(383\) 6.00000 + 10.3923i 0.306586 + 0.531022i 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 0 0
\(385\) 8.00000 + 6.92820i 0.407718 + 0.353094i
\(386\) 22.0000 1.11977
\(387\) 0 0
\(388\) 6.00000 + 10.3923i 0.304604 + 0.527589i
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 32.0000 1.61214
\(395\) −1.00000 1.73205i −0.0503155 0.0871489i
\(396\) 0 0
\(397\) 4.50000 7.79423i 0.225849 0.391181i −0.730725 0.682672i \(-0.760818\pi\)
0.956574 + 0.291491i \(0.0941512\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 18.0000 + 31.1769i 0.898877 + 1.55690i 0.828932 + 0.559350i \(0.188949\pi\)
0.0699455 + 0.997551i \(0.477717\pi\)
\(402\) 0 0
\(403\) −4.50000 + 7.79423i −0.224161 + 0.388258i
\(404\) −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
\(409\) 5.00000 0.247234 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) 40.0000 1.97546
\(411\) 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
\(416\) 4.00000 6.92820i 0.196116 0.339683i
\(417\) 0 0
\(418\) 2.00000 + 3.46410i 0.0978232 + 0.169435i
\(419\) −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
\(427\) 20.0000 + 17.3205i 0.967868 + 0.838198i
\(428\) 8.00000 13.8564i 0.386695 0.669775i
\(429\) 0 0
\(430\) 10.0000 17.3205i 0.482243 0.835269i
\(431\) 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) 0 0
\(433\) 31.0000 1.48976 0.744882 0.667196i \(-0.232506\pi\)
0.744882 + 0.667196i \(0.232506\pi\)
\(434\) 36.0000 + 31.1769i 1.72806 + 1.49654i
\(435\) 0 0
\(436\) −9.00000 15.5885i −0.431022 0.746552i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) −32.0000 −1.51695
\(446\) −16.0000 27.7128i −0.757622 1.31224i
\(447\) 0 0
\(448\) −16.0000 13.8564i −0.755929 0.654654i
\(449\) −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
\(452\) −10.0000 + 17.3205i −0.470360 + 0.814688i
\(453\) 0 0
\(454\) −18.0000 + 31.1769i −0.844782 + 1.46321i
\(455\) −4.00000 3.46410i −0.187523 0.162400i
\(456\) 0 0
\(457\) −11.0000 −0.514558 −0.257279 0.966337i \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(458\) 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 \(0.0374014\pi\)
\(464\) 8.00000 + 13.8564i 0.371391 + 0.643268i
\(465\) 0 0
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) −3.00000 + 5.19615i −0.138823 + 0.240449i −0.927052 0.374934i \(-0.877665\pi\)
0.788228 + 0.615383i \(0.210999\pi\)
\(468\) 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
\(473\) −10.0000 −0.459800
\(474\) 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
\(479\) 14.0000 24.2487i 0.639676 1.10795i −0.345827 0.938298i \(-0.612402\pi\)
0.985504 0.169654i \(-0.0542649\pi\)
\(480\) 0 0
\(481\) −1.50000 2.59808i −0.0683941 0.118462i
\(482\) −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 −0.967632 0.252367i \(-0.918791\pi\)
0.265260 0.964177i \(-0.414542\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −22.0000 + 17.3205i −0.993859 + 0.782461i
\(491\) 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
\(497\) −12.0000 10.3923i −0.538274 0.466159i
\(498\) 0 0
\(499\) −18.5000 32.0429i −0.828174 1.43444i −0.899469 0.436984i \(-0.856047\pi\)
0.0712957 0.997455i \(-0.477287\pi\)
\(500\) 24.0000 1.07331
\(501\) 0 0
\(502\) −16.0000 −0.714115
\(503\) −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
\(508\) −30.0000 −1.33103
\(509\) −1.00000 1.73205i −0.0443242 0.0767718i 0.843012 0.537895i \(-0.180780\pi\)
−0.887336 + 0.461123i \(0.847447\pi\)
\(510\) 0 0
\(511\) −1.50000 + 7.79423i −0.0663561 + 0.344796i
\(512\) 32.0000 1.41421
\(513\) 0 0
\(514\) −26.0000 45.0333i −1.14681 1.98633i
\(515\) −7.00000 + 12.1244i −0.308457 + 0.534263i
\(516\) 0 0
\(517\) −6.00000 + 10.3923i −0.263880 + 0.457053i
\(518\) −15.0000 + 5.19615i −0.659062 + 0.228306i
\(519\) 0 0
\(520\) 0 0
\(521\) −6.00000 10.3923i −0.262865 0.455295i 0.704137 0.710064i \(-0.251334\pi\)
−0.967002 + 0.254769i \(0.918001\pi\)
\(522\) 0 0
\(523\) −15.5000 + 26.8468i −0.677768 + 1.17393i 0.297884 + 0.954602i \(0.403719\pi\)
−0.975652 + 0.219326i \(0.929614\pi\)
\(524\) 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
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 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
\(535\) 16.0000 0.691740
\(536\) 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 −0.586278 0.810110i \(-0.699407\pi\)
0.994715 + 0.102677i \(0.0327407\pi\)
\(542\) −16.0000 + 27.7128i −0.687259 + 1.19037i
\(543\) 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
\(551\) 4.00000 0.170406
\(552\) 0 0
\(553\) −2.00000 1.73205i −0.0850487 0.0736543i
\(554\) −13.0000 + 22.5167i −0.552317 + 0.956641i
\(555\) 0 0
\(556\) 3.00000 5.19615i 0.127228 0.220366i
\(557\) 1.00000 + 1.73205i 0.0423714 + 0.0733893i 0.886433 0.462856i \(-0.153175\pi\)
−0.844062 + 0.536246i \(0.819842\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) 4.00000 20.7846i 0.169031 0.878310i
\(561\) 0 0
\(562\) 4.00000 + 6.92820i 0.168730 + 0.292249i
\(563\) −26.0000 −1.09577 −0.547885 0.836554i \(-0.684567\pi\)
−0.547885 + 0.836554i \(0.684567\pi\)
\(564\) 0 0
\(565\) −20.0000 −0.841406
\(566\) −22.0000 −0.924729
\(567\) 0 0
\(568\) 0 0
\(569\) −26.0000 −1.08998 −0.544988 0.838444i \(-0.683466\pi\)
−0.544988 + 0.838444i \(0.683466\pi\)
\(570\) 0 0
\(571\) −19.0000 −0.795125 −0.397563 0.917575i \(-0.630144\pi\)
−0.397563 + 0.917575i \(0.630144\pi\)
\(572\) 2.00000 + 3.46410i 0.0836242 + 0.144841i
\(573\) 0 0
\(574\) 50.0000 17.3205i 2.08696 0.722944i
\(575\) 0 0
\(576\) 0 0
\(577\) 8.50000 + 14.7224i 0.353860 + 0.612903i 0.986922 0.161198i \(-0.0515357\pi\)
−0.633062 + 0.774101i \(0.718202\pi\)
\(578\) 17.0000 29.4449i 0.707107 1.22474i
\(579\) 0 0
\(580\) 8.00000 13.8564i 0.332182 0.575356i
\(581\) 3.00000 15.5885i 0.124461 0.646718i
\(582\) 0 0
\(583\) −24.0000 −0.993978
\(584\) 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
\(590\) −24.0000 41.5692i −0.988064 1.71138i
\(591\) 0 0
\(592\) 6.00000 10.3923i 0.246598 0.427121i
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 + 20.7846i 0.491539 + 0.851371i
\(597\) 0 0
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 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
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 0 0
\(607\) −11.5000 19.9186i −0.466771 0.808470i 0.532509 0.846424i \(-0.321249\pi\)
−0.999279 + 0.0379540i \(0.987916\pi\)
\(608\) 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 −0.972924 0.231127i \(-0.925759\pi\)
0.286300 0.958140i \(-0.407575\pi\)
\(614\) −34.0000 −1.37213
\(615\) 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
\(619\) 14.5000 25.1147i 0.582804 1.00945i −0.412341 0.911030i \(-0.635289\pi\)
0.995145 0.0984169i \(-0.0313779\pi\)
\(620\) 18.0000 + 31.1769i 0.722897 + 1.25210i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) −40.0000 + 13.8564i −1.60257 + 0.555145i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) −2.00000 −0.0799361
\(627\) 0 0
\(628\) −28.0000 −1.11732
\(629\) 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
\(634\) 48.0000 1.90632
\(635\) −15.0000 25.9808i −0.595257 1.03102i
\(636\) 0 0
\(637\) −6.50000 2.59808i −0.257539 0.102940i
\(638\) −16.0000 −0.633446
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 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 \(-0.179184\pi\)
−0.885013 + 0.465566i \(0.845851\pi\)
\(648\) 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
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 0 0
\(655\) −14.0000 + 24.2487i −0.547025 + 0.947476i
\(656\) −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
\(661\) −41.0000 −1.59472 −0.797358 0.603507i \(-0.793769\pi\)
−0.797358 + 0.603507i \(0.793769\pi\)
\(662\) −50.0000 −1.94331
\(663\) 0 0
\(664\) 0 0
\(665\) −4.00000 3.46410i −0.155113 0.134332i
\(666\) 0 0
\(667\) 0 0
\(668\) 14.0000 24.2487i 0.541676 0.938211i
\(669\) 0 0
\(670\) −10.0000 17.3205i −0.386334 0.669150i
\(671\) 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
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) 0 0
\(679\) −3.00000 + 15.5885i −0.115129 + 0.598230i
\(680\) 0 0
\(681\) 0 0
\(682\) 18.0000 31.1769i 0.689256 1.19383i
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 0 0
\(685\) 24.0000 0.916993
\(686\) −20.0000 + 31.1769i −0.763604 + 1.19034i
\(687\) 0 0
\(688\) 10.0000 + 17.3205i 0.381246 + 0.660338i
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) −37.0000 −1.40755 −0.703773 0.710425i \(-0.748503\pi\)
−0.703773 + 0.710425i \(0.748503\pi\)
\(692\) 16.0000 0.608229
\(693\) 0 0
\(694\) 64.0000 2.42941
\(695\) 6.00000 0.227593
\(696\) 0 0
\(697\) 0 0
\(698\) 14.0000 + 24.2487i 0.529908 + 0.917827i
\(699\) 0 0
\(700\) 5.00000 1.73205i 0.188982 0.0654654i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −1.50000 2.59808i −0.0565736 0.0979883i
\(704\) −8.00000 + 13.8564i −0.301511 + 0.522233i
\(705\) 0 0
\(706\) −34.0000 + 58.8897i −1.27961 + 2.21634i
\(707\) −5.00000 + 1.73205i −0.188044 + 0.0651405i
\(708\) 0 0
\(709\) 30.0000 1.12667 0.563337 0.826227i \(-0.309517\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(710\) −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
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) 0 0
\(718\) −20.0000 + 34.6410i −0.746393 + 1.29279i
\(719\) 9.00000 15.5885i 0.335643 0.581351i −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 0 0
\(721\) −3.50000 + 18.1865i −0.130347 + 0.677302i
\(722\) 18.0000 + 31.1769i 0.669891 + 1.16028i
\(723\) 0 0
\(724\) 26.0000 0.966282
\(725\) −4.00000 −0.148556
\(726\) 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
\(733\) 7.50000 + 12.9904i 0.277019 + 0.479811i 0.970642 0.240527i \(-0.0773202\pi\)
−0.693624 + 0.720338i \(0.743987\pi\)
\(734\) 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 0.970360 0.241665i \(-0.0776935\pi\)
−0.694468 + 0.719524i \(0.744360\pi\)
\(740\) −12.0000 −0.441129
\(741\) 0 0
\(742\) 12.0000 62.3538i 0.440534 2.28908i
\(743\) −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
\(745\) −12.0000 + 20.7846i −0.439646 + 0.761489i
\(746\) −23.0000 39.8372i −0.842090 1.45854i
\(747\) 0 0
\(748\) 0 0
\(749\) 20.0000 6.92820i 0.730784 0.253151i
\(750\) 0 0
\(751\) −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i \(-0.242893\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(752\) 24.0000 0.875190
\(753\) 0 0
\(754\) 8.00000 0.291343
\(755\) 32.0000 1.16460
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 6.00000 0.217930
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 + 41.5692i 0.869999 + 1.50688i 0.861996 + 0.506915i \(0.169214\pi\)
0.00800331 + 0.999968i \(0.497452\pi\)
\(762\) 0 0
\(763\) 4.50000 23.3827i 0.162911 0.846510i
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) 12.0000 + 20.7846i 0.433578 + 0.750978i
\(767\) 6.00000 10.3923i 0.216647 0.375244i
\(768\) 0 0
\(769\) 24.5000 42.4352i 0.883493 1.53025i 0.0360609 0.999350i \(-0.488519\pi\)
0.847432 0.530904i \(-0.178148\pi\)
\(770\) 16.0000 + 13.8564i 0.576600 + 0.499350i
\(771\) 0 0
\(772\) 22.0000 0.791797
\(773\) 17.0000 + 29.4449i 0.611448 + 1.05906i 0.990997 + 0.133887i \(0.0427458\pi\)
−0.379549 + 0.925172i \(0.623921\pi\)
\(774\) 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
\(779\) 5.00000 + 8.66025i 0.179144 + 0.310286i
\(780\) 0 0
\(781\) −6.00000 + 10.3923i −0.214697 + 0.371866i
\(782\) 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
\(787\) 40.0000 1.42585 0.712923 0.701242i \(-0.247371\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) 32.0000 1.13995
\(789\) 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