Properties

Label 567.2.f.g.379.1
Level $567$
Weight $2$
Character 567.379
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.f (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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 379.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 567.379
Dual form 567.2.f.g.190.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +2.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{16} -6.00000 q^{17} +4.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(2.00000 + 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{25} +2.00000 q^{26} +1.00000 q^{28} +(1.00000 - 1.73205i) q^{29} +(2.50000 + 4.33013i) q^{32} +(-3.00000 + 5.19615i) q^{34} +2.00000 q^{35} +6.00000 q^{37} +(2.00000 - 3.46410i) q^{38} +(3.00000 + 5.19615i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(2.00000 - 3.46410i) q^{43} -4.00000 q^{44} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} +6.00000 q^{53} -8.00000 q^{55} +(1.50000 - 2.59808i) q^{56} +(-1.00000 - 1.73205i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +7.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(1.00000 - 1.73205i) q^{70} -6.00000 q^{73} +(3.00000 - 5.19615i) q^{74} +(2.00000 + 3.46410i) q^{76} +(2.00000 + 3.46410i) q^{77} +(8.00000 - 13.8564i) q^{79} +2.00000 q^{80} -2.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-6.00000 + 10.3923i) q^{88} -14.0000 q^{89} +2.00000 q^{91} +(4.00000 + 6.92820i) q^{95} +(-9.00000 + 15.5885i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{4} + 2q^{5} + q^{7} + 6q^{8} + O(q^{10}) \) \( 2q + q^{2} + q^{4} + 2q^{5} + q^{7} + 6q^{8} + 4q^{10} - 4q^{11} + 2q^{13} - q^{14} + q^{16} - 12q^{17} + 8q^{19} - 2q^{20} + 4q^{22} + q^{25} + 4q^{26} + 2q^{28} + 2q^{29} + 5q^{32} - 6q^{34} + 4q^{35} + 12q^{37} + 4q^{38} + 6q^{40} - 2q^{41} + 4q^{43} - 8q^{44} - q^{49} - q^{50} - 2q^{52} + 12q^{53} - 16q^{55} + 3q^{56} - 2q^{58} - 12q^{59} + 2q^{61} + 14q^{64} - 4q^{65} - 4q^{67} - 6q^{68} + 2q^{70} - 12q^{73} + 6q^{74} + 4q^{76} + 4q^{77} + 16q^{79} + 4q^{80} - 4q^{82} + 12q^{83} - 12q^{85} - 4q^{86} - 12q^{88} - 28q^{89} + 4q^{91} + 8q^{95} - 18q^{97} - 2q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i −0.633316 0.773893i \(-0.718307\pi\)
0.986869 + 0.161521i \(0.0516399\pi\)
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 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
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) 2.00000 0.632456
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) −1.00000 + 1.73205i −0.223607 + 0.387298i
\(21\) 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
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 1.00000 1.73205i 0.185695 0.321634i −0.758115 0.652121i \(-0.773880\pi\)
0.943811 + 0.330487i \(0.107213\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 2.50000 + 4.33013i 0.441942 + 0.765466i
\(33\) 0 0
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) 0 0
\(40\) 3.00000 + 5.19615i 0.474342 + 0.821584i
\(41\) −1.00000 1.73205i −0.156174 0.270501i 0.777312 0.629115i \(-0.216583\pi\)
−0.933486 + 0.358614i \(0.883249\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −8.00000 −1.07872
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) 0 0
\(58\) −1.00000 1.73205i −0.131306 0.227429i
\(59\) −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
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) 0 0
\(67\) −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i \(-0.245238\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 0 0
\(70\) 1.00000 1.73205i 0.119523 0.207020i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 3.00000 5.19615i 0.348743 0.604040i
\(75\) 0 0
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) 2.00000 + 3.46410i 0.227921 + 0.394771i
\(78\) 0 0
\(79\) 8.00000 13.8564i 0.900070 1.55897i 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) 2.00000 0.223607
\(81\) 0 0
\(82\) −2.00000 −0.220863
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) −6.00000 10.3923i −0.650791 1.12720i
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) −6.00000 + 10.3923i −0.639602 + 1.10782i
\(89\) −14.0000 −1.48400 −0.741999 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 0 0
\(97\) −9.00000 + 15.5885i −0.913812 + 1.58277i −0.105180 + 0.994453i \(0.533542\pi\)
−0.808632 + 0.588315i \(0.799792\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −7.00000 + 12.1244i −0.696526 + 1.20642i 0.273138 + 0.961975i \(0.411939\pi\)
−0.969664 + 0.244443i \(0.921395\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) 3.00000 + 5.19615i 0.294174 + 0.509525i
\(105\) 0 0
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) −4.00000 + 6.92820i −0.381385 + 0.660578i
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) 7.00000 + 12.1244i 0.658505 + 1.14056i 0.981003 + 0.193993i \(0.0621440\pi\)
−0.322498 + 0.946570i \(0.604523\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2.00000 0.185695
\(117\) 0 0
\(118\) −12.0000 −1.10469
\(119\) −3.00000 + 5.19615i −0.275010 + 0.476331i
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) −1.00000 1.73205i −0.0905357 0.156813i
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −1.50000 + 2.59808i −0.132583 + 0.229640i
\(129\) 0 0
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i \(-0.222575\pi\)
−0.940072 + 0.340977i \(0.889242\pi\)
\(132\) 0 0
\(133\) 2.00000 3.46410i 0.173422 0.300376i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −18.0000 −1.54349
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) −6.00000 10.3923i −0.508913 0.881464i −0.999947 0.0103230i \(-0.996714\pi\)
0.491033 0.871141i \(-0.336619\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) 0 0
\(142\) 0 0
\(143\) −8.00000 −0.668994
\(144\) 0 0
\(145\) 4.00000 0.332182
\(146\) −3.00000 + 5.19615i −0.248282 + 0.430037i
\(147\) 0 0
\(148\) 3.00000 + 5.19615i 0.246598 + 0.427121i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) 12.0000 0.973329
\(153\) 0 0
\(154\) 4.00000 0.322329
\(155\) 0 0
\(156\) 0 0
\(157\) 1.00000 + 1.73205i 0.0798087 + 0.138233i 0.903167 0.429289i \(-0.141236\pi\)
−0.823359 + 0.567521i \(0.807902\pi\)
\(158\) −8.00000 13.8564i −0.636446 1.10236i
\(159\) 0 0
\(160\) −5.00000 + 8.66025i −0.395285 + 0.684653i
\(161\) 0 0
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 1.00000 1.73205i 0.0780869 0.135250i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 4.00000 + 6.92820i 0.309529 + 0.536120i 0.978259 0.207385i \(-0.0664952\pi\)
−0.668730 + 0.743505i \(0.733162\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) −12.0000 −0.920358
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) 5.00000 8.66025i 0.380143 0.658427i −0.610939 0.791677i \(-0.709208\pi\)
0.991082 + 0.133250i \(0.0425415\pi\)
\(174\) 0 0
\(175\) −0.500000 0.866025i −0.0377964 0.0654654i
\(176\) 2.00000 + 3.46410i 0.150756 + 0.261116i
\(177\) 0 0
\(178\) −7.00000 + 12.1244i −0.524672 + 0.908759i
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 0 0
\(181\) −26.0000 −1.93256 −0.966282 0.257485i \(-0.917106\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 1.00000 1.73205i 0.0741249 0.128388i
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 + 10.3923i 0.441129 + 0.764057i
\(186\) 0 0
\(187\) 12.0000 20.7846i 0.877527 1.51992i
\(188\) 0 0
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 4.00000 6.92820i 0.289430 0.501307i −0.684244 0.729253i \(-0.739868\pi\)
0.973674 + 0.227946i \(0.0732010\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 9.00000 + 15.5885i 0.646162 + 1.11919i
\(195\) 0 0
\(196\) 0.500000 0.866025i 0.0357143 0.0618590i
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 1.50000 2.59808i 0.106066 0.183712i
\(201\) 0 0
\(202\) 7.00000 + 12.1244i 0.492518 + 0.853067i
\(203\) −1.00000 1.73205i −0.0701862 0.121566i
\(204\) 0 0
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) −8.00000 + 13.8564i −0.553372 + 0.958468i
\(210\) 0 0
\(211\) −2.00000 3.46410i −0.137686 0.238479i 0.788935 0.614477i \(-0.210633\pi\)
−0.926620 + 0.375999i \(0.877300\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) 8.00000 0.545595
\(216\) 0 0
\(217\) 0 0
\(218\) −9.00000 + 15.5885i −0.609557 + 1.05578i
\(219\) 0 0
\(220\) −4.00000 6.92820i −0.269680 0.467099i
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) 0 0
\(223\) −8.00000 + 13.8564i −0.535720 + 0.927894i 0.463409 + 0.886145i \(0.346626\pi\)
−0.999128 + 0.0417488i \(0.986707\pi\)
\(224\) 5.00000 0.334077
\(225\) 0 0
\(226\) 14.0000 0.931266
\(227\) 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) 0 0
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) 0 0
\(238\) 3.00000 + 5.19615i 0.194461 + 0.336817i
\(239\) −12.0000 20.7846i −0.776215 1.34444i −0.934109 0.356988i \(-0.883804\pi\)
0.157893 0.987456i \(-0.449530\pi\)
\(240\) 0 0
\(241\) −1.00000 + 1.73205i −0.0644157 + 0.111571i −0.896435 0.443176i \(-0.853852\pi\)
0.832019 + 0.554747i \(0.187185\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 1.00000 1.73205i 0.0638877 0.110657i
\(246\) 0 0
\(247\) 4.00000 + 6.92820i 0.254514 + 0.440831i
\(248\) 0 0
\(249\) 0 0
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −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
\(259\) 3.00000 5.19615i 0.186411 0.322873i
\(260\) −4.00000 −0.248069
\(261\) 0 0
\(262\) −4.00000 −0.247121
\(263\) −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) 0 0
\(265\) 6.00000 + 10.3923i 0.368577 + 0.638394i
\(266\) −2.00000 3.46410i −0.122628 0.212398i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) −3.00000 + 5.19615i −0.181902 + 0.315063i
\(273\) 0 0
\(274\) −3.00000 5.19615i −0.181237 0.313911i
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) 0 0
\(277\) −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i \(0.396503\pi\)
−0.980373 + 0.197153i \(0.936830\pi\)
\(278\) −12.0000 −0.719712
\(279\) 0 0
\(280\) 6.00000 0.358569
\(281\) 11.0000 19.0526i 0.656205 1.13658i −0.325385 0.945582i \(-0.605494\pi\)
0.981590 0.190999i \(-0.0611727\pi\)
\(282\) 0 0
\(283\) 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i \(0.0359589\pi\)
−0.399188 + 0.916869i \(0.630708\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −4.00000 + 6.92820i −0.236525 + 0.409673i
\(287\) −2.00000 −0.118056
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 2.00000 3.46410i 0.117444 0.203419i
\(291\) 0 0
\(292\) −3.00000 5.19615i −0.175562 0.304082i
\(293\) −7.00000 12.1244i −0.408944 0.708312i 0.585827 0.810436i \(-0.300770\pi\)
−0.994772 + 0.102123i \(0.967436\pi\)
\(294\) 0 0
\(295\) 12.0000 20.7846i 0.698667 1.21013i
\(296\) 18.0000 1.04623
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −2.00000 3.46410i −0.115278 0.199667i
\(302\) 4.00000 + 6.92820i 0.230174 + 0.398673i
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 4.00000 0.229039
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) −2.00000 + 3.46410i −0.113961 + 0.197386i
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 0 0
\(313\) −13.0000 + 22.5167i −0.734803 + 1.27272i 0.220006 + 0.975499i \(0.429392\pi\)
−0.954810 + 0.297218i \(0.903941\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 0 0
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 7.00000 + 12.1244i 0.391312 + 0.677772i
\(321\) 0 0
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) 0 0
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 12.0000 0.658586
\(333\) 0 0
\(334\) 8.00000 0.437741
\(335\) 4.00000 6.92820i 0.218543 0.378528i
\(336\) 0 0
\(337\) 7.00000 + 12.1244i 0.381314 + 0.660456i 0.991250 0.131995i \(-0.0421382\pi\)
−0.609936 + 0.792451i \(0.708805\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 0 0
\(340\) 6.00000 10.3923i 0.325396 0.563602i
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 6.00000 10.3923i 0.323498 0.560316i
\(345\) 0 0
\(346\) −5.00000 8.66025i −0.268802 0.465578i
\(347\) 14.0000 + 24.2487i 0.751559 + 1.30174i 0.947067 + 0.321037i \(0.104031\pi\)
−0.195507 + 0.980702i \(0.562635\pi\)
\(348\) 0 0
\(349\) 1.00000 1.73205i 0.0535288 0.0927146i −0.838019 0.545640i \(-0.816286\pi\)
0.891548 + 0.452926i \(0.149620\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 0 0
\(352\) −20.0000 −1.06600
\(353\) −5.00000 + 8.66025i −0.266123 + 0.460939i −0.967857 0.251500i \(-0.919076\pi\)
0.701734 + 0.712439i \(0.252409\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −7.00000 12.1244i −0.370999 0.642590i
\(357\) 0 0
\(358\) −2.00000 + 3.46410i −0.105703 + 0.183083i
\(359\) 32.0000 1.68890 0.844448 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −13.0000 + 22.5167i −0.683265 + 1.18345i
\(363\) 0 0
\(364\) 1.00000 + 1.73205i 0.0524142 + 0.0907841i
\(365\) −6.00000 10.3923i −0.314054 0.543958i
\(366\) 0 0
\(367\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 12.0000 0.623850
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) −12.0000 20.7846i −0.620505 1.07475i
\(375\) 0 0
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) −4.00000 + 6.92820i −0.205196 + 0.355409i
\(381\) 0 0
\(382\) −4.00000 6.92820i −0.204658 0.354478i
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 0 0
\(385\) −4.00000 + 6.92820i −0.203859 + 0.353094i
\(386\) −2.00000 −0.101797
\(387\) 0 0
\(388\) −18.0000 −0.913812
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.50000 2.59808i −0.0757614 0.131223i
\(393\) 0 0
\(394\) 11.0000 19.0526i 0.554172 0.959854i
\(395\) 32.0000 1.61009
\(396\) 0 0
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) 12.0000 20.7846i 0.601506 1.04184i
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i \(0.102830\pi\)
−0.199207 + 0.979957i \(0.563837\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −14.0000 −0.696526
\(405\) 0 0
\(406\) −2.00000 −0.0992583
\(407\) −12.0000 + 20.7846i −0.594818 + 1.03025i
\(408\) 0 0
\(409\) 11.0000 + 19.0526i 0.543915 + 0.942088i 0.998674 + 0.0514740i \(0.0163919\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(410\) −2.00000 3.46410i −0.0987730 0.171080i
\(411\) 0 0
\(412\) 4.00000 6.92820i 0.197066 0.341328i
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) −5.00000 + 8.66025i −0.245145 + 0.424604i
\(417\) 0 0
\(418\) 8.00000 + 13.8564i 0.391293 + 0.677739i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) −19.0000 + 32.9090i −0.926003 + 1.60388i −0.136064 + 0.990700i \(0.543445\pi\)
−0.789940 + 0.613185i \(0.789888\pi\)
\(422\) −4.00000 −0.194717
\(423\) 0 0
\(424\) 18.0000 0.874157
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 0 0
\(427\) −1.00000 1.73205i −0.0483934 0.0838198i
\(428\) 2.00000 + 3.46410i 0.0966736 + 0.167444i
\(429\) 0 0
\(430\) 4.00000 6.92820i 0.192897 0.334108i
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −9.00000 15.5885i −0.431022 0.746552i
\(437\) 0 0
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) −24.0000 −1.14416
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 0 0
\(445\) −14.0000 24.2487i −0.663664 1.14950i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) 0 0
\(448\) 3.50000 6.06218i 0.165359 0.286411i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) −7.00000 + 12.1244i −0.329252 + 0.570282i
\(453\) 0 0
\(454\) −6.00000 10.3923i −0.281594 0.487735i
\(455\) 2.00000 + 3.46410i 0.0937614 + 0.162400i
\(456\) 0 0
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 10.0000 0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) 5.00000 8.66025i 0.232873 0.403348i −0.725779 0.687928i \(-0.758521\pi\)
0.958652 + 0.284579i \(0.0918539\pi\)
\(462\) 0 0
\(463\) −8.00000 13.8564i −0.371792 0.643962i 0.618050 0.786139i \(-0.287923\pi\)
−0.989841 + 0.142177i \(0.954590\pi\)
\(464\) −1.00000 1.73205i −0.0464238 0.0804084i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 0 0
\(471\) 0 0
\(472\) −18.0000 31.1769i −0.828517 1.43503i
\(473\) 8.00000 + 13.8564i 0.367840 + 0.637118i
\(474\) 0 0
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) −6.00000 −0.275010
\(477\) 0 0
\(478\) −24.0000 −1.09773
\(479\) 8.00000 13.8564i 0.365529 0.633115i −0.623332 0.781958i \(-0.714221\pi\)
0.988861 + 0.148842i \(0.0475547\pi\)
\(480\) 0 0
\(481\) 6.00000 + 10.3923i 0.273576 + 0.473848i
\(482\) 1.00000 + 1.73205i 0.0455488 + 0.0788928i
\(483\) 0 0
\(484\) 2.50000 4.33013i 0.113636 0.196824i
\(485\) −36.0000 −1.63468
\(486\) 0 0
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) 3.00000 5.19615i 0.135804 0.235219i
\(489\) 0 0
\(490\) −1.00000 1.73205i −0.0451754 0.0782461i
\(491\) −10.0000 17.3205i −0.451294 0.781664i 0.547173 0.837020i \(-0.315704\pi\)
−0.998467 + 0.0553560i \(0.982371\pi\)
\(492\) 0 0
\(493\) −6.00000 + 10.3923i −0.270226 + 0.468046i
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i \(-0.195204\pi\)
−0.907314 + 0.420455i \(0.861871\pi\)
\(500\) 6.00000 + 10.3923i 0.268328 + 0.464758i
\(501\) 0 0
\(502\) −10.0000 + 17.3205i −0.446322 + 0.773052i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) −28.0000 −1.24598
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.00000 + 8.66025i 0.221621 + 0.383859i 0.955300 0.295637i \(-0.0955319\pi\)
−0.733679 + 0.679496i \(0.762199\pi\)
\(510\) 0 0
\(511\) −3.00000 + 5.19615i −0.132712 + 0.229864i
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) −26.0000 −1.14681
\(515\) 8.00000 13.8564i 0.352522 0.610586i
\(516\) 0 0
\(517\) 0 0
\(518\) −3.00000 5.19615i −0.131812 0.228306i
\(519\) 0 0
\(520\) −6.00000 + 10.3923i −0.263117 + 0.455733i
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 2.00000 3.46410i 0.0873704 0.151330i
\(525\) 0 0
\(526\) 8.00000 + 13.8564i 0.348817 + 0.604168i
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 12.0000 0.521247
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) 2.00000 3.46410i 0.0866296 0.150047i
\(534\) 0 0
\(535\) 4.00000 + 6.92820i 0.172935 + 0.299532i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 0 0
\(538\) 3.00000 5.19615i 0.129339 0.224022i
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) −15.0000 25.9808i −0.643120 1.11392i
\(545\) −18.0000 31.1769i −0.771035 1.33547i
\(546\) 0 0
\(547\) −2.00000 + 3.46410i −0.0855138 + 0.148114i −0.905610 0.424111i \(-0.860587\pi\)
0.820096 + 0.572226i \(0.193920\pi\)
\(548\) 6.00000 0.256307
\(549\) 0 0
\(550\) 4.00000 0.170561
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) −8.00000 13.8564i −0.340195 0.589234i
\(554\) 11.0000 + 19.0526i 0.467345 + 0.809466i
\(555\) 0 0
\(556\) 6.00000 10.3923i 0.254457 0.440732i
\(557\) −2.00000 −0.0847427 −0.0423714 0.999102i \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 1.00000 1.73205i 0.0422577 0.0731925i
\(561\) 0 0
\(562\) −11.0000 19.0526i −0.464007 0.803684i
\(563\) −2.00000 3.46410i −0.0842900 0.145994i 0.820798 0.571218i \(-0.193529\pi\)
−0.905088 + 0.425223i \(0.860196\pi\)
\(564\) 0 0
\(565\) −14.0000 + 24.2487i −0.588984 + 1.02015i
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) 0 0
\(569\) −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i \(-0.900553\pi\)
0.741981 + 0.670421i \(0.233886\pi\)
\(570\) 0 0
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) −4.00000 6.92820i −0.167248 0.289683i
\(573\) 0 0
\(574\) −1.00000 + 1.73205i −0.0417392 + 0.0722944i
\(575\) 0 0
\(576\) 0 0
\(577\) 34.0000 1.41544 0.707719 0.706494i \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) 0 0
\(580\) 2.00000 + 3.46410i 0.0830455 + 0.143839i
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) −12.0000 + 20.7846i −0.496989 + 0.860811i
\(584\) −18.0000 −0.744845
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) −14.0000 + 24.2487i −0.577842 + 1.00085i 0.417885 + 0.908500i \(0.362772\pi\)
−0.995726 + 0.0923513i \(0.970562\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −12.0000 20.7846i −0.494032 0.855689i
\(591\) 0 0
\(592\) 3.00000 5.19615i 0.123299 0.213561i
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) −24.0000 41.5692i −0.980613 1.69847i −0.660006 0.751260i \(-0.729446\pi\)
−0.320607 0.947212i \(-0.603887\pi\)
\(600\) 0 0
\(601\) 3.00000 5.19615i 0.122373 0.211955i −0.798330 0.602220i \(-0.794283\pi\)
0.920703 + 0.390264i \(0.127616\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) −8.00000 −0.325515
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) 0 0
\(607\) 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i \(-0.0614000\pi\)
−0.656744 + 0.754114i \(0.728067\pi\)
\(608\) 10.0000 + 17.3205i 0.405554 + 0.702439i
\(609\) 0 0
\(610\) 2.00000 3.46410i 0.0809776 0.140257i
\(611\) 0 0
\(612\) 0 0
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 2.00000 3.46410i 0.0807134 0.139800i
\(615\) 0 0
\(616\) 6.00000 + 10.3923i 0.241747 + 0.418718i
\(617\) 3.00000 + 5.19615i 0.120775 + 0.209189i 0.920074 0.391745i \(-0.128129\pi\)
−0.799298 + 0.600935i \(0.794795\pi\)
\(618\) 0 0
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −7.00000 + 12.1244i −0.280449 + 0.485752i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 13.0000 + 22.5167i 0.519584 + 0.899947i
\(627\) 0 0
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) −36.0000 −1.43541
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 24.0000 41.5692i 0.954669 1.65353i
\(633\) 0 0
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.00000 1.73205i 0.0396214 0.0686264i
\(638\) 8.00000 0.316723
\(639\) 0 0
\(640\) −6.00000 −0.237171
\(641\) −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) 0 0
\(643\) −10.0000 17.3205i −0.394362 0.683054i 0.598658 0.801005i \(-0.295701\pi\)
−0.993019 + 0.117951i \(0.962368\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) −40.0000 −1.57256 −0.786281 0.617869i \(-0.787996\pi\)
−0.786281 + 0.617869i \(0.787996\pi\)
\(648\) 0 0
\(649\) 48.0000 1.88416
\(650\) 1.00000 1.73205i 0.0392232 0.0679366i
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) 0 0
\(655\) 4.00000 6.92820i 0.156293 0.270707i
\(656\) −2.00000 −0.0780869
\(657\) 0 0
\(658\) 0 0
\(659\) −6.00000 + 10.3923i −0.233727 + 0.404827i −0.958902 0.283738i \(-0.908425\pi\)
0.725175 + 0.688565i \(0.241759\pi\)
\(660\) 0 0
\(661\) −11.0000 19.0526i −0.427850 0.741059i 0.568831 0.822454i \(-0.307396\pi\)
−0.996682 + 0.0813955i \(0.974062\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) 0 0
\(664\) 18.0000 31.1769i 0.698535 1.20990i
\(665\) 8.00000 0.310227
\(666\) 0 0
\(667\) 0 0
\(668\) −4.00000 + 6.92820i −0.154765 + 0.268060i
\(669\) 0 0
\(670\) −4.00000 6.92820i −0.154533 0.267660i
\(671\) 4.00000 + 6.92820i 0.154418 + 0.267460i
\(672\) 0 0
\(673\) −17.0000 + 29.4449i −0.655302 + 1.13502i 0.326516 + 0.945192i \(0.394125\pi\)
−0.981818 + 0.189824i \(0.939208\pi\)
\(674\) 14.0000 0.539260
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 9.00000 15.5885i 0.345898 0.599113i −0.639618 0.768693i \(-0.720908\pi\)
0.985517 + 0.169580i \(0.0542410\pi\)
\(678\) 0 0
\(679\) 9.00000 + 15.5885i 0.345388 + 0.598230i
\(680\) −18.0000 31.1769i −0.690268 1.19558i
\(681\) 0 0
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −10.0000 + 17.3205i −0.380418 + 0.658903i −0.991122 0.132956i \(-0.957553\pi\)
0.610704 + 0.791859i \(0.290887\pi\)
\(692\) 10.0000 0.380143
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) 12.0000 20.7846i 0.455186 0.788405i
\(696\) 0 0
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) −1.00000 1.73205i −0.0378506 0.0655591i
\(699\) 0 0
\(700\) 0.500000 0.866025i 0.0188982 0.0327327i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 24.0000 0.905177
\(704\) −14.0000 + 24.2487i −0.527645 + 0.913908i
\(705\) 0 0
\(706\) 5.00000 + 8.66025i 0.188177 + 0.325933i
\(707\) 7.00000 + 12.1244i 0.263262 + 0.455983i
\(708\) 0 0
\(709\) −3.00000 + 5.19615i −0.112667 + 0.195146i −0.916845 0.399244i \(-0.869273\pi\)
0.804178 + 0.594389i \(0.202606\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −42.0000 −1.57402
\(713\) 0 0
\(714\) 0 0
\(715\) −8.00000 13.8564i −0.299183 0.518200i
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) 0 0
\(718\) 16.0000 27.7128i 0.597115 1.03423i
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) −1.50000 + 2.59808i −0.0558242 + 0.0966904i
\(723\) 0 0
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) −1.00000 1.73205i −0.0371391 0.0643268i
\(726\) 0 0
\(727\) 20.0000 34.6410i 0.741759 1.28476i −0.209935 0.977715i \(-0.567325\pi\)
0.951694 0.307049i \(-0.0993415\pi\)
\(728\) 6.00000 0.222375
\(729\) 0 0
\(730\) −12.0000 −0.444140
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 0 0
\(733\) 9.00000 + 15.5885i 0.332423 + 0.575773i 0.982986 0.183679i \(-0.0588007\pi\)
−0.650564 + 0.759452i \(0.725467\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.0000 0.589368
\(738\) 0 0
\(739\) 36.0000 1.32428 0.662141 0.749380i \(-0.269648\pi\)
0.662141 + 0.749380i \(0.269648\pi\)
\(740\) −6.00000 + 10.3923i −0.220564 + 0.382029i
\(741\) 0 0
\(742\) −3.00000 5.19615i −0.110133 0.190757i
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 6.00000 10.3923i 0.219823 0.380745i
\(746\) 10.0000 0.366126
\(747\) 0 0
\(748\) 24.0000 0.877527
\(749\) 2.00000 3.46410i 0.0730784 0.126576i
\(750\) 0 0
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 2.00000 3.46410i 0.0728357 0.126155i
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 6.00000 10.3923i 0.217930 0.377466i
\(759\) 0 0
\(760\) 12.0000 + 20.7846i 0.435286 + 0.753937i
\(761\) −9.00000 15.5885i −0.326250 0.565081i 0.655515 0.755182i \(-0.272452\pi\)
−0.981764 + 0.190101i \(0.939118\pi\)
\(762\) 0 0
\(763\) −9.00000 + 15.5885i −0.325822 + 0.564340i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 0 0
\(767\) 12.0000 20.7846i 0.433295 0.750489i
\(768\) 0 0
\(769\) −1.00000 1.73205i −0.0360609 0.0624593i 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 4.00000 + 6.92820i 0.144150 + 0.249675i
\(771\) 0 0
\(772\) 1.00000 1.73205i 0.0359908 0.0623379i
\(773\) 14.0000 0.503545 0.251773 0.967786i \(-0.418987\pi\)
0.251773 + 0.967786i \(0.418987\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −27.0000 + 46.7654i −0.969244 + 1.67878i
\(777\) 0 0
\(778\) 3.00000 + 5.19615i 0.107555 + 0.186291i
\(779\) −4.00000 6.92820i −0.143315 0.248229i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −1.00000 −0.0357143
\(785\) −2.00000 + 3.46410i −0.0713831 + 0.123639i
\(786\) 0 0
\(787\) 22.0000 + 38.1051i 0.784215 + 1.35830i 0.929467 + 0.368906i \(0.120268\pi\)
−0.145251 + 0.989395i \(0.546399\pi\)
\(788\) 11.0000 + 19.0526i 0.391859 + 0.678719i
\(789\) 0 0
\(790\) 16.0000 27.7128i 0.569254 0.985978i
\(791\) 14.0000 0.497783
\(792\) 0 0
\(793\) 4.00000 0.142044
\(794\) −9.00000 + 15.5885i −0.319398 + 0.553214i
\(795\) 0 0
\(796\) 12.0000 + 20.7846i 0.425329 + 0.736691i
\(797\) 13.0000 + 22.5167i 0.460484 + 0.797581i 0.998985 0.0450436i \(-0.0143427\pi\)
−0.538501 + 0.842625i \(0.681009\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 5.00000 0.176777
\(801\) 0 0
\(802\) 30.0000 1.05934
\(803\) 12.0000 20.7846i 0.423471 0.733473i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −21.0000 + 36.3731i −0.738777 + 1.27960i