Properties

Label 567.2.f.b.190.1
Level $567$
Weight $2$
Character 567.190
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 190.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 567.190
Dual form 567.2.f.b.379.1

$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 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 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 0 0
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 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 \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 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 \(-0.226120\pi\)
−0.943811 + 0.330487i \(0.892787\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −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 \(-0.783417\pi\)
0.933486 + 0.358614i \(0.116751\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 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 \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 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 −0.150148 0.988663i \(-0.547975\pi\)
0.931282 0.364299i \(-0.118692\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 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 −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 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 0.827401 + 0.561611i \(0.189818\pi\)
0.0726692 + 0.997356i \(0.476848\pi\)
\(80\) −2.00000 −0.223607
\(81\) 0 0
\(82\) −2.00000 −0.220863
\(83\) −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) 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 \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 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 −0.808632 0.588315i \(-0.799792\pi\)
−0.105180 0.994453i \(-0.533542\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) −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 \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 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 0.322498 + 0.946570i \(0.395477\pi\)
−0.981003 + 0.193993i \(0.937856\pi\)
\(114\) 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 \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 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 \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 0 0
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) −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 \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) −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 −0.823359 0.567521i \(-0.807902\pi\)
0.903167 + 0.429289i \(0.141236\pi\)
\(158\) 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 \(-0.933505\pi\)
0.668730 + 0.743505i \(0.266838\pi\)
\(168\) 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 \(-0.290792\pi\)
−0.991082 + 0.133250i \(0.957459\pi\)
\(174\) 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 \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 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 \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −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 \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 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 −0.926620 0.375999i \(-0.877300\pi\)
0.788935 + 0.614477i \(0.210633\pi\)
\(212\) −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 −0.999128 0.0417488i \(-0.986707\pi\)
0.463409 0.886145i \(-0.346626\pi\)
\(224\) −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 \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 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 −0.157893 0.987456i \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 0 0
\(241\) −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i \(-0.187185\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) 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 \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) 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 −0.101305 0.994855i \(-0.532302\pi\)
0.912222 0.409695i \(-0.134365\pi\)
\(258\) 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 \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) 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 \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 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 −0.980373 0.197153i \(-0.936830\pi\)
0.319447 0.947604i \(-0.396503\pi\)
\(278\) 12.0000 0.719712
\(279\) 0 0
\(280\) 6.00000 0.358569
\(281\) −11.0000 19.0526i −0.656205 1.13658i −0.981590 0.190999i \(-0.938827\pi\)
0.325385 0.945582i \(-0.394506\pi\)
\(282\) 0 0
\(283\) 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i \(-0.630708\pi\)
0.993626 0.112728i \(-0.0359589\pi\)
\(284\) 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 \(-0.699230\pi\)
0.994772 + 0.102123i \(0.0325637\pi\)
\(294\) 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 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) −13.0000 22.5167i −0.734803 1.27272i −0.954810 0.297218i \(-0.903941\pi\)
0.220006 0.975499i \(-0.429392\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) 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 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) −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 −0.609936 0.792451i \(-0.708805\pi\)
0.991250 + 0.131995i \(0.0421382\pi\)
\(338\) 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 0.195507 + 0.980702i \(0.437365\pi\)
−0.947067 + 0.321037i \(0.895969\pi\)
\(348\) 0 0
\(349\) 1.00000 + 1.73205i 0.0535288 + 0.0927146i 0.891548 0.452926i \(-0.149620\pi\)
−0.838019 + 0.545640i \(0.816286\pi\)
\(350\) 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 \(-0.0809239\pi\)
−0.701734 + 0.712439i \(0.747591\pi\)
\(354\) 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 \(-0.820071\pi\)
−0.844448 + 0.535638i \(0.820071\pi\)
\(360\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 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 −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 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 \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 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 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 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 −0.454759 0.890614i \(-0.650275\pi\)
0.998674 0.0514740i \(-0.0163919\pi\)
\(410\) 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 \(-0.928027\pi\)
0.681426 + 0.731887i \(0.261360\pi\)
\(420\) 0 0
\(421\) −19.0000 32.9090i −0.926003 1.60388i −0.789940 0.613185i \(-0.789888\pi\)
−0.136064 0.990700i \(-0.543445\pi\)
\(422\) 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 \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 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 0.996284 + 0.0861252i \(0.0274485\pi\)
−0.423556 + 0.905870i \(0.639218\pi\)
\(440\) 24.0000 1.14416
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) 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 \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 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 0.725059 0.688686i \(-0.241812\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) −10.0000 −0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) −5.00000 8.66025i −0.232873 0.403348i 0.725779 0.687928i \(-0.241479\pi\)
−0.958652 + 0.284579i \(0.908146\pi\)
\(462\) 0 0
\(463\) −8.00000 + 13.8564i −0.371792 + 0.643962i −0.989841 0.142177i \(-0.954590\pi\)
0.618050 + 0.786139i \(0.287923\pi\)
\(464\) 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 \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) 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 \(-0.285779\pi\)
−0.988861 + 0.148842i \(0.952445\pi\)
\(480\) 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 \(-0.684296\pi\)
0.998467 + 0.0553560i \(0.0176294\pi\)
\(492\) 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 −0.907314 0.420455i \(-0.861871\pi\)
0.817781 + 0.575529i \(0.195204\pi\)
\(500\) −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 \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 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 \(-0.904468\pi\)
0.733679 + 0.679496i \(0.237801\pi\)
\(510\) 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 \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 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 0.820096 0.572226i \(-0.193920\pi\)
−0.905610 + 0.424111i \(0.860587\pi\)
\(548\) −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 \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 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 \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 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 \(-0.0994469\pi\)
−0.741981 + 0.670421i \(0.766114\pi\)
\(570\) 0 0
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) 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 0.995726 + 0.0923513i \(0.0294383\pi\)
−0.417885 + 0.908500i \(0.637228\pi\)
\(588\) 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 \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 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 0.320607 0.947212i \(-0.396113\pi\)
0.660006 0.751260i \(-0.270554\pi\)
\(600\) 0 0
\(601\) 3.00000 + 5.19615i 0.122373 + 0.211955i 0.920703 0.390264i \(-0.127616\pi\)
−0.798330 + 0.602220i \(0.794283\pi\)
\(602\) 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 −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) −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 \(-0.871871\pi\)
0.799298 + 0.600935i \(0.205205\pi\)
\(618\) 0 0
\(619\) 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i \(-0.0350048\pi\)
−0.592025 + 0.805919i \(0.701671\pi\)
\(620\) 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 \(-0.0509845\pi\)
−0.631721 + 0.775196i \(0.717651\pi\)
\(642\) 0 0
\(643\) −10.0000 + 17.3205i −0.394362 + 0.683054i −0.993019 0.117951i \(-0.962368\pi\)
0.598658 + 0.801005i \(0.295701\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) 40.0000 1.57256 0.786281 0.617869i \(-0.212004\pi\)
0.786281 + 0.617869i \(0.212004\pi\)
\(648\) 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 \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 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 \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 0 0
\(661\) −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) 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 −0.981818 0.189824i \(-0.939208\pi\)
0.326516 0.945192i \(-0.394125\pi\)
\(674\) −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 \(-0.279092\pi\)
−0.985517 + 0.169580i \(0.945759\pi\)
\(678\) 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 \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 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 0.610704 0.791859i \(-0.290887\pi\)
−0.991122 + 0.132956i \(0.957553\pi\)
\(692\) −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 \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 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 0.804178 0.594389i \(-0.202606\pi\)
−0.916845 + 0.399244i \(0.869273\pi\)
\(710\) 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 \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) 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 0.951694 + 0.307049i \(0.0993415\pi\)
−0.209935 + 0.977715i \(0.567325\pi\)
\(728\) −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 −0.650564 0.759452i \(-0.725467\pi\)
0.982986 + 0.183679i \(0.0588007\pi\)
\(734\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 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 −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 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 \(-0.727548\pi\)
0.981764 + 0.190101i \(0.0608816\pi\)
\(762\) 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 −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) −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 \(-0.581013\pi\)
−0.251773 + 0.967786i \(0.581013\pi\)
\(774\) 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 −0.145251 0.989395i \(-0.546399\pi\)
0.929467 0.368906i \(-0.120268\pi\)
\(788\) −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
\(794\)