Properties

Label 441.2.e.b.361.1
Level $441$
Weight $2$
Character 441.361
Analytic conductor $3.521$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.2.e.b.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} -3.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} -3.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +2.00000 q^{13} +(0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +2.00000 q^{20} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +2.00000 q^{29} +(-2.50000 + 4.33013i) q^{32} -6.00000 q^{34} +(-3.00000 - 5.19615i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-3.00000 - 5.19615i) q^{40} +2.00000 q^{41} -4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} -1.00000 q^{50} +(1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +8.00000 q^{55} +(-1.00000 - 1.73205i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +7.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-3.00000 + 5.19615i) q^{73} +(-3.00000 + 5.19615i) q^{74} +4.00000 q^{76} +(8.00000 + 13.8564i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-1.00000 - 1.73205i) q^{82} -12.0000 q^{83} +12.0000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-6.00000 + 10.3923i) q^{88} +(7.00000 + 12.1244i) q^{89} +(-4.00000 + 6.92820i) q^{95} -18.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{4} + 2q^{5} - 6q^{8} + O(q^{10}) \) \( 2q - q^{2} + q^{4} + 2q^{5} - 6q^{8} + 2q^{10} + 4q^{11} + 4q^{13} + q^{16} + 6q^{17} + 4q^{19} + 4q^{20} - 8q^{22} + q^{25} - 2q^{26} + 4q^{29} - 5q^{32} - 12q^{34} - 6q^{37} + 4q^{38} - 6q^{40} + 4q^{41} - 8q^{43} - 4q^{44} - 2q^{50} + 2q^{52} + 6q^{53} + 16q^{55} - 2q^{58} - 12q^{59} - 2q^{61} + 14q^{64} + 4q^{65} - 4q^{67} - 6q^{68} - 6q^{73} - 6q^{74} + 8q^{76} + 16q^{79} - 2q^{80} - 2q^{82} - 24q^{83} + 24q^{85} + 4q^{86} - 12q^{88} + 14q^{89} - 8q^{95} - 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −3.00000 −1.06066
\(9\) 0 0
\(10\) 1.00000 1.73205i 0.316228 0.547723i
\(11\) 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0 0
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 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
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 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
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 0 0
\(37\) −3.00000 5.19615i −0.493197 0.854242i 0.506772 0.862080i \(-0.330838\pi\)
−0.999969 + 0.00783774i \(0.997505\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) 0 0
\(40\) −3.00000 5.19615i −0.474342 0.821584i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) 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 0
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 1.73205i −0.131306 0.227429i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 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
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −3.00000 + 5.19615i −0.351123 + 0.608164i −0.986447 0.164083i \(-0.947534\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(74\) −3.00000 + 5.19615i −0.348743 + 0.604040i
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i \(0.189818\pi\)
0.0726692 + 0.997356i \(0.476848\pi\)
\(80\) −1.00000 + 1.73205i −0.111803 + 0.193649i
\(81\) 0 0
\(82\) −1.00000 1.73205i −0.110432 0.191273i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) 0 0
\(88\) −6.00000 + 10.3923i −0.639602 + 1.10782i
\(89\) 7.00000 + 12.1244i 0.741999 + 1.28518i 0.951584 + 0.307389i \(0.0994552\pi\)
−0.209585 + 0.977790i \(0.567211\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) 0 0
\(97\) −18.0000 −1.82762 −0.913812 0.406138i \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −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 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(108\) 0 0
\(109\) 9.00000 15.5885i 0.862044 1.49310i −0.00790932 0.999969i \(-0.502518\pi\)
0.869953 0.493135i \(-0.164149\pi\)
\(110\) −4.00000 6.92820i −0.381385 0.660578i
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.00000 1.73205i 0.0928477 0.160817i
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) 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
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) −9.00000 + 15.5885i −0.771744 + 1.33670i
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.00000 6.92820i 0.334497 0.579365i
\(144\) 0 0
\(145\) 2.00000 + 3.46410i 0.166091 + 0.287678i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) −6.00000 10.3923i −0.486664 0.842927i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) 8.00000 13.8564i 0.636446 1.10236i
\(159\) 0 0
\(160\) −10.0000 −0.790569
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) 1.00000 1.73205i 0.0780869 0.135250i
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −6.00000 10.3923i −0.460179 0.797053i
\(171\) 0 0
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 5.00000 + 8.66025i 0.380143 + 0.658427i 0.991082 0.133250i \(-0.0425415\pi\)
−0.610939 + 0.791677i \(0.709208\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 7.00000 12.1244i 0.524672 0.908759i
\(179\) −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) 0 0
\(181\) 26.0000 1.93256 0.966282 0.257485i \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 0 0
\(183\) 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 0
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 0 0
\(199\) 12.0000 20.7846i 0.850657 1.47338i −0.0299585 0.999551i \(-0.509538\pi\)
0.880616 0.473831i \(-0.157129\pi\)
\(200\) −1.50000 + 2.59808i −0.106066 + 0.183712i
\(201\) 0 0
\(202\) 14.0000 0.985037
\(203\) 0 0
\(204\) 0 0
\(205\) 2.00000 + 3.46410i 0.139686 + 0.241943i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 0 0
\(208\) 1.00000 + 1.73205i 0.0693375 + 0.120096i
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 0 0
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) −4.00000 6.92820i −0.272798 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) −18.0000 −1.21911
\(219\) 0 0
\(220\) 4.00000 6.92820i 0.269680 0.467099i
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.00000 12.1244i −0.465633 0.806500i
\(227\) 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 0.652183 0.758062i \(-0.273853\pi\)
−0.982592 + 0.185776i \(0.940520\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.00000 + 10.3923i 0.390567 + 0.676481i
\(237\) 0 0
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 1.00000 1.73205i 0.0644157 0.111571i −0.832019 0.554747i \(-0.812815\pi\)
0.896435 + 0.443176i \(0.146148\pi\)
\(242\) −2.50000 + 4.33013i −0.160706 + 0.278351i
\(243\) 0 0
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 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
\(259\) 0 0
\(260\) 4.00000 0.248069
\(261\) 0 0
\(262\) −2.00000 + 3.46410i −0.123560 + 0.214013i
\(263\) 8.00000 13.8564i 0.493301 0.854423i −0.506669 0.862141i \(-0.669123\pi\)
0.999970 + 0.00771799i \(0.00245674\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −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 \(0.936830\pi\)
\(278\) 6.00000 + 10.3923i 0.359856 + 0.623289i
\(279\) 0 0
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 0 0
\(283\) −10.0000 + 17.3205i −0.594438 + 1.02960i 0.399188 + 0.916869i \(0.369292\pi\)
−0.993626 + 0.112728i \(0.964041\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 0 0
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 2.00000 3.46410i 0.117444 0.203419i
\(291\) 0 0
\(292\) 3.00000 + 5.19615i 0.175562 + 0.304082i
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) −24.0000 −1.39733
\(296\) 9.00000 + 15.5885i 0.523114 + 0.906061i
\(297\) 0 0
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 2.00000 3.46410i 0.114520 0.198354i
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) 13.0000 + 22.5167i 0.734803 + 1.27272i 0.954810 + 0.297218i \(0.0960589\pi\)
−0.220006 + 0.975499i \(0.570608\pi\)
\(314\) 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
\(325\) 1.00000 1.73205i 0.0554700 0.0960769i
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) 0 0
\(328\) −6.00000 −0.331295
\(329\) 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 \(0.798271\pi\)
\(332\) −6.00000 + 10.3923i −0.329293 + 0.570352i
\(333\) 0 0
\(334\) 4.00000 + 6.92820i 0.218870 + 0.379094i
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 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
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 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
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000 + 17.3205i 0.533002 + 0.923186i
\(353\) −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
\(356\) 14.0000 0.741999
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) 16.0000 + 27.7128i 0.844448 + 1.46263i 0.886100 + 0.463494i \(0.153404\pi\)
−0.0416523 + 0.999132i \(0.513262\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −13.0000 22.5167i −0.683265 1.18345i
\(363\) 0 0
\(364\) 0 0
\(365\) −12.0000 −0.628109
\(366\) 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
\(371\) 0 0
\(372\) 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
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) 0 0
\(388\) −9.00000 + 15.5885i −0.456906 + 0.791384i
\(389\) 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
\(394\) 11.0000 + 19.0526i 0.554172 + 0.959854i
\(395\) −16.0000 + 27.7128i −0.805047 + 1.39438i
\(396\) 0 0
\(397\) −9.00000 15.5885i −0.451697 0.782362i 0.546795 0.837267i \(-0.315848\pi\)
−0.998492 + 0.0549046i \(0.982515\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 7.00000 + 12.1244i 0.348263 + 0.603209i
\(405\) 0 0
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) −11.0000 + 19.0526i −0.543915 + 0.942088i 0.454759 + 0.890614i \(0.349725\pi\)
−0.998674 + 0.0514740i \(0.983608\pi\)
\(410\) 2.00000 3.46410i 0.0987730 0.171080i
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 20.7846i −0.589057 1.02028i
\(416\) −5.00000 + 8.66025i −0.245145 + 0.424604i
\(417\) 0 0
\(418\) −8.00000 13.8564i −0.391293 0.677739i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) −2.00000 3.46410i −0.0973585 0.168630i
\(423\) 0 0
\(424\) −9.00000 + 15.5885i −0.437079 + 0.757042i
\(425\) −3.00000 5.19615i −0.145521 0.252050i
\(426\) 0 0
\(427\) 0 0
\(428\) 4.00000 0.193347
\(429\) 0 0
\(430\) −4.00000 + 6.92820i −0.192897 + 0.334108i
\(431\) −12.0000 + 20.7846i −0.578020 + 1.00116i 0.417687 + 0.908591i \(0.362841\pi\)
−0.995706 + 0.0925683i \(0.970492\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 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 \(-0.972552\pi\)
0.423556 0.905870i \(-0.360782\pi\)
\(440\) −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
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 4.00000 6.92820i 0.188353 0.326236i
\(452\) 7.00000 12.1244i 0.329252 0.570282i
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 0 0
\(457\) −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i \(-0.241812\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) 0 0
\(460\) 0 0
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 1.00000 + 1.73205i 0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) −18.0000 31.1769i −0.832941 1.44270i −0.895696 0.444667i \(-0.853322\pi\)
0.0627555 0.998029i \(-0.480011\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 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
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 12.0000 + 20.7846i 0.548867 + 0.950666i
\(479\) 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
\(482\) −2.00000 −0.0910975
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) −18.0000 31.1769i −0.817338 1.41567i
\(486\) 0 0
\(487\) 4.00000 6.92820i 0.181257 0.313947i −0.761052 0.648691i \(-0.775317\pi\)
0.942309 + 0.334744i \(0.108650\pi\)
\(488\) 3.00000 + 5.19615i 0.135804 + 0.235219i
\(489\) 0 0
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) 6.00000 10.3923i 0.270226 0.468046i
\(494\) 4.00000 6.92820i 0.179969 0.311715i
\(495\) 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
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) 0 0
\(514\) −13.0000 + 22.5167i −0.573405 + 0.993167i
\(515\) −8.00000 + 13.8564i −0.352522 + 0.610586i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −6.00000 10.3923i −0.263117 0.455733i
\(521\) −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i \(-0.962345\pi\)
0.598714 + 0.800963i \(0.295679\pi\)
\(522\) 0 0
\(523\) −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i \(-0.310721\pi\)
−0.997478 + 0.0709788i \(0.977388\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −6.00000 10.3923i −0.260623 0.451413i
\(531\) 0 0
\(532\) 0 0
\(533\) 4.00000 0.173259
\(534\) 0 0
\(535\) −4.00000 + 6.92820i −0.172935 + 0.299532i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 0 0
\(538\) 6.00000 0.258678
\(539\) 0 0
\(540\) 0 0
\(541\) 17.0000 + 29.4449i 0.730887 + 1.26593i 0.956504 + 0.291718i \(0.0942267\pi\)
−0.225617 + 0.974216i \(0.572440\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) 15.0000 + 25.9808i 0.643120 + 1.11392i
\(545\) 36.0000 1.54207
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 0 0
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) 4.00000 + 6.92820i 0.170406 + 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) 0 0
\(556\) −6.00000 + 10.3923i −0.254457 + 0.440732i
\(557\) −1.00000 + 1.73205i −0.0423714 + 0.0733893i −0.886433 0.462856i \(-0.846825\pi\)
0.844062 + 0.536246i \(0.180158\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) −11.0000 19.0526i −0.464007 0.803684i
\(563\) −2.00000 + 3.46410i −0.0842900 + 0.145994i −0.905088 0.425223i \(-0.860196\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(564\) 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
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 17.0000 29.4449i 0.707719 1.22581i −0.257982 0.966150i \(-0.583058\pi\)
0.965701 0.259656i \(-0.0836092\pi\)
\(578\) −9.50000 + 16.4545i −0.395148 + 0.684416i
\(579\) 0 0
\(580\) 4.00000 0.166091
\(581\) 0 0
\(582\) 0 0
\(583\) −12.0000 20.7846i −0.496989 0.860811i
\(584\) 9.00000 15.5885i 0.372423 0.645055i
\(585\) 0 0
\(586\) −7.00000 12.1244i −0.289167 0.500853i
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 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
\(593\) 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) 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
\(601\) 6.00000 0.244745 0.122373 0.992484i \(-0.460950\pi\)
0.122373 + 0.992484i \(0.460950\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.00000 + 6.92820i 0.162758 + 0.281905i
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) 0 0
\(607\) −8.00000 13.8564i −0.324710 0.562414i 0.656744 0.754114i \(-0.271933\pi\)
−0.981454 + 0.191700i \(0.938600\pi\)
\(608\) −20.0000 −0.811107
\(609\) 0 0
\(610\) −4.00000 −0.161955
\(611\) 0 0
\(612\) 0 0
\(613\) 13.0000 22.5167i 0.525065 0.909439i −0.474509 0.880251i \(-0.657374\pi\)
0.999574 0.0291886i \(-0.00929235\pi\)
\(614\) 2.00000 + 3.46410i 0.0807134 + 0.139800i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) −10.0000 + 17.3205i −0.401934 + 0.696170i −0.993959 0.109749i \(-0.964995\pi\)
0.592025 + 0.805919i \(0.298329\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) 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
\(637\) 0 0
\(638\) −8.00000 −0.316723
\(639\) 0 0
\(640\) −3.00000 + 5.19615i −0.118585 + 0.205396i
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 0 0
\(643\) −20.0000 −0.788723 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) 20.0000 34.6410i 0.786281 1.36188i −0.141950 0.989874i \(-0.545337\pi\)
0.928231 0.372005i \(-0.121330\pi\)
\(648\) 0 0
\(649\) 24.0000 + 41.5692i 0.942082 + 1.63173i
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −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
\(655\) 4.00000 6.92820i 0.156293 0.270707i
\(656\) 1.00000 + 1.73205i 0.0390434 + 0.0676252i
\(657\) 0 0
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 11.0000 19.0526i 0.427850 0.741059i −0.568831 0.822454i \(-0.692604\pi\)
0.996682 + 0.0813955i \(0.0259377\pi\)
\(662\) 2.00000 3.46410i 0.0777322 0.134636i
\(663\) 0 0
\(664\) 36.0000 1.39707
\(665\) 0 0
\(666\) 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
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 7.00000 + 12.1244i 0.269630 + 0.467013i
\(675\) 0 0
\(676\) −4.50000 + 7.79423i −0.173077 + 0.299778i
\(677\) 9.00000 + 15.5885i 0.345898 + 0.599113i 0.985517 0.169580i \(-0.0542410\pi\)
−0.639618 + 0.768693i \(0.720908\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −36.0000 −1.38054
\(681\) 0 0
\(682\) 0 0
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 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 \(-0.0424468\pi\)
−0.610704 + 0.791859i \(0.709113\pi\)
\(692\) 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 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 12.0000 20.7846i 0.452589 0.783906i
\(704\) 14.0000 24.2487i 0.527645 0.913908i
\(705\) 0 0
\(706\) 10.0000 0.376355
\(707\) 0 0
\(708\) 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
\(712\) −21.0000 36.3731i −0.787008 1.36314i
\(713\) 0 0
\(714\) 0 0
\(715\) 16.0000 0.598366
\(716\) 2.00000 + 3.46410i 0.0747435 + 0.129460i
\(717\) 0 0
\(718\) 16.0000 27.7128i 0.597115 1.03423i
\(719\) 24.0000 + 41.5692i 0.895049 + 1.55027i 0.833744 + 0.552151i \(0.186193\pi\)
0.0613050 + 0.998119i \(0.480474\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) 0 0
\(724\) 13.0000 22.5167i 0.483141 0.836825i
\(725\) 1.00000 1.73205i 0.0371391 0.0643268i
\(726\) 0 0
\(727\) 40.0000 1.48352 0.741759 0.670667i \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 6.00000 + 10.3923i 0.222070 + 0.384636i
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 0 0
\(733\) −9.00000 15.5885i −0.332423 0.575773i 0.650564 0.759452i \(-0.274533\pi\)
−0.982986 + 0.183679i \(0.941199\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.00000 + 13.8564i 0.294684 + 0.510407i
\(738\) 0 0
\(739\) −18.0000 + 31.1769i −0.662141 + 1.14686i 0.317911 + 0.948120i \(0.397019\pi\)
−0.980052 + 0.198741i \(0.936315\pi\)
\(740\) −6.00000 10.3923i −0.220564 0.382029i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −6.00000 + 10.3923i −0.219823 + 0.380745i
\(746\) 5.00000 8.66025i 0.183063 0.317074i
\(747\) 0 0
\(748\) −24.0000 −0.877527
\(749\) 0 0
\(750\) 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
\(763\) 0 0
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) 0 0
\(767\) −12.0000 + 20.7846i −0.433295 + 0.750489i
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.00000 + 1.73205i 0.0359908 + 0.0623379i
\(773\) −7.00000 + 12.1244i −0.251773 + 0.436083i −0.964014 0.265852i \(-0.914347\pi\)
0.712241 + 0.701935i \(0.247680\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 54.0000 1.93849
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) 4.00000 + 6.92820i 0.143315 + 0.248229i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) −22.0000 + 38.1051i −0.784215 + 1.35830i 0.145251 + 0.989395i \(0.453601\pi\)
−0.929467 + 0.368906i \(0.879732\pi\)
\(788\) −11.0000 + 19.0526i −0.391859 + 0.678719i
\(789\) 0 0
\(790\) 32.0000 1.13851
\(791\) 0 0
\(792\) 0 0
\(793\) −2.00000 3.46410i −0.0710221 0.123014i
\(794\) −9.00000 + 15.5885i −0.319398 + 0.553214i
\(795\) 0 0
\(796\) −12.0000 20.7846i −0.425329 0.736691i
\(797\) −26.0000 −0.920967 −0.460484 0.887668i \(-0.652324\pi\)
−0.460484 + 0.887668i \(0.652324\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.50000 + 4.33013i 0.0883883 + 0.153093i
\(801\) 0 0
\(802\) −15.0000 + 25.9808i −0.529668 + 0.917413i
\(803\) 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
\(809\) 21.0000 36.3731i 0.738321 1.27881i −0.214930 0.976629i \(-0.568952\pi\)
0.953251 0.302180i \(-0.0977142\pi\)
\(810\) 0