Properties

Label 2352.2.q.e.961.1
Level $2352$
Weight $2$
Character 2352.961
Analytic conductor $18.781$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2352.961
Dual form 2352.2.q.e.1537.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(-3.00000 - 5.19615i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -2.00000 q^{29} +(2.00000 - 3.46410i) q^{33} +(-3.00000 + 5.19615i) q^{37} +(-1.00000 - 1.73205i) q^{39} -2.00000 q^{41} +4.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(-3.00000 + 5.19615i) q^{51} +(-3.00000 - 5.19615i) q^{53} -8.00000 q^{55} +4.00000 q^{57} +(-6.00000 - 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-8.00000 + 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +12.0000 q^{85} +(1.00000 + 1.73205i) q^{87} +(-7.00000 + 12.1244i) q^{89} +(-4.00000 - 6.92820i) q^{95} -18.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 2q^{5} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - 2q^{5} - q^{9} + 4q^{11} + 4q^{13} + 4q^{15} - 6q^{17} - 4q^{19} + q^{25} + 2q^{27} - 4q^{29} + 4q^{33} - 6q^{37} - 2q^{39} - 4q^{41} + 8q^{43} - 2q^{45} - 6q^{51} - 6q^{53} - 16q^{55} + 8q^{57} - 12q^{59} - 2q^{61} - 4q^{65} + 4q^{67} - 6q^{73} + q^{75} - 16q^{79} - q^{81} - 24q^{83} + 24q^{85} + 2q^{87} - 14q^{89} - 8q^{95} - 36q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) −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 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 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
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 0 0
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 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
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0 0
\(33\) 2.00000 3.46410i 0.348155 0.603023i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.00000 + 5.19615i −0.493197 + 0.854242i −0.999969 0.00783774i \(-0.997505\pi\)
0.506772 + 0.862080i \(0.330838\pi\)
\(38\) 0 0
\(39\) −1.00000 1.73205i −0.160128 0.277350i
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) 0 0
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) 0 0
\(59\) −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 −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 0 0
\(69\) 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 0.635323 0.772246i \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −8.00000 + 13.8564i −0.900070 + 1.55897i −0.0726692 + 0.997356i \(0.523152\pi\)
−0.827401 + 0.561611i \(0.810182\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −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
\(86\) 0 0
\(87\) 1.00000 + 1.73205i 0.107211 + 0.185695i
\(88\) 0 0
\(89\) −7.00000 + 12.1244i −0.741999 + 1.28518i 0.209585 + 0.977790i \(0.432789\pi\)
−0.951584 + 0.307389i \(0.900545\pi\)
\(90\) 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
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) 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 \(0.295621\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.00000 3.46410i 0.193347 0.334887i −0.753010 0.658009i \(-0.771399\pi\)
0.946357 + 0.323122i \(0.104732\pi\)
\(108\) 0 0
\(109\) 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i \(0.164149\pi\)
−0.00790932 + 0.999969i \(0.502518\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 + 1.73205i −0.0924500 + 0.160128i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) 1.00000 + 1.73205i 0.0901670 + 0.156174i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) 0 0
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1.00000 + 1.73205i −0.0860663 + 0.149071i
\(136\) 0 0
\(137\) 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 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
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) 0 0
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 4.00000 + 6.92820i 0.311400 + 0.539360i
\(166\) 0 0
\(167\) −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
\(170\) 0 0
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) 0 0
\(173\) −5.00000 + 8.66025i −0.380143 + 0.658427i −0.991082 0.133250i \(-0.957459\pi\)
0.610939 + 0.791677i \(0.290792\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) 0 0
\(179\) −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) 0 0
\(181\) 26.0000 1.93256 0.966282 0.257485i \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 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
\(190\) 0 0
\(191\) −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 0 0
\(195\) 4.00000 0.286446
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i \(-0.842871\pi\)
0.0299585 0.999551i \(-0.490462\pi\)
\(200\) 0 0
\(201\) 2.00000 3.46410i 0.141069 0.244339i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.00000 + 6.92820i −0.272798 + 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3.00000 + 5.19615i −0.202721 + 0.351123i
\(220\) 0 0
\(221\) −6.00000 10.3923i −0.403604 0.699062i
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 0 0
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) 0 0
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 16.0000 1.03931
\(238\) 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 0.896435 0.443176i \(-0.146148\pi\)
−0.832019 + 0.554747i \(0.812815\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.00000 + 6.92820i −0.254514 + 0.440831i
\(248\) 0 0
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 0 0
\(251\) −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
\(255\) −6.00000 10.3923i −0.375735 0.650791i
\(256\) 0 0
\(257\) 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
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000 1.73205i 0.0618984 0.107211i
\(262\) 0 0
\(263\) 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
\(265\) 12.0000 0.737154
\(266\) 0 0
\(267\) 14.0000 0.856786
\(268\) 0 0
\(269\) 3.00000 + 5.19615i 0.182913 + 0.316815i 0.942871 0.333157i \(-0.108114\pi\)
−0.759958 + 0.649972i \(0.774781\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −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 \(-0.396503\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 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
\(285\) −4.00000 + 6.92820i −0.236940 + 0.410391i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 9.00000 + 15.5885i 0.527589 + 0.913812i
\(292\) 0 0
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 2.00000 + 3.46410i 0.116052 + 0.201008i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 7.00000 12.1244i 0.402139 0.696526i
\(304\) 0 0
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 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 \(-0.570608\pi\)
0.954810 0.297218i \(-0.0960589\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 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
\(320\) 0 0
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) 1.00000 + 1.73205i 0.0554700 + 0.0960769i
\(326\) 0 0
\(327\) 9.00000 15.5885i 0.497701 0.862044i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 0 0
\(333\) −3.00000 5.19615i −0.164399 0.284747i
\(334\) 0 0
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 0 0
\(339\) 7.00000 + 12.1244i 0.380188 + 0.658505i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.0000 24.2487i −0.751559 1.30174i −0.947067 0.321037i \(-0.895969\pi\)
0.195507 0.980702i \(-0.437365\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) 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
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 16.0000 27.7128i 0.844448 1.46263i −0.0416523 0.999132i \(-0.513262\pi\)
0.886100 0.463494i \(-0.153404\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 0 0
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) 0 0
\(367\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 0 0
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 0 0
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) 0 0
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.00000 + 3.46410i −0.101666 + 0.176090i
\(388\) 0 0
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) 0 0
\(395\) −16.0000 27.7128i −0.805047 1.39438i
\(396\) 0 0
\(397\) −9.00000 + 15.5885i −0.451697 + 0.782362i −0.998492 0.0549046i \(-0.982515\pi\)
0.546795 + 0.837267i \(0.315848\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.0000 25.9808i 0.749064 1.29742i −0.199207 0.979957i \(-0.563837\pi\)
0.948272 0.317460i \(-0.102830\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 2.00000 0.0993808
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) −11.0000 19.0526i −0.543915 0.942088i −0.998674 0.0514740i \(-0.983608\pi\)
0.454759 0.890614i \(-0.349725\pi\)
\(410\) 0 0
\(411\) 3.00000 5.19615i 0.147979 0.256307i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 12.0000 20.7846i 0.589057 1.02028i
\(416\) 0 0
\(417\) −6.00000 10.3923i −0.293821 0.508913i
\(418\) 0 0
\(419\) −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 \(0.123221\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.00000 5.19615i 0.145521 0.252050i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 4.00000 6.92820i 0.193122 0.334497i
\(430\) 0 0
\(431\) −12.0000 20.7846i −0.578020 1.00116i −0.995706 0.0925683i \(-0.970492\pi\)
0.417687 0.908591i \(-0.362841\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) −4.00000 −0.191785
\(436\) 0 0
\(437\) 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 \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 18.0000 31.1769i 0.855206 1.48126i −0.0212481 0.999774i \(-0.506764\pi\)
0.876454 0.481486i \(-0.159903\pi\)
\(444\) 0 0
\(445\) −14.0000 24.2487i −0.663664 1.14950i
\(446\) 0 0
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −4.00000 6.92820i −0.188353 0.326236i
\(452\) 0 0
\(453\) 4.00000 6.92820i 0.187936 0.325515i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 0 0
\(459\) −3.00000 5.19615i −0.140028 0.242536i
\(460\) 0 0
\(461\) 10.0000 0.465746 0.232873 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.0000 + 31.1769i −0.832941 + 1.44270i 0.0627555 + 0.998029i \(0.480011\pi\)
−0.895696 + 0.444667i \(0.853322\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 + 1.73205i −0.0460776 + 0.0798087i
\(472\) 0 0
\(473\) 8.00000 + 13.8564i 0.367840 + 0.637118i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) 8.00000 + 13.8564i 0.365529 + 0.633115i 0.988861 0.148842i \(-0.0475547\pi\)
−0.623332 + 0.781958i \(0.714221\pi\)
\(480\) 0 0
\(481\) −6.00000 + 10.3923i −0.273576 + 0.473848i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 18.0000 31.1769i 0.817338 1.41567i
\(486\) 0 0
\(487\) −4.00000 6.92820i −0.181257 0.313947i 0.761052 0.648691i \(-0.224683\pi\)
−0.942309 + 0.334744i \(0.891350\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 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
\(494\) 0 0
\(495\) 4.00000 6.92820i 0.179787 0.311400i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0 0
\(501\) 4.00000 + 6.92820i 0.178707 + 0.309529i
\(502\) 0 0
\(503\) 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
\(507\) 4.50000 + 7.79423i 0.199852 + 0.346154i
\(508\) 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
\(511\) 0 0
\(512\) 0 0
\(513\) −2.00000 + 3.46410i −0.0883022 + 0.152944i
\(514\) 0 0
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 10.0000 0.438951
\(520\) 0 0
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 0 0
\(523\) 10.0000 17.3205i 0.437269 0.757373i −0.560208 0.828352i \(-0.689279\pi\)
0.997478 + 0.0709788i \(0.0226123\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −4.00000 −0.173259
\(534\) 0 0
\(535\) 4.00000 + 6.92820i 0.172935 + 0.299532i
\(536\) 0 0
\(537\) −2.00000 + 3.46410i −0.0863064 + 0.149487i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i \(-0.572440\pi\)
0.956504 0.291718i \(-0.0942267\pi\)
\(542\) 0 0
\(543\) −13.0000 22.5167i −0.557883 0.966282i
\(544\) 0 0
\(545\) −36.0000 −1.54207
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) 0 0
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −6.00000 + 10.3923i −0.254686 + 0.441129i
\(556\) 0 0
\(557\) 1.00000 + 1.73205i 0.0423714 + 0.0733893i 0.886433 0.462856i \(-0.153175\pi\)
−0.844062 + 0.536246i \(0.819842\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) 0 0
\(563\) −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
\(566\) 0 0
\(567\) 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 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 17.0000 + 29.4449i 0.707719 + 1.22581i 0.965701 + 0.259656i \(0.0836092\pi\)
−0.257982 + 0.966150i \(0.583058\pi\)
\(578\) 0 0
\(579\) −1.00000 + 1.73205i −0.0415586 + 0.0719816i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) 0 0
\(585\) −2.00000 3.46410i −0.0826898 0.143223i
\(586\) 0 0
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −11.0000 19.0526i −0.452480 0.783718i
\(592\) 0 0
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −12.0000 + 20.7846i −0.491127 + 0.850657i
\(598\) 0 0
\(599\) 24.0000 + 41.5692i 0.980613 + 1.69847i 0.660006 + 0.751260i \(0.270554\pi\)
0.320607 + 0.947212i \(0.396113\pi\)
\(600\) 0 0
\(601\) 6.00000 0.244745 0.122373 0.992484i \(-0.460950\pi\)
0.122373 + 0.992484i \(0.460950\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) −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 \(0.0614000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 13.0000 + 22.5167i 0.525065 + 0.909439i 0.999574 + 0.0291886i \(0.00929235\pi\)
−0.474509 + 0.880251i \(0.657374\pi\)
\(614\) 0 0
\(615\) −4.00000 −0.161296
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 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
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 8.00000 + 13.8564i 0.319489 + 0.553372i
\(628\) 0 0
\(629\) 36.0000 1.43541
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) 2.00000 + 3.46410i 0.0794929 + 0.137686i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) 0 0
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) 20.0000 + 34.6410i 0.786281 + 1.36188i 0.928231 + 0.372005i \(0.121330\pi\)
−0.141950 + 0.989874i \(0.545337\pi\)
\(648\) 0 0
\(649\) 24.0000 41.5692i 0.942082 1.63173i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) −4.00000 6.92820i −0.156293 0.270707i
\(656\) 0 0
\(657\) 6.00000 0.234082
\(658\) 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 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 0 0
\(663\) −6.00000 + 10.3923i −0.233021 + 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) 0 0
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 0 0
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 0 0
\(677\) −9.00000 + 15.5885i −0.345898 + 0.599113i −0.985517 0.169580i \(-0.945759\pi\)
0.639618 + 0.768693i \(0.279092\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 6.00000 10.3923i 0.229920 0.398234i
\(682\) 0 0
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 10.0000 0.381524
\(688\) 0 0
\(689\) −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 \(0.290887\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12.0000 + 20.7846i −0.455186 + 0.788405i
\(696\) 0 0
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) 0 0
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) −12.0000 20.7846i −0.452589 0.783906i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 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
\(711\) −8.00000 13.8564i −0.300023 0.519656i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −16.0000 −0.598366
\(716\) 0 0
\(717\) 12.0000 + 20.7846i 0.448148 + 0.776215i
\(718\) 0 0
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.00000 1.73205i 0.0371904 0.0644157i
\(724\) 0 0
\(725\) −1.00000 1.73205i −0.0371391 0.0643268i
\(726\) 0 0
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) −9.00000 + 15.5885i −0.332423 + 0.575773i −0.982986 0.183679i \(-0.941199\pi\)
0.650564 + 0.759452i \(0.274533\pi\)
\(734\) 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 0.980052 + 0.198741i \(0.0636852\pi\)
−0.317911 + 0.948120i \(0.602981\pi\)
\(740\) 0 0
\(741\) 8.00000 0.293887
\(742\) 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
\(746\) 0 0
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 0 0
\(753\) 10.0000 + 17.3205i 0.364420 + 0.631194i
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 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
\(763\) 0 0
\(764\) 0 0
\(765\) −6.00000 + 10.3923i −0.216930 + 0.375735i
\(766\) 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
\(771\) −26.0000 −0.936367
\(772\) 0 0
\(773\) 7.00000 + 12.1244i 0.251773 + 0.436083i 0.964014 0.265852i \(-0.0856532\pi\)
−0.712241 + 0.701935i \(0.752320\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.00000 6.92820i 0.143315 0.248229i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) 4.00000 0.142766
\(786\) 0 0
\(787\) 22.0000 + 38.1051i 0.784215 + 1.35830i 0.929467 + 0.368906i \(0.120268\pi\)
−0.145251 + 0.989395i \(0.546399\pi\)
\(788\) 0 0
\(789\) 8.00000 13.8564i 0.284808 0.493301i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.00000 + 3.46410i −0.0710221 + 0.123014i
\(794\) 0 0
\(795\) −6.00000 10.3923i −0.212798 0.368577i
\(796\) 0 0
\(797\) 26.0000 0.920967 0.460484 0.887668i \(-0.347676\pi\)
0.460484 + 0.887668i \(0.347676\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −7.00000 12.1244i −0.247333 0.428393i
\(802\) 0 0
\(803\) 12.0000 20.7846i 0.423471 0.733473i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 3.00000 5.19615i 0.105605 0.182913i
\(808\) 0 0
\(809\) −21.0000 36.3731i −0.738321 1.27881i −0.953251 0.302180i \(-0.902286\pi\)
0.214930 0.976629i \(-0.431048\pi\)
\(810\) 0 0
\(811\) 44.0000 1.54505 0.772524 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(812\) 0 0
\(813\) 16.0000 0.561144
\(814\) 0 0
\(815\) 4.00000 + 6.92820i 0.140114 + 0.242684i