Properties

Label 1064.2.q.d.305.1
Level $1064$
Weight $2$
Character 1064.305
Analytic conductor $8.496$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.49608277506\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 305.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1064.305
Dual form 1064.2.q.d.457.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{11} +(3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +6.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(7.50000 - 2.59808i) q^{35} +6.00000 q^{41} +9.00000 q^{43} +(4.50000 - 7.79423i) q^{45} +(1.50000 + 2.59808i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{53} -3.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-7.50000 + 2.59808i) q^{63} +(4.00000 - 6.92820i) q^{67} +6.00000 q^{71} +(7.50000 - 12.9904i) q^{73} +(2.00000 + 1.73205i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{83} -18.0000 q^{85} +(4.00000 + 6.92820i) q^{89} +(1.50000 - 2.59808i) q^{95} -6.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{5} - q^{7} + 3 q^{9} + q^{11} + 6 q^{17} + q^{19} + 3 q^{23} - 4 q^{25} + 12 q^{29} - 2 q^{31} + 15 q^{35} + 12 q^{41} + 18 q^{43} + 9 q^{45} + 3 q^{47} - 13 q^{49} + 2 q^{53} - 6 q^{55} + 12 q^{59} - 11 q^{61} - 15 q^{63} + 8 q^{67} + 12 q^{71} + 15 q^{73} + 4 q^{77} + 12 q^{79} - 9 q^{81} + 14 q^{83} - 36 q^{85} + 8 q^{89} + 3 q^{95} - 12 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(799\) \(913\) \(1009\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0 0
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 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
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 7.50000 2.59808i 1.26773 0.439155i
\(36\) 0 0
\(37\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 9.00000 1.37249 0.686244 0.727372i \(-0.259258\pi\)
0.686244 + 0.727372i \(0.259258\pi\)
\(44\) 0 0
\(45\) 4.50000 7.79423i 0.670820 1.16190i
\(46\) 0 0
\(47\) 1.50000 + 2.59808i 0.218797 + 0.378968i 0.954441 0.298401i \(-0.0964533\pi\)
−0.735643 + 0.677369i \(0.763120\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 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
\(61\) −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i \(-0.917971\pi\)
0.262776 0.964857i \(-0.415362\pi\)
\(62\) 0 0
\(63\) −7.50000 + 2.59808i −0.944911 + 0.327327i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000 6.92820i 0.488678 0.846415i −0.511237 0.859440i \(-0.670813\pi\)
0.999915 + 0.0130248i \(0.00414604\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 7.50000 12.9904i 0.877809 1.52041i 0.0240681 0.999710i \(-0.492338\pi\)
0.853740 0.520699i \(-0.174329\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.00000 + 1.73205i 0.227921 + 0.197386i
\(78\) 0 0
\(79\) 6.00000 + 10.3923i 0.675053 + 1.16923i 0.976453 + 0.215728i \(0.0692125\pi\)
−0.301401 + 0.953498i \(0.597454\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 7.00000 0.768350 0.384175 0.923260i \(-0.374486\pi\)
0.384175 + 0.923260i \(0.374486\pi\)
\(84\) 0 0
\(85\) −18.0000 −1.95237
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.00000 + 6.92820i 0.423999 + 0.734388i 0.996326 0.0856373i \(-0.0272926\pi\)
−0.572327 + 0.820025i \(0.693959\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.50000 2.59808i 0.153897 0.266557i
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 0 0
\(103\) 7.00000 + 12.1244i 0.689730 + 1.19465i 0.971925 + 0.235291i \(0.0756043\pi\)
−0.282194 + 0.959357i \(0.591062\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 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
\(109\) −2.00000 + 3.46410i −0.191565 + 0.331801i −0.945769 0.324840i \(-0.894690\pi\)
0.754204 + 0.656640i \(0.228023\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 12.0000 + 10.3923i 1.10004 + 0.952661i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.00000 + 6.92820i 0.349482 + 0.605320i 0.986157 0.165812i \(-0.0530244\pi\)
−0.636676 + 0.771132i \(0.719691\pi\)
\(132\) 0 0
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 0 0
\(139\) −17.0000 −1.44192 −0.720961 0.692976i \(-0.756299\pi\)
−0.720961 + 0.692976i \(0.756299\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −9.00000 15.5885i −0.747409 1.29455i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i \(-0.127452\pi\)
−0.798019 + 0.602632i \(0.794119\pi\)
\(150\) 0 0
\(151\) −3.00000 + 5.19615i −0.244137 + 0.422857i −0.961888 0.273442i \(-0.911838\pi\)
0.717752 + 0.696299i \(0.245171\pi\)
\(152\) 0 0
\(153\) 18.0000 1.45521
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) 0 0
\(157\) 3.50000 6.06218i 0.279330 0.483814i −0.691888 0.722005i \(-0.743221\pi\)
0.971219 + 0.238190i \(0.0765542\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −7.50000 + 2.59808i −0.591083 + 0.204757i
\(162\) 0 0
\(163\) 9.50000 + 16.4545i 0.744097 + 1.28881i 0.950615 + 0.310372i \(0.100454\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −14.0000 −1.08335 −0.541676 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) −1.50000 + 2.59808i −0.114708 + 0.198680i
\(172\) 0 0
\(173\) −4.00000 6.92820i −0.304114 0.526742i 0.672949 0.739689i \(-0.265027\pi\)
−0.977064 + 0.212947i \(0.931694\pi\)
\(174\) 0 0
\(175\) −8.00000 6.92820i −0.604743 0.523723i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i \(-0.711416\pi\)
0.990134 + 0.140122i \(0.0447496\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −3.00000 5.19615i −0.219382 0.379980i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.50000 4.33013i −0.180894 0.313317i 0.761291 0.648410i \(-0.224566\pi\)
−0.942185 + 0.335093i \(0.891232\pi\)
\(192\) 0 0
\(193\) 10.0000 17.3205i 0.719816 1.24676i −0.241257 0.970461i \(-0.577560\pi\)
0.961073 0.276296i \(-0.0891071\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) −2.50000 + 4.33013i −0.177220 + 0.306955i −0.940927 0.338608i \(-0.890044\pi\)
0.763707 + 0.645563i \(0.223377\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.00000 + 15.5885i −0.210559 + 1.09410i
\(204\) 0 0
\(205\) −9.00000 15.5885i −0.628587 1.08875i
\(206\) 0 0
\(207\) −4.50000 + 7.79423i −0.312772 + 0.541736i
\(208\) 0 0
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −13.5000 23.3827i −0.920692 1.59469i
\(216\) 0 0
\(217\) −4.00000 3.46410i −0.271538 0.235159i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −2.00000 −0.133930 −0.0669650 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) 0 0
\(225\) −12.0000 −0.800000
\(226\) 0 0
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i \(-0.318310\pi\)
−0.998886 + 0.0471787i \(0.984977\pi\)
\(234\) 0 0
\(235\) 4.50000 7.79423i 0.293548 0.508439i
\(236\) 0 0
\(237\) 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
\(241\) −2.00000 + 3.46410i −0.128831 + 0.223142i −0.923224 0.384262i \(-0.874456\pi\)
0.794393 + 0.607404i \(0.207789\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.00000 + 20.7846i 0.191663 + 1.32788i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) 3.00000 0.188608
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.0000 + 19.0526i 0.686161 + 1.18847i 0.973070 + 0.230508i \(0.0740389\pi\)
−0.286909 + 0.957958i \(0.592628\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 9.00000 + 15.5885i 0.557086 + 0.964901i
\(262\) 0 0
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) −7.50000 12.9904i −0.455593 0.789109i 0.543130 0.839649i \(-0.317239\pi\)
−0.998722 + 0.0505395i \(0.983906\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) 0 0
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) 0 0
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −0.500000 + 0.866025i −0.0297219 + 0.0514799i −0.880504 0.474039i \(-0.842796\pi\)
0.850782 + 0.525519i \(0.176129\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.00000 + 15.5885i −0.177084 + 0.920158i
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) −36.0000 −2.09600
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −4.50000 + 23.3827i −0.259376 + 1.34776i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −16.5000 + 28.5788i −0.944787 + 1.63642i
\(306\) 0 0
\(307\) 22.0000 1.25561 0.627803 0.778372i \(-0.283954\pi\)
0.627803 + 0.778372i \(0.283954\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 6.50000 + 11.2583i 0.367402 + 0.636358i 0.989158 0.146852i \(-0.0469141\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) 18.0000 + 15.5885i 1.01419 + 0.878310i
\(316\) 0 0
\(317\) 1.00000 + 1.73205i 0.0561656 + 0.0972817i 0.892741 0.450570i \(-0.148779\pi\)
−0.836576 + 0.547852i \(0.815446\pi\)
\(318\) 0 0
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −7.50000 + 2.59808i −0.413488 + 0.143237i
\(330\) 0 0
\(331\) 11.0000 + 19.0526i 0.604615 + 1.04722i 0.992112 + 0.125353i \(0.0400062\pi\)
−0.387498 + 0.921871i \(0.626660\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −24.0000 −1.31126
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.00000 + 1.73205i 0.0541530 + 0.0937958i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.50000 4.33013i 0.134207 0.232453i −0.791087 0.611703i \(-0.790485\pi\)
0.925294 + 0.379250i \(0.123818\pi\)
\(348\) 0 0
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 15.0000 25.9808i 0.798369 1.38282i −0.122308 0.992492i \(-0.539030\pi\)
0.920677 0.390324i \(-0.127637\pi\)
\(354\) 0 0
\(355\) −9.00000 15.5885i −0.477670 0.827349i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.50000 + 4.33013i 0.131945 + 0.228535i 0.924426 0.381361i \(-0.124544\pi\)
−0.792481 + 0.609896i \(0.791211\pi\)
\(360\) 0 0
\(361\) −0.500000 + 0.866025i −0.0263158 + 0.0455803i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −45.0000 −2.35541
\(366\) 0 0
\(367\) 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 0 0
\(369\) 9.00000 + 15.5885i 0.468521 + 0.811503i
\(370\) 0 0
\(371\) 4.00000 + 3.46410i 0.207670 + 0.179847i
\(372\) 0 0
\(373\) −16.0000 27.7128i −0.828449 1.43492i −0.899255 0.437425i \(-0.855891\pi\)
0.0708063 0.997490i \(-0.477443\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.00000 + 6.92820i 0.204390 + 0.354015i 0.949938 0.312437i \(-0.101145\pi\)
−0.745548 + 0.666452i \(0.767812\pi\)
\(384\) 0 0
\(385\) 1.50000 7.79423i 0.0764471 0.397231i
\(386\) 0 0
\(387\) 13.5000 + 23.3827i 0.686244 + 1.18861i
\(388\) 0 0
\(389\) −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 18.0000 31.1769i 0.905678 1.56868i
\(396\) 0 0
\(397\) −17.0000 29.4449i −0.853206 1.47780i −0.878300 0.478110i \(-0.841322\pi\)
0.0250943 0.999685i \(-0.492011\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 27.0000 1.34164
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.00000 + 1.73205i −0.0494468 + 0.0856444i −0.889689 0.456566i \(-0.849079\pi\)
0.840243 + 0.542211i \(0.182412\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 24.0000 + 20.7846i 1.18096 + 1.02274i
\(414\) 0 0
\(415\) −10.5000 18.1865i −0.515425 0.892742i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.00000 −0.244266 −0.122133 0.992514i \(-0.538973\pi\)
−0.122133 + 0.992514i \(0.538973\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) 0 0
\(425\) 12.0000 + 20.7846i 0.582086 + 1.00820i
\(426\) 0 0
\(427\) 27.5000 9.52628i 1.33082 0.461009i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.00000 5.19615i 0.144505 0.250290i −0.784683 0.619897i \(-0.787174\pi\)
0.929188 + 0.369607i \(0.120508\pi\)
\(432\) 0 0
\(433\) −24.0000 −1.15337 −0.576683 0.816968i \(-0.695653\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.50000 + 2.59808i −0.0717547 + 0.124283i
\(438\) 0 0
\(439\) −10.0000 17.3205i −0.477274 0.826663i 0.522387 0.852709i \(-0.325042\pi\)
−0.999661 + 0.0260459i \(0.991708\pi\)
\(440\) 0 0
\(441\) −3.00000 20.7846i −0.142857 0.989743i
\(442\) 0 0
\(443\) −14.0000 24.2487i −0.665160 1.15209i −0.979242 0.202695i \(-0.935030\pi\)
0.314082 0.949396i \(-0.398303\pi\)
\(444\) 0 0
\(445\) 12.0000 20.7846i 0.568855 0.985285i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) 0 0
\(451\) 3.00000 5.19615i 0.141264 0.244677i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 12.5000 + 21.6506i 0.584725 + 1.01277i 0.994910 + 0.100771i \(0.0321310\pi\)
−0.410184 + 0.912003i \(0.634536\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.00000 0.0465746 0.0232873 0.999729i \(-0.492587\pi\)
0.0232873 + 0.999729i \(0.492587\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.5000 28.5788i −0.763529 1.32247i −0.941021 0.338349i \(-0.890132\pi\)
0.177492 0.984122i \(-0.443202\pi\)
\(468\) 0 0
\(469\) 16.0000 + 13.8564i 0.738811 + 0.639829i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.50000 7.79423i 0.206910 0.358379i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i \(-0.855166\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.00000 + 15.5885i 0.408669 + 0.707835i
\(486\) 0 0
\(487\) −13.0000 + 22.5167i −0.589086 + 1.02033i 0.405266 + 0.914199i \(0.367179\pi\)
−0.994352 + 0.106129i \(0.966154\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −33.0000 −1.48927 −0.744635 0.667472i \(-0.767376\pi\)
−0.744635 + 0.667472i \(0.767376\pi\)
\(492\) 0 0
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) 0 0
\(495\) −4.50000 7.79423i −0.202260 0.350325i
\(496\) 0 0
\(497\) −3.00000 + 15.5885i −0.134568 + 0.699238i
\(498\) 0 0
\(499\) 6.50000 + 11.2583i 0.290980 + 0.503992i 0.974042 0.226369i \(-0.0726854\pi\)
−0.683062 + 0.730361i \(0.739352\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.00000 0.0445878 0.0222939 0.999751i \(-0.492903\pi\)
0.0222939 + 0.999751i \(0.492903\pi\)
\(504\) 0 0
\(505\) 27.0000 1.20148
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) 30.0000 + 25.9808i 1.32712 + 1.14932i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 21.0000 36.3731i 0.925371 1.60279i
\(516\) 0 0
\(517\) 3.00000 0.131940
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.00000 10.3923i 0.262865 0.455295i −0.704137 0.710064i \(-0.748666\pi\)
0.967002 + 0.254769i \(0.0819994\pi\)
\(522\) 0 0
\(523\) −9.00000 15.5885i −0.393543 0.681636i 0.599371 0.800471i \(-0.295417\pi\)
−0.992914 + 0.118835i \(0.962084\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 36.0000 1.56227
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 6.00000 10.3923i 0.259403 0.449299i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.50000 + 4.33013i −0.236902 + 0.186512i
\(540\) 0 0
\(541\) −5.50000 9.52628i −0.236463 0.409567i 0.723234 0.690604i \(-0.242655\pi\)
−0.959697 + 0.281037i \(0.909322\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.0000 0.514024
\(546\) 0 0
\(547\) −2.00000 −0.0855138 −0.0427569 0.999086i \(-0.513614\pi\)
−0.0427569 + 0.999086i \(0.513614\pi\)
\(548\) 0 0
\(549\) 16.5000 28.5788i 0.704203 1.21972i
\(550\) 0 0
\(551\) 3.00000 + 5.19615i 0.127804 + 0.221364i
\(552\) 0 0
\(553\) −30.0000 + 10.3923i −1.27573 + 0.441926i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.50000 12.9904i 0.317785 0.550420i −0.662240 0.749291i \(-0.730394\pi\)
0.980026 + 0.198871i \(0.0637276\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.0000 + 20.7846i −0.505740 + 0.875967i 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) 0 0
\(565\) 27.0000 + 46.7654i 1.13590 + 1.96743i
\(566\) 0 0
\(567\) −18.0000 15.5885i −0.755929 0.654654i
\(568\) 0 0
\(569\) 9.00000 + 15.5885i 0.377300 + 0.653502i 0.990668 0.136295i \(-0.0435194\pi\)
−0.613369 + 0.789797i \(0.710186\pi\)
\(570\) 0 0
\(571\) −11.5000 + 19.9186i −0.481260 + 0.833567i −0.999769 0.0215055i \(-0.993154\pi\)
0.518509 + 0.855072i \(0.326487\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −3.50000 + 6.06218i −0.145707 + 0.252372i −0.929636 0.368478i \(-0.879879\pi\)
0.783930 + 0.620850i \(0.213212\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.50000 + 18.1865i −0.145204 + 0.754505i
\(582\) 0 0
\(583\) −1.00000 1.73205i −0.0414158 0.0717342i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.50000 2.59808i −0.0615976 0.106690i 0.833582 0.552396i \(-0.186286\pi\)
−0.895180 + 0.445705i \(0.852953\pi\)
\(594\) 0 0
\(595\) 9.00000 46.7654i 0.368964 1.91719i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.00000 + 12.1244i −0.286012 + 0.495388i −0.972854 0.231419i \(-0.925663\pi\)
0.686842 + 0.726807i \(0.258996\pi\)
\(600\) 0 0
\(601\) −16.0000 −0.652654 −0.326327 0.945257i \(-0.605811\pi\)
−0.326327 + 0.945257i \(0.605811\pi\)
\(602\) 0 0
\(603\) 24.0000 0.977356
\(604\) 0 0
\(605\) 15.0000 25.9808i 0.609837 1.05627i
\(606\) 0 0
\(607\) −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 3.00000 5.19615i 0.121169 0.209871i −0.799060 0.601251i \(-0.794669\pi\)
0.920229 + 0.391381i \(0.128002\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 45.0000 1.81163 0.905816 0.423672i \(-0.139259\pi\)
0.905816 + 0.423672i \(0.139259\pi\)
\(618\) 0 0
\(619\) 0.500000 0.866025i 0.0200967 0.0348085i −0.855802 0.517303i \(-0.826936\pi\)
0.875899 + 0.482495i \(0.160269\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −20.0000 + 6.92820i −0.801283 + 0.277573i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −23.0000 −0.915616 −0.457808 0.889051i \(-0.651365\pi\)
−0.457808 + 0.889051i \(0.651365\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 24.0000 + 41.5692i 0.952411 + 1.64962i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 9.00000 + 15.5885i 0.356034 + 0.616670i
\(640\) 0 0
\(641\) −22.0000 + 38.1051i −0.868948 + 1.50506i −0.00587459 + 0.999983i \(0.501870\pi\)
−0.863073 + 0.505079i \(0.831463\pi\)
\(642\) 0 0
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12.5000 + 21.6506i −0.491426 + 0.851174i −0.999951 0.00987260i \(-0.996857\pi\)
0.508526 + 0.861047i \(0.330191\pi\)
\(648\) 0 0
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.00000 12.1244i −0.273931 0.474463i 0.695934 0.718106i \(-0.254991\pi\)
−0.969865 + 0.243643i \(0.921657\pi\)
\(654\) 0 0
\(655\) 12.0000 20.7846i 0.468879 0.812122i
\(656\) 0 0
\(657\) 45.0000 1.75562
\(658\) 0 0
\(659\) 50.0000 1.94772 0.973862 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6.00000 + 5.19615i 0.232670 + 0.201498i
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −11.0000 −0.424650
\(672\) 0 0
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 24.0000 + 41.5692i 0.922395 + 1.59763i 0.795698 + 0.605693i \(0.207104\pi\)
0.126697 + 0.991941i \(0.459562\pi\)
\(678\) 0 0
\(679\) 3.00000 15.5885i 0.115129 0.598230i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 21.0000 36.3731i 0.803543 1.39178i −0.113728 0.993512i \(-0.536279\pi\)
0.917270 0.398265i \(-0.130387\pi\)
\(684\) 0 0
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 2.00000 + 3.46410i 0.0760836 + 0.131781i 0.901557 0.432660i \(-0.142425\pi\)
−0.825473 + 0.564441i \(0.809092\pi\)
\(692\) 0 0
\(693\) −1.50000 + 7.79423i −0.0569803 + 0.296078i
\(694\) 0 0
\(695\) 25.5000 + 44.1673i 0.967270 + 1.67536i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19.0000 −0.717620 −0.358810 0.933411i \(-0.616817\pi\)
−0.358810 + 0.933411i \(0.616817\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −18.0000 15.5885i −0.676960 0.586264i
\(708\) 0 0
\(709\) −6.50000 11.2583i −0.244113 0.422815i 0.717769 0.696281i \(-0.245163\pi\)
−0.961882 + 0.273466i \(0.911830\pi\)
\(710\) 0 0
\(711\) −18.0000 + 31.1769i −0.675053 + 1.16923i
\(712\) 0 0
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.0000 27.7128i −0.596699 1.03351i −0.993305 0.115524i \(-0.963145\pi\)
0.396605 0.917989i \(-0.370188\pi\)
\(720\) 0 0
\(721\) −35.0000 + 12.1244i −1.30347 + 0.451535i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −12.0000 + 20.7846i −0.445669 + 0.771921i
\(726\) 0 0
\(727\) −33.0000 −1.22390 −0.611951 0.790896i \(-0.709615\pi\)
−0.611951 + 0.790896i \(0.709615\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 27.0000 46.7654i 0.998631 1.72968i
\(732\) 0 0
\(733\) −13.0000 22.5167i −0.480166 0.831672i 0.519575 0.854425i \(-0.326090\pi\)
−0.999741 + 0.0227529i \(0.992757\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.00000 6.92820i −0.147342 0.255204i
\(738\) 0 0
\(739\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) 0 0
\(745\) 4.50000 7.79423i 0.164867 0.285558i
\(746\) 0 0
\(747\) 10.5000 + 18.1865i 0.384175 + 0.665410i
\(748\) 0 0
\(749\) −10.0000 + 3.46410i −0.365392 + 0.126576i
\(750\) 0 0
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 18.0000 0.655087
\(756\) 0 0
\(757\) −53.0000 −1.92632 −0.963159 0.268933i \(-0.913329\pi\)
−0.963159 + 0.268933i \(0.913329\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12.5000 21.6506i −0.453125 0.784835i 0.545454 0.838141i \(-0.316357\pi\)
−0.998578 + 0.0533061i \(0.983024\pi\)
\(762\) 0 0
\(763\) −8.00000 6.92820i −0.289619 0.250818i
\(764\) 0 0
\(765\) −27.0000 46.7654i −0.976187 1.69081i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 19.0000 0.685158 0.342579 0.939489i \(-0.388700\pi\)
0.342579 + 0.939489i \(0.388700\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 18.0000 31.1769i 0.647415 1.12136i −0.336323 0.941747i \(-0.609183\pi\)
0.983738 0.179609i \(-0.0574833\pi\)
\(774\) 0 0
\(775\) −4.00000 6.92820i −0.143684 0.248868i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.00000 + 5.19615i 0.107486 + 0.186171i
\(780\) 0 0
\(781\) 3.00000 5.19615i 0.107348 0.185933i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −21.0000 −0.749522
\(786\) 0 0
\(787\) −26.0000 + 45.0333i −0.926800 + 1.60526i −0.138159 + 0.990410i \(0.544119\pi\)
−0.788641 + 0.614855i \(0.789215\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9.00000 46.7654i 0.320003 1.66279i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 44.0000 1.55856 0.779280 0.626676i \(-0.215585\pi\)
0.779280 + 0.626676i \(0.215585\pi\)
\(798\) 0 0
\(799\) 18.0000 0.636794
\(800\) 0 0
\(801\) −12.0000 + 20.7846i