Properties

Label 1600.2.n.e.1407.1
Level $1600$
Weight $2$
Character 1600.1407
Analytic conductor $12.776$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.n (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1407.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1600.1407
Dual form 1600.2.n.e.1343.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{3} +(1.00000 - 1.00000i) q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{3} +(1.00000 - 1.00000i) q^{7} -1.00000i q^{9} +6.00000i q^{11} +(-1.00000 + 1.00000i) q^{13} +(-1.00000 - 1.00000i) q^{17} -4.00000 q^{19} -2.00000 q^{21} +(-5.00000 - 5.00000i) q^{23} +(-4.00000 + 4.00000i) q^{27} -8.00000i q^{29} +2.00000i q^{31} +(6.00000 - 6.00000i) q^{33} +(-5.00000 - 5.00000i) q^{37} +2.00000 q^{39} +6.00000 q^{41} +(3.00000 + 3.00000i) q^{43} +(-7.00000 + 7.00000i) q^{47} +5.00000i q^{49} +2.00000i q^{51} +(-1.00000 + 1.00000i) q^{53} +(4.00000 + 4.00000i) q^{57} -4.00000 q^{59} -2.00000 q^{61} +(-1.00000 - 1.00000i) q^{63} +(-7.00000 + 7.00000i) q^{67} +10.0000i q^{69} -6.00000i q^{71} +(-9.00000 + 9.00000i) q^{73} +(6.00000 + 6.00000i) q^{77} -8.00000 q^{79} +5.00000 q^{81} +(-5.00000 - 5.00000i) q^{83} +(-8.00000 + 8.00000i) q^{87} +2.00000i q^{91} +(2.00000 - 2.00000i) q^{93} +(3.00000 + 3.00000i) q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} + 2 q^{7} - 2 q^{13} - 2 q^{17} - 8 q^{19} - 4 q^{21} - 10 q^{23} - 8 q^{27} + 12 q^{33} - 10 q^{37} + 4 q^{39} + 12 q^{41} + 6 q^{43} - 14 q^{47} - 2 q^{53} + 8 q^{57} - 8 q^{59} - 4 q^{61} - 2 q^{63} - 14 q^{67} - 18 q^{73} + 12 q^{77} - 16 q^{79} + 10 q^{81} - 10 q^{83} - 16 q^{87} + 4 q^{93} + 6 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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
\(3\) −1.00000 1.00000i −0.577350 0.577350i 0.356822 0.934172i \(-0.383860\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 1.00000i 0.377964 0.377964i −0.492403 0.870367i \(-0.663881\pi\)
0.870367 + 0.492403i \(0.163881\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 6.00000i 1.80907i 0.426401 + 0.904534i \(0.359781\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.00000i −0.277350 + 0.277350i −0.832050 0.554700i \(-0.812833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.00000 1.00000i −0.242536 0.242536i 0.575363 0.817898i \(-0.304861\pi\)
−0.817898 + 0.575363i \(0.804861\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) −5.00000 5.00000i −1.04257 1.04257i −0.999053 0.0435195i \(-0.986143\pi\)
−0.0435195 0.999053i \(-0.513857\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4.00000 + 4.00000i −0.769800 + 0.769800i
\(28\) 0 0
\(29\) 8.00000i 1.48556i −0.669534 0.742781i \(-0.733506\pi\)
0.669534 0.742781i \(-0.266494\pi\)
\(30\) 0 0
\(31\) 2.00000i 0.359211i 0.983739 + 0.179605i \(0.0574821\pi\)
−0.983739 + 0.179605i \(0.942518\pi\)
\(32\) 0 0
\(33\) 6.00000 6.00000i 1.04447 1.04447i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.00000 5.00000i −0.821995 0.821995i 0.164399 0.986394i \(-0.447432\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 3.00000 + 3.00000i 0.457496 + 0.457496i 0.897833 0.440337i \(-0.145141\pi\)
−0.440337 + 0.897833i \(0.645141\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.00000 + 7.00000i −1.02105 + 1.02105i −0.0212814 + 0.999774i \(0.506775\pi\)
−0.999774 + 0.0212814i \(0.993225\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) 2.00000i 0.280056i
\(52\) 0 0
\(53\) −1.00000 + 1.00000i −0.137361 + 0.137361i −0.772444 0.635083i \(-0.780966\pi\)
0.635083 + 0.772444i \(0.280966\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.00000 + 4.00000i 0.529813 + 0.529813i
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) −1.00000 1.00000i −0.125988 0.125988i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.00000 + 7.00000i −0.855186 + 0.855186i −0.990766 0.135580i \(-0.956710\pi\)
0.135580 + 0.990766i \(0.456710\pi\)
\(68\) 0 0
\(69\) 10.0000i 1.20386i
\(70\) 0 0
\(71\) 6.00000i 0.712069i −0.934473 0.356034i \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) 0 0
\(73\) −9.00000 + 9.00000i −1.05337 + 1.05337i −0.0548772 + 0.998493i \(0.517477\pi\)
−0.998493 + 0.0548772i \(0.982523\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.00000 + 6.00000i 0.683763 + 0.683763i
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) −5.00000 5.00000i −0.548821 0.548821i 0.377279 0.926100i \(-0.376860\pi\)
−0.926100 + 0.377279i \(0.876860\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −8.00000 + 8.00000i −0.857690 + 0.857690i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 2.00000i 0.209657i
\(92\) 0 0
\(93\) 2.00000 2.00000i 0.207390 0.207390i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 3.00000 + 3.00000i 0.304604 + 0.304604i 0.842812 0.538208i \(-0.180899\pi\)
−0.538208 + 0.842812i \(0.680899\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 3.00000 + 3.00000i 0.295599 + 0.295599i 0.839287 0.543688i \(-0.182973\pi\)
−0.543688 + 0.839287i \(0.682973\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 + 3.00000i −0.290021 + 0.290021i −0.837088 0.547068i \(-0.815744\pi\)
0.547068 + 0.837088i \(0.315744\pi\)
\(108\) 0 0
\(109\) 4.00000i 0.383131i −0.981480 0.191565i \(-0.938644\pi\)
0.981480 0.191565i \(-0.0613564\pi\)
\(110\) 0 0
\(111\) 10.0000i 0.949158i
\(112\) 0 0
\(113\) 3.00000 3.00000i 0.282216 0.282216i −0.551776 0.833992i \(-0.686050\pi\)
0.833992 + 0.551776i \(0.186050\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 + 1.00000i 0.0924500 + 0.0924500i
\(118\) 0 0
\(119\) −2.00000 −0.183340
\(120\) 0 0
\(121\) −25.0000 −2.27273
\(122\) 0 0
\(123\) −6.00000 6.00000i −0.541002 0.541002i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.00000 5.00000i 0.443678 0.443678i −0.449568 0.893246i \(-0.648422\pi\)
0.893246 + 0.449568i \(0.148422\pi\)
\(128\) 0 0
\(129\) 6.00000i 0.528271i
\(130\) 0 0
\(131\) 2.00000i 0.174741i −0.996176 0.0873704i \(-0.972154\pi\)
0.996176 0.0873704i \(-0.0278464\pi\)
\(132\) 0 0
\(133\) −4.00000 + 4.00000i −0.346844 + 0.346844i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −13.0000 13.0000i −1.11066 1.11066i −0.993061 0.117604i \(-0.962479\pi\)
−0.117604 0.993061i \(-0.537521\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) 14.0000 1.17901
\(142\) 0 0
\(143\) −6.00000 6.00000i −0.501745 0.501745i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.00000 5.00000i 0.412393 0.412393i
\(148\) 0 0
\(149\) 12.0000i 0.983078i 0.870855 + 0.491539i \(0.163566\pi\)
−0.870855 + 0.491539i \(0.836434\pi\)
\(150\) 0 0
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) 0 0
\(153\) −1.00000 + 1.00000i −0.0808452 + 0.0808452i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 3.00000 + 3.00000i 0.239426 + 0.239426i 0.816612 0.577186i \(-0.195849\pi\)
−0.577186 + 0.816612i \(0.695849\pi\)
\(158\) 0 0
\(159\) 2.00000 0.158610
\(160\) 0 0
\(161\) −10.0000 −0.788110
\(162\) 0 0
\(163\) −1.00000 1.00000i −0.0783260 0.0783260i 0.666858 0.745184i \(-0.267639\pi\)
−0.745184 + 0.666858i \(0.767639\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.00000 5.00000i 0.386912 0.386912i −0.486673 0.873584i \(-0.661790\pi\)
0.873584 + 0.486673i \(0.161790\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) 4.00000i 0.305888i
\(172\) 0 0
\(173\) 7.00000 7.00000i 0.532200 0.532200i −0.389026 0.921227i \(-0.627189\pi\)
0.921227 + 0.389026i \(0.127189\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.00000 + 4.00000i 0.300658 + 0.300658i
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 2.00000 + 2.00000i 0.147844 + 0.147844i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 6.00000 6.00000i 0.438763 0.438763i
\(188\) 0 0
\(189\) 8.00000i 0.581914i
\(190\) 0 0
\(191\) 10.0000i 0.723575i 0.932261 + 0.361787i \(0.117833\pi\)
−0.932261 + 0.361787i \(0.882167\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.00000i −0.0719816 + 0.0719816i −0.742181 0.670199i \(-0.766209\pi\)
0.670199 + 0.742181i \(0.266209\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.00000 1.00000i −0.0712470 0.0712470i 0.670585 0.741832i \(-0.266043\pi\)
−0.741832 + 0.670585i \(0.766043\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 14.0000 0.987484
\(202\) 0 0
\(203\) −8.00000 8.00000i −0.561490 0.561490i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −5.00000 + 5.00000i −0.347524 + 0.347524i
\(208\) 0 0
\(209\) 24.0000i 1.66011i
\(210\) 0 0
\(211\) 10.0000i 0.688428i −0.938891 0.344214i \(-0.888145\pi\)
0.938891 0.344214i \(-0.111855\pi\)
\(212\) 0 0
\(213\) −6.00000 + 6.00000i −0.411113 + 0.411113i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 2.00000 + 2.00000i 0.135769 + 0.135769i
\(218\) 0 0
\(219\) 18.0000 1.21633
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) 0 0
\(223\) 19.0000 + 19.0000i 1.27233 + 1.27233i 0.944860 + 0.327474i \(0.106197\pi\)
0.327474 + 0.944860i \(0.393803\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.0000 13.0000i 0.862840 0.862840i −0.128827 0.991667i \(-0.541121\pi\)
0.991667 + 0.128827i \(0.0411211\pi\)
\(228\) 0 0
\(229\) 16.0000i 1.05731i −0.848837 0.528655i \(-0.822697\pi\)
0.848837 0.528655i \(-0.177303\pi\)
\(230\) 0 0
\(231\) 12.0000i 0.789542i
\(232\) 0 0
\(233\) −13.0000 + 13.0000i −0.851658 + 0.851658i −0.990337 0.138679i \(-0.955714\pi\)
0.138679 + 0.990337i \(0.455714\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 8.00000 + 8.00000i 0.519656 + 0.519656i
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) 7.00000 + 7.00000i 0.449050 + 0.449050i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.00000 4.00000i 0.254514 0.254514i
\(248\) 0 0
\(249\) 10.0000i 0.633724i
\(250\) 0 0
\(251\) 18.0000i 1.13615i −0.822977 0.568075i \(-0.807688\pi\)
0.822977 0.568075i \(-0.192312\pi\)
\(252\) 0 0
\(253\) 30.0000 30.0000i 1.88608 1.88608i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.0000 + 11.0000i 0.686161 + 0.686161i 0.961381 0.275220i \(-0.0887507\pi\)
−0.275220 + 0.961381i \(0.588751\pi\)
\(258\) 0 0
\(259\) −10.0000 −0.621370
\(260\) 0 0
\(261\) −8.00000 −0.495188
\(262\) 0 0
\(263\) −9.00000 9.00000i −0.554964 0.554964i 0.372906 0.927869i \(-0.378362\pi\)
−0.927869 + 0.372906i \(0.878362\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.00000i 0.243884i 0.992537 + 0.121942i \(0.0389122\pi\)
−0.992537 + 0.121942i \(0.961088\pi\)
\(270\) 0 0
\(271\) 22.0000i 1.33640i −0.743980 0.668202i \(-0.767064\pi\)
0.743980 0.668202i \(-0.232936\pi\)
\(272\) 0 0
\(273\) 2.00000 2.00000i 0.121046 0.121046i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −9.00000 9.00000i −0.540758 0.540758i 0.382993 0.923751i \(-0.374893\pi\)
−0.923751 + 0.382993i \(0.874893\pi\)
\(278\) 0 0
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) 15.0000 + 15.0000i 0.891657 + 0.891657i 0.994679 0.103022i \(-0.0328511\pi\)
−0.103022 + 0.994679i \(0.532851\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.00000 6.00000i 0.354169 0.354169i
\(288\) 0 0
\(289\) 15.0000i 0.882353i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) 0 0
\(293\) −17.0000 + 17.0000i −0.993151 + 0.993151i −0.999977 0.00682610i \(-0.997827\pi\)
0.00682610 + 0.999977i \(0.497827\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −24.0000 24.0000i −1.39262 1.39262i
\(298\) 0 0
\(299\) 10.0000 0.578315
\(300\) 0 0
\(301\) 6.00000 0.345834
\(302\) 0 0
\(303\) 6.00000 + 6.00000i 0.344691 + 0.344691i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −7.00000 + 7.00000i −0.399511 + 0.399511i −0.878061 0.478549i \(-0.841163\pi\)
0.478549 + 0.878061i \(0.341163\pi\)
\(308\) 0 0
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 22.0000i 1.24751i −0.781622 0.623753i \(-0.785607\pi\)
0.781622 0.623753i \(-0.214393\pi\)
\(312\) 0 0
\(313\) 15.0000 15.0000i 0.847850 0.847850i −0.142014 0.989865i \(-0.545358\pi\)
0.989865 + 0.142014i \(0.0453579\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −25.0000 25.0000i −1.40414 1.40414i −0.786318 0.617822i \(-0.788015\pi\)
−0.617822 0.786318i \(-0.711985\pi\)
\(318\) 0 0
\(319\) 48.0000 2.68748
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) 4.00000 + 4.00000i 0.222566 + 0.222566i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −4.00000 + 4.00000i −0.221201 + 0.221201i
\(328\) 0 0
\(329\) 14.0000i 0.771845i
\(330\) 0 0
\(331\) 18.0000i 0.989369i −0.869072 0.494685i \(-0.835284\pi\)
0.869072 0.494685i \(-0.164716\pi\)
\(332\) 0 0
\(333\) −5.00000 + 5.00000i −0.273998 + 0.273998i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.00000 1.00000i −0.0544735 0.0544735i 0.679345 0.733819i \(-0.262264\pi\)
−0.733819 + 0.679345i \(0.762264\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.00000 9.00000i 0.483145 0.483145i −0.422989 0.906135i \(-0.639019\pi\)
0.906135 + 0.422989i \(0.139019\pi\)
\(348\) 0 0
\(349\) 32.0000i 1.71292i −0.516213 0.856460i \(-0.672659\pi\)
0.516213 0.856460i \(-0.327341\pi\)
\(350\) 0 0
\(351\) 8.00000i 0.427008i
\(352\) 0 0
\(353\) 15.0000 15.0000i 0.798369 0.798369i −0.184469 0.982838i \(-0.559057\pi\)
0.982838 + 0.184469i \(0.0590565\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.00000 + 2.00000i 0.105851 + 0.105851i
\(358\) 0 0
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 25.0000 + 25.0000i 1.31216 + 1.31216i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 13.0000 13.0000i 0.678594 0.678594i −0.281088 0.959682i \(-0.590695\pi\)
0.959682 + 0.281088i \(0.0906952\pi\)
\(368\) 0 0
\(369\) 6.00000i 0.312348i
\(370\) 0 0
\(371\) 2.00000i 0.103835i
\(372\) 0 0
\(373\) −21.0000 + 21.0000i −1.08734 + 1.08734i −0.0915371 + 0.995802i \(0.529178\pi\)
−0.995802 + 0.0915371i \(0.970822\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 + 8.00000i 0.412021 + 0.412021i
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) −10.0000 −0.512316
\(382\) 0 0
\(383\) −13.0000 13.0000i −0.664269 0.664269i 0.292114 0.956383i \(-0.405641\pi\)
−0.956383 + 0.292114i \(0.905641\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.00000 3.00000i 0.152499 0.152499i
\(388\) 0 0
\(389\) 12.0000i 0.608424i 0.952604 + 0.304212i \(0.0983931\pi\)
−0.952604 + 0.304212i \(0.901607\pi\)
\(390\) 0 0
\(391\) 10.0000i 0.505722i
\(392\) 0 0
\(393\) −2.00000 + 2.00000i −0.100887 + 0.100887i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 19.0000 + 19.0000i 0.953583 + 0.953583i 0.998969 0.0453868i \(-0.0144520\pi\)
−0.0453868 + 0.998969i \(0.514452\pi\)
\(398\) 0 0
\(399\) 8.00000 0.400501
\(400\) 0 0
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 0 0
\(403\) −2.00000 2.00000i −0.0996271 0.0996271i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 30.0000 30.0000i 1.48704 1.48704i
\(408\) 0 0
\(409\) 20.0000i 0.988936i 0.869196 + 0.494468i \(0.164637\pi\)
−0.869196 + 0.494468i \(0.835363\pi\)
\(410\) 0 0
\(411\) 26.0000i 1.28249i
\(412\) 0 0
\(413\) −4.00000 + 4.00000i −0.196827 + 0.196827i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 12.0000 + 12.0000i 0.587643 + 0.587643i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 0 0
\(423\) 7.00000 + 7.00000i 0.340352 + 0.340352i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −2.00000 + 2.00000i −0.0967868 + 0.0967868i
\(428\) 0 0
\(429\) 12.0000i 0.579365i
\(430\) 0 0
\(431\) 38.0000i 1.83040i −0.403005 0.915198i \(-0.632034\pi\)
0.403005 0.915198i \(-0.367966\pi\)
\(432\) 0 0
\(433\) −5.00000 + 5.00000i −0.240285 + 0.240285i −0.816968 0.576683i \(-0.804347\pi\)
0.576683 + 0.816968i \(0.304347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 20.0000 + 20.0000i 0.956730 + 0.956730i
\(438\) 0 0
\(439\) 32.0000 1.52728 0.763638 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) −17.0000 17.0000i −0.807694 0.807694i 0.176590 0.984284i \(-0.443493\pi\)
−0.984284 + 0.176590i \(0.943493\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.0000 12.0000i 0.567581 0.567581i
\(448\) 0 0
\(449\) 4.00000i 0.188772i 0.995536 + 0.0943858i \(0.0300887\pi\)
−0.995536 + 0.0943858i \(0.969911\pi\)
\(450\) 0 0
\(451\) 36.0000i 1.69517i
\(452\) 0 0
\(453\) 18.0000 18.0000i 0.845714 0.845714i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 15.0000 + 15.0000i 0.701670 + 0.701670i 0.964769 0.263099i \(-0.0847444\pi\)
−0.263099 + 0.964769i \(0.584744\pi\)
\(458\) 0 0
\(459\) 8.00000 0.373408
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −17.0000 17.0000i −0.790057 0.790057i 0.191446 0.981503i \(-0.438682\pi\)
−0.981503 + 0.191446i \(0.938682\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.00000 5.00000i 0.231372 0.231372i −0.581893 0.813265i \(-0.697688\pi\)
0.813265 + 0.581893i \(0.197688\pi\)
\(468\) 0 0
\(469\) 14.0000i 0.646460i
\(470\) 0 0
\(471\) 6.00000i 0.276465i
\(472\) 0 0
\(473\) −18.0000 + 18.0000i −0.827641 + 0.827641i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.00000 + 1.00000i 0.0457869 + 0.0457869i
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 10.0000 0.455961
\(482\) 0 0
\(483\) 10.0000 + 10.0000i 0.455016 + 0.455016i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −15.0000 + 15.0000i −0.679715 + 0.679715i −0.959936 0.280221i \(-0.909592\pi\)
0.280221 + 0.959936i \(0.409592\pi\)
\(488\) 0 0
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) 2.00000i 0.0902587i −0.998981 0.0451294i \(-0.985630\pi\)
0.998981 0.0451294i \(-0.0143700\pi\)
\(492\) 0 0
\(493\) −8.00000 + 8.00000i −0.360302 + 0.360302i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.00000 6.00000i −0.269137 0.269137i
\(498\) 0 0
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) −10.0000 −0.446767
\(502\) 0 0
\(503\) 11.0000 + 11.0000i 0.490466 + 0.490466i 0.908453 0.417987i \(-0.137264\pi\)
−0.417987 + 0.908453i \(0.637264\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 11.0000 11.0000i 0.488527 0.488527i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 18.0000i 0.796273i
\(512\) 0 0
\(513\) 16.0000 16.0000i 0.706417 0.706417i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −42.0000 42.0000i −1.84716 1.84716i
\(518\) 0 0
\(519\) −14.0000 −0.614532
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −25.0000 25.0000i −1.09317 1.09317i −0.995188 0.0979859i \(-0.968760\pi\)
−0.0979859 0.995188i \(-0.531240\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00000 2.00000i 0.0871214 0.0871214i
\(528\) 0 0
\(529\) 27.0000i 1.17391i
\(530\) 0 0
\(531\) 4.00000i 0.173585i
\(532\) 0 0
\(533\) −6.00000 + 6.00000i −0.259889 + 0.259889i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −12.0000 12.0000i −0.517838 0.517838i
\(538\) 0 0
\(539\) −30.0000 −1.29219
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 0 0
\(543\) −10.0000 10.0000i −0.429141 0.429141i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3.00000 + 3.00000i −0.128271 + 0.128271i −0.768328 0.640057i \(-0.778911\pi\)
0.640057 + 0.768328i \(0.278911\pi\)
\(548\) 0 0
\(549\) 2.00000i 0.0853579i
\(550\) 0 0
\(551\) 32.0000i 1.36325i
\(552\) 0 0
\(553\) −8.00000 + 8.00000i −0.340195 + 0.340195i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15.0000 + 15.0000i 0.635570 + 0.635570i 0.949460 0.313889i \(-0.101632\pi\)
−0.313889 + 0.949460i \(0.601632\pi\)
\(558\) 0 0
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) −12.0000 −0.506640
\(562\) 0 0
\(563\) 15.0000 + 15.0000i 0.632175 + 0.632175i 0.948613 0.316438i \(-0.102487\pi\)
−0.316438 + 0.948613i \(0.602487\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 5.00000 5.00000i 0.209980 0.209980i
\(568\) 0 0
\(569\) 20.0000i 0.838444i −0.907884 0.419222i \(-0.862303\pi\)
0.907884 0.419222i \(-0.137697\pi\)
\(570\) 0 0
\(571\) 26.0000i 1.08807i −0.839064 0.544033i \(-0.816897\pi\)
0.839064 0.544033i \(-0.183103\pi\)
\(572\) 0 0
\(573\) 10.0000 10.0000i 0.417756 0.417756i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 3.00000 + 3.00000i 0.124892 + 0.124892i 0.766790 0.641898i \(-0.221853\pi\)
−0.641898 + 0.766790i \(0.721853\pi\)
\(578\) 0 0
\(579\) 2.00000 0.0831172
\(580\) 0 0
\(581\) −10.0000 −0.414870
\(582\) 0 0
\(583\) −6.00000 6.00000i −0.248495 0.248495i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 25.0000 25.0000i 1.03186 1.03186i 0.0323850 0.999475i \(-0.489690\pi\)
0.999475 0.0323850i \(-0.0103103\pi\)
\(588\) 0 0
\(589\) 8.00000i 0.329634i
\(590\) 0 0
\(591\) 2.00000i 0.0822690i
\(592\) 0 0
\(593\) 23.0000 23.0000i 0.944497 0.944497i −0.0540419 0.998539i \(-0.517210\pi\)
0.998539 + 0.0540419i \(0.0172104\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 7.00000 + 7.00000i 0.285062 + 0.285062i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −15.0000 + 15.0000i −0.608831 + 0.608831i −0.942641 0.333809i \(-0.891666\pi\)
0.333809 + 0.942641i \(0.391666\pi\)
\(608\) 0 0
\(609\) 16.0000i 0.648353i
\(610\) 0 0
\(611\) 14.0000i 0.566379i
\(612\) 0 0
\(613\) 3.00000 3.00000i 0.121169 0.121169i −0.643922 0.765091i \(-0.722694\pi\)
0.765091 + 0.643922i \(0.222694\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.0000 + 11.0000i 0.442843 + 0.442843i 0.892966 0.450123i \(-0.148620\pi\)
−0.450123 + 0.892966i \(0.648620\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) 40.0000 1.60514
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −24.0000 + 24.0000i −0.958468 + 0.958468i
\(628\) 0 0
\(629\) 10.0000i 0.398726i
\(630\) 0 0
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 0 0
\(633\) −10.0000 + 10.0000i −0.397464 + 0.397464i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.00000 5.00000i −0.198107 0.198107i
\(638\) 0 0
\(639\) −6.00000 −0.237356
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) 11.0000 + 11.0000i 0.433798 + 0.433798i 0.889918 0.456120i \(-0.150761\pi\)
−0.456120 + 0.889918i \(0.650761\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −31.0000 + 31.0000i −1.21874 + 1.21874i −0.250661 + 0.968075i \(0.580648\pi\)
−0.968075 + 0.250661i \(0.919352\pi\)
\(648\) 0 0
\(649\) 24.0000i 0.942082i
\(650\) 0 0
\(651\) 4.00000i 0.156772i
\(652\) 0 0
\(653\) −5.00000 + 5.00000i −0.195665 + 0.195665i −0.798139 0.602474i \(-0.794182\pi\)
0.602474 + 0.798139i \(0.294182\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 9.00000 + 9.00000i 0.351123 + 0.351123i
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 0 0
\(661\) 30.0000 1.16686 0.583432 0.812162i \(-0.301709\pi\)
0.583432 + 0.812162i \(0.301709\pi\)
\(662\) 0 0
\(663\) −2.00000 2.00000i −0.0776736 0.0776736i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −40.0000 + 40.0000i −1.54881 + 1.54881i
\(668\) 0 0
\(669\) 38.0000i 1.46916i
\(670\) 0 0
\(671\) 12.0000i 0.463255i
\(672\) 0 0
\(673\) −29.0000 + 29.0000i −1.11787 + 1.11787i −0.125814 + 0.992054i \(0.540154\pi\)
−0.992054 + 0.125814i \(0.959846\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.0000 + 15.0000i 0.576497 + 0.576497i 0.933936 0.357439i \(-0.116350\pi\)
−0.357439 + 0.933936i \(0.616350\pi\)
\(678\) 0 0
\(679\) 6.00000 0.230259
\(680\) 0 0
\(681\) −26.0000 −0.996322
\(682\) 0 0
\(683\) −13.0000 13.0000i −0.497431 0.497431i 0.413206 0.910637i \(-0.364409\pi\)
−0.910637 + 0.413206i \(0.864409\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −16.0000 + 16.0000i −0.610438 + 0.610438i
\(688\) 0 0
\(689\) 2.00000i 0.0761939i
\(690\) 0 0
\(691\) 10.0000i 0.380418i −0.981744 0.190209i \(-0.939083\pi\)
0.981744 0.190209i \(-0.0609166\pi\)
\(692\) 0 0
\(693\) 6.00000 6.00000i 0.227921 0.227921i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −6.00000 6.00000i −0.227266 0.227266i
\(698\) 0 0
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) 20.0000 + 20.0000i 0.754314 + 0.754314i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.00000 + 6.00000i −0.225653 + 0.225653i
\(708\) 0 0
\(709\) 24.0000i 0.901339i 0.892691 + 0.450669i \(0.148815\pi\)
−0.892691 + 0.450669i \(0.851185\pi\)
\(710\) 0 0
\(711\) 8.00000i 0.300023i
\(712\) 0 0
\(713\) 10.0000 10.0000i 0.374503 0.374503i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 16.0000 + 16.0000i 0.597531 + 0.597531i
\(718\) 0 0
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) 0 0
\(723\) −14.0000 14.0000i −0.520666 0.520666i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −15.0000 + 15.0000i −0.556319 + 0.556319i −0.928257 0.371938i \(-0.878693\pi\)
0.371938 + 0.928257i \(0.378693\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 6.00000i 0.221918i
\(732\) 0 0
\(733\) −9.00000 + 9.00000i −0.332423 + 0.332423i −0.853506 0.521083i \(-0.825528\pi\)
0.521083 + 0.853506i \(0.325528\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −42.0000 42.0000i −1.54709 1.54709i
\(738\) 0 0
\(739\) 28.0000 1.03000 0.514998 0.857191i \(-0.327793\pi\)
0.514998 + 0.857191i \(0.327793\pi\)
\(740\) 0 0
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) −9.00000 9.00000i −0.330178 0.330178i 0.522476 0.852654i \(-0.325008\pi\)
−0.852654 + 0.522476i \(0.825008\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.00000 + 5.00000i −0.182940 + 0.182940i
\(748\) 0 0
\(749\) 6.00000i 0.219235i
\(750\) 0 0
\(751\) 26.0000i 0.948753i 0.880322 + 0.474377i \(0.157327\pi\)
−0.880322 + 0.474377i \(0.842673\pi\)
\(752\) 0 0
\(753\) −18.0000 + 18.0000i −0.655956 + 0.655956i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.00000 1.00000i −0.0363456 0.0363456i 0.688700 0.725046i \(-0.258182\pi\)
−0.725046 + 0.688700i \(0.758182\pi\)
\(758\) 0 0
\(759\) −60.0000 −2.17786
\(760\) 0 0
\(761\) 50.0000 1.81250 0.906249 0.422744i \(-0.138933\pi\)
0.906249 + 0.422744i \(0.138933\pi\)
\(762\) 0 0
\(763\) −4.00000 4.00000i −0.144810 0.144810i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.00000 4.00000i 0.144432 0.144432i
\(768\) 0 0
\(769\) 8.00000i 0.288487i −0.989542 0.144244i \(-0.953925\pi\)
0.989542 0.144244i \(-0.0460749\pi\)
\(770\) 0 0
\(771\) 22.0000i 0.792311i
\(772\) 0 0
\(773\) 35.0000 35.0000i 1.25886 1.25886i 0.307226 0.951637i \(-0.400599\pi\)
0.951637 0.307226i \(-0.0994007\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 10.0000 + 10.0000i 0.358748 + 0.358748i
\(778\) 0 0
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) 0 0
\(783\) 32.0000 + 32.0000i 1.14359 + 1.14359i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 9.00000 9.00000i 0.320815 0.320815i −0.528265 0.849080i \(-0.677157\pi\)
0.849080 + 0.528265i \(0.177157\pi\)
\(788\) 0 0
\(789\) 18.0000i 0.640817i
\(790\) 0 0
\(791\) 6.00000i 0.213335i
\(792\) 0 0
\(793\) 2.00000 2.00000i 0.0710221 0.0710221i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −17.0000 17.0000i −0.602171 0.602171i 0.338717 0.940888i \(-0.390007\pi\)
−0.940888 + 0.338717i \(0.890007\pi\)
\(798\) 0 0
\(799\) 14.0000 0.495284
\(800\) 0