Properties

Label 20.4.e.a.7.1
Level 20
Weight 4
Character 20.7
Analytic conductor 1.180
Analytic rank 0
Dimension 2
CM disc. -4
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 20.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(1.18003820011\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{U}(1)[D_{4}]$

Embedding invariants

Embedding label 7.1
Root \(1.00000i\)
Character \(\chi\) = 20.7
Dual form 20.4.e.a.3.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(2.00000 + 2.00000i) q^{2}\) \(+8.00000i q^{4}\) \(+(-2.00000 - 11.0000i) q^{5}\) \(+(-16.0000 + 16.0000i) q^{8}\) \(-27.0000i q^{9}\) \(+O(q^{10})\) \(q\)\(+(2.00000 + 2.00000i) q^{2}\) \(+8.00000i q^{4}\) \(+(-2.00000 - 11.0000i) q^{5}\) \(+(-16.0000 + 16.0000i) q^{8}\) \(-27.0000i q^{9}\) \(+(18.0000 - 26.0000i) q^{10}\) \(+(-37.0000 + 37.0000i) q^{13}\) \(-64.0000 q^{16}\) \(+(99.0000 + 99.0000i) q^{17}\) \(+(54.0000 - 54.0000i) q^{18}\) \(+(88.0000 - 16.0000i) q^{20}\) \(+(-117.000 + 44.0000i) q^{25}\) \(-148.000 q^{26}\) \(-284.000i q^{29}\) \(+(-128.000 - 128.000i) q^{32}\) \(+396.000i q^{34}\) \(+216.000 q^{36}\) \(+(-91.0000 - 91.0000i) q^{37}\) \(+(208.000 + 144.000i) q^{40}\) \(+472.000 q^{41}\) \(+(-297.000 + 54.0000i) q^{45}\) \(+343.000i q^{49}\) \(+(-322.000 - 146.000i) q^{50}\) \(+(-296.000 - 296.000i) q^{52}\) \(+(-27.0000 + 27.0000i) q^{53}\) \(+(568.000 - 568.000i) q^{58}\) \(-468.000 q^{61}\) \(-512.000i q^{64}\) \(+(481.000 + 333.000i) q^{65}\) \(+(-792.000 + 792.000i) q^{68}\) \(+(432.000 + 432.000i) q^{72}\) \(+(253.000 - 253.000i) q^{73}\) \(-364.000i q^{74}\) \(+(128.000 + 704.000i) q^{80}\) \(-729.000 q^{81}\) \(+(944.000 + 944.000i) q^{82}\) \(+(891.000 - 1287.00i) q^{85}\) \(+176.000i q^{89}\) \(+(-702.000 - 486.000i) q^{90}\) \(+(-611.000 - 611.000i) q^{97}\) \(+(-686.000 + 686.000i) q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 32q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 32q^{8} \) \(\mathstrut +\mathstrut 36q^{10} \) \(\mathstrut -\mathstrut 74q^{13} \) \(\mathstrut -\mathstrut 128q^{16} \) \(\mathstrut +\mathstrut 198q^{17} \) \(\mathstrut +\mathstrut 108q^{18} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut -\mathstrut 234q^{25} \) \(\mathstrut -\mathstrut 296q^{26} \) \(\mathstrut -\mathstrut 256q^{32} \) \(\mathstrut +\mathstrut 432q^{36} \) \(\mathstrut -\mathstrut 182q^{37} \) \(\mathstrut +\mathstrut 416q^{40} \) \(\mathstrut +\mathstrut 944q^{41} \) \(\mathstrut -\mathstrut 594q^{45} \) \(\mathstrut -\mathstrut 644q^{50} \) \(\mathstrut -\mathstrut 592q^{52} \) \(\mathstrut -\mathstrut 54q^{53} \) \(\mathstrut +\mathstrut 1136q^{58} \) \(\mathstrut -\mathstrut 936q^{61} \) \(\mathstrut +\mathstrut 962q^{65} \) \(\mathstrut -\mathstrut 1584q^{68} \) \(\mathstrut +\mathstrut 864q^{72} \) \(\mathstrut +\mathstrut 506q^{73} \) \(\mathstrut +\mathstrut 256q^{80} \) \(\mathstrut -\mathstrut 1458q^{81} \) \(\mathstrut +\mathstrut 1888q^{82} \) \(\mathstrut +\mathstrut 1782q^{85} \) \(\mathstrut -\mathstrut 1404q^{90} \) \(\mathstrut -\mathstrut 1222q^{97} \) \(\mathstrut -\mathstrut 1372q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(3\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(4\) 8.00000i 1.00000i
\(5\) −2.00000 11.0000i −0.178885 0.983870i
\(6\) 0 0
\(7\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(8\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(9\) 27.0000i 1.00000i
\(10\) 18.0000 26.0000i 0.569210 0.822192i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) −37.0000 + 37.0000i −0.789381 + 0.789381i −0.981393 0.192012i \(-0.938499\pi\)
0.192012 + 0.981393i \(0.438499\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −64.0000 −1.00000
\(17\) 99.0000 + 99.0000i 1.41241 + 1.41241i 0.741874 + 0.670540i \(0.233937\pi\)
0.670540 + 0.741874i \(0.266063\pi\)
\(18\) 54.0000 54.0000i 0.707107 0.707107i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 88.0000 16.0000i 0.983870 0.178885i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(24\) 0 0
\(25\) −117.000 + 44.0000i −0.936000 + 0.352000i
\(26\) −148.000 −1.11635
\(27\) 0 0
\(28\) 0 0
\(29\) 284.000i 1.81853i −0.416214 0.909267i \(-0.636643\pi\)
0.416214 0.909267i \(-0.363357\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −128.000 128.000i −0.707107 0.707107i
\(33\) 0 0
\(34\) 396.000i 1.99745i
\(35\) 0 0
\(36\) 216.000 1.00000
\(37\) −91.0000 91.0000i −0.404333 0.404333i 0.475424 0.879757i \(-0.342295\pi\)
−0.879757 + 0.475424i \(0.842295\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 208.000 + 144.000i 0.822192 + 0.569210i
\(41\) 472.000 1.79790 0.898951 0.438048i \(-0.144330\pi\)
0.898951 + 0.438048i \(0.144330\pi\)
\(42\) 0 0
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 0 0
\(45\) −297.000 + 54.0000i −0.983870 + 0.178885i
\(46\) 0 0
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) 0 0
\(49\) 343.000i 1.00000i
\(50\) −322.000 146.000i −0.910754 0.412950i
\(51\) 0 0
\(52\) −296.000 296.000i −0.789381 0.789381i
\(53\) −27.0000 + 27.0000i −0.0699761 + 0.0699761i −0.741229 0.671253i \(-0.765757\pi\)
0.671253 + 0.741229i \(0.265757\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 568.000 568.000i 1.28590 1.28590i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −468.000 −0.982316 −0.491158 0.871071i \(-0.663426\pi\)
−0.491158 + 0.871071i \(0.663426\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 512.000i 1.00000i
\(65\) 481.000 + 333.000i 0.917857 + 0.635439i
\(66\) 0 0
\(67\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) −792.000 + 792.000i −1.41241 + 1.41241i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 432.000 + 432.000i 0.707107 + 0.707107i
\(73\) 253.000 253.000i 0.405636 0.405636i −0.474578 0.880214i \(-0.657399\pi\)
0.880214 + 0.474578i \(0.157399\pi\)
\(74\) 364.000i 0.571813i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 128.000 + 704.000i 0.178885 + 0.983870i
\(81\) −729.000 −1.00000
\(82\) 944.000 + 944.000i 1.27131 + 1.27131i
\(83\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) 0 0
\(85\) 891.000 1287.00i 1.13697 1.64229i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 176.000i 0.209618i 0.994492 + 0.104809i \(0.0334231\pi\)
−0.994492 + 0.104809i \(0.966577\pi\)
\(90\) −702.000 486.000i −0.822192 0.569210i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −611.000 611.000i −0.639563 0.639563i 0.310884 0.950448i \(-0.399375\pi\)
−0.950448 + 0.310884i \(0.899375\pi\)
\(98\) −686.000 + 686.000i −0.707107 + 0.707107i
\(99\) 0 0
\(100\) −352.000 936.000i −0.352000 0.936000i
\(101\) −598.000 −0.589141 −0.294570 0.955630i \(-0.595177\pi\)
−0.294570 + 0.955630i \(0.595177\pi\)
\(102\) 0 0
\(103\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) 1184.00i 1.11635i
\(105\) 0 0
\(106\) −108.000 −0.0989612
\(107\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) 0 0
\(109\) 1746.00i 1.53428i 0.641480 + 0.767140i \(0.278321\pi\)
−0.641480 + 0.767140i \(0.721679\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −337.000 + 337.000i −0.280551 + 0.280551i −0.833329 0.552778i \(-0.813568\pi\)
0.552778 + 0.833329i \(0.313568\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2272.00 1.81853
\(117\) 999.000 + 999.000i 0.789381 + 0.789381i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1331.00 1.00000
\(122\) −936.000 936.000i −0.694602 0.694602i
\(123\) 0 0
\(124\) 0 0
\(125\) 718.000 + 1199.00i 0.513759 + 0.857935i
\(126\) 0 0
\(127\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) 1024.00 1024.00i 0.707107 0.707107i
\(129\) 0 0
\(130\) 296.000 + 1628.00i 0.199699 + 1.09835i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −3168.00 −1.99745
\(137\) −2191.00 2191.00i −1.36635 1.36635i −0.865583 0.500766i \(-0.833052\pi\)
−0.500766 0.865583i \(-0.666948\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1728.00i 1.00000i
\(145\) −3124.00 + 568.000i −1.78920 + 0.325309i
\(146\) 1012.00 0.573656
\(147\) 0 0
\(148\) 728.000 728.000i 0.404333 0.404333i
\(149\) 3514.00i 1.93207i −0.258415 0.966034i \(-0.583200\pi\)
0.258415 0.966034i \(-0.416800\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 2673.00 2673.00i 1.41241 1.41241i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1819.00 + 1819.00i 0.924662 + 0.924662i 0.997354 0.0726920i \(-0.0231590\pi\)
−0.0726920 + 0.997354i \(0.523159\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −1152.00 + 1664.00i −0.569210 + 0.822192i
\(161\) 0 0
\(162\) −1458.00 1458.00i −0.707107 0.707107i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 3776.00i 1.79790i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 0 0
\(169\) 541.000i 0.246245i
\(170\) 4356.00 792.000i 1.96523 0.357315i
\(171\) 0 0
\(172\) 0 0
\(173\) −3047.00 + 3047.00i −1.33907 + 1.33907i −0.442108 + 0.896962i \(0.645769\pi\)
−0.896962 + 0.442108i \(0.854231\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −352.000 + 352.000i −0.148222 + 0.148222i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −432.000 2376.00i −0.178885 0.983870i
\(181\) 3942.00 1.61882 0.809410 0.587243i \(-0.199787\pi\)
0.809410 + 0.587243i \(0.199787\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −819.000 + 1183.00i −0.325482 + 0.470140i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) −2717.00 + 2717.00i −1.01334 + 1.01334i −0.0134266 + 0.999910i \(0.504274\pi\)
−0.999910 + 0.0134266i \(0.995726\pi\)
\(194\) 2444.00i 0.904479i
\(195\) 0 0
\(196\) −2744.00 −1.00000
\(197\) 3289.00 + 3289.00i 1.18950 + 1.18950i 0.977206 + 0.212295i \(0.0680936\pi\)
0.212295 + 0.977206i \(0.431906\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 1168.00 2576.00i 0.412950 0.910754i
\(201\) 0 0
\(202\) −1196.00 1196.00i −0.416585 0.416585i
\(203\) 0 0
\(204\) 0 0
\(205\) −944.000 5192.00i −0.321619 1.76890i
\(206\) 0 0
\(207\) 0 0
\(208\) 2368.00 2368.00i 0.789381 0.789381i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −216.000 216.000i −0.0699761 0.0699761i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −3492.00 + 3492.00i −1.08490 + 1.08490i
\(219\) 0 0
\(220\) 0 0
\(221\) −7326.00 −2.22986
\(222\) 0 0
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 0 0
\(225\) 1188.00 + 3159.00i 0.352000 + 0.936000i
\(226\) −1348.00 −0.396759
\(227\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(228\) 0 0
\(229\) 2684.00i 0.774514i −0.921972 0.387257i \(-0.873423\pi\)
0.921972 0.387257i \(-0.126577\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4544.00 + 4544.00i 1.28590 + 1.28590i
\(233\) 3843.00 3843.00i 1.08053 1.08053i 0.0840693 0.996460i \(-0.473208\pi\)
0.996460 0.0840693i \(-0.0267917\pi\)
\(234\) 3996.00i 1.11635i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 5272.00 1.40913 0.704563 0.709641i \(-0.251143\pi\)
0.704563 + 0.709641i \(0.251143\pi\)
\(242\) 2662.00 + 2662.00i 0.707107 + 0.707107i
\(243\) 0 0
\(244\) 3744.00i 0.982316i
\(245\) 3773.00 686.000i 0.983870 0.178885i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −962.000 + 3834.00i −0.243369 + 0.969934i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 4096.00 1.00000
\(257\) −3281.00 3281.00i −0.796355 0.796355i 0.186164 0.982519i \(-0.440394\pi\)
−0.982519 + 0.186164i \(0.940394\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2664.00 + 3848.00i −0.635439 + 0.917857i
\(261\) −7668.00 −1.81853
\(262\) 0 0
\(263\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(264\) 0 0
\(265\) 351.000 + 243.000i 0.0813651 + 0.0563297i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3406.00i 0.771998i 0.922499 + 0.385999i \(0.126143\pi\)
−0.922499 + 0.385999i \(0.873857\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −6336.00 6336.00i −1.41241 1.41241i
\(273\) 0 0
\(274\) 8764.00i 1.93231i
\(275\) 0 0
\(276\) 0 0
\(277\) −5221.00 5221.00i −1.13249 1.13249i −0.989762 0.142727i \(-0.954413\pi\)
−0.142727 0.989762i \(-0.545587\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5792.00 1.22961 0.614807 0.788677i \(-0.289234\pi\)
0.614807 + 0.788677i \(0.289234\pi\)
\(282\) 0 0
\(283\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −3456.00 + 3456.00i −0.707107 + 0.707107i
\(289\) 14689.0i 2.98982i
\(290\) −7384.00 5112.00i −1.49518 1.03513i
\(291\) 0 0
\(292\) 2024.00 + 2024.00i 0.405636 + 0.405636i
\(293\) 2983.00 2983.00i 0.594774 0.594774i −0.344143 0.938917i \(-0.611831\pi\)
0.938917 + 0.344143i \(0.111831\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2912.00 0.571813
\(297\) 0 0
\(298\) 7028.00 7028.00i 1.36618 1.36618i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 936.000 + 5148.00i 0.175722 + 0.966471i
\(306\) 10692.0 1.99745
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −937.000 + 937.000i −0.169209 + 0.169209i −0.786632 0.617423i \(-0.788177\pi\)
0.617423 + 0.786632i \(0.288177\pi\)
\(314\) 7276.00i 1.30767i
\(315\) 0 0
\(316\) 0 0
\(317\) 2799.00 + 2799.00i 0.495923 + 0.495923i 0.910166 0.414243i \(-0.135954\pi\)
−0.414243 + 0.910166i \(0.635954\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −5632.00 + 1024.00i −0.983870 + 0.178885i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 5832.00i 1.00000i
\(325\) 2701.00 5957.00i 0.460999 1.01672i
\(326\) 0 0
\(327\) 0 0
\(328\) −7552.00 + 7552.00i −1.27131 + 1.27131i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −2457.00 + 2457.00i −0.404333 + 0.404333i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −6391.00 6391.00i −1.03306 1.03306i −0.999435 0.0336216i \(-0.989296\pi\)
−0.0336216 0.999435i \(-0.510704\pi\)
\(338\) 1082.00 1082.00i 0.174121 0.174121i
\(339\) 0 0
\(340\) 10296.0 + 7128.00i 1.64229 + 1.13697i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −12188.0 −1.89373
\(347\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(348\) 0 0
\(349\) 8964.00i 1.37488i −0.726243 0.687438i \(-0.758735\pi\)
0.726243 0.687438i \(-0.241265\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8073.00 8073.00i 1.21723 1.21723i 0.248633 0.968598i \(-0.420019\pi\)
0.968598 0.248633i \(-0.0799813\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1408.00 −0.209618
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 3888.00 5616.00i 0.569210 0.822192i
\(361\) −6859.00 −1.00000
\(362\) 7884.00 + 7884.00i 1.14468 + 1.14468i
\(363\) 0 0
\(364\) 0 0
\(365\) −3289.00 2277.00i −0.471655 0.326530i
\(366\) 0 0
\(367\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(368\) 0 0
\(369\) 12744.0i 1.79790i
\(370\) −4004.00 + 728.000i −0.562589 + 0.102289i
\(371\) 0 0
\(372\) 0 0
\(373\) −9647.00 + 9647.00i −1.33915 + 1.33915i −0.442265 + 0.896884i \(0.645825\pi\)
−0.896884 + 0.442265i \(0.854175\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10508.0 + 10508.0i 1.43552 + 1.43552i
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10868.0 −1.43307
\(387\) 0 0
\(388\) 4888.00 4888.00i 0.639563 0.639563i
\(389\) 374.000i 0.0487469i −0.999703 0.0243735i \(-0.992241\pi\)
0.999703 0.0243735i \(-0.00775908\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −5488.00 5488.00i −0.707107 0.707107i
\(393\) 0 0
\(394\) 13156.0i 1.68221i
\(395\) 0 0
\(396\) 0 0
\(397\) 11089.0 + 11089.0i 1.40187 + 1.40187i 0.794168 + 0.607699i \(0.207907\pi\)
0.607699 + 0.794168i \(0.292093\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 7488.00 2816.00i 0.936000 0.352000i
\(401\) −2398.00 −0.298629 −0.149315 0.988790i \(-0.547707\pi\)
−0.149315 + 0.988790i \(0.547707\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 4784.00i 0.589141i
\(405\) 1458.00 + 8019.00i 0.178885 + 0.983870i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 7146.00i 0.863929i 0.901891 + 0.431964i \(0.142179\pi\)
−0.901891 + 0.431964i \(0.857821\pi\)
\(410\) 8496.00 12272.0i 1.02338 1.47822i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 9472.00 1.11635
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 13412.0 1.55264 0.776319 0.630340i \(-0.217084\pi\)
0.776319 + 0.630340i \(0.217084\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 864.000i 0.0989612i
\(425\) −15939.0 7227.00i −1.81919 0.824849i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) −11107.0 + 11107.0i −1.23272 + 1.23272i −0.269807 + 0.962914i \(0.586960\pi\)
−0.962914 + 0.269807i \(0.913040\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −13968.0 −1.53428
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 9261.00 1.00000
\(442\) −14652.0 14652.0i −1.57675 1.57675i
\(443\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(444\) 0 0
\(445\) 1936.00 352.000i 0.206236 0.0374975i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 16114.0i 1.69369i −0.531840 0.846845i \(-0.678499\pi\)
0.531840 0.846845i \(-0.321501\pi\)
\(450\) −3942.00 + 8694.00i −0.412950 + 0.910754i
\(451\) 0 0
\(452\) −2696.00 2696.00i −0.280551 0.280551i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −13481.0 13481.0i −1.37990 1.37990i −0.844768 0.535132i \(-0.820262\pi\)
−0.535132 0.844768i \(-0.679738\pi\)
\(458\) 5368.00 5368.00i 0.547664 0.547664i
\(459\) 0 0
\(460\) 0 0
\(461\) −2318.00 −0.234187 −0.117093 0.993121i \(-0.537358\pi\)
−0.117093 + 0.993121i \(0.537358\pi\)
\(462\) 0 0
\(463\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) 18176.0i 1.81853i
\(465\) 0 0
\(466\) 15372.0 1.52810
\(467\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(468\) −7992.00 + 7992.00i −0.789381 + 0.789381i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 729.000 + 729.000i 0.0699761 + 0.0699761i
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 6734.00 0.638345
\(482\) 10544.0 + 10544.0i 0.996403 + 0.996403i
\(483\) 0 0
\(484\) 10648.0i 1.00000i
\(485\) −5499.00 + 7943.00i −0.514839 + 0.743656i
\(486\) 0 0
\(487\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(488\) 7488.00 7488.00i 0.694602 0.694602i
\(489\) 0 0
\(490\) 8918.00 + 6174.00i 0.822192 + 0.569210i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 28116.0 28116.0i 2.56852 2.56852i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −9592.00 + 5744.00i −0.857935 + 0.513759i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 0 0
\(505\) 1196.00 + 6578.00i 0.105389 + 0.579638i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17996.0i 1.56711i 0.621323 + 0.783555i \(0.286596\pi\)
−0.621323 + 0.783555i \(0.713404\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 8192.00 + 8192.00i 0.707107 + 0.707107i
\(513\) 0 0
\(514\) 13124.0i 1.12622i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −13024.0 + 2368.00i −1.09835 + 0.199699i
\(521\) −23738.0 −1.99612 −0.998062 0.0622265i \(-0.980180\pi\)
−0.998062 + 0.0622265i \(0.980180\pi\)
\(522\) −15336.0 15336.0i −1.28590 1.28590i
\(523\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 12167.0i 1.00000i
\(530\) 216.000 + 1188.00i 0.0177027 + 0.0973649i
\(531\) 0 0
\(532\) 0 0
\(533\) −17464.0 + 17464.0i −1.41923 + 1.41923i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −6812.00 + 6812.00i −0.545885 + 0.545885i
\(539\) 0 0
\(540\) 0 0
\(541\) 5922.00 0.470622 0.235311 0.971920i \(-0.424389\pi\)
0.235311 + 0.971920i \(0.424389\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 25344.0i 1.99745i
\(545\) 19206.0 3492.00i 1.50953 0.274460i
\(546\) 0 0
\(547\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) 17528.0 17528.0i 1.36635 1.36635i
\(549\) 12636.0i 0.982316i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 20884.0i 1.60158i
\(555\) 0 0
\(556\) 0 0
\(557\) −16731.0 16731.0i −1.27274 1.27274i −0.944646 0.328093i \(-0.893594\pi\)
−0.328093 0.944646i \(-0.606406\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 11584.0 + 11584.0i 0.869469 + 0.869469i
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) 0 0
\(565\) 4381.00 + 3033.00i 0.326212 + 0.225839i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 26806.0i 1.97498i 0.157669 + 0.987492i \(0.449602\pi\)
−0.157669 + 0.987492i \(0.550398\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −13824.0 −1.00000
\(577\) 15479.0 + 15479.0i 1.11681 + 1.11681i 0.992207 + 0.124603i \(0.0397657\pi\)
0.124603 + 0.992207i \(0.460234\pi\)
\(578\) −29378.0 + 29378.0i −2.11412 + 2.11412i
\(579\) 0 0
\(580\) −4544.00 24992.0i −0.325309 1.78920i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 8096.00i 0.573656i
\(585\) 8991.00 12987.0i 0.635439 0.917857i
\(586\) 11932.0 0.841137
\(587\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 5824.00 + 5824.00i 0.404333 + 0.404333i
\(593\) 4433.00 4433.00i 0.306984 0.306984i −0.536755 0.843738i \(-0.680350\pi\)
0.843738 + 0.536755i \(0.180350\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 28112.0 1.93207
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −24048.0 −1.63218 −0.816089 0.577927i \(-0.803862\pi\)
−0.816089 + 0.577927i \(0.803862\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2662.00 14641.0i −0.178885 0.983870i
\(606\) 0 0
\(607\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −8424.00 + 12168.0i −0.559144 + 0.807652i
\(611\) 0 0
\(612\) 21384.0 + 21384.0i 1.41241 + 1.41241i
\(613\) −1837.00 + 1837.00i −0.121037 + 0.121037i −0.765031 0.643994i \(-0.777276\pi\)
0.643994 + 0.765031i \(0.277276\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5499.00 + 5499.00i 0.358803 + 0.358803i 0.863372 0.504569i \(-0.168348\pi\)
−0.504569 + 0.863372i \(0.668348\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 11753.0 10296.0i 0.752192 0.658944i
\(626\) −3748.00 −0.239297
\(627\) 0 0
\(628\) −14552.0 + 14552.0i −0.924662 + 0.924662i
\(629\) 18018.0i 1.14217i
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 11196.0i 0.701341i
\(635\) 0 0
\(636\) 0 0
\(637\) −12691.0 12691.0i −0.789381 0.789381i
\(638\) 0 0
\(639\) 0 0
\(640\) −13312.0 9216.00i −0.822192 0.569210i
\(641\) 14872.0 0.916394 0.458197 0.888851i \(-0.348495\pi\)
0.458197 + 0.888851i \(0.348495\pi\)
\(642\) 0 0
\(643\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(648\) 11664.0 11664.0i 0.707107 0.707107i
\(649\) 0 0
\(650\) 17316.0 6512.00i 1.04491 0.392956i
\(651\) 0 0
\(652\) 0 0
\(653\) 16173.0 16173.0i 0.969217 0.969217i −0.0303236 0.999540i \(-0.509654\pi\)
0.999540 + 0.0303236i \(0.00965378\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −30208.0 −1.79790
\(657\) −6831.00 6831.00i −0.405636 0.405636i
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −22068.0 −1.29856 −0.649278 0.760551i \(-0.724929\pi\)
−0.649278 + 0.760551i \(0.724929\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −9828.00 −0.571813
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −19547.0 + 19547.0i −1.11959 + 1.11959i −0.127784 + 0.991802i \(0.540786\pi\)
−0.991802 + 0.127784i \(0.959214\pi\)
\(674\) 25564.0i 1.46096i
\(675\) 0 0
\(676\) 4328.00 0.246245
\(677\) −15471.0 15471.0i −0.878285 0.878285i 0.115072 0.993357i \(-0.463290\pi\)
−0.993357 + 0.115072i \(0.963290\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6336.00 + 34848.0i 0.357315 + 1.96523i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(684\) 0 0
\(685\) −19719.0 + 28483.0i −1.09989 + 1.58873i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1998.00i 0.110476i
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) −24376.0 24376.0i −1.33907 1.33907i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 46728.0 + 46728.0i 2.53938 + 2.53938i
\(698\) 17928.0 17928.0i 0.972185 0.972185i
\(699\) 0 0
\(700\) 0 0
\(701\) 31252.0 1.68384 0.841920 0.539602i \(-0.181425\pi\)
0.841920 + 0.539602i \(0.181425\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 32292.0 1.72142
\(707\) 0 0
\(708\) 0 0
\(709\) 8404.00i 0.445161i −0.974914 0.222580i \(-0.928552\pi\)
0.974914 0.222580i \(-0.0714479\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −2816.00 2816.00i −0.148222 0.148222i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 19008.0 3456.00i 0.983870 0.178885i
\(721\) 0 0
\(722\) −13718.0 13718.0i −0.707107 0.707107i
\(723\) 0 0
\(724\) 31536.0i 1.61882i
\(725\) 12496.0 + 33228.0i 0.640124 + 1.70215i
\(726\) 0 0
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 0 0
\(729\) 19683.0i 1.00000i
\(730\) −2024.00 11132.0i −0.102619 0.564402i
\(731\) 0 0
\(732\) 0 0
\(733\) 14993.0 14993.0i 0.755497 0.755497i −0.220003 0.975499i \(-0.570607\pi\)
0.975499 + 0.220003i \(0.0706066\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 25488.0 25488.0i 1.27131 1.27131i
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) −9464.00 6552.00i −0.470140 0.325482i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(744\) 0 0
\(745\) −38654.0 + 7028.00i −1.90090 + 0.345619i
\(746\) −38588.0 −1.89384
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 42032.0i 2.03013i
\(755\) 0 0
\(756\) 0 0
\(757\) −28781.0 28781.0i −1.38185 1.38185i −0.841327 0.540527i \(-0.818225\pi\)
−0.540527 0.841327i \(-0.681775\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 31882.0 1.51869 0.759344 0.650689i \(-0.225520\pi\)
0.759344 + 0.650689i \(0.225520\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −34749.0 24057.0i −1.64229 1.13697i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 41544.0i 1.94813i −0.226260 0.974067i \(-0.572650\pi\)
0.226260 0.974067i \(-0.427350\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −21736.0 21736.0i −1.01334 1.01334i
\(773\) −28197.0 + 28197.0i −1.31200 + 1.31200i −0.392060 + 0.919940i \(0.628237\pi\)
−0.919940 + 0.392060i \(0.871763\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 19552.0 0.904479
\(777\) 0 0
\(778\) 748.000 748.000i 0.0344693 0.0344693i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 21952.0i 1.00000i
\(785\) 16371.0 23647.0i 0.744339 1.07516i
\(786\) 0 0
\(787\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(788\) −26312.0 + 26312.0i −1.18950 + 1.18950i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 17316.0 17316.0i 0.775421 0.775421i
\(794\) 44356.0i 1.98254i
\(795\) 0 0
\(796\) 0 0
\(797\) 12839.0 + 12839.0i 0.570616 + 0.570616i 0.932300 0.361685i \(-0.117798\pi\)
−0.361685 + 0.932300i \(0.617798\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 20608.0 + 9344.00i 0.910754 + 0.412950i
\(801\) 4752.00 0.209618
\(802\) −4796.00 4796.00i −0.211163 0.211163i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 9568.00 9568.00i 0.416585 0.416585i
\(809\) 39704.0i 1.72549i −0.505643 0.862743i \(-0.668745\pi\)
0.505643 0.862743i \(-0.331255\pi\)
\(810\) −13122.0 + 18954.0i −0.569210 + 0.822192i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0