Properties

Label 1600.2.q.f.49.3
Level $1600$
Weight $2$
Character 1600.49
Analytic conductor $12.776$
Analytic rank $0$
Dimension $12$
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.q (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 400)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 49.3
Root \(-0.507829 + 1.31989i\) of defining polynomial
Character \(\chi\) \(=\) 1600.49
Dual form 1600.2.q.f.849.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0623209 + 0.0623209i) q^{3} -0.375877 q^{7} -2.99223i q^{9} +O(q^{10})\) \(q+(0.0623209 + 0.0623209i) q^{3} -0.375877 q^{7} -2.99223i q^{9} +(-2.36756 - 2.36756i) q^{11} +(-1.76442 - 1.76442i) q^{13} +4.64955i q^{17} +(-2.34965 + 2.34965i) q^{19} +(-0.0234250 - 0.0234250i) q^{21} +2.07779 q^{23} +(0.373441 - 0.373441i) q^{27} +(-2.55422 + 2.55422i) q^{29} -8.51714 q^{31} -0.295096i q^{33} +(-7.62613 + 7.62613i) q^{37} -0.219921i q^{39} +3.77709i q^{41} +(6.21191 - 6.21191i) q^{43} +9.71696i q^{47} -6.85872 q^{49} +(-0.289764 + 0.289764i) q^{51} +(-3.03609 + 3.03609i) q^{53} -0.292864 q^{57} +(-8.11663 - 8.11663i) q^{59} +(0.728329 - 0.728329i) q^{61} +1.12471i q^{63} +(-0.969239 - 0.969239i) q^{67} +(0.129490 + 0.129490i) q^{69} -9.14230i q^{71} +7.56793 q^{73} +(0.889909 + 0.889909i) q^{77} +11.8065 q^{79} -8.93015 q^{81} +(-10.6393 - 10.6393i) q^{83} -0.318363 q^{87} -15.7111i q^{89} +(0.663205 + 0.663205i) q^{91} +(-0.530796 - 0.530796i) q^{93} +3.86020i q^{97} +(-7.08428 + 7.08428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{3} - 12q^{7} + O(q^{10}) \) \( 12q + 2q^{3} - 12q^{7} + 2q^{11} + 4q^{13} - 14q^{19} - 20q^{21} - 12q^{23} - 10q^{27} + 4q^{31} - 8q^{37} - 4q^{49} - 10q^{51} - 16q^{53} - 16q^{57} + 20q^{59} + 4q^{61} - 50q^{67} + 40q^{73} - 8q^{77} + 12q^{79} - 8q^{81} - 2q^{83} + 64q^{87} + 44q^{93} + 12q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 0.0623209 + 0.0623209i 0.0359810 + 0.0359810i 0.724868 0.688887i \(-0.241901\pi\)
−0.688887 + 0.724868i \(0.741901\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.375877 −0.142068 −0.0710340 0.997474i \(-0.522630\pi\)
−0.0710340 + 0.997474i \(0.522630\pi\)
\(8\) 0 0
\(9\) 2.99223i 0.997411i
\(10\) 0 0
\(11\) −2.36756 2.36756i −0.713845 0.713845i 0.253492 0.967337i \(-0.418421\pi\)
−0.967337 + 0.253492i \(0.918421\pi\)
\(12\) 0 0
\(13\) −1.76442 1.76442i −0.489363 0.489363i 0.418742 0.908105i \(-0.362471\pi\)
−0.908105 + 0.418742i \(0.862471\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.64955i 1.12768i 0.825883 + 0.563841i \(0.190677\pi\)
−0.825883 + 0.563841i \(0.809323\pi\)
\(18\) 0 0
\(19\) −2.34965 + 2.34965i −0.539047 + 0.539047i −0.923249 0.384202i \(-0.874476\pi\)
0.384202 + 0.923249i \(0.374476\pi\)
\(20\) 0 0
\(21\) −0.0234250 0.0234250i −0.00511175 0.00511175i
\(22\) 0 0
\(23\) 2.07779 0.433250 0.216625 0.976255i \(-0.430495\pi\)
0.216625 + 0.976255i \(0.430495\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0.373441 0.373441i 0.0718688 0.0718688i
\(28\) 0 0
\(29\) −2.55422 + 2.55422i −0.474307 + 0.474307i −0.903305 0.428998i \(-0.858867\pi\)
0.428998 + 0.903305i \(0.358867\pi\)
\(30\) 0 0
\(31\) −8.51714 −1.52972 −0.764862 0.644194i \(-0.777193\pi\)
−0.764862 + 0.644194i \(0.777193\pi\)
\(32\) 0 0
\(33\) 0.295096i 0.0513697i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.62613 + 7.62613i −1.25373 + 1.25373i −0.299691 + 0.954036i \(0.596884\pi\)
−0.954036 + 0.299691i \(0.903116\pi\)
\(38\) 0 0
\(39\) 0.219921i 0.0352155i
\(40\) 0 0
\(41\) 3.77709i 0.589882i 0.955515 + 0.294941i \(0.0953001\pi\)
−0.955515 + 0.294941i \(0.904700\pi\)
\(42\) 0 0
\(43\) 6.21191 6.21191i 0.947307 0.947307i −0.0513725 0.998680i \(-0.516360\pi\)
0.998680 + 0.0513725i \(0.0163596\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.71696i 1.41736i 0.705528 + 0.708682i \(0.250710\pi\)
−0.705528 + 0.708682i \(0.749290\pi\)
\(48\) 0 0
\(49\) −6.85872 −0.979817
\(50\) 0 0
\(51\) −0.289764 + 0.289764i −0.0405751 + 0.0405751i
\(52\) 0 0
\(53\) −3.03609 + 3.03609i −0.417040 + 0.417040i −0.884182 0.467143i \(-0.845283\pi\)
0.467143 + 0.884182i \(0.345283\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.292864 −0.0387908
\(58\) 0 0
\(59\) −8.11663 8.11663i −1.05670 1.05670i −0.998293 0.0584019i \(-0.981400\pi\)
−0.0584019 0.998293i \(-0.518600\pi\)
\(60\) 0 0
\(61\) 0.728329 0.728329i 0.0932529 0.0932529i −0.658941 0.752194i \(-0.728995\pi\)
0.752194 + 0.658941i \(0.228995\pi\)
\(62\) 0 0
\(63\) 1.12471i 0.141700i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −0.969239 0.969239i −0.118411 0.118411i 0.645418 0.763829i \(-0.276683\pi\)
−0.763829 + 0.645418i \(0.776683\pi\)
\(68\) 0 0
\(69\) 0.129490 + 0.129490i 0.0155887 + 0.0155887i
\(70\) 0 0
\(71\) 9.14230i 1.08499i −0.840058 0.542496i \(-0.817479\pi\)
0.840058 0.542496i \(-0.182521\pi\)
\(72\) 0 0
\(73\) 7.56793 0.885759 0.442879 0.896581i \(-0.353957\pi\)
0.442879 + 0.896581i \(0.353957\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.889909 + 0.889909i 0.101415 + 0.101415i
\(78\) 0 0
\(79\) 11.8065 1.32834 0.664169 0.747583i \(-0.268786\pi\)
0.664169 + 0.747583i \(0.268786\pi\)
\(80\) 0 0
\(81\) −8.93015 −0.992239
\(82\) 0 0
\(83\) −10.6393 10.6393i −1.16782 1.16782i −0.982720 0.185101i \(-0.940739\pi\)
−0.185101 0.982720i \(-0.559261\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.318363 −0.0341320
\(88\) 0 0
\(89\) 15.7111i 1.66538i −0.553741 0.832689i \(-0.686800\pi\)
0.553741 0.832689i \(-0.313200\pi\)
\(90\) 0 0
\(91\) 0.663205 + 0.663205i 0.0695228 + 0.0695228i
\(92\) 0 0
\(93\) −0.530796 0.530796i −0.0550410 0.0550410i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 3.86020i 0.391943i 0.980610 + 0.195972i \(0.0627861\pi\)
−0.980610 + 0.195972i \(0.937214\pi\)
\(98\) 0 0
\(99\) −7.08428 + 7.08428i −0.711997 + 0.711997i
\(100\) 0 0
\(101\) −6.87437 6.87437i −0.684026 0.684026i 0.276879 0.960905i \(-0.410700\pi\)
−0.960905 + 0.276879i \(0.910700\pi\)
\(102\) 0 0
\(103\) −1.15407 −0.113714 −0.0568571 0.998382i \(-0.518108\pi\)
−0.0568571 + 0.998382i \(0.518108\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.70435 + 5.70435i −0.551460 + 0.551460i −0.926862 0.375402i \(-0.877505\pi\)
0.375402 + 0.926862i \(0.377505\pi\)
\(108\) 0 0
\(109\) −11.1863 + 11.1863i −1.07145 + 1.07145i −0.0742092 + 0.997243i \(0.523643\pi\)
−0.997243 + 0.0742092i \(0.976357\pi\)
\(110\) 0 0
\(111\) −0.950534 −0.0902207
\(112\) 0 0
\(113\) 4.08163i 0.383967i −0.981398 0.191984i \(-0.938508\pi\)
0.981398 0.191984i \(-0.0614920\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −5.27956 + 5.27956i −0.488096 + 0.488096i
\(118\) 0 0
\(119\) 1.74766i 0.160208i
\(120\) 0 0
\(121\) 0.210643i 0.0191493i
\(122\) 0 0
\(123\) −0.235392 + 0.235392i −0.0212245 + 0.0212245i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 17.0918i 1.51665i 0.651876 + 0.758326i \(0.273982\pi\)
−0.651876 + 0.758326i \(0.726018\pi\)
\(128\) 0 0
\(129\) 0.774263 0.0681701
\(130\) 0 0
\(131\) 3.56424 3.56424i 0.311409 0.311409i −0.534046 0.845455i \(-0.679329\pi\)
0.845455 + 0.534046i \(0.179329\pi\)
\(132\) 0 0
\(133\) 0.883179 0.883179i 0.0765813 0.0765813i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.6995 1.42673 0.713366 0.700792i \(-0.247170\pi\)
0.713366 + 0.700792i \(0.247170\pi\)
\(138\) 0 0
\(139\) −7.56455 7.56455i −0.641616 0.641616i 0.309336 0.950953i \(-0.399893\pi\)
−0.950953 + 0.309336i \(0.899893\pi\)
\(140\) 0 0
\(141\) −0.605569 + 0.605569i −0.0509982 + 0.0509982i
\(142\) 0 0
\(143\) 8.35474i 0.698658i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.427441 0.427441i −0.0352548 0.0352548i
\(148\) 0 0
\(149\) 10.2542 + 10.2542i 0.840056 + 0.840056i 0.988866 0.148810i \(-0.0475444\pi\)
−0.148810 + 0.988866i \(0.547544\pi\)
\(150\) 0 0
\(151\) 19.0430i 1.54970i 0.632147 + 0.774849i \(0.282174\pi\)
−0.632147 + 0.774849i \(0.717826\pi\)
\(152\) 0 0
\(153\) 13.9125 1.12476
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −10.1335 10.1335i −0.808741 0.808741i 0.175702 0.984443i \(-0.443780\pi\)
−0.984443 + 0.175702i \(0.943780\pi\)
\(158\) 0 0
\(159\) −0.378424 −0.0300110
\(160\) 0 0
\(161\) −0.780994 −0.0615509
\(162\) 0 0
\(163\) 7.35501 + 7.35501i 0.576089 + 0.576089i 0.933823 0.357735i \(-0.116451\pi\)
−0.357735 + 0.933823i \(0.616451\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.02936 −0.621331 −0.310665 0.950519i \(-0.600552\pi\)
−0.310665 + 0.950519i \(0.600552\pi\)
\(168\) 0 0
\(169\) 6.77363i 0.521048i
\(170\) 0 0
\(171\) 7.03070 + 7.03070i 0.537651 + 0.537651i
\(172\) 0 0
\(173\) −10.4326 10.4326i −0.793177 0.793177i 0.188832 0.982009i \(-0.439530\pi\)
−0.982009 + 0.188832i \(0.939530\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.01167i 0.0760418i
\(178\) 0 0
\(179\) −8.30280 + 8.30280i −0.620580 + 0.620580i −0.945680 0.325099i \(-0.894602\pi\)
0.325099 + 0.945680i \(0.394602\pi\)
\(180\) 0 0
\(181\) −10.4772 10.4772i −0.778765 0.778765i 0.200856 0.979621i \(-0.435628\pi\)
−0.979621 + 0.200856i \(0.935628\pi\)
\(182\) 0 0
\(183\) 0.0907802 0.00671066
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 11.0081 11.0081i 0.804990 0.804990i
\(188\) 0 0
\(189\) −0.140368 + 0.140368i −0.0102103 + 0.0102103i
\(190\) 0 0
\(191\) −1.68079 −0.121618 −0.0608089 0.998149i \(-0.519368\pi\)
−0.0608089 + 0.998149i \(0.519368\pi\)
\(192\) 0 0
\(193\) 1.61403i 0.116181i −0.998311 0.0580903i \(-0.981499\pi\)
0.998311 0.0580903i \(-0.0185011\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.10322 5.10322i 0.363589 0.363589i −0.501543 0.865133i \(-0.667234\pi\)
0.865133 + 0.501543i \(0.167234\pi\)
\(198\) 0 0
\(199\) 11.1545i 0.790725i −0.918525 0.395362i \(-0.870619\pi\)
0.918525 0.395362i \(-0.129381\pi\)
\(200\) 0 0
\(201\) 0.120808i 0.00852111i
\(202\) 0 0
\(203\) 0.960072 0.960072i 0.0673839 0.0673839i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.21724i 0.432128i
\(208\) 0 0
\(209\) 11.1259 0.769591
\(210\) 0 0
\(211\) 2.48377 2.48377i 0.170989 0.170989i −0.616425 0.787414i \(-0.711419\pi\)
0.787414 + 0.616425i \(0.211419\pi\)
\(212\) 0 0
\(213\) 0.569756 0.569756i 0.0390391 0.0390391i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.20140 0.217325
\(218\) 0 0
\(219\) 0.471640 + 0.471640i 0.0318705 + 0.0318705i
\(220\) 0 0
\(221\) 8.20377 8.20377i 0.551846 0.551846i
\(222\) 0 0
\(223\) 21.1384i 1.41553i 0.706448 + 0.707765i \(0.250297\pi\)
−0.706448 + 0.707765i \(0.749703\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.4885 14.4885i −0.961634 0.961634i 0.0376566 0.999291i \(-0.488011\pi\)
−0.999291 + 0.0376566i \(0.988011\pi\)
\(228\) 0 0
\(229\) 10.0956 + 10.0956i 0.667138 + 0.667138i 0.957053 0.289914i \(-0.0936268\pi\)
−0.289914 + 0.957053i \(0.593627\pi\)
\(230\) 0 0
\(231\) 0.110920i 0.00729799i
\(232\) 0 0
\(233\) −3.44995 −0.226014 −0.113007 0.993594i \(-0.536048\pi\)
−0.113007 + 0.993594i \(0.536048\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.735793 + 0.735793i 0.0477949 + 0.0477949i
\(238\) 0 0
\(239\) 18.0060 1.16471 0.582354 0.812935i \(-0.302132\pi\)
0.582354 + 0.812935i \(0.302132\pi\)
\(240\) 0 0
\(241\) 12.6235 0.813154 0.406577 0.913617i \(-0.366722\pi\)
0.406577 + 0.913617i \(0.366722\pi\)
\(242\) 0 0
\(243\) −1.67686 1.67686i −0.107571 0.107571i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.29155 0.527578
\(248\) 0 0
\(249\) 1.32611i 0.0840386i
\(250\) 0 0
\(251\) 9.17919 + 9.17919i 0.579386 + 0.579386i 0.934734 0.355348i \(-0.115638\pi\)
−0.355348 + 0.934734i \(0.615638\pi\)
\(252\) 0 0
\(253\) −4.91929 4.91929i −0.309273 0.309273i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 16.2897i 1.01612i −0.861321 0.508061i \(-0.830363\pi\)
0.861321 0.508061i \(-0.169637\pi\)
\(258\) 0 0
\(259\) 2.86648 2.86648i 0.178115 0.178115i
\(260\) 0 0
\(261\) 7.64282 + 7.64282i 0.473079 + 0.473079i
\(262\) 0 0
\(263\) −10.4898 −0.646831 −0.323416 0.946257i \(-0.604831\pi\)
−0.323416 + 0.946257i \(0.604831\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.979132 0.979132i 0.0599219 0.0599219i
\(268\) 0 0
\(269\) 8.46636 8.46636i 0.516203 0.516203i −0.400217 0.916420i \(-0.631065\pi\)
0.916420 + 0.400217i \(0.131065\pi\)
\(270\) 0 0
\(271\) 8.92117 0.541923 0.270961 0.962590i \(-0.412658\pi\)
0.270961 + 0.962590i \(0.412658\pi\)
\(272\) 0 0
\(273\) 0.0826631i 0.00500300i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 9.36430 9.36430i 0.562646 0.562646i −0.367412 0.930058i \(-0.619756\pi\)
0.930058 + 0.367412i \(0.119756\pi\)
\(278\) 0 0
\(279\) 25.4853i 1.52576i
\(280\) 0 0
\(281\) 3.12921i 0.186673i 0.995635 + 0.0933365i \(0.0297532\pi\)
−0.995635 + 0.0933365i \(0.970247\pi\)
\(282\) 0 0
\(283\) −2.07308 + 2.07308i −0.123232 + 0.123232i −0.766033 0.642801i \(-0.777772\pi\)
0.642801 + 0.766033i \(0.277772\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.41972i 0.0838035i
\(288\) 0 0
\(289\) −4.61834 −0.271667
\(290\) 0 0
\(291\) −0.240571 + 0.240571i −0.0141025 + 0.0141025i
\(292\) 0 0
\(293\) −12.3528 + 12.3528i −0.721659 + 0.721659i −0.968943 0.247284i \(-0.920462\pi\)
0.247284 + 0.968943i \(0.420462\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1.76829 −0.102606
\(298\) 0 0
\(299\) −3.66610 3.66610i −0.212016 0.212016i
\(300\) 0 0
\(301\) −2.33491 + 2.33491i −0.134582 + 0.134582i
\(302\) 0 0
\(303\) 0.856834i 0.0492238i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 10.5938 + 10.5938i 0.604619 + 0.604619i 0.941535 0.336916i \(-0.109384\pi\)
−0.336916 + 0.941535i \(0.609384\pi\)
\(308\) 0 0
\(309\) −0.0719229 0.0719229i −0.00409155 0.00409155i
\(310\) 0 0
\(311\) 19.4153i 1.10094i −0.834854 0.550471i \(-0.814448\pi\)
0.834854 0.550471i \(-0.185552\pi\)
\(312\) 0 0
\(313\) −2.56569 −0.145022 −0.0725108 0.997368i \(-0.523101\pi\)
−0.0725108 + 0.997368i \(0.523101\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.32418 + 7.32418i 0.411367 + 0.411367i 0.882215 0.470848i \(-0.156052\pi\)
−0.470848 + 0.882215i \(0.656052\pi\)
\(318\) 0 0
\(319\) 12.0945 0.677163
\(320\) 0 0
\(321\) −0.711000 −0.0396842
\(322\) 0 0
\(323\) −10.9248 10.9248i −0.607873 0.607873i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1.39428 −0.0771038
\(328\) 0 0
\(329\) 3.65238i 0.201362i
\(330\) 0 0
\(331\) −4.17652 4.17652i −0.229562 0.229562i 0.582948 0.812510i \(-0.301899\pi\)
−0.812510 + 0.582948i \(0.801899\pi\)
\(332\) 0 0
\(333\) 22.8191 + 22.8191i 1.25048 + 1.25048i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 12.4540i 0.678410i −0.940712 0.339205i \(-0.889842\pi\)
0.940712 0.339205i \(-0.110158\pi\)
\(338\) 0 0
\(339\) 0.254371 0.254371i 0.0138155 0.0138155i
\(340\) 0 0
\(341\) 20.1648 + 20.1648i 1.09199 + 1.09199i
\(342\) 0 0
\(343\) 5.20917 0.281269
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 17.5107 17.5107i 0.940024 0.940024i −0.0582766 0.998300i \(-0.518561\pi\)
0.998300 + 0.0582766i \(0.0185605\pi\)
\(348\) 0 0
\(349\) −8.42042 + 8.42042i −0.450735 + 0.450735i −0.895598 0.444863i \(-0.853252\pi\)
0.444863 + 0.895598i \(0.353252\pi\)
\(350\) 0 0
\(351\) −1.31782 −0.0703398
\(352\) 0 0
\(353\) 9.71293i 0.516967i 0.966016 + 0.258484i \(0.0832228\pi\)
−0.966016 + 0.258484i \(0.916777\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0.108916 0.108916i 0.00576443 0.00576443i
\(358\) 0 0
\(359\) 6.77551i 0.357598i −0.983886 0.178799i \(-0.942779\pi\)
0.983886 0.178799i \(-0.0572212\pi\)
\(360\) 0 0
\(361\) 7.95830i 0.418858i
\(362\) 0 0
\(363\) −0.0131274 + 0.0131274i −0.000689012 + 0.000689012i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 34.4591i 1.79875i −0.437176 0.899376i \(-0.644021\pi\)
0.437176 0.899376i \(-0.355979\pi\)
\(368\) 0 0
\(369\) 11.3019 0.588355
\(370\) 0 0
\(371\) 1.14120 1.14120i 0.0592480 0.0592480i
\(372\) 0 0
\(373\) −3.55187 + 3.55187i −0.183909 + 0.183909i −0.793057 0.609148i \(-0.791512\pi\)
0.609148 + 0.793057i \(0.291512\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.01345 0.464216
\(378\) 0 0
\(379\) 26.4464 + 26.4464i 1.35846 + 1.35846i 0.875817 + 0.482644i \(0.160323\pi\)
0.482644 + 0.875817i \(0.339677\pi\)
\(380\) 0 0
\(381\) −1.06518 + 1.06518i −0.0545706 + 0.0545706i
\(382\) 0 0
\(383\) 30.8614i 1.57695i −0.615069 0.788473i \(-0.710872\pi\)
0.615069 0.788473i \(-0.289128\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −18.5875 18.5875i −0.944854 0.944854i
\(388\) 0 0
\(389\) −9.50959 9.50959i −0.482155 0.482155i 0.423664 0.905819i \(-0.360744\pi\)
−0.905819 + 0.423664i \(0.860744\pi\)
\(390\) 0 0
\(391\) 9.66080i 0.488568i
\(392\) 0 0
\(393\) 0.444253 0.0224096
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −24.8540 24.8540i −1.24739 1.24739i −0.956870 0.290518i \(-0.906172\pi\)
−0.290518 0.956870i \(-0.593828\pi\)
\(398\) 0 0
\(399\) 0.110081 0.00551094
\(400\) 0 0
\(401\) 4.69303 0.234359 0.117179 0.993111i \(-0.462615\pi\)
0.117179 + 0.993111i \(0.462615\pi\)
\(402\) 0 0
\(403\) 15.0278 + 15.0278i 0.748590 + 0.748590i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 36.1106 1.78993
\(408\) 0 0
\(409\) 28.2641i 1.39757i 0.715331 + 0.698786i \(0.246276\pi\)
−0.715331 + 0.698786i \(0.753724\pi\)
\(410\) 0 0
\(411\) 1.04073 + 1.04073i 0.0513352 + 0.0513352i
\(412\) 0 0
\(413\) 3.05085 + 3.05085i 0.150123 + 0.150123i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.942858i 0.0461720i
\(418\) 0 0
\(419\) 23.0355 23.0355i 1.12536 1.12536i 0.134433 0.990923i \(-0.457079\pi\)
0.990923 0.134433i \(-0.0429213\pi\)
\(420\) 0 0
\(421\) 5.40760 + 5.40760i 0.263550 + 0.263550i 0.826495 0.562945i \(-0.190332\pi\)
−0.562945 + 0.826495i \(0.690332\pi\)
\(422\) 0 0
\(423\) 29.0754 1.41369
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.273762 + 0.273762i −0.0132483 + 0.0132483i
\(428\) 0 0
\(429\) −0.520675 + 0.520675i −0.0251384 + 0.0251384i
\(430\) 0 0
\(431\) 12.6839 0.610961 0.305481 0.952198i \(-0.401183\pi\)
0.305481 + 0.952198i \(0.401183\pi\)
\(432\) 0 0
\(433\) 23.8511i 1.14621i 0.819482 + 0.573104i \(0.194261\pi\)
−0.819482 + 0.573104i \(0.805739\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.88208 + 4.88208i −0.233542 + 0.233542i
\(438\) 0 0
\(439\) 4.65878i 0.222352i −0.993801 0.111176i \(-0.964538\pi\)
0.993801 0.111176i \(-0.0354617\pi\)
\(440\) 0 0
\(441\) 20.5229i 0.977280i
\(442\) 0 0
\(443\) −8.74048 + 8.74048i −0.415273 + 0.415273i −0.883571 0.468298i \(-0.844867\pi\)
0.468298 + 0.883571i \(0.344867\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.27810i 0.0604520i
\(448\) 0 0
\(449\) 7.28525 0.343812 0.171906 0.985113i \(-0.445007\pi\)
0.171906 + 0.985113i \(0.445007\pi\)
\(450\) 0 0
\(451\) 8.94247 8.94247i 0.421085 0.421085i
\(452\) 0 0
\(453\) −1.18678 + 1.18678i −0.0557596 + 0.0557596i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −25.2194 −1.17971 −0.589857 0.807508i \(-0.700816\pi\)
−0.589857 + 0.807508i \(0.700816\pi\)
\(458\) 0 0
\(459\) 1.73633 + 1.73633i 0.0810451 + 0.0810451i
\(460\) 0 0
\(461\) 13.6698 13.6698i 0.636667 0.636667i −0.313064 0.949732i \(-0.601356\pi\)
0.949732 + 0.313064i \(0.101356\pi\)
\(462\) 0 0
\(463\) 2.77045i 0.128754i 0.997926 + 0.0643768i \(0.0205060\pi\)
−0.997926 + 0.0643768i \(0.979494\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.9587 + 17.9587i 0.831031 + 0.831031i 0.987658 0.156627i \(-0.0500621\pi\)
−0.156627 + 0.987658i \(0.550062\pi\)
\(468\) 0 0
\(469\) 0.364314 + 0.364314i 0.0168225 + 0.0168225i
\(470\) 0 0
\(471\) 1.26306i 0.0581986i
\(472\) 0 0
\(473\) −29.4141 −1.35246
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 9.08470 + 9.08470i 0.415960 + 0.415960i
\(478\) 0 0
\(479\) −22.4540 −1.02595 −0.512975 0.858403i \(-0.671457\pi\)
−0.512975 + 0.858403i \(0.671457\pi\)
\(480\) 0 0
\(481\) 26.9114 1.22705
\(482\) 0 0
\(483\) −0.0486722 0.0486722i −0.00221466 0.00221466i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −27.7615 −1.25799 −0.628997 0.777408i \(-0.716534\pi\)
−0.628997 + 0.777408i \(0.716534\pi\)
\(488\) 0 0
\(489\) 0.916741i 0.0414565i
\(490\) 0 0
\(491\) −16.8993 16.8993i −0.762656 0.762656i 0.214146 0.976802i \(-0.431303\pi\)
−0.976802 + 0.214146i \(0.931303\pi\)
\(492\) 0 0
\(493\) −11.8760 11.8760i −0.534867 0.534867i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.43638i 0.154143i
\(498\) 0 0
\(499\) −1.81950 + 1.81950i −0.0814520 + 0.0814520i −0.746659 0.665207i \(-0.768343\pi\)
0.665207 + 0.746659i \(0.268343\pi\)
\(500\) 0 0
\(501\) −0.500397 0.500397i −0.0223561 0.0223561i
\(502\) 0 0
\(503\) −42.2076 −1.88195 −0.940973 0.338482i \(-0.890087\pi\)
−0.940973 + 0.338482i \(0.890087\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.422139 0.422139i 0.0187478 0.0187478i
\(508\) 0 0
\(509\) 21.9831 21.9831i 0.974382 0.974382i −0.0252980 0.999680i \(-0.508053\pi\)
0.999680 + 0.0252980i \(0.00805345\pi\)
\(510\) 0 0
\(511\) −2.84461 −0.125838
\(512\) 0 0
\(513\) 1.75491i 0.0774812i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 23.0054 23.0054i 1.01178 1.01178i
\(518\) 0 0
\(519\) 1.30034i 0.0570786i
\(520\) 0 0
\(521\) 28.1418i 1.23291i −0.787388 0.616457i \(-0.788567\pi\)
0.787388 0.616457i \(-0.211433\pi\)
\(522\) 0 0
\(523\) 9.58093 9.58093i 0.418945 0.418945i −0.465895 0.884840i \(-0.654268\pi\)
0.884840 + 0.465895i \(0.154268\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 39.6009i 1.72504i
\(528\) 0 0
\(529\) −18.6828 −0.812295
\(530\) 0 0
\(531\) −24.2868 + 24.2868i −1.05396 + 1.05396i
\(532\) 0 0
\(533\) 6.66438 6.66438i 0.288666 0.288666i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.03488 −0.0446582
\(538\) 0 0
\(539\) 16.2384 + 16.2384i 0.699437 + 0.699437i
\(540\) 0 0
\(541\) −26.9128 + 26.9128i −1.15707 + 1.15707i −0.171972 + 0.985102i \(0.555014\pi\)
−0.985102 + 0.171972i \(0.944986\pi\)
\(542\) 0 0
\(543\) 1.30590i 0.0560415i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 10.6627 + 10.6627i 0.455902 + 0.455902i 0.897308 0.441406i \(-0.145520\pi\)
−0.441406 + 0.897308i \(0.645520\pi\)
\(548\) 0 0
\(549\) −2.17933 2.17933i −0.0930115 0.0930115i
\(550\) 0 0
\(551\) 12.0030i 0.511347i
\(552\) 0 0
\(553\) −4.43780 −0.188714
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.8060 + 22.8060i 0.966320 + 0.966320i 0.999451 0.0331307i \(-0.0105477\pi\)
−0.0331307 + 0.999451i \(0.510548\pi\)
\(558\) 0 0
\(559\) −21.9209 −0.927153
\(560\) 0 0
\(561\) 1.37207 0.0579287
\(562\) 0 0
\(563\) −0.472513 0.472513i −0.0199140 0.0199140i 0.697080 0.716994i \(-0.254482\pi\)
−0.716994 + 0.697080i \(0.754482\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 3.35664 0.140965
\(568\) 0 0
\(569\) 3.14792i 0.131967i 0.997821 + 0.0659837i \(0.0210185\pi\)
−0.997821 + 0.0659837i \(0.978981\pi\)
\(570\) 0 0
\(571\) −5.78162 5.78162i −0.241953 0.241953i 0.575704 0.817658i \(-0.304728\pi\)
−0.817658 + 0.575704i \(0.804728\pi\)
\(572\) 0 0
\(573\) −0.104748 0.104748i −0.00437593 0.00437593i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 29.0110i 1.20774i 0.797081 + 0.603872i \(0.206376\pi\)
−0.797081 + 0.603872i \(0.793624\pi\)
\(578\) 0 0
\(579\) 0.100588 0.100588i 0.00418029 0.00418029i
\(580\) 0 0
\(581\) 3.99908 + 3.99908i 0.165910 + 0.165910i
\(582\) 0 0
\(583\) 14.3762 0.595403
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.4099 + 20.4099i −0.842408 + 0.842408i −0.989172 0.146764i \(-0.953114\pi\)
0.146764 + 0.989172i \(0.453114\pi\)
\(588\) 0 0
\(589\) 20.0123 20.0123i 0.824592 0.824592i
\(590\) 0 0
\(591\) 0.636074 0.0261646
\(592\) 0 0
\(593\) 28.9098i 1.18718i −0.804766 0.593592i \(-0.797709\pi\)
0.804766 0.593592i \(-0.202291\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.695161 0.695161i 0.0284511 0.0284511i
\(598\) 0 0
\(599\) 11.7893i 0.481696i 0.970563 + 0.240848i \(0.0774256\pi\)
−0.970563 + 0.240848i \(0.922574\pi\)
\(600\) 0 0
\(601\) 17.7398i 0.723621i −0.932252 0.361810i \(-0.882159\pi\)
0.932252 0.361810i \(-0.117841\pi\)
\(602\) 0 0
\(603\) −2.90019 + 2.90019i −0.118105 + 0.118105i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 25.8393i 1.04878i 0.851477 + 0.524392i \(0.175707\pi\)
−0.851477 + 0.524392i \(0.824293\pi\)
\(608\) 0 0
\(609\) 0.119665 0.00484907
\(610\) 0 0
\(611\) 17.1448 17.1448i 0.693605 0.693605i
\(612\) 0 0
\(613\) 31.5411 31.5411i 1.27393 1.27393i 0.329929 0.944006i \(-0.392975\pi\)
0.944006 0.329929i \(-0.107025\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15.0637 −0.606440 −0.303220 0.952921i \(-0.598062\pi\)
−0.303220 + 0.952921i \(0.598062\pi\)
\(618\) 0 0
\(619\) −10.4975 10.4975i −0.421929 0.421929i 0.463938 0.885868i \(-0.346436\pi\)
−0.885868 + 0.463938i \(0.846436\pi\)
\(620\) 0 0
\(621\) 0.775933 0.775933i 0.0311371 0.0311371i
\(622\) 0 0
\(623\) 5.90545i 0.236597i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0.693373 + 0.693373i 0.0276906 + 0.0276906i
\(628\) 0 0
\(629\) −35.4581 35.4581i −1.41381 1.41381i
\(630\) 0 0
\(631\) 43.6349i 1.73708i 0.495621 + 0.868539i \(0.334940\pi\)
−0.495621 + 0.868539i \(0.665060\pi\)
\(632\) 0 0
\(633\) 0.309581 0.0123047
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 12.1017 + 12.1017i 0.479486 + 0.479486i
\(638\) 0 0
\(639\) −27.3559 −1.08218
\(640\) 0 0
\(641\) −34.2710 −1.35362 −0.676812 0.736156i \(-0.736639\pi\)
−0.676812 + 0.736156i \(0.736639\pi\)
\(642\) 0 0
\(643\) 30.1937 + 30.1937i 1.19072 + 1.19072i 0.976865 + 0.213857i \(0.0686027\pi\)
0.213857 + 0.976865i \(0.431397\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.7474 −0.619096 −0.309548 0.950884i \(-0.600178\pi\)
−0.309548 + 0.950884i \(0.600178\pi\)
\(648\) 0 0
\(649\) 38.4331i 1.50863i
\(650\) 0 0
\(651\) 0.199514 + 0.199514i 0.00781956 + 0.00781956i
\(652\) 0 0
\(653\) 5.80619 + 5.80619i 0.227214 + 0.227214i 0.811528 0.584314i \(-0.198636\pi\)
−0.584314 + 0.811528i \(0.698636\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 22.6450i 0.883465i
\(658\) 0 0
\(659\) 1.76782 1.76782i 0.0688647 0.0688647i −0.671836 0.740700i \(-0.734494\pi\)
0.740700 + 0.671836i \(0.234494\pi\)
\(660\) 0 0
\(661\) −12.4824 12.4824i −0.485509 0.485509i 0.421377 0.906886i \(-0.361547\pi\)
−0.906886 + 0.421377i \(0.861547\pi\)
\(662\) 0 0
\(663\) 1.02253 0.0397119
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −5.30714 + 5.30714i −0.205493 + 0.205493i
\(668\) 0 0
\(669\) −1.31736 + 1.31736i −0.0509322 + 0.0509322i
\(670\) 0 0
\(671\) −3.44872 −0.133136
\(672\) 0 0
\(673\) 14.1113i 0.543950i −0.962304 0.271975i \(-0.912323\pi\)
0.962304 0.271975i \(-0.0876768\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8.31191 + 8.31191i −0.319453 + 0.319453i −0.848557 0.529104i \(-0.822528\pi\)
0.529104 + 0.848557i \(0.322528\pi\)
\(678\) 0 0
\(679\) 1.45096i 0.0556827i
\(680\) 0 0
\(681\) 1.80587i 0.0692011i
\(682\) 0 0
\(683\) −30.0811 + 30.0811i −1.15102 + 1.15102i −0.164673 + 0.986348i \(0.552657\pi\)
−0.986348 + 0.164673i \(0.947343\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.25834i 0.0480086i
\(688\) 0 0
\(689\) 10.7139 0.408167
\(690\) 0 0
\(691\) −24.0212 + 24.0212i −0.913810 + 0.913810i −0.996570 0.0827600i \(-0.973627\pi\)
0.0827600 + 0.996570i \(0.473627\pi\)
\(692\) 0 0
\(693\) 2.66282 2.66282i 0.101152 0.101152i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −17.5618 −0.665200
\(698\) 0 0
\(699\) −0.215004 0.215004i −0.00813219 0.00813219i
\(700\) 0 0
\(701\) 10.0971 10.0971i 0.381363 0.381363i −0.490230 0.871593i \(-0.663087\pi\)
0.871593 + 0.490230i \(0.163087\pi\)
\(702\) 0 0
\(703\) 35.8375i 1.35164i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.58392 + 2.58392i 0.0971782 + 0.0971782i
\(708\) 0 0
\(709\) 4.67310 + 4.67310i 0.175502 + 0.175502i 0.789392 0.613890i \(-0.210396\pi\)
−0.613890 + 0.789392i \(0.710396\pi\)
\(710\) 0 0
\(711\) 35.3279i 1.32490i
\(712\) 0 0
\(713\) −17.6968 −0.662752
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.12215 + 1.12215i 0.0419074 + 0.0419074i
\(718\) 0 0
\(719\) −23.5339 −0.877667 −0.438833 0.898568i \(-0.644608\pi\)
−0.438833 + 0.898568i \(0.644608\pi\)
\(720\) 0 0
\(721\) 0.433789 0.0161552
\(722\) 0 0
\(723\) 0.786710 + 0.786710i 0.0292581 + 0.0292581i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −16.6692 −0.618226 −0.309113 0.951025i \(-0.600032\pi\)
−0.309113 + 0.951025i \(0.600032\pi\)
\(728\) 0 0
\(729\) 26.5814i 0.984498i
\(730\) 0 0
\(731\) 28.8826 + 28.8826i 1.06826 + 1.06826i
\(732\) 0 0
\(733\) 27.4684 + 27.4684i 1.01457 + 1.01457i 0.999892 + 0.0146760i \(0.00467168\pi\)
0.0146760 + 0.999892i \(0.495328\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.58945i 0.169055i
\(738\) 0 0
\(739\) 22.7939 22.7939i 0.838486 0.838486i −0.150174 0.988660i \(-0.547983\pi\)
0.988660 + 0.150174i \(0.0479832\pi\)
\(740\) 0 0
\(741\) 0.516736 + 0.516736i 0.0189828 + 0.0189828i
\(742\) 0 0
\(743\) 16.4964 0.605196 0.302598 0.953118i \(-0.402146\pi\)
0.302598 + 0.953118i \(0.402146\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −31.8354 + 31.8354i −1.16480 + 1.16480i
\(748\) 0 0
\(749\) 2.14413 2.14413i 0.0783449 0.0783449i
\(750\) 0 0
\(751\) 21.6997 0.791833 0.395917 0.918286i \(-0.370427\pi\)
0.395917 + 0.918286i \(0.370427\pi\)
\(752\) 0 0
\(753\) 1.14411i 0.0416937i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.73819 + 1.73819i −0.0631757 + 0.0631757i −0.737989 0.674813i \(-0.764224\pi\)
0.674813 + 0.737989i \(0.264224\pi\)
\(758\) 0 0
\(759\) 0.613149i 0.0222559i
\(760\) 0 0
\(761\) 46.5311i 1.68675i −0.537323 0.843376i \(-0.680565\pi\)
0.537323 0.843376i \(-0.319435\pi\)
\(762\) 0 0
\(763\) 4.20467 4.20467i 0.152219 0.152219i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 28.6423i 1.03421i
\(768\) 0 0
\(769\) −15.4731 −0.557976 −0.278988 0.960295i \(-0.589999\pi\)
−0.278988 + 0.960295i \(0.589999\pi\)
\(770\) 0 0
\(771\) 1.01519 1.01519i 0.0365610 0.0365610i
\(772\) 0 0
\(773\) −5.69848 + 5.69848i −0.204960 + 0.204960i −0.802121 0.597161i \(-0.796295\pi\)
0.597161 + 0.802121i \(0.296295\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0.357284 0.0128175
\(778\) 0 0
\(779\) −8.87484 8.87484i −0.317974 0.317974i
\(780\) 0 0
\(781\) −21.6449 + 21.6449i −0.774516 + 0.774516i
\(782\) 0 0
\(783\) 1.90770i 0.0681757i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 18.1351 + 18.1351i 0.646448 + 0.646448i 0.952133 0.305685i \(-0.0988855\pi\)
−0.305685 + 0.952133i \(0.598885\pi\)
\(788\) 0 0
\(789\) −0.653736 0.653736i −0.0232736 0.0232736i
\(790\) 0 0
\(791\) 1.53419i 0.0545495i
\(792\) 0 0
\(793\) −2.57016 −0.0912690
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4.51575 4.51575i −0.159956 0.159956i 0.622591 0.782547i \(-0.286080\pi\)
−0.782547 + 0.622591i \(0.786080\pi\)
\(798\) 0 0
\(799\) −45.1795 −1.59834
\(800\) 0 0
\(801\) −47.0114 −1.66107
\(802\) 0