Properties

Label 1600.2.q.f.49.5
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 49.5
Root \(1.35979 + 0.388551i\) of defining polynomial
Character \(\chi\) \(=\) 1600.49
Dual form 1600.2.q.f.849.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.03997 + 1.03997i) q^{3} +1.49668 q^{7} -0.836925i q^{9} +O(q^{10})\) \(q+(1.03997 + 1.03997i) q^{3} +1.49668 q^{7} -0.836925i q^{9} +(-0.423260 - 0.423260i) q^{11} +(-1.85704 - 1.85704i) q^{13} -6.50950i q^{17} +(-1.75725 + 1.75725i) q^{19} +(1.55650 + 1.55650i) q^{21} +7.19295 q^{23} +(3.99029 - 3.99029i) q^{27} +(6.57892 - 6.57892i) q^{29} +6.75252 q^{31} -0.880355i q^{33} +(1.95300 - 1.95300i) q^{37} -3.86254i q^{39} +7.70745i q^{41} +(-6.13581 + 6.13581i) q^{43} -6.65476i q^{47} -4.75994 q^{49} +(6.76969 - 6.76969i) q^{51} +(-5.29390 + 5.29390i) q^{53} -3.65497 q^{57} +(5.91841 + 5.91841i) q^{59} +(-1.43686 + 1.43686i) q^{61} -1.25261i q^{63} +(-6.35614 - 6.35614i) q^{67} +(7.48045 + 7.48045i) q^{69} +4.08932i q^{71} +2.43800 q^{73} +(-0.633485 - 0.633485i) q^{77} +11.6722 q^{79} +5.78878 q^{81} +(-2.81439 - 2.81439i) q^{83} +13.6838 q^{87} +10.5543i q^{89} +(-2.77940 - 2.77940i) q^{91} +(7.02242 + 7.02242i) q^{93} -18.1512i q^{97} +(-0.354237 + 0.354237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{3} - 12q^{7} + O(q^{10}) \) \( 12q + 2q^{3} - 12q^{7} + 2q^{11} + 4q^{13} - 14q^{19} - 20q^{21} - 12q^{23} - 10q^{27} + 4q^{31} - 8q^{37} - 4q^{49} - 10q^{51} - 16q^{53} - 16q^{57} + 20q^{59} + 4q^{61} - 50q^{67} + 40q^{73} - 8q^{77} + 12q^{79} - 8q^{81} - 2q^{83} + 64q^{87} + 44q^{93} + 12q^{99} + O(q^{100}) \)

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
\(3\) 1.03997 + 1.03997i 0.600427 + 0.600427i 0.940426 0.339999i \(-0.110427\pi\)
−0.339999 + 0.940426i \(0.610427\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.49668 0.565693 0.282846 0.959165i \(-0.408721\pi\)
0.282846 + 0.959165i \(0.408721\pi\)
\(8\) 0 0
\(9\) 0.836925i 0.278975i
\(10\) 0 0
\(11\) −0.423260 0.423260i −0.127618 0.127618i 0.640413 0.768031i \(-0.278763\pi\)
−0.768031 + 0.640413i \(0.778763\pi\)
\(12\) 0 0
\(13\) −1.85704 1.85704i −0.515051 0.515051i 0.401019 0.916070i \(-0.368656\pi\)
−0.916070 + 0.401019i \(0.868656\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.50950i 1.57879i −0.613888 0.789393i \(-0.710395\pi\)
0.613888 0.789393i \(-0.289605\pi\)
\(18\) 0 0
\(19\) −1.75725 + 1.75725i −0.403141 + 0.403141i −0.879338 0.476198i \(-0.842015\pi\)
0.476198 + 0.879338i \(0.342015\pi\)
\(20\) 0 0
\(21\) 1.55650 + 1.55650i 0.339657 + 0.339657i
\(22\) 0 0
\(23\) 7.19295 1.49983 0.749917 0.661532i \(-0.230094\pi\)
0.749917 + 0.661532i \(0.230094\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.99029 3.99029i 0.767931 0.767931i
\(28\) 0 0
\(29\) 6.57892 6.57892i 1.22167 1.22167i 0.254639 0.967036i \(-0.418043\pi\)
0.967036 0.254639i \(-0.0819565\pi\)
\(30\) 0 0
\(31\) 6.75252 1.21279 0.606394 0.795164i \(-0.292615\pi\)
0.606394 + 0.795164i \(0.292615\pi\)
\(32\) 0 0
\(33\) 0.880355i 0.153250i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.95300 1.95300i 0.321071 0.321071i −0.528107 0.849178i \(-0.677098\pi\)
0.849178 + 0.528107i \(0.177098\pi\)
\(38\) 0 0
\(39\) 3.86254i 0.618501i
\(40\) 0 0
\(41\) 7.70745i 1.20370i 0.798609 + 0.601851i \(0.205570\pi\)
−0.798609 + 0.601851i \(0.794430\pi\)
\(42\) 0 0
\(43\) −6.13581 + 6.13581i −0.935702 + 0.935702i −0.998054 0.0623522i \(-0.980140\pi\)
0.0623522 + 0.998054i \(0.480140\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.65476i 0.970697i −0.874321 0.485348i \(-0.838693\pi\)
0.874321 0.485348i \(-0.161307\pi\)
\(48\) 0 0
\(49\) −4.75994 −0.679992
\(50\) 0 0
\(51\) 6.76969 6.76969i 0.947946 0.947946i
\(52\) 0 0
\(53\) −5.29390 + 5.29390i −0.727173 + 0.727173i −0.970056 0.242882i \(-0.921907\pi\)
0.242882 + 0.970056i \(0.421907\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.65497 −0.484113
\(58\) 0 0
\(59\) 5.91841 + 5.91841i 0.770511 + 0.770511i 0.978196 0.207685i \(-0.0665929\pi\)
−0.207685 + 0.978196i \(0.566593\pi\)
\(60\) 0 0
\(61\) −1.43686 + 1.43686i −0.183971 + 0.183971i −0.793084 0.609113i \(-0.791526\pi\)
0.609113 + 0.793084i \(0.291526\pi\)
\(62\) 0 0
\(63\) 1.25261i 0.157814i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.35614 6.35614i −0.776526 0.776526i 0.202712 0.979238i \(-0.435024\pi\)
−0.979238 + 0.202712i \(0.935024\pi\)
\(68\) 0 0
\(69\) 7.48045 + 7.48045i 0.900540 + 0.900540i
\(70\) 0 0
\(71\) 4.08932i 0.485313i 0.970112 + 0.242657i \(0.0780188\pi\)
−0.970112 + 0.242657i \(0.921981\pi\)
\(72\) 0 0
\(73\) 2.43800 0.285346 0.142673 0.989770i \(-0.454430\pi\)
0.142673 + 0.989770i \(0.454430\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.633485 0.633485i −0.0721924 0.0721924i
\(78\) 0 0
\(79\) 11.6722 1.31323 0.656615 0.754226i \(-0.271988\pi\)
0.656615 + 0.754226i \(0.271988\pi\)
\(80\) 0 0
\(81\) 5.78878 0.643198
\(82\) 0 0
\(83\) −2.81439 2.81439i −0.308919 0.308919i 0.535571 0.844490i \(-0.320096\pi\)
−0.844490 + 0.535571i \(0.820096\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 13.6838 1.46705
\(88\) 0 0
\(89\) 10.5543i 1.11876i 0.828912 + 0.559379i \(0.188960\pi\)
−0.828912 + 0.559379i \(0.811040\pi\)
\(90\) 0 0
\(91\) −2.77940 2.77940i −0.291360 0.291360i
\(92\) 0 0
\(93\) 7.02242 + 7.02242i 0.728191 + 0.728191i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 18.1512i 1.84298i −0.388407 0.921488i \(-0.626975\pi\)
0.388407 0.921488i \(-0.373025\pi\)
\(98\) 0 0
\(99\) −0.354237 + 0.354237i −0.0356021 + 0.0356021i
\(100\) 0 0
\(101\) −1.04036 1.04036i −0.103520 0.103520i 0.653450 0.756970i \(-0.273321\pi\)
−0.756970 + 0.653450i \(0.773321\pi\)
\(102\) 0 0
\(103\) 0.955267 0.0941253 0.0470626 0.998892i \(-0.485014\pi\)
0.0470626 + 0.998892i \(0.485014\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.20266 + 7.20266i −0.696308 + 0.696308i −0.963612 0.267305i \(-0.913867\pi\)
0.267305 + 0.963612i \(0.413867\pi\)
\(108\) 0 0
\(109\) 5.67807 5.67807i 0.543861 0.543861i −0.380798 0.924658i \(-0.624351\pi\)
0.924658 + 0.380798i \(0.124351\pi\)
\(110\) 0 0
\(111\) 4.06212 0.385560
\(112\) 0 0
\(113\) 1.94751i 0.183206i 0.995796 + 0.0916029i \(0.0291991\pi\)
−0.995796 + 0.0916029i \(0.970801\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.55420 + 1.55420i −0.143686 + 0.143686i
\(118\) 0 0
\(119\) 9.74266i 0.893108i
\(120\) 0 0
\(121\) 10.6417i 0.967427i
\(122\) 0 0
\(123\) −8.01552 + 8.01552i −0.722735 + 0.722735i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.31796i 0.116950i −0.998289 0.0584750i \(-0.981376\pi\)
0.998289 0.0584750i \(-0.0186238\pi\)
\(128\) 0 0
\(129\) −12.7621 −1.12364
\(130\) 0 0
\(131\) −1.03026 + 1.03026i −0.0900139 + 0.0900139i −0.750680 0.660666i \(-0.770274\pi\)
0.660666 + 0.750680i \(0.270274\pi\)
\(132\) 0 0
\(133\) −2.63004 + 2.63004i −0.228054 + 0.228054i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.75559 0.320862 0.160431 0.987047i \(-0.448712\pi\)
0.160431 + 0.987047i \(0.448712\pi\)
\(138\) 0 0
\(139\) 12.9485 + 12.9485i 1.09828 + 1.09828i 0.994612 + 0.103669i \(0.0330584\pi\)
0.103669 + 0.994612i \(0.466942\pi\)
\(140\) 0 0
\(141\) 6.92075 6.92075i 0.582832 0.582832i
\(142\) 0 0
\(143\) 1.57202i 0.131459i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.95020 4.95020i −0.408285 0.408285i
\(148\) 0 0
\(149\) 15.8472 + 15.8472i 1.29825 + 1.29825i 0.929545 + 0.368709i \(0.120200\pi\)
0.368709 + 0.929545i \(0.379800\pi\)
\(150\) 0 0
\(151\) 11.5316i 0.938424i 0.883085 + 0.469212i \(0.155462\pi\)
−0.883085 + 0.469212i \(0.844538\pi\)
\(152\) 0 0
\(153\) −5.44797 −0.440442
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.41891 + 5.41891i 0.432476 + 0.432476i 0.889470 0.456994i \(-0.151074\pi\)
−0.456994 + 0.889470i \(0.651074\pi\)
\(158\) 0 0
\(159\) −11.0110 −0.873229
\(160\) 0 0
\(161\) 10.7656 0.848445
\(162\) 0 0
\(163\) −6.47288 6.47288i −0.506995 0.506995i 0.406608 0.913603i \(-0.366711\pi\)
−0.913603 + 0.406608i \(0.866711\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.29734 −0.642068 −0.321034 0.947068i \(-0.604030\pi\)
−0.321034 + 0.947068i \(0.604030\pi\)
\(168\) 0 0
\(169\) 6.10279i 0.469445i
\(170\) 0 0
\(171\) 1.47069 + 1.47069i 0.112466 + 0.112466i
\(172\) 0 0
\(173\) 11.9420 + 11.9420i 0.907935 + 0.907935i 0.996105 0.0881700i \(-0.0281019\pi\)
−0.0881700 + 0.996105i \(0.528102\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.3099i 0.925271i
\(178\) 0 0
\(179\) −10.8703 + 10.8703i −0.812481 + 0.812481i −0.985005 0.172524i \(-0.944808\pi\)
0.172524 + 0.985005i \(0.444808\pi\)
\(180\) 0 0
\(181\) −4.09403 4.09403i −0.304307 0.304307i 0.538389 0.842696i \(-0.319033\pi\)
−0.842696 + 0.538389i \(0.819033\pi\)
\(182\) 0 0
\(183\) −2.98858 −0.220922
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.75521 + 2.75521i −0.201481 + 0.201481i
\(188\) 0 0
\(189\) 5.97219 5.97219i 0.434413 0.434413i
\(190\) 0 0
\(191\) −19.2542 −1.39319 −0.696594 0.717466i \(-0.745302\pi\)
−0.696594 + 0.717466i \(0.745302\pi\)
\(192\) 0 0
\(193\) 24.8152i 1.78624i −0.449820 0.893119i \(-0.648512\pi\)
0.449820 0.893119i \(-0.351488\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.81324 + 2.81324i −0.200435 + 0.200435i −0.800186 0.599751i \(-0.795266\pi\)
0.599751 + 0.800186i \(0.295266\pi\)
\(198\) 0 0
\(199\) 21.2194i 1.50420i −0.659048 0.752101i \(-0.729041\pi\)
0.659048 0.752101i \(-0.270959\pi\)
\(200\) 0 0
\(201\) 13.2204i 0.932495i
\(202\) 0 0
\(203\) 9.84655 9.84655i 0.691092 0.691092i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.01996i 0.418416i
\(208\) 0 0
\(209\) 1.48755 0.102896
\(210\) 0 0
\(211\) −15.5715 + 15.5715i −1.07199 + 1.07199i −0.0747872 + 0.997200i \(0.523828\pi\)
−0.997200 + 0.0747872i \(0.976172\pi\)
\(212\) 0 0
\(213\) −4.25277 + 4.25277i −0.291395 + 0.291395i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 10.1064 0.686065
\(218\) 0 0
\(219\) 2.53545 + 2.53545i 0.171330 + 0.171330i
\(220\) 0 0
\(221\) −12.0884 + 12.0884i −0.813155 + 0.813155i
\(222\) 0 0
\(223\) 7.88779i 0.528205i 0.964495 + 0.264103i \(0.0850758\pi\)
−0.964495 + 0.264103i \(0.914924\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.98838 5.98838i −0.397463 0.397463i 0.479874 0.877337i \(-0.340682\pi\)
−0.877337 + 0.479874i \(0.840682\pi\)
\(228\) 0 0
\(229\) −19.4584 19.4584i −1.28585 1.28585i −0.937286 0.348563i \(-0.886670\pi\)
−0.348563 0.937286i \(-0.613330\pi\)
\(230\) 0 0
\(231\) 1.31761i 0.0866925i
\(232\) 0 0
\(233\) −2.68717 −0.176042 −0.0880212 0.996119i \(-0.528054\pi\)
−0.0880212 + 0.996119i \(0.528054\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 12.1388 + 12.1388i 0.788499 + 0.788499i
\(238\) 0 0
\(239\) −12.6359 −0.817346 −0.408673 0.912681i \(-0.634008\pi\)
−0.408673 + 0.912681i \(0.634008\pi\)
\(240\) 0 0
\(241\) 7.53314 0.485252 0.242626 0.970120i \(-0.421991\pi\)
0.242626 + 0.970120i \(0.421991\pi\)
\(242\) 0 0
\(243\) −5.95070 5.95070i −0.381738 0.381738i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.52658 0.415276
\(248\) 0 0
\(249\) 5.85376i 0.370967i
\(250\) 0 0
\(251\) 9.95683 + 9.95683i 0.628470 + 0.628470i 0.947683 0.319213i \(-0.103419\pi\)
−0.319213 + 0.947683i \(0.603419\pi\)
\(252\) 0 0
\(253\) −3.04449 3.04449i −0.191405 0.191405i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.51630i 0.281719i −0.990030 0.140860i \(-0.955013\pi\)
0.990030 0.140860i \(-0.0449866\pi\)
\(258\) 0 0
\(259\) 2.92302 2.92302i 0.181628 0.181628i
\(260\) 0 0
\(261\) −5.50606 5.50606i −0.340817 0.340817i
\(262\) 0 0
\(263\) 20.2127 1.24637 0.623185 0.782075i \(-0.285838\pi\)
0.623185 + 0.782075i \(0.285838\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −10.9762 + 10.9762i −0.671732 + 0.671732i
\(268\) 0 0
\(269\) −16.9430 + 16.9430i −1.03304 + 1.03304i −0.0335999 + 0.999435i \(0.510697\pi\)
−0.999435 + 0.0335999i \(0.989303\pi\)
\(270\) 0 0
\(271\) 3.64054 0.221147 0.110573 0.993868i \(-0.464731\pi\)
0.110573 + 0.993868i \(0.464731\pi\)
\(272\) 0 0
\(273\) 5.78099i 0.349881i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −16.0090 + 16.0090i −0.961888 + 0.961888i −0.999300 0.0374115i \(-0.988089\pi\)
0.0374115 + 0.999300i \(0.488089\pi\)
\(278\) 0 0
\(279\) 5.65135i 0.338338i
\(280\) 0 0
\(281\) 5.51857i 0.329210i 0.986360 + 0.164605i \(0.0526350\pi\)
−0.986360 + 0.164605i \(0.947365\pi\)
\(282\) 0 0
\(283\) 2.36694 2.36694i 0.140700 0.140700i −0.633249 0.773949i \(-0.718279\pi\)
0.773949 + 0.633249i \(0.218279\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 11.5356i 0.680925i
\(288\) 0 0
\(289\) −25.3736 −1.49257
\(290\) 0 0
\(291\) 18.8767 18.8767i 1.10657 1.10657i
\(292\) 0 0
\(293\) 19.1812 19.1812i 1.12058 1.12058i 0.128922 0.991655i \(-0.458848\pi\)
0.991655 0.128922i \(-0.0411517\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.37786 −0.196003
\(298\) 0 0
\(299\) −13.3576 13.3576i −0.772491 0.772491i
\(300\) 0 0
\(301\) −9.18335 + 9.18335i −0.529320 + 0.529320i
\(302\) 0 0
\(303\) 2.16390i 0.124313i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 19.9292 + 19.9292i 1.13742 + 1.13742i 0.988911 + 0.148507i \(0.0474469\pi\)
0.148507 + 0.988911i \(0.452553\pi\)
\(308\) 0 0
\(309\) 0.993449 + 0.993449i 0.0565153 + 0.0565153i
\(310\) 0 0
\(311\) 5.73314i 0.325096i 0.986701 + 0.162548i \(0.0519713\pi\)
−0.986701 + 0.162548i \(0.948029\pi\)
\(312\) 0 0
\(313\) −0.212621 −0.0120180 −0.00600902 0.999982i \(-0.501913\pi\)
−0.00600902 + 0.999982i \(0.501913\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.21582 + 3.21582i 0.180618 + 0.180618i 0.791625 0.611007i \(-0.209235\pi\)
−0.611007 + 0.791625i \(0.709235\pi\)
\(318\) 0 0
\(319\) −5.56919 −0.311815
\(320\) 0 0
\(321\) −14.9811 −0.836164
\(322\) 0 0
\(323\) 11.4388 + 11.4388i 0.636473 + 0.636473i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 11.8101 0.653097
\(328\) 0 0
\(329\) 9.96006i 0.549116i
\(330\) 0 0
\(331\) −22.0295 22.0295i −1.21085 1.21085i −0.970747 0.240106i \(-0.922818\pi\)
−0.240106 0.970747i \(-0.577182\pi\)
\(332\) 0 0
\(333\) −1.63451 1.63451i −0.0895708 0.0895708i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 11.2122i 0.610767i 0.952229 + 0.305384i \(0.0987847\pi\)
−0.952229 + 0.305384i \(0.901215\pi\)
\(338\) 0 0
\(339\) −2.02535 + 2.02535i −0.110002 + 0.110002i
\(340\) 0 0
\(341\) −2.85807 2.85807i −0.154773 0.154773i
\(342\) 0 0
\(343\) −17.6009 −0.950359
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.23653 + 1.23653i −0.0663803 + 0.0663803i −0.739518 0.673137i \(-0.764946\pi\)
0.673137 + 0.739518i \(0.264946\pi\)
\(348\) 0 0
\(349\) 5.61778 5.61778i 0.300713 0.300713i −0.540580 0.841293i \(-0.681795\pi\)
0.841293 + 0.540580i \(0.181795\pi\)
\(350\) 0 0
\(351\) −14.8203 −0.791047
\(352\) 0 0
\(353\) 0.748709i 0.0398497i 0.999801 + 0.0199249i \(0.00634270\pi\)
−0.999801 + 0.0199249i \(0.993657\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 10.1321 10.1321i 0.536246 0.536246i
\(358\) 0 0
\(359\) 2.69883i 0.142439i −0.997461 0.0712195i \(-0.977311\pi\)
0.997461 0.0712195i \(-0.0226891\pi\)
\(360\) 0 0
\(361\) 12.8241i 0.674955i
\(362\) 0 0
\(363\) 11.0671 11.0671i 0.580870 0.580870i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 20.6101i 1.07584i 0.842996 + 0.537920i \(0.180790\pi\)
−0.842996 + 0.537920i \(0.819210\pi\)
\(368\) 0 0
\(369\) 6.45056 0.335802
\(370\) 0 0
\(371\) −7.92329 + 7.92329i −0.411357 + 0.411357i
\(372\) 0 0
\(373\) −5.24143 + 5.24143i −0.271391 + 0.271391i −0.829660 0.558269i \(-0.811466\pi\)
0.558269 + 0.829660i \(0.311466\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −24.4347 −1.25845
\(378\) 0 0
\(379\) 5.41344 + 5.41344i 0.278070 + 0.278070i 0.832338 0.554268i \(-0.187002\pi\)
−0.554268 + 0.832338i \(0.687002\pi\)
\(380\) 0 0
\(381\) 1.37064 1.37064i 0.0702199 0.0702199i
\(382\) 0 0
\(383\) 29.5087i 1.50782i −0.656975 0.753912i \(-0.728164\pi\)
0.656975 0.753912i \(-0.271836\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 5.13521 + 5.13521i 0.261037 + 0.261037i
\(388\) 0 0
\(389\) −1.37884 1.37884i −0.0699099 0.0699099i 0.671287 0.741197i \(-0.265742\pi\)
−0.741197 + 0.671287i \(0.765742\pi\)
\(390\) 0 0
\(391\) 46.8225i 2.36792i
\(392\) 0 0
\(393\) −2.14287 −0.108094
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −21.9750 21.9750i −1.10289 1.10289i −0.994060 0.108832i \(-0.965289\pi\)
−0.108832 0.994060i \(-0.534711\pi\)
\(398\) 0 0
\(399\) −5.47033 −0.273859
\(400\) 0 0
\(401\) −31.4584 −1.57096 −0.785479 0.618889i \(-0.787583\pi\)
−0.785479 + 0.618889i \(0.787583\pi\)
\(402\) 0 0
\(403\) −12.5397 12.5397i −0.624648 0.624648i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.65325 −0.0819487
\(408\) 0 0
\(409\) 12.8017i 0.633003i 0.948592 + 0.316502i \(0.102508\pi\)
−0.948592 + 0.316502i \(0.897492\pi\)
\(410\) 0 0
\(411\) 3.90570 + 3.90570i 0.192654 + 0.192654i
\(412\) 0 0
\(413\) 8.85797 + 8.85797i 0.435872 + 0.435872i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 26.9322i 1.31888i
\(418\) 0 0
\(419\) −11.4979 + 11.4979i −0.561709 + 0.561709i −0.929793 0.368084i \(-0.880014\pi\)
0.368084 + 0.929793i \(0.380014\pi\)
\(420\) 0 0
\(421\) 12.5714 + 12.5714i 0.612690 + 0.612690i 0.943646 0.330956i \(-0.107371\pi\)
−0.330956 + 0.943646i \(0.607371\pi\)
\(422\) 0 0
\(423\) −5.56953 −0.270800
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −2.15052 + 2.15052i −0.104071 + 0.104071i
\(428\) 0 0
\(429\) −1.63486 + 1.63486i −0.0789316 + 0.0789316i
\(430\) 0 0
\(431\) 15.2579 0.734946 0.367473 0.930034i \(-0.380223\pi\)
0.367473 + 0.930034i \(0.380223\pi\)
\(432\) 0 0
\(433\) 12.1705i 0.584877i 0.956284 + 0.292439i \(0.0944667\pi\)
−0.956284 + 0.292439i \(0.905533\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.6398 + 12.6398i −0.604644 + 0.604644i
\(438\) 0 0
\(439\) 39.7535i 1.89733i 0.316283 + 0.948665i \(0.397565\pi\)
−0.316283 + 0.948665i \(0.602435\pi\)
\(440\) 0 0
\(441\) 3.98371i 0.189701i
\(442\) 0 0
\(443\) −3.62318 + 3.62318i −0.172142 + 0.172142i −0.787920 0.615778i \(-0.788842\pi\)
0.615778 + 0.787920i \(0.288842\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 32.9612i 1.55901i
\(448\) 0 0
\(449\) 5.38425 0.254098 0.127049 0.991896i \(-0.459449\pi\)
0.127049 + 0.991896i \(0.459449\pi\)
\(450\) 0 0
\(451\) 3.26225 3.26225i 0.153614 0.153614i
\(452\) 0 0
\(453\) −11.9925 + 11.9925i −0.563455 + 0.563455i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.3039 0.669108 0.334554 0.942377i \(-0.391414\pi\)
0.334554 + 0.942377i \(0.391414\pi\)
\(458\) 0 0
\(459\) −25.9748 25.9748i −1.21240 1.21240i
\(460\) 0 0
\(461\) −4.50363 + 4.50363i −0.209755 + 0.209755i −0.804163 0.594408i \(-0.797386\pi\)
0.594408 + 0.804163i \(0.297386\pi\)
\(462\) 0 0
\(463\) 19.3500i 0.899271i 0.893212 + 0.449636i \(0.148446\pi\)
−0.893212 + 0.449636i \(0.851554\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.1773 + 17.1773i 0.794871 + 0.794871i 0.982282 0.187410i \(-0.0600094\pi\)
−0.187410 + 0.982282i \(0.560009\pi\)
\(468\) 0 0
\(469\) −9.51312 9.51312i −0.439275 0.439275i
\(470\) 0 0
\(471\) 11.2710i 0.519341i
\(472\) 0 0
\(473\) 5.19408 0.238824
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 4.43060 + 4.43060i 0.202863 + 0.202863i
\(478\) 0 0
\(479\) 5.54474 0.253346 0.126673 0.991945i \(-0.459570\pi\)
0.126673 + 0.991945i \(0.459570\pi\)
\(480\) 0 0
\(481\) −7.25361 −0.330736
\(482\) 0 0
\(483\) 11.1959 + 11.1959i 0.509429 + 0.509429i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −31.7138 −1.43709 −0.718546 0.695480i \(-0.755192\pi\)
−0.718546 + 0.695480i \(0.755192\pi\)
\(488\) 0 0
\(489\) 13.4632i 0.608827i
\(490\) 0 0
\(491\) −7.39419 7.39419i −0.333695 0.333695i 0.520293 0.853988i \(-0.325823\pi\)
−0.853988 + 0.520293i \(0.825823\pi\)
\(492\) 0 0
\(493\) −42.8255 42.8255i −1.92876 1.92876i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.12041i 0.274538i
\(498\) 0 0
\(499\) 14.0103 14.0103i 0.627189 0.627189i −0.320171 0.947360i \(-0.603740\pi\)
0.947360 + 0.320171i \(0.103740\pi\)
\(500\) 0 0
\(501\) −8.62899 8.62899i −0.385515 0.385515i
\(502\) 0 0
\(503\) 8.43795 0.376230 0.188115 0.982147i \(-0.439762\pi\)
0.188115 + 0.982147i \(0.439762\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.34671 6.34671i 0.281868 0.281868i
\(508\) 0 0
\(509\) −2.09367 + 2.09367i −0.0928004 + 0.0928004i −0.751983 0.659183i \(-0.770902\pi\)
0.659183 + 0.751983i \(0.270902\pi\)
\(510\) 0 0
\(511\) 3.64891 0.161418
\(512\) 0 0
\(513\) 14.0239i 0.619169i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2.81669 + 2.81669i −0.123878 + 0.123878i
\(518\) 0 0
\(519\) 24.8387i 1.09030i
\(520\) 0 0
\(521\) 28.2558i 1.23791i 0.785428 + 0.618954i \(0.212443\pi\)
−0.785428 + 0.618954i \(0.787557\pi\)
\(522\) 0 0
\(523\) −10.1929 + 10.1929i −0.445703 + 0.445703i −0.893923 0.448220i \(-0.852058\pi\)
0.448220 + 0.893923i \(0.352058\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 43.9555i 1.91473i
\(528\) 0 0
\(529\) 28.7385 1.24950
\(530\) 0 0
\(531\) 4.95326 4.95326i 0.214953 0.214953i
\(532\) 0 0
\(533\) 14.3131 14.3131i 0.619967 0.619967i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −22.6095 −0.975671
\(538\) 0 0
\(539\) 2.01469 + 2.01469i 0.0867790 + 0.0867790i
\(540\) 0 0
\(541\) 3.86053 3.86053i 0.165977 0.165977i −0.619231 0.785209i \(-0.712556\pi\)
0.785209 + 0.619231i \(0.212556\pi\)
\(542\) 0 0
\(543\) 8.51534i 0.365428i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.6231 20.6231i −0.881781 0.881781i 0.111935 0.993716i \(-0.464295\pi\)
−0.993716 + 0.111935i \(0.964295\pi\)
\(548\) 0 0
\(549\) 1.20254 + 1.20254i 0.0513233 + 0.0513233i
\(550\) 0 0
\(551\) 23.1216i 0.985014i
\(552\) 0 0
\(553\) 17.4696 0.742884
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.28512 1.28512i −0.0544523 0.0544523i 0.679356 0.733809i \(-0.262259\pi\)
−0.733809 + 0.679356i \(0.762259\pi\)
\(558\) 0 0
\(559\) 22.7889 0.963868
\(560\) 0 0
\(561\) −5.73068 −0.241949
\(562\) 0 0
\(563\) 21.9152 + 21.9152i 0.923615 + 0.923615i 0.997283 0.0736677i \(-0.0234704\pi\)
−0.0736677 + 0.997283i \(0.523470\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 8.66397 0.363852
\(568\) 0 0
\(569\) 35.6668i 1.49523i 0.664132 + 0.747615i \(0.268801\pi\)
−0.664132 + 0.747615i \(0.731199\pi\)
\(570\) 0 0
\(571\) −5.60524 5.60524i −0.234572 0.234572i 0.580026 0.814598i \(-0.303042\pi\)
−0.814598 + 0.580026i \(0.803042\pi\)
\(572\) 0 0
\(573\) −20.0238 20.0238i −0.836507 0.836507i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.43681i 0.101446i −0.998713 0.0507230i \(-0.983847\pi\)
0.998713 0.0507230i \(-0.0161526\pi\)
\(578\) 0 0
\(579\) 25.8071 25.8071i 1.07251 1.07251i
\(580\) 0 0
\(581\) −4.21225 4.21225i −0.174753 0.174753i
\(582\) 0 0
\(583\) 4.48139 0.185600
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.415982 0.415982i 0.0171694 0.0171694i −0.698470 0.715639i \(-0.746135\pi\)
0.715639 + 0.698470i \(0.246135\pi\)
\(588\) 0 0
\(589\) −11.8659 + 11.8659i −0.488924 + 0.488924i
\(590\) 0 0
\(591\) −5.85136 −0.240693
\(592\) 0 0
\(593\) 15.3439i 0.630098i 0.949075 + 0.315049i \(0.102021\pi\)
−0.949075 + 0.315049i \(0.897979\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 22.0675 22.0675i 0.903163 0.903163i
\(598\) 0 0
\(599\) 43.3487i 1.77118i 0.464468 + 0.885590i \(0.346246\pi\)
−0.464468 + 0.885590i \(0.653754\pi\)
\(600\) 0 0
\(601\) 38.7291i 1.57979i −0.613239 0.789897i \(-0.710134\pi\)
0.613239 0.789897i \(-0.289866\pi\)
\(602\) 0 0
\(603\) −5.31961 + 5.31961i −0.216631 + 0.216631i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 34.9068i 1.41682i 0.705800 + 0.708412i \(0.250588\pi\)
−0.705800 + 0.708412i \(0.749412\pi\)
\(608\) 0 0
\(609\) 20.4802 0.829901
\(610\) 0 0
\(611\) −12.3582 + 12.3582i −0.499958 + 0.499958i
\(612\) 0 0
\(613\) −0.151779 + 0.151779i −0.00613031 + 0.00613031i −0.710165 0.704035i \(-0.751380\pi\)
0.704035 + 0.710165i \(0.251380\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.288199 −0.0116025 −0.00580123 0.999983i \(-0.501847\pi\)
−0.00580123 + 0.999983i \(0.501847\pi\)
\(618\) 0 0
\(619\) −11.5307 11.5307i −0.463460 0.463460i 0.436328 0.899788i \(-0.356279\pi\)
−0.899788 + 0.436328i \(0.856279\pi\)
\(620\) 0 0
\(621\) 28.7019 28.7019i 1.15177 1.15177i
\(622\) 0 0
\(623\) 15.7965i 0.632873i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.54700 + 1.54700i 0.0617814 + 0.0617814i
\(628\) 0 0
\(629\) −12.7131 12.7131i −0.506903 0.506903i
\(630\) 0 0
\(631\) 14.2062i 0.565541i −0.959188 0.282771i \(-0.908746\pi\)
0.959188 0.282771i \(-0.0912536\pi\)
\(632\) 0 0
\(633\) −32.3878 −1.28730
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 8.83942 + 8.83942i 0.350230 + 0.350230i
\(638\) 0 0
\(639\) 3.42245 0.135390
\(640\) 0 0
\(641\) 19.7372 0.779572 0.389786 0.920905i \(-0.372549\pi\)
0.389786 + 0.920905i \(0.372549\pi\)
\(642\) 0 0
\(643\) −5.80043 5.80043i −0.228747 0.228747i 0.583422 0.812169i \(-0.301713\pi\)
−0.812169 + 0.583422i \(0.801713\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −46.3186 −1.82097 −0.910485 0.413541i \(-0.864292\pi\)
−0.910485 + 0.413541i \(0.864292\pi\)
\(648\) 0 0
\(649\) 5.01005i 0.196662i
\(650\) 0 0
\(651\) 10.5103 + 10.5103i 0.411932 + 0.411932i
\(652\) 0 0
\(653\) 4.42354 + 4.42354i 0.173106 + 0.173106i 0.788343 0.615236i \(-0.210939\pi\)
−0.615236 + 0.788343i \(0.710939\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.04042i 0.0796045i
\(658\) 0 0
\(659\) −15.2461 + 15.2461i −0.593905 + 0.593905i −0.938684 0.344779i \(-0.887954\pi\)
0.344779 + 0.938684i \(0.387954\pi\)
\(660\) 0 0
\(661\) 19.1271 + 19.1271i 0.743958 + 0.743958i 0.973337 0.229379i \(-0.0736696\pi\)
−0.229379 + 0.973337i \(0.573670\pi\)
\(662\) 0 0
\(663\) −25.1432 −0.976481
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 47.3218 47.3218i 1.83231 1.83231i
\(668\) 0 0
\(669\) −8.20306 + 8.20306i −0.317149 + 0.317149i
\(670\) 0 0
\(671\) 1.21633 0.0469559
\(672\) 0 0
\(673\) 18.5586i 0.715382i 0.933840 + 0.357691i \(0.116436\pi\)
−0.933840 + 0.357691i \(0.883564\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.71844 2.71844i 0.104478 0.104478i −0.652935 0.757414i \(-0.726463\pi\)
0.757414 + 0.652935i \(0.226463\pi\)
\(678\) 0 0
\(679\) 27.1666i 1.04256i
\(680\) 0 0
\(681\) 12.4555i 0.477295i
\(682\) 0 0
\(683\) 12.6646 12.6646i 0.484598 0.484598i −0.421999 0.906596i \(-0.638671\pi\)
0.906596 + 0.421999i \(0.138671\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 40.4723i 1.54412i
\(688\) 0 0
\(689\) 19.6620 0.749063
\(690\) 0 0
\(691\) −26.8892 + 26.8892i −1.02291 + 1.02291i −0.0231826 + 0.999731i \(0.507380\pi\)
−0.999731 + 0.0231826i \(0.992620\pi\)
\(692\) 0 0
\(693\) −0.530180 + 0.530180i −0.0201399 + 0.0201399i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 50.1717 1.90039
\(698\) 0 0
\(699\) −2.79458 2.79458i −0.105701 0.105701i
\(700\) 0 0
\(701\) 25.3725 25.3725i 0.958305 0.958305i −0.0408602 0.999165i \(-0.513010\pi\)
0.999165 + 0.0408602i \(0.0130098\pi\)
\(702\) 0 0
\(703\) 6.86382i 0.258874i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.55709 1.55709i −0.0585606 0.0585606i
\(708\) 0 0
\(709\) −16.1117 16.1117i −0.605089 0.605089i 0.336570 0.941659i \(-0.390733\pi\)
−0.941659 + 0.336570i \(0.890733\pi\)
\(710\) 0 0
\(711\) 9.76879i 0.366358i
\(712\) 0 0
\(713\) 48.5705 1.81898
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −13.1409 13.1409i −0.490757 0.490757i
\(718\) 0 0
\(719\) 29.1676 1.08777 0.543884 0.839160i \(-0.316953\pi\)
0.543884 + 0.839160i \(0.316953\pi\)
\(720\) 0 0
\(721\) 1.42973 0.0532460
\(722\) 0 0
\(723\) 7.83424 + 7.83424i 0.291358 + 0.291358i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 4.13463 0.153345 0.0766724 0.997056i \(-0.475570\pi\)
0.0766724 + 0.997056i \(0.475570\pi\)
\(728\) 0 0
\(729\) 29.7434i 1.10161i
\(730\) 0 0
\(731\) 39.9411 + 39.9411i 1.47727 + 1.47727i
\(732\) 0 0
\(733\) 19.3838 + 19.3838i 0.715957 + 0.715957i 0.967775 0.251817i \(-0.0810282\pi\)
−0.251817 + 0.967775i \(0.581028\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.38060i 0.198197i
\(738\) 0 0
\(739\) 23.9820 23.9820i 0.882194 0.882194i −0.111564 0.993757i \(-0.535586\pi\)
0.993757 + 0.111564i \(0.0355859\pi\)
\(740\) 0 0
\(741\) 6.78744 + 6.78744i 0.249343 + 0.249343i
\(742\) 0 0
\(743\) −10.3473 −0.379604 −0.189802 0.981822i \(-0.560785\pi\)
−0.189802 + 0.981822i \(0.560785\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.35543 + 2.35543i −0.0861808 + 0.0861808i
\(748\) 0 0
\(749\) −10.7801 + 10.7801i −0.393896 + 0.393896i
\(750\) 0 0
\(751\) 37.0217 1.35094 0.675470 0.737387i \(-0.263941\pi\)
0.675470 + 0.737387i \(0.263941\pi\)
\(752\) 0 0
\(753\) 20.7096i 0.754700i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 30.4305 30.4305i 1.10601 1.10601i 0.112345 0.993669i \(-0.464164\pi\)
0.993669 0.112345i \(-0.0358361\pi\)
\(758\) 0 0
\(759\) 6.33235i 0.229850i
\(760\) 0 0
\(761\) 43.1054i 1.56257i 0.624174 + 0.781285i \(0.285436\pi\)
−0.624174 + 0.781285i \(0.714564\pi\)
\(762\) 0 0
\(763\) 8.49827 8.49827i 0.307658 0.307658i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 21.9815i 0.793705i
\(768\) 0 0
\(769\) 31.2507 1.12693 0.563465 0.826140i \(-0.309468\pi\)
0.563465 + 0.826140i \(0.309468\pi\)
\(770\) 0 0
\(771\) 4.69682 4.69682i 0.169152 0.169152i
\(772\) 0 0
\(773\) 24.4047 24.4047i 0.877778 0.877778i −0.115527 0.993304i \(-0.536856\pi\)
0.993304 + 0.115527i \(0.0368556\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.07970 0.218108
\(778\) 0 0
\(779\) −13.5439 13.5439i −0.485261 0.485261i
\(780\) 0 0
\(781\) 1.73085 1.73085i 0.0619345 0.0619345i
\(782\) 0 0
\(783\) 52.5036i 1.87632i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 17.2122 + 17.2122i 0.613549 + 0.613549i 0.943869 0.330320i \(-0.107157\pi\)
−0.330320 + 0.943869i \(0.607157\pi\)
\(788\) 0 0
\(789\) 21.0206 + 21.0206i 0.748354 + 0.748354i
\(790\) 0 0
\(791\) 2.91480i 0.103638i
\(792\) 0 0
\(793\) 5.33662 0.189509
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −20.3220 20.3220i −0.719841 0.719841i 0.248731 0.968573i \(-0.419986\pi\)
−0.968573 + 0.248731i \(0.919986\pi\)
\(798\) 0 0
\(799\) −43.3192 −1.53252
\(800\) 0 0
\(801\) 8.83319 0.312105
\(802\) 0 0