Properties

Label 1600.2.l.g.401.5
Level $1600$
Weight $2$
Character 1600.401
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.l (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 401.5
Root \(1.35979 + 0.388551i\) of defining polynomial
Character \(\chi\) \(=\) 1600.401
Dual form 1600.2.l.g.1201.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.03997 + 1.03997i) q^{3} -1.49668i q^{7} -0.836925i q^{9} +O(q^{10})\) \(q+(1.03997 + 1.03997i) q^{3} -1.49668i q^{7} -0.836925i q^{9} +(-0.423260 + 0.423260i) q^{11} +(-1.85704 - 1.85704i) q^{13} +6.50950 q^{17} +(1.75725 + 1.75725i) q^{19} +(1.55650 - 1.55650i) q^{21} +7.19295i q^{23} +(3.99029 - 3.99029i) q^{27} +(-6.57892 - 6.57892i) q^{29} +6.75252 q^{31} -0.880355 q^{33} +(1.95300 - 1.95300i) q^{37} -3.86254i q^{39} -7.70745i q^{41} +(6.13581 - 6.13581i) q^{43} +6.65476 q^{47} +4.75994 q^{49} +(6.76969 + 6.76969i) q^{51} +(5.29390 - 5.29390i) q^{53} +3.65497i q^{57} +(-5.91841 + 5.91841i) q^{59} +(-1.43686 - 1.43686i) q^{61} -1.25261 q^{63} +(6.35614 + 6.35614i) q^{67} +(-7.48045 + 7.48045i) q^{69} -4.08932i q^{71} +2.43800i q^{73} +(0.633485 + 0.633485i) q^{77} -11.6722 q^{79} +5.78878 q^{81} +(-2.81439 - 2.81439i) q^{83} -13.6838i q^{87} +10.5543i q^{89} +(-2.77940 + 2.77940i) q^{91} +(7.02242 + 7.02242i) q^{93} +18.1512 q^{97} +(0.354237 + 0.354237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{3} + O(q^{10}) \) \( 12q + 2q^{3} + 2q^{11} + 4q^{13} + 8q^{17} + 14q^{19} - 20q^{21} - 10q^{27} + 4q^{31} - 28q^{33} - 8q^{37} + 8q^{47} + 4q^{49} - 10q^{51} + 16q^{53} - 20q^{59} + 4q^{61} - 8q^{63} + 50q^{67} + 8q^{77} - 12q^{79} - 8q^{81} - 2q^{83} + 44q^{93} - 12q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(7\) 1.49668i 0.565693i −0.959165 0.282846i \(-0.908721\pi\)
0.959165 0.282846i \(-0.0912786\pi\)
\(8\) 0 0
\(9\) 0.836925i 0.278975i
\(10\) 0 0
\(11\) −0.423260 + 0.423260i −0.127618 + 0.127618i −0.768031 0.640413i \(-0.778763\pi\)
0.640413 + 0.768031i \(0.278763\pi\)
\(12\) 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
\(17\) 6.50950 1.57879 0.789393 0.613888i \(-0.210395\pi\)
0.789393 + 0.613888i \(0.210395\pi\)
\(18\) 0 0
\(19\) 1.75725 + 1.75725i 0.403141 + 0.403141i 0.879338 0.476198i \(-0.157985\pi\)
−0.476198 + 0.879338i \(0.657985\pi\)
\(20\) 0 0
\(21\) 1.55650 1.55650i 0.339657 0.339657i
\(22\) 0 0
\(23\) 7.19295i 1.49983i 0.661532 + 0.749917i \(0.269906\pi\)
−0.661532 + 0.749917i \(0.730094\pi\)
\(24\) 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 −0.967036 0.254639i \(-0.918043\pi\)
−0.254639 0.967036i \(-0.581957\pi\)
\(30\) 0 0
\(31\) 6.75252 1.21279 0.606394 0.795164i \(-0.292615\pi\)
0.606394 + 0.795164i \(0.292615\pi\)
\(32\) 0 0
\(33\) −0.880355 −0.153250
\(34\) 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 \(-0.794430\pi\)
0.798609 0.601851i \(-0.205570\pi\)
\(42\) 0 0
\(43\) 6.13581 6.13581i 0.935702 0.935702i −0.0623522 0.998054i \(-0.519860\pi\)
0.998054 + 0.0623522i \(0.0198602\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.65476 0.970697 0.485348 0.874321i \(-0.338693\pi\)
0.485348 + 0.874321i \(0.338693\pi\)
\(48\) 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 −0.242882 0.970056i \(-0.578093\pi\)
0.970056 + 0.242882i \(0.0780929\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.65497i 0.484113i
\(58\) 0 0
\(59\) −5.91841 + 5.91841i −0.770511 + 0.770511i −0.978196 0.207685i \(-0.933407\pi\)
0.207685 + 0.978196i \(0.433407\pi\)
\(60\) 0 0
\(61\) −1.43686 1.43686i −0.183971 0.183971i 0.609113 0.793084i \(-0.291526\pi\)
−0.793084 + 0.609113i \(0.791526\pi\)
\(62\) 0 0
\(63\) −1.25261 −0.157814
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.35614 + 6.35614i 0.776526 + 0.776526i 0.979238 0.202712i \(-0.0649756\pi\)
−0.202712 + 0.979238i \(0.564976\pi\)
\(68\) 0 0
\(69\) −7.48045 + 7.48045i −0.900540 + 0.900540i
\(70\) 0 0
\(71\) 4.08932i 0.485313i −0.970112 0.242657i \(-0.921981\pi\)
0.970112 0.242657i \(-0.0780188\pi\)
\(72\) 0 0
\(73\) 2.43800i 0.285346i 0.989770 + 0.142673i \(0.0455698\pi\)
−0.989770 + 0.142673i \(0.954430\pi\)
\(74\) 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 \(-0.728012\pi\)
−0.656615 + 0.754226i \(0.728012\pi\)
\(80\) 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
\(87\) 13.6838i 1.46705i
\(88\) 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
\(97\) 18.1512 1.84298 0.921488 0.388407i \(-0.126975\pi\)
0.921488 + 0.388407i \(0.126975\pi\)
\(98\) 0 0
\(99\) 0.354237 + 0.354237i 0.0356021 + 0.0356021i
\(100\) 0 0
\(101\) −1.04036 + 1.04036i −0.103520 + 0.103520i −0.756970 0.653450i \(-0.773321\pi\)
0.653450 + 0.756970i \(0.273321\pi\)
\(102\) 0 0
\(103\) 0.955267i 0.0941253i 0.998892 + 0.0470626i \(0.0149860\pi\)
−0.998892 + 0.0470626i \(0.985014\pi\)
\(104\) 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 \(-0.375649\pi\)
−0.924658 + 0.380798i \(0.875649\pi\)
\(110\) 0 0
\(111\) 4.06212 0.385560
\(112\) 0 0
\(113\) 1.94751 0.183206 0.0916029 0.995796i \(-0.470801\pi\)
0.0916029 + 0.995796i \(0.470801\pi\)
\(114\) 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
\(127\) 1.31796 0.116950 0.0584750 0.998289i \(-0.481376\pi\)
0.0584750 + 0.998289i \(0.481376\pi\)
\(128\) 0 0
\(129\) 12.7621 1.12364
\(130\) 0 0
\(131\) −1.03026 1.03026i −0.0900139 0.0900139i 0.660666 0.750680i \(-0.270274\pi\)
−0.750680 + 0.660666i \(0.770274\pi\)
\(132\) 0 0
\(133\) 2.63004 2.63004i 0.228054 0.228054i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.75559i 0.320862i −0.987047 0.160431i \(-0.948712\pi\)
0.987047 0.160431i \(-0.0512884\pi\)
\(138\) 0 0
\(139\) −12.9485 + 12.9485i −1.09828 + 1.09828i −0.103669 + 0.994612i \(0.533058\pi\)
−0.994612 + 0.103669i \(0.966942\pi\)
\(140\) 0 0
\(141\) 6.92075 + 6.92075i 0.582832 + 0.582832i
\(142\) 0 0
\(143\) 1.57202 0.131459
\(144\) 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 −0.368709 + 0.929545i \(0.620200\pi\)
−0.929545 + 0.368709i \(0.879800\pi\)
\(150\) 0 0
\(151\) 11.5316i 0.938424i −0.883085 0.469212i \(-0.844538\pi\)
0.883085 0.469212i \(-0.155462\pi\)
\(152\) 0 0
\(153\) 5.44797i 0.440442i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −5.41891 5.41891i −0.432476 0.432476i 0.456994 0.889470i \(-0.348926\pi\)
−0.889470 + 0.456994i \(0.848926\pi\)
\(158\) 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
\(167\) 8.29734i 0.642068i 0.947068 + 0.321034i \(0.104030\pi\)
−0.947068 + 0.321034i \(0.895970\pi\)
\(168\) 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
\(177\) −12.3099 −0.925271
\(178\) 0 0
\(179\) 10.8703 + 10.8703i 0.812481 + 0.812481i 0.985005 0.172524i \(-0.0551922\pi\)
−0.172524 + 0.985005i \(0.555192\pi\)
\(180\) 0 0
\(181\) −4.09403 + 4.09403i −0.304307 + 0.304307i −0.842696 0.538389i \(-0.819033\pi\)
0.538389 + 0.842696i \(0.319033\pi\)
\(182\) 0 0
\(183\) 2.98858i 0.220922i
\(184\) 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
\(193\) −24.8152 −1.78624 −0.893119 0.449820i \(-0.851488\pi\)
−0.893119 + 0.449820i \(0.851488\pi\)
\(194\) 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
\(207\) 6.01996 0.418416
\(208\) 0 0
\(209\) −1.48755 −0.102896
\(210\) 0 0
\(211\) −15.5715 15.5715i −1.07199 1.07199i −0.997200 0.0747872i \(-0.976172\pi\)
−0.0747872 0.997200i \(-0.523828\pi\)
\(212\) 0 0
\(213\) 4.25277 4.25277i 0.291395 0.291395i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 10.1064i 0.686065i
\(218\) 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
\(223\) 7.88779 0.528205 0.264103 0.964495i \(-0.414924\pi\)
0.264103 + 0.964495i \(0.414924\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.98838 + 5.98838i 0.397463 + 0.397463i 0.877337 0.479874i \(-0.159318\pi\)
−0.479874 + 0.877337i \(0.659318\pi\)
\(228\) 0 0
\(229\) 19.4584 19.4584i 1.28585 1.28585i 0.348563 0.937286i \(-0.386670\pi\)
0.937286 0.348563i \(-0.113330\pi\)
\(230\) 0 0
\(231\) 1.31761i 0.0866925i
\(232\) 0 0
\(233\) 2.68717i 0.176042i −0.996119 0.0880212i \(-0.971946\pi\)
0.996119 0.0880212i \(-0.0280543\pi\)
\(234\) 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 \(-0.365992\pi\)
0.408673 + 0.912681i \(0.365992\pi\)
\(240\) 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
\(247\) 6.52658i 0.415276i
\(248\) 0 0
\(249\) 5.85376i 0.370967i
\(250\) 0 0
\(251\) 9.95683 9.95683i 0.628470 0.628470i −0.319213 0.947683i \(-0.603419\pi\)
0.947683 + 0.319213i \(0.103419\pi\)
\(252\) 0 0
\(253\) −3.04449 3.04449i −0.191405 0.191405i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.51630 0.281719 0.140860 0.990030i \(-0.455013\pi\)
0.140860 + 0.990030i \(0.455013\pi\)
\(258\) 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
\(263\) 20.2127i 1.24637i 0.782075 + 0.623185i \(0.214162\pi\)
−0.782075 + 0.623185i \(0.785838\pi\)
\(264\) 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 0.999435 + 0.0335999i \(0.0106972\pi\)
0.0335999 + 0.999435i \(0.489303\pi\)
\(270\) 0 0
\(271\) 3.64054 0.221147 0.110573 0.993868i \(-0.464731\pi\)
0.110573 + 0.993868i \(0.464731\pi\)
\(272\) 0 0
\(273\) −5.78099 −0.349881
\(274\) 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 \(-0.947365\pi\)
0.986360 0.164605i \(-0.0526350\pi\)
\(282\) 0 0
\(283\) −2.36694 + 2.36694i −0.140700 + 0.140700i −0.773949 0.633249i \(-0.781721\pi\)
0.633249 + 0.773949i \(0.281721\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.5356 −0.680925
\(288\) 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 \(0.541152\pi\)
−0.991655 + 0.128922i \(0.958848\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.37786i 0.196003i
\(298\) 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
\(303\) −2.16390 −0.124313
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −19.9292 19.9292i −1.13742 1.13742i −0.988911 0.148507i \(-0.952553\pi\)
−0.148507 0.988911i \(-0.547447\pi\)
\(308\) 0 0
\(309\) −0.993449 + 0.993449i −0.0565153 + 0.0565153i
\(310\) 0 0
\(311\) 5.73314i 0.325096i −0.986701 0.162548i \(-0.948029\pi\)
0.986701 0.162548i \(-0.0519713\pi\)
\(312\) 0 0
\(313\) 0.212621i 0.0120180i −0.999982 0.00600902i \(-0.998087\pi\)
0.999982 0.00600902i \(-0.00191274\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.21582 3.21582i −0.180618 0.180618i 0.611007 0.791625i \(-0.290765\pi\)
−0.791625 + 0.611007i \(0.790765\pi\)
\(318\) 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
\(327\) 11.8101i 0.653097i
\(328\) 0 0
\(329\) 9.96006i 0.549116i
\(330\) 0 0
\(331\) −22.0295 + 22.0295i −1.21085 + 1.21085i −0.240106 + 0.970747i \(0.577182\pi\)
−0.970747 + 0.240106i \(0.922818\pi\)
\(332\) 0 0
\(333\) −1.63451 1.63451i −0.0895708 0.0895708i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.2122 −0.610767 −0.305384 0.952229i \(-0.598785\pi\)
−0.305384 + 0.952229i \(0.598785\pi\)
\(338\) 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
\(343\) 17.6009i 0.950359i
\(344\) 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 \(-0.318205\pi\)
−0.841293 + 0.540580i \(0.818205\pi\)
\(350\) 0 0
\(351\) −14.8203 −0.791047
\(352\) 0 0
\(353\) 0.748709 0.0398497 0.0199249 0.999801i \(-0.493657\pi\)
0.0199249 + 0.999801i \(0.493657\pi\)
\(354\) 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
\(367\) −20.6101 −1.07584 −0.537920 0.842996i \(-0.680790\pi\)
−0.537920 + 0.842996i \(0.680790\pi\)
\(368\) 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 −0.558269 0.829660i \(-0.688534\pi\)
0.829660 + 0.558269i \(0.188534\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 24.4347i 1.25845i
\(378\) 0 0
\(379\) −5.41344 + 5.41344i −0.278070 + 0.278070i −0.832338 0.554268i \(-0.812998\pi\)
0.554268 + 0.832338i \(0.312998\pi\)
\(380\) 0 0
\(381\) 1.37064 + 1.37064i 0.0702199 + 0.0702199i
\(382\) 0 0
\(383\) −29.5087 −1.50782 −0.753912 0.656975i \(-0.771836\pi\)
−0.753912 + 0.656975i \(0.771836\pi\)
\(384\) 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 \(-0.734258\pi\)
0.741197 + 0.671287i \(0.234258\pi\)
\(390\) 0 0
\(391\) 46.8225i 2.36792i
\(392\) 0 0
\(393\) 2.14287i 0.108094i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 21.9750 + 21.9750i 1.10289 + 1.10289i 0.994060 + 0.108832i \(0.0347111\pi\)
0.108832 + 0.994060i \(0.465289\pi\)
\(398\) 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
\(407\) 1.65325i 0.0819487i
\(408\) 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
\(417\) −26.9322 −1.31888
\(418\) 0 0
\(419\) 11.4979 + 11.4979i 0.561709 + 0.561709i 0.929793 0.368084i \(-0.119986\pi\)
−0.368084 + 0.929793i \(0.619986\pi\)
\(420\) 0 0
\(421\) 12.5714 12.5714i 0.612690 0.612690i −0.330956 0.943646i \(-0.607371\pi\)
0.943646 + 0.330956i \(0.107371\pi\)
\(422\) 0 0
\(423\) 5.56953i 0.270800i
\(424\) 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
\(433\) 12.1705 0.584877 0.292439 0.956284i \(-0.405533\pi\)
0.292439 + 0.956284i \(0.405533\pi\)
\(434\) 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 −0.615778 0.787920i \(-0.711158\pi\)
0.787920 + 0.615778i \(0.211158\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −32.9612 −1.55901
\(448\) 0 0
\(449\) −5.38425 −0.254098 −0.127049 0.991896i \(-0.540551\pi\)
−0.127049 + 0.991896i \(0.540551\pi\)
\(450\) 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
\(457\) 14.3039i 0.669108i −0.942377 0.334554i \(-0.891414\pi\)
0.942377 0.334554i \(-0.108586\pi\)
\(458\) 0 0
\(459\) 25.9748 25.9748i 1.21240 1.21240i
\(460\) 0 0
\(461\) −4.50363 4.50363i −0.209755 0.209755i 0.594408 0.804163i \(-0.297386\pi\)
−0.804163 + 0.594408i \(0.797386\pi\)
\(462\) 0 0
\(463\) 19.3500 0.899271 0.449636 0.893212i \(-0.351554\pi\)
0.449636 + 0.893212i \(0.351554\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.1773 17.1773i −0.794871 0.794871i 0.187410 0.982282i \(-0.439991\pi\)
−0.982282 + 0.187410i \(0.939991\pi\)
\(468\) 0 0
\(469\) 9.51312 9.51312i 0.439275 0.439275i
\(470\) 0 0
\(471\) 11.2710i 0.519341i
\(472\) 0 0
\(473\) 5.19408i 0.238824i
\(474\) 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 \(-0.540430\pi\)
−0.126673 + 0.991945i \(0.540430\pi\)
\(480\) 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
\(487\) 31.7138i 1.43709i 0.695480 + 0.718546i \(0.255192\pi\)
−0.695480 + 0.718546i \(0.744808\pi\)
\(488\) 0 0
\(489\) 13.4632i 0.608827i
\(490\) 0 0
\(491\) −7.39419 + 7.39419i −0.333695 + 0.333695i −0.853988 0.520293i \(-0.825823\pi\)
0.520293 + 0.853988i \(0.325823\pi\)
\(492\) 0 0
\(493\) −42.8255 42.8255i −1.92876 1.92876i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.12041 −0.274538
\(498\) 0 0
\(499\) −14.0103 14.0103i −0.627189 0.627189i 0.320171 0.947360i \(-0.396260\pi\)
−0.947360 + 0.320171i \(0.896260\pi\)
\(500\) 0 0
\(501\) −8.62899 + 8.62899i −0.385515 + 0.385515i
\(502\) 0 0
\(503\) 8.43795i 0.376230i 0.982147 + 0.188115i \(0.0602377\pi\)
−0.982147 + 0.188115i \(0.939762\pi\)
\(504\) 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 \(-0.229098\pi\)
−0.659183 + 0.751983i \(0.729098\pi\)
\(510\) 0 0
\(511\) 3.64891 0.161418
\(512\) 0 0
\(513\) 14.0239 0.619169
\(514\) 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 \(-0.787557\pi\)
0.785428 0.618954i \(-0.212443\pi\)
\(522\) 0 0
\(523\) 10.1929 10.1929i 0.445703 0.445703i −0.448220 0.893923i \(-0.647942\pi\)
0.893923 + 0.448220i \(0.147942\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 43.9555 1.91473
\(528\) 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
\(537\) 22.6095i 0.975671i
\(538\) 0 0
\(539\) −2.01469 + 2.01469i −0.0867790 + 0.0867790i
\(540\) 0 0
\(541\) 3.86053 + 3.86053i 0.165977 + 0.165977i 0.785209 0.619231i \(-0.212556\pi\)
−0.619231 + 0.785209i \(0.712556\pi\)
\(542\) 0 0
\(543\) −8.51534 −0.365428
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 20.6231 + 20.6231i 0.881781 + 0.881781i 0.993716 0.111935i \(-0.0357048\pi\)
−0.111935 + 0.993716i \(0.535705\pi\)
\(548\) 0 0
\(549\) −1.20254 + 1.20254i −0.0513233 + 0.0513233i
\(550\) 0 0
\(551\) 23.1216i 0.985014i
\(552\) 0 0
\(553\) 17.4696i 0.742884i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.28512 + 1.28512i 0.0544523 + 0.0544523i 0.733809 0.679356i \(-0.237741\pi\)
−0.679356 + 0.733809i \(0.737741\pi\)
\(558\) 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
\(567\) 8.66397i 0.363852i
\(568\) 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 −0.814598 0.580026i \(-0.803042\pi\)
0.580026 + 0.814598i \(0.303042\pi\)
\(572\) 0 0
\(573\) −20.0238 20.0238i −0.836507 0.836507i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.43681 0.101446 0.0507230 0.998713i \(-0.483847\pi\)
0.0507230 + 0.998713i \(0.483847\pi\)
\(578\) 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
\(583\) 4.48139i 0.185600i
\(584\) 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
\(593\) 15.3439 0.630098 0.315049 0.949075i \(-0.397979\pi\)
0.315049 + 0.949075i \(0.397979\pi\)
\(594\) 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 \(0.289866\pi\)
−0.613239 + 0.789897i \(0.710134\pi\)
\(602\) 0 0
\(603\) 5.31961 5.31961i 0.216631 0.216631i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −34.9068 −1.41682 −0.708412 0.705800i \(-0.750588\pi\)
−0.708412 + 0.705800i \(0.750588\pi\)
\(608\) 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 −0.704035 0.710165i \(-0.748620\pi\)
0.710165 + 0.704035i \(0.248620\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.288199i 0.0116025i 0.999983 + 0.00580123i \(0.00184660\pi\)
−0.999983 + 0.00580123i \(0.998153\pi\)
\(618\) 0 0
\(619\) 11.5307 11.5307i 0.463460 0.463460i −0.436328 0.899788i \(-0.643721\pi\)
0.899788 + 0.436328i \(0.143721\pi\)
\(620\) 0 0
\(621\) 28.7019 + 28.7019i 1.15177 + 1.15177i
\(622\) 0 0
\(623\) 15.7965 0.632873
\(624\) 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 \(0.0912536\pi\)
−0.959188 + 0.282771i \(0.908746\pi\)
\(632\) 0 0
\(633\) 32.3878i 1.28730i
\(634\) 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
\(647\) 46.3186i 1.82097i 0.413541 + 0.910485i \(0.364292\pi\)
−0.413541 + 0.910485i \(0.635708\pi\)
\(648\) 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
\(657\) 2.04042 0.0796045
\(658\) 0 0
\(659\) 15.2461 + 15.2461i 0.593905 + 0.593905i 0.938684 0.344779i \(-0.112046\pi\)
−0.344779 + 0.938684i \(0.612046\pi\)
\(660\) 0 0
\(661\) 19.1271 19.1271i 0.743958 0.743958i −0.229379 0.973337i \(-0.573670\pi\)
0.973337 + 0.229379i \(0.0736696\pi\)
\(662\) 0 0
\(663\) 25.1432i 0.976481i
\(664\) 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
\(673\) 18.5586 0.715382 0.357691 0.933840i \(-0.383564\pi\)
0.357691 + 0.933840i \(0.383564\pi\)
\(674\) 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 −0.906596 0.421999i \(-0.861329\pi\)
0.421999 + 0.906596i \(0.361329\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 40.4723 1.54412
\(688\) 0 0
\(689\) −19.6620 −0.749063
\(690\) 0 0
\(691\) −26.8892 26.8892i −1.02291 1.02291i −0.999731 0.0231826i \(-0.992620\pi\)
−0.0231826 0.999731i \(-0.507380\pi\)
\(692\) 0 0
\(693\) 0.530180 0.530180i 0.0201399 0.0201399i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 50.1717i 1.90039i
\(698\) 0 0
\(699\) 2.79458 2.79458i 0.105701 0.105701i
\(700\) 0 0
\(701\) 25.3725 + 25.3725i 0.958305 + 0.958305i 0.999165 0.0408602i \(-0.0130098\pi\)
−0.0408602 + 0.999165i \(0.513010\pi\)
\(702\) 0 0
\(703\) 6.86382 0.258874
\(704\) 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 \(-0.609267\pi\)
0.941659 + 0.336570i \(0.109267\pi\)
\(710\) 0 0
\(711\) 9.76879i 0.366358i
\(712\) 0 0
\(713\) 48.5705i 1.81898i
\(714\) 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 \(-0.683047\pi\)
−0.543884 + 0.839160i \(0.683047\pi\)
\(720\) 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
\(727\) 4.13463i 0.153345i −0.997056 0.0766724i \(-0.975570\pi\)
0.997056 0.0766724i \(-0.0244296\pi\)
\(728\) 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
\(737\) −5.38060 −0.198197
\(738\) 0 0
\(739\) −23.9820 23.9820i −0.882194 0.882194i 0.111564 0.993757i \(-0.464414\pi\)
−0.993757 + 0.111564i \(0.964414\pi\)
\(740\) 0 0
\(741\) 6.78744 6.78744i 0.249343 0.249343i
\(742\) 0 0
\(743\) 10.3473i 0.379604i −0.981822 0.189802i \(-0.939215\pi\)
0.981822 0.189802i \(-0.0607846\pi\)
\(744\) 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
\(753\) 20.7096 0.754700
\(754\) 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 \(-0.714564\pi\)
0.624174 0.781285i \(-0.285436\pi\)
\(762\) 0 0
\(763\) −8.49827 + 8.49827i −0.307658 + 0.307658i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 21.9815 0.793705
\(768\) 0 0
\(769\) −31.2507 −1.12693 −0.563465 0.826140i \(-0.690532\pi\)
−0.563465 + 0.826140i \(0.690532\pi\)
\(770\) 0 0
\(771\) 4.69682 + 4.69682i 0.169152 + 0.169152i
\(772\) 0 0
\(773\) −24.4047 + 24.4047i −0.877778 + 0.877778i −0.993304 0.115527i \(-0.963144\pi\)
0.115527 + 0.993304i \(0.463144\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.07970i 0.218108i
\(778\) 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
\(783\) −52.5036 −1.87632
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −17.2122 17.2122i −0.613549 0.613549i 0.330320 0.943869i \(-0.392843\pi\)
−0.943869 + 0.330320i \(0.892843\pi\)
\(788\) 0 0
\(789\) −21.0206 + 21.0206i −0.748354 + 0.748354i
\(790\) 0 0
\(791\) 2.91480i 0.103638i
\(792\) 0 0
\(793\) 5.33662i 0.189509i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20.3220 + 20.3220i 0.719841 + 0.719841i 0.968573 0.248731i \(-0.0800136\pi\)
−0.248731 + 0.968573i \(0.580014\pi\)
\(798\) 0 0
\(799\) 43.3192 1.53252
\(800\) 0 0
\(801\) 8.83319 0.312105
\(802\) 0 0
\(803\) −1.03191 1.03191i −0.0364153