Properties

Label 225.4.f.d.143.5
Level $225$
Weight $4$
Character 225.143
Analytic conductor $13.275$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: 16.0.11007531417600000000.1
Defining polynomial: \(x^{16} - 7 x^{12} + 48 x^{8} - 7 x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 143.5
Root \(1.56290 + 0.418778i\) of defining polynomial
Character \(\chi\) \(=\) 225.143
Dual form 225.4.f.d.107.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.07047 + 1.07047i) q^{2} -5.70820i q^{4} +(-7.85846 + 7.85846i) q^{7} +(14.6742 - 14.6742i) q^{8} +O(q^{10})\) \(q+(1.07047 + 1.07047i) q^{2} -5.70820i q^{4} +(-7.85846 + 7.85846i) q^{7} +(14.6742 - 14.6742i) q^{8} -33.7047i q^{11} +(25.7196 + 25.7196i) q^{13} -16.8244 q^{14} -14.2492 q^{16} +(-66.3461 - 66.3461i) q^{17} -128.915i q^{19} +(36.0797 - 36.0797i) q^{22} +(110.948 - 110.948i) q^{23} +55.0640i q^{26} +(44.8577 + 44.8577i) q^{28} -268.817 q^{29} -2.91486 q^{31} +(-132.647 - 132.647i) q^{32} -142.043i q^{34} +(115.736 - 115.736i) q^{37} +(137.999 - 137.999i) q^{38} -251.610i q^{41} +(340.781 + 340.781i) q^{43} -192.393 q^{44} +237.532 q^{46} +(126.292 + 126.292i) q^{47} +219.489i q^{49} +(146.813 - 146.813i) q^{52} +(254.947 - 254.947i) q^{53} +230.633i q^{56} +(-287.759 - 287.759i) q^{58} -131.161 q^{59} +225.170 q^{61} +(-3.12025 - 3.12025i) q^{62} -169.994i q^{64} +(-236.271 + 236.271i) q^{67} +(-378.717 + 378.717i) q^{68} -29.8233i q^{71} +(41.4328 + 41.4328i) q^{73} +247.784 q^{74} -735.872 q^{76} +(264.867 + 264.867i) q^{77} +450.170i q^{79} +(269.340 - 269.340i) q^{82} +(-729.807 + 729.807i) q^{83} +729.588i q^{86} +(-494.588 - 494.588i) q^{88} +1478.30 q^{89} -404.234 q^{91} +(-633.313 - 633.313i) q^{92} +270.383i q^{94} +(-1291.69 + 1291.69i) q^{97} +(-234.956 + 234.956i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q + 416 q^{16} + 1456 q^{31} - 4464 q^{46} + 6608 q^{61} - 9520 q^{76} + 7056 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.07047 + 1.07047i 0.378467 + 0.378467i 0.870549 0.492082i \(-0.163764\pi\)
−0.492082 + 0.870549i \(0.663764\pi\)
\(3\) 0 0
\(4\) 5.70820i 0.713525i
\(5\) 0 0
\(6\) 0 0
\(7\) −7.85846 + 7.85846i −0.424317 + 0.424317i −0.886687 0.462370i \(-0.846999\pi\)
0.462370 + 0.886687i \(0.346999\pi\)
\(8\) 14.6742 14.6742i 0.648513 0.648513i
\(9\) 0 0
\(10\) 0 0
\(11\) 33.7047i 0.923850i −0.886919 0.461925i \(-0.847159\pi\)
0.886919 0.461925i \(-0.152841\pi\)
\(12\) 0 0
\(13\) 25.7196 + 25.7196i 0.548719 + 0.548719i 0.926070 0.377351i \(-0.123165\pi\)
−0.377351 + 0.926070i \(0.623165\pi\)
\(14\) −16.8244 −0.321180
\(15\) 0 0
\(16\) −14.2492 −0.222644
\(17\) −66.3461 66.3461i −0.946547 0.946547i 0.0520952 0.998642i \(-0.483410\pi\)
−0.998642 + 0.0520952i \(0.983410\pi\)
\(18\) 0 0
\(19\) 128.915i 1.55658i −0.627903 0.778292i \(-0.716086\pi\)
0.627903 0.778292i \(-0.283914\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 36.0797 36.0797i 0.349647 0.349647i
\(23\) 110.948 110.948i 1.00584 1.00584i 0.00585236 0.999983i \(-0.498137\pi\)
0.999983 0.00585236i \(-0.00186287\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 55.0640i 0.415344i
\(27\) 0 0
\(28\) 44.8577 + 44.8577i 0.302761 + 0.302761i
\(29\) −268.817 −1.72131 −0.860655 0.509189i \(-0.829946\pi\)
−0.860655 + 0.509189i \(0.829946\pi\)
\(30\) 0 0
\(31\) −2.91486 −0.0168879 −0.00844393 0.999964i \(-0.502688\pi\)
−0.00844393 + 0.999964i \(0.502688\pi\)
\(32\) −132.647 132.647i −0.732776 0.732776i
\(33\) 0 0
\(34\) 142.043i 0.716474i
\(35\) 0 0
\(36\) 0 0
\(37\) 115.736 115.736i 0.514242 0.514242i −0.401581 0.915823i \(-0.631539\pi\)
0.915823 + 0.401581i \(0.131539\pi\)
\(38\) 137.999 137.999i 0.589116 0.589116i
\(39\) 0 0
\(40\) 0 0
\(41\) 251.610i 0.958410i −0.877703 0.479205i \(-0.840925\pi\)
0.877703 0.479205i \(-0.159075\pi\)
\(42\) 0 0
\(43\) 340.781 + 340.781i 1.20857 + 1.20857i 0.971490 + 0.237081i \(0.0761906\pi\)
0.237081 + 0.971490i \(0.423809\pi\)
\(44\) −192.393 −0.659190
\(45\) 0 0
\(46\) 237.532 0.761351
\(47\) 126.292 + 126.292i 0.391949 + 0.391949i 0.875382 0.483432i \(-0.160610\pi\)
−0.483432 + 0.875382i \(0.660610\pi\)
\(48\) 0 0
\(49\) 219.489i 0.639910i
\(50\) 0 0
\(51\) 0 0
\(52\) 146.813 146.813i 0.391525 0.391525i
\(53\) 254.947 254.947i 0.660747 0.660747i −0.294809 0.955556i \(-0.595256\pi\)
0.955556 + 0.294809i \(0.0952560\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 230.633i 0.550350i
\(57\) 0 0
\(58\) −287.759 287.759i −0.651459 0.651459i
\(59\) −131.161 −0.289418 −0.144709 0.989474i \(-0.546225\pi\)
−0.144709 + 0.989474i \(0.546225\pi\)
\(60\) 0 0
\(61\) 225.170 0.472625 0.236312 0.971677i \(-0.424061\pi\)
0.236312 + 0.971677i \(0.424061\pi\)
\(62\) −3.12025 3.12025i −0.00639149 0.00639149i
\(63\) 0 0
\(64\) 169.994i 0.332019i
\(65\) 0 0
\(66\) 0 0
\(67\) −236.271 + 236.271i −0.430823 + 0.430823i −0.888908 0.458085i \(-0.848535\pi\)
0.458085 + 0.888908i \(0.348535\pi\)
\(68\) −378.717 + 378.717i −0.675385 + 0.675385i
\(69\) 0 0
\(70\) 0 0
\(71\) 29.8233i 0.0498503i −0.999689 0.0249252i \(-0.992065\pi\)
0.999689 0.0249252i \(-0.00793475\pi\)
\(72\) 0 0
\(73\) 41.4328 + 41.4328i 0.0664293 + 0.0664293i 0.739541 0.673112i \(-0.235043\pi\)
−0.673112 + 0.739541i \(0.735043\pi\)
\(74\) 247.784 0.389247
\(75\) 0 0
\(76\) −735.872 −1.11066
\(77\) 264.867 + 264.867i 0.392005 + 0.392005i
\(78\) 0 0
\(79\) 450.170i 0.641115i 0.947229 + 0.320558i \(0.103870\pi\)
−0.947229 + 0.320558i \(0.896130\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 269.340 269.340i 0.362727 0.362727i
\(83\) −729.807 + 729.807i −0.965142 + 0.965142i −0.999413 0.0342709i \(-0.989089\pi\)
0.0342709 + 0.999413i \(0.489089\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 729.588i 0.914808i
\(87\) 0 0
\(88\) −494.588 494.588i −0.599128 0.599128i
\(89\) 1478.30 1.76067 0.880337 0.474349i \(-0.157317\pi\)
0.880337 + 0.474349i \(0.157317\pi\)
\(90\) 0 0
\(91\) −404.234 −0.465662
\(92\) −633.313 633.313i −0.717689 0.717689i
\(93\) 0 0
\(94\) 270.383i 0.296680i
\(95\) 0 0
\(96\) 0 0
\(97\) −1291.69 + 1291.69i −1.35207 + 1.35207i −0.468734 + 0.883339i \(0.655290\pi\)
−0.883339 + 0.468734i \(0.844710\pi\)
\(98\) −234.956 + 234.956i −0.242185 + 0.242185i
\(99\) 0 0
\(100\) 0 0
\(101\) 1342.18i 1.32229i −0.750256 0.661147i \(-0.770070\pi\)
0.750256 0.661147i \(-0.229930\pi\)
\(102\) 0 0
\(103\) −888.748 888.748i −0.850203 0.850203i 0.139955 0.990158i \(-0.455304\pi\)
−0.990158 + 0.139955i \(0.955304\pi\)
\(104\) 754.829 0.711702
\(105\) 0 0
\(106\) 545.823 0.500142
\(107\) 1367.01 + 1367.01i 1.23509 + 1.23509i 0.961985 + 0.273101i \(0.0880494\pi\)
0.273101 + 0.961985i \(0.411951\pi\)
\(108\) 0 0
\(109\) 155.177i 0.136360i 0.997673 + 0.0681799i \(0.0217192\pi\)
−0.997673 + 0.0681799i \(0.978281\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 111.977 111.977i 0.0944717 0.0944717i
\(113\) −241.613 + 241.613i −0.201142 + 0.201142i −0.800489 0.599347i \(-0.795427\pi\)
0.599347 + 0.800489i \(0.295427\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1534.46i 1.22820i
\(117\) 0 0
\(118\) −140.403 140.403i −0.109535 0.109535i
\(119\) 1042.76 0.803272
\(120\) 0 0
\(121\) 194.994 0.146502
\(122\) 241.037 + 241.037i 0.178873 + 0.178873i
\(123\) 0 0
\(124\) 16.6386i 0.0120499i
\(125\) 0 0
\(126\) 0 0
\(127\) −597.467 + 597.467i −0.417454 + 0.417454i −0.884325 0.466871i \(-0.845381\pi\)
0.466871 + 0.884325i \(0.345381\pi\)
\(128\) −879.201 + 879.201i −0.607118 + 0.607118i
\(129\) 0 0
\(130\) 0 0
\(131\) 1289.40i 0.859966i −0.902837 0.429983i \(-0.858520\pi\)
0.902837 0.429983i \(-0.141480\pi\)
\(132\) 0 0
\(133\) 1013.07 + 1013.07i 0.660485 + 0.660485i
\(134\) −505.841 −0.326105
\(135\) 0 0
\(136\) −1947.15 −1.22770
\(137\) 672.223 + 672.223i 0.419211 + 0.419211i 0.884932 0.465721i \(-0.154205\pi\)
−0.465721 + 0.884932i \(0.654205\pi\)
\(138\) 0 0
\(139\) 1028.98i 0.627891i 0.949441 + 0.313945i \(0.101651\pi\)
−0.949441 + 0.313945i \(0.898349\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 31.9248 31.9248i 0.0188667 0.0188667i
\(143\) 866.873 866.873i 0.506934 0.506934i
\(144\) 0 0
\(145\) 0 0
\(146\) 88.7048i 0.0502826i
\(147\) 0 0
\(148\) −660.647 660.647i −0.366925 0.366925i
\(149\) −1475.95 −0.811509 −0.405754 0.913982i \(-0.632991\pi\)
−0.405754 + 0.913982i \(0.632991\pi\)
\(150\) 0 0
\(151\) 3253.22 1.75327 0.876633 0.481160i \(-0.159784\pi\)
0.876633 + 0.481160i \(0.159784\pi\)
\(152\) −1891.72 1891.72i −1.00946 1.00946i
\(153\) 0 0
\(154\) 567.062i 0.296722i
\(155\) 0 0
\(156\) 0 0
\(157\) 2284.72 2284.72i 1.16141 1.16141i 0.177237 0.984168i \(-0.443284\pi\)
0.984168 0.177237i \(-0.0567160\pi\)
\(158\) −481.892 + 481.892i −0.242641 + 0.242641i
\(159\) 0 0
\(160\) 0 0
\(161\) 1743.76i 0.853586i
\(162\) 0 0
\(163\) 65.0158 + 65.0158i 0.0312419 + 0.0312419i 0.722555 0.691313i \(-0.242968\pi\)
−0.691313 + 0.722555i \(0.742968\pi\)
\(164\) −1436.24 −0.683850
\(165\) 0 0
\(166\) −1562.47 −0.730549
\(167\) −111.465 111.465i −0.0516493 0.0516493i 0.680810 0.732460i \(-0.261628\pi\)
−0.732460 + 0.680810i \(0.761628\pi\)
\(168\) 0 0
\(169\) 874.000i 0.397815i
\(170\) 0 0
\(171\) 0 0
\(172\) 1945.24 1945.24i 0.862346 0.862346i
\(173\) 2261.53 2261.53i 0.993878 0.993878i −0.00610303 0.999981i \(-0.501943\pi\)
0.999981 + 0.00610303i \(0.00194267\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 480.266i 0.205690i
\(177\) 0 0
\(178\) 1582.47 + 1582.47i 0.666357 + 0.666357i
\(179\) −771.589 −0.322186 −0.161093 0.986939i \(-0.551502\pi\)
−0.161093 + 0.986939i \(0.551502\pi\)
\(180\) 0 0
\(181\) 1010.32 0.414897 0.207449 0.978246i \(-0.433484\pi\)
0.207449 + 0.978246i \(0.433484\pi\)
\(182\) −432.719 432.719i −0.176238 0.176238i
\(183\) 0 0
\(184\) 3256.13i 1.30459i
\(185\) 0 0
\(186\) 0 0
\(187\) −2236.18 + 2236.18i −0.874467 + 0.874467i
\(188\) 720.902 720.902i 0.279666 0.279666i
\(189\) 0 0
\(190\) 0 0
\(191\) 1285.52i 0.487000i −0.969901 0.243500i \(-0.921704\pi\)
0.969901 0.243500i \(-0.0782956\pi\)
\(192\) 0 0
\(193\) 1987.54 + 1987.54i 0.741275 + 0.741275i 0.972823 0.231548i \(-0.0743792\pi\)
−0.231548 + 0.972823i \(0.574379\pi\)
\(194\) −2765.42 −1.02343
\(195\) 0 0
\(196\) 1252.89 0.456592
\(197\) −91.4449 91.4449i −0.0330720 0.0330720i 0.690377 0.723449i \(-0.257444\pi\)
−0.723449 + 0.690377i \(0.757444\pi\)
\(198\) 0 0
\(199\) 1163.72i 0.414543i −0.978283 0.207272i \(-0.933542\pi\)
0.978283 0.207272i \(-0.0664584\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 1436.76 1436.76i 0.500445 0.500445i
\(203\) 2112.49 2112.49i 0.730381 0.730381i
\(204\) 0 0
\(205\) 0 0
\(206\) 1902.75i 0.643548i
\(207\) 0 0
\(208\) −366.485 366.485i −0.122169 0.122169i
\(209\) −4345.04 −1.43805
\(210\) 0 0
\(211\) −2121.60 −0.692212 −0.346106 0.938195i \(-0.612496\pi\)
−0.346106 + 0.938195i \(0.612496\pi\)
\(212\) −1455.29 1455.29i −0.471460 0.471460i
\(213\) 0 0
\(214\) 2926.69i 0.934879i
\(215\) 0 0
\(216\) 0 0
\(217\) 22.9063 22.9063i 0.00716580 0.00716580i
\(218\) −166.111 + 166.111i −0.0516077 + 0.0516077i
\(219\) 0 0
\(220\) 0 0
\(221\) 3412.80i 1.03878i
\(222\) 0 0
\(223\) 1439.60 + 1439.60i 0.432298 + 0.432298i 0.889410 0.457111i \(-0.151116\pi\)
−0.457111 + 0.889410i \(0.651116\pi\)
\(224\) 2084.80 0.621859
\(225\) 0 0
\(226\) −517.277 −0.152251
\(227\) −501.434 501.434i −0.146614 0.146614i 0.629990 0.776604i \(-0.283059\pi\)
−0.776604 + 0.629990i \(0.783059\pi\)
\(228\) 0 0
\(229\) 6371.08i 1.83848i −0.393692 0.919242i \(-0.628802\pi\)
0.393692 0.919242i \(-0.371198\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3944.66 + 3944.66i −1.11629 + 1.11629i
\(233\) 3586.88 3586.88i 1.00852 1.00852i 0.00855336 0.999963i \(-0.497277\pi\)
0.999963 0.00855336i \(-0.00272265\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 748.692i 0.206507i
\(237\) 0 0
\(238\) 1116.24 + 1116.24i 0.304012 + 0.304012i
\(239\) 5726.18 1.54977 0.774886 0.632100i \(-0.217807\pi\)
0.774886 + 0.632100i \(0.217807\pi\)
\(240\) 0 0
\(241\) 4533.68 1.21178 0.605892 0.795547i \(-0.292816\pi\)
0.605892 + 0.795547i \(0.292816\pi\)
\(242\) 208.734 + 208.734i 0.0554461 + 0.0554461i
\(243\) 0 0
\(244\) 1285.32i 0.337230i
\(245\) 0 0
\(246\) 0 0
\(247\) 3315.64 3315.64i 0.854127 0.854127i
\(248\) −42.7731 + 42.7731i −0.0109520 + 0.0109520i
\(249\) 0 0
\(250\) 0 0
\(251\) 2022.81i 0.508679i 0.967115 + 0.254340i \(0.0818581\pi\)
−0.967115 + 0.254340i \(0.918142\pi\)
\(252\) 0 0
\(253\) −3739.46 3739.46i −0.929241 0.929241i
\(254\) −1279.14 −0.315985
\(255\) 0 0
\(256\) −3242.26 −0.791567
\(257\) −2225.48 2225.48i −0.540161 0.540161i 0.383415 0.923576i \(-0.374748\pi\)
−0.923576 + 0.383415i \(0.874748\pi\)
\(258\) 0 0
\(259\) 1819.02i 0.436404i
\(260\) 0 0
\(261\) 0 0
\(262\) 1380.26 1380.26i 0.325469 0.325469i
\(263\) −5187.30 + 5187.30i −1.21621 + 1.21621i −0.247257 + 0.968950i \(0.579529\pi\)
−0.968950 + 0.247257i \(0.920471\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2168.92i 0.499944i
\(267\) 0 0
\(268\) 1348.69 + 1348.69i 0.307403 + 0.307403i
\(269\) −1505.47 −0.341228 −0.170614 0.985338i \(-0.554575\pi\)
−0.170614 + 0.985338i \(0.554575\pi\)
\(270\) 0 0
\(271\) −3810.34 −0.854102 −0.427051 0.904227i \(-0.640448\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(272\) 945.381 + 945.381i 0.210743 + 0.210743i
\(273\) 0 0
\(274\) 1439.18i 0.317315i
\(275\) 0 0
\(276\) 0 0
\(277\) −4620.91 + 4620.91i −1.00232 + 1.00232i −0.00232589 + 0.999997i \(0.500740\pi\)
−0.999997 + 0.00232589i \(0.999260\pi\)
\(278\) −1101.49 + 1101.49i −0.237636 + 0.237636i
\(279\) 0 0
\(280\) 0 0
\(281\) 1168.20i 0.248004i 0.992282 + 0.124002i \(0.0395730\pi\)
−0.992282 + 0.124002i \(0.960427\pi\)
\(282\) 0 0
\(283\) −4505.94 4505.94i −0.946468 0.946468i 0.0521705 0.998638i \(-0.483386\pi\)
−0.998638 + 0.0521705i \(0.983386\pi\)
\(284\) −170.237 −0.0355695
\(285\) 0 0
\(286\) 1855.92 0.383715
\(287\) 1977.26 + 1977.26i 0.406670 + 0.406670i
\(288\) 0 0
\(289\) 3890.62i 0.791902i
\(290\) 0 0
\(291\) 0 0
\(292\) 236.507 236.507i 0.0473990 0.0473990i
\(293\) −3623.76 + 3623.76i −0.722533 + 0.722533i −0.969120 0.246588i \(-0.920691\pi\)
0.246588 + 0.969120i \(0.420691\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3396.67i 0.666985i
\(297\) 0 0
\(298\) −1579.96 1579.96i −0.307129 0.307129i
\(299\) 5707.07 1.10384
\(300\) 0 0
\(301\) −5356.02 −1.02563
\(302\) 3482.46 + 3482.46i 0.663553 + 0.663553i
\(303\) 0 0
\(304\) 1836.94i 0.346564i
\(305\) 0 0
\(306\) 0 0
\(307\) 1210.91 1210.91i 0.225114 0.225114i −0.585534 0.810648i \(-0.699115\pi\)
0.810648 + 0.585534i \(0.199115\pi\)
\(308\) 1511.92 1511.92i 0.279706 0.279706i
\(309\) 0 0
\(310\) 0 0
\(311\) 6608.74i 1.20498i 0.798128 + 0.602488i \(0.205824\pi\)
−0.798128 + 0.602488i \(0.794176\pi\)
\(312\) 0 0
\(313\) 4399.41 + 4399.41i 0.794471 + 0.794471i 0.982218 0.187746i \(-0.0601183\pi\)
−0.187746 + 0.982218i \(0.560118\pi\)
\(314\) 4891.43 0.879107
\(315\) 0 0
\(316\) 2569.66 0.457452
\(317\) 484.443 + 484.443i 0.0858329 + 0.0858329i 0.748720 0.662887i \(-0.230669\pi\)
−0.662887 + 0.748720i \(0.730669\pi\)
\(318\) 0 0
\(319\) 9060.38i 1.59023i
\(320\) 0 0
\(321\) 0 0
\(322\) −1866.63 + 1866.63i −0.323054 + 0.323054i
\(323\) −8553.00 + 8553.00i −1.47338 + 1.47338i
\(324\) 0 0
\(325\) 0 0
\(326\) 139.194i 0.0236480i
\(327\) 0 0
\(328\) −3692.16 3692.16i −0.621541 0.621541i
\(329\) −1984.93 −0.332622
\(330\) 0 0
\(331\) 9323.92 1.54830 0.774152 0.632999i \(-0.218176\pi\)
0.774152 + 0.632999i \(0.218176\pi\)
\(332\) 4165.89 + 4165.89i 0.688653 + 0.688653i
\(333\) 0 0
\(334\) 238.639i 0.0390951i
\(335\) 0 0
\(336\) 0 0
\(337\) 4993.89 4993.89i 0.807224 0.807224i −0.176989 0.984213i \(-0.556636\pi\)
0.984213 + 0.176989i \(0.0566357\pi\)
\(338\) 935.588 935.588i 0.150560 0.150560i
\(339\) 0 0
\(340\) 0 0
\(341\) 98.2443i 0.0156018i
\(342\) 0 0
\(343\) −4420.30 4420.30i −0.695842 0.695842i
\(344\) 10001.3 1.56755
\(345\) 0 0
\(346\) 4841.78 0.752300
\(347\) 4772.75 + 4772.75i 0.738370 + 0.738370i 0.972263 0.233892i \(-0.0751463\pi\)
−0.233892 + 0.972263i \(0.575146\pi\)
\(348\) 0 0
\(349\) 2130.21i 0.326726i 0.986566 + 0.163363i \(0.0522342\pi\)
−0.986566 + 0.163363i \(0.947766\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4470.82 + 4470.82i −0.676975 + 0.676975i
\(353\) 3735.22 3735.22i 0.563189 0.563189i −0.367023 0.930212i \(-0.619623\pi\)
0.930212 + 0.367023i \(0.119623\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 8438.46i 1.25629i
\(357\) 0 0
\(358\) −825.960 825.960i −0.121937 0.121937i
\(359\) −818.350 −0.120309 −0.0601544 0.998189i \(-0.519159\pi\)
−0.0601544 + 0.998189i \(0.519159\pi\)
\(360\) 0 0
\(361\) −9760.04 −1.42295
\(362\) 1081.51 + 1081.51i 0.157025 + 0.157025i
\(363\) 0 0
\(364\) 2307.45i 0.332261i
\(365\) 0 0
\(366\) 0 0
\(367\) −6106.19 + 6106.19i −0.868502 + 0.868502i −0.992307 0.123805i \(-0.960490\pi\)
0.123805 + 0.992307i \(0.460490\pi\)
\(368\) −1580.92 + 1580.92i −0.223943 + 0.223943i
\(369\) 0 0
\(370\) 0 0
\(371\) 4006.98i 0.560733i
\(372\) 0 0
\(373\) −741.335 741.335i −0.102908 0.102908i 0.653778 0.756686i \(-0.273183\pi\)
−0.756686 + 0.653778i \(0.773183\pi\)
\(374\) −4787.50 −0.661914
\(375\) 0 0
\(376\) 3706.47 0.508368
\(377\) −6913.87 6913.87i −0.944515 0.944515i
\(378\) 0 0
\(379\) 56.6115i 0.00767266i 0.999993 + 0.00383633i \(0.00122115\pi\)
−0.999993 + 0.00383633i \(0.998779\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1376.11 1376.11i 0.184313 0.184313i
\(383\) −4830.26 + 4830.26i −0.644425 + 0.644425i −0.951640 0.307215i \(-0.900603\pi\)
0.307215 + 0.951640i \(0.400603\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4255.18i 0.561096i
\(387\) 0 0
\(388\) 7373.22 + 7373.22i 0.964739 + 0.964739i
\(389\) −1186.46 −0.154643 −0.0773213 0.997006i \(-0.524637\pi\)
−0.0773213 + 0.997006i \(0.524637\pi\)
\(390\) 0 0
\(391\) −14721.9 −1.90414
\(392\) 3220.82 + 3220.82i 0.414990 + 0.414990i
\(393\) 0 0
\(394\) 195.777i 0.0250333i
\(395\) 0 0
\(396\) 0 0
\(397\) 8913.20 8913.20i 1.12680 1.12680i 0.136108 0.990694i \(-0.456540\pi\)
0.990694 0.136108i \(-0.0434595\pi\)
\(398\) 1245.73 1245.73i 0.156891 0.156891i
\(399\) 0 0
\(400\) 0 0
\(401\) 5637.87i 0.702099i 0.936357 + 0.351050i \(0.114175\pi\)
−0.936357 + 0.351050i \(0.885825\pi\)
\(402\) 0 0
\(403\) −74.9690 74.9690i −0.00926668 0.00926668i
\(404\) −7661.43 −0.943491
\(405\) 0 0
\(406\) 4522.69 0.552850
\(407\) −3900.86 3900.86i −0.475083 0.475083i
\(408\) 0 0
\(409\) 12265.1i 1.48282i −0.671055 0.741408i \(-0.734159\pi\)
0.671055 0.741408i \(-0.265841\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −5073.15 + 5073.15i −0.606642 + 0.606642i
\(413\) 1030.72 1030.72i 0.122805 0.122805i
\(414\) 0 0
\(415\) 0 0
\(416\) 6823.25i 0.804176i
\(417\) 0 0
\(418\) −4651.21 4651.21i −0.544254 0.544254i
\(419\) 9519.10 1.10988 0.554938 0.831891i \(-0.312742\pi\)
0.554938 + 0.831891i \(0.312742\pi\)
\(420\) 0 0
\(421\) 4787.83 0.554263 0.277131 0.960832i \(-0.410616\pi\)
0.277131 + 0.960832i \(0.410616\pi\)
\(422\) −2271.10 2271.10i −0.261979 0.261979i
\(423\) 0 0
\(424\) 7482.26i 0.857006i
\(425\) 0 0
\(426\) 0 0
\(427\) −1769.49 + 1769.49i −0.200543 + 0.200543i
\(428\) 7803.20 7803.20i 0.881266 0.881266i
\(429\) 0 0
\(430\) 0 0
\(431\) 8308.56i 0.928560i −0.885689 0.464280i \(-0.846313\pi\)
0.885689 0.464280i \(-0.153687\pi\)
\(432\) 0 0
\(433\) 4885.19 + 4885.19i 0.542188 + 0.542188i 0.924170 0.381982i \(-0.124758\pi\)
−0.381982 + 0.924170i \(0.624758\pi\)
\(434\) 49.0408 0.00542404
\(435\) 0 0
\(436\) 885.779 0.0972962
\(437\) −14302.8 14302.8i −1.56567 1.56567i
\(438\) 0 0
\(439\) 4105.93i 0.446391i −0.974774 0.223195i \(-0.928351\pi\)
0.974774 0.223195i \(-0.0716488\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3653.28 3653.28i 0.393143 0.393143i
\(443\) 1722.96 1722.96i 0.184786 0.184786i −0.608652 0.793438i \(-0.708289\pi\)
0.793438 + 0.608652i \(0.208289\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 3082.08i 0.327221i
\(447\) 0 0
\(448\) 1335.89 + 1335.89i 0.140881 + 0.140881i
\(449\) −15259.1 −1.60383 −0.801917 0.597436i \(-0.796186\pi\)
−0.801917 + 0.597436i \(0.796186\pi\)
\(450\) 0 0
\(451\) −8480.42 −0.885427
\(452\) 1379.18 + 1379.18i 0.143520 + 0.143520i
\(453\) 0 0
\(454\) 1073.54i 0.110977i
\(455\) 0 0
\(456\) 0 0
\(457\) 5301.02 5301.02i 0.542607 0.542607i −0.381685 0.924292i \(-0.624656\pi\)
0.924292 + 0.381685i \(0.124656\pi\)
\(458\) 6820.03 6820.03i 0.695806 0.695806i
\(459\) 0 0
\(460\) 0 0
\(461\) 4117.47i 0.415986i 0.978130 + 0.207993i \(0.0666932\pi\)
−0.978130 + 0.207993i \(0.933307\pi\)
\(462\) 0 0
\(463\) −3550.72 3550.72i −0.356406 0.356406i 0.506081 0.862486i \(-0.331094\pi\)
−0.862486 + 0.506081i \(0.831094\pi\)
\(464\) 3830.43 0.383240
\(465\) 0 0
\(466\) 7679.27 0.763381
\(467\) −2539.40 2539.40i −0.251626 0.251626i 0.570011 0.821637i \(-0.306939\pi\)
−0.821637 + 0.570011i \(0.806939\pi\)
\(468\) 0 0
\(469\) 3713.46i 0.365611i
\(470\) 0 0
\(471\) 0 0
\(472\) −1924.67 + 1924.67i −0.187691 + 0.187691i
\(473\) 11485.9 11485.9i 1.11654 1.11654i
\(474\) 0 0
\(475\) 0 0
\(476\) 5952.27i 0.573155i
\(477\) 0 0
\(478\) 6129.68 + 6129.68i 0.586538 + 0.586538i
\(479\) −15920.6 −1.51865 −0.759324 0.650712i \(-0.774470\pi\)
−0.759324 + 0.650712i \(0.774470\pi\)
\(480\) 0 0
\(481\) 5953.40 0.564349
\(482\) 4853.15 + 4853.15i 0.458620 + 0.458620i
\(483\) 0 0
\(484\) 1113.06i 0.104533i
\(485\) 0 0
\(486\) 0 0
\(487\) −2724.10 + 2724.10i −0.253472 + 0.253472i −0.822393 0.568920i \(-0.807361\pi\)
0.568920 + 0.822393i \(0.307361\pi\)
\(488\) 3304.19 3304.19i 0.306503 0.306503i
\(489\) 0 0
\(490\) 0 0
\(491\) 4422.67i 0.406502i −0.979127 0.203251i \(-0.934849\pi\)
0.979127 0.203251i \(-0.0651507\pi\)
\(492\) 0 0
\(493\) 17834.9 + 17834.9i 1.62930 + 1.62930i
\(494\) 7098.57 0.646518
\(495\) 0 0
\(496\) 41.5344 0.00375998
\(497\) 234.365 + 234.365i 0.0211523 + 0.0211523i
\(498\) 0 0
\(499\) 653.980i 0.0586697i 0.999570 + 0.0293348i \(0.00933891\pi\)
−0.999570 + 0.0293348i \(0.990661\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −2165.35 + 2165.35i −0.192518 + 0.192518i
\(503\) −7109.17 + 7109.17i −0.630183 + 0.630183i −0.948114 0.317931i \(-0.897012\pi\)
0.317931 + 0.948114i \(0.397012\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 8005.93i 0.703374i
\(507\) 0 0
\(508\) 3410.46 + 3410.46i 0.297864 + 0.297864i
\(509\) −15370.7 −1.33849 −0.669246 0.743041i \(-0.733383\pi\)
−0.669246 + 0.743041i \(0.733383\pi\)
\(510\) 0 0
\(511\) −651.196 −0.0563742
\(512\) 3562.88 + 3562.88i 0.307536 + 0.307536i
\(513\) 0 0
\(514\) 4764.59i 0.408866i
\(515\) 0 0
\(516\) 0 0
\(517\) 4256.64 4256.64i 0.362102 0.362102i
\(518\) −1947.20 + 1947.20i −0.165164 + 0.165164i
\(519\) 0 0
\(520\) 0 0
\(521\) 8014.41i 0.673930i −0.941517 0.336965i \(-0.890600\pi\)
0.941517 0.336965i \(-0.109400\pi\)
\(522\) 0 0
\(523\) −8470.99 8470.99i −0.708242 0.708242i 0.257924 0.966165i \(-0.416962\pi\)
−0.966165 + 0.257924i \(0.916962\pi\)
\(524\) −7360.17 −0.613608
\(525\) 0 0
\(526\) −11105.7 −0.920588
\(527\) 193.389 + 193.389i 0.0159851 + 0.0159851i
\(528\) 0 0
\(529\) 12451.8i 1.02341i
\(530\) 0 0
\(531\) 0 0
\(532\) 5782.82 5782.82i 0.471273 0.471273i
\(533\) 6471.31 6471.31i 0.525898 0.525898i
\(534\) 0 0
\(535\) 0 0
\(536\) 6934.18i 0.558789i
\(537\) 0 0
\(538\) −1611.56 1611.56i −0.129144 0.129144i
\(539\) 7397.81 0.591181
\(540\) 0 0
\(541\) 16590.7 1.31846 0.659231 0.751941i \(-0.270882\pi\)
0.659231 + 0.751941i \(0.270882\pi\)
\(542\) −4078.84 4078.84i −0.323249 0.323249i
\(543\) 0 0
\(544\) 17601.2i 1.38721i
\(545\) 0 0
\(546\) 0 0
\(547\) 7105.34 7105.34i 0.555397 0.555397i −0.372596 0.927994i \(-0.621532\pi\)
0.927994 + 0.372596i \(0.121532\pi\)
\(548\) 3837.19 3837.19i 0.299118 0.299118i
\(549\) 0 0
\(550\) 0 0
\(551\) 34654.5i 2.67936i
\(552\) 0 0
\(553\) −3537.65 3537.65i −0.272036 0.272036i
\(554\) −9893.05 −0.758692
\(555\) 0 0
\(556\) 5873.62 0.448016
\(557\) 1686.40 + 1686.40i 0.128286 + 0.128286i 0.768334 0.640049i \(-0.221086\pi\)
−0.640049 + 0.768334i \(0.721086\pi\)
\(558\) 0 0
\(559\) 17529.5i 1.32633i
\(560\) 0 0
\(561\) 0 0
\(562\) −1250.52 + 1250.52i −0.0938614 + 0.0938614i
\(563\) −4011.17 + 4011.17i −0.300268 + 0.300268i −0.841119 0.540851i \(-0.818102\pi\)
0.540851 + 0.841119i \(0.318102\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 9646.91i 0.716414i
\(567\) 0 0
\(568\) −437.632 437.632i −0.0323286 0.0323286i
\(569\) 11917.1 0.878012 0.439006 0.898484i \(-0.355331\pi\)
0.439006 + 0.898484i \(0.355331\pi\)
\(570\) 0 0
\(571\) 5233.00 0.383528 0.191764 0.981441i \(-0.438579\pi\)
0.191764 + 0.981441i \(0.438579\pi\)
\(572\) −4948.29 4948.29i −0.361710 0.361710i
\(573\) 0 0
\(574\) 4233.19i 0.307822i
\(575\) 0 0
\(576\) 0 0
\(577\) 471.420 471.420i 0.0340130 0.0340130i −0.689896 0.723909i \(-0.742344\pi\)
0.723909 + 0.689896i \(0.242344\pi\)
\(578\) −4164.77 + 4164.77i −0.299709 + 0.299709i
\(579\) 0 0
\(580\) 0 0
\(581\) 11470.3i 0.819052i
\(582\) 0 0
\(583\) −8592.90 8592.90i −0.610431 0.610431i
\(584\) 1215.98 0.0861605
\(585\) 0 0
\(586\) −7758.22 −0.546910
\(587\) 11088.0 + 11088.0i 0.779645 + 0.779645i 0.979770 0.200125i \(-0.0641349\pi\)
−0.200125 + 0.979770i \(0.564135\pi\)
\(588\) 0 0
\(589\) 375.768i 0.0262874i
\(590\) 0 0
\(591\) 0 0
\(592\) −1649.16 + 1649.16i −0.114493 + 0.114493i
\(593\) −4249.89 + 4249.89i −0.294303 + 0.294303i −0.838778 0.544474i \(-0.816729\pi\)
0.544474 + 0.838778i \(0.316729\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8425.04i 0.579032i
\(597\) 0 0
\(598\) 6109.23 + 6109.23i 0.417768 + 0.417768i
\(599\) 25049.7 1.70868 0.854341 0.519712i \(-0.173961\pi\)
0.854341 + 0.519712i \(0.173961\pi\)
\(600\) 0 0
\(601\) −23667.8 −1.60637 −0.803186 0.595728i \(-0.796864\pi\)
−0.803186 + 0.595728i \(0.796864\pi\)
\(602\) −5733.44 5733.44i −0.388169 0.388169i
\(603\) 0 0
\(604\) 18570.0i 1.25100i
\(605\) 0 0
\(606\) 0 0
\(607\) 1377.34 1377.34i 0.0920997 0.0920997i −0.659556 0.751656i \(-0.729256\pi\)
0.751656 + 0.659556i \(0.229256\pi\)
\(608\) −17100.1 + 17100.1i −1.14063 + 1.14063i
\(609\) 0 0
\(610\) 0 0
\(611\) 6496.38i 0.430140i
\(612\) 0 0
\(613\) −6308.16 6308.16i −0.415635 0.415635i 0.468061 0.883696i \(-0.344953\pi\)
−0.883696 + 0.468061i \(0.844953\pi\)
\(614\) 2592.47 0.170397
\(615\) 0 0
\(616\) 7773.41 0.508441
\(617\) −699.955 699.955i −0.0456712 0.0456712i 0.683902 0.729574i \(-0.260281\pi\)
−0.729574 + 0.683902i \(0.760281\pi\)
\(618\) 0 0
\(619\) 19461.7i 1.26370i 0.775089 + 0.631852i \(0.217705\pi\)
−0.775089 + 0.631852i \(0.782295\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −7074.43 + 7074.43i −0.456043 + 0.456043i
\(623\) −11617.2 + 11617.2i −0.747084 + 0.747084i
\(624\) 0 0
\(625\) 0 0
\(626\) 9418.84i 0.601362i
\(627\) 0 0
\(628\) −13041.7 13041.7i −0.828692 0.828692i
\(629\) −15357.3 −0.973509
\(630\) 0 0
\(631\) 7257.30 0.457858 0.228929 0.973443i \(-0.426478\pi\)
0.228929 + 0.973443i \(0.426478\pi\)
\(632\) 6605.88 + 6605.88i 0.415772 + 0.415772i
\(633\) 0 0
\(634\) 1037.16i 0.0649699i
\(635\) 0 0
\(636\) 0 0
\(637\) −5645.18 + 5645.18i −0.351131 + 0.351131i
\(638\) −9698.83 + 9698.83i −0.601850 + 0.601850i
\(639\) 0 0
\(640\) 0 0
\(641\) 21156.1i 1.30361i −0.758385 0.651807i \(-0.774011\pi\)
0.758385 0.651807i \(-0.225989\pi\)
\(642\) 0 0
\(643\) 8931.56 + 8931.56i 0.547786 + 0.547786i 0.925800 0.378014i \(-0.123393\pi\)
−0.378014 + 0.925800i \(0.623393\pi\)
\(644\) 9953.73 0.609055
\(645\) 0 0
\(646\) −18311.4 −1.11525
\(647\) 16740.1 + 16740.1i 1.01719 + 1.01719i 0.999850 + 0.0173412i \(0.00552015\pi\)
0.0173412 + 0.999850i \(0.494480\pi\)
\(648\) 0 0
\(649\) 4420.73i 0.267379i
\(650\) 0 0
\(651\) 0 0
\(652\) 371.123 371.123i 0.0222919 0.0222919i
\(653\) 12157.8 12157.8i 0.728592 0.728592i −0.241747 0.970339i \(-0.577720\pi\)
0.970339 + 0.241747i \(0.0777205\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3585.24i 0.213384i
\(657\) 0 0
\(658\) −2124.80 2124.80i −0.125886 0.125886i
\(659\) 28300.0 1.67285 0.836427 0.548079i \(-0.184641\pi\)
0.836427 + 0.548079i \(0.184641\pi\)
\(660\) 0 0
\(661\) 4326.04 0.254559 0.127280 0.991867i \(-0.459375\pi\)
0.127280 + 0.991867i \(0.459375\pi\)
\(662\) 9980.94 + 9980.94i 0.585982 + 0.585982i
\(663\) 0 0
\(664\) 21418.6i 1.25181i
\(665\) 0 0
\(666\) 0 0
\(667\) −29824.6 + 29824.6i −1.73135 + 1.73135i
\(668\) −636.266 + 636.266i −0.0368531 + 0.0368531i
\(669\) 0 0
\(670\) 0 0
\(671\) 7589.30i 0.436634i
\(672\) 0 0
\(673\) −11089.2 11089.2i −0.635153 0.635153i 0.314203 0.949356i \(-0.398263\pi\)
−0.949356 + 0.314203i \(0.898263\pi\)
\(674\) 10691.6 0.611015
\(675\) 0 0
\(676\) −4988.97 −0.283851
\(677\) −3104.83 3104.83i −0.176260 0.176260i 0.613463 0.789723i \(-0.289776\pi\)
−0.789723 + 0.613463i \(0.789776\pi\)
\(678\) 0 0
\(679\) 20301.4i 1.14742i
\(680\) 0 0
\(681\) 0 0
\(682\) −105.167 + 105.167i −0.00590478 + 0.00590478i
\(683\) −2278.90 + 2278.90i −0.127672 + 0.127672i −0.768055 0.640384i \(-0.778775\pi\)
0.640384 + 0.768055i \(0.278775\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 9463.56i 0.526706i
\(687\) 0 0
\(688\) −4855.86 4855.86i −0.269081 0.269081i
\(689\) 13114.3 0.725129
\(690\) 0 0
\(691\) 6466.55 0.356004 0.178002 0.984030i \(-0.443037\pi\)
0.178002 + 0.984030i \(0.443037\pi\)
\(692\) −12909.3 12909.3i −0.709158 0.709158i
\(693\) 0 0
\(694\) 10218.1i 0.558897i
\(695\) 0 0
\(696\) 0 0
\(697\) −16693.3 + 16693.3i −0.907180 + 0.907180i
\(698\) −2280.32 + 2280.32i −0.123655 + 0.123655i
\(699\) 0 0
\(700\) 0 0
\(701\) 31472.6i 1.69573i 0.530214 + 0.847864i \(0.322112\pi\)
−0.530214 + 0.847864i \(0.677888\pi\)
\(702\) 0 0
\(703\) −14920.2 14920.2i −0.800461 0.800461i
\(704\) −5729.59 −0.306736
\(705\) 0 0
\(706\) 7996.86 0.426297
\(707\) 10547.5 + 10547.5i 0.561072 + 0.561072i
\(708\) 0 0
\(709\) 21493.4i 1.13851i −0.822162 0.569254i \(-0.807232\pi\)
0.822162 0.569254i \(-0.192768\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 21692.9 21692.9i 1.14182 1.14182i
\(713\) −323.397 + 323.397i −0.0169864 + 0.0169864i
\(714\) 0 0
\(715\) 0 0
\(716\) 4404.39i 0.229888i
\(717\) 0 0
\(718\) −876.016 876.016i −0.0455329 0.0455329i
\(719\) 34918.3 1.81117 0.905587 0.424160i \(-0.139431\pi\)
0.905587 + 0.424160i \(0.139431\pi\)
\(720\) 0 0
\(721\) 13968.4 0.721511
\(722\) −10447.8 10447.8i −0.538541 0.538541i
\(723\) 0 0
\(724\) 5767.11i 0.296040i
\(725\) 0 0
\(726\) 0 0
\(727\) 14767.9 14767.9i 0.753388 0.753388i −0.221722 0.975110i \(-0.571168\pi\)
0.975110 + 0.221722i \(0.0711678\pi\)
\(728\) −5931.79 + 5931.79i −0.301988 + 0.301988i
\(729\) 0 0
\(730\) 0 0
\(731\) 45218.9i 2.28794i
\(732\) 0 0
\(733\) 15017.4 + 15017.4i 0.756726 + 0.756726i 0.975725 0.218999i \(-0.0702790\pi\)
−0.218999 + 0.975725i \(0.570279\pi\)
\(734\) −13072.9 −0.657399
\(735\) 0 0
\(736\) −29433.7 −1.47410
\(737\) 7963.46 + 7963.46i 0.398016 + 0.398016i
\(738\) 0 0
\(739\) 30967.6i 1.54149i 0.637143 + 0.770746i \(0.280116\pi\)
−0.637143 + 0.770746i \(0.719884\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −4289.33 + 4289.33i −0.212219 + 0.212219i
\(743\) −9588.32 + 9588.32i −0.473434 + 0.473434i −0.903024 0.429590i \(-0.858658\pi\)
0.429590 + 0.903024i \(0.358658\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1587.15i 0.0778949i
\(747\) 0 0
\(748\) 12764.5 + 12764.5i 0.623955 + 0.623955i
\(749\) −21485.3 −1.04814
\(750\) 0 0
\(751\) 8514.08 0.413693 0.206846 0.978373i \(-0.433680\pi\)
0.206846 + 0.978373i \(0.433680\pi\)
\(752\) −1799.57 1799.57i −0.0872652 0.0872652i
\(753\) 0 0
\(754\) 14802.1i 0.714936i
\(755\) 0 0
\(756\) 0 0
\(757\) −7031.43 + 7031.43i −0.337598 + 0.337598i −0.855463 0.517865i \(-0.826727\pi\)
0.517865 + 0.855463i \(0.326727\pi\)
\(758\) −60.6007 + 60.6007i −0.00290385 + 0.00290385i
\(759\) 0 0
\(760\) 0 0
\(761\) 15458.2i 0.736346i 0.929757 + 0.368173i \(0.120017\pi\)
−0.929757 + 0.368173i \(0.879983\pi\)
\(762\) 0 0
\(763\) −1219.45 1219.45i −0.0578598 0.0578598i
\(764\) −7338.01 −0.347487
\(765\) 0 0
\(766\) −10341.3 −0.487787
\(767\) −3373.40 3373.40i −0.158809 0.158809i
\(768\) 0 0
\(769\) 10361.1i 0.485865i 0.970043 + 0.242933i \(0.0781094\pi\)
−0.970043 + 0.242933i \(0.921891\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11345.3 11345.3i 0.528919 0.528919i
\(773\) 18766.0 18766.0i 0.873179 0.873179i −0.119638 0.992818i \(-0.538173\pi\)
0.992818 + 0.119638i \(0.0381734\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 37908.9i 1.75367i
\(777\) 0 0
\(778\) −1270.07 1270.07i −0.0585271 0.0585271i
\(779\) −32436.2 −1.49185
\(780\) 0 0
\(781\) −1005.18 −0.0460542
\(782\) −15759.3 15759.3i −0.720654 0.720654i
\(783\) 0 0
\(784\) 3127.55i 0.142472i
\(785\) 0 0
\(786\) 0 0
\(787\) −7235.25 + 7235.25i −0.327711 + 0.327711i −0.851716 0.524004i \(-0.824438\pi\)
0.524004 + 0.851716i \(0.324438\pi\)
\(788\) −521.986 + 521.986i −0.0235977 + 0.0235977i
\(789\) 0 0
\(790\) 0 0
\(791\) 3797.41i 0.170696i
\(792\) 0 0
\(793\) 5791.30 + 5791.30i 0.259338 + 0.259338i
\(794\) 19082.6 0.852915
\(795\) 0 0