Properties

Label 1900.2.i.d.501.1
Level $1900$
Weight $2$
Character 1900.501
Analytic conductor $15.172$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 9 x^{6} + 2 x^{5} + 65 x^{4} - 20 x^{3} + 25 x^{2} + 6 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 501.1
Root \(-1.26041 - 2.18309i\) of defining polynomial
Character \(\chi\) \(=\) 1900.501
Dual form 1900.2.i.d.201.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.26041 - 2.18309i) q^{3} -2.72743 q^{7} +(-1.67727 + 2.90511i) q^{9} +O(q^{10})\) \(q+(-1.26041 - 2.18309i) q^{3} -2.72743 q^{7} +(-1.67727 + 2.90511i) q^{9} +3.31421 q^{11} +(1.62412 - 2.81306i) q^{13} +(-1.17727 - 2.03909i) q^{17} +(-3.11494 - 3.04912i) q^{19} +(3.43768 + 5.95423i) q^{21} +(1.07396 - 1.86016i) q^{23} +0.893714 q^{27} +(1.96702 - 3.40697i) q^{29} -10.1896 q^{31} +(-4.17727 - 7.23524i) q^{33} +3.68579 q^{37} -8.18825 q^{39} +(0.363714 + 0.629971i) q^{41} +(-1.18645 - 2.05499i) q^{43} +(-5.51164 + 9.54644i) q^{47} +0.438860 q^{49} +(-2.96768 + 5.14017i) q^{51} +(-4.49148 + 7.77947i) q^{53} +(-2.73041 + 10.6434i) q^{57} +(5.48784 + 9.50521i) q^{59} +(4.22743 - 7.32212i) q^{61} +(4.57462 - 7.92348i) q^{63} +(-4.87535 + 8.44436i) q^{67} -5.41453 q^{69} +(-3.45850 - 5.99029i) q^{71} +(-1.24025 - 2.14818i) q^{73} -9.03927 q^{77} +(-5.99948 - 10.3914i) q^{79} +(3.90535 + 6.76427i) q^{81} -4.68711 q^{83} -9.91699 q^{87} +(-4.27205 + 7.39941i) q^{89} +(-4.42968 + 7.67243i) q^{91} +(12.8430 + 22.2448i) q^{93} +(3.61494 + 6.26127i) q^{97} +(-5.55882 + 9.62816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{3} - 5q^{9} + O(q^{10}) \) \( 8q + q^{3} - 5q^{9} + 4q^{11} - 9q^{13} - q^{17} + 3q^{19} + 8q^{21} - 20q^{27} + 5q^{29} - 20q^{31} - 25q^{33} + 52q^{37} - 54q^{39} - 8q^{41} - 7q^{43} - 16q^{47} + 20q^{49} + 12q^{51} - 5q^{53} - 27q^{57} + 11q^{59} + 12q^{61} + 3q^{63} + 6q^{69} + 14q^{71} + 4q^{73} + 44q^{77} + 13q^{79} - 24q^{81} - 10q^{83} + 4q^{87} + 5q^{89} - 46q^{91} + 28q^{93} + q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −1.26041 2.18309i −0.727698 1.26041i −0.957854 0.287256i \(-0.907257\pi\)
0.230156 0.973154i \(-0.426076\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.72743 −1.03087 −0.515435 0.856928i \(-0.672370\pi\)
−0.515435 + 0.856928i \(0.672370\pi\)
\(8\) 0 0
\(9\) −1.67727 + 2.90511i −0.559089 + 0.968370i
\(10\) 0 0
\(11\) 3.31421 0.999273 0.499636 0.866235i \(-0.333467\pi\)
0.499636 + 0.866235i \(0.333467\pi\)
\(12\) 0 0
\(13\) 1.62412 2.81306i 0.450451 0.780204i −0.547963 0.836502i \(-0.684597\pi\)
0.998414 + 0.0562987i \(0.0179299\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.17727 2.03909i −0.285529 0.494551i 0.687208 0.726460i \(-0.258836\pi\)
−0.972737 + 0.231910i \(0.925503\pi\)
\(18\) 0 0
\(19\) −3.11494 3.04912i −0.714617 0.699516i
\(20\) 0 0
\(21\) 3.43768 + 5.95423i 0.750163 + 1.29932i
\(22\) 0 0
\(23\) 1.07396 1.86016i 0.223937 0.387870i −0.732063 0.681237i \(-0.761442\pi\)
0.956000 + 0.293367i \(0.0947758\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0.893714 0.171995
\(28\) 0 0
\(29\) 1.96702 3.40697i 0.365266 0.632659i −0.623553 0.781781i \(-0.714311\pi\)
0.988819 + 0.149122i \(0.0476447\pi\)
\(30\) 0 0
\(31\) −10.1896 −1.83010 −0.915050 0.403340i \(-0.867849\pi\)
−0.915050 + 0.403340i \(0.867849\pi\)
\(32\) 0 0
\(33\) −4.17727 7.23524i −0.727169 1.25949i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.68579 0.605940 0.302970 0.953000i \(-0.402022\pi\)
0.302970 + 0.953000i \(0.402022\pi\)
\(38\) 0 0
\(39\) −8.18825 −1.31117
\(40\) 0 0
\(41\) 0.363714 + 0.629971i 0.0568025 + 0.0983849i 0.893028 0.450000i \(-0.148576\pi\)
−0.836226 + 0.548385i \(0.815243\pi\)
\(42\) 0 0
\(43\) −1.18645 2.05499i −0.180931 0.313383i 0.761267 0.648439i \(-0.224578\pi\)
−0.942198 + 0.335057i \(0.891245\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.51164 + 9.54644i −0.803955 + 1.39249i 0.113039 + 0.993591i \(0.463942\pi\)
−0.916994 + 0.398901i \(0.869392\pi\)
\(48\) 0 0
\(49\) 0.438860 0.0626942
\(50\) 0 0
\(51\) −2.96768 + 5.14017i −0.415558 + 0.719767i
\(52\) 0 0
\(53\) −4.49148 + 7.77947i −0.616952 + 1.06859i 0.373087 + 0.927797i \(0.378299\pi\)
−0.990039 + 0.140796i \(0.955034\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.73041 + 10.6434i −0.361652 + 1.40975i
\(58\) 0 0
\(59\) 5.48784 + 9.50521i 0.714456 + 1.23747i 0.963169 + 0.268896i \(0.0866589\pi\)
−0.248714 + 0.968577i \(0.580008\pi\)
\(60\) 0 0
\(61\) 4.22743 7.32212i 0.541267 0.937501i −0.457565 0.889176i \(-0.651278\pi\)
0.998832 0.0483251i \(-0.0153884\pi\)
\(62\) 0 0
\(63\) 4.57462 7.92348i 0.576348 0.998264i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.87535 + 8.44436i −0.595619 + 1.03164i 0.397840 + 0.917455i \(0.369760\pi\)
−0.993459 + 0.114188i \(0.963573\pi\)
\(68\) 0 0
\(69\) −5.41453 −0.651833
\(70\) 0 0
\(71\) −3.45850 5.99029i −0.410448 0.710917i 0.584491 0.811400i \(-0.301294\pi\)
−0.994939 + 0.100484i \(0.967961\pi\)
\(72\) 0 0
\(73\) −1.24025 2.14818i −0.145160 0.251425i 0.784272 0.620417i \(-0.213036\pi\)
−0.929433 + 0.368992i \(0.879703\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.03927 −1.03012
\(78\) 0 0
\(79\) −5.99948 10.3914i −0.674994 1.16912i −0.976471 0.215650i \(-0.930813\pi\)
0.301477 0.953474i \(-0.402520\pi\)
\(80\) 0 0
\(81\) 3.90535 + 6.76427i 0.433928 + 0.751586i
\(82\) 0 0
\(83\) −4.68711 −0.514477 −0.257238 0.966348i \(-0.582813\pi\)
−0.257238 + 0.966348i \(0.582813\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −9.91699 −1.06321
\(88\) 0 0
\(89\) −4.27205 + 7.39941i −0.452836 + 0.784336i −0.998561 0.0536291i \(-0.982921\pi\)
0.545725 + 0.837965i \(0.316254\pi\)
\(90\) 0 0
\(91\) −4.42968 + 7.67243i −0.464357 + 0.804289i
\(92\) 0 0
\(93\) 12.8430 + 22.2448i 1.33176 + 2.30668i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 3.61494 + 6.26127i 0.367042 + 0.635735i 0.989102 0.147235i \(-0.0470372\pi\)
−0.622060 + 0.782970i \(0.713704\pi\)
\(98\) 0 0
\(99\) −5.55882 + 9.62816i −0.558682 + 0.967666i
\(100\) 0 0
\(101\) 2.88818 5.00247i 0.287384 0.497764i −0.685800 0.727790i \(-0.740548\pi\)
0.973185 + 0.230026i \(0.0738810\pi\)
\(102\) 0 0
\(103\) 15.0576 1.48367 0.741836 0.670581i \(-0.233955\pi\)
0.741836 + 0.670581i \(0.233955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.1896 1.46843 0.734215 0.678917i \(-0.237550\pi\)
0.734215 + 0.678917i \(0.237550\pi\)
\(108\) 0 0
\(109\) 6.31057 + 10.9302i 0.604443 + 1.04693i 0.992139 + 0.125139i \(0.0399376\pi\)
−0.387696 + 0.921787i \(0.626729\pi\)
\(110\) 0 0
\(111\) −4.64560 8.04642i −0.440941 0.763732i
\(112\) 0 0
\(113\) 6.10761 0.574555 0.287278 0.957847i \(-0.407250\pi\)
0.287278 + 0.957847i \(0.407250\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 5.44818 + 9.43652i 0.503684 + 0.872406i
\(118\) 0 0
\(119\) 3.21091 + 5.56146i 0.294344 + 0.509818i
\(120\) 0 0
\(121\) −0.0159950 −0.00145409
\(122\) 0 0
\(123\) 0.916857 1.58804i 0.0826702 0.143189i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −4.56114 + 7.90013i −0.404736 + 0.701023i −0.994291 0.106705i \(-0.965970\pi\)
0.589555 + 0.807728i \(0.299303\pi\)
\(128\) 0 0
\(129\) −2.99082 + 5.18025i −0.263327 + 0.456096i
\(130\) 0 0
\(131\) −11.1328 19.2825i −0.972676 1.68472i −0.687402 0.726277i \(-0.741249\pi\)
−0.285274 0.958446i \(-0.592085\pi\)
\(132\) 0 0
\(133\) 8.49578 + 8.31625i 0.736678 + 0.721110i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.81355 + 6.60527i −0.325814 + 0.564326i −0.981677 0.190554i \(-0.938972\pi\)
0.655863 + 0.754880i \(0.272305\pi\)
\(138\) 0 0
\(139\) −8.45916 + 14.6517i −0.717496 + 1.24274i 0.244493 + 0.969651i \(0.421379\pi\)
−0.961989 + 0.273089i \(0.911955\pi\)
\(140\) 0 0
\(141\) 27.7877 2.34015
\(142\) 0 0
\(143\) 5.38269 9.32309i 0.450123 0.779636i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.553143 0.958072i −0.0456225 0.0790204i
\(148\) 0 0
\(149\) 6.19809 + 10.7354i 0.507767 + 0.879478i 0.999960 + 0.00899193i \(0.00286226\pi\)
−0.492193 + 0.870486i \(0.663804\pi\)
\(150\) 0 0
\(151\) −14.4549 −1.17632 −0.588160 0.808745i \(-0.700147\pi\)
−0.588160 + 0.808745i \(0.700147\pi\)
\(152\) 0 0
\(153\) 7.89836 0.638544
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.10642 15.7728i −0.726772 1.25881i −0.958241 0.285963i \(-0.907687\pi\)
0.231469 0.972842i \(-0.425647\pi\)
\(158\) 0 0
\(159\) 22.6444 1.79582
\(160\) 0 0
\(161\) −2.92916 + 5.07345i −0.230850 + 0.399844i
\(162\) 0 0
\(163\) −19.2642 −1.50889 −0.754446 0.656362i \(-0.772094\pi\)
−0.754446 + 0.656362i \(0.772094\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.84289 4.92404i 0.219990 0.381033i −0.734815 0.678268i \(-0.762731\pi\)
0.954805 + 0.297234i \(0.0960643\pi\)
\(168\) 0 0
\(169\) 1.22445 + 2.12080i 0.0941881 + 0.163139i
\(170\) 0 0
\(171\) 14.0826 3.93507i 1.07692 0.300922i
\(172\) 0 0
\(173\) −4.57760 7.92864i −0.348029 0.602804i 0.637870 0.770144i \(-0.279816\pi\)
−0.985899 + 0.167340i \(0.946482\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 13.8338 23.9609i 1.03982 1.80101i
\(178\) 0 0
\(179\) 12.1810 0.910448 0.455224 0.890377i \(-0.349559\pi\)
0.455224 + 0.890377i \(0.349559\pi\)
\(180\) 0 0
\(181\) −7.70608 + 13.3473i −0.572789 + 0.992099i 0.423489 + 0.905901i \(0.360805\pi\)
−0.996278 + 0.0861980i \(0.972528\pi\)
\(182\) 0 0
\(183\) −21.3132 −1.57551
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −3.90171 6.75796i −0.285321 0.494191i
\(188\) 0 0
\(189\) −2.43754 −0.177305
\(190\) 0 0
\(191\) −16.2482 −1.17568 −0.587841 0.808977i \(-0.700022\pi\)
−0.587841 + 0.808977i \(0.700022\pi\)
\(192\) 0 0
\(193\) 0.425514 + 0.737011i 0.0306292 + 0.0530512i 0.880934 0.473240i \(-0.156916\pi\)
−0.850305 + 0.526291i \(0.823582\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −19.9843 −1.42382 −0.711910 0.702270i \(-0.752170\pi\)
−0.711910 + 0.702270i \(0.752170\pi\)
\(198\) 0 0
\(199\) 3.22861 5.59212i 0.228870 0.396415i −0.728603 0.684936i \(-0.759830\pi\)
0.957474 + 0.288521i \(0.0931636\pi\)
\(200\) 0 0
\(201\) 24.5798 1.73372
\(202\) 0 0
\(203\) −5.36490 + 9.29227i −0.376542 + 0.652190i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.60264 + 6.23996i 0.250401 + 0.433707i
\(208\) 0 0
\(209\) −10.3236 10.1054i −0.714097 0.699007i
\(210\) 0 0
\(211\) −5.27205 9.13146i −0.362943 0.628635i 0.625501 0.780223i \(-0.284895\pi\)
−0.988444 + 0.151588i \(0.951561\pi\)
\(212\) 0 0
\(213\) −8.71825 + 15.1004i −0.597364 + 1.03467i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 27.7913 1.88660
\(218\) 0 0
\(219\) −3.12645 + 5.41516i −0.211266 + 0.365923i
\(220\) 0 0
\(221\) −7.64811 −0.514467
\(222\) 0 0
\(223\) 4.86319 + 8.42329i 0.325663 + 0.564065i 0.981646 0.190710i \(-0.0610791\pi\)
−0.655983 + 0.754776i \(0.727746\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −22.5798 −1.49867 −0.749336 0.662190i \(-0.769627\pi\)
−0.749336 + 0.662190i \(0.769627\pi\)
\(228\) 0 0
\(229\) −16.2239 −1.07211 −0.536053 0.844184i \(-0.680085\pi\)
−0.536053 + 0.844184i \(0.680085\pi\)
\(230\) 0 0
\(231\) 11.3932 + 19.7336i 0.749617 + 1.29837i
\(232\) 0 0
\(233\) −9.33139 16.1624i −0.611320 1.05884i −0.991018 0.133727i \(-0.957306\pi\)
0.379699 0.925110i \(-0.376028\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −15.1236 + 26.1948i −0.982383 + 1.70154i
\(238\) 0 0
\(239\) 0.602780 0.0389906 0.0194953 0.999810i \(-0.493794\pi\)
0.0194953 + 0.999810i \(0.493794\pi\)
\(240\) 0 0
\(241\) −10.9408 + 18.9500i −0.704759 + 1.22068i 0.262020 + 0.965062i \(0.415611\pi\)
−0.966779 + 0.255615i \(0.917722\pi\)
\(242\) 0 0
\(243\) 11.1853 19.3734i 0.717535 1.24281i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −13.6364 + 3.81039i −0.867665 + 0.242449i
\(248\) 0 0
\(249\) 5.90768 + 10.2324i 0.374384 + 0.648452i
\(250\) 0 0
\(251\) −4.13629 + 7.16426i −0.261080 + 0.452204i −0.966529 0.256557i \(-0.917412\pi\)
0.705449 + 0.708761i \(0.250745\pi\)
\(252\) 0 0
\(253\) 3.55934 6.16496i 0.223774 0.387588i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.09544 12.2897i 0.442602 0.766608i −0.555280 0.831663i \(-0.687389\pi\)
0.997882 + 0.0650550i \(0.0207223\pi\)
\(258\) 0 0
\(259\) −10.0527 −0.624645
\(260\) 0 0
\(261\) 6.59842 + 11.4288i 0.408432 + 0.707425i
\(262\) 0 0
\(263\) −9.27153 16.0588i −0.571707 0.990225i −0.996391 0.0848836i \(-0.972948\pi\)
0.424684 0.905342i \(-0.360385\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 21.5381 1.31811
\(268\) 0 0
\(269\) −3.33371 5.77416i −0.203260 0.352057i 0.746317 0.665591i \(-0.231820\pi\)
−0.949577 + 0.313534i \(0.898487\pi\)
\(270\) 0 0
\(271\) −11.0331 19.1099i −0.670214 1.16085i −0.977843 0.209339i \(-0.932869\pi\)
0.307629 0.951506i \(-0.400464\pi\)
\(272\) 0 0
\(273\) 22.3328 1.35165
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 24.4624 1.46980 0.734902 0.678173i \(-0.237228\pi\)
0.734902 + 0.678173i \(0.237228\pi\)
\(278\) 0 0
\(279\) 17.0906 29.6018i 1.02319 1.77221i
\(280\) 0 0
\(281\) −9.33139 + 16.1624i −0.556664 + 0.964170i 0.441108 + 0.897454i \(0.354586\pi\)
−0.997772 + 0.0667164i \(0.978748\pi\)
\(282\) 0 0
\(283\) 2.24811 + 3.89384i 0.133636 + 0.231465i 0.925076 0.379783i \(-0.124001\pi\)
−0.791439 + 0.611248i \(0.790668\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.992002 1.71820i −0.0585561 0.101422i
\(288\) 0 0
\(289\) 5.72809 9.92134i 0.336946 0.583608i
\(290\) 0 0
\(291\) 9.11262 15.7835i 0.534191 0.925246i
\(292\) 0 0
\(293\) −1.27021 −0.0742063 −0.0371031 0.999311i \(-0.511813\pi\)
−0.0371031 + 0.999311i \(0.511813\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 2.96196 0.171870
\(298\) 0 0
\(299\) −3.48850 6.04225i −0.201745 0.349433i
\(300\) 0 0
\(301\) 3.23595 + 5.60483i 0.186517 + 0.323057i
\(302\) 0 0
\(303\) −14.5611 −0.836516
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −4.32638 7.49350i −0.246919 0.427677i 0.715750 0.698356i \(-0.246085\pi\)
−0.962669 + 0.270680i \(0.912752\pi\)
\(308\) 0 0
\(309\) −18.9788 32.8722i −1.07967 1.87004i
\(310\) 0 0
\(311\) 23.8497 1.35239 0.676196 0.736721i \(-0.263627\pi\)
0.676196 + 0.736721i \(0.263627\pi\)
\(312\) 0 0
\(313\) −0.388175 + 0.672340i −0.0219410 + 0.0380029i −0.876787 0.480878i \(-0.840318\pi\)
0.854846 + 0.518881i \(0.173651\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.92116 + 11.9878i −0.388731 + 0.673302i −0.992279 0.124025i \(-0.960420\pi\)
0.603548 + 0.797327i \(0.293753\pi\)
\(318\) 0 0
\(319\) 6.51911 11.2914i 0.365000 0.632199i
\(320\) 0 0
\(321\) −19.1451 33.1603i −1.06857 1.85082i
\(322\) 0 0
\(323\) −2.55030 + 9.94126i −0.141902 + 0.553147i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 15.9078 27.5531i 0.879704 1.52369i
\(328\) 0 0
\(329\) 15.0326 26.0372i 0.828774 1.43548i
\(330\) 0 0
\(331\) 28.6993 1.57746 0.788728 0.614742i \(-0.210740\pi\)
0.788728 + 0.614742i \(0.210740\pi\)
\(332\) 0 0
\(333\) −6.18205 + 10.7076i −0.338774 + 0.586774i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −17.6628 30.5928i −0.962153 1.66650i −0.717077 0.696994i \(-0.754520\pi\)
−0.245076 0.969504i \(-0.578813\pi\)
\(338\) 0 0
\(339\) −7.69809 13.3335i −0.418103 0.724175i
\(340\) 0 0
\(341\) −33.7704 −1.82877
\(342\) 0 0
\(343\) 17.8950 0.966241
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 13.0031 + 22.5221i 0.698044 + 1.20905i 0.969144 + 0.246496i \(0.0792793\pi\)
−0.271100 + 0.962551i \(0.587387\pi\)
\(348\) 0 0
\(349\) 2.44757 0.131015 0.0655077 0.997852i \(-0.479133\pi\)
0.0655077 + 0.997852i \(0.479133\pi\)
\(350\) 0 0
\(351\) 1.45150 2.51408i 0.0774755 0.134191i
\(352\) 0 0
\(353\) 4.85103 0.258194 0.129097 0.991632i \(-0.458792\pi\)
0.129097 + 0.991632i \(0.458792\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 8.09412 14.0194i 0.428386 0.741987i
\(358\) 0 0
\(359\) 3.67376 + 6.36314i 0.193894 + 0.335834i 0.946537 0.322594i \(-0.104555\pi\)
−0.752644 + 0.658428i \(0.771222\pi\)
\(360\) 0 0
\(361\) 0.405741 + 18.9957i 0.0213548 + 0.999772i
\(362\) 0 0
\(363\) 0.0201603 + 0.0349186i 0.00105814 + 0.00183275i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 6.51784 11.2892i 0.340228 0.589293i −0.644247 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561623\pi\)
\(368\) 0 0
\(369\) −2.44018 −0.127031
\(370\) 0 0
\(371\) 12.2502 21.2179i 0.635998 1.10158i
\(372\) 0 0
\(373\) 28.5514 1.47833 0.739167 0.673522i \(-0.235219\pi\)
0.739167 + 0.673522i \(0.235219\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.38936 11.0667i −0.329069 0.569964i
\(378\) 0 0
\(379\) 13.2128 0.678698 0.339349 0.940661i \(-0.389793\pi\)
0.339349 + 0.940661i \(0.389793\pi\)
\(380\) 0 0
\(381\) 22.9956 1.17810
\(382\) 0 0
\(383\) −18.8309 32.6160i −0.962212 1.66660i −0.716925 0.697150i \(-0.754451\pi\)
−0.245287 0.969450i \(-0.578882\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 7.95995 0.404627
\(388\) 0 0
\(389\) 12.8223 22.2090i 0.650119 1.12604i −0.332975 0.942936i \(-0.608052\pi\)
0.983094 0.183103i \(-0.0586142\pi\)
\(390\) 0 0
\(391\) −5.05736 −0.255762
\(392\) 0 0
\(393\) −28.0637 + 48.6078i −1.41563 + 2.45194i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −16.6366 28.8154i −0.834965 1.44620i −0.894059 0.447949i \(-0.852155\pi\)
0.0590940 0.998252i \(-0.481179\pi\)
\(398\) 0 0
\(399\) 7.44699 29.0290i 0.372816 1.45327i
\(400\) 0 0
\(401\) −4.70674 8.15232i −0.235044 0.407107i 0.724242 0.689546i \(-0.242190\pi\)
−0.959285 + 0.282439i \(0.908857\pi\)
\(402\) 0 0
\(403\) −16.5491 + 28.6639i −0.824370 + 1.42785i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12.2155 0.605499
\(408\) 0 0
\(409\) 1.25545 2.17450i 0.0620779 0.107522i −0.833316 0.552797i \(-0.813561\pi\)
0.895394 + 0.445275i \(0.146894\pi\)
\(410\) 0 0
\(411\) 19.2266 0.948376
\(412\) 0 0
\(413\) −14.9677 25.9248i −0.736511 1.27567i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 42.6480 2.08848
\(418\) 0 0
\(419\) −39.5638 −1.93282 −0.966409 0.257011i \(-0.917262\pi\)
−0.966409 + 0.257011i \(0.917262\pi\)
\(420\) 0 0
\(421\) 7.07892 + 12.2611i 0.345006 + 0.597567i 0.985355 0.170517i \(-0.0545437\pi\)
−0.640349 + 0.768084i \(0.721210\pi\)
\(422\) 0 0
\(423\) −18.4890 32.0238i −0.898965 1.55705i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −11.5300 + 19.9705i −0.557976 + 0.966442i
\(428\) 0 0
\(429\) −27.1376 −1.31022
\(430\) 0 0
\(431\) 3.26287 5.65145i 0.157167 0.272221i −0.776679 0.629897i \(-0.783097\pi\)
0.933846 + 0.357676i \(0.116431\pi\)
\(432\) 0 0
\(433\) −4.30073 + 7.44908i −0.206680 + 0.357980i −0.950667 0.310214i \(-0.899599\pi\)
0.743987 + 0.668194i \(0.232933\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9.01718 + 2.51965i −0.431350 + 0.120531i
\(438\) 0 0
\(439\) 5.77939 + 10.0102i 0.275835 + 0.477760i 0.970345 0.241722i \(-0.0777123\pi\)
−0.694510 + 0.719483i \(0.744379\pi\)
\(440\) 0 0
\(441\) −0.736084 + 1.27494i −0.0350516 + 0.0607112i
\(442\) 0 0
\(443\) −5.69629 + 9.86626i −0.270639 + 0.468760i −0.969026 0.246960i \(-0.920568\pi\)
0.698387 + 0.715721i \(0.253902\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 15.6243 27.0620i 0.739002 1.27999i
\(448\) 0 0
\(449\) 17.2252 0.812909 0.406455 0.913671i \(-0.366765\pi\)
0.406455 + 0.913671i \(0.366765\pi\)
\(450\) 0 0
\(451\) 1.20542 + 2.08786i 0.0567612 + 0.0983133i
\(452\) 0 0
\(453\) 18.2190 + 31.5563i 0.856005 + 1.48264i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 26.1885 1.22505 0.612524 0.790452i \(-0.290154\pi\)
0.612524 + 0.790452i \(0.290154\pi\)
\(458\) 0 0
\(459\) −1.05214 1.82236i −0.0491097 0.0850605i
\(460\) 0 0
\(461\) −20.2166 35.0162i −0.941580 1.63086i −0.762458 0.647038i \(-0.776008\pi\)
−0.179122 0.983827i \(-0.557326\pi\)
\(462\) 0 0
\(463\) −9.48542 −0.440825 −0.220412 0.975407i \(-0.570740\pi\)
−0.220412 + 0.975407i \(0.570740\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 39.2462 1.81610 0.908048 0.418867i \(-0.137573\pi\)
0.908048 + 0.418867i \(0.137573\pi\)
\(468\) 0 0
\(469\) 13.2972 23.0314i 0.614006 1.06349i
\(470\) 0 0
\(471\) −22.9557 + 39.7604i −1.05774 + 1.83206i
\(472\) 0 0
\(473\) −3.93214 6.81066i −0.180800 0.313155i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −15.0668 26.0965i −0.689862 1.19488i
\(478\) 0 0
\(479\) −2.72677 + 4.72290i −0.124589 + 0.215795i −0.921572 0.388207i \(-0.873095\pi\)
0.796983 + 0.604002i \(0.206428\pi\)
\(480\) 0 0
\(481\) 5.98617 10.3684i 0.272946 0.472756i
\(482\) 0 0
\(483\) 14.7677 0.671956
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −25.0662 −1.13586 −0.567930 0.823077i \(-0.692256\pi\)
−0.567930 + 0.823077i \(0.692256\pi\)
\(488\) 0 0
\(489\) 24.2808 + 42.0557i 1.09802 + 1.90182i
\(490\) 0 0
\(491\) −14.8412 25.7057i −0.669773 1.16008i −0.977967 0.208758i \(-0.933058\pi\)
0.308194 0.951324i \(-0.400275\pi\)
\(492\) 0 0
\(493\) −9.26281 −0.417176
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9.43280 + 16.3381i 0.423119 + 0.732863i
\(498\) 0 0
\(499\) 6.85519 + 11.8735i 0.306881 + 0.531533i 0.977678 0.210108i \(-0.0673814\pi\)
−0.670798 + 0.741640i \(0.734048\pi\)
\(500\) 0 0
\(501\) −14.3328 −0.640344
\(502\) 0 0
\(503\) 18.3253 31.7404i 0.817086 1.41523i −0.0907343 0.995875i \(-0.528921\pi\)
0.907820 0.419359i \(-0.137745\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.08661 5.34616i 0.137081 0.237431i
\(508\) 0 0
\(509\) 6.32519 10.9556i 0.280359 0.485596i −0.691114 0.722746i \(-0.742880\pi\)
0.971473 + 0.237149i \(0.0762131\pi\)
\(510\) 0 0
\(511\) 3.38269 + 5.85899i 0.149641 + 0.259187i
\(512\) 0 0
\(513\) −2.78387 2.72504i −0.122911 0.120314i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −18.2667 + 31.6389i −0.803371 + 1.39148i
\(518\) 0 0
\(519\) −11.5393 + 19.9867i −0.506520 + 0.877318i
\(520\) 0 0
\(521\) 16.3339 0.715601 0.357800 0.933798i \(-0.383527\pi\)
0.357800 + 0.933798i \(0.383527\pi\)
\(522\) 0 0
\(523\) −4.56734 + 7.91086i −0.199716 + 0.345918i −0.948436 0.316968i \(-0.897335\pi\)
0.748720 + 0.662886i \(0.230669\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 11.9958 + 20.7774i 0.522547 + 0.905078i
\(528\) 0 0
\(529\) 9.19321 + 15.9231i 0.399705 + 0.692309i
\(530\) 0 0
\(531\) −36.8183 −1.59778
\(532\) 0 0
\(533\) 2.36286 0.102347
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −15.3530 26.5922i −0.662531 1.14754i
\(538\) 0 0
\(539\) 1.45447 0.0626486
\(540\) 0 0
\(541\) 1.45954 2.52800i 0.0627507 0.108687i −0.832943 0.553358i \(-0.813346\pi\)
0.895694 + 0.444671i \(0.146679\pi\)
\(542\) 0 0
\(543\) 38.8513 1.66727
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.73973 + 3.01329i −0.0743853 + 0.128839i −0.900819 0.434195i \(-0.857033\pi\)
0.826433 + 0.563034i \(0.190366\pi\)
\(548\) 0 0
\(549\) 14.1810 + 24.5623i 0.605232 + 1.04829i
\(550\) 0 0
\(551\) −16.5154 + 4.61486i −0.703580 + 0.196600i
\(552\) 0 0
\(553\) 16.3631 + 28.3418i 0.695831 + 1.20522i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.96280 13.7920i 0.337395 0.584385i −0.646547 0.762874i \(-0.723788\pi\)
0.983942 + 0.178489i \(0.0571210\pi\)
\(558\) 0 0
\(559\) −7.70775 −0.326003
\(560\) 0 0
\(561\) −9.83551 + 17.0356i −0.415256 + 0.719244i
\(562\) 0 0
\(563\) −19.6274 −0.827195 −0.413598 0.910460i \(-0.635728\pi\)
−0.413598 + 0.910460i \(0.635728\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −10.6516 18.4491i −0.447324 0.774788i
\(568\) 0 0
\(569\) −11.7544 −0.492770 −0.246385 0.969172i \(-0.579243\pi\)
−0.246385 + 0.969172i \(0.579243\pi\)
\(570\) 0 0
\(571\) 32.4868 1.35953 0.679766 0.733429i \(-0.262081\pi\)
0.679766 + 0.733429i \(0.262081\pi\)
\(572\) 0 0
\(573\) 20.4795 + 35.4715i 0.855541 + 1.48184i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −25.7287 −1.07110 −0.535551 0.844503i \(-0.679896\pi\)
−0.535551 + 0.844503i \(0.679896\pi\)
\(578\) 0 0
\(579\) 1.07264 1.85787i 0.0445775 0.0772106i
\(580\) 0 0
\(581\) 12.7837 0.530359
\(582\) 0 0
\(583\) −14.8857 + 25.7828i −0.616503 + 1.06782i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.8279 36.0750i −0.859659 1.48897i −0.872255 0.489052i \(-0.837343\pi\)
0.0125958 0.999921i \(-0.495991\pi\)
\(588\) 0 0
\(589\) 31.7399 + 31.0692i 1.30782 + 1.28018i
\(590\) 0 0
\(591\) 25.1884 + 43.6276i 1.03611 + 1.79460i
\(592\) 0 0
\(593\) 8.83267 15.2986i 0.362714 0.628239i −0.625692 0.780070i \(-0.715183\pi\)
0.988407 + 0.151831i \(0.0485168\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −16.2775 −0.666193
\(598\) 0 0
\(599\) 13.1925 22.8502i 0.539033 0.933632i −0.459924 0.887959i \(-0.652123\pi\)
0.998956 0.0456738i \(-0.0145435\pi\)
\(600\) 0 0
\(601\) 9.46838 0.386223 0.193112 0.981177i \(-0.438142\pi\)
0.193112 + 0.981177i \(0.438142\pi\)
\(602\) 0 0
\(603\) −16.3545 28.3269i −0.666008 1.15356i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 8.26529 0.335478 0.167739 0.985831i \(-0.446353\pi\)
0.167739 + 0.985831i \(0.446353\pi\)
\(608\) 0 0
\(609\) 27.0479 1.09604
\(610\) 0 0
\(611\) 17.9032 + 31.0092i 0.724285 + 1.25450i
\(612\) 0 0
\(613\) 3.40417 + 5.89620i 0.137493 + 0.238145i 0.926547 0.376179i \(-0.122762\pi\)
−0.789054 + 0.614324i \(0.789429\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.00668 5.20772i 0.121044 0.209655i −0.799135 0.601151i \(-0.794709\pi\)
0.920180 + 0.391496i \(0.128042\pi\)
\(618\) 0 0
\(619\) 13.2299 0.531754 0.265877 0.964007i \(-0.414338\pi\)
0.265877 + 0.964007i \(0.414338\pi\)
\(620\) 0 0
\(621\) 0.959816 1.66245i 0.0385161 0.0667118i
\(622\) 0 0
\(623\) 11.6517 20.1813i 0.466816 0.808548i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −9.04916 + 35.2743i −0.361389 + 1.40872i
\(628\) 0 0
\(629\) −4.33915 7.51564i −0.173013 0.299668i
\(630\) 0 0
\(631\) 11.8932 20.5996i 0.473460 0.820058i −0.526078 0.850436i \(-0.676338\pi\)
0.999538 + 0.0303788i \(0.00967135\pi\)
\(632\) 0 0
\(633\) −13.2899 + 23.0188i −0.528226 + 0.914914i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.712762 1.23454i 0.0282407 0.0489143i
\(638\) 0 0
\(639\) 23.2033 0.917908
\(640\) 0 0
\(641\) −6.14239 10.6389i −0.242610 0.420212i 0.718847 0.695168i \(-0.244670\pi\)
−0.961457 + 0.274956i \(0.911337\pi\)
\(642\) 0 0
\(643\) 14.5776 + 25.2492i 0.574885 + 0.995729i 0.996054 + 0.0887474i \(0.0282864\pi\)
−0.421170 + 0.906982i \(0.638380\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 36.7499 1.44479 0.722394 0.691481i \(-0.243042\pi\)
0.722394 + 0.691481i \(0.243042\pi\)
\(648\) 0 0
\(649\) 18.1879 + 31.5023i 0.713936 + 1.23657i
\(650\) 0 0
\(651\) −35.0284 60.6710i −1.37287 2.37788i
\(652\) 0 0
\(653\) −24.7707 −0.969351 −0.484675 0.874694i \(-0.661062\pi\)
−0.484675 + 0.874694i \(0.661062\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 8.32092 0.324630
\(658\) 0 0
\(659\) −11.1156 + 19.2528i −0.433002 + 0.749982i −0.997130 0.0757053i \(-0.975879\pi\)
0.564128 + 0.825687i \(0.309213\pi\)
\(660\) 0 0
\(661\) −20.4684 + 35.4524i −0.796130 + 1.37894i 0.125990 + 0.992032i \(0.459789\pi\)
−0.922119 + 0.386905i \(0.873544\pi\)
\(662\) 0 0
\(663\) 9.63975 + 16.6965i 0.374377 + 0.648440i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.22501 7.31793i −0.163593 0.283351i
\(668\) 0 0
\(669\) 12.2592 21.2336i 0.473969 0.820939i
\(670\) 0 0
\(671\) 14.0106 24.2671i 0.540873 0.936819i
\(672\) 0 0
\(673\) 33.5992 1.29515 0.647577 0.762000i \(-0.275783\pi\)
0.647577 + 0.762000i \(0.275783\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −29.5883 −1.13717 −0.568585 0.822624i \(-0.692509\pi\)
−0.568585 + 0.822624i \(0.692509\pi\)
\(678\) 0 0
\(679\) −9.85949 17.0771i −0.378373 0.655361i
\(680\) 0 0
\(681\) 28.4598 + 49.2938i 1.09058 + 1.88894i
\(682\) 0 0
\(683\) −41.0567 −1.57099 −0.785495 0.618868i \(-0.787592\pi\)
−0.785495 + 0.618868i \(0.787592\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 20.4488 + 35.4183i 0.780170 + 1.35129i
\(688\) 0 0
\(689\) 14.5894 + 25.2696i 0.555813 + 0.962697i
\(690\) 0 0
\(691\) 1.22497 0.0466000 0.0233000 0.999729i \(-0.492583\pi\)
0.0233000 + 0.999729i \(0.492583\pi\)
\(692\) 0 0
\(693\) 15.1613 26.2601i 0.575929 0.997538i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0.856376 1.48329i 0.0324375 0.0561835i
\(698\) 0 0
\(699\) −23.5228 + 40.7426i −0.889712 + 1.54103i
\(700\) 0 0
\(701\) −22.0101 38.1226i −0.831309 1.43987i −0.897001 0.442029i \(-0.854259\pi\)
0.0656918 0.997840i \(-0.479075\pi\)
\(702\) 0 0
\(703\) −11.4810 11.2384i −0.433015 0.423865i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.87729 + 13.6439i −0.296256 + 0.513130i
\(708\) 0 0
\(709\) −8.16255 + 14.1379i −0.306551 + 0.530962i −0.977605 0.210446i \(-0.932508\pi\)
0.671055 + 0.741408i \(0.265842\pi\)
\(710\) 0 0
\(711\) 40.2509 1.50953
\(712\) 0 0
\(713\) −10.9432 + 18.9542i −0.409827 + 0.709841i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.759750 1.31593i −0.0283734 0.0491442i
\(718\) 0 0
\(719\) −5.08574 8.80876i −0.189666 0.328511i 0.755473 0.655180i \(-0.227407\pi\)
−0.945139 + 0.326669i \(0.894074\pi\)
\(720\) 0 0
\(721\) −41.0686 −1.52947
\(722\) 0 0
\(723\) 55.1595 2.05141
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 4.02148 + 6.96541i 0.149148 + 0.258333i 0.930913 0.365241i \(-0.119013\pi\)
−0.781765 + 0.623574i \(0.785680\pi\)
\(728\) 0 0
\(729\) −32.9600 −1.22074
\(730\) 0 0
\(731\) −2.79353 + 4.83853i −0.103322 + 0.178960i
\(732\) 0 0
\(733\) −41.2325 −1.52296 −0.761479 0.648190i \(-0.775526\pi\)
−0.761479 + 0.648190i \(0.775526\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.1580 + 27.9864i −0.595186 + 1.03089i
\(738\) 0 0
\(739\) −16.5253 28.6227i −0.607893 1.05290i −0.991587 0.129442i \(-0.958681\pi\)
0.383694 0.923460i \(-0.374652\pi\)
\(740\) 0 0
\(741\) 25.5059 + 24.9669i 0.936983 + 0.917184i
\(742\) 0 0
\(743\) 17.3933 + 30.1261i 0.638099 + 1.10522i 0.985849 + 0.167633i \(0.0536124\pi\)
−0.347750 + 0.937587i \(0.613054\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 7.86153 13.6166i 0.287638 0.498204i
\(748\) 0 0
\(749\) −41.4284 −1.51376
\(750\) 0 0
\(751\) 21.7350 37.6462i 0.793123 1.37373i −0.130902 0.991395i \(-0.541787\pi\)
0.924024 0.382334i \(-0.124879\pi\)
\(752\) 0 0
\(753\) 20.8537 0.759950
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −3.08494 5.34328i −0.112124 0.194205i 0.804502 0.593949i \(-0.202432\pi\)
−0.916626 + 0.399745i \(0.869099\pi\)
\(758\) 0 0
\(759\) −17.9449 −0.651359
\(760\) 0 0
\(761\) −9.81318 −0.355728 −0.177864 0.984055i \(-0.556919\pi\)
−0.177864 + 0.984055i \(0.556919\pi\)
\(762\) 0 0
\(763\) −17.2116 29.8114i −0.623103 1.07925i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 35.6517 1.28731
\(768\) 0 0
\(769\) 20.7452 35.9317i 0.748090 1.29573i −0.200647 0.979664i \(-0.564305\pi\)
0.948737 0.316066i \(-0.102362\pi\)
\(770\) 0 0
\(771\) −35.7727 −1.28832
\(772\) 0 0
\(773\) 20.8584 36.1279i 0.750226 1.29943i −0.197487 0.980306i \(-0.563278\pi\)
0.947713 0.319124i \(-0.103389\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 12.6705 + 21.9460i 0.454553 + 0.787309i
\(778\) 0 0
\(779\) 0.787908 3.07133i 0.0282297 0.110042i
\(780\) 0 0
\(781\) −11.4622 19.8531i −0.410149 0.710400i
\(782\) 0 0
\(783\) 1.75795 3.04486i 0.0628240 0.108814i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 13.0342 0.464621 0.232310 0.972642i \(-0.425371\pi\)
0.232310 + 0.972642i \(0.425371\pi\)
\(788\) 0 0
\(789\) −23.3718 + 40.4812i −0.832060 + 1.44117i
\(790\) 0 0
\(791\) −16.6580 −0.592292
\(792\) 0 0
\(793\) −13.7317 23.7841i −0.487628 0.844596i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33.1911 −1.17569 −0.587844 0.808974i \(-0.700023\pi\)
−0.587844 + 0.808974i \(0.700023\pi\)
\(798\) 0 0
\(799\) 25.9547 0.918210
\(800\) 0 0
\(801\) −14.3307 24.8216i −0.506351 0.877026i