Properties

Label 1900.2.i.d.201.1
Level $1900$
Weight $2$
Character 1900.201
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 201.1
Root \(-1.26041 + 2.18309i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.d.501.1

$q$-expansion

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

Character values

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

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.230156 + 0.973154i \(0.426076\pi\)
−0.957854 + 0.287256i \(0.907257\pi\)
\(4\) 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 0.998414 0.0562987i \(-0.0179299\pi\)
−0.547963 + 0.836502i \(0.684597\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.17727 + 2.03909i −0.285529 + 0.494551i −0.972737 0.231910i \(-0.925503\pi\)
0.687208 + 0.726460i \(0.258836\pi\)
\(18\) 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 0.956000 0.293367i \(-0.0947758\pi\)
−0.732063 + 0.681237i \(0.761442\pi\)
\(24\) 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 0.988819 0.149122i \(-0.0476447\pi\)
−0.623553 + 0.781781i \(0.714311\pi\)
\(30\) 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 −0.836226 0.548385i \(-0.815243\pi\)
0.893028 + 0.450000i \(0.148576\pi\)
\(42\) 0 0
\(43\) −1.18645 + 2.05499i −0.180931 + 0.313383i −0.942198 0.335057i \(-0.891245\pi\)
0.761267 + 0.648439i \(0.224578\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.51164 9.54644i −0.803955 1.39249i −0.916994 0.398901i \(-0.869392\pi\)
0.113039 0.993591i \(-0.463942\pi\)
\(48\) 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 −0.990039 0.140796i \(-0.955034\pi\)
0.373087 0.927797i \(-0.378299\pi\)
\(54\) 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 −0.248714 0.968577i \(-0.580008\pi\)
0.963169 0.268896i \(-0.0866589\pi\)
\(60\) 0 0
\(61\) 4.22743 + 7.32212i 0.541267 + 0.937501i 0.998832 + 0.0483251i \(0.0153884\pi\)
−0.457565 + 0.889176i \(0.651278\pi\)
\(62\) 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 −0.993459 0.114188i \(-0.963573\pi\)
0.397840 0.917455i \(-0.369760\pi\)
\(68\) 0 0
\(69\) −5.41453 −0.651833
\(70\) 0 0
\(71\) −3.45850 + 5.99029i −0.410448 + 0.710917i −0.994939 0.100484i \(-0.967961\pi\)
0.584491 + 0.811400i \(0.301294\pi\)
\(72\) 0 0
\(73\) −1.24025 + 2.14818i −0.145160 + 0.251425i −0.929433 0.368992i \(-0.879703\pi\)
0.784272 + 0.620417i \(0.213036\pi\)
\(74\) 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 0.301477 + 0.953474i \(0.402520\pi\)
−0.976471 + 0.215650i \(0.930813\pi\)
\(80\) 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 0.545725 0.837965i \(-0.316254\pi\)
−0.998561 + 0.0536291i \(0.982921\pi\)
\(90\) 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 −0.622060 0.782970i \(-0.713704\pi\)
0.989102 + 0.147235i \(0.0470372\pi\)
\(98\) 0 0
\(99\) −5.55882 9.62816i −0.558682 0.967666i
\(100\) 0 0
\(101\) 2.88818 + 5.00247i 0.287384 + 0.497764i 0.973185 0.230026i \(-0.0738810\pi\)
−0.685800 + 0.727790i \(0.740548\pi\)
\(102\) 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 −0.387696 0.921787i \(-0.626729\pi\)
0.992139 0.125139i \(-0.0399376\pi\)
\(110\) 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 0.589555 0.807728i \(-0.299303\pi\)
−0.994291 + 0.106705i \(0.965970\pi\)
\(128\) 0 0
\(129\) −2.99082 5.18025i −0.263327 0.456096i
\(130\) 0 0
\(131\) −11.1328 + 19.2825i −0.972676 + 1.68472i −0.285274 + 0.958446i \(0.592085\pi\)
−0.687402 + 0.726277i \(0.741249\pi\)
\(132\) 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 0.655863 0.754880i \(-0.272305\pi\)
−0.981677 + 0.190554i \(0.938972\pi\)
\(138\) 0 0
\(139\) −8.45916 14.6517i −0.717496 1.24274i −0.961989 0.273089i \(-0.911955\pi\)
0.244493 0.969651i \(-0.421379\pi\)
\(140\) 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 −0.492193 0.870486i \(-0.663804\pi\)
0.999960 0.00899193i \(-0.00286226\pi\)
\(150\) 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 0.231469 + 0.972842i \(0.425647\pi\)
−0.958241 + 0.285963i \(0.907687\pi\)
\(158\) 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 0.954805 0.297234i \(-0.0960643\pi\)
−0.734815 + 0.678268i \(0.762731\pi\)
\(168\) 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 −0.985899 0.167340i \(-0.946482\pi\)
0.637870 + 0.770144i \(0.279816\pi\)
\(174\) 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 −0.996278 0.0861980i \(-0.972528\pi\)
0.423489 0.905901i \(-0.360805\pi\)
\(182\) 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 −0.850305 0.526291i \(-0.823582\pi\)
0.880934 + 0.473240i \(0.156916\pi\)
\(194\) 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 0.957474 0.288521i \(-0.0931636\pi\)
−0.728603 + 0.684936i \(0.759830\pi\)
\(200\) 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 −0.988444 0.151588i \(-0.951561\pi\)
0.625501 + 0.780223i \(0.284895\pi\)
\(212\) 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 −0.655983 0.754776i \(-0.727746\pi\)
0.981646 + 0.190710i \(0.0610791\pi\)
\(224\) 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 0.379699 + 0.925110i \(0.376028\pi\)
−0.991018 + 0.133727i \(0.957306\pi\)
\(234\) 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 −0.966779 0.255615i \(-0.917722\pi\)
0.262020 0.965062i \(-0.415611\pi\)
\(242\) 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 0.705449 0.708761i \(-0.250745\pi\)
−0.966529 + 0.256557i \(0.917412\pi\)
\(252\) 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 0.997882 0.0650550i \(-0.0207223\pi\)
−0.555280 + 0.831663i \(0.687389\pi\)
\(258\) 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 0.424684 + 0.905342i \(0.360385\pi\)
−0.996391 + 0.0848836i \(0.972948\pi\)
\(264\) 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 −0.949577 0.313534i \(-0.898487\pi\)
0.746317 + 0.665591i \(0.231820\pi\)
\(270\) 0 0
\(271\) −11.0331 + 19.1099i −0.670214 + 1.16085i 0.307629 + 0.951506i \(0.400464\pi\)
−0.977843 + 0.209339i \(0.932869\pi\)
\(272\) 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 −0.997772 0.0667164i \(-0.978748\pi\)
0.441108 0.897454i \(-0.354586\pi\)
\(282\) 0 0
\(283\) 2.24811 3.89384i 0.133636 0.231465i −0.791439 0.611248i \(-0.790668\pi\)
0.925076 + 0.379783i \(0.124001\pi\)
\(284\) 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 −0.962669 0.270680i \(-0.912752\pi\)
0.715750 + 0.698356i \(0.246085\pi\)
\(308\) 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 0.854846 0.518881i \(-0.173651\pi\)
−0.876787 + 0.480878i \(0.840318\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.92116 11.9878i −0.388731 0.673302i 0.603548 0.797327i \(-0.293753\pi\)
−0.992279 + 0.124025i \(0.960420\pi\)
\(318\) 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 −0.245076 + 0.969504i \(0.578813\pi\)
−0.717077 + 0.696994i \(0.754520\pi\)
\(338\) 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 −0.271100 0.962551i \(-0.587387\pi\)
0.969144 0.246496i \(-0.0792793\pi\)
\(348\) 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 −0.752644 0.658428i \(-0.771222\pi\)
0.946537 + 0.322594i \(0.104555\pi\)
\(360\) 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 0.984475 0.175525i \(-0.0561623\pi\)
−0.644247 + 0.764818i \(0.722829\pi\)
\(368\) 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 −0.245287 + 0.969450i \(0.578882\pi\)
−0.716925 + 0.697150i \(0.754451\pi\)
\(384\) 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 0.983094 + 0.183103i \(0.0586142\pi\)
−0.332975 + 0.942936i \(0.608052\pi\)
\(390\) 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 0.0590940 + 0.998252i \(0.481179\pi\)
−0.894059 + 0.447949i \(0.852155\pi\)
\(398\) 0 0
\(399\) 7.44699 + 29.0290i 0.372816 + 1.45327i
\(400\) 0 0
\(401\) −4.70674 + 8.15232i −0.235044 + 0.407107i −0.959285 0.282439i \(-0.908857\pi\)
0.724242 + 0.689546i \(0.242190\pi\)
\(402\) 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 0.895394 0.445275i \(-0.146894\pi\)
−0.833316 + 0.552797i \(0.813561\pi\)
\(410\) 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 −0.640349 0.768084i \(-0.721210\pi\)
0.985355 + 0.170517i \(0.0545437\pi\)
\(422\) 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 0.933846 0.357676i \(-0.116431\pi\)
−0.776679 + 0.629897i \(0.783097\pi\)
\(432\) 0 0
\(433\) −4.30073 7.44908i −0.206680 0.357980i 0.743987 0.668194i \(-0.232933\pi\)
−0.950667 + 0.310214i \(0.899599\pi\)
\(434\) 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 −0.694510 0.719483i \(-0.744379\pi\)
0.970345 + 0.241722i \(0.0777123\pi\)
\(440\) 0 0
\(441\) −0.736084 1.27494i −0.0350516 0.0607112i
\(442\) 0 0
\(443\) −5.69629 9.86626i −0.270639 0.468760i 0.698387 0.715721i \(-0.253902\pi\)
−0.969026 + 0.246960i \(0.920568\pi\)
\(444\) 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 −0.179122 + 0.983827i \(0.557326\pi\)
−0.762458 + 0.647038i \(0.776008\pi\)
\(462\) 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 0.796983 0.604002i \(-0.206428\pi\)
−0.921572 + 0.388207i \(0.873095\pi\)
\(480\) 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 0.308194 + 0.951324i \(0.400275\pi\)
−0.977967 + 0.208758i \(0.933058\pi\)
\(492\) 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 −0.670798 0.741640i \(-0.734048\pi\)
0.977678 + 0.210108i \(0.0673814\pi\)
\(500\) 0 0
\(501\) −14.3328 −0.640344
\(502\) 0 0
\(503\) 18.3253 + 31.7404i 0.817086 + 1.41523i 0.907820 + 0.419359i \(0.137745\pi\)
−0.0907343 + 0.995875i \(0.528921\pi\)
\(504\) 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 0.971473 0.237149i \(-0.0762131\pi\)
−0.691114 + 0.722746i \(0.742880\pi\)
\(510\) 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 0.748720 0.662886i \(-0.230669\pi\)
−0.948436 + 0.316968i \(0.897335\pi\)
\(524\) 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 0.895694 0.444671i \(-0.146679\pi\)
−0.832943 + 0.553358i \(0.813346\pi\)
\(542\) 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 0.826433 0.563034i \(-0.190366\pi\)
−0.900819 + 0.434195i \(0.857033\pi\)
\(548\) 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 0.983942 0.178489i \(-0.0571210\pi\)
−0.646547 + 0.762874i \(0.723788\pi\)
\(558\) 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 0.0125958 + 0.999921i \(0.495991\pi\)
−0.872255 + 0.489052i \(0.837343\pi\)
\(588\) 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 0.988407 0.151831i \(-0.0485168\pi\)
−0.625692 + 0.780070i \(0.715183\pi\)
\(594\) 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 0.998956 + 0.0456738i \(0.0145435\pi\)
−0.459924 + 0.887959i \(0.652123\pi\)
\(600\) 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 −0.789054 0.614324i \(-0.789429\pi\)
0.926547 + 0.376179i \(0.122762\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.00668 + 5.20772i 0.121044 + 0.209655i 0.920180 0.391496i \(-0.128042\pi\)
−0.799135 + 0.601151i \(0.794709\pi\)
\(618\) 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 0.999538 0.0303788i \(-0.00967135\pi\)
−0.526078 + 0.850436i \(0.676338\pi\)
\(632\) 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 −0.961457 0.274956i \(-0.911337\pi\)
0.718847 + 0.695168i \(0.244670\pi\)
\(642\) 0 0
\(643\) 14.5776 25.2492i 0.574885 0.995729i −0.421170 0.906982i \(-0.638380\pi\)
0.996054 0.0887474i \(-0.0282864\pi\)
\(644\) 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 0.564128 0.825687i \(-0.309213\pi\)
−0.997130 + 0.0757053i \(0.975879\pi\)
\(660\) 0 0
\(661\) −20.4684 35.4524i −0.796130 1.37894i −0.922119 0.386905i \(-0.873544\pi\)
0.125990 0.992032i \(-0.459789\pi\)
\(662\) 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 0.0656918 + 0.997840i \(0.479075\pi\)
−0.897001 + 0.442029i \(0.854259\pi\)
\(702\) 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 0.671055 0.741408i \(-0.265842\pi\)
−0.977605 + 0.210446i \(0.932508\pi\)
\(710\) 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 −0.945139 0.326669i \(-0.894074\pi\)
0.755473 + 0.655180i \(0.227407\pi\)
\(720\) 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 −0.781765 0.623574i \(-0.785680\pi\)
0.930913 + 0.365241i \(0.119013\pi\)
\(728\) 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 0.383694 + 0.923460i \(0.374652\pi\)
−0.991587 + 0.129442i \(0.958681\pi\)
\(740\) 0 0
\(741\) 25.5059 24.9669i 0.936983 0.917184i
\(742\) 0 0
\(743\) 17.3933 30.1261i 0.638099 1.10522i −0.347750 0.937587i \(-0.613054\pi\)
0.985849 0.167633i \(-0.0536124\pi\)
\(744\) 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 0.924024 + 0.382334i \(0.124879\pi\)
−0.130902 + 0.991395i \(0.541787\pi\)
\(752\) 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 −0.916626 0.399745i \(-0.869099\pi\)
0.804502 + 0.593949i \(0.202432\pi\)
\(758\) 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 0.948737 + 0.316066i \(0.102362\pi\)
−0.200647 + 0.979664i \(0.564305\pi\)
\(770\) 0 0
\(771\) −35.7727 −1.28832
\(772\) 0 0
\(773\) 20.8584 + 36.1279i 0.750226 + 1.29943i 0.947713 + 0.319124i \(0.103389\pi\)
−0.197487 + 0.980306i \(0.563278\pi\)
\(774\) 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