Properties

Label 2100.2.q.k.1201.1
Level $2100$
Weight $2$
Character 2100.1201
Analytic conductor $16.769$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1201.1
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2100.1201
Dual form 2100.2.q.k.1801.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.62132 + 2.09077i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.62132 + 2.09077i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.12132 - 3.67423i) q^{11} -3.24264 q^{13} +(2.12132 - 3.67423i) q^{17} +(3.50000 + 6.06218i) q^{19} +(1.00000 + 2.44949i) q^{21} +(-2.12132 - 3.67423i) q^{23} -1.00000 q^{27} -1.75736 q^{29} +(4.74264 - 8.21449i) q^{31} +(-2.12132 - 3.67423i) q^{33} +(1.62132 + 2.80821i) q^{37} +(-1.62132 + 2.80821i) q^{39} -4.24264 q^{41} -3.24264 q^{43} +(-3.00000 - 5.19615i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(-2.12132 - 3.67423i) q^{51} +(4.24264 - 7.34847i) q^{53} +7.00000 q^{57} +(5.12132 - 8.87039i) q^{59} +(-2.24264 - 3.88437i) q^{61} +(2.62132 + 0.358719i) q^{63} +(-2.62132 + 4.54026i) q^{67} -4.24264 q^{69} -12.7279 q^{71} +(4.62132 - 8.00436i) q^{73} +(4.24264 + 10.3923i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +10.2426 q^{83} +(-0.878680 + 1.52192i) q^{87} +(5.12132 + 8.87039i) q^{89} +(5.25736 - 6.77962i) q^{91} +(-4.74264 - 8.21449i) q^{93} +0.485281 q^{97} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} + 2 q^{7} - 2 q^{9} + 4 q^{13} + 14 q^{19} + 4 q^{21} - 4 q^{27} - 24 q^{29} + 2 q^{31} - 2 q^{37} + 2 q^{39} + 4 q^{43} - 12 q^{47} + 10 q^{49} + 28 q^{57} + 12 q^{59} + 8 q^{61} + 2 q^{63} - 2 q^{67} + 10 q^{73} - 22 q^{79} - 2 q^{81} + 24 q^{83} - 12 q^{87} + 12 q^{89} + 38 q^{91} - 2 q^{93} - 32 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.62132 + 2.09077i −0.612801 + 0.790237i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.12132 3.67423i 0.639602 1.10782i −0.345918 0.938265i \(-0.612432\pi\)
0.985520 0.169559i \(-0.0542342\pi\)
\(12\) 0 0
\(13\) −3.24264 −0.899347 −0.449673 0.893193i \(-0.648460\pi\)
−0.449673 + 0.893193i \(0.648460\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.12132 3.67423i 0.514496 0.891133i −0.485363 0.874313i \(-0.661312\pi\)
0.999859 0.0168199i \(-0.00535420\pi\)
\(18\) 0 0
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) 1.00000 + 2.44949i 0.218218 + 0.534522i
\(22\) 0 0
\(23\) −2.12132 3.67423i −0.442326 0.766131i 0.555536 0.831493i \(-0.312513\pi\)
−0.997862 + 0.0653618i \(0.979180\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.75736 −0.326333 −0.163167 0.986599i \(-0.552171\pi\)
−0.163167 + 0.986599i \(0.552171\pi\)
\(30\) 0 0
\(31\) 4.74264 8.21449i 0.851803 1.47537i −0.0277757 0.999614i \(-0.508842\pi\)
0.879579 0.475753i \(-0.157824\pi\)
\(32\) 0 0
\(33\) −2.12132 3.67423i −0.369274 0.639602i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.62132 + 2.80821i 0.266543 + 0.461667i 0.967967 0.251078i \(-0.0807851\pi\)
−0.701423 + 0.712745i \(0.747452\pi\)
\(38\) 0 0
\(39\) −1.62132 + 2.80821i −0.259619 + 0.449673i
\(40\) 0 0
\(41\) −4.24264 −0.662589 −0.331295 0.943527i \(-0.607485\pi\)
−0.331295 + 0.943527i \(0.607485\pi\)
\(42\) 0 0
\(43\) −3.24264 −0.494498 −0.247249 0.968952i \(-0.579527\pi\)
−0.247249 + 0.968952i \(0.579527\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) −1.74264 6.77962i −0.248949 0.968517i
\(50\) 0 0
\(51\) −2.12132 3.67423i −0.297044 0.514496i
\(52\) 0 0
\(53\) 4.24264 7.34847i 0.582772 1.00939i −0.412378 0.911013i \(-0.635302\pi\)
0.995149 0.0983769i \(-0.0313651\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 7.00000 0.927173
\(58\) 0 0
\(59\) 5.12132 8.87039i 0.666739 1.15483i −0.312072 0.950059i \(-0.601023\pi\)
0.978811 0.204767i \(-0.0656438\pi\)
\(60\) 0 0
\(61\) −2.24264 3.88437i −0.287141 0.497342i 0.685985 0.727615i \(-0.259371\pi\)
−0.973126 + 0.230273i \(0.926038\pi\)
\(62\) 0 0
\(63\) 2.62132 + 0.358719i 0.330255 + 0.0451944i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.62132 + 4.54026i −0.320245 + 0.554681i −0.980539 0.196327i \(-0.937099\pi\)
0.660293 + 0.751008i \(0.270432\pi\)
\(68\) 0 0
\(69\) −4.24264 −0.510754
\(70\) 0 0
\(71\) −12.7279 −1.51053 −0.755263 0.655422i \(-0.772491\pi\)
−0.755263 + 0.655422i \(0.772491\pi\)
\(72\) 0 0
\(73\) 4.62132 8.00436i 0.540885 0.936840i −0.457969 0.888968i \(-0.651423\pi\)
0.998854 0.0478714i \(-0.0152438\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.24264 + 10.3923i 0.483494 + 1.18431i
\(78\) 0 0
\(79\) −5.50000 9.52628i −0.618798 1.07179i −0.989705 0.143120i \(-0.954286\pi\)
0.370907 0.928670i \(-0.379047\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 10.2426 1.12428 0.562138 0.827043i \(-0.309979\pi\)
0.562138 + 0.827043i \(0.309979\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.878680 + 1.52192i −0.0942043 + 0.163167i
\(88\) 0 0
\(89\) 5.12132 + 8.87039i 0.542859 + 0.940259i 0.998738 + 0.0502176i \(0.0159915\pi\)
−0.455879 + 0.890042i \(0.650675\pi\)
\(90\) 0 0
\(91\) 5.25736 6.77962i 0.551121 0.710697i
\(92\) 0 0
\(93\) −4.74264 8.21449i −0.491789 0.851803i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.485281 0.0492729 0.0246364 0.999696i \(-0.492157\pi\)
0.0246364 + 0.999696i \(0.492157\pi\)
\(98\) 0 0
\(99\) −4.24264 −0.426401
\(100\) 0 0
\(101\) 3.87868 6.71807i 0.385943 0.668473i −0.605956 0.795498i \(-0.707209\pi\)
0.991900 + 0.127025i \(0.0405428\pi\)
\(102\) 0 0
\(103\) −8.62132 14.9326i −0.849484 1.47135i −0.881670 0.471867i \(-0.843580\pi\)
0.0321856 0.999482i \(-0.489753\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.36396 + 11.0227i 0.615227 + 1.06561i 0.990345 + 0.138628i \(0.0442691\pi\)
−0.375117 + 0.926977i \(0.622398\pi\)
\(108\) 0 0
\(109\) 4.74264 8.21449i 0.454263 0.786806i −0.544383 0.838837i \(-0.683236\pi\)
0.998645 + 0.0520310i \(0.0165695\pi\)
\(110\) 0 0
\(111\) 3.24264 0.307778
\(112\) 0 0
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.62132 + 2.80821i 0.149891 + 0.259619i
\(118\) 0 0
\(119\) 4.24264 + 10.3923i 0.388922 + 0.952661i
\(120\) 0 0
\(121\) −3.50000 6.06218i −0.318182 0.551107i
\(122\) 0 0
\(123\) −2.12132 + 3.67423i −0.191273 + 0.331295i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.75736 0.244676 0.122338 0.992488i \(-0.460961\pi\)
0.122338 + 0.992488i \(0.460961\pi\)
\(128\) 0 0
\(129\) −1.62132 + 2.80821i −0.142749 + 0.247249i
\(130\) 0 0
\(131\) −7.24264 12.5446i −0.632792 1.09603i −0.986978 0.160854i \(-0.948575\pi\)
0.354186 0.935175i \(-0.384758\pi\)
\(132\) 0 0
\(133\) −18.3492 2.51104i −1.59108 0.217734i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.12132 3.67423i 0.181237 0.313911i −0.761065 0.648675i \(-0.775323\pi\)
0.942302 + 0.334764i \(0.108657\pi\)
\(138\) 0 0
\(139\) −15.4853 −1.31344 −0.656722 0.754133i \(-0.728058\pi\)
−0.656722 + 0.754133i \(0.728058\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −6.87868 + 11.9142i −0.575224 + 0.996317i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.74264 1.88064i −0.556124 0.155112i
\(148\) 0 0
\(149\) 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) 0 0
\(151\) −11.2426 + 19.4728i −0.914913 + 1.58468i −0.107885 + 0.994163i \(0.534408\pi\)
−0.807028 + 0.590513i \(0.798926\pi\)
\(152\) 0 0
\(153\) −4.24264 −0.342997
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3.24264 + 5.61642i −0.258791 + 0.448239i −0.965918 0.258847i \(-0.916657\pi\)
0.707127 + 0.707086i \(0.249991\pi\)
\(158\) 0 0
\(159\) −4.24264 7.34847i −0.336463 0.582772i
\(160\) 0 0
\(161\) 11.1213 + 1.52192i 0.876483 + 0.119944i
\(162\) 0 0
\(163\) 4.00000 + 6.92820i 0.313304 + 0.542659i 0.979076 0.203497i \(-0.0652307\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −18.7279 −1.44921 −0.724605 0.689164i \(-0.757978\pi\)
−0.724605 + 0.689164i \(0.757978\pi\)
\(168\) 0 0
\(169\) −2.48528 −0.191175
\(170\) 0 0
\(171\) 3.50000 6.06218i 0.267652 0.463586i
\(172\) 0 0
\(173\) −10.2426 17.7408i −0.778734 1.34881i −0.932672 0.360726i \(-0.882529\pi\)
0.153938 0.988080i \(-0.450804\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.12132 8.87039i −0.384942 0.666739i
\(178\) 0 0
\(179\) 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i \(-0.761346\pi\)
0.956088 + 0.293079i \(0.0946798\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 0 0
\(183\) −4.48528 −0.331562
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −9.00000 15.5885i −0.658145 1.13994i
\(188\) 0 0
\(189\) 1.62132 2.09077i 0.117934 0.152081i
\(190\) 0 0
\(191\) −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i \(-0.236317\pi\)
−0.953912 + 0.300088i \(0.902984\pi\)
\(192\) 0 0
\(193\) 3.37868 5.85204i 0.243203 0.421239i −0.718422 0.695607i \(-0.755135\pi\)
0.961625 + 0.274368i \(0.0884687\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.2426 1.15724 0.578620 0.815597i \(-0.303591\pi\)
0.578620 + 0.815597i \(0.303591\pi\)
\(198\) 0 0
\(199\) −5.24264 + 9.08052i −0.371641 + 0.643701i −0.989818 0.142338i \(-0.954538\pi\)
0.618177 + 0.786039i \(0.287871\pi\)
\(200\) 0 0
\(201\) 2.62132 + 4.54026i 0.184894 + 0.320245i
\(202\) 0 0
\(203\) 2.84924 3.67423i 0.199978 0.257881i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2.12132 + 3.67423i −0.147442 + 0.255377i
\(208\) 0 0
\(209\) 29.6985 2.05429
\(210\) 0 0
\(211\) 22.4853 1.54795 0.773975 0.633216i \(-0.218265\pi\)
0.773975 + 0.633216i \(0.218265\pi\)
\(212\) 0 0
\(213\) −6.36396 + 11.0227i −0.436051 + 0.755263i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 9.48528 + 23.2341i 0.643903 + 1.57723i
\(218\) 0 0
\(219\) −4.62132 8.00436i −0.312280 0.540885i
\(220\) 0 0
\(221\) −6.87868 + 11.9142i −0.462710 + 0.801437i
\(222\) 0 0
\(223\) 7.51472 0.503223 0.251611 0.967828i \(-0.419040\pi\)
0.251611 + 0.967828i \(0.419040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.60660 + 13.1750i −0.504868 + 0.874457i 0.495116 + 0.868827i \(0.335125\pi\)
−0.999984 + 0.00563010i \(0.998208\pi\)
\(228\) 0 0
\(229\) 3.50000 + 6.06218i 0.231287 + 0.400600i 0.958187 0.286143i \(-0.0923732\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 11.1213 + 1.52192i 0.731729 + 0.100135i
\(232\) 0 0
\(233\) 7.24264 + 12.5446i 0.474481 + 0.821825i 0.999573 0.0292201i \(-0.00930237\pi\)
−0.525092 + 0.851046i \(0.675969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −11.0000 −0.714527
\(238\) 0 0
\(239\) 10.9706 0.709627 0.354813 0.934937i \(-0.384544\pi\)
0.354813 + 0.934937i \(0.384544\pi\)
\(240\) 0 0
\(241\) 2.00000 3.46410i 0.128831 0.223142i −0.794393 0.607404i \(-0.792211\pi\)
0.923224 + 0.384262i \(0.125544\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −11.3492 19.6575i −0.722135 1.25077i
\(248\) 0 0
\(249\) 5.12132 8.87039i 0.324550 0.562138i
\(250\) 0 0
\(251\) −18.7279 −1.18210 −0.591048 0.806636i \(-0.701286\pi\)
−0.591048 + 0.806636i \(0.701286\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.12132 + 8.87039i 0.319459 + 0.553320i 0.980375 0.197140i \(-0.0631654\pi\)
−0.660916 + 0.750460i \(0.729832\pi\)
\(258\) 0 0
\(259\) −8.50000 1.16320i −0.528164 0.0722776i
\(260\) 0 0
\(261\) 0.878680 + 1.52192i 0.0543889 + 0.0942043i
\(262\) 0 0
\(263\) −4.24264 + 7.34847i −0.261612 + 0.453126i −0.966671 0.256023i \(-0.917588\pi\)
0.705058 + 0.709150i \(0.250921\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 10.2426 0.626839
\(268\) 0 0
\(269\) 1.24264 2.15232i 0.0757651 0.131229i −0.825654 0.564177i \(-0.809193\pi\)
0.901419 + 0.432948i \(0.142527\pi\)
\(270\) 0 0
\(271\) 11.7279 + 20.3134i 0.712421 + 1.23395i 0.963946 + 0.266098i \(0.0857344\pi\)
−0.251525 + 0.967851i \(0.580932\pi\)
\(272\) 0 0
\(273\) −3.24264 7.94282i −0.196254 0.480721i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.86396 15.3528i 0.532584 0.922462i −0.466692 0.884420i \(-0.654554\pi\)
0.999276 0.0380425i \(-0.0121122\pi\)
\(278\) 0 0
\(279\) −9.48528 −0.567869
\(280\) 0 0
\(281\) 28.9706 1.72824 0.864119 0.503287i \(-0.167876\pi\)
0.864119 + 0.503287i \(0.167876\pi\)
\(282\) 0 0
\(283\) 11.8640 20.5490i 0.705239 1.22151i −0.261366 0.965240i \(-0.584173\pi\)
0.966605 0.256270i \(-0.0824938\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.87868 8.87039i 0.406036 0.523602i
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) 0.242641 0.420266i 0.0142238 0.0246364i
\(292\) 0 0
\(293\) 4.97056 0.290383 0.145192 0.989404i \(-0.453620\pi\)
0.145192 + 0.989404i \(0.453620\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2.12132 + 3.67423i −0.123091 + 0.213201i
\(298\) 0 0
\(299\) 6.87868 + 11.9142i 0.397804 + 0.689017i
\(300\) 0 0
\(301\) 5.25736 6.77962i 0.303029 0.390771i
\(302\) 0 0
\(303\) −3.87868 6.71807i −0.222824 0.385943i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −3.24264 −0.185067 −0.0925336 0.995710i \(-0.529497\pi\)
−0.0925336 + 0.995710i \(0.529497\pi\)
\(308\) 0 0
\(309\) −17.2426 −0.980900
\(310\) 0 0
\(311\) −10.6066 + 18.3712i −0.601445 + 1.04173i 0.391157 + 0.920324i \(0.372075\pi\)
−0.992602 + 0.121410i \(0.961258\pi\)
\(312\) 0 0
\(313\) 11.8640 + 20.5490i 0.670591 + 1.16150i 0.977737 + 0.209835i \(0.0672926\pi\)
−0.307146 + 0.951662i \(0.599374\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.3640 21.4150i −0.694429 1.20279i −0.970373 0.241613i \(-0.922324\pi\)
0.275943 0.961174i \(-0.411010\pi\)
\(318\) 0 0
\(319\) −3.72792 + 6.45695i −0.208724 + 0.361520i
\(320\) 0 0
\(321\) 12.7279 0.710403
\(322\) 0 0
\(323\) 29.6985 1.65247
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −4.74264 8.21449i −0.262269 0.454263i
\(328\) 0 0
\(329\) 15.7279 + 2.15232i 0.867108 + 0.118661i
\(330\) 0 0
\(331\) −8.50000 14.7224i −0.467202 0.809218i 0.532096 0.846684i \(-0.321405\pi\)
−0.999298 + 0.0374662i \(0.988071\pi\)
\(332\) 0 0
\(333\) 1.62132 2.80821i 0.0888478 0.153889i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 13.7279 0.747808 0.373904 0.927467i \(-0.378019\pi\)
0.373904 + 0.927467i \(0.378019\pi\)
\(338\) 0 0
\(339\) 9.00000 15.5885i 0.488813 0.846649i
\(340\) 0 0
\(341\) −20.1213 34.8511i −1.08963 1.88730i
\(342\) 0 0
\(343\) 17.0000 + 7.34847i 0.917914 + 0.396780i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.0000 + 20.7846i −0.644194 + 1.11578i 0.340293 + 0.940319i \(0.389474\pi\)
−0.984487 + 0.175457i \(0.943860\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 3.24264 0.173079
\(352\) 0 0
\(353\) −5.12132 + 8.87039i −0.272580 + 0.472123i −0.969522 0.245005i \(-0.921210\pi\)
0.696941 + 0.717128i \(0.254544\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 11.1213 + 1.52192i 0.588603 + 0.0805484i
\(358\) 0 0
\(359\) −0.878680 1.52192i −0.0463749 0.0803237i 0.841906 0.539624i \(-0.181434\pi\)
−0.888281 + 0.459300i \(0.848100\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 17.8640 30.9413i 0.932491 1.61512i 0.153443 0.988157i \(-0.450964\pi\)
0.779048 0.626965i \(-0.215703\pi\)
\(368\) 0 0
\(369\) 2.12132 + 3.67423i 0.110432 + 0.191273i
\(370\) 0 0
\(371\) 8.48528 + 20.7846i 0.440534 + 1.07908i
\(372\) 0 0
\(373\) 8.86396 + 15.3528i 0.458959 + 0.794939i 0.998906 0.0467591i \(-0.0148893\pi\)
−0.539948 + 0.841699i \(0.681556\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.69848 0.293487
\(378\) 0 0
\(379\) −20.4558 −1.05075 −0.525373 0.850872i \(-0.676074\pi\)
−0.525373 + 0.850872i \(0.676074\pi\)
\(380\) 0 0
\(381\) 1.37868 2.38794i 0.0706319 0.122338i
\(382\) 0 0
\(383\) 12.7279 + 22.0454i 0.650366 + 1.12647i 0.983034 + 0.183424i \(0.0587180\pi\)
−0.332668 + 0.943044i \(0.607949\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.62132 + 2.80821i 0.0824163 + 0.142749i
\(388\) 0 0
\(389\) 10.6066 18.3712i 0.537776 0.931455i −0.461247 0.887272i \(-0.652598\pi\)
0.999023 0.0441839i \(-0.0140687\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) −14.4853 −0.730686
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.37868 7.58410i −0.219760 0.380635i 0.734975 0.678094i \(-0.237194\pi\)
−0.954734 + 0.297460i \(0.903861\pi\)
\(398\) 0 0
\(399\) −11.3492 + 14.6354i −0.568173 + 0.732686i
\(400\) 0 0
\(401\) 1.75736 + 3.04384i 0.0877583 + 0.152002i 0.906563 0.422070i \(-0.138696\pi\)
−0.818805 + 0.574072i \(0.805363\pi\)
\(402\) 0 0
\(403\) −15.3787 + 26.6367i −0.766067 + 1.32687i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 13.7574 0.681927
\(408\) 0 0
\(409\) −8.50000 + 14.7224i −0.420298 + 0.727977i −0.995968 0.0897044i \(-0.971408\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(410\) 0 0
\(411\) −2.12132 3.67423i −0.104637 0.181237i
\(412\) 0 0
\(413\) 10.2426 + 25.0892i 0.504007 + 1.23456i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.74264 + 13.4106i −0.379159 + 0.656722i
\(418\) 0 0
\(419\) −14.4853 −0.707652 −0.353826 0.935311i \(-0.615120\pi\)
−0.353826 + 0.935311i \(0.615120\pi\)
\(420\) 0 0
\(421\) 31.4853 1.53450 0.767249 0.641349i \(-0.221625\pi\)
0.767249 + 0.641349i \(0.221625\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 11.7574 + 1.60896i 0.568978 + 0.0778629i
\(428\) 0 0
\(429\) 6.87868 + 11.9142i 0.332106 + 0.575224i
\(430\) 0 0
\(431\) −9.72792 + 16.8493i −0.468578 + 0.811600i −0.999355 0.0359112i \(-0.988567\pi\)
0.530777 + 0.847511i \(0.321900\pi\)
\(432\) 0 0
\(433\) −33.2426 −1.59754 −0.798770 0.601637i \(-0.794515\pi\)
−0.798770 + 0.601637i \(0.794515\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 14.8492 25.7196i 0.710336 1.23034i
\(438\) 0 0
\(439\) 5.00000 + 8.66025i 0.238637 + 0.413331i 0.960323 0.278889i \(-0.0899661\pi\)
−0.721686 + 0.692220i \(0.756633\pi\)
\(440\) 0 0
\(441\) −5.00000 + 4.89898i −0.238095 + 0.233285i
\(442\) 0 0
\(443\) 10.2426 + 17.7408i 0.486643 + 0.842890i 0.999882 0.0153558i \(-0.00488809\pi\)
−0.513240 + 0.858245i \(0.671555\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.0000 0.567581
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −9.00000 + 15.5885i −0.423793 + 0.734032i
\(452\) 0 0
\(453\) 11.2426 + 19.4728i 0.528225 + 0.914913i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 16.1066 + 27.8975i 0.753435 + 1.30499i 0.946149 + 0.323733i \(0.104938\pi\)
−0.192714 + 0.981255i \(0.561729\pi\)
\(458\) 0 0
\(459\) −2.12132 + 3.67423i −0.0990148 + 0.171499i
\(460\) 0 0
\(461\) 18.7279 0.872246 0.436123 0.899887i \(-0.356351\pi\)
0.436123 + 0.899887i \(0.356351\pi\)
\(462\) 0 0
\(463\) −10.2721 −0.477384 −0.238692 0.971095i \(-0.576719\pi\)
−0.238692 + 0.971095i \(0.576719\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.48528 9.50079i −0.253829 0.439644i 0.710748 0.703447i \(-0.248357\pi\)
−0.964577 + 0.263803i \(0.915023\pi\)
\(468\) 0 0
\(469\) −5.24264 12.8418i −0.242083 0.592979i
\(470\) 0 0
\(471\) 3.24264 + 5.61642i 0.149413 + 0.258791i
\(472\) 0 0
\(473\) −6.87868 + 11.9142i −0.316282 + 0.547817i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −8.48528 −0.388514
\(478\) 0 0
\(479\) −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) 0 0
\(481\) −5.25736 9.10601i −0.239715 0.415198i
\(482\) 0 0
\(483\) 6.87868 8.87039i 0.312991 0.403617i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −18.8640 + 32.6733i −0.854808 + 1.48057i 0.0220157 + 0.999758i \(0.492992\pi\)
−0.876823 + 0.480813i \(0.840342\pi\)
\(488\) 0 0
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) 15.5147 0.700169 0.350085 0.936718i \(-0.386153\pi\)
0.350085 + 0.936718i \(0.386153\pi\)
\(492\) 0 0
\(493\) −3.72792 + 6.45695i −0.167897 + 0.290806i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.6360 26.6112i 0.925653 1.19367i
\(498\) 0 0
\(499\) −9.74264 16.8747i −0.436140 0.755417i 0.561247 0.827648i \(-0.310322\pi\)
−0.997388 + 0.0722305i \(0.976988\pi\)
\(500\) 0 0
\(501\) −9.36396 + 16.2189i −0.418351 + 0.724605i
\(502\) 0 0
\(503\) 26.4853 1.18092 0.590460 0.807067i \(-0.298946\pi\)
0.590460 + 0.807067i \(0.298946\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.24264 + 2.15232i −0.0551876 + 0.0955877i
\(508\) 0 0
\(509\) 9.72792 + 16.8493i 0.431183 + 0.746830i 0.996975 0.0777173i \(-0.0247632\pi\)
−0.565793 + 0.824547i \(0.691430\pi\)
\(510\) 0 0
\(511\) 9.24264 + 22.6398i 0.408870 + 1.00152i
\(512\) 0 0
\(513\) −3.50000 6.06218i −0.154529 0.267652i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −25.4558 −1.11955
\(518\) 0 0
\(519\) −20.4853 −0.899204
\(520\) 0 0
\(521\) 6.72792 11.6531i 0.294756 0.510532i −0.680172 0.733052i \(-0.738095\pi\)
0.974928 + 0.222520i \(0.0714284\pi\)
\(522\) 0 0
\(523\) −2.62132 4.54026i −0.114622 0.198532i 0.803006 0.595970i \(-0.203232\pi\)
−0.917629 + 0.397439i \(0.869899\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.1213 34.8511i −0.876498 1.51814i
\(528\) 0 0
\(529\) 2.50000 4.33013i 0.108696 0.188266i
\(530\) 0 0
\(531\) −10.2426 −0.444493
\(532\) 0 0
\(533\) 13.7574 0.595897
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −3.00000 5.19615i −0.129460 0.224231i
\(538\) 0 0
\(539\) −28.6066 7.97887i −1.23217 0.343674i
\(540\) 0 0
\(541\) 20.4706 + 35.4561i 0.880098 + 1.52437i 0.851231 + 0.524792i \(0.175857\pi\)
0.0288675 + 0.999583i \(0.490810\pi\)
\(542\) 0 0
\(543\) −6.50000 + 11.2583i −0.278942 + 0.483141i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −33.4558 −1.43047 −0.715234 0.698885i \(-0.753680\pi\)
−0.715234 + 0.698885i \(0.753680\pi\)
\(548\) 0 0
\(549\) −2.24264 + 3.88437i −0.0957136 + 0.165781i
\(550\) 0 0
\(551\) −6.15076 10.6534i −0.262031 0.453851i
\(552\) 0 0
\(553\) 28.8345 + 3.94591i 1.22617 + 0.167797i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.0000 + 25.9808i −0.635570 + 1.10084i 0.350824 + 0.936442i \(0.385902\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(558\) 0 0
\(559\) 10.5147 0.444725
\(560\) 0 0
\(561\) −18.0000 −0.759961
\(562\) 0 0
\(563\) −3.00000 + 5.19615i −0.126435 + 0.218992i −0.922293 0.386492i \(-0.873687\pi\)
0.795858 + 0.605483i \(0.207020\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1.00000 2.44949i −0.0419961 0.102869i
\(568\) 0 0
\(569\) 20.8492 + 36.1119i 0.874046 + 1.51389i 0.857776 + 0.514024i \(0.171846\pi\)
0.0162699 + 0.999868i \(0.494821\pi\)
\(570\) 0 0
\(571\) 14.4706 25.0637i 0.605574 1.04889i −0.386386 0.922337i \(-0.626277\pi\)
0.991960 0.126548i \(-0.0403898\pi\)
\(572\) 0 0
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 6.37868 11.0482i 0.265548 0.459942i −0.702159 0.712020i \(-0.747780\pi\)
0.967707 + 0.252078i \(0.0811138\pi\)
\(578\) 0 0
\(579\) −3.37868 5.85204i −0.140413 0.243203i
\(580\) 0 0
\(581\) −16.6066 + 21.4150i −0.688958 + 0.888444i
\(582\) 0 0
\(583\) −18.0000 31.1769i −0.745484 1.29122i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −45.2132 −1.86615 −0.933074 0.359684i \(-0.882885\pi\)
−0.933074 + 0.359684i \(0.882885\pi\)
\(588\) 0 0
\(589\) 66.3970 2.73584
\(590\) 0 0
\(591\) 8.12132 14.0665i 0.334066 0.578620i
\(592\) 0 0
\(593\) 1.60660 + 2.78272i 0.0659752 + 0.114272i 0.897126 0.441774i \(-0.145651\pi\)
−0.831151 + 0.556047i \(0.812318\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.24264 + 9.08052i 0.214567 + 0.371641i
\(598\) 0 0
\(599\) 16.2426 28.1331i 0.663656 1.14949i −0.315991 0.948762i \(-0.602337\pi\)
0.979648 0.200724i \(-0.0643296\pi\)
\(600\) 0 0
\(601\) −3.48528 −0.142168 −0.0710838 0.997470i \(-0.522646\pi\)
−0.0710838 + 0.997470i \(0.522646\pi\)
\(602\) 0 0
\(603\) 5.24264 0.213497
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −14.6213 25.3249i −0.593461 1.02790i −0.993762 0.111521i \(-0.964428\pi\)
0.400301 0.916384i \(-0.368906\pi\)
\(608\) 0 0
\(609\) −1.75736 4.30463i −0.0712118 0.174433i
\(610\) 0 0
\(611\) 9.72792 + 16.8493i 0.393550 + 0.681648i
\(612\) 0 0
\(613\) −2.72792 + 4.72490i −0.110180 + 0.190837i −0.915843 0.401537i \(-0.868476\pi\)
0.805663 + 0.592374i \(0.201809\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26.4853 1.06626 0.533129 0.846034i \(-0.321016\pi\)
0.533129 + 0.846034i \(0.321016\pi\)
\(618\) 0 0
\(619\) 5.98528 10.3668i 0.240569 0.416677i −0.720308 0.693655i \(-0.755999\pi\)
0.960876 + 0.276977i \(0.0893327\pi\)
\(620\) 0 0
\(621\) 2.12132 + 3.67423i 0.0851257 + 0.147442i
\(622\) 0 0
\(623\) −26.8492 3.67423i −1.07569 0.147205i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 14.8492 25.7196i 0.593022 1.02714i
\(628\) 0 0
\(629\) 13.7574 0.548542
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 11.2426 19.4728i 0.446855 0.773975i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5.65076 + 21.9839i 0.223891 + 0.871032i
\(638\) 0 0
\(639\) 6.36396 + 11.0227i 0.251754 + 0.436051i
\(640\) 0 0
\(641\) −17.1213 + 29.6550i −0.676251 + 1.17130i 0.299850 + 0.953986i \(0.403063\pi\)
−0.976101 + 0.217316i \(0.930270\pi\)
\(642\) 0 0
\(643\) 19.7279 0.777993 0.388997 0.921239i \(-0.372822\pi\)
0.388997 + 0.921239i \(0.372822\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.12132 8.87039i 0.201340 0.348731i −0.747621 0.664126i \(-0.768804\pi\)
0.948960 + 0.315395i \(0.102137\pi\)
\(648\) 0 0
\(649\) −21.7279 37.6339i −0.852896 1.47726i
\(650\) 0 0
\(651\) 24.8640 + 3.40256i 0.974495 + 0.133357i
\(652\) 0 0
\(653\) 5.12132 + 8.87039i 0.200413 + 0.347125i 0.948661 0.316293i \(-0.102438\pi\)
−0.748249 + 0.663418i \(0.769105\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −9.24264 −0.360590
\(658\) 0 0
\(659\) 40.9706 1.59599 0.797993 0.602666i \(-0.205895\pi\)
0.797993 + 0.602666i \(0.205895\pi\)
\(660\) 0 0
\(661\) 1.01472 1.75754i 0.0394680 0.0683605i −0.845617 0.533791i \(-0.820767\pi\)
0.885085 + 0.465430i \(0.154100\pi\)
\(662\) 0 0
\(663\) 6.87868 + 11.9142i 0.267146 + 0.462710i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3.72792 + 6.45695i 0.144346 + 0.250014i
\(668\) 0 0
\(669\) 3.75736 6.50794i 0.145268 0.251611i
\(670\) 0 0
\(671\) −19.0294 −0.734623
\(672\) 0 0
\(673\) −29.7279 −1.14593 −0.572964 0.819581i \(-0.694206\pi\)
−0.572964 + 0.819581i \(0.694206\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.36396 + 11.0227i 0.244587 + 0.423637i 0.962015 0.272995i \(-0.0880143\pi\)
−0.717428 + 0.696632i \(0.754681\pi\)
\(678\) 0 0
\(679\) −0.786797 + 1.01461i −0.0301945 + 0.0389372i
\(680\) 0 0
\(681\) 7.60660 + 13.1750i 0.291486 + 0.504868i
\(682\) 0 0
\(683\) 16.6066 28.7635i 0.635434 1.10060i −0.350989 0.936380i \(-0.614155\pi\)
0.986423 0.164224i \(-0.0525121\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7.00000 0.267067
\(688\) 0 0
\(689\) −13.7574 + 23.8284i −0.524114 + 0.907791i
\(690\) 0 0
\(691\) −13.4706 23.3317i −0.512444 0.887580i −0.999896 0.0144296i \(-0.995407\pi\)
0.487452 0.873150i \(-0.337927\pi\)
\(692\) 0 0
\(693\) 6.87868 8.87039i 0.261299 0.336958i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9.00000 + 15.5885i −0.340899 + 0.590455i
\(698\) 0 0
\(699\) 14.4853 0.547884
\(700\) 0 0
\(701\) 8.78680 0.331873 0.165936 0.986136i \(-0.446935\pi\)
0.165936 + 0.986136i \(0.446935\pi\)
\(702\) 0 0
\(703\) −11.3492 + 19.6575i −0.428045 + 0.741395i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 7.75736 + 19.0016i 0.291746 + 0.714628i
\(708\) 0 0
\(709\) 18.2426 + 31.5972i 0.685117 + 1.18666i 0.973400 + 0.229112i \(0.0735822\pi\)
−0.288283 + 0.957545i \(0.593085\pi\)
\(710\) 0 0
\(711\) −5.50000 + 9.52628i −0.206266 + 0.357263i
\(712\) 0 0
\(713\) −40.2426 −1.50710
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 5.48528 9.50079i 0.204852 0.354813i
\(718\) 0 0
\(719\) −13.2426 22.9369i −0.493867 0.855403i 0.506108 0.862470i \(-0.331084\pi\)
−0.999975 + 0.00706717i \(0.997750\pi\)
\(720\) 0 0
\(721\) 45.1985 + 6.18527i 1.68328 + 0.230352i
\(722\) 0 0
\(723\) −2.00000 3.46410i −0.0743808 0.128831i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −0.757359 −0.0280889 −0.0140445 0.999901i \(-0.504471\pi\)
−0.0140445 + 0.999901i \(0.504471\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −6.87868 + 11.9142i −0.254417 + 0.440663i
\(732\) 0 0
\(733\) 0.893398 + 1.54741i 0.0329984 + 0.0571549i 0.882053 0.471150i \(-0.156161\pi\)
−0.849055 + 0.528305i \(0.822828\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 11.1213 + 19.2627i 0.409659 + 0.709550i
\(738\) 0 0
\(739\) 7.74264 13.4106i 0.284818 0.493319i −0.687747 0.725950i \(-0.741400\pi\)
0.972565 + 0.232632i \(0.0747336\pi\)
\(740\) 0 0
\(741\) −22.6985 −0.833850
\(742\) 0 0
\(743\) −15.2132 −0.558118 −0.279059 0.960274i \(-0.590023\pi\)
−0.279059 + 0.960274i \(0.590023\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.12132 8.87039i −0.187379 0.324550i
\(748\) 0 0
\(749\) −33.3640 4.56575i −1.21909 0.166829i
\(750\) 0 0
\(751\) −22.4706 38.9202i −0.819962 1.42022i −0.905709 0.423900i \(-0.860661\pi\)
0.0857467 0.996317i \(-0.472672\pi\)
\(752\) 0 0
\(753\) −9.36396 + 16.2189i −0.341242 + 0.591048i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −9.02944 −0.328180 −0.164090 0.986445i \(-0.552469\pi\)
−0.164090 + 0.986445i \(0.552469\pi\)
\(758\) 0 0
\(759\) −9.00000 + 15.5885i −0.326679 + 0.565825i
\(760\) 0 0
\(761\) −23.1213 40.0473i −0.838147 1.45171i −0.891442 0.453135i \(-0.850306\pi\)
0.0532948 0.998579i \(-0.483028\pi\)
\(762\) 0 0
\(763\) 9.48528 + 23.2341i 0.343390 + 0.841131i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −16.6066 + 28.7635i −0.599630 + 1.03859i
\(768\) 0 0
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 10.2426 0.368880
\(772\) 0 0
\(773\) 5.84924 10.1312i 0.210383 0.364393i −0.741452 0.671006i \(-0.765862\pi\)
0.951834 + 0.306613i \(0.0991957\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −5.25736 + 6.77962i −0.188607 + 0.243217i
\(778\) 0 0
\(779\) −14.8492 25.7196i −0.532029 0.921502i
\(780\) 0 0
\(781\) −27.0000 + 46.7654i −0.966136 + 1.67340i
\(782\) 0 0
\(783\) 1.75736 0.0628029
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 14.2426 24.6690i 0.507695 0.879354i −0.492265 0.870445i \(-0.663831\pi\)
0.999960 0.00890869i \(-0.00283576\pi\)
\(788\) 0 0
\(789\) 4.24264 + 7.34847i 0.151042 + 0.261612i
\(790\) 0 0
\(791\) −29.1838 + 37.6339i −1.03766 + 1.33811i
\(792\) 0 0
\(793\) 7.27208 + 12.5956i 0.258239 + 0.447283i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 31.7574 1.12490 0.562452 0.826830i \(-0.309858\pi\)
0.562452 + 0.826830i \(0.309858\pi\)
\(798\) 0 0
\(799\) −25.4558 −0.900563
\(800\) 0 0
\(801\) 5.12132 8.87039i