Properties

Label 448.2.p.d.255.1
Level $448$
Weight $2$
Character 448.255
Analytic conductor $3.577$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.57729801055\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 255.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 448.255
Dual form 448.2.p.d.383.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 1.50000i) q^{3} +(1.50000 - 0.866025i) q^{5} +(-1.73205 + 2.00000i) q^{7} +O(q^{10})\) \(q+(-0.866025 + 1.50000i) q^{3} +(1.50000 - 0.866025i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(-0.866025 - 0.500000i) q^{11} +3.46410i q^{13} +3.00000i q^{15} +(-1.50000 - 0.866025i) q^{17} +(2.59808 + 4.50000i) q^{19} +(-1.50000 - 4.33013i) q^{21} +(0.866025 - 0.500000i) q^{23} +(-1.00000 + 1.73205i) q^{25} -5.19615 q^{27} -4.00000 q^{29} +(-0.866025 + 1.50000i) q^{31} +(1.50000 - 0.866025i) q^{33} +(-0.866025 + 4.50000i) q^{35} +(1.50000 + 2.59808i) q^{37} +(-5.19615 - 3.00000i) q^{39} +3.46410i q^{41} -2.00000i q^{43} +(4.33013 + 7.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(2.59808 - 1.50000i) q^{51} +(-0.500000 + 0.866025i) q^{53} -1.73205 q^{55} -9.00000 q^{57} +(2.59808 - 4.50000i) q^{59} +(4.50000 - 2.59808i) q^{61} +(3.00000 + 5.19615i) q^{65} +(-2.59808 - 1.50000i) q^{67} +1.73205i q^{69} -14.0000i q^{71} +(7.50000 + 4.33013i) q^{73} +(-1.73205 - 3.00000i) q^{75} +(2.50000 - 0.866025i) q^{77} +(7.79423 - 4.50000i) q^{79} +(4.50000 - 7.79423i) q^{81} +13.8564 q^{83} -3.00000 q^{85} +(3.46410 - 6.00000i) q^{87} +(13.5000 - 7.79423i) q^{89} +(-6.92820 - 6.00000i) q^{91} +(-1.50000 - 2.59808i) q^{93} +(7.79423 + 4.50000i) q^{95} +17.3205i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{5} - 6 q^{17} - 6 q^{21} - 4 q^{25} - 16 q^{29} + 6 q^{33} + 6 q^{37} - 4 q^{49} - 2 q^{53} - 36 q^{57} + 18 q^{61} + 12 q^{65} + 30 q^{73} + 10 q^{77} + 18 q^{81} - 12 q^{85} + 54 q^{89} - 6 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) −0.866025 + 1.50000i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i \(-0.540075\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) 0 0
\(7\) −1.73205 + 2.00000i −0.654654 + 0.755929i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.866025 0.500000i −0.261116 0.150756i 0.363727 0.931505i \(-0.381504\pi\)
−0.624844 + 0.780750i \(0.714837\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) 0 0
\(15\) 3.00000i 0.774597i
\(16\) 0 0
\(17\) −1.50000 0.866025i −0.363803 0.210042i 0.306944 0.951727i \(-0.400693\pi\)
−0.670748 + 0.741685i \(0.734027\pi\)
\(18\) 0 0
\(19\) 2.59808 + 4.50000i 0.596040 + 1.03237i 0.993399 + 0.114708i \(0.0365932\pi\)
−0.397360 + 0.917663i \(0.630073\pi\)
\(20\) 0 0
\(21\) −1.50000 4.33013i −0.327327 0.944911i
\(22\) 0 0
\(23\) 0.866025 0.500000i 0.180579 0.104257i −0.406986 0.913434i \(-0.633420\pi\)
0.587565 + 0.809177i \(0.300087\pi\)
\(24\) 0 0
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) 0 0
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −0.866025 + 1.50000i −0.155543 + 0.269408i −0.933257 0.359211i \(-0.883046\pi\)
0.777714 + 0.628619i \(0.216379\pi\)
\(32\) 0 0
\(33\) 1.50000 0.866025i 0.261116 0.150756i
\(34\) 0 0
\(35\) −0.866025 + 4.50000i −0.146385 + 0.760639i
\(36\) 0 0
\(37\) 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i \(-0.0873538\pi\)
−0.715981 + 0.698119i \(0.754020\pi\)
\(38\) 0 0
\(39\) −5.19615 3.00000i −0.832050 0.480384i
\(40\) 0 0
\(41\) 3.46410i 0.541002i 0.962720 + 0.270501i \(0.0871893\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.33013 + 7.50000i 0.631614 + 1.09399i 0.987222 + 0.159352i \(0.0509405\pi\)
−0.355608 + 0.934635i \(0.615726\pi\)
\(48\) 0 0
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) 0 0
\(51\) 2.59808 1.50000i 0.363803 0.210042i
\(52\) 0 0
\(53\) −0.500000 + 0.866025i −0.0686803 + 0.118958i −0.898321 0.439340i \(-0.855212\pi\)
0.829640 + 0.558298i \(0.188546\pi\)
\(54\) 0 0
\(55\) −1.73205 −0.233550
\(56\) 0 0
\(57\) −9.00000 −1.19208
\(58\) 0 0
\(59\) 2.59808 4.50000i 0.338241 0.585850i −0.645861 0.763455i \(-0.723502\pi\)
0.984102 + 0.177605i \(0.0568349\pi\)
\(60\) 0 0
\(61\) 4.50000 2.59808i 0.576166 0.332650i −0.183442 0.983030i \(-0.558724\pi\)
0.759608 + 0.650381i \(0.225391\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.00000 + 5.19615i 0.372104 + 0.644503i
\(66\) 0 0
\(67\) −2.59808 1.50000i −0.317406 0.183254i 0.332830 0.942987i \(-0.391996\pi\)
−0.650236 + 0.759733i \(0.725330\pi\)
\(68\) 0 0
\(69\) 1.73205i 0.208514i
\(70\) 0 0
\(71\) 14.0000i 1.66149i −0.556650 0.830747i \(-0.687914\pi\)
0.556650 0.830747i \(-0.312086\pi\)
\(72\) 0 0
\(73\) 7.50000 + 4.33013i 0.877809 + 0.506803i 0.869935 0.493166i \(-0.164160\pi\)
0.00787336 + 0.999969i \(0.497494\pi\)
\(74\) 0 0
\(75\) −1.73205 3.00000i −0.200000 0.346410i
\(76\) 0 0
\(77\) 2.50000 0.866025i 0.284901 0.0986928i
\(78\) 0 0
\(79\) 7.79423 4.50000i 0.876919 0.506290i 0.00727784 0.999974i \(-0.497683\pi\)
0.869641 + 0.493684i \(0.164350\pi\)
\(80\) 0 0
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) 0 0
\(83\) 13.8564 1.52094 0.760469 0.649374i \(-0.224969\pi\)
0.760469 + 0.649374i \(0.224969\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 3.46410 6.00000i 0.371391 0.643268i
\(88\) 0 0
\(89\) 13.5000 7.79423i 1.43100 0.826187i 0.433800 0.901009i \(-0.357172\pi\)
0.997197 + 0.0748225i \(0.0238390\pi\)
\(90\) 0 0
\(91\) −6.92820 6.00000i −0.726273 0.628971i
\(92\) 0 0
\(93\) −1.50000 2.59808i −0.155543 0.269408i
\(94\) 0 0
\(95\) 7.79423 + 4.50000i 0.799671 + 0.461690i
\(96\) 0 0
\(97\) 17.3205i 1.75863i 0.476240 + 0.879316i \(0.342000\pi\)
−0.476240 + 0.879316i \(0.658000\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.50000 + 4.33013i 0.746278 + 0.430864i 0.824347 0.566084i \(-0.191542\pi\)
−0.0780696 + 0.996948i \(0.524876\pi\)
\(102\) 0 0
\(103\) −4.33013 7.50000i −0.426660 0.738997i 0.569914 0.821705i \(-0.306977\pi\)
−0.996574 + 0.0827075i \(0.973643\pi\)
\(104\) 0 0
\(105\) −6.00000 5.19615i −0.585540 0.507093i
\(106\) 0 0
\(107\) 11.2583 6.50000i 1.08838 0.628379i 0.155238 0.987877i \(-0.450386\pi\)
0.933146 + 0.359498i \(0.117052\pi\)
\(108\) 0 0
\(109\) 4.50000 7.79423i 0.431022 0.746552i −0.565940 0.824447i \(-0.691487\pi\)
0.996962 + 0.0778949i \(0.0248199\pi\)
\(110\) 0 0
\(111\) −5.19615 −0.493197
\(112\) 0 0
\(113\) −16.0000 −1.50515 −0.752577 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) 0.866025 1.50000i 0.0807573 0.139876i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.33013 1.50000i 0.396942 0.137505i
\(120\) 0 0
\(121\) −5.00000 8.66025i −0.454545 0.787296i
\(122\) 0 0
\(123\) −5.19615 3.00000i −0.468521 0.270501i
\(124\) 0 0
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 6.00000i 0.532414i 0.963916 + 0.266207i \(0.0857705\pi\)
−0.963916 + 0.266207i \(0.914230\pi\)
\(128\) 0 0
\(129\) 3.00000 + 1.73205i 0.264135 + 0.152499i
\(130\) 0 0
\(131\) −2.59808 4.50000i −0.226995 0.393167i 0.729921 0.683531i \(-0.239557\pi\)
−0.956916 + 0.290365i \(0.906223\pi\)
\(132\) 0 0
\(133\) −13.5000 2.59808i −1.17060 0.225282i
\(134\) 0 0
\(135\) −7.79423 + 4.50000i −0.670820 + 0.387298i
\(136\) 0 0
\(137\) −0.500000 + 0.866025i −0.0427179 + 0.0739895i −0.886594 0.462549i \(-0.846935\pi\)
0.843876 + 0.536538i \(0.180268\pi\)
\(138\) 0 0
\(139\) −6.92820 −0.587643 −0.293821 0.955860i \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) 0 0
\(141\) −15.0000 −1.26323
\(142\) 0 0
\(143\) 1.73205 3.00000i 0.144841 0.250873i
\(144\) 0 0
\(145\) −6.00000 + 3.46410i −0.498273 + 0.287678i
\(146\) 0 0
\(147\) 11.2583 + 4.50000i 0.928571 + 0.371154i
\(148\) 0 0
\(149\) 0.500000 + 0.866025i 0.0409616 + 0.0709476i 0.885779 0.464107i \(-0.153625\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(150\) 0 0
\(151\) −6.06218 3.50000i −0.493333 0.284826i 0.232623 0.972567i \(-0.425269\pi\)
−0.725956 + 0.687741i \(0.758602\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.00000i 0.240966i
\(156\) 0 0
\(157\) −1.50000 0.866025i −0.119713 0.0691164i 0.438948 0.898513i \(-0.355351\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 0 0
\(159\) −0.866025 1.50000i −0.0686803 0.118958i
\(160\) 0 0
\(161\) −0.500000 + 2.59808i −0.0394055 + 0.204757i
\(162\) 0 0
\(163\) −18.1865 + 10.5000i −1.42448 + 0.822423i −0.996678 0.0814491i \(-0.974045\pi\)
−0.427802 + 0.903873i \(0.640712\pi\)
\(164\) 0 0
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) 0 0
\(167\) 17.3205 1.34030 0.670151 0.742225i \(-0.266230\pi\)
0.670151 + 0.742225i \(0.266230\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.5000 6.06218i 0.798300 0.460899i −0.0445762 0.999006i \(-0.514194\pi\)
0.842876 + 0.538107i \(0.180860\pi\)
\(174\) 0 0
\(175\) −1.73205 5.00000i −0.130931 0.377964i
\(176\) 0 0
\(177\) 4.50000 + 7.79423i 0.338241 + 0.585850i
\(178\) 0 0
\(179\) 16.4545 + 9.50000i 1.22987 + 0.710063i 0.967002 0.254770i \(-0.0819996\pi\)
0.262864 + 0.964833i \(0.415333\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 0 0
\(183\) 9.00000i 0.665299i
\(184\) 0 0
\(185\) 4.50000 + 2.59808i 0.330847 + 0.191014i
\(186\) 0 0
\(187\) 0.866025 + 1.50000i 0.0633300 + 0.109691i
\(188\) 0 0
\(189\) 9.00000 10.3923i 0.654654 0.755929i
\(190\) 0 0
\(191\) −0.866025 + 0.500000i −0.0626634 + 0.0361787i −0.531004 0.847369i \(-0.678185\pi\)
0.468341 + 0.883548i \(0.344852\pi\)
\(192\) 0 0
\(193\) 7.50000 12.9904i 0.539862 0.935068i −0.459049 0.888411i \(-0.651810\pi\)
0.998911 0.0466572i \(-0.0148568\pi\)
\(194\) 0 0
\(195\) −10.3923 −0.744208
\(196\) 0 0
\(197\) −16.0000 −1.13995 −0.569976 0.821661i \(-0.693048\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(198\) 0 0
\(199\) −11.2583 + 19.5000i −0.798082 + 1.38232i 0.122782 + 0.992434i \(0.460818\pi\)
−0.920864 + 0.389885i \(0.872515\pi\)
\(200\) 0 0
\(201\) 4.50000 2.59808i 0.317406 0.183254i
\(202\) 0 0
\(203\) 6.92820 8.00000i 0.486265 0.561490i
\(204\) 0 0
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.19615i 0.359425i
\(210\) 0 0
\(211\) 10.0000i 0.688428i −0.938891 0.344214i \(-0.888145\pi\)
0.938891 0.344214i \(-0.111855\pi\)
\(212\) 0 0
\(213\) 21.0000 + 12.1244i 1.43890 + 0.830747i
\(214\) 0 0
\(215\) −1.73205 3.00000i −0.118125 0.204598i
\(216\) 0 0
\(217\) −1.50000 4.33013i −0.101827 0.293948i
\(218\) 0 0
\(219\) −12.9904 + 7.50000i −0.877809 + 0.506803i
\(220\) 0 0
\(221\) 3.00000 5.19615i 0.201802 0.349531i
\(222\) 0 0
\(223\) −6.92820 −0.463947 −0.231973 0.972722i \(-0.574518\pi\)
−0.231973 + 0.972722i \(0.574518\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.52628 + 16.5000i −0.632281 + 1.09514i 0.354803 + 0.934941i \(0.384548\pi\)
−0.987084 + 0.160202i \(0.948785\pi\)
\(228\) 0 0
\(229\) 13.5000 7.79423i 0.892105 0.515057i 0.0174746 0.999847i \(-0.494437\pi\)
0.874630 + 0.484790i \(0.161104\pi\)
\(230\) 0 0
\(231\) −0.866025 + 4.50000i −0.0569803 + 0.296078i
\(232\) 0 0
\(233\) 3.50000 + 6.06218i 0.229293 + 0.397146i 0.957599 0.288106i \(-0.0930254\pi\)
−0.728306 + 0.685252i \(0.759692\pi\)
\(234\) 0 0
\(235\) 12.9904 + 7.50000i 0.847399 + 0.489246i
\(236\) 0 0
\(237\) 15.5885i 1.01258i
\(238\) 0 0
\(239\) 20.0000i 1.29369i 0.762620 + 0.646846i \(0.223912\pi\)
−0.762620 + 0.646846i \(0.776088\pi\)
\(240\) 0 0
\(241\) −4.50000 2.59808i −0.289870 0.167357i 0.348013 0.937490i \(-0.386857\pi\)
−0.637883 + 0.770133i \(0.720190\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −7.50000 9.52628i −0.479157 0.608612i
\(246\) 0 0
\(247\) −15.5885 + 9.00000i −0.991870 + 0.572656i
\(248\) 0 0
\(249\) −12.0000 + 20.7846i −0.760469 + 1.31717i
\(250\) 0 0
\(251\) −3.46410 −0.218652 −0.109326 0.994006i \(-0.534869\pi\)
−0.109326 + 0.994006i \(0.534869\pi\)
\(252\) 0 0
\(253\) −1.00000 −0.0628695
\(254\) 0 0
\(255\) 2.59808 4.50000i 0.162698 0.281801i
\(256\) 0 0
\(257\) 4.50000 2.59808i 0.280702 0.162064i −0.353039 0.935609i \(-0.614852\pi\)
0.633741 + 0.773545i \(0.281518\pi\)
\(258\) 0 0
\(259\) −7.79423 1.50000i −0.484310 0.0932055i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 19.9186 + 11.5000i 1.22823 + 0.709120i 0.966660 0.256063i \(-0.0824256\pi\)
0.261573 + 0.965184i \(0.415759\pi\)
\(264\) 0 0
\(265\) 1.73205i 0.106399i
\(266\) 0 0
\(267\) 27.0000i 1.65237i
\(268\) 0 0
\(269\) −19.5000 11.2583i −1.18894 0.686433i −0.230871 0.972984i \(-0.574158\pi\)
−0.958065 + 0.286552i \(0.907491\pi\)
\(270\) 0 0
\(271\) −7.79423 13.5000i −0.473466 0.820067i 0.526073 0.850439i \(-0.323664\pi\)
−0.999539 + 0.0303728i \(0.990331\pi\)
\(272\) 0 0
\(273\) 15.0000 5.19615i 0.907841 0.314485i
\(274\) 0 0
\(275\) 1.73205 1.00000i 0.104447 0.0603023i
\(276\) 0 0
\(277\) −6.50000 + 11.2583i −0.390547 + 0.676448i −0.992522 0.122068i \(-0.961047\pi\)
0.601975 + 0.798515i \(0.294381\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 0 0
\(283\) −6.06218 + 10.5000i −0.360359 + 0.624160i −0.988020 0.154327i \(-0.950679\pi\)
0.627661 + 0.778487i \(0.284012\pi\)
\(284\) 0 0
\(285\) −13.5000 + 7.79423i −0.799671 + 0.461690i
\(286\) 0 0
\(287\) −6.92820 6.00000i −0.408959 0.354169i
\(288\) 0 0
\(289\) −7.00000 12.1244i −0.411765 0.713197i
\(290\) 0 0
\(291\) −25.9808 15.0000i −1.52302 0.879316i
\(292\) 0 0
\(293\) 20.7846i 1.21425i −0.794606 0.607125i \(-0.792323\pi\)
0.794606 0.607125i \(-0.207677\pi\)
\(294\) 0 0
\(295\) 9.00000i 0.524000i
\(296\) 0 0
\(297\) 4.50000 + 2.59808i 0.261116 + 0.150756i
\(298\) 0 0
\(299\) 1.73205 + 3.00000i 0.100167 + 0.173494i
\(300\) 0 0
\(301\) 4.00000 + 3.46410i 0.230556 + 0.199667i
\(302\) 0 0
\(303\) −12.9904 + 7.50000i −0.746278 + 0.430864i
\(304\) 0 0
\(305\) 4.50000 7.79423i 0.257669 0.446296i
\(306\) 0 0
\(307\) 20.7846 1.18624 0.593120 0.805114i \(-0.297896\pi\)
0.593120 + 0.805114i \(0.297896\pi\)
\(308\) 0 0
\(309\) 15.0000 0.853320
\(310\) 0 0
\(311\) 4.33013 7.50000i 0.245539 0.425286i −0.716744 0.697336i \(-0.754368\pi\)
0.962283 + 0.272050i \(0.0877017\pi\)
\(312\) 0 0
\(313\) 1.50000 0.866025i 0.0847850 0.0489506i −0.457008 0.889463i \(-0.651079\pi\)
0.541793 + 0.840512i \(0.317746\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.50000 + 9.52628i 0.308911 + 0.535049i 0.978124 0.208021i \(-0.0667022\pi\)
−0.669214 + 0.743070i \(0.733369\pi\)
\(318\) 0 0
\(319\) 3.46410 + 2.00000i 0.193952 + 0.111979i
\(320\) 0 0
\(321\) 22.5167i 1.25676i
\(322\) 0 0
\(323\) 9.00000i 0.500773i
\(324\) 0 0
\(325\) −6.00000 3.46410i −0.332820 0.192154i
\(326\) 0 0
\(327\) 7.79423 + 13.5000i 0.431022 + 0.746552i
\(328\) 0 0
\(329\) −22.5000 4.33013i −1.24047 0.238728i
\(330\) 0 0
\(331\) 6.06218 3.50000i 0.333207 0.192377i −0.324057 0.946038i \(-0.605047\pi\)
0.657264 + 0.753660i \(0.271714\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.19615 −0.283896
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 13.8564 24.0000i 0.752577 1.30350i
\(340\) 0 0
\(341\) 1.50000 0.866025i 0.0812296 0.0468979i
\(342\) 0 0
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) 0 0
\(345\) 1.50000 + 2.59808i 0.0807573 + 0.139876i
\(346\) 0 0
\(347\) 11.2583 + 6.50000i 0.604379 + 0.348938i 0.770762 0.637123i \(-0.219876\pi\)
−0.166383 + 0.986061i \(0.553209\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) 0 0
\(351\) 18.0000i 0.960769i
\(352\) 0 0
\(353\) −25.5000 14.7224i −1.35723 0.783596i −0.367979 0.929834i \(-0.619950\pi\)
−0.989249 + 0.146238i \(0.953283\pi\)
\(354\) 0 0
\(355\) −12.1244 21.0000i −0.643494 1.11456i
\(356\) 0 0
\(357\) −1.50000 + 7.79423i −0.0793884 + 0.412514i
\(358\) 0 0
\(359\) 19.9186 11.5000i 1.05126 0.606947i 0.128260 0.991741i \(-0.459061\pi\)
0.923003 + 0.384794i \(0.125727\pi\)
\(360\) 0 0
\(361\) −4.00000 + 6.92820i −0.210526 + 0.364642i
\(362\) 0 0
\(363\) 17.3205 0.909091
\(364\) 0 0
\(365\) 15.0000 0.785136
\(366\) 0 0
\(367\) 0.866025 1.50000i 0.0452062 0.0782994i −0.842537 0.538639i \(-0.818939\pi\)
0.887743 + 0.460339i \(0.152272\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.866025 2.50000i −0.0449618 0.129794i
\(372\) 0 0
\(373\) −14.5000 25.1147i −0.750782 1.30039i −0.947444 0.319921i \(-0.896344\pi\)
0.196663 0.980471i \(-0.436990\pi\)
\(374\) 0 0
\(375\) −18.1865 10.5000i −0.939149 0.542218i
\(376\) 0 0
\(377\) 13.8564i 0.713641i
\(378\) 0 0
\(379\) 8.00000i 0.410932i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) 0 0
\(381\) −9.00000 5.19615i −0.461084 0.266207i
\(382\) 0 0
\(383\) −2.59808 4.50000i −0.132755 0.229939i 0.791982 0.610544i \(-0.209049\pi\)
−0.924738 + 0.380605i \(0.875716\pi\)
\(384\) 0 0
\(385\) 3.00000 3.46410i 0.152894 0.176547i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.50000 + 16.4545i −0.481669 + 0.834275i −0.999779 0.0210389i \(-0.993303\pi\)
0.518110 + 0.855314i \(0.326636\pi\)
\(390\) 0 0
\(391\) −1.73205 −0.0875936
\(392\) 0 0
\(393\) 9.00000 0.453990
\(394\) 0 0
\(395\) 7.79423 13.5000i 0.392170 0.679259i
\(396\) 0 0
\(397\) −16.5000 + 9.52628i −0.828111 + 0.478110i −0.853206 0.521575i \(-0.825345\pi\)
0.0250943 + 0.999685i \(0.492011\pi\)
\(398\) 0 0
\(399\) 15.5885 18.0000i 0.780399 0.901127i
\(400\) 0 0
\(401\) 11.5000 + 19.9186i 0.574283 + 0.994687i 0.996119 + 0.0880147i \(0.0280523\pi\)
−0.421837 + 0.906672i \(0.638614\pi\)
\(402\) 0 0
\(403\) −5.19615 3.00000i −0.258839 0.149441i
\(404\) 0 0
\(405\) 15.5885i 0.774597i
\(406\) 0 0
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) 22.5000 + 12.9904i 1.11255 + 0.642333i 0.939490 0.342578i \(-0.111300\pi\)
0.173064 + 0.984911i \(0.444633\pi\)
\(410\) 0 0
\(411\) −0.866025 1.50000i −0.0427179 0.0739895i
\(412\) 0 0
\(413\) 4.50000 + 12.9904i 0.221431 + 0.639215i
\(414\) 0 0
\(415\) 20.7846 12.0000i 1.02028 0.589057i
\(416\) 0 0
\(417\) 6.00000 10.3923i 0.293821 0.508913i
\(418\) 0 0
\(419\) −20.7846 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.00000 1.73205i 0.145521 0.0840168i
\(426\) 0 0
\(427\) −2.59808 + 13.5000i −0.125730 + 0.653311i
\(428\) 0 0
\(429\) 3.00000 + 5.19615i 0.144841 + 0.250873i
\(430\) 0 0
\(431\) −19.9186 11.5000i −0.959444 0.553936i −0.0634424 0.997985i \(-0.520208\pi\)
−0.896002 + 0.444050i \(0.853541\pi\)
\(432\) 0 0
\(433\) 10.3923i 0.499422i 0.968320 + 0.249711i \(0.0803357\pi\)
−0.968320 + 0.249711i \(0.919664\pi\)
\(434\) 0 0
\(435\) 12.0000i 0.575356i
\(436\) 0 0
\(437\) 4.50000 + 2.59808i 0.215264 + 0.124283i
\(438\) 0 0
\(439\) 11.2583 + 19.5000i 0.537331 + 0.930684i 0.999047 + 0.0436563i \(0.0139007\pi\)
−0.461716 + 0.887028i \(0.652766\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.7224 8.50000i 0.699484 0.403847i −0.107671 0.994187i \(-0.534339\pi\)
0.807155 + 0.590339i \(0.201006\pi\)
\(444\) 0 0
\(445\) 13.5000 23.3827i 0.639961 1.10845i
\(446\) 0 0
\(447\) −1.73205 −0.0819232
\(448\) 0 0
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) 0 0
\(451\) 1.73205 3.00000i 0.0815591 0.141264i
\(452\) 0 0
\(453\) 10.5000 6.06218i 0.493333 0.284826i
\(454\) 0 0
\(455\) −15.5885 3.00000i −0.730798 0.140642i
\(456\) 0 0
\(457\) −7.50000 12.9904i −0.350835 0.607664i 0.635561 0.772051i \(-0.280769\pi\)
−0.986396 + 0.164386i \(0.947436\pi\)
\(458\) 0 0
\(459\) 7.79423 + 4.50000i 0.363803 + 0.210042i
\(460\) 0 0
\(461\) 17.3205i 0.806696i −0.915047 0.403348i \(-0.867846\pi\)
0.915047 0.403348i \(-0.132154\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i −0.716965 0.697109i \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) 0 0
\(465\) −4.50000 2.59808i −0.208683 0.120483i
\(466\) 0 0
\(467\) 4.33013 + 7.50000i 0.200374 + 0.347059i 0.948649 0.316330i \(-0.102451\pi\)
−0.748275 + 0.663389i \(0.769117\pi\)
\(468\) 0 0
\(469\) 7.50000 2.59808i 0.346318 0.119968i
\(470\) 0 0
\(471\) 2.59808 1.50000i 0.119713 0.0691164i
\(472\) 0 0
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) 0 0
\(475\) −10.3923 −0.476832
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.06218 + 10.5000i −0.276988 + 0.479757i −0.970635 0.240558i \(-0.922670\pi\)
0.693647 + 0.720315i \(0.256003\pi\)
\(480\) 0 0
\(481\) −9.00000 + 5.19615i −0.410365 + 0.236924i
\(482\) 0 0
\(483\) −3.46410 3.00000i −0.157622 0.136505i
\(484\) 0 0
\(485\) 15.0000 + 25.9808i 0.681115 + 1.17973i
\(486\) 0 0
\(487\) 26.8468 + 15.5000i 1.21654 + 0.702372i 0.964177 0.265260i \(-0.0854576\pi\)
0.252367 + 0.967632i \(0.418791\pi\)
\(488\) 0 0
\(489\) 36.3731i 1.64485i
\(490\) 0 0
\(491\) 32.0000i 1.44414i −0.691820 0.722070i \(-0.743191\pi\)
0.691820 0.722070i \(-0.256809\pi\)
\(492\) 0 0
\(493\) 6.00000 + 3.46410i 0.270226 + 0.156015i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 28.0000 + 24.2487i 1.25597 + 1.08770i
\(498\) 0 0
\(499\) 30.3109 17.5000i 1.35690 0.783408i 0.367697 0.929946i \(-0.380146\pi\)
0.989205 + 0.146538i \(0.0468131\pi\)
\(500\) 0 0
\(501\) −15.0000 + 25.9808i −0.670151 + 1.16073i
\(502\) 0 0
\(503\) 6.92820 0.308913 0.154457 0.988000i \(-0.450637\pi\)
0.154457 + 0.988000i \(0.450637\pi\)
\(504\) 0 0
\(505\) 15.0000 0.667491
\(506\) 0 0
\(507\) −0.866025 + 1.50000i −0.0384615 + 0.0666173i
\(508\) 0 0
\(509\) −10.5000 + 6.06218i −0.465404 + 0.268701i −0.714314 0.699825i \(-0.753261\pi\)
0.248910 + 0.968527i \(0.419928\pi\)
\(510\) 0 0
\(511\) −21.6506 + 7.50000i −0.957768 + 0.331780i
\(512\) 0 0
\(513\) −13.5000 23.3827i −0.596040 1.03237i
\(514\) 0 0
\(515\) −12.9904 7.50000i −0.572425 0.330489i
\(516\) 0 0
\(517\) 8.66025i 0.380878i
\(518\) 0 0
\(519\) 21.0000i 0.921798i
\(520\) 0 0
\(521\) 1.50000 + 0.866025i 0.0657162 + 0.0379413i 0.532498 0.846431i \(-0.321253\pi\)
−0.466782 + 0.884372i \(0.654587\pi\)
\(522\) 0 0
\(523\) 12.9904 + 22.5000i 0.568030 + 0.983856i 0.996761 + 0.0804241i \(0.0256275\pi\)
−0.428731 + 0.903432i \(0.641039\pi\)
\(524\) 0 0
\(525\) 9.00000 + 1.73205i 0.392792 + 0.0755929i
\(526\) 0 0
\(527\) 2.59808 1.50000i 0.113174 0.0653410i
\(528\) 0 0
\(529\) −11.0000 + 19.0526i −0.478261 + 0.828372i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 11.2583 19.5000i 0.486740 0.843059i
\(536\) 0 0
\(537\) −28.5000 + 16.4545i −1.22987 + 0.710063i
\(538\) 0 0
\(539\) −2.59808 + 6.50000i −0.111907 + 0.279975i
\(540\) 0 0
\(541\) −9.50000 16.4545i −0.408437 0.707433i 0.586278 0.810110i \(-0.300593\pi\)
−0.994715 + 0.102677i \(0.967259\pi\)
\(542\) 0 0
\(543\) −10.3923 6.00000i −0.445976 0.257485i
\(544\) 0 0
\(545\) 15.5885i 0.667736i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −10.3923 18.0000i −0.442727 0.766826i
\(552\) 0 0
\(553\) −4.50000 + 23.3827i −0.191359 + 0.994333i
\(554\) 0 0
\(555\) −7.79423 + 4.50000i −0.330847 + 0.191014i
\(556\) 0 0
\(557\) 18.5000 32.0429i 0.783870 1.35770i −0.145802 0.989314i \(-0.546576\pi\)
0.929672 0.368389i \(-0.120091\pi\)
\(558\) 0 0
\(559\) 6.92820 0.293032
\(560\) 0 0
\(561\) −3.00000 −0.126660
\(562\) 0 0
\(563\) −11.2583 + 19.5000i −0.474482 + 0.821827i −0.999573 0.0292191i \(-0.990698\pi\)
0.525091 + 0.851046i \(0.324031\pi\)
\(564\) 0 0
\(565\) −24.0000 + 13.8564i −1.00969 + 0.582943i
\(566\) 0 0
\(567\) 7.79423 + 22.5000i 0.327327 + 0.944911i
\(568\) 0 0
\(569\) 6.50000 + 11.2583i 0.272494 + 0.471974i 0.969500 0.245092i \(-0.0788181\pi\)
−0.697006 + 0.717066i \(0.745485\pi\)
\(570\) 0 0
\(571\) −18.1865 10.5000i −0.761083 0.439411i 0.0686016 0.997644i \(-0.478146\pi\)
−0.829684 + 0.558233i \(0.811480\pi\)
\(572\) 0 0
\(573\) 1.73205i 0.0723575i
\(574\) 0 0
\(575\) 2.00000i 0.0834058i
\(576\) 0 0
\(577\) −28.5000 16.4545i −1.18647 0.685009i −0.228968 0.973434i \(-0.573535\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 0 0
\(579\) 12.9904 + 22.5000i 0.539862 + 0.935068i
\(580\) 0 0
\(581\) −24.0000 + 27.7128i −0.995688 + 1.14972i
\(582\) 0 0
\(583\) 0.866025 0.500000i 0.0358671 0.0207079i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.92820 0.285958 0.142979 0.989726i \(-0.454332\pi\)
0.142979 + 0.989726i \(0.454332\pi\)
\(588\) 0 0
\(589\) −9.00000 −0.370839
\(590\) 0 0
\(591\) 13.8564 24.0000i 0.569976 0.987228i
\(592\) 0 0
\(593\) −13.5000 + 7.79423i −0.554379 + 0.320071i −0.750886 0.660432i \(-0.770373\pi\)
0.196508 + 0.980502i \(0.437040\pi\)
\(594\) 0 0
\(595\) 5.19615 6.00000i 0.213021 0.245976i
\(596\) 0 0
\(597\) −19.5000 33.7750i −0.798082 1.38232i
\(598\) 0 0
\(599\) −14.7224 8.50000i −0.601542 0.347301i 0.168106 0.985769i \(-0.446235\pi\)
−0.769648 + 0.638468i \(0.779568\pi\)
\(600\) 0 0
\(601\) 38.1051i 1.55434i −0.629291 0.777170i \(-0.716654\pi\)
0.629291 0.777170i \(-0.283346\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −15.0000 8.66025i −0.609837 0.352089i
\(606\) 0 0
\(607\) 7.79423 + 13.5000i 0.316358 + 0.547948i 0.979725 0.200346i \(-0.0642066\pi\)
−0.663367 + 0.748294i \(0.730873\pi\)
\(608\) 0 0
\(609\) 6.00000 + 17.3205i 0.243132 + 0.701862i
\(610\) 0 0
\(611\) −25.9808 + 15.0000i −1.05107 + 0.606835i
\(612\) 0 0
\(613\) −15.5000 + 26.8468i −0.626039 + 1.08433i 0.362300 + 0.932062i \(0.381992\pi\)
−0.988339 + 0.152270i \(0.951342\pi\)
\(614\) 0 0
\(615\) −10.3923 −0.419058
\(616\) 0 0
\(617\) 20.0000 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(618\) 0 0
\(619\) −7.79423 + 13.5000i −0.313276 + 0.542611i −0.979070 0.203526i \(-0.934760\pi\)
0.665793 + 0.746136i \(0.268093\pi\)
\(620\) 0 0
\(621\) −4.50000 + 2.59808i −0.180579 + 0.104257i
\(622\) 0 0
\(623\) −7.79423 + 40.5000i −0.312269 + 1.62260i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) 7.79423 + 4.50000i 0.311272 + 0.179713i
\(628\) 0 0
\(629\) 5.19615i 0.207184i
\(630\) 0 0
\(631\) 30.0000i 1.19428i 0.802137 + 0.597141i \(0.203697\pi\)
−0.802137 + 0.597141i \(0.796303\pi\)
\(632\) 0 0
\(633\) 15.0000 + 8.66025i 0.596196 + 0.344214i
\(634\) 0 0
\(635\) 5.19615 + 9.00000i 0.206203 + 0.357154i
\(636\) 0 0
\(637\) 24.0000 3.46410i 0.950915 0.137253i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6.50000 11.2583i 0.256735 0.444677i −0.708631 0.705580i \(-0.750687\pi\)
0.965365 + 0.260902i \(0.0840201\pi\)
\(642\) 0 0
\(643\) −13.8564 −0.546443 −0.273222 0.961951i \(-0.588089\pi\)
−0.273222 + 0.961951i \(0.588089\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) −16.4545 + 28.5000i −0.646892 + 1.12045i 0.336968 + 0.941516i \(0.390598\pi\)
−0.983861 + 0.178935i \(0.942735\pi\)
\(648\) 0 0
\(649\) −4.50000 + 2.59808i −0.176640 + 0.101983i
\(650\) 0 0
\(651\) 7.79423 + 1.50000i 0.305480 + 0.0587896i
\(652\) 0 0
\(653\) 15.5000 + 26.8468i 0.606562 + 1.05060i 0.991803 + 0.127780i \(0.0407851\pi\)
−0.385241 + 0.922816i \(0.625882\pi\)
\(654\) 0 0
\(655\) −7.79423 4.50000i −0.304546 0.175830i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 38.0000i 1.48027i 0.672458 + 0.740135i \(0.265238\pi\)
−0.672458 + 0.740135i \(0.734762\pi\)
\(660\) 0 0
\(661\) 34.5000 + 19.9186i 1.34189 + 0.774743i 0.987085 0.160196i \(-0.0512125\pi\)
0.354809 + 0.934939i \(0.384546\pi\)
\(662\) 0 0
\(663\) 5.19615 + 9.00000i 0.201802 + 0.349531i
\(664\) 0 0
\(665\) −22.5000 + 7.79423i −0.872513 + 0.302247i
\(666\) 0 0
\(667\) −3.46410 + 2.00000i −0.134131 + 0.0774403i
\(668\) 0 0
\(669\) 6.00000 10.3923i 0.231973 0.401790i
\(670\) 0 0
\(671\) −5.19615 −0.200595
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) 5.19615 9.00000i 0.200000 0.346410i
\(676\) 0 0
\(677\) 37.5000 21.6506i 1.44124 0.832102i 0.443309 0.896369i \(-0.353804\pi\)
0.997933 + 0.0642672i \(0.0204710\pi\)
\(678\) 0 0
\(679\) −34.6410 30.0000i −1.32940 1.15129i
\(680\) 0 0
\(681\) −16.5000 28.5788i −0.632281 1.09514i
\(682\) 0 0
\(683\) −21.6506 12.5000i −0.828439 0.478299i 0.0248792 0.999690i \(-0.492080\pi\)
−0.853318 + 0.521391i \(0.825413\pi\)
\(684\) 0 0
\(685\) 1.73205i 0.0661783i
\(686\) 0 0
\(687\) 27.0000i 1.03011i
\(688\) 0 0
\(689\) −3.00000 1.73205i −0.114291 0.0659859i
\(690\) 0 0
\(691\) −6.06218 10.5000i −0.230616 0.399439i 0.727373 0.686242i \(-0.240741\pi\)
−0.957990 + 0.286803i \(0.907407\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10.3923 + 6.00000i −0.394203 + 0.227593i
\(696\) 0 0
\(697\) 3.00000 5.19615i 0.113633 0.196818i
\(698\) 0 0
\(699\) −12.1244 −0.458585
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) −7.79423 + 13.5000i −0.293965 + 0.509162i
\(704\) 0 0
\(705\) −22.5000 + 12.9904i −0.847399 + 0.489246i
\(706\) 0 0
\(707\) −21.6506 + 7.50000i −0.814256 + 0.282067i
\(708\) 0 0
\(709\) −4.50000 7.79423i −0.169001 0.292718i 0.769068 0.639167i \(-0.220721\pi\)
−0.938069 + 0.346449i \(0.887387\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.73205i 0.0648658i
\(714\) 0 0
\(715\) 6.00000i 0.224387i
\(716\) 0 0
\(717\) −30.0000 17.3205i −1.12037 0.646846i
\(718\) 0 0
\(719\) 12.9904 + 22.5000i 0.484459 + 0.839108i 0.999841 0.0178527i \(-0.00568298\pi\)
−0.515381 + 0.856961i \(0.672350\pi\)
\(720\) 0 0
\(721\) 22.5000 + 4.33013i 0.837944 + 0.161262i
\(722\) 0 0
\(723\) 7.79423 4.50000i 0.289870 0.167357i
\(724\) 0 0
\(725\) 4.00000 6.92820i 0.148556 0.257307i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −1.73205 + 3.00000i −0.0640622 + 0.110959i
\(732\) 0 0
\(733\) −37.5000 + 21.6506i −1.38509 + 0.799684i −0.992757 0.120137i \(-0.961667\pi\)
−0.392337 + 0.919822i \(0.628333\pi\)
\(734\) 0 0
\(735\) 20.7846 3.00000i 0.766652 0.110657i
\(736\) 0 0
\(737\) 1.50000 + 2.59808i 0.0552532 + 0.0957014i
\(738\) 0 0
\(739\) 44.1673 + 25.5000i 1.62472 + 0.938033i 0.985634 + 0.168898i \(0.0540208\pi\)
0.639087 + 0.769135i \(0.279313\pi\)
\(740\) 0 0
\(741\) 31.1769i 1.14531i
\(742\) 0 0
\(743\) 34.0000i 1.24734i −0.781688 0.623670i \(-0.785641\pi\)
0.781688 0.623670i \(-0.214359\pi\)
\(744\) 0 0
\(745\) 1.50000 + 0.866025i 0.0549557 + 0.0317287i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.50000 + 33.7750i −0.237505 + 1.23411i
\(750\) 0 0
\(751\) −21.6506 + 12.5000i −0.790043 + 0.456131i −0.839978 0.542621i \(-0.817432\pi\)
0.0499348 + 0.998752i \(0.484099\pi\)
\(752\) 0 0
\(753\) 3.00000 5.19615i 0.109326 0.189358i
\(754\) 0 0
\(755\) −12.1244 −0.441250
\(756\) 0 0
\(757\) 48.0000 1.74459 0.872295 0.488980i \(-0.162631\pi\)
0.872295 + 0.488980i \(0.162631\pi\)
\(758\) 0 0
\(759\) 0.866025 1.50000i 0.0314347 0.0544466i
\(760\) 0 0
\(761\) 16.5000 9.52628i 0.598125 0.345327i −0.170179 0.985413i \(-0.554435\pi\)
0.768303 + 0.640086i \(0.221101\pi\)
\(762\) 0 0
\(763\) 7.79423 + 22.5000i 0.282170 + 0.814555i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15.5885 + 9.00000i 0.562867 + 0.324971i
\(768\) 0 0
\(769\) 3.46410i 0.124919i 0.998048 + 0.0624593i \(0.0198944\pi\)
−0.998048 + 0.0624593i \(0.980106\pi\)
\(770\) 0 0
\(771\) 9.00000i 0.324127i
\(772\) 0 0
\(773\) −22.5000 12.9904i −0.809269 0.467232i 0.0374331 0.999299i \(-0.488082\pi\)
−0.846702 + 0.532068i \(0.821415\pi\)
\(774\) 0 0
\(775\) −1.73205 3.00000i −0.0622171 0.107763i
\(776\) 0 0
\(777\) 9.00000 10.3923i 0.322873 0.372822i
\(778\) 0 0
\(779\) −15.5885 + 9.00000i −0.558514 + 0.322458i
\(780\) 0 0
\(781\) −7.00000 + 12.1244i −0.250480 + 0.433844i
\(782\) 0 0
\(783\) 20.7846 0.742781
\(784\) 0 0
\(785\) −3.00000 −0.107075
\(786\) 0 0
\(787\) 2.59808 4.50000i 0.0926114 0.160408i −0.815998 0.578055i \(-0.803812\pi\)
0.908609 + 0.417647i \(0.137145\pi\)
\(788\) 0 0
\(789\) −34.5000 + 19.9186i −1.22823 + 0.709120i
\(790\) 0 0
\(791\) 27.7128 32.0000i 0.985354 1.13779i
\(792\) 0 0
\(793\) 9.00000 + 15.5885i 0.319599 + 0.553562i
\(794\) 0 0
\(795\) −2.59808 1.50000i −0.0921443 0.0531995i
\(796\) 0 0