Properties

Label 1568.2.i.n.1537.1
Level $1568$
Weight $2$
Character 1568.1537
Analytic conductor $12.521$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.5205430369\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 224)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1537.1
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 1568.1537
Dual form 1568.2.i.n.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.61803 + 2.80252i) q^{3} +(-0.618034 - 1.07047i) q^{5} +(-3.73607 - 6.47106i) q^{9} +O(q^{10})\) \(q+(-1.61803 + 2.80252i) q^{3} +(-0.618034 - 1.07047i) q^{5} +(-3.73607 - 6.47106i) q^{9} +(-1.23607 + 2.14093i) q^{11} -5.23607 q^{13} +4.00000 q^{15} +(-2.23607 + 3.87298i) q^{17} +(1.61803 + 2.80252i) q^{19} +(-2.00000 - 3.46410i) q^{23} +(1.73607 - 3.00696i) q^{25} +14.4721 q^{27} +4.47214 q^{29} +(3.23607 - 5.60503i) q^{31} +(-4.00000 - 6.92820i) q^{33} +(-2.23607 - 3.87298i) q^{37} +(8.47214 - 14.6742i) q^{39} -0.472136 q^{41} -2.47214 q^{43} +(-4.61803 + 7.99867i) q^{45} +(0.763932 + 1.32317i) q^{47} +(-7.23607 - 12.5332i) q^{51} +(5.00000 - 8.66025i) q^{53} +3.05573 q^{55} -10.4721 q^{57} +(-2.38197 + 4.12569i) q^{59} +(3.38197 + 5.85774i) q^{61} +(3.23607 + 5.60503i) q^{65} +(-2.00000 + 3.46410i) q^{67} +12.9443 q^{69} +12.9443 q^{71} +(7.47214 - 12.9421i) q^{73} +(5.61803 + 9.73072i) q^{75} +(2.47214 + 4.28187i) q^{79} +(-12.2082 + 21.1452i) q^{81} +4.76393 q^{83} +5.52786 q^{85} +(-7.23607 + 12.5332i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(10.4721 + 18.1383i) q^{93} +(2.00000 - 3.46410i) q^{95} -3.52786 q^{97} +18.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{5} - 6q^{9} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{5} - 6q^{9} + 4q^{11} - 12q^{13} + 16q^{15} + 2q^{19} - 8q^{23} - 2q^{25} + 40q^{27} + 4q^{31} - 16q^{33} + 16q^{39} + 16q^{41} + 8q^{43} - 14q^{45} + 12q^{47} - 20q^{51} + 20q^{53} + 48q^{55} - 24q^{57} - 14q^{59} + 18q^{61} + 4q^{65} - 8q^{67} + 16q^{69} + 16q^{71} + 12q^{73} + 18q^{75} - 8q^{79} - 22q^{81} + 28q^{83} + 40q^{85} - 20q^{87} - 12q^{89} + 24q^{93} + 8q^{95} - 32q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(1471\) \(1473\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.61803 + 2.80252i −0.934172 + 1.61803i −0.158069 + 0.987428i \(0.550527\pi\)
−0.776103 + 0.630606i \(0.782806\pi\)
\(4\) 0 0
\(5\) −0.618034 1.07047i −0.276393 0.478727i 0.694092 0.719886i \(-0.255806\pi\)
−0.970486 + 0.241159i \(0.922473\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −3.73607 6.47106i −1.24536 2.15702i
\(10\) 0 0
\(11\) −1.23607 + 2.14093i −0.372689 + 0.645515i −0.989978 0.141221i \(-0.954897\pi\)
0.617290 + 0.786736i \(0.288231\pi\)
\(12\) 0 0
\(13\) −5.23607 −1.45222 −0.726112 0.687576i \(-0.758675\pi\)
−0.726112 + 0.687576i \(0.758675\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) 0 0
\(17\) −2.23607 + 3.87298i −0.542326 + 0.939336i 0.456444 + 0.889752i \(0.349123\pi\)
−0.998770 + 0.0495842i \(0.984210\pi\)
\(18\) 0 0
\(19\) 1.61803 + 2.80252i 0.371202 + 0.642942i 0.989751 0.142805i \(-0.0456123\pi\)
−0.618548 + 0.785747i \(0.712279\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0 0
\(25\) 1.73607 3.00696i 0.347214 0.601392i
\(26\) 0 0
\(27\) 14.4721 2.78516
\(28\) 0 0
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) 0 0
\(31\) 3.23607 5.60503i 0.581215 1.00669i −0.414121 0.910222i \(-0.635911\pi\)
0.995336 0.0964719i \(-0.0307558\pi\)
\(32\) 0 0
\(33\) −4.00000 6.92820i −0.696311 1.20605i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.23607 3.87298i −0.367607 0.636715i 0.621584 0.783348i \(-0.286490\pi\)
−0.989191 + 0.146633i \(0.953156\pi\)
\(38\) 0 0
\(39\) 8.47214 14.6742i 1.35663 2.34975i
\(40\) 0 0
\(41\) −0.472136 −0.0737352 −0.0368676 0.999320i \(-0.511738\pi\)
−0.0368676 + 0.999320i \(0.511738\pi\)
\(42\) 0 0
\(43\) −2.47214 −0.376997 −0.188499 0.982073i \(-0.560362\pi\)
−0.188499 + 0.982073i \(0.560362\pi\)
\(44\) 0 0
\(45\) −4.61803 + 7.99867i −0.688416 + 1.19237i
\(46\) 0 0
\(47\) 0.763932 + 1.32317i 0.111431 + 0.193004i 0.916347 0.400384i \(-0.131123\pi\)
−0.804916 + 0.593388i \(0.797790\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −7.23607 12.5332i −1.01325 1.75500i
\(52\) 0 0
\(53\) 5.00000 8.66025i 0.686803 1.18958i −0.286064 0.958211i \(-0.592347\pi\)
0.972867 0.231367i \(-0.0743197\pi\)
\(54\) 0 0
\(55\) 3.05573 0.412034
\(56\) 0 0
\(57\) −10.4721 −1.38707
\(58\) 0 0
\(59\) −2.38197 + 4.12569i −0.310106 + 0.537119i −0.978385 0.206792i \(-0.933698\pi\)
0.668279 + 0.743910i \(0.267031\pi\)
\(60\) 0 0
\(61\) 3.38197 + 5.85774i 0.433016 + 0.750006i 0.997131 0.0756898i \(-0.0241159\pi\)
−0.564115 + 0.825696i \(0.690783\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.23607 + 5.60503i 0.401385 + 0.695219i
\(66\) 0 0
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 0 0
\(69\) 12.9443 1.55831
\(70\) 0 0
\(71\) 12.9443 1.53620 0.768101 0.640328i \(-0.221202\pi\)
0.768101 + 0.640328i \(0.221202\pi\)
\(72\) 0 0
\(73\) 7.47214 12.9421i 0.874547 1.51476i 0.0173032 0.999850i \(-0.494492\pi\)
0.857244 0.514910i \(-0.172175\pi\)
\(74\) 0 0
\(75\) 5.61803 + 9.73072i 0.648715 + 1.12361i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.47214 + 4.28187i 0.278137 + 0.481747i 0.970922 0.239397i \(-0.0769497\pi\)
−0.692785 + 0.721144i \(0.743616\pi\)
\(80\) 0 0
\(81\) −12.2082 + 21.1452i −1.35647 + 2.34947i
\(82\) 0 0
\(83\) 4.76393 0.522909 0.261455 0.965216i \(-0.415798\pi\)
0.261455 + 0.965216i \(0.415798\pi\)
\(84\) 0 0
\(85\) 5.52786 0.599581
\(86\) 0 0
\(87\) −7.23607 + 12.5332i −0.775788 + 1.34370i
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 10.4721 + 18.1383i 1.08591 + 1.88085i
\(94\) 0 0
\(95\) 2.00000 3.46410i 0.205196 0.355409i
\(96\) 0 0
\(97\) −3.52786 −0.358200 −0.179100 0.983831i \(-0.557319\pi\)
−0.179100 + 0.983831i \(0.557319\pi\)
\(98\) 0 0
\(99\) 18.4721 1.85652
\(100\) 0 0
\(101\) 5.85410 10.1396i 0.582505 1.00893i −0.412677 0.910878i \(-0.635406\pi\)
0.995181 0.0980505i \(-0.0312607\pi\)
\(102\) 0 0
\(103\) −7.23607 12.5332i −0.712991 1.23494i −0.963729 0.266882i \(-0.914007\pi\)
0.250738 0.968055i \(-0.419327\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.47214 + 7.74597i 0.432338 + 0.748831i 0.997074 0.0764405i \(-0.0243555\pi\)
−0.564736 + 0.825271i \(0.691022\pi\)
\(108\) 0 0
\(109\) 0.236068 0.408882i 0.0226112 0.0391638i −0.854498 0.519454i \(-0.826135\pi\)
0.877110 + 0.480290i \(0.159469\pi\)
\(110\) 0 0
\(111\) 14.4721 1.37363
\(112\) 0 0
\(113\) −3.52786 −0.331874 −0.165937 0.986136i \(-0.553065\pi\)
−0.165937 + 0.986136i \(0.553065\pi\)
\(114\) 0 0
\(115\) −2.47214 + 4.28187i −0.230528 + 0.399286i
\(116\) 0 0
\(117\) 19.5623 + 33.8829i 1.80854 + 3.13248i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 2.44427 + 4.23360i 0.222207 + 0.384873i
\(122\) 0 0
\(123\) 0.763932 1.32317i 0.0688814 0.119306i
\(124\) 0 0
\(125\) −10.4721 −0.936656
\(126\) 0 0
\(127\) −8.94427 −0.793676 −0.396838 0.917889i \(-0.629892\pi\)
−0.396838 + 0.917889i \(0.629892\pi\)
\(128\) 0 0
\(129\) 4.00000 6.92820i 0.352180 0.609994i
\(130\) 0 0
\(131\) −0.854102 1.47935i −0.0746232 0.129251i 0.826299 0.563232i \(-0.190442\pi\)
−0.900922 + 0.433980i \(0.857109\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −8.94427 15.4919i −0.769800 1.33333i
\(136\) 0 0
\(137\) 1.47214 2.54981i 0.125773 0.217845i −0.796262 0.604952i \(-0.793192\pi\)
0.922035 + 0.387107i \(0.126526\pi\)
\(138\) 0 0
\(139\) 3.23607 0.274480 0.137240 0.990538i \(-0.456177\pi\)
0.137240 + 0.990538i \(0.456177\pi\)
\(140\) 0 0
\(141\) −4.94427 −0.416383
\(142\) 0 0
\(143\) 6.47214 11.2101i 0.541227 0.937433i
\(144\) 0 0
\(145\) −2.76393 4.78727i −0.229532 0.397561i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.47214 + 12.9421i 0.612141 + 1.06026i 0.990879 + 0.134756i \(0.0430249\pi\)
−0.378738 + 0.925504i \(0.623642\pi\)
\(150\) 0 0
\(151\) −4.47214 + 7.74597i −0.363937 + 0.630358i −0.988605 0.150533i \(-0.951901\pi\)
0.624668 + 0.780891i \(0.285234\pi\)
\(152\) 0 0
\(153\) 33.4164 2.70156
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) 2.61803 4.53457i 0.208942 0.361898i −0.742440 0.669913i \(-0.766331\pi\)
0.951381 + 0.308015i \(0.0996647\pi\)
\(158\) 0 0
\(159\) 16.1803 + 28.0252i 1.28318 + 2.22254i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −11.7082 20.2792i −0.917057 1.58839i −0.803861 0.594817i \(-0.797224\pi\)
−0.113196 0.993573i \(-0.536109\pi\)
\(164\) 0 0
\(165\) −4.94427 + 8.56373i −0.384911 + 0.666685i
\(166\) 0 0
\(167\) 3.41641 0.264370 0.132185 0.991225i \(-0.457801\pi\)
0.132185 + 0.991225i \(0.457801\pi\)
\(168\) 0 0
\(169\) 14.4164 1.10895
\(170\) 0 0
\(171\) 12.0902 20.9408i 0.924558 1.60138i
\(172\) 0 0
\(173\) −3.85410 6.67550i −0.293022 0.507529i 0.681501 0.731817i \(-0.261328\pi\)
−0.974523 + 0.224288i \(0.927994\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.70820 13.3510i −0.579384 1.00352i
\(178\) 0 0
\(179\) 12.4721 21.6024i 0.932211 1.61464i 0.152678 0.988276i \(-0.451210\pi\)
0.779533 0.626361i \(-0.215456\pi\)
\(180\) 0 0
\(181\) −10.1803 −0.756699 −0.378349 0.925663i \(-0.623508\pi\)
−0.378349 + 0.925663i \(0.623508\pi\)
\(182\) 0 0
\(183\) −21.8885 −1.61805
\(184\) 0 0
\(185\) −2.76393 + 4.78727i −0.203208 + 0.351967i
\(186\) 0 0
\(187\) −5.52786 9.57454i −0.404237 0.700160i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.47214 + 11.2101i 0.468307 + 0.811132i 0.999344 0.0362168i \(-0.0115307\pi\)
−0.531037 + 0.847349i \(0.678197\pi\)
\(192\) 0 0
\(193\) 4.23607 7.33708i 0.304919 0.528135i −0.672324 0.740257i \(-0.734704\pi\)
0.977243 + 0.212122i \(0.0680373\pi\)
\(194\) 0 0
\(195\) −20.9443 −1.49985
\(196\) 0 0
\(197\) −6.94427 −0.494759 −0.247379 0.968919i \(-0.579569\pi\)
−0.247379 + 0.968919i \(0.579569\pi\)
\(198\) 0 0
\(199\) −5.70820 + 9.88690i −0.404644 + 0.700864i −0.994280 0.106805i \(-0.965938\pi\)
0.589636 + 0.807669i \(0.299271\pi\)
\(200\) 0 0
\(201\) −6.47214 11.2101i −0.456509 0.790697i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.291796 + 0.505406i 0.0203799 + 0.0352991i
\(206\) 0 0
\(207\) −14.9443 + 25.8842i −1.03870 + 1.79908i
\(208\) 0 0
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) −20.9443 + 36.2765i −1.43508 + 2.48563i
\(214\) 0 0
\(215\) 1.52786 + 2.64634i 0.104199 + 0.180479i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 24.1803 + 41.8816i 1.63396 + 2.83009i
\(220\) 0 0
\(221\) 11.7082 20.2792i 0.787579 1.36413i
\(222\) 0 0
\(223\) 4.94427 0.331093 0.165546 0.986202i \(-0.447061\pi\)
0.165546 + 0.986202i \(0.447061\pi\)
\(224\) 0 0
\(225\) −25.9443 −1.72962
\(226\) 0 0
\(227\) −6.38197 + 11.0539i −0.423586 + 0.733672i −0.996287 0.0860918i \(-0.972562\pi\)
0.572701 + 0.819764i \(0.305896\pi\)
\(228\) 0 0
\(229\) −12.7984 22.1674i −0.845740 1.46487i −0.884977 0.465635i \(-0.845826\pi\)
0.0392364 0.999230i \(-0.487507\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.94427 17.2240i −0.651471 1.12838i −0.982766 0.184854i \(-0.940819\pi\)
0.331295 0.943527i \(-0.392514\pi\)
\(234\) 0 0
\(235\) 0.944272 1.63553i 0.0615975 0.106690i
\(236\) 0 0
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) 21.8885 1.41585 0.707926 0.706287i \(-0.249631\pi\)
0.707926 + 0.706287i \(0.249631\pi\)
\(240\) 0 0
\(241\) 1.76393 3.05522i 0.113625 0.196804i −0.803604 0.595164i \(-0.797087\pi\)
0.917229 + 0.398360i \(0.130420\pi\)
\(242\) 0 0
\(243\) −17.7984 30.8277i −1.14177 1.97760i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −8.47214 14.6742i −0.539069 0.933695i
\(248\) 0 0
\(249\) −7.70820 + 13.3510i −0.488488 + 0.846085i
\(250\) 0 0
\(251\) −17.7082 −1.11773 −0.558866 0.829258i \(-0.688763\pi\)
−0.558866 + 0.829258i \(0.688763\pi\)
\(252\) 0 0
\(253\) 9.88854 0.621687
\(254\) 0 0
\(255\) −8.94427 + 15.4919i −0.560112 + 0.970143i
\(256\) 0 0
\(257\) −7.00000 12.1244i −0.436648 0.756297i 0.560781 0.827964i \(-0.310501\pi\)
−0.997429 + 0.0716680i \(0.977168\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −16.7082 28.9395i −1.03421 1.79131i
\(262\) 0 0
\(263\) −14.4721 + 25.0665i −0.892390 + 1.54567i −0.0553884 + 0.998465i \(0.517640\pi\)
−0.837002 + 0.547200i \(0.815694\pi\)
\(264\) 0 0
\(265\) −12.3607 −0.759311
\(266\) 0 0
\(267\) 19.4164 1.18826
\(268\) 0 0
\(269\) 9.09017 15.7446i 0.554237 0.959967i −0.443725 0.896163i \(-0.646343\pi\)
0.997962 0.0638044i \(-0.0203234\pi\)
\(270\) 0 0
\(271\) −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i \(-0.906676\pi\)
0.228380 0.973572i \(-0.426657\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.29180 + 7.43361i 0.258805 + 0.448263i
\(276\) 0 0
\(277\) 13.9443 24.1522i 0.837830 1.45116i −0.0538751 0.998548i \(-0.517157\pi\)
0.891705 0.452617i \(-0.149509\pi\)
\(278\) 0 0
\(279\) −48.3607 −2.89528
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 0 0
\(283\) 8.09017 14.0126i 0.480911 0.832962i −0.518849 0.854866i \(-0.673639\pi\)
0.999760 + 0.0219039i \(0.00697279\pi\)
\(284\) 0 0
\(285\) 6.47214 + 11.2101i 0.383376 + 0.664027i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.50000 2.59808i −0.0882353 0.152828i
\(290\) 0 0
\(291\) 5.70820 9.88690i 0.334621 0.579580i
\(292\) 0 0
\(293\) 17.2361 1.00694 0.503471 0.864012i \(-0.332056\pi\)
0.503471 + 0.864012i \(0.332056\pi\)
\(294\) 0 0
\(295\) 5.88854 0.342844
\(296\) 0 0
\(297\) −17.8885 + 30.9839i −1.03800 + 1.79787i
\(298\) 0 0
\(299\) 10.4721 + 18.1383i 0.605619 + 1.04896i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 18.9443 + 32.8124i 1.08832 + 1.88503i
\(304\) 0 0
\(305\) 4.18034 7.24056i 0.239366 0.414593i
\(306\) 0 0
\(307\) −24.1803 −1.38004 −0.690022 0.723788i \(-0.742399\pi\)
−0.690022 + 0.723788i \(0.742399\pi\)
\(308\) 0 0
\(309\) 46.8328 2.66423
\(310\) 0 0
\(311\) 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i \(-0.760501\pi\)
0.956864 + 0.290537i \(0.0938340\pi\)
\(312\) 0 0
\(313\) 0.236068 + 0.408882i 0.0133434 + 0.0231114i 0.872620 0.488400i \(-0.162419\pi\)
−0.859277 + 0.511511i \(0.829086\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.4721 23.3344i −0.756671 1.31059i −0.944540 0.328398i \(-0.893491\pi\)
0.187869 0.982194i \(-0.439842\pi\)
\(318\) 0 0
\(319\) −5.52786 + 9.57454i −0.309501 + 0.536071i
\(320\) 0 0
\(321\) −28.9443 −1.61551
\(322\) 0 0
\(323\) −14.4721 −0.805251
\(324\) 0 0
\(325\) −9.09017 + 15.7446i −0.504232 + 0.873355i
\(326\) 0 0
\(327\) 0.763932 + 1.32317i 0.0422455 + 0.0731714i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6.76393 11.7155i −0.371779 0.643941i 0.618060 0.786131i \(-0.287919\pi\)
−0.989839 + 0.142190i \(0.954586\pi\)
\(332\) 0 0
\(333\) −16.7082 + 28.9395i −0.915604 + 1.58587i
\(334\) 0 0
\(335\) 4.94427 0.270134
\(336\) 0 0
\(337\) −34.3607 −1.87175 −0.935873 0.352338i \(-0.885387\pi\)
−0.935873 + 0.352338i \(0.885387\pi\)
\(338\) 0 0
\(339\) 5.70820 9.88690i 0.310027 0.536983i
\(340\) 0 0
\(341\) 8.00000 + 13.8564i 0.433224 + 0.750366i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −8.00000 13.8564i −0.430706 0.746004i
\(346\) 0 0
\(347\) 1.23607 2.14093i 0.0663556 0.114931i −0.830939 0.556364i \(-0.812196\pi\)
0.897295 + 0.441432i \(0.145529\pi\)
\(348\) 0 0
\(349\) 4.65248 0.249041 0.124521 0.992217i \(-0.460261\pi\)
0.124521 + 0.992217i \(0.460261\pi\)
\(350\) 0 0
\(351\) −75.7771 −4.04468
\(352\) 0 0
\(353\) 9.94427 17.2240i 0.529280 0.916740i −0.470137 0.882594i \(-0.655795\pi\)
0.999417 0.0341465i \(-0.0108713\pi\)
\(354\) 0 0
\(355\) −8.00000 13.8564i −0.424596 0.735422i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.472136 0.817763i −0.0249184 0.0431599i 0.853297 0.521425i \(-0.174599\pi\)
−0.878216 + 0.478265i \(0.841266\pi\)
\(360\) 0 0
\(361\) 4.26393 7.38535i 0.224417 0.388702i
\(362\) 0 0
\(363\) −15.8197 −0.830317
\(364\) 0 0
\(365\) −18.4721 −0.966876
\(366\) 0 0
\(367\) 15.4164 26.7020i 0.804730 1.39383i −0.111743 0.993737i \(-0.535643\pi\)
0.916473 0.400096i \(-0.131023\pi\)
\(368\) 0 0
\(369\) 1.76393 + 3.05522i 0.0918266 + 0.159048i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 7.47214 + 12.9421i 0.386893 + 0.670118i 0.992030 0.126004i \(-0.0402151\pi\)
−0.605137 + 0.796121i \(0.706882\pi\)
\(374\) 0 0
\(375\) 16.9443 29.3483i 0.874998 1.51554i
\(376\) 0 0
\(377\) −23.4164 −1.20601
\(378\) 0 0
\(379\) −31.4164 −1.61375 −0.806876 0.590721i \(-0.798844\pi\)
−0.806876 + 0.590721i \(0.798844\pi\)
\(380\) 0 0
\(381\) 14.4721 25.0665i 0.741430 1.28419i
\(382\) 0 0
\(383\) 5.70820 + 9.88690i 0.291676 + 0.505197i 0.974206 0.225660i \(-0.0724539\pi\)
−0.682530 + 0.730857i \(0.739121\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 9.23607 + 15.9973i 0.469496 + 0.813190i
\(388\) 0 0
\(389\) −2.23607 + 3.87298i −0.113373 + 0.196368i −0.917128 0.398592i \(-0.869499\pi\)
0.803755 + 0.594960i \(0.202832\pi\)
\(390\) 0 0
\(391\) 17.8885 0.904663
\(392\) 0 0
\(393\) 5.52786 0.278844
\(394\) 0 0
\(395\) 3.05573 5.29268i 0.153750 0.266303i
\(396\) 0 0
\(397\) −5.38197 9.32184i −0.270113 0.467850i 0.698777 0.715339i \(-0.253728\pi\)
−0.968891 + 0.247489i \(0.920394\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.2361 + 28.1217i 0.810791 + 1.40433i 0.912311 + 0.409497i \(0.134296\pi\)
−0.101521 + 0.994833i \(0.532371\pi\)
\(402\) 0 0
\(403\) −16.9443 + 29.3483i −0.844054 + 1.46194i
\(404\) 0 0
\(405\) 30.1803 1.49967
\(406\) 0 0
\(407\) 11.0557 0.548012
\(408\) 0 0
\(409\) 2.70820 4.69075i 0.133912 0.231943i −0.791269 0.611468i \(-0.790579\pi\)
0.925181 + 0.379525i \(0.123913\pi\)
\(410\) 0 0
\(411\) 4.76393 + 8.25137i 0.234987 + 0.407010i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −2.94427 5.09963i −0.144529 0.250331i
\(416\) 0 0
\(417\) −5.23607 + 9.06914i −0.256411 + 0.444117i
\(418\) 0 0
\(419\) 0.180340 0.00881018 0.00440509 0.999990i \(-0.498598\pi\)
0.00440509 + 0.999990i \(0.498598\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 0 0
\(423\) 5.70820 9.88690i 0.277542 0.480717i
\(424\) 0 0
\(425\) 7.76393 + 13.4475i 0.376606 + 0.652301i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 20.9443 + 36.2765i 1.01120 + 1.75145i
\(430\) 0 0
\(431\) 14.0000 24.2487i 0.674356 1.16802i −0.302300 0.953213i \(-0.597755\pi\)
0.976657 0.214807i \(-0.0689121\pi\)
\(432\) 0 0
\(433\) 17.4164 0.836979 0.418490 0.908222i \(-0.362560\pi\)
0.418490 + 0.908222i \(0.362560\pi\)
\(434\) 0 0
\(435\) 17.8885 0.857690
\(436\) 0 0
\(437\) 6.47214 11.2101i 0.309604 0.536250i
\(438\) 0 0
\(439\) −16.0000 27.7128i −0.763638 1.32266i −0.940963 0.338508i \(-0.890078\pi\)
0.177325 0.984152i \(-0.443256\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.9443 18.9560i −0.519978 0.900628i −0.999730 0.0232244i \(-0.992607\pi\)
0.479752 0.877404i \(-0.340727\pi\)
\(444\) 0 0
\(445\) −3.70820 + 6.42280i −0.175786 + 0.304470i
\(446\) 0 0
\(447\) −48.3607 −2.28738
\(448\) 0 0
\(449\) 27.8885 1.31614 0.658071 0.752956i \(-0.271373\pi\)
0.658071 + 0.752956i \(0.271373\pi\)
\(450\) 0 0
\(451\) 0.583592 1.01081i 0.0274803 0.0475972i
\(452\) 0 0
\(453\) −14.4721 25.0665i −0.679960 1.17773i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.23607 + 14.2653i 0.385267 + 0.667302i 0.991806 0.127752i \(-0.0407760\pi\)
−0.606539 + 0.795054i \(0.707443\pi\)
\(458\) 0 0
\(459\) −32.3607 + 56.0503i −1.51047 + 2.61621i
\(460\) 0 0
\(461\) −8.29180 −0.386187 −0.193094 0.981180i \(-0.561852\pi\)
−0.193094 + 0.981180i \(0.561852\pi\)
\(462\) 0 0
\(463\) 35.7771 1.66270 0.831351 0.555748i \(-0.187568\pi\)
0.831351 + 0.555748i \(0.187568\pi\)
\(464\) 0 0
\(465\) 12.9443 22.4201i 0.600276 1.03971i
\(466\) 0 0
\(467\) 13.0344 + 22.5763i 0.603162 + 1.04471i 0.992339 + 0.123544i \(0.0394261\pi\)
−0.389177 + 0.921163i \(0.627241\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 8.47214 + 14.6742i 0.390375 + 0.676150i
\(472\) 0 0
\(473\) 3.05573 5.29268i 0.140503 0.243358i
\(474\) 0 0
\(475\) 11.2361 0.515546
\(476\) 0 0
\(477\) −74.7214 −3.42126
\(478\) 0 0
\(479\) −17.7082 + 30.6715i −0.809108 + 1.40142i 0.104374 + 0.994538i \(0.466716\pi\)
−0.913482 + 0.406879i \(0.866617\pi\)
\(480\) 0 0
\(481\) 11.7082 + 20.2792i 0.533848 + 0.924652i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.18034 + 3.77646i 0.0990041 + 0.171480i
\(486\) 0 0
\(487\) −10.0000 + 17.3205i −0.453143 + 0.784867i −0.998579 0.0532853i \(-0.983031\pi\)
0.545436 + 0.838152i \(0.316364\pi\)
\(488\) 0 0
\(489\) 75.7771 3.42676
\(490\) 0 0
\(491\) 2.11146 0.0952887 0.0476443 0.998864i \(-0.484829\pi\)
0.0476443 + 0.998864i \(0.484829\pi\)
\(492\) 0 0
\(493\) −10.0000 + 17.3205i −0.450377 + 0.780076i
\(494\) 0 0
\(495\) −11.4164 19.7738i −0.513129 0.888766i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 6.94427 + 12.0278i 0.310868 + 0.538440i 0.978551 0.206007i \(-0.0660469\pi\)
−0.667682 + 0.744446i \(0.732714\pi\)
\(500\) 0 0
\(501\) −5.52786 + 9.57454i −0.246967 + 0.427759i
\(502\) 0 0
\(503\) −12.9443 −0.577157 −0.288578 0.957456i \(-0.593183\pi\)
−0.288578 + 0.957456i \(0.593183\pi\)
\(504\) 0 0
\(505\) −14.4721 −0.644002
\(506\) 0 0
\(507\) −23.3262 + 40.4022i −1.03595 + 1.79433i
\(508\) 0 0
\(509\) −0.437694 0.758108i −0.0194004 0.0336026i 0.856162 0.516707i \(-0.172842\pi\)
−0.875563 + 0.483105i \(0.839509\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 23.4164 + 40.5584i 1.03386 + 1.79070i
\(514\) 0 0
\(515\) −8.94427 + 15.4919i −0.394132 + 0.682656i
\(516\) 0 0
\(517\) −3.77709 −0.166116
\(518\) 0 0
\(519\) 24.9443 1.09493
\(520\) 0 0
\(521\) −16.7082 + 28.9395i −0.732000 + 1.26786i 0.224028 + 0.974583i \(0.428079\pi\)
−0.956027 + 0.293278i \(0.905254\pi\)
\(522\) 0 0
\(523\) −8.85410 15.3358i −0.387163 0.670586i 0.604904 0.796299i \(-0.293212\pi\)
−0.992067 + 0.125713i \(0.959878\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.4721 + 25.0665i 0.630416 + 1.09191i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 35.5967 1.54477
\(532\) 0 0
\(533\) 2.47214 0.107080
\(534\) 0 0
\(535\) 5.52786 9.57454i 0.238990 0.413944i
\(536\) 0 0
\(537\) 40.3607 + 69.9067i 1.74169 + 3.01670i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 11.4721 + 19.8703i 0.493226 + 0.854292i 0.999970 0.00780476i \(-0.00248436\pi\)
−0.506744 + 0.862097i \(0.669151\pi\)
\(542\) 0 0
\(543\) 16.4721 28.5306i 0.706887 1.22436i
\(544\) 0 0
\(545\) −0.583592 −0.0249983
\(546\) 0 0
\(547\) −31.4164 −1.34327 −0.671634 0.740883i \(-0.734407\pi\)
−0.671634 + 0.740883i \(0.734407\pi\)
\(548\) 0 0
\(549\) 25.2705 43.7698i 1.07852 1.86805i
\(550\) 0 0
\(551\) 7.23607 + 12.5332i 0.308267 + 0.533934i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −8.94427 15.4919i −0.379663 0.657596i
\(556\) 0 0
\(557\) −13.4721 + 23.3344i −0.570833 + 0.988711i 0.425648 + 0.904889i \(0.360046\pi\)
−0.996481 + 0.0838224i \(0.973287\pi\)
\(558\) 0 0
\(559\) 12.9443 0.547484
\(560\) 0 0
\(561\) 35.7771 1.51051
\(562\) 0 0
\(563\) −20.0902 + 34.7972i −0.846700 + 1.46653i 0.0374372 + 0.999299i \(0.488081\pi\)
−0.884137 + 0.467228i \(0.845253\pi\)
\(564\) 0 0
\(565\) 2.18034 + 3.77646i 0.0917276 + 0.158877i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.18034 + 15.9008i 0.384860 + 0.666597i 0.991750 0.128189i \(-0.0409164\pi\)
−0.606890 + 0.794786i \(0.707583\pi\)
\(570\) 0 0
\(571\) 2.76393 4.78727i 0.115667 0.200341i −0.802379 0.596815i \(-0.796433\pi\)
0.918046 + 0.396474i \(0.129766\pi\)
\(572\) 0 0
\(573\) −41.8885 −1.74992
\(574\) 0 0
\(575\) −13.8885 −0.579192
\(576\) 0 0
\(577\) −3.00000 + 5.19615i −0.124892 + 0.216319i −0.921691 0.387926i \(-0.873192\pi\)
0.796799 + 0.604245i \(0.206525\pi\)
\(578\) 0 0
\(579\) 13.7082 + 23.7433i 0.569694 + 0.986738i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 12.3607 + 21.4093i 0.511927 + 0.886684i
\(584\) 0 0
\(585\) 24.1803 41.8816i 0.999734 1.73159i
\(586\) 0 0
\(587\) −9.70820 −0.400700 −0.200350 0.979724i \(-0.564208\pi\)
−0.200350 + 0.979724i \(0.564208\pi\)
\(588\) 0 0
\(589\) 20.9443 0.862994
\(590\) 0 0
\(591\) 11.2361 19.4614i 0.462190 0.800537i
\(592\) 0 0
\(593\) −10.4164 18.0417i −0.427751 0.740886i 0.568922 0.822391i \(-0.307361\pi\)
−0.996673 + 0.0815055i \(0.974027\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −18.4721 31.9947i −0.756014 1.30945i
\(598\) 0 0
\(599\) 8.94427 15.4919i 0.365453 0.632983i −0.623396 0.781907i \(-0.714247\pi\)
0.988849 + 0.148923i \(0.0475807\pi\)
\(600\) 0 0
\(601\) 41.7771 1.70412 0.852061 0.523442i \(-0.175352\pi\)
0.852061 + 0.523442i \(0.175352\pi\)
\(602\) 0 0
\(603\) 29.8885 1.21716
\(604\) 0 0
\(605\) 3.02129 5.23302i 0.122833 0.212753i
\(606\) 0 0
\(607\) −12.9443 22.4201i −0.525392 0.910005i −0.999563 0.0295724i \(-0.990585\pi\)
0.474171 0.880433i \(-0.342748\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.00000 6.92820i −0.161823 0.280285i
\(612\) 0 0
\(613\) −1.29180 + 2.23746i −0.0521752 + 0.0903700i −0.890933 0.454134i \(-0.849949\pi\)
0.838758 + 0.544504i \(0.183282\pi\)
\(614\) 0 0
\(615\) −1.88854 −0.0761534
\(616\) 0 0
\(617\) −10.3607 −0.417105 −0.208553 0.978011i \(-0.566875\pi\)
−0.208553 + 0.978011i \(0.566875\pi\)
\(618\) 0 0
\(619\) 5.03444 8.71991i 0.202351 0.350483i −0.746934 0.664898i \(-0.768475\pi\)
0.949286 + 0.314415i \(0.101808\pi\)
\(620\) 0 0
\(621\) −28.9443 50.1329i −1.16149 2.01177i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −2.20820 3.82472i −0.0883282 0.152989i
\(626\) 0 0
\(627\) 12.9443 22.4201i 0.516944 0.895374i
\(628\) 0 0
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) −27.0557 −1.07707 −0.538536 0.842603i \(-0.681022\pi\)
−0.538536 + 0.842603i \(0.681022\pi\)
\(632\) 0 0
\(633\) 19.4164 33.6302i 0.771733 1.33668i
\(634\) 0 0
\(635\) 5.52786 + 9.57454i 0.219367 + 0.379954i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −48.3607 83.7632i −1.91312 3.31362i
\(640\) 0 0
\(641\) −20.7082 + 35.8677i −0.817925 + 1.41669i 0.0892837 + 0.996006i \(0.471542\pi\)
−0.907209 + 0.420681i \(0.861791\pi\)
\(642\) 0 0
\(643\) 30.2918 1.19459 0.597296 0.802021i \(-0.296242\pi\)
0.597296 + 0.802021i \(0.296242\pi\)
\(644\) 0 0
\(645\) −9.88854 −0.389361
\(646\) 0 0
\(647\) 12.1803 21.0970i 0.478859 0.829407i −0.520848 0.853650i \(-0.674384\pi\)
0.999706 + 0.0242423i \(0.00771733\pi\)
\(648\) 0 0
\(649\) −5.88854 10.1993i −0.231146 0.400356i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.70820 15.0831i −0.340778 0.590245i 0.643799 0.765195i \(-0.277357\pi\)
−0.984577 + 0.174949i \(0.944024\pi\)
\(654\) 0 0
\(655\) −1.05573 + 1.82857i −0.0412507 + 0.0714483i
\(656\) 0 0
\(657\) −111.666 −4.35649
\(658\) 0 0
\(659\) −25.3050 −0.985741 −0.492870 0.870103i \(-0.664052\pi\)
−0.492870 + 0.870103i \(0.664052\pi\)
\(660\) 0 0
\(661\) 4.32624 7.49326i 0.168271 0.291454i −0.769541 0.638597i \(-0.779515\pi\)
0.937812 + 0.347143i \(0.112848\pi\)
\(662\) 0 0
\(663\) 37.8885 + 65.6249i 1.47147 + 2.54866i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.94427 15.4919i −0.346324 0.599850i
\(668\) 0 0
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) 0 0
\(671\) −16.7214 −0.645521
\(672\) 0 0
\(673\) 14.9443 0.576059 0.288030 0.957621i \(-0.407000\pi\)
0.288030 + 0.957621i \(0.407000\pi\)
\(674\) 0 0
\(675\) 25.1246 43.5171i 0.967047 1.67497i
\(676\) 0 0
\(677\) 21.0902 + 36.5292i 0.810561 + 1.40393i 0.912472 + 0.409139i \(0.134171\pi\)
−0.101911 + 0.994794i \(0.532496\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −20.6525 35.7711i −0.791405 1.37075i
\(682\) 0 0
\(683\) 23.8885 41.3762i 0.914070 1.58322i 0.105812 0.994386i \(-0.466256\pi\)
0.808258 0.588829i \(-0.200411\pi\)
\(684\) 0 0
\(685\) −3.63932 −0.139051
\(686\) 0 0
\(687\) 82.8328 3.16027
\(688\) 0 0
\(689\) −26.1803 + 45.3457i −0.997392 + 1.72753i
\(690\) 0 0
\(691\) 4.09017 + 7.08438i 0.155597 + 0.269503i 0.933276 0.359159i \(-0.116936\pi\)
−0.777679 + 0.628662i \(0.783603\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.00000 3.46410i −0.0758643 0.131401i
\(696\) 0 0
\(697\) 1.05573 1.82857i 0.0399886 0.0692622i
\(698\) 0 0
\(699\) 64.3607 2.43434
\(700\) 0 0
\(701\) −14.5836 −0.550815 −0.275407 0.961328i \(-0.588813\pi\)
−0.275407 + 0.961328i \(0.588813\pi\)
\(702\) 0 0
\(703\) 7.23607 12.5332i 0.272913 0.472700i
\(704\) 0 0
\(705\) 3.05573 + 5.29268i 0.115085 + 0.199334i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −23.1803 40.1495i −0.870556 1.50785i −0.861423 0.507889i \(-0.830426\pi\)
−0.00913331 0.999958i \(-0.502907\pi\)
\(710\) 0 0
\(711\) 18.4721 31.9947i 0.692759 1.19989i
\(712\) 0 0
\(713\) −25.8885 −0.969534
\(714\) 0 0
\(715\) −16.0000 −0.598366
\(716\) 0 0
\(717\) −35.4164 + 61.3430i −1.32265 + 2.29090i
\(718\) 0 0
\(719\) −23.5967 40.8708i −0.880010 1.52422i −0.851328 0.524634i \(-0.824202\pi\)
−0.0286822 0.999589i \(-0.509131\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 5.70820 + 9.88690i 0.212290 + 0.367698i
\(724\) 0 0
\(725\) 7.76393 13.4475i 0.288345 0.499429i
\(726\) 0 0
\(727\) 32.3607 1.20019 0.600096 0.799928i \(-0.295129\pi\)
0.600096 + 0.799928i \(0.295129\pi\)
\(728\) 0 0
\(729\) 41.9443 1.55349
\(730\) 0 0
\(731\) 5.52786 9.57454i 0.204455 0.354127i
\(732\) 0 0
\(733\) −4.61803 7.99867i −0.170571 0.295438i 0.768049 0.640391i \(-0.221228\pi\)
−0.938620 + 0.344954i \(0.887895\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.94427 8.56373i −0.182125 0.315449i
\(738\) 0 0
\(739\) −11.7082 + 20.2792i −0.430693 + 0.745983i −0.996933 0.0782579i \(-0.975064\pi\)
0.566240 + 0.824240i \(0.308398\pi\)
\(740\) 0 0
\(741\) 54.8328 2.01433
\(742\) 0 0
\(743\) 7.05573 0.258850 0.129425 0.991589i \(-0.458687\pi\)
0.129425 + 0.991589i \(0.458687\pi\)
\(744\) 0 0
\(745\) 9.23607 15.9973i 0.338383 0.586097i
\(746\) 0 0
\(747\) −17.7984 30.8277i −0.651208 1.12793i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −18.0000 31.1769i −0.656829 1.13766i −0.981432 0.191811i \(-0.938564\pi\)
0.324603 0.945851i \(-0.394769\pi\)
\(752\) 0 0
\(753\) 28.6525 49.6275i 1.04415 1.80853i
\(754\) 0 0
\(755\) 11.0557 0.402359
\(756\) 0 0
\(757\) −23.3050 −0.847033 −0.423516 0.905888i \(-0.639204\pi\)
−0.423516 + 0.905888i \(0.639204\pi\)
\(758\) 0 0
\(759\) −16.0000 + 27.7128i −0.580763 + 1.00591i
\(760\) 0 0
\(761\) −6.23607 10.8012i −0.226057 0.391543i 0.730579 0.682828i \(-0.239250\pi\)
−0.956636 + 0.291286i \(0.905917\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −20.6525 35.7711i −0.746692 1.29331i
\(766\) 0 0
\(767\) 12.4721 21.6024i 0.450343 0.780016i
\(768\) 0 0
\(769\) −26.3607 −0.950590 −0.475295 0.879826i \(-0.657659\pi\)
−0.475295 + 0.879826i \(0.657659\pi\)
\(770\) 0 0
\(771\) 45.3050 1.63162
\(772\) 0 0
\(773\) 8.90983 15.4323i 0.320464 0.555060i −0.660120 0.751161i \(-0.729494\pi\)
0.980584 + 0.196100i \(0.0628277\pi\)
\(774\) 0 0
\(775\) −11.2361 19.4614i −0.403611 0.699076i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.763932 1.32317i −0.0273707 0.0474075i
\(780\) 0 0
\(781\) −16.0000 + 27.7128i −0.572525 + 0.991642i
\(782\) 0 0
\(783\) 64.7214 2.31295
\(784\) 0 0
\(785\) −6.47214 −0.231000
\(786\) 0 0
\(787\) −12.8541 + 22.2640i −0.458199 + 0.793624i −0.998866 0.0476126i \(-0.984839\pi\)
0.540667 + 0.841237i \(0.318172\pi\)
\(788\) 0 0
\(789\) −46.8328 81.1168i −1.66729 2.88784i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −17.7082 30.6715i −0.628837 1.08918i
\(794\) 0 0
\(795\) 20.0000 34.6410i 0.709327 1.22859i
\(796\) 0 0
\(797\) 29.8197 1.05627 0.528133 0.849161i \(-0.322892\pi\)
0.528133 + 0.849161i \(0.322892\pi\)
\(798\) 0 0
\(799\) −6.83282 −0.241728