Properties

Label 768.2.o.b.95.7
Level 768
Weight 2
Character 768.95
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 95.7
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0499748 + 1.73133i) q^{3} +(1.06973 - 0.443098i) q^{5} +(2.37247 + 2.37247i) q^{7} +(-2.99501 - 0.173046i) q^{9} +O(q^{10})\) \(q+(-0.0499748 + 1.73133i) q^{3} +(1.06973 - 0.443098i) q^{5} +(2.37247 + 2.37247i) q^{7} +(-2.99501 - 0.173046i) q^{9} +(-5.50127 + 2.27870i) q^{11} +(-0.346353 + 0.836171i) q^{13} +(0.713689 + 1.87421i) q^{15} -0.685064 q^{17} +(3.35074 + 1.38792i) q^{19} +(-4.22609 + 3.98896i) q^{21} +(2.05133 + 2.05133i) q^{23} +(-2.58754 + 2.58754i) q^{25} +(0.449274 - 5.17669i) q^{27} +(1.98869 - 4.80112i) q^{29} +6.36503i q^{31} +(-3.67025 - 9.63838i) q^{33} +(3.58914 + 1.48667i) q^{35} +(-0.112738 - 0.272172i) q^{37} +(-1.43038 - 0.641440i) q^{39} +(-3.26585 + 3.26585i) q^{41} +(0.993018 + 2.39736i) q^{43} +(-3.28053 + 1.14197i) q^{45} -11.7975i q^{47} +4.25719i q^{49} +(0.0342360 - 1.18607i) q^{51} +(1.56192 + 3.77080i) q^{53} +(-4.87520 + 4.87520i) q^{55} +(-2.57040 + 5.73187i) q^{57} +(2.20815 + 5.33094i) q^{59} +(1.53549 + 0.636020i) q^{61} +(-6.69500 - 7.51609i) q^{63} +1.04795i q^{65} +(-4.69605 + 11.3373i) q^{67} +(-3.65405 + 3.44902i) q^{69} +(-7.99150 + 7.99150i) q^{71} +(-2.34760 - 2.34760i) q^{73} +(-4.35057 - 4.60920i) q^{75} +(-18.4577 - 7.64543i) q^{77} +8.91043 q^{79} +(8.94011 + 1.03655i) q^{81} +(3.06920 - 7.40970i) q^{83} +(-0.732836 + 0.303551i) q^{85} +(8.21294 + 3.68301i) q^{87} +(-1.99332 - 1.99332i) q^{89} +(-2.80550 + 1.16208i) q^{91} +(-11.0200 - 0.318091i) q^{93} +4.19938 q^{95} +8.66510 q^{97} +(16.8706 - 5.87274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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
\(3\) −0.0499748 + 1.73133i −0.0288530 + 0.999584i
\(4\) 0 0
\(5\) 1.06973 0.443098i 0.478400 0.198160i −0.130435 0.991457i \(-0.541637\pi\)
0.608834 + 0.793297i \(0.291637\pi\)
\(6\) 0 0
\(7\) 2.37247 + 2.37247i 0.896708 + 0.896708i 0.995143 0.0984354i \(-0.0313838\pi\)
−0.0984354 + 0.995143i \(0.531384\pi\)
\(8\) 0 0
\(9\) −2.99501 0.173046i −0.998335 0.0576820i
\(10\) 0 0
\(11\) −5.50127 + 2.27870i −1.65869 + 0.687054i −0.997977 0.0635809i \(-0.979748\pi\)
−0.660718 + 0.750635i \(0.729748\pi\)
\(12\) 0 0
\(13\) −0.346353 + 0.836171i −0.0960612 + 0.231912i −0.964604 0.263701i \(-0.915057\pi\)
0.868543 + 0.495613i \(0.165057\pi\)
\(14\) 0 0
\(15\) 0.713689 + 1.87421i 0.184274 + 0.483918i
\(16\) 0 0
\(17\) −0.685064 −0.166152 −0.0830762 0.996543i \(-0.526474\pi\)
−0.0830762 + 0.996543i \(0.526474\pi\)
\(18\) 0 0
\(19\) 3.35074 + 1.38792i 0.768712 + 0.318411i 0.732351 0.680928i \(-0.238423\pi\)
0.0363614 + 0.999339i \(0.488423\pi\)
\(20\) 0 0
\(21\) −4.22609 + 3.98896i −0.922207 + 0.870462i
\(22\) 0 0
\(23\) 2.05133 + 2.05133i 0.427732 + 0.427732i 0.887855 0.460123i \(-0.152195\pi\)
−0.460123 + 0.887855i \(0.652195\pi\)
\(24\) 0 0
\(25\) −2.58754 + 2.58754i −0.517508 + 0.517508i
\(26\) 0 0
\(27\) 0.449274 5.17669i 0.0864629 0.996255i
\(28\) 0 0
\(29\) 1.98869 4.80112i 0.369291 0.891546i −0.624576 0.780964i \(-0.714728\pi\)
0.993867 0.110582i \(-0.0352716\pi\)
\(30\) 0 0
\(31\) 6.36503i 1.14319i 0.820535 + 0.571596i \(0.193676\pi\)
−0.820535 + 0.571596i \(0.806324\pi\)
\(32\) 0 0
\(33\) −3.67025 9.63838i −0.638909 1.67783i
\(34\) 0 0
\(35\) 3.58914 + 1.48667i 0.606676 + 0.251293i
\(36\) 0 0
\(37\) −0.112738 0.272172i −0.0185339 0.0447449i 0.914342 0.404944i \(-0.132709\pi\)
−0.932876 + 0.360199i \(0.882709\pi\)
\(38\) 0 0
\(39\) −1.43038 0.641440i −0.229044 0.102713i
\(40\) 0 0
\(41\) −3.26585 + 3.26585i −0.510040 + 0.510040i −0.914539 0.404499i \(-0.867446\pi\)
0.404499 + 0.914539i \(0.367446\pi\)
\(42\) 0 0
\(43\) 0.993018 + 2.39736i 0.151434 + 0.365594i 0.981332 0.192321i \(-0.0616016\pi\)
−0.829898 + 0.557915i \(0.811602\pi\)
\(44\) 0 0
\(45\) −3.28053 + 1.14197i −0.489033 + 0.170235i
\(46\) 0 0
\(47\) 11.7975i 1.72084i −0.509589 0.860418i \(-0.670203\pi\)
0.509589 0.860418i \(-0.329797\pi\)
\(48\) 0 0
\(49\) 4.25719i 0.608171i
\(50\) 0 0
\(51\) 0.0342360 1.18607i 0.00479399 0.166083i
\(52\) 0 0
\(53\) 1.56192 + 3.77080i 0.214546 + 0.517959i 0.994112 0.108361i \(-0.0345602\pi\)
−0.779566 + 0.626320i \(0.784560\pi\)
\(54\) 0 0
\(55\) −4.87520 + 4.87520i −0.657372 + 0.657372i
\(56\) 0 0
\(57\) −2.57040 + 5.73187i −0.340458 + 0.759205i
\(58\) 0 0
\(59\) 2.20815 + 5.33094i 0.287476 + 0.694029i 0.999971 0.00764882i \(-0.00243472\pi\)
−0.712495 + 0.701678i \(0.752435\pi\)
\(60\) 0 0
\(61\) 1.53549 + 0.636020i 0.196599 + 0.0814341i 0.478811 0.877918i \(-0.341068\pi\)
−0.282212 + 0.959352i \(0.591068\pi\)
\(62\) 0 0
\(63\) −6.69500 7.51609i −0.843491 0.946939i
\(64\) 0 0
\(65\) 1.04795i 0.129982i
\(66\) 0 0
\(67\) −4.69605 + 11.3373i −0.573714 + 1.38507i 0.324657 + 0.945832i \(0.394751\pi\)
−0.898371 + 0.439237i \(0.855249\pi\)
\(68\) 0 0
\(69\) −3.65405 + 3.44902i −0.439895 + 0.415213i
\(70\) 0 0
\(71\) −7.99150 + 7.99150i −0.948416 + 0.948416i −0.998733 0.0503173i \(-0.983977\pi\)
0.0503173 + 0.998733i \(0.483977\pi\)
\(72\) 0 0
\(73\) −2.34760 2.34760i −0.274766 0.274766i 0.556250 0.831015i \(-0.312240\pi\)
−0.831015 + 0.556250i \(0.812240\pi\)
\(74\) 0 0
\(75\) −4.35057 4.60920i −0.502361 0.532224i
\(76\) 0 0
\(77\) −18.4577 7.64543i −2.10345 0.871278i
\(78\) 0 0
\(79\) 8.91043 1.00250 0.501251 0.865302i \(-0.332873\pi\)
0.501251 + 0.865302i \(0.332873\pi\)
\(80\) 0 0
\(81\) 8.94011 + 1.03655i 0.993346 + 0.115172i
\(82\) 0 0
\(83\) 3.06920 7.40970i 0.336888 0.813320i −0.661123 0.750278i \(-0.729920\pi\)
0.998011 0.0630420i \(-0.0200802\pi\)
\(84\) 0 0
\(85\) −0.732836 + 0.303551i −0.0794872 + 0.0329247i
\(86\) 0 0
\(87\) 8.21294 + 3.68301i 0.880520 + 0.394861i
\(88\) 0 0
\(89\) −1.99332 1.99332i −0.211291 0.211291i 0.593525 0.804816i \(-0.297736\pi\)
−0.804816 + 0.593525i \(0.797736\pi\)
\(90\) 0 0
\(91\) −2.80550 + 1.16208i −0.294096 + 0.121819i
\(92\) 0 0
\(93\) −11.0200 0.318091i −1.14272 0.0329845i
\(94\) 0 0
\(95\) 4.19938 0.430848
\(96\) 0 0
\(97\) 8.66510 0.879807 0.439904 0.898045i \(-0.355013\pi\)
0.439904 + 0.898045i \(0.355013\pi\)
\(98\) 0 0
\(99\) 16.8706 5.87274i 1.69556 0.590233i
\(100\) 0 0
\(101\) 15.6920 6.49983i 1.56141 0.646758i 0.576077 0.817395i \(-0.304583\pi\)
0.985334 + 0.170637i \(0.0545827\pi\)
\(102\) 0 0
\(103\) −5.39788 5.39788i −0.531869 0.531869i 0.389259 0.921128i \(-0.372731\pi\)
−0.921128 + 0.389259i \(0.872731\pi\)
\(104\) 0 0
\(105\) −2.75329 + 6.13969i −0.268693 + 0.599173i
\(106\) 0 0
\(107\) −0.0169596 + 0.00702491i −0.00163955 + 0.000679124i −0.383503 0.923540i \(-0.625282\pi\)
0.381864 + 0.924219i \(0.375282\pi\)
\(108\) 0 0
\(109\) 4.94357 11.9348i 0.473508 1.14315i −0.489094 0.872231i \(-0.662672\pi\)
0.962602 0.270919i \(-0.0873276\pi\)
\(110\) 0 0
\(111\) 0.476854 0.181584i 0.0452610 0.0172352i
\(112\) 0 0
\(113\) 10.4984 0.987609 0.493804 0.869573i \(-0.335606\pi\)
0.493804 + 0.869573i \(0.335606\pi\)
\(114\) 0 0
\(115\) 3.10332 + 1.28544i 0.289386 + 0.119868i
\(116\) 0 0
\(117\) 1.18203 2.44440i 0.109278 0.225985i
\(118\) 0 0
\(119\) −1.62529 1.62529i −0.148990 0.148990i
\(120\) 0 0
\(121\) 17.2933 17.2933i 1.57212 1.57212i
\(122\) 0 0
\(123\) −5.49105 5.81747i −0.495112 0.524544i
\(124\) 0 0
\(125\) −3.83694 + 9.26318i −0.343186 + 0.828524i
\(126\) 0 0
\(127\) 0.793212i 0.0703862i −0.999381 0.0351931i \(-0.988795\pi\)
0.999381 0.0351931i \(-0.0112046\pi\)
\(128\) 0 0
\(129\) −4.20024 + 1.59943i −0.369811 + 0.140822i
\(130\) 0 0
\(131\) −9.39267 3.89057i −0.820641 0.339921i −0.0674502 0.997723i \(-0.521486\pi\)
−0.753191 + 0.657802i \(0.771486\pi\)
\(132\) 0 0
\(133\) 4.65672 + 11.2423i 0.403789 + 0.974832i
\(134\) 0 0
\(135\) −1.81318 5.73676i −0.156054 0.493741i
\(136\) 0 0
\(137\) 2.95969 2.95969i 0.252863 0.252863i −0.569280 0.822144i \(-0.692778\pi\)
0.822144 + 0.569280i \(0.192778\pi\)
\(138\) 0 0
\(139\) 1.91155 + 4.61488i 0.162135 + 0.391429i 0.983979 0.178284i \(-0.0570545\pi\)
−0.821844 + 0.569713i \(0.807054\pi\)
\(140\) 0 0
\(141\) 20.4253 + 0.589576i 1.72012 + 0.0496512i
\(142\) 0 0
\(143\) 5.38924i 0.450671i
\(144\) 0 0
\(145\) 6.01711i 0.499694i
\(146\) 0 0
\(147\) −7.37061 0.212753i −0.607917 0.0175475i
\(148\) 0 0
\(149\) 5.53451 + 13.3615i 0.453405 + 1.09462i 0.971019 + 0.239002i \(0.0768202\pi\)
−0.517614 + 0.855614i \(0.673180\pi\)
\(150\) 0 0
\(151\) 2.96063 2.96063i 0.240932 0.240932i −0.576303 0.817236i \(-0.695505\pi\)
0.817236 + 0.576303i \(0.195505\pi\)
\(152\) 0 0
\(153\) 2.05177 + 0.118548i 0.165876 + 0.00958400i
\(154\) 0 0
\(155\) 2.82033 + 6.80889i 0.226535 + 0.546903i
\(156\) 0 0
\(157\) 16.1213 + 6.67768i 1.28662 + 0.532937i 0.917977 0.396633i \(-0.129822\pi\)
0.368646 + 0.929570i \(0.379822\pi\)
\(158\) 0 0
\(159\) −6.60656 + 2.51575i −0.523934 + 0.199512i
\(160\) 0 0
\(161\) 9.73343i 0.767102i
\(162\) 0 0
\(163\) 4.62172 11.1578i 0.362001 0.873949i −0.633006 0.774147i \(-0.718179\pi\)
0.995007 0.0998018i \(-0.0318209\pi\)
\(164\) 0 0
\(165\) −8.19695 8.68422i −0.638131 0.676066i
\(166\) 0 0
\(167\) −1.28603 + 1.28603i −0.0995157 + 0.0995157i −0.755112 0.655596i \(-0.772417\pi\)
0.655596 + 0.755112i \(0.272417\pi\)
\(168\) 0 0
\(169\) 8.61317 + 8.61317i 0.662551 + 0.662551i
\(170\) 0 0
\(171\) −9.79530 4.73666i −0.749065 0.362222i
\(172\) 0 0
\(173\) −0.0565964 0.0234430i −0.00430295 0.00178234i 0.380531 0.924768i \(-0.375741\pi\)
−0.384834 + 0.922986i \(0.625741\pi\)
\(174\) 0 0
\(175\) −12.2777 −0.928107
\(176\) 0 0
\(177\) −9.33996 + 3.55662i −0.702034 + 0.267332i
\(178\) 0 0
\(179\) −1.17461 + 2.83576i −0.0877946 + 0.211955i −0.961678 0.274180i \(-0.911594\pi\)
0.873884 + 0.486135i \(0.161594\pi\)
\(180\) 0 0
\(181\) 20.8334 8.62949i 1.54854 0.641425i 0.565485 0.824758i \(-0.308689\pi\)
0.983051 + 0.183334i \(0.0586889\pi\)
\(182\) 0 0
\(183\) −1.17790 + 2.62665i −0.0870726 + 0.194168i
\(184\) 0 0
\(185\) −0.241198 0.241198i −0.0177333 0.0177333i
\(186\) 0 0
\(187\) 3.76872 1.56105i 0.275596 0.114156i
\(188\) 0 0
\(189\) 13.3474 11.2156i 0.970882 0.815818i
\(190\) 0 0
\(191\) 23.0566 1.66832 0.834158 0.551525i \(-0.185954\pi\)
0.834158 + 0.551525i \(0.185954\pi\)
\(192\) 0 0
\(193\) 7.52832 0.541900 0.270950 0.962593i \(-0.412662\pi\)
0.270950 + 0.962593i \(0.412662\pi\)
\(194\) 0 0
\(195\) −1.81435 0.0523711i −0.129928 0.00375037i
\(196\) 0 0
\(197\) −2.14750 + 0.889524i −0.153003 + 0.0633760i −0.457871 0.889019i \(-0.651388\pi\)
0.304868 + 0.952395i \(0.401388\pi\)
\(198\) 0 0
\(199\) 7.46994 + 7.46994i 0.529530 + 0.529530i 0.920432 0.390902i \(-0.127837\pi\)
−0.390902 + 0.920432i \(0.627837\pi\)
\(200\) 0 0
\(201\) −19.3939 8.69699i −1.36794 0.613439i
\(202\) 0 0
\(203\) 16.1086 6.67240i 1.13060 0.468311i
\(204\) 0 0
\(205\) −2.04650 + 4.94068i −0.142934 + 0.345072i
\(206\) 0 0
\(207\) −5.78877 6.49872i −0.402348 0.451692i
\(208\) 0 0
\(209\) −21.5960 −1.49382
\(210\) 0 0
\(211\) −15.9819 6.61994i −1.10024 0.455735i −0.242676 0.970107i \(-0.578025\pi\)
−0.857567 + 0.514372i \(0.828025\pi\)
\(212\) 0 0
\(213\) −13.4365 14.2353i −0.920657 0.975386i
\(214\) 0 0
\(215\) 2.12453 + 2.12453i 0.144892 + 0.144892i
\(216\) 0 0
\(217\) −15.1008 + 15.1008i −1.02511 + 1.02511i
\(218\) 0 0
\(219\) 4.18179 3.94715i 0.282579 0.266723i
\(220\) 0 0
\(221\) 0.237274 0.572831i 0.0159608 0.0385328i
\(222\) 0 0
\(223\) 18.2244i 1.22040i −0.792248 0.610199i \(-0.791090\pi\)
0.792248 0.610199i \(-0.208910\pi\)
\(224\) 0 0
\(225\) 8.19746 7.30193i 0.546497 0.486795i
\(226\) 0 0
\(227\) −10.8455 4.49234i −0.719840 0.298167i −0.00747022 0.999972i \(-0.502378\pi\)
−0.712369 + 0.701805i \(0.752378\pi\)
\(228\) 0 0
\(229\) −5.20986 12.5777i −0.344277 0.831159i −0.997273 0.0737978i \(-0.976488\pi\)
0.652996 0.757362i \(-0.273512\pi\)
\(230\) 0 0
\(231\) 14.1592 31.5743i 0.931606 2.07744i
\(232\) 0 0
\(233\) 11.7233 11.7233i 0.768016 0.768016i −0.209741 0.977757i \(-0.567262\pi\)
0.977757 + 0.209741i \(0.0672620\pi\)
\(234\) 0 0
\(235\) −5.22743 12.6201i −0.341000 0.823247i
\(236\) 0 0
\(237\) −0.445297 + 15.4269i −0.0289252 + 1.00208i
\(238\) 0 0
\(239\) 21.5949i 1.39685i 0.715681 + 0.698427i \(0.246117\pi\)
−0.715681 + 0.698427i \(0.753883\pi\)
\(240\) 0 0
\(241\) 14.6095i 0.941078i −0.882379 0.470539i \(-0.844059\pi\)
0.882379 0.470539i \(-0.155941\pi\)
\(242\) 0 0
\(243\) −2.24138 + 15.4265i −0.143785 + 0.989609i
\(244\) 0 0
\(245\) 1.88636 + 4.55406i 0.120515 + 0.290949i
\(246\) 0 0
\(247\) −2.32108 + 2.32108i −0.147687 + 0.147687i
\(248\) 0 0
\(249\) 12.6752 + 5.68409i 0.803261 + 0.360215i
\(250\) 0 0
\(251\) −1.08581 2.62137i −0.0685355 0.165459i 0.885900 0.463876i \(-0.153542\pi\)
−0.954436 + 0.298416i \(0.903542\pi\)
\(252\) 0 0
\(253\) −15.9593 6.61055i −1.00335 0.415602i
\(254\) 0 0
\(255\) −0.488923 1.28395i −0.0306175 0.0804041i
\(256\) 0 0
\(257\) 1.35436i 0.0844827i 0.999107 + 0.0422414i \(0.0134498\pi\)
−0.999107 + 0.0422414i \(0.986550\pi\)
\(258\) 0 0
\(259\) 0.378254 0.913186i 0.0235036 0.0567426i
\(260\) 0 0
\(261\) −6.78695 + 14.0353i −0.420102 + 0.868760i
\(262\) 0 0
\(263\) −3.52372 + 3.52372i −0.217282 + 0.217282i −0.807352 0.590070i \(-0.799100\pi\)
0.590070 + 0.807352i \(0.299100\pi\)
\(264\) 0 0
\(265\) 3.34167 + 3.34167i 0.205277 + 0.205277i
\(266\) 0 0
\(267\) 3.55070 3.35147i 0.217299 0.205107i
\(268\) 0 0
\(269\) 16.4741 + 6.82380i 1.00444 + 0.416055i 0.823425 0.567425i \(-0.192060\pi\)
0.181020 + 0.983479i \(0.442060\pi\)
\(270\) 0 0
\(271\) −8.50293 −0.516516 −0.258258 0.966076i \(-0.583149\pi\)
−0.258258 + 0.966076i \(0.583149\pi\)
\(272\) 0 0
\(273\) −1.87173 4.91532i −0.113282 0.297489i
\(274\) 0 0
\(275\) 8.33852 20.1310i 0.502832 1.21394i
\(276\) 0 0
\(277\) −20.2028 + 8.36828i −1.21387 + 0.502801i −0.895456 0.445150i \(-0.853150\pi\)
−0.318414 + 0.947952i \(0.603150\pi\)
\(278\) 0 0
\(279\) 1.10144 19.0633i 0.0659416 1.14129i
\(280\) 0 0
\(281\) −10.3342 10.3342i −0.616487 0.616487i 0.328142 0.944629i \(-0.393578\pi\)
−0.944629 + 0.328142i \(0.893578\pi\)
\(282\) 0 0
\(283\) −8.67342 + 3.59265i −0.515581 + 0.213561i −0.625275 0.780405i \(-0.715013\pi\)
0.109694 + 0.993965i \(0.465013\pi\)
\(284\) 0 0
\(285\) −0.209864 + 7.27052i −0.0124312 + 0.430668i
\(286\) 0 0
\(287\) −15.4962 −0.914714
\(288\) 0 0
\(289\) −16.5307 −0.972393
\(290\) 0 0
\(291\) −0.433037 + 15.0021i −0.0253851 + 0.879441i
\(292\) 0 0
\(293\) −11.3816 + 4.71442i −0.664922 + 0.275420i −0.689508 0.724278i \(-0.742173\pi\)
0.0245862 + 0.999698i \(0.492173\pi\)
\(294\) 0 0
\(295\) 4.72426 + 4.72426i 0.275057 + 0.275057i
\(296\) 0 0
\(297\) 9.32455 + 29.5021i 0.541065 + 1.71189i
\(298\) 0 0
\(299\) −2.42575 + 1.00478i −0.140285 + 0.0581078i
\(300\) 0 0
\(301\) −3.33175 + 8.04355i −0.192039 + 0.463623i
\(302\) 0 0
\(303\) 10.4692 + 27.4928i 0.601437 + 1.57942i
\(304\) 0 0
\(305\) 1.92438 0.110190
\(306\) 0 0
\(307\) 12.6145 + 5.22511i 0.719950 + 0.298213i 0.712415 0.701759i \(-0.247601\pi\)
0.00753514 + 0.999972i \(0.497601\pi\)
\(308\) 0 0
\(309\) 9.61527 9.07575i 0.546994 0.516302i
\(310\) 0 0
\(311\) −18.8020 18.8020i −1.06617 1.06617i −0.997650 0.0685162i \(-0.978174\pi\)
−0.0685162 0.997650i \(1.47817\pi\)
\(312\) 0 0
\(313\) 4.30835 4.30835i 0.243522 0.243522i −0.574783 0.818306i \(-0.694914\pi\)
0.818306 + 0.574783i \(0.194914\pi\)
\(314\) 0 0
\(315\) −10.4922 5.07368i −0.591171 0.285869i
\(316\) 0 0
\(317\) −0.543402 + 1.31189i −0.0305205 + 0.0736830i −0.938405 0.345538i \(-0.887697\pi\)
0.907884 + 0.419221i \(0.137697\pi\)
\(318\) 0 0
\(319\) 30.9439i 1.73252i
\(320\) 0 0
\(321\) −0.0113149 0.0297138i −0.000631535 0.00165846i
\(322\) 0 0
\(323\) −2.29547 0.950815i −0.127723 0.0529047i
\(324\) 0 0
\(325\) −1.26742 3.05983i −0.0703040 0.169729i
\(326\) 0 0
\(327\) 20.4161 + 9.15540i 1.12901 + 0.506295i
\(328\) 0 0
\(329\) 27.9891 27.9891i 1.54309 1.54309i
\(330\) 0 0
\(331\) 5.18815 + 12.5253i 0.285167 + 0.688453i 0.999941 0.0109024i \(-0.00347041\pi\)
−0.714774 + 0.699356i \(0.753470\pi\)
\(332\) 0 0
\(333\) 0.290551 + 0.834667i 0.0159221 + 0.0457395i
\(334\) 0 0
\(335\) 14.2087i 0.776303i
\(336\) 0 0
\(337\) 19.9878i 1.08881i 0.838824 + 0.544403i \(0.183244\pi\)
−0.838824 + 0.544403i \(0.816756\pi\)
\(338\) 0 0
\(339\) −0.524657 + 18.1762i −0.0284955 + 0.987197i
\(340\) 0 0
\(341\) −14.5040 35.0157i −0.785435 1.89621i
\(342\) 0 0
\(343\) 6.50721 6.50721i 0.351357 0.351357i
\(344\) 0 0
\(345\) −2.38060 + 5.30863i −0.128167 + 0.285807i
\(346\) 0 0
\(347\) 5.84634 + 14.1143i 0.313848 + 0.757696i 0.999555 + 0.0298187i \(0.00949299\pi\)
−0.685707 + 0.727877i \(0.740507\pi\)
\(348\) 0 0
\(349\) −7.90170 3.27299i −0.422969 0.175199i 0.161038 0.986948i \(-0.448516\pi\)
−0.584007 + 0.811749i \(0.698516\pi\)
\(350\) 0 0
\(351\) 4.17299 + 2.16864i 0.222738 + 0.115753i
\(352\) 0 0
\(353\) 28.4566i 1.51459i 0.653072 + 0.757296i \(0.273480\pi\)
−0.653072 + 0.757296i \(0.726520\pi\)
\(354\) 0 0
\(355\) −5.00776 + 12.0898i −0.265784 + 0.641659i
\(356\) 0 0
\(357\) 2.89514 2.73269i 0.153227 0.144629i
\(358\) 0 0
\(359\) −3.48589 + 3.48589i −0.183978 + 0.183978i −0.793087 0.609109i \(-0.791527\pi\)
0.609109 + 0.793087i \(0.291527\pi\)
\(360\) 0 0
\(361\) −4.13391 4.13391i −0.217574 0.217574i
\(362\) 0 0
\(363\) 29.0762 + 30.8046i 1.52610 + 1.61682i
\(364\) 0 0
\(365\) −3.55152 1.47109i −0.185895 0.0770003i
\(366\) 0 0
\(367\) 7.37411 0.384925 0.192463 0.981304i \(-0.438353\pi\)
0.192463 + 0.981304i \(0.438353\pi\)
\(368\) 0 0
\(369\) 10.3464 9.21609i 0.538611 0.479771i
\(370\) 0 0
\(371\) −5.24050 + 12.6517i −0.272073 + 0.656843i
\(372\) 0 0
\(373\) 7.72861 3.20130i 0.400172 0.165757i −0.173515 0.984831i \(-0.555512\pi\)
0.573687 + 0.819074i \(0.305512\pi\)
\(374\) 0 0
\(375\) −15.8459 7.10593i −0.818277 0.366948i
\(376\) 0 0
\(377\) 3.32577 + 3.32577i 0.171286 + 0.171286i
\(378\) 0 0
\(379\) 22.6759 9.39268i 1.16478 0.482470i 0.285319 0.958433i \(-0.407900\pi\)
0.879465 + 0.475963i \(0.157900\pi\)
\(380\) 0 0
\(381\) 1.37331 + 0.0396406i 0.0703569 + 0.00203085i
\(382\) 0 0
\(383\) −11.3729 −0.581129 −0.290565 0.956855i \(-0.593843\pi\)
−0.290565 + 0.956855i \(0.593843\pi\)
\(384\) 0 0
\(385\) −23.1325 −1.17894
\(386\) 0 0
\(387\) −2.55924 7.35194i −0.130094 0.373720i
\(388\) 0 0
\(389\) −11.2635 + 4.66550i −0.571083 + 0.236550i −0.649489 0.760371i \(-0.725017\pi\)
0.0784059 + 0.996922i \(0.475017\pi\)
\(390\) 0 0
\(391\) −1.40529 1.40529i −0.0710687 0.0710687i
\(392\) 0 0
\(393\) 7.20526 16.0674i 0.363457 0.810492i
\(394\) 0 0
\(395\) 9.53179 3.94820i 0.479596 0.198655i
\(396\) 0 0
\(397\) −3.65241 + 8.81769i −0.183309 + 0.442547i −0.988645 0.150272i \(-0.951985\pi\)
0.805336 + 0.592819i \(0.201985\pi\)
\(398\) 0 0
\(399\) −19.6969 + 7.50048i −0.986076 + 0.375494i
\(400\) 0 0
\(401\) 5.46170 0.272744 0.136372 0.990658i \(-0.456456\pi\)
0.136372 + 0.990658i \(0.456456\pi\)
\(402\) 0 0
\(403\) −5.32225 2.20455i −0.265120 0.109816i
\(404\) 0 0
\(405\) 10.0228 2.85252i 0.498038 0.141743i
\(406\) 0 0
\(407\) 1.24040 + 1.24040i 0.0614843 + 0.0614843i
\(408\) 0 0
\(409\) −21.6474 + 21.6474i −1.07039 + 1.07039i −0.0730670 + 0.997327i \(0.523279\pi\)
−0.997327 + 0.0730670i \(0.976721\pi\)
\(410\) 0 0
\(411\) 4.97629 + 5.27211i 0.245462 + 0.260054i
\(412\) 0 0
\(413\) −7.40871 + 17.8862i −0.364559 + 0.880123i
\(414\) 0 0
\(415\) 9.28636i 0.455849i
\(416\) 0 0
\(417\) −8.08541 + 3.07889i −0.395944 + 0.150774i
\(418\) 0 0
\(419\) −16.1057 6.67119i −0.786814 0.325909i −0.0471519 0.998888i \(-0.515014\pi\)
−0.739662 + 0.672979i \(0.765014\pi\)
\(420\) 0 0
\(421\) −11.0865 26.7651i −0.540321 1.30445i −0.924497 0.381190i \(-0.875514\pi\)
0.384176 0.923260i \(-0.374486\pi\)
\(422\) 0 0
\(423\) −2.04150 + 35.3334i −0.0992612 + 1.71797i
\(424\) 0 0
\(425\) 1.77263 1.77263i 0.0859852 0.0859852i
\(426\) 0 0
\(427\) 2.13396 + 5.15183i 0.103270 + 0.249315i
\(428\) 0 0
\(429\) 9.33055 + 0.269326i 0.450483 + 0.0130032i
\(430\) 0 0
\(431\) 20.4774i 0.986361i −0.869927 0.493180i \(-0.835834\pi\)
0.869927 0.493180i \(-0.164166\pi\)
\(432\) 0 0
\(433\) 14.6756i 0.705262i 0.935762 + 0.352631i \(0.114713\pi\)
−0.935762 + 0.352631i \(0.885287\pi\)
\(434\) 0 0
\(435\) 10.4176 + 0.300704i 0.499486 + 0.0144177i
\(436\) 0 0
\(437\) 4.02639 + 9.72056i 0.192608 + 0.464997i
\(438\) 0 0
\(439\) 4.86825 4.86825i 0.232349 0.232349i −0.581324 0.813672i \(-0.697465\pi\)
0.813672 + 0.581324i \(0.197465\pi\)
\(440\) 0 0
\(441\) 0.736690 12.7503i 0.0350805 0.607158i
\(442\) 0 0
\(443\) 6.00738 + 14.5031i 0.285419 + 0.689063i 0.999944 0.0105468i \(-0.00335721\pi\)
−0.714525 + 0.699610i \(0.753357\pi\)
\(444\) 0 0
\(445\) −3.01555 1.24908i −0.142951 0.0592122i
\(446\) 0 0
\(447\) −23.4097 + 8.91432i −1.10724 + 0.421633i
\(448\) 0 0
\(449\) 1.76611i 0.0833480i 0.999131 + 0.0416740i \(0.0132691\pi\)
−0.999131 + 0.0416740i \(0.986731\pi\)
\(450\) 0 0
\(451\) 10.5244 25.4082i 0.495576 1.19643i
\(452\) 0 0
\(453\) 4.97787 + 5.27378i 0.233881 + 0.247784i
\(454\) 0 0
\(455\) −2.48622 + 2.48622i −0.116556 + 0.116556i
\(456\) 0 0
\(457\) −22.3579 22.3579i −1.04586 1.04586i −0.998897 0.0469601i \(-0.985047\pi\)
−0.0469601 0.998897i \(-0.514953\pi\)
\(458\) 0 0
\(459\) −0.307782 + 3.54637i −0.0143660 + 0.165530i
\(460\) 0 0
\(461\) −0.811938 0.336316i −0.0378157 0.0156638i 0.363695 0.931518i \(-0.381515\pi\)
−0.401511 + 0.915854i \(0.631515\pi\)
\(462\) 0 0
\(463\) 14.0009 0.650678 0.325339 0.945597i \(-0.394522\pi\)
0.325339 + 0.945597i \(0.394522\pi\)
\(464\) 0 0
\(465\) −11.9294 + 4.54265i −0.553211 + 0.210661i
\(466\) 0 0
\(467\) −5.94695 + 14.3572i −0.275192 + 0.664373i −0.999690 0.0249045i \(-0.992072\pi\)
0.724498 + 0.689277i \(0.242072\pi\)
\(468\) 0 0
\(469\) −38.0385 + 15.7561i −1.75646 + 0.727548i
\(470\) 0 0
\(471\) −12.3669 + 27.5776i −0.569838 + 1.27071i
\(472\) 0 0
\(473\) −10.9257 10.9257i −0.502365 0.502365i
\(474\) 0 0
\(475\) −12.2615 + 5.07887i −0.562595 + 0.233034i
\(476\) 0 0
\(477\) −4.02543 11.5639i −0.184312 0.529473i
\(478\) 0 0
\(479\) 34.4708 1.57501 0.787505 0.616309i \(-0.211373\pi\)
0.787505 + 0.616309i \(0.211373\pi\)
\(480\) 0 0
\(481\) 0.266630 0.0121573
\(482\) 0 0
\(483\) −16.8518 0.486427i −0.766782 0.0221332i
\(484\) 0 0
\(485\) 9.26935 3.83949i 0.420899 0.174342i
\(486\) 0 0
\(487\) −13.6710 13.6710i −0.619490 0.619490i 0.325911 0.945401i \(-0.394329\pi\)
−0.945401 + 0.325911i \(0.894329\pi\)
\(488\) 0 0
\(489\) 19.0869 + 8.55934i 0.863140 + 0.387067i
\(490\) 0 0
\(491\) 16.0034 6.62882i 0.722223 0.299154i 0.00887095 0.999961i \(-0.497176\pi\)
0.713352 + 0.700806i \(0.247176\pi\)
\(492\) 0 0
\(493\) −1.36238 + 3.28908i −0.0613585 + 0.148133i
\(494\) 0 0
\(495\) 15.4449 13.7576i 0.694196 0.618359i
\(496\) 0 0
\(497\) −37.9191 −1.70090
\(498\) 0 0
\(499\) 6.36166 + 2.63509i 0.284787 + 0.117963i 0.520504 0.853859i \(-0.325744\pi\)
−0.235717 + 0.971822i \(0.575744\pi\)
\(500\) 0 0
\(501\) −2.16227 2.29080i −0.0966029 0.102346i
\(502\) 0 0
\(503\) 16.8510 + 16.8510i 0.751350 + 0.751350i 0.974731 0.223381i \(-0.0717095\pi\)
−0.223381 + 0.974731i \(0.571709\pi\)
\(504\) 0 0
\(505\) 13.9062 13.9062i 0.618817 0.618817i
\(506\) 0 0
\(507\) −15.3427 + 14.4818i −0.681392 + 0.643159i
\(508\) 0 0
\(509\) 6.71610 16.2141i 0.297686 0.718678i −0.702291 0.711890i \(-0.747839\pi\)
0.999977 0.00678764i \(-0.00216059\pi\)
\(510\) 0 0
\(511\) 11.1392i 0.492769i
\(512\) 0 0
\(513\) 8.69024 16.7222i 0.383684 0.738302i
\(514\) 0 0
\(515\) −8.16609 3.38250i −0.359841 0.149051i
\(516\) 0 0
\(517\) 26.8828 + 64.9009i 1.18231 + 2.85434i
\(518\) 0 0
\(519\) 0.0434160 0.0968155i 0.00190575 0.00424973i
\(520\) 0 0
\(521\) −18.2126 + 18.2126i −0.797908 + 0.797908i −0.982765 0.184858i \(-0.940818\pi\)
0.184858 + 0.982765i \(0.440818\pi\)
\(522\) 0 0
\(523\) 0.472480 + 1.14067i 0.0206601 + 0.0498779i 0.933873 0.357605i \(-0.116407\pi\)
−0.913213 + 0.407483i \(0.866407\pi\)
\(524\) 0 0
\(525\) 0.613576 21.2567i 0.0267787 0.927721i
\(526\) 0 0
\(527\) 4.36045i 0.189944i
\(528\) 0 0
\(529\) 14.5841i 0.634090i
\(530\) 0 0
\(531\) −5.69091 16.3483i −0.246965 0.709455i
\(532\) 0 0
\(533\) −1.59967 3.86195i −0.0692895 0.167280i
\(534\) 0 0
\(535\) −0.0150296 + 0.0150296i −0.000649785 + 0.000649785i
\(536\) 0 0
\(537\) −4.85094 2.17536i −0.209333 0.0938735i
\(538\) 0 0
\(539\) −9.70087 23.4200i −0.417846 1.00877i
\(540\) 0 0
\(541\) −14.2297 5.89412i −0.611781 0.253408i 0.0552087 0.998475i \(-0.482418\pi\)
−0.666990 + 0.745067i \(0.732418\pi\)
\(542\) 0 0
\(543\) 13.8993 + 36.5008i 0.596478 + 1.56640i
\(544\) 0 0
\(545\) 14.9576i 0.640713i
\(546\) 0 0
\(547\) 6.24323 15.0725i 0.266941 0.644453i −0.732395 0.680880i \(-0.761598\pi\)
0.999336 + 0.0364266i \(0.0115975\pi\)
\(548\) 0 0
\(549\) −4.48874 2.17059i −0.191575 0.0926387i
\(550\) 0 0
\(551\) 13.3272 13.3272i 0.567756 0.567756i
\(552\) 0 0
\(553\) 21.1397 + 21.1397i 0.898952 + 0.898952i
\(554\) 0 0
\(555\) 0.429648 0.405540i 0.0182375 0.0172142i
\(556\) 0 0
\(557\) −7.09223 2.93770i −0.300507 0.124474i 0.227335 0.973817i \(-0.426999\pi\)
−0.527842 + 0.849342i \(0.676999\pi\)
\(558\) 0 0
\(559\) −2.34854 −0.0993325
\(560\) 0 0
\(561\) 2.51436 + 6.60291i 0.106156 + 0.278775i
\(562\) 0 0
\(563\) −0.517007 + 1.24817i −0.0217892 + 0.0526039i −0.934400 0.356226i \(-0.884063\pi\)
0.912610 + 0.408830i \(0.134063\pi\)
\(564\) 0 0
\(565\) 11.2305 4.65183i 0.472471 0.195704i
\(566\) 0 0
\(567\) 18.7509 + 23.6693i 0.787465 + 0.994016i
\(568\) 0 0
\(569\) 4.40004 + 4.40004i 0.184459 + 0.184459i 0.793296 0.608836i \(-0.208363\pi\)
−0.608836 + 0.793296i \(0.708363\pi\)
\(570\) 0 0
\(571\) −23.9135 + 9.90528i −1.00075 + 0.414523i −0.822071 0.569385i \(-0.807181\pi\)
−0.178676 + 0.983908i \(0.557181\pi\)
\(572\) 0 0
\(573\) −1.15225 + 39.9186i −0.0481359 + 1.66762i
\(574\) 0 0
\(575\) −10.6158 −0.442709
\(576\) 0 0
\(577\) −7.45244 −0.310249 −0.155124 0.987895i \(-0.549578\pi\)
−0.155124 + 0.987895i \(0.549578\pi\)
\(578\) 0 0
\(579\) −0.376226 + 13.0340i −0.0156354 + 0.541675i
\(580\) 0 0
\(581\) 24.8608 10.2977i 1.03140 0.427220i
\(582\) 0 0
\(583\) −17.1850 17.1850i −0.711732 0.711732i
\(584\) 0 0
\(585\) 0.181343 3.13861i 0.00749762 0.129766i
\(586\) 0 0
\(587\) −39.1257 + 16.2064i −1.61489 + 0.668910i −0.993420 0.114526i \(-0.963465\pi\)
−0.621472 + 0.783436i \(0.713465\pi\)
\(588\) 0 0
\(589\) −8.83416 + 21.3275i −0.364005 + 0.878786i
\(590\) 0 0
\(591\) −1.43274 3.76249i −0.0589350 0.154768i
\(592\) 0 0
\(593\) 42.7694 1.75633 0.878164 0.478359i \(-0.158768\pi\)
0.878164 + 0.478359i \(0.158768\pi\)
\(594\) 0 0
\(595\) −2.45879 1.01847i −0.100801 0.0417530i
\(596\) 0 0
\(597\) −13.3062 + 12.5596i −0.544588 + 0.514031i
\(598\) 0 0
\(599\) −21.3145 21.3145i −0.870885 0.870885i 0.121684 0.992569i \(-0.461171\pi\)
−0.992569 + 0.121684i \(0.961171\pi\)
\(600\) 0 0
\(601\) −4.26621 + 4.26621i −0.174022 + 0.174022i −0.788744 0.614722i \(-0.789268\pi\)
0.614722 + 0.788744i \(0.289268\pi\)
\(602\) 0 0
\(603\) 16.0266 33.1426i 0.652652 1.34967i
\(604\) 0 0
\(605\) 10.8366 26.1618i 0.440570 1.06363i
\(606\) 0 0
\(607\) 30.5562i 1.24024i −0.784508 0.620118i \(-0.787085\pi\)
0.784508 0.620118i \(-0.212915\pi\)
\(608\) 0 0
\(609\) 10.7471 + 28.2228i 0.435495 + 1.14364i
\(610\) 0 0
\(611\) 9.86469 + 4.08609i 0.399083 + 0.165305i
\(612\) 0 0
\(613\) −13.4587 32.4921i −0.543590 1.31234i −0.922174 0.386775i \(-0.873589\pi\)
0.378584 0.925567i \(-0.376411\pi\)
\(614\) 0 0
\(615\) −8.45168 3.79007i −0.340804 0.152830i
\(616\) 0 0
\(617\) −32.1395 + 32.1395i −1.29389 + 1.29389i −0.361524 + 0.932363i \(0.617743\pi\)
−0.932363 + 0.361524i \(0.882257\pi\)
\(618\) 0 0
\(619\) −14.9456 36.0820i −0.600716 1.45026i −0.872846 0.487996i \(-0.837728\pi\)
0.272129 0.962261i \(-0.412272\pi\)
\(620\) 0 0
\(621\) 11.5407 9.69750i 0.463113 0.389147i
\(622\) 0 0
\(623\) 9.45815i 0.378933i
\(624\) 0 0
\(625\) 6.68739i 0.267496i
\(626\) 0 0
\(627\) 1.07925 37.3897i 0.0431013 1.49320i
\(628\) 0 0
\(629\) 0.0772324 + 0.186456i 0.00307946 + 0.00743447i
\(630\) 0 0
\(631\) 20.5960 20.5960i 0.819912 0.819912i −0.166183 0.986095i \(-0.553144\pi\)
0.986095 + 0.166183i \(0.0531442\pi\)
\(632\) 0 0
\(633\) 12.2600 27.3392i 0.487291 1.08664i
\(634\) 0 0
\(635\) −0.351471 0.848526i −0.0139477 0.0336727i
\(636\) 0 0
\(637\) −3.55974 1.47449i −0.141042 0.0584216i
\(638\) 0 0
\(639\) 25.3175 22.5517i 1.00154 0.892130i
\(640\) 0 0
\(641\) 12.6916i 0.501289i 0.968079 + 0.250645i \(0.0806426\pi\)
−0.968079 + 0.250645i \(0.919357\pi\)
\(642\) 0 0
\(643\) −0.974363 + 2.35232i −0.0384251 + 0.0927665i −0.941927 0.335818i \(-0.890987\pi\)
0.903502 + 0.428584i \(0.140987\pi\)
\(644\) 0 0
\(645\) −3.78444 + 3.57209i −0.149012 + 0.140651i
\(646\) 0 0
\(647\) 22.3823 22.3823i 0.879941 0.879941i −0.113587 0.993528i \(-0.536234\pi\)
0.993528 + 0.113587i \(0.0362341\pi\)
\(648\) 0 0
\(649\) −24.2952 24.2952i −0.953670 0.953670i
\(650\) 0 0
\(651\) −25.3898 26.8992i −0.995106 1.05426i
\(652\) 0 0
\(653\) 2.02663 + 0.839459i 0.0793083 + 0.0328506i 0.421985 0.906603i \(-0.361334\pi\)
−0.342677 + 0.939453i \(0.611334\pi\)
\(654\) 0 0
\(655\) −11.7716 −0.459953
\(656\) 0 0
\(657\) 6.62483 + 7.43731i 0.258459 + 0.290157i
\(658\) 0 0
\(659\) −4.65284 + 11.2330i −0.181249 + 0.437574i −0.988224 0.153011i \(-0.951103\pi\)
0.806975 + 0.590585i \(0.201103\pi\)
\(660\) 0 0
\(661\) 22.0472 9.13226i 0.857538 0.355204i 0.0897938 0.995960i \(-0.471379\pi\)
0.767744 + 0.640757i \(0.221379\pi\)
\(662\) 0 0
\(663\) 0.979901 + 0.439427i 0.0380562 + 0.0170659i
\(664\) 0 0
\(665\) 9.96289 + 9.96289i 0.386344 + 0.386344i
\(666\) 0 0
\(667\) 13.9282 5.76923i 0.539300 0.223386i
\(668\) 0 0
\(669\) 31.5525 + 0.910763i 1.21989 + 0.0352121i
\(670\) 0 0
\(671\) −9.89643 −0.382048
\(672\) 0 0
\(673\) 1.77155 0.0682883 0.0341441 0.999417i \(-0.489129\pi\)
0.0341441 + 0.999417i \(0.489129\pi\)
\(674\) 0 0
\(675\) 12.2324 + 14.5574i 0.470825 + 0.560315i
\(676\) 0 0
\(677\) 31.1005 12.8822i 1.19529 0.495105i 0.305815 0.952091i \(-0.401071\pi\)
0.889474 + 0.456986i \(0.151071\pi\)
\(678\) 0 0
\(679\) 20.5577 + 20.5577i 0.788930 + 0.788930i
\(680\) 0 0
\(681\) 8.31973 18.5526i 0.318813 0.710937i
\(682\) 0 0
\(683\) 2.51740 1.04274i 0.0963256 0.0398994i −0.334000 0.942573i \(-0.608399\pi\)
0.430326 + 0.902674i \(0.358399\pi\)
\(684\) 0 0
\(685\) 1.85465 4.47752i 0.0708624 0.171077i
\(686\) 0 0
\(687\) 22.0365 8.39142i 0.840747 0.320153i
\(688\) 0 0
\(689\) −3.69401 −0.140731
\(690\) 0 0
\(691\) −36.0335 14.9256i −1.37078 0.567795i −0.428779 0.903409i \(-0.641056\pi\)
−0.942000 + 0.335614i \(0.891056\pi\)
\(692\) 0 0
\(693\) 53.9579 + 26.0921i 2.04969 + 0.991158i
\(694\) 0 0
\(695\) 4.08969 + 4.08969i 0.155131 + 0.155131i
\(696\) 0 0
\(697\) 2.23732 2.23732i 0.0847444 0.0847444i
\(698\) 0 0
\(699\) 19.7110 + 20.8827i 0.745537 + 0.789856i
\(700\) 0 0
\(701\) −1.39440 + 3.36638i −0.0526658 + 0.127147i −0.948023 0.318203i \(-0.896921\pi\)
0.895357 + 0.445350i \(0.146921\pi\)
\(702\) 0 0
\(703\) 1.06845i 0.0402973i
\(704\) 0 0
\(705\) 22.1109 8.41972i 0.832743 0.317105i
\(706\) 0 0
\(707\) 52.6494 + 21.8081i 1.98008 + 0.820177i
\(708\) 0 0
\(709\) −9.10175 21.9736i −0.341824 0.825235i −0.997531 0.0702205i \(-0.977630\pi\)
0.655708 0.755015i \(-0.272370\pi\)
\(710\) 0 0
\(711\) −26.6868 1.54191i −1.00083 0.0578263i
\(712\) 0 0
\(713\) −13.0568 + 13.0568i −0.488980 + 0.488980i
\(714\) 0 0
\(715\) −2.38796 5.76505i −0.0893047 0.215601i
\(716\) 0 0
\(717\) −37.3878 1.07920i −1.39627 0.0403034i
\(718\) 0 0
\(719\) 19.5450i 0.728907i 0.931222 + 0.364453i \(0.118744\pi\)
−0.931222 + 0.364453i \(0.881256\pi\)
\(720\) 0 0
\(721\) 25.6126i 0.953863i
\(722\) 0 0
\(723\) 25.2938 + 0.730106i 0.940686 + 0.0271529i
\(724\) 0 0
\(725\) 7.27728 + 17.5689i 0.270271 + 0.652493i
\(726\) 0 0
\(727\) −20.8914 + 20.8914i −0.774821 + 0.774821i −0.978945 0.204124i \(-0.934565\pi\)
0.204124 + 0.978945i \(0.434565\pi\)
\(728\) 0 0
\(729\) −26.5963 4.65151i −0.985048 0.172278i
\(730\) 0 0
\(731\) −0.680281 1.64234i −0.0251611 0.0607443i
\(732\) 0 0
\(733\) 9.09957 + 3.76916i 0.336100 + 0.139217i 0.544350 0.838859i \(-0.316777\pi\)
−0.208249 + 0.978076i \(0.566777\pi\)
\(734\) 0 0
\(735\) −7.97886 + 3.03831i −0.294305 + 0.112070i
\(736\) 0 0
\(737\) 73.0703i 2.69158i
\(738\) 0 0
\(739\) −8.03797 + 19.4054i −0.295682 + 0.713839i 0.704311 + 0.709892i \(0.251256\pi\)
−0.999992 + 0.00394665i \(0.998744\pi\)
\(740\) 0 0
\(741\) −3.90256 4.13455i −0.143364 0.151886i
\(742\) 0 0
\(743\) −14.8827 + 14.8827i −0.545995 + 0.545995i −0.925280 0.379285i \(-0.876170\pi\)
0.379285 + 0.925280i \(0.376170\pi\)
\(744\) 0 0
\(745\) 11.8409 + 11.8409i 0.433817 + 0.433817i
\(746\) 0 0
\(747\) −10.4745 + 21.6610i −0.383241 + 0.792533i
\(748\) 0 0
\(749\) −0.0569026 0.0235698i −0.00207917 0.000861222i
\(750\) 0 0
\(751\) −47.9945 −1.75135 −0.875673 0.482905i \(-0.839582\pi\)
−0.875673 + 0.482905i \(0.839582\pi\)
\(752\) 0 0
\(753\) 4.59272 1.74889i 0.167368 0.0637330i
\(754\) 0 0
\(755\) 1.85523 4.47893i 0.0675189 0.163005i
\(756\) 0 0
\(757\) 4.61422 1.91127i 0.167707 0.0694663i −0.297251 0.954799i \(-0.596070\pi\)
0.464957 + 0.885333i \(0.346070\pi\)
\(758\) 0 0
\(759\) 12.2426 27.3004i 0.444379 0.990943i
\(760\) 0 0
\(761\) 35.4112 + 35.4112i 1.28365 + 1.28365i 0.938573 + 0.345081i \(0.112149\pi\)
0.345081 + 0.938573i \(0.387851\pi\)
\(762\) 0 0
\(763\) 40.0435 16.5865i 1.44967 0.600473i
\(764\) 0 0
\(765\) 2.24738 0.782322i 0.0812541 0.0282849i
\(766\) 0 0
\(767\) −5.22237 −0.188569
\(768\) 0 0
\(769\) 49.1306 1.77169 0.885847 0.463978i \(-0.153578\pi\)
0.885847 + 0.463978i \(0.153578\pi\)
\(770\) 0 0
\(771\) −2.34485 0.0676840i −0.0844476 0.00243758i
\(772\) 0 0
\(773\) −48.9331 + 20.2688i −1.76000 + 0.729017i −0.763467 + 0.645847i \(0.776504\pi\)
−0.996535 + 0.0831696i \(0.973496\pi\)
\(774\) 0 0
\(775\) −16.4698 16.4698i −0.591611 0.591611i
\(776\) 0 0
\(777\) 1.56212 + 0.700519i 0.0560408 + 0.0251310i
\(778\) 0 0
\(779\) −15.4757 + 6.41026i −0.554476 + 0.229672i
\(780\) 0 0
\(781\) 25.7531 62.1736i 0.921520 2.22474i
\(782\) 0 0
\(783\)