Properties

Label 768.2.o.b.95.4
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 95.4
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.18890 + 1.25957i) q^{3} +(-1.06973 + 0.443098i) q^{5} +(2.37247 + 2.37247i) q^{7} +(-0.173046 - 2.99501i) q^{9} +O(q^{10})\) \(q+(-1.18890 + 1.25957i) q^{3} +(-1.06973 + 0.443098i) q^{5} +(2.37247 + 2.37247i) q^{7} +(-0.173046 - 2.99501i) q^{9} +(5.50127 - 2.27870i) q^{11} +(-0.346353 + 0.836171i) q^{13} +(0.713689 - 1.87421i) q^{15} +0.685064 q^{17} +(3.35074 + 1.38792i) q^{19} +(-5.80891 + 0.167674i) q^{21} +(-2.05133 - 2.05133i) q^{23} +(-2.58754 + 2.58754i) q^{25} +(3.97816 + 3.34279i) q^{27} +(-1.98869 + 4.80112i) q^{29} +6.36503i q^{31} +(-3.67025 + 9.63838i) q^{33} +(-3.58914 - 1.48667i) q^{35} +(-0.112738 - 0.272172i) q^{37} +(-0.641440 - 1.43038i) q^{39} +(3.26585 - 3.26585i) q^{41} +(0.993018 + 2.39736i) q^{43} +(1.51219 + 3.12718i) q^{45} +11.7975i q^{47} +4.25719i q^{49} +(-0.814471 + 0.862888i) q^{51} +(-1.56192 - 3.77080i) q^{53} +(-4.87520 + 4.87520i) q^{55} +(-5.73187 + 2.57040i) q^{57} +(-2.20815 - 5.33094i) q^{59} +(1.53549 + 0.636020i) q^{61} +(6.69500 - 7.51609i) q^{63} -1.04795i q^{65} +(-4.69605 + 11.3373i) q^{67} +(5.02262 - 0.144978i) q^{69} +(7.99150 - 7.99150i) q^{71} +(-2.34760 - 2.34760i) q^{73} +(-0.182875 - 6.33551i) q^{75} +(18.4577 + 7.64543i) q^{77} +8.91043 q^{79} +(-8.94011 + 1.03655i) q^{81} +(-3.06920 + 7.40970i) q^{83} +(-0.732836 + 0.303551i) q^{85} +(-3.68301 - 8.21294i) q^{87} +(1.99332 + 1.99332i) q^{89} +(-2.80550 + 1.16208i) q^{91} +(-8.01722 - 7.56737i) q^{93} -4.19938 q^{95} +8.66510 q^{97} +(-7.77669 - 16.0820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) −1.18890 + 1.25957i −0.686410 + 0.727215i
\(4\) 0 0
\(5\) −1.06973 + 0.443098i −0.478400 + 0.198160i −0.608834 0.793297i \(-0.708363\pi\)
0.130435 + 0.991457i \(0.458363\pi\)
\(6\) 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
\(9\) −0.173046 2.99501i −0.0576820 0.998335i
\(10\) 0 0
\(11\) 5.50127 2.27870i 1.65869 0.687054i 0.660718 0.750635i \(-0.270252\pi\)
0.997977 + 0.0635809i \(0.0202521\pi\)
\(12\) 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 \(-0.473526\pi\)
0.0830762 + 0.996543i \(0.473526\pi\)
\(18\) 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
\(21\) −5.80891 + 0.167674i −1.26761 + 0.0365895i
\(22\) 0 0
\(23\) −2.05133 2.05133i −0.427732 0.427732i 0.460123 0.887855i \(-0.347805\pi\)
−0.887855 + 0.460123i \(0.847805\pi\)
\(24\) 0 0
\(25\) −2.58754 + 2.58754i −0.517508 + 0.517508i
\(26\) 0 0
\(27\) 3.97816 + 3.34279i 0.765597 + 0.643320i
\(28\) 0 0
\(29\) −1.98869 + 4.80112i −0.369291 + 0.891546i 0.624576 + 0.780964i \(0.285272\pi\)
−0.993867 + 0.110582i \(0.964728\pi\)
\(30\) 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
\(39\) −0.641440 1.43038i −0.102713 0.229044i
\(40\) 0 0
\(41\) 3.26585 3.26585i 0.510040 0.510040i −0.404499 0.914539i \(-0.632554\pi\)
0.914539 + 0.404499i \(0.132554\pi\)
\(42\) 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
\(45\) 1.51219 + 3.12718i 0.225425 + 0.466173i
\(46\) 0 0
\(47\) 11.7975i 1.72084i 0.509589 + 0.860418i \(0.329797\pi\)
−0.509589 + 0.860418i \(0.670203\pi\)
\(48\) 0 0
\(49\) 4.25719i 0.608171i
\(50\) 0 0
\(51\) −0.814471 + 0.862888i −0.114049 + 0.120828i
\(52\) 0 0
\(53\) −1.56192 3.77080i −0.214546 0.517959i 0.779566 0.626320i \(-0.215440\pi\)
−0.994112 + 0.108361i \(0.965440\pi\)
\(54\) 0 0
\(55\) −4.87520 + 4.87520i −0.657372 + 0.657372i
\(56\) 0 0
\(57\) −5.73187 + 2.57040i −0.759205 + 0.340458i
\(58\) 0 0
\(59\) −2.20815 5.33094i −0.287476 0.694029i 0.712495 0.701678i \(-0.247565\pi\)
−0.999971 + 0.00764882i \(0.997565\pi\)
\(60\) 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
\(69\) 5.02262 0.144978i 0.604653 0.0174533i
\(70\) 0 0
\(71\) 7.99150 7.99150i 0.948416 0.948416i −0.0503173 0.998733i \(-0.516023\pi\)
0.998733 + 0.0503173i \(0.0160232\pi\)
\(72\) 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
\(75\) −0.182875 6.33551i −0.0211165 0.731562i
\(76\) 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 \(0.270080\pi\)
−0.998011 + 0.0630420i \(0.979920\pi\)
\(84\) 0 0
\(85\) −0.732836 + 0.303551i −0.0794872 + 0.0329247i
\(86\) 0 0
\(87\) −3.68301 8.21294i −0.394861 0.880520i
\(88\) 0 0
\(89\) 1.99332 + 1.99332i 0.211291 + 0.211291i 0.804816 0.593525i \(-0.202264\pi\)
−0.593525 + 0.804816i \(0.702264\pi\)
\(90\) 0 0
\(91\) −2.80550 + 1.16208i −0.294096 + 0.121819i
\(92\) 0 0
\(93\) −8.01722 7.56737i −0.831347 0.784699i
\(94\) 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
\(99\) −7.77669 16.0820i −0.781586 1.61630i
\(100\) 0 0
\(101\) −15.6920 + 6.49983i −1.56141 + 0.646758i −0.985334 0.170637i \(-0.945417\pi\)
−0.576077 + 0.817395i \(0.695417\pi\)
\(102\) 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
\(105\) 6.13969 2.75329i 0.599173 0.268693i
\(106\) 0 0
\(107\) 0.0169596 0.00702491i 0.00163955 0.000679124i −0.381864 0.924219i \(-0.624718\pi\)
0.383503 + 0.923540i \(0.374718\pi\)
\(108\) 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 \(-0.664394\pi\)
−0.493804 + 0.869573i \(0.664394\pi\)
\(114\) 0 0
\(115\) 3.10332 + 1.28544i 0.289386 + 0.119868i
\(116\) 0 0
\(117\) 2.56427 + 0.892634i 0.237067 + 0.0825241i
\(118\) 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
\(123\) 0.230814 + 7.99633i 0.0208118 + 0.721005i
\(124\) 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 0.753191 0.657802i \(-0.228514\pi\)
0.0674502 + 0.997723i \(0.478514\pi\)
\(132\) 0 0
\(133\) 4.65672 + 11.2423i 0.403789 + 0.974832i
\(134\) 0 0
\(135\) −5.73676 1.81318i −0.493741 0.156054i
\(136\) 0 0
\(137\) −2.95969 + 2.95969i −0.252863 + 0.252863i −0.822144 0.569280i \(-0.807222\pi\)
0.569280 + 0.822144i \(0.307222\pi\)
\(138\) 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
\(141\) −14.8597 14.0260i −1.25142 1.18120i
\(142\) 0 0
\(143\) 5.38924i 0.450671i
\(144\) 0 0
\(145\) 6.01711i 0.499694i
\(146\) 0 0
\(147\) −5.36224 5.06137i −0.442270 0.417455i
\(148\) 0 0
\(149\) −5.53451 13.3615i −0.453405 1.09462i −0.971019 0.239002i \(-0.923180\pi\)
0.517614 0.855614i \(1.67318\pi\)
\(150\) 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
\(153\) −0.118548 2.05177i −0.00958400 0.165876i
\(154\) 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
\(165\) −0.344556 11.9368i −0.0268236 0.929278i
\(166\) 0 0
\(167\) 1.28603 1.28603i 0.0995157 0.0995157i −0.655596 0.755112i \(-0.727583\pi\)
0.755112 + 0.655596i \(0.227583\pi\)
\(168\) 0 0
\(169\) 8.61317 + 8.61317i 0.662551 + 0.662551i
\(170\) 0 0
\(171\) 3.57700 10.2756i 0.273540 0.785799i
\(172\) 0 0
\(173\) 0.0565964 + 0.0234430i 0.00430295 + 0.00178234i 0.384834 0.922986i \(-0.374259\pi\)
−0.380531 + 0.924768i \(0.624259\pi\)
\(174\) 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 −0.873884 0.486135i \(-0.838406\pi\)
0.961678 + 0.274180i \(0.0884064\pi\)
\(180\) 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
\(183\) −2.62665 + 1.17790i −0.194168 + 0.0870726i
\(184\) 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
\(189\) 1.50739 + 17.3687i 0.109647 + 1.26339i
\(190\) 0 0
\(191\) −23.0566 −1.66832 −0.834158 0.551525i \(-0.814046\pi\)
−0.834158 + 0.551525i \(0.814046\pi\)
\(192\) 0 0
\(193\) 7.52832 0.541900 0.270950 0.962593i \(-0.412662\pi\)
0.270950 + 0.962593i \(0.412662\pi\)
\(194\) 0 0
\(195\) 1.31997 + 1.24590i 0.0945249 + 0.0892211i
\(196\) 0 0
\(197\) 2.14750 0.889524i 0.153003 0.0633760i −0.304868 0.952395i \(-0.598612\pi\)
0.457871 + 0.889019i \(0.348612\pi\)
\(198\) 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
\(201\) −8.69699 19.3939i −0.613439 1.36794i
\(202\) 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
\(213\) 0.564800 + 19.5669i 0.0386994 + 1.34070i
\(214\) 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
\(219\) 5.74803 0.165917i 0.388416 0.0112116i
\(220\) 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 0.712369 0.701805i \(-0.247622\pi\)
0.00747022 + 0.999972i \(0.497622\pi\)
\(228\) 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
\(231\) −31.5743 + 14.1592i −2.07744 + 0.931606i
\(232\) 0 0
\(233\) −11.7233 + 11.7233i −0.768016 + 0.768016i −0.977757 0.209741i \(-0.932738\pi\)
0.209741 + 0.977757i \(0.432738\pi\)
\(234\) 0 0
\(235\) −5.22743 12.6201i −0.341000 0.823247i
\(236\) 0 0
\(237\) −10.5936 + 11.2233i −0.688128 + 0.729034i
\(238\) 0 0
\(239\) 21.5949i 1.39685i −0.715681 0.698427i \(-0.753883\pi\)
0.715681 0.698427i \(-0.246117\pi\)
\(240\) 0 0
\(241\) 14.6095i 0.941078i −0.882379 0.470539i \(-0.844059\pi\)
0.882379 0.470539i \(-0.155941\pi\)
\(242\) 0 0
\(243\) 9.32327 12.4931i 0.598088 0.801430i
\(244\) 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
\(249\) −5.68409 12.6752i −0.360215 0.803261i
\(250\) 0 0
\(251\) 1.08581 + 2.62137i 0.0685355 + 0.165459i 0.954436 0.298416i \(-0.0964584\pi\)
−0.885900 + 0.463876i \(0.846458\pi\)
\(252\) 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 \(-0.986550\pi\)
0.999107 0.0422414i \(-0.0134498\pi\)
\(258\) 0 0
\(259\) 0.378254 0.913186i 0.0235036 0.0567426i
\(260\) 0 0
\(261\) 14.7235 + 5.12532i 0.911363 + 0.317250i
\(262\) 0 0
\(263\) 3.52372 3.52372i 0.217282 0.217282i −0.590070 0.807352i \(-0.700900\pi\)
0.807352 + 0.590070i \(0.200900\pi\)
\(264\) 0 0
\(265\) 3.34167 + 3.34167i 0.205277 + 0.205277i
\(266\) 0 0
\(267\) −4.88057 + 0.140878i −0.298686 + 0.00862158i
\(268\) 0 0
\(269\) −16.4741 6.82380i −1.00444 0.416055i −0.181020 0.983479i \(-0.557940\pi\)
−0.823425 + 0.567425i \(0.807940\pi\)
\(270\) 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
\(279\) 19.0633 1.10144i 1.14129 0.0659416i
\(280\) 0 0
\(281\) 10.3342 + 10.3342i 0.616487 + 0.616487i 0.944629 0.328142i \(-0.106422\pi\)
−0.328142 + 0.944629i \(0.606422\pi\)
\(282\) 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
\(285\) 4.99264 5.28943i 0.295738 0.313319i
\(286\) 0 0
\(287\) 15.4962 0.914714
\(288\) 0 0
\(289\) −16.5307 −0.972393
\(290\) 0 0
\(291\) −10.3019 + 10.9143i −0.603909 + 0.639809i
\(292\) 0 0
\(293\) 11.3816 4.71442i 0.664922 0.275420i −0.0245862 0.999698i \(-0.507827\pi\)
0.689508 + 0.724278i \(0.257827\pi\)
\(294\) 0 0
\(295\) 4.72426 + 4.72426i 0.275057 + 0.275057i
\(296\) 0 0
\(297\) 29.5021 + 9.32455i 1.71189 + 0.541065i
\(298\) 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
\(309\) 13.2166 0.381496i 0.751863 0.0217025i
\(310\) 0 0
\(311\) 18.8020 + 18.8020i 1.06617 + 1.06617i 0.997650 + 0.0685162i \(0.0218265\pi\)
0.0685162 + 0.997650i \(0.478174\pi\)
\(312\) 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
\(315\) −3.83150 + 11.0068i −0.215881 + 0.620161i
\(316\) 0 0
\(317\) 0.543402 1.31189i 0.0305205 0.0736830i −0.907884 0.419221i \(-0.862303\pi\)
0.938405 + 0.345538i \(0.112303\pi\)
\(318\) 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
\(327\) 9.15540 + 20.4161i 0.506295 + 1.12901i
\(328\) 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
\(333\) −0.795649 + 0.384748i −0.0436013 + 0.0210840i
\(334\) 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
\(339\) 12.4815 13.2235i 0.677905 0.718203i
\(340\) 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
\(345\) −5.30863 + 2.38060i −0.285807 + 0.128167i
\(346\) 0 0
\(347\) −5.84634 14.1143i −0.313848 0.757696i −0.999555 0.0298187i \(-0.990507\pi\)
0.685707 0.727877i \(1.74051\pi\)
\(348\) 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 \(-0.726520\pi\)
0.653072 0.757296i \(-0.273480\pi\)
\(354\) 0 0
\(355\) −5.00776 + 12.0898i −0.265784 + 0.641659i
\(356\) 0 0
\(357\) −3.97948 + 0.114868i −0.210616 + 0.00607944i
\(358\) 0 0
\(359\) 3.48589 3.48589i 0.183978 0.183978i −0.609109 0.793087i \(-0.708473\pi\)
0.793087 + 0.609109i \(0.208473\pi\)
\(360\) 0 0
\(361\) −4.13391 4.13391i −0.217574 0.217574i
\(362\) 0 0
\(363\) 1.22221 + 42.3421i 0.0641491 + 2.22238i
\(364\) 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
\(375\) 7.10593 + 15.8459i 0.366948 + 0.818277i
\(376\) 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
\(381\) 0.999108 + 0.943047i 0.0511858 + 0.0483138i
\(382\) 0 0
\(383\) 11.3729 0.581129 0.290565 0.956855i \(-0.406157\pi\)
0.290565 + 0.956855i \(0.406157\pi\)
\(384\) 0 0
\(385\) −23.1325 −1.17894
\(386\) 0 0
\(387\) 7.00826 3.38895i 0.356250 0.172270i
\(388\) 0 0
\(389\) 11.2635 4.66550i 0.571083 0.236550i −0.0784059 0.996922i \(-0.524983\pi\)
0.649489 + 0.760371i \(0.274983\pi\)
\(390\) 0 0
\(391\) −1.40529 1.40529i −0.0710687 0.0710687i
\(392\) 0 0
\(393\) −16.0674 + 7.20526i −0.810492 + 0.363457i
\(394\) 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 \(-0.543544\pi\)
−0.136372 + 0.990658i \(0.543544\pi\)
\(402\) 0 0
\(403\) −5.32225 2.20455i −0.265120 0.109816i
\(404\) 0 0
\(405\) 9.10425 5.07018i 0.452394 0.251939i
\(406\) 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
\(411\) −0.209176 7.24671i −0.0103179 0.357454i
\(412\) 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 0.739662 0.672979i \(-0.234986\pi\)
0.0471519 + 0.998888i \(0.484986\pi\)
\(420\) 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
\(423\) 35.3334 2.04150i 1.71797 0.0992612i
\(424\) 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
\(429\) −6.78813 6.40725i −0.327734 0.309345i
\(430\) 0 0
\(431\) 20.4774i 0.986361i 0.869927 + 0.493180i \(0.164166\pi\)
−0.869927 + 0.493180i \(0.835834\pi\)
\(432\) 0 0
\(433\) 14.6756i 0.705262i 0.935762 + 0.352631i \(0.114713\pi\)
−0.935762 + 0.352631i \(0.885287\pi\)
\(434\) 0 0
\(435\) 7.57899 + 7.15373i 0.363385 + 0.342995i
\(436\) 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
\(441\) 12.7503 0.736690i 0.607158 0.0350805i
\(442\) 0 0
\(443\) −6.00738 14.5031i −0.285419 0.689063i 0.714525 0.699610i \(-0.246643\pi\)
−0.999944 + 0.0105468i \(0.996643\pi\)
\(444\) 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 \(-0.986731\pi\)
0.999131 0.0416740i \(-0.0132691\pi\)
\(450\) 0 0
\(451\) 10.5244 25.4082i 0.495576 1.19643i
\(452\) 0 0
\(453\) 0.209243 + 7.24901i 0.00983108 + 0.340588i
\(454\) 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
\(459\) 2.72529 + 2.29003i 0.127206 + 0.106889i
\(460\) 0 0
\(461\) 0.811938 + 0.336316i 0.0378157 + 0.0156638i 0.401511 0.915854i \(-0.368485\pi\)
−0.363695 + 0.931518i \(0.618485\pi\)
\(462\) 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 −0.724498 0.689277i \(-0.757928\pi\)
0.999690 + 0.0249045i \(0.00792818\pi\)
\(468\) 0 0
\(469\) −38.0385 + 15.7561i −1.75646 + 0.727548i
\(470\) 0 0
\(471\) −27.5776 + 12.3669i −1.27071 + 0.569838i
\(472\) 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
\(477\) −11.0233 + 5.33047i −0.504722 + 0.244066i
\(478\) 0 0
\(479\) −34.4708 −1.57501 −0.787505 0.616309i \(-0.788627\pi\)
−0.787505 + 0.616309i \(0.788627\pi\)
\(480\) 0 0
\(481\) 0.266630 0.0121573
\(482\) 0 0
\(483\) 12.2600 + 11.5720i 0.557847 + 0.526546i
\(484\) 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
\(489\) 8.55934 + 19.0869i 0.387067 + 0.863140i
\(490\) 0 0
\(491\) −16.0034 + 6.62882i −0.722223 + 0.299154i −0.713352 0.700806i \(-0.752824\pi\)
−0.00887095 + 0.999961i \(0.502824\pi\)
\(492\) 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
\(501\) 0.0908900 + 3.14880i 0.00406067 + 0.140678i
\(502\) 0 0
\(503\) −16.8510 16.8510i −0.751350 0.751350i 0.223381 0.974731i \(-0.428291\pi\)
−0.974731 + 0.223381i \(0.928291\pi\)
\(504\) 0 0
\(505\) 13.9062 13.9062i 0.618817 0.618817i
\(506\) 0 0
\(507\) −21.0891 + 0.608736i −0.936599 + 0.0270349i
\(508\) 0 0
\(509\) −6.71610 + 16.2141i −0.297686 + 0.718678i 0.702291 + 0.711890i \(0.252161\pi\)
−0.999977 + 0.00678764i \(0.997839\pi\)
\(510\) 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
\(519\) −0.0968155 + 0.0434160i −0.00424973 + 0.00190575i
\(520\) 0 0
\(521\) 18.2126 18.2126i 0.797908 0.797908i −0.184858 0.982765i \(-0.559182\pi\)
0.982765 + 0.184858i \(0.0591824\pi\)
\(522\) 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
\(525\) 14.5969 15.4647i 0.637062 0.674933i
\(526\) 0 0
\(527\) 4.36045i 0.189944i
\(528\) 0 0
\(529\) 14.5841i 0.634090i
\(530\) 0 0
\(531\) −15.5841 + 7.53590i −0.676291 + 0.327030i
\(532\) 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
\(537\) 2.17536 + 4.85094i 0.0938735 + 0.209333i
\(538\) 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
\(549\) 1.63917 4.70886i 0.0699582 0.200969i
\(550\) 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
\(555\) −0.590567 + 0.0170467i −0.0250682 + 0.000723593i
\(556\) 0 0
\(557\) 7.09223 + 2.93770i 0.300507 + 0.124474i 0.527842 0.849342i \(-0.323001\pi\)
−0.227335 + 0.973817i \(0.573001\pi\)
\(558\) 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 −0.912610 0.408830i \(-0.865937\pi\)
0.934400 + 0.356226i \(0.115937\pi\)
\(564\) 0 0
\(565\) 11.2305 4.65183i 0.472471 0.195704i
\(566\) 0 0
\(567\) −23.6693 18.7509i −0.994016 0.787465i
\(568\) 0 0
\(569\) −4.40004 4.40004i −0.184459 0.184459i 0.608836 0.793296i \(-0.291637\pi\)
−0.793296 + 0.608836i \(0.791637\pi\)
\(570\) 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
\(573\) 27.4119 29.0415i 1.14515 1.21322i
\(574\) 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
\(579\) −8.95040 + 9.48246i −0.371966 + 0.394078i
\(580\) 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
\(585\) −3.13861 + 0.181343i −0.129766 + 0.00749762i
\(586\) 0 0
\(587\) 39.1257 16.2064i 1.61489 0.668910i 0.621472 0.783436i \(-0.286535\pi\)
0.993420 + 0.114526i \(0.0365349\pi\)
\(588\) 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 \(-0.841232\pi\)
−0.878164 + 0.478359i \(0.841232\pi\)
\(594\) 0 0
\(595\) −2.45879 1.01847i −0.100801 0.0417530i
\(596\) 0 0
\(597\) −18.2899 + 0.527938i −0.748556 + 0.0216071i
\(598\) 0 0
\(599\) 21.3145 + 21.3145i 0.870885 + 0.870885i 0.992569 0.121684i \(-0.0388294\pi\)
−0.121684 + 0.992569i \(0.538829\pi\)
\(600\) 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
\(603\) 34.7678 + 12.1028i 1.41586 + 0.492865i
\(604\) 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
\(615\) −3.79007 8.45168i −0.152830 0.340804i
\(616\) 0 0
\(617\) 32.1395 32.1395i 1.29389 1.29389i 0.361524 0.932363i \(-0.382257\pi\)
0.932363 0.361524i \(-0.117743\pi\)
\(618\) 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
\(621\) −1.30335 15.0177i −0.0523018 0.602639i
\(622\) 0 0
\(623\) 9.45815i 0.378933i
\(624\) 0 0
\(625\) 6.68739i 0.267496i
\(626\) 0 0
\(627\) −25.6754 + 27.2017i −1.02538 + 1.08633i
\(628\) 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
\(633\) 27.3392 12.2600i 1.08664 0.487291i
\(634\) 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 \(-0.919357\pi\)
0.968079 0.250645i \(-0.0806426\pi\)
\(642\) 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
\(645\) 5.20185 0.150151i 0.204823 0.00591221i
\(646\) 0 0
\(647\) −22.3823 + 22.3823i −0.879941 + 0.879941i −0.993528 0.113587i \(-0.963766\pi\)
0.113587 + 0.993528i \(0.463766\pi\)
\(648\) 0 0
\(649\) −24.2952 24.2952i −0.953670 0.953670i
\(650\) 0 0
\(651\) −1.06725 36.9739i −0.0418289 1.44912i
\(652\) 0 0
\(653\) −2.02663 0.839459i −0.0793083 0.0328506i 0.342677 0.939453i \(-0.388666\pi\)
−0.421985 + 0.906603i \(0.638666\pi\)
\(654\) 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 −0.806975 0.590585i \(-0.798897\pi\)
0.988224 + 0.153011i \(0.0488971\pi\)
\(660\) 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
\(663\) −0.439427 0.979901i −0.0170659 0.0380562i
\(664\) 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
\(669\) 22.9550 + 21.6670i 0.887491 + 0.837694i
\(670\) 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
\(675\) −18.9432 + 1.64404i −0.729126 + 0.0632793i
\(676\) 0 0
\(677\) −31.1005 + 12.8822i −1.19529 + 0.495105i −0.889474 0.456986i \(-0.848929\pi\)
−0.305815 + 0.952091i \(0.598929\pi\)
\(678\) 0 0
\(679\) 20.5577 + 20.5577i 0.788930 + 0.788930i
\(680\) 0 0
\(681\) −18.5526 + 8.31973i −0.710937 + 0.318813i
\(682\) 0 0
\(683\) −2.51740 + 1.04274i −0.0963256 + 0.0398994i −0.430326 0.902674i \(-0.641601\pi\)
0.334000 + 0.942573i \(0.391601\pi\)
\(684\) 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
\(693\) 19.7041 56.6039i 0.748496 2.15021i
\(694\) 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
\(699\) −0.828543 28.7040i −0.0313384 1.08569i
\(700\) 0 0
\(701\) 1.39440 3.36638i 0.0526658 0.127147i −0.895357 0.445350i \(-0.853079\pi\)
0.948023 + 0.318203i \(0.103079\pi\)
\(702\) 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
\(711\) −1.54191 26.6868i −0.0578263 1.00083i
\(712\) 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
\(717\) 27.2003 + 25.6741i 1.01581 + 0.958816i
\(718\) 0 0
\(719\) 19.5450i 0.728907i −0.931222 0.364453i \(-0.881256\pi\)
0.931222 0.364453i \(-0.118744\pi\)
\(720\) 0 0
\(721\) 25.6126i 0.953863i
\(722\) 0 0
\(723\) 18.4017 + 17.3692i 0.684366 + 0.645966i
\(724\) 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
\(729\) 4.65151 + 26.5963i 0.172278 + 0.985048i
\(730\) 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
\(741\) −0.164043 5.68309i −0.00602625 0.208774i
\(742\) 0 0
\(743\) 14.8827 14.8827i 0.545995 0.545995i −0.379285 0.925280i \(-0.623830\pi\)
0.925280 + 0.379285i \(0.123830\pi\)
\(744\) 0 0
\(745\) 11.8409 + 11.8409i 0.433817 + 0.433817i
\(746\) 0 0
\(747\) 22.7232 + 7.91004i 0.831398 + 0.289413i
\(748\) 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
\(759\) 27.3004 12.2426i 0.990943 0.444379i
\(760\) 0 0
\(761\) −35.4112 35.4112i −1.28365 1.28365i −0.938573 0.345081i \(-0.887851\pi\)
−0.345081 0.938573i \(1.38785\pi\)
\(762\) 0 0
\(763\) 40.0435 16.5865i 1.44967 0.600473i
\(764\) 0 0
\(765\) 1.03595 + 2.14232i 0.0374549 + 0.0774557i
\(766\) 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
\(771\) 1.70592 + 1.61020i 0.0614371 + 0.0579898i
\(772\) 0 0
\(773\) 48.9331 20.2688i 1.76000 0.729017i 0.763467 0.645847i \(-0.223496\pi\)
0.996535 0.0831696i \(-0.0265043\pi\)
\(774\) 0 0
\(775\) −16.4698 16.4698i −0.591611 0.591611i
\(776\) 0 0
\(777\) 0.700519 + 1.56212i 0.0251310 + 0.0560408i
\(778\) 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
\(783\) −23.9605 +