Properties

Label 384.2.j.b.289.3
Level $384$
Weight $2$
Character 384.289
Analytic conductor $3.066$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 289.3
Root \(0.500000 + 1.44392i\) of defining polynomial
Character \(\chi\) \(=\) 384.289
Dual form 384.2.j.b.97.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{3} +(-1.74912 + 1.74912i) q^{5} +2.55765i q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{3} +(-1.74912 + 1.74912i) q^{5} +2.55765i q^{7} +1.00000i q^{9} +(-0.473626 + 0.473626i) q^{11} +(-2.88784 - 2.88784i) q^{13} -2.47363 q^{15} -6.44549 q^{17} +(4.55765 + 4.55765i) q^{19} +(-1.80853 + 1.80853i) q^{21} +2.82843i q^{23} -1.11882i q^{25} +(-0.707107 + 0.707107i) q^{27} +(3.07931 + 3.07931i) q^{29} +6.55765 q^{31} -0.669808 q^{33} +(-4.47363 - 4.47363i) q^{35} +(2.72922 - 2.72922i) q^{37} -4.08402i q^{39} +0.788632i q^{41} +(0.389604 - 0.389604i) q^{43} +(-1.74912 - 1.74912i) q^{45} +2.82843 q^{47} +0.458440 q^{49} +(-4.55765 - 4.55765i) q^{51} +(2.57754 - 2.57754i) q^{53} -1.65685i q^{55} +6.44549i q^{57} +(-4.00000 + 4.00000i) q^{59} +(4.38607 + 4.38607i) q^{61} -2.55765 q^{63} +10.1023 q^{65} +(2.11882 + 2.11882i) q^{67} +(-2.00000 + 2.00000i) q^{69} -5.11529i q^{71} -14.7721i q^{73} +(0.791128 - 0.791128i) q^{75} +(-1.21137 - 1.21137i) q^{77} -6.32000 q^{79} -1.00000 q^{81} +(-0.641669 - 0.641669i) q^{83} +(11.2739 - 11.2739i) q^{85} +4.35480i q^{87} +6.31724i q^{89} +(7.38607 - 7.38607i) q^{91} +(4.63696 + 4.63696i) q^{93} -15.9437 q^{95} +12.6533 q^{97} +(-0.473626 - 0.473626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 8q^{11} - 8q^{15} + 8q^{19} + 16q^{29} + 24q^{31} - 24q^{35} + 16q^{37} + 8q^{43} - 8q^{49} - 8q^{51} - 16q^{53} - 32q^{59} - 16q^{61} + 8q^{63} - 16q^{65} + 16q^{67} - 16q^{69} - 16q^{75} - 16q^{77} - 24q^{79} - 8q^{81} + 40q^{83} + 16q^{85} + 8q^{91} - 48q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 0 0
\(5\) −1.74912 + 1.74912i −0.782229 + 0.782229i −0.980207 0.197977i \(-0.936563\pi\)
0.197977 + 0.980207i \(0.436563\pi\)
\(6\) 0 0
\(7\) 2.55765i 0.966700i 0.875427 + 0.483350i \(0.160580\pi\)
−0.875427 + 0.483350i \(0.839420\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) −0.473626 + 0.473626i −0.142804 + 0.142804i −0.774894 0.632091i \(-0.782197\pi\)
0.632091 + 0.774894i \(0.282197\pi\)
\(12\) 0 0
\(13\) −2.88784 2.88784i −0.800943 0.800943i 0.182300 0.983243i \(-0.441646\pi\)
−0.983243 + 0.182300i \(0.941646\pi\)
\(14\) 0 0
\(15\) −2.47363 −0.638687
\(16\) 0 0
\(17\) −6.44549 −1.56326 −0.781630 0.623742i \(-0.785611\pi\)
−0.781630 + 0.623742i \(0.785611\pi\)
\(18\) 0 0
\(19\) 4.55765 + 4.55765i 1.04560 + 1.04560i 0.998910 + 0.0466864i \(0.0148661\pi\)
0.0466864 + 0.998910i \(0.485134\pi\)
\(20\) 0 0
\(21\) −1.80853 + 1.80853i −0.394654 + 0.394654i
\(22\) 0 0
\(23\) 2.82843i 0.589768i 0.955533 + 0.294884i \(0.0952810\pi\)
−0.955533 + 0.294884i \(0.904719\pi\)
\(24\) 0 0
\(25\) 1.11882i 0.223765i
\(26\) 0 0
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) 3.07931 + 3.07931i 0.571813 + 0.571813i 0.932635 0.360821i \(-0.117504\pi\)
−0.360821 + 0.932635i \(0.617504\pi\)
\(30\) 0 0
\(31\) 6.55765 1.17779 0.588894 0.808210i \(-0.299563\pi\)
0.588894 + 0.808210i \(0.299563\pi\)
\(32\) 0 0
\(33\) −0.669808 −0.116599
\(34\) 0 0
\(35\) −4.47363 4.47363i −0.756181 0.756181i
\(36\) 0 0
\(37\) 2.72922 2.72922i 0.448681 0.448681i −0.446235 0.894916i \(-0.647235\pi\)
0.894916 + 0.446235i \(0.147235\pi\)
\(38\) 0 0
\(39\) 4.08402i 0.653967i
\(40\) 0 0
\(41\) 0.788632i 0.123164i 0.998102 + 0.0615818i \(0.0196145\pi\)
−0.998102 + 0.0615818i \(0.980385\pi\)
\(42\) 0 0
\(43\) 0.389604 0.389604i 0.0594141 0.0594141i −0.676775 0.736190i \(-0.736623\pi\)
0.736190 + 0.676775i \(0.236623\pi\)
\(44\) 0 0
\(45\) −1.74912 1.74912i −0.260743 0.260743i
\(46\) 0 0
\(47\) 2.82843 0.412568 0.206284 0.978492i \(-0.433863\pi\)
0.206284 + 0.978492i \(0.433863\pi\)
\(48\) 0 0
\(49\) 0.458440 0.0654915
\(50\) 0 0
\(51\) −4.55765 4.55765i −0.638198 0.638198i
\(52\) 0 0
\(53\) 2.57754 2.57754i 0.354053 0.354053i −0.507562 0.861615i \(-0.669453\pi\)
0.861615 + 0.507562i \(0.169453\pi\)
\(54\) 0 0
\(55\) 1.65685i 0.223410i
\(56\) 0 0
\(57\) 6.44549i 0.853726i
\(58\) 0 0
\(59\) −4.00000 + 4.00000i −0.520756 + 0.520756i −0.917800 0.397044i \(-0.870036\pi\)
0.397044 + 0.917800i \(0.370036\pi\)
\(60\) 0 0
\(61\) 4.38607 + 4.38607i 0.561579 + 0.561579i 0.929756 0.368177i \(-0.120018\pi\)
−0.368177 + 0.929756i \(0.620018\pi\)
\(62\) 0 0
\(63\) −2.55765 −0.322233
\(64\) 0 0
\(65\) 10.1023 1.25304
\(66\) 0 0
\(67\) 2.11882 + 2.11882i 0.258856 + 0.258856i 0.824589 0.565733i \(-0.191407\pi\)
−0.565733 + 0.824589i \(0.691407\pi\)
\(68\) 0 0
\(69\) −2.00000 + 2.00000i −0.240772 + 0.240772i
\(70\) 0 0
\(71\) 5.11529i 0.607074i −0.952820 0.303537i \(-0.901832\pi\)
0.952820 0.303537i \(-0.0981676\pi\)
\(72\) 0 0
\(73\) 14.7721i 1.72895i −0.502676 0.864475i \(-0.667651\pi\)
0.502676 0.864475i \(-0.332349\pi\)
\(74\) 0 0
\(75\) 0.791128 0.791128i 0.0913516 0.0913516i
\(76\) 0 0
\(77\) −1.21137 1.21137i −0.138048 0.138048i
\(78\) 0 0
\(79\) −6.32000 −0.711055 −0.355528 0.934666i \(-0.615699\pi\)
−0.355528 + 0.934666i \(0.615699\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) −0.641669 0.641669i −0.0704323 0.0704323i 0.671013 0.741445i \(-0.265859\pi\)
−0.741445 + 0.671013i \(0.765859\pi\)
\(84\) 0 0
\(85\) 11.2739 11.2739i 1.22283 1.22283i
\(86\) 0 0
\(87\) 4.35480i 0.466884i
\(88\) 0 0
\(89\) 6.31724i 0.669626i 0.942285 + 0.334813i \(0.108673\pi\)
−0.942285 + 0.334813i \(0.891327\pi\)
\(90\) 0 0
\(91\) 7.38607 7.38607i 0.774271 0.774271i
\(92\) 0 0
\(93\) 4.63696 + 4.63696i 0.480830 + 0.480830i
\(94\) 0 0
\(95\) −15.9437 −1.63579
\(96\) 0 0
\(97\) 12.6533 1.28475 0.642375 0.766390i \(-0.277949\pi\)
0.642375 + 0.766390i \(0.277949\pi\)
\(98\) 0 0
\(99\) −0.473626 0.473626i −0.0476012 0.0476012i
\(100\) 0 0
\(101\) −7.52480 + 7.52480i −0.748745 + 0.748745i −0.974244 0.225498i \(-0.927599\pi\)
0.225498 + 0.974244i \(0.427599\pi\)
\(102\) 0 0
\(103\) 3.33686i 0.328790i −0.986395 0.164395i \(-0.947433\pi\)
0.986395 0.164395i \(-0.0525672\pi\)
\(104\) 0 0
\(105\) 6.32666i 0.617419i
\(106\) 0 0
\(107\) 14.0625 14.0625i 1.35948 1.35948i 0.484918 0.874560i \(-0.338849\pi\)
0.874560 0.484918i \(-0.161151\pi\)
\(108\) 0 0
\(109\) −2.76901 2.76901i −0.265224 0.265224i 0.561949 0.827172i \(-0.310052\pi\)
−0.827172 + 0.561949i \(0.810052\pi\)
\(110\) 0 0
\(111\) 3.85970 0.366347
\(112\) 0 0
\(113\) 2.23765 0.210500 0.105250 0.994446i \(-0.466436\pi\)
0.105250 + 0.994446i \(0.466436\pi\)
\(114\) 0 0
\(115\) −4.94725 4.94725i −0.461334 0.461334i
\(116\) 0 0
\(117\) 2.88784 2.88784i 0.266981 0.266981i
\(118\) 0 0
\(119\) 16.4853i 1.51120i
\(120\) 0 0
\(121\) 10.5514i 0.959214i
\(122\) 0 0
\(123\) −0.557647 + 0.557647i −0.0502814 + 0.0502814i
\(124\) 0 0
\(125\) −6.78863 6.78863i −0.607194 0.607194i
\(126\) 0 0
\(127\) 12.2145 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(128\) 0 0
\(129\) 0.550984 0.0485114
\(130\) 0 0
\(131\) 3.77568 + 3.77568i 0.329883 + 0.329883i 0.852542 0.522659i \(-0.175060\pi\)
−0.522659 + 0.852542i \(0.675060\pi\)
\(132\) 0 0
\(133\) −11.6569 + 11.6569i −1.01078 + 1.01078i
\(134\) 0 0
\(135\) 2.47363i 0.212896i
\(136\) 0 0
\(137\) 5.10587i 0.436224i −0.975924 0.218112i \(-0.930010\pi\)
0.975924 0.218112i \(-0.0699898\pi\)
\(138\) 0 0
\(139\) −11.7757 + 11.7757i −0.998800 + 0.998800i −0.999999 0.00119925i \(-0.999618\pi\)
0.00119925 + 0.999999i \(0.499618\pi\)
\(140\) 0 0
\(141\) 2.00000 + 2.00000i 0.168430 + 0.168430i
\(142\) 0 0
\(143\) 2.73551 0.228755
\(144\) 0 0
\(145\) −10.7721 −0.894578
\(146\) 0 0
\(147\) 0.324166 + 0.324166i 0.0267368 + 0.0267368i
\(148\) 0 0
\(149\) 7.90774 7.90774i 0.647827 0.647827i −0.304640 0.952467i \(-0.598536\pi\)
0.952467 + 0.304640i \(0.0985363\pi\)
\(150\) 0 0
\(151\) 14.6506i 1.19225i 0.802893 + 0.596123i \(0.203293\pi\)
−0.802893 + 0.596123i \(0.796707\pi\)
\(152\) 0 0
\(153\) 6.44549i 0.521087i
\(154\) 0 0
\(155\) −11.4701 + 11.4701i −0.921300 + 0.921300i
\(156\) 0 0
\(157\) 3.15196 + 3.15196i 0.251553 + 0.251553i 0.821607 0.570054i \(-0.193078\pi\)
−0.570054 + 0.821607i \(0.693078\pi\)
\(158\) 0 0
\(159\) 3.64520 0.289083
\(160\) 0 0
\(161\) −7.23412 −0.570128
\(162\) 0 0
\(163\) −5.50490 5.50490i −0.431177 0.431177i 0.457852 0.889029i \(-0.348619\pi\)
−0.889029 + 0.457852i \(0.848619\pi\)
\(164\) 0 0
\(165\) 1.17157 1.17157i 0.0912068 0.0912068i
\(166\) 0 0
\(167\) 20.1814i 1.56168i 0.624730 + 0.780841i \(0.285209\pi\)
−0.624730 + 0.780841i \(0.714791\pi\)
\(168\) 0 0
\(169\) 3.67923i 0.283018i
\(170\) 0 0
\(171\) −4.55765 + 4.55765i −0.348532 + 0.348532i
\(172\) 0 0
\(173\) −4.35322 4.35322i −0.330969 0.330969i 0.521985 0.852955i \(-0.325192\pi\)
−0.852955 + 0.521985i \(0.825192\pi\)
\(174\) 0 0
\(175\) 2.86156 0.216313
\(176\) 0 0
\(177\) −5.65685 −0.425195
\(178\) 0 0
\(179\) 13.2833 + 13.2833i 0.992843 + 0.992843i 0.999975 0.00713130i \(-0.00226998\pi\)
−0.00713130 + 0.999975i \(0.502270\pi\)
\(180\) 0 0
\(181\) −6.34628 + 6.34628i −0.471715 + 0.471715i −0.902469 0.430754i \(-0.858248\pi\)
0.430754 + 0.902469i \(0.358248\pi\)
\(182\) 0 0
\(183\) 6.20285i 0.458528i
\(184\) 0 0
\(185\) 9.54745i 0.701943i
\(186\) 0 0
\(187\) 3.05275 3.05275i 0.223239 0.223239i
\(188\) 0 0
\(189\) −1.80853 1.80853i −0.131551 0.131551i
\(190\) 0 0
\(191\) 5.60058 0.405243 0.202622 0.979257i \(-0.435054\pi\)
0.202622 + 0.979257i \(0.435054\pi\)
\(192\) 0 0
\(193\) −19.4514 −1.40014 −0.700071 0.714074i \(-0.746848\pi\)
−0.700071 + 0.714074i \(0.746848\pi\)
\(194\) 0 0
\(195\) 7.14343 + 7.14343i 0.511552 + 0.511552i
\(196\) 0 0
\(197\) −1.23793 + 1.23793i −0.0881988 + 0.0881988i −0.749830 0.661631i \(-0.769865\pi\)
0.661631 + 0.749830i \(0.269865\pi\)
\(198\) 0 0
\(199\) 0.993710i 0.0704422i 0.999380 + 0.0352211i \(0.0112135\pi\)
−0.999380 + 0.0352211i \(0.988786\pi\)
\(200\) 0 0
\(201\) 2.99647i 0.211355i
\(202\) 0 0
\(203\) −7.87579 + 7.87579i −0.552772 + 0.552772i
\(204\) 0 0
\(205\) −1.37941 1.37941i −0.0963422 0.0963422i
\(206\) 0 0
\(207\) −2.82843 −0.196589
\(208\) 0 0
\(209\) −4.31724 −0.298630
\(210\) 0 0
\(211\) −4.22432 4.22432i −0.290814 0.290814i 0.546588 0.837402i \(-0.315927\pi\)
−0.837402 + 0.546588i \(0.815927\pi\)
\(212\) 0 0
\(213\) 3.61706 3.61706i 0.247837 0.247837i
\(214\) 0 0
\(215\) 1.36293i 0.0929509i
\(216\) 0 0
\(217\) 16.7721i 1.13857i
\(218\) 0 0
\(219\) 10.4455 10.4455i 0.705841 0.705841i
\(220\) 0 0
\(221\) 18.6135 + 18.6135i 1.25208 + 1.25208i
\(222\) 0 0
\(223\) −23.7659 −1.59148 −0.795740 0.605639i \(-0.792918\pi\)
−0.795740 + 0.605639i \(0.792918\pi\)
\(224\) 0 0
\(225\) 1.11882 0.0745883
\(226\) 0 0
\(227\) 0.641669 + 0.641669i 0.0425891 + 0.0425891i 0.728081 0.685492i \(-0.240413\pi\)
−0.685492 + 0.728081i \(0.740413\pi\)
\(228\) 0 0
\(229\) −5.34275 + 5.34275i −0.353059 + 0.353059i −0.861246 0.508188i \(-0.830316\pi\)
0.508188 + 0.861246i \(0.330316\pi\)
\(230\) 0 0
\(231\) 1.71313i 0.112716i
\(232\) 0 0
\(233\) 23.2271i 1.52166i −0.648954 0.760828i \(-0.724793\pi\)
0.648954 0.760828i \(-0.275207\pi\)
\(234\) 0 0
\(235\) −4.94725 + 4.94725i −0.322723 + 0.322723i
\(236\) 0 0
\(237\) −4.46891 4.46891i −0.290287 0.290287i
\(238\) 0 0
\(239\) 26.9213 1.74140 0.870698 0.491817i \(-0.163667\pi\)
0.870698 + 0.491817i \(0.163667\pi\)
\(240\) 0 0
\(241\) −10.3494 −0.666664 −0.333332 0.942809i \(-0.608173\pi\)
−0.333332 + 0.942809i \(0.608173\pi\)
\(242\) 0 0
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 0 0
\(245\) −0.801866 + 0.801866i −0.0512293 + 0.0512293i
\(246\) 0 0
\(247\) 26.3235i 1.67492i
\(248\) 0 0
\(249\) 0.907457i 0.0575077i
\(250\) 0 0
\(251\) 9.75696 9.75696i 0.615854 0.615854i −0.328611 0.944465i \(-0.606581\pi\)
0.944465 + 0.328611i \(0.106581\pi\)
\(252\) 0 0
\(253\) −1.33962 1.33962i −0.0842209 0.0842209i
\(254\) 0 0
\(255\) 15.9437 0.998435
\(256\) 0 0
\(257\) 16.9965 1.06021 0.530105 0.847932i \(-0.322152\pi\)
0.530105 + 0.847932i \(0.322152\pi\)
\(258\) 0 0
\(259\) 6.98038 + 6.98038i 0.433740 + 0.433740i
\(260\) 0 0
\(261\) −3.07931 + 3.07931i −0.190604 + 0.190604i
\(262\) 0 0
\(263\) 29.9929i 1.84944i 0.380643 + 0.924722i \(0.375703\pi\)
−0.380643 + 0.924722i \(0.624297\pi\)
\(264\) 0 0
\(265\) 9.01686i 0.553901i
\(266\) 0 0
\(267\) −4.46696 + 4.46696i −0.273374 + 0.273374i
\(268\) 0 0
\(269\) −20.6003 20.6003i −1.25602 1.25602i −0.952976 0.303046i \(-0.901996\pi\)
−0.303046 0.952976i \(-0.598004\pi\)
\(270\) 0 0
\(271\) −26.6506 −1.61891 −0.809453 0.587184i \(-0.800236\pi\)
−0.809453 + 0.587184i \(0.800236\pi\)
\(272\) 0 0
\(273\) 10.4455 0.632190
\(274\) 0 0
\(275\) 0.529904 + 0.529904i 0.0319544 + 0.0319544i
\(276\) 0 0
\(277\) −12.1220 + 12.1220i −0.728338 + 0.728338i −0.970289 0.241951i \(-0.922213\pi\)
0.241951 + 0.970289i \(0.422213\pi\)
\(278\) 0 0
\(279\) 6.55765i 0.392596i
\(280\) 0 0
\(281\) 2.76588i 0.164999i −0.996591 0.0824993i \(-0.973710\pi\)
0.996591 0.0824993i \(-0.0262902\pi\)
\(282\) 0 0
\(283\) −4.48528 + 4.48528i −0.266622 + 0.266622i −0.827738 0.561115i \(-0.810372\pi\)
0.561115 + 0.827738i \(0.310372\pi\)
\(284\) 0 0
\(285\) −11.2739 11.2739i −0.667809 0.667809i
\(286\) 0 0
\(287\) −2.01704 −0.119062
\(288\) 0 0
\(289\) 24.5443 1.44378
\(290\) 0 0
\(291\) 8.94725 + 8.94725i 0.524497 + 0.524497i
\(292\) 0 0
\(293\) 8.20793 8.20793i 0.479512 0.479512i −0.425463 0.904976i \(-0.639889\pi\)
0.904976 + 0.425463i \(0.139889\pi\)
\(294\) 0 0
\(295\) 13.9929i 0.814700i
\(296\) 0 0
\(297\) 0.669808i 0.0388662i
\(298\) 0 0
\(299\) 8.16804 8.16804i 0.472370 0.472370i
\(300\) 0 0
\(301\) 0.996470 + 0.996470i 0.0574356 + 0.0574356i
\(302\) 0 0
\(303\) −10.6417 −0.611348
\(304\) 0 0
\(305\) −15.3435 −0.878567
\(306\) 0 0
\(307\) −10.4549 10.4549i −0.596693 0.596693i 0.342738 0.939431i \(-0.388646\pi\)
−0.939431 + 0.342738i \(0.888646\pi\)
\(308\) 0 0
\(309\) 2.35951 2.35951i 0.134228 0.134228i
\(310\) 0 0
\(311\) 15.0761i 0.854885i −0.904043 0.427442i \(-0.859415\pi\)
0.904043 0.427442i \(-0.140585\pi\)
\(312\) 0 0
\(313\) 23.0027i 1.30019i −0.759852 0.650096i \(-0.774729\pi\)
0.759852 0.650096i \(-0.225271\pi\)
\(314\) 0 0
\(315\) 4.47363 4.47363i 0.252060 0.252060i
\(316\) 0 0
\(317\) 6.75892 + 6.75892i 0.379618 + 0.379618i 0.870964 0.491346i \(-0.163495\pi\)
−0.491346 + 0.870964i \(0.663495\pi\)
\(318\) 0 0
\(319\) −2.91688 −0.163314
\(320\) 0 0
\(321\) 19.8874 1.11001
\(322\) 0 0
\(323\) −29.3763 29.3763i −1.63454 1.63454i
\(324\) 0 0
\(325\) −3.23099 + 3.23099i −0.179223 + 0.179223i
\(326\) 0 0
\(327\) 3.91598i 0.216554i
\(328\) 0 0
\(329\) 7.23412i 0.398830i
\(330\) 0 0
\(331\) 19.6631 19.6631i 1.08078 1.08078i 0.0843464 0.996436i \(-0.473120\pi\)
0.996436 0.0843464i \(-0.0268802\pi\)
\(332\) 0 0
\(333\) 2.72922 + 2.72922i 0.149560 + 0.149560i
\(334\) 0 0
\(335\) −7.41215 −0.404969
\(336\) 0 0
\(337\) 3.00980 0.163954 0.0819771 0.996634i \(-0.473877\pi\)
0.0819771 + 0.996634i \(0.473877\pi\)
\(338\) 0 0
\(339\) 1.58226 + 1.58226i 0.0859364 + 0.0859364i
\(340\) 0 0
\(341\) −3.10587 + 3.10587i −0.168192 + 0.168192i
\(342\) 0 0
\(343\) 19.0761i 1.03001i
\(344\) 0 0
\(345\) 6.99647i 0.376677i
\(346\) 0 0
\(347\) −6.27521 + 6.27521i −0.336871 + 0.336871i −0.855188 0.518317i \(-0.826559\pi\)
0.518317 + 0.855188i \(0.326559\pi\)
\(348\) 0 0
\(349\) 4.74255 + 4.74255i 0.253863 + 0.253863i 0.822552 0.568690i \(-0.192549\pi\)
−0.568690 + 0.822552i \(0.692549\pi\)
\(350\) 0 0
\(351\) 4.08402 0.217989
\(352\) 0 0
\(353\) −8.75882 −0.466185 −0.233093 0.972455i \(-0.574884\pi\)
−0.233093 + 0.972455i \(0.574884\pi\)
\(354\) 0 0
\(355\) 8.94725 + 8.94725i 0.474871 + 0.474871i
\(356\) 0 0
\(357\) 11.6569 11.6569i 0.616946 0.616946i
\(358\) 0 0
\(359\) 32.7917i 1.73068i −0.501184 0.865341i \(-0.667102\pi\)
0.501184 0.865341i \(-0.332898\pi\)
\(360\) 0 0
\(361\) 22.5443i 1.18654i
\(362\) 0 0
\(363\) −7.46094 + 7.46094i −0.391598 + 0.391598i
\(364\) 0 0
\(365\) 25.8382 + 25.8382i 1.35243 + 1.35243i
\(366\) 0 0
\(367\) 20.6435 1.07758 0.538791 0.842439i \(-0.318881\pi\)
0.538791 + 0.842439i \(0.318881\pi\)
\(368\) 0 0
\(369\) −0.788632 −0.0410546
\(370\) 0 0
\(371\) 6.59245 + 6.59245i 0.342263 + 0.342263i
\(372\) 0 0
\(373\) 16.6167 16.6167i 0.860378 0.860378i −0.131004 0.991382i \(-0.541820\pi\)
0.991382 + 0.131004i \(0.0418200\pi\)
\(374\) 0 0
\(375\) 9.60058i 0.495772i
\(376\) 0 0
\(377\) 17.7851i 0.915979i
\(378\) 0 0
\(379\) −7.77844 + 7.77844i −0.399552 + 0.399552i −0.878075 0.478523i \(-0.841172\pi\)
0.478523 + 0.878075i \(0.341172\pi\)
\(380\) 0 0
\(381\) 8.63696 + 8.63696i 0.442485 + 0.442485i
\(382\) 0 0
\(383\) −17.2037 −0.879070 −0.439535 0.898225i \(-0.644857\pi\)
−0.439535 + 0.898225i \(0.644857\pi\)
\(384\) 0 0
\(385\) 4.23765 0.215971
\(386\) 0 0
\(387\) 0.389604 + 0.389604i 0.0198047 + 0.0198047i
\(388\) 0 0
\(389\) 23.8515 23.8515i 1.20932 1.20932i 0.238069 0.971248i \(-0.423486\pi\)
0.971248 0.238069i \(-0.0765143\pi\)
\(390\) 0 0
\(391\) 18.2306i 0.921961i
\(392\) 0 0
\(393\) 5.33962i 0.269348i
\(394\) 0 0
\(395\) 11.0544 11.0544i 0.556208 0.556208i
\(396\) 0 0
\(397\) 10.2673 + 10.2673i 0.515299 + 0.515299i 0.916145 0.400847i \(-0.131284\pi\)
−0.400847 + 0.916145i \(0.631284\pi\)
\(398\) 0 0
\(399\) −16.4853 −0.825296
\(400\) 0 0
\(401\) 32.2274 1.60936 0.804681 0.593708i \(-0.202337\pi\)
0.804681 + 0.593708i \(0.202337\pi\)
\(402\) 0 0
\(403\) −18.9374 18.9374i −0.943341 0.943341i
\(404\) 0 0
\(405\) 1.74912 1.74912i 0.0869143 0.0869143i
\(406\) 0 0
\(407\) 2.58526i 0.128146i
\(408\) 0 0
\(409\) 11.5702i 0.572110i 0.958213 + 0.286055i \(0.0923440\pi\)
−0.958213 + 0.286055i \(0.907656\pi\)
\(410\) 0 0
\(411\) 3.61040 3.61040i 0.178088 0.178088i
\(412\) 0 0
\(413\) −10.2306 10.2306i −0.503414 0.503414i
\(414\) 0 0
\(415\) 2.24471 0.110188
\(416\) 0 0
\(417\) −16.6533 −0.815517
\(418\) 0 0
\(419\) −6.74717 6.74717i −0.329621 0.329621i 0.522822 0.852442i \(-0.324879\pi\)
−0.852442 + 0.522822i \(0.824879\pi\)
\(420\) 0 0
\(421\) 17.2239 17.2239i 0.839443 0.839443i −0.149343 0.988785i \(-0.547716\pi\)
0.988785 + 0.149343i \(0.0477158\pi\)
\(422\) 0 0
\(423\) 2.82843i 0.137523i
\(424\) 0 0
\(425\) 7.21137i 0.349803i
\(426\) 0 0
\(427\) −11.2180 + 11.2180i −0.542879 + 0.542879i
\(428\) 0 0
\(429\) 1.93430 + 1.93430i 0.0933888 + 0.0933888i
\(430\) 0 0
\(431\) 40.7088 1.96087 0.980437 0.196832i \(-0.0630654\pi\)
0.980437 + 0.196832i \(0.0630654\pi\)
\(432\) 0 0
\(433\) 7.31371 0.351474 0.175737 0.984437i \(-0.443769\pi\)
0.175737 + 0.984437i \(0.443769\pi\)
\(434\) 0 0
\(435\) −7.61706 7.61706i −0.365210 0.365210i
\(436\) 0 0
\(437\) −12.8910 + 12.8910i −0.616659 + 0.616659i
\(438\) 0 0
\(439\) 17.7122i 0.845356i 0.906280 + 0.422678i \(0.138910\pi\)
−0.906280 + 0.422678i \(0.861090\pi\)
\(440\) 0 0
\(441\) 0.458440i 0.0218305i
\(442\) 0 0
\(443\) −15.6944 + 15.6944i −0.745664 + 0.745664i −0.973662 0.227997i \(-0.926782\pi\)
0.227997 + 0.973662i \(0.426782\pi\)
\(444\) 0 0
\(445\) −11.0496 11.0496i −0.523801 0.523801i
\(446\) 0 0
\(447\) 11.1832 0.528949
\(448\) 0 0
\(449\) −28.3400 −1.33745 −0.668723 0.743511i \(-0.733159\pi\)
−0.668723 + 0.743511i \(0.733159\pi\)
\(450\) 0 0
\(451\) −0.373517 0.373517i −0.0175882 0.0175882i
\(452\) 0 0
\(453\) −10.3595 + 10.3595i −0.486732 + 0.486732i
\(454\) 0 0
\(455\) 25.8382i 1.21131i
\(456\) 0 0
\(457\) 17.3396i 0.811113i −0.914070 0.405557i \(-0.867078\pi\)
0.914070 0.405557i \(-0.132922\pi\)
\(458\) 0 0
\(459\) 4.55765 4.55765i 0.212733 0.212733i
\(460\) 0 0
\(461\) 1.69284 + 1.69284i 0.0788434 + 0.0788434i 0.745429 0.666585i \(-0.232245\pi\)
−0.666585 + 0.745429i \(0.732245\pi\)
\(462\) 0 0
\(463\) 2.70238 0.125590 0.0627951 0.998026i \(-0.479999\pi\)
0.0627951 + 0.998026i \(0.479999\pi\)
\(464\) 0 0
\(465\) −16.2212 −0.752239
\(466\) 0 0
\(467\) 17.1136 + 17.1136i 0.791924 + 0.791924i 0.981807 0.189883i \(-0.0608108\pi\)
−0.189883 + 0.981807i \(0.560811\pi\)
\(468\) 0 0
\(469\) −5.41921 + 5.41921i −0.250236 + 0.250236i
\(470\) 0 0
\(471\) 4.45754i 0.205393i
\(472\) 0 0
\(473\) 0.369053i 0.0169691i
\(474\) 0 0
\(475\) 5.09921 5.09921i 0.233968 0.233968i
\(476\) 0 0
\(477\) 2.57754 + 2.57754i 0.118018 + 0.118018i
\(478\) 0 0
\(479\) −22.2251 −1.01549 −0.507745 0.861508i \(-0.669521\pi\)
−0.507745 + 0.861508i \(0.669521\pi\)
\(480\) 0 0
\(481\) −15.7631 −0.718735
\(482\) 0 0
\(483\) −5.11529 5.11529i −0.232754 0.232754i
\(484\) 0 0
\(485\) −22.1322 + 22.1322i −1.00497 + 1.00497i
\(486\) 0 0
\(487\) 13.9839i 0.633672i −0.948480 0.316836i \(-0.897380\pi\)
0.948480 0.316836i \(-0.102620\pi\)
\(488\) 0 0
\(489\) 7.78510i 0.352055i
\(490\) 0 0
\(491\) −7.23412 + 7.23412i −0.326471 + 0.326471i −0.851243 0.524772i \(-0.824151\pi\)
0.524772 + 0.851243i \(0.324151\pi\)
\(492\) 0 0
\(493\) −19.8476 19.8476i −0.893893 0.893893i
\(494\) 0 0
\(495\) 1.65685 0.0744701
\(496\) 0 0
\(497\) 13.0831 0.586858
\(498\) 0 0
\(499\) −2.59078 2.59078i −0.115979 0.115979i 0.646735 0.762715i \(-0.276134\pi\)
−0.762715 + 0.646735i \(0.776134\pi\)
\(500\) 0 0
\(501\) −14.2704 + 14.2704i −0.637554 + 0.637554i
\(502\) 0 0
\(503\) 39.6443i 1.76765i −0.467817 0.883825i \(-0.654959\pi\)
0.467817 0.883825i \(-0.345041\pi\)
\(504\) 0 0
\(505\) 26.3235i 1.17138i
\(506\) 0 0
\(507\) −2.60161 + 2.60161i −0.115542 + 0.115542i
\(508\) 0 0
\(509\) −20.2875 20.2875i −0.899229 0.899229i 0.0961393 0.995368i \(-0.469351\pi\)
−0.995368 + 0.0961393i \(0.969351\pi\)
\(510\) 0 0
\(511\) 37.7819 1.67137
\(512\) 0 0
\(513\) −6.44549 −0.284575
\(514\) 0 0
\(515\) 5.83655 + 5.83655i 0.257189 + 0.257189i
\(516\) 0 0
\(517\) −1.33962 + 1.33962i −0.0589162 + 0.0589162i
\(518\) 0 0
\(519\) 6.15639i 0.270235i
\(520\) 0 0
\(521\) 23.1784i 1.01546i 0.861515 + 0.507732i \(0.169516\pi\)
−0.861515 + 0.507732i \(0.830484\pi\)
\(522\) 0 0
\(523\) 5.78550 5.78550i 0.252982 0.252982i −0.569210 0.822192i \(-0.692751\pi\)
0.822192 + 0.569210i \(0.192751\pi\)
\(524\) 0 0
\(525\) 2.02343 + 2.02343i 0.0883096 + 0.0883096i
\(526\) 0 0
\(527\) −42.2672 −1.84119
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) 0 0
\(531\) −4.00000 4.00000i −0.173585 0.173585i
\(532\) 0 0
\(533\) 2.27744 2.27744i 0.0986470 0.0986470i
\(534\) 0 0
\(535\) 49.1941i 2.12685i
\(536\) 0 0
\(537\) 18.7855i 0.810653i
\(538\) 0 0
\(539\) −0.217129 + 0.217129i −0.00935241 + 0.00935241i
\(540\) 0 0
\(541\) −4.55175 4.55175i −0.195695 0.195695i 0.602457 0.798152i \(-0.294189\pi\)
−0.798152 + 0.602457i \(0.794189\pi\)
\(542\) 0 0
\(543\) −8.97499 −0.385154
\(544\) 0 0
\(545\) 9.68667 0.414931
\(546\) 0 0
\(547\) 27.7355 + 27.7355i 1.18588 + 1.18588i 0.978195 + 0.207689i \(0.0665942\pi\)
0.207689 + 0.978195i \(0.433406\pi\)
\(548\) 0 0
\(549\) −4.38607 + 4.38607i −0.187193 + 0.187193i
\(550\) 0 0
\(551\) 28.0688i 1.19577i
\(552\) 0 0
\(553\) 16.1643i 0.687377i
\(554\) 0 0
\(555\) −6.75107 + 6.75107i −0.286567 + 0.286567i
\(556\) 0 0
\(557\) 1.17538 + 1.17538i 0.0498026 + 0.0498026i 0.731569 0.681767i \(-0.238788\pi\)
−0.681767 + 0.731569i \(0.738788\pi\)
\(558\) 0 0
\(559\) −2.25023 −0.0951745
\(560\) 0 0
\(561\) 4.31724 0.182274
\(562\) 0 0
\(563\) 28.7346 + 28.7346i 1.21102 + 1.21102i 0.970692 + 0.240326i \(0.0772544\pi\)
0.240326 + 0.970692i \(0.422746\pi\)
\(564\) 0 0
\(565\) −3.91391 + 3.91391i −0.164659 + 0.164659i
\(566\) 0 0
\(567\) 2.55765i 0.107411i
\(568\) 0 0
\(569\) 27.0004i 1.13191i 0.824435 + 0.565957i \(0.191493\pi\)
−0.824435 + 0.565957i \(0.808507\pi\)
\(570\) 0 0
\(571\) 14.8284 14.8284i 0.620550 0.620550i −0.325122 0.945672i \(-0.605405\pi\)
0.945672 + 0.325122i \(0.105405\pi\)
\(572\) 0 0
\(573\) 3.96021 + 3.96021i 0.165440 + 0.165440i
\(574\) 0 0
\(575\) 3.16451 0.131969
\(576\) 0 0
\(577\) −37.6372 −1.56686 −0.783429 0.621481i \(-0.786531\pi\)
−0.783429 + 0.621481i \(0.786531\pi\)
\(578\) 0 0
\(579\) −13.7542 13.7542i −0.571605 0.571605i
\(580\) 0 0
\(581\) 1.64116 1.64116i 0.0680869 0.0680869i
\(582\) 0 0
\(583\) 2.44158i 0.101120i
\(584\) 0 0
\(585\) 10.1023i 0.417680i
\(586\) 0 0
\(587\) 31.2574 31.2574i 1.29013 1.29013i 0.355429 0.934703i \(-0.384335\pi\)
0.934703 0.355429i \(-0.115665\pi\)
\(588\) 0 0
\(589\) 29.8874 + 29.8874i 1.23149 + 1.23149i
\(590\) 0 0
\(591\) −1.75070 −0.0720140
\(592\) 0 0
\(593\) −3.59611 −0.147675 −0.0738373 0.997270i \(-0.523525\pi\)
−0.0738373 + 0.997270i \(0.523525\pi\)
\(594\) 0 0
\(595\) 28.8347 + 28.8347i 1.18211 + 1.18211i
\(596\) 0 0
\(597\) −0.702659 + 0.702659i −0.0287579 + 0.0287579i
\(598\) 0 0
\(599\) 22.0296i 0.900104i 0.893002 + 0.450052i \(0.148595\pi\)
−0.893002 + 0.450052i \(0.851405\pi\)
\(600\) 0 0
\(601\) 10.7721i 0.439405i −0.975567 0.219703i \(-0.929491\pi\)
0.975567 0.219703i \(-0.0705087\pi\)
\(602\) 0 0
\(603\) −2.11882 + 2.11882i −0.0862852 + 0.0862852i
\(604\) 0 0
\(605\) −18.4556 18.4556i −0.750325 0.750325i
\(606\) 0 0
\(607\) 5.47453 0.222204 0.111102 0.993809i \(-0.464562\pi\)
0.111102 + 0.993809i \(0.464562\pi\)
\(608\) 0 0
\(609\) −11.1380 −0.451336
\(610\) 0 0
\(611\) −8.16804 8.16804i −0.330444 0.330444i
\(612\) 0 0
\(613\) 10.5049 10.5049i 0.424289 0.424289i −0.462389 0.886677i \(-0.653007\pi\)
0.886677 + 0.462389i \(0.153007\pi\)
\(614\) 0 0
\(615\) 1.95078i 0.0786631i
\(616\) 0 0
\(617\) 22.2235i 0.894686i 0.894363 + 0.447343i \(0.147630\pi\)
−0.894363 + 0.447343i \(0.852370\pi\)
\(618\) 0 0
\(619\) −11.6398 + 11.6398i −0.467843 + 0.467843i −0.901215 0.433372i \(-0.857324\pi\)
0.433372 + 0.901215i \(0.357324\pi\)
\(620\) 0 0
\(621\) −2.00000 2.00000i −0.0802572 0.0802572i
\(622\) 0 0
\(623\) −16.1573 −0.647327
\(624\) 0 0
\(625\) 29.3424 1.17369
\(626\) 0 0
\(627\) −3.05275 3.05275i −0.121915 0.121915i
\(628\) 0 0
\(629\) −17.5912 + 17.5912i −0.701405 + 0.701405i
\(630\) 0 0
\(631\) 4.06977i 0.162015i −0.996713 0.0810075i \(-0.974186\pi\)
0.996713 0.0810075i \(-0.0258138\pi\)
\(632\) 0 0
\(633\) 5.97409i 0.237449i
\(634\) 0 0
\(635\) −21.3646 + 21.3646i −0.847828 + 0.847828i
\(636\) 0 0
\(637\) −1.32390 1.32390i −0.0524549 0.0524549i
\(638\) 0 0
\(639\) 5.11529 0.202358
\(640\) 0 0
\(641\) −8.41958 −0.332553 −0.166277 0.986079i \(-0.553174\pi\)
−0.166277 + 0.986079i \(0.553174\pi\)
\(642\) 0 0
\(643\) 7.37275 + 7.37275i 0.290753 + 0.290753i 0.837378 0.546625i \(-0.184088\pi\)
−0.546625 + 0.837378i \(0.684088\pi\)
\(644\) 0 0
\(645\) −0.963735 + 0.963735i −0.0379470 + 0.0379470i
\(646\) 0 0
\(647\) 11.6132i 0.456560i −0.973595 0.228280i \(-0.926690\pi\)
0.973595 0.228280i \(-0.0733102\pi\)
\(648\) 0 0
\(649\) 3.78901i 0.148731i
\(650\) 0 0
\(651\) −11.8597 + 11.8597i −0.464818 + 0.464818i
\(652\) 0 0
\(653\) 1.93049 + 1.93049i 0.0755458 + 0.0755458i 0.743870 0.668324i \(-0.232988\pi\)
−0.668324 + 0.743870i \(0.732988\pi\)
\(654\) 0 0
\(655\) −13.2082 −0.516088
\(656\) 0 0
\(657\) 14.7721 0.576316
\(658\) 0 0
\(659\) −22.3102 22.3102i −0.869081 0.869081i 0.123290 0.992371i \(-0.460656\pi\)
−0.992371 + 0.123290i \(0.960656\pi\)
\(660\) 0 0
\(661\) −10.7033 + 10.7033i −0.416311 + 0.416311i −0.883930 0.467619i \(-0.845112\pi\)
0.467619 + 0.883930i \(0.345112\pi\)
\(662\) 0 0
\(663\) 26.3235i 1.02232i
\(664\) 0 0
\(665\) 40.7784i 1.58132i
\(666\) 0 0
\(667\) −8.70960 + 8.70960i −0.337237 + 0.337237i
\(668\) 0 0
\(669\) −16.8050 16.8050i −0.649719 0.649719i
\(670\) 0 0
\(671\) −4.15472 −0.160391
\(672\) 0 0
\(673\) −20.6345 −0.795401 −0.397700 0.917515i \(-0.630192\pi\)
−0.397700 + 0.917515i \(0.630192\pi\)
\(674\) 0 0
\(675\) 0.791128 + 0.791128i 0.0304505 + 0.0304505i
\(676\) 0 0
\(677\) −26.8246 + 26.8246i −1.03095 + 1.03095i −0.0314484 + 0.999505i \(0.510012\pi\)
−0.999505 + 0.0314484i \(0.989988\pi\)
\(678\) 0 0
\(679\) 32.3627i 1.24197i
\(680\) 0 0
\(681\) 0.907457i 0.0347738i
\(682\) 0 0
\(683\) −12.9026 + 12.9026i −0.493705 + 0.493705i −0.909472 0.415766i \(-0.863513\pi\)
0.415766 + 0.909472i \(0.363513\pi\)
\(684\) 0 0
\(685\) 8.93077 + 8.93077i 0.341227 + 0.341227i
\(686\) 0 0
\(687\) −7.55579 −0.288271
\(688\) 0 0
\(689\) −14.8871 −0.567152
\(690\) 0 0
\(691\) 21.3923 + 21.3923i 0.813803 + 0.813803i 0.985202 0.171399i \(-0.0548286\pi\)
−0.171399 + 0.985202i \(0.554829\pi\)
\(692\) 0 0
\(693\) 1.21137 1.21137i 0.0460161 0.0460161i
\(694\) 0 0
\(695\) 41.1941i 1.56258i
\(696\) 0 0
\(697\) 5.08312i 0.192537i
\(698\) 0 0
\(699\) 16.4240 16.4240i 0.621213 0.621213i
\(700\) 0 0
\(701\) −14.2040 14.2040i −0.536479 0.536479i 0.386014 0.922493i \(-0.373852\pi\)
−0.922493 + 0.386014i \(0.873852\pi\)
\(702\) 0 0
\(703\) 24.8776 0.938278
\(704\) 0 0
\(705\) −6.99647 −0.263502
\(706\) 0 0
\(707\) −19.2458 19.2458i −0.723812 0.723812i
\(708\) 0 0
\(709\) 29.5474 29.5474i 1.10968 1.10968i 0.116485 0.993192i \(-0.462837\pi\)
0.993192 0.116485i \(-0.0371626\pi\)
\(710\) 0 0
\(711\) 6.32000i 0.237018i
\(712\) 0 0
\(713\) 18.5478i 0.694622i
\(714\) 0 0
\(715\) −4.78473 + 4.78473i −0.178939 + 0.178939i
\(716\) 0 0
\(717\) 19.0363 + 19.0363i 0.710922 + 0.710922i
\(718\) 0 0
\(719\) 28.3683 1.05796 0.528979 0.848635i \(-0.322575\pi\)
0.528979 + 0.848635i \(0.322575\pi\)
\(720\) 0 0
\(721\) 8.53450 0.317841
\(722\) 0 0
\(723\) −7.31814 7.31814i −0.272165 0.272165i
\(724\) 0 0
\(725\) 3.44521 3.44521i 0.127952 0.127952i
\(726\) 0 0
\(727\) 20.4843i 0.759722i −0.925044 0.379861i \(-0.875972\pi\)
0.925044 0.379861i \(-0.124028\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −2.51119 + 2.51119i −0.0928797 + 0.0928797i
\(732\) 0 0
\(733\) −33.9961 33.9961i −1.25567 1.25567i −0.953138 0.302536i \(-0.902167\pi\)
−0.302536 0.953138i \(-0.597833\pi\)
\(734\) 0 0
\(735\) −1.13401 −0.0418286
\(736\) 0 0
\(737\) −2.00706 −0.0739310
\(738\) 0 0
\(739\) −15.1645 15.1645i −0.557836 0.557836i 0.370855 0.928691i \(-0.379065\pi\)
−0.928691 + 0.370855i \(0.879065\pi\)
\(740\) 0 0
\(741\) 18.6135 18.6135i 0.683785 0.683785i
\(742\) 0 0
\(743\) 2.17431i 0.0797677i −0.999204 0.0398839i \(-0.987301\pi\)
0.999204 0.0398839i \(-0.0126988\pi\)
\(744\) 0 0
\(745\) 27.6631i 1.01350i
\(746\) 0 0
\(747\) 0.641669 0.641669i 0.0234774 0.0234774i
\(748\) 0 0
\(749\) 35.9670 + 35.9670i 1.31421 + 1.31421i
\(750\) 0 0
\(751\) 29.8980 1.09099 0.545497 0.838113i \(-0.316341\pi\)
0.545497 + 0.838113i \(0.316341\pi\)
\(752\) 0 0
\(753\) 13.7984 0.502843
\(754\) 0 0
\(755\) −25.6256 25.6256i −0.932610 0.932610i
\(756\) 0 0
\(757\) 15.3294 15.3294i 0.557157 0.557157i −0.371340 0.928497i \(-0.621101\pi\)
0.928497 + 0.371340i \(0.121101\pi\)
\(758\) 0 0
\(759\) 1.89450i 0.0687661i
\(760\) 0 0
\(761\) 4.29449i 0.155675i −0.996966 0.0778375i \(-0.975198\pi\)
0.996966 0.0778375i \(-0.0248015\pi\)
\(762\) 0 0
\(763\) 7.08216 7.08216i 0.256392 0.256392i
\(764\) 0 0
\(765\) 11.2739 + 11.2739i 0.407609 + 0.407609i
\(766\) 0 0
\(767\) 23.1027 0.834191
\(768\) 0 0
\(769\) 33.8819 1.22181 0.610907 0.791703i \(-0.290805\pi\)
0.610907 + 0.791703i \(0.290805\pi\)
\(770\) 0 0
\(771\) 12.0183 + 12.0183i 0.432829 + 0.432829i
\(772\) 0 0
\(773\) 35.0230 35.0230i 1.25969 1.25969i 0.308450 0.951240i \(-0.400190\pi\)
0.951240 0.308450i \(-0.0998104\pi\)
\(774\) 0 0
\(775\) 7.33686i 0.263548i
\(776\) 0 0
\(777\) 9.87175i 0.354147i
\(778\) 0 0
\(779\) −3.59431 + 3.59431i −0.128779 + 0.128779i
\(780\) 0 0
\(781\) 2.42274 + 2.42274i 0.0866923 + 0.0866923i
\(782\) 0 0
\(783\) −4.35480 −0.155628
\(784\) 0 0
\(785\) −11.0263 −0.393545
\(786\) 0 0
\(787\) −24.1090 24.1090i −0.859393 0.859393i 0.131873 0.991267i \(-0.457901\pi\)
−0.991267 + 0.131873i \(0.957901\pi\)
\(788\) 0 0
\(789\) −21.2082 + 21.2082i −0.755032 + 0.755032i
\(790\) 0 0
\(791\) 5.72312i 0.203491i
\(792\) 0 0
\(793\) 25.3326i 0.899585i
\(794\) 0 0
\(795\) −6.37588 + 6.37588i −0.226129 + 0.226129i
\(796\) 0 0
\(797\) 28.7722 + 28.7722i 1.01917 + 1.01917i 0.999813 + 0.0193524i \(0.00616044\pi\)
0.0193524 + 0.999813i \(0.493840\pi\)
\(798\) 0 0
\(799\) −18.2306