Properties

Label 192.2.j.a.49.4
Level $192$
Weight $2$
Character 192.49
Analytic conductor $1.533$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.53312771881\)
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 49.4
Root \(0.500000 + 1.44392i\) of defining polynomial
Character \(\chi\) \(=\) 192.49
Dual form 192.2.j.a.145.4

$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 0 0
\(5\) 1.74912 + 1.74912i 0.782229 + 0.782229i 0.980207 0.197977i \(-0.0634373\pi\)
−0.197977 + 0.980207i \(0.563437\pi\)
\(6\) 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 0.632091 0.774894i \(-0.282197\pi\)
−0.774894 + 0.632091i \(0.782197\pi\)
\(12\) 0 0
\(13\) 2.88784 2.88784i 0.800943 0.800943i −0.182300 0.983243i \(-0.558354\pi\)
0.983243 + 0.182300i \(0.0583543\pi\)
\(14\) 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 0.0466864 0.998910i \(-0.485134\pi\)
0.998910 0.0466864i \(-0.0148661\pi\)
\(20\) 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 \(-0.882496\pi\)
0.360821 + 0.932635i \(0.382496\pi\)
\(30\) 0 0
\(31\) −6.55765 −1.17779 −0.588894 0.808210i \(-0.700437\pi\)
−0.588894 + 0.808210i \(0.700437\pi\)
\(32\) 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 \(-0.352765\pi\)
−0.894916 + 0.446235i \(0.852765\pi\)
\(38\) 0 0
\(39\) 4.08402i 0.653967i
\(40\) 0 0
\(41\) 0.788632i 0.123164i −0.998102 0.0615818i \(-0.980385\pi\)
0.998102 0.0615818i \(-0.0196145\pi\)
\(42\) 0 0
\(43\) 0.389604 + 0.389604i 0.0594141 + 0.0594141i 0.736190 0.676775i \(-0.236623\pi\)
−0.676775 + 0.736190i \(0.736623\pi\)
\(44\) 0 0
\(45\) 1.74912 1.74912i 0.260743 0.260743i
\(46\) 0 0
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) 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 \(-0.330547\pi\)
−0.861615 + 0.507562i \(0.830547\pi\)
\(54\) 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 0.397044 0.917800i \(-0.370036\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(60\) 0 0
\(61\) −4.38607 + 4.38607i −0.561579 + 0.561579i −0.929756 0.368177i \(-0.879982\pi\)
0.368177 + 0.929756i \(0.379982\pi\)
\(62\) 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 −0.565733 0.824589i \(-0.691407\pi\)
0.824589 + 0.565733i \(0.191407\pi\)
\(68\) 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 \(0.332349\pi\)
−0.502676 + 0.864475i \(0.667651\pi\)
\(74\) 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 \(-0.384301\pi\)
0.355528 + 0.934666i \(0.384301\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) −0.641669 + 0.641669i −0.0704323 + 0.0704323i −0.741445 0.671013i \(-0.765859\pi\)
0.671013 + 0.741445i \(0.265859\pi\)
\(84\) 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 \(-0.891327\pi\)
0.942285 0.334813i \(-0.108673\pi\)
\(90\) 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 \(-0.0724010\pi\)
−0.225498 + 0.974244i \(0.572401\pi\)
\(102\) 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 0.874560 + 0.484918i \(0.161151\pi\)
0.484918 + 0.874560i \(0.338849\pi\)
\(108\) 0 0
\(109\) 2.76901 2.76901i 0.265224 0.265224i −0.561949 0.827172i \(-0.689948\pi\)
0.827172 + 0.561949i \(0.189948\pi\)
\(110\) 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 \(-0.682307\pi\)
−0.541931 + 0.840423i \(0.682307\pi\)
\(128\) 0 0
\(129\) 0.550984 0.0485114
\(130\) 0 0
\(131\) 3.77568 3.77568i 0.329883 0.329883i −0.522659 0.852542i \(-0.675060\pi\)
0.852542 + 0.522659i \(0.175060\pi\)
\(132\) 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 \(0.0699898\pi\)
−0.975924 + 0.218112i \(0.930010\pi\)
\(138\) 0 0
\(139\) −11.7757 11.7757i −0.998800 0.998800i 0.00119925 0.999999i \(-0.499618\pi\)
−0.999999 + 0.00119925i \(0.999618\pi\)
\(140\) 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 \(-0.401464\pi\)
−0.952467 + 0.304640i \(0.901464\pi\)
\(150\) 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 \(-0.806922\pi\)
0.570054 + 0.821607i \(0.306922\pi\)
\(158\) 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 −0.889029 0.457852i \(-0.848619\pi\)
0.457852 + 0.889029i \(0.348619\pi\)
\(164\) 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 \(-0.674808\pi\)
0.852955 + 0.521985i \(0.174808\pi\)
\(174\) 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 −0.00713130 0.999975i \(-0.502270\pi\)
0.999975 + 0.00713130i \(0.00226998\pi\)
\(180\) 0 0
\(181\) 6.34628 + 6.34628i 0.471715 + 0.471715i 0.902469 0.430754i \(-0.141752\pi\)
−0.430754 + 0.902469i \(0.641752\pi\)
\(182\) 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 \(-0.564946\pi\)
−0.202622 + 0.979257i \(0.564946\pi\)
\(192\) 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 \(-0.230135\pi\)
−0.661631 + 0.749830i \(0.730135\pi\)
\(198\) 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 −0.837402 0.546588i \(-0.815927\pi\)
0.546588 + 0.837402i \(0.315927\pi\)
\(212\) 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 \(-0.207082\pi\)
0.795740 + 0.605639i \(0.207082\pi\)
\(224\) 0 0
\(225\) 1.11882 0.0745883
\(226\) 0 0
\(227\) 0.641669 0.641669i 0.0425891 0.0425891i −0.685492 0.728081i \(-0.740413\pi\)
0.728081 + 0.685492i \(0.240413\pi\)
\(228\) 0 0
\(229\) 5.34275 + 5.34275i 0.353059 + 0.353059i 0.861246 0.508188i \(-0.169684\pi\)
−0.508188 + 0.861246i \(0.669684\pi\)
\(230\) 0 0
\(231\) 1.71313i 0.112716i
\(232\) 0 0
\(233\) 23.2271i 1.52166i 0.648954 + 0.760828i \(0.275207\pi\)
−0.648954 + 0.760828i \(0.724793\pi\)
\(234\) 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 \(-0.836333\pi\)
−0.870698 + 0.491817i \(0.836333\pi\)
\(240\) 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 0.944465 0.328611i \(-0.106581\pi\)
−0.328611 + 0.944465i \(0.606581\pi\)
\(252\) 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 0.303046 0.952976i \(-0.401996\pi\)
0.952976 0.303046i \(-0.0980037\pi\)
\(270\) 0 0
\(271\) 26.6506 1.61891 0.809453 0.587184i \(-0.199764\pi\)
0.809453 + 0.587184i \(0.199764\pi\)
\(272\) 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 \(-0.0777872\pi\)
−0.241951 + 0.970289i \(0.577787\pi\)
\(278\) 0 0
\(279\) 6.55765i 0.392596i
\(280\) 0 0
\(281\) 2.76588i 0.164999i 0.996591 + 0.0824993i \(0.0262902\pi\)
−0.996591 + 0.0824993i \(0.973710\pi\)
\(282\) 0 0
\(283\) −4.48528 4.48528i −0.266622 0.266622i 0.561115 0.827738i \(-0.310372\pi\)
−0.827738 + 0.561115i \(0.810372\pi\)
\(284\) 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 \(-0.360111\pi\)
−0.904976 + 0.425463i \(0.860111\pi\)
\(294\) 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 −0.939431 0.342738i \(-0.888646\pi\)
0.342738 + 0.939431i \(0.388646\pi\)
\(308\) 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 \(0.225271\pi\)
−0.759852 + 0.650096i \(0.774729\pi\)
\(314\) 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 \(-0.836505\pi\)
0.491346 + 0.870964i \(0.336505\pi\)
\(318\) 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 0.996436 + 0.0843464i \(0.0268802\pi\)
0.0843464 + 0.996436i \(0.473120\pi\)
\(332\) 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 0.518317 0.855188i \(-0.326559\pi\)
−0.855188 + 0.518317i \(0.826559\pi\)
\(348\) 0 0
\(349\) −4.74255 + 4.74255i −0.253863 + 0.253863i −0.822552 0.568690i \(-0.807451\pi\)
0.568690 + 0.822552i \(0.307451\pi\)
\(350\) 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 \(-0.681119\pi\)
−0.538791 + 0.842439i \(0.681119\pi\)
\(368\) 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 \(-0.458180\pi\)
−0.991382 + 0.131004i \(0.958180\pi\)
\(374\) 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 0.478523 0.878075i \(-0.341172\pi\)
−0.878075 + 0.478523i \(0.841172\pi\)
\(380\) 0 0
\(381\) −8.63696 + 8.63696i −0.442485 + 0.442485i
\(382\) 0 0
\(383\) 17.2037 0.879070 0.439535 0.898225i \(-0.355143\pi\)
0.439535 + 0.898225i \(0.355143\pi\)
\(384\) 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 −0.971248 0.238069i \(-0.923486\pi\)
−0.238069 0.971248i \(-0.576514\pi\)
\(390\) 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 \(-0.868716\pi\)
0.400847 + 0.916145i \(0.368716\pi\)
\(398\) 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 \(-0.907656\pi\)
0.958213 0.286055i \(-0.0923440\pi\)
\(410\) 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 −0.852442 0.522822i \(-0.824879\pi\)
0.522822 + 0.852442i \(0.324879\pi\)
\(420\) 0 0
\(421\) −17.2239 17.2239i −0.839443 0.839443i 0.149343 0.988785i \(-0.452284\pi\)
−0.988785 + 0.149343i \(0.952284\pi\)
\(422\) 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 \(-0.936935\pi\)
−0.980437 + 0.196832i \(0.936935\pi\)
\(432\) 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 0.227997 0.973662i \(-0.426782\pi\)
−0.973662 + 0.227997i \(0.926782\pi\)
\(444\) 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 \(0.132922\pi\)
−0.914070 + 0.405557i \(0.867078\pi\)
\(458\) 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 \(-0.767755\pi\)
0.666585 + 0.745429i \(0.267755\pi\)
\(462\) 0 0
\(463\) −2.70238 −0.125590 −0.0627951 0.998026i \(-0.520001\pi\)
−0.0627951 + 0.998026i \(0.520001\pi\)
\(464\) 0 0
\(465\) −16.2212 −0.752239
\(466\) 0 0
\(467\) 17.1136 17.1136i 0.791924 0.791924i −0.189883 0.981807i \(-0.560811\pi\)
0.981807 + 0.189883i \(0.0608108\pi\)
\(468\) 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 \(-0.330479\pi\)
0.507745 + 0.861508i \(0.330479\pi\)
\(480\) 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 0.524772 0.851243i \(-0.324151\pi\)
−0.851243 + 0.524772i \(0.824151\pi\)
\(492\) 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 −0.762715 0.646735i \(-0.776134\pi\)
0.646735 + 0.762715i \(0.276134\pi\)
\(500\) 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 \(-0.530649\pi\)
0.995368 + 0.0961393i \(0.0306494\pi\)
\(510\) 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 \(-0.830484\pi\)
0.861515 0.507732i \(-0.169516\pi\)
\(522\) 0 0
\(523\) 5.78550 + 5.78550i 0.252982 + 0.252982i 0.822192 0.569210i \(-0.192751\pi\)
−0.569210 + 0.822192i \(0.692751\pi\)
\(524\) 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 \(-0.705811\pi\)
0.798152 + 0.602457i \(0.205811\pi\)
\(542\) 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 0.207689 0.978195i \(-0.433406\pi\)
0.978195 0.207689i \(-0.0665942\pi\)
\(548\) 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 \(-0.761212\pi\)
0.681767 + 0.731569i \(0.261212\pi\)
\(558\) 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 0.240326 0.970692i \(-0.422746\pi\)
0.970692 0.240326i \(-0.0772544\pi\)
\(564\) 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 \(-0.808507\pi\)
0.824435 0.565957i \(-0.191493\pi\)
\(570\) 0 0
\(571\) 14.8284 + 14.8284i 0.620550 + 0.620550i 0.945672 0.325122i \(-0.105405\pi\)
−0.325122 + 0.945672i \(0.605405\pi\)
\(572\) 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 0.934703 + 0.355429i \(0.115665\pi\)
0.355429 + 0.934703i \(0.384335\pi\)
\(588\) 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 \(0.0705087\pi\)
−0.975567 + 0.219703i \(0.929491\pi\)
\(602\) 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 \(-0.535438\pi\)
−0.111102 + 0.993809i \(0.535438\pi\)
\(608\) 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 \(-0.346993\pi\)
−0.886677 + 0.462389i \(0.846993\pi\)
\(614\) 0 0
\(615\) 1.95078i 0.0786631i
\(616\) 0 0
\(617\) 22.2235i 0.894686i −0.894363 0.447343i \(-0.852370\pi\)
0.894363 0.447343i \(-0.147630\pi\)
\(618\) 0 0
\(619\) −11.6398 11.6398i −0.467843 0.467843i 0.433372 0.901215i \(-0.357324\pi\)
−0.901215 + 0.433372i \(0.857324\pi\)
\(620\) 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 −0.546625 0.837378i \(-0.684088\pi\)
0.837378 + 0.546625i \(0.184088\pi\)
\(644\) 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 \(-0.767012\pi\)
0.668324 + 0.743870i \(0.267012\pi\)
\(654\) 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 −0.992371 0.123290i \(-0.960656\pi\)
0.123290 + 0.992371i \(0.460656\pi\)
\(660\) 0 0
\(661\) 10.7033 + 10.7033i 0.416311 + 0.416311i 0.883930 0.467619i \(-0.154888\pi\)
−0.467619 + 0.883930i \(0.654888\pi\)
\(662\) 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 0.999505 + 0.0314484i \(0.0100120\pi\)
0.0314484 + 0.999505i \(0.489988\pi\)
\(678\) 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 0.415766 0.909472i \(-0.363513\pi\)
−0.909472 + 0.415766i \(0.863513\pi\)
\(684\) 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 −0.171399 0.985202i \(-0.554829\pi\)
0.985202 + 0.171399i \(0.0548286\pi\)
\(692\) 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 \(-0.626148\pi\)
0.922493 + 0.386014i \(0.126148\pi\)
\(702\) 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 −0.993192 0.116485i \(-0.962837\pi\)
−0.116485 0.993192i \(-0.537163\pi\)
\(710\) 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 \(-0.677425\pi\)
−0.528979 + 0.848635i \(0.677425\pi\)
\(720\) 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 0.302536 0.953138i \(-0.402167\pi\)
0.953138 0.302536i \(-0.0978331\pi\)
\(734\) 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 −0.928691 0.370855i \(-0.879065\pi\)
0.370855 + 0.928691i \(0.379065\pi\)
\(740\) 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 \(-0.683659\pi\)
−0.545497 + 0.838113i \(0.683659\pi\)
\(752\) 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 \(-0.378899\pi\)
−0.928497 + 0.371340i \(0.878899\pi\)
\(758\) 0 0
\(759\) 1.89450i 0.0687661i
\(760\) 0 0
\(761\) 4.29449i 0.155675i 0.996966 + 0.0778375i \(0.0248015\pi\)
−0.996966 + 0.0778375i \(0.975198\pi\)
\(762\) 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 −0.951240 0.308450i \(-0.900190\pi\)
−0.308450 0.951240i \(-0.599810\pi\)
\(774\) 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 −0.991267 0.131873i \(-0.957901\pi\)
0.131873 + 0.991267i \(0.457901\pi\)
\(788\) 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 −0.0193524 + 0.999813i \(0.506160\pi\)
−0.999813 + 0.0193524i \(0.993840\pi\)
\(798\) 0 0
\(799\) 18.2306