Properties

Label 912.2.q.l.577.2
Level $912$
Weight $2$
Character 912.577
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 577.2
Root \(1.71903 + 0.211943i\) of defining polynomial
Character \(\chi\) \(=\) 912.577
Dual form 912.2.q.l.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-0.675970 - 1.17081i) q^{5} -0.351939 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-0.675970 - 1.17081i) q^{5} -0.351939 q^{7} +(-0.500000 + 0.866025i) q^{9} -5.52420 q^{11} +(2.58613 - 4.47931i) q^{13} +(0.675970 - 1.17081i) q^{15} +(2.43807 - 3.61328i) q^{19} +(-0.175970 - 0.304788i) q^{21} +(4.41016 - 7.63862i) q^{23} +(1.58613 - 2.74726i) q^{25} -1.00000 q^{27} +(-1.35194 + 2.34163i) q^{29} +0.524200 q^{31} +(-2.76210 - 4.78410i) q^{33} +(0.237900 + 0.412055i) q^{35} -1.00000 q^{37} +5.17226 q^{39} +(1.35194 + 2.34163i) q^{41} +(-3.26210 - 5.65012i) q^{43} +1.35194 q^{45} +(-3.00000 + 5.19615i) q^{47} -6.87614 q^{49} +(2.02791 - 3.51244i) q^{53} +(3.73419 + 6.46781i) q^{55} +(4.34823 + 0.304788i) q^{57} +(-2.76210 - 4.78410i) q^{59} +(0.938069 - 1.62478i) q^{61} +(0.175970 - 0.304788i) q^{63} -6.99258 q^{65} +(5.99629 - 10.3859i) q^{67} +8.82032 q^{69} +(2.52420 + 4.37204i) q^{71} +(-3.85194 - 6.67175i) q^{73} +3.17226 q^{75} +1.94418 q^{77} +(3.91016 + 6.77260i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.34452 q^{83} -2.70388 q^{87} +(2.32403 - 4.02534i) q^{89} +(-0.910161 + 1.57644i) q^{91} +(0.262100 + 0.453970i) q^{93} +(-5.87854 - 0.412055i) q^{95} +(6.90645 + 11.9623i) q^{97} +(2.76210 - 4.78410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} + 2 q^{15} - 4 q^{19} + q^{21} + 14 q^{23} - 5 q^{25} - 6 q^{27} - 4 q^{29} - 30 q^{31} + 18 q^{35} - 6 q^{37} + 2 q^{39} + 4 q^{41} - 3 q^{43} + 4 q^{45} - 18 q^{47} - 4 q^{49} + 6 q^{53} + 12 q^{55} - 5 q^{57} - 13 q^{61} - q^{63} + 12 q^{65} + 9 q^{67} + 28 q^{69} - 18 q^{71} - 19 q^{73} - 10 q^{75} + 24 q^{77} + 11 q^{79} - 3 q^{81} + 8 q^{83} - 8 q^{87} + 16 q^{89} + 7 q^{91} - 15 q^{93} - 2 q^{95} + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −0.675970 1.17081i −0.302303 0.523604i 0.674354 0.738408i \(-0.264422\pi\)
−0.976657 + 0.214804i \(0.931089\pi\)
\(6\) 0 0
\(7\) −0.351939 −0.133021 −0.0665103 0.997786i \(-0.521187\pi\)
−0.0665103 + 0.997786i \(0.521187\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −5.52420 −1.66561 −0.832804 0.553567i \(-0.813266\pi\)
−0.832804 + 0.553567i \(0.813266\pi\)
\(12\) 0 0
\(13\) 2.58613 4.47931i 0.717263 1.24234i −0.244817 0.969569i \(-0.578728\pi\)
0.962080 0.272767i \(-0.0879389\pi\)
\(14\) 0 0
\(15\) 0.675970 1.17081i 0.174535 0.302303i
\(16\) 0 0
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 2.43807 3.61328i 0.559331 0.828944i
\(20\) 0 0
\(21\) −0.175970 0.304788i −0.0383997 0.0665103i
\(22\) 0 0
\(23\) 4.41016 7.63862i 0.919582 1.59276i 0.119531 0.992830i \(-0.461861\pi\)
0.800051 0.599932i \(-0.204806\pi\)
\(24\) 0 0
\(25\) 1.58613 2.74726i 0.317226 0.549452i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.35194 + 2.34163i −0.251049 + 0.434829i −0.963815 0.266573i \(-0.914109\pi\)
0.712766 + 0.701402i \(0.247442\pi\)
\(30\) 0 0
\(31\) 0.524200 0.0941490 0.0470745 0.998891i \(-0.485010\pi\)
0.0470745 + 0.998891i \(0.485010\pi\)
\(32\) 0 0
\(33\) −2.76210 4.78410i −0.480820 0.832804i
\(34\) 0 0
\(35\) 0.237900 + 0.412055i 0.0402125 + 0.0696500i
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) 5.17226 0.828225
\(40\) 0 0
\(41\) 1.35194 + 2.34163i 0.211137 + 0.365701i 0.952071 0.305878i \(-0.0989499\pi\)
−0.740933 + 0.671579i \(0.765617\pi\)
\(42\) 0 0
\(43\) −3.26210 5.65012i −0.497466 0.861636i 0.502530 0.864560i \(-0.332403\pi\)
−0.999996 + 0.00292406i \(0.999069\pi\)
\(44\) 0 0
\(45\) 1.35194 0.201535
\(46\) 0 0
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) −6.87614 −0.982306
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.02791 3.51244i 0.278555 0.482471i −0.692471 0.721446i \(-0.743478\pi\)
0.971026 + 0.238975i \(0.0768113\pi\)
\(54\) 0 0
\(55\) 3.73419 + 6.46781i 0.503518 + 0.872119i
\(56\) 0 0
\(57\) 4.34823 + 0.304788i 0.575937 + 0.0403702i
\(58\) 0 0
\(59\) −2.76210 4.78410i −0.359595 0.622836i 0.628298 0.777972i \(-0.283752\pi\)
−0.987893 + 0.155136i \(0.950418\pi\)
\(60\) 0 0
\(61\) 0.938069 1.62478i 0.120107 0.208032i −0.799702 0.600397i \(-0.795009\pi\)
0.919810 + 0.392364i \(0.128343\pi\)
\(62\) 0 0
\(63\) 0.175970 0.304788i 0.0221701 0.0383997i
\(64\) 0 0
\(65\) −6.99258 −0.867323
\(66\) 0 0
\(67\) 5.99629 10.3859i 0.732564 1.26884i −0.223221 0.974768i \(-0.571657\pi\)
0.955784 0.294069i \(-0.0950096\pi\)
\(68\) 0 0
\(69\) 8.82032 1.06184
\(70\) 0 0
\(71\) 2.52420 + 4.37204i 0.299567 + 0.518866i 0.976037 0.217605i \(-0.0698243\pi\)
−0.676470 + 0.736471i \(0.736491\pi\)
\(72\) 0 0
\(73\) −3.85194 6.67175i −0.450835 0.780870i 0.547603 0.836738i \(-0.315541\pi\)
−0.998438 + 0.0558687i \(0.982207\pi\)
\(74\) 0 0
\(75\) 3.17226 0.366301
\(76\) 0 0
\(77\) 1.94418 0.221560
\(78\) 0 0
\(79\) 3.91016 + 6.77260i 0.439927 + 0.761977i 0.997683 0.0680283i \(-0.0216708\pi\)
−0.557756 + 0.830005i \(0.688337\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −8.34452 −0.915930 −0.457965 0.888970i \(-0.651422\pi\)
−0.457965 + 0.888970i \(0.651422\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.70388 −0.289886
\(88\) 0 0
\(89\) 2.32403 4.02534i 0.246347 0.426685i −0.716163 0.697933i \(-0.754103\pi\)
0.962509 + 0.271248i \(0.0874365\pi\)
\(90\) 0 0
\(91\) −0.910161 + 1.57644i −0.0954108 + 0.165256i
\(92\) 0 0
\(93\) 0.262100 + 0.453970i 0.0271785 + 0.0470745i
\(94\) 0 0
\(95\) −5.87854 0.412055i −0.603126 0.0422760i
\(96\) 0 0
\(97\) 6.90645 + 11.9623i 0.701244 + 1.21459i 0.968030 + 0.250834i \(0.0807049\pi\)
−0.266786 + 0.963756i \(0.585962\pi\)
\(98\) 0 0
\(99\) 2.76210 4.78410i 0.277601 0.480820i
\(100\) 0 0
\(101\) 1.17226 2.03041i 0.116644 0.202034i −0.801792 0.597604i \(-0.796120\pi\)
0.918436 + 0.395570i \(0.129453\pi\)
\(102\) 0 0
\(103\) 16.1042 1.58680 0.793398 0.608703i \(-0.208310\pi\)
0.793398 + 0.608703i \(0.208310\pi\)
\(104\) 0 0
\(105\) −0.237900 + 0.412055i −0.0232167 + 0.0402125i
\(106\) 0 0
\(107\) 0.592243 0.0572543 0.0286272 0.999590i \(-0.490886\pi\)
0.0286272 + 0.999590i \(0.490886\pi\)
\(108\) 0 0
\(109\) 6.79001 + 11.7606i 0.650365 + 1.12647i 0.983034 + 0.183422i \(0.0587173\pi\)
−0.332669 + 0.943043i \(0.607949\pi\)
\(110\) 0 0
\(111\) −0.500000 0.866025i −0.0474579 0.0821995i
\(112\) 0 0
\(113\) −12.9926 −1.22224 −0.611120 0.791538i \(-0.709281\pi\)
−0.611120 + 0.791538i \(0.709281\pi\)
\(114\) 0 0
\(115\) −11.9245 −1.11197
\(116\) 0 0
\(117\) 2.58613 + 4.47931i 0.239088 + 0.414112i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 19.5168 1.77425
\(122\) 0 0
\(123\) −1.35194 + 2.34163i −0.121900 + 0.211137i
\(124\) 0 0
\(125\) −11.0484 −0.988199
\(126\) 0 0
\(127\) 5.35194 9.26983i 0.474908 0.822564i −0.524679 0.851300i \(-0.675815\pi\)
0.999587 + 0.0287355i \(0.00914807\pi\)
\(128\) 0 0
\(129\) 3.26210 5.65012i 0.287212 0.497466i
\(130\) 0 0
\(131\) −1.64806 2.85453i −0.143992 0.249401i 0.785005 0.619490i \(-0.212661\pi\)
−0.928996 + 0.370089i \(0.879327\pi\)
\(132\) 0 0
\(133\) −0.858052 + 1.27166i −0.0744026 + 0.110267i
\(134\) 0 0
\(135\) 0.675970 + 1.17081i 0.0581782 + 0.100768i
\(136\) 0 0
\(137\) −8.52420 + 14.7643i −0.728272 + 1.26140i 0.229342 + 0.973346i \(0.426343\pi\)
−0.957613 + 0.288057i \(0.906991\pi\)
\(138\) 0 0
\(139\) −8.96598 + 15.5295i −0.760484 + 1.31720i 0.182117 + 0.983277i \(0.441705\pi\)
−0.942601 + 0.333921i \(0.891628\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −14.2863 + 24.7446i −1.19468 + 2.06925i
\(144\) 0 0
\(145\) 3.65548 0.303571
\(146\) 0 0
\(147\) −3.43807 5.95491i −0.283567 0.491153i
\(148\) 0 0
\(149\) −0.972091 1.68371i −0.0796368 0.137935i 0.823456 0.567379i \(-0.192043\pi\)
−0.903093 + 0.429444i \(0.858709\pi\)
\(150\) 0 0
\(151\) −13.6406 −1.11006 −0.555030 0.831830i \(-0.687293\pi\)
−0.555030 + 0.831830i \(0.687293\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.354343 0.613740i −0.0284615 0.0492968i
\(156\) 0 0
\(157\) −8.32032 14.4112i −0.664034 1.15014i −0.979546 0.201219i \(-0.935510\pi\)
0.315512 0.948921i \(-0.397824\pi\)
\(158\) 0 0
\(159\) 4.05582 0.321647
\(160\) 0 0
\(161\) −1.55211 + 2.68833i −0.122323 + 0.211870i
\(162\) 0 0
\(163\) 1.99258 0.156071 0.0780355 0.996951i \(-0.475135\pi\)
0.0780355 + 0.996951i \(0.475135\pi\)
\(164\) 0 0
\(165\) −3.73419 + 6.46781i −0.290706 + 0.503518i
\(166\) 0 0
\(167\) 1.29372 2.24078i 0.100111 0.173397i −0.811619 0.584187i \(-0.801414\pi\)
0.911730 + 0.410790i \(0.134747\pi\)
\(168\) 0 0
\(169\) −6.87614 11.9098i −0.528934 0.916140i
\(170\) 0 0
\(171\) 1.91016 + 3.91807i 0.146074 + 0.299622i
\(172\) 0 0
\(173\) −8.82032 15.2772i −0.670597 1.16151i −0.977735 0.209843i \(-0.932705\pi\)
0.307139 0.951665i \(-0.400628\pi\)
\(174\) 0 0
\(175\) −0.558221 + 0.966868i −0.0421976 + 0.0730883i
\(176\) 0 0
\(177\) 2.76210 4.78410i 0.207612 0.359595i
\(178\) 0 0
\(179\) −2.22808 −0.166534 −0.0832672 0.996527i \(-0.526535\pi\)
−0.0832672 + 0.996527i \(0.526535\pi\)
\(180\) 0 0
\(181\) −4.73419 + 8.19986i −0.351890 + 0.609491i −0.986581 0.163275i \(-0.947794\pi\)
0.634691 + 0.772766i \(0.281127\pi\)
\(182\) 0 0
\(183\) 1.87614 0.138688
\(184\) 0 0
\(185\) 0.675970 + 1.17081i 0.0496983 + 0.0860799i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.351939 0.0255998
\(190\) 0 0
\(191\) 22.5726 1.63330 0.816648 0.577136i \(-0.195830\pi\)
0.816648 + 0.577136i \(0.195830\pi\)
\(192\) 0 0
\(193\) 6.93807 + 12.0171i 0.499413 + 0.865009i 1.00000 0.000677488i \(-0.000215651\pi\)
−0.500587 + 0.865686i \(0.666882\pi\)
\(194\) 0 0
\(195\) −3.49629 6.05575i −0.250375 0.433662i
\(196\) 0 0
\(197\) 8.30354 0.591603 0.295801 0.955249i \(-0.404413\pi\)
0.295801 + 0.955249i \(0.404413\pi\)
\(198\) 0 0
\(199\) −3.44178 + 5.96134i −0.243981 + 0.422588i −0.961845 0.273596i \(-0.911787\pi\)
0.717863 + 0.696184i \(0.245120\pi\)
\(200\) 0 0
\(201\) 11.9926 0.845891
\(202\) 0 0
\(203\) 0.475800 0.824110i 0.0333946 0.0578412i
\(204\) 0 0
\(205\) 1.82774 3.16574i 0.127655 0.221105i
\(206\) 0 0
\(207\) 4.41016 + 7.63862i 0.306527 + 0.530921i
\(208\) 0 0
\(209\) −13.4684 + 19.9605i −0.931627 + 1.38070i
\(210\) 0 0
\(211\) −4.31792 7.47885i −0.297258 0.514865i 0.678250 0.734831i \(-0.262739\pi\)
−0.975508 + 0.219966i \(0.929405\pi\)
\(212\) 0 0
\(213\) −2.52420 + 4.37204i −0.172955 + 0.299567i
\(214\) 0 0
\(215\) −4.41016 + 7.63862i −0.300770 + 0.520950i
\(216\) 0 0
\(217\) −0.184486 −0.0125238
\(218\) 0 0
\(219\) 3.85194 6.67175i 0.260290 0.450835i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 6.13824 + 10.6317i 0.411047 + 0.711954i 0.995004 0.0998301i \(-0.0318299\pi\)
−0.583958 + 0.811784i \(0.698497\pi\)
\(224\) 0 0
\(225\) 1.58613 + 2.74726i 0.105742 + 0.183151i
\(226\) 0 0
\(227\) −0.475800 −0.0315800 −0.0157900 0.999875i \(-0.505026\pi\)
−0.0157900 + 0.999875i \(0.505026\pi\)
\(228\) 0 0
\(229\) −5.17226 −0.341793 −0.170896 0.985289i \(-0.554666\pi\)
−0.170896 + 0.985289i \(0.554666\pi\)
\(230\) 0 0
\(231\) 0.972091 + 1.68371i 0.0639589 + 0.110780i
\(232\) 0 0
\(233\) 5.34452 + 9.25698i 0.350131 + 0.606445i 0.986272 0.165128i \(-0.0528037\pi\)
−0.636141 + 0.771573i \(0.719470\pi\)
\(234\) 0 0
\(235\) 8.11164 0.529145
\(236\) 0 0
\(237\) −3.91016 + 6.77260i −0.253992 + 0.439927i
\(238\) 0 0
\(239\) 0.475800 0.0307770 0.0153885 0.999882i \(-0.495101\pi\)
0.0153885 + 0.999882i \(0.495101\pi\)
\(240\) 0 0
\(241\) 0.320321 0.554813i 0.0206337 0.0357386i −0.855524 0.517763i \(-0.826765\pi\)
0.876158 + 0.482024i \(0.160098\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 4.64806 + 8.05068i 0.296954 + 0.514339i
\(246\) 0 0
\(247\) −9.87985 20.2653i −0.628640 1.28945i
\(248\) 0 0
\(249\) −4.17226 7.22657i −0.264406 0.457965i
\(250\) 0 0
\(251\) −2.52420 + 4.37204i −0.159326 + 0.275961i −0.934626 0.355633i \(-0.884265\pi\)
0.775300 + 0.631593i \(0.217599\pi\)
\(252\) 0 0
\(253\) −24.3626 + 42.1973i −1.53166 + 2.65292i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −10.3724 + 17.9656i −0.647014 + 1.12066i 0.336818 + 0.941570i \(0.390649\pi\)
−0.983832 + 0.179092i \(0.942684\pi\)
\(258\) 0 0
\(259\) 0.351939 0.0218684
\(260\) 0 0
\(261\) −1.35194 2.34163i −0.0836829 0.144943i
\(262\) 0 0
\(263\) 8.52420 + 14.7643i 0.525625 + 0.910409i 0.999555 + 0.0298460i \(0.00950169\pi\)
−0.473930 + 0.880563i \(0.657165\pi\)
\(264\) 0 0
\(265\) −5.48322 −0.336831
\(266\) 0 0
\(267\) 4.64806 0.284457
\(268\) 0 0
\(269\) −4.55211 7.88448i −0.277547 0.480725i 0.693228 0.720719i \(-0.256188\pi\)
−0.970775 + 0.239993i \(0.922855\pi\)
\(270\) 0 0
\(271\) 13.2207 + 22.8989i 0.803098 + 1.39101i 0.917568 + 0.397580i \(0.130150\pi\)
−0.114470 + 0.993427i \(0.536517\pi\)
\(272\) 0 0
\(273\) −1.82032 −0.110171
\(274\) 0 0
\(275\) −8.76210 + 15.1764i −0.528374 + 0.915171i
\(276\) 0 0
\(277\) 26.1574 1.57165 0.785824 0.618451i \(-0.212239\pi\)
0.785824 + 0.618451i \(0.212239\pi\)
\(278\) 0 0
\(279\) −0.262100 + 0.453970i −0.0156915 + 0.0271785i
\(280\) 0 0
\(281\) 12.2002 21.1313i 0.727801 1.26059i −0.230010 0.973188i \(-0.573876\pi\)
0.957811 0.287400i \(-0.0927909\pi\)
\(282\) 0 0
\(283\) −0.172260 0.298364i −0.0102398 0.0177359i 0.860860 0.508842i \(-0.169926\pi\)
−0.871100 + 0.491106i \(0.836593\pi\)
\(284\) 0 0
\(285\) −2.58242 5.29699i −0.152969 0.313767i
\(286\) 0 0
\(287\) −0.475800 0.824110i −0.0280856 0.0486457i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) −6.90645 + 11.9623i −0.404863 + 0.701244i
\(292\) 0 0
\(293\) 17.2813 1.00958 0.504792 0.863241i \(-0.331569\pi\)
0.504792 + 0.863241i \(0.331569\pi\)
\(294\) 0 0
\(295\) −3.73419 + 6.46781i −0.217413 + 0.376570i
\(296\) 0 0
\(297\) 5.52420 0.320547
\(298\) 0 0
\(299\) −22.8105 39.5089i −1.31917 2.28486i
\(300\) 0 0
\(301\) 1.14806 + 1.98850i 0.0661731 + 0.114615i
\(302\) 0 0
\(303\) 2.34452 0.134689
\(304\) 0 0
\(305\) −2.53643 −0.145235
\(306\) 0 0
\(307\) 4.43807 + 7.68696i 0.253294 + 0.438718i 0.964431 0.264336i \(-0.0851527\pi\)
−0.711137 + 0.703054i \(0.751819\pi\)
\(308\) 0 0
\(309\) 8.05211 + 13.9467i 0.458068 + 0.793398i
\(310\) 0 0
\(311\) 11.1648 0.633100 0.316550 0.948576i \(-0.397475\pi\)
0.316550 + 0.948576i \(0.397475\pi\)
\(312\) 0 0
\(313\) 2.25839 3.91165i 0.127652 0.221099i −0.795115 0.606459i \(-0.792589\pi\)
0.922766 + 0.385360i \(0.125923\pi\)
\(314\) 0 0
\(315\) −0.475800 −0.0268083
\(316\) 0 0
\(317\) 2.50371 4.33655i 0.140622 0.243565i −0.787109 0.616814i \(-0.788423\pi\)
0.927731 + 0.373249i \(0.121756\pi\)
\(318\) 0 0
\(319\) 7.46838 12.9356i 0.418149 0.724256i
\(320\) 0 0
\(321\) 0.296122 + 0.512898i 0.0165279 + 0.0286272i
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −8.20388 14.2095i −0.455069 0.788203i
\(326\) 0 0
\(327\) −6.79001 + 11.7606i −0.375488 + 0.650365i
\(328\) 0 0
\(329\) 1.05582 1.82873i 0.0582091 0.100821i
\(330\) 0 0
\(331\) 10.1797 0.559526 0.279763 0.960069i \(-0.409744\pi\)
0.279763 + 0.960069i \(0.409744\pi\)
\(332\) 0 0
\(333\) 0.500000 0.866025i 0.0273998 0.0474579i
\(334\) 0 0
\(335\) −16.2132 −0.885824
\(336\) 0 0
\(337\) −11.7584 20.3661i −0.640520 1.10941i −0.985317 0.170736i \(-0.945385\pi\)
0.344796 0.938677i \(-0.387948\pi\)
\(338\) 0 0
\(339\) −6.49629 11.2519i −0.352830 0.611120i
\(340\) 0 0
\(341\) −2.89578 −0.156815
\(342\) 0 0
\(343\) 4.88356 0.263687
\(344\) 0 0
\(345\) −5.96227 10.3270i −0.320998 0.555984i
\(346\) 0 0
\(347\) 6.23790 + 10.8044i 0.334868 + 0.580008i 0.983459 0.181128i \(-0.0579749\pi\)
−0.648591 + 0.761137i \(0.724642\pi\)
\(348\) 0 0
\(349\) 6.23550 0.333778 0.166889 0.985976i \(-0.446628\pi\)
0.166889 + 0.985976i \(0.446628\pi\)
\(350\) 0 0
\(351\) −2.58613 + 4.47931i −0.138037 + 0.239088i
\(352\) 0 0
\(353\) 29.8081 1.58652 0.793262 0.608880i \(-0.208381\pi\)
0.793262 + 0.608880i \(0.208381\pi\)
\(354\) 0 0
\(355\) 3.41256 5.91073i 0.181120 0.313709i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.87614 11.9098i −0.362909 0.628576i 0.625529 0.780201i \(-0.284883\pi\)
−0.988438 + 0.151624i \(0.951550\pi\)
\(360\) 0 0
\(361\) −7.11164 17.6189i −0.374297 0.927309i
\(362\) 0 0
\(363\) 9.75839 + 16.9020i 0.512183 + 0.887126i
\(364\) 0 0
\(365\) −5.20759 + 9.01981i −0.272578 + 0.472118i
\(366\) 0 0
\(367\) 9.25468 16.0296i 0.483090 0.836737i −0.516721 0.856154i \(-0.672848\pi\)
0.999811 + 0.0194166i \(0.00618090\pi\)
\(368\) 0 0
\(369\) −2.70388 −0.140758
\(370\) 0 0
\(371\) −0.713701 + 1.23617i −0.0370535 + 0.0641785i
\(372\) 0 0
\(373\) 6.53162 0.338194 0.169097 0.985599i \(-0.445915\pi\)
0.169097 + 0.985599i \(0.445915\pi\)
\(374\) 0 0
\(375\) −5.52420 9.56819i −0.285268 0.494099i
\(376\) 0 0
\(377\) 6.99258 + 12.1115i 0.360136 + 0.623774i
\(378\) 0 0
\(379\) −24.8687 −1.27742 −0.638710 0.769447i \(-0.720532\pi\)
−0.638710 + 0.769447i \(0.720532\pi\)
\(380\) 0 0
\(381\) 10.7039 0.548376
\(382\) 0 0
\(383\) −4.99018 8.64324i −0.254986 0.441649i 0.709906 0.704297i \(-0.248738\pi\)
−0.964892 + 0.262648i \(0.915404\pi\)
\(384\) 0 0
\(385\) −1.31421 2.27628i −0.0669783 0.116010i
\(386\) 0 0
\(387\) 6.52420 0.331644
\(388\) 0 0
\(389\) 8.54469 14.7998i 0.433233 0.750382i −0.563917 0.825832i \(-0.690706\pi\)
0.997150 + 0.0754502i \(0.0240394\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 1.64806 2.85453i 0.0831337 0.143992i
\(394\) 0 0
\(395\) 5.28630 9.15614i 0.265983 0.460695i
\(396\) 0 0
\(397\) 0.821627 + 1.42310i 0.0412363 + 0.0714233i 0.885907 0.463863i \(-0.153537\pi\)
−0.844671 + 0.535286i \(0.820204\pi\)
\(398\) 0 0
\(399\) −1.53031 0.107267i −0.0766115 0.00537006i
\(400\) 0 0
\(401\) 3.67597 + 6.36697i 0.183569 + 0.317951i 0.943093 0.332528i \(-0.107902\pi\)
−0.759524 + 0.650479i \(0.774568\pi\)
\(402\) 0 0
\(403\) 1.35565 2.34805i 0.0675297 0.116965i
\(404\) 0 0
\(405\) −0.675970 + 1.17081i −0.0335892 + 0.0581782i
\(406\) 0 0
\(407\) 5.52420 0.273824
\(408\) 0 0
\(409\) −1.03773 + 1.79740i −0.0513125 + 0.0888758i −0.890541 0.454903i \(-0.849674\pi\)
0.839228 + 0.543779i \(0.183007\pi\)
\(410\) 0 0
\(411\) −17.0484 −0.840936
\(412\) 0 0
\(413\) 0.972091 + 1.68371i 0.0478335 + 0.0828500i
\(414\) 0 0
\(415\) 5.64064 + 9.76988i 0.276888 + 0.479585i
\(416\) 0 0
\(417\) −17.9320 −0.878132
\(418\) 0 0
\(419\) −8.22808 −0.401968 −0.200984 0.979595i \(-0.564414\pi\)
−0.200984 + 0.979595i \(0.564414\pi\)
\(420\) 0 0
\(421\) −2.79001 4.83244i −0.135977 0.235519i 0.789993 0.613115i \(-0.210084\pi\)
−0.925970 + 0.377597i \(0.876751\pi\)
\(422\) 0 0
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.330143 + 0.571825i −0.0159768 + 0.0276726i
\(428\) 0 0
\(429\) −28.5726 −1.37950
\(430\) 0 0
\(431\) 14.0484 24.3325i 0.676688 1.17206i −0.299285 0.954164i \(-0.596748\pi\)
0.975973 0.217893i \(-0.0699185\pi\)
\(432\) 0 0
\(433\) −14.1661 + 24.5365i −0.680782 + 1.17915i 0.293961 + 0.955817i \(0.405026\pi\)
−0.974743 + 0.223331i \(0.928307\pi\)
\(434\) 0 0
\(435\) 1.82774 + 3.16574i 0.0876334 + 0.151786i
\(436\) 0 0
\(437\) −16.8482 34.5587i −0.805960 1.65316i
\(438\) 0 0
\(439\) −5.16855 8.95219i −0.246681 0.427265i 0.715922 0.698181i \(-0.246007\pi\)
−0.962603 + 0.270916i \(0.912673\pi\)
\(440\) 0 0
\(441\) 3.43807 5.95491i 0.163718 0.283567i
\(442\) 0 0
\(443\) −0.475800 + 0.824110i −0.0226060 + 0.0391547i −0.877107 0.480295i \(-0.840530\pi\)
0.854501 + 0.519450i \(0.173863\pi\)
\(444\) 0 0
\(445\) −6.28390 −0.297885
\(446\) 0 0
\(447\) 0.972091 1.68371i 0.0459783 0.0796368i
\(448\) 0 0
\(449\) −21.8639 −1.03182 −0.515911 0.856642i \(-0.672546\pi\)
−0.515911 + 0.856642i \(0.672546\pi\)
\(450\) 0 0
\(451\) −7.46838 12.9356i −0.351672 0.609114i
\(452\) 0 0
\(453\) −6.82032 11.8131i −0.320447 0.555030i
\(454\) 0 0
\(455\) 2.46096 0.115372
\(456\) 0 0
\(457\) 21.7645 1.01810 0.509050 0.860737i \(-0.329997\pi\)
0.509050 + 0.860737i \(0.329997\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.5521 18.2768i −0.491461 0.851235i 0.508491 0.861067i \(-0.330204\pi\)
−0.999952 + 0.00983244i \(0.996870\pi\)
\(462\) 0 0
\(463\) −5.16745 −0.240152 −0.120076 0.992765i \(-0.538314\pi\)
−0.120076 + 0.992765i \(0.538314\pi\)
\(464\) 0 0
\(465\) 0.354343 0.613740i 0.0164323 0.0284615i
\(466\) 0 0
\(467\) 36.8007 1.70293 0.851466 0.524410i \(-0.175714\pi\)
0.851466 + 0.524410i \(0.175714\pi\)
\(468\) 0 0
\(469\) −2.11033 + 3.65520i −0.0974460 + 0.168781i
\(470\) 0 0
\(471\) 8.32032 14.4112i 0.383380 0.664034i
\(472\) 0 0
\(473\) 18.0205 + 31.2124i 0.828583 + 1.43515i
\(474\) 0 0
\(475\) −6.05953 12.4291i −0.278030 0.570288i
\(476\) 0 0
\(477\) 2.02791 + 3.51244i 0.0928516 + 0.160824i
\(478\) 0 0
\(479\) 7.28870 12.6244i 0.333029 0.576824i −0.650075 0.759870i \(-0.725263\pi\)
0.983104 + 0.183046i \(0.0585958\pi\)
\(480\) 0 0
\(481\) −2.58613 + 4.47931i −0.117917 + 0.204239i
\(482\) 0 0
\(483\) −3.10422 −0.141247
\(484\) 0 0
\(485\) 9.33710 16.1723i 0.423976 0.734348i
\(486\) 0 0
\(487\) −7.04840 −0.319393 −0.159697 0.987166i \(-0.551052\pi\)
−0.159697 + 0.987166i \(0.551052\pi\)
\(488\) 0 0
\(489\) 0.996291 + 1.72563i 0.0450538 + 0.0780355i
\(490\) 0 0
\(491\) 5.22808 + 9.05530i 0.235940 + 0.408660i 0.959545 0.281554i \(-0.0908498\pi\)
−0.723606 + 0.690214i \(0.757516\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −7.46838 −0.335679
\(496\) 0 0
\(497\) −0.888365 1.53869i −0.0398486 0.0690198i
\(498\) 0 0
\(499\) 2.23659 + 3.87390i 0.100124 + 0.173419i 0.911735 0.410778i \(-0.134743\pi\)
−0.811612 + 0.584197i \(0.801409\pi\)
\(500\) 0 0
\(501\) 2.58744 0.115598
\(502\) 0 0
\(503\) 11.5242 19.9605i 0.513839 0.889995i −0.486032 0.873941i \(-0.661556\pi\)
0.999871 0.0160539i \(-0.00511034\pi\)
\(504\) 0 0
\(505\) −3.16965 −0.141048
\(506\) 0 0
\(507\) 6.87614 11.9098i 0.305380 0.528934i
\(508\) 0 0
\(509\) 13.1723 22.8150i 0.583850 1.01126i −0.411168 0.911560i \(-0.634879\pi\)
0.995018 0.0996984i \(-0.0317878\pi\)
\(510\) 0 0
\(511\) 1.35565 + 2.34805i 0.0599704 + 0.103872i
\(512\) 0 0
\(513\) −2.43807 + 3.61328i −0.107643 + 0.159530i
\(514\) 0 0
\(515\) −10.8860 18.8550i −0.479693 0.830852i
\(516\) 0 0
\(517\) 16.5726 28.7046i 0.728862 1.26243i
\(518\) 0 0
\(519\) 8.82032 15.2772i 0.387169 0.670597i
\(520\) 0 0
\(521\) 42.6332 1.86780 0.933898 0.357540i \(-0.116385\pi\)
0.933898 + 0.357540i \(0.116385\pi\)
\(522\) 0 0
\(523\) −5.94047 + 10.2892i −0.259759 + 0.449915i −0.966177 0.257879i \(-0.916976\pi\)
0.706418 + 0.707794i \(0.250310\pi\)
\(524\) 0 0
\(525\) −1.11644 −0.0487256
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −27.3990 47.4565i −1.19126 2.06333i
\(530\) 0 0
\(531\) 5.52420 0.239730
\(532\) 0 0
\(533\) 13.9852 0.605765
\(534\) 0 0
\(535\) −0.400338 0.693406i −0.0173081 0.0299786i
\(536\) 0 0
\(537\) −1.11404 1.92957i −0.0480743 0.0832672i
\(538\) 0 0
\(539\) 37.9852 1.63614
\(540\) 0 0
\(541\) −16.9610 + 29.3773i −0.729209 + 1.26303i 0.228009 + 0.973659i \(0.426778\pi\)
−0.957218 + 0.289368i \(0.906555\pi\)
\(542\) 0 0
\(543\) −9.46838 −0.406327
\(544\) 0 0
\(545\) 9.17968 15.8997i 0.393214 0.681067i
\(546\) 0 0
\(547\) −4.49760 + 7.79007i −0.192303 + 0.333079i −0.946013 0.324128i \(-0.894929\pi\)
0.753710 + 0.657207i \(0.228262\pi\)
\(548\) 0 0
\(549\) 0.938069 + 1.62478i 0.0400358 + 0.0693441i
\(550\) 0 0
\(551\) 5.16484 + 10.5940i 0.220030 + 0.451319i
\(552\) 0 0
\(553\) −1.37614 2.38354i −0.0585194 0.101359i
\(554\) 0 0
\(555\) −0.675970 + 1.17081i −0.0286933 + 0.0496983i
\(556\) 0 0
\(557\) −4.94418 + 8.56358i −0.209492 + 0.362850i −0.951555 0.307480i \(-0.900514\pi\)
0.742063 + 0.670330i \(0.233848\pi\)
\(558\) 0 0
\(559\) −33.7449 −1.42726
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 36.4413 1.53582 0.767909 0.640559i \(-0.221297\pi\)
0.767909 + 0.640559i \(0.221297\pi\)
\(564\) 0 0
\(565\) 8.78259 + 15.2119i 0.369486 + 0.639969i
\(566\) 0 0
\(567\) 0.175970 + 0.304788i 0.00739003 + 0.0127999i
\(568\) 0 0
\(569\) −27.2717 −1.14329 −0.571644 0.820502i \(-0.693694\pi\)
−0.571644 + 0.820502i \(0.693694\pi\)
\(570\) 0 0
\(571\) 16.1042 0.673940 0.336970 0.941515i \(-0.390598\pi\)
0.336970 + 0.941515i \(0.390598\pi\)
\(572\) 0 0
\(573\) 11.2863 + 19.5484i 0.471492 + 0.816648i
\(574\) 0 0
\(575\) −13.9902 24.2317i −0.583431 1.01053i
\(576\) 0 0
\(577\) −27.3323 −1.13786 −0.568929 0.822387i \(-0.692642\pi\)
−0.568929 + 0.822387i \(0.692642\pi\)
\(578\) 0 0
\(579\) −6.93807 + 12.0171i −0.288336 + 0.499413i
\(580\) 0 0
\(581\) 2.93676 0.121838
\(582\) 0 0
\(583\) −11.2026 + 19.4034i −0.463963 + 0.803608i
\(584\) 0 0
\(585\) 3.49629 6.05575i 0.144554 0.250375i
\(586\) 0 0
\(587\) 13.0508 + 22.6047i 0.538664 + 0.932994i 0.998976 + 0.0452367i \(0.0144042\pi\)
−0.460312 + 0.887757i \(0.652262\pi\)
\(588\) 0 0
\(589\) 1.27803 1.89408i 0.0526605 0.0780443i
\(590\) 0 0
\(591\) 4.15177 + 7.19108i 0.170781 + 0.295801i
\(592\) 0 0
\(593\) 4.55211 7.88448i 0.186933 0.323777i −0.757293 0.653075i \(-0.773479\pi\)
0.944226 + 0.329298i \(0.106812\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.88356 −0.281725
\(598\) 0 0
\(599\) −13.2937 + 23.0254i −0.543167 + 0.940792i 0.455553 + 0.890209i \(0.349441\pi\)
−0.998720 + 0.0505836i \(0.983892\pi\)
\(600\) 0 0
\(601\) 31.2691 1.27549 0.637746 0.770247i \(-0.279867\pi\)
0.637746 + 0.770247i \(0.279867\pi\)
\(602\) 0 0
\(603\) 5.99629 + 10.3859i 0.244188 + 0.422946i
\(604\) 0 0
\(605\) −13.1928 22.8505i −0.536362 0.929006i
\(606\) 0 0
\(607\) −18.8687 −0.765858 −0.382929 0.923778i \(-0.625085\pi\)
−0.382929 + 0.923778i \(0.625085\pi\)
\(608\) 0 0
\(609\) 0.951601 0.0385608
\(610\) 0 0
\(611\) 15.5168 + 26.8759i 0.627742 + 1.08728i
\(612\) 0 0
\(613\) 9.61033 + 16.6456i 0.388158 + 0.672309i 0.992202 0.124642i \(-0.0397783\pi\)
−0.604044 + 0.796951i \(0.706445\pi\)
\(614\) 0 0
\(615\) 3.65548 0.147403
\(616\) 0 0
\(617\) −11.2608 + 19.5043i −0.453343 + 0.785212i −0.998591 0.0530621i \(-0.983102\pi\)
0.545249 + 0.838274i \(0.316435\pi\)
\(618\) 0 0
\(619\) −5.99258 −0.240862 −0.120431 0.992722i \(-0.538428\pi\)
−0.120431 + 0.992722i \(0.538428\pi\)
\(620\) 0 0
\(621\) −4.41016 + 7.63862i −0.176974 + 0.306527i
\(622\) 0 0
\(623\) −0.817917 + 1.41667i −0.0327692 + 0.0567579i
\(624\) 0 0
\(625\) −0.462269 0.800673i −0.0184908 0.0320269i
\(626\) 0 0
\(627\) −24.0205 1.68371i −0.959286 0.0672410i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.700169 + 1.21273i −0.0278733 + 0.0482780i −0.879626 0.475667i \(-0.842207\pi\)
0.851752 + 0.523945i \(0.175540\pi\)
\(632\) 0 0
\(633\) 4.31792 7.47885i 0.171622 0.297258i
\(634\) 0 0
\(635\) −14.4710 −0.574264
\(636\) 0 0
\(637\) −17.7826 + 30.8003i −0.704572 + 1.22035i
\(638\) 0 0
\(639\) −5.04840 −0.199712
\(640\) 0 0
\(641\) −5.30354 9.18600i −0.209477 0.362825i 0.742073 0.670319i \(-0.233843\pi\)
−0.951550 + 0.307494i \(0.900510\pi\)
\(642\) 0 0
\(643\) −21.9963 38.0987i −0.867449 1.50247i −0.864595 0.502470i \(-0.832425\pi\)
−0.00285431 0.999996i \(-0.500909\pi\)
\(644\) 0 0
\(645\) −8.82032 −0.347300
\(646\) 0 0
\(647\) 8.11164 0.318901 0.159451 0.987206i \(-0.449028\pi\)
0.159451 + 0.987206i \(0.449028\pi\)
\(648\) 0 0
\(649\) 15.2584 + 26.4283i 0.598944 + 1.03740i
\(650\) 0 0
\(651\) −0.0922432 0.159770i −0.00361530 0.00626188i
\(652\) 0 0
\(653\) 34.6890 1.35749 0.678744 0.734375i \(-0.262525\pi\)
0.678744 + 0.734375i \(0.262525\pi\)
\(654\) 0 0
\(655\) −2.22808 + 3.85914i −0.0870582 + 0.150789i
\(656\) 0 0
\(657\) 7.70388 0.300557
\(658\) 0 0
\(659\) 15.5218 26.8845i 0.604643 1.04727i −0.387464 0.921885i \(-0.626649\pi\)
0.992108 0.125388i \(-0.0400177\pi\)
\(660\) 0 0
\(661\) 7.34452 12.7211i 0.285669 0.494793i −0.687102 0.726561i \(-0.741118\pi\)
0.972771 + 0.231768i \(0.0744510\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.06889 + 0.145018i 0.0802281 + 0.00562357i
\(666\) 0 0
\(667\) 11.9245 + 20.6539i 0.461720 + 0.799722i
\(668\) 0 0
\(669\) −6.13824 + 10.6317i −0.237318 + 0.411047i
\(670\) 0 0
\(671\) −5.18208 + 8.97563i −0.200052 + 0.346500i
\(672\) 0 0
\(673\) −12.3567 −0.476318 −0.238159 0.971226i \(-0.576544\pi\)
−0.238159 + 0.971226i \(0.576544\pi\)
\(674\) 0 0
\(675\) −1.58613 + 2.74726i −0.0610502 + 0.105742i
\(676\) 0 0
\(677\) 32.7858 1.26006 0.630031 0.776570i \(-0.283042\pi\)
0.630031 + 0.776570i \(0.283042\pi\)
\(678\) 0 0
\(679\) −2.43065 4.21001i −0.0932798 0.161565i
\(680\) 0 0
\(681\) −0.237900 0.412055i −0.00911636 0.0157900i
\(682\) 0 0
\(683\) −41.3977 −1.58404 −0.792020 0.610495i \(-0.790970\pi\)
−0.792020 + 0.610495i \(0.790970\pi\)
\(684\) 0 0
\(685\) 23.0484 0.880634
\(686\) 0 0
\(687\) −2.58613 4.47931i −0.0986670 0.170896i
\(688\) 0 0
\(689\) −10.4889 18.1673i −0.399594 0.692117i
\(690\) 0 0
\(691\) 42.9368 1.63339 0.816696 0.577069i \(-0.195803\pi\)
0.816696 + 0.577069i \(0.195803\pi\)
\(692\) 0 0
\(693\) −0.972091 + 1.68371i −0.0369267 + 0.0639589i
\(694\) 0 0
\(695\) 24.2429 0.919586
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −5.34452 + 9.25698i −0.202148 + 0.350131i
\(700\) 0 0
\(701\) 1.03533 + 1.79324i 0.0391038 + 0.0677297i 0.884915 0.465753i \(-0.154216\pi\)
−0.845811 + 0.533482i \(0.820883\pi\)
\(702\) 0 0
\(703\) −2.43807 + 3.61328i −0.0919535 + 0.136278i
\(704\) 0 0
\(705\) 4.05582 + 7.02488i 0.152751 + 0.264572i
\(706\) 0 0
\(707\) −0.412564 + 0.714582i −0.0155161 + 0.0268746i
\(708\) 0 0
\(709\) 6.28259 10.8818i 0.235948 0.408673i −0.723600 0.690220i \(-0.757514\pi\)
0.959548 + 0.281546i \(0.0908473\pi\)
\(710\) 0 0
\(711\) −7.82032 −0.293285
\(712\) 0 0
\(713\) 2.31180 4.00416i 0.0865778 0.149957i
\(714\) 0 0
\(715\) 38.6284 1.44462
\(716\) 0 0
\(717\) 0.237900 + 0.412055i 0.00888455 + 0.0153885i
\(718\) 0 0
\(719\) −25.1550 43.5698i −0.938124 1.62488i −0.768966 0.639289i \(-0.779229\pi\)
−0.169158 0.985589i \(-0.554105\pi\)
\(720\) 0 0
\(721\) −5.66771 −0.211076
\(722\) 0 0
\(723\) 0.640642 0.0238257
\(724\) 0 0
\(725\) 4.28870 + 7.42825i 0.159278 + 0.275878i
\(726\) 0 0
\(727\) −16.6672 28.8685i −0.618154 1.07067i −0.989822 0.142308i \(-0.954548\pi\)
0.371668 0.928366i \(-0.378786\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −25.8129 −0.953421 −0.476711 0.879060i \(-0.658171\pi\)
−0.476711 + 0.879060i \(0.658171\pi\)
\(734\) 0 0
\(735\) −4.64806 + 8.05068i −0.171446 + 0.296954i
\(736\) 0 0
\(737\) −33.1247 + 57.3737i −1.22016 + 2.11339i
\(738\) 0 0
\(739\) 24.2802 + 42.0545i 0.893161 + 1.54700i 0.836064 + 0.548632i \(0.184851\pi\)
0.0570970 + 0.998369i \(0.481816\pi\)
\(740\) 0 0
\(741\) 12.6103 18.6888i 0.463252 0.686552i
\(742\) 0 0
\(743\) 7.33470 + 12.7041i 0.269084 + 0.466067i 0.968626 0.248525i \(-0.0799457\pi\)
−0.699542 + 0.714592i \(0.746612\pi\)
\(744\) 0 0
\(745\) −1.31421 + 2.27628i −0.0481489 + 0.0833963i
\(746\) 0 0
\(747\) 4.17226 7.22657i 0.152655 0.264406i
\(748\) 0 0
\(749\) −0.208434 −0.00761600
\(750\) 0 0
\(751\) 3.87243 6.70724i 0.141307 0.244751i −0.786682 0.617358i \(-0.788203\pi\)
0.927989 + 0.372607i \(0.121536\pi\)
\(752\) 0 0
\(753\) −5.04840 −0.183974
\(754\) 0 0
\(755\) 9.22066 + 15.9707i 0.335574 + 0.581231i
\(756\) 0 0
\(757\) 15.8626 + 27.4748i 0.576536 + 0.998590i 0.995873 + 0.0907593i \(0.0289294\pi\)
−0.419337 + 0.907831i \(0.637737\pi\)
\(758\) 0 0
\(759\) −48.7252 −1.76861
\(760\) 0 0
\(761\) −37.2255 −1.34942 −0.674711 0.738082i \(-0.735732\pi\)
−0.674711 + 0.738082i \(0.735732\pi\)
\(762\) 0 0
\(763\) −2.38967 4.13903i −0.0865119 0.149843i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −28.5726 −1.03170
\(768\) 0 0
\(769\) 11.2645 19.5107i 0.406208 0.703574i −0.588253 0.808677i \(-0.700184\pi\)
0.994461 + 0.105103i \(0.0335174\pi\)
\(770\) 0 0
\(771\) −20.7449 −0.747108
\(772\) 0 0
\(773\) 25.5726 44.2930i 0.919782 1.59311i 0.120038 0.992769i \(-0.461698\pi\)
0.799744 0.600341i \(-0.204968\pi\)
\(774\) 0 0
\(775\) 0.831449 1.44011i 0.0298665 0.0517303i
\(776\) 0 0
\(777\) 0.175970 + 0.304788i 0.00631287 + 0.0109342i
\(778\) 0 0
\(779\) 11.7571 + 0.824110i 0.421241 + 0.0295268i
\(780\) 0 0
\(781\) −13.9442 24.1520i −0.498962 0.864228i
\(782\) 0 0
\(783\) 1.35194 2.34163i 0.0483144 0.0836829i
\(784\) 0 0
\(785\) −11.2486 + 19.4831i −0.401479 + 0.695381i
\(786\) 0 0
\(787\) 1.16745 0.0416152 0.0208076 0.999783i \(-0.493376\pi\)
0.0208076 + 0.999783i \(0.493376\pi\)
\(788\) 0 0
\(789\) −8.52420 + 14.7643i −0.303470 + 0.525625i
\(790\) 0 0
\(791\) 4.57260 0.162583
\(792\) 0 0
\(793\) −4.85194 8.40381i −0.172297 0.298428i
\(794\) 0 0
\(795\) −2.74161 4.74861i −0.0972349 0.168416i
\(796\) 0 0
\(797\) 37.1600 1.31628 0.658138 0.752897i \(-0.271344\pi\)