Properties

Label 912.2.q.l.49.1
Level $912$
Weight $2$
Character 912.49
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 49.1
Root \(0.403374 + 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 912.49
Dual form 912.2.q.l.577.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.66044 + 2.87597i) q^{5} -2.32088 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.66044 + 2.87597i) q^{5} -2.32088 q^{7} +(-0.500000 - 0.866025i) q^{9} +1.70739 q^{11} +(-2.01414 - 3.48859i) q^{13} +(1.66044 + 2.87597i) q^{15} +(-0.193252 - 4.35461i) q^{19} +(-1.16044 + 2.00994i) q^{21} +(-1.17458 - 2.03443i) q^{23} +(-3.01414 - 5.22064i) q^{25} -1.00000 q^{27} +(-3.32088 - 5.75194i) q^{29} -6.70739 q^{31} +(0.853695 - 1.47864i) q^{33} +(3.85369 - 6.67479i) q^{35} -1.00000 q^{37} -4.02827 q^{39} +(3.32088 - 5.75194i) q^{41} +(0.353695 - 0.612617i) q^{43} +3.32088 q^{45} +(-3.00000 - 5.19615i) q^{47} -1.61350 q^{49} +(4.98133 + 8.62791i) q^{53} +(-2.83502 + 4.91040i) q^{55} +(-3.86783 - 2.00994i) q^{57} +(0.853695 - 1.47864i) q^{59} +(-1.69325 - 2.93280i) q^{61} +(1.16044 + 2.00994i) q^{63} +13.3774 q^{65} +(-4.18872 - 7.25507i) q^{67} -2.34916 q^{69} +(-4.70739 + 8.15344i) q^{71} +(-5.82088 + 10.0821i) q^{73} -6.02827 q^{75} -3.96265 q^{77} +(-1.67458 + 2.90046i) q^{79} +(-0.500000 + 0.866025i) q^{81} +10.0565 q^{83} -6.64177 q^{87} +(1.33956 + 2.32018i) q^{89} +(4.67458 + 8.09661i) q^{91} +(-3.35369 + 5.80877i) q^{93} +(12.8446 + 6.67479i) q^{95} +(-8.86330 + 15.3517i) q^{97} +(-0.853695 - 1.47864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(5\) −1.66044 + 2.87597i −0.742572 + 1.28617i 0.208748 + 0.977969i \(0.433061\pi\)
−0.951320 + 0.308204i \(0.900272\pi\)
\(6\) 0 0
\(7\) −2.32088 −0.877212 −0.438606 0.898679i \(-0.644528\pi\)
−0.438606 + 0.898679i \(0.644528\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 1.70739 0.514797 0.257399 0.966305i \(-0.417135\pi\)
0.257399 + 0.966305i \(0.417135\pi\)
\(12\) 0 0
\(13\) −2.01414 3.48859i −0.558621 0.967560i −0.997612 0.0690685i \(-0.977997\pi\)
0.438991 0.898492i \(-0.355336\pi\)
\(14\) 0 0
\(15\) 1.66044 + 2.87597i 0.428724 + 0.742572i
\(16\) 0 0
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) −0.193252 4.35461i −0.0443351 0.999017i
\(20\) 0 0
\(21\) −1.16044 + 2.00994i −0.253229 + 0.438606i
\(22\) 0 0
\(23\) −1.17458 2.03443i −0.244917 0.424208i 0.717191 0.696876i \(-0.245427\pi\)
−0.962108 + 0.272668i \(0.912094\pi\)
\(24\) 0 0
\(25\) −3.01414 5.22064i −0.602827 1.04413i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −3.32088 5.75194i −0.616673 1.06811i −0.990089 0.140444i \(-0.955147\pi\)
0.373416 0.927664i \(-0.378186\pi\)
\(30\) 0 0
\(31\) −6.70739 −1.20468 −0.602341 0.798239i \(-0.705765\pi\)
−0.602341 + 0.798239i \(0.705765\pi\)
\(32\) 0 0
\(33\) 0.853695 1.47864i 0.148609 0.257399i
\(34\) 0 0
\(35\) 3.85369 6.67479i 0.651393 1.12825i
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) −4.02827 −0.645040
\(40\) 0 0
\(41\) 3.32088 5.75194i 0.518635 0.898302i −0.481131 0.876649i \(-0.659774\pi\)
0.999766 0.0216532i \(-0.00689298\pi\)
\(42\) 0 0
\(43\) 0.353695 0.612617i 0.0539379 0.0934232i −0.837796 0.545984i \(-0.816156\pi\)
0.891734 + 0.452561i \(0.149489\pi\)
\(44\) 0 0
\(45\) 3.32088 0.495048
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) −1.61350 −0.230499
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.98133 + 8.62791i 0.684238 + 1.18513i 0.973676 + 0.227938i \(0.0731983\pi\)
−0.289438 + 0.957197i \(0.593468\pi\)
\(54\) 0 0
\(55\) −2.83502 + 4.91040i −0.382274 + 0.662118i
\(56\) 0 0
\(57\) −3.86783 2.00994i −0.512307 0.266224i
\(58\) 0 0
\(59\) 0.853695 1.47864i 0.111142 0.192503i −0.805089 0.593154i \(-0.797883\pi\)
0.916231 + 0.400651i \(0.131216\pi\)
\(60\) 0 0
\(61\) −1.69325 2.93280i −0.216799 0.375506i 0.737029 0.675861i \(-0.236228\pi\)
−0.953828 + 0.300355i \(0.902895\pi\)
\(62\) 0 0
\(63\) 1.16044 + 2.00994i 0.146202 + 0.253229i
\(64\) 0 0
\(65\) 13.3774 1.65927
\(66\) 0 0
\(67\) −4.18872 7.25507i −0.511733 0.886348i −0.999907 0.0136016i \(-0.995670\pi\)
0.488174 0.872746i \(-0.337663\pi\)
\(68\) 0 0
\(69\) −2.34916 −0.282805
\(70\) 0 0
\(71\) −4.70739 + 8.15344i −0.558664 + 0.967635i 0.438944 + 0.898514i \(0.355353\pi\)
−0.997608 + 0.0691206i \(0.977981\pi\)
\(72\) 0 0
\(73\) −5.82088 + 10.0821i −0.681283 + 1.18002i 0.293307 + 0.956018i \(0.405244\pi\)
−0.974590 + 0.223998i \(0.928089\pi\)
\(74\) 0 0
\(75\) −6.02827 −0.696085
\(76\) 0 0
\(77\) −3.96265 −0.451586
\(78\) 0 0
\(79\) −1.67458 + 2.90046i −0.188405 + 0.326327i −0.944719 0.327882i \(-0.893665\pi\)
0.756314 + 0.654209i \(0.226998\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 10.0565 1.10385 0.551925 0.833894i \(-0.313894\pi\)
0.551925 + 0.833894i \(0.313894\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −6.64177 −0.712072
\(88\) 0 0
\(89\) 1.33956 + 2.32018i 0.141993 + 0.245939i 0.928247 0.371964i \(-0.121316\pi\)
−0.786254 + 0.617903i \(0.787982\pi\)
\(90\) 0 0
\(91\) 4.67458 + 8.09661i 0.490029 + 0.848755i
\(92\) 0 0
\(93\) −3.35369 + 5.80877i −0.347762 + 0.602341i
\(94\) 0 0
\(95\) 12.8446 + 6.67479i 1.31783 + 0.684820i
\(96\) 0 0
\(97\) −8.86330 + 15.3517i −0.899931 + 1.55873i −0.0723511 + 0.997379i \(0.523050\pi\)
−0.827580 + 0.561347i \(0.810283\pi\)
\(98\) 0 0
\(99\) −0.853695 1.47864i −0.0857995 0.148609i
\(100\) 0 0
\(101\) −8.02827 13.9054i −0.798843 1.38364i −0.920370 0.391049i \(-0.872112\pi\)
0.121527 0.992588i \(-0.461221\pi\)
\(102\) 0 0
\(103\) 7.54787 0.743714 0.371857 0.928290i \(-0.378721\pi\)
0.371857 + 0.928290i \(0.378721\pi\)
\(104\) 0 0
\(105\) −3.85369 6.67479i −0.376082 0.651393i
\(106\) 0 0
\(107\) −7.28354 −0.704126 −0.352063 0.935976i \(-0.614520\pi\)
−0.352063 + 0.935976i \(0.614520\pi\)
\(108\) 0 0
\(109\) 6.12763 10.6134i 0.586921 1.01658i −0.407712 0.913110i \(-0.633673\pi\)
0.994633 0.103466i \(-0.0329933\pi\)
\(110\) 0 0
\(111\) −0.500000 + 0.866025i −0.0474579 + 0.0821995i
\(112\) 0 0
\(113\) 7.37743 0.694010 0.347005 0.937863i \(-0.387199\pi\)
0.347005 + 0.937863i \(0.387199\pi\)
\(114\) 0 0
\(115\) 7.80128 0.727473
\(116\) 0 0
\(117\) −2.01414 + 3.48859i −0.186207 + 0.322520i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.08482 −0.734984
\(122\) 0 0
\(123\) −3.32088 5.75194i −0.299434 0.518635i
\(124\) 0 0
\(125\) 3.41478 0.305427
\(126\) 0 0
\(127\) 7.32088 + 12.6801i 0.649623 + 1.12518i 0.983213 + 0.182462i \(0.0584068\pi\)
−0.333589 + 0.942718i \(0.608260\pi\)
\(128\) 0 0
\(129\) −0.353695 0.612617i −0.0311411 0.0539379i
\(130\) 0 0
\(131\) 0.320884 0.555788i 0.0280358 0.0485594i −0.851667 0.524083i \(-0.824408\pi\)
0.879703 + 0.475524i \(0.157741\pi\)
\(132\) 0 0
\(133\) 0.448517 + 10.1066i 0.0388913 + 0.876349i
\(134\) 0 0
\(135\) 1.66044 2.87597i 0.142908 0.247524i
\(136\) 0 0
\(137\) −1.29261 2.23887i −0.110435 0.191279i 0.805511 0.592581i \(-0.201891\pi\)
−0.915946 + 0.401302i \(0.868558\pi\)
\(138\) 0 0
\(139\) −9.28807 16.0874i −0.787804 1.36452i −0.927309 0.374296i \(-0.877885\pi\)
0.139505 0.990221i \(-0.455449\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −3.43892 5.95638i −0.287577 0.498097i
\(144\) 0 0
\(145\) 22.0565 1.83170
\(146\) 0 0
\(147\) −0.806748 + 1.39733i −0.0665394 + 0.115250i
\(148\) 0 0
\(149\) 1.98133 3.43176i 0.162317 0.281141i −0.773382 0.633940i \(-0.781437\pi\)
0.935699 + 0.352799i \(0.114770\pi\)
\(150\) 0 0
\(151\) 8.69832 0.707859 0.353929 0.935272i \(-0.384845\pi\)
0.353929 + 0.935272i \(0.384845\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 11.1372 19.2903i 0.894564 1.54943i
\(156\) 0 0
\(157\) 2.84916 4.93489i 0.227388 0.393847i −0.729645 0.683826i \(-0.760315\pi\)
0.957033 + 0.289979i \(0.0936482\pi\)
\(158\) 0 0
\(159\) 9.96265 0.790090
\(160\) 0 0
\(161\) 2.72606 + 4.72168i 0.214844 + 0.372120i
\(162\) 0 0
\(163\) −18.3774 −1.43943 −0.719716 0.694269i \(-0.755728\pi\)
−0.719716 + 0.694269i \(0.755728\pi\)
\(164\) 0 0
\(165\) 2.83502 + 4.91040i 0.220706 + 0.382274i
\(166\) 0 0
\(167\) 10.8163 + 18.7345i 0.836994 + 1.44972i 0.892396 + 0.451252i \(0.149023\pi\)
−0.0554023 + 0.998464i \(0.517644\pi\)
\(168\) 0 0
\(169\) −1.61350 + 2.79466i −0.124115 + 0.214974i
\(170\) 0 0
\(171\) −3.67458 + 2.34467i −0.281002 + 0.179301i
\(172\) 0 0
\(173\) 2.34916 4.06886i 0.178603 0.309350i −0.762799 0.646636i \(-0.776175\pi\)
0.941402 + 0.337286i \(0.109509\pi\)
\(174\) 0 0
\(175\) 6.99546 + 12.1165i 0.528807 + 0.915921i
\(176\) 0 0
\(177\) −0.853695 1.47864i −0.0641676 0.111142i
\(178\) 0 0
\(179\) 1.06562 0.0796482 0.0398241 0.999207i \(-0.487320\pi\)
0.0398241 + 0.999207i \(0.487320\pi\)
\(180\) 0 0
\(181\) 1.83502 + 3.17835i 0.136396 + 0.236245i 0.926130 0.377205i \(-0.123115\pi\)
−0.789734 + 0.613450i \(0.789781\pi\)
\(182\) 0 0
\(183\) −3.38650 −0.250338
\(184\) 0 0
\(185\) 1.66044 2.87597i 0.122078 0.211446i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 2.32088 0.168820
\(190\) 0 0
\(191\) 0.877832 0.0635177 0.0317588 0.999496i \(-0.489889\pi\)
0.0317588 + 0.999496i \(0.489889\pi\)
\(192\) 0 0
\(193\) 4.30675 7.45951i 0.310006 0.536947i −0.668357 0.743841i \(-0.733002\pi\)
0.978363 + 0.206894i \(0.0663354\pi\)
\(194\) 0 0
\(195\) 6.68872 11.5852i 0.478989 0.829633i
\(196\) 0 0
\(197\) 24.7357 1.76234 0.881172 0.472797i \(-0.156756\pi\)
0.881172 + 0.472797i \(0.156756\pi\)
\(198\) 0 0
\(199\) −10.9955 19.0447i −0.779448 1.35004i −0.932260 0.361788i \(-0.882166\pi\)
0.152813 0.988255i \(-0.451167\pi\)
\(200\) 0 0
\(201\) −8.37743 −0.590899
\(202\) 0 0
\(203\) 7.70739 + 13.3496i 0.540953 + 0.936958i
\(204\) 0 0
\(205\) 11.0283 + 19.1015i 0.770248 + 1.33411i
\(206\) 0 0
\(207\) −1.17458 + 2.03443i −0.0816389 + 0.141403i
\(208\) 0 0
\(209\) −0.329957 7.43502i −0.0228236 0.514291i
\(210\) 0 0
\(211\) −6.60896 + 11.4471i −0.454979 + 0.788048i −0.998687 0.0512272i \(-0.983687\pi\)
0.543708 + 0.839275i \(0.317020\pi\)
\(212\) 0 0
\(213\) 4.70739 + 8.15344i 0.322545 + 0.558664i
\(214\) 0 0
\(215\) 1.17458 + 2.03443i 0.0801056 + 0.138747i
\(216\) 0 0
\(217\) 15.5671 1.05676
\(218\) 0 0
\(219\) 5.82088 + 10.0821i 0.393339 + 0.681283i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −2.74020 + 4.74616i −0.183497 + 0.317827i −0.943069 0.332597i \(-0.892075\pi\)
0.759572 + 0.650423i \(0.225409\pi\)
\(224\) 0 0
\(225\) −3.01414 + 5.22064i −0.200942 + 0.348043i
\(226\) 0 0
\(227\) −7.70739 −0.511557 −0.255779 0.966735i \(-0.582332\pi\)
−0.255779 + 0.966735i \(0.582332\pi\)
\(228\) 0 0
\(229\) 4.02827 0.266196 0.133098 0.991103i \(-0.457508\pi\)
0.133098 + 0.991103i \(0.457508\pi\)
\(230\) 0 0
\(231\) −1.98133 + 3.43176i −0.130362 + 0.225793i
\(232\) 0 0
\(233\) −13.0565 + 22.6146i −0.855363 + 1.48153i 0.0209451 + 0.999781i \(0.493332\pi\)
−0.876308 + 0.481751i \(0.840001\pi\)
\(234\) 0 0
\(235\) 19.9253 1.29978
\(236\) 0 0
\(237\) 1.67458 + 2.90046i 0.108776 + 0.188405i
\(238\) 0 0
\(239\) 7.70739 0.498550 0.249275 0.968433i \(-0.419808\pi\)
0.249275 + 0.968433i \(0.419808\pi\)
\(240\) 0 0
\(241\) −10.8492 18.7913i −0.698856 1.21045i −0.968863 0.247595i \(-0.920360\pi\)
0.270008 0.962858i \(-0.412974\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 2.67912 4.64036i 0.171162 0.296462i
\(246\) 0 0
\(247\) −14.8022 + 9.44496i −0.941842 + 0.600969i
\(248\) 0 0
\(249\) 5.02827 8.70923i 0.318654 0.551925i
\(250\) 0 0
\(251\) 4.70739 + 8.15344i 0.297128 + 0.514640i 0.975478 0.220099i \(-0.0706379\pi\)
−0.678350 + 0.734739i \(0.737305\pi\)
\(252\) 0 0
\(253\) −2.00546 3.47357i −0.126082 0.218381i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.07522 + 8.79054i 0.316584 + 0.548339i 0.979773 0.200113i \(-0.0641309\pi\)
−0.663189 + 0.748452i \(0.730798\pi\)
\(258\) 0 0
\(259\) 2.32088 0.144213
\(260\) 0 0
\(261\) −3.32088 + 5.75194i −0.205558 + 0.356036i
\(262\) 0 0
\(263\) 1.29261 2.23887i 0.0797058 0.138054i −0.823417 0.567436i \(-0.807935\pi\)
0.903123 + 0.429382i \(0.141269\pi\)
\(264\) 0 0
\(265\) −33.0848 −2.03238
\(266\) 0 0
\(267\) 2.67912 0.163959
\(268\) 0 0
\(269\) −0.273937 + 0.474473i −0.0167023 + 0.0289292i −0.874256 0.485466i \(-0.838650\pi\)
0.857553 + 0.514395i \(0.171983\pi\)
\(270\) 0 0
\(271\) −10.4431 + 18.0879i −0.634370 + 1.09876i 0.352278 + 0.935895i \(0.385407\pi\)
−0.986648 + 0.162866i \(0.947926\pi\)
\(272\) 0 0
\(273\) 9.34916 0.565837
\(274\) 0 0
\(275\) −5.14631 8.91366i −0.310334 0.537514i
\(276\) 0 0
\(277\) −23.7831 −1.42899 −0.714495 0.699640i \(-0.753344\pi\)
−0.714495 + 0.699640i \(0.753344\pi\)
\(278\) 0 0
\(279\) 3.35369 + 5.80877i 0.200780 + 0.347762i
\(280\) 0 0
\(281\) 5.95305 + 10.3110i 0.355129 + 0.615102i 0.987140 0.159858i \(-0.0511035\pi\)
−0.632011 + 0.774960i \(0.717770\pi\)
\(282\) 0 0
\(283\) 9.02827 15.6374i 0.536675 0.929549i −0.462405 0.886669i \(-0.653013\pi\)
0.999080 0.0428799i \(-0.0136533\pi\)
\(284\) 0 0
\(285\) 12.2029 7.78637i 0.722835 0.461225i
\(286\) 0 0
\(287\) −7.70739 + 13.3496i −0.454953 + 0.788001i
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0 0
\(291\) 8.86330 + 15.3517i 0.519576 + 0.899931i
\(292\) 0 0
\(293\) −27.3966 −1.60053 −0.800264 0.599648i \(-0.795307\pi\)
−0.800264 + 0.599648i \(0.795307\pi\)
\(294\) 0 0
\(295\) 2.83502 + 4.91040i 0.165061 + 0.285895i
\(296\) 0 0
\(297\) −1.70739 −0.0990728
\(298\) 0 0
\(299\) −4.73153 + 8.19524i −0.273631 + 0.473943i
\(300\) 0 0
\(301\) −0.820884 + 1.42181i −0.0473150 + 0.0819520i
\(302\) 0 0
\(303\) −16.0565 −0.922425
\(304\) 0 0
\(305\) 11.2462 0.643955
\(306\) 0 0
\(307\) 1.80675 3.12938i 0.103117 0.178603i −0.809851 0.586636i \(-0.800452\pi\)
0.912967 + 0.408033i \(0.133785\pi\)
\(308\) 0 0
\(309\) 3.77394 6.53665i 0.214692 0.371857i
\(310\) 0 0
\(311\) −18.4057 −1.04369 −0.521846 0.853040i \(-0.674756\pi\)
−0.521846 + 0.853040i \(0.674756\pi\)
\(312\) 0 0
\(313\) −11.5424 19.9920i −0.652416 1.13002i −0.982535 0.186078i \(-0.940422\pi\)
0.330119 0.943939i \(-0.392911\pi\)
\(314\) 0 0
\(315\) −7.70739 −0.434262
\(316\) 0 0
\(317\) 12.6887 + 21.9775i 0.712669 + 1.23438i 0.963852 + 0.266440i \(0.0858473\pi\)
−0.251182 + 0.967940i \(0.580819\pi\)
\(318\) 0 0
\(319\) −5.67004 9.82080i −0.317461 0.549859i
\(320\) 0 0
\(321\) −3.64177 + 6.30773i −0.203264 + 0.352063i
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −12.1418 + 21.0302i −0.673504 + 1.16654i
\(326\) 0 0
\(327\) −6.12763 10.6134i −0.338859 0.586921i
\(328\) 0 0
\(329\) 6.96265 + 12.0597i 0.383864 + 0.664871i
\(330\) 0 0
\(331\) 21.3492 1.17346 0.586728 0.809784i \(-0.300416\pi\)
0.586728 + 0.809784i \(0.300416\pi\)
\(332\) 0 0
\(333\) 0.500000 + 0.866025i 0.0273998 + 0.0474579i
\(334\) 0 0
\(335\) 27.8205 1.52000
\(336\) 0 0
\(337\) 2.04241 3.53756i 0.111257 0.192703i −0.805020 0.593247i \(-0.797846\pi\)
0.916277 + 0.400544i \(0.131179\pi\)
\(338\) 0 0
\(339\) 3.68872 6.38904i 0.200344 0.347005i
\(340\) 0 0
\(341\) −11.4521 −0.620167
\(342\) 0 0
\(343\) 19.9909 1.07941
\(344\) 0 0
\(345\) 3.90064 6.75611i 0.210003 0.363737i
\(346\) 0 0
\(347\) 9.85369 17.0671i 0.528974 0.916210i −0.470455 0.882424i \(-0.655910\pi\)
0.999429 0.0337860i \(-0.0107565\pi\)
\(348\) 0 0
\(349\) 23.3118 1.24785 0.623926 0.781483i \(-0.285537\pi\)
0.623926 + 0.781483i \(0.285537\pi\)
\(350\) 0 0
\(351\) 2.01414 + 3.48859i 0.107507 + 0.186207i
\(352\) 0 0
\(353\) 25.1896 1.34071 0.670355 0.742041i \(-0.266142\pi\)
0.670355 + 0.742041i \(0.266142\pi\)
\(354\) 0 0
\(355\) −15.6327 27.0766i −0.829697 1.43708i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.61350 + 2.79466i −0.0851570 + 0.147496i −0.905458 0.424436i \(-0.860473\pi\)
0.820301 + 0.571932i \(0.193806\pi\)
\(360\) 0 0
\(361\) −18.9253 + 1.68308i −0.996069 + 0.0885831i
\(362\) 0 0
\(363\) −4.04241 + 7.00166i −0.212172 + 0.367492i
\(364\) 0 0
\(365\) −19.3305 33.4814i −1.01180 1.75250i
\(366\) 0 0
\(367\) −14.7311 25.5151i −0.768959 1.33188i −0.938128 0.346288i \(-0.887442\pi\)
0.169170 0.985587i \(-0.445891\pi\)
\(368\) 0 0
\(369\) −6.64177 −0.345757
\(370\) 0 0
\(371\) −11.5611 20.0244i −0.600222 1.03961i
\(372\) 0 0
\(373\) 19.6700 1.01848 0.509238 0.860626i \(-0.329927\pi\)
0.509238 + 0.860626i \(0.329927\pi\)
\(374\) 0 0
\(375\) 1.70739 2.95729i 0.0881692 0.152714i
\(376\) 0 0
\(377\) −13.3774 + 23.1704i −0.688973 + 1.19334i
\(378\) 0 0
\(379\) 0.763937 0.0392408 0.0196204 0.999808i \(-0.493754\pi\)
0.0196204 + 0.999808i \(0.493754\pi\)
\(380\) 0 0
\(381\) 14.6418 0.750121
\(382\) 0 0
\(383\) 1.91932 3.32435i 0.0980724 0.169866i −0.812814 0.582523i \(-0.802066\pi\)
0.910887 + 0.412656i \(0.135399\pi\)
\(384\) 0 0
\(385\) 6.57976 11.3965i 0.335335 0.580818i
\(386\) 0 0
\(387\) −0.707389 −0.0359586
\(388\) 0 0
\(389\) −16.1035 27.8921i −0.816480 1.41418i −0.908261 0.418405i \(-0.862589\pi\)
0.0917810 0.995779i \(-0.470744\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −0.320884 0.555788i −0.0161865 0.0280358i
\(394\) 0 0
\(395\) −5.56108 9.63208i −0.279809 0.484643i
\(396\) 0 0
\(397\) 13.2977 23.0322i 0.667391 1.15596i −0.311240 0.950331i \(-0.600744\pi\)
0.978631 0.205624i \(-0.0659224\pi\)
\(398\) 0 0
\(399\) 8.97679 + 4.66485i 0.449402 + 0.233535i
\(400\) 0 0
\(401\) 4.66044 8.07212i 0.232731 0.403103i −0.725880 0.687822i \(-0.758567\pi\)
0.958611 + 0.284719i \(0.0919004\pi\)
\(402\) 0 0
\(403\) 13.5096 + 23.3993i 0.672961 + 1.16560i
\(404\) 0 0
\(405\) −1.66044 2.87597i −0.0825080 0.142908i
\(406\) 0 0
\(407\) −1.70739 −0.0846321
\(408\) 0 0
\(409\) −10.9006 18.8805i −0.539002 0.933579i −0.998958 0.0456372i \(-0.985468\pi\)
0.459956 0.887942i \(-0.347865\pi\)
\(410\) 0 0
\(411\) −2.58522 −0.127520
\(412\) 0 0
\(413\) −1.98133 + 3.43176i −0.0974947 + 0.168866i
\(414\) 0 0
\(415\) −16.6983 + 28.9223i −0.819688 + 1.41974i
\(416\) 0 0
\(417\) −18.5761 −0.909678
\(418\) 0 0
\(419\) −4.93438 −0.241060 −0.120530 0.992710i \(-0.538459\pi\)
−0.120530 + 0.992710i \(0.538459\pi\)
\(420\) 0 0
\(421\) −2.12763 + 3.68517i −0.103694 + 0.179604i −0.913204 0.407503i \(-0.866400\pi\)
0.809510 + 0.587107i \(0.199733\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.92984 + 6.80669i 0.190178 + 0.329399i
\(428\) 0 0
\(429\) −6.87783 −0.332065
\(430\) 0 0
\(431\) −0.414779 0.718418i −0.0199792 0.0346050i 0.855863 0.517203i \(-0.173027\pi\)
−0.875842 + 0.482598i \(0.839693\pi\)
\(432\) 0 0
\(433\) −8.24113 14.2741i −0.396043 0.685967i 0.597190 0.802099i \(-0.296284\pi\)
−0.993234 + 0.116132i \(0.962950\pi\)
\(434\) 0 0
\(435\) 11.0283 19.1015i 0.528765 0.915848i
\(436\) 0 0
\(437\) −8.63217 + 5.50800i −0.412933 + 0.263483i
\(438\) 0 0
\(439\) 14.2170 24.6245i 0.678540 1.17527i −0.296881 0.954915i \(-0.595946\pi\)
0.975421 0.220351i \(-0.0707203\pi\)
\(440\) 0 0
\(441\) 0.806748 + 1.39733i 0.0384166 + 0.0665394i
\(442\) 0 0
\(443\) −7.70739 13.3496i −0.366189 0.634258i 0.622777 0.782399i \(-0.286004\pi\)
−0.988966 + 0.148141i \(0.952671\pi\)
\(444\) 0 0
\(445\) −8.89703 −0.421760
\(446\) 0 0
\(447\) −1.98133 3.43176i −0.0937135 0.162317i
\(448\) 0 0
\(449\) −23.1523 −1.09262 −0.546312 0.837582i \(-0.683969\pi\)
−0.546312 + 0.837582i \(0.683969\pi\)
\(450\) 0 0
\(451\) 5.67004 9.82080i 0.266992 0.462444i
\(452\) 0 0
\(453\) 4.34916 7.53296i 0.204341 0.353929i
\(454\) 0 0
\(455\) −31.0475 −1.45553
\(456\) 0 0
\(457\) 4.68819 0.219304 0.109652 0.993970i \(-0.465026\pi\)
0.109652 + 0.993970i \(0.465026\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.27394 + 10.8668i −0.292206 + 0.506116i −0.974331 0.225119i \(-0.927723\pi\)
0.682125 + 0.731236i \(0.261056\pi\)
\(462\) 0 0
\(463\) −22.8880 −1.06369 −0.531847 0.846841i \(-0.678502\pi\)
−0.531847 + 0.846841i \(0.678502\pi\)
\(464\) 0 0
\(465\) −11.1372 19.2903i −0.516477 0.894564i
\(466\) 0 0
\(467\) 11.8122 0.546604 0.273302 0.961928i \(-0.411884\pi\)
0.273302 + 0.961928i \(0.411884\pi\)
\(468\) 0 0
\(469\) 9.72153 + 16.8382i 0.448898 + 0.777515i
\(470\) 0 0
\(471\) −2.84916 4.93489i −0.131282 0.227388i
\(472\) 0 0
\(473\) 0.603895 1.04598i 0.0277671 0.0480940i
\(474\) 0 0
\(475\) −22.1514 + 14.1343i −1.01637 + 0.648526i
\(476\) 0 0
\(477\) 4.98133 8.62791i 0.228079 0.395045i
\(478\) 0 0
\(479\) −17.0192 29.4781i −0.777627 1.34689i −0.933306 0.359082i \(-0.883090\pi\)
0.155679 0.987808i \(-0.450244\pi\)
\(480\) 0 0
\(481\) 2.01414 + 3.48859i 0.0918367 + 0.159066i
\(482\) 0 0
\(483\) 5.45213 0.248080
\(484\) 0 0
\(485\) −29.4340 50.9811i −1.33653 2.31493i
\(486\) 0 0
\(487\) 7.41478 0.335996 0.167998 0.985787i \(-0.446270\pi\)
0.167998 + 0.985787i \(0.446270\pi\)
\(488\) 0 0
\(489\) −9.18872 + 15.9153i −0.415528 + 0.719716i
\(490\) 0 0
\(491\) 1.93438 3.35044i 0.0872973 0.151203i −0.819071 0.573693i \(-0.805510\pi\)
0.906368 + 0.422489i \(0.138844\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 5.67004 0.254849
\(496\) 0 0
\(497\) 10.9253 18.9232i 0.490067 0.848821i
\(498\) 0 0
\(499\) −17.7931 + 30.8186i −0.796530 + 1.37963i 0.125333 + 0.992115i \(0.460000\pi\)
−0.921863 + 0.387516i \(0.873333\pi\)
\(500\) 0 0
\(501\) 21.6327 0.966478
\(502\) 0 0
\(503\) 4.29261 + 7.43502i 0.191398 + 0.331511i 0.945714 0.325001i \(-0.105365\pi\)
−0.754316 + 0.656512i \(0.772031\pi\)
\(504\) 0 0
\(505\) 53.3219 2.37280
\(506\) 0 0
\(507\) 1.61350 + 2.79466i 0.0716578 + 0.124115i
\(508\) 0 0
\(509\) 3.97173 + 6.87923i 0.176044 + 0.304917i 0.940522 0.339733i \(-0.110337\pi\)
−0.764478 + 0.644649i \(0.777003\pi\)
\(510\) 0 0
\(511\) 13.5096 23.3993i 0.597630 1.03512i
\(512\) 0 0
\(513\) 0.193252 + 4.35461i 0.00853230 + 0.192261i
\(514\) 0 0
\(515\) −12.5328 + 21.7075i −0.552262 + 0.956545i
\(516\) 0 0
\(517\) −5.12217 8.87186i −0.225273 0.390184i
\(518\) 0 0
\(519\) −2.34916 4.06886i −0.103117 0.178603i
\(520\) 0 0
\(521\) −0.0757489 −0.00331862 −0.00165931 0.999999i \(-0.500528\pi\)
−0.00165931 + 0.999999i \(0.500528\pi\)
\(522\) 0 0
\(523\) 10.1514 + 17.5827i 0.443888 + 0.768837i 0.997974 0.0636224i \(-0.0202653\pi\)
−0.554086 + 0.832460i \(0.686932\pi\)
\(524\) 0 0
\(525\) 13.9909 0.610614
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 8.74073 15.1394i 0.380032 0.658234i
\(530\) 0 0
\(531\) −1.70739 −0.0740944
\(532\) 0 0
\(533\) −26.7549 −1.15888
\(534\) 0 0
\(535\) 12.0939 20.9472i 0.522865 0.905628i
\(536\) 0 0
\(537\) 0.532810 0.922854i 0.0229925 0.0398241i
\(538\) 0 0
\(539\) −2.75486 −0.118660
\(540\) 0 0
\(541\) 16.5475 + 28.6611i 0.711432 + 1.23224i 0.964320 + 0.264740i \(0.0852862\pi\)
−0.252888 + 0.967495i \(0.581381\pi\)
\(542\) 0 0
\(543\) 3.67004 0.157497
\(544\) 0 0
\(545\) 20.3492 + 35.2458i 0.871662 + 1.50976i
\(546\) 0 0
\(547\) −17.9581 31.1044i −0.767834 1.32993i −0.938735 0.344639i \(-0.888001\pi\)
0.170902 0.985288i \(-0.445332\pi\)
\(548\) 0 0
\(549\) −1.69325 + 2.93280i −0.0722663 + 0.125169i
\(550\) 0 0
\(551\) −24.4057 + 15.5727i −1.03972 + 0.663421i
\(552\) 0 0
\(553\) 3.88650 6.73162i 0.165271 0.286258i
\(554\) 0 0
\(555\) −1.66044 2.87597i −0.0704818 0.122078i
\(556\) 0 0
\(557\) 0.962653 + 1.66736i 0.0407889 + 0.0706485i 0.885699 0.464260i \(-0.153680\pi\)
−0.844910 + 0.534908i \(0.820346\pi\)
\(558\) 0 0
\(559\) −2.84956 −0.120523
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −10.8861 −0.458795 −0.229397 0.973333i \(-0.573676\pi\)
−0.229397 + 0.973333i \(0.573676\pi\)
\(564\) 0 0
\(565\) −12.2498 + 21.2173i −0.515353 + 0.892618i
\(566\) 0 0
\(567\) 1.16044 2.00994i 0.0487340 0.0844098i
\(568\) 0 0
\(569\) −36.4358 −1.52747 −0.763735 0.645530i \(-0.776636\pi\)
−0.763735 + 0.645530i \(0.776636\pi\)
\(570\) 0 0
\(571\) 7.54787 0.315869 0.157934 0.987450i \(-0.449517\pi\)
0.157934 + 0.987450i \(0.449517\pi\)
\(572\) 0 0
\(573\) 0.438916 0.760225i 0.0183360 0.0317588i
\(574\) 0 0
\(575\) −7.08068 + 12.2641i −0.295285 + 0.511449i
\(576\) 0 0
\(577\) −15.4823 −0.644535 −0.322267 0.946649i \(-0.604445\pi\)
−0.322267 + 0.946649i \(0.604445\pi\)
\(578\) 0 0
\(579\) −4.30675 7.45951i −0.178982 0.310006i
\(580\) 0 0
\(581\) −23.3401 −0.968310
\(582\) 0 0
\(583\) 8.50506 + 14.7312i 0.352244 + 0.610104i
\(584\) 0 0
\(585\) −6.68872 11.5852i −0.276544 0.478989i
\(586\) 0 0
\(587\) −14.8729 + 25.7606i −0.613870 + 1.06325i 0.376712 + 0.926331i \(0.377055\pi\)
−0.990582 + 0.136924i \(0.956279\pi\)
\(588\) 0 0
\(589\) 1.29622 + 29.2081i 0.0534098 + 1.20350i
\(590\) 0 0
\(591\) 12.3678 21.4217i 0.508745 0.881172i
\(592\) 0 0
\(593\) 0.273937 + 0.474473i 0.0112493 + 0.0194843i 0.871595 0.490226i \(-0.163086\pi\)
−0.860346 + 0.509711i \(0.829753\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −21.9909 −0.900029
\(598\) 0 0
\(599\) −22.8163 39.5191i −0.932251 1.61471i −0.779465 0.626446i \(-0.784509\pi\)
−0.152786 0.988259i \(-0.548825\pi\)
\(600\) 0 0
\(601\) −6.85783 −0.279737 −0.139868 0.990170i \(-0.544668\pi\)
−0.139868 + 0.990170i \(0.544668\pi\)
\(602\) 0 0
\(603\) −4.18872 + 7.25507i −0.170578 + 0.295449i
\(604\) 0 0
\(605\) 13.4244 23.2517i 0.545779 0.945316i
\(606\) 0 0
\(607\) 6.76394 0.274540 0.137270 0.990534i \(-0.456167\pi\)
0.137270 + 0.990534i \(0.456167\pi\)
\(608\) 0 0
\(609\) 15.4148 0.624638
\(610\) 0 0
\(611\) −12.0848 + 20.9315i −0.488900 + 0.846799i
\(612\) 0 0
\(613\) −2.22153 + 3.84780i −0.0897266 + 0.155411i −0.907396 0.420278i \(-0.861933\pi\)
0.817669 + 0.575689i \(0.195266\pi\)
\(614\) 0 0
\(615\) 22.0565 0.889406
\(616\) 0 0
\(617\) 16.0005 + 27.7137i 0.644157 + 1.11571i 0.984496 + 0.175410i \(0.0561250\pi\)
−0.340339 + 0.940303i \(0.610542\pi\)
\(618\) 0 0
\(619\) 14.3774 0.577878 0.288939 0.957348i \(-0.406698\pi\)
0.288939 + 0.957348i \(0.406698\pi\)
\(620\) 0 0
\(621\) 1.17458 + 2.03443i 0.0471342 + 0.0816389i
\(622\) 0 0
\(623\) −3.10896 5.38487i −0.124558 0.215740i
\(624\) 0 0
\(625\) 9.40064 16.2824i 0.376026 0.651296i
\(626\) 0 0
\(627\) −6.60389 3.43176i −0.263734 0.137051i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 5.54695 + 9.60759i 0.220820 + 0.382472i 0.955057 0.296421i \(-0.0957932\pi\)
−0.734237 + 0.678893i \(0.762460\pi\)
\(632\) 0 0
\(633\) 6.60896 + 11.4471i 0.262683 + 0.454979i
\(634\) 0 0
\(635\) −48.6236 −1.92957
\(636\) 0 0
\(637\) 3.24980 + 5.62882i 0.128762 + 0.223022i
\(638\) 0 0
\(639\) 9.41478 0.372443
\(640\) 0 0
\(641\) −21.7357 + 37.6473i −0.858507 + 1.48698i 0.0148458 + 0.999890i \(0.495274\pi\)
−0.873353 + 0.487088i \(0.838059\pi\)
\(642\) 0 0
\(643\) −11.8113 + 20.4577i −0.465792 + 0.806775i −0.999237 0.0390599i \(-0.987564\pi\)
0.533445 + 0.845835i \(0.320897\pi\)
\(644\) 0 0
\(645\) 2.34916 0.0924980
\(646\) 0 0
\(647\) 19.9253 0.783345 0.391672 0.920105i \(-0.371897\pi\)
0.391672 + 0.920105i \(0.371897\pi\)
\(648\) 0 0
\(649\) 1.45759 2.52462i 0.0572154 0.0990999i
\(650\) 0 0
\(651\) 7.78354 13.4815i 0.305061 0.528381i
\(652\) 0 0
\(653\) −2.11310 −0.0826918 −0.0413459 0.999145i \(-0.513165\pi\)
−0.0413459 + 0.999145i \(0.513165\pi\)
\(654\) 0 0
\(655\) 1.06562 + 1.84571i 0.0416372 + 0.0721178i
\(656\) 0 0
\(657\) 11.6418 0.454189
\(658\) 0 0
\(659\) 21.7507 + 37.6734i 0.847288 + 1.46755i 0.883619 + 0.468206i \(0.155100\pi\)
−0.0363312 + 0.999340i \(0.511567\pi\)
\(660\) 0 0
\(661\) −11.0565 19.1505i −0.430050 0.744868i 0.566827 0.823837i \(-0.308171\pi\)
−0.996877 + 0.0789685i \(0.974837\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −29.8109 15.4914i −1.15602 0.600732i
\(666\) 0 0
\(667\) −7.80128 + 13.5122i −0.302067 + 0.523195i
\(668\) 0 0
\(669\) 2.74020 + 4.74616i 0.105942 + 0.183497i
\(670\) 0 0
\(671\) −2.89104 5.00743i −0.111607 0.193310i
\(672\) 0 0
\(673\) 12.5953 0.485515 0.242758 0.970087i \(-0.421948\pi\)
0.242758 + 0.970087i \(0.421948\pi\)
\(674\) 0 0
\(675\) 3.01414 + 5.22064i 0.116014 + 0.200942i
\(676\) 0 0
\(677\) −32.9427 −1.26609 −0.633045 0.774115i \(-0.718195\pi\)
−0.633045 + 0.774115i \(0.718195\pi\)
\(678\) 0 0
\(679\) 20.5707 35.6295i 0.789430 1.36733i
\(680\) 0 0
\(681\) −3.85369 + 6.67479i −0.147674 + 0.255779i
\(682\) 0 0
\(683\) 18.3876 0.703580 0.351790 0.936079i \(-0.385573\pi\)
0.351790 + 0.936079i \(0.385573\pi\)
\(684\) 0 0
\(685\) 8.58522 0.328024
\(686\) 0 0
\(687\) 2.01414 3.48859i 0.0768441 0.133098i
\(688\) 0 0
\(689\) 20.0661 34.7556i 0.764459 1.32408i
\(690\) 0 0
\(691\) 16.6599 0.633773 0.316887 0.948463i \(-0.397363\pi\)
0.316887 + 0.948463i \(0.397363\pi\)
\(692\) 0 0
\(693\) 1.98133 + 3.43176i 0.0752644 + 0.130362i
\(694\) 0 0
\(695\) 61.6892 2.34001
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 13.0565 + 22.6146i 0.493844 + 0.855363i
\(700\) 0 0
\(701\) 24.3588 42.1906i 0.920018 1.59352i 0.120633 0.992697i \(-0.461507\pi\)
0.799384 0.600820i \(-0.205159\pi\)
\(702\) 0 0
\(703\) 0.193252 + 4.35461i 0.00728865 + 0.164237i
\(704\) 0 0
\(705\) 9.96265 17.2558i 0.375215 0.649892i
\(706\) 0 0
\(707\) 18.6327 + 32.2728i 0.700755 + 1.21374i
\(708\) 0 0
\(709\) −14.7498 25.5474i −0.553940 0.959453i −0.997985 0.0634483i \(-0.979790\pi\)
0.444045 0.896005i \(-0.353543\pi\)
\(710\) 0 0
\(711\) 3.34916 0.125603
\(712\) 0 0
\(713\) 7.87836 + 13.6457i 0.295047 + 0.511036i
\(714\) 0 0
\(715\) 22.8405 0.854186
\(716\) 0 0
\(717\) 3.85369 6.67479i 0.143919 0.249275i
\(718\) 0 0
\(719\) 11.3250 19.6155i 0.422352 0.731535i −0.573817 0.818984i \(-0.694538\pi\)
0.996169 + 0.0874484i \(0.0278713\pi\)
\(720\) 0 0
\(721\) −17.5177 −0.652395
\(722\) 0 0
\(723\) −21.6983 −0.806969
\(724\) 0 0
\(725\) −20.0192 + 34.6743i −0.743494 + 1.28777i
\(726\) 0 0
\(727\) 26.3638 45.6635i 0.977780 1.69356i 0.307342 0.951599i \(-0.400560\pi\)
0.670438 0.741966i \(-0.266106\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 5.72659 0.211516 0.105758 0.994392i \(-0.466273\pi\)
0.105758 + 0.994392i \(0.466273\pi\)
\(734\) 0 0
\(735\) −2.67912 4.64036i −0.0988207 0.171162i
\(736\) 0 0
\(737\) −7.15177 12.3872i −0.263439 0.456289i
\(738\) 0 0
\(739\) 16.7083 28.9397i 0.614625 1.06456i −0.375825 0.926691i \(-0.622641\pi\)
0.990450 0.137872i \(-0.0440261\pi\)
\(740\) 0 0
\(741\) 0.778474 + 17.5416i 0.0285979 + 0.644406i
\(742\) 0 0
\(743\) −17.9759 + 31.1351i −0.659470 + 1.14224i 0.321282 + 0.946983i \(0.395886\pi\)
−0.980753 + 0.195253i \(0.937447\pi\)
\(744\) 0 0
\(745\) 6.57976 + 11.3965i 0.241064 + 0.417534i
\(746\) 0 0
\(747\) −5.02827 8.70923i −0.183975 0.318654i
\(748\) 0 0
\(749\) 16.9043 0.617668
\(750\) 0 0
\(751\) −11.5752 20.0489i −0.422386 0.731594i 0.573787 0.819005i \(-0.305474\pi\)
−0.996172 + 0.0874112i \(0.972141\pi\)
\(752\) 0 0
\(753\) 9.41478 0.343094
\(754\) 0 0
\(755\) −14.4431 + 25.0161i −0.525637 + 0.910429i
\(756\) 0 0
\(757\) −6.49454 + 11.2489i −0.236048 + 0.408847i −0.959577 0.281447i \(-0.909186\pi\)
0.723529 + 0.690294i \(0.242519\pi\)
\(758\) 0 0
\(759\) −4.01093 −0.145587
\(760\) 0 0
\(761\) 13.3593 0.484274 0.242137 0.970242i \(-0.422152\pi\)
0.242137 + 0.970242i \(0.422152\pi\)
\(762\) 0 0
\(763\) −14.2215 + 24.6324i −0.514854 + 0.891753i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6.87783 −0.248344
\(768\) 0 0
\(769\) −5.81181 10.0664i −0.209579 0.363002i 0.742003 0.670397i \(-0.233876\pi\)
−0.951582 + 0.307395i \(0.900543\pi\)
\(770\) 0 0
\(771\) 10.1504 0.365559
\(772\) 0 0
\(773\) 3.87783 + 6.71660i 0.139476 + 0.241579i 0.927298 0.374323i \(-0.122125\pi\)
−0.787822 + 0.615902i \(0.788792\pi\)
\(774\) 0 0
\(775\) 20.2170 + 35.0169i 0.726216 + 1.25784i
\(776\) 0 0
\(777\) 1.16044 2.00994i 0.0416306 0.0721064i
\(778\) 0 0
\(779\) −25.6892 13.3496i −0.920413 0.478299i
\(780\) 0 0
\(781\) −8.03735 + 13.9211i −0.287599 + 0.498136i
\(782\) 0 0
\(783\) 3.32088 + 5.75194i 0.118679 + 0.205558i
\(784\) 0 0
\(785\) 9.46173 + 16.3882i 0.337703 + 0.584920i
\(786\) 0 0
\(787\) 18.8880 0.673283 0.336642 0.941633i \(-0.390709\pi\)
0.336642 + 0.941633i \(0.390709\pi\)
\(788\) 0 0
\(789\) −1.29261 2.23887i −0.0460182 0.0797058i
\(790\) 0 0
\(791\) −17.1222 −0.608794
\(792\) 0 0
\(793\) −6.82088 + 11.8141i −0.242217 + 0.419532i
\(794\) 0 0
\(795\) −16.5424 + 28.6523i −0.586699 + 1.01619i
\(796\) 0 0
\(797\) 34.5105 1.22243 0.611213 0.791466i \(-0.290682\pi\)
0.611213 + 0.791466i