Properties

Label 1456.2.r.j.625.2
Level $1456$
Weight $2$
Character 1456.625
Analytic conductor $11.626$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 625.2
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 1456.625
Dual form 1456.2.r.j.417.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.11803 + 1.93649i) q^{3} +(1.11803 - 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(1.11803 + 1.93649i) q^{3} +(1.11803 - 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +5.00000 q^{15} +(3.73607 + 6.47106i) q^{17} +(1.50000 - 2.59808i) q^{19} +(-1.11803 + 5.80948i) q^{21} +(-1.88197 + 3.25966i) q^{23} +2.23607 q^{27} -4.47214 q^{29} +(2.50000 + 4.33013i) q^{31} +(3.35410 - 5.80948i) q^{33} +(5.59017 - 1.93649i) q^{35} +(4.35410 - 7.54153i) q^{37} +(-1.11803 - 1.93649i) q^{39} +4.47214 q^{41} +8.00000 q^{43} +(2.23607 + 3.87298i) q^{45} +(0.736068 - 1.27491i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-8.35410 + 14.4697i) q^{51} +(-0.736068 - 1.27491i) q^{53} -6.70820 q^{55} +6.70820 q^{57} +(3.73607 + 6.47106i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-5.00000 + 1.73205i) q^{63} +(-1.11803 + 1.93649i) q^{65} +(-1.50000 - 2.59808i) q^{67} -8.41641 q^{69} -8.94427 q^{71} +(-5.35410 - 9.27358i) q^{73} +(1.50000 - 7.79423i) q^{77} +(5.35410 - 9.27358i) q^{79} +(5.50000 + 9.52628i) q^{81} +16.7082 q^{85} +(-5.00000 - 8.66025i) q^{87} +(1.11803 - 1.93649i) q^{89} +(-2.00000 - 1.73205i) q^{91} +(-5.59017 + 9.68246i) q^{93} +(-3.35410 - 5.80948i) q^{95} -17.4164 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q + 8 q^{7} - 4 q^{9} - 6 q^{11} - 4 q^{13} + 20 q^{15} + 6 q^{17} + 6 q^{19} - 12 q^{23} + 10 q^{31} + 4 q^{37} + 32 q^{43} - 6 q^{47} + 4 q^{49} - 20 q^{51} + 6 q^{53} + 6 q^{59} - 6 q^{61} - 20 q^{63} - 6 q^{67} + 20 q^{69} - 8 q^{73} + 6 q^{77} + 8 q^{79} + 22 q^{81} + 40 q^{85} - 20 q^{87} - 8 q^{91} - 16 q^{97} + 24 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.11803 + 1.93649i 0.645497 + 1.11803i 0.984186 + 0.177136i \(0.0566831\pi\)
−0.338689 + 0.940898i \(0.609984\pi\)
\(4\) 0 0
\(5\) 1.11803 1.93649i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 0 0
\(9\) −1.00000 + 1.73205i −0.333333 + 0.577350i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 5.00000 1.29099
\(16\) 0 0
\(17\) 3.73607 + 6.47106i 0.906130 + 1.56946i 0.819394 + 0.573231i \(0.194310\pi\)
0.0867359 + 0.996231i \(0.472356\pi\)
\(18\) 0 0
\(19\) 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i \(-0.721509\pi\)
0.985194 + 0.171442i \(0.0548427\pi\)
\(20\) 0 0
\(21\) −1.11803 + 5.80948i −0.243975 + 1.26773i
\(22\) 0 0
\(23\) −1.88197 + 3.25966i −0.392417 + 0.679686i −0.992768 0.120051i \(-0.961694\pi\)
0.600351 + 0.799737i \(0.295028\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.23607 0.430331
\(28\) 0 0
\(29\) −4.47214 −0.830455 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(30\) 0 0
\(31\) 2.50000 + 4.33013i 0.449013 + 0.777714i 0.998322 0.0579057i \(-0.0184423\pi\)
−0.549309 + 0.835619i \(0.685109\pi\)
\(32\) 0 0
\(33\) 3.35410 5.80948i 0.583874 1.01130i
\(34\) 0 0
\(35\) 5.59017 1.93649i 0.944911 0.327327i
\(36\) 0 0
\(37\) 4.35410 7.54153i 0.715810 1.23982i −0.246836 0.969057i \(-0.579391\pi\)
0.962646 0.270762i \(-0.0872757\pi\)
\(38\) 0 0
\(39\) −1.11803 1.93649i −0.179029 0.310087i
\(40\) 0 0
\(41\) 4.47214 0.698430 0.349215 0.937043i \(-0.386448\pi\)
0.349215 + 0.937043i \(0.386448\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 2.23607 + 3.87298i 0.333333 + 0.577350i
\(46\) 0 0
\(47\) 0.736068 1.27491i 0.107367 0.185964i −0.807336 0.590092i \(-0.799091\pi\)
0.914703 + 0.404128i \(0.132425\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) −8.35410 + 14.4697i −1.16981 + 2.02617i
\(52\) 0 0
\(53\) −0.736068 1.27491i −0.101107 0.175122i 0.811034 0.584999i \(-0.198905\pi\)
−0.912141 + 0.409877i \(0.865572\pi\)
\(54\) 0 0
\(55\) −6.70820 −0.904534
\(56\) 0 0
\(57\) 6.70820 0.888523
\(58\) 0 0
\(59\) 3.73607 + 6.47106i 0.486395 + 0.842460i 0.999878 0.0156395i \(-0.00497842\pi\)
−0.513483 + 0.858100i \(0.671645\pi\)
\(60\) 0 0
\(61\) −1.50000 + 2.59808i −0.192055 + 0.332650i −0.945931 0.324367i \(-0.894849\pi\)
0.753876 + 0.657017i \(0.228182\pi\)
\(62\) 0 0
\(63\) −5.00000 + 1.73205i −0.629941 + 0.218218i
\(64\) 0 0
\(65\) −1.11803 + 1.93649i −0.138675 + 0.240192i
\(66\) 0 0
\(67\) −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) 0 0
\(69\) −8.41641 −1.01322
\(70\) 0 0
\(71\) −8.94427 −1.06149 −0.530745 0.847532i \(-0.678088\pi\)
−0.530745 + 0.847532i \(0.678088\pi\)
\(72\) 0 0
\(73\) −5.35410 9.27358i −0.626650 1.08539i −0.988219 0.153045i \(-0.951092\pi\)
0.361569 0.932345i \(-0.382241\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.50000 7.79423i 0.170941 0.888235i
\(78\) 0 0
\(79\) 5.35410 9.27358i 0.602384 1.04336i −0.390076 0.920783i \(-0.627551\pi\)
0.992459 0.122576i \(-0.0391155\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 16.7082 1.81226
\(86\) 0 0
\(87\) −5.00000 8.66025i −0.536056 0.928477i
\(88\) 0 0
\(89\) 1.11803 1.93649i 0.118511 0.205268i −0.800667 0.599110i \(-0.795521\pi\)
0.919178 + 0.393842i \(0.128854\pi\)
\(90\) 0 0
\(91\) −2.00000 1.73205i −0.209657 0.181568i
\(92\) 0 0
\(93\) −5.59017 + 9.68246i −0.579674 + 1.00402i
\(94\) 0 0
\(95\) −3.35410 5.80948i −0.344124 0.596040i
\(96\) 0 0
\(97\) −17.4164 −1.76837 −0.884184 0.467139i \(-0.845285\pi\)
−0.884184 + 0.467139i \(0.845285\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 0 0
\(103\) 5.35410 9.27358i 0.527555 0.913753i −0.471929 0.881637i \(-0.656442\pi\)
0.999484 0.0321160i \(-0.0102246\pi\)
\(104\) 0 0
\(105\) 10.0000 + 8.66025i 0.975900 + 0.845154i
\(106\) 0 0
\(107\) −7.11803 + 12.3288i −0.688126 + 1.19187i 0.284317 + 0.958730i \(0.408233\pi\)
−0.972443 + 0.233139i \(0.925100\pi\)
\(108\) 0 0
\(109\) −5.35410 9.27358i −0.512830 0.888248i −0.999889 0.0148787i \(-0.995264\pi\)
0.487059 0.873369i \(-0.338070\pi\)
\(110\) 0 0
\(111\) 19.4721 1.84821
\(112\) 0 0
\(113\) −14.9443 −1.40584 −0.702919 0.711269i \(-0.748121\pi\)
−0.702919 + 0.711269i \(0.748121\pi\)
\(114\) 0 0
\(115\) 4.20820 + 7.28882i 0.392417 + 0.679686i
\(116\) 0 0
\(117\) 1.00000 1.73205i 0.0924500 0.160128i
\(118\) 0 0
\(119\) −3.73607 + 19.4132i −0.342485 + 1.77960i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) 5.00000 + 8.66025i 0.450835 + 0.780869i
\(124\) 0 0
\(125\) 11.1803 1.00000
\(126\) 0 0
\(127\) −15.4164 −1.36798 −0.683992 0.729489i \(-0.739758\pi\)
−0.683992 + 0.729489i \(0.739758\pi\)
\(128\) 0 0
\(129\) 8.94427 + 15.4919i 0.787499 + 1.36399i
\(130\) 0 0
\(131\) −1.88197 + 3.25966i −0.164428 + 0.284798i −0.936452 0.350796i \(-0.885911\pi\)
0.772024 + 0.635593i \(0.219245\pi\)
\(132\) 0 0
\(133\) 7.50000 2.59808i 0.650332 0.225282i
\(134\) 0 0
\(135\) 2.50000 4.33013i 0.215166 0.372678i
\(136\) 0 0
\(137\) 1.88197 + 3.25966i 0.160787 + 0.278492i 0.935151 0.354249i \(-0.115263\pi\)
−0.774364 + 0.632740i \(0.781930\pi\)
\(138\) 0 0
\(139\) −3.41641 −0.289776 −0.144888 0.989448i \(-0.546282\pi\)
−0.144888 + 0.989448i \(0.546282\pi\)
\(140\) 0 0
\(141\) 3.29180 0.277219
\(142\) 0 0
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) 0 0
\(145\) −5.00000 + 8.66025i −0.415227 + 0.719195i
\(146\) 0 0
\(147\) −12.2984 + 9.68246i −1.01435 + 0.798596i
\(148\) 0 0
\(149\) 6.35410 11.0056i 0.520548 0.901616i −0.479166 0.877724i \(-0.659061\pi\)
0.999715 0.0238920i \(-0.00760577\pi\)
\(150\) 0 0
\(151\) −3.20820 5.55677i −0.261080 0.452204i 0.705449 0.708760i \(-0.250745\pi\)
−0.966529 + 0.256557i \(0.917412\pi\)
\(152\) 0 0
\(153\) −14.9443 −1.20817
\(154\) 0 0
\(155\) 11.1803 0.898027
\(156\) 0 0
\(157\) −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i \(-0.256779\pi\)
−0.971219 + 0.238190i \(0.923446\pi\)
\(158\) 0 0
\(159\) 1.64590 2.85078i 0.130528 0.226081i
\(160\) 0 0
\(161\) −9.40983 + 3.25966i −0.741598 + 0.256897i
\(162\) 0 0
\(163\) 5.20820 9.02087i 0.407938 0.706569i −0.586721 0.809789i \(-0.699581\pi\)
0.994659 + 0.103220i \(0.0329146\pi\)
\(164\) 0 0
\(165\) −7.50000 12.9904i −0.583874 1.01130i
\(166\) 0 0
\(167\) −13.5279 −1.04682 −0.523409 0.852082i \(-0.675340\pi\)
−0.523409 + 0.852082i \(0.675340\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 3.00000 + 5.19615i 0.229416 + 0.397360i
\(172\) 0 0
\(173\) −5.20820 + 9.02087i −0.395972 + 0.685844i −0.993225 0.116209i \(-0.962926\pi\)
0.597252 + 0.802053i \(0.296259\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −8.35410 + 14.4697i −0.627933 + 1.08761i
\(178\) 0 0
\(179\) 10.0623 + 17.4284i 0.752092 + 1.30266i 0.946807 + 0.321802i \(0.104288\pi\)
−0.194715 + 0.980860i \(0.562378\pi\)
\(180\) 0 0
\(181\) 1.41641 0.105281 0.0526404 0.998614i \(-0.483236\pi\)
0.0526404 + 0.998614i \(0.483236\pi\)
\(182\) 0 0
\(183\) −6.70820 −0.495885
\(184\) 0 0
\(185\) −9.73607 16.8634i −0.715810 1.23982i
\(186\) 0 0
\(187\) 11.2082 19.4132i 0.819625 1.41963i
\(188\) 0 0
\(189\) 4.47214 + 3.87298i 0.325300 + 0.281718i
\(190\) 0 0
\(191\) −5.59017 + 9.68246i −0.404491 + 0.700598i −0.994262 0.106972i \(-0.965884\pi\)
0.589772 + 0.807570i \(0.299218\pi\)
\(192\) 0 0
\(193\) 6.35410 + 11.0056i 0.457378 + 0.792202i 0.998821 0.0485349i \(-0.0154552\pi\)
−0.541443 + 0.840737i \(0.682122\pi\)
\(194\) 0 0
\(195\) −5.00000 −0.358057
\(196\) 0 0
\(197\) −26.9443 −1.91970 −0.959850 0.280514i \(-0.909495\pi\)
−0.959850 + 0.280514i \(0.909495\pi\)
\(198\) 0 0
\(199\) −3.64590 6.31488i −0.258451 0.447650i 0.707376 0.706837i \(-0.249879\pi\)
−0.965827 + 0.259187i \(0.916545\pi\)
\(200\) 0 0
\(201\) 3.35410 5.80948i 0.236580 0.409769i
\(202\) 0 0
\(203\) −8.94427 7.74597i −0.627765 0.543660i
\(204\) 0 0
\(205\) 5.00000 8.66025i 0.349215 0.604858i
\(206\) 0 0
\(207\) −3.76393 6.51932i −0.261611 0.453124i
\(208\) 0 0
\(209\) −9.00000 −0.622543
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −10.0000 17.3205i −0.685189 1.18678i
\(214\) 0 0
\(215\) 8.94427 15.4919i 0.609994 1.05654i
\(216\) 0 0
\(217\) −2.50000 + 12.9904i −0.169711 + 0.881845i
\(218\) 0 0
\(219\) 11.9721 20.7363i 0.809002 1.40123i
\(220\) 0 0
\(221\) −3.73607 6.47106i −0.251315 0.435291i
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.97214 10.3440i −0.396385 0.686558i 0.596892 0.802321i \(-0.296402\pi\)
−0.993277 + 0.115763i \(0.963069\pi\)
\(228\) 0 0
\(229\) 8.06231 13.9643i 0.532772 0.922788i −0.466495 0.884524i \(-0.654484\pi\)
0.999268 0.0382649i \(-0.0121831\pi\)
\(230\) 0 0
\(231\) 16.7705 5.80948i 1.10342 0.382235i
\(232\) 0 0
\(233\) 2.97214 5.14789i 0.194711 0.337250i −0.752095 0.659055i \(-0.770956\pi\)
0.946806 + 0.321806i \(0.104290\pi\)
\(234\) 0 0
\(235\) −1.64590 2.85078i −0.107367 0.185964i
\(236\) 0 0
\(237\) 23.9443 1.55535
\(238\) 0 0
\(239\) 7.41641 0.479728 0.239864 0.970807i \(-0.422897\pi\)
0.239864 + 0.970807i \(0.422897\pi\)
\(240\) 0 0
\(241\) 4.35410 + 7.54153i 0.280472 + 0.485792i 0.971501 0.237035i \(-0.0761756\pi\)
−0.691029 + 0.722827i \(0.742842\pi\)
\(242\) 0 0
\(243\) −8.94427 + 15.4919i −0.573775 + 0.993808i
\(244\) 0 0
\(245\) 14.5344 + 5.80948i 0.928571 + 0.371154i
\(246\) 0 0
\(247\) −1.50000 + 2.59808i −0.0954427 + 0.165312i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −10.4721 −0.660995 −0.330498 0.943807i \(-0.607217\pi\)
−0.330498 + 0.943807i \(0.607217\pi\)
\(252\) 0 0
\(253\) 11.2918 0.709909
\(254\) 0 0
\(255\) 18.6803 + 32.3553i 1.16981 + 2.02617i
\(256\) 0 0
\(257\) 8.97214 15.5402i 0.559666 0.969371i −0.437858 0.899044i \(-0.644263\pi\)
0.997524 0.0703264i \(-0.0224041\pi\)
\(258\) 0 0
\(259\) 21.7705 7.54153i 1.35275 0.468608i
\(260\) 0 0
\(261\) 4.47214 7.74597i 0.276818 0.479463i
\(262\) 0 0
\(263\) −7.06231 12.2323i −0.435480 0.754274i 0.561854 0.827236i \(-0.310088\pi\)
−0.997335 + 0.0729620i \(0.976755\pi\)
\(264\) 0 0
\(265\) −3.29180 −0.202213
\(266\) 0 0
\(267\) 5.00000 0.305995
\(268\) 0 0
\(269\) −2.26393 3.92125i −0.138034 0.239083i 0.788718 0.614755i \(-0.210745\pi\)
−0.926753 + 0.375672i \(0.877412\pi\)
\(270\) 0 0
\(271\) 3.20820 5.55677i 0.194885 0.337550i −0.751978 0.659188i \(-0.770900\pi\)
0.946863 + 0.321638i \(0.104233\pi\)
\(272\) 0 0
\(273\) 1.11803 5.80948i 0.0676665 0.351605i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −13.2082 22.8773i −0.793604 1.37456i −0.923722 0.383064i \(-0.874869\pi\)
0.130118 0.991499i \(-0.458464\pi\)
\(278\) 0 0
\(279\) −10.0000 −0.598684
\(280\) 0 0
\(281\) 9.05573 0.540219 0.270110 0.962830i \(-0.412940\pi\)
0.270110 + 0.962830i \(0.412940\pi\)
\(282\) 0 0
\(283\) −7.06231 12.2323i −0.419811 0.727133i 0.576110 0.817372i \(-0.304570\pi\)
−0.995920 + 0.0902393i \(0.971237\pi\)
\(284\) 0 0
\(285\) 7.50000 12.9904i 0.444262 0.769484i
\(286\) 0 0
\(287\) 8.94427 + 7.74597i 0.527964 + 0.457230i
\(288\) 0 0
\(289\) −19.4164 + 33.6302i −1.14214 + 1.97825i
\(290\) 0 0
\(291\) −19.4721 33.7267i −1.14148 1.97710i
\(292\) 0 0
\(293\) 2.94427 0.172006 0.0860031 0.996295i \(-0.472591\pi\)
0.0860031 + 0.996295i \(0.472591\pi\)
\(294\) 0 0
\(295\) 16.7082 0.972789
\(296\) 0 0
\(297\) −3.35410 5.80948i −0.194625 0.337100i
\(298\) 0 0
\(299\) 1.88197 3.25966i 0.108837 0.188511i
\(300\) 0 0
\(301\) 16.0000 + 13.8564i 0.922225 + 0.798670i
\(302\) 0 0
\(303\) −10.0623 + 17.4284i −0.578064 + 1.00124i
\(304\) 0 0
\(305\) 3.35410 + 5.80948i 0.192055 + 0.332650i
\(306\) 0 0
\(307\) 7.41641 0.423277 0.211638 0.977348i \(-0.432120\pi\)
0.211638 + 0.977348i \(0.432120\pi\)
\(308\) 0 0
\(309\) 23.9443 1.36214
\(310\) 0 0
\(311\) −16.1180 27.9173i −0.913970 1.58304i −0.808403 0.588630i \(-0.799667\pi\)
−0.105567 0.994412i \(-0.533666\pi\)
\(312\) 0 0
\(313\) 16.2082 28.0734i 0.916142 1.58680i 0.110921 0.993829i \(-0.464620\pi\)
0.805221 0.592975i \(-0.202047\pi\)
\(314\) 0 0
\(315\) −2.23607 + 11.6190i −0.125988 + 0.654654i
\(316\) 0 0
\(317\) 1.88197 3.25966i 0.105702 0.183081i −0.808323 0.588739i \(-0.799624\pi\)
0.914025 + 0.405659i \(0.132958\pi\)
\(318\) 0 0
\(319\) 6.70820 + 11.6190i 0.375587 + 0.650536i
\(320\) 0 0
\(321\) −31.8328 −1.77673
\(322\) 0 0
\(323\) 22.4164 1.24728
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 11.9721 20.7363i 0.662061 1.14672i
\(328\) 0 0
\(329\) 3.68034 1.27491i 0.202904 0.0702879i
\(330\) 0 0
\(331\) −14.2082 + 24.6093i −0.780954 + 1.35265i 0.150433 + 0.988620i \(0.451933\pi\)
−0.931387 + 0.364031i \(0.881400\pi\)
\(332\) 0 0
\(333\) 8.70820 + 15.0831i 0.477207 + 0.826546i
\(334\) 0 0
\(335\) −6.70820 −0.366508
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) −16.7082 28.9395i −0.907465 1.57178i
\(340\) 0 0
\(341\) 7.50000 12.9904i 0.406148 0.703469i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) −9.40983 + 16.2983i −0.506608 + 0.877471i
\(346\) 0 0
\(347\) −17.5344 30.3705i −0.941298 1.63038i −0.762999 0.646400i \(-0.776274\pi\)
−0.178299 0.983976i \(-0.557060\pi\)
\(348\) 0 0
\(349\) −2.58359 −0.138297 −0.0691483 0.997606i \(-0.522028\pi\)
−0.0691483 + 0.997606i \(0.522028\pi\)
\(350\) 0 0
\(351\) −2.23607 −0.119352
\(352\) 0 0
\(353\) −15.3541 26.5941i −0.817216 1.41546i −0.907725 0.419565i \(-0.862183\pi\)
0.0905091 0.995896i \(-0.471151\pi\)
\(354\) 0 0
\(355\) −10.0000 + 17.3205i −0.530745 + 0.919277i
\(356\) 0 0
\(357\) −41.7705 + 14.4697i −2.21073 + 0.765819i
\(358\) 0 0
\(359\) −2.97214 + 5.14789i −0.156863 + 0.271695i −0.933736 0.357963i \(-0.883472\pi\)
0.776873 + 0.629658i \(0.216805\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) 0 0
\(363\) 4.47214 0.234726
\(364\) 0 0
\(365\) −23.9443 −1.25330
\(366\) 0 0
\(367\) 0.354102 + 0.613323i 0.0184840 + 0.0320152i 0.875119 0.483907i \(-0.160783\pi\)
−0.856635 + 0.515922i \(0.827449\pi\)
\(368\) 0 0
\(369\) −4.47214 + 7.74597i −0.232810 + 0.403239i
\(370\) 0 0
\(371\) 0.736068 3.82472i 0.0382147 0.198570i
\(372\) 0 0
\(373\) 14.2082 24.6093i 0.735673 1.27422i −0.218755 0.975780i \(-0.570199\pi\)
0.954427 0.298443i \(-0.0964673\pi\)
\(374\) 0 0
\(375\) 12.5000 + 21.6506i 0.645497 + 1.11803i
\(376\) 0 0
\(377\) 4.47214 0.230327
\(378\) 0 0
\(379\) −11.4164 −0.586421 −0.293211 0.956048i \(-0.594724\pi\)
−0.293211 + 0.956048i \(0.594724\pi\)
\(380\) 0 0
\(381\) −17.2361 29.8537i −0.883031 1.52945i
\(382\) 0 0
\(383\) 7.50000 12.9904i 0.383232 0.663777i −0.608290 0.793715i \(-0.708144\pi\)
0.991522 + 0.129937i \(0.0414776\pi\)
\(384\) 0 0
\(385\) −13.4164 11.6190i −0.683763 0.592157i
\(386\) 0 0
\(387\) −8.00000 + 13.8564i −0.406663 + 0.704361i
\(388\) 0 0
\(389\) 3.73607 + 6.47106i 0.189426 + 0.328096i 0.945059 0.326900i \(-0.106004\pi\)
−0.755633 + 0.654995i \(0.772671\pi\)
\(390\) 0 0
\(391\) −28.1246 −1.42232
\(392\) 0 0
\(393\) −8.41641 −0.424552
\(394\) 0 0
\(395\) −11.9721 20.7363i −0.602384 1.04336i
\(396\) 0 0
\(397\) −7.06231 + 12.2323i −0.354447 + 0.613920i −0.987023 0.160578i \(-0.948664\pi\)
0.632576 + 0.774498i \(0.281998\pi\)
\(398\) 0 0
\(399\) 13.4164 + 11.6190i 0.671660 + 0.581675i
\(400\) 0 0
\(401\) −4.88197 + 8.45581i −0.243794 + 0.422263i −0.961792 0.273782i \(-0.911725\pi\)
0.717998 + 0.696045i \(0.245059\pi\)
\(402\) 0 0
\(403\) −2.50000 4.33013i −0.124534 0.215699i
\(404\) 0 0
\(405\) 24.5967 1.22222
\(406\) 0 0
\(407\) −26.1246 −1.29495
\(408\) 0 0
\(409\) 2.35410 + 4.07742i 0.116403 + 0.201616i 0.918340 0.395793i \(-0.129530\pi\)
−0.801937 + 0.597409i \(0.796197\pi\)
\(410\) 0 0
\(411\) −4.20820 + 7.28882i −0.207575 + 0.359531i
\(412\) 0 0
\(413\) −3.73607 + 19.4132i −0.183840 + 0.955260i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −3.81966 6.61585i −0.187050 0.323979i
\(418\) 0 0
\(419\) −15.0557 −0.735520 −0.367760 0.929921i \(-0.619875\pi\)
−0.367760 + 0.929921i \(0.619875\pi\)
\(420\) 0 0
\(421\) −13.4164 −0.653876 −0.326938 0.945046i \(-0.606017\pi\)
−0.326938 + 0.945046i \(0.606017\pi\)
\(422\) 0 0
\(423\) 1.47214 + 2.54981i 0.0715777 + 0.123976i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −7.50000 + 2.59808i −0.362950 + 0.125730i
\(428\) 0 0
\(429\) −3.35410 + 5.80948i −0.161938 + 0.280484i
\(430\) 0 0
\(431\) 6.68034 + 11.5707i 0.321781 + 0.557340i 0.980856 0.194737i \(-0.0623853\pi\)
−0.659075 + 0.752077i \(0.729052\pi\)
\(432\) 0 0
\(433\) 2.58359 0.124160 0.0620798 0.998071i \(-0.480227\pi\)
0.0620798 + 0.998071i \(0.480227\pi\)
\(434\) 0 0
\(435\) −22.3607 −1.07211
\(436\) 0 0
\(437\) 5.64590 + 9.77898i 0.270080 + 0.467792i
\(438\) 0 0
\(439\) −8.06231 + 13.9643i −0.384793 + 0.666481i −0.991740 0.128261i \(-0.959060\pi\)
0.606948 + 0.794742i \(0.292394\pi\)
\(440\) 0 0
\(441\) −13.0000 5.19615i −0.619048 0.247436i
\(442\) 0 0
\(443\) −1.11803 + 1.93649i −0.0531194 + 0.0920055i −0.891362 0.453291i \(-0.850250\pi\)
0.838243 + 0.545297i \(0.183583\pi\)
\(444\) 0 0
\(445\) −2.50000 4.33013i −0.118511 0.205268i
\(446\) 0 0
\(447\) 28.4164 1.34405
\(448\) 0 0
\(449\) 10.3607 0.488951 0.244475 0.969656i \(-0.421384\pi\)
0.244475 + 0.969656i \(0.421384\pi\)
\(450\) 0 0
\(451\) −6.70820 11.6190i −0.315877 0.547115i
\(452\) 0 0
\(453\) 7.17376 12.4253i 0.337053 0.583792i
\(454\) 0 0
\(455\) −5.59017 + 1.93649i −0.262071 + 0.0907841i
\(456\) 0 0
\(457\) −17.0623 + 29.5528i −0.798141 + 1.38242i 0.122684 + 0.992446i \(0.460850\pi\)
−0.920825 + 0.389975i \(0.872484\pi\)
\(458\) 0 0
\(459\) 8.35410 + 14.4697i 0.389936 + 0.675389i
\(460\) 0 0
\(461\) −10.3607 −0.482545 −0.241272 0.970457i \(-0.577565\pi\)
−0.241272 + 0.970457i \(0.577565\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 0 0
\(465\) 12.5000 + 21.6506i 0.579674 + 1.00402i
\(466\) 0 0
\(467\) −10.8262 + 18.7516i −0.500979 + 0.867720i 0.499021 + 0.866590i \(0.333693\pi\)
−0.999999 + 0.00113029i \(0.999640\pi\)
\(468\) 0 0
\(469\) 1.50000 7.79423i 0.0692636 0.359904i
\(470\) 0 0
\(471\) 7.82624 13.5554i 0.360614 0.624602i
\(472\) 0 0
\(473\) −12.0000 20.7846i −0.551761 0.955677i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 2.94427 0.134809
\(478\) 0 0
\(479\) −14.9164 25.8360i −0.681548 1.18048i −0.974508 0.224351i \(-0.927974\pi\)
0.292960 0.956125i \(-0.405360\pi\)
\(480\) 0 0
\(481\) −4.35410 + 7.54153i −0.198530 + 0.343864i
\(482\) 0 0
\(483\) −16.8328 14.5776i −0.765920 0.663306i
\(484\) 0 0
\(485\) −19.4721 + 33.7267i −0.884184 + 1.53145i
\(486\) 0 0
\(487\) 15.9164 + 27.5680i 0.721241 + 1.24923i 0.960503 + 0.278271i \(0.0897614\pi\)
−0.239261 + 0.970955i \(0.576905\pi\)
\(488\) 0 0
\(489\) 23.2918 1.05329
\(490\) 0 0
\(491\) 34.4721 1.55571 0.777853 0.628446i \(-0.216309\pi\)
0.777853 + 0.628446i \(0.216309\pi\)
\(492\) 0 0
\(493\) −16.7082 28.9395i −0.752500 1.30337i
\(494\) 0 0
\(495\) 6.70820 11.6190i 0.301511 0.522233i
\(496\) 0 0
\(497\) −17.8885 15.4919i −0.802411 0.694908i
\(498\) 0 0
\(499\) −0.208204 + 0.360620i −0.00932049 + 0.0161436i −0.870648 0.491907i \(-0.836300\pi\)
0.861328 + 0.508050i \(0.169634\pi\)
\(500\) 0 0
\(501\) −15.1246 26.1966i −0.675718 1.17038i
\(502\) 0 0
\(503\) −3.05573 −0.136248 −0.0681241 0.997677i \(-0.521701\pi\)
−0.0681241 + 0.997677i \(0.521701\pi\)
\(504\) 0 0
\(505\) 20.1246 0.895533
\(506\) 0 0
\(507\) 1.11803 + 1.93649i 0.0496536 + 0.0860026i
\(508\) 0 0
\(509\) 7.88197 13.6520i 0.349362 0.605113i −0.636774 0.771050i \(-0.719732\pi\)
0.986136 + 0.165938i \(0.0530650\pi\)
\(510\) 0 0
\(511\) 5.35410 27.8207i 0.236852 1.23072i
\(512\) 0 0
\(513\) 3.35410 5.80948i 0.148087 0.256495i
\(514\) 0 0
\(515\) −11.9721 20.7363i −0.527555 0.913753i
\(516\) 0 0
\(517\) −4.41641 −0.194233
\(518\) 0 0
\(519\) −23.2918 −1.02240
\(520\) 0 0
\(521\) 0.0278640 + 0.0482619i 0.00122075 + 0.00211439i 0.866635 0.498942i \(-0.166278\pi\)
−0.865414 + 0.501057i \(0.832945\pi\)
\(522\) 0 0
\(523\) 9.64590 16.7072i 0.421786 0.730554i −0.574329 0.818625i \(-0.694737\pi\)
0.996114 + 0.0880707i \(0.0280701\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −18.6803 + 32.3553i −0.813728 + 1.40942i
\(528\) 0 0
\(529\) 4.41641 + 7.64944i 0.192018 + 0.332584i
\(530\) 0 0
\(531\) −14.9443 −0.648526
\(532\) 0 0
\(533\) −4.47214 −0.193710
\(534\) 0 0
\(535\) 15.9164 + 27.5680i 0.688126 + 1.19187i
\(536\) 0 0
\(537\) −22.5000 + 38.9711i −0.970947 + 1.68173i
\(538\) 0 0
\(539\) 16.5000 12.9904i 0.710705 0.559535i
\(540\) 0 0
\(541\) −7.35410 + 12.7377i −0.316178 + 0.547636i −0.979687 0.200532i \(-0.935733\pi\)
0.663510 + 0.748168i \(0.269066\pi\)
\(542\) 0 0
\(543\) 1.58359 + 2.74286i 0.0679584 + 0.117707i
\(544\) 0 0
\(545\) −23.9443 −1.02566
\(546\) 0 0
\(547\) 31.4164 1.34327 0.671634 0.740883i \(-0.265593\pi\)
0.671634 + 0.740883i \(0.265593\pi\)
\(548\) 0 0
\(549\) −3.00000 5.19615i −0.128037 0.221766i
\(550\) 0 0
\(551\) −6.70820 + 11.6190i −0.285779 + 0.494984i
\(552\) 0 0
\(553\) 26.7705 9.27358i 1.13840 0.394353i
\(554\) 0 0
\(555\) 21.7705 37.7076i 0.924107 1.60060i
\(556\) 0 0
\(557\) 2.64590 + 4.58283i 0.112110 + 0.194181i 0.916621 0.399758i \(-0.130906\pi\)
−0.804511 + 0.593938i \(0.797572\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 50.1246 2.11626
\(562\) 0 0
\(563\) −18.2984 31.6937i −0.771185 1.33573i −0.936914 0.349560i \(-0.886331\pi\)
0.165730 0.986171i \(-0.447002\pi\)
\(564\) 0 0
\(565\) −16.7082 + 28.9395i −0.702919 + 1.21749i
\(566\) 0 0
\(567\) −5.50000 + 28.5788i −0.230978 + 1.20020i
\(568\) 0 0
\(569\) −8.26393 + 14.3136i −0.346442 + 0.600055i −0.985615 0.169008i \(-0.945944\pi\)
0.639173 + 0.769063i \(0.279277\pi\)
\(570\) 0 0
\(571\) 2.06231 + 3.57202i 0.0863048 + 0.149484i 0.905946 0.423392i \(-0.139161\pi\)
−0.819642 + 0.572877i \(0.805827\pi\)
\(572\) 0 0
\(573\) −25.0000 −1.04439
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 16.3541 + 28.3261i 0.680830 + 1.17923i 0.974728 + 0.223396i \(0.0717142\pi\)
−0.293898 + 0.955837i \(0.594953\pi\)
\(578\) 0 0
\(579\) −14.2082 + 24.6093i −0.590473 + 1.02273i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2.20820 + 3.82472i −0.0914545 + 0.158404i
\(584\) 0 0
\(585\) −2.23607 3.87298i −0.0924500 0.160128i
\(586\) 0 0
\(587\) 41.8885 1.72893 0.864463 0.502697i \(-0.167659\pi\)
0.864463 + 0.502697i \(0.167659\pi\)
\(588\) 0 0
\(589\) 15.0000 0.618064
\(590\) 0 0
\(591\) −30.1246 52.1774i −1.23916 2.14629i
\(592\) 0 0
\(593\) −16.1180 + 27.9173i −0.661888 + 1.14642i 0.318231 + 0.948013i \(0.396911\pi\)
−0.980119 + 0.198411i \(0.936422\pi\)
\(594\) 0 0
\(595\) 33.4164 + 28.9395i 1.36994 + 1.18640i
\(596\) 0 0
\(597\) 8.15248 14.1205i 0.333659 0.577914i
\(598\) 0 0
\(599\) 20.5344 + 35.5667i 0.839015 + 1.45322i 0.890719 + 0.454553i \(0.150201\pi\)
−0.0517049 + 0.998662i \(0.516466\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 6.00000 0.244339
\(604\) 0 0
\(605\) −2.23607 3.87298i −0.0909091 0.157459i
\(606\) 0 0
\(607\) −8.06231 + 13.9643i −0.327239 + 0.566794i −0.981963 0.189074i \(-0.939452\pi\)
0.654724 + 0.755868i \(0.272785\pi\)
\(608\) 0 0
\(609\) 5.00000 25.9808i 0.202610 1.05279i
\(610\) 0 0
\(611\) −0.736068 + 1.27491i −0.0297781 + 0.0515772i
\(612\) 0 0
\(613\) −11.0623 19.1605i −0.446802 0.773884i 0.551373 0.834259i \(-0.314104\pi\)
−0.998176 + 0.0603742i \(0.980771\pi\)
\(614\) 0 0
\(615\) 22.3607 0.901670
\(616\) 0 0
\(617\) 4.47214 0.180041 0.0900207 0.995940i \(-0.471307\pi\)
0.0900207 + 0.995940i \(0.471307\pi\)
\(618\) 0 0
\(619\) 8.50000 + 14.7224i 0.341644 + 0.591744i 0.984738 0.174042i \(-0.0556830\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 0 0
\(621\) −4.20820 + 7.28882i −0.168869 + 0.292490i
\(622\) 0 0
\(623\) 5.59017 1.93649i 0.223965 0.0775839i
\(624\) 0 0
\(625\) 12.5000 21.6506i 0.500000 0.866025i
\(626\) 0 0
\(627\) −10.0623 17.4284i −0.401850 0.696024i
\(628\) 0 0
\(629\) 65.0689 2.59447
\(630\) 0 0
\(631\) 30.8328 1.22744 0.613718 0.789526i \(-0.289673\pi\)
0.613718 + 0.789526i \(0.289673\pi\)
\(632\) 0 0
\(633\) −4.47214 7.74597i −0.177751 0.307875i
\(634\) 0 0
\(635\) −17.2361 + 29.8537i −0.683992 + 1.18471i
\(636\) 0 0
\(637\) −1.00000 6.92820i −0.0396214 0.274505i
\(638\) 0 0
\(639\) 8.94427 15.4919i 0.353830 0.612851i
\(640\) 0 0
\(641\) 2.97214 + 5.14789i 0.117392 + 0.203329i 0.918734 0.394878i \(-0.129213\pi\)
−0.801341 + 0.598208i \(0.795880\pi\)
\(642\) 0 0
\(643\) 18.8328 0.742694 0.371347 0.928494i \(-0.378896\pi\)
0.371347 + 0.928494i \(0.378896\pi\)
\(644\) 0 0
\(645\) 40.0000 1.57500
\(646\) 0 0
\(647\) 7.88197 + 13.6520i 0.309872 + 0.536714i 0.978334 0.207032i \(-0.0663804\pi\)
−0.668462 + 0.743746i \(0.733047\pi\)
\(648\) 0 0
\(649\) 11.2082 19.4132i 0.439960 0.762034i
\(650\) 0 0
\(651\) −27.9508 + 9.68246i −1.09548 + 0.379485i
\(652\) 0 0
\(653\) −6.73607 + 11.6672i −0.263603 + 0.456573i −0.967197 0.254029i \(-0.918244\pi\)
0.703594 + 0.710602i \(0.251577\pi\)
\(654\) 0 0
\(655\) 4.20820 + 7.28882i 0.164428 + 0.284798i
\(656\) 0 0
\(657\) 21.4164 0.835534
\(658\) 0 0
\(659\) −8.94427 −0.348419 −0.174210 0.984709i \(-0.555737\pi\)
−0.174210 + 0.984709i \(0.555737\pi\)
\(660\) 0 0
\(661\) −3.35410 5.80948i −0.130459 0.225962i 0.793394 0.608708i \(-0.208312\pi\)
−0.923854 + 0.382746i \(0.874979\pi\)
\(662\) 0 0
\(663\) 8.35410 14.4697i 0.324446 0.561958i
\(664\) 0 0
\(665\) 3.35410 17.4284i 0.130066 0.675845i
\(666\) 0 0
\(667\) 8.41641 14.5776i 0.325885 0.564449i
\(668\) 0 0
\(669\) 4.47214 + 7.74597i 0.172903 + 0.299476i
\(670\) 0 0
\(671\) 9.00000 0.347441
\(672\) 0 0
\(673\) 17.4164 0.671353 0.335677 0.941977i \(-0.391035\pi\)
0.335677 + 0.941977i \(0.391035\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.4443 + 28.4823i −0.632005 + 1.09466i 0.355137 + 0.934814i \(0.384434\pi\)
−0.987141 + 0.159850i \(0.948899\pi\)
\(678\) 0 0
\(679\) −34.8328 30.1661i −1.33676 1.15767i
\(680\) 0 0
\(681\) 13.3541 23.1300i 0.511730 0.886343i
\(682\) 0 0
\(683\) −2.26393 3.92125i −0.0866270 0.150042i 0.819456 0.573142i \(-0.194275\pi\)
−0.906083 + 0.423099i \(0.860942\pi\)
\(684\) 0 0
\(685\) 8.41641 0.321574
\(686\) 0 0
\(687\) 36.0557 1.37561
\(688\) 0 0
\(689\) 0.736068 + 1.27491i 0.0280420 + 0.0485701i
\(690\) 0 0
\(691\) 0.916408 1.58726i 0.0348618 0.0603824i −0.848068 0.529887i \(-0.822234\pi\)
0.882930 + 0.469505i \(0.155568\pi\)
\(692\) 0 0
\(693\) 12.0000 + 10.3923i 0.455842 + 0.394771i
\(694\) 0 0
\(695\) −3.81966 + 6.61585i −0.144888 + 0.250953i
\(696\) 0 0
\(697\) 16.7082 + 28.9395i 0.632868 + 1.09616i
\(698\) 0 0
\(699\) 13.2918 0.502742
\(700\) 0 0
\(701\) 22.3607 0.844551 0.422276 0.906467i \(-0.361231\pi\)
0.422276 + 0.906467i \(0.361231\pi\)
\(702\) 0 0
\(703\) −13.0623 22.6246i −0.492654 0.853302i
\(704\) 0 0
\(705\) 3.68034 6.37454i 0.138610 0.240079i
\(706\) 0 0
\(707\) −4.50000 + 23.3827i −0.169240 + 0.879396i
\(708\) 0 0
\(709\) 4.93769 8.55234i 0.185439 0.321190i −0.758285 0.651923i \(-0.773963\pi\)
0.943724 + 0.330733i \(0.107296\pi\)
\(710\) 0 0
\(711\) 10.7082 + 18.5472i 0.401589 + 0.695573i
\(712\) 0 0
\(713\) −18.8197 −0.704802
\(714\) 0 0
\(715\) 6.70820 0.250873
\(716\) 0 0
\(717\) 8.29180 + 14.3618i 0.309663 + 0.536352i
\(718\) 0 0
\(719\) 5.64590 9.77898i 0.210556 0.364694i −0.741332 0.671138i \(-0.765806\pi\)
0.951889 + 0.306444i \(0.0991391\pi\)
\(720\) 0 0
\(721\) 26.7705 9.27358i 0.996986 0.345366i
\(722\) 0 0
\(723\) −9.73607 + 16.8634i −0.362088 + 0.627155i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −14.8328 −0.550119 −0.275059 0.961427i \(-0.588698\pi\)
−0.275059 + 0.961427i \(0.588698\pi\)
\(728\) 0 0
\(729\) −7.00000 −0.259259
\(730\) 0 0
\(731\) 29.8885 + 51.7685i 1.10547 + 1.91473i
\(732\) 0 0
\(733\) −7.64590 + 13.2431i −0.282408 + 0.489144i −0.971977 0.235075i \(-0.924466\pi\)
0.689570 + 0.724219i \(0.257800\pi\)
\(734\) 0 0
\(735\) 5.00000 + 34.6410i 0.184428 + 1.27775i
\(736\) 0 0
\(737\) −4.50000 + 7.79423i −0.165760 + 0.287104i
\(738\) 0 0
\(739\) 17.9164 + 31.0321i 0.659066 + 1.14154i 0.980858 + 0.194725i \(0.0623814\pi\)
−0.321792 + 0.946810i \(0.604285\pi\)
\(740\) 0 0
\(741\) −6.70820 −0.246432
\(742\) 0 0
\(743\) −15.0557 −0.552341 −0.276171 0.961109i \(-0.589065\pi\)
−0.276171 + 0.961109i \(0.589065\pi\)
\(744\) 0 0
\(745\) −14.2082 24.6093i −0.520548 0.901616i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −35.5902 + 12.3288i −1.30044 + 0.450484i
\(750\) 0 0
\(751\) 15.0623 26.0887i 0.549631 0.951989i −0.448668 0.893698i \(-0.648102\pi\)
0.998300 0.0582911i \(-0.0185651\pi\)
\(752\) 0 0
\(753\) −11.7082 20.2792i −0.426671 0.739015i
\(754\) 0 0
\(755\) −14.3475 −0.522160
\(756\) 0 0
\(757\) 0.832816 0.0302692 0.0151346 0.999885i \(-0.495182\pi\)
0.0151346 + 0.999885i \(0.495182\pi\)
\(758\) 0 0
\(759\) 12.6246 + 21.8665i 0.458244 + 0.793703i
\(760\) 0 0
\(761\) −16.7705 + 29.0474i −0.607931 + 1.05297i 0.383650 + 0.923478i \(0.374667\pi\)
−0.991581 + 0.129488i \(0.958667\pi\)
\(762\) 0 0
\(763\) 5.35410 27.8207i 0.193832 1.00718i
\(764\) 0 0
\(765\) −16.7082 + 28.9395i −0.604086 + 1.04631i
\(766\) 0 0
\(767\) −3.73607 6.47106i −0.134902 0.233656i
\(768\) 0 0
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) 0 0
\(771\) 40.1246 1.44505
\(772\) 0 0
\(773\) −5.53444 9.58593i −0.199060 0.344782i 0.749164 0.662385i \(-0.230456\pi\)
−0.948224 + 0.317603i \(0.897122\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 38.9443 + 33.7267i 1.39712 + 1.20994i
\(778\) 0 0
\(779\) 6.70820 11.6190i 0.240346 0.416292i
\(780\) 0 0
\(781\) 13.4164 + 23.2379i 0.480077 + 0.831517i
\(782\) 0 0
\(783\) −10.0000 −0.357371
\(784\) 0 0
\(785\) −15.6525 −0.558661
\(786\) 0 0
\(787\) −3.20820 5.55677i −0.114360 0.198078i 0.803164 0.595758i \(-0.203148\pi\)
−0.917524 + 0.397681i \(0.869815\pi\)
\(788\) 0 0
\(789\) 15.7918 27.3522i 0.562203 0.973764i
\(790\) 0 0
\(791\) −29.8885 25.8842i −1.06271 0.920338i
\(792\) 0 0
\(793\) 1.50000 2.59808i 0.0532666 0.0922604i
\(794\) 0 0
\(795\) −3.68034 6.37454i −0.130528 0.226081i
\(796\) 0 0
\(797\) 26.9443