Properties

Label 756.2.ck.a.5.14
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.14
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.277790 + 1.70963i) q^{3} +(0.630118 - 3.57358i) q^{5} +(-2.41159 + 1.08823i) q^{7} +(-2.84567 + 0.949836i) q^{9} +O(q^{10})\) \(q+(0.277790 + 1.70963i) q^{3} +(0.630118 - 3.57358i) q^{5} +(-2.41159 + 1.08823i) q^{7} +(-2.84567 + 0.949836i) q^{9} +(-5.37077 + 0.947012i) q^{11} +(3.07790 - 3.66809i) q^{13} +(6.28454 + 0.0845642i) q^{15} -3.33090 q^{17} -5.54597i q^{19} +(-2.53039 - 3.82062i) q^{21} +(-4.97574 + 5.92986i) q^{23} +(-7.67496 - 2.79346i) q^{25} +(-2.41437 - 4.60118i) q^{27} +(-4.08440 - 4.86760i) q^{29} +(1.15746 + 3.18009i) q^{31} +(-3.11099 - 8.91896i) q^{33} +(2.36929 + 9.30371i) q^{35} +(0.690046 + 1.19519i) q^{37} +(7.12609 + 4.24310i) q^{39} +(4.74638 + 3.98269i) q^{41} +(-1.78595 - 0.650033i) q^{43} +(1.60121 + 10.7677i) q^{45} +(-5.57250 - 2.02822i) q^{47} +(4.63151 - 5.24873i) q^{49} +(-0.925291 - 5.69461i) q^{51} +(6.01547 - 3.47303i) q^{53} +19.7896i q^{55} +(9.48155 - 1.54061i) q^{57} +(-8.58135 - 7.20060i) q^{59} +(-0.712093 + 1.95646i) q^{61} +(5.82893 - 5.38735i) q^{63} +(-11.1688 - 13.3104i) q^{65} +(1.69045 - 9.58704i) q^{67} +(-11.5201 - 6.85942i) q^{69} +(-1.02203 - 0.590072i) q^{71} +(3.38838 + 1.95628i) q^{73} +(2.64375 - 13.8973i) q^{75} +(11.9215 - 8.12844i) q^{77} +(1.24492 + 7.06031i) q^{79} +(7.19562 - 5.40583i) q^{81} +(7.60660 - 6.38269i) q^{83} +(-2.09886 + 11.9032i) q^{85} +(7.18718 - 8.33498i) q^{87} -6.67102 q^{89} +(-3.43088 + 12.1954i) q^{91} +(-5.11525 + 2.86222i) q^{93} +(-19.8189 - 3.49462i) q^{95} +(-3.89819 + 10.7102i) q^{97} +(14.3839 - 7.79623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.277790 + 1.70963i 0.160382 + 0.987055i
\(4\) 0 0
\(5\) 0.630118 3.57358i 0.281798 1.59815i −0.434708 0.900572i \(-0.643148\pi\)
0.716505 0.697582i \(-0.245741\pi\)
\(6\) 0 0
\(7\) −2.41159 + 1.08823i −0.911494 + 0.411313i
\(8\) 0 0
\(9\) −2.84567 + 0.949836i −0.948555 + 0.316612i
\(10\) 0 0
\(11\) −5.37077 + 0.947012i −1.61935 + 0.285535i −0.908524 0.417833i \(-0.862790\pi\)
−0.710825 + 0.703368i \(0.751678\pi\)
\(12\) 0 0
\(13\) 3.07790 3.66809i 0.853655 1.01735i −0.145952 0.989292i \(-0.546624\pi\)
0.999606 0.0280542i \(-0.00893109\pi\)
\(14\) 0 0
\(15\) 6.28454 + 0.0845642i 1.62266 + 0.0218344i
\(16\) 0 0
\(17\) −3.33090 −0.807862 −0.403931 0.914789i \(-0.632356\pi\)
−0.403931 + 0.914789i \(0.632356\pi\)
\(18\) 0 0
\(19\) 5.54597i 1.27233i −0.771552 0.636166i \(-0.780519\pi\)
0.771552 0.636166i \(-0.219481\pi\)
\(20\) 0 0
\(21\) −2.53039 3.82062i −0.552176 0.833728i
\(22\) 0 0
\(23\) −4.97574 + 5.92986i −1.03751 + 1.23646i −0.0664127 + 0.997792i \(0.521155\pi\)
−0.971101 + 0.238669i \(0.923289\pi\)
\(24\) 0 0
\(25\) −7.67496 2.79346i −1.53499 0.558691i
\(26\) 0 0
\(27\) −2.41437 4.60118i −0.464645 0.885497i
\(28\) 0 0
\(29\) −4.08440 4.86760i −0.758454 0.903890i 0.239295 0.970947i \(-0.423084\pi\)
−0.997749 + 0.0670565i \(0.978639\pi\)
\(30\) 0 0
\(31\) 1.15746 + 3.18009i 0.207886 + 0.571161i 0.999189 0.0402624i \(-0.0128194\pi\)
−0.791303 + 0.611424i \(0.790597\pi\)
\(32\) 0 0
\(33\) −3.11099 8.91896i −0.541553 1.55259i
\(34\) 0 0
\(35\) 2.36929 + 9.30371i 0.400484 + 1.57261i
\(36\) 0 0
\(37\) 0.690046 + 1.19519i 0.113443 + 0.196489i 0.917156 0.398528i \(-0.130479\pi\)
−0.803713 + 0.595017i \(0.797145\pi\)
\(38\) 0 0
\(39\) 7.12609 + 4.24310i 1.14109 + 0.679440i
\(40\) 0 0
\(41\) 4.74638 + 3.98269i 0.741260 + 0.621991i 0.933176 0.359420i \(-0.117026\pi\)
−0.191916 + 0.981411i \(0.561470\pi\)
\(42\) 0 0
\(43\) −1.78595 0.650033i −0.272355 0.0991291i 0.202232 0.979338i \(-0.435180\pi\)
−0.474587 + 0.880209i \(0.657403\pi\)
\(44\) 0 0
\(45\) 1.60121 + 10.7677i 0.238694 + 1.60516i
\(46\) 0 0
\(47\) −5.57250 2.02822i −0.812832 0.295847i −0.0980389 0.995183i \(-0.531257\pi\)
−0.714793 + 0.699336i \(0.753479\pi\)
\(48\) 0 0
\(49\) 4.63151 5.24873i 0.661644 0.749818i
\(50\) 0 0
\(51\) −0.925291 5.69461i −0.129567 0.797404i
\(52\) 0 0
\(53\) 6.01547 3.47303i 0.826288 0.477057i −0.0262922 0.999654i \(-0.508370\pi\)
0.852580 + 0.522597i \(0.175037\pi\)
\(54\) 0 0
\(55\) 19.7896i 2.66843i
\(56\) 0 0
\(57\) 9.48155 1.54061i 1.25586 0.204059i
\(58\) 0 0
\(59\) −8.58135 7.20060i −1.11720 0.937439i −0.118737 0.992926i \(-0.537884\pi\)
−0.998459 + 0.0554869i \(0.982329\pi\)
\(60\) 0 0
\(61\) −0.712093 + 1.95646i −0.0911741 + 0.250499i −0.976895 0.213719i \(-0.931442\pi\)
0.885721 + 0.464218i \(0.153665\pi\)
\(62\) 0 0
\(63\) 5.82893 5.38735i 0.734376 0.678743i
\(64\) 0 0
\(65\) −11.1688 13.3104i −1.38532 1.65096i
\(66\) 0 0
\(67\) 1.69045 9.58704i 0.206522 1.17124i −0.688505 0.725231i \(-0.741733\pi\)
0.895027 0.446012i \(-0.147156\pi\)
\(68\) 0 0
\(69\) −11.5201 6.85942i −1.38685 0.825777i
\(70\) 0 0
\(71\) −1.02203 0.590072i −0.121293 0.0700286i 0.438126 0.898914i \(-0.355642\pi\)
−0.559419 + 0.828885i \(0.688976\pi\)
\(72\) 0 0
\(73\) 3.38838 + 1.95628i 0.396580 + 0.228965i 0.685007 0.728536i \(-0.259799\pi\)
−0.288428 + 0.957502i \(0.593132\pi\)
\(74\) 0 0
\(75\) 2.64375 13.8973i 0.305274 1.60472i
\(76\) 0 0
\(77\) 11.9215 8.12844i 1.35858 0.926322i
\(78\) 0 0
\(79\) 1.24492 + 7.06031i 0.140065 + 0.794347i 0.971198 + 0.238274i \(0.0765815\pi\)
−0.831133 + 0.556073i \(0.812307\pi\)
\(80\) 0 0
\(81\) 7.19562 5.40583i 0.799514 0.600648i
\(82\) 0 0
\(83\) 7.60660 6.38269i 0.834932 0.700592i −0.121485 0.992593i \(-0.538766\pi\)
0.956418 + 0.292002i \(0.0943213\pi\)
\(84\) 0 0
\(85\) −2.09886 + 11.9032i −0.227654 + 1.29109i
\(86\) 0 0
\(87\) 7.18718 8.33498i 0.770547 0.893604i
\(88\) 0 0
\(89\) −6.67102 −0.707126 −0.353563 0.935411i \(-0.615030\pi\)
−0.353563 + 0.935411i \(0.615030\pi\)
\(90\) 0 0
\(91\) −3.43088 + 12.1954i −0.359654 + 1.27842i
\(92\) 0 0
\(93\) −5.11525 + 2.86222i −0.530426 + 0.296799i
\(94\) 0 0
\(95\) −19.8189 3.49462i −2.03338 0.358540i
\(96\) 0 0
\(97\) −3.89819 + 10.7102i −0.395802 + 1.08746i 0.568508 + 0.822678i \(0.307521\pi\)
−0.964309 + 0.264778i \(0.914701\pi\)
\(98\) 0 0
\(99\) 14.3839 7.79623i 1.44564 0.783551i
\(100\) 0 0
\(101\) −0.268163 + 0.225015i −0.0266832 + 0.0223899i −0.656032 0.754733i \(-0.727766\pi\)
0.629349 + 0.777123i \(0.283322\pi\)
\(102\) 0 0
\(103\) 15.9438 + 2.81132i 1.57099 + 0.277007i 0.890233 0.455506i \(-0.150542\pi\)
0.680753 + 0.732513i \(0.261653\pi\)
\(104\) 0 0
\(105\) −15.2477 + 6.63509i −1.48803 + 0.647519i
\(106\) 0 0
\(107\) 2.20395 + 1.27245i 0.213064 + 0.123012i 0.602734 0.797942i \(-0.294078\pi\)
−0.389671 + 0.920954i \(0.627411\pi\)
\(108\) 0 0
\(109\) −2.93214 5.07862i −0.280848 0.486444i 0.690746 0.723098i \(-0.257282\pi\)
−0.971594 + 0.236654i \(0.923949\pi\)
\(110\) 0 0
\(111\) −1.85165 + 1.51174i −0.175751 + 0.143488i
\(112\) 0 0
\(113\) 3.59529 + 9.87798i 0.338217 + 0.929242i 0.985900 + 0.167333i \(0.0535156\pi\)
−0.647684 + 0.761909i \(0.724262\pi\)
\(114\) 0 0
\(115\) 18.0555 + 21.5177i 1.68368 + 2.00654i
\(116\) 0 0
\(117\) −5.27457 + 13.3617i −0.487634 + 1.23529i
\(118\) 0 0
\(119\) 8.03276 3.62479i 0.736362 0.332284i
\(120\) 0 0
\(121\) 17.6118 6.41015i 1.60107 0.582741i
\(122\) 0 0
\(123\) −5.49042 + 9.22090i −0.495055 + 0.831421i
\(124\) 0 0
\(125\) −5.74700 + 9.95409i −0.514027 + 0.890321i
\(126\) 0 0
\(127\) −5.79930 10.0447i −0.514605 0.891322i −0.999856 0.0169471i \(-0.994605\pi\)
0.485252 0.874375i \(-0.338728\pi\)
\(128\) 0 0
\(129\) 0.615196 3.23389i 0.0541650 0.284728i
\(130\) 0 0
\(131\) 1.18226 + 0.992033i 0.103294 + 0.0866743i 0.692972 0.720964i \(-0.256301\pi\)
−0.589678 + 0.807639i \(0.700745\pi\)
\(132\) 0 0
\(133\) 6.03529 + 13.3746i 0.523326 + 1.15972i
\(134\) 0 0
\(135\) −17.9640 + 5.72864i −1.54610 + 0.493043i
\(136\) 0 0
\(137\) −0.508156 + 1.39615i −0.0434147 + 0.119281i −0.959505 0.281690i \(-0.909105\pi\)
0.916091 + 0.400971i \(0.131327\pi\)
\(138\) 0 0
\(139\) −17.2879 3.04832i −1.46634 0.258555i −0.617234 0.786780i \(-0.711747\pi\)
−0.849105 + 0.528224i \(0.822858\pi\)
\(140\) 0 0
\(141\) 1.91953 10.0903i 0.161653 0.849758i
\(142\) 0 0
\(143\) −13.0569 + 22.6153i −1.09188 + 1.89119i
\(144\) 0 0
\(145\) −19.9684 + 11.5288i −1.65829 + 0.957412i
\(146\) 0 0
\(147\) 10.2600 + 6.46012i 0.846228 + 0.532822i
\(148\) 0 0
\(149\) 1.32136 + 3.63041i 0.108250 + 0.297415i 0.981977 0.189003i \(-0.0605256\pi\)
−0.873726 + 0.486418i \(0.838303\pi\)
\(150\) 0 0
\(151\) 0.227371 + 1.28949i 0.0185032 + 0.104937i 0.992661 0.120933i \(-0.0385887\pi\)
−0.974157 + 0.225870i \(0.927478\pi\)
\(152\) 0 0
\(153\) 9.47863 3.16381i 0.766302 0.255779i
\(154\) 0 0
\(155\) 12.0936 2.13244i 0.971385 0.171281i
\(156\) 0 0
\(157\) −14.5617 + 17.3540i −1.16215 + 1.38500i −0.253555 + 0.967321i \(0.581600\pi\)
−0.908596 + 0.417676i \(0.862845\pi\)
\(158\) 0 0
\(159\) 7.60863 + 9.31944i 0.603404 + 0.739080i
\(160\) 0 0
\(161\) 5.54638 19.7151i 0.437116 1.55377i
\(162\) 0 0
\(163\) 8.18989 14.1853i 0.641481 1.11108i −0.343621 0.939109i \(-0.611653\pi\)
0.985102 0.171970i \(-0.0550132\pi\)
\(164\) 0 0
\(165\) −33.8329 + 5.49736i −2.63389 + 0.427969i
\(166\) 0 0
\(167\) 10.1535 3.69558i 0.785704 0.285973i 0.0821551 0.996620i \(-0.473820\pi\)
0.703549 + 0.710647i \(0.251597\pi\)
\(168\) 0 0
\(169\) −1.72404 9.77751i −0.132618 0.752116i
\(170\) 0 0
\(171\) 5.26776 + 15.7820i 0.402836 + 1.20688i
\(172\) 0 0
\(173\) −6.04200 + 5.06984i −0.459365 + 0.385453i −0.842897 0.538075i \(-0.819152\pi\)
0.383533 + 0.923527i \(0.374707\pi\)
\(174\) 0 0
\(175\) 21.5487 1.61546i 1.62893 0.122117i
\(176\) 0 0
\(177\) 9.92655 16.6712i 0.746125 1.25308i
\(178\) 0 0
\(179\) 18.3182i 1.36916i 0.728936 + 0.684582i \(0.240015\pi\)
−0.728936 + 0.684582i \(0.759985\pi\)
\(180\) 0 0
\(181\) −12.1885 + 7.03703i −0.905963 + 0.523058i −0.879130 0.476582i \(-0.841876\pi\)
−0.0268333 + 0.999640i \(0.508542\pi\)
\(182\) 0 0
\(183\) −3.54263 0.673930i −0.261879 0.0498183i
\(184\) 0 0
\(185\) 4.70593 1.71282i 0.345987 0.125929i
\(186\) 0 0
\(187\) 17.8895 3.15440i 1.30821 0.230673i
\(188\) 0 0
\(189\) 10.8296 + 8.46876i 0.787737 + 0.616011i
\(190\) 0 0
\(191\) −12.8418 + 2.26435i −0.929197 + 0.163843i −0.617708 0.786407i \(-0.711939\pi\)
−0.311489 + 0.950250i \(0.600828\pi\)
\(192\) 0 0
\(193\) −9.60938 + 3.49753i −0.691698 + 0.251758i −0.663862 0.747855i \(-0.731084\pi\)
−0.0278360 + 0.999613i \(0.508862\pi\)
\(194\) 0 0
\(195\) 19.6533 22.7920i 1.40740 1.63217i
\(196\) 0 0
\(197\) −3.72816 + 2.15245i −0.265620 + 0.153356i −0.626896 0.779103i \(-0.715675\pi\)
0.361275 + 0.932459i \(0.382341\pi\)
\(198\) 0 0
\(199\) 19.8295i 1.40568i −0.711350 0.702838i \(-0.751916\pi\)
0.711350 0.702838i \(-0.248084\pi\)
\(200\) 0 0
\(201\) 16.8599 + 0.226865i 1.18920 + 0.0160018i
\(202\) 0 0
\(203\) 15.1470 + 7.29387i 1.06311 + 0.511929i
\(204\) 0 0
\(205\) 17.2232 14.4520i 1.20292 1.00937i
\(206\) 0 0
\(207\) 8.52690 21.6005i 0.592661 1.50134i
\(208\) 0 0
\(209\) 5.25210 + 29.7861i 0.363295 + 2.06035i
\(210\) 0 0
\(211\) 10.3867 3.78043i 0.715047 0.260256i 0.0412251 0.999150i \(-0.486874\pi\)
0.673821 + 0.738894i \(0.264652\pi\)
\(212\) 0 0
\(213\) 0.724893 1.91122i 0.0496689 0.130954i
\(214\) 0 0
\(215\) −3.44830 + 5.97264i −0.235172 + 0.407330i
\(216\) 0 0
\(217\) −6.25198 6.40949i −0.424412 0.435104i
\(218\) 0 0
\(219\) −2.40326 + 6.33630i −0.162397 + 0.428168i
\(220\) 0 0
\(221\) −10.2522 + 12.2181i −0.689635 + 0.821875i
\(222\) 0 0
\(223\) 10.1929 1.79728i 0.682567 0.120355i 0.178396 0.983959i \(-0.442909\pi\)
0.504171 + 0.863604i \(0.331798\pi\)
\(224\) 0 0
\(225\) 24.4937 + 0.659289i 1.63291 + 0.0439526i
\(226\) 0 0
\(227\) −3.56670 20.2278i −0.236730 1.34257i −0.838939 0.544226i \(-0.816823\pi\)
0.602208 0.798339i \(-0.294288\pi\)
\(228\) 0 0
\(229\) 0.382724 + 1.05153i 0.0252911 + 0.0694867i 0.951696 0.307043i \(-0.0993395\pi\)
−0.926405 + 0.376530i \(0.877117\pi\)
\(230\) 0 0
\(231\) 17.2083 + 18.1234i 1.13222 + 1.19243i
\(232\) 0 0
\(233\) 2.76526 1.59653i 0.181159 0.104592i −0.406678 0.913571i \(-0.633313\pi\)
0.587837 + 0.808979i \(0.299980\pi\)
\(234\) 0 0
\(235\) −10.7593 + 18.6357i −0.701862 + 1.21566i
\(236\) 0 0
\(237\) −11.7247 + 4.08964i −0.761600 + 0.265651i
\(238\) 0 0
\(239\) −7.88449 1.39025i −0.510006 0.0899277i −0.0872770 0.996184i \(-0.527817\pi\)
−0.422729 + 0.906256i \(0.638928\pi\)
\(240\) 0 0
\(241\) −5.02001 + 13.7924i −0.323367 + 0.888444i 0.666380 + 0.745612i \(0.267843\pi\)
−0.989747 + 0.142831i \(0.954379\pi\)
\(242\) 0 0
\(243\) 11.2408 + 10.8002i 0.721100 + 0.692831i
\(244\) 0 0
\(245\) −15.8383 19.8584i −1.01187 1.26871i
\(246\) 0 0
\(247\) −20.3431 17.0699i −1.29440 1.08613i
\(248\) 0 0
\(249\) 13.0251 + 11.2314i 0.825431 + 0.711762i
\(250\) 0 0
\(251\) −12.8272 22.2173i −0.809645 1.40235i −0.913110 0.407713i \(-0.866326\pi\)
0.103466 0.994633i \(-0.467007\pi\)
\(252\) 0 0
\(253\) 21.1079 36.5600i 1.32704 2.29851i
\(254\) 0 0
\(255\) −20.9332 0.281675i −1.31089 0.0176392i
\(256\) 0 0
\(257\) −0.877450 + 0.319366i −0.0547338 + 0.0199215i −0.369242 0.929333i \(-0.620383\pi\)
0.314508 + 0.949255i \(0.398160\pi\)
\(258\) 0 0
\(259\) −2.96475 2.13139i −0.184221 0.132438i
\(260\) 0 0
\(261\) 16.2463 + 9.97205i 1.00562 + 0.617254i
\(262\) 0 0
\(263\) −10.6594 12.7034i −0.657287 0.783324i 0.329707 0.944083i \(-0.393050\pi\)
−0.986994 + 0.160759i \(0.948606\pi\)
\(264\) 0 0
\(265\) −8.62069 23.6852i −0.529565 1.45497i
\(266\) 0 0
\(267\) −1.85314 11.4050i −0.113410 0.697973i
\(268\) 0 0
\(269\) −1.93665 3.35438i −0.118080 0.204520i 0.800927 0.598762i \(-0.204341\pi\)
−0.919007 + 0.394242i \(0.871007\pi\)
\(270\) 0 0
\(271\) 24.5867 + 14.1952i 1.49354 + 0.862295i 0.999973 0.00741404i \(-0.00235998\pi\)
0.493566 + 0.869709i \(0.335693\pi\)
\(272\) 0 0
\(273\) −21.8027 2.47778i −1.31956 0.149962i
\(274\) 0 0
\(275\) 43.8659 + 7.73474i 2.64521 + 0.466422i
\(276\) 0 0
\(277\) 6.59930 5.53747i 0.396513 0.332714i −0.422631 0.906302i \(-0.638893\pi\)
0.819144 + 0.573588i \(0.194449\pi\)
\(278\) 0 0
\(279\) −6.31430 7.95008i −0.378028 0.475959i
\(280\) 0 0
\(281\) 3.95484 10.8658i 0.235926 0.648201i −0.764070 0.645134i \(-0.776802\pi\)
0.999995 0.00306676i \(-0.000976183\pi\)
\(282\) 0 0
\(283\) −6.43295 1.13430i −0.382399 0.0674273i −0.0208556 0.999782i \(-0.506639\pi\)
−0.361544 + 0.932355i \(0.617750\pi\)
\(284\) 0 0
\(285\) 0.468990 34.8538i 0.0277806 2.06456i
\(286\) 0 0
\(287\) −15.7804 4.43944i −0.931487 0.262052i
\(288\) 0 0
\(289\) −5.90510 −0.347359
\(290\) 0 0
\(291\) −19.3934 3.68928i −1.13686 0.216269i
\(292\) 0 0
\(293\) 2.53946 14.4020i 0.148357 0.841372i −0.816254 0.577693i \(-0.803953\pi\)
0.964611 0.263679i \(-0.0849359\pi\)
\(294\) 0 0
\(295\) −31.1392 + 26.1289i −1.81299 + 1.52128i
\(296\) 0 0
\(297\) 17.3244 + 22.4255i 1.00526 + 1.30126i
\(298\) 0 0
\(299\) 6.43646 + 36.5030i 0.372230 + 2.11102i
\(300\) 0 0
\(301\) 5.01436 0.375915i 0.289023 0.0216674i
\(302\) 0 0
\(303\) −0.459186 0.395952i −0.0263795 0.0227469i
\(304\) 0 0
\(305\) 6.54286 + 3.77752i 0.374643 + 0.216300i
\(306\) 0 0
\(307\) 7.18349 + 4.14739i 0.409984 + 0.236704i 0.690783 0.723062i \(-0.257266\pi\)
−0.280799 + 0.959767i \(0.590599\pi\)
\(308\) 0 0
\(309\) −0.377289 + 28.0389i −0.0214632 + 1.59508i
\(310\) 0 0
\(311\) 3.30946 18.7689i 0.187662 1.06429i −0.734825 0.678257i \(-0.762736\pi\)
0.922487 0.386028i \(-0.126153\pi\)
\(312\) 0 0
\(313\) −7.42127 8.84433i −0.419475 0.499911i 0.514380 0.857562i \(-0.328022\pi\)
−0.933855 + 0.357651i \(0.883578\pi\)
\(314\) 0 0
\(315\) −15.5792 24.2248i −0.877789 1.36491i
\(316\) 0 0
\(317\) −6.33640 + 17.4091i −0.355888 + 0.977793i 0.624554 + 0.780982i \(0.285281\pi\)
−0.980441 + 0.196811i \(0.936941\pi\)
\(318\) 0 0
\(319\) 26.5461 + 22.2748i 1.48629 + 1.24715i
\(320\) 0 0
\(321\) −1.56318 + 4.12141i −0.0872483 + 0.230034i
\(322\) 0 0
\(323\) 18.4731i 1.02787i
\(324\) 0 0
\(325\) −33.8694 + 19.5545i −1.87873 + 1.08469i
\(326\) 0 0
\(327\) 7.86804 6.42367i 0.435104 0.355230i
\(328\) 0 0
\(329\) 15.6457 1.17293i 0.862577 0.0646655i
\(330\) 0 0
\(331\) 21.9733 + 7.99762i 1.20776 + 0.439589i 0.865926 0.500172i \(-0.166730\pi\)
0.341834 + 0.939760i \(0.388952\pi\)
\(332\) 0 0
\(333\) −3.09888 2.74569i −0.169817 0.150463i
\(334\) 0 0
\(335\) −33.1948 12.0819i −1.81363 0.660107i
\(336\) 0 0
\(337\) −19.4319 16.3053i −1.05852 0.888207i −0.0645595 0.997914i \(-0.520564\pi\)
−0.993964 + 0.109707i \(0.965009\pi\)
\(338\) 0 0
\(339\) −15.8890 + 8.89062i −0.862969 + 0.482872i
\(340\) 0 0
\(341\) −9.22803 15.9834i −0.499726 0.865551i
\(342\) 0 0
\(343\) −5.45746 + 17.6979i −0.294675 + 0.955597i
\(344\) 0 0
\(345\) −31.7717 + 36.8456i −1.71053 + 1.98370i
\(346\) 0 0
\(347\) −9.46873 26.0151i −0.508308 1.39657i −0.882981 0.469408i \(-0.844467\pi\)
0.374673 0.927157i \(-0.377755\pi\)
\(348\) 0 0
\(349\) 14.4724 + 17.2475i 0.774690 + 0.923240i 0.998681 0.0513514i \(-0.0163529\pi\)
−0.223990 + 0.974591i \(0.571908\pi\)
\(350\) 0 0
\(351\) −24.3087 5.30583i −1.29750 0.283204i
\(352\) 0 0
\(353\) 21.0176 + 7.64979i 1.11866 + 0.407157i 0.834161 0.551520i \(-0.185952\pi\)
0.284494 + 0.958678i \(0.408174\pi\)
\(354\) 0 0
\(355\) −2.75267 + 3.28051i −0.146097 + 0.174111i
\(356\) 0 0
\(357\) 8.42847 + 12.7261i 0.446082 + 0.673537i
\(358\) 0 0
\(359\) 12.2285i 0.645394i 0.946502 + 0.322697i \(0.104590\pi\)
−0.946502 + 0.322697i \(0.895410\pi\)
\(360\) 0 0
\(361\) −11.7577 −0.618828
\(362\) 0 0
\(363\) 15.8514 + 28.3289i 0.831981 + 1.48688i
\(364\) 0 0
\(365\) 9.12600 10.8759i 0.477677 0.569273i
\(366\) 0 0
\(367\) −11.3381 + 1.99921i −0.591843 + 0.104358i −0.461545 0.887117i \(-0.652705\pi\)
−0.130298 + 0.991475i \(0.541594\pi\)
\(368\) 0 0
\(369\) −17.2895 6.82511i −0.900056 0.355301i
\(370\) 0 0
\(371\) −10.7274 + 14.9217i −0.556937 + 0.774698i
\(372\) 0 0
\(373\) 3.57680 20.2850i 0.185199 1.05032i −0.740499 0.672057i \(-0.765411\pi\)
0.925699 0.378261i \(-0.123478\pi\)
\(374\) 0 0
\(375\) −18.6143 7.06009i −0.961236 0.364581i
\(376\) 0 0
\(377\) −30.4262 −1.56703
\(378\) 0 0
\(379\) −23.0701 −1.18503 −0.592516 0.805559i \(-0.701865\pi\)
−0.592516 + 0.805559i \(0.701865\pi\)
\(380\) 0 0
\(381\) 15.5617 12.7050i 0.797250 0.650895i
\(382\) 0 0
\(383\) 1.26488 7.17350i 0.0646324 0.366549i −0.935287 0.353889i \(-0.884859\pi\)
0.999920 0.0126597i \(-0.00402981\pi\)
\(384\) 0 0
\(385\) −21.5357 47.7244i −1.09756 2.43226i
\(386\) 0 0
\(387\) 5.69964 + 0.153416i 0.289729 + 0.00779855i
\(388\) 0 0
\(389\) −16.3643 + 2.88546i −0.829701 + 0.146299i −0.572340 0.820017i \(-0.693964\pi\)
−0.257361 + 0.966315i \(0.582853\pi\)
\(390\) 0 0
\(391\) 16.5737 19.7518i 0.838168 0.998890i
\(392\) 0 0
\(393\) −1.36759 + 2.29680i −0.0689857 + 0.115858i
\(394\) 0 0
\(395\) 26.0150 1.30896
\(396\) 0 0
\(397\) 33.8573i 1.69925i −0.527387 0.849625i \(-0.676828\pi\)
0.527387 0.849625i \(-0.323172\pi\)
\(398\) 0 0
\(399\) −21.1890 + 14.0334i −1.06078 + 0.702551i
\(400\) 0 0
\(401\) 18.6906 22.2746i 0.933364 1.11234i −0.0600993 0.998192i \(-0.519142\pi\)
0.993464 0.114148i \(-0.0364138\pi\)
\(402\) 0 0
\(403\) 15.2274 + 5.54232i 0.758531 + 0.276083i
\(404\) 0 0
\(405\) −14.7841 29.1204i −0.734626 1.44701i
\(406\) 0 0
\(407\) −4.83794 5.76564i −0.239808 0.285792i
\(408\) 0 0
\(409\) 1.79133 + 4.92163i 0.0885754 + 0.243359i 0.976069 0.217461i \(-0.0697776\pi\)
−0.887494 + 0.460820i \(0.847555\pi\)
\(410\) 0 0
\(411\) −2.52806 0.480923i −0.124700 0.0237222i
\(412\) 0 0
\(413\) 28.5306 + 8.02640i 1.40390 + 0.394953i
\(414\) 0 0
\(415\) −18.0160 31.2046i −0.884371 1.53177i
\(416\) 0 0
\(417\) 0.409096 30.4027i 0.0200335 1.48882i
\(418\) 0 0
\(419\) 10.1018 + 8.47646i 0.493507 + 0.414102i 0.855281 0.518164i \(-0.173384\pi\)
−0.361774 + 0.932266i \(0.617829\pi\)
\(420\) 0 0
\(421\) 15.3884 + 5.60092i 0.749985 + 0.272972i 0.688599 0.725142i \(-0.258226\pi\)
0.0613855 + 0.998114i \(0.480448\pi\)
\(422\) 0 0
\(423\) 17.7839 + 0.478685i 0.864685 + 0.0232745i
\(424\) 0 0
\(425\) 25.5645 + 9.30472i 1.24006 + 0.451345i
\(426\) 0 0
\(427\) −0.411805 5.49309i −0.0199286 0.265829i
\(428\) 0 0
\(429\) −42.2909 16.0402i −2.04182 0.774430i
\(430\) 0 0
\(431\) 8.99505 5.19329i 0.433276 0.250152i −0.267465 0.963568i \(-0.586186\pi\)
0.700741 + 0.713415i \(0.252853\pi\)
\(432\) 0 0
\(433\) 31.5263i 1.51506i −0.652802 0.757528i \(-0.726407\pi\)
0.652802 0.757528i \(-0.273593\pi\)
\(434\) 0 0
\(435\) −25.2569 30.9360i −1.21098 1.48327i
\(436\) 0 0
\(437\) 32.8868 + 27.5953i 1.57319 + 1.32006i
\(438\) 0 0
\(439\) −10.9952 + 30.2091i −0.524773 + 1.44180i 0.340376 + 0.940289i \(0.389446\pi\)
−0.865150 + 0.501514i \(0.832777\pi\)
\(440\) 0 0
\(441\) −8.19429 + 19.3353i −0.390204 + 0.920728i
\(442\) 0 0
\(443\) −10.5359 12.5562i −0.500574 0.596561i 0.455300 0.890338i \(-0.349532\pi\)
−0.955874 + 0.293777i \(0.905088\pi\)
\(444\) 0 0
\(445\) −4.20353 + 23.8394i −0.199266 + 1.13010i
\(446\) 0 0
\(447\) −5.83959 + 3.26753i −0.276203 + 0.154549i
\(448\) 0 0
\(449\) −27.4796 15.8654i −1.29684 0.748733i −0.316986 0.948430i \(-0.602671\pi\)
−0.979858 + 0.199697i \(0.936004\pi\)
\(450\) 0 0
\(451\) −29.2634 16.8952i −1.37796 0.795565i
\(452\) 0 0
\(453\) −2.14138 + 0.746926i −0.100611 + 0.0350937i
\(454\) 0 0
\(455\) 41.4193 + 19.9451i 1.94177 + 0.935039i
\(456\) 0 0
\(457\) −6.52474 37.0037i −0.305215 1.73096i −0.622493 0.782626i \(-0.713880\pi\)
0.317278 0.948333i \(-0.397231\pi\)
\(458\) 0 0
\(459\) 8.04201 + 15.3261i 0.375369 + 0.715360i
\(460\) 0 0
\(461\) 18.5831 15.5931i 0.865504 0.726244i −0.0976428 0.995222i \(-0.531130\pi\)
0.963146 + 0.268978i \(0.0866858\pi\)
\(462\) 0 0
\(463\) 3.22506 18.2902i 0.149881 0.850019i −0.813436 0.581654i \(-0.802406\pi\)
0.963317 0.268364i \(-0.0864831\pi\)
\(464\) 0 0
\(465\) 7.00517 + 20.0833i 0.324857 + 0.931340i
\(466\) 0 0
\(467\) −0.199729 −0.00924236 −0.00462118 0.999989i \(-0.501471\pi\)
−0.00462118 + 0.999989i \(0.501471\pi\)
\(468\) 0 0
\(469\) 6.35623 + 24.9596i 0.293503 + 1.15253i
\(470\) 0 0
\(471\) −33.7139 20.0744i −1.55346 0.924978i
\(472\) 0 0
\(473\) 10.2075 + 1.79986i 0.469342 + 0.0827577i
\(474\) 0 0
\(475\) −15.4924 + 42.5650i −0.710840 + 1.95302i
\(476\) 0 0
\(477\) −13.8192 + 15.5968i −0.632737 + 0.714128i
\(478\) 0 0
\(479\) 10.0571 8.43895i 0.459523 0.385585i −0.383433 0.923569i \(-0.625258\pi\)
0.842955 + 0.537983i \(0.180814\pi\)
\(480\) 0 0
\(481\) 6.50797 + 1.14753i 0.296738 + 0.0523229i
\(482\) 0 0
\(483\) 35.2463 + 4.00559i 1.60376 + 0.182261i
\(484\) 0 0
\(485\) 35.8174 + 20.6792i 1.62639 + 0.938994i
\(486\) 0 0
\(487\) −15.3472 26.5821i −0.695448 1.20455i −0.970030 0.242987i \(-0.921873\pi\)
0.274582 0.961564i \(-0.411461\pi\)
\(488\) 0 0
\(489\) 26.5267 + 10.0611i 1.19958 + 0.454980i
\(490\) 0 0
\(491\) −6.76951 18.5991i −0.305504 0.839365i −0.993519 0.113668i \(-0.963740\pi\)
0.688015 0.725696i \(-0.258482\pi\)
\(492\) 0 0
\(493\) 13.6047 + 16.2135i 0.612726 + 0.730219i
\(494\) 0 0
\(495\) −18.7969 56.3146i −0.844857 2.53115i
\(496\) 0 0
\(497\) 3.10686 + 0.310801i 0.139362 + 0.0139413i
\(498\) 0 0
\(499\) −17.8458 + 6.49533i −0.798887 + 0.290771i −0.709025 0.705183i \(-0.750865\pi\)
−0.0898617 + 0.995954i \(0.528643\pi\)
\(500\) 0 0
\(501\) 9.13863 + 16.3322i 0.408284 + 0.729668i
\(502\) 0 0
\(503\) 5.81026 10.0637i 0.259067 0.448717i −0.706925 0.707288i \(-0.749918\pi\)
0.965992 + 0.258571i \(0.0832517\pi\)
\(504\) 0 0
\(505\) 0.635136 + 1.10009i 0.0282632 + 0.0489533i
\(506\) 0 0
\(507\) 16.2370 5.66356i 0.721110 0.251528i
\(508\) 0 0
\(509\) −0.957091 0.803094i −0.0424223 0.0355965i 0.621330 0.783549i \(-0.286593\pi\)
−0.663752 + 0.747952i \(0.731037\pi\)
\(510\) 0 0
\(511\) −10.3003 1.03041i −0.455656 0.0455824i
\(512\) 0 0
\(513\) −25.5180 + 13.3900i −1.12665 + 0.591182i
\(514\) 0 0
\(515\) 20.0929 55.2049i 0.885400 2.43262i
\(516\) 0 0
\(517\) 31.8494 + 5.61590i 1.40073 + 0.246987i
\(518\) 0 0
\(519\) −10.3460 8.92123i −0.454137 0.391598i
\(520\) 0 0
\(521\) −15.1411 + 26.2251i −0.663342 + 1.14894i 0.316390 + 0.948629i \(0.397529\pi\)
−0.979732 + 0.200313i \(0.935804\pi\)
\(522\) 0 0
\(523\) 33.3913 19.2785i 1.46010 0.842989i 0.461085 0.887356i \(-0.347460\pi\)
0.999015 + 0.0443672i \(0.0141271\pi\)
\(524\) 0 0
\(525\) 8.74787 + 36.3916i 0.381788 + 1.58826i
\(526\) 0 0
\(527\) −3.85538 10.5926i −0.167943 0.461420i
\(528\) 0 0
\(529\) −6.41130 36.3603i −0.278752 1.58088i
\(530\) 0 0
\(531\) 31.2590 + 12.3396i 1.35653 + 0.535495i
\(532\) 0 0
\(533\) 29.2177 5.15187i 1.26556 0.223152i
\(534\) 0 0
\(535\) 5.93595 7.07419i 0.256633 0.305844i
\(536\) 0 0
\(537\) −31.3173 + 5.08860i −1.35144 + 0.219589i
\(538\) 0 0
\(539\) −19.9042 + 32.5758i −0.857333 + 1.40314i
\(540\) 0 0
\(541\) −16.4143 + 28.4305i −0.705707 + 1.22232i 0.260728 + 0.965412i \(0.416037\pi\)
−0.966436 + 0.256909i \(0.917296\pi\)
\(542\) 0 0
\(543\) −15.4166 18.8830i −0.661588 0.810347i
\(544\) 0 0
\(545\) −19.9965 + 7.27811i −0.856554 + 0.311760i
\(546\) 0 0
\(547\) 2.00894 + 11.3933i 0.0858961 + 0.487141i 0.997160 + 0.0753172i \(0.0239969\pi\)
−0.911264 + 0.411824i \(0.864892\pi\)
\(548\) 0 0
\(549\) 0.168062 6.24380i 0.00717273 0.266479i
\(550\) 0 0
\(551\) −26.9955 + 22.6519i −1.15005 + 0.965005i
\(552\) 0 0
\(553\) −10.6855 15.6718i −0.454393 0.666432i
\(554\) 0 0
\(555\) 4.23555 + 7.56959i 0.179789 + 0.321311i
\(556\) 0 0
\(557\) 32.9309i 1.39533i 0.716426 + 0.697663i \(0.245777\pi\)
−0.716426 + 0.697663i \(0.754223\pi\)
\(558\) 0 0
\(559\) −7.88135 + 4.55030i −0.333345 + 0.192457i
\(560\) 0 0
\(561\) 10.3624 + 29.7082i 0.437501 + 1.25428i
\(562\) 0 0
\(563\) −32.2541 + 11.7395i −1.35935 + 0.494763i −0.915853 0.401513i \(-0.868484\pi\)
−0.443497 + 0.896276i \(0.646262\pi\)
\(564\) 0 0
\(565\) 37.5652 6.62376i 1.58038 0.278664i
\(566\) 0 0
\(567\) −11.4701 + 20.8671i −0.481698 + 0.876337i
\(568\) 0 0
\(569\) 30.0162 5.29267i 1.25835 0.221880i 0.495584 0.868560i \(-0.334954\pi\)
0.762762 + 0.646679i \(0.223843\pi\)
\(570\) 0 0
\(571\) 2.68710 0.978023i 0.112452 0.0409290i −0.285182 0.958474i \(-0.592054\pi\)
0.397633 + 0.917545i \(0.369832\pi\)
\(572\) 0 0
\(573\) −7.43851 21.3256i −0.310748 0.890891i
\(574\) 0 0
\(575\) 54.7534 31.6119i 2.28337 1.31831i
\(576\) 0 0
\(577\) 14.5845i 0.607162i −0.952806 0.303581i \(-0.901818\pi\)
0.952806 0.303581i \(-0.0981823\pi\)
\(578\) 0 0
\(579\) −8.64887 15.4569i −0.359435 0.642367i
\(580\) 0 0
\(581\) −11.3981 + 23.6702i −0.472874 + 0.982003i
\(582\) 0 0
\(583\) −29.0187 + 24.3496i −1.20183 + 1.00846i
\(584\) 0 0
\(585\) 44.4253 + 27.2685i 1.83676 + 1.12742i
\(586\) 0 0
\(587\) −1.69475 9.61138i −0.0699497 0.396704i −0.999601 0.0282626i \(-0.991003\pi\)
0.929651 0.368442i \(-0.120109\pi\)
\(588\) 0 0
\(589\) 17.6367 6.41922i 0.726707 0.264500i
\(590\) 0 0
\(591\) −4.71554 5.77584i −0.193972 0.237586i
\(592\) 0 0
\(593\) −8.66155 + 15.0022i −0.355687 + 0.616068i −0.987235 0.159269i \(-0.949086\pi\)
0.631548 + 0.775337i \(0.282420\pi\)
\(594\) 0 0
\(595\) −7.89188 30.9897i −0.323536 1.27046i
\(596\) 0 0
\(597\) 33.9011 5.50844i 1.38748 0.225445i
\(598\) 0 0
\(599\) −15.1161 + 18.0147i −0.617628 + 0.736060i −0.980661 0.195716i \(-0.937297\pi\)
0.363033 + 0.931776i \(0.381741\pi\)
\(600\) 0 0
\(601\) 0.356342 0.0628327i 0.0145355 0.00256300i −0.166376 0.986062i \(-0.553206\pi\)
0.180911 + 0.983499i \(0.442095\pi\)
\(602\) 0 0
\(603\) 4.29565 + 28.8871i 0.174932 + 1.17638i
\(604\) 0 0
\(605\) −11.8097 66.9762i −0.480133 2.72297i
\(606\) 0 0
\(607\) 2.83802 + 7.79739i 0.115192 + 0.316486i 0.983869 0.178893i \(-0.0572515\pi\)
−0.868677 + 0.495379i \(0.835029\pi\)
\(608\) 0 0
\(609\) −8.26214 + 27.9218i −0.334799 + 1.13145i
\(610\) 0 0
\(611\) −24.5913 + 14.1978i −0.994856 + 0.574380i
\(612\) 0 0
\(613\) −13.1528 + 22.7813i −0.531236 + 0.920127i 0.468100 + 0.883676i \(0.344939\pi\)
−0.999335 + 0.0364515i \(0.988395\pi\)
\(614\) 0 0
\(615\) 29.4920 + 25.4307i 1.18923 + 1.02547i
\(616\) 0 0
\(617\) 5.77193 + 1.01775i 0.232369 + 0.0409730i 0.288620 0.957444i \(-0.406804\pi\)
−0.0562509 + 0.998417i \(0.517915\pi\)
\(618\) 0 0
\(619\) 6.60976 18.1602i 0.265669 0.729919i −0.733091 0.680131i \(-0.761923\pi\)
0.998760 0.0497885i \(-0.0158547\pi\)
\(620\) 0 0
\(621\) 39.2976 + 8.57743i 1.57696 + 0.344200i
\(622\) 0 0
\(623\) 16.0877 7.25961i 0.644542 0.290850i
\(624\) 0 0
\(625\) 0.667031 + 0.559705i 0.0266812 + 0.0223882i
\(626\) 0 0
\(627\) −49.4643 + 17.2534i −1.97541 + 0.689036i
\(628\) 0 0
\(629\) −2.29847 3.98107i −0.0916462 0.158736i
\(630\) 0 0
\(631\) −5.39911 + 9.35153i −0.214935 + 0.372279i −0.953252 0.302175i \(-0.902287\pi\)
0.738317 + 0.674453i \(0.235621\pi\)
\(632\) 0 0
\(633\) 9.34845 + 16.7072i 0.371567 + 0.664050i
\(634\) 0 0
\(635\) −39.5497 + 14.3949i −1.56948 + 0.571245i
\(636\) 0 0
\(637\) −4.99752 33.1438i −0.198009 1.31321i
\(638\) 0 0
\(639\) 3.46884 + 0.708382i 0.137225 + 0.0280231i
\(640\) 0 0
\(641\) 4.57485 + 5.45210i 0.180696 + 0.215345i 0.848788 0.528734i \(-0.177333\pi\)
−0.668092 + 0.744079i \(0.732889\pi\)
\(642\) 0 0
\(643\) −13.7176 37.6889i −0.540971 1.48630i −0.845591 0.533831i \(-0.820752\pi\)
0.304621 0.952474i \(-0.401470\pi\)
\(644\) 0 0
\(645\) −11.1689 4.23618i −0.439775 0.166799i
\(646\) 0 0
\(647\) 9.02415 + 15.6303i 0.354776 + 0.614490i 0.987080 0.160231i \(-0.0512239\pi\)
−0.632304 + 0.774721i \(0.717891\pi\)
\(648\) 0 0
\(649\) 52.9075 + 30.5462i 2.07680 + 1.19904i
\(650\) 0 0
\(651\) 9.22111 12.4691i 0.361404 0.488701i
\(652\) 0 0
\(653\) −1.86090 0.328127i −0.0728226 0.0128406i 0.137118 0.990555i \(-0.456216\pi\)
−0.209941 + 0.977714i \(0.567327\pi\)
\(654\) 0 0
\(655\) 4.29007 3.59980i 0.167627 0.140656i
\(656\) 0 0
\(657\) −11.5003 2.34852i −0.448671 0.0916244i
\(658\) 0 0
\(659\) −7.91790 + 21.7542i −0.308438 + 0.847425i 0.684524 + 0.728990i \(0.260010\pi\)
−0.992962 + 0.118435i \(0.962212\pi\)
\(660\) 0 0
\(661\) −15.6928 2.76706i −0.610378 0.107626i −0.140089 0.990139i \(-0.544739\pi\)
−0.470288 + 0.882513i \(0.655850\pi\)
\(662\) 0 0
\(663\) −23.7363 14.1333i −0.921841 0.548894i
\(664\) 0 0
\(665\) 51.5981 13.1400i 2.00089 0.509548i
\(666\) 0 0
\(667\) 49.1871 1.90453
\(668\) 0 0
\(669\) 5.90418 + 16.9268i 0.228269 + 0.654429i
\(670\) 0 0
\(671\) 1.97170 11.1821i 0.0761166 0.431679i
\(672\) 0 0
\(673\) −24.9316 + 20.9201i −0.961043 + 0.806411i −0.981122 0.193387i \(-0.938053\pi\)
0.0200793 + 0.999798i \(0.493608\pi\)
\(674\) 0 0
\(675\) 5.67696 + 42.0583i 0.218506 + 1.61882i
\(676\) 0 0
\(677\) −6.21630 35.2544i −0.238912 1.35494i −0.834217 0.551436i \(-0.814080\pi\)
0.595306 0.803499i \(-0.297031\pi\)
\(678\) 0 0
\(679\) −2.25433 30.0707i −0.0865134 1.15401i
\(680\) 0 0
\(681\) 33.5912 11.7168i 1.28722 0.448989i
\(682\) 0 0
\(683\) 21.7726 + 12.5704i 0.833105 + 0.480993i 0.854915 0.518769i \(-0.173609\pi\)
−0.0218096 + 0.999762i \(0.506943\pi\)
\(684\) 0 0
\(685\) 4.66904 + 2.69567i 0.178395 + 0.102996i
\(686\) 0 0
\(687\) −1.69140 + 0.946419i −0.0645310 + 0.0361081i
\(688\) 0 0
\(689\) 5.77557 32.7549i 0.220032 1.24786i
\(690\) 0 0
\(691\) 17.8024 + 21.2160i 0.677234 + 0.807096i 0.989749 0.142817i \(-0.0456161\pi\)
−0.312515 + 0.949913i \(0.601172\pi\)
\(692\) 0 0
\(693\) −26.2040 + 34.4543i −0.995407 + 1.30881i
\(694\) 0 0
\(695\) −21.7868 + 59.8588i −0.826421 + 2.27057i
\(696\) 0 0
\(697\) −15.8097 13.2659i −0.598836 0.502483i
\(698\) 0 0
\(699\) 3.49763 + 4.28408i 0.132293 + 0.162039i
\(700\) 0 0
\(701\) 36.4801i 1.37783i −0.724840 0.688917i \(-0.758087\pi\)
0.724840 0.688917i \(-0.241913\pi\)
\(702\) 0 0
\(703\) 6.62851 3.82697i 0.249999 0.144337i
\(704\) 0 0
\(705\) −34.8490 13.2177i −1.31249 0.497806i
\(706\) 0 0
\(707\) 0.401830 0.834468i 0.0151124 0.0313834i
\(708\) 0 0
\(709\) −45.4492 16.5422i −1.70688 0.621254i −0.710301 0.703898i \(-0.751441\pi\)
−0.996579 + 0.0826445i \(0.973663\pi\)
\(710\) 0 0
\(711\) −10.2488 18.9088i −0.384359 0.709135i
\(712\) 0 0
\(713\) −24.6167 8.95975i −0.921903 0.335545i
\(714\) 0 0
\(715\) 72.5901 + 60.9104i 2.71472 + 2.27792i
\(716\) 0 0
\(717\) 0.186576 13.8658i 0.00696783 0.517826i
\(718\) 0 0
\(719\) 12.5049 + 21.6590i 0.466352 + 0.807746i 0.999261 0.0384266i \(-0.0122346\pi\)
−0.532909 + 0.846173i \(0.678901\pi\)
\(720\) 0 0
\(721\) −41.5092 + 10.5708i −1.54588 + 0.393676i
\(722\) 0 0
\(723\) −24.9743 4.75097i −0.928805 0.176691i
\(724\) 0 0
\(725\) 17.7502 + 48.7682i 0.659225 + 1.81121i
\(726\) 0 0
\(727\) −24.6457 29.3716i −0.914058 1.08933i −0.995697 0.0926696i \(-0.970460\pi\)
0.0816392 0.996662i \(-0.473984\pi\)
\(728\) 0 0
\(729\) −15.3417 + 22.2179i −0.568210 + 0.822883i
\(730\) 0 0
\(731\) 5.94882 + 2.16519i 0.220025 + 0.0800826i
\(732\) 0 0
\(733\) 6.65784 7.93450i 0.245913 0.293067i −0.628942 0.777452i \(-0.716512\pi\)
0.874855 + 0.484384i \(0.160956\pi\)
\(734\) 0 0
\(735\) 29.5507 32.5942i 1.09000 1.20225i
\(736\) 0 0
\(737\) 53.0907i 1.95562i
\(738\) 0 0
\(739\) 26.9803 0.992486 0.496243 0.868184i \(-0.334713\pi\)
0.496243 + 0.868184i \(0.334713\pi\)
\(740\) 0 0
\(741\) 23.5321 39.5210i 0.864473 1.45184i
\(742\) 0 0
\(743\) −3.94022 + 4.69577i −0.144553 + 0.172271i −0.833463 0.552576i \(-0.813645\pi\)
0.688910 + 0.724847i \(0.258089\pi\)
\(744\) 0 0
\(745\) 13.8062 2.43440i 0.505819 0.0891895i
\(746\) 0 0
\(747\) −15.5833 + 25.3880i −0.570164 + 0.928899i
\(748\) 0 0
\(749\) −6.69973 0.670220i −0.244803 0.0244893i
\(750\) 0 0
\(751\) 0.534990 3.03408i 0.0195221 0.110715i −0.973490 0.228731i \(-0.926542\pi\)
0.993012 + 0.118016i \(0.0376534\pi\)
\(752\) 0 0
\(753\) 34.4201 28.1015i 1.25434 1.02408i
\(754\) 0 0
\(755\) 4.75135 0.172919
\(756\) 0 0
\(757\) 5.55567 0.201924 0.100962 0.994890i \(-0.467808\pi\)
0.100962 + 0.994890i \(0.467808\pi\)
\(758\) 0 0
\(759\) 68.3676 + 25.9307i 2.48159 + 0.941226i
\(760\) 0 0
\(761\) −3.33014 + 18.8862i −0.120718 + 0.684624i 0.863042 + 0.505132i \(0.168556\pi\)
−0.983760 + 0.179491i \(0.942555\pi\)
\(762\) 0 0
\(763\) 12.5978 + 9.05669i 0.456072 + 0.327874i
\(764\) 0 0
\(765\) −5.33347 35.8662i −0.192832 1.29675i
\(766\) 0 0
\(767\) −52.8250 + 9.31447i −1.90740 + 0.336326i
\(768\) 0 0
\(769\) −2.74887 + 3.27598i −0.0991269 + 0.118135i −0.813327 0.581807i \(-0.802346\pi\)
0.714200 + 0.699941i \(0.246791\pi\)
\(770\) 0 0
\(771\) −0.789744 1.41140i −0.0284419 0.0508302i
\(772\) 0 0
\(773\) −34.2221 −1.23088 −0.615442 0.788182i \(-0.711023\pi\)
−0.615442 + 0.788182i \(0.711023\pi\)
\(774\) 0 0
\(775\) 27.6404i 0.992871i
\(776\) 0 0
\(777\) 2.82030 5.66071i 0.101178 0.203077i