Properties

Label 1008.2.r.k.673.1
Level $1008$
Weight $2$
Character 1008.673
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.k.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.349814 + 1.69636i) q^{3} +(1.79418 + 3.10761i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.75526 - 1.18682i) q^{9} +O(q^{10})\) \(q+(-0.349814 + 1.69636i) q^{3} +(1.79418 + 3.10761i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.75526 - 1.18682i) q^{9} +(-1.40545 + 2.43430i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-5.89926 + 1.95649i) q^{15} -4.11126 q^{17} +0.888736 q^{19} +(-1.29418 - 1.15113i) q^{21} +(2.93818 + 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} +(2.97710 - 4.25874i) q^{27} +(0.849814 - 1.47192i) q^{29} +(-3.49381 - 6.05146i) q^{31} +(-3.63781 - 3.23569i) q^{33} -3.58836 q^{35} +4.76509 q^{37} +(1.64400 - 0.545231i) q^{39} +(2.70582 + 4.68661i) q^{41} +(2.60507 - 4.51212i) q^{43} +(-1.25526 - 10.6917i) q^{45} +(-1.33310 + 2.30900i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(1.43818 - 6.97418i) q^{51} -0.123644 q^{53} -10.0865 q^{55} +(-0.310892 + 1.50761i) q^{57} +(-4.43818 - 7.68715i) q^{59} +(-1.93818 + 3.35702i) q^{61} +(2.40545 - 1.79272i) q^{63} +(1.79418 - 3.10761i) q^{65} +(6.15452 + 10.6599i) q^{67} +(-9.66071 + 3.20397i) q^{69} +2.87636 q^{71} -10.6414 q^{73} +(-10.1934 - 9.06668i) q^{75} +(-1.40545 - 2.43430i) q^{77} +(-3.54325 + 6.13709i) q^{79} +(6.18292 + 6.53999i) q^{81} +(-2.05563 + 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +(2.19963 + 1.95649i) q^{87} +9.60940 q^{89} +1.00000 q^{91} +(11.4876 - 3.80987i) q^{93} +(1.59455 + 2.76185i) q^{95} +(-3.66071 + 6.34053i) q^{97} +(6.76145 - 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 4q^{3} + 5q^{5} - 3q^{7} - 4q^{9} + O(q^{10}) \) \( 6q + 4q^{3} + 5q^{5} - 3q^{7} - 4q^{9} - 2q^{11} - 3q^{13} - 11q^{15} - 24q^{17} + 6q^{19} - 2q^{21} - 6q^{25} + 7q^{27} - q^{29} - 3q^{31} + 8q^{33} - 10q^{35} - 6q^{37} - 2q^{39} + 22q^{41} - 3q^{43} + 5q^{45} - 9q^{47} - 3q^{49} - 9q^{51} - 36q^{53} + 12q^{55} + 11q^{57} - 9q^{59} + 6q^{61} + 8q^{63} + 5q^{65} - 39q^{69} - 18q^{71} + 6q^{73} - 31q^{75} - 2q^{77} + 15q^{79} + 32q^{81} - 12q^{83} - 9q^{85} + q^{87} - 4q^{89} + 6q^{91} + 33q^{93} + 16q^{95} - 3q^{97} + 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.349814 + 1.69636i −0.201965 + 0.979393i
\(4\) 0 0
\(5\) 1.79418 + 3.10761i 0.802383 + 1.38977i 0.918044 + 0.396479i \(0.129768\pi\)
−0.115661 + 0.993289i \(0.536899\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) −2.75526 1.18682i −0.918420 0.395607i
\(10\) 0 0
\(11\) −1.40545 + 2.43430i −0.423758 + 0.733970i −0.996304 0.0859026i \(-0.972623\pi\)
0.572546 + 0.819873i \(0.305956\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) −5.89926 + 1.95649i −1.52318 + 0.505163i
\(16\) 0 0
\(17\) −4.11126 −0.997128 −0.498564 0.866853i \(-0.666139\pi\)
−0.498564 + 0.866853i \(0.666139\pi\)
\(18\) 0 0
\(19\) 0.888736 0.203890 0.101945 0.994790i \(-0.467493\pi\)
0.101945 + 0.994790i \(0.467493\pi\)
\(20\) 0 0
\(21\) −1.29418 1.15113i −0.282414 0.251196i
\(22\) 0 0
\(23\) 2.93818 + 5.08907i 0.612652 + 1.06115i 0.990792 + 0.135396i \(0.0432308\pi\)
−0.378139 + 0.925749i \(0.623436\pi\)
\(24\) 0 0
\(25\) −3.93818 + 6.82112i −0.787636 + 1.36422i
\(26\) 0 0
\(27\) 2.97710 4.25874i 0.572943 0.819595i
\(28\) 0 0
\(29\) 0.849814 1.47192i 0.157807 0.273329i −0.776271 0.630399i \(-0.782891\pi\)
0.934077 + 0.357071i \(0.116224\pi\)
\(30\) 0 0
\(31\) −3.49381 6.05146i −0.627507 1.08687i −0.988050 0.154131i \(-0.950742\pi\)
0.360544 0.932742i \(-0.382591\pi\)
\(32\) 0 0
\(33\) −3.63781 3.23569i −0.633261 0.563262i
\(34\) 0 0
\(35\) −3.58836 −0.606544
\(36\) 0 0
\(37\) 4.76509 0.783376 0.391688 0.920098i \(-0.371891\pi\)
0.391688 + 0.920098i \(0.371891\pi\)
\(38\) 0 0
\(39\) 1.64400 0.545231i 0.263250 0.0873068i
\(40\) 0 0
\(41\) 2.70582 + 4.68661i 0.422578 + 0.731926i 0.996191 0.0872002i \(-0.0277920\pi\)
−0.573613 + 0.819126i \(0.694459\pi\)
\(42\) 0 0
\(43\) 2.60507 4.51212i 0.397270 0.688092i −0.596118 0.802897i \(-0.703291\pi\)
0.993388 + 0.114805i \(0.0366243\pi\)
\(44\) 0 0
\(45\) −1.25526 10.6917i −0.187123 1.59382i
\(46\) 0 0
\(47\) −1.33310 + 2.30900i −0.194453 + 0.336803i −0.946721 0.322055i \(-0.895627\pi\)
0.752268 + 0.658857i \(0.228960\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 1.43818 6.97418i 0.201385 0.976580i
\(52\) 0 0
\(53\) −0.123644 −0.0169838 −0.00849190 0.999964i \(-0.502703\pi\)
−0.00849190 + 0.999964i \(0.502703\pi\)
\(54\) 0 0
\(55\) −10.0865 −1.36006
\(56\) 0 0
\(57\) −0.310892 + 1.50761i −0.0411787 + 0.199688i
\(58\) 0 0
\(59\) −4.43818 7.68715i −0.577802 1.00078i −0.995731 0.0923022i \(-0.970577\pi\)
0.417929 0.908479i \(-0.362756\pi\)
\(60\) 0 0
\(61\) −1.93818 + 3.35702i −0.248158 + 0.429823i −0.963015 0.269448i \(-0.913159\pi\)
0.714857 + 0.699271i \(0.246492\pi\)
\(62\) 0 0
\(63\) 2.40545 1.79272i 0.303058 0.225861i
\(64\) 0 0
\(65\) 1.79418 3.10761i 0.222541 0.385452i
\(66\) 0 0
\(67\) 6.15452 + 10.6599i 0.751894 + 1.30232i 0.946904 + 0.321517i \(0.104193\pi\)
−0.195010 + 0.980801i \(0.562474\pi\)
\(68\) 0 0
\(69\) −9.66071 + 3.20397i −1.16301 + 0.385713i
\(70\) 0 0
\(71\) 2.87636 0.341361 0.170680 0.985326i \(-0.445403\pi\)
0.170680 + 0.985326i \(0.445403\pi\)
\(72\) 0 0
\(73\) −10.6414 −1.24549 −0.622744 0.782426i \(-0.713982\pi\)
−0.622744 + 0.782426i \(0.713982\pi\)
\(74\) 0 0
\(75\) −10.1934 9.06668i −1.17704 1.04693i
\(76\) 0 0
\(77\) −1.40545 2.43430i −0.160165 0.277415i
\(78\) 0 0
\(79\) −3.54325 + 6.13709i −0.398647 + 0.690477i −0.993559 0.113314i \(-0.963853\pi\)
0.594912 + 0.803791i \(0.297187\pi\)
\(80\) 0 0
\(81\) 6.18292 + 6.53999i 0.686991 + 0.726666i
\(82\) 0 0
\(83\) −2.05563 + 3.56046i −0.225635 + 0.390811i −0.956510 0.291700i \(-0.905779\pi\)
0.730875 + 0.682512i \(0.239112\pi\)
\(84\) 0 0
\(85\) −7.37636 12.7762i −0.800078 1.38578i
\(86\) 0 0
\(87\) 2.19963 + 1.95649i 0.235825 + 0.209757i
\(88\) 0 0
\(89\) 9.60940 1.01859 0.509297 0.860591i \(-0.329905\pi\)
0.509297 + 0.860591i \(0.329905\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 11.4876 3.80987i 1.19121 0.395065i
\(94\) 0 0
\(95\) 1.59455 + 2.76185i 0.163598 + 0.283360i
\(96\) 0 0
\(97\) −3.66071 + 6.34053i −0.371688 + 0.643783i −0.989825 0.142287i \(-0.954554\pi\)
0.618137 + 0.786070i \(0.287888\pi\)
\(98\) 0 0
\(99\) 6.76145 5.03913i 0.679551 0.506452i
\(100\) 0 0
\(101\) −1.73236 + 3.00054i −0.172376 + 0.298564i −0.939250 0.343233i \(-0.888478\pi\)
0.766874 + 0.641798i \(0.221811\pi\)
\(102\) 0 0
\(103\) −7.93818 13.7493i −0.782172 1.35476i −0.930674 0.365849i \(-0.880779\pi\)
0.148502 0.988912i \(-0.452555\pi\)
\(104\) 0 0
\(105\) 1.25526 6.08715i 0.122501 0.594045i
\(106\) 0 0
\(107\) 5.35346 0.517538 0.258769 0.965939i \(-0.416683\pi\)
0.258769 + 0.965939i \(0.416683\pi\)
\(108\) 0 0
\(109\) −18.8640 −1.80684 −0.903421 0.428755i \(-0.858952\pi\)
−0.903421 + 0.428755i \(0.858952\pi\)
\(110\) 0 0
\(111\) −1.66690 + 8.08330i −0.158215 + 0.767233i
\(112\) 0 0
\(113\) 9.27561 + 16.0658i 0.872576 + 1.51135i 0.859322 + 0.511434i \(0.170886\pi\)
0.0132538 + 0.999912i \(0.495781\pi\)
\(114\) 0 0
\(115\) −10.5433 + 18.2614i −0.983163 + 1.70289i
\(116\) 0 0
\(117\) 0.349814 + 2.97954i 0.0323403 + 0.275458i
\(118\) 0 0
\(119\) 2.05563 3.56046i 0.188439 0.326387i
\(120\) 0 0
\(121\) 1.54944 + 2.68371i 0.140858 + 0.243974i
\(122\) 0 0
\(123\) −8.89671 + 2.95059i −0.802189 + 0.266046i
\(124\) 0 0
\(125\) −10.3214 −0.923175
\(126\) 0 0
\(127\) −9.98762 −0.886258 −0.443129 0.896458i \(-0.646132\pi\)
−0.443129 + 0.896458i \(0.646132\pi\)
\(128\) 0 0
\(129\) 6.74288 + 5.99754i 0.593678 + 0.528054i
\(130\) 0 0
\(131\) 8.02654 + 13.9024i 0.701282 + 1.21466i 0.968017 + 0.250886i \(0.0807220\pi\)
−0.266734 + 0.963770i \(0.585945\pi\)
\(132\) 0 0
\(133\) −0.444368 + 0.769668i −0.0385316 + 0.0667387i
\(134\) 0 0
\(135\) 18.5760 + 1.61072i 1.59877 + 0.138629i
\(136\) 0 0
\(137\) 6.49381 11.2476i 0.554804 0.960948i −0.443115 0.896465i \(-0.646127\pi\)
0.997919 0.0644834i \(-0.0205400\pi\)
\(138\) 0 0
\(139\) 0.555632 + 0.962383i 0.0471281 + 0.0816283i 0.888627 0.458630i \(-0.151660\pi\)
−0.841499 + 0.540259i \(0.818326\pi\)
\(140\) 0 0
\(141\) −3.45056 3.06914i −0.290589 0.258468i
\(142\) 0 0
\(143\) 2.81089 0.235059
\(144\) 0 0
\(145\) 6.09888 0.506485
\(146\) 0 0
\(147\) 1.64400 0.545231i 0.135595 0.0449699i
\(148\) 0 0
\(149\) −4.21634 7.30291i −0.345416 0.598278i 0.640013 0.768364i \(-0.278929\pi\)
−0.985429 + 0.170086i \(0.945595\pi\)
\(150\) 0 0
\(151\) −7.42580 + 12.8619i −0.604303 + 1.04668i 0.387858 + 0.921719i \(0.373215\pi\)
−0.992161 + 0.124964i \(0.960118\pi\)
\(152\) 0 0
\(153\) 11.3276 + 4.87933i 0.915782 + 0.394470i
\(154\) 0 0
\(155\) 12.5371 21.7148i 1.00700 1.74418i
\(156\) 0 0
\(157\) −1.44437 2.50172i −0.115273 0.199659i 0.802616 0.596496i \(-0.203441\pi\)
−0.917889 + 0.396837i \(0.870108\pi\)
\(158\) 0 0
\(159\) 0.0432524 0.209744i 0.00343014 0.0166338i
\(160\) 0 0
\(161\) −5.87636 −0.463122
\(162\) 0 0
\(163\) 10.3090 0.807466 0.403733 0.914877i \(-0.367713\pi\)
0.403733 + 0.914877i \(0.367713\pi\)
\(164\) 0 0
\(165\) 3.52840 17.1103i 0.274686 1.33204i
\(166\) 0 0
\(167\) 6.07598 + 10.5239i 0.470174 + 0.814365i 0.999418 0.0341045i \(-0.0108579\pi\)
−0.529244 + 0.848469i \(0.677525\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) −2.44870 1.05477i −0.187257 0.0806602i
\(172\) 0 0
\(173\) 3.30470 5.72391i 0.251252 0.435181i −0.712619 0.701551i \(-0.752491\pi\)
0.963871 + 0.266370i \(0.0858244\pi\)
\(174\) 0 0
\(175\) −3.93818 6.82112i −0.297698 0.515629i
\(176\) 0 0
\(177\) 14.5927 4.83967i 1.09685 0.363772i
\(178\) 0 0
\(179\) 3.84294 0.287234 0.143617 0.989633i \(-0.454127\pi\)
0.143617 + 0.989633i \(0.454127\pi\)
\(180\) 0 0
\(181\) 18.5426 1.37826 0.689129 0.724639i \(-0.257993\pi\)
0.689129 + 0.724639i \(0.257993\pi\)
\(182\) 0 0
\(183\) −5.01671 4.46218i −0.370846 0.329854i
\(184\) 0 0
\(185\) 8.54944 + 14.8081i 0.628567 + 1.08871i
\(186\) 0 0
\(187\) 5.77816 10.0081i 0.422541 0.731862i
\(188\) 0 0
\(189\) 2.19963 + 4.70761i 0.159999 + 0.342429i
\(190\) 0 0
\(191\) 2.31708 4.01330i 0.167658 0.290392i −0.769938 0.638119i \(-0.779713\pi\)
0.937596 + 0.347726i \(0.113046\pi\)
\(192\) 0 0
\(193\) 12.6483 + 21.9075i 0.910446 + 1.57694i 0.813435 + 0.581656i \(0.197595\pi\)
0.0970118 + 0.995283i \(0.469072\pi\)
\(194\) 0 0
\(195\) 4.64400 + 4.13066i 0.332563 + 0.295803i
\(196\) 0 0
\(197\) 10.7207 0.763816 0.381908 0.924200i \(-0.375267\pi\)
0.381908 + 0.924200i \(0.375267\pi\)
\(198\) 0 0
\(199\) 8.76647 0.621439 0.310719 0.950502i \(-0.399430\pi\)
0.310719 + 0.950502i \(0.399430\pi\)
\(200\) 0 0
\(201\) −20.2360 + 6.71127i −1.42734 + 0.473376i
\(202\) 0 0
\(203\) 0.849814 + 1.47192i 0.0596453 + 0.103309i
\(204\) 0 0
\(205\) −9.70946 + 16.8173i −0.678138 + 1.17457i
\(206\) 0 0
\(207\) −2.05563 17.5088i −0.142876 1.21695i
\(208\) 0 0
\(209\) −1.24907 + 2.16345i −0.0864000 + 0.149649i
\(210\) 0 0
\(211\) 5.26509 + 9.11941i 0.362464 + 0.627806i 0.988366 0.152096i \(-0.0486023\pi\)
−0.625902 + 0.779902i \(0.715269\pi\)
\(212\) 0 0
\(213\) −1.00619 + 4.87933i −0.0689430 + 0.334326i
\(214\) 0 0
\(215\) 18.6959 1.27505
\(216\) 0 0
\(217\) 6.98762 0.474351
\(218\) 0 0
\(219\) 3.72253 18.0517i 0.251545 1.21982i
\(220\) 0 0
\(221\) 2.05563 + 3.56046i 0.138277 + 0.239502i
\(222\) 0 0
\(223\) −2.83379 + 4.90827i −0.189765 + 0.328682i −0.945172 0.326574i \(-0.894106\pi\)
0.755407 + 0.655256i \(0.227439\pi\)
\(224\) 0 0
\(225\) 18.9462 14.1201i 1.26308 0.941338i
\(226\) 0 0
\(227\) −5.54944 + 9.61192i −0.368329 + 0.637965i −0.989304 0.145865i \(-0.953403\pi\)
0.620975 + 0.783830i \(0.286737\pi\)
\(228\) 0 0
\(229\) −9.82141 17.0112i −0.649017 1.12413i −0.983358 0.181679i \(-0.941847\pi\)
0.334341 0.942452i \(-0.391486\pi\)
\(230\) 0 0
\(231\) 4.62110 1.53259i 0.304046 0.100837i
\(232\) 0 0
\(233\) 8.96286 0.587177 0.293588 0.955932i \(-0.405151\pi\)
0.293588 + 0.955932i \(0.405151\pi\)
\(234\) 0 0
\(235\) −9.56732 −0.624103
\(236\) 0 0
\(237\) −9.17123 8.15747i −0.595735 0.529884i
\(238\) 0 0
\(239\) 5.61126 + 9.71899i 0.362963 + 0.628670i 0.988447 0.151567i \(-0.0484320\pi\)
−0.625484 + 0.780237i \(0.715099\pi\)
\(240\) 0 0
\(241\) 3.49312 6.05026i 0.225012 0.389732i −0.731311 0.682044i \(-0.761091\pi\)
0.956323 + 0.292312i \(0.0944246\pi\)
\(242\) 0 0
\(243\) −13.2570 + 8.20066i −0.850440 + 0.526073i
\(244\) 0 0
\(245\) 1.79418 3.10761i 0.114626 0.198538i
\(246\) 0 0
\(247\) −0.444368 0.769668i −0.0282745 0.0489728i
\(248\) 0 0
\(249\) −5.32072 4.73259i −0.337187 0.299915i
\(250\) 0 0
\(251\) −4.62041 −0.291638 −0.145819 0.989311i \(-0.546582\pi\)
−0.145819 + 0.989311i \(0.546582\pi\)
\(252\) 0 0
\(253\) −16.5178 −1.03847
\(254\) 0 0
\(255\) 24.2534 8.04364i 1.51881 0.503712i
\(256\) 0 0
\(257\) 0.712008 + 1.23323i 0.0444138 + 0.0769270i 0.887378 0.461043i \(-0.152525\pi\)
−0.842964 + 0.537970i \(0.819191\pi\)
\(258\) 0 0
\(259\) −2.38255 + 4.12669i −0.148044 + 0.256420i
\(260\) 0 0
\(261\) −4.08836 + 3.04695i −0.253063 + 0.188601i
\(262\) 0 0
\(263\) 8.13162 14.0844i 0.501417 0.868480i −0.498582 0.866843i \(-0.666146\pi\)
0.999999 0.00163692i \(-0.000521048\pi\)
\(264\) 0 0
\(265\) −0.221840 0.384237i −0.0136275 0.0236035i
\(266\) 0 0
\(267\) −3.36151 + 16.3010i −0.205721 + 0.997604i
\(268\) 0 0
\(269\) −18.6538 −1.13734 −0.568672 0.822564i \(-0.692543\pi\)
−0.568672 + 0.822564i \(0.692543\pi\)
\(270\) 0 0
\(271\) −3.96286 −0.240727 −0.120363 0.992730i \(-0.538406\pi\)
−0.120363 + 0.992730i \(0.538406\pi\)
\(272\) 0 0
\(273\) −0.349814 + 1.69636i −0.0211717 + 0.102668i
\(274\) 0 0
\(275\) −11.0698 19.1734i −0.667534 1.15620i
\(276\) 0 0
\(277\) 1.16690 2.02112i 0.0701120 0.121438i −0.828838 0.559488i \(-0.810998\pi\)
0.898950 + 0.438051i \(0.144331\pi\)
\(278\) 0 0
\(279\) 2.44437 + 20.8199i 0.146340 + 1.24645i
\(280\) 0 0
\(281\) −13.9975 + 24.2443i −0.835018 + 1.44629i 0.0589978 + 0.998258i \(0.481210\pi\)
−0.894016 + 0.448035i \(0.852124\pi\)
\(282\) 0 0
\(283\) 5.16002 + 8.93741i 0.306731 + 0.531274i 0.977645 0.210261i \(-0.0674314\pi\)
−0.670914 + 0.741535i \(0.734098\pi\)
\(284\) 0 0
\(285\) −5.24288 + 1.73880i −0.310561 + 0.102998i
\(286\) 0 0
\(287\) −5.41164 −0.319439
\(288\) 0 0
\(289\) −0.0975070 −0.00573571
\(290\) 0 0
\(291\) −9.47524 8.42787i −0.555448 0.494051i
\(292\) 0 0
\(293\) 15.3480 + 26.5834i 0.896637 + 1.55302i 0.831765 + 0.555127i \(0.187330\pi\)
0.0648718 + 0.997894i \(0.479336\pi\)
\(294\) 0 0
\(295\) 15.9258 27.5843i 0.927236 1.60602i
\(296\) 0 0
\(297\) 6.18292 + 13.2326i 0.358769 + 0.767833i
\(298\) 0 0
\(299\) 2.93818 5.08907i 0.169919 0.294309i
\(300\) 0 0
\(301\) 2.60507 + 4.51212i 0.150154 + 0.260074i
\(302\) 0 0
\(303\) −4.48398 3.98833i −0.257598 0.229124i
\(304\) 0 0
\(305\) −13.9098 −0.796471
\(306\) 0 0
\(307\) 11.4437 0.653125 0.326563 0.945176i \(-0.394110\pi\)
0.326563 + 0.945176i \(0.394110\pi\)
\(308\) 0 0
\(309\) 26.1007 8.65628i 1.48482 0.492439i
\(310\) 0 0
\(311\) 5.98143 + 10.3601i 0.339176 + 0.587470i 0.984278 0.176627i \(-0.0565185\pi\)
−0.645102 + 0.764096i \(0.723185\pi\)
\(312\) 0 0
\(313\) 6.77197 11.7294i 0.382774 0.662985i −0.608683 0.793413i \(-0.708302\pi\)
0.991458 + 0.130429i \(0.0416353\pi\)
\(314\) 0 0
\(315\) 9.88688 + 4.25874i 0.557062 + 0.239953i
\(316\) 0 0
\(317\) 14.9814 25.9486i 0.841441 1.45742i −0.0472355 0.998884i \(-0.515041\pi\)
0.888676 0.458535i \(-0.151626\pi\)
\(318\) 0 0
\(319\) 2.38874 + 4.13741i 0.133744 + 0.231651i
\(320\) 0 0
\(321\) −1.87271 + 9.08138i −0.104525 + 0.506873i
\(322\) 0 0
\(323\) −3.65383 −0.203304
\(324\) 0 0
\(325\) 7.87636 0.436902
\(326\) 0 0
\(327\) 6.59888 32.0001i 0.364919 1.76961i
\(328\) 0 0
\(329\) −1.33310 2.30900i −0.0734964 0.127299i
\(330\) 0 0
\(331\) 1.04325 1.80697i 0.0573423 0.0993198i −0.835929 0.548837i \(-0.815071\pi\)
0.893272 + 0.449517i \(0.148404\pi\)
\(332\) 0 0
\(333\) −13.1291 5.65531i −0.719469 0.309909i
\(334\) 0 0
\(335\) −22.0846 + 38.2517i −1.20661 + 2.08992i
\(336\) 0 0
\(337\) 8.10439 + 14.0372i 0.441474 + 0.764655i 0.997799 0.0663093i \(-0.0211224\pi\)
−0.556325 + 0.830965i \(0.687789\pi\)
\(338\) 0 0
\(339\) −30.4981 + 10.1147i −1.65643 + 0.549355i
\(340\) 0 0
\(341\) 19.6414 1.06364
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −27.2898 24.2732i −1.46923 1.30683i
\(346\) 0 0
\(347\) 5.63348 + 9.75747i 0.302421 + 0.523808i 0.976684 0.214683i \(-0.0688719\pi\)
−0.674263 + 0.738491i \(0.735539\pi\)
\(348\) 0 0
\(349\) 0.0988844 0.171273i 0.00529316 0.00916803i −0.863367 0.504577i \(-0.831648\pi\)
0.868660 + 0.495409i \(0.164982\pi\)
\(350\) 0 0
\(351\) −5.17673 0.448873i −0.276313 0.0239591i
\(352\) 0 0
\(353\) 6.25093 10.8269i 0.332703 0.576259i −0.650338 0.759645i \(-0.725373\pi\)
0.983041 + 0.183386i \(0.0587059\pi\)
\(354\) 0 0
\(355\) 5.16071 + 8.93861i 0.273902 + 0.474412i
\(356\) 0 0
\(357\) 5.32072 + 4.73259i 0.281603 + 0.250475i
\(358\) 0 0
\(359\) −20.0197 −1.05660 −0.528299 0.849059i \(-0.677170\pi\)
−0.528299 + 0.849059i \(0.677170\pi\)
\(360\) 0 0
\(361\) −18.2101 −0.958429
\(362\) 0 0
\(363\) −5.09455 + 1.68961i −0.267395 + 0.0886814i
\(364\) 0 0
\(365\) −19.0927 33.0695i −0.999357 1.73094i
\(366\) 0 0
\(367\) 15.0364 26.0438i 0.784892 1.35947i −0.144171 0.989553i \(-0.546052\pi\)
0.929063 0.369921i \(-0.120615\pi\)
\(368\) 0 0
\(369\) −1.89307 16.1242i −0.0985491 0.839390i
\(370\) 0 0
\(371\) 0.0618219 0.107079i 0.00320963 0.00555925i
\(372\) 0 0
\(373\) −3.50619 6.07290i −0.181544 0.314443i 0.760863 0.648913i \(-0.224776\pi\)
−0.942406 + 0.334470i \(0.891443\pi\)
\(374\) 0 0
\(375\) 3.61058 17.5088i 0.186449 0.904151i
\(376\) 0 0
\(377\) −1.69963 −0.0875353
\(378\) 0 0
\(379\) 19.0741 0.979772 0.489886 0.871787i \(-0.337038\pi\)
0.489886 + 0.871787i \(0.337038\pi\)
\(380\) 0 0
\(381\) 3.49381 16.9426i 0.178993 0.867995i
\(382\) 0 0
\(383\) 1.60507 + 2.78007i 0.0820155 + 0.142055i 0.904116 0.427288i \(-0.140531\pi\)
−0.822100 + 0.569343i \(0.807198\pi\)
\(384\) 0 0
\(385\) 5.04325 8.73517i 0.257028 0.445185i
\(386\) 0 0
\(387\) −12.5327 + 9.34031i −0.637075 + 0.474795i
\(388\) 0 0
\(389\) −2.56801 + 4.44793i −0.130203 + 0.225519i −0.923755 0.382984i \(-0.874896\pi\)
0.793552 + 0.608503i \(0.208230\pi\)
\(390\) 0 0
\(391\) −12.0796 20.9225i −0.610893 1.05810i
\(392\) 0 0
\(393\) −26.3912 + 8.75264i −1.33126 + 0.441512i
\(394\) 0 0
\(395\) −25.4290 −1.27947
\(396\) 0 0
\(397\) 22.9381 1.15123 0.575615 0.817721i \(-0.304763\pi\)
0.575615 + 0.817721i \(0.304763\pi\)
\(398\) 0 0
\(399\) −1.15019 1.02305i −0.0575813 0.0512164i
\(400\) 0 0
\(401\) 9.10507 + 15.7705i 0.454686 + 0.787539i 0.998670 0.0515566i \(-0.0164183\pi\)
−0.543984 + 0.839095i \(0.683085\pi\)
\(402\) 0 0
\(403\) −3.49381 + 6.05146i −0.174039 + 0.301445i
\(404\) 0 0
\(405\) −9.23050 + 30.9481i −0.458667 + 1.53782i
\(406\) 0 0
\(407\) −6.69708 + 11.5997i −0.331962 + 0.574975i
\(408\) 0 0
\(409\) 7.66621 + 13.2783i 0.379070 + 0.656568i 0.990927 0.134400i \(-0.0429108\pi\)
−0.611858 + 0.790968i \(0.709577\pi\)
\(410\) 0 0
\(411\) 16.8083 + 14.9504i 0.829094 + 0.737449i
\(412\) 0 0
\(413\) 8.87636 0.436777
\(414\) 0 0
\(415\) −14.7527 −0.724182
\(416\) 0 0
\(417\) −1.82691 + 0.605896i −0.0894644 + 0.0296708i
\(418\) 0 0
\(419\) 5.28435 + 9.15276i 0.258157 + 0.447142i 0.965748 0.259481i \(-0.0835513\pi\)
−0.707591 + 0.706622i \(0.750218\pi\)
\(420\) 0 0
\(421\) 18.0858 31.3256i 0.881449 1.52671i 0.0317181 0.999497i \(-0.489902\pi\)
0.849731 0.527217i \(-0.176765\pi\)
\(422\) 0 0
\(423\) 6.41342 4.77975i 0.311831 0.232399i
\(424\) 0 0
\(425\) 16.1909 28.0434i 0.785374 1.36031i
\(426\) 0 0
\(427\) −1.93818 3.35702i −0.0937950 0.162458i
\(428\) 0 0
\(429\) −0.983290 + 4.76828i −0.0474737 + 0.230215i
\(430\) 0 0
\(431\) −35.0989 −1.69065 −0.845327 0.534249i \(-0.820594\pi\)
−0.845327 + 0.534249i \(0.820594\pi\)
\(432\) 0 0
\(433\) −41.1730 −1.97865 −0.989324 0.145731i \(-0.953447\pi\)
−0.989324 + 0.145731i \(0.953447\pi\)
\(434\) 0 0
\(435\) −2.13348 + 10.3459i −0.102292 + 0.496047i
\(436\) 0 0
\(437\) 2.61126 + 4.52284i 0.124914 + 0.216357i
\(438\) 0 0
\(439\) −2.33929 + 4.05178i −0.111648 + 0.193381i −0.916435 0.400184i \(-0.868946\pi\)
0.804787 + 0.593564i \(0.202280\pi\)
\(440\) 0 0
\(441\) 0.349814 + 2.97954i 0.0166578 + 0.141883i
\(442\) 0 0
\(443\) 15.0865 26.1306i 0.716781 1.24150i −0.245487 0.969400i \(-0.578948\pi\)
0.962268 0.272102i \(-0.0877188\pi\)
\(444\) 0 0
\(445\) 17.2410 + 29.8623i 0.817303 + 1.41561i
\(446\) 0 0
\(447\) 13.8633 4.59776i 0.655711 0.217466i
\(448\) 0 0
\(449\) 0.333792 0.0157526 0.00787632 0.999969i \(-0.497493\pi\)
0.00787632 + 0.999969i \(0.497493\pi\)
\(450\) 0 0
\(451\) −15.2115 −0.716283
\(452\) 0 0
\(453\) −19.2207 17.0961i −0.903066 0.803244i
\(454\) 0 0
\(455\) 1.79418 + 3.10761i 0.0841125 + 0.145687i
\(456\) 0 0
\(457\) 9.65452 16.7221i 0.451619 0.782227i −0.546868 0.837219i \(-0.684180\pi\)
0.998487 + 0.0549917i \(0.0175132\pi\)
\(458\) 0 0
\(459\) −12.2396 + 17.5088i −0.571298 + 0.817241i
\(460\) 0 0
\(461\) −19.5538 + 33.8681i −0.910710 + 1.57740i −0.0976463 + 0.995221i \(0.531131\pi\)
−0.813064 + 0.582175i \(0.802202\pi\)
\(462\) 0 0
\(463\) 10.9382 + 18.9455i 0.508340 + 0.880471i 0.999953 + 0.00965741i \(0.00307410\pi\)
−0.491613 + 0.870814i \(0.663593\pi\)
\(464\) 0 0
\(465\) 32.4505 + 28.8635i 1.50486 + 1.33851i
\(466\) 0 0
\(467\) 12.3200 0.570103 0.285052 0.958512i \(-0.407989\pi\)
0.285052 + 0.958512i \(0.407989\pi\)
\(468\) 0 0
\(469\) −12.3090 −0.568378
\(470\) 0 0
\(471\) 4.74907 1.57503i 0.218826 0.0725735i
\(472\) 0 0
\(473\) 7.32258 + 12.6831i 0.336693 + 0.583169i
\(474\) 0 0
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0.340671 + 0.146743i 0.0155983 + 0.00671890i
\(478\) 0 0
\(479\) 6.74474 11.6822i 0.308175 0.533775i −0.669788 0.742552i \(-0.733615\pi\)
0.977963 + 0.208777i \(0.0669484\pi\)
\(480\) 0 0
\(481\) −2.38255 4.12669i −0.108635 0.188161i
\(482\) 0 0
\(483\) 2.05563 9.96840i 0.0935345 0.453578i
\(484\) 0 0
\(485\) −26.2719 −1.19295
\(486\) 0 0
\(487\) −7.54394 −0.341849 −0.170924 0.985284i \(-0.554675\pi\)
−0.170924 + 0.985284i \(0.554675\pi\)
\(488\) 0 0
\(489\) −3.60624 + 17.4878i −0.163080 + 0.790826i
\(490\) 0 0
\(491\) −8.06979 13.9773i −0.364185 0.630786i 0.624460 0.781057i \(-0.285319\pi\)
−0.988645 + 0.150270i \(0.951986\pi\)
\(492\) 0 0
\(493\) −3.49381 + 6.05146i −0.157353 + 0.272544i
\(494\) 0 0
\(495\) 27.7909 + 11.9709i 1.24911 + 0.538050i
\(496\) 0 0
\(497\) −1.43818 + 2.49100i −0.0645111 + 0.111737i
\(498\) 0 0
\(499\) −15.4327 26.7302i −0.690862 1.19661i −0.971556 0.236810i \(-0.923898\pi\)
0.280694 0.959797i \(-0.409435\pi\)
\(500\) 0 0
\(501\) −19.9778 + 6.62563i −0.892542 + 0.296011i
\(502\) 0 0
\(503\) −24.6304 −1.09822 −0.549109 0.835751i \(-0.685033\pi\)
−0.549109 + 0.835751i \(0.685033\pi\)
\(504\) 0 0
\(505\) −12.4327 −0.553247
\(506\) 0 0
\(507\) 15.5302 + 13.8135i 0.689720 + 0.613480i
\(508\) 0 0
\(509\) −6.79487 11.7691i −0.301177 0.521654i 0.675226 0.737611i \(-0.264046\pi\)
−0.976403 + 0.215957i \(0.930713\pi\)
\(510\) 0 0
\(511\) 5.32072 9.21576i 0.235375 0.407681i
\(512\) 0 0
\(513\) 2.64586 3.78490i 0.116817 0.167107i
\(514\) 0 0
\(515\) 28.4851 49.3376i 1.25520 2.17407i
\(516\) 0 0
\(517\) −3.74721 6.49036i −0.164802 0.285446i
\(518\) 0 0
\(519\) 8.55377 + 7.60826i 0.375469 + 0.333966i
\(520\) 0 0
\(521\) −39.1730 −1.71620 −0.858100 0.513482i \(-0.828355\pi\)
−0.858100 + 0.513482i \(0.828355\pi\)
\(522\) 0 0
\(523\) −19.1236 −0.836219 −0.418109 0.908397i \(-0.637307\pi\)
−0.418109 + 0.908397i \(0.637307\pi\)
\(524\) 0 0
\(525\) 12.9487 4.29443i 0.565128 0.187424i
\(526\) 0 0
\(527\) 14.3640 + 24.8791i 0.625705 + 1.08375i
\(528\) 0 0
\(529\) −5.76578 + 9.98663i −0.250686 + 0.434201i
\(530\) 0 0
\(531\) 3.10507 + 26.4474i 0.134749 + 1.14772i
\(532\) 0 0
\(533\) 2.70582 4.68661i 0.117202 0.203000i
\(534\) 0 0
\(535\) 9.60507 + 16.6365i 0.415264 + 0.719258i
\(536\) 0 0
\(537\) −1.34431 + 6.51899i −0.0580114 + 0.281315i
\(538\) 0 0
\(539\) 2.81089 0.121074
\(540\) 0 0
\(541\) 2.53018 0.108781 0.0543906 0.998520i \(-0.482678\pi\)
0.0543906 + 0.998520i \(0.482678\pi\)
\(542\) 0 0
\(543\) −6.48645 + 31.4548i −0.278360 + 1.34986i
\(544\) 0 0
\(545\) −33.8454 58.6220i −1.44978 2.51109i
\(546\) 0 0
\(547\) 8.92580 15.4599i 0.381640 0.661019i −0.609657 0.792665i \(-0.708693\pi\)
0.991297 + 0.131646i \(0.0420262\pi\)
\(548\) 0 0
\(549\) 9.32437 6.94920i 0.397954 0.296585i
\(550\) 0 0
\(551\) 0.755260 1.30815i 0.0321752 0.0557290i
\(552\) 0 0
\(553\) −3.54325 6.13709i −0.150674 0.260976i
\(554\) 0 0
\(555\) −28.1105 + 9.32284i −1.19322 + 0.395733i
\(556\) 0 0
\(557\) 41.3607 1.75251 0.876255 0.481847i \(-0.160034\pi\)
0.876255 + 0.481847i \(0.160034\pi\)
\(558\) 0 0
\(559\) −5.21015 −0.220366
\(560\) 0 0
\(561\) 14.9560 + 13.3028i 0.631442 + 0.561644i
\(562\) 0 0
\(563\) −10.3683 17.9584i −0.436972 0.756858i 0.560482 0.828166i \(-0.310616\pi\)
−0.997454 + 0.0713087i \(0.977282\pi\)
\(564\) 0 0
\(565\) −33.2843 + 57.6501i −1.40028 + 2.42536i
\(566\) 0 0
\(567\) −8.75526 + 2.08457i −0.367686 + 0.0875436i
\(568\) 0 0
\(569\) 0.134164 0.232379i 0.00562446 0.00974185i −0.863199 0.504863i \(-0.831543\pi\)
0.868824 + 0.495121i \(0.164876\pi\)
\(570\) 0 0
\(571\) 17.9684 + 31.1221i 0.751953 + 1.30242i 0.946875 + 0.321601i \(0.104221\pi\)
−0.194923 + 0.980819i \(0.562446\pi\)
\(572\) 0 0
\(573\) 5.99745 + 5.33451i 0.250547 + 0.222852i
\(574\) 0 0
\(575\) −46.2843 −1.93019
\(576\) 0 0
\(577\) 5.43130 0.226108 0.113054 0.993589i \(-0.463937\pi\)
0.113054 + 0.993589i \(0.463937\pi\)
\(578\) 0 0
\(579\) −41.5876 + 13.7925i −1.72832 + 0.573198i
\(580\) 0 0
\(581\) −2.05563 3.56046i −0.0852820 0.147713i
\(582\) 0 0
\(583\) 0.173775 0.300987i 0.00719702 0.0124656i
\(584\) 0 0
\(585\) −8.63162 + 6.43292i −0.356873 + 0.265968i
\(586\) 0 0
\(587\) 17.5822 30.4532i 0.725694 1.25694i −0.232994 0.972478i \(-0.574852\pi\)
0.958688 0.284461i \(-0.0918145\pi\)
\(588\) 0 0
\(589\) −3.10507 5.37815i −0.127942 0.221603i
\(590\) 0 0
\(591\) −3.75024 + 18.1861i −0.154264 + 0.748076i
\(592\) 0 0
\(593\) −33.5068 −1.37596 −0.687980 0.725730i \(-0.741502\pi\)
−0.687980 + 0.725730i \(0.741502\pi\)
\(594\) 0 0
\(595\) 14.7527 0.604802
\(596\) 0 0
\(597\) −3.06663 + 14.8711i −0.125509 + 0.608632i
\(598\) 0 0
\(599\) 3.12364 + 5.41031i 0.127629 + 0.221059i 0.922757 0.385381i \(-0.125930\pi\)
−0.795129 + 0.606441i \(0.792597\pi\)
\(600\) 0 0
\(601\) −11.2040 + 19.4058i −0.457019 + 0.791580i −0.998802 0.0489384i \(-0.984416\pi\)
0.541783 + 0.840519i \(0.317750\pi\)
\(602\) 0 0
\(603\) −4.30587 36.6752i −0.175349 1.49353i
\(604\) 0 0
\(605\) −5.55996 + 9.63014i −0.226045 + 0.391521i
\(606\) 0 0
\(607\) 7.47524 + 12.9475i 0.303411 + 0.525523i 0.976906 0.213669i \(-0.0685413\pi\)
−0.673496 + 0.739191i \(0.735208\pi\)
\(608\) 0 0
\(609\) −2.79418 + 0.926690i −0.113226 + 0.0375514i
\(610\) 0 0
\(611\) 2.66621 0.107863
\(612\) 0 0
\(613\) 35.1978 1.42162 0.710812 0.703382i \(-0.248328\pi\)
0.710812 + 0.703382i \(0.248328\pi\)
\(614\) 0 0
\(615\) −25.1316 22.3536i −1.01340 0.901386i
\(616\) 0 0
\(617\) 1.00619 + 1.74277i 0.0405077 + 0.0701614i 0.885568 0.464509i \(-0.153769\pi\)
−0.845061 + 0.534670i \(0.820436\pi\)
\(618\) 0 0
\(619\) 19.6909 34.1056i 0.791444 1.37082i −0.133629 0.991031i \(-0.542663\pi\)
0.925073 0.379789i \(-0.124004\pi\)
\(620\) 0 0
\(621\) 30.4203 + 2.63774i 1.22072 + 0.105849i
\(622\) 0 0
\(623\) −4.80470 + 8.32199i −0.192496 + 0.333413i
\(624\) 0 0
\(625\) 1.17240 + 2.03065i 0.0468959 + 0.0812261i
\(626\) 0 0
\(627\) −3.23305 2.87568i −0.129116 0.114843i
\(628\) 0 0
\(629\) −19.5906 −0.781126
\(630\) 0 0
\(631\) −44.3832 −1.76687 −0.883433 0.468558i \(-0.844774\pi\)
−0.883433 + 0.468558i \(0.844774\pi\)
\(632\) 0 0
\(633\) −17.3116 + 5.74138i −0.688074 + 0.228200i
\(634\) 0 0
\(635\) −17.9196 31.0377i −0.711118 1.23169i
\(636\) 0 0
\(637\) −0.500000 + 0.866025i −0.0198107 + 0.0343132i
\(638\) 0 0
\(639\) −7.92511 3.41372i −0.313512 0.135045i
\(640\) 0 0
\(641\) 7.49312 12.9785i 0.295961 0.512619i −0.679247 0.733909i \(-0.737694\pi\)
0.975208 + 0.221291i \(0.0710270\pi\)
\(642\) 0 0
\(643\) −5.32691 9.22649i −0.210073 0.363857i 0.741664 0.670771i \(-0.234037\pi\)
−0.951737 + 0.306914i \(0.900703\pi\)
\(644\) 0 0
\(645\) −6.54009 + 31.7150i −0.257516 + 1.24878i
\(646\) 0 0
\(647\) −2.12955 −0.0837213 −0.0418606 0.999123i \(-0.513329\pi\)
−0.0418606 + 0.999123i \(0.513329\pi\)
\(648\) 0 0
\(649\) 24.9505 0.979392
\(650\) 0 0
\(651\) −2.44437 + 11.8535i −0.0958023 + 0.464575i
\(652\) 0 0
\(653\) −5.58582 9.67492i −0.218590 0.378609i 0.735787 0.677213i \(-0.236812\pi\)
−0.954377 + 0.298604i \(0.903479\pi\)
\(654\) 0 0
\(655\) −28.8022 + 49.8868i −1.12539 + 1.94924i
\(656\) 0 0
\(657\) 29.3200 + 12.6295i 1.14388 + 0.492723i
\(658\) 0 0
\(659\) −5.65452 + 9.79391i −0.220269 + 0.381517i −0.954890 0.296961i \(-0.904027\pi\)
0.734621 + 0.678478i \(0.237360\pi\)
\(660\) 0 0
\(661\) −16.1785 28.0220i −0.629271 1.08993i −0.987698 0.156372i \(-0.950020\pi\)
0.358427 0.933558i \(-0.383313\pi\)
\(662\) 0 0
\(663\) −6.75890 + 2.24159i −0.262494 + 0.0870561i
\(664\) 0 0
\(665\) −3.18911 −0.123668
\(666\) 0 0
\(667\) 9.98762 0.386722
\(668\) 0 0
\(669\) −7.33489 6.52411i −0.283583 0.252237i
\(670\) 0 0
\(671\) −5.44801 9.43623i −0.210318 0.364282i
\(672\) 0 0
\(673\) 12.0803 20.9237i 0.465662 0.806550i −0.533569 0.845756i \(-0.679150\pi\)
0.999231 + 0.0392063i \(0.0124830\pi\)
\(674\) 0 0
\(675\) 17.3251 + 37.0788i 0.666842 + 1.42717i
\(676\) 0 0
\(677\) −12.5371 + 21.7148i −0.481838 + 0.834569i −0.999783 0.0208457i \(-0.993364\pi\)
0.517944 + 0.855414i \(0.326697\pi\)
\(678\) 0 0
\(679\) −3.66071 6.34053i −0.140485 0.243327i
\(680\) 0 0
\(681\) −14.3640 12.7762i −0.550429 0.489586i
\(682\) 0 0
\(683\) 47.6784 1.82436 0.912182 0.409785i \(-0.134396\pi\)
0.912182 + 0.409785i \(0.134396\pi\)
\(684\) 0 0
\(685\) 46.6043 1.78066
\(686\) 0 0
\(687\) 32.2927 10.7099i 1.23204 0.408607i
\(688\) 0 0
\(689\) 0.0618219 + 0.107079i 0.00235523 + 0.00407937i
\(690\) 0 0
\(691\) −12.3400 + 21.3735i −0.469435 + 0.813085i −0.999389 0.0349408i \(-0.988876\pi\)
0.529954 + 0.848026i \(0.322209\pi\)
\(692\) 0 0
\(693\) 0.983290 + 8.37515i 0.0373521 + 0.318146i
\(694\) 0 0
\(695\) −1.99381 + 3.45338i −0.0756295 + 0.130994i
\(696\) 0 0
\(697\) −11.1243 19.2679i −0.421364 0.729824i
\(698\) 0 0
\(699\) −3.13533 + 15.2042i −0.118589 + 0.575076i
\(700\) 0 0
\(701\) −29.6784 −1.12094 −0.560469 0.828175i \(-0.689379\pi\)
−0.560469 + 0.828175i \(0.689379\pi\)
\(702\) 0 0
\(703\) 4.23491 0.159723
\(704\) 0 0
\(705\) 3.34678 16.2296i 0.126047 0.611242i
\(706\) 0 0
\(707\) −1.73236 3.00054i −0.0651521 0.112847i
\(708\) 0 0
\(709\) 14.6291 25.3383i 0.549406 0.951599i −0.448909 0.893577i \(-0.648187\pi\)
0.998315 0.0580220i \(-0.0184794\pi\)
\(710\) 0 0
\(711\) 17.0462 12.7041i 0.639283 0.476440i
\(712\) 0 0
\(713\) 20.5309 35.5605i 0.768887 1.33175i
\(714\) 0 0
\(715\) 5.04325 + 8.73517i 0.188607 + 0.326677i
\(716\) 0 0
\(717\) −18.4498 + 6.11887i −0.689020 + 0.228513i
\(718\) 0 0
\(719\) −1.07413 −0.0400581 −0.0200291 0.999799i \(-0.506376\pi\)
−0.0200291 + 0.999799i \(0.506376\pi\)
\(720\) 0 0
\(721\) 15.8764 0.591266
\(722\) 0 0
\(723\) 9.04147 + 8.04205i 0.336256 + 0.299087i
\(724\) 0 0
\(725\) 6.69344 + 11.5934i 0.248588 + 0.430567i
\(726\) 0 0
\(727\) 12.7163 22.0253i 0.471623 0.816875i −0.527850 0.849338i \(-0.677002\pi\)
0.999473 + 0.0324628i \(0.0103350\pi\)
\(728\) 0 0
\(729\) −9.27375 25.3574i −0.343472 0.939163i
\(730\) 0 0
\(731\) −10.7101 + 18.5505i −0.396129 + 0.686116i
\(732\) 0 0
\(733\) 5.69777 + 9.86883i 0.210452 + 0.364513i 0.951856 0.306545i \(-0.0991731\pi\)
−0.741404 + 0.671059i \(0.765840\pi\)
\(734\) 0 0
\(735\) 4.64400 + 4.13066i 0.171296 + 0.152362i
\(736\) 0 0
\(737\) −34.5994 −1.27448
\(738\) 0 0
\(739\) 29.9395 1.10134 0.550671 0.834723i \(-0.314372\pi\)
0.550671 + 0.834723i \(0.314372\pi\)
\(740\) 0 0
\(741\) 1.46108 0.484566i 0.0536740 0.0178010i
\(742\) 0 0
\(743\) −9.50069 16.4557i −0.348546 0.603700i 0.637445 0.770496i \(-0.279991\pi\)
−0.985991 + 0.166796i \(0.946658\pi\)
\(744\) 0 0
\(745\) 15.1298 26.2055i 0.554311 0.960096i
\(746\) 0 0
\(747\) 9.88942 7.37033i 0.361835 0.269666i
\(748\) 0 0
\(749\) −2.67673 + 4.63623i −0.0978055 + 0.169404i
\(750\) 0 0
\(751\) 0.0130684 + 0.0226352i 0.000476873 + 0.000825969i 0.866264 0.499587i \(-0.166515\pi\)
−0.865787 + 0.500413i \(0.833182\pi\)
\(752\) 0 0
\(753\) 1.61628 7.83786i 0.0589006 0.285628i
\(754\) 0 0
\(755\) −53.2929 −1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) 0 0
\(759\) 5.77816 28.0201i 0.209734 1.01707i
\(760\) 0 0
\(761\) 7.32141 + 12.6811i 0.265401 + 0.459688i 0.967669 0.252225i \(-0.0811623\pi\)
−0.702268 + 0.711913i \(0.747829\pi\)
\(762\) 0 0
\(763\) 9.43199 16.3367i 0.341461 0.591428i
\(764\) 0 0
\(765\) 5.16071 + 43.9562i 0.186586 + 1.58924i
\(766\) 0 0
\(767\) −4.43818 + 7.68715i −0.160253 + 0.277567i
\(768\) 0 0
\(769\) −24.5672 42.5517i −0.885918 1.53445i −0.844658 0.535306i \(-0.820196\pi\)
−0.0412592 0.999148i \(-0.513137\pi\)
\(770\) 0 0
\(771\) −2.34108 + 0.776418i −0.0843118 + 0.0279620i
\(772\) 0 0
\(773\) 12.4413 0.447484 0.223742 0.974648i \(-0.428173\pi\)
0.223742 + 0.974648i \(0.428173\pi\)
\(774\) 0 0
\(775\) 55.0370 1.97699
\(776\) 0 0
\(777\) −6.16690 5.48523i −0.221236 0.196781i
\(778\) 0 0
\(779\) 2.40476 + 4.16516i 0.0861594 + 0.149232i
\(780\) 0 0
\(781\) −4.04256 + 7.00193i −0.144654 + 0.250549i
\(782\) 0 0
\(783\) −3.73855 8.00119i −0.133605 0.285939i
\(784\) 0 0
\(785\) 5.18292 8.97708i 0.184986 0.320406i
\(786\) 0 0
\(787\) −16.4567 28.5038i −0.586617 1.01605i −0.994672 0.103093i \(-0.967126\pi\)
0.408055 0.912957i \(-0.366207\pi\)
\(788\) 0 0
\(789\) 21.0476 + 18.7210i 0.749314 + 0.666487i
\(790\) 0 0
\(791\) −18.5512 −0.659606
\(792\) 0 0
\(793\) 3.87636 0.137653
\(794\) 0 0
\(795\) 0.729407 0.241908i 0.0258694 0.00857958i
\(796\) 0 0
\(797\) −13.1989 22.8612i −0.467530 0.809786i 0.531781 0.846882i \(-0.321523\pi\)
−0.999312 + 0.0370953i \(0.988189\pi\)
\(798\) 0 0
\(799\) 5.48074 9.49292i 0.193895 0.335835i
\(800\) 0