Properties

Label 560.2.ci.c.33.2
Level $560$
Weight $2$
Character 560.33
Analytic conductor $4.472$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.ci (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 61 x^{12} + 266 x^{10} + 852 x^{8} + 1438 x^{6} + 1933 x^{4} + 3038 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.2
Root \(-1.45333 - 1.51725i\) of defining polynomial
Character \(\chi\) \(=\) 560.33
Dual form 560.2.ci.c.17.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.13459 - 0.304013i) q^{3} +(0.264946 - 2.22032i) q^{5} +(-0.698943 - 2.55176i) q^{7} +(-1.40320 - 0.810140i) q^{9} +O(q^{10})\) \(q+(-1.13459 - 0.304013i) q^{3} +(0.264946 - 2.22032i) q^{5} +(-0.698943 - 2.55176i) q^{7} +(-1.40320 - 0.810140i) q^{9} +(0.371536 + 0.643519i) q^{11} +(-2.05532 + 2.05532i) q^{13} +(-0.975610 + 2.43860i) q^{15} +(-1.69789 + 6.33660i) q^{17} +(0.946027 - 1.63857i) q^{19} +(0.0172465 + 3.10769i) q^{21} +(-5.11112 + 1.36952i) q^{23} +(-4.85961 - 1.17653i) q^{25} +(3.83750 + 3.83750i) q^{27} -9.69135i q^{29} +(-2.96403 + 1.71129i) q^{31} +(-0.225903 - 0.843083i) q^{33} +(-5.85090 + 0.875795i) q^{35} +(-0.691342 - 2.58012i) q^{37} +(2.95680 - 1.70711i) q^{39} -0.817699i q^{41} +(-1.59589 - 1.59589i) q^{43} +(-2.17054 + 2.90091i) q^{45} +(-4.54913 + 1.21894i) q^{47} +(-6.02296 + 3.56707i) q^{49} +(3.85282 - 6.67328i) q^{51} +(1.29040 - 4.81583i) q^{53} +(1.52725 - 0.654429i) q^{55} +(-1.57150 + 1.57150i) q^{57} +(-1.27487 - 2.20815i) q^{59} +(5.25989 + 3.03680i) q^{61} +(-1.08652 + 4.14688i) q^{63} +(4.01892 + 5.10802i) q^{65} +(-13.2248 - 3.54358i) q^{67} +6.21538 q^{69} +16.0173 q^{71} +(-8.54906 - 2.29071i) q^{73} +(5.15599 + 2.81226i) q^{75} +(1.38242 - 1.39785i) q^{77} +(-5.70091 - 3.29142i) q^{79} +(-0.756928 - 1.31104i) q^{81} +(9.23519 - 9.23519i) q^{83} +(13.6194 + 5.44871i) q^{85} +(-2.94629 + 10.9957i) q^{87} +(-3.01603 + 5.22392i) q^{89} +(6.68124 + 3.80814i) q^{91} +(3.88322 - 1.04051i) q^{93} +(-3.38749 - 2.53461i) q^{95} +(-3.16693 - 3.16693i) q^{97} -1.20398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 12q^{5} - 8q^{7} + O(q^{10}) \) \( 16q - 12q^{5} - 8q^{7} + 12q^{11} - 16q^{15} - 36q^{17} - 28q^{21} + 4q^{23} + 12q^{25} - 24q^{31} + 48q^{33} - 8q^{35} + 4q^{37} + 8q^{43} - 12q^{45} - 12q^{47} + 16q^{51} - 28q^{53} + 8q^{57} - 12q^{61} + 36q^{63} - 8q^{65} - 32q^{67} - 16q^{71} - 12q^{73} + 48q^{75} + 16q^{77} + 24q^{85} + 24q^{87} + 16q^{91} + 28q^{93} - 20q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.13459 0.304013i −0.655056 0.175522i −0.0840425 0.996462i \(-0.526783\pi\)
−0.571014 + 0.820940i \(0.693450\pi\)
\(4\) 0 0
\(5\) 0.264946 2.22032i 0.118487 0.992956i
\(6\) 0 0
\(7\) −0.698943 2.55176i −0.264175 0.964475i
\(8\) 0 0
\(9\) −1.40320 0.810140i −0.467734 0.270047i
\(10\) 0 0
\(11\) 0.371536 + 0.643519i 0.112022 + 0.194028i 0.916586 0.399839i \(-0.130934\pi\)
−0.804563 + 0.593867i \(0.797601\pi\)
\(12\) 0 0
\(13\) −2.05532 + 2.05532i −0.570044 + 0.570044i −0.932141 0.362097i \(-0.882061\pi\)
0.362097 + 0.932141i \(0.382061\pi\)
\(14\) 0 0
\(15\) −0.975610 + 2.43860i −0.251901 + 0.629645i
\(16\) 0 0
\(17\) −1.69789 + 6.33660i −0.411798 + 1.53685i 0.379365 + 0.925247i \(0.376143\pi\)
−0.791163 + 0.611605i \(0.790524\pi\)
\(18\) 0 0
\(19\) 0.946027 1.63857i 0.217033 0.375913i −0.736866 0.676039i \(-0.763695\pi\)
0.953900 + 0.300126i \(0.0970286\pi\)
\(20\) 0 0
\(21\) 0.0172465 + 3.10769i 0.00376349 + 0.678154i
\(22\) 0 0
\(23\) −5.11112 + 1.36952i −1.06574 + 0.285565i −0.748743 0.662861i \(-0.769342\pi\)
−0.317000 + 0.948426i \(0.602675\pi\)
\(24\) 0 0
\(25\) −4.85961 1.17653i −0.971921 0.235306i
\(26\) 0 0
\(27\) 3.83750 + 3.83750i 0.738528 + 0.738528i
\(28\) 0 0
\(29\) 9.69135i 1.79964i −0.436263 0.899819i \(-0.643698\pi\)
0.436263 0.899819i \(-0.356302\pi\)
\(30\) 0 0
\(31\) −2.96403 + 1.71129i −0.532356 + 0.307356i −0.741975 0.670427i \(-0.766111\pi\)
0.209619 + 0.977783i \(0.432778\pi\)
\(32\) 0 0
\(33\) −0.225903 0.843083i −0.0393247 0.146762i
\(34\) 0 0
\(35\) −5.85090 + 0.875795i −0.988982 + 0.148036i
\(36\) 0 0
\(37\) −0.691342 2.58012i −0.113656 0.424170i 0.885527 0.464588i \(-0.153798\pi\)
−0.999183 + 0.0404183i \(0.987131\pi\)
\(38\) 0 0
\(39\) 2.95680 1.70711i 0.473466 0.273356i
\(40\) 0 0
\(41\) 0.817699i 0.127703i −0.997959 0.0638515i \(-0.979662\pi\)
0.997959 0.0638515i \(-0.0203384\pi\)
\(42\) 0 0
\(43\) −1.59589 1.59589i −0.243371 0.243371i 0.574872 0.818243i \(-0.305052\pi\)
−0.818243 + 0.574872i \(0.805052\pi\)
\(44\) 0 0
\(45\) −2.17054 + 2.90091i −0.323565 + 0.432442i
\(46\) 0 0
\(47\) −4.54913 + 1.21894i −0.663560 + 0.177800i −0.574852 0.818257i \(-0.694940\pi\)
−0.0887076 + 0.996058i \(0.528274\pi\)
\(48\) 0 0
\(49\) −6.02296 + 3.56707i −0.860423 + 0.509581i
\(50\) 0 0
\(51\) 3.85282 6.67328i 0.539502 0.934445i
\(52\) 0 0
\(53\) 1.29040 4.81583i 0.177250 0.661505i −0.818908 0.573925i \(-0.805420\pi\)
0.996158 0.0875798i \(-0.0279133\pi\)
\(54\) 0 0
\(55\) 1.52725 0.654429i 0.205935 0.0882432i
\(56\) 0 0
\(57\) −1.57150 + 1.57150i −0.208150 + 0.208150i
\(58\) 0 0
\(59\) −1.27487 2.20815i −0.165975 0.287476i 0.771026 0.636803i \(-0.219744\pi\)
−0.937001 + 0.349327i \(0.886410\pi\)
\(60\) 0 0
\(61\) 5.25989 + 3.03680i 0.673460 + 0.388822i 0.797386 0.603469i \(-0.206215\pi\)
−0.123927 + 0.992291i \(0.539549\pi\)
\(62\) 0 0
\(63\) −1.08652 + 4.14688i −0.136889 + 0.522458i
\(64\) 0 0
\(65\) 4.01892 + 5.10802i 0.498485 + 0.633572i
\(66\) 0 0
\(67\) −13.2248 3.54358i −1.61567 0.432917i −0.665944 0.746002i \(-0.731971\pi\)
−0.949725 + 0.313084i \(0.898638\pi\)
\(68\) 0 0
\(69\) 6.21538 0.748244
\(70\) 0 0
\(71\) 16.0173 1.90090 0.950450 0.310879i \(-0.100623\pi\)
0.950450 + 0.310879i \(0.100623\pi\)
\(72\) 0 0
\(73\) −8.54906 2.29071i −1.00059 0.268108i −0.278898 0.960321i \(-0.589969\pi\)
−0.721693 + 0.692213i \(0.756636\pi\)
\(74\) 0 0
\(75\) 5.15599 + 2.81226i 0.595362 + 0.324732i
\(76\) 0 0
\(77\) 1.38242 1.39785i 0.157542 0.159300i
\(78\) 0 0
\(79\) −5.70091 3.29142i −0.641402 0.370314i 0.143752 0.989614i \(-0.454083\pi\)
−0.785155 + 0.619300i \(0.787417\pi\)
\(80\) 0 0
\(81\) −0.756928 1.31104i −0.0841031 0.145671i
\(82\) 0 0
\(83\) 9.23519 9.23519i 1.01369 1.01369i 0.0137887 0.999905i \(-0.495611\pi\)
0.999905 0.0137887i \(-0.00438921\pi\)
\(84\) 0 0
\(85\) 13.6194 + 5.44871i 1.47723 + 0.590995i
\(86\) 0 0
\(87\) −2.94629 + 10.9957i −0.315876 + 1.17886i
\(88\) 0 0
\(89\) −3.01603 + 5.22392i −0.319699 + 0.553735i −0.980425 0.196892i \(-0.936915\pi\)
0.660726 + 0.750627i \(0.270248\pi\)
\(90\) 0 0
\(91\) 6.68124 + 3.80814i 0.700385 + 0.399201i
\(92\) 0 0
\(93\) 3.88322 1.04051i 0.402671 0.107895i
\(94\) 0 0
\(95\) −3.38749 2.53461i −0.347549 0.260046i
\(96\) 0 0
\(97\) −3.16693 3.16693i −0.321553 0.321553i 0.527810 0.849363i \(-0.323013\pi\)
−0.849363 + 0.527810i \(0.823013\pi\)
\(98\) 0 0
\(99\) 1.20398i 0.121005i
\(100\) 0 0
\(101\) 9.68359 5.59083i 0.963554 0.556308i 0.0662887 0.997800i \(-0.478884\pi\)
0.897265 + 0.441493i \(0.145551\pi\)
\(102\) 0 0
\(103\) −0.627940 2.34351i −0.0618728 0.230912i 0.928064 0.372420i \(-0.121472\pi\)
−0.989937 + 0.141507i \(0.954805\pi\)
\(104\) 0 0
\(105\) 6.90463 + 0.785078i 0.673823 + 0.0766157i
\(106\) 0 0
\(107\) 1.71868 + 6.41422i 0.166151 + 0.620086i 0.997891 + 0.0649189i \(0.0206789\pi\)
−0.831739 + 0.555167i \(0.812654\pi\)
\(108\) 0 0
\(109\) 7.76000 4.48024i 0.743274 0.429129i −0.0799848 0.996796i \(-0.525487\pi\)
0.823258 + 0.567667i \(0.192154\pi\)
\(110\) 0 0
\(111\) 3.13756i 0.297804i
\(112\) 0 0
\(113\) 0.307790 + 0.307790i 0.0289545 + 0.0289545i 0.721436 0.692481i \(-0.243482\pi\)
−0.692481 + 0.721436i \(0.743482\pi\)
\(114\) 0 0
\(115\) 1.68660 + 11.7112i 0.157276 + 1.09207i
\(116\) 0 0
\(117\) 4.54913 1.21894i 0.420568 0.112691i
\(118\) 0 0
\(119\) 17.3562 0.0963204i 1.59104 0.00882967i
\(120\) 0 0
\(121\) 5.22392 9.04810i 0.474902 0.822554i
\(122\) 0 0
\(123\) −0.248591 + 0.927753i −0.0224147 + 0.0836527i
\(124\) 0 0
\(125\) −3.89980 + 10.4781i −0.348808 + 0.937194i
\(126\) 0 0
\(127\) 11.1823 11.1823i 0.992267 0.992267i −0.00770296 0.999970i \(-0.502452\pi\)
0.999970 + 0.00770296i \(0.00245195\pi\)
\(128\) 0 0
\(129\) 1.32551 + 2.29585i 0.116705 + 0.202139i
\(130\) 0 0
\(131\) 8.30763 + 4.79641i 0.725841 + 0.419064i 0.816899 0.576781i \(-0.195692\pi\)
−0.0910579 + 0.995846i \(0.529025\pi\)
\(132\) 0 0
\(133\) −4.84245 1.26877i −0.419893 0.110016i
\(134\) 0 0
\(135\) 9.53720 7.50374i 0.820832 0.645819i
\(136\) 0 0
\(137\) −8.99233 2.40949i −0.768267 0.205856i −0.146661 0.989187i \(-0.546853\pi\)
−0.621606 + 0.783330i \(0.713519\pi\)
\(138\) 0 0
\(139\) −22.1714 −1.88056 −0.940278 0.340408i \(-0.889435\pi\)
−0.940278 + 0.340408i \(0.889435\pi\)
\(140\) 0 0
\(141\) 5.53198 0.465877
\(142\) 0 0
\(143\) −2.08627 0.559013i −0.174462 0.0467470i
\(144\) 0 0
\(145\) −21.5179 2.56768i −1.78696 0.213235i
\(146\) 0 0
\(147\) 7.91803 2.21611i 0.653068 0.182781i
\(148\) 0 0
\(149\) −3.41418 1.97118i −0.279701 0.161485i 0.353587 0.935402i \(-0.384962\pi\)
−0.633288 + 0.773916i \(0.718295\pi\)
\(150\) 0 0
\(151\) −9.97267 17.2732i −0.811564 1.40567i −0.911769 0.410703i \(-0.865283\pi\)
0.100205 0.994967i \(-0.468050\pi\)
\(152\) 0 0
\(153\) 7.51602 7.51602i 0.607634 0.607634i
\(154\) 0 0
\(155\) 3.01429 + 7.03449i 0.242113 + 0.565024i
\(156\) 0 0
\(157\) −1.93165 + 7.20903i −0.154163 + 0.575343i 0.845013 + 0.534746i \(0.179593\pi\)
−0.999176 + 0.0405972i \(0.987074\pi\)
\(158\) 0 0
\(159\) −2.92815 + 5.07170i −0.232217 + 0.402212i
\(160\) 0 0
\(161\) 7.06707 + 12.0851i 0.556963 + 0.952442i
\(162\) 0 0
\(163\) 11.7520 3.14893i 0.920486 0.246644i 0.232693 0.972550i \(-0.425246\pi\)
0.687793 + 0.725907i \(0.258580\pi\)
\(164\) 0 0
\(165\) −1.93176 + 0.278205i −0.150387 + 0.0216583i
\(166\) 0 0
\(167\) 1.45564 + 1.45564i 0.112641 + 0.112641i 0.761181 0.648540i \(-0.224620\pi\)
−0.648540 + 0.761181i \(0.724620\pi\)
\(168\) 0 0
\(169\) 4.55129i 0.350099i
\(170\) 0 0
\(171\) −2.65494 + 1.53283i −0.203028 + 0.117218i
\(172\) 0 0
\(173\) 2.43499 + 9.08750i 0.185129 + 0.690910i 0.994603 + 0.103754i \(0.0330856\pi\)
−0.809474 + 0.587155i \(0.800248\pi\)
\(174\) 0 0
\(175\) 0.394370 + 13.2229i 0.0298116 + 0.999556i
\(176\) 0 0
\(177\) 0.775156 + 2.89292i 0.0582643 + 0.217445i
\(178\) 0 0
\(179\) 3.89494 2.24874i 0.291121 0.168079i −0.347326 0.937744i \(-0.612910\pi\)
0.638447 + 0.769665i \(0.279577\pi\)
\(180\) 0 0
\(181\) 17.8850i 1.32938i −0.747118 0.664691i \(-0.768563\pi\)
0.747118 0.664691i \(-0.231437\pi\)
\(182\) 0 0
\(183\) −5.04460 5.04460i −0.372907 0.372907i
\(184\) 0 0
\(185\) −5.91186 + 0.851405i −0.434649 + 0.0625965i
\(186\) 0 0
\(187\) −4.70855 + 1.26165i −0.344323 + 0.0922612i
\(188\) 0 0
\(189\) 7.11019 12.4746i 0.517190 0.907392i
\(190\) 0 0
\(191\) −1.38774 + 2.40364i −0.100413 + 0.173921i −0.911855 0.410512i \(-0.865350\pi\)
0.811442 + 0.584433i \(0.198683\pi\)
\(192\) 0 0
\(193\) −1.33034 + 4.96491i −0.0957602 + 0.357382i −0.997134 0.0756607i \(-0.975893\pi\)
0.901373 + 0.433043i \(0.142560\pi\)
\(194\) 0 0
\(195\) −3.00693 7.01731i −0.215330 0.502520i
\(196\) 0 0
\(197\) 1.34043 1.34043i 0.0955019 0.0955019i −0.657742 0.753244i \(-0.728488\pi\)
0.753244 + 0.657742i \(0.228488\pi\)
\(198\) 0 0
\(199\) −7.25148 12.5599i −0.514043 0.890349i −0.999867 0.0162926i \(-0.994814\pi\)
0.485824 0.874057i \(-0.338520\pi\)
\(200\) 0 0
\(201\) 13.9275 + 8.04103i 0.982368 + 0.567171i
\(202\) 0 0
\(203\) −24.7300 + 6.77370i −1.73571 + 0.475420i
\(204\) 0 0
\(205\) −1.81555 0.216646i −0.126803 0.0151312i
\(206\) 0 0
\(207\) 8.28144 + 2.21901i 0.575600 + 0.154232i
\(208\) 0 0
\(209\) 1.40593 0.0972504
\(210\) 0 0
\(211\) −10.0324 −0.690660 −0.345330 0.938481i \(-0.612233\pi\)
−0.345330 + 0.938481i \(0.612233\pi\)
\(212\) 0 0
\(213\) −18.1730 4.86945i −1.24520 0.333649i
\(214\) 0 0
\(215\) −3.96620 + 3.12055i −0.270493 + 0.212820i
\(216\) 0 0
\(217\) 6.43848 + 6.36741i 0.437073 + 0.432248i
\(218\) 0 0
\(219\) 9.00328 + 5.19804i 0.608385 + 0.351251i
\(220\) 0 0
\(221\) −9.53406 16.5135i −0.641330 1.11082i
\(222\) 0 0
\(223\) −3.13756 + 3.13756i −0.210107 + 0.210107i −0.804313 0.594206i \(-0.797466\pi\)
0.594206 + 0.804313i \(0.297466\pi\)
\(224\) 0 0
\(225\) 5.86586 + 5.58787i 0.391058 + 0.372525i
\(226\) 0 0
\(227\) −0.173634 + 0.648012i −0.0115245 + 0.0430101i −0.971449 0.237250i \(-0.923754\pi\)
0.959924 + 0.280260i \(0.0904207\pi\)
\(228\) 0 0
\(229\) 6.60166 11.4344i 0.436250 0.755608i −0.561146 0.827717i \(-0.689640\pi\)
0.997397 + 0.0721088i \(0.0229729\pi\)
\(230\) 0 0
\(231\) −1.99345 + 1.16572i −0.131159 + 0.0766986i
\(232\) 0 0
\(233\) 8.36389 2.24110i 0.547937 0.146819i 0.0257782 0.999668i \(-0.491794\pi\)
0.522158 + 0.852849i \(0.325127\pi\)
\(234\) 0 0
\(235\) 1.50115 + 10.4235i 0.0979243 + 0.679952i
\(236\) 0 0
\(237\) 5.46757 + 5.46757i 0.355157 + 0.355157i
\(238\) 0 0
\(239\) 4.00294i 0.258929i 0.991584 + 0.129464i \(0.0413258\pi\)
−0.991584 + 0.129464i \(0.958674\pi\)
\(240\) 0 0
\(241\) −15.0040 + 8.66256i −0.966493 + 0.558005i −0.898165 0.439658i \(-0.855100\pi\)
−0.0683274 + 0.997663i \(0.521766\pi\)
\(242\) 0 0
\(243\) −3.75364 14.0088i −0.240796 0.898663i
\(244\) 0 0
\(245\) 6.32426 + 14.3180i 0.404042 + 0.914740i
\(246\) 0 0
\(247\) 1.42339 + 5.31218i 0.0905683 + 0.338006i
\(248\) 0 0
\(249\) −13.2858 + 7.67055i −0.841952 + 0.486101i
\(250\) 0 0
\(251\) 5.49938i 0.347118i −0.984824 0.173559i \(-0.944473\pi\)
0.984824 0.173559i \(-0.0555267\pi\)
\(252\) 0 0
\(253\) −2.78028 2.78028i −0.174795 0.174795i
\(254\) 0 0
\(255\) −13.7960 10.3225i −0.863939 0.646422i
\(256\) 0 0
\(257\) 15.9473 4.27307i 0.994766 0.266547i 0.275515 0.961297i \(-0.411152\pi\)
0.719251 + 0.694750i \(0.244485\pi\)
\(258\) 0 0
\(259\) −6.10065 + 3.56750i −0.379076 + 0.221674i
\(260\) 0 0
\(261\) −7.85135 + 13.5989i −0.485986 + 0.841753i
\(262\) 0 0
\(263\) 2.55217 9.52484i 0.157374 0.587327i −0.841517 0.540231i \(-0.818337\pi\)
0.998890 0.0470956i \(-0.0149965\pi\)
\(264\) 0 0
\(265\) −10.3508 4.14102i −0.635843 0.254381i
\(266\) 0 0
\(267\) 5.01010 5.01010i 0.306613 0.306613i
\(268\) 0 0
\(269\) 4.47922 + 7.75824i 0.273103 + 0.473028i 0.969655 0.244478i \(-0.0786167\pi\)
−0.696552 + 0.717506i \(0.745283\pi\)
\(270\) 0 0
\(271\) 19.7889 + 11.4251i 1.20209 + 0.694027i 0.961020 0.276480i \(-0.0891680\pi\)
0.241071 + 0.970507i \(0.422501\pi\)
\(272\) 0 0
\(273\) −6.42276 6.35186i −0.388723 0.384432i
\(274\) 0 0
\(275\) −1.04840 3.56437i −0.0632209 0.214940i
\(276\) 0 0
\(277\) −20.7995 5.57320i −1.24972 0.334861i −0.427491 0.904019i \(-0.640603\pi\)
−0.822228 + 0.569158i \(0.807269\pi\)
\(278\) 0 0
\(279\) 5.54552 0.332002
\(280\) 0 0
\(281\) −5.64885 −0.336982 −0.168491 0.985703i \(-0.553889\pi\)
−0.168491 + 0.985703i \(0.553889\pi\)
\(282\) 0 0
\(283\) 2.82870 + 0.757948i 0.168149 + 0.0450553i 0.341911 0.939732i \(-0.388926\pi\)
−0.173762 + 0.984788i \(0.555592\pi\)
\(284\) 0 0
\(285\) 3.07286 + 3.90559i 0.182021 + 0.231347i
\(286\) 0 0
\(287\) −2.08657 + 0.571524i −0.123166 + 0.0337360i
\(288\) 0 0
\(289\) −22.5473 13.0177i −1.32631 0.765747i
\(290\) 0 0
\(291\) 2.63038 + 4.55596i 0.154196 + 0.267075i
\(292\) 0 0
\(293\) −10.7875 + 10.7875i −0.630212 + 0.630212i −0.948121 0.317909i \(-0.897019\pi\)
0.317909 + 0.948121i \(0.397019\pi\)
\(294\) 0 0
\(295\) −5.24056 + 2.24558i −0.305117 + 0.130743i
\(296\) 0 0
\(297\) −1.04374 + 3.89528i −0.0605637 + 0.226027i
\(298\) 0 0
\(299\) 7.69020 13.3198i 0.444736 0.770305i
\(300\) 0 0
\(301\) −2.95689 + 5.18776i −0.170432 + 0.299018i
\(302\) 0 0
\(303\) −12.6866 + 3.39936i −0.728826 + 0.195288i
\(304\) 0 0
\(305\) 8.13624 10.8740i 0.465880 0.622645i
\(306\) 0 0
\(307\) −6.89201 6.89201i −0.393348 0.393348i 0.482531 0.875879i \(-0.339718\pi\)
−0.875879 + 0.482531i \(0.839718\pi\)
\(308\) 0 0
\(309\) 2.84982i 0.162121i
\(310\) 0 0
\(311\) 0.109136 0.0630096i 0.00618852 0.00357294i −0.496903 0.867806i \(-0.665529\pi\)
0.503091 + 0.864233i \(0.332196\pi\)
\(312\) 0 0
\(313\) −3.02662 11.2955i −0.171075 0.638459i −0.997187 0.0749536i \(-0.976119\pi\)
0.826112 0.563505i \(-0.190548\pi\)
\(314\) 0 0
\(315\) 8.91951 + 3.51112i 0.502558 + 0.197829i
\(316\) 0 0
\(317\) −2.83308 10.5732i −0.159122 0.593851i −0.998717 0.0506382i \(-0.983874\pi\)
0.839595 0.543212i \(-0.182792\pi\)
\(318\) 0 0
\(319\) 6.23657 3.60068i 0.349181 0.201600i
\(320\) 0 0
\(321\) 7.80001i 0.435354i
\(322\) 0 0
\(323\) 8.77670 + 8.77670i 0.488349 + 0.488349i
\(324\) 0 0
\(325\) 12.4062 7.56992i 0.688173 0.419904i
\(326\) 0 0
\(327\) −10.1665 + 2.72410i −0.562208 + 0.150643i
\(328\) 0 0
\(329\) 6.29002 + 10.7563i 0.346780 + 0.593016i
\(330\) 0 0
\(331\) −2.73019 + 4.72883i −0.150065 + 0.259920i −0.931251 0.364378i \(-0.881282\pi\)
0.781186 + 0.624298i \(0.214615\pi\)
\(332\) 0 0
\(333\) −1.12017 + 4.18052i −0.0613848 + 0.229091i
\(334\) 0 0
\(335\) −11.3717 + 28.4244i −0.621304 + 1.55299i
\(336\) 0 0
\(337\) 20.4823 20.4823i 1.11574 1.11574i 0.123385 0.992359i \(-0.460625\pi\)
0.992359 0.123385i \(-0.0393751\pi\)
\(338\) 0 0
\(339\) −0.255644 0.442788i −0.0138847 0.0240490i
\(340\) 0 0
\(341\) −2.20249 1.27161i −0.119272 0.0688615i
\(342\) 0 0
\(343\) 13.3120 + 12.8760i 0.718781 + 0.695237i
\(344\) 0 0
\(345\) 1.64674 13.8001i 0.0886576 0.742973i
\(346\) 0 0
\(347\) −20.8040 5.57442i −1.11682 0.299250i −0.347223 0.937783i \(-0.612875\pi\)
−0.769595 + 0.638532i \(0.779542\pi\)
\(348\) 0 0
\(349\) −12.5744 −0.673093 −0.336546 0.941667i \(-0.609259\pi\)
−0.336546 + 0.941667i \(0.609259\pi\)
\(350\) 0 0
\(351\) −15.7746 −0.841987
\(352\) 0 0
\(353\) 0.666012 + 0.178457i 0.0354482 + 0.00949832i 0.276500 0.961014i \(-0.410826\pi\)
−0.241051 + 0.970512i \(0.577492\pi\)
\(354\) 0 0
\(355\) 4.24371 35.5634i 0.225233 1.88751i
\(356\) 0 0
\(357\) −19.7215 5.16723i −1.04377 0.273479i
\(358\) 0 0
\(359\) −19.1381 11.0494i −1.01007 0.583165i −0.0988582 0.995102i \(-0.531519\pi\)
−0.911212 + 0.411937i \(0.864852\pi\)
\(360\) 0 0
\(361\) 7.71007 + 13.3542i 0.405793 + 0.702854i
\(362\) 0 0
\(363\) −8.67775 + 8.67775i −0.455464 + 0.455464i
\(364\) 0 0
\(365\) −7.35115 + 18.3747i −0.384777 + 0.961775i
\(366\) 0 0
\(367\) −3.47100 + 12.9539i −0.181185 + 0.676191i 0.814230 + 0.580542i \(0.197159\pi\)
−0.995415 + 0.0956487i \(0.969507\pi\)
\(368\) 0 0
\(369\) −0.662450 + 1.14740i −0.0344858 + 0.0597311i
\(370\) 0 0
\(371\) −13.1908 + 0.0732036i −0.684830 + 0.00380054i
\(372\) 0 0
\(373\) 14.4564 3.87359i 0.748526 0.200567i 0.135662 0.990755i \(-0.456684\pi\)
0.612864 + 0.790188i \(0.290017\pi\)
\(374\) 0 0
\(375\) 7.61017 10.7028i 0.392987 0.552691i
\(376\) 0 0
\(377\) 19.9189 + 19.9189i 1.02587 + 1.02587i
\(378\) 0 0
\(379\) 1.71784i 0.0882395i 0.999026 + 0.0441198i \(0.0140483\pi\)
−0.999026 + 0.0441198i \(0.985952\pi\)
\(380\) 0 0
\(381\) −16.0869 + 9.28776i −0.824156 + 0.475827i
\(382\) 0 0
\(383\) 2.70676 + 10.1017i 0.138309 + 0.516175i 0.999962 + 0.00867837i \(0.00276245\pi\)
−0.861654 + 0.507497i \(0.830571\pi\)
\(384\) 0 0
\(385\) −2.73741 3.43977i −0.139511 0.175307i
\(386\) 0 0
\(387\) 0.946464 + 3.53225i 0.0481114 + 0.179554i
\(388\) 0 0
\(389\) 18.8548 10.8858i 0.955978 0.551934i 0.0610449 0.998135i \(-0.480557\pi\)
0.894933 + 0.446201i \(0.147223\pi\)
\(390\) 0 0
\(391\) 34.7124i 1.75548i
\(392\) 0 0
\(393\) −7.96759 7.96759i −0.401912 0.401912i
\(394\) 0 0
\(395\) −8.81843 + 11.7858i −0.443703 + 0.593006i
\(396\) 0 0
\(397\) −30.6188 + 8.20427i −1.53671 + 0.411761i −0.925202 0.379476i \(-0.876104\pi\)
−0.611510 + 0.791237i \(0.709438\pi\)
\(398\) 0 0
\(399\) 5.10848 + 2.91170i 0.255744 + 0.145767i
\(400\) 0 0
\(401\) −6.98528 + 12.0989i −0.348828 + 0.604188i −0.986042 0.166499i \(-0.946754\pi\)
0.637213 + 0.770687i \(0.280087\pi\)
\(402\) 0 0
\(403\) 2.57480 9.60930i 0.128260 0.478673i
\(404\) 0 0
\(405\) −3.11146 + 1.33327i −0.154610 + 0.0662505i
\(406\) 0 0
\(407\) 1.40350 1.40350i 0.0695690 0.0695690i
\(408\) 0 0
\(409\) −9.36960 16.2286i −0.463297 0.802454i 0.535826 0.844328i \(-0.320000\pi\)
−0.999123 + 0.0418748i \(0.986667\pi\)
\(410\) 0 0
\(411\) 9.47010 + 5.46757i 0.467126 + 0.269695i
\(412\) 0 0
\(413\) −4.74360 + 4.79654i −0.233417 + 0.236022i
\(414\) 0 0
\(415\) −18.0582 22.9519i −0.886443 1.12666i
\(416\) 0 0
\(417\) 25.1555 + 6.74040i 1.23187 + 0.330079i
\(418\) 0 0
\(419\) 31.5744 1.54251 0.771255 0.636526i \(-0.219629\pi\)
0.771255 + 0.636526i \(0.219629\pi\)
\(420\) 0 0
\(421\) −13.5569 −0.660722 −0.330361 0.943855i \(-0.607171\pi\)
−0.330361 + 0.943855i \(0.607171\pi\)
\(422\) 0 0
\(423\) 7.37087 + 1.97502i 0.358384 + 0.0960287i
\(424\) 0 0
\(425\) 15.7063 28.7958i 0.761866 1.39680i
\(426\) 0 0
\(427\) 4.07282 15.5445i 0.197097 0.752252i
\(428\) 0 0
\(429\) 2.19711 + 1.26850i 0.106078 + 0.0612439i
\(430\) 0 0
\(431\) 6.63518 + 11.4925i 0.319605 + 0.553572i 0.980406 0.196989i \(-0.0631164\pi\)
−0.660800 + 0.750562i \(0.729783\pi\)
\(432\) 0 0
\(433\) 12.0535 12.0535i 0.579252 0.579252i −0.355445 0.934697i \(-0.615671\pi\)
0.934697 + 0.355445i \(0.115671\pi\)
\(434\) 0 0
\(435\) 23.6334 + 9.45497i 1.13313 + 0.453331i
\(436\) 0 0
\(437\) −2.59121 + 9.67052i −0.123954 + 0.462604i
\(438\) 0 0
\(439\) −17.5238 + 30.3521i −0.836366 + 1.44863i 0.0565475 + 0.998400i \(0.481991\pi\)
−0.892913 + 0.450228i \(0.851343\pi\)
\(440\) 0 0
\(441\) 11.3413 0.125883i 0.540060 0.00599443i
\(442\) 0 0
\(443\) −0.0609189 + 0.0163232i −0.00289435 + 0.000775538i −0.260266 0.965537i \(-0.583810\pi\)
0.257372 + 0.966313i \(0.417144\pi\)
\(444\) 0 0
\(445\) 10.7997 + 8.08060i 0.511954 + 0.383057i
\(446\) 0 0
\(447\) 3.27444 + 3.27444i 0.154876 + 0.154876i
\(448\) 0 0
\(449\) 24.5207i 1.15720i 0.815611 + 0.578601i \(0.196401\pi\)
−0.815611 + 0.578601i \(0.803599\pi\)
\(450\) 0 0
\(451\) 0.526205 0.303804i 0.0247780 0.0143056i
\(452\) 0 0
\(453\) 6.06364 + 22.6298i 0.284894 + 1.06324i
\(454\) 0 0
\(455\) 10.2254 13.8255i 0.479376 0.648151i
\(456\) 0 0
\(457\) 5.19531 + 19.3892i 0.243027 + 0.906987i 0.974365 + 0.224973i \(0.0722293\pi\)
−0.731339 + 0.682015i \(0.761104\pi\)
\(458\) 0 0
\(459\) −30.8324 + 17.8011i −1.43913 + 0.830884i
\(460\) 0 0
\(461\) 11.6940i 0.544642i −0.962207 0.272321i \(-0.912209\pi\)
0.962207 0.272321i \(-0.0877912\pi\)
\(462\) 0 0
\(463\) −2.77226 2.77226i −0.128838 0.128838i 0.639747 0.768585i \(-0.279039\pi\)
−0.768585 + 0.639747i \(0.779039\pi\)
\(464\) 0 0
\(465\) −1.28141 8.89765i −0.0594239 0.412619i
\(466\) 0 0
\(467\) 20.2080 5.41472i 0.935116 0.250563i 0.241081 0.970505i \(-0.422498\pi\)
0.694035 + 0.719942i \(0.255831\pi\)
\(468\) 0 0
\(469\) 0.201026 + 36.2233i 0.00928250 + 1.67264i
\(470\) 0 0
\(471\) 4.38327 7.59205i 0.201971 0.349823i
\(472\) 0 0
\(473\) 0.434055 1.61992i 0.0199579 0.0744838i
\(474\) 0 0
\(475\) −6.52514 + 6.84976i −0.299394 + 0.314289i
\(476\) 0 0
\(477\) −5.71218 + 5.71218i −0.261543 + 0.261543i
\(478\) 0 0
\(479\) 12.1419 + 21.0303i 0.554775 + 0.960899i 0.997921 + 0.0644496i \(0.0205292\pi\)
−0.443145 + 0.896450i \(0.646137\pi\)
\(480\) 0 0
\(481\) 6.72392 + 3.88206i 0.306584 + 0.177007i
\(482\) 0 0
\(483\) −4.34420 15.8602i −0.197668 0.721663i
\(484\) 0 0
\(485\) −7.87065 + 6.19252i −0.357388 + 0.281188i
\(486\) 0 0
\(487\) 2.46890 + 0.661539i 0.111876 + 0.0299772i 0.314323 0.949316i \(-0.398223\pi\)
−0.202446 + 0.979293i \(0.564889\pi\)
\(488\) 0 0
\(489\) −14.2910 −0.646262
\(490\) 0 0
\(491\) −14.5668 −0.657391 −0.328695 0.944436i \(-0.606609\pi\)
−0.328695 + 0.944436i \(0.606609\pi\)
\(492\) 0 0
\(493\) 61.4102 + 16.4548i 2.76578 + 0.741088i
\(494\) 0 0
\(495\) −2.67323 0.318991i −0.120153 0.0143376i
\(496\) 0 0
\(497\) −11.1951 40.8722i −0.502171 1.83337i
\(498\) 0 0
\(499\) 26.0565 + 15.0437i 1.16645 + 0.673450i 0.952841 0.303469i \(-0.0981450\pi\)
0.213608 + 0.976919i \(0.431478\pi\)
\(500\) 0 0
\(501\) −1.20902 2.09409i −0.0540152 0.0935572i
\(502\) 0 0
\(503\) 24.6819 24.6819i 1.10051 1.10051i 0.106161 0.994349i \(-0.466144\pi\)
0.994349 0.106161i \(-0.0338558\pi\)
\(504\) 0 0
\(505\) −9.84777 22.9819i −0.438220 1.02268i
\(506\) 0 0
\(507\) 1.38365 5.16386i 0.0614501 0.229335i
\(508\) 0 0
\(509\) 6.22521 10.7824i 0.275927 0.477920i −0.694441 0.719549i \(-0.744348\pi\)
0.970369 + 0.241629i \(0.0776817\pi\)
\(510\) 0 0
\(511\) 0.129951 + 23.4162i 0.00574869 + 1.03587i
\(512\) 0 0
\(513\) 9.91839 2.65762i 0.437908 0.117337i
\(514\) 0 0
\(515\) −5.36969 + 0.773324i −0.236617 + 0.0340767i
\(516\) 0 0
\(517\) −2.47458 2.47458i −0.108832 0.108832i
\(518\) 0 0
\(519\) 11.0509i 0.485079i
\(520\) 0 0
\(521\) 30.6011 17.6676i 1.34066 0.774030i 0.353756 0.935338i \(-0.384904\pi\)
0.986904 + 0.161308i \(0.0515711\pi\)
\(522\) 0 0
\(523\) 4.25513 + 15.8804i 0.186064 + 0.694400i 0.994400 + 0.105679i \(0.0337016\pi\)
−0.808336 + 0.588721i \(0.799632\pi\)
\(524\) 0 0
\(525\) 3.57247 15.1225i 0.155916 0.659998i
\(526\) 0 0
\(527\) −5.81115 21.6875i −0.253137 0.944722i
\(528\) 0 0
\(529\) 4.32938 2.49957i 0.188234 0.108677i
\(530\) 0 0
\(531\) 4.13131i 0.179283i
\(532\) 0 0
\(533\) 1.68063 + 1.68063i 0.0727964 + 0.0727964i
\(534\) 0 0
\(535\) 14.6969 2.11660i 0.635404 0.0915086i
\(536\) 0 0
\(537\) −5.10281 + 1.36729i −0.220202 + 0.0590031i
\(538\) 0 0
\(539\) −4.53322 2.55059i −0.195260 0.109862i
\(540\) 0 0
\(541\) 13.2572 22.9621i 0.569970 0.987218i −0.426598 0.904441i \(-0.640288\pi\)
0.996568 0.0827763i \(-0.0263787\pi\)
\(542\) 0 0
\(543\) −5.43727 + 20.2922i −0.233336 + 0.870820i
\(544\) 0 0
\(545\) −7.89157 18.4167i −0.338038 0.788884i
\(546\) 0 0
\(547\) 1.07403 1.07403i 0.0459223 0.0459223i −0.683773 0.729695i \(-0.739662\pi\)
0.729695 + 0.683773i \(0.239662\pi\)
\(548\) 0 0
\(549\) −4.92046 8.52249i −0.210000 0.363731i
\(550\) 0 0
\(551\) −15.8799 9.16828i −0.676507 0.390582i
\(552\) 0 0
\(553\) −4.41431 + 16.8479i −0.187715 + 0.716444i
\(554\) 0 0
\(555\) 6.96638 + 0.831285i 0.295706 + 0.0352861i
\(556\) 0 0
\(557\) −15.0145 4.02313i −0.636186 0.170466i −0.0737108 0.997280i \(-0.523484\pi\)
−0.562475 + 0.826814i \(0.690151\pi\)
\(558\) 0 0
\(559\) 6.56014 0.277464
\(560\) 0 0
\(561\) 5.72584 0.241745
\(562\) 0 0
\(563\) 26.5108 + 7.10355i 1.11730 + 0.299379i 0.769789 0.638298i \(-0.220361\pi\)
0.347508 + 0.937677i \(0.387028\pi\)
\(564\) 0 0
\(565\) 0.764940 0.601844i 0.0321813 0.0253198i
\(566\) 0 0
\(567\) −2.81641 + 2.84784i −0.118278 + 0.119598i
\(568\) 0 0
\(569\) 5.85207 + 3.37869i 0.245332 + 0.141642i 0.617625 0.786473i \(-0.288095\pi\)
−0.372293 + 0.928115i \(0.621428\pi\)
\(570\) 0 0
\(571\) 5.87721 + 10.1796i 0.245953 + 0.426004i 0.962399 0.271639i \(-0.0875656\pi\)
−0.716446 + 0.697643i \(0.754232\pi\)
\(572\) 0 0
\(573\) 2.30526 2.30526i 0.0963034 0.0963034i
\(574\) 0 0
\(575\) 26.4493 0.641957i 1.10301 0.0267715i
\(576\) 0 0
\(577\) 0.583767 2.17865i 0.0243025 0.0906983i −0.952709 0.303883i \(-0.901717\pi\)
0.977012 + 0.213184i \(0.0683835\pi\)
\(578\) 0 0
\(579\) 3.01879 5.22870i 0.125457 0.217297i
\(580\) 0 0
\(581\) −30.0209 17.1111i −1.24547 0.709889i
\(582\) 0 0
\(583\) 3.57851 0.958858i 0.148207 0.0397118i
\(584\) 0 0
\(585\) −1.50115 10.4235i −0.0620649 0.430957i
\(586\) 0 0
\(587\) 12.8372 + 12.8372i 0.529847 + 0.529847i 0.920527 0.390680i \(-0.127760\pi\)
−0.390680 + 0.920527i \(0.627760\pi\)
\(588\) 0 0
\(589\) 6.47569i 0.266826i
\(590\) 0 0
\(591\) −1.92835 + 1.11333i −0.0793218 + 0.0457965i
\(592\) 0 0
\(593\) 9.40957 + 35.1170i 0.386405 + 1.44208i 0.835940 + 0.548820i \(0.184923\pi\)
−0.449535 + 0.893262i \(0.648410\pi\)
\(594\) 0 0
\(595\) 4.38460 38.5618i 0.179751 1.58088i
\(596\) 0 0
\(597\) 4.40908 + 16.4549i 0.180452 + 0.673455i
\(598\) 0 0
\(599\) 30.9792 17.8858i 1.26578 0.730796i 0.291589 0.956544i \(-0.405816\pi\)
0.974186 + 0.225748i \(0.0724826\pi\)
\(600\) 0 0
\(601\) 45.6631i 1.86264i 0.364204 + 0.931319i \(0.381341\pi\)
−0.364204 + 0.931319i \(0.618659\pi\)
\(602\) 0 0
\(603\) 15.6863 + 15.6863i 0.638796 + 0.638796i
\(604\) 0 0
\(605\) −18.7056 13.9960i −0.760490 0.569019i
\(606\) 0 0
\(607\) 1.13151 0.303188i 0.0459267 0.0123060i −0.235783 0.971806i \(-0.575765\pi\)
0.281709 + 0.959500i \(0.409099\pi\)
\(608\) 0 0
\(609\) 30.1177 0.167142i 1.22043 0.00677293i
\(610\) 0 0
\(611\) 6.84463 11.8553i 0.276904 0.479612i
\(612\) 0 0
\(613\) −3.60737 + 13.4629i −0.145700 + 0.543760i 0.854023 + 0.520235i \(0.174156\pi\)
−0.999723 + 0.0235253i \(0.992511\pi\)
\(614\) 0 0
\(615\) 1.99404 + 0.797755i 0.0804076 + 0.0321686i
\(616\) 0 0
\(617\) 22.7725 22.7725i 0.916788 0.916788i −0.0800065 0.996794i \(-0.525494\pi\)
0.996794 + 0.0800065i \(0.0254941\pi\)
\(618\) 0 0
\(619\) −11.3386 19.6391i −0.455738 0.789361i 0.542992 0.839738i \(-0.317291\pi\)
−0.998730 + 0.0503763i \(0.983958\pi\)
\(620\) 0 0
\(621\) −24.8695 14.3584i −0.997978 0.576183i
\(622\) 0 0
\(623\) 15.4382 + 4.04497i 0.618520 + 0.162058i
\(624\) 0 0
\(625\) 22.2316 + 11.4349i 0.889263 + 0.457397i
\(626\) 0 0
\(627\) −1.59516 0.427421i −0.0637045 0.0170696i
\(628\) 0 0
\(629\) 17.5231 0.698690
\(630\) 0 0
\(631\) −32.4210 −1.29066 −0.645330 0.763904i \(-0.723280\pi\)
−0.645330 + 0.763904i \(0.723280\pi\)
\(632\) 0 0
\(633\) 11.3827 + 3.04998i 0.452421 + 0.121226i
\(634\) 0 0
\(635\) −21.8655 27.7909i −0.867706 1.10285i
\(636\) 0 0
\(637\) 5.04765 19.7106i 0.199995 0.780963i
\(638\) 0 0
\(639\) −22.4755 12.9762i −0.889116 0.513331i
\(640\) 0 0
\(641\) 0.428070 + 0.741439i 0.0169077 + 0.0292851i 0.874355 0.485286i \(-0.161285\pi\)
−0.857448 + 0.514571i \(0.827951\pi\)
\(642\) 0 0
\(643\) −16.4254 + 16.4254i −0.647754 + 0.647754i −0.952450 0.304696i \(-0.901445\pi\)
0.304696 + 0.952450i \(0.401445\pi\)
\(644\) 0 0
\(645\) 5.44871 2.33478i 0.214543 0.0919317i
\(646\) 0 0
\(647\) 12.2805 45.8316i 0.482798 1.80183i −0.106982 0.994261i \(-0.534119\pi\)
0.589779 0.807564i \(-0.299215\pi\)
\(648\) 0 0
\(649\) 0.947323 1.64081i 0.0371857 0.0644075i
\(650\) 0 0
\(651\) −5.36927 9.18179i −0.210438 0.359863i
\(652\) 0 0
\(653\) −25.3781 + 6.80004i −0.993121 + 0.266106i −0.718561 0.695464i \(-0.755199\pi\)
−0.274560 + 0.961570i \(0.588532\pi\)
\(654\) 0 0
\(655\) 12.8506 17.1748i 0.502115 0.671074i
\(656\) 0 0
\(657\) 10.1403 + 10.1403i 0.395609 + 0.395609i
\(658\) 0 0
\(659\) 26.2355i 1.02199i 0.859583 + 0.510996i \(0.170723\pi\)
−0.859583 + 0.510996i \(0.829277\pi\)
\(660\) 0 0
\(661\) −12.6197 + 7.28597i −0.490848 + 0.283391i −0.724926 0.688827i \(-0.758126\pi\)
0.234078 + 0.972218i \(0.424793\pi\)
\(662\) 0 0
\(663\) 5.79695 + 21.6345i 0.225135 + 0.840215i
\(664\) 0 0
\(665\) −4.10006 + 10.4156i −0.158993 + 0.403900i
\(666\) 0 0
\(667\) 13.2725 + 49.5336i 0.513913 + 1.91795i
\(668\) 0 0
\(669\) 4.51371 2.60599i 0.174510 0.100753i
\(670\) 0 0
\(671\) 4.51312i 0.174227i
\(672\) 0 0
\(673\) −16.4201 16.4201i −0.632950 0.632950i 0.315857 0.948807i \(-0.397708\pi\)
−0.948807 + 0.315857i \(0.897708\pi\)
\(674\) 0 0
\(675\) −14.1338 23.1637i −0.544011 0.891571i
\(676\) 0 0
\(677\) −21.9882 + 5.89172i −0.845075 + 0.226437i −0.655280 0.755386i \(-0.727449\pi\)
−0.189796 + 0.981824i \(0.560783\pi\)
\(678\) 0 0
\(679\) −5.86774 + 10.2947i −0.225183 + 0.395076i
\(680\) 0 0
\(681\) 0.394008 0.682442i 0.0150984 0.0261512i
\(682\) 0 0
\(683\) −7.93034 + 29.5964i −0.303446 + 1.13248i 0.630829 + 0.775922i \(0.282715\pi\)
−0.934275 + 0.356554i \(0.883952\pi\)
\(684\) 0 0
\(685\) −7.73231 + 19.3274i −0.295436 + 0.738463i
\(686\) 0 0
\(687\) −10.9664 + 10.9664i −0.418394 + 0.418394i
\(688\) 0 0
\(689\) 7.24590 + 12.5503i 0.276047 + 0.478127i
\(690\) 0 0
\(691\) −27.7284 16.0090i −1.05484 0.609012i −0.130839 0.991404i \(-0.541767\pi\)
−0.924000 + 0.382392i \(0.875100\pi\)
\(692\) 0 0
\(693\) −3.07228 + 0.841516i −0.116706 + 0.0319665i
\(694\) 0 0
\(695\) −5.87423 + 49.2276i −0.222822 + 1.86731i
\(696\) 0 0
\(697\) 5.18143 + 1.38836i 0.196261 + 0.0525879i
\(698\) 0 0
\(699\) −10.1709 −0.384699
\(700\) 0 0
\(701\) −18.5294 −0.699844 −0.349922 0.936779i \(-0.613792\pi\)
−0.349922 + 0.936779i \(0.613792\pi\)
\(702\) 0 0
\(703\) −4.88174 1.30806i −0.184118 0.0493343i
\(704\) 0 0
\(705\) 1.46568 12.2827i 0.0552006 0.462595i
\(706\) 0 0
\(707\) −21.0347 20.8025i −0.791092 0.782360i
\(708\) 0 0
\(709\) 23.1074 + 13.3411i 0.867818 + 0.501035i 0.866622 0.498965i \(-0.166286\pi\)
0.00119522 + 0.999999i \(0.499620\pi\)
\(710\) 0 0
\(711\) 5.33302 + 9.23706i 0.200004 + 0.346417i
\(712\) 0 0
\(713\) 12.8059 12.8059i 0.479585 0.479585i
\(714\) 0 0
\(715\) −1.79393 + 4.48406i −0.0670893 + 0.167694i
\(716\) 0 0
\(717\) 1.21695 4.54170i 0.0454477 0.169613i
\(718\) 0 0
\(719\) −15.9890 + 27.6937i −0.596288 + 1.03280i 0.397076 + 0.917786i \(0.370025\pi\)
−0.993364 + 0.115015i \(0.963308\pi\)
\(720\) 0 0
\(721\) −5.54117 + 3.24033i −0.206364 + 0.120676i
\(722\) 0 0
\(723\) 19.6569 5.26706i 0.731049 0.195884i
\(724\) 0 0
\(725\) −11.4021 + 47.0961i −0.423465 + 1.74911i
\(726\) 0 0
\(727\) 21.4539 + 21.4539i 0.795683 + 0.795683i 0.982412 0.186729i \(-0.0597885\pi\)
−0.186729 + 0.982412i \(0.559789\pi\)
\(728\) 0 0
\(729\) 21.5770i 0.799146i
\(730\) 0 0
\(731\) 12.8222 7.40288i 0.474245 0.273805i
\(732\) 0 0
\(733\) −3.36789 12.5691i −0.124396 0.464252i 0.875422 0.483360i \(-0.160584\pi\)
−0.999817 + 0.0191085i \(0.993917\pi\)
\(734\) 0 0
\(735\) −2.82261 18.1677i −0.104113 0.670125i
\(736\) 0 0
\(737\) −2.63314 9.82700i −0.0969928 0.361982i
\(738\) 0 0
\(739\) −3.12136 + 1.80212i −0.114821 + 0.0662920i −0.556311 0.830974i \(-0.687784\pi\)
0.441490 + 0.897266i \(0.354450\pi\)
\(740\) 0 0
\(741\) 6.45988i 0.237309i
\(742\) 0 0
\(743\) −31.1070 31.1070i −1.14121 1.14121i −0.988230 0.152977i \(-0.951114\pi\)
−0.152977 0.988230i \(-0.548886\pi\)
\(744\) 0 0
\(745\) −5.28121 + 7.05831i −0.193489 + 0.258596i
\(746\) 0 0
\(747\) −20.4406 + 5.47705i −0.747884 + 0.200395i
\(748\) 0 0
\(749\) 15.1663 8.86884i 0.554164 0.324060i
\(750\) 0 0
\(751\) −25.5141 + 44.1917i −0.931023 + 1.61258i −0.149447 + 0.988770i \(0.547749\pi\)
−0.781576 + 0.623810i \(0.785584\pi\)
\(752\) 0 0
\(753\) −1.67188 + 6.23954i −0.0609267 + 0.227382i
\(754\) 0 0
\(755\) −40.9941 + 17.5660i −1.49193 + 0.639293i
\(756\) 0 0
\(757\) 26.8141 26.8141i 0.974576 0.974576i −0.0251083 0.999685i \(-0.507993\pi\)
0.999685 + 0.0251083i \(0.00799305\pi\)
\(758\) 0 0
\(759\) 2.30924 + 3.99972i 0.0838200 + 0.145181i
\(760\) 0 0
\(761\) −25.8753 14.9391i −0.937980 0.541543i −0.0486532 0.998816i \(-0.515493\pi\)
−0.889326 + 0.457273i \(0.848826\pi\)
\(762\) 0 0
\(763\) −16.8563 16.6702i −0.610239 0.603503i
\(764\) 0 0
\(765\) −14.6966 18.6793i −0.531357 0.675351i
\(766\) 0 0
\(767\) 7.15874 + 1.91818i 0.258487 + 0.0692614i
\(768\) 0 0
\(769\) −44.7341 −1.61315 −0.806576 0.591130i \(-0.798682\pi\)
−0.806576 + 0.591130i \(0.798682\pi\)
\(770\) 0 0
\(771\) −19.3927 −0.698413
\(772\) 0 0
\(773\) −23.3328 6.25202i −0.839224 0.224869i −0.186490 0.982457i \(-0.559711\pi\)
−0.652734 + 0.757587i \(0.726378\pi\)
\(774\) 0 0
\(775\) 16.4174 4.82891i 0.589731 0.173460i
\(776\) 0 0
\(777\) 8.00631 2.19298i 0.287225 0.0786726i
\(778\) 0 0
\(779\) −1.33985 0.773565i −0.0480052 0.0277158i
\(780\) 0 0
\(781\) 5.95099 + 10.3074i 0.212943 + 0.368828i
\(782\) 0 0
\(783\) 37.1906 37.1906i 1.32908 1.32908i
\(784\) 0 0
\(785\) 15.4945 + 6.19889i 0.553024 + 0.221248i
\(786\) 0 0
\(787\) −3.28689 + 12.2669i −0.117165 + 0.437266i −0.999440 0.0334688i \(-0.989345\pi\)
0.882275 + 0.470735i \(0.156011\pi\)
\(788\) 0 0
\(789\) −5.79134 + 10.0309i −0.206177 + 0.357110i
\(790\) 0 0
\(791\) 0.570279 1.00054i 0.0202768 0.0355749i
\(792\) 0 0
\(793\) −17.0524 + 4.56917i −0.605547 + 0.162256i