Properties

Label 252.2.w.a.5.8
Level $252$
Weight $2$
Character 252.5
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.w (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.8
Root \(-0.544978 + 1.64408i\) of defining polynomial
Character \(\chi\) \(=\) 252.5
Dual form 252.2.w.a.101.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.70992 + 0.276016i) q^{3} +(-1.95741 - 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +(2.84763 + 0.943929i) q^{9} +O(q^{10})\) \(q+(1.70992 + 0.276016i) q^{3} +(-1.95741 - 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +(2.84763 + 0.943929i) q^{9} +(-3.19958 - 1.84728i) q^{11} +(0.480242 + 0.277268i) q^{13} +(-2.41122 - 6.33747i) q^{15} +(2.91916 + 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} +(1.66177 - 4.27066i) q^{21} +(-1.96965 + 1.13718i) q^{23} +(-5.16291 + 8.94242i) q^{25} +(4.60867 + 2.40003i) q^{27} +(3.53638 - 2.04173i) q^{29} +8.08443i q^{31} +(-4.96114 - 4.04183i) q^{33} +(-9.85583 + 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +(0.744643 + 0.606659i) q^{39} +(3.59234 - 6.22212i) q^{41} +(-0.754009 - 1.30598i) q^{43} +(-2.37374 - 11.5021i) q^{45} -2.82833 q^{47} +(-6.38563 - 2.86770i) q^{49} +(3.59594 + 9.45130i) q^{51} +(-0.0415658 + 0.0239980i) q^{53} +14.4635i q^{55} +(7.17031 + 5.84164i) q^{57} -8.91313 q^{59} +6.96680i q^{61} +(4.02026 - 6.84379i) q^{63} -2.17091i q^{65} +1.17480 q^{67} +(-3.68181 + 1.40082i) q^{69} +6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(-11.2964 + 13.8658i) q^{75} +(-6.55234 + 7.25364i) q^{77} -3.94747 q^{79} +(7.21799 + 5.37592i) q^{81} +(3.84674 + 6.66275i) q^{83} +(11.4280 - 19.7938i) q^{85} +(6.61047 - 2.51509i) q^{87} +(-2.71300 + 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +(-2.23143 + 13.8237i) q^{93} -20.9041i q^{95} +(13.9874 - 8.07563i) q^{97} +(-7.36753 - 8.28055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + 6q^{9} + O(q^{10}) \) \( 16q - q^{7} + 6q^{9} - 6q^{11} - 3q^{13} - 3q^{15} + 9q^{17} + 6q^{21} + 21q^{23} - 8q^{25} + 9q^{27} + 6q^{29} - 15q^{35} + q^{37} - 3q^{39} - 6q^{41} - 2q^{43} - 30q^{45} - 36q^{47} - 5q^{49} - 33q^{51} + 15q^{57} - 30q^{59} - 15q^{63} + 14q^{67} + 21q^{69} - 57q^{75} + 3q^{77} + 2q^{79} + 18q^{81} + 6q^{85} + 48q^{87} + 21q^{89} + 9q^{91} + 21q^{93} - 3q^{97} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) 1.70992 + 0.276016i 0.987221 + 0.159358i
\(4\) 0 0
\(5\) −1.95741 3.39033i −0.875381 1.51620i −0.856357 0.516385i \(-0.827278\pi\)
−0.0190238 0.999819i \(-0.506056\pi\)
\(6\) 0 0
\(7\) 0.554241 2.58705i 0.209483 0.977812i
\(8\) 0 0
\(9\) 2.84763 + 0.943929i 0.949210 + 0.314643i
\(10\) 0 0
\(11\) −3.19958 1.84728i −0.964710 0.556976i −0.0670908 0.997747i \(-0.521372\pi\)
−0.897620 + 0.440771i \(0.854705\pi\)
\(12\) 0 0
\(13\) 0.480242 + 0.277268i 0.133195 + 0.0769002i 0.565117 0.825011i \(-0.308831\pi\)
−0.431922 + 0.901911i \(0.642164\pi\)
\(14\) 0 0
\(15\) −2.41122 6.33747i −0.622575 1.63633i
\(16\) 0 0
\(17\) 2.91916 + 5.05613i 0.708000 + 1.22629i 0.965598 + 0.260040i \(0.0837356\pi\)
−0.257598 + 0.966252i \(0.582931\pi\)
\(18\) 0 0
\(19\) 4.62434 + 2.66986i 1.06090 + 0.612509i 0.925680 0.378307i \(-0.123494\pi\)
0.135216 + 0.990816i \(0.456827\pi\)
\(20\) 0 0
\(21\) 1.66177 4.27066i 0.362629 0.931934i
\(22\) 0 0
\(23\) −1.96965 + 1.13718i −0.410700 + 0.237118i −0.691090 0.722768i \(-0.742869\pi\)
0.280390 + 0.959886i \(0.409536\pi\)
\(24\) 0 0
\(25\) −5.16291 + 8.94242i −1.03258 + 1.78848i
\(26\) 0 0
\(27\) 4.60867 + 2.40003i 0.886939 + 0.461887i
\(28\) 0 0
\(29\) 3.53638 2.04173i 0.656690 0.379140i −0.134325 0.990937i \(-0.542887\pi\)
0.791014 + 0.611797i \(0.209553\pi\)
\(30\) 0 0
\(31\) 8.08443i 1.45201i 0.687691 + 0.726004i \(0.258624\pi\)
−0.687691 + 0.726004i \(0.741376\pi\)
\(32\) 0 0
\(33\) −4.96114 4.04183i −0.863624 0.703592i
\(34\) 0 0
\(35\) −9.85583 + 3.18485i −1.66594 + 0.538338i
\(36\) 0 0
\(37\) 3.89849 6.75239i 0.640909 1.11009i −0.344322 0.938852i \(-0.611891\pi\)
0.985230 0.171235i \(-0.0547756\pi\)
\(38\) 0 0
\(39\) 0.744643 + 0.606659i 0.119238 + 0.0971432i
\(40\) 0 0
\(41\) 3.59234 6.22212i 0.561030 0.971732i −0.436377 0.899764i \(-0.643739\pi\)
0.997407 0.0719684i \(-0.0229281\pi\)
\(42\) 0 0
\(43\) −0.754009 1.30598i −0.114985 0.199160i 0.802789 0.596264i \(-0.203349\pi\)
−0.917774 + 0.397103i \(0.870015\pi\)
\(44\) 0 0
\(45\) −2.37374 11.5021i −0.353857 1.71463i
\(46\) 0 0
\(47\) −2.82833 −0.412554 −0.206277 0.978494i \(-0.566135\pi\)
−0.206277 + 0.978494i \(0.566135\pi\)
\(48\) 0 0
\(49\) −6.38563 2.86770i −0.912233 0.409671i
\(50\) 0 0
\(51\) 3.59594 + 9.45130i 0.503533 + 1.32345i
\(52\) 0 0
\(53\) −0.0415658 + 0.0239980i −0.00570950 + 0.00329638i −0.502852 0.864373i \(-0.667716\pi\)
0.497143 + 0.867669i \(0.334383\pi\)
\(54\) 0 0
\(55\) 14.4635i 1.95026i
\(56\) 0 0
\(57\) 7.17031 + 5.84164i 0.949731 + 0.773744i
\(58\) 0 0
\(59\) −8.91313 −1.16039 −0.580195 0.814477i \(-0.697024\pi\)
−0.580195 + 0.814477i \(0.697024\pi\)
\(60\) 0 0
\(61\) 6.96680i 0.892008i 0.895031 + 0.446004i \(0.147153\pi\)
−0.895031 + 0.446004i \(0.852847\pi\)
\(62\) 0 0
\(63\) 4.02026 6.84379i 0.506506 0.862237i
\(64\) 0 0
\(65\) 2.17091i 0.269268i
\(66\) 0 0
\(67\) 1.17480 0.143525 0.0717626 0.997422i \(-0.477138\pi\)
0.0717626 + 0.997422i \(0.477138\pi\)
\(68\) 0 0
\(69\) −3.68181 + 1.40082i −0.443238 + 0.168639i
\(70\) 0 0
\(71\) 6.71061i 0.796403i 0.917298 + 0.398202i \(0.130366\pi\)
−0.917298 + 0.398202i \(0.869634\pi\)
\(72\) 0 0
\(73\) −3.52692 + 2.03627i −0.412795 + 0.238327i −0.691990 0.721907i \(-0.743266\pi\)
0.279195 + 0.960234i \(0.409932\pi\)
\(74\) 0 0
\(75\) −11.2964 + 13.8658i −1.30440 + 1.60108i
\(76\) 0 0
\(77\) −6.55234 + 7.25364i −0.746709 + 0.826628i
\(78\) 0 0
\(79\) −3.94747 −0.444125 −0.222063 0.975032i \(-0.571279\pi\)
−0.222063 + 0.975032i \(0.571279\pi\)
\(80\) 0 0
\(81\) 7.21799 + 5.37592i 0.801999 + 0.597325i
\(82\) 0 0
\(83\) 3.84674 + 6.66275i 0.422235 + 0.731332i 0.996158 0.0875774i \(-0.0279125\pi\)
−0.573923 + 0.818909i \(0.694579\pi\)
\(84\) 0 0
\(85\) 11.4280 19.7938i 1.23954 2.14694i
\(86\) 0 0
\(87\) 6.61047 2.51509i 0.708717 0.269646i
\(88\) 0 0
\(89\) −2.71300 + 4.69905i −0.287577 + 0.498099i −0.973231 0.229829i \(-0.926183\pi\)
0.685654 + 0.727928i \(0.259517\pi\)
\(90\) 0 0
\(91\) 0.983474 1.08874i 0.103096 0.114130i
\(92\) 0 0
\(93\) −2.23143 + 13.8237i −0.231389 + 1.43345i
\(94\) 0 0
\(95\) 20.9041i 2.14471i
\(96\) 0 0
\(97\) 13.9874 8.07563i 1.42021 0.819956i 0.423890 0.905714i \(-0.360664\pi\)
0.996316 + 0.0857571i \(0.0273309\pi\)
\(98\) 0 0
\(99\) −7.36753 8.28055i −0.740464 0.832227i
\(100\) 0 0
\(101\) 0.811750 1.40599i 0.0807722 0.139901i −0.822810 0.568317i \(-0.807595\pi\)
0.903582 + 0.428416i \(0.140928\pi\)
\(102\) 0 0
\(103\) −0.342653 + 0.197831i −0.0337626 + 0.0194929i −0.516786 0.856114i \(-0.672872\pi\)
0.483024 + 0.875607i \(0.339539\pi\)
\(104\) 0 0
\(105\) −17.7317 + 2.72546i −1.73044 + 0.265978i
\(106\) 0 0
\(107\) −4.90777 2.83350i −0.474452 0.273925i 0.243650 0.969863i \(-0.421655\pi\)
−0.718101 + 0.695938i \(0.754989\pi\)
\(108\) 0 0
\(109\) −6.75667 11.7029i −0.647171 1.12093i −0.983795 0.179294i \(-0.942619\pi\)
0.336624 0.941639i \(-0.390715\pi\)
\(110\) 0 0
\(111\) 8.52987 10.4700i 0.809619 0.993766i
\(112\) 0 0
\(113\) 1.13651 + 0.656162i 0.106913 + 0.0617265i 0.552503 0.833511i \(-0.313673\pi\)
−0.445590 + 0.895237i \(0.647006\pi\)
\(114\) 0 0
\(115\) 7.71082 + 4.45184i 0.719038 + 0.415137i
\(116\) 0 0
\(117\) 1.10583 + 1.24287i 0.102234 + 0.114903i
\(118\) 0 0
\(119\) 14.6984 4.74969i 1.34740 0.435403i
\(120\) 0 0
\(121\) 1.32489 + 2.29477i 0.120444 + 0.208615i
\(122\) 0 0
\(123\) 7.86002 9.64777i 0.708714 0.869910i
\(124\) 0 0
\(125\) 20.8496 1.86485
\(126\) 0 0
\(127\) −17.3935 −1.54342 −0.771710 0.635975i \(-0.780598\pi\)
−0.771710 + 0.635975i \(0.780598\pi\)
\(128\) 0 0
\(129\) −0.928820 2.44124i −0.0817780 0.214939i
\(130\) 0 0
\(131\) 5.45361 + 9.44593i 0.476484 + 0.825295i 0.999637 0.0269442i \(-0.00857764\pi\)
−0.523153 + 0.852239i \(0.675244\pi\)
\(132\) 0 0
\(133\) 9.47007 10.4836i 0.821159 0.909047i
\(134\) 0 0
\(135\) −0.884146 20.3228i −0.0760952 1.74911i
\(136\) 0 0
\(137\) 7.62547 + 4.40257i 0.651488 + 0.376137i 0.789026 0.614360i \(-0.210586\pi\)
−0.137538 + 0.990496i \(0.543919\pi\)
\(138\) 0 0
\(139\) −14.2352 8.21869i −1.20741 0.697100i −0.245220 0.969468i \(-0.578860\pi\)
−0.962193 + 0.272367i \(0.912193\pi\)
\(140\) 0 0
\(141\) −4.83621 0.780664i −0.407282 0.0657438i
\(142\) 0 0
\(143\) −1.02438 1.77428i −0.0856631 0.148373i
\(144\) 0 0
\(145\) −13.8443 7.99301i −1.14971 0.663783i
\(146\) 0 0
\(147\) −10.1274 6.66606i −0.835292 0.549807i
\(148\) 0 0
\(149\) 12.5814 7.26390i 1.03071 0.595082i 0.113523 0.993535i \(-0.463786\pi\)
0.917188 + 0.398454i \(0.130453\pi\)
\(150\) 0 0
\(151\) −2.80307 + 4.85505i −0.228110 + 0.395099i −0.957248 0.289268i \(-0.906588\pi\)
0.729138 + 0.684367i \(0.239921\pi\)
\(152\) 0 0
\(153\) 3.54005 + 17.1535i 0.286196 + 1.38678i
\(154\) 0 0
\(155\) 27.4089 15.8246i 2.20154 1.27106i
\(156\) 0 0
\(157\) 17.8299i 1.42298i 0.702697 + 0.711489i \(0.251979\pi\)
−0.702697 + 0.711489i \(0.748021\pi\)
\(158\) 0 0
\(159\) −0.0776978 + 0.0295618i −0.00616184 + 0.00234440i
\(160\) 0 0
\(161\) 1.85027 + 5.72584i 0.145822 + 0.451260i
\(162\) 0 0
\(163\) −0.576994 + 0.999383i −0.0451937 + 0.0782777i −0.887737 0.460350i \(-0.847724\pi\)
0.842544 + 0.538628i \(0.181057\pi\)
\(164\) 0 0
\(165\) −3.99217 + 24.7314i −0.310790 + 1.92534i
\(166\) 0 0
\(167\) −8.95550 + 15.5114i −0.692997 + 1.20031i 0.277854 + 0.960623i \(0.410377\pi\)
−0.970851 + 0.239683i \(0.922957\pi\)
\(168\) 0 0
\(169\) −6.34625 10.9920i −0.488173 0.845540i
\(170\) 0 0
\(171\) 10.6482 + 11.9678i 0.814292 + 0.915203i
\(172\) 0 0
\(173\) 7.49629 0.569932 0.284966 0.958538i \(-0.408018\pi\)
0.284966 + 0.958538i \(0.408018\pi\)
\(174\) 0 0
\(175\) 20.2730 + 18.3130i 1.53249 + 1.38433i
\(176\) 0 0
\(177\) −15.2407 2.46017i −1.14556 0.184918i
\(178\) 0 0
\(179\) 0.624382 0.360487i 0.0466685 0.0269441i −0.476484 0.879183i \(-0.658089\pi\)
0.523153 + 0.852239i \(0.324756\pi\)
\(180\) 0 0
\(181\) 5.07121i 0.376940i −0.982079 0.188470i \(-0.939647\pi\)
0.982079 0.188470i \(-0.0603529\pi\)
\(182\) 0 0
\(183\) −1.92295 + 11.9127i −0.142149 + 0.880609i
\(184\) 0 0
\(185\) −30.5238 −2.24416
\(186\) 0 0
\(187\) 21.5700i 1.57736i
\(188\) 0 0
\(189\) 8.76331 10.5927i 0.637437 0.770502i
\(190\) 0 0
\(191\) 12.7022i 0.919101i 0.888152 + 0.459551i \(0.151989\pi\)
−0.888152 + 0.459551i \(0.848011\pi\)
\(192\) 0 0
\(193\) −22.8153 −1.64228 −0.821140 0.570726i \(-0.806662\pi\)
−0.821140 + 0.570726i \(0.806662\pi\)
\(194\) 0 0
\(195\) 0.599205 3.71207i 0.0429100 0.265827i
\(196\) 0 0
\(197\) 0.0311360i 0.00221835i 0.999999 + 0.00110918i \(0.000353062\pi\)
−0.999999 + 0.00110918i \(0.999647\pi\)
\(198\) 0 0
\(199\) 19.9144 11.4976i 1.41169 0.815042i 0.416146 0.909298i \(-0.363380\pi\)
0.995548 + 0.0942556i \(0.0300471\pi\)
\(200\) 0 0
\(201\) 2.00882 + 0.324265i 0.141691 + 0.0228719i
\(202\) 0 0
\(203\) −3.32205 10.2804i −0.233162 0.721543i
\(204\) 0 0
\(205\) −28.1268 −1.96446
\(206\) 0 0
\(207\) −6.68225 + 1.37905i −0.464448 + 0.0958506i
\(208\) 0 0
\(209\) −9.86397 17.0849i −0.682305 1.18179i
\(210\) 0 0
\(211\) 8.55841 14.8236i 0.589185 1.02050i −0.405154 0.914248i \(-0.632782\pi\)
0.994339 0.106250i \(-0.0338845\pi\)
\(212\) 0 0
\(213\) −1.85224 + 11.4746i −0.126913 + 0.786226i
\(214\) 0 0
\(215\) −2.95181 + 5.11268i −0.201312 + 0.348682i
\(216\) 0 0
\(217\) 20.9148 + 4.48072i 1.41979 + 0.304171i
\(218\) 0 0
\(219\) −6.59278 + 2.50836i −0.445499 + 0.169499i
\(220\) 0 0
\(221\) 3.23755i 0.217781i
\(222\) 0 0
\(223\) 1.25230 0.723016i 0.0838602 0.0484167i −0.457484 0.889218i \(-0.651249\pi\)
0.541344 + 0.840801i \(0.317916\pi\)
\(224\) 0 0
\(225\) −23.1431 + 20.5913i −1.54287 + 1.37275i
\(226\) 0 0
\(227\) −2.23596 + 3.87280i −0.148406 + 0.257047i −0.930639 0.365940i \(-0.880748\pi\)
0.782232 + 0.622987i \(0.214081\pi\)
\(228\) 0 0
\(229\) 2.24072 1.29368i 0.148071 0.0854888i −0.424134 0.905599i \(-0.639421\pi\)
0.572205 + 0.820111i \(0.306088\pi\)
\(230\) 0 0
\(231\) −13.2061 + 10.5946i −0.868896 + 0.697071i
\(232\) 0 0
\(233\) 15.0756 + 8.70389i 0.987634 + 0.570211i 0.904566 0.426333i \(-0.140195\pi\)
0.0830679 + 0.996544i \(0.473528\pi\)
\(234\) 0 0
\(235\) 5.53620 + 9.58898i 0.361142 + 0.625516i
\(236\) 0 0
\(237\) −6.74985 1.08957i −0.438450 0.0707750i
\(238\) 0 0
\(239\) 4.23642 + 2.44590i 0.274031 + 0.158212i 0.630718 0.776012i \(-0.282760\pi\)
−0.356687 + 0.934224i \(0.616094\pi\)
\(240\) 0 0
\(241\) 7.04282 + 4.06618i 0.453668 + 0.261925i 0.709378 0.704828i \(-0.248976\pi\)
−0.255710 + 0.966754i \(0.582309\pi\)
\(242\) 0 0
\(243\) 10.8583 + 11.1847i 0.696562 + 0.717497i
\(244\) 0 0
\(245\) 2.77686 + 27.2627i 0.177407 + 1.74175i
\(246\) 0 0
\(247\) 1.48053 + 2.56436i 0.0942041 + 0.163166i
\(248\) 0 0
\(249\) 4.73858 + 12.4545i 0.300295 + 0.789272i
\(250\) 0 0
\(251\) −25.9341 −1.63694 −0.818472 0.574546i \(-0.805179\pi\)
−0.818472 + 0.574546i \(0.805179\pi\)
\(252\) 0 0
\(253\) 8.40274 0.528276
\(254\) 0 0
\(255\) 25.0043 30.6915i 1.56583 1.92198i
\(256\) 0 0
\(257\) 15.4115 + 26.6935i 0.961344 + 1.66510i 0.719131 + 0.694874i \(0.244540\pi\)
0.242213 + 0.970223i \(0.422127\pi\)
\(258\) 0 0
\(259\) −15.3081 13.8280i −0.951196 0.859233i
\(260\) 0 0
\(261\) 11.9976 2.47600i 0.742630 0.153261i
\(262\) 0 0
\(263\) −15.6625 9.04276i −0.965792 0.557600i −0.0678413 0.997696i \(-0.521611\pi\)
−0.897951 + 0.440096i \(0.854944\pi\)
\(264\) 0 0
\(265\) 0.162723 + 0.0939479i 0.00999597 + 0.00577117i
\(266\) 0 0
\(267\) −5.93602 + 7.28616i −0.363278 + 0.445906i
\(268\) 0 0
\(269\) −10.8203 18.7413i −0.659725 1.14268i −0.980687 0.195585i \(-0.937339\pi\)
0.320961 0.947092i \(-0.395994\pi\)
\(270\) 0 0
\(271\) −12.3453 7.12756i −0.749923 0.432968i 0.0757430 0.997127i \(-0.475867\pi\)
−0.825666 + 0.564159i \(0.809200\pi\)
\(272\) 0 0
\(273\) 1.98217 1.59019i 0.119966 0.0962428i
\(274\) 0 0
\(275\) 33.0383 19.0747i 1.99229 1.15025i
\(276\) 0 0
\(277\) −4.40164 + 7.62386i −0.264469 + 0.458073i −0.967424 0.253160i \(-0.918530\pi\)
0.702956 + 0.711234i \(0.251863\pi\)
\(278\) 0 0
\(279\) −7.63113 + 23.0215i −0.456864 + 1.37826i
\(280\) 0 0
\(281\) −16.6889 + 9.63537i −0.995579 + 0.574798i −0.906937 0.421266i \(-0.861586\pi\)
−0.0886417 + 0.996064i \(0.528253\pi\)
\(282\) 0 0
\(283\) 9.61660i 0.571647i 0.958282 + 0.285824i \(0.0922672\pi\)
−0.958282 + 0.285824i \(0.907733\pi\)
\(284\) 0 0
\(285\) 5.76987 35.7442i 0.341777 2.11731i
\(286\) 0 0
\(287\) −14.1059 12.7421i −0.832645 0.752144i
\(288\) 0 0
\(289\) −8.54297 + 14.7969i −0.502528 + 0.870404i
\(290\) 0 0
\(291\) 26.1463 9.94791i 1.53272 0.583157i
\(292\) 0 0
\(293\) 1.22598 2.12346i 0.0716225 0.124054i −0.827990 0.560743i \(-0.810516\pi\)
0.899613 + 0.436689i \(0.143849\pi\)
\(294\) 0 0
\(295\) 17.4467 + 30.2185i 1.01578 + 1.75939i
\(296\) 0 0
\(297\) −10.3123 16.1926i −0.598380 0.939590i
\(298\) 0 0
\(299\) −1.26121 −0.0729376
\(300\) 0 0
\(301\) −3.79654 + 1.22683i −0.218829 + 0.0707132i
\(302\) 0 0
\(303\) 1.77610 2.18007i 0.102034 0.125242i
\(304\) 0 0
\(305\) 23.6198 13.6369i 1.35247 0.780846i
\(306\) 0 0
\(307\) 10.6839i 0.609760i −0.952391 0.304880i \(-0.901384\pi\)
0.952391 0.304880i \(-0.0986163\pi\)
\(308\) 0 0
\(309\) −0.640513 + 0.243697i −0.0364375 + 0.0138634i
\(310\) 0 0
\(311\) −20.7665 −1.17756 −0.588780 0.808293i \(-0.700392\pi\)
−0.588780 + 0.808293i \(0.700392\pi\)
\(312\) 0 0
\(313\) 3.93117i 0.222203i 0.993809 + 0.111101i \(0.0354378\pi\)
−0.993809 + 0.111101i \(0.964562\pi\)
\(314\) 0 0
\(315\) −31.0720 0.233929i −1.75071 0.0131804i
\(316\) 0 0
\(317\) 2.29057i 0.128651i −0.997929 0.0643256i \(-0.979510\pi\)
0.997929 0.0643256i \(-0.0204896\pi\)
\(318\) 0 0
\(319\) −15.0866 −0.844687
\(320\) 0 0
\(321\) −7.60978 6.19967i −0.424736 0.346032i
\(322\) 0 0
\(323\) 31.1750i 1.73462i
\(324\) 0 0
\(325\) −4.95889 + 2.86302i −0.275070 + 0.158812i
\(326\) 0 0
\(327\) −8.32315 21.8759i −0.460271 1.20974i
\(328\) 0 0
\(329\) −1.56757 + 7.31702i −0.0864232 + 0.403400i
\(330\) 0 0
\(331\) 6.93577 0.381224 0.190612 0.981665i \(-0.438953\pi\)
0.190612 + 0.981665i \(0.438953\pi\)
\(332\) 0 0
\(333\) 17.4753 15.5484i 0.957638 0.852047i
\(334\) 0 0
\(335\) −2.29957 3.98298i −0.125639 0.217613i
\(336\) 0 0
\(337\) −9.59771 + 16.6237i −0.522821 + 0.905552i 0.476827 + 0.878997i \(0.341787\pi\)
−0.999647 + 0.0265545i \(0.991546\pi\)
\(338\) 0 0
\(339\) 1.76222 + 1.43568i 0.0957106 + 0.0779752i
\(340\) 0 0
\(341\) 14.9342 25.8668i 0.808733 1.40077i
\(342\) 0 0
\(343\) −10.9580 + 14.9305i −0.591679 + 0.806174i
\(344\) 0 0
\(345\) 11.9561 + 9.74059i 0.643694 + 0.524416i
\(346\) 0 0
\(347\) 8.49036i 0.455786i −0.973686 0.227893i \(-0.926816\pi\)
0.973686 0.227893i \(-0.0731837\pi\)
\(348\) 0 0
\(349\) −16.5478 + 9.55386i −0.885782 + 0.511407i −0.872560 0.488506i \(-0.837542\pi\)
−0.0132216 + 0.999913i \(0.504209\pi\)
\(350\) 0 0
\(351\) 1.54782 + 2.43043i 0.0826167 + 0.129727i
\(352\) 0 0
\(353\) 6.82951 11.8291i 0.363498 0.629597i −0.625036 0.780596i \(-0.714916\pi\)
0.988534 + 0.150999i \(0.0482490\pi\)
\(354\) 0 0
\(355\) 22.7512 13.1354i 1.20751 0.697156i
\(356\) 0 0
\(357\) 26.4440 4.06458i 1.39956 0.215121i
\(358\) 0 0
\(359\) −14.8909 8.59724i −0.785909 0.453745i 0.0526113 0.998615i \(-0.483246\pi\)
−0.838520 + 0.544870i \(0.816579\pi\)
\(360\) 0 0
\(361\) 4.75635 + 8.23824i 0.250334 + 0.433592i
\(362\) 0 0
\(363\) 1.63205 + 4.28955i 0.0856604 + 0.225143i
\(364\) 0 0
\(365\) 13.8073 + 7.97162i 0.722705 + 0.417254i
\(366\) 0 0
\(367\) 14.6001 + 8.42936i 0.762118 + 0.440009i 0.830056 0.557680i \(-0.188309\pi\)
−0.0679376 + 0.997690i \(0.521642\pi\)
\(368\) 0 0
\(369\) 16.1029 14.3274i 0.838284 0.745854i
\(370\) 0 0
\(371\) 0.0390466 + 0.120833i 0.00202720 + 0.00627335i
\(372\) 0 0
\(373\) 0.704288 + 1.21986i 0.0364667 + 0.0631621i 0.883683 0.468086i \(-0.155056\pi\)
−0.847216 + 0.531248i \(0.821723\pi\)
\(374\) 0 0
\(375\) 35.6511 + 5.75484i 1.84102 + 0.297179i
\(376\) 0 0
\(377\) 2.26442 0.116624
\(378\) 0 0
\(379\) −0.598572 −0.0307466 −0.0153733 0.999882i \(-0.504894\pi\)
−0.0153733 + 0.999882i \(0.504894\pi\)
\(380\) 0 0
\(381\) −29.7414 4.80088i −1.52370 0.245956i
\(382\) 0 0
\(383\) −4.26039 7.37921i −0.217696 0.377060i 0.736407 0.676538i \(-0.236521\pi\)
−0.954103 + 0.299478i \(0.903187\pi\)
\(384\) 0 0
\(385\) 37.4179 + 8.01628i 1.90699 + 0.408548i
\(386\) 0 0
\(387\) −0.914384 4.43068i −0.0464807 0.225224i
\(388\) 0 0
\(389\) −29.9624 17.2988i −1.51915 0.877084i −0.999746 0.0225587i \(-0.992819\pi\)
−0.519409 0.854526i \(-0.673848\pi\)
\(390\) 0 0
\(391\) −11.4994 6.63920i −0.581551 0.335759i
\(392\) 0 0
\(393\) 6.71799 + 17.6570i 0.338878 + 0.890680i
\(394\) 0 0
\(395\) 7.72683 + 13.3833i 0.388779 + 0.673385i
\(396\) 0 0
\(397\) 27.9571 + 16.1411i 1.40313 + 0.810097i 0.994712 0.102699i \(-0.0327478\pi\)
0.408416 + 0.912796i \(0.366081\pi\)
\(398\) 0 0
\(399\) 19.0867 15.3123i 0.955529 0.766572i
\(400\) 0 0
\(401\) 11.3473 6.55139i 0.566659 0.327161i −0.189155 0.981947i \(-0.560575\pi\)
0.755814 + 0.654787i \(0.227242\pi\)
\(402\) 0 0
\(403\) −2.24155 + 3.88248i −0.111660 + 0.193400i
\(404\) 0 0
\(405\) 4.09760 34.9943i 0.203611 1.73888i
\(406\) 0 0
\(407\) −24.9471 + 14.4032i −1.23658 + 0.713941i
\(408\) 0 0
\(409\) 37.3538i 1.84703i −0.383568 0.923513i \(-0.625305\pi\)
0.383568 0.923513i \(-0.374695\pi\)
\(410\) 0 0
\(411\) 11.8237 + 9.63278i 0.583222 + 0.475150i
\(412\) 0 0
\(413\) −4.94002 + 23.0587i −0.243082 + 1.13464i
\(414\) 0 0
\(415\) 15.0593 26.0835i 0.739232 1.28039i
\(416\) 0 0
\(417\) −22.0725 17.9824i −1.08089 0.880603i
\(418\) 0 0
\(419\) 14.1954 24.5871i 0.693490 1.20116i −0.277198 0.960813i \(-0.589406\pi\)
0.970687 0.240346i \(-0.0772610\pi\)
\(420\) 0 0
\(421\) −17.3359 30.0267i −0.844901 1.46341i −0.885707 0.464245i \(-0.846326\pi\)
0.0408054 0.999167i \(-0.487008\pi\)
\(422\) 0 0
\(423\) −8.05403 2.66974i −0.391600 0.129807i
\(424\) 0 0
\(425\) −60.2854 −2.92427
\(426\) 0 0
\(427\) 18.0235 + 3.86129i 0.872216 + 0.186861i
\(428\) 0 0
\(429\) −1.26188 3.31662i −0.0609240 0.160128i
\(430\) 0 0
\(431\) 13.1844 7.61200i 0.635069 0.366657i −0.147643 0.989041i \(-0.547169\pi\)
0.782713 + 0.622383i \(0.213835\pi\)
\(432\) 0 0
\(433\) 3.97041i 0.190806i 0.995439 + 0.0954028i \(0.0304139\pi\)
−0.995439 + 0.0954028i \(0.969586\pi\)
\(434\) 0 0
\(435\) −21.4664 17.4886i −1.02924 0.838516i
\(436\) 0 0
\(437\) −12.1444 −0.580947
\(438\) 0 0
\(439\) 9.49060i 0.452962i 0.974016 + 0.226481i \(0.0727221\pi\)
−0.974016 + 0.226481i \(0.927278\pi\)
\(440\) 0 0
\(441\) −15.4770 14.1937i −0.737001 0.675892i
\(442\) 0 0
\(443\) 32.7883i 1.55782i 0.627135 + 0.778910i \(0.284227\pi\)
−0.627135 + 0.778910i \(0.715773\pi\)
\(444\) 0 0
\(445\) 21.2418 1.00696
\(446\) 0 0
\(447\) 23.5182 8.94798i 1.11237 0.423225i
\(448\) 0 0
\(449\) 0.658896i 0.0310952i −0.999879 0.0155476i \(-0.995051\pi\)
0.999879 0.0155476i \(-0.00494916\pi\)
\(450\) 0 0
\(451\) −22.9880 + 13.2721i −1.08246 + 0.624960i
\(452\) 0 0
\(453\) −6.13308 + 7.52804i −0.288157 + 0.353698i
\(454\) 0 0
\(455\) −5.61624 1.20321i −0.263293 0.0564071i
\(456\) 0 0
\(457\) 15.8903 0.743316 0.371658 0.928370i \(-0.378789\pi\)
0.371658 + 0.928370i \(0.378789\pi\)
\(458\) 0 0
\(459\) 1.31856 + 30.3081i 0.0615451 + 1.41466i
\(460\) 0 0
\(461\) −9.81626 17.0023i −0.457189 0.791874i 0.541622 0.840622i \(-0.317810\pi\)
−0.998811 + 0.0487477i \(0.984477\pi\)
\(462\) 0 0
\(463\) 0.600159 1.03951i 0.0278918 0.0483099i −0.851743 0.523960i \(-0.824454\pi\)
0.879634 + 0.475651i \(0.157787\pi\)
\(464\) 0 0
\(465\) 51.2348 19.4934i 2.37596 0.903983i
\(466\) 0 0
\(467\) 19.2809 33.3955i 0.892213 1.54536i 0.0549972 0.998487i \(-0.482485\pi\)
0.837216 0.546872i \(-0.184182\pi\)
\(468\) 0 0
\(469\) 0.651124 3.03927i 0.0300661 0.140341i
\(470\) 0 0
\(471\) −4.92133 + 30.4876i −0.226763 + 1.40479i
\(472\) 0 0
\(473\) 5.57146i 0.256176i
\(474\) 0 0
\(475\) −47.7501 + 27.5685i −2.19093 + 1.26493i
\(476\) 0 0
\(477\) −0.141016 + 0.0291023i −0.00645670 + 0.00133250i
\(478\) 0 0
\(479\) −3.61289 + 6.25771i −0.165077 + 0.285922i −0.936683 0.350179i \(-0.886121\pi\)
0.771606 + 0.636101i \(0.219454\pi\)
\(480\) 0 0
\(481\) 3.74444 2.16185i 0.170732 0.0985720i
\(482\) 0 0
\(483\) 1.58338 + 10.3014i 0.0720465 + 0.468731i
\(484\) 0 0
\(485\) −54.7582 31.6147i −2.48644 1.43555i
\(486\) 0 0
\(487\) 4.85770 + 8.41378i 0.220123 + 0.381265i 0.954845 0.297104i \(-0.0960207\pi\)
−0.734722 + 0.678368i \(0.762687\pi\)
\(488\) 0 0
\(489\) −1.26246 + 1.54960i −0.0570903 + 0.0700754i
\(490\) 0 0
\(491\) 17.2480 + 9.95814i 0.778392 + 0.449405i 0.835860 0.548943i \(-0.184969\pi\)
−0.0574682 + 0.998347i \(0.518303\pi\)
\(492\) 0 0
\(493\) 20.6465 + 11.9203i 0.929872 + 0.536862i
\(494\) 0 0
\(495\) −13.6526 + 41.1868i −0.613637 + 1.85121i
\(496\) 0 0
\(497\) 17.3607 + 3.71930i 0.778733 + 0.166833i
\(498\) 0 0
\(499\) −17.1920 29.7774i −0.769619 1.33302i −0.937770 0.347258i \(-0.887113\pi\)
0.168150 0.985761i \(-0.446221\pi\)
\(500\) 0 0
\(501\) −19.5945 + 24.0513i −0.875420 + 1.07453i
\(502\) 0 0
\(503\) 1.22542 0.0546388 0.0273194 0.999627i \(-0.491303\pi\)
0.0273194 + 0.999627i \(0.491303\pi\)
\(504\) 0 0
\(505\) −6.35571 −0.282826
\(506\) 0 0
\(507\) −7.81758 20.5471i −0.347191 0.912529i
\(508\) 0 0
\(509\) 5.05078 + 8.74820i 0.223872 + 0.387757i 0.955980 0.293431i \(-0.0947970\pi\)
−0.732109 + 0.681188i \(0.761464\pi\)
\(510\) 0 0
\(511\) 3.31316 + 10.2529i 0.146565 + 0.453561i
\(512\) 0 0
\(513\) 14.9043 + 23.4031i 0.658041 + 1.03327i
\(514\) 0 0
\(515\) 1.34143 + 0.774473i 0.0591103 + 0.0341274i
\(516\) 0 0
\(517\) 9.04947 + 5.22471i 0.397995 + 0.229783i
\(518\) 0 0
\(519\) 12.8180 + 2.06910i 0.562649 + 0.0908233i
\(520\) 0 0
\(521\) 10.5390 + 18.2541i 0.461723 + 0.799728i 0.999047 0.0436480i \(-0.0138980\pi\)
−0.537324 + 0.843376i \(0.680565\pi\)
\(522\) 0 0
\(523\) 17.0733 + 9.85727i 0.746563 + 0.431028i 0.824451 0.565934i \(-0.191484\pi\)
−0.0778877 + 0.996962i \(0.524818\pi\)
\(524\) 0 0
\(525\) 29.6104 + 36.9093i 1.29231 + 1.61085i
\(526\) 0 0
\(527\) −40.8760 + 23.5997i −1.78058 + 1.02802i
\(528\) 0 0
\(529\) −8.91366 + 15.4389i −0.387550 + 0.671257i
\(530\) 0 0
\(531\) −25.3813 8.41336i −1.10145 0.365109i
\(532\) 0 0
\(533\) 3.45039 1.99208i 0.149453 0.0862866i
\(534\) 0 0
\(535\) 22.1853i 0.959154i
\(536\) 0 0
\(537\) 1.16714 0.444063i 0.0503658 0.0191627i
\(538\) 0 0
\(539\) 15.1339 + 20.9715i 0.651864 + 0.903306i
\(540\) 0 0
\(541\) −4.22475 + 7.31748i −0.181636 + 0.314603i −0.942438 0.334381i \(-0.891473\pi\)
0.760802 + 0.648984i \(0.224806\pi\)
\(542\) 0 0
\(543\) 1.39974 8.67135i 0.0600685 0.372123i
\(544\) 0 0
\(545\) −26.4511 + 45.8147i −1.13304 + 1.96249i
\(546\) 0 0
\(547\) −4.02889 6.97824i −0.172263 0.298368i 0.766948 0.641709i \(-0.221774\pi\)
−0.939211 + 0.343342i \(0.888441\pi\)
\(548\) 0 0
\(549\) −6.57617 + 19.8389i −0.280664 + 0.846703i
\(550\) 0 0
\(551\) 21.8046 0.928906
\(552\) 0 0
\(553\) −2.18785 + 10.2123i −0.0930369 + 0.434271i
\(554\) 0 0
\(555\) −52.1932 8.42507i −2.21548 0.357624i
\(556\) 0 0
\(557\) −18.2294 + 10.5247i −0.772403 + 0.445947i −0.833731 0.552170i \(-0.813800\pi\)
0.0613279 + 0.998118i \(0.480466\pi\)
\(558\) 0 0
\(559\) 0.836249i 0.0353696i
\(560\) 0 0
\(561\) 5.95367 36.8829i 0.251364 1.55720i
\(562\) 0 0
\(563\) 41.2821 1.73983 0.869916 0.493200i \(-0.164173\pi\)
0.869916 + 0.493200i \(0.164173\pi\)
\(564\) 0 0
\(565\) 5.13751i 0.216137i
\(566\) 0 0
\(567\) 17.9083 15.6937i 0.752077 0.659075i
\(568\) 0 0
\(569\) 36.1064i 1.51366i −0.653612 0.756829i \(-0.726747\pi\)
0.653612 0.756829i \(-0.273253\pi\)
\(570\) 0 0
\(571\) −19.2422 −0.805262 −0.402631 0.915362i \(-0.631904\pi\)
−0.402631 + 0.915362i \(0.631904\pi\)
\(572\) 0 0
\(573\) −3.50602 + 21.7198i −0.146466 + 0.907356i
\(574\) 0 0
\(575\) 23.4846i 0.979375i
\(576\) 0 0
\(577\) −25.8102 + 14.9015i −1.07449 + 0.620359i −0.929406 0.369060i \(-0.879680\pi\)
−0.145088 + 0.989419i \(0.546346\pi\)
\(578\) 0 0
\(579\) −39.0123 6.29739i −1.62129 0.261711i
\(580\) 0 0
\(581\) 19.3689 6.25893i 0.803556 0.259664i
\(582\) 0 0
\(583\) 0.177324 0.00734402
\(584\) 0 0
\(585\) 2.04918 6.18194i 0.0847233 0.255592i
\(586\) 0 0
\(587\) 4.72218 + 8.17905i 0.194905 + 0.337586i 0.946869 0.321618i \(-0.104227\pi\)
−0.751964 + 0.659204i \(0.770893\pi\)
\(588\) 0 0
\(589\) −21.5843 + 37.3852i −0.889367 + 1.54043i
\(590\) 0 0
\(591\) −0.00859405 + 0.0532400i −0.000353512 + 0.00219000i
\(592\) 0 0
\(593\) 12.4176 21.5079i 0.509929 0.883223i −0.490005 0.871720i \(-0.663005\pi\)
0.999934 0.0115033i \(-0.00366171\pi\)
\(594\) 0 0
\(595\) −44.8738 40.5353i −1.83965 1.66179i
\(596\) 0 0
\(597\) 37.2255 14.1632i 1.52354 0.579662i
\(598\) 0 0
\(599\) 11.8995i 0.486199i −0.970001 0.243100i \(-0.921836\pi\)
0.970001 0.243100i \(-0.0781642\pi\)
\(600\) 0 0
\(601\) 22.1276 12.7754i 0.902604 0.521118i 0.0245596 0.999698i \(-0.492182\pi\)
0.878044 + 0.478580i \(0.158848\pi\)
\(602\) 0 0
\(603\) 3.34541 + 1.10893i 0.136236 + 0.0451592i
\(604\) 0 0
\(605\) 5.18669 8.98361i 0.210869 0.365236i
\(606\) 0 0
\(607\) −19.5544 + 11.2897i −0.793687 + 0.458235i −0.841259 0.540632i \(-0.818185\pi\)
0.0475718 + 0.998868i \(0.484852\pi\)
\(608\) 0 0
\(609\) −2.84287 18.4956i −0.115199 0.749478i
\(610\) 0 0
\(611\) −1.35828 0.784204i −0.0549502 0.0317255i
\(612\) 0 0
\(613\) −11.4294 19.7963i −0.461628 0.799564i 0.537414 0.843319i \(-0.319401\pi\)
−0.999042 + 0.0437549i \(0.986068\pi\)
\(614\) 0 0
\(615\) −48.0944 7.76344i −1.93935 0.313052i
\(616\) 0 0
\(617\) 1.78792 + 1.03226i 0.0719791 + 0.0415572i 0.535558 0.844499i \(-0.320101\pi\)
−0.463578 + 0.886056i \(0.653435\pi\)
\(618\) 0 0
\(619\) −28.2233 16.2947i −1.13439 0.654940i −0.189354 0.981909i \(-0.560639\pi\)
−0.945035 + 0.326969i \(0.893973\pi\)
\(620\) 0 0
\(621\) −11.8067 + 0.513653i −0.473787 + 0.0206122i
\(622\) 0 0
\(623\) 10.6530 + 9.62307i 0.426804 + 0.385540i
\(624\) 0 0
\(625\) −14.9967 25.9751i −0.599870 1.03901i
\(626\) 0 0
\(627\) −12.1509 31.9364i −0.485259 1.27542i
\(628\) 0 0
\(629\) 45.5213 1.81505
\(630\) 0 0
\(631\) 38.4706 1.53149 0.765744 0.643145i \(-0.222371\pi\)
0.765744 + 0.643145i \(0.222371\pi\)
\(632\) 0 0
\(633\) 18.7257 22.9849i 0.744281 0.913566i
\(634\) 0 0
\(635\) 34.0461 + 58.9696i 1.35108 + 2.34014i
\(636\) 0 0
\(637\) −2.27153 3.14772i −0.0900012 0.124717i
\(638\) 0 0
\(639\) −6.33434 + 19.1093i −0.250583 + 0.755954i
\(640\) 0 0
\(641\) 41.3645 + 23.8818i 1.63380 + 0.943274i 0.982907 + 0.184104i \(0.0589384\pi\)
0.650892 + 0.759170i \(0.274395\pi\)
\(642\) 0 0
\(643\) 29.2346 + 16.8786i 1.15290 + 0.665626i 0.949592 0.313489i \(-0.101498\pi\)
0.203306 + 0.979115i \(0.434831\pi\)
\(644\) 0 0
\(645\) −6.45853 + 7.92752i −0.254304 + 0.312146i
\(646\) 0 0
\(647\) 0.536008 + 0.928393i 0.0210727 + 0.0364989i 0.876369 0.481640i \(-0.159959\pi\)
−0.855297 + 0.518138i \(0.826625\pi\)
\(648\) 0 0
\(649\) 28.5183 + 16.4650i 1.11944 + 0.646309i
\(650\) 0 0
\(651\) 34.5258 + 13.4345i 1.35317 + 0.526539i
\(652\) 0 0
\(653\) 28.8503 16.6567i 1.12900 0.651828i 0.185317 0.982679i \(-0.440669\pi\)
0.943683 + 0.330851i \(0.107336\pi\)
\(654\) 0 0
\(655\) 21.3499 36.9791i 0.834210 1.44489i
\(656\) 0 0
\(657\) −11.9654 + 2.46937i −0.466817 + 0.0963394i
\(658\) 0 0
\(659\) −8.41890 + 4.86065i −0.327954 + 0.189344i −0.654932 0.755688i \(-0.727303\pi\)
0.326979 + 0.945032i \(0.393969\pi\)
\(660\) 0 0
\(661\) 17.0729i 0.664060i 0.943269 + 0.332030i \(0.107734\pi\)
−0.943269 + 0.332030i \(0.892266\pi\)
\(662\) 0 0
\(663\) −0.893617 + 5.53595i −0.0347052 + 0.214998i
\(664\) 0 0
\(665\) −54.0799 11.5859i −2.09713 0.449282i
\(666\) 0 0
\(667\) −4.64362 + 8.04298i −0.179802 + 0.311426i
\(668\) 0 0
\(669\) 2.34089 0.890642i 0.0905041 0.0344342i
\(670\) 0 0
\(671\) 12.8696 22.2909i 0.496827 0.860529i
\(672\) 0 0
\(673\) −18.3359 31.7588i −0.706798 1.22421i −0.966039 0.258398i \(-0.916805\pi\)
0.259240 0.965813i \(-0.416528\pi\)
\(674\) 0 0
\(675\) −45.2563 + 28.8215i −1.74191 + 1.10934i
\(676\) 0 0
\(677\) −40.3538 −1.55092 −0.775461 0.631395i \(-0.782483\pi\)
−0.775461 + 0.631395i \(0.782483\pi\)
\(678\) 0 0
\(679\) −13.1397 40.6619i −0.504254 1.56046i
\(680\) 0 0
\(681\) −4.89227 + 6.00501i −0.187472 + 0.230112i
\(682\) 0 0
\(683\) 8.23662 4.75541i 0.315165 0.181961i −0.334070 0.942548i \(-0.608422\pi\)
0.649236 + 0.760587i \(0.275089\pi\)
\(684\) 0 0
\(685\) 34.4705i 1.31705i
\(686\) 0 0
\(687\) 4.18852 1.59361i 0.159802 0.0608000i
\(688\) 0 0
\(689\) −0.0266155 −0.00101397
\(690\) 0 0
\(691\) 7.70784i 0.293220i −0.989194 0.146610i \(-0.953164\pi\)
0.989194 0.146610i \(-0.0468363\pi\)
\(692\) 0 0
\(693\) −25.5056 + 14.4707i −0.968876 + 0.549697i
\(694\) 0 0
\(695\) 64.3494i 2.44091i
\(696\) 0 0
\(697\) 41.9465 1.58884
\(698\) 0 0
\(699\) 23.3756 + 19.0440i 0.884145 + 0.720311i
\(700\) 0 0
\(701\) 15.6388i 0.590671i −0.955394 0.295336i \(-0.904569\pi\)
0.955394 0.295336i \(-0.0954314\pi\)
\(702\) 0 0
\(703\) 36.0559 20.8169i 1.35988 0.785124i
\(704\) 0 0
\(705\) 6.81973 + 17.9244i 0.256846 + 0.675073i
\(706\) 0 0
\(707\) −3.18747 2.87930i −0.119877 0.108287i
\(708\) 0 0
\(709\) 13.4405 0.504769 0.252384 0.967627i \(-0.418785\pi\)
0.252384 + 0.967627i \(0.418785\pi\)
\(710\) 0 0
\(711\) −11.2409 3.72614i −0.421568 0.139741i
\(712\) 0 0
\(713\) −9.19343 15.9235i −0.344297 0.596339i
\(714\) 0 0
\(715\) −4.01027 + 6.94599i −0.149976 + 0.259765i
\(716\) 0 0
\(717\) 6.56881 + 5.35160i 0.245317 + 0.199859i
\(718\) 0 0
\(719\) 20.0309 34.6946i 0.747027 1.29389i −0.202214 0.979341i \(-0.564814\pi\)
0.949242 0.314548i \(-0.101853\pi\)
\(720\) 0 0
\(721\) 0.321886 + 0.996107i 0.0119877 + 0.0370970i
\(722\) 0 0
\(723\) 10.9203 + 8.89675i 0.406131 + 0.330874i
\(724\) 0 0
\(725\) 42.1651i 1.56597i
\(726\) 0 0
\(727\) 43.2091 24.9468i 1.60254 0.925225i 0.611560 0.791198i \(-0.290542\pi\)
0.990978 0.134027i \(-0.0427910\pi\)
\(728\) 0 0
\(729\) 15.4797 + 22.1219i 0.573322 + 0.819330i
\(730\) 0 0
\(731\) 4.40214 7.62473i 0.162819 0.282011i
\(732\) 0 0
\(733\) −9.91430 + 5.72402i −0.366193 + 0.211422i −0.671794 0.740738i \(-0.734476\pi\)
0.305601 + 0.952160i \(0.401143\pi\)
\(734\) 0 0
\(735\) −2.77674 + 47.3834i −0.102422 + 1.74776i
\(736\) 0 0
\(737\) −3.75888 2.17019i −0.138460 0.0799400i
\(738\) 0 0
\(739\) 4.46303 + 7.73020i 0.164175 + 0.284360i 0.936362 0.351036i \(-0.114170\pi\)
−0.772187 + 0.635396i \(0.780837\pi\)
\(740\) 0 0
\(741\) 1.82378 + 4.79349i 0.0669984 + 0.176093i
\(742\) 0 0
\(743\) −45.8621 26.4785i −1.68252 0.971403i −0.959979 0.280074i \(-0.909641\pi\)
−0.722540 0.691329i \(-0.757026\pi\)
\(744\) 0 0
\(745\) −49.2541 28.4369i −1.80453 1.04185i
\(746\) 0 0
\(747\) 4.66493 + 22.6041i 0.170681 + 0.827041i
\(748\) 0 0
\(749\) −10.0505 + 11.1262i −0.367237 + 0.406542i
\(750\) 0 0
\(751\) 13.2326 + 22.9195i 0.482865 + 0.836346i 0.999806 0.0196744i \(-0.00626295\pi\)
−0.516942 + 0.856021i \(0.672930\pi\)
\(752\) 0 0
\(753\) −44.3451 7.15823i −1.61603 0.260860i
\(754\) 0 0
\(755\) 21.9470 0.798733
\(756\) 0 0
\(757\) 8.46749 0.307756 0.153878 0.988090i \(-0.450824\pi\)
0.153878 + 0.988090i \(0.450824\pi\)
\(758\) 0 0
\(759\) 14.3680 + 2.31929i 0.521525 + 0.0841849i
\(760\) 0 0
\(761\) −26.9968 46.7599i −0.978635 1.69505i −0.667377 0.744720i \(-0.732583\pi\)
−0.311258 0.950325i \(-0.600750\pi\)
\(762\) 0 0
\(763\) −34.0208 + 10.9936i −1.23163 + 0.397995i
\(764\) 0 0
\(765\) 51.2267 45.5783i 1.85210 1.64789i
\(766\) 0 0
\(767\) −4.28046 2.47132i −0.154558 0.0892343i
\(768\) 0 0
\(769\) 30.1912 + 17.4309i 1.08872 + 0.628575i 0.933236 0.359263i \(-0.116972\pi\)
0.155487 + 0.987838i \(0.450305\pi\)
\(770\) 0 0
\(771\) 18.9846 + 49.8976i 0.683713 + 1.79702i
\(772\) 0 0
\(773\) −1.06375 1.84246i −0.0382603 0.0662688i 0.846261 0.532768i \(-0.178848\pi\)
−0.884521 + 0.466499i \(0.845515\pi\)
\(774\) 0 0
\(775\) −72.2944 41.7392i −2.59689 1.49932i
\(776\) 0 0
\(777\) −22.3587 27.8701i −0.802115 0.999833i
\(778\) 0 0
\(779\) 33.2244 19.1821i 1.19039 0.687272i
\(780\) 0 0
\(781\) 12.3964 21.4712i 0.443577 0.768298i
\(782\) 0 0
\(783\) 21.1982 0.922233i 0.757563 0.0329579i
\(784\) 0 0
\(785\) 60.4492 34.9004i 2.15752 1.24565i
\(786\) 0 0
\(787\) 28.3429i 1.01032i −0.863027 0.505158i \(-0.831434\pi\)
0.863027 0.505158i \(-0.168566\pi\)
\(788\) 0 0
\(789\) −24.2856 19.7855i −0.864592 0.704381i
\(790\) 0 0
\(791\) 2.32742 2.57652i 0.0827535 0.0916106i
\(792\) 0 0
\(793\) −1.93167 + 3.34575i −0.0685956 + 0.118811i
\(794\) 0 0
\(795\) 0.252311 + 0.205557i 0.00894854 + 0.00729036i
\(796\) 0