Properties

Label 1152.2.i.k.385.5
Level $1152$
Weight $2$
Character 1152.385
Analytic conductor $9.199$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 385.5
Root \(-0.433633 + 1.67689i\) of defining polynomial
Character \(\chi\) \(=\) 1152.385
Dual form 1152.2.i.k.769.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.23541 - 1.21398i) q^{3} +(2.22043 + 3.84590i) q^{5} +(1.45488 - 2.51992i) q^{7} +(0.0524919 - 2.99954i) q^{9} +O(q^{10})\) \(q+(1.23541 - 1.21398i) q^{3} +(2.22043 + 3.84590i) q^{5} +(1.45488 - 2.51992i) q^{7} +(0.0524919 - 2.99954i) q^{9} +(1.08263 - 1.87517i) q^{11} +(1.96377 + 3.40135i) q^{13} +(7.41200 + 2.05571i) q^{15} +1.79720 q^{17} -1.76882 q^{19} +(-1.26177 - 4.87934i) q^{21} +(-3.44197 - 5.96166i) q^{23} +(-7.36062 + 12.7490i) q^{25} +(-3.57654 - 3.76940i) q^{27} +(2.87353 - 4.97710i) q^{29} +(3.27671 + 5.67542i) q^{31} +(-0.938929 - 3.63091i) q^{33} +12.9218 q^{35} +2.51332 q^{37} +(6.55525 + 1.81809i) q^{39} +(-3.68420 - 6.38122i) q^{41} +(-2.53640 + 4.39317i) q^{43} +(11.6525 - 6.45839i) q^{45} +(-4.98598 + 8.63597i) q^{47} +(-0.733339 - 1.27018i) q^{49} +(2.22029 - 2.18177i) q^{51} +3.30620 q^{53} +9.61562 q^{55} +(-2.18523 + 2.14732i) q^{57} +(2.30090 + 3.98528i) q^{59} +(-1.87353 + 3.24505i) q^{61} +(-7.48224 - 4.49624i) q^{63} +(-8.72084 + 15.1049i) q^{65} +(-2.36045 - 4.08841i) q^{67} +(-11.4896 - 3.18663i) q^{69} +0.907539 q^{71} -1.87740 q^{73} +(6.38362 + 24.6859i) q^{75} +(-3.15019 - 5.45629i) q^{77} +(1.23661 - 2.14187i) q^{79} +(-8.99449 - 0.314903i) q^{81} +(1.09251 - 1.89227i) q^{83} +(3.99056 + 6.91185i) q^{85} +(-2.49211 - 9.63718i) q^{87} -5.30620 q^{89} +11.4282 q^{91} +(10.9380 + 3.03363i) q^{93} +(-3.92754 - 6.80271i) q^{95} +(4.45302 - 7.71286i) q^{97} +(-5.56782 - 3.34583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + 4 q^{11} + 10 q^{13} + 4 q^{15} + 4 q^{17} + 4 q^{19} + 2 q^{21} + 8 q^{23} - 14 q^{25} - 14 q^{27} - 2 q^{29} + 8 q^{31} - 10 q^{33} + 8 q^{35} + 22 q^{39} - 2 q^{41} - 2 q^{43} + 10 q^{45} - 14 q^{47} - 18 q^{49} - 38 q^{51} + 24 q^{53} - 16 q^{55} - 38 q^{57} + 6 q^{59} + 14 q^{61} - 16 q^{63} - 8 q^{65} + 4 q^{67} - 50 q^{69} - 28 q^{71} + 60 q^{73} + 50 q^{75} + 2 q^{77} + 16 q^{79} + 22 q^{81} + 24 q^{83} + 16 q^{85} - 36 q^{87} - 48 q^{89} - 52 q^{91} + 42 q^{93} - 20 q^{95} - 14 q^{97} + 68 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 1.23541 1.21398i 0.713266 0.700893i
\(4\) 0 0
\(5\) 2.22043 + 3.84590i 0.993006 + 1.71994i 0.598746 + 0.800939i \(0.295666\pi\)
0.394260 + 0.918999i \(0.371001\pi\)
\(6\) 0 0
\(7\) 1.45488 2.51992i 0.549892 0.952441i −0.448389 0.893838i \(-0.648002\pi\)
0.998281 0.0586028i \(-0.0186645\pi\)
\(8\) 0 0
\(9\) 0.0524919 2.99954i 0.0174973 0.999847i
\(10\) 0 0
\(11\) 1.08263 1.87517i 0.326425 0.565385i −0.655374 0.755304i \(-0.727489\pi\)
0.981800 + 0.189919i \(0.0608225\pi\)
\(12\) 0 0
\(13\) 1.96377 + 3.40135i 0.544652 + 0.943366i 0.998629 + 0.0523518i \(0.0166717\pi\)
−0.453976 + 0.891014i \(0.649995\pi\)
\(14\) 0 0
\(15\) 7.41200 + 2.05571i 1.91377 + 0.530782i
\(16\) 0 0
\(17\) 1.79720 0.435885 0.217943 0.975962i \(-0.430065\pi\)
0.217943 + 0.975962i \(0.430065\pi\)
\(18\) 0 0
\(19\) −1.76882 −0.405795 −0.202898 0.979200i \(-0.565036\pi\)
−0.202898 + 0.979200i \(0.565036\pi\)
\(20\) 0 0
\(21\) −1.26177 4.87934i −0.275340 1.06476i
\(22\) 0 0
\(23\) −3.44197 5.96166i −0.717700 1.24309i −0.961909 0.273370i \(-0.911862\pi\)
0.244209 0.969723i \(-0.421472\pi\)
\(24\) 0 0
\(25\) −7.36062 + 12.7490i −1.47212 + 2.54979i
\(26\) 0 0
\(27\) −3.57654 3.76940i −0.688306 0.725421i
\(28\) 0 0
\(29\) 2.87353 4.97710i 0.533601 0.924224i −0.465629 0.884980i \(-0.654172\pi\)
0.999230 0.0392435i \(-0.0124948\pi\)
\(30\) 0 0
\(31\) 3.27671 + 5.67542i 0.588514 + 1.01934i 0.994427 + 0.105425i \(0.0336201\pi\)
−0.405913 + 0.913912i \(0.633047\pi\)
\(32\) 0 0
\(33\) −0.938929 3.63091i −0.163447 0.632060i
\(34\) 0 0
\(35\) 12.9218 2.18419
\(36\) 0 0
\(37\) 2.51332 0.413187 0.206593 0.978427i \(-0.433762\pi\)
0.206593 + 0.978427i \(0.433762\pi\)
\(38\) 0 0
\(39\) 6.55525 + 1.81809i 1.04968 + 0.291128i
\(40\) 0 0
\(41\) −3.68420 6.38122i −0.575376 0.996580i −0.996001 0.0893453i \(-0.971523\pi\)
0.420625 0.907235i \(-0.361811\pi\)
\(42\) 0 0
\(43\) −2.53640 + 4.39317i −0.386797 + 0.669953i −0.992017 0.126106i \(-0.959752\pi\)
0.605219 + 0.796059i \(0.293085\pi\)
\(44\) 0 0
\(45\) 11.6525 6.45839i 1.73705 0.962760i
\(46\) 0 0
\(47\) −4.98598 + 8.63597i −0.727280 + 1.25969i 0.230748 + 0.973013i \(0.425883\pi\)
−0.958029 + 0.286673i \(0.907451\pi\)
\(48\) 0 0
\(49\) −0.733339 1.27018i −0.104763 0.181454i
\(50\) 0 0
\(51\) 2.22029 2.18177i 0.310902 0.305509i
\(52\) 0 0
\(53\) 3.30620 0.454141 0.227070 0.973878i \(-0.427085\pi\)
0.227070 + 0.973878i \(0.427085\pi\)
\(54\) 0 0
\(55\) 9.61562 1.29657
\(56\) 0 0
\(57\) −2.18523 + 2.14732i −0.289440 + 0.284419i
\(58\) 0 0
\(59\) 2.30090 + 3.98528i 0.299552 + 0.518839i 0.976033 0.217621i \(-0.0698296\pi\)
−0.676482 + 0.736459i \(0.736496\pi\)
\(60\) 0 0
\(61\) −1.87353 + 3.24505i −0.239881 + 0.415485i −0.960680 0.277658i \(-0.910442\pi\)
0.720799 + 0.693144i \(0.243775\pi\)
\(62\) 0 0
\(63\) −7.48224 4.49624i −0.942674 0.566473i
\(64\) 0 0
\(65\) −8.72084 + 15.1049i −1.08169 + 1.87354i
\(66\) 0 0
\(67\) −2.36045 4.08841i −0.288374 0.499479i 0.685047 0.728498i \(-0.259781\pi\)
−0.973422 + 0.229019i \(0.926448\pi\)
\(68\) 0 0
\(69\) −11.4896 3.18663i −1.38319 0.383625i
\(70\) 0 0
\(71\) 0.907539 0.107705 0.0538525 0.998549i \(-0.482850\pi\)
0.0538525 + 0.998549i \(0.482850\pi\)
\(72\) 0 0
\(73\) −1.87740 −0.219733 −0.109866 0.993946i \(-0.535042\pi\)
−0.109866 + 0.993946i \(0.535042\pi\)
\(74\) 0 0
\(75\) 6.38362 + 24.6859i 0.737117 + 2.85048i
\(76\) 0 0
\(77\) −3.15019 5.45629i −0.358998 0.621802i
\(78\) 0 0
\(79\) 1.23661 2.14187i 0.139129 0.240979i −0.788038 0.615627i \(-0.788903\pi\)
0.927167 + 0.374648i \(0.122236\pi\)
\(80\) 0 0
\(81\) −8.99449 0.314903i −0.999388 0.0349892i
\(82\) 0 0
\(83\) 1.09251 1.89227i 0.119918 0.207704i −0.799817 0.600244i \(-0.795070\pi\)
0.919735 + 0.392540i \(0.128403\pi\)
\(84\) 0 0
\(85\) 3.99056 + 6.91185i 0.432837 + 0.749696i
\(86\) 0 0
\(87\) −2.49211 9.63718i −0.267183 1.03321i
\(88\) 0 0
\(89\) −5.30620 −0.562456 −0.281228 0.959641i \(-0.590742\pi\)
−0.281228 + 0.959641i \(0.590742\pi\)
\(90\) 0 0
\(91\) 11.4282 1.19800
\(92\) 0 0
\(93\) 10.9380 + 3.03363i 1.13421 + 0.314572i
\(94\) 0 0
\(95\) −3.92754 6.80271i −0.402958 0.697943i
\(96\) 0 0
\(97\) 4.45302 7.71286i 0.452136 0.783123i −0.546382 0.837536i \(-0.683995\pi\)
0.998519 + 0.0544132i \(0.0173288\pi\)
\(98\) 0 0
\(99\) −5.56782 3.34583i −0.559587 0.336268i
\(100\) 0 0
\(101\) −0.689326 + 1.19395i −0.0685905 + 0.118802i −0.898281 0.439421i \(-0.855184\pi\)
0.829691 + 0.558224i \(0.188517\pi\)
\(102\) 0 0
\(103\) 2.54512 + 4.40828i 0.250778 + 0.434361i 0.963740 0.266842i \(-0.0859801\pi\)
−0.712962 + 0.701203i \(0.752647\pi\)
\(104\) 0 0
\(105\) 15.9638 15.6869i 1.55791 1.53088i
\(106\) 0 0
\(107\) 17.2062 1.66338 0.831692 0.555238i \(-0.187373\pi\)
0.831692 + 0.555238i \(0.187373\pi\)
\(108\) 0 0
\(109\) 6.59351 0.631544 0.315772 0.948835i \(-0.397737\pi\)
0.315772 + 0.948835i \(0.397737\pi\)
\(110\) 0 0
\(111\) 3.10498 3.05112i 0.294712 0.289600i
\(112\) 0 0
\(113\) −8.90072 15.4165i −0.837309 1.45026i −0.892137 0.451766i \(-0.850794\pi\)
0.0548276 0.998496i \(-0.482539\pi\)
\(114\) 0 0
\(115\) 15.2853 26.4749i 1.42536 2.46880i
\(116\) 0 0
\(117\) 10.3056 5.71187i 0.952751 0.528063i
\(118\) 0 0
\(119\) 2.61471 4.52881i 0.239690 0.415155i
\(120\) 0 0
\(121\) 3.15582 + 5.46604i 0.286893 + 0.496913i
\(122\) 0 0
\(123\) −12.2982 3.41089i −1.10889 0.307550i
\(124\) 0 0
\(125\) −43.1706 −3.86130
\(126\) 0 0
\(127\) −18.2258 −1.61728 −0.808639 0.588305i \(-0.799795\pi\)
−0.808639 + 0.588305i \(0.799795\pi\)
\(128\) 0 0
\(129\) 2.19973 + 8.50653i 0.193676 + 0.748958i
\(130\) 0 0
\(131\) −4.33057 7.50076i −0.378363 0.655345i 0.612461 0.790501i \(-0.290180\pi\)
−0.990824 + 0.135156i \(0.956846\pi\)
\(132\) 0 0
\(133\) −2.57342 + 4.45729i −0.223144 + 0.386496i
\(134\) 0 0
\(135\) 6.55525 22.1247i 0.564186 1.90419i
\(136\) 0 0
\(137\) −0.774446 + 1.34138i −0.0661654 + 0.114602i −0.897210 0.441603i \(-0.854410\pi\)
0.831045 + 0.556205i \(0.187743\pi\)
\(138\) 0 0
\(139\) −9.78618 16.9502i −0.830053 1.43769i −0.897996 0.440005i \(-0.854977\pi\)
0.0679426 0.997689i \(-0.478357\pi\)
\(140\) 0 0
\(141\) 4.32418 + 16.7219i 0.364161 + 1.40824i
\(142\) 0 0
\(143\) 8.50416 0.711154
\(144\) 0 0
\(145\) 25.5219 2.11948
\(146\) 0 0
\(147\) −2.44796 0.678937i −0.201904 0.0559978i
\(148\) 0 0
\(149\) −0.945984 1.63849i −0.0774980 0.134230i 0.824672 0.565612i \(-0.191360\pi\)
−0.902170 + 0.431381i \(0.858026\pi\)
\(150\) 0 0
\(151\) −4.27927 + 7.41191i −0.348242 + 0.603173i −0.985937 0.167116i \(-0.946555\pi\)
0.637695 + 0.770289i \(0.279888\pi\)
\(152\) 0 0
\(153\) 0.0943385 5.39078i 0.00762682 0.435819i
\(154\) 0 0
\(155\) −14.5514 + 25.2038i −1.16880 + 2.02441i
\(156\) 0 0
\(157\) 2.22265 + 3.84974i 0.177387 + 0.307242i 0.940985 0.338449i \(-0.109902\pi\)
−0.763598 + 0.645692i \(0.776569\pi\)
\(158\) 0 0
\(159\) 4.08452 4.01366i 0.323923 0.318304i
\(160\) 0 0
\(161\) −20.0306 −1.57863
\(162\) 0 0
\(163\) −18.8817 −1.47893 −0.739465 0.673195i \(-0.764922\pi\)
−0.739465 + 0.673195i \(0.764922\pi\)
\(164\) 0 0
\(165\) 11.8793 11.6732i 0.924800 0.908757i
\(166\) 0 0
\(167\) 4.31394 + 7.47197i 0.333823 + 0.578198i 0.983258 0.182219i \(-0.0583279\pi\)
−0.649435 + 0.760417i \(0.724995\pi\)
\(168\) 0 0
\(169\) −1.21280 + 2.10063i −0.0932924 + 0.161587i
\(170\) 0 0
\(171\) −0.0928488 + 5.30565i −0.00710033 + 0.405733i
\(172\) 0 0
\(173\) −3.91423 + 6.77965i −0.297594 + 0.515447i −0.975585 0.219623i \(-0.929517\pi\)
0.677991 + 0.735070i \(0.262851\pi\)
\(174\) 0 0
\(175\) 21.4176 + 37.0964i 1.61902 + 2.80422i
\(176\) 0 0
\(177\) 7.68062 + 2.13021i 0.577311 + 0.160116i
\(178\) 0 0
\(179\) −13.6390 −1.01943 −0.509714 0.860344i \(-0.670249\pi\)
−0.509714 + 0.860344i \(0.670249\pi\)
\(180\) 0 0
\(181\) −0.504672 −0.0375120 −0.0187560 0.999824i \(-0.505971\pi\)
−0.0187560 + 0.999824i \(0.505971\pi\)
\(182\) 0 0
\(183\) 1.62485 + 6.28340i 0.120112 + 0.464482i
\(184\) 0 0
\(185\) 5.58064 + 9.66596i 0.410297 + 0.710655i
\(186\) 0 0
\(187\) 1.94571 3.37006i 0.142284 0.246443i
\(188\) 0 0
\(189\) −14.7020 + 3.52860i −1.06941 + 0.256668i
\(190\) 0 0
\(191\) −10.0083 + 17.3349i −0.724175 + 1.25431i 0.235138 + 0.971962i \(0.424446\pi\)
−0.959313 + 0.282345i \(0.908888\pi\)
\(192\) 0 0
\(193\) −1.08462 1.87862i −0.0780726 0.135226i 0.824346 0.566087i \(-0.191543\pi\)
−0.902418 + 0.430861i \(0.858210\pi\)
\(194\) 0 0
\(195\) 7.56329 + 29.2478i 0.541618 + 2.09448i
\(196\) 0 0
\(197\) −5.67460 −0.404298 −0.202149 0.979355i \(-0.564793\pi\)
−0.202149 + 0.979355i \(0.564793\pi\)
\(198\) 0 0
\(199\) −11.5032 −0.815439 −0.407719 0.913107i \(-0.633676\pi\)
−0.407719 + 0.913107i \(0.633676\pi\)
\(200\) 0 0
\(201\) −7.87939 2.18534i −0.555769 0.154142i
\(202\) 0 0
\(203\) −8.36126 14.4821i −0.586846 1.01645i
\(204\) 0 0
\(205\) 16.3610 28.3381i 1.14270 1.97922i
\(206\) 0 0
\(207\) −18.0629 + 10.0114i −1.25546 + 0.695839i
\(208\) 0 0
\(209\) −1.91498 + 3.31684i −0.132462 + 0.229431i
\(210\) 0 0
\(211\) 10.3177 + 17.8707i 0.710297 + 1.23027i 0.964746 + 0.263184i \(0.0847726\pi\)
−0.254449 + 0.967086i \(0.581894\pi\)
\(212\) 0 0
\(213\) 1.12119 1.10174i 0.0768224 0.0754897i
\(214\) 0 0
\(215\) −22.5276 −1.53637
\(216\) 0 0
\(217\) 19.0688 1.29448
\(218\) 0 0
\(219\) −2.31936 + 2.27913i −0.156728 + 0.154009i
\(220\) 0 0
\(221\) 3.52929 + 6.11292i 0.237406 + 0.411199i
\(222\) 0 0
\(223\) 2.54291 4.40444i 0.170286 0.294943i −0.768234 0.640169i \(-0.778864\pi\)
0.938520 + 0.345226i \(0.112198\pi\)
\(224\) 0 0
\(225\) 37.8547 + 22.7477i 2.52364 + 1.51651i
\(226\) 0 0
\(227\) 9.14484 15.8393i 0.606964 1.05129i −0.384773 0.923011i \(-0.625720\pi\)
0.991738 0.128282i \(-0.0409462\pi\)
\(228\) 0 0
\(229\) 9.62341 + 16.6682i 0.635933 + 1.10147i 0.986317 + 0.164862i \(0.0527178\pi\)
−0.350384 + 0.936606i \(0.613949\pi\)
\(230\) 0 0
\(231\) −10.5156 2.91650i −0.691878 0.191891i
\(232\) 0 0
\(233\) 16.4263 1.07612 0.538061 0.842906i \(-0.319157\pi\)
0.538061 + 0.842906i \(0.319157\pi\)
\(234\) 0 0
\(235\) −44.2841 −2.88878
\(236\) 0 0
\(237\) −1.07247 4.14732i −0.0696644 0.269397i
\(238\) 0 0
\(239\) −9.08563 15.7368i −0.587700 1.01793i −0.994533 0.104424i \(-0.966700\pi\)
0.406833 0.913503i \(-0.366633\pi\)
\(240\) 0 0
\(241\) −11.4344 + 19.8050i −0.736556 + 1.27575i 0.217481 + 0.976065i \(0.430216\pi\)
−0.954037 + 0.299688i \(0.903117\pi\)
\(242\) 0 0
\(243\) −11.4942 + 10.5301i −0.737353 + 0.675507i
\(244\) 0 0
\(245\) 3.25666 5.64070i 0.208060 0.360371i
\(246\) 0 0
\(247\) −3.47356 6.01639i −0.221017 0.382813i
\(248\) 0 0
\(249\) −0.947493 3.66402i −0.0600449 0.232198i
\(250\) 0 0
\(251\) −0.139530 −0.00880707 −0.00440353 0.999990i \(-0.501402\pi\)
−0.00440353 + 0.999990i \(0.501402\pi\)
\(252\) 0 0
\(253\) −14.9055 −0.937102
\(254\) 0 0
\(255\) 13.3209 + 3.69452i 0.834185 + 0.231360i
\(256\) 0 0
\(257\) −7.17682 12.4306i −0.447678 0.775400i 0.550557 0.834798i \(-0.314415\pi\)
−0.998234 + 0.0593974i \(0.981082\pi\)
\(258\) 0 0
\(259\) 3.65657 6.33336i 0.227208 0.393536i
\(260\) 0 0
\(261\) −14.7782 8.88052i −0.914745 0.549690i
\(262\) 0 0
\(263\) −0.968751 + 1.67793i −0.0597357 + 0.103465i −0.894347 0.447374i \(-0.852359\pi\)
0.834611 + 0.550840i \(0.185692\pi\)
\(264\) 0 0
\(265\) 7.34118 + 12.7153i 0.450965 + 0.781094i
\(266\) 0 0
\(267\) −6.55534 + 6.44163i −0.401181 + 0.394221i
\(268\) 0 0
\(269\) 9.91415 0.604477 0.302238 0.953232i \(-0.402266\pi\)
0.302238 + 0.953232i \(0.402266\pi\)
\(270\) 0 0
\(271\) −4.56777 −0.277472 −0.138736 0.990329i \(-0.544304\pi\)
−0.138736 + 0.990329i \(0.544304\pi\)
\(272\) 0 0
\(273\) 14.1185 13.8736i 0.854493 0.839670i
\(274\) 0 0
\(275\) 15.9377 + 27.6048i 0.961077 + 1.66463i
\(276\) 0 0
\(277\) −14.4728 + 25.0676i −0.869585 + 1.50616i −0.00716263 + 0.999974i \(0.502280\pi\)
−0.862422 + 0.506190i \(0.831053\pi\)
\(278\) 0 0
\(279\) 17.1957 9.53070i 1.02948 0.570588i
\(280\) 0 0
\(281\) 11.1351 19.2865i 0.664262 1.15054i −0.315223 0.949018i \(-0.602079\pi\)
0.979485 0.201518i \(-0.0645875\pi\)
\(282\) 0 0
\(283\) 6.79946 + 11.7770i 0.404186 + 0.700071i 0.994226 0.107303i \(-0.0342215\pi\)
−0.590040 + 0.807374i \(0.700888\pi\)
\(284\) 0 0
\(285\) −13.1105 3.63618i −0.776599 0.215389i
\(286\) 0 0
\(287\) −21.4403 −1.26558
\(288\) 0 0
\(289\) −13.7701 −0.810004
\(290\) 0 0
\(291\) −3.86196 14.9345i −0.226392 0.875474i
\(292\) 0 0
\(293\) −7.21821 12.5023i −0.421693 0.730393i 0.574413 0.818566i \(-0.305230\pi\)
−0.996105 + 0.0881730i \(0.971897\pi\)
\(294\) 0 0
\(295\) −10.2180 + 17.6980i −0.594913 + 1.03042i
\(296\) 0 0
\(297\) −10.9403 + 2.62576i −0.634823 + 0.152362i
\(298\) 0 0
\(299\) 13.5185 23.4147i 0.781794 1.35411i
\(300\) 0 0
\(301\) 7.38030 + 12.7831i 0.425394 + 0.736804i
\(302\) 0 0
\(303\) 0.597829 + 2.31185i 0.0343444 + 0.132812i
\(304\) 0 0
\(305\) −16.6401 −0.952812
\(306\) 0 0
\(307\) −16.5451 −0.944280 −0.472140 0.881524i \(-0.656518\pi\)
−0.472140 + 0.881524i \(0.656518\pi\)
\(308\) 0 0
\(309\) 8.49585 + 2.35631i 0.483312 + 0.134046i
\(310\) 0 0
\(311\) −5.19366 8.99568i −0.294505 0.510098i 0.680364 0.732874i \(-0.261822\pi\)
−0.974870 + 0.222776i \(0.928488\pi\)
\(312\) 0 0
\(313\) −6.76501 + 11.7173i −0.382381 + 0.662303i −0.991402 0.130851i \(-0.958229\pi\)
0.609021 + 0.793154i \(0.291562\pi\)
\(314\) 0 0
\(315\) 0.678291 38.7595i 0.0382174 2.18385i
\(316\) 0 0
\(317\) −11.9869 + 20.7619i −0.673251 + 1.16611i 0.303726 + 0.952760i \(0.401769\pi\)
−0.976977 + 0.213346i \(0.931564\pi\)
\(318\) 0 0
\(319\) −6.22194 10.7767i −0.348362 0.603380i
\(320\) 0 0
\(321\) 21.2567 20.8880i 1.18644 1.16585i
\(322\) 0 0
\(323\) −3.17893 −0.176880
\(324\) 0 0
\(325\) −57.8183 −3.20718
\(326\) 0 0
\(327\) 8.14571 8.00441i 0.450459 0.442645i
\(328\) 0 0
\(329\) 14.5080 + 25.1286i 0.799851 + 1.38538i
\(330\) 0 0
\(331\) −1.29103 + 2.23612i −0.0709612 + 0.122908i −0.899323 0.437285i \(-0.855940\pi\)
0.828362 + 0.560194i \(0.189273\pi\)
\(332\) 0 0
\(333\) 0.131929 7.53879i 0.00722965 0.413123i
\(334\) 0 0
\(335\) 10.4824 18.1561i 0.572715 0.991972i
\(336\) 0 0
\(337\) −1.79736 3.11313i −0.0979087 0.169583i 0.812910 0.582389i \(-0.197882\pi\)
−0.910819 + 0.412806i \(0.864549\pi\)
\(338\) 0 0
\(339\) −29.7114 8.24042i −1.61370 0.447558i
\(340\) 0 0
\(341\) 14.1899 0.768424
\(342\) 0 0
\(343\) 16.1006 0.869351
\(344\) 0 0
\(345\) −13.2564 51.2636i −0.713702 2.75994i
\(346\) 0 0
\(347\) 5.85180 + 10.1356i 0.314141 + 0.544108i 0.979255 0.202634i \(-0.0649502\pi\)
−0.665114 + 0.746742i \(0.731617\pi\)
\(348\) 0 0
\(349\) 9.34856 16.1922i 0.500417 0.866747i −0.499583 0.866266i \(-0.666513\pi\)
1.00000 0.000481224i \(-0.000153178\pi\)
\(350\) 0 0
\(351\) 5.79754 19.5673i 0.309450 1.04443i
\(352\) 0 0
\(353\) 14.3410 24.8394i 0.763295 1.32207i −0.177848 0.984058i \(-0.556914\pi\)
0.941143 0.338008i \(-0.109753\pi\)
\(354\) 0 0
\(355\) 2.01513 + 3.49030i 0.106952 + 0.185246i
\(356\) 0 0
\(357\) −2.26765 8.76916i −0.120017 0.464113i
\(358\) 0 0
\(359\) −15.8202 −0.834958 −0.417479 0.908687i \(-0.637086\pi\)
−0.417479 + 0.908687i \(0.637086\pi\)
\(360\) 0 0
\(361\) −15.8713 −0.835330
\(362\) 0 0
\(363\) 10.5344 + 2.92171i 0.552914 + 0.153350i
\(364\) 0 0
\(365\) −4.16863 7.22028i −0.218196 0.377927i
\(366\) 0 0
\(367\) 13.1383 22.7563i 0.685815 1.18787i −0.287364 0.957821i \(-0.592779\pi\)
0.973180 0.230046i \(-0.0738876\pi\)
\(368\) 0 0
\(369\) −19.3341 + 10.7160i −1.00649 + 0.557850i
\(370\) 0 0
\(371\) 4.81011 8.33136i 0.249729 0.432543i
\(372\) 0 0
\(373\) 10.8735 + 18.8335i 0.563010 + 0.975162i 0.997232 + 0.0743558i \(0.0236901\pi\)
−0.434222 + 0.900806i \(0.642977\pi\)
\(374\) 0 0
\(375\) −53.3336 + 52.4084i −2.75413 + 2.70636i
\(376\) 0 0
\(377\) 22.5718 1.16251
\(378\) 0 0
\(379\) 32.8861 1.68925 0.844623 0.535362i \(-0.179825\pi\)
0.844623 + 0.535362i \(0.179825\pi\)
\(380\) 0 0
\(381\) −22.5164 + 22.1258i −1.15355 + 1.13354i
\(382\) 0 0
\(383\) 5.81269 + 10.0679i 0.297015 + 0.514444i 0.975452 0.220214i \(-0.0706757\pi\)
−0.678437 + 0.734659i \(0.737342\pi\)
\(384\) 0 0
\(385\) 13.9896 24.2306i 0.712974 1.23491i
\(386\) 0 0
\(387\) 13.0444 + 7.83864i 0.663082 + 0.398461i
\(388\) 0 0
\(389\) −3.61687 + 6.26460i −0.183383 + 0.317628i −0.943030 0.332707i \(-0.892038\pi\)
0.759648 + 0.650335i \(0.225371\pi\)
\(390\) 0 0
\(391\) −6.18591 10.7143i −0.312835 0.541846i
\(392\) 0 0
\(393\) −14.4558 4.00931i −0.729200 0.202243i
\(394\) 0 0
\(395\) 10.9832 0.552625
\(396\) 0 0
\(397\) 29.8911 1.50019 0.750095 0.661330i \(-0.230008\pi\)
0.750095 + 0.661330i \(0.230008\pi\)
\(398\) 0 0
\(399\) 2.23184 + 8.63069i 0.111732 + 0.432075i
\(400\) 0 0
\(401\) 3.03226 + 5.25202i 0.151424 + 0.262273i 0.931751 0.363098i \(-0.118281\pi\)
−0.780327 + 0.625371i \(0.784948\pi\)
\(402\) 0 0
\(403\) −12.8694 + 22.2905i −0.641071 + 1.11037i
\(404\) 0 0
\(405\) −18.7605 35.2911i −0.932219 1.75363i
\(406\) 0 0
\(407\) 2.72099 4.71290i 0.134875 0.233610i
\(408\) 0 0
\(409\) −14.4396 25.0101i −0.713993 1.23667i −0.963347 0.268259i \(-0.913552\pi\)
0.249354 0.968412i \(-0.419782\pi\)
\(410\) 0 0
\(411\) 0.671651 + 2.59732i 0.0331301 + 0.128116i
\(412\) 0 0
\(413\) 13.3901 0.658884
\(414\) 0 0
\(415\) 9.70332 0.476317
\(416\) 0 0
\(417\) −32.6672 9.06020i −1.59972 0.443680i
\(418\) 0 0
\(419\) 5.63281 + 9.75631i 0.275181 + 0.476627i 0.970181 0.242383i \(-0.0779290\pi\)
−0.695000 + 0.719010i \(0.744596\pi\)
\(420\) 0 0
\(421\) −6.03050 + 10.4451i −0.293909 + 0.509065i −0.974730 0.223384i \(-0.928289\pi\)
0.680822 + 0.732449i \(0.261623\pi\)
\(422\) 0 0
\(423\) 25.6422 + 15.4090i 1.24677 + 0.749210i
\(424\) 0 0
\(425\) −13.2285 + 22.9125i −0.641677 + 1.11142i
\(426\) 0 0
\(427\) 5.45151 + 9.44229i 0.263817 + 0.456944i
\(428\) 0 0
\(429\) 10.5062 10.3239i 0.507242 0.498443i
\(430\) 0 0
\(431\) −25.5079 −1.22867 −0.614336 0.789045i \(-0.710576\pi\)
−0.614336 + 0.789045i \(0.710576\pi\)
\(432\) 0 0
\(433\) 29.4513 1.41534 0.707670 0.706543i \(-0.249746\pi\)
0.707670 + 0.706543i \(0.249746\pi\)
\(434\) 0 0
\(435\) 31.5301 30.9831i 1.51175 1.48553i
\(436\) 0 0
\(437\) 6.08823 + 10.5451i 0.291239 + 0.504441i
\(438\) 0 0
\(439\) 17.8086 30.8454i 0.849959 1.47217i −0.0312845 0.999511i \(-0.509960\pi\)
0.881244 0.472662i \(-0.156707\pi\)
\(440\) 0 0
\(441\) −3.84845 + 2.13301i −0.183260 + 0.101572i
\(442\) 0 0
\(443\) −6.60886 + 11.4469i −0.313996 + 0.543857i −0.979224 0.202783i \(-0.935001\pi\)
0.665227 + 0.746641i \(0.268335\pi\)
\(444\) 0 0
\(445\) −11.7820 20.4071i −0.558522 0.967389i
\(446\) 0 0
\(447\) −3.15778 0.875807i −0.149358 0.0414242i
\(448\) 0 0
\(449\) −5.83739 −0.275483 −0.137742 0.990468i \(-0.543984\pi\)
−0.137742 + 0.990468i \(0.543984\pi\)
\(450\) 0 0
\(451\) −15.9545 −0.751269
\(452\) 0 0
\(453\) 3.71127 + 14.3517i 0.174370 + 0.674303i
\(454\) 0 0
\(455\) 25.3755 + 43.9517i 1.18962 + 2.06049i
\(456\) 0 0
\(457\) −13.5037 + 23.3891i −0.631677 + 1.09410i 0.355532 + 0.934664i \(0.384300\pi\)
−0.987209 + 0.159433i \(0.949034\pi\)
\(458\) 0 0
\(459\) −6.42777 6.77437i −0.300022 0.316200i
\(460\) 0 0
\(461\) 1.78550 3.09258i 0.0831591 0.144036i −0.821446 0.570286i \(-0.806832\pi\)
0.904605 + 0.426250i \(0.140166\pi\)
\(462\) 0 0
\(463\) −19.8396 34.3631i −0.922023 1.59699i −0.796281 0.604927i \(-0.793202\pi\)
−0.125742 0.992063i \(-0.540131\pi\)
\(464\) 0 0
\(465\) 12.6199 + 48.8022i 0.585236 + 2.26315i
\(466\) 0 0
\(467\) −18.8522 −0.872376 −0.436188 0.899855i \(-0.643672\pi\)
−0.436188 + 0.899855i \(0.643672\pi\)
\(468\) 0 0
\(469\) −13.7366 −0.634299
\(470\) 0 0
\(471\) 7.41940 + 2.05776i 0.341868 + 0.0948167i
\(472\) 0 0
\(473\) 5.49197 + 9.51237i 0.252521 + 0.437379i
\(474\) 0 0
\(475\) 13.0196 22.5506i 0.597381 1.03469i
\(476\) 0 0
\(477\) 0.173549 9.91707i 0.00794624 0.454071i
\(478\) 0 0
\(479\) 11.0879 19.2049i 0.506621 0.877492i −0.493350 0.869831i \(-0.664228\pi\)
0.999971 0.00766167i \(-0.00243881\pi\)
\(480\) 0 0
\(481\) 4.93558 + 8.54867i 0.225043 + 0.389786i
\(482\) 0 0
\(483\) −24.7460 + 24.3168i −1.12598 + 1.10645i
\(484\) 0 0
\(485\) 39.5505 1.79590
\(486\) 0 0
\(487\) −17.9432 −0.813086 −0.406543 0.913632i \(-0.633266\pi\)
−0.406543 + 0.913632i \(0.633266\pi\)
\(488\) 0 0
\(489\) −23.3267 + 22.9221i −1.05487 + 1.03657i
\(490\) 0 0
\(491\) 1.71919 + 2.97773i 0.0775861 + 0.134383i 0.902208 0.431301i \(-0.141945\pi\)
−0.824622 + 0.565684i \(0.808612\pi\)
\(492\) 0 0
\(493\) 5.16431 8.94485i 0.232589 0.402856i
\(494\) 0 0
\(495\) 0.504742 28.8425i 0.0226865 1.29637i
\(496\) 0 0
\(497\) 1.32036 2.28693i 0.0592262 0.102583i
\(498\) 0 0
\(499\) 5.41124 + 9.37254i 0.242240 + 0.419572i 0.961352 0.275322i \(-0.0887845\pi\)
−0.719112 + 0.694894i \(0.755451\pi\)
\(500\) 0 0
\(501\) 14.4003 + 3.99392i 0.643360 + 0.178435i
\(502\) 0 0
\(503\) 9.71510 0.433175 0.216587 0.976263i \(-0.430507\pi\)
0.216587 + 0.976263i \(0.430507\pi\)
\(504\) 0 0
\(505\) −6.12240 −0.272443
\(506\) 0 0
\(507\) 1.05182 + 4.06747i 0.0467130 + 0.180643i
\(508\) 0 0
\(509\) −17.5991 30.4825i −0.780066 1.35111i −0.931903 0.362708i \(-0.881852\pi\)
0.151837 0.988406i \(-0.451481\pi\)
\(510\) 0 0
\(511\) −2.73138 + 4.73090i −0.120829 + 0.209283i
\(512\) 0 0
\(513\) 6.32626 + 6.66739i 0.279311 + 0.294372i
\(514\) 0 0
\(515\) −11.3025 + 19.5766i −0.498049 + 0.862646i
\(516\) 0 0
\(517\) 10.7960 + 18.6991i 0.474806 + 0.822387i
\(518\) 0 0
\(519\) 3.39468 + 13.1275i 0.149010 + 0.576233i
\(520\) 0 0
\(521\) −7.57440 −0.331840 −0.165920 0.986139i \(-0.553059\pi\)
−0.165920 + 0.986139i \(0.553059\pi\)
\(522\) 0 0
\(523\) 10.0630 0.440025 0.220013 0.975497i \(-0.429390\pi\)
0.220013 + 0.975497i \(0.429390\pi\)
\(524\) 0 0
\(525\) 71.4939 + 19.8288i 3.12025 + 0.865398i
\(526\) 0 0
\(527\) 5.88890 + 10.1999i 0.256525 + 0.444314i
\(528\) 0 0
\(529\) −12.1943 + 21.1211i −0.530187 + 0.918310i
\(530\) 0 0
\(531\) 12.0748 6.69245i 0.524001 0.290427i
\(532\) 0 0
\(533\) 14.4699 25.0625i 0.626759 1.08558i
\(534\) 0 0
\(535\) 38.2051 + 66.1732i 1.65175 + 2.86092i
\(536\) 0 0
\(537\) −16.8498 + 16.5575i −0.727124 + 0.714511i
\(538\) 0 0
\(539\) −3.17574 −0.136789
\(540\) 0 0
\(541\) −26.2133 −1.12700 −0.563498 0.826117i \(-0.690545\pi\)
−0.563498 + 0.826117i \(0.690545\pi\)
\(542\) 0 0
\(543\) −0.623479 + 0.612663i −0.0267560 + 0.0262919i
\(544\) 0 0
\(545\) 14.6404 + 25.3580i 0.627127 + 1.08622i
\(546\) 0 0
\(547\) 9.57620 16.5865i 0.409449 0.709186i −0.585379 0.810760i \(-0.699054\pi\)
0.994828 + 0.101574i \(0.0323878\pi\)
\(548\) 0 0
\(549\) 9.63530 + 5.79006i 0.411225 + 0.247114i
\(550\) 0 0
\(551\) −5.08276 + 8.80359i −0.216533 + 0.375046i
\(552\) 0 0
\(553\) −3.59823 6.23232i −0.153012 0.265025i
\(554\) 0 0
\(555\) 18.6287 + 5.16665i 0.790744 + 0.219312i
\(556\) 0 0
\(557\) 22.5019 0.953435 0.476717 0.879057i \(-0.341827\pi\)
0.476717 + 0.879057i \(0.341827\pi\)
\(558\) 0 0
\(559\) −19.9236 −0.842680
\(560\) 0 0
\(561\) −1.68745 6.52547i −0.0712440 0.275506i
\(562\) 0 0
\(563\) 12.7085 + 22.0118i 0.535599 + 0.927685i 0.999134 + 0.0416066i \(0.0132476\pi\)
−0.463535 + 0.886079i \(0.653419\pi\)
\(564\) 0 0
\(565\) 39.5268 68.4625i 1.66291 2.88024i
\(566\) 0 0
\(567\) −13.8794 + 22.2073i −0.582881 + 0.932618i
\(568\) 0 0
\(569\) 9.14798 15.8448i 0.383503 0.664247i −0.608057 0.793893i \(-0.708051\pi\)
0.991560 + 0.129646i \(0.0413842\pi\)
\(570\) 0 0
\(571\) 1.27484 + 2.20808i 0.0533503 + 0.0924054i 0.891467 0.453085i \(-0.149677\pi\)
−0.838117 + 0.545491i \(0.816343\pi\)
\(572\) 0 0
\(573\) 8.67986 + 33.5656i 0.362606 + 1.40222i
\(574\) 0 0
\(575\) 101.340 4.22617
\(576\) 0 0
\(577\) 2.22842 0.0927702 0.0463851 0.998924i \(-0.485230\pi\)
0.0463851 + 0.998924i \(0.485230\pi\)
\(578\) 0 0
\(579\) −3.62056 1.00416i −0.150465 0.0417314i
\(580\) 0 0
\(581\) −3.17892 5.50606i −0.131884 0.228430i
\(582\) 0 0
\(583\) 3.57939 6.19968i 0.148243 0.256765i
\(584\) 0 0
\(585\) 44.8501 + 26.9514i 1.85432 + 1.11430i
\(586\) 0 0
\(587\) 15.2694 26.4473i 0.630234 1.09160i −0.357270 0.934001i \(-0.616292\pi\)
0.987504 0.157596i \(-0.0503743\pi\)
\(588\) 0 0
\(589\) −5.79591 10.0388i −0.238816 0.413642i
\(590\) 0 0
\(591\) −7.01048 + 6.88887i −0.288372 + 0.283370i
\(592\) 0 0
\(593\) −5.96281 −0.244863 −0.122432 0.992477i \(-0.539069\pi\)
−0.122432 + 0.992477i \(0.539069\pi\)
\(594\) 0 0
\(595\) 23.2231 0.952055
\(596\) 0 0
\(597\) −14.2112 + 13.9647i −0.581625 + 0.571536i
\(598\) 0 0
\(599\) −4.29265 7.43508i −0.175393 0.303789i 0.764904 0.644144i \(-0.222786\pi\)
−0.940297 + 0.340355i \(0.889453\pi\)
\(600\) 0 0
\(601\) 1.44648 2.50538i 0.0590033 0.102197i −0.835015 0.550227i \(-0.814541\pi\)
0.894018 + 0.448031i \(0.147874\pi\)
\(602\) 0 0
\(603\) −12.3873 + 6.86565i −0.504448 + 0.279591i
\(604\) 0 0
\(605\) −14.0146 + 24.2739i −0.569773 + 0.986876i
\(606\) 0 0
\(607\) 9.96773 + 17.2646i 0.404577 + 0.700749i 0.994272 0.106877i \(-0.0340853\pi\)
−0.589695 + 0.807626i \(0.700752\pi\)
\(608\) 0 0
\(609\) −27.9107 7.74099i −1.13100 0.313681i
\(610\) 0 0
\(611\) −39.1653 −1.58446
\(612\) 0 0
\(613\) 35.4941 1.43359 0.716797 0.697282i \(-0.245607\pi\)
0.716797 + 0.697282i \(0.245607\pi\)
\(614\) 0 0
\(615\) −14.1894 54.8713i −0.572171 2.21262i
\(616\) 0 0
\(617\) −15.6891 27.1743i −0.631618 1.09399i −0.987221 0.159357i \(-0.949058\pi\)
0.355603 0.934637i \(-0.384276\pi\)
\(618\) 0 0
\(619\) 16.7289 28.9752i 0.672389 1.16461i −0.304835 0.952405i \(-0.598601\pi\)
0.977225 0.212207i \(-0.0680652\pi\)
\(620\) 0 0
\(621\) −10.1615 + 34.2963i −0.407768 + 1.37626i
\(622\) 0 0
\(623\) −7.71987 + 13.3712i −0.309290 + 0.535706i
\(624\) 0 0
\(625\) −59.0543 102.285i −2.36217 4.09140i
\(626\) 0 0
\(627\) 1.66080 + 6.42243i 0.0663259 + 0.256487i
\(628\) 0 0
\(629\) 4.51694 0.180102
\(630\) 0 0
\(631\) −8.12216 −0.323338 −0.161669 0.986845i \(-0.551688\pi\)
−0.161669 + 0.986845i \(0.551688\pi\)
\(632\) 0 0
\(633\) 34.4413 + 9.55225i 1.36892 + 0.379668i
\(634\) 0 0
\(635\) −40.4691 70.0945i −1.60597 2.78162i
\(636\) 0 0
\(637\) 2.88022 4.98869i 0.114119 0.197659i
\(638\) 0 0
\(639\) 0.0476384 2.72220i 0.00188455 0.107689i
\(640\) 0 0
\(641\) −10.4782 + 18.1488i −0.413865 + 0.716836i −0.995309 0.0967511i \(-0.969155\pi\)
0.581443 + 0.813587i \(0.302488\pi\)
\(642\) 0 0
\(643\) 16.3547 + 28.3272i 0.644967 + 1.11712i 0.984309 + 0.176453i \(0.0564623\pi\)
−0.339342 + 0.940663i \(0.610204\pi\)
\(644\) 0 0
\(645\) −27.8309 + 27.3481i −1.09584 + 1.07683i
\(646\) 0 0
\(647\) 18.7820 0.738395 0.369198 0.929351i \(-0.379633\pi\)
0.369198 + 0.929351i \(0.379633\pi\)
\(648\) 0 0
\(649\) 9.96410 0.391125
\(650\) 0 0
\(651\) 23.5579 23.1492i 0.923307 0.907290i
\(652\) 0 0
\(653\) 4.85977 + 8.41736i 0.190177 + 0.329397i 0.945309 0.326176i \(-0.105760\pi\)
−0.755132 + 0.655573i \(0.772427\pi\)
\(654\) 0 0
\(655\) 19.2314 33.3098i 0.751435 1.30152i
\(656\) 0 0
\(657\) −0.0985482 + 5.63133i −0.00384473 + 0.219699i
\(658\) 0 0
\(659\) 16.1773 28.0198i 0.630177 1.09150i −0.357338 0.933975i \(-0.616316\pi\)
0.987515 0.157523i \(-0.0503510\pi\)
\(660\) 0 0
\(661\) −13.0319 22.5719i −0.506883 0.877946i −0.999968 0.00796563i \(-0.997464\pi\)
0.493086 0.869981i \(-0.335869\pi\)
\(662\) 0 0
\(663\) 11.7811 + 3.26748i 0.457540 + 0.126898i
\(664\) 0 0
\(665\) −22.8564 −0.886333
\(666\) 0 0
\(667\) −39.5624 −1.53186
\(668\) 0 0
\(669\) −2.20538 8.52835i −0.0852648 0.329725i
\(670\) 0 0
\(671\) 4.05668 + 7.02637i 0.156606 + 0.271250i
\(672\) 0 0
\(673\) 16.6951 28.9167i 0.643549 1.11466i −0.341086 0.940032i \(-0.610795\pi\)
0.984635 0.174627i \(-0.0558719\pi\)
\(674\) 0 0
\(675\) 74.3815 17.8521i 2.86294 0.687128i
\(676\) 0 0
\(677\) −12.6991 + 21.9955i −0.488065 + 0.845354i −0.999906 0.0137265i \(-0.995631\pi\)
0.511840 + 0.859081i \(0.328964\pi\)
\(678\) 0 0
\(679\) −12.9572 22.4425i −0.497252 0.861266i
\(680\) 0 0
\(681\) −7.93101 30.6698i −0.303917 1.17527i
\(682\) 0 0
\(683\) −37.2800 −1.42648 −0.713241 0.700919i \(-0.752773\pi\)
−0.713241 + 0.700919i \(0.752773\pi\)
\(684\) 0 0
\(685\) −6.87841 −0.262811
\(686\) 0 0
\(687\) 32.1238 + 8.90950i 1.22560 + 0.339919i
\(688\) 0 0
\(689\) 6.49261 + 11.2455i 0.247349 + 0.428421i
\(690\) 0 0
\(691\) −6.41730 + 11.1151i −0.244126 + 0.422838i −0.961885 0.273453i \(-0.911834\pi\)
0.717760 + 0.696291i \(0.245168\pi\)
\(692\) 0 0
\(693\) −16.5317 + 9.16271i −0.627988 + 0.348063i
\(694\) 0 0
\(695\) 43.4591 75.2733i 1.64850 2.85528i
\(696\) 0 0
\(697\) −6.62125 11.4683i −0.250798 0.434395i
\(698\) 0 0
\(699\) 20.2933 19.9412i 0.767561 0.754247i
\(700\) 0 0
\(701\) −6.89156 −0.260290 −0.130145 0.991495i \(-0.541544\pi\)
−0.130145 + 0.991495i \(0.541544\pi\)
\(702\) 0 0
\(703\) −4.44561 −0.167669
\(704\) 0 0
\(705\) −54.7092 + 53.7601i −2.06047 + 2.02472i
\(706\) 0 0
\(707\) 2.00577 + 3.47410i 0.0754347 + 0.130657i
\(708\) 0 0
\(709\) 10.1178 17.5246i 0.379983 0.658150i −0.611076 0.791572i \(-0.709263\pi\)
0.991059 + 0.133422i \(0.0425964\pi\)
\(710\) 0 0
\(711\) −6.35971 3.82169i −0.238508 0.143325i
\(712\) 0 0
\(713\) 22.5566 39.0693i 0.844753 1.46316i
\(714\) 0 0
\(715\) 18.8829 + 32.7061i 0.706180 + 1.22314i
\(716\) 0 0
\(717\) −30.3287 8.41162i −1.13264 0.314138i
\(718\) 0 0
\(719\) 44.1706 1.64729 0.823643 0.567108i \(-0.191938\pi\)
0.823643 + 0.567108i \(0.191938\pi\)
\(720\) 0 0
\(721\) 14.8114 0.551604
\(722\) 0 0
\(723\) 9.91670 + 38.3486i 0.368806 + 1.42620i
\(724\) 0 0
\(725\) 42.3019 + 73.2690i 1.57105 + 2.72114i
\(726\) 0 0
\(727\) 7.29193 12.6300i 0.270443 0.468421i −0.698532 0.715578i \(-0.746163\pi\)
0.968975 + 0.247158i \(0.0794965\pi\)
\(728\) 0 0
\(729\) −1.41670 + 26.9628i −0.0524705 + 0.998622i
\(730\) 0 0
\(731\) −4.55842 + 7.89542i −0.168599 + 0.292023i
\(732\) 0 0
\(733\) 16.4444 + 28.4826i 0.607388 + 1.05203i 0.991669 + 0.128811i \(0.0411161\pi\)
−0.384281 + 0.923216i \(0.625551\pi\)
\(734\) 0 0
\(735\) −2.82439 10.9221i −0.104179 0.402868i
\(736\) 0 0
\(737\) −10.2220 −0.376531
\(738\) 0 0
\(739\) 35.3966 1.30208 0.651042 0.759041i \(-0.274332\pi\)
0.651042 + 0.759041i \(0.274332\pi\)
\(740\) 0 0
\(741\) −11.5951 3.21588i −0.425956 0.118138i
\(742\) 0 0
\(743\) 18.8177 + 32.5932i 0.690353 + 1.19573i 0.971722 + 0.236127i \(0.0758782\pi\)
−0.281369 + 0.959600i \(0.590788\pi\)
\(744\) 0 0
\(745\) 4.20098 7.27631i 0.153912 0.266584i
\(746\) 0 0
\(747\) −5.61861 3.37634i −0.205574 0.123534i
\(748\) 0 0
\(749\) 25.0329 43.3582i 0.914682 1.58427i
\(750\) 0 0
\(751\) 8.38950 + 14.5310i 0.306137 + 0.530245i 0.977514 0.210871i \(-0.0676300\pi\)
−0.671377 + 0.741116i \(0.734297\pi\)
\(752\) 0 0
\(753\) −0.172377 + 0.169387i −0.00628178 + 0.00617281i
\(754\) 0 0
\(755\) −38.0073 −1.38323
\(756\) 0 0
\(757\) 19.4825 0.708103 0.354051 0.935226i \(-0.384804\pi\)
0.354051 + 0.935226i \(0.384804\pi\)
\(758\) 0 0
\(759\) −18.4145 + 18.0950i −0.668403 + 0.656809i
\(760\) 0 0
\(761\) −9.49573 16.4471i −0.344220 0.596206i 0.640992 0.767548i \(-0.278523\pi\)
−0.985212 + 0.171341i \(0.945190\pi\)
\(762\) 0 0
\(763\) 9.59276 16.6151i 0.347281 0.601508i
\(764\) 0 0
\(765\) 20.9419 11.6070i 0.757154 0.419653i
\(766\) 0 0
\(767\) −9.03688 + 15.6523i −0.326303 + 0.565173i
\(768\) 0 0
\(769\) 21.2098 + 36.7365i 0.764846 + 1.32475i 0.940328 + 0.340270i \(0.110518\pi\)
−0.175482 + 0.984483i \(0.556148\pi\)
\(770\) 0 0
\(771\) −23.9569 6.64441i −0.862786 0.239293i
\(772\) 0 0
\(773\) 2.55333 0.0918368 0.0459184 0.998945i \(-0.485379\pi\)
0.0459184 + 0.998945i \(0.485379\pi\)
\(774\) 0 0
\(775\) −96.4744 −3.46546
\(776\) 0 0
\(777\) −3.17122 12.2633i −0.113767 0.439944i
\(778\) 0 0
\(779\) 6.51670 + 11.2872i 0.233485 + 0.404408i
\(780\) 0 0
\(781\) 0.982529 1.70179i 0.0351577 0.0608949i
\(782\) 0 0
\(783\) −29.0379 + 6.96932i −1.03773 + 0.249063i
\(784\) 0 0
\(785\) −9.87046 + 17.0961i −0.352292 + 0.610188i
\(786\) 0 0
\(787\) −6.70128 11.6069i −0.238875 0.413743i 0.721517 0.692397i \(-0.243445\pi\)
−0.960392 + 0.278654i \(0.910112\pi\)
\(788\) 0 0
\(789\) 0.840165 + 3.24898i 0.0299107 + 0.115667i
\(790\) 0 0
\(791\) −51.7978 −1.84172
\(792\) 0 0
\(793\) −14.7167 −0.522606
\(794\) 0 0
\(795\) 24.5055 + 6.79658i 0.869122 + 0.241050i
\(796\) 0 0
\(797\) &min