Properties

Label 1152.2.i.k.769.5
Level $1152$
Weight $2$
Character 1152.769
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 769.5
Root \(-0.433633 - 1.67689i\) of defining polynomial
Character \(\chi\) \(=\) 1152.769
Dual form 1152.2.i.k.385.5

$q$-expansion

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

Character values

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

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

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 0.394260 0.918999i \(-0.371001\pi\)
0.598746 0.800939i \(-0.295666\pi\)
\(6\) 0 0
\(7\) 1.45488 + 2.51992i 0.549892 + 0.952441i 0.998281 + 0.0586028i \(0.0186645\pi\)
−0.448389 + 0.893838i \(0.648002\pi\)
\(8\) 0 0
\(9\) 0.0524919 + 2.99954i 0.0174973 + 0.999847i
\(10\) 0 0
\(11\) 1.08263 + 1.87517i 0.326425 + 0.565385i 0.981800 0.189919i \(-0.0608225\pi\)
−0.655374 + 0.755304i \(0.727489\pi\)
\(12\) 0 0
\(13\) 1.96377 3.40135i 0.544652 0.943366i −0.453976 0.891014i \(-0.649995\pi\)
0.998629 0.0523518i \(-0.0166717\pi\)
\(14\) 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 0.244209 + 0.969723i \(0.421472\pi\)
−0.961909 + 0.273370i \(0.911862\pi\)
\(24\) 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 0.999230 + 0.0392435i \(0.0124948\pi\)
−0.465629 + 0.884980i \(0.654172\pi\)
\(30\) 0 0
\(31\) 3.27671 5.67542i 0.588514 1.01934i −0.405913 0.913912i \(-0.633047\pi\)
0.994427 0.105425i \(-0.0336201\pi\)
\(32\) 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 0.420625 + 0.907235i \(0.361811\pi\)
−0.996001 + 0.0893453i \(0.971523\pi\)
\(42\) 0 0
\(43\) −2.53640 4.39317i −0.386797 0.669953i 0.605219 0.796059i \(-0.293085\pi\)
−0.992017 + 0.126106i \(0.959752\pi\)
\(44\) 0 0
\(45\) 11.6525 + 6.45839i 1.73705 + 0.962760i
\(46\) 0 0
\(47\) −4.98598 8.63597i −0.727280 1.25969i −0.958029 0.286673i \(-0.907451\pi\)
0.230748 0.973013i \(-0.425883\pi\)
\(48\) 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 −0.676482 0.736459i \(-0.736496\pi\)
0.976033 + 0.217621i \(0.0698296\pi\)
\(60\) 0 0
\(61\) −1.87353 3.24505i −0.239881 0.415485i 0.720799 0.693144i \(-0.243775\pi\)
−0.960680 + 0.277658i \(0.910442\pi\)
\(62\) 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 −0.973422 0.229019i \(-0.926448\pi\)
0.685047 + 0.728498i \(0.259781\pi\)
\(68\) 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 0.927167 0.374648i \(-0.122236\pi\)
−0.788038 + 0.615627i \(0.788903\pi\)
\(80\) 0 0
\(81\) −8.99449 + 0.314903i −0.999388 + 0.0349892i
\(82\) 0 0
\(83\) 1.09251 + 1.89227i 0.119918 + 0.207704i 0.919735 0.392540i \(-0.128403\pi\)
−0.799817 + 0.600244i \(0.795070\pi\)
\(84\) 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 0.998519 0.0544132i \(-0.0173288\pi\)
−0.546382 + 0.837536i \(0.683995\pi\)
\(98\) 0 0
\(99\) −5.56782 + 3.34583i −0.559587 + 0.336268i
\(100\) 0 0
\(101\) −0.689326 1.19395i −0.0685905 0.118802i 0.829691 0.558224i \(-0.188517\pi\)
−0.898281 + 0.439421i \(0.855184\pi\)
\(102\) 0 0
\(103\) 2.54512 4.40828i 0.250778 0.434361i −0.712962 0.701203i \(-0.752647\pi\)
0.963740 + 0.266842i \(0.0859801\pi\)
\(104\) 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 0.0548276 + 0.998496i \(0.482539\pi\)
−0.892137 + 0.451766i \(0.850794\pi\)
\(114\) 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 −0.990824 0.135156i \(-0.956846\pi\)
0.612461 + 0.790501i \(0.290180\pi\)
\(132\) 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 0.831045 0.556205i \(-0.187743\pi\)
−0.897210 + 0.441603i \(0.854410\pi\)
\(138\) 0 0
\(139\) −9.78618 + 16.9502i −0.830053 + 1.43769i 0.0679426 + 0.997689i \(0.478357\pi\)
−0.897996 + 0.440005i \(0.854977\pi\)
\(140\) 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 −0.902170 0.431381i \(-0.858026\pi\)
0.824672 + 0.565612i \(0.191360\pi\)
\(150\) 0 0
\(151\) −4.27927 7.41191i −0.348242 0.603173i 0.637695 0.770289i \(-0.279888\pi\)
−0.985937 + 0.167116i \(0.946555\pi\)
\(152\) 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 −0.763598 0.645692i \(-0.776569\pi\)
0.940985 + 0.338449i \(0.109902\pi\)
\(158\) 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 −0.649435 0.760417i \(-0.724995\pi\)
0.983258 + 0.182219i \(0.0583279\pi\)
\(168\) 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 0.677991 0.735070i \(-0.262851\pi\)
−0.975585 + 0.219623i \(0.929517\pi\)
\(174\) 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 −0.959313 0.282345i \(-0.908888\pi\)
0.235138 0.971962i \(-0.424446\pi\)
\(192\) 0 0
\(193\) −1.08462 + 1.87862i −0.0780726 + 0.135226i −0.902418 0.430861i \(-0.858210\pi\)
0.824346 + 0.566087i \(0.191543\pi\)
\(194\) 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 −0.254449 0.967086i \(-0.581894\pi\)
0.964746 0.263184i \(-0.0847726\pi\)
\(212\) 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 0.938520 0.345226i \(-0.112198\pi\)
−0.768234 + 0.640169i \(0.778864\pi\)
\(224\) 0 0
\(225\) 37.8547 22.7477i 2.52364 1.51651i
\(226\) 0 0
\(227\) 9.14484 + 15.8393i 0.606964 + 1.05129i 0.991738 + 0.128282i \(0.0409462\pi\)
−0.384773 + 0.923011i \(0.625720\pi\)
\(228\) 0 0
\(229\) 9.62341 16.6682i 0.635933 1.10147i −0.350384 0.936606i \(-0.613949\pi\)
0.986317 0.164862i \(-0.0527178\pi\)
\(230\) 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 0.406833 + 0.913503i \(0.366633\pi\)
−0.994533 + 0.104424i \(0.966700\pi\)
\(240\) 0 0
\(241\) −11.4344 19.8050i −0.736556 1.27575i −0.954037 0.299688i \(-0.903117\pi\)
0.217481 0.976065i \(-0.430216\pi\)
\(242\) 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 −0.998234 0.0593974i \(-0.981082\pi\)
0.550557 + 0.834798i \(0.314415\pi\)
\(258\) 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 0.834611 0.550840i \(-0.185692\pi\)
−0.894347 + 0.447374i \(0.852359\pi\)
\(264\) 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 −0.862422 0.506190i \(-0.831053\pi\)
−0.00716263 0.999974i \(-0.502280\pi\)
\(278\) 0 0
\(279\) 17.1957 + 9.53070i 1.02948 + 0.570588i
\(280\) 0 0
\(281\) 11.1351 + 19.2865i 0.664262 + 1.15054i 0.979485 + 0.201518i \(0.0645875\pi\)
−0.315223 + 0.949018i \(0.602079\pi\)
\(282\) 0 0
\(283\) 6.79946 11.7770i 0.404186 0.700071i −0.590040 0.807374i \(-0.700888\pi\)
0.994226 + 0.107303i \(0.0342215\pi\)
\(284\) 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 −0.996105 0.0881730i \(-0.971897\pi\)
0.574413 + 0.818566i \(0.305230\pi\)
\(294\) 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 −0.974870 0.222776i \(-0.928488\pi\)
0.680364 + 0.732874i \(0.261822\pi\)
\(312\) 0 0
\(313\) −6.76501 11.7173i −0.382381 0.662303i 0.609021 0.793154i \(-0.291562\pi\)
−0.991402 + 0.130851i \(0.958229\pi\)
\(314\) 0 0
\(315\) 0.678291 + 38.7595i 0.0382174 + 2.18385i
\(316\) 0 0
\(317\) −11.9869 20.7619i −0.673251 1.16611i −0.976977 0.213346i \(-0.931564\pi\)
0.303726 0.952760i \(-0.401769\pi\)
\(318\) 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 0.828362 0.560194i \(-0.189273\pi\)
−0.899323 + 0.437285i \(0.855940\pi\)
\(332\) 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 −0.910819 0.412806i \(-0.864549\pi\)
0.812910 + 0.582389i \(0.197882\pi\)
\(338\) 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 −0.665114 0.746742i \(-0.731617\pi\)
0.979255 + 0.202634i \(0.0649502\pi\)
\(348\) 0 0
\(349\) 9.34856 + 16.1922i 0.500417 + 0.866747i 1.00000 0.000481224i \(0.000153178\pi\)
−0.499583 + 0.866266i \(0.666513\pi\)
\(350\) 0 0
\(351\) 5.79754 + 19.5673i 0.309450 + 1.04443i
\(352\) 0 0
\(353\) 14.3410 + 24.8394i 0.763295 + 1.32207i 0.941143 + 0.338008i \(0.109753\pi\)
−0.177848 + 0.984058i \(0.556914\pi\)
\(354\) 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 0.973180 + 0.230046i \(0.0738876\pi\)
−0.287364 + 0.957821i \(0.592779\pi\)
\(368\) 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 −0.434222 0.900806i \(-0.642977\pi\)
0.997232 0.0743558i \(-0.0236901\pi\)
\(374\) 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 −0.678437 0.734659i \(-0.737342\pi\)
0.975452 + 0.220214i \(0.0706757\pi\)
\(384\) 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 0.759648 0.650335i \(-0.225371\pi\)
−0.943030 + 0.332707i \(0.892038\pi\)
\(390\) 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 −0.780327 0.625371i \(-0.784948\pi\)
0.931751 + 0.363098i \(0.118281\pi\)
\(402\) 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 0.249354 + 0.968412i \(0.419782\pi\)
−0.963347 + 0.268259i \(0.913552\pi\)
\(410\) 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 −0.695000 0.719010i \(-0.744596\pi\)
0.970181 + 0.242383i \(0.0779290\pi\)
\(420\) 0 0
\(421\) −6.03050 10.4451i −0.293909 0.509065i 0.680822 0.732449i \(-0.261623\pi\)
−0.974730 + 0.223384i \(0.928289\pi\)
\(422\) 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 0.881244 + 0.472662i \(0.156707\pi\)
−0.0312845 + 0.999511i \(0.509960\pi\)
\(440\) 0 0
\(441\) −3.84845 2.13301i −0.183260 0.101572i
\(442\) 0 0
\(443\) −6.60886 11.4469i −0.313996 0.543857i 0.665227 0.746641i \(-0.268335\pi\)
−0.979224 + 0.202783i \(0.935001\pi\)
\(444\) 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 −0.987209 0.159433i \(-0.949034\pi\)
0.355532 0.934664i \(-0.384300\pi\)
\(458\) 0 0
\(459\) −6.42777 + 6.77437i −0.300022 + 0.316200i
\(460\) 0 0
\(461\) 1.78550 + 3.09258i 0.0831591 + 0.144036i 0.904605 0.426250i \(-0.140166\pi\)
−0.821446 + 0.570286i \(0.806832\pi\)
\(462\) 0 0
\(463\) −19.8396 + 34.3631i −0.922023 + 1.59699i −0.125742 + 0.992063i \(0.540131\pi\)
−0.796281 + 0.604927i \(0.793202\pi\)
\(464\) 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 0.999971 + 0.00766167i \(0.00243881\pi\)
−0.493350 + 0.869831i \(0.664228\pi\)
\(480\) 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 −0.824622 0.565684i \(-0.808612\pi\)
0.902208 + 0.431301i \(0.141945\pi\)
\(492\) 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 −0.719112 0.694894i \(-0.755451\pi\)
0.961352 + 0.275322i \(0.0887845\pi\)
\(500\) 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 0.151837 + 0.988406i \(0.451481\pi\)
−0.931903 + 0.362708i \(0.881852\pi\)
\(510\) 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 0.994828 0.101574i \(-0.0323878\pi\)
−0.585379 + 0.810760i \(0.699054\pi\)
\(548\) 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 −0.463535 0.886079i \(-0.653419\pi\)
0.999134 0.0416066i \(-0.0132476\pi\)
\(564\) 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 0.991560 0.129646i \(-0.0413842\pi\)
−0.608057 + 0.793893i \(0.708051\pi\)
\(570\) 0 0
\(571\) 1.27484 2.20808i 0.0533503 0.0924054i −0.838117 0.545491i \(-0.816343\pi\)
0.891467 + 0.453085i \(0.149677\pi\)
\(572\) 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 0.987504 + 0.157596i \(0.0503743\pi\)
−0.357270 + 0.934001i \(0.616292\pi\)
\(588\) 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 −0.940297 0.340355i \(-0.889453\pi\)
0.764904 + 0.644144i \(0.222786\pi\)
\(600\) 0 0
\(601\) 1.44648 + 2.50538i 0.0590033 + 0.102197i 0.894018 0.448031i \(-0.147874\pi\)
−0.835015 + 0.550227i \(0.814541\pi\)
\(602\) 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 −0.589695 0.807626i \(-0.700752\pi\)
0.994272 + 0.106877i \(0.0340853\pi\)
\(608\) 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 0.355603 + 0.934637i \(0.384276\pi\)
−0.987221 + 0.159357i \(0.949058\pi\)
\(618\) 0 0
\(619\) 16.7289 + 28.9752i 0.672389 + 1.16461i 0.977225 + 0.212207i \(0.0680652\pi\)
−0.304835 + 0.952405i \(0.598601\pi\)
\(620\) 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 0.581443 0.813587i \(-0.302488\pi\)
−0.995309 + 0.0967511i \(0.969155\pi\)
\(642\) 0 0
\(643\) 16.3547 28.3272i 0.644967 1.11712i −0.339342 0.940663i \(-0.610204\pi\)
0.984309 0.176453i \(-0.0564623\pi\)
\(644\) 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 −0.755132 0.655573i \(-0.772427\pi\)
0.945309 + 0.326176i \(0.105760\pi\)
\(654\) 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 0.987515 + 0.157523i \(0.0503510\pi\)
−0.357338 + 0.933975i \(0.616316\pi\)
\(660\) 0 0
\(661\) −13.0319 + 22.5719i −0.506883 + 0.877946i 0.493086 + 0.869981i \(0.335869\pi\)
−0.999968 + 0.00796563i \(0.997464\pi\)
\(662\) 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 0.984635 + 0.174627i \(0.0558719\pi\)
−0.341086 + 0.940032i \(0.610795\pi\)
\(674\) 0 0
\(675\) 74.3815 + 17.8521i 2.86294 + 0.687128i
\(676\) 0 0
\(677\) −12.6991 21.9955i −0.488065 0.845354i 0.511840 0.859081i \(-0.328964\pi\)
−0.999906 + 0.0137265i \(0.995631\pi\)
\(678\) 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 0.717760 0.696291i \(-0.245168\pi\)
−0.961885 + 0.273453i \(0.911834\pi\)
\(692\) 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 0.991059 0.133422i \(-0.0425964\pi\)
−0.611076 + 0.791572i \(0.709263\pi\)
\(710\) 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 0.968975 0.247158i \(-0.0794965\pi\)
−0.698532 + 0.715578i \(0.746163\pi\)
\(728\) 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 −0.384281 0.923216i \(-0.625551\pi\)
0.991669 0.128811i \(-0.0411161\pi\)
\(734\) 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 −0.281369 0.959600i \(-0.590788\pi\)
0.971722 0.236127i \(-0.0758782\pi\)
\(744\) 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 −0.671377 0.741116i \(-0.734297\pi\)
0.977514 + 0.210871i \(0.0676300\pi\)
\(752\) 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 −0.985212 0.171341i \(-0.945190\pi\)
0.640992 + 0.767548i \(0.278523\pi\)
\(762\) 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 −0.175482 0.984483i \(-0.556148\pi\)
0.940328 0.340270i \(-0.110518\pi\)
\(770\) 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 −0.960392 0.278654i \(-0.910112\pi\)
0.721517 + 0.692397i \(0.243445\pi\)
\(788\) 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
\(797\) −16.0873 +