Properties

Label 252.2.x.a.41.4
Level $252$
Weight $2$
Character 252.41
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.x (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: \(x^{16} - 3 x^{14} - 9 x^{12} - 9 x^{10} + 225 x^{8} - 81 x^{6} - 729 x^{4} - 2187 x^{2} + 6561\)
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 41.4
Root \(1.71965 + 0.206851i\) of defining polynomial
Character \(\chi\) \(=\) 252.41
Dual form 252.2.x.a.209.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.680689 - 1.59269i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-2.64522 + 0.0532130i) q^{7} +(-2.07332 + 2.16825i) q^{9} +O(q^{10})\) \(q+(-0.680689 - 1.59269i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-2.64522 + 0.0532130i) q^{7} +(-2.07332 + 2.16825i) q^{9} +(-1.23222 + 0.711425i) q^{11} +(0.850739 + 0.491174i) q^{13} +(-7.19970 - 0.866025i) q^{15} -0.370947 q^{17} -4.97471i q^{19} +(1.88532 + 4.17679i) q^{21} +(4.98775 + 2.87968i) q^{23} +(-6.26427 - 10.8500i) q^{25} +(4.86465 + 1.82626i) q^{27} +(7.31732 - 4.22466i) q^{29} +(-6.28007 - 3.62580i) q^{31} +(1.97184 + 1.47829i) q^{33} +(-5.34444 + 9.70241i) q^{35} +3.46445 q^{37} +(0.203200 - 1.68930i) q^{39} +(1.06981 - 1.85297i) q^{41} +(3.00875 + 5.21130i) q^{43} +(3.52145 + 12.0564i) q^{45} +(4.13542 + 7.16276i) q^{47} +(6.99434 - 0.281520i) q^{49} +(0.252500 + 0.590804i) q^{51} +4.97245i q^{53} +5.95706i q^{55} +(-7.92317 + 3.38623i) q^{57} +(2.27883 - 3.94705i) q^{59} +(-6.50416 + 3.75518i) q^{61} +(5.36901 - 5.84583i) q^{63} +(3.56180 - 2.05640i) q^{65} +(5.03205 - 8.71577i) q^{67} +(1.19133 - 9.90411i) q^{69} -10.9555i q^{71} +9.52848i q^{73} +(-13.0167 + 17.3626i) q^{75} +(3.22164 - 1.94744i) q^{77} +(4.25553 + 7.37079i) q^{79} +(-0.402651 - 8.99099i) q^{81} +(-0.972254 - 1.68399i) q^{83} +(-0.776524 + 1.34498i) q^{85} +(-11.7094 - 8.77855i) q^{87} +7.80735 q^{89} +(-2.27652 - 1.25399i) q^{91} +(-1.50000 + 12.4702i) q^{93} +(-18.0373 - 10.4138i) q^{95} +(3.34099 - 1.92892i) q^{97} +(1.01225 - 4.14679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + O(q^{10}) \) \( 16q - q^{7} + 6q^{11} - 12q^{15} + 9q^{21} + 6q^{23} - 8q^{25} - 12q^{29} + 4q^{37} + 18q^{39} + 4q^{43} - 5q^{49} - 18q^{51} - 42q^{57} - 27q^{63} - 24q^{65} + 14q^{67} - 21q^{77} + 20q^{79} - 36q^{81} + 6q^{85} - 18q^{91} - 24q^{93} - 60q^{95} + 90q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.680689 1.59269i −0.392996 0.919540i
\(4\) 0 0
\(5\) 2.09336 3.62580i 0.936177 1.62151i 0.163656 0.986518i \(-0.447671\pi\)
0.772521 0.634989i \(-0.218995\pi\)
\(6\) 0 0
\(7\) −2.64522 + 0.0532130i −0.999798 + 0.0201126i
\(8\) 0 0
\(9\) −2.07332 + 2.16825i −0.691108 + 0.722751i
\(10\) 0 0
\(11\) −1.23222 + 0.711425i −0.371529 + 0.214503i −0.674126 0.738616i \(-0.735480\pi\)
0.302597 + 0.953119i \(0.402146\pi\)
\(12\) 0 0
\(13\) 0.850739 + 0.491174i 0.235952 + 0.136227i 0.613315 0.789838i \(-0.289836\pi\)
−0.377363 + 0.926066i \(0.623169\pi\)
\(14\) 0 0
\(15\) −7.19970 0.866025i −1.85895 0.223607i
\(16\) 0 0
\(17\) −0.370947 −0.0899679 −0.0449840 0.998988i \(-0.514324\pi\)
−0.0449840 + 0.998988i \(0.514324\pi\)
\(18\) 0 0
\(19\) 4.97471i 1.14128i −0.821201 0.570638i \(-0.806696\pi\)
0.821201 0.570638i \(-0.193304\pi\)
\(20\) 0 0
\(21\) 1.88532 + 4.17679i 0.411411 + 0.911450i
\(22\) 0 0
\(23\) 4.98775 + 2.87968i 1.04002 + 0.600455i 0.919838 0.392298i \(-0.128320\pi\)
0.120179 + 0.992752i \(0.461653\pi\)
\(24\) 0 0
\(25\) −6.26427 10.8500i −1.25285 2.17001i
\(26\) 0 0
\(27\) 4.86465 + 1.82626i 0.936202 + 0.351463i
\(28\) 0 0
\(29\) 7.31732 4.22466i 1.35879 0.784499i 0.369332 0.929298i \(-0.379587\pi\)
0.989461 + 0.144798i \(0.0462534\pi\)
\(30\) 0 0
\(31\) −6.28007 3.62580i −1.12793 0.651213i −0.184519 0.982829i \(-0.559073\pi\)
−0.943414 + 0.331616i \(0.892406\pi\)
\(32\) 0 0
\(33\) 1.97184 + 1.47829i 0.343253 + 0.257338i
\(34\) 0 0
\(35\) −5.34444 + 9.70241i −0.903375 + 1.64001i
\(36\) 0 0
\(37\) 3.46445 0.569552 0.284776 0.958594i \(-0.408081\pi\)
0.284776 + 0.958594i \(0.408081\pi\)
\(38\) 0 0
\(39\) 0.203200 1.68930i 0.0325380 0.270504i
\(40\) 0 0
\(41\) 1.06981 1.85297i 0.167077 0.289386i −0.770314 0.637665i \(-0.779901\pi\)
0.937391 + 0.348279i \(0.113234\pi\)
\(42\) 0 0
\(43\) 3.00875 + 5.21130i 0.458830 + 0.794716i 0.998899 0.0469039i \(-0.0149354\pi\)
−0.540070 + 0.841620i \(0.681602\pi\)
\(44\) 0 0
\(45\) 3.52145 + 12.0564i 0.524946 + 1.79726i
\(46\) 0 0
\(47\) 4.13542 + 7.16276i 0.603213 + 1.04480i 0.992331 + 0.123608i \(0.0394466\pi\)
−0.389118 + 0.921188i \(0.627220\pi\)
\(48\) 0 0
\(49\) 6.99434 0.281520i 0.999191 0.0402171i
\(50\) 0 0
\(51\) 0.252500 + 0.590804i 0.0353570 + 0.0827291i
\(52\) 0 0
\(53\) 4.97245i 0.683019i 0.939878 + 0.341509i \(0.110938\pi\)
−0.939878 + 0.341509i \(0.889062\pi\)
\(54\) 0 0
\(55\) 5.95706i 0.803250i
\(56\) 0 0
\(57\) −7.92317 + 3.38623i −1.04945 + 0.448517i
\(58\) 0 0
\(59\) 2.27883 3.94705i 0.296678 0.513862i −0.678696 0.734420i \(-0.737454\pi\)
0.975374 + 0.220558i \(0.0707878\pi\)
\(60\) 0 0
\(61\) −6.50416 + 3.75518i −0.832772 + 0.480801i −0.854801 0.518956i \(-0.826321\pi\)
0.0220288 + 0.999757i \(0.492987\pi\)
\(62\) 0 0
\(63\) 5.36901 5.84583i 0.676432 0.736505i
\(64\) 0 0
\(65\) 3.56180 2.05640i 0.441786 0.255066i
\(66\) 0 0
\(67\) 5.03205 8.71577i 0.614763 1.06480i −0.375663 0.926756i \(-0.622585\pi\)
0.990426 0.138044i \(-0.0440816\pi\)
\(68\) 0 0
\(69\) 1.19133 9.90411i 0.143419 1.19231i
\(70\) 0 0
\(71\) 10.9555i 1.30018i −0.759857 0.650090i \(-0.774731\pi\)
0.759857 0.650090i \(-0.225269\pi\)
\(72\) 0 0
\(73\) 9.52848i 1.11522i 0.830102 + 0.557612i \(0.188282\pi\)
−0.830102 + 0.557612i \(0.811718\pi\)
\(74\) 0 0
\(75\) −13.0167 + 17.3626i −1.50304 + 2.00486i
\(76\) 0 0
\(77\) 3.22164 1.94744i 0.367140 0.221932i
\(78\) 0 0
\(79\) 4.25553 + 7.37079i 0.478784 + 0.829278i 0.999704 0.0243272i \(-0.00774434\pi\)
−0.520920 + 0.853606i \(0.674411\pi\)
\(80\) 0 0
\(81\) −0.402651 8.99099i −0.0447390 0.998999i
\(82\) 0 0
\(83\) −0.972254 1.68399i −0.106719 0.184842i 0.807720 0.589566i \(-0.200701\pi\)
−0.914439 + 0.404724i \(0.867368\pi\)
\(84\) 0 0
\(85\) −0.776524 + 1.34498i −0.0842259 + 0.145884i
\(86\) 0 0
\(87\) −11.7094 8.77855i −1.25538 0.941159i
\(88\) 0 0
\(89\) 7.80735 0.827578 0.413789 0.910373i \(-0.364205\pi\)
0.413789 + 0.910373i \(0.364205\pi\)
\(90\) 0 0
\(91\) −2.27652 1.25399i −0.238645 0.131454i
\(92\) 0 0
\(93\) −1.50000 + 12.4702i −0.155543 + 1.29310i
\(94\) 0 0
\(95\) −18.0373 10.4138i −1.85059 1.06844i
\(96\) 0 0
\(97\) 3.34099 1.92892i 0.339226 0.195852i −0.320704 0.947180i \(-0.603919\pi\)
0.659930 + 0.751327i \(0.270586\pi\)
\(98\) 0 0
\(99\) 1.01225 4.14679i 0.101735 0.416768i
\(100\) 0 0
\(101\) 4.50637 + 7.80526i 0.448401 + 0.776653i 0.998282 0.0585901i \(-0.0186605\pi\)
−0.549882 + 0.835243i \(0.685327\pi\)
\(102\) 0 0
\(103\) −5.96343 3.44299i −0.587594 0.339248i 0.176551 0.984291i \(-0.443506\pi\)
−0.764146 + 0.645044i \(0.776839\pi\)
\(104\) 0 0
\(105\) 19.0908 + 1.90771i 1.86308 + 0.186173i
\(106\) 0 0
\(107\) 11.3630i 1.09850i 0.835658 + 0.549250i \(0.185087\pi\)
−0.835658 + 0.549250i \(0.814913\pi\)
\(108\) 0 0
\(109\) −15.9930 −1.53185 −0.765926 0.642929i \(-0.777719\pi\)
−0.765926 + 0.642929i \(0.777719\pi\)
\(110\) 0 0
\(111\) −2.35821 5.51779i −0.223832 0.523726i
\(112\) 0 0
\(113\) 2.17043 + 1.25310i 0.204177 + 0.117881i 0.598602 0.801046i \(-0.295723\pi\)
−0.394426 + 0.918928i \(0.629056\pi\)
\(114\) 0 0
\(115\) 20.8823 12.0564i 1.94728 1.12426i
\(116\) 0 0
\(117\) −2.82885 + 0.826254i −0.261527 + 0.0763872i
\(118\) 0 0
\(119\) 0.981235 0.0197392i 0.0899497 0.00180949i
\(120\) 0 0
\(121\) −4.48775 + 7.77301i −0.407977 + 0.706637i
\(122\) 0 0
\(123\) −3.67942 0.442584i −0.331762 0.0399065i
\(124\) 0 0
\(125\) −31.5199 −2.81922
\(126\) 0 0
\(127\) −1.91140 −0.169609 −0.0848046 0.996398i \(-0.527027\pi\)
−0.0848046 + 0.996398i \(0.527027\pi\)
\(128\) 0 0
\(129\) 6.25197 8.33928i 0.550455 0.734233i
\(130\) 0 0
\(131\) 4.32591 7.49270i 0.377957 0.654640i −0.612808 0.790232i \(-0.709960\pi\)
0.990765 + 0.135592i \(0.0432935\pi\)
\(132\) 0 0
\(133\) 0.264719 + 13.1592i 0.0229541 + 1.14105i
\(134\) 0 0
\(135\) 16.8051 13.8152i 1.44635 1.18902i
\(136\) 0 0
\(137\) 10.0973 5.82971i 0.862675 0.498065i −0.00223233 0.999998i \(-0.500711\pi\)
0.864907 + 0.501932i \(0.167377\pi\)
\(138\) 0 0
\(139\) 4.82663 + 2.78666i 0.409390 + 0.236361i 0.690528 0.723306i \(-0.257378\pi\)
−0.281138 + 0.959667i \(0.590712\pi\)
\(140\) 0 0
\(141\) 8.59312 11.4621i 0.723672 0.965280i
\(142\) 0 0
\(143\) −1.39773 −0.116884
\(144\) 0 0
\(145\) 35.3748i 2.93772i
\(146\) 0 0
\(147\) −5.20934 10.9482i −0.429659 0.902991i
\(148\) 0 0
\(149\) −13.4024 7.73789i −1.09797 0.633913i −0.162282 0.986744i \(-0.551886\pi\)
−0.935687 + 0.352832i \(0.885219\pi\)
\(150\) 0 0
\(151\) 8.31732 + 14.4060i 0.676854 + 1.17235i 0.975923 + 0.218114i \(0.0699905\pi\)
−0.299069 + 0.954231i \(0.596676\pi\)
\(152\) 0 0
\(153\) 0.769094 0.804308i 0.0621776 0.0650244i
\(154\) 0 0
\(155\) −26.2928 + 15.1802i −2.11189 + 1.21930i
\(156\) 0 0
\(157\) −14.5559 8.40387i −1.16169 0.670702i −0.209981 0.977705i \(-0.567340\pi\)
−0.951708 + 0.307004i \(0.900674\pi\)
\(158\) 0 0
\(159\) 7.91958 3.38469i 0.628063 0.268424i
\(160\) 0 0
\(161\) −13.3469 7.35196i −1.05188 0.579416i
\(162\) 0 0
\(163\) 3.51105 0.275007 0.137503 0.990501i \(-0.456092\pi\)
0.137503 + 0.990501i \(0.456092\pi\)
\(164\) 0 0
\(165\) 9.48775 4.05491i 0.738620 0.315674i
\(166\) 0 0
\(167\) −4.05253 + 7.01918i −0.313594 + 0.543160i −0.979138 0.203198i \(-0.934866\pi\)
0.665544 + 0.746359i \(0.268200\pi\)
\(168\) 0 0
\(169\) −6.01750 10.4226i −0.462884 0.801739i
\(170\) 0 0
\(171\) 10.7864 + 10.3142i 0.824859 + 0.788746i
\(172\) 0 0
\(173\) 6.54844 + 11.3422i 0.497868 + 0.862334i 0.999997 0.00245951i \(-0.000782886\pi\)
−0.502128 + 0.864793i \(0.667450\pi\)
\(174\) 0 0
\(175\) 17.1477 + 28.3674i 1.29625 + 2.14437i
\(176\) 0 0
\(177\) −7.83760 0.942756i −0.589110 0.0708619i
\(178\) 0 0
\(179\) 12.7179i 0.950578i −0.879830 0.475289i \(-0.842344\pi\)
0.879830 0.475289i \(-0.157656\pi\)
\(180\) 0 0
\(181\) 26.5518i 1.97358i 0.161998 + 0.986791i \(0.448206\pi\)
−0.161998 + 0.986791i \(0.551794\pi\)
\(182\) 0 0
\(183\) 10.4081 + 7.80300i 0.769392 + 0.576814i
\(184\) 0 0
\(185\) 7.25232 12.5614i 0.533201 0.923532i
\(186\) 0 0
\(187\) 0.457090 0.263901i 0.0334257 0.0192983i
\(188\) 0 0
\(189\) −12.9652 4.57198i −0.943081 0.332563i
\(190\) 0 0
\(191\) −1.09735 + 0.633555i −0.0794014 + 0.0458424i −0.539175 0.842194i \(-0.681264\pi\)
0.459774 + 0.888036i \(0.347931\pi\)
\(192\) 0 0
\(193\) −9.31732 + 16.1381i −0.670676 + 1.16164i 0.307037 + 0.951697i \(0.400662\pi\)
−0.977713 + 0.209947i \(0.932671\pi\)
\(194\) 0 0
\(195\) −5.69969 4.27307i −0.408163 0.306001i
\(196\) 0 0
\(197\) 5.94312i 0.423430i 0.977331 + 0.211715i \(0.0679049\pi\)
−0.977331 + 0.211715i \(0.932095\pi\)
\(198\) 0 0
\(199\) 5.62675i 0.398870i 0.979911 + 0.199435i \(0.0639106\pi\)
−0.979911 + 0.199435i \(0.936089\pi\)
\(200\) 0 0
\(201\) −17.3068 2.08177i −1.22073 0.146837i
\(202\) 0 0
\(203\) −19.1311 + 11.5645i −1.34274 + 0.811670i
\(204\) 0 0
\(205\) −4.47900 7.75786i −0.312827 0.541832i
\(206\) 0 0
\(207\) −16.5851 + 4.84420i −1.15274 + 0.336695i
\(208\) 0 0
\(209\) 3.53913 + 6.12996i 0.244807 + 0.424018i
\(210\) 0 0
\(211\) 1.05305 1.82393i 0.0724948 0.125565i −0.827499 0.561467i \(-0.810237\pi\)
0.899994 + 0.435902i \(0.143571\pi\)
\(212\) 0 0
\(213\) −17.4487 + 7.45730i −1.19557 + 0.510966i
\(214\) 0 0
\(215\) 25.1935 1.71818
\(216\) 0 0
\(217\) 16.8051 + 9.25684i 1.14080 + 0.628395i
\(218\) 0 0
\(219\) 15.1759 6.48593i 1.02549 0.438279i
\(220\) 0 0
\(221\) −0.315579 0.182200i −0.0212281 0.0122561i
\(222\) 0 0
\(223\) −5.52351 + 3.18900i −0.369882 + 0.213551i −0.673407 0.739272i \(-0.735170\pi\)
0.303525 + 0.952823i \(0.401836\pi\)
\(224\) 0 0
\(225\) 36.5135 + 8.91312i 2.43423 + 0.594208i
\(226\) 0 0
\(227\) 5.72365 + 9.91365i 0.379892 + 0.657992i 0.991046 0.133520i \(-0.0426279\pi\)
−0.611154 + 0.791511i \(0.709295\pi\)
\(228\) 0 0
\(229\) 4.88696 + 2.82149i 0.322940 + 0.186449i 0.652702 0.757615i \(-0.273635\pi\)
−0.329762 + 0.944064i \(0.606969\pi\)
\(230\) 0 0
\(231\) −5.29461 3.80547i −0.348360 0.250382i
\(232\) 0 0
\(233\) 12.4463i 0.815385i −0.913119 0.407693i \(-0.866333\pi\)
0.913119 0.407693i \(-0.133667\pi\)
\(234\) 0 0
\(235\) 34.6276 2.25886
\(236\) 0 0
\(237\) 8.84269 11.7950i 0.574394 0.766164i
\(238\) 0 0
\(239\) 3.52450 + 2.03487i 0.227981 + 0.131625i 0.609640 0.792678i \(-0.291314\pi\)
−0.381659 + 0.924303i \(0.624647\pi\)
\(240\) 0 0
\(241\) −4.26195 + 2.46064i −0.274537 + 0.158504i −0.630947 0.775826i \(-0.717334\pi\)
0.356411 + 0.934329i \(0.384000\pi\)
\(242\) 0 0
\(243\) −14.0458 + 6.76137i −0.901037 + 0.433742i
\(244\) 0 0
\(245\) 13.6209 25.9494i 0.870207 1.65784i
\(246\) 0 0
\(247\) 2.44345 4.23218i 0.155473 0.269287i
\(248\) 0 0
\(249\) −2.02028 + 2.69477i −0.128030 + 0.170774i
\(250\) 0 0
\(251\) 4.65020 0.293518 0.146759 0.989172i \(-0.453116\pi\)
0.146759 + 0.989172i \(0.453116\pi\)
\(252\) 0 0
\(253\) −8.19470 −0.515196
\(254\) 0 0
\(255\) 2.67071 + 0.321250i 0.167246 + 0.0201174i
\(256\) 0 0
\(257\) 5.44701 9.43450i 0.339775 0.588508i −0.644615 0.764507i \(-0.722982\pi\)
0.984390 + 0.175999i \(0.0563156\pi\)
\(258\) 0 0
\(259\) −9.16421 + 0.184354i −0.569436 + 0.0114552i
\(260\) 0 0
\(261\) −6.01105 + 24.6249i −0.372075 + 1.52424i
\(262\) 0 0
\(263\) 15.6489 9.03488i 0.964951 0.557114i 0.0672574 0.997736i \(-0.478575\pi\)
0.897693 + 0.440621i \(0.145242\pi\)
\(264\) 0 0
\(265\) 18.0291 + 10.4091i 1.10752 + 0.639427i
\(266\) 0 0
\(267\) −5.31438 12.4347i −0.325235 0.760991i
\(268\) 0 0
\(269\) −2.98410 −0.181944 −0.0909718 0.995853i \(-0.528997\pi\)
−0.0909718 + 0.995853i \(0.528997\pi\)
\(270\) 0 0
\(271\) 10.3608i 0.629375i −0.949195 0.314688i \(-0.898100\pi\)
0.949195 0.314688i \(-0.101900\pi\)
\(272\) 0 0
\(273\) −0.447615 + 4.47938i −0.0270909 + 0.271104i
\(274\) 0 0
\(275\) 15.4380 + 8.91312i 0.930945 + 0.537481i
\(276\) 0 0
\(277\) 5.94345 + 10.2944i 0.357107 + 0.618528i 0.987476 0.157768i \(-0.0504297\pi\)
−0.630369 + 0.776296i \(0.717096\pi\)
\(278\) 0 0
\(279\) 20.8823 6.09932i 1.25019 0.365157i
\(280\) 0 0
\(281\) −12.0740 + 6.97095i −0.720277 + 0.415852i −0.814855 0.579665i \(-0.803183\pi\)
0.0945775 + 0.995518i \(0.469850\pi\)
\(282\) 0 0
\(283\) −2.19593 1.26782i −0.130535 0.0753642i 0.433311 0.901245i \(-0.357345\pi\)
−0.563845 + 0.825880i \(0.690679\pi\)
\(284\) 0 0
\(285\) −4.30823 + 35.8164i −0.255197 + 2.12158i
\(286\) 0 0
\(287\) −2.73129 + 4.95844i −0.161223 + 0.292687i
\(288\) 0 0
\(289\) −16.8624 −0.991906
\(290\) 0 0
\(291\) −5.34635 4.00816i −0.313408 0.234963i
\(292\) 0 0
\(293\) −3.95496 + 6.85020i −0.231052 + 0.400193i −0.958118 0.286374i \(-0.907550\pi\)
0.727066 + 0.686567i \(0.240883\pi\)
\(294\) 0 0
\(295\) −9.54080 16.5251i −0.555487 0.962131i
\(296\) 0 0
\(297\) −7.29358 + 1.21047i −0.423216 + 0.0702388i
\(298\) 0 0
\(299\) 2.82885 + 4.89971i 0.163596 + 0.283357i
\(300\) 0 0
\(301\) −8.23610 13.6249i −0.474721 0.785327i
\(302\) 0 0
\(303\) 9.36393 12.4902i 0.537944 0.717544i
\(304\) 0 0
\(305\) 31.4437i 1.80046i
\(306\) 0 0
\(307\) 13.9676i 0.797170i −0.917131 0.398585i \(-0.869501\pi\)
0.917131 0.398585i \(-0.130499\pi\)
\(308\) 0 0
\(309\) −1.42437 + 11.8415i −0.0810296 + 0.673640i
\(310\) 0 0
\(311\) −16.3163 + 28.2607i −0.925215 + 1.60252i −0.134001 + 0.990981i \(0.542782\pi\)
−0.791215 + 0.611539i \(0.790551\pi\)
\(312\) 0 0
\(313\) −13.6110 + 7.85832i −0.769340 + 0.444178i −0.832639 0.553816i \(-0.813171\pi\)
0.0632994 + 0.997995i \(0.479838\pi\)
\(314\) 0 0
\(315\) −9.95654 31.7043i −0.560988 1.78634i
\(316\) 0 0
\(317\) −25.1366 + 14.5126i −1.41181 + 0.815111i −0.995559 0.0941377i \(-0.969991\pi\)
−0.416254 + 0.909248i \(0.636657\pi\)
\(318\) 0 0
\(319\) −6.01105 + 10.4114i −0.336554 + 0.582929i
\(320\) 0 0
\(321\) 18.0977 7.73465i 1.01012 0.431706i
\(322\) 0 0
\(323\) 1.84535i 0.102678i
\(324\) 0 0
\(325\) 12.3074i 0.682692i
\(326\) 0 0
\(327\) 10.8863 + 25.4719i 0.602011 + 1.40860i
\(328\) 0 0
\(329\) −11.3202 18.7270i −0.624105 1.03245i
\(330\) 0 0
\(331\) −6.58510 11.4057i −0.361950 0.626915i 0.626332 0.779556i \(-0.284555\pi\)
−0.988282 + 0.152641i \(0.951222\pi\)
\(332\) 0 0
\(333\) −7.18292 + 7.51180i −0.393622 + 0.411644i
\(334\) 0 0
\(335\) −21.0677 36.4904i −1.15105 1.99368i
\(336\) 0 0
\(337\) 8.31732 14.4060i 0.453073 0.784746i −0.545502 0.838110i \(-0.683661\pi\)
0.998575 + 0.0533635i \(0.0169942\pi\)
\(338\) 0 0
\(339\) 0.518409 4.30979i 0.0281561 0.234076i
\(340\) 0 0
\(341\) 10.3179 0.558747
\(342\) 0 0
\(343\) −18.4866 + 1.11687i −0.998180 + 0.0603053i
\(344\) 0 0
\(345\) −33.4164 25.0523i −1.79908 1.34877i
\(346\) 0 0
\(347\) 21.4012 + 12.3560i 1.14888 + 0.663305i 0.948614 0.316437i \(-0.102487\pi\)
0.200264 + 0.979742i \(0.435820\pi\)
\(348\) 0 0
\(349\) 26.7994 15.4727i 1.43454 0.828232i 0.437078 0.899424i \(-0.356013\pi\)
0.997463 + 0.0711915i \(0.0226802\pi\)
\(350\) 0 0
\(351\) 3.24153 + 3.94306i 0.173020 + 0.210465i
\(352\) 0 0
\(353\) −11.6758 20.2231i −0.621440 1.07637i −0.989218 0.146452i \(-0.953215\pi\)
0.367778 0.929914i \(-0.380119\pi\)
\(354\) 0 0
\(355\) −39.7225 22.9338i −2.10825 1.21720i
\(356\) 0 0
\(357\) −0.699355 1.54937i −0.0370138 0.0820012i
\(358\) 0 0
\(359\) 21.2351i 1.12075i −0.828240 0.560374i \(-0.810657\pi\)
0.828240 0.560374i \(-0.189343\pi\)
\(360\) 0 0
\(361\) −5.74775 −0.302513
\(362\) 0 0
\(363\) 15.4348 + 1.85659i 0.810115 + 0.0974458i
\(364\) 0 0
\(365\) 34.5483 + 19.9465i 1.80834 + 1.04405i
\(366\) 0 0
\(367\) −12.0178 + 6.93846i −0.627322 + 0.362185i −0.779714 0.626135i \(-0.784636\pi\)
0.152392 + 0.988320i \(0.451302\pi\)
\(368\) 0 0
\(369\) 1.79964 + 6.16144i 0.0936857 + 0.320752i
\(370\) 0 0
\(371\) −0.264599 13.1532i −0.0137373 0.682881i
\(372\) 0 0
\(373\) 16.0728 27.8390i 0.832221 1.44145i −0.0640529 0.997947i \(-0.520403\pi\)
0.896273 0.443502i \(-0.146264\pi\)
\(374\) 0 0
\(375\) 21.4552 + 50.2014i 1.10794 + 2.59239i
\(376\) 0 0
\(377\) 8.30017 0.427481
\(378\) 0 0
\(379\) 1.95340 0.100339 0.0501696 0.998741i \(-0.484024\pi\)
0.0501696 + 0.998741i \(0.484024\pi\)
\(380\) 0 0
\(381\) 1.30107 + 3.04427i 0.0666558 + 0.155962i
\(382\) 0 0
\(383\) −0.788167 + 1.36514i −0.0402734 + 0.0697557i −0.885460 0.464717i \(-0.846156\pi\)
0.845186 + 0.534472i \(0.179490\pi\)
\(384\) 0 0
\(385\) −0.316993 15.7577i −0.0161555 0.803087i
\(386\) 0 0
\(387\) −17.5375 4.28100i −0.891483 0.217615i
\(388\) 0 0
\(389\) 9.74447 5.62597i 0.494064 0.285248i −0.232195 0.972669i \(-0.574591\pi\)
0.726259 + 0.687421i \(0.241257\pi\)
\(390\) 0 0
\(391\) −1.85019 1.06821i −0.0935682 0.0540216i
\(392\) 0 0
\(393\) −14.8782 1.78964i −0.750503 0.0902753i
\(394\) 0 0
\(395\) 35.6333 1.79291
\(396\) 0 0
\(397\) 0.632961i 0.0317674i 0.999874 + 0.0158837i \(0.00505615\pi\)
−0.999874 + 0.0158837i \(0.994944\pi\)
\(398\) 0 0
\(399\) 20.7783 9.37893i 1.04022 0.469534i
\(400\) 0 0
\(401\) 7.38032 + 4.26103i 0.368555 + 0.212786i 0.672827 0.739800i \(-0.265080\pi\)
−0.304272 + 0.952585i \(0.598413\pi\)
\(402\) 0 0
\(403\) −3.56180 6.16921i −0.177426 0.307310i
\(404\) 0 0
\(405\) −33.4424 17.3614i −1.66177 0.862695i
\(406\) 0 0
\(407\) −4.26897 + 2.46469i −0.211605 + 0.122170i
\(408\) 0 0
\(409\) −12.1822 7.03338i −0.602370 0.347778i 0.167603 0.985855i \(-0.446397\pi\)
−0.769973 + 0.638076i \(0.779731\pi\)
\(410\) 0 0
\(411\) −16.1581 12.1137i −0.797019 0.597526i
\(412\) 0 0
\(413\) −5.81796 + 10.5621i −0.286283 + 0.519725i
\(414\) 0 0
\(415\) −8.14109 −0.399630
\(416\) 0 0
\(417\) 1.15285 9.58418i 0.0564551 0.469339i
\(418\) 0 0
\(419\) 10.9339 18.9381i 0.534156 0.925185i −0.465048 0.885286i \(-0.653963\pi\)
0.999204 0.0398995i \(-0.0127038\pi\)
\(420\) 0 0
\(421\) 13.3616 + 23.1430i 0.651206 + 1.12792i 0.982831 + 0.184510i \(0.0590698\pi\)
−0.331625 + 0.943411i \(0.607597\pi\)
\(422\) 0 0
\(423\) −24.1048 5.88408i −1.17201 0.286094i
\(424\) 0 0
\(425\) 2.32371 + 4.02479i 0.112717 + 0.195231i
\(426\) 0 0
\(427\) 17.0051 10.2794i 0.822933 0.497453i
\(428\) 0 0
\(429\) 0.951422 + 2.22616i 0.0459351 + 0.107480i
\(430\) 0 0
\(431\) 19.9400i 0.960476i 0.877138 + 0.480238i \(0.159450\pi\)
−0.877138 + 0.480238i \(0.840550\pi\)
\(432\) 0 0
\(433\) 20.2826i 0.974719i 0.873201 + 0.487359i \(0.162040\pi\)
−0.873201 + 0.487359i \(0.837960\pi\)
\(434\) 0 0
\(435\) −56.3412 + 24.0793i −2.70135 + 1.15451i
\(436\) 0 0
\(437\) 14.3256 24.8126i 0.685285 1.18695i
\(438\) 0 0
\(439\) 24.5936 14.1991i 1.17379 0.677687i 0.219219 0.975676i \(-0.429649\pi\)
0.954569 + 0.297989i \(0.0963158\pi\)
\(440\) 0 0
\(441\) −13.8911 + 15.7492i −0.661482 + 0.749961i
\(442\) 0 0
\(443\) 10.6570 6.15281i 0.506328 0.292329i −0.224995 0.974360i \(-0.572236\pi\)
0.731323 + 0.682031i \(0.238903\pi\)
\(444\) 0 0
\(445\) 16.3436 28.3079i 0.774759 1.34192i
\(446\) 0 0
\(447\) −3.20118 + 26.6130i −0.151411 + 1.25875i
\(448\) 0 0
\(449\) 36.1924i 1.70803i −0.520251 0.854013i \(-0.674162\pi\)
0.520251 0.854013i \(-0.325838\pi\)
\(450\) 0 0
\(451\) 3.04437i 0.143354i
\(452\) 0 0
\(453\) 17.2828 23.0529i 0.812018 1.08312i
\(454\) 0 0
\(455\) −9.31229 + 5.62917i −0.436567 + 0.263899i
\(456\) 0 0
\(457\) 4.20892 + 7.29007i 0.196885 + 0.341015i 0.947517 0.319706i \(-0.103584\pi\)
−0.750632 + 0.660721i \(0.770251\pi\)
\(458\) 0 0
\(459\) −1.80453 0.677445i −0.0842281 0.0316204i
\(460\) 0 0
\(461\) 9.07730 + 15.7224i 0.422772 + 0.732263i 0.996209 0.0869865i \(-0.0277237\pi\)
−0.573437 + 0.819249i \(0.694390\pi\)
\(462\) 0 0
\(463\) −7.64690 + 13.2448i −0.355381 + 0.615539i −0.987183 0.159591i \(-0.948982\pi\)
0.631802 + 0.775130i \(0.282316\pi\)
\(464\) 0 0
\(465\) 42.0745 + 31.5433i 1.95116 + 1.46279i
\(466\) 0 0
\(467\) 26.7864 1.23953 0.619763 0.784789i \(-0.287229\pi\)
0.619763 + 0.784789i \(0.287229\pi\)
\(468\) 0 0
\(469\) −12.8471 + 23.3229i −0.593223 + 1.07695i
\(470\) 0 0
\(471\) −3.47670 + 28.9035i −0.160198 + 1.33180i
\(472\) 0 0
\(473\) −7.41490 4.28100i −0.340938 0.196840i
\(474\) 0 0
\(475\) −53.9758 + 31.1630i −2.47658 + 1.42985i
\(476\) 0 0
\(477\) −10.7815 10.3095i −0.493653 0.472040i
\(478\) 0 0
\(479\) −14.2775 24.7294i −0.652357 1.12992i −0.982549 0.186002i \(-0.940447\pi\)
0.330193 0.943914i \(-0.392886\pi\)
\(480\) 0 0
\(481\) 2.94734 + 1.70165i 0.134387 + 0.0775884i
\(482\) 0 0
\(483\) −2.62430 + 26.2619i −0.119410 + 1.19496i
\(484\) 0 0
\(485\) 16.1517i 0.733409i
\(486\) 0 0
\(487\) −13.1527 −0.596006 −0.298003 0.954565i \(-0.596321\pi\)
−0.298003 + 0.954565i \(0.596321\pi\)
\(488\) 0 0
\(489\) −2.38994 5.59202i −0.108077 0.252880i
\(490\) 0 0
\(491\) 28.6854 + 16.5615i 1.29455 + 0.747411i 0.979458 0.201649i \(-0.0646301\pi\)
0.315096 + 0.949060i \(0.397963\pi\)
\(492\) 0 0
\(493\) −2.71434 + 1.56712i −0.122248 + 0.0705798i
\(494\) 0 0
\(495\) −12.9164 12.3509i −0.580550 0.555132i
\(496\) 0 0
\(497\) 0.582976 + 28.9797i 0.0261500 + 1.29992i
\(498\) 0 0
\(499\) 3.27652 5.67511i 0.146677 0.254053i −0.783320 0.621619i \(-0.786475\pi\)
0.929997 + 0.367566i \(0.119809\pi\)
\(500\) 0 0
\(501\) 13.9379 + 1.67654i 0.622699 + 0.0749022i
\(502\) 0 0
\(503\) −12.4969 −0.557210 −0.278605 0.960406i \(-0.589872\pi\)
−0.278605 + 0.960406i \(0.589872\pi\)
\(504\) 0 0
\(505\) 37.7337 1.67913
\(506\) 0 0
\(507\) −12.5039 + 16.6786i −0.555320 + 0.740721i
\(508\) 0 0
\(509\) −3.30237 + 5.71987i −0.146375 + 0.253529i −0.929885 0.367850i \(-0.880094\pi\)
0.783510 + 0.621379i \(0.213427\pi\)
\(510\) 0 0
\(511\) −0.507039 25.2049i −0.0224301 1.11500i
\(512\) 0 0
\(513\) 9.08510 24.2002i 0.401117 1.06847i
\(514\) 0 0
\(515\) −24.9672 + 14.4148i −1.10018 + 0.635192i
\(516\) 0 0
\(517\) −10.1915 5.88408i −0.448223 0.258782i
\(518\) 0 0
\(519\) 13.6072 18.1502i 0.597290 0.796704i
\(520\) 0 0
\(521\) 15.9784 0.700026 0.350013 0.936745i \(-0.386177\pi\)
0.350013 + 0.936745i \(0.386177\pi\)
\(522\) 0 0
\(523\) 11.7615i 0.514293i 0.966372 + 0.257147i \(0.0827824\pi\)
−0.966372 + 0.257147i \(0.917218\pi\)
\(524\) 0 0
\(525\) 33.5082 46.6204i 1.46242 2.03468i
\(526\) 0 0
\(527\) 2.32957 + 1.34498i 0.101478 + 0.0585882i
\(528\) 0 0
\(529\) 5.08510 + 8.80765i 0.221091 + 0.382941i
\(530\) 0 0
\(531\) 3.83345 + 13.1246i 0.166358 + 0.569559i
\(532\) 0 0
\(533\) 1.82026 1.05093i 0.0788444 0.0455208i
\(534\) 0 0
\(535\) 41.1999 + 23.7867i 1.78122 + 1.02839i
\(536\) 0 0
\(537\) −20.2556 + 8.65691i −0.874094 + 0.373573i
\(538\) 0 0
\(539\) −8.41831 + 5.32284i −0.362602 + 0.229271i
\(540\) 0 0
\(541\) −0.411960 −0.0177115 −0.00885576 0.999961i \(-0.502819\pi\)
−0.00885576 + 0.999961i \(0.502819\pi\)
\(542\) 0 0
\(543\) 42.2888 18.0735i 1.81479 0.775610i
\(544\) 0 0
\(545\) −33.4790 + 57.9874i −1.43408 + 2.48391i
\(546\) 0 0
\(547\) 11.9166 + 20.6402i 0.509519 + 0.882513i 0.999939 + 0.0110266i \(0.00350995\pi\)
−0.490420 + 0.871486i \(0.663157\pi\)
\(548\) 0 0
\(549\) 5.34305 21.8884i 0.228036 0.934173i
\(550\) 0 0
\(551\) −21.0165 36.4016i −0.895331 1.55076i
\(552\) 0 0
\(553\) −11.6490 19.2709i −0.495366 0.819481i
\(554\) 0 0
\(555\) −24.9430 3.00030i −1.05877 0.127356i
\(556\) 0 0
\(557\) 42.9474i 1.81974i 0.414896 + 0.909869i \(0.363818\pi\)
−0.414896 + 0.909869i \(0.636182\pi\)
\(558\) 0 0
\(559\) 5.91128i 0.250020i
\(560\) 0 0
\(561\) −0.731449 0.548368i −0.0308818 0.0231521i
\(562\) 0 0
\(563\) −15.9454 + 27.6182i −0.672019 + 1.16397i 0.305312 + 0.952252i \(0.401239\pi\)
−0.977331 + 0.211718i \(0.932094\pi\)
\(564\) 0 0
\(565\) 9.08695 5.24635i 0.382291 0.220716i
\(566\) 0 0
\(567\) 1.54354 + 23.7617i 0.0648224 + 0.997897i
\(568\) 0 0
\(569\) 0.428895 0.247623i 0.0179802 0.0103809i −0.490983 0.871169i \(-0.663362\pi\)
0.508963 + 0.860788i \(0.330029\pi\)
\(570\) 0 0
\(571\) −1.34182 + 2.32411i −0.0561535 + 0.0972608i −0.892736 0.450581i \(-0.851217\pi\)
0.836582 + 0.547841i \(0.184550\pi\)
\(572\) 0 0
\(573\) 1.75601 + 1.31648i 0.0733584 + 0.0549969i
\(574\) 0 0
\(575\) 72.1564i 3.00913i
\(576\) 0 0
\(577\) 42.0259i 1.74956i −0.484518 0.874781i \(-0.661005\pi\)
0.484518 0.874781i \(-0.338995\pi\)
\(578\) 0 0
\(579\) 32.0452 + 3.85460i 1.33175 + 0.160192i
\(580\) 0 0
\(581\) 2.66143 + 4.40279i 0.110415 + 0.182658i
\(582\) 0 0
\(583\) −3.53753 6.12717i −0.146509 0.253762i
\(584\) 0 0
\(585\) −2.92595 + 11.9865i −0.120973 + 0.495580i
\(586\) 0 0
\(587\) −1.71916 2.97768i −0.0709575 0.122902i 0.828364 0.560191i \(-0.189272\pi\)
−0.899321 + 0.437289i \(0.855939\pi\)
\(588\) 0 0
\(589\) −18.0373 + 31.2415i −0.743214 + 1.28728i
\(590\) 0 0
\(591\) 9.46555 4.04542i 0.389361 0.166406i
\(592\) 0 0
\(593\) −9.10251 −0.373795 −0.186898 0.982379i \(-0.559843\pi\)
−0.186898 + 0.982379i \(0.559843\pi\)
\(594\) 0 0
\(595\) 1.98250 3.59908i 0.0812747 0.147548i
\(596\) 0 0
\(597\) 8.96167 3.83007i 0.366777 0.156754i
\(598\) 0 0
\(599\) 6.71186 + 3.87510i 0.274239 + 0.158332i 0.630813 0.775935i \(-0.282722\pi\)
−0.356573 + 0.934267i \(0.616055\pi\)
\(600\) 0 0
\(601\) 22.0034 12.7037i 0.897536 0.518193i 0.0211361 0.999777i \(-0.493272\pi\)
0.876400 + 0.481584i \(0.159938\pi\)
\(602\) 0 0
\(603\) 8.46492 + 28.9814i 0.344718 + 1.18021i
\(604\) 0 0
\(605\) 18.7889 + 32.5433i 0.763878 + 1.32308i
\(606\) 0 0
\(607\) −11.7094 6.76042i −0.475270 0.274397i 0.243173 0.969983i \(-0.421812\pi\)
−0.718443 + 0.695586i \(0.755145\pi\)
\(608\) 0 0
\(609\) 31.4410 + 22.5981i 1.27405 + 0.915720i
\(610\) 0 0
\(611\) 8.12485i 0.328696i
\(612\) 0 0
\(613\) 4.83635 0.195338 0.0976691 0.995219i \(-0.468861\pi\)
0.0976691 + 0.995219i \(0.468861\pi\)
\(614\) 0 0
\(615\) −9.30706 + 12.4144i −0.375297 + 0.500595i
\(616\) 0 0
\(617\) 5.30333 + 3.06188i 0.213504 + 0.123267i 0.602939 0.797787i \(-0.293996\pi\)
−0.389435 + 0.921054i \(0.627330\pi\)
\(618\) 0 0
\(619\) −4.94313 + 2.85392i −0.198681 + 0.114709i −0.596040 0.802955i \(-0.703260\pi\)
0.397359 + 0.917663i \(0.369927\pi\)
\(620\) 0 0
\(621\) 19.0046 + 23.1175i 0.762629 + 0.927675i
\(622\) 0 0
\(623\) −20.6521 + 0.415453i −0.827410 + 0.0166448i
\(624\) 0 0
\(625\) −34.6609 + 60.0344i −1.38644 + 2.40138i
\(626\) 0 0
\(627\) 7.35407 9.80934i 0.293693 0.391747i
\(628\) 0 0
\(629\) −1.28513 −0.0512414
\(630\) 0 0
\(631\) −19.0525 −0.758468 −0.379234 0.925301i \(-0.623812\pi\)
−0.379234 + 0.925301i \(0.623812\pi\)
\(632\) 0 0
\(633\) −3.62176 0.435648i −0.143952 0.0173155i
\(634\) 0 0
\(635\) −4.00124 + 6.93035i −0.158784 + 0.275022i
\(636\) 0 0
\(637\) 6.08863 + 3.19594i 0.241240 + 0.126628i
\(638\) 0 0
\(639\) 23.7543 + 22.7143i 0.939707 + 0.898565i
\(640\) 0 0
\(641\) 13.2820 7.66837i 0.524607 0.302882i −0.214210 0.976788i \(-0.568718\pi\)
0.738818 + 0.673905i \(0.235384\pi\)
\(642\) 0 0
\(643\) 11.3209 + 6.53612i 0.446453 + 0.257759i 0.706331 0.707882i \(-0.250349\pi\)
−0.259878 + 0.965641i \(0.583682\pi\)
\(644\) 0 0
\(645\) −17.1490 40.1255i −0.675239 1.57994i
\(646\) 0 0
\(647\) −35.7066 −1.40377 −0.701885 0.712290i \(-0.747658\pi\)
−0.701885 + 0.712290i \(0.747658\pi\)
\(648\) 0 0
\(649\) 6.48486i 0.254553i
\(650\) 0 0
\(651\) 3.30425 33.0663i 0.129504 1.29597i
\(652\) 0 0
\(653\) −23.6131 13.6330i −0.924051 0.533501i −0.0391261 0.999234i \(-0.512457\pi\)
−0.884925 + 0.465733i \(0.845791\pi\)
\(654\) 0 0
\(655\) −18.1113 31.3698i −0.707669 1.22572i
\(656\) 0 0
\(657\) −20.6602 19.7556i −0.806030 0.770741i
\(658\) 0 0
\(659\) −14.7911 + 8.53963i −0.576179 + 0.332657i −0.759613 0.650375i \(-0.774612\pi\)
0.183435 + 0.983032i \(0.441278\pi\)
\(660\) 0 0
\(661\) 40.6657 + 23.4784i 1.58171 + 0.913203i 0.994609 + 0.103692i \(0.0330657\pi\)
0.587105 + 0.809511i \(0.300268\pi\)
\(662\) 0 0
\(663\) −0.0753764 + 0.626641i −0.00292738 + 0.0243367i
\(664\) 0 0
\(665\) 48.2667 + 26.5870i 1.87170 + 1.03100i
\(666\) 0 0
\(667\) 48.6626 1.88422
\(668\) 0 0
\(669\) 8.83888 + 6.62652i 0.341731 + 0.256196i
\(670\) 0 0
\(671\) 5.34305 9.25444i 0.206266 0.357264i
\(672\) 0 0
\(673\) 7.76077 + 13.4421i 0.299156 + 0.518153i 0.975943 0.218026i \(-0.0699616\pi\)
−0.676787 + 0.736179i \(0.736628\pi\)
\(674\) 0 0
\(675\) −10.6585 64.2218i −0.410247 2.47190i
\(676\) 0 0
\(677\) 9.07869 + 15.7248i 0.348922 + 0.604351i 0.986058 0.166400i \(-0.0532143\pi\)
−0.637136 + 0.770751i \(0.719881\pi\)
\(678\) 0 0
\(679\) −8.73499 + 5.28019i −0.335218 + 0.202635i
\(680\) 0 0
\(681\) 11.8933 15.8641i 0.455754 0.607914i
\(682\) 0 0
\(683\) 20.1917i 0.772615i −0.922370 0.386308i \(-0.873750\pi\)
0.922370 0.386308i \(-0.126250\pi\)
\(684\) 0 0
\(685\) 48.8146i 1.86511i
\(686\) 0 0
\(687\) 1.16726 9.70398i 0.0445336 0.370230i
\(688\) 0 0
\(689\) −2.44234 + 4.23026i −0.0930458 + 0.161160i
\(690\) 0 0
\(691\) 0.0695792 0.0401716i 0.00264692 0.00152820i −0.498676 0.866788i \(-0.666180\pi\)
0.501323 + 0.865260i \(0.332847\pi\)
\(692\) 0 0
\(693\) −2.45696 + 11.0230i −0.0933321 + 0.418730i
\(694\) 0 0
\(695\) 20.2077 11.6669i 0.766523 0.442552i
\(696\) 0 0
\(697\) −0.396844 + 0.687355i −0.0150316 + 0.0260354i
\(698\) 0 0
\(699\) −19.8231 + 8.47207i −0.749780 + 0.320443i
\(700\) 0 0
\(701\) 35.1490i 1.32756i −0.747928 0.663780i \(-0.768951\pi\)
0.747928 0.663780i \(-0.231049\pi\)
\(702\) 0 0
\(703\) 17.2346i 0.650016i
\(704\) 0 0
\(705\) −23.5707 55.1511i −0.887722 2.07711i
\(706\) 0 0
\(707\) −12.3357 20.4068i −0.463930 0.767477i
\(708\) 0 0
\(709\) −0.782968 1.35614i −0.0294050 0.0509309i 0.850948 0.525249i \(-0.176028\pi\)
−0.880353 + 0.474318i \(0.842695\pi\)
\(710\) 0 0
\(711\) −24.8048 6.05497i −0.930254 0.227079i
\(712\) 0 0
\(713\) −20.8823 36.1691i −0.782047 1.35455i
\(714\) 0 0
\(715\) −2.92595 + 5.06790i −0.109424 + 0.189529i
\(716\) 0 0
\(717\) 0.841830 6.99855i 0.0314387 0.261366i
\(718\) 0 0
\(719\) −25.8787 −0.965112 −0.482556 0.875865i \(-0.660291\pi\)
−0.482556 + 0.875865i \(0.660291\pi\)
\(720\) 0 0
\(721\) 15.9578 + 8.79012i 0.594299 + 0.327361i
\(722\) 0 0
\(723\) 6.82010 + 5.11304i 0.253642 + 0.190156i
\(724\) 0 0
\(725\) −91.6754 52.9288i −3.40474 1.96573i
\(726\) 0 0
\(727\) −0.990545 + 0.571891i −0.0367373 + 0.0212103i −0.518256 0.855225i \(-0.673419\pi\)
0.481519 + 0.876436i \(0.340085\pi\)
\(728\) 0 0
\(729\) 20.3296 + 17.7682i 0.752947 + 0.658081i
\(730\) 0 0
\(731\) −1.11609 1.93312i −0.0412800 0.0714990i
\(732\) 0 0
\(733\) 20.1408 + 11.6283i 0.743916 + 0.429500i 0.823491 0.567329i \(-0.192023\pi\)
−0.0795755 + 0.996829i \(0.525356\pi\)
\(734\) 0 0
\(735\) −50.6009 4.03042i −1.86644 0.148664i
\(736\) 0 0
\(737\) 14.3197i 0.527473i
\(738\) 0 0
\(739\) −36.1516 −1.32986 −0.664929 0.746907i \(-0.731538\pi\)
−0.664929 + 0.746907i \(0.731538\pi\)
\(740\) 0 0
\(741\) −8.40378 1.01086i −0.308721 0.0371349i
\(742\) 0 0
\(743\) 6.43940 + 3.71779i 0.236239 + 0.136392i 0.613447 0.789736i \(-0.289783\pi\)
−0.377208 + 0.926129i \(0.623116\pi\)
\(744\) 0 0
\(745\) −56.1121 + 32.3963i −2.05579 + 1.18691i
\(746\) 0 0
\(747\) 5.66712 + 1.38337i 0.207349 + 0.0506149i
\(748\) 0 0
\(749\) −0.604658 30.0575i −0.0220937 1.09828i
\(750\) 0 0
\(751\) −3.67798 + 6.37044i −0.134211 + 0.232461i −0.925296 0.379246i \(-0.876183\pi\)
0.791085 + 0.611707i \(0.209517\pi\)
\(752\) 0 0
\(753\) −3.16534 7.40633i −0.115352 0.269902i
\(754\) 0 0
\(755\) 69.6445 2.53462
\(756\) 0 0
\(757\) 7.65326 0.278163 0.139081 0.990281i \(-0.455585\pi\)
0.139081 + 0.990281i \(0.455585\pi\)
\(758\) 0 0
\(759\) 5.57804 + 13.0516i 0.202470 + 0.473744i
\(760\) 0 0
\(761\) −21.7203 + 37.6207i −0.787362 + 1.36375i 0.140217 + 0.990121i \(0.455220\pi\)
−0.927578 + 0.373629i \(0.878113\pi\)
\(762\) 0 0
\(763\) 42.3049 0.851035i 1.53154 0.0308095i
\(764\) 0 0
\(765\) −1.30627 4.47228i −0.0472283 0.161696i
\(766\) 0 0
\(767\) 3.87738 2.23860i 0.140004 0.0808313i
\(768\) 0 0
\(769\) 18.8491 + 10.8825i 0.679716 + 0.392434i 0.799748 0.600336i \(-0.204966\pi\)
−0.120032 + 0.992770i \(0.538300\pi\)
\(770\) 0 0
\(771\) −18.7340 2.25344i −0.674687 0.0811557i
\(772\) 0 0
\(773\) 14.5147 0.522056 0.261028 0.965331i \(-0.415938\pi\)
0.261028 + 0.965331i \(0.415938\pi\)
\(774\) 0 0
\(775\) 90.8520i 3.26350i
\(776\) 0 0
\(777\) 6.53160 + 14.4703i 0.234320 + 0.519118i
\(778\) 0 0
\(779\) −9.21800 5.32202i −0.330269 0.190681i
\(780\) 0 0
\(781\) 7.79402 + 13.4996i 0.278892 + 0.483055i
\(782\) 0 0
\(783\) 43.3115 7.18816i 1.54783 0.256884i
\(784\) 0 0
\(785\) −60.9415 + 35.1846i −2.17509 + 1.25579i
\(786\) 0 0
\(787\) −11.4291 6.59861i −0.407405 0.235215i 0.282269 0.959335i \(-0.408913\pi\)
−0.689674 + 0.724120i \(0.742246\pi\)
\(788\) 0 0
\(789\) −25.0418 18.7739i −0.891511 0.668367i
\(790\) 0 0
\(791\) −5.80793 3.19922i −0.206506 0.113751i
\(792\) 0 0
\(793\) −7.37778 −0.261993
\(794\) 0 0
\(795\) 4.30627 35.8002i 0.152728 1.26970i
\(796\) 0 0