Properties

Label 252.2.x.a.41.5
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 41.5
Root \(-1.71965 - 0.206851i\) of defining polynomial
Character \(\chi\) \(=\) 252.41
Dual form 252.2.x.a.209.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.680689 + 1.59269i) q^{3} +(-2.09336 + 3.62580i) q^{5} +(1.36869 - 2.26422i) q^{7} +(-2.07332 + 2.16825i) q^{9} +O(q^{10})\) \(q+(0.680689 + 1.59269i) q^{3} +(-2.09336 + 3.62580i) q^{5} +(1.36869 - 2.26422i) q^{7} +(-2.07332 + 2.16825i) q^{9} +(-1.23222 + 0.711425i) q^{11} +(-0.850739 - 0.491174i) q^{13} +(-7.19970 - 0.866025i) q^{15} +0.370947 q^{17} +4.97471i q^{19} +(4.53785 + 0.638674i) q^{21} +(4.98775 + 2.87968i) q^{23} +(-6.26427 - 10.8500i) q^{25} +(-4.86465 - 1.82626i) q^{27} +(7.31732 - 4.22466i) q^{29} +(6.28007 + 3.62580i) q^{31} +(-1.97184 - 1.47829i) q^{33} +(5.34444 + 9.70241i) q^{35} +3.46445 q^{37} +(0.203200 - 1.68930i) q^{39} +(-1.06981 + 1.85297i) q^{41} +(3.00875 + 5.21130i) q^{43} +(-3.52145 - 12.0564i) q^{45} +(-4.13542 - 7.16276i) q^{47} +(-3.25337 - 6.19803i) q^{49} +(0.252500 + 0.590804i) q^{51} +4.97245i q^{53} -5.95706i q^{55} +(-7.92317 + 3.38623i) q^{57} +(-2.27883 + 3.94705i) q^{59} +(6.50416 - 3.75518i) q^{61} +(2.07166 + 7.66213i) q^{63} +(3.56180 - 2.05640i) q^{65} +(5.03205 - 8.71577i) q^{67} +(-1.19133 + 9.90411i) q^{69} -10.9555i q^{71} -9.52848i q^{73} +(13.0167 - 17.3626i) q^{75} +(-0.0757141 + 3.76374i) q^{77} +(4.25553 + 7.37079i) q^{79} +(-0.402651 - 8.99099i) q^{81} +(0.972254 + 1.68399i) q^{83} +(-0.776524 + 1.34498i) q^{85} +(11.7094 + 8.77855i) q^{87} -7.80735 q^{89} +(-2.27652 + 1.25399i) q^{91} +(-1.50000 + 12.4702i) q^{93} +(-18.0373 - 10.4138i) q^{95} +(-3.34099 + 1.92892i) q^{97} +(1.01225 - 4.14679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - q^{7} + O(q^{10}) \) \( 16q - q^{7} + 6q^{11} - 12q^{15} + 9q^{21} + 6q^{23} - 8q^{25} - 12q^{29} + 4q^{37} + 18q^{39} + 4q^{43} - 5q^{49} - 18q^{51} - 42q^{57} - 27q^{63} - 24q^{65} + 14q^{67} - 21q^{77} + 20q^{79} - 36q^{81} + 6q^{85} - 18q^{91} - 24q^{93} - 60q^{95} + 90q^{99} + O(q^{100}) \)

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 \(0.552329\pi\)
−0.772521 + 0.634989i \(0.781005\pi\)
\(6\) 0 0
\(7\) 1.36869 2.26422i 0.517317 0.855794i
\(8\) 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 0.377363 0.926066i \(-0.376831\pi\)
−0.613315 + 0.789838i \(0.710164\pi\)
\(14\) 0 0
\(15\) −7.19970 0.866025i −1.85895 0.223607i
\(16\) 0 0
\(17\) 0.370947 0.0899679 0.0449840 0.998988i \(-0.485676\pi\)
0.0449840 + 0.998988i \(0.485676\pi\)
\(18\) 0 0
\(19\) 4.97471i 1.14128i 0.821201 + 0.570638i \(0.193304\pi\)
−0.821201 + 0.570638i \(0.806696\pi\)
\(20\) 0 0
\(21\) 4.53785 + 0.638674i 0.990240 + 0.139370i
\(22\) 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 0.943414 0.331616i \(-0.107594\pi\)
0.184519 + 0.982829i \(0.440927\pi\)
\(32\) 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 −0.937391 0.348279i \(-0.886766\pi\)
0.770314 + 0.637665i \(0.220099\pi\)
\(42\) 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 \(-0.960553\pi\)
0.389118 0.921188i \(-0.372780\pi\)
\(48\) 0 0
\(49\) −3.25337 6.19803i −0.464766 0.885433i
\(50\) 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 −0.975374 0.220558i \(-0.929212\pi\)
0.678696 + 0.734420i \(0.262546\pi\)
\(60\) 0 0
\(61\) 6.50416 3.75518i 0.832772 0.480801i −0.0220288 0.999757i \(-0.507013\pi\)
0.854801 + 0.518956i \(0.173679\pi\)
\(62\) 0 0
\(63\) 2.07166 + 7.66213i 0.261004 + 0.965338i
\(64\) 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 \(-0.811718\pi\)
0.830102 0.557612i \(-0.188282\pi\)
\(74\) 0 0
\(75\) 13.0167 17.3626i 1.50304 2.00486i
\(76\) 0 0
\(77\) −0.0757141 + 3.76374i −0.00862842 + 0.428918i
\(78\) 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 0.914439 0.404724i \(-0.132632\pi\)
−0.807720 + 0.589566i \(0.799299\pi\)
\(84\) 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 \(-0.635795\pi\)
−0.413789 + 0.910373i \(0.635795\pi\)
\(90\) 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 −0.659930 0.751327i \(-0.729414\pi\)
0.320704 + 0.947180i \(0.396081\pi\)
\(98\) 0 0
\(99\) 1.01225 4.14679i 0.101735 0.416768i
\(100\) 0 0
\(101\) −4.50637 7.80526i −0.448401 0.776653i 0.549882 0.835243i \(-0.314673\pi\)
−0.998282 + 0.0585901i \(0.981340\pi\)
\(102\) 0 0
\(103\) 5.96343 + 3.44299i 0.587594 + 0.339248i 0.764146 0.645044i \(-0.223161\pi\)
−0.176551 + 0.984291i \(0.556494\pi\)
\(104\) 0 0
\(105\) −11.8150 + 15.1164i −1.15303 + 1.47521i
\(106\) 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
\(119\) 0.507712 0.839905i 0.0465419 0.0769940i
\(120\) 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 −0.990765 0.135592i \(-0.956707\pi\)
0.612808 + 0.790232i \(0.290040\pi\)
\(132\) 0 0
\(133\) 11.2638 + 6.80885i 0.976698 + 0.590402i
\(134\) 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 0.281138 0.959667i \(-0.409288\pi\)
−0.690528 + 0.723306i \(0.742622\pi\)
\(140\) 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
\(147\) 7.65702 9.40054i 0.631540 0.775343i
\(148\) 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 0.951708 0.307004i \(-0.0993264\pi\)
0.209981 + 0.977705i \(0.432660\pi\)
\(158\) 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 −0.665544 0.746359i \(-0.731800\pi\)
0.979138 + 0.203198i \(0.0651336\pi\)
\(168\) 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 0.502128 0.864793i \(-0.332550\pi\)
−0.999997 + 0.00245951i \(0.999217\pi\)
\(174\) 0 0
\(175\) −33.1407 0.666682i −2.50520 0.0503964i
\(176\) 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 \(-0.551794\pi\)
0.161998 0.986791i \(-0.448206\pi\)
\(182\) 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
\(189\) −10.7932 + 8.51504i −0.785093 + 0.619378i
\(190\) 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 \(-0.936089\pi\)
0.979911 0.199435i \(-0.0639106\pi\)
\(200\) 0 0
\(201\) 17.3068 + 2.08177i 1.22073 + 0.146837i
\(202\) 0 0
\(203\) 0.449613 22.3503i 0.0315567 1.56868i
\(204\) 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 −0.303525 0.952823i \(-0.598164\pi\)
0.673407 + 0.739272i \(0.264830\pi\)
\(224\) 0 0
\(225\) 36.5135 + 8.91312i 2.43423 + 0.594208i
\(226\) 0 0
\(227\) −5.72365 9.91365i −0.379892 0.657992i 0.611154 0.791511i \(-0.290705\pi\)
−0.991046 + 0.133520i \(0.957372\pi\)
\(228\) 0 0
\(229\) −4.88696 2.82149i −0.322940 0.186449i 0.329762 0.944064i \(-0.393031\pi\)
−0.652702 + 0.757615i \(0.726365\pi\)
\(230\) 0 0
\(231\) −6.04602 + 2.44135i −0.397799 + 0.160629i
\(232\) 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 −0.356411 0.934329i \(-0.616000\pi\)
0.630947 + 0.775826i \(0.282666\pi\)
\(242\) 0 0
\(243\) 14.0458 6.76137i 0.901037 0.433742i
\(244\) 0 0
\(245\) 29.2833 + 1.17864i 1.87084 + 0.0753007i
\(246\) 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 \(-0.546884\pi\)
−0.146759 + 0.989172i \(0.546884\pi\)
\(252\) 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 −0.984390 0.175999i \(-0.943684\pi\)
0.644615 + 0.764507i \(0.277018\pi\)
\(258\) 0 0
\(259\) 4.74176 7.84426i 0.294639 0.487419i
\(260\) 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 \(-0.471003\pi\)
0.0909718 + 0.995853i \(0.471003\pi\)
\(270\) 0 0
\(271\) 10.3608i 0.629375i 0.949195 + 0.314688i \(0.101900\pi\)
−0.949195 + 0.314688i \(0.898100\pi\)
\(272\) 0 0
\(273\) −3.54683 2.77222i −0.214664 0.167782i
\(274\) 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 0.563845 0.825880i \(-0.309321\pi\)
−0.433311 + 0.901245i \(0.642655\pi\)
\(284\) 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 −0.727066 0.686567i \(-0.759117\pi\)
0.958118 + 0.286374i \(0.0924501\pi\)
\(294\) 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
\(301\) 15.9176 + 0.320209i 0.917474 + 0.0184565i
\(302\) 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 \(0.130499\pi\)
−0.917131 + 0.398585i \(0.869501\pi\)
\(308\) 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 \(-0.457218\pi\)
0.791215 0.611539i \(-0.209449\pi\)
\(312\) 0 0
\(313\) 13.6110 7.85832i 0.769340 0.444178i −0.0632994 0.997995i \(-0.520162\pi\)
0.832639 + 0.553816i \(0.186829\pi\)
\(314\) 0 0
\(315\) −32.1181 8.52815i −1.80965 0.480507i
\(316\) 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
\(329\) −21.8782 0.440117i −1.20618 0.0242644i
\(330\) 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 −0.997463 0.0711915i \(-0.977320\pi\)
−0.437078 + 0.899424i \(0.643987\pi\)
\(350\) 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 \(0.0467853\pi\)
−0.367778 + 0.929914i \(0.619881\pi\)
\(354\) 0 0
\(355\) 39.7225 + 22.9338i 2.10825 + 1.21720i
\(356\) 0 0
\(357\) 1.68330 + 0.236914i 0.0890898 + 0.0125388i
\(358\) 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 −0.152392 0.988320i \(-0.548698\pi\)
0.779714 + 0.626135i \(0.215364\pi\)
\(368\) 0 0
\(369\) −1.79964 6.16144i −0.0936857 0.320752i
\(370\) 0 0
\(371\) 11.2587 + 6.80576i 0.584523 + 0.353337i
\(372\) 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 −0.845186 0.534472i \(-0.820510\pi\)
0.885460 + 0.464717i \(0.153844\pi\)
\(384\) 0 0
\(385\) −13.4881 8.15338i −0.687416 0.415535i
\(386\) 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 \(-0.994944\pi\)
0.999874 0.0158837i \(-0.00505615\pi\)
\(398\) 0 0
\(399\) −3.17722 + 22.5745i −0.159060 + 1.13014i
\(400\) 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 0.769973 0.638076i \(-0.220269\pi\)
−0.167603 + 0.985855i \(0.553603\pi\)
\(410\) 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 \(0.346037\pi\)
−0.999204 + 0.0398995i \(0.987296\pi\)
\(420\) 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
\(427\) 0.399648 19.8665i 0.0193403 0.961408i
\(428\) 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 \(-0.837960\pi\)
0.873201 0.487359i \(-0.162040\pi\)
\(434\) 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 −0.954569 0.297989i \(-0.903684\pi\)
−0.219219 + 0.975676i \(0.570351\pi\)
\(440\) 0 0
\(441\) 20.1842 + 5.79641i 0.961152 + 0.276020i
\(442\) 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
\(455\) 0.218855 10.8793i 0.0102601 0.510028i
\(456\) 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 0.573437 0.819249i \(-0.305610\pi\)
−0.996209 + 0.0869865i \(0.972276\pi\)
\(462\) 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 \(-0.712771\pi\)
−0.619763 + 0.784789i \(0.712771\pi\)
\(468\) 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 \(0.0595529\pi\)
−0.330193 + 0.943914i \(0.607114\pi\)
\(480\) 0 0
\(481\) −2.94734 1.70165i −0.134387 0.0775884i
\(482\) 0 0
\(483\) 20.7945 + 16.2531i 0.946182 + 0.739542i
\(484\) 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
\(497\) −24.8057 14.9947i −1.11269 0.672605i
\(498\) 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 \(-0.410128\pi\)
0.278605 + 0.960406i \(0.410128\pi\)
\(504\) 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 −0.783510 0.621379i \(-0.786573\pi\)
0.929885 + 0.367850i \(0.119906\pi\)
\(510\) 0 0
\(511\) −21.5746 13.0416i −0.954402 0.576924i
\(512\) 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 \(-0.613823\pi\)
−0.350013 + 0.936745i \(0.613823\pi\)
\(522\) 0 0
\(523\) 11.7615i 0.514293i −0.966372 0.257147i \(-0.917218\pi\)
0.966372 0.257147i \(-0.0827824\pi\)
\(524\) 0 0
\(525\) −21.4967 53.2367i −0.938193 2.32344i
\(526\) 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
\(553\) 22.5136 + 0.452899i 0.957374 + 0.0192592i
\(554\) 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 \(-0.598761\pi\)
0.977331 0.211718i \(-0.0679058\pi\)
\(564\) 0 0
\(565\) −9.08695 + 5.24635i −0.382291 + 0.220716i
\(566\) 0 0
\(567\) −20.9087 11.3942i −0.878081 0.478512i
\(568\) 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 \(0.338995\pi\)
−0.484518 + 0.874781i \(0.661005\pi\)
\(578\) 0 0
\(579\) −32.0452 3.85460i −1.33175 0.160192i
\(580\) 0 0
\(581\) 5.14364 + 0.103473i 0.213394 + 0.00429279i
\(582\) 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 0.899321 0.437289i \(-0.144061\pi\)
−0.828364 + 0.560191i \(0.810728\pi\)
\(588\) 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 \(-0.440157\pi\)
0.186898 + 0.982379i \(0.440157\pi\)
\(594\) 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 −0.876400 0.481584i \(-0.840062\pi\)
−0.0211361 + 0.999777i \(0.506728\pi\)
\(602\) 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 0.718443 0.695586i \(-0.244855\pi\)
−0.243173 + 0.969983i \(0.578188\pi\)
\(608\) 0 0
\(609\) 35.9031 14.4975i 1.45487 0.587468i
\(610\) 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 −0.397359 0.917663i \(-0.630073\pi\)
0.596040 + 0.802955i \(0.296740\pi\)
\(620\) 0 0
\(621\) −19.0046 23.1175i −0.762629 0.927675i
\(622\) 0 0
\(623\) −10.6859 + 17.6775i −0.428120 + 0.708236i
\(624\) 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
\(637\) −0.276550 + 6.87087i −0.0109573 + 0.272234i
\(638\) 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 0.259878 0.965641i \(-0.416318\pi\)
−0.706331 + 0.707882i \(0.749651\pi\)
\(644\) 0 0
\(645\) −17.1490 40.1255i −0.675239 1.57994i
\(646\) 0 0
\(647\) 35.7066 1.40377 0.701885 0.712290i \(-0.252342\pi\)
0.701885 + 0.712290i \(0.252342\pi\)
\(648\) 0 0
\(649\) 6.48486i 0.254553i
\(650\) 0 0
\(651\) 26.1823 + 20.4642i 1.02617 + 0.802057i
\(652\) 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 \(-0.966934\pi\)
−0.587105 0.809511i \(-0.699732\pi\)
\(662\) 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 0.637136 0.770751i \(-0.280119\pi\)
−0.986058 + 0.166400i \(0.946786\pi\)
\(678\) 0 0
\(679\) −0.205287 + 10.2048i −0.00787820 + 0.391625i
\(680\) 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 −0.501323 0.865260i \(-0.667153\pi\)
0.498676 + 0.866788i \(0.333820\pi\)
\(692\) 0 0
\(693\) −8.00377 7.96763i −0.304038 0.302665i
\(694\) 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
\(707\) −23.8406 0.479595i −0.896620 0.0180370i
\(708\) 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 \(-0.339709\pi\)
0.482556 + 0.875865i \(0.339709\pi\)
\(720\) 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 −0.481519 0.876436i \(-0.659915\pi\)
0.518256 + 0.855225i \(0.326581\pi\)
\(728\) 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 0.0795755 0.996829i \(-0.474644\pi\)
−0.823491 + 0.567329i \(0.807977\pi\)
\(734\) 0 0
\(735\) 18.0556 + 47.4415i 0.665990 + 1.74990i
\(736\) 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
\(749\) 25.7283 + 15.5524i 0.940090 + 0.568273i
\(750\) 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 \(-0.544780\pi\)
0.927578 0.373629i \(-0.121887\pi\)
\(762\) 0 0
\(763\) −21.8895 + 36.2116i −0.792452 + 1.31095i
\(764\) 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 0.120032 0.992770i \(-0.461700\pi\)
−0.799748 + 0.600336i \(0.795034\pi\)
\(770\) 0 0
\(771\) −18.7340 2.25344i −0.674687 0.0811557i
\(772\) 0 0
\(773\) −14.5147 −0.522056 −0.261028 0.965331i \(-0.584062\pi\)
−0.261028 + 0.965331i \(0.584062\pi\)
\(774\) 0 0
\(775\) 90.8520i 3.26350i
\(776\) 0 0
\(777\) 15.7211 + 2.21265i 0.563993 + 0.0793784i
\(778\) 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 0.689674 0.724120i \(-0.257754\pi\)
−0.282269 + 0.959335i \(0.591087\pi\)
\(788\) 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