Properties

Label 144.2.k.b.37.1
Level $144$
Weight $2$
Character 144.37
Analytic conductor $1.150$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 - 0.0297061i\) of defining polynomial
Character \(\chi\) \(=\) 144.37
Dual form 144.2.k.b.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.874559 + 1.11137i) q^{2} +(-0.470294 - 1.94392i) q^{4} +(0.334904 + 0.334904i) q^{5} +4.55765i q^{7} +(2.57172 + 1.17740i) q^{8} +O(q^{10})\) \(q+(-0.874559 + 1.11137i) q^{2} +(-0.470294 - 1.94392i) q^{4} +(0.334904 + 0.334904i) q^{5} +4.55765i q^{7} +(2.57172 + 1.17740i) q^{8} +(-0.665096 + 0.0793096i) q^{10} +(2.47363 + 2.47363i) q^{11} +(-0.0594122 + 0.0594122i) q^{13} +(-5.06524 - 3.98593i) q^{14} +(-3.55765 + 1.82843i) q^{16} -3.61706 q^{17} +(2.55765 - 2.55765i) q^{19} +(0.493523 - 0.808530i) q^{20} +(-4.91245 + 0.585786i) q^{22} +2.82843i q^{23} -4.77568i q^{25} +(-0.0140696 - 0.117988i) q^{26} +(8.85970 - 2.14343i) q^{28} +(5.16333 - 5.16333i) q^{29} -0.557647 q^{31} +(1.07931 - 5.55294i) q^{32} +(3.16333 - 4.01990i) q^{34} +(-1.52637 + 1.52637i) q^{35} +(4.38607 + 4.38607i) q^{37} +(0.605684 + 5.07931i) q^{38} +(0.466962 + 1.25559i) q^{40} -9.27391i q^{41} +(-1.61040 - 1.61040i) q^{43} +(3.64520 - 5.97186i) q^{44} +(-3.14343 - 2.47363i) q^{46} -2.82843 q^{47} -13.7721 q^{49} +(5.30755 + 4.17661i) q^{50} +(0.143434 + 0.0875513i) q^{52} +(0.493523 + 0.493523i) q^{53} +1.65685i q^{55} +(-5.36618 + 11.7210i) q^{56} +(1.22274 + 10.2540i) q^{58} +(-4.00000 - 4.00000i) q^{59} +(2.72922 - 2.72922i) q^{61} +(0.487695 - 0.619753i) q^{62} +(5.22746 + 6.05588i) q^{64} -0.0397948 q^{65} +(3.77568 - 3.77568i) q^{67} +(1.70108 + 7.03127i) q^{68} +(-0.361465 - 3.03127i) q^{70} +9.11529i q^{71} +0.541560i q^{73} +(-8.71044 + 1.03868i) q^{74} +(-6.17471 - 3.76901i) q^{76} +(-11.2739 + 11.2739i) q^{77} -10.9937 q^{79} +(-1.80382 - 0.579123i) q^{80} +(10.3068 + 8.11058i) q^{82} +(10.6417 - 10.6417i) q^{83} +(-1.21137 - 1.21137i) q^{85} +(3.19813 - 0.381362i) q^{86} +(3.44902 + 9.27391i) q^{88} +14.6533i q^{89} +(-0.270780 - 0.270780i) q^{91} +(5.49824 - 1.33019i) q^{92} +(2.47363 - 3.14343i) q^{94} +1.71313 q^{95} +4.31724 q^{97} +(12.0446 - 15.3060i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} + 12q^{8} + O(q^{10}) \) \( 8q - 4q^{4} + 12q^{8} - 8q^{10} + 8q^{11} - 12q^{14} - 8q^{19} - 16q^{20} - 20q^{26} + 8q^{28} + 16q^{29} + 24q^{31} - 24q^{35} - 16q^{37} + 8q^{38} + 16q^{40} - 8q^{43} + 40q^{44} - 8q^{46} - 8q^{49} + 36q^{50} - 16q^{52} - 16q^{53} - 16q^{58} - 32q^{59} + 16q^{61} + 12q^{62} + 8q^{64} + 16q^{65} - 16q^{67} - 32q^{68} + 32q^{70} - 52q^{74} + 8q^{76} - 16q^{77} - 24q^{79} - 8q^{80} + 40q^{82} + 40q^{83} - 16q^{85} + 16q^{86} + 32q^{88} - 8q^{91} + 16q^{92} + 8q^{94} + 48q^{95} + 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.874559 + 1.11137i −0.618406 + 0.785858i
\(3\) 0 0
\(4\) −0.470294 1.94392i −0.235147 0.971960i
\(5\) 0.334904 + 0.334904i 0.149774 + 0.149774i 0.778017 0.628243i \(-0.216226\pi\)
−0.628243 + 0.778017i \(0.716226\pi\)
\(6\) 0 0
\(7\) 4.55765i 1.72263i 0.508072 + 0.861314i \(0.330358\pi\)
−0.508072 + 0.861314i \(0.669642\pi\)
\(8\) 2.57172 + 1.17740i 0.909239 + 0.416274i
\(9\) 0 0
\(10\) −0.665096 + 0.0793096i −0.210322 + 0.0250799i
\(11\) 2.47363 + 2.47363i 0.745826 + 0.745826i 0.973692 0.227866i \(-0.0731749\pi\)
−0.227866 + 0.973692i \(0.573175\pi\)
\(12\) 0 0
\(13\) −0.0594122 + 0.0594122i −0.0164780 + 0.0164780i −0.715298 0.698820i \(-0.753709\pi\)
0.698820 + 0.715298i \(0.253709\pi\)
\(14\) −5.06524 3.98593i −1.35374 1.06528i
\(15\) 0 0
\(16\) −3.55765 + 1.82843i −0.889412 + 0.457107i
\(17\) −3.61706 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(18\) 0 0
\(19\) 2.55765 2.55765i 0.586765 0.586765i −0.349989 0.936754i \(-0.613815\pi\)
0.936754 + 0.349989i \(0.113815\pi\)
\(20\) 0.493523 0.808530i 0.110355 0.180793i
\(21\) 0 0
\(22\) −4.91245 + 0.585786i −1.04734 + 0.124890i
\(23\) 2.82843i 0.589768i 0.955533 + 0.294884i \(0.0952810\pi\)
−0.955533 + 0.294884i \(0.904719\pi\)
\(24\) 0 0
\(25\) 4.77568i 0.955136i
\(26\) −0.0140696 0.117988i −0.00275927 0.0231394i
\(27\) 0 0
\(28\) 8.85970 2.14343i 1.67433 0.405071i
\(29\) 5.16333 5.16333i 0.958807 0.958807i −0.0403780 0.999184i \(-0.512856\pi\)
0.999184 + 0.0403780i \(0.0128562\pi\)
\(30\) 0 0
\(31\) −0.557647 −0.100156 −0.0500782 0.998745i \(-0.515947\pi\)
−0.0500782 + 0.998745i \(0.515947\pi\)
\(32\) 1.07931 5.55294i 0.190797 0.981630i
\(33\) 0 0
\(34\) 3.16333 4.01990i 0.542507 0.689407i
\(35\) −1.52637 + 1.52637i −0.258004 + 0.258004i
\(36\) 0 0
\(37\) 4.38607 + 4.38607i 0.721066 + 0.721066i 0.968822 0.247756i \(-0.0796932\pi\)
−0.247756 + 0.968822i \(0.579693\pi\)
\(38\) 0.605684 + 5.07931i 0.0982549 + 0.823973i
\(39\) 0 0
\(40\) 0.466962 + 1.25559i 0.0738332 + 0.198527i
\(41\) 9.27391i 1.44834i −0.689620 0.724171i \(-0.742223\pi\)
0.689620 0.724171i \(-0.257777\pi\)
\(42\) 0 0
\(43\) −1.61040 1.61040i −0.245583 0.245583i 0.573572 0.819155i \(-0.305557\pi\)
−0.819155 + 0.573572i \(0.805557\pi\)
\(44\) 3.64520 5.97186i 0.549534 0.900292i
\(45\) 0 0
\(46\) −3.14343 2.47363i −0.463474 0.364716i
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) 0 0
\(49\) −13.7721 −1.96745
\(50\) 5.30755 + 4.17661i 0.750601 + 0.590662i
\(51\) 0 0
\(52\) 0.143434 + 0.0875513i 0.0198907 + 0.0121412i
\(53\) 0.493523 + 0.493523i 0.0677906 + 0.0677906i 0.740189 0.672399i \(-0.234736\pi\)
−0.672399 + 0.740189i \(0.734736\pi\)
\(54\) 0 0
\(55\) 1.65685i 0.223410i
\(56\) −5.36618 + 11.7210i −0.717086 + 1.56628i
\(57\) 0 0
\(58\) 1.22274 + 10.2540i 0.160554 + 1.34642i
\(59\) −4.00000 4.00000i −0.520756 0.520756i 0.397044 0.917800i \(-0.370036\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(60\) 0 0
\(61\) 2.72922 2.72922i 0.349441 0.349441i −0.510460 0.859901i \(-0.670525\pi\)
0.859901 + 0.510460i \(0.170525\pi\)
\(62\) 0.487695 0.619753i 0.0619374 0.0787088i
\(63\) 0 0
\(64\) 5.22746 + 6.05588i 0.653432 + 0.756985i
\(65\) −0.0397948 −0.00493593
\(66\) 0 0
\(67\) 3.77568 3.77568i 0.461273 0.461273i −0.437800 0.899072i \(-0.644242\pi\)
0.899072 + 0.437800i \(0.144242\pi\)
\(68\) 1.70108 + 7.03127i 0.206286 + 0.852667i
\(69\) 0 0
\(70\) −0.361465 3.03127i −0.0432033 0.362306i
\(71\) 9.11529i 1.08179i 0.841091 + 0.540893i \(0.181914\pi\)
−0.841091 + 0.540893i \(0.818086\pi\)
\(72\) 0 0
\(73\) 0.541560i 0.0633848i 0.999498 + 0.0316924i \(0.0100897\pi\)
−0.999498 + 0.0316924i \(0.989910\pi\)
\(74\) −8.71044 + 1.03868i −1.01257 + 0.120744i
\(75\) 0 0
\(76\) −6.17471 3.76901i −0.708287 0.432336i
\(77\) −11.2739 + 11.2739i −1.28478 + 1.28478i
\(78\) 0 0
\(79\) −10.9937 −1.23689 −0.618445 0.785828i \(-0.712237\pi\)
−0.618445 + 0.785828i \(0.712237\pi\)
\(80\) −1.80382 0.579123i −0.201673 0.0647479i
\(81\) 0 0
\(82\) 10.3068 + 8.11058i 1.13819 + 0.895664i
\(83\) 10.6417 10.6417i 1.16807 1.16807i 0.185415 0.982660i \(-0.440637\pi\)
0.982660 0.185415i \(-0.0593628\pi\)
\(84\) 0 0
\(85\) −1.21137 1.21137i −0.131391 0.131391i
\(86\) 3.19813 0.381362i 0.344864 0.0411234i
\(87\) 0 0
\(88\) 3.44902 + 9.27391i 0.367666 + 0.988603i
\(89\) 14.6533i 1.55325i 0.629964 + 0.776625i \(0.283070\pi\)
−0.629964 + 0.776625i \(0.716930\pi\)
\(90\) 0 0
\(91\) −0.270780 0.270780i −0.0283854 0.0283854i
\(92\) 5.49824 1.33019i 0.573231 0.138682i
\(93\) 0 0
\(94\) 2.47363 3.14343i 0.255135 0.324220i
\(95\) 1.71313 0.175764
\(96\) 0 0
\(97\) 4.31724 0.438349 0.219175 0.975686i \(-0.429664\pi\)
0.219175 + 0.975686i \(0.429664\pi\)
\(98\) 12.0446 15.3060i 1.21668 1.54614i
\(99\) 0 0
\(100\) −9.28354 + 2.24597i −0.928354 + 0.224597i
\(101\) 0.453728 + 0.453728i 0.0451477 + 0.0451477i 0.729320 0.684173i \(-0.239836\pi\)
−0.684173 + 0.729320i \(0.739836\pi\)
\(102\) 0 0
\(103\) 1.33686i 0.131724i −0.997829 0.0658622i \(-0.979020\pi\)
0.997829 0.0658622i \(-0.0209798\pi\)
\(104\) −0.222743 + 0.0828394i −0.0218418 + 0.00812307i
\(105\) 0 0
\(106\) −0.980103 + 0.116873i −0.0951960 + 0.0113517i
\(107\) −6.06255 6.06255i −0.586088 0.586088i 0.350481 0.936570i \(-0.386018\pi\)
−0.936570 + 0.350481i \(0.886018\pi\)
\(108\) 0 0
\(109\) 5.71627 5.71627i 0.547519 0.547519i −0.378203 0.925722i \(-0.623458\pi\)
0.925722 + 0.378203i \(0.123458\pi\)
\(110\) −1.84138 1.44902i −0.175569 0.138158i
\(111\) 0 0
\(112\) −8.33333 16.2145i −0.787425 1.53213i
\(113\) 9.55136 0.898516 0.449258 0.893402i \(-0.351688\pi\)
0.449258 + 0.893402i \(0.351688\pi\)
\(114\) 0 0
\(115\) −0.947252 + 0.947252i −0.0883317 + 0.0883317i
\(116\) −12.4654 7.60882i −1.15738 0.706461i
\(117\) 0 0
\(118\) 7.94372 0.947252i 0.731279 0.0872016i
\(119\) 16.4853i 1.51120i
\(120\) 0 0
\(121\) 1.23765i 0.112514i
\(122\) 0.646314 + 5.42004i 0.0585146 + 0.490707i
\(123\) 0 0
\(124\) 0.262258 + 1.08402i 0.0235515 + 0.0973480i
\(125\) 3.27391 3.27391i 0.292828 0.292828i
\(126\) 0 0
\(127\) 5.09921 0.452481 0.226241 0.974071i \(-0.427356\pi\)
0.226241 + 0.974071i \(0.427356\pi\)
\(128\) −11.3021 + 0.513421i −0.998970 + 0.0453804i
\(129\) 0 0
\(130\) 0.0348029 0.0442268i 0.00305241 0.00387894i
\(131\) −2.11882 + 2.11882i −0.185123 + 0.185123i −0.793584 0.608461i \(-0.791787\pi\)
0.608461 + 0.793584i \(0.291787\pi\)
\(132\) 0 0
\(133\) 11.6569 + 11.6569i 1.01078 + 1.01078i
\(134\) 0.894129 + 7.49824i 0.0772410 + 0.647749i
\(135\) 0 0
\(136\) −9.30205 4.25873i −0.797644 0.365183i
\(137\) 3.37941i 0.288723i −0.989525 0.144361i \(-0.953887\pi\)
0.989525 0.144361i \(-0.0461127\pi\)
\(138\) 0 0
\(139\) 5.88118 + 5.88118i 0.498835 + 0.498835i 0.911075 0.412240i \(-0.135254\pi\)
−0.412240 + 0.911075i \(0.635254\pi\)
\(140\) 3.68499 + 2.24930i 0.311439 + 0.190101i
\(141\) 0 0
\(142\) −10.1305 7.97186i −0.850131 0.668984i
\(143\) −0.293927 −0.0245794
\(144\) 0 0
\(145\) 3.45844 0.287208
\(146\) −0.601874 0.473626i −0.0498115 0.0391975i
\(147\) 0 0
\(148\) 6.46343 10.5889i 0.531291 0.870404i
\(149\) 9.99176 + 9.99176i 0.818557 + 0.818557i 0.985899 0.167342i \(-0.0535185\pi\)
−0.167342 + 0.985899i \(0.553518\pi\)
\(150\) 0 0
\(151\) 9.97685i 0.811905i −0.913894 0.405952i \(-0.866940\pi\)
0.913894 0.405952i \(-0.133060\pi\)
\(152\) 9.58892 3.56617i 0.777764 0.289255i
\(153\) 0 0
\(154\) −2.66981 22.3892i −0.215139 1.80417i
\(155\) −0.186758 0.186758i −0.0150008 0.0150008i
\(156\) 0 0
\(157\) −16.1618 + 16.1618i −1.28985 + 1.28985i −0.354971 + 0.934877i \(0.615509\pi\)
−0.934877 + 0.354971i \(0.884491\pi\)
\(158\) 9.61465 12.2181i 0.764900 0.972020i
\(159\) 0 0
\(160\) 2.22117 1.49824i 0.175599 0.118446i
\(161\) −12.8910 −1.01595
\(162\) 0 0
\(163\) −7.50490 + 7.50490i −0.587829 + 0.587829i −0.937043 0.349214i \(-0.886449\pi\)
0.349214 + 0.937043i \(0.386449\pi\)
\(164\) −18.0277 + 4.36147i −1.40773 + 0.340573i
\(165\) 0 0
\(166\) 2.52008 + 21.1336i 0.195596 + 1.64029i
\(167\) 5.83822i 0.451775i −0.974153 0.225888i \(-0.927472\pi\)
0.974153 0.225888i \(-0.0725282\pi\)
\(168\) 0 0
\(169\) 12.9929i 0.999457i
\(170\) 2.40569 0.286867i 0.184508 0.0220017i
\(171\) 0 0
\(172\) −2.37312 + 3.88784i −0.180949 + 0.296445i
\(173\) 3.62530 3.62530i 0.275627 0.275627i −0.555734 0.831360i \(-0.687563\pi\)
0.831360 + 0.555734i \(0.187563\pi\)
\(174\) 0 0
\(175\) 21.7659 1.64534
\(176\) −13.3231 4.27744i −1.00427 0.322424i
\(177\) 0 0
\(178\) −16.2853 12.8152i −1.22063 0.960539i
\(179\) −9.28334 + 9.28334i −0.693869 + 0.693869i −0.963081 0.269212i \(-0.913237\pi\)
0.269212 + 0.963081i \(0.413237\pi\)
\(180\) 0 0
\(181\) −10.8316 10.8316i −0.805104 0.805104i 0.178785 0.983888i \(-0.442783\pi\)
−0.983888 + 0.178785i \(0.942783\pi\)
\(182\) 0.537750 0.0641242i 0.0398607 0.00475320i
\(183\) 0 0
\(184\) −3.33019 + 7.27391i −0.245505 + 0.536240i
\(185\) 2.93783i 0.215993i
\(186\) 0 0
\(187\) −8.94725 8.94725i −0.654288 0.654288i
\(188\) 1.33019 + 5.49824i 0.0970142 + 0.401000i
\(189\) 0 0
\(190\) −1.49824 + 1.90393i −0.108693 + 0.138125i
\(191\) 8.63001 0.624446 0.312223 0.950009i \(-0.398926\pi\)
0.312223 + 0.950009i \(0.398926\pi\)
\(192\) 0 0
\(193\) 11.4514 0.824288 0.412144 0.911119i \(-0.364780\pi\)
0.412144 + 0.911119i \(0.364780\pi\)
\(194\) −3.77568 + 4.79806i −0.271078 + 0.344480i
\(195\) 0 0
\(196\) 6.47696 + 26.7720i 0.462640 + 1.91228i
\(197\) −7.48999 7.48999i −0.533640 0.533640i 0.388014 0.921654i \(-0.373161\pi\)
−0.921654 + 0.388014i \(0.873161\pi\)
\(198\) 0 0
\(199\) 3.68000i 0.260868i 0.991457 + 0.130434i \(0.0416371\pi\)
−0.991457 + 0.130434i \(0.958363\pi\)
\(200\) 5.62289 12.2817i 0.397598 0.868447i
\(201\) 0 0
\(202\) −0.901073 + 0.107449i −0.0633993 + 0.00756007i
\(203\) 23.5326 + 23.5326i 1.65167 + 1.65167i
\(204\) 0 0
\(205\) 3.10587 3.10587i 0.216923 0.216923i
\(206\) 1.48574 + 1.16916i 0.103517 + 0.0814592i
\(207\) 0 0
\(208\) 0.102737 0.319999i 0.00712351 0.0221879i
\(209\) 12.6533 0.875249
\(210\) 0 0
\(211\) 10.1188 10.1188i 0.696609 0.696609i −0.267069 0.963677i \(-0.586055\pi\)
0.963677 + 0.267069i \(0.0860551\pi\)
\(212\) 0.727268 1.19147i 0.0499490 0.0818305i
\(213\) 0 0
\(214\) 12.0398 1.43569i 0.823023 0.0981417i
\(215\) 1.07866i 0.0735637i
\(216\) 0 0
\(217\) 2.54156i 0.172532i
\(218\) 1.35369 + 11.3521i 0.0916832 + 0.768862i
\(219\) 0 0
\(220\) 3.22079 0.779208i 0.217146 0.0525342i
\(221\) 0.214897 0.214897i 0.0144556 0.0144556i
\(222\) 0 0
\(223\) −4.86156 −0.325554 −0.162777 0.986663i \(-0.552045\pi\)
−0.162777 + 0.986663i \(0.552045\pi\)
\(224\) 25.3083 + 4.91911i 1.69098 + 0.328672i
\(225\) 0 0
\(226\) −8.35322 + 10.6151i −0.555648 + 0.706106i
\(227\) −10.6417 + 10.6417i −0.706312 + 0.706312i −0.965758 0.259445i \(-0.916460\pi\)
0.259445 + 0.965758i \(0.416460\pi\)
\(228\) 0 0
\(229\) −20.1712 20.1712i −1.33295 1.33295i −0.902720 0.430229i \(-0.858433\pi\)
−0.430229 0.902720i \(-0.641567\pi\)
\(230\) −0.224321 1.88118i −0.0147913 0.124041i
\(231\) 0 0
\(232\) 19.3579 7.19932i 1.27091 0.472658i
\(233\) 13.5702i 0.889014i 0.895775 + 0.444507i \(0.146621\pi\)
−0.895775 + 0.444507i \(0.853379\pi\)
\(234\) 0 0
\(235\) −0.947252 0.947252i −0.0617919 0.0617919i
\(236\) −5.89450 + 9.65685i −0.383699 + 0.628608i
\(237\) 0 0
\(238\) 18.3213 + 14.4173i 1.18759 + 0.934538i
\(239\) −29.3629 −1.89933 −0.949665 0.313267i \(-0.898576\pi\)
−0.949665 + 0.313267i \(0.898576\pi\)
\(240\) 0 0
\(241\) 24.0063 1.54638 0.773190 0.634175i \(-0.218660\pi\)
0.773190 + 0.634175i \(0.218660\pi\)
\(242\) −1.37549 1.08240i −0.0884197 0.0695791i
\(243\) 0 0
\(244\) −6.58892 4.02185i −0.421812 0.257473i
\(245\) −4.61235 4.61235i −0.294672 0.294672i
\(246\) 0 0
\(247\) 0.303911i 0.0193374i
\(248\) −1.43411 0.656574i −0.0910661 0.0416925i
\(249\) 0 0
\(250\) 0.775305 + 6.50176i 0.0490346 + 0.411208i
\(251\) −15.7570 15.7570i −0.994571 0.994571i 0.00541463 0.999985i \(-0.498276\pi\)
−0.999985 + 0.00541463i \(0.998276\pi\)
\(252\) 0 0
\(253\) −6.99647 + 6.99647i −0.439864 + 0.439864i
\(254\) −4.45956 + 5.66711i −0.279817 + 0.355586i
\(255\) 0 0
\(256\) 9.31371 13.0098i 0.582107 0.813112i
\(257\) −8.66038 −0.540220 −0.270110 0.962829i \(-0.587060\pi\)
−0.270110 + 0.962829i \(0.587060\pi\)
\(258\) 0 0
\(259\) −19.9902 + 19.9902i −1.24213 + 1.24213i
\(260\) 0.0187152 + 0.0773578i 0.00116067 + 0.00479753i
\(261\) 0 0
\(262\) −0.501765 4.20784i −0.0309991 0.259961i
\(263\) 13.3208i 0.821394i 0.911772 + 0.410697i \(0.134715\pi\)
−0.911772 + 0.410697i \(0.865285\pi\)
\(264\) 0 0
\(265\) 0.330566i 0.0203065i
\(266\) −23.1497 + 2.76049i −1.41940 + 0.169257i
\(267\) 0 0
\(268\) −9.11529 5.56394i −0.556805 0.339872i
\(269\) 11.6714 11.6714i 0.711616 0.711616i −0.255257 0.966873i \(-0.582160\pi\)
0.966873 + 0.255257i \(0.0821602\pi\)
\(270\) 0 0
\(271\) −21.9769 −1.33500 −0.667499 0.744610i \(-0.732635\pi\)
−0.667499 + 0.744610i \(0.732635\pi\)
\(272\) 12.8682 6.61353i 0.780251 0.401004i
\(273\) 0 0
\(274\) 3.75578 + 2.95549i 0.226895 + 0.178548i
\(275\) 11.8132 11.8132i 0.712365 0.712365i
\(276\) 0 0
\(277\) −10.9504 10.9504i −0.657945 0.657945i 0.296949 0.954893i \(-0.404031\pi\)
−0.954893 + 0.296949i \(0.904031\pi\)
\(278\) −11.6796 + 1.39274i −0.700496 + 0.0835309i
\(279\) 0 0
\(280\) −5.72256 + 2.12825i −0.341988 + 0.127187i
\(281\) 22.8910i 1.36556i −0.730624 0.682780i \(-0.760771\pi\)
0.730624 0.682780i \(-0.239229\pi\)
\(282\) 0 0
\(283\) 4.48528 + 4.48528i 0.266622 + 0.266622i 0.827738 0.561115i \(-0.189628\pi\)
−0.561115 + 0.827738i \(0.689628\pi\)
\(284\) 17.7194 4.28687i 1.05145 0.254379i
\(285\) 0 0
\(286\) 0.257057 0.326662i 0.0152001 0.0193159i
\(287\) 42.2672 2.49496
\(288\) 0 0
\(289\) −3.91688 −0.230405
\(290\) −3.02461 + 3.84361i −0.177611 + 0.225705i
\(291\) 0 0
\(292\) 1.05275 0.254692i 0.0616074 0.0149047i
\(293\) −21.6221 21.6221i −1.26318 1.26318i −0.949543 0.313636i \(-0.898453\pi\)
−0.313636 0.949543i \(-0.601547\pi\)
\(294\) 0 0
\(295\) 2.67923i 0.155991i
\(296\) 6.11557 + 16.4439i 0.355461 + 0.955783i
\(297\) 0 0
\(298\) −19.8429 + 2.36618i −1.14947 + 0.137069i
\(299\) −0.168043 0.168043i −0.00971818 0.00971818i
\(300\) 0 0
\(301\) 7.33962 7.33962i 0.423048 0.423048i
\(302\) 11.0880 + 8.72534i 0.638042 + 0.502087i
\(303\) 0 0
\(304\) −4.42274 + 13.7757i −0.253661 + 0.790089i
\(305\) 1.82805 0.104674
\(306\) 0 0
\(307\) −12.1118 + 12.1118i −0.691255 + 0.691255i −0.962508 0.271253i \(-0.912562\pi\)
0.271253 + 0.962508i \(0.412562\pi\)
\(308\) 27.2176 + 16.6135i 1.55087 + 0.946644i
\(309\) 0 0
\(310\) 0.370889 0.0442268i 0.0210651 0.00251191i
\(311\) 26.8651i 1.52338i −0.647943 0.761689i \(-0.724370\pi\)
0.647943 0.761689i \(-0.275630\pi\)
\(312\) 0 0
\(313\) 19.6890i 1.11289i −0.830885 0.556445i \(-0.812165\pi\)
0.830885 0.556445i \(-0.187835\pi\)
\(314\) −3.82731 32.0961i −0.215988 1.81129i
\(315\) 0 0
\(316\) 5.17027 + 21.3709i 0.290851 + 1.20221i
\(317\) −21.3447 + 21.3447i −1.19884 + 1.19884i −0.224323 + 0.974515i \(0.572017\pi\)
−0.974515 + 0.224323i \(0.927983\pi\)
\(318\) 0 0
\(319\) 25.5443 1.43021
\(320\) −0.277444 + 3.77883i −0.0155096 + 0.211243i
\(321\) 0 0
\(322\) 11.2739 14.3267i 0.628271 0.798394i
\(323\) −9.25116 + 9.25116i −0.514748 + 0.514748i
\(324\) 0 0
\(325\) 0.283734 + 0.283734i 0.0157387 + 0.0157387i
\(326\) −1.77726 14.9042i −0.0984331 0.825468i
\(327\) 0 0
\(328\) 10.9191 23.8499i 0.602907 1.31689i
\(329\) 12.8910i 0.710702i
\(330\) 0 0
\(331\) 14.6926 + 14.6926i 0.807576 + 0.807576i 0.984266 0.176690i \(-0.0565391\pi\)
−0.176690 + 0.984266i \(0.556539\pi\)
\(332\) −25.6913 15.6818i −1.40999 0.860653i
\(333\) 0 0
\(334\) 6.48844 + 5.10587i 0.355032 + 0.279381i
\(335\) 2.52898 0.138173
\(336\) 0 0
\(337\) −23.0098 −1.25342 −0.626712 0.779251i \(-0.715600\pi\)
−0.626712 + 0.779251i \(0.715600\pi\)
\(338\) −14.4400 11.3631i −0.785432 0.618071i
\(339\) 0 0
\(340\) −1.78510 + 2.92450i −0.0968108 + 0.158603i
\(341\) −1.37941 1.37941i −0.0746993 0.0746993i
\(342\) 0 0
\(343\) 30.8651i 1.66656i
\(344\) −2.24540 6.03756i −0.121064 0.325524i
\(345\) 0 0
\(346\) 0.858518 + 7.19960i 0.0461542 + 0.387053i
\(347\) 10.9026 + 10.9026i 0.585284 + 0.585284i 0.936350 0.351067i \(-0.114181\pi\)
−0.351067 + 0.936350i \(0.614181\pi\)
\(348\) 0 0
\(349\) 20.0563 20.0563i 1.07359 1.07359i 0.0765186 0.997068i \(-0.475620\pi\)
0.997068 0.0765186i \(-0.0243805\pi\)
\(350\) −19.0355 + 24.1900i −1.01749 + 1.29301i
\(351\) 0 0
\(352\) 16.4057 11.0661i 0.874426 0.589824i
\(353\) 12.2117 0.649965 0.324983 0.945720i \(-0.394642\pi\)
0.324983 + 0.945720i \(0.394642\pi\)
\(354\) 0 0
\(355\) −3.05275 + 3.05275i −0.162023 + 0.162023i
\(356\) 28.4849 6.89137i 1.50970 0.365242i
\(357\) 0 0
\(358\) −2.19841 18.4361i −0.116190 0.974376i
\(359\) 33.4780i 1.76690i 0.468522 + 0.883452i \(0.344786\pi\)
−0.468522 + 0.883452i \(0.655214\pi\)
\(360\) 0 0
\(361\) 5.91688i 0.311415i
\(362\) 21.5107 2.56505i 1.13058 0.134816i
\(363\) 0 0
\(364\) −0.399028 + 0.653720i −0.0209148 + 0.0342643i
\(365\) −0.181370 + 0.181370i −0.00949337 + 0.00949337i
\(366\) 0 0
\(367\) −0.702379 −0.0366639 −0.0183319 0.999832i \(-0.505836\pi\)
−0.0183319 + 0.999832i \(0.505836\pi\)
\(368\) −5.17157 10.0625i −0.269587 0.524546i
\(369\) 0 0
\(370\) −3.26502 2.56930i −0.169740 0.133572i
\(371\) −2.24930 + 2.24930i −0.116778 + 0.116778i
\(372\) 0 0
\(373\) 18.9598 + 18.9598i 0.981702 + 0.981702i 0.999836 0.0181339i \(-0.00577250\pi\)
−0.0181339 + 0.999836i \(0.505773\pi\)
\(374\) 17.7686 2.11882i 0.918793 0.109562i
\(375\) 0 0
\(376\) −7.27391 3.33019i −0.375123 0.171742i
\(377\) 0.613530i 0.0315984i
\(378\) 0 0
\(379\) −1.77844 1.77844i −0.0913523 0.0913523i 0.659954 0.751306i \(-0.270576\pi\)
−0.751306 + 0.659954i \(0.770576\pi\)
\(380\) −0.805676 3.33019i −0.0413303 0.170835i
\(381\) 0 0
\(382\) −7.54745 + 9.59115i −0.386161 + 0.490726i
\(383\) −25.4880 −1.30238 −0.651188 0.758916i \(-0.725729\pi\)
−0.651188 + 0.758916i \(0.725729\pi\)
\(384\) 0 0
\(385\) −7.55136 −0.384853
\(386\) −10.0149 + 12.7267i −0.509745 + 0.647774i
\(387\) 0 0
\(388\) −2.03037 8.39236i −0.103076 0.426058i
\(389\) 11.7049 + 11.7049i 0.593462 + 0.593462i 0.938565 0.345103i \(-0.112156\pi\)
−0.345103 + 0.938565i \(0.612156\pi\)
\(390\) 0 0
\(391\) 10.2306i 0.517383i
\(392\) −35.4181 16.2153i −1.78888 0.818998i
\(393\) 0 0
\(394\) 14.8746 1.77373i 0.749372 0.0893591i
\(395\) −3.68184 3.68184i −0.185253 0.185253i
\(396\) 0 0
\(397\) −9.04646 + 9.04646i −0.454029 + 0.454029i −0.896689 0.442661i \(-0.854035\pi\)
0.442661 + 0.896689i \(0.354035\pi\)
\(398\) −4.08985 3.21838i −0.205006 0.161323i
\(399\) 0 0
\(400\) 8.73198 + 16.9902i 0.436599 + 0.849509i
\(401\) 18.0853 0.903137 0.451568 0.892237i \(-0.350865\pi\)
0.451568 + 0.892237i \(0.350865\pi\)
\(402\) 0 0
\(403\) 0.0331311 0.0331311i 0.00165038 0.00165038i
\(404\) 0.668626 1.09540i 0.0332654 0.0544980i
\(405\) 0 0
\(406\) −46.7342 + 5.57283i −2.31938 + 0.276575i
\(407\) 21.6990i 1.07558i
\(408\) 0 0
\(409\) 25.2271i 1.24740i 0.781665 + 0.623699i \(0.214371\pi\)
−0.781665 + 0.623699i \(0.785629\pi\)
\(410\) 0.735510 + 6.16804i 0.0363243 + 0.304618i
\(411\) 0 0
\(412\) −2.59874 + 0.628715i −0.128031 + 0.0309746i
\(413\) 18.2306 18.2306i 0.897069 0.897069i
\(414\) 0 0
\(415\) 7.12787 0.349894
\(416\) 0.265788 + 0.394036i 0.0130313 + 0.0193192i
\(417\) 0 0
\(418\) −11.0661 + 14.0625i −0.541259 + 0.687822i
\(419\) −7.25283 + 7.25283i −0.354324 + 0.354324i −0.861716 0.507392i \(-0.830610\pi\)
0.507392 + 0.861716i \(0.330610\pi\)
\(420\) 0 0
\(421\) 2.39550 + 2.39550i 0.116749 + 0.116749i 0.763068 0.646318i \(-0.223692\pi\)
−0.646318 + 0.763068i \(0.723692\pi\)
\(422\) 2.39627 + 20.0953i 0.116648 + 0.978223i
\(423\) 0 0
\(424\) 0.688127 + 1.85028i 0.0334184 + 0.0898574i
\(425\) 17.2739i 0.837908i
\(426\) 0 0
\(427\) 12.4388 + 12.4388i 0.601957 + 0.601957i
\(428\) −8.93392 + 14.6363i −0.431838 + 0.707471i
\(429\) 0 0
\(430\) 1.19879 + 0.943348i 0.0578107 + 0.0454923i
\(431\) 4.42454 0.213123 0.106561 0.994306i \(-0.466016\pi\)
0.106561 + 0.994306i \(0.466016\pi\)
\(432\) 0 0
\(433\) 7.31371 0.351474 0.175737 0.984437i \(-0.443769\pi\)
0.175737 + 0.984437i \(0.443769\pi\)
\(434\) 2.82462 + 2.22274i 0.135586 + 0.106695i
\(435\) 0 0
\(436\) −13.8003 8.42364i −0.660914 0.403419i
\(437\) 7.23412 + 7.23412i 0.346055 + 0.346055i
\(438\) 0 0
\(439\) 29.6533i 1.41527i 0.706576 + 0.707637i \(0.250239\pi\)
−0.706576 + 0.707637i \(0.749761\pi\)
\(440\) −1.95078 + 4.26096i −0.0929999 + 0.203133i
\(441\) 0 0
\(442\) 0.0508905 + 0.426771i 0.00242061 + 0.0202994i
\(443\) −10.3056 10.3056i −0.489633 0.489633i 0.418557 0.908190i \(-0.362536\pi\)
−0.908190 + 0.418557i \(0.862536\pi\)
\(444\) 0 0
\(445\) −4.90746 + 4.90746i −0.232636 + 0.232636i
\(446\) 4.25172 5.40300i 0.201325 0.255839i
\(447\) 0 0
\(448\) −27.6006 + 23.8249i −1.30400 + 1.12562i
\(449\) 6.48844 0.306208 0.153104 0.988210i \(-0.451073\pi\)
0.153104 + 0.988210i \(0.451073\pi\)
\(450\) 0 0
\(451\) 22.9402 22.9402i 1.08021 1.08021i
\(452\) −4.49195 18.5671i −0.211283 0.873322i
\(453\) 0 0
\(454\) −2.52008 21.1336i −0.118273 0.991850i
\(455\) 0.181370i 0.00850278i
\(456\) 0 0
\(457\) 9.00353i 0.421167i 0.977576 + 0.210584i \(0.0675364\pi\)
−0.977576 + 0.210584i \(0.932464\pi\)
\(458\) 40.0586 4.77679i 1.87181 0.223205i
\(459\) 0 0
\(460\) 2.28687 + 1.39589i 0.106626 + 0.0650839i
\(461\) −14.6218 + 14.6218i −0.681004 + 0.681004i −0.960226 0.279223i \(-0.909923\pi\)
0.279223 + 0.960226i \(0.409923\pi\)
\(462\) 0 0
\(463\) −18.6435 −0.866437 −0.433219 0.901289i \(-0.642622\pi\)
−0.433219 + 0.901289i \(0.642622\pi\)
\(464\) −8.92854 + 27.8101i −0.414497 + 1.29105i
\(465\) 0 0
\(466\) −15.0815 11.8679i −0.698639 0.549772i
\(467\) 23.5138 23.5138i 1.08809 1.08809i 0.0923633 0.995725i \(-0.470558\pi\)
0.995725 0.0923633i \(-0.0294421\pi\)
\(468\) 0 0
\(469\) 17.2082 + 17.2082i 0.794601 + 0.794601i
\(470\) 1.88118 0.224321i 0.0867722 0.0103472i
\(471\) 0 0
\(472\) −5.57726 14.9965i −0.256714 0.690268i
\(473\) 7.96703i 0.366325i
\(474\) 0 0
\(475\) −12.2145 12.2145i −0.560440 0.560440i
\(476\) −32.0461 + 7.75293i −1.46883 + 0.355355i
\(477\) 0 0
\(478\) 25.6796 32.6331i 1.17456 1.49260i
\(479\) 1.08864 0.0497412 0.0248706 0.999691i \(-0.492083\pi\)
0.0248706 + 0.999691i \(0.492083\pi\)
\(480\) 0 0
\(481\) −0.521173 −0.0237634
\(482\) −20.9949 + 26.6799i −0.956291 + 1.21524i
\(483\) 0 0
\(484\) 2.40589 0.582059i 0.109359 0.0264572i
\(485\) 1.44586 + 1.44586i 0.0656531 + 0.0656531i
\(486\) 0 0
\(487\) 35.3298i 1.60095i 0.599369 + 0.800473i \(0.295418\pi\)
−0.599369 + 0.800473i \(0.704582\pi\)
\(488\) 10.2322 3.80540i 0.463188 0.172262i
\(489\) 0 0
\(490\) 9.15980 1.09226i 0.413798 0.0493434i
\(491\) 12.8910 + 12.8910i 0.581761 + 0.581761i 0.935387 0.353626i \(-0.115051\pi\)
−0.353626 + 0.935387i \(0.615051\pi\)
\(492\) 0 0
\(493\) −18.6761 + 18.6761i −0.841128 + 0.841128i
\(494\) −0.337758 0.265788i −0.0151964 0.0119584i
\(495\) 0 0
\(496\) 1.98391 1.01962i 0.0890803 0.0457822i
\(497\) −41.5443 −1.86352
\(498\) 0 0
\(499\) 14.3798 14.3798i 0.643728 0.643728i −0.307742 0.951470i \(-0.599573\pi\)
0.951470 + 0.307742i \(0.0995734\pi\)
\(500\) −7.90393 4.82452i −0.353474 0.215759i
\(501\) 0 0
\(502\) 31.2922 3.73145i 1.39664 0.166543i
\(503\) 30.2969i 1.35087i −0.737420 0.675435i \(-0.763956\pi\)
0.737420 0.675435i \(-0.236044\pi\)
\(504\) 0 0
\(505\) 0.303911i 0.0135239i
\(506\) −1.65685 13.8945i −0.0736562 0.617686i
\(507\) 0 0
\(508\) −2.39813 9.91245i −0.106400 0.439794i
\(509\) −10.5825 + 10.5825i −0.469063 + 0.469063i −0.901611 0.432548i \(-0.857615\pi\)
0.432548 + 0.901611i \(0.357615\pi\)
\(510\) 0 0
\(511\) −2.46824 −0.109188
\(512\) 6.31333 + 21.7288i 0.279013 + 0.960287i
\(513\) 0 0
\(514\) 7.57401 9.62491i 0.334075 0.424536i
\(515\) 0.447718 0.447718i 0.0197288 0.0197288i
\(516\) 0 0
\(517\) −6.99647 6.99647i −0.307704 0.307704i
\(518\) −4.73393 39.6991i −0.207997 1.74428i
\(519\) 0 0
\(520\) −0.102341 0.0468544i −0.00448794 0.00205470i
\(521\) 24.9049i 1.09110i 0.838078 + 0.545551i \(0.183680\pi\)
−0.838078 + 0.545551i \(0.816320\pi\)
\(522\) 0 0
\(523\) −12.9008 12.9008i −0.564112 0.564112i 0.366361 0.930473i \(-0.380604\pi\)
−0.930473 + 0.366361i \(0.880604\pi\)
\(524\) 5.11529 + 3.12235i 0.223463 + 0.136401i
\(525\) 0 0
\(526\) −14.8043 11.6498i −0.645499 0.507955i
\(527\) 2.01704 0.0878638
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) −0.367381 0.289099i −0.0159580 0.0125577i
\(531\) 0 0
\(532\) 17.1778 28.1421i 0.744754 1.22012i
\(533\) 0.550984 + 0.550984i 0.0238657 + 0.0238657i
\(534\) 0 0
\(535\) 4.06074i 0.175561i
\(536\) 14.1555 5.26449i 0.611423 0.227391i
\(537\) 0 0
\(538\) 2.76393 + 23.1785i 0.119161 + 0.999297i
\(539\) −34.0671 34.0671i −1.46738 1.46738i
\(540\) 0 0
\(541\) 18.2767 18.2767i 0.785776 0.785776i −0.195023 0.980799i \(-0.562478\pi\)
0.980799 + 0.195023i \(0.0624782\pi\)
\(542\) 19.2200 24.4245i 0.825572 1.04912i
\(543\) 0 0
\(544\) −3.90393 + 20.0853i −0.167379 + 0.861150i
\(545\) 3.82880 0.164008
\(546\) 0 0
\(547\) 13.7355 13.7355i 0.587287 0.587287i −0.349609 0.936896i \(-0.613685\pi\)
0.936896 + 0.349609i \(0.113685\pi\)
\(548\) −6.56930 + 1.58932i −0.280627 + 0.0678922i
\(549\) 0 0
\(550\) 2.79753 + 23.4603i 0.119287 + 1.00035i
\(551\) 26.4120i 1.12519i
\(552\) 0 0
\(553\) 50.1055i 2.13070i
\(554\) 21.7467 2.59319i 0.923929 0.110174i
\(555\) 0 0
\(556\) 8.66665 14.1984i 0.367548 0.602147i
\(557\) 27.5525 27.5525i 1.16744 1.16744i 0.184631 0.982808i \(-0.440891\pi\)
0.982808 0.184631i \(-0.0591089\pi\)
\(558\) 0 0
\(559\) 0.191354 0.00809342
\(560\) 2.63944 8.22117i 0.111537 0.347408i
\(561\) 0 0
\(562\) 25.4404 + 20.0195i 1.07314 + 0.844472i
\(563\) 19.8928 19.8928i 0.838383 0.838383i −0.150263 0.988646i \(-0.548012\pi\)
0.988646 + 0.150263i \(0.0480121\pi\)
\(564\) 0 0
\(565\) 3.19879 + 3.19879i 0.134574 + 0.134574i
\(566\) −8.90746 + 1.06217i −0.374408 + 0.0446464i
\(567\) 0 0
\(568\) −10.7324 + 23.4420i −0.450320 + 0.983603i
\(569\) 13.4849i 0.565317i 0.959221 + 0.282658i \(0.0912163\pi\)
−0.959221 + 0.282658i \(0.908784\pi\)
\(570\) 0 0
\(571\) −14.8284 14.8284i −0.620550 0.620550i 0.325122 0.945672i \(-0.394595\pi\)
−0.945672 + 0.325122i \(0.894595\pi\)
\(572\) 0.138232 + 0.571371i 0.00577977 + 0.0238902i
\(573\) 0 0
\(574\) −36.9652 + 46.9746i −1.54290 + 1.96068i
\(575\) 13.5077 0.563308
\(576\) 0 0
\(577\) −11.6176 −0.483648 −0.241824 0.970320i \(-0.577746\pi\)
−0.241824 + 0.970320i \(0.577746\pi\)
\(578\) 3.42554 4.35311i 0.142484 0.181066i
\(579\) 0 0
\(580\) −1.62648 6.72293i −0.0675360 0.279154i
\(581\) 48.5010 + 48.5010i 2.01216 + 2.01216i
\(582\) 0 0
\(583\) 2.44158i 0.101120i
\(584\) −0.637633 + 1.39274i −0.0263854 + 0.0576319i
\(585\) 0 0
\(586\) 42.9401 5.12040i 1.77384 0.211522i
\(587\) 17.0268 + 17.0268i 0.702773 + 0.702773i 0.965005 0.262232i \(-0.0844585\pi\)
−0.262232 + 0.965005i \(0.584459\pi\)
\(588\) 0 0
\(589\) −1.42627 + 1.42627i −0.0587682 + 0.0587682i
\(590\) 2.97762 + 2.34315i 0.122587 + 0.0964658i
\(591\) 0 0
\(592\) −23.6237 7.58449i −0.970929 0.311721i
\(593\) −41.5372 −1.70573 −0.852865 0.522132i \(-0.825137\pi\)
−0.852865 + 0.522132i \(0.825137\pi\)
\(594\) 0 0
\(595\) 5.52099 5.52099i 0.226338 0.226338i
\(596\) 14.7241 24.1222i 0.603123 0.988085i
\(597\) 0 0
\(598\) 0.333722 0.0397948i 0.0136469 0.00162733i
\(599\) 6.43160i 0.262788i −0.991330 0.131394i \(-0.958055\pi\)
0.991330 0.131394i \(-0.0419453\pi\)
\(600\) 0 0
\(601\) 3.45844i 0.141073i −0.997509 0.0705364i \(-0.977529\pi\)
0.997509 0.0705364i \(-0.0224711\pi\)
\(602\) 1.73812 + 14.5760i 0.0708403 + 0.594072i
\(603\) 0 0
\(604\) −19.3942 + 4.69205i −0.789139 + 0.190917i
\(605\) −0.414494 + 0.414494i −0.0168516 + 0.0168516i
\(606\) 0 0
\(607\) −30.1019 −1.22180 −0.610900 0.791708i \(-0.709192\pi\)
−0.610900 + 0.791708i \(0.709192\pi\)
\(608\) −11.4420 16.9629i −0.464033 0.687938i
\(609\) 0 0
\(610\) −1.59874 + 2.03165i −0.0647311 + 0.0822590i
\(611\) 0.168043 0.168043i 0.00679829 0.00679829i
\(612\) 0 0
\(613\) 2.50490 + 2.50490i 0.101172 + 0.101172i 0.755881 0.654709i \(-0.227209\pi\)
−0.654709 + 0.755881i \(0.727209\pi\)
\(614\) −2.86822 24.0531i −0.115752 0.970705i
\(615\) 0 0
\(616\) −42.2672 + 15.7194i −1.70300 + 0.633353i
\(617\) 22.9098i 0.922315i −0.887318 0.461157i \(-0.847434\pi\)
0.887318 0.461157i \(-0.152566\pi\)
\(618\) 0 0
\(619\) −28.6104 28.6104i −1.14995 1.14995i −0.986562 0.163386i \(-0.947758\pi\)
−0.163386 0.986562i \(-0.552242\pi\)
\(620\) −0.275212 + 0.450874i −0.0110528 + 0.0181076i
\(621\) 0 0
\(622\) 29.8571 + 23.4951i 1.19716 + 0.942067i
\(623\) −66.7847 −2.67567
\(624\) 0 0
\(625\) −21.6855 −0.867420
\(626\) 21.8818 + 17.2192i 0.874574 + 0.688218i
\(627\) 0 0
\(628\) 39.0179 + 23.8164i 1.55698 + 0.950377i
\(629\) −15.8647 15.8647i −0.632567 0.632567i
\(630\) 0 0
\(631\) 11.1851i 0.445270i 0.974902 + 0.222635i \(0.0714659\pi\)
−0.974902 + 0.222635i \(0.928534\pi\)
\(632\) −28.2727 12.9440i −1.12463 0.514885i
\(633\) 0 0
\(634\) −5.05470 42.3891i −0.200748 1.68349i
\(635\) 1.70774 + 1.70774i 0.0677698 + 0.0677698i
\(636\) 0 0
\(637\) 0.818234 0.818234i 0.0324196 0.0324196i
\(638\) −22.3400 + 28.3892i −0.884449 + 1.12394i
\(639\) 0 0
\(640\) −3.95705 3.61316i −0.156416 0.142823i
\(641\) 6.69312 0.264362 0.132181 0.991226i \(-0.457802\pi\)
0.132181 + 0.991226i \(0.457802\pi\)
\(642\) 0 0
\(643\) −17.9410 + 17.9410i −0.707522 + 0.707522i −0.966014 0.258491i \(-0.916775\pi\)
0.258491 + 0.966014i \(0.416775\pi\)
\(644\) 6.06255 + 25.0590i 0.238898 + 0.987464i
\(645\) 0 0
\(646\) −2.19079 18.3722i −0.0861957 0.722843i
\(647\) 6.72999i 0.264583i −0.991211 0.132292i \(-0.957766\pi\)
0.991211 0.132292i \(-0.0422335\pi\)
\(648\) 0 0
\(649\) 19.7890i 0.776786i
\(650\) −0.563475 + 0.0671918i −0.0221013 + 0.00263548i
\(651\) 0 0
\(652\) 18.1184 + 11.0594i 0.709572 + 0.433120i
\(653\) −26.1731 + 26.1731i −1.02423 + 1.02423i −0.0245347 + 0.999699i \(0.507810\pi\)
−0.999699 + 0.0245347i \(0.992190\pi\)
\(654\) 0 0
\(655\) −1.41921 −0.0554529
\(656\) 16.9567 + 32.9933i 0.662047 + 1.28817i
\(657\) 0 0
\(658\) 14.3267 + 11.2739i 0.558511 + 0.439503i
\(659\) −13.9741 + 13.9741i −0.544353 + 0.544353i −0.924802 0.380449i \(-0.875770\pi\)
0.380449 + 0.924802i \(0.375770\pi\)
\(660\) 0 0
\(661\) 11.9241 + 11.9241i 0.463794 + 0.463794i 0.899897 0.436103i \(-0.143642\pi\)
−0.436103 + 0.899897i \(0.643642\pi\)
\(662\) −29.1784 + 3.47939i −1.13405 + 0.135230i
\(663\) 0 0
\(664\) 39.8969 14.8379i 1.54830 0.575820i
\(665\) 7.80785i 0.302776i
\(666\) 0 0
\(667\) 14.6041 + 14.6041i 0.565473 + 0.565473i
\(668\) −11.3490 + 2.74568i −0.439108 + 0.106234i
\(669\) 0 0
\(670\) −2.21174 + 2.81064i −0.0854470 + 0.108584i
\(671\) 13.5021 0.521244
\(672\) 0 0
\(673\) −37.3066 −1.43807 −0.719033 0.694976i \(-0.755415\pi\)
−0.719033 + 0.694976i \(0.755415\pi\)
\(674\) 20.1234 25.5724i 0.775125 0.985013i
\(675\) 0 0
\(676\) 25.2572 6.11050i 0.971432 0.235019i
\(677\) −0.447461 0.447461i −0.0171973 0.0171973i 0.698456 0.715653i \(-0.253871\pi\)
−0.715653 + 0.698456i \(0.753871\pi\)
\(678\) 0 0
\(679\) 19.6764i 0.755113i
\(680\) −1.68903 4.54156i −0.0647713 0.174161i
\(681\) 0 0
\(682\) 2.73941 0.326662i 0.104898 0.0125085i
\(683\) 4.27521 + 4.27521i 0.163586 + 0.163586i 0.784153 0.620567i \(-0.213098\pi\)
−0.620567 + 0.784153i \(0.713098\pi\)
\(684\) 0 0
\(685\) 1.13178 1.13178i 0.0432430 0.0432430i
\(686\) 34.3026 + 26.9933i 1.30968 + 1.03061i
\(687\) 0 0
\(688\) 8.67371 + 2.78473i 0.330682 + 0.106167i
\(689\) −0.0586426 −0.00223410
\(690\) 0 0
\(691\) 20.0786 20.0786i 0.763827 0.763827i −0.213185 0.977012i \(-0.568384\pi\)
0.977012 + 0.213185i \(0.0683836\pi\)
\(692\) −8.75225 5.34234i −0.332711 0.203085i
\(693\) 0 0
\(694\) −21.6519 + 2.58188i −0.821893 + 0.0980069i
\(695\) 3.93926i 0.149425i
\(696\) 0 0
\(697\) 33.5443i 1.27058i
\(698\) 4.74958 + 39.8303i 0.179774 + 1.50760i
\(699\) 0 0
\(700\) −10.2364 42.3111i −0.386898 1.59921i
\(701\) 10.4467 10.4467i 0.394565 0.394565i −0.481746 0.876311i \(-0.659997\pi\)
0.876311 + 0.481746i \(0.159997\pi\)
\(702\) 0 0
\(703\) 22.4361 0.846192
\(704\) −2.04922 + 27.9108i −0.0772328 + 1.05193i
\(705\) 0 0
\(706\) −10.6799 + 13.5718i −0.401943 + 0.510781i
\(707\) −2.06793 + 2.06793i −0.0777727 + 0.0777727i
\(708\) 0 0
\(709\) 16.0916 + 16.0916i 0.604332 + 0.604332i 0.941459 0.337127i \(-0.109455\pi\)
−0.337127 + 0.941459i \(0.609455\pi\)
\(710\) −0.722930 6.06255i −0.0271311 0.227523i
\(711\) 0 0
\(712\) −17.2528 + 37.6842i −0.646577 + 1.41228i
\(713\) 1.57726i 0.0590690i
\(714\) 0 0
\(715\) −0.0984373 0.0984373i −0.00368135 0.00368135i
\(716\) 22.4120 + 13.6802i 0.837574 + 0.511252i
\(717\) 0 0
\(718\) −37.2065 29.2785i −1.38854 1.09266i
\(719\) 30.9957 1.15594 0.577972 0.816057i \(-0.303844\pi\)
0.577972 + 0.816057i \(0.303844\pi\)
\(720\) 0 0
\(721\) 6.09292 0.226912
\(722\) −6.57585 5.17466i −0.244728 0.192581i
\(723\) 0 0
\(724\) −15.9617 + 26.1497i −0.593211 + 0.971846i
\(725\) −24.6584 24.6584i −0.915790 0.915790i
\(726\) 0 0
\(727\) 41.1117i 1.52475i −0.647135 0.762375i \(-0.724033\pi\)
0.647135 0.762375i \(-0.275967\pi\)
\(728\) −0.377553 1.01519i −0.0139930 0.0376253i
\(729\) 0 0
\(730\) −0.0429509 0.360189i −0.00158968 0.0133312i
\(731\) 5.82490 + 5.82490i 0.215442 + 0.215442i
\(732\) 0 0
\(733\) 0.146061 0.146061i 0.00539490 0.00539490i −0.704404 0.709799i \(-0.748786\pi\)
0.709799 + 0.704404i \(0.248786\pi\)
\(734\) 0.614272 0.780604i 0.0226732 0.0288126i
\(735\) 0 0
\(736\) 15.7061 + 3.05275i 0.578934 + 0.112526i
\(737\) 18.6792 0.688058
\(738\) 0 0
\(739\) −1.50766 + 1.50766i −0.0554601 + 0.0554601i −0.734293 0.678833i \(-0.762486\pi\)
0.678833 + 0.734293i \(0.262486\pi\)
\(740\) 5.71090 1.38164i 0.209937 0.0507902i
\(741\) 0 0
\(742\) −0.532664 4.46696i −0.0195547 0.163987i
\(743\) 40.5175i 1.48644i 0.669046 + 0.743221i \(0.266703\pi\)
−0.669046 + 0.743221i \(0.733297\pi\)
\(744\) 0 0
\(745\) 6.69256i 0.245196i
\(746\) −37.6529 + 4.48993i −1.37857 + 0.164388i
\(747\) 0 0
\(748\) −13.1849 + 21.6006i −0.482088 + 0.789795i
\(749\) 27.6309 27.6309i 1.00961 1.00961i
\(750\) 0 0
\(751\) −12.5843 −0.459208 −0.229604 0.973284i \(-0.573743\pi\)
−0.229604 + 0.973284i \(0.573743\pi\)
\(752\) 10.0625 5.17157i 0.366943 0.188588i
\(753\) 0 0
\(754\) −0.681859 0.536568i −0.0248319 0.0195406i
\(755\) 3.34129 3.34129i 0.121602 0.121602i
\(756\) 0 0
\(757\) −7.49900 7.49900i −0.272556 0.272556i 0.557572 0.830128i \(-0.311733\pi\)
−0.830128 + 0.557572i \(0.811733\pi\)
\(758\) 3.53186 0.421157i 0.128283 0.0152971i
\(759\) 0 0
\(760\) 4.40569 + 2.01704i 0.159811 + 0.0731659i
\(761\) 42.8182i 1.55216i −0.630635 0.776079i \(-0.717206\pi\)
0.630635 0.776079i \(-0.282794\pi\)
\(762\) 0 0
\(763\) 26.0527 + 26.0527i 0.943172 + 0.943172i
\(764\) −4.05864 16.7761i −0.146837 0.606936i
\(765\) 0 0
\(766\) 22.2908 28.3267i 0.805398 1.02348i
\(767\) 0.475298 0.0171620
\(768\) 0 0
\(769\) 12.7455 0.459614 0.229807 0.973236i \(-0.426190\pi\)
0.229807 + 0.973236i \(0.426190\pi\)
\(770\) 6.60411 8.39236i 0.237995 0.302440i
\(771\) 0 0
\(772\) −5.38551 22.2606i −0.193829 0.801175i
\(773\) 22.8765 + 22.8765i 0.822809 + 0.822809i 0.986510 0.163701i \(-0.0523432\pi\)
−0.163701 + 0.986510i \(0.552343\pi\)
\(774\) 0 0
\(775\) 2.66314i 0.0956630i
\(776\) 11.1027 + 5.08312i 0.398564 + 0.182473i
\(777\) 0 0
\(778\) −23.2451 + 2.77187i −0.833377 + 0.0993763i
\(779\) −23.7194 23.7194i −0.849836 0.849836i
\(780\) 0 0
\(781\) −22.5478 + 22.5478i −0.806825 + 0.806825i
\(782\) 11.3700 + 8.94725i 0.406590 + 0.319953i
\(783\) 0 0
\(784\) 48.9964 25.1814i 1.74987 0.899335i
\(785\) −10.8253 −0.386370
\(786\) 0 0
\(787\) 5.20470 5.20470i 0.185528 0.185528i −0.608232 0.793759i \(-0.708121\pi\)
0.793759 + 0.608232i \(0.208121\pi\)
\(788\)