Properties

Label 105.2.j.a.8.1
Level 105
Weight 2
Character 105.8
Analytic conductor 0.838
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.1
Character \(\chi\) = 105.8
Dual form 105.2.j.a.92.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.79963 - 1.79963i) q^{2} +(-1.66094 + 0.491204i) q^{3} +4.47734i q^{4} +(1.87996 + 1.21069i) q^{5} +(3.87306 + 2.10509i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(4.45829 - 4.45829i) q^{8} +(2.51744 - 1.63172i) q^{9} +O(q^{10})\) \(q+(-1.79963 - 1.79963i) q^{2} +(-1.66094 + 0.491204i) q^{3} +4.47734i q^{4} +(1.87996 + 1.21069i) q^{5} +(3.87306 + 2.10509i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(4.45829 - 4.45829i) q^{8} +(2.51744 - 1.63172i) q^{9} +(-1.20443 - 5.56202i) q^{10} +1.56870i q^{11} +(-2.19929 - 7.43658i) q^{12} +(2.21881 + 2.21881i) q^{13} +2.54506 q^{14} +(-3.71719 - 1.08744i) q^{15} -7.09187 q^{16} +(3.60725 + 3.60725i) q^{17} +(-7.46695 - 1.59396i) q^{18} +1.68040i q^{19} +(-5.42066 + 8.41719i) q^{20} +(0.827127 - 1.52180i) q^{21} +(2.82308 - 2.82308i) q^{22} +(0.995850 - 0.995850i) q^{23} +(-5.21502 + 9.59488i) q^{24} +(2.06847 + 4.55208i) q^{25} -7.98606i q^{26} +(-3.37980 + 3.94676i) q^{27} +(-3.16595 - 3.16595i) q^{28} -8.91955 q^{29} +(4.73258 + 8.64655i) q^{30} +2.74834 q^{31} +(3.84616 + 3.84616i) q^{32} +(-0.770553 - 2.60552i) q^{33} -12.9834i q^{34} +(-2.18542 + 0.473244i) q^{35} +(7.30576 + 11.2714i) q^{36} +(0.440360 - 0.440360i) q^{37} +(3.02410 - 3.02410i) q^{38} +(-4.77519 - 2.59542i) q^{39} +(13.7790 - 2.98379i) q^{40} -6.44292i q^{41} +(-4.22719 + 1.25015i) q^{42} +(-5.47734 - 5.47734i) q^{43} -7.02360 q^{44} +(6.70817 - 0.0197326i) q^{45} -3.58432 q^{46} +(3.69358 + 3.69358i) q^{47} +(11.7792 - 3.48356i) q^{48} -1.00000i q^{49} +(4.46958 - 11.9145i) q^{50} +(-7.76331 - 4.21952i) q^{51} +(-9.93435 + 9.93435i) q^{52} +(2.83358 - 2.83358i) q^{53} +(13.1851 - 1.02033i) q^{54} +(-1.89921 + 2.94909i) q^{55} +6.30497i q^{56} +(-0.825420 - 2.79104i) q^{57} +(16.0519 + 16.0519i) q^{58} +5.54871 q^{59} +(4.86882 - 16.6431i) q^{60} +7.40665 q^{61} +(-4.94599 - 4.94599i) q^{62} +(-0.626296 + 2.93390i) q^{63} +0.340400i q^{64} +(1.48498 + 6.85754i) q^{65} +(-3.30226 + 6.07568i) q^{66} +(-3.75240 + 3.75240i) q^{67} +(-16.1509 + 16.1509i) q^{68} +(-1.16488 + 2.14321i) q^{69} +(4.78460 + 3.08128i) q^{70} +3.61943i q^{71} +(3.94878 - 18.4981i) q^{72} +(-5.89737 - 5.89737i) q^{73} -1.58497 q^{74} +(-5.67160 - 6.54469i) q^{75} -7.52372 q^{76} +(-1.10924 - 1.10924i) q^{77} +(3.92279 + 13.2644i) q^{78} -17.0572i q^{79} +(-13.3324 - 8.58604i) q^{80} +(3.67497 - 8.21551i) q^{81} +(-11.5949 + 11.5949i) q^{82} +(3.21312 - 3.21312i) q^{83} +(6.81359 + 3.70333i) q^{84} +(2.41421 + 11.1487i) q^{85} +19.7144i q^{86} +(14.8148 - 4.38132i) q^{87} +(6.99372 + 6.99372i) q^{88} -9.40273 q^{89} +(-12.1077 - 12.0367i) q^{90} -3.13787 q^{91} +(4.45876 + 4.45876i) q^{92} +(-4.56482 + 1.35000i) q^{93} -13.2941i q^{94} +(-2.03444 + 3.15908i) q^{95} +(-8.27749 - 4.49899i) q^{96} +(4.39640 - 4.39640i) q^{97} +(-1.79963 + 1.79963i) q^{98} +(2.55968 + 3.94911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{3} + O(q^{10}) \) \( 24q - 4q^{3} - 16q^{10} + 16q^{12} - 8q^{13} - 16q^{15} - 16q^{16} - 20q^{18} + 4q^{21} + 8q^{22} - 16q^{25} - 16q^{27} + 20q^{30} + 28q^{33} + 16q^{36} - 16q^{37} + 64q^{40} - 20q^{42} - 40q^{43} + 20q^{45} - 64q^{46} + 16q^{48} - 20q^{51} + 40q^{55} + 4q^{57} + 40q^{58} + 32q^{60} + 32q^{61} - 8q^{63} - 16q^{66} + 24q^{67} - 8q^{70} - 8q^{72} + 32q^{73} - 60q^{75} + 32q^{76} + 60q^{78} + 52q^{81} - 80q^{82} + 24q^{85} + 4q^{87} + 96q^{88} - 24q^{90} - 24q^{91} - 76q^{93} - 96q^{96} + 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79963 1.79963i −1.27253 1.27253i −0.944756 0.327775i \(-0.893701\pi\)
−0.327775 0.944756i \(-0.606299\pi\)
\(3\) −1.66094 + 0.491204i −0.958944 + 0.283597i
\(4\) 4.47734i 2.23867i
\(5\) 1.87996 + 1.21069i 0.840742 + 0.541436i
\(6\) 3.87306 + 2.10509i 1.58117 + 0.859399i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 4.45829 4.45829i 1.57624 1.57624i
\(9\) 2.51744 1.63172i 0.839146 0.543907i
\(10\) −1.20443 5.56202i −0.380876 1.75886i
\(11\) 1.56870i 0.472981i 0.971634 + 0.236491i \(0.0759973\pi\)
−0.971634 + 0.236491i \(0.924003\pi\)
\(12\) −2.19929 7.43658i −0.634880 2.14676i
\(13\) 2.21881 + 2.21881i 0.615386 + 0.615386i 0.944345 0.328958i \(-0.106697\pi\)
−0.328958 + 0.944345i \(0.606697\pi\)
\(14\) 2.54506 0.680196
\(15\) −3.71719 1.08744i −0.959774 0.280775i
\(16\) −7.09187 −1.77297
\(17\) 3.60725 + 3.60725i 0.874886 + 0.874886i 0.993000 0.118114i \(-0.0376849\pi\)
−0.118114 + 0.993000i \(0.537685\pi\)
\(18\) −7.46695 1.59396i −1.75998 0.375700i
\(19\) 1.68040i 0.385510i 0.981247 + 0.192755i \(0.0617423\pi\)
−0.981247 + 0.192755i \(0.938258\pi\)
\(20\) −5.42066 + 8.41719i −1.21210 + 1.88214i
\(21\) 0.827127 1.52180i 0.180494 0.332083i
\(22\) 2.82308 2.82308i 0.601883 0.601883i
\(23\) 0.995850 0.995850i 0.207649 0.207649i −0.595618 0.803268i \(-0.703093\pi\)
0.803268 + 0.595618i \(0.203093\pi\)
\(24\) −5.21502 + 9.59488i −1.06451 + 1.95855i
\(25\) 2.06847 + 4.55208i 0.413694 + 0.910416i
\(26\) 7.98606i 1.56620i
\(27\) −3.37980 + 3.94676i −0.650443 + 0.759555i
\(28\) −3.16595 3.16595i −0.598309 0.598309i
\(29\) −8.91955 −1.65632 −0.828159 0.560493i \(-0.810612\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(30\) 4.73258 + 8.64655i 0.864047 + 1.57864i
\(31\) 2.74834 0.493616 0.246808 0.969064i \(-0.420618\pi\)
0.246808 + 0.969064i \(0.420618\pi\)
\(32\) 3.84616 + 3.84616i 0.679912 + 0.679912i
\(33\) −0.770553 2.60552i −0.134136 0.453562i
\(34\) 12.9834i 2.22664i
\(35\) −2.18542 + 0.473244i −0.369403 + 0.0799928i
\(36\) 7.30576 + 11.2714i 1.21763 + 1.87857i
\(37\) 0.440360 0.440360i 0.0723947 0.0723947i −0.669982 0.742377i \(-0.733698\pi\)
0.742377 + 0.669982i \(0.233698\pi\)
\(38\) 3.02410 3.02410i 0.490574 0.490574i
\(39\) −4.77519 2.59542i −0.764643 0.415599i
\(40\) 13.7790 2.98379i 2.17865 0.471778i
\(41\) 6.44292i 1.00622i −0.864224 0.503108i \(-0.832190\pi\)
0.864224 0.503108i \(-0.167810\pi\)
\(42\) −4.22719 + 1.25015i −0.652270 + 0.192902i
\(43\) −5.47734 5.47734i −0.835286 0.835286i 0.152948 0.988234i \(-0.451123\pi\)
−0.988234 + 0.152948i \(0.951123\pi\)
\(44\) −7.02360 −1.05885
\(45\) 6.70817 0.0197326i 0.999996 0.00294156i
\(46\) −3.58432 −0.528480
\(47\) 3.69358 + 3.69358i 0.538763 + 0.538763i 0.923166 0.384402i \(-0.125592\pi\)
−0.384402 + 0.923166i \(0.625592\pi\)
\(48\) 11.7792 3.48356i 1.70018 0.502808i
\(49\) 1.00000i 0.142857i
\(50\) 4.46958 11.9145i 0.632095 1.68497i
\(51\) −7.76331 4.21952i −1.08708 0.590851i
\(52\) −9.93435 + 9.93435i −1.37765 + 1.37765i
\(53\) 2.83358 2.83358i 0.389222 0.389222i −0.485188 0.874410i \(-0.661249\pi\)
0.874410 + 0.485188i \(0.161249\pi\)
\(54\) 13.1851 1.02033i 1.79427 0.138849i
\(55\) −1.89921 + 2.94909i −0.256089 + 0.397655i
\(56\) 6.30497i 0.842537i
\(57\) −0.825420 2.79104i −0.109330 0.369683i
\(58\) 16.0519 + 16.0519i 2.10772 + 2.10772i
\(59\) 5.54871 0.722381 0.361191 0.932492i \(-0.382370\pi\)
0.361191 + 0.932492i \(0.382370\pi\)
\(60\) 4.86882 16.6431i 0.628562 2.14861i
\(61\) 7.40665 0.948325 0.474162 0.880437i \(-0.342751\pi\)
0.474162 + 0.880437i \(0.342751\pi\)
\(62\) −4.94599 4.94599i −0.628141 0.628141i
\(63\) −0.626296 + 2.93390i −0.0789058 + 0.369636i
\(64\) 0.340400i 0.0425500i
\(65\) 1.48498 + 6.85754i 0.184189 + 0.850574i
\(66\) −3.30226 + 6.07568i −0.406480 + 0.747864i
\(67\) −3.75240 + 3.75240i −0.458429 + 0.458429i −0.898139 0.439711i \(-0.855081\pi\)
0.439711 + 0.898139i \(0.355081\pi\)
\(68\) −16.1509 + 16.1509i −1.95858 + 1.95858i
\(69\) −1.16488 + 2.14321i −0.140235 + 0.258012i
\(70\) 4.78460 + 3.08128i 0.571869 + 0.368283i
\(71\) 3.61943i 0.429548i 0.976664 + 0.214774i \(0.0689015\pi\)
−0.976664 + 0.214774i \(0.931099\pi\)
\(72\) 3.94878 18.4981i 0.465368 2.18003i
\(73\) −5.89737 5.89737i −0.690235 0.690235i 0.272049 0.962284i \(-0.412299\pi\)
−0.962284 + 0.272049i \(0.912299\pi\)
\(74\) −1.58497 −0.184249
\(75\) −5.67160 6.54469i −0.654900 0.755715i
\(76\) −7.52372 −0.863030
\(77\) −1.10924 1.10924i −0.126410 0.126410i
\(78\) 3.92279 + 13.2644i 0.444168 + 1.50189i
\(79\) 17.0572i 1.91909i −0.281558 0.959544i \(-0.590851\pi\)
0.281558 0.959544i \(-0.409149\pi\)
\(80\) −13.3324 8.58604i −1.49061 0.959949i
\(81\) 3.67497 8.21551i 0.408330 0.912834i
\(82\) −11.5949 + 11.5949i −1.28044 + 1.28044i
\(83\) 3.21312 3.21312i 0.352686 0.352686i −0.508422 0.861108i \(-0.669771\pi\)
0.861108 + 0.508422i \(0.169771\pi\)
\(84\) 6.81359 + 3.70333i 0.743423 + 0.404066i
\(85\) 2.41421 + 11.1487i 0.261858 + 1.20925i
\(86\) 19.7144i 2.12585i
\(87\) 14.8148 4.38132i 1.58832 0.469727i
\(88\) 6.99372 + 6.99372i 0.745533 + 0.745533i
\(89\) −9.40273 −0.996688 −0.498344 0.866979i \(-0.666058\pi\)
−0.498344 + 0.866979i \(0.666058\pi\)
\(90\) −12.1077 12.0367i −1.27627 1.26878i
\(91\) −3.13787 −0.328938
\(92\) 4.45876 + 4.45876i 0.464858 + 0.464858i
\(93\) −4.56482 + 1.35000i −0.473350 + 0.139988i
\(94\) 13.2941i 1.37119i
\(95\) −2.03444 + 3.15908i −0.208729 + 0.324115i
\(96\) −8.27749 4.49899i −0.844818 0.459176i
\(97\) 4.39640 4.39640i 0.446386 0.446386i −0.447765 0.894151i \(-0.647780\pi\)
0.894151 + 0.447765i \(0.147780\pi\)
\(98\) −1.79963 + 1.79963i −0.181790 + 0.181790i
\(99\) 2.55968 + 3.94911i 0.257258 + 0.396900i
\(100\) −20.3812 + 9.26123i −2.03812 + 0.926123i
\(101\) 1.01132i 0.100630i −0.998733 0.0503152i \(-0.983977\pi\)
0.998733 0.0503152i \(-0.0160226\pi\)
\(102\) 6.37751 + 21.5647i 0.631468 + 2.13522i
\(103\) −4.03058 4.03058i −0.397145 0.397145i 0.480080 0.877225i \(-0.340608\pi\)
−0.877225 + 0.480080i \(0.840608\pi\)
\(104\) 19.7842 1.94000
\(105\) 3.39738 1.85951i 0.331551 0.181470i
\(106\) −10.1988 −0.990593
\(107\) 2.81760 + 2.81760i 0.272388 + 0.272388i 0.830061 0.557673i \(-0.188306\pi\)
−0.557673 + 0.830061i \(0.688306\pi\)
\(108\) −17.6710 15.1325i −1.70039 1.45613i
\(109\) 6.42246i 0.615160i 0.951522 + 0.307580i \(0.0995192\pi\)
−0.951522 + 0.307580i \(0.900481\pi\)
\(110\) 8.72514 1.88940i 0.831910 0.180147i
\(111\) −0.515104 + 0.947718i −0.0488915 + 0.0899534i
\(112\) 5.01471 5.01471i 0.473845 0.473845i
\(113\) 3.29246 3.29246i 0.309729 0.309729i −0.535075 0.844804i \(-0.679717\pi\)
0.844804 + 0.535075i \(0.179717\pi\)
\(114\) −3.53739 + 6.50830i −0.331307 + 0.609558i
\(115\) 3.07782 0.666490i 0.287008 0.0621505i
\(116\) 39.9358i 3.70795i
\(117\) 9.20618 + 1.96523i 0.851112 + 0.181686i
\(118\) −9.98563 9.98563i −0.919252 0.919252i
\(119\) −5.10142 −0.467646
\(120\) −21.4204 + 11.7242i −1.95541 + 1.07027i
\(121\) 8.53918 0.776289
\(122\) −13.3292 13.3292i −1.20677 1.20677i
\(123\) 3.16479 + 10.7013i 0.285360 + 0.964904i
\(124\) 12.3052i 1.10504i
\(125\) −1.62252 + 11.0620i −0.145123 + 0.989414i
\(126\) 6.40703 4.15283i 0.570784 0.369963i
\(127\) 14.2818 14.2818i 1.26730 1.26730i 0.319826 0.947476i \(-0.396376\pi\)
0.947476 0.319826i \(-0.103624\pi\)
\(128\) 8.30492 8.30492i 0.734058 0.734058i
\(129\) 11.7880 + 6.40703i 1.03788 + 0.564108i
\(130\) 9.66863 15.0134i 0.847995 1.31677i
\(131\) 4.89729i 0.427878i 0.976847 + 0.213939i \(0.0686294\pi\)
−0.976847 + 0.213939i \(0.931371\pi\)
\(132\) 11.6658 3.45002i 1.01538 0.300286i
\(133\) −1.18822 1.18822i −0.103032 0.103032i
\(134\) 13.5059 1.16673
\(135\) −11.1322 + 3.32786i −0.958105 + 0.286417i
\(136\) 32.1643 2.75807
\(137\) −4.55880 4.55880i −0.389485 0.389485i 0.485019 0.874504i \(-0.338813\pi\)
−0.874504 + 0.485019i \(0.838813\pi\)
\(138\) 5.95334 1.76064i 0.506782 0.149875i
\(139\) 10.2045i 0.865536i 0.901505 + 0.432768i \(0.142463\pi\)
−0.901505 + 0.432768i \(0.857537\pi\)
\(140\) −2.11887 9.78484i −0.179077 0.826970i
\(141\) −7.94911 4.32050i −0.669435 0.363852i
\(142\) 6.51364 6.51364i 0.546613 0.546613i
\(143\) −3.48065 + 3.48065i −0.291066 + 0.291066i
\(144\) −17.8533 + 11.5720i −1.48778 + 0.964329i
\(145\) −16.7684 10.7988i −1.39254 0.896791i
\(146\) 21.2262i 1.75669i
\(147\) 0.491204 + 1.66094i 0.0405139 + 0.136992i
\(148\) 1.97164 + 1.97164i 0.162068 + 0.162068i
\(149\) −0.923124 −0.0756253 −0.0378126 0.999285i \(-0.512039\pi\)
−0.0378126 + 0.999285i \(0.512039\pi\)
\(150\) −1.57123 + 21.9848i −0.128291 + 1.79505i
\(151\) −13.7310 −1.11741 −0.558705 0.829366i \(-0.688702\pi\)
−0.558705 + 0.829366i \(0.688702\pi\)
\(152\) 7.49171 + 7.49171i 0.607658 + 0.607658i
\(153\) 14.9670 + 3.19499i 1.21001 + 0.258300i
\(154\) 3.99244i 0.321720i
\(155\) 5.16675 + 3.32738i 0.415004 + 0.267262i
\(156\) 11.6205 21.3801i 0.930389 1.71178i
\(157\) −13.7211 + 13.7211i −1.09506 + 1.09506i −0.100086 + 0.994979i \(0.531912\pi\)
−0.994979 + 0.100086i \(0.968088\pi\)
\(158\) −30.6967 + 30.6967i −2.44210 + 2.44210i
\(159\) −3.31453 + 6.09826i −0.262859 + 0.483624i
\(160\) 2.57411 + 11.8871i 0.203501 + 0.939759i
\(161\) 1.40834i 0.110993i
\(162\) −21.3985 + 8.17128i −1.68122 + 0.641997i
\(163\) 6.60566 + 6.60566i 0.517395 + 0.517395i 0.916782 0.399387i \(-0.130777\pi\)
−0.399387 + 0.916782i \(0.630777\pi\)
\(164\) 28.8471 2.25258
\(165\) 1.70586 5.83116i 0.132801 0.453955i
\(166\) −11.5649 −0.897607
\(167\) −3.11442 3.11442i −0.241001 0.241001i 0.576263 0.817264i \(-0.304510\pi\)
−0.817264 + 0.576263i \(0.804510\pi\)
\(168\) −3.09703 10.4722i −0.238941 0.807946i
\(169\) 3.15379i 0.242599i
\(170\) 15.7189 24.4083i 1.20558 1.87203i
\(171\) 2.74195 + 4.23030i 0.209682 + 0.323499i
\(172\) 24.5239 24.5239i 1.86993 1.86993i
\(173\) 8.12870 8.12870i 0.618013 0.618013i −0.327008 0.945022i \(-0.606040\pi\)
0.945022 + 0.327008i \(0.106040\pi\)
\(174\) −34.5460 18.7764i −2.61892 1.42344i
\(175\) −4.68144 1.75618i −0.353883 0.132755i
\(176\) 11.1250i 0.838580i
\(177\) −9.21608 + 2.72555i −0.692723 + 0.204865i
\(178\) 16.9214 + 16.9214i 1.26832 + 1.26832i
\(179\) 16.5980 1.24059 0.620297 0.784367i \(-0.287012\pi\)
0.620297 + 0.784367i \(0.287012\pi\)
\(180\) 0.0883493 + 30.0348i 0.00658517 + 2.23866i
\(181\) 11.6532 0.866174 0.433087 0.901352i \(-0.357424\pi\)
0.433087 + 0.901352i \(0.357424\pi\)
\(182\) 5.64700 + 5.64700i 0.418583 + 0.418583i
\(183\) −12.3020 + 3.63818i −0.909390 + 0.268942i
\(184\) 8.87958i 0.654611i
\(185\) 1.36100 0.294719i 0.100062 0.0216681i
\(186\) 10.6445 + 5.78550i 0.780491 + 0.424213i
\(187\) −5.65869 + 5.65869i −0.413805 + 0.413805i
\(188\) −16.5374 + 16.5374i −1.20611 + 1.20611i
\(189\) −0.400905 5.18066i −0.0291615 0.376838i
\(190\) 9.34642 2.02393i 0.678060 0.146831i
\(191\) 12.8543i 0.930108i −0.885282 0.465054i \(-0.846035\pi\)
0.885282 0.465054i \(-0.153965\pi\)
\(192\) −0.167206 0.565384i −0.0120671 0.0408031i
\(193\) −8.06158 8.06158i −0.580285 0.580285i 0.354696 0.934982i \(-0.384584\pi\)
−0.934982 + 0.354696i \(0.884584\pi\)
\(194\) −15.8238 −1.13608
\(195\) −5.83491 10.6605i −0.417847 0.763417i
\(196\) 4.47734 0.319810
\(197\) −18.7512 18.7512i −1.33597 1.33597i −0.899929 0.436036i \(-0.856382\pi\)
−0.436036 0.899929i \(-0.643618\pi\)
\(198\) 2.50045 11.7134i 0.177699 0.832436i
\(199\) 4.20728i 0.298246i 0.988819 + 0.149123i \(0.0476451\pi\)
−0.988819 + 0.149123i \(0.952355\pi\)
\(200\) 29.5163 + 11.0727i 2.08712 + 0.782956i
\(201\) 4.38931 8.07570i 0.309598 0.569616i
\(202\) −1.82001 + 1.82001i −0.128055 + 0.128055i
\(203\) 6.30707 6.30707i 0.442670 0.442670i
\(204\) 18.8922 34.7590i 1.32272 2.43361i
\(205\) 7.80037 12.1124i 0.544802 0.845967i
\(206\) 14.5071i 1.01076i
\(207\) 0.882040 4.13194i 0.0613060 0.287190i
\(208\) −15.7355 15.7355i −1.09106 1.09106i
\(209\) −2.63605 −0.182339
\(210\) −9.46047 2.76759i −0.652834 0.190982i
\(211\) −21.5211 −1.48158 −0.740788 0.671739i \(-0.765548\pi\)
−0.740788 + 0.671739i \(0.765548\pi\)
\(212\) 12.6869 + 12.6869i 0.871338 + 0.871338i
\(213\) −1.77788 6.01166i −0.121818 0.411912i
\(214\) 10.1413i 0.693244i
\(215\) −3.66580 16.9285i −0.250006 1.15451i
\(216\) 2.52769 + 32.6639i 0.171988 + 2.22250i
\(217\) −1.94337 + 1.94337i −0.131924 + 0.131924i
\(218\) 11.5581 11.5581i 0.782810 0.782810i
\(219\) 12.6920 + 6.89836i 0.857645 + 0.466148i
\(220\) −13.2041 8.50339i −0.890218 0.573299i
\(221\) 16.0076i 1.07679i
\(222\) 2.63254 0.778544i 0.176684 0.0522525i
\(223\) 12.4001 + 12.4001i 0.830375 + 0.830375i 0.987568 0.157193i \(-0.0502445\pi\)
−0.157193 + 0.987568i \(0.550244\pi\)
\(224\) −5.43929 −0.363428
\(225\) 12.6350 + 8.08441i 0.842331 + 0.538961i
\(226\) −11.8504 −0.788279
\(227\) −8.70556 8.70556i −0.577809 0.577809i 0.356490 0.934299i \(-0.383973\pi\)
−0.934299 + 0.356490i \(0.883973\pi\)
\(228\) 12.4964 3.69568i 0.827597 0.244753i
\(229\) 4.46342i 0.294951i 0.989066 + 0.147476i \(0.0471148\pi\)
−0.989066 + 0.147476i \(0.952885\pi\)
\(230\) −6.73837 4.33950i −0.444315 0.286138i
\(231\) 2.38724 + 1.29752i 0.157069 + 0.0853703i
\(232\) −39.7659 + 39.7659i −2.61076 + 2.61076i
\(233\) −5.64161 + 5.64161i −0.369594 + 0.369594i −0.867329 0.497735i \(-0.834165\pi\)
0.497735 + 0.867329i \(0.334165\pi\)
\(234\) −13.0310 20.1044i −0.851865 1.31427i
\(235\) 2.47199 + 11.4155i 0.161255 + 0.744667i
\(236\) 24.8435i 1.61717i
\(237\) 8.37859 + 28.3310i 0.544248 + 1.84030i
\(238\) 9.18066 + 9.18066i 0.595094 + 0.595094i
\(239\) 11.8594 0.767124 0.383562 0.923515i \(-0.374697\pi\)
0.383562 + 0.923515i \(0.374697\pi\)
\(240\) 26.3618 + 7.71196i 1.70165 + 0.497805i
\(241\) −18.0723 −1.16414 −0.582071 0.813138i \(-0.697757\pi\)
−0.582071 + 0.813138i \(0.697757\pi\)
\(242\) −15.3674 15.3674i −0.987851 0.987851i
\(243\) −2.06841 + 15.4506i −0.132689 + 0.991158i
\(244\) 33.1621i 2.12298i
\(245\) 1.21069 1.87996i 0.0773480 0.120106i
\(246\) 13.5629 24.9538i 0.864741 1.59100i
\(247\) −3.72849 + 3.72849i −0.237238 + 0.237238i
\(248\) 12.2529 12.2529i 0.778059 0.778059i
\(249\) −3.75850 + 6.91510i −0.238185 + 0.438226i
\(250\) 22.8274 16.9875i 1.44373 1.07439i
\(251\) 3.19253i 0.201511i 0.994911 + 0.100755i \(0.0321259\pi\)
−0.994911 + 0.100755i \(0.967874\pi\)
\(252\) −13.1360 2.80414i −0.827493 0.176644i
\(253\) 1.56219 + 1.56219i 0.0982141 + 0.0982141i
\(254\) −51.4038 −3.22536
\(255\) −9.48616 17.3315i −0.594046 1.08534i
\(256\) −29.2108 −1.82567
\(257\) 11.8118 + 11.8118i 0.736799 + 0.736799i 0.971957 0.235158i \(-0.0755607\pi\)
−0.235158 + 0.971957i \(0.575561\pi\)
\(258\) −9.68378 32.7443i −0.602886 2.03857i
\(259\) 0.622763i 0.0386966i
\(260\) −30.7035 + 6.64874i −1.90415 + 0.412337i
\(261\) −22.4544 + 14.5542i −1.38989 + 0.900883i
\(262\) 8.81331 8.81331i 0.544488 0.544488i
\(263\) 13.1502 13.1502i 0.810874 0.810874i −0.173891 0.984765i \(-0.555634\pi\)
0.984765 + 0.173891i \(0.0556339\pi\)
\(264\) −15.0515 8.18080i −0.926356 0.503493i
\(265\) 8.75757 1.89642i 0.537974 0.116496i
\(266\) 4.27672i 0.262223i
\(267\) 15.6174 4.61866i 0.955767 0.282658i
\(268\) −16.8008 16.8008i −1.02627 1.02627i
\(269\) −29.3405 −1.78892 −0.894461 0.447146i \(-0.852441\pi\)
−0.894461 + 0.447146i \(0.852441\pi\)
\(270\) 26.0227 + 14.0449i 1.58369 + 0.854744i
\(271\) 3.18366 0.193394 0.0966968 0.995314i \(-0.469172\pi\)
0.0966968 + 0.995314i \(0.469172\pi\)
\(272\) −25.5821 25.5821i −1.55114 1.55114i
\(273\) 5.21181 1.54133i 0.315433 0.0932858i
\(274\) 16.4083i 0.991263i
\(275\) −7.14085 + 3.24481i −0.430610 + 0.195669i
\(276\) −9.59588 5.21556i −0.577604 0.313940i
\(277\) 16.8636 16.8636i 1.01324 1.01324i 0.0133247 0.999911i \(-0.495758\pi\)
0.999911 0.0133247i \(-0.00424152\pi\)
\(278\) 18.3644 18.3644i 1.10142 1.10142i
\(279\) 6.91877 4.48452i 0.414216 0.268481i
\(280\) −7.63336 + 11.8531i −0.456180 + 0.708356i
\(281\) 24.8052i 1.47975i 0.672742 + 0.739877i \(0.265116\pi\)
−0.672742 + 0.739877i \(0.734884\pi\)
\(282\) 6.53014 + 22.0808i 0.388864 + 1.31489i
\(283\) 5.41918 + 5.41918i 0.322137 + 0.322137i 0.849586 0.527449i \(-0.176852\pi\)
−0.527449 + 0.849586i \(0.676852\pi\)
\(284\) −16.2054 −0.961615
\(285\) 1.82733 6.24636i 0.108242 0.370003i
\(286\) 12.5277 0.740781
\(287\) 4.55583 + 4.55583i 0.268922 + 0.268922i
\(288\) 15.9583 + 3.40661i 0.940354 + 0.200736i
\(289\) 9.02446i 0.530850i
\(290\) 10.7430 + 49.6107i 0.630851 + 2.91324i
\(291\) −5.14262 + 9.46168i −0.301466 + 0.554653i
\(292\) 26.4045 26.4045i 1.54521 1.54521i
\(293\) 8.60739 8.60739i 0.502849 0.502849i −0.409473 0.912322i \(-0.634288\pi\)
0.912322 + 0.409473i \(0.134288\pi\)
\(294\) 2.10509 3.87306i 0.122771 0.225882i
\(295\) 10.4313 + 6.71776i 0.607336 + 0.391123i
\(296\) 3.92650i 0.228223i
\(297\) −6.19129 5.30190i −0.359255 0.307647i
\(298\) 1.66128 + 1.66128i 0.0962355 + 0.0962355i
\(299\) 4.41920 0.255569
\(300\) 29.3028 25.3937i 1.69180 1.46610i
\(301\) 7.74612 0.446479
\(302\) 24.7107 + 24.7107i 1.42194 + 1.42194i
\(303\) 0.496766 + 1.67975i 0.0285385 + 0.0964989i
\(304\) 11.9172i 0.683497i
\(305\) 13.9242 + 8.96715i 0.797296 + 0.513457i
\(306\) −21.1853 32.6849i −1.21108 1.86847i
\(307\) −11.8525 + 11.8525i −0.676457 + 0.676457i −0.959197 0.282740i \(-0.908757\pi\)
0.282740 + 0.959197i \(0.408757\pi\)
\(308\) 4.96644 4.96644i 0.282989 0.282989i
\(309\) 8.67440 + 4.71471i 0.493469 + 0.268211i
\(310\) −3.31019 15.2863i −0.188006 0.868203i
\(311\) 29.2800i 1.66032i −0.557528 0.830158i \(-0.688250\pi\)
0.557528 0.830158i \(-0.311750\pi\)
\(312\) −32.8603 + 9.71807i −1.86035 + 0.550177i
\(313\) 1.22577 + 1.22577i 0.0692848 + 0.0692848i 0.740900 0.671615i \(-0.234399\pi\)
−0.671615 + 0.740900i \(0.734399\pi\)
\(314\) 49.3859 2.78701
\(315\) −4.72944 + 4.75735i −0.266474 + 0.268046i
\(316\) 76.3710 4.29620
\(317\) −4.30159 4.30159i −0.241601 0.241601i 0.575911 0.817512i \(-0.304647\pi\)
−0.817512 + 0.575911i \(0.804647\pi\)
\(318\) 16.9395 5.00968i 0.949922 0.280929i
\(319\) 13.9921i 0.783408i
\(320\) −0.412119 + 0.639937i −0.0230381 + 0.0357736i
\(321\) −6.06388 3.29585i −0.338453 0.183956i
\(322\) 2.53450 2.53450i 0.141242 0.141242i
\(323\) −6.06162 + 6.06162i −0.337278 + 0.337278i
\(324\) 36.7836 + 16.4541i 2.04353 + 0.914116i
\(325\) −5.51066 + 14.6897i −0.305676 + 0.814839i
\(326\) 23.7755i 1.31680i
\(327\) −3.15474 10.6673i −0.174458 0.589904i
\(328\) −28.7244 28.7244i −1.58604 1.58604i
\(329\) −5.22351 −0.287981
\(330\) −13.5638 + 7.42400i −0.746665 + 0.408678i
\(331\) 33.2602 1.82815 0.914074 0.405548i \(-0.132919\pi\)
0.914074 + 0.405548i \(0.132919\pi\)
\(332\) 14.3862 + 14.3862i 0.789547 + 0.789547i
\(333\) 0.390034 1.82712i 0.0213737 0.100126i
\(334\) 11.2096i 0.613363i
\(335\) −11.5973 + 2.51136i −0.633630 + 0.137210i
\(336\) −5.86588 + 10.7924i −0.320010 + 0.588772i
\(337\) 10.3056 10.3056i 0.561383 0.561383i −0.368317 0.929700i \(-0.620066\pi\)
0.929700 + 0.368317i \(0.120066\pi\)
\(338\) −5.67565 + 5.67565i −0.308715 + 0.308715i
\(339\) −3.85131 + 7.08585i −0.209174 + 0.384851i
\(340\) −49.9166 + 10.8092i −2.70711 + 0.586214i
\(341\) 4.31132i 0.233471i
\(342\) 2.67849 12.5475i 0.144836 0.678489i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −48.8391 −2.63323
\(345\) −4.78469 + 2.61884i −0.257599 + 0.140993i
\(346\) −29.2573 −1.57288
\(347\) 19.2241 + 19.2241i 1.03200 + 1.03200i 0.999471 + 0.0325323i \(0.0103572\pi\)
0.0325323 + 0.999471i \(0.489643\pi\)
\(348\) 19.6166 + 66.3310i 1.05156 + 3.55571i
\(349\) 30.1301i 1.61283i −0.591353 0.806413i \(-0.701406\pi\)
0.591353 0.806413i \(-0.298594\pi\)
\(350\) 5.26438 + 11.5853i 0.281393 + 0.619262i
\(351\) −16.2562 + 1.25799i −0.867694 + 0.0671463i
\(352\) −6.03348 + 6.03348i −0.321586 + 0.321586i
\(353\) −17.0339 + 17.0339i −0.906625 + 0.906625i −0.995998 0.0893729i \(-0.971514\pi\)
0.0893729 + 0.995998i \(0.471514\pi\)
\(354\) 21.4905 + 11.6805i 1.14221 + 0.620814i
\(355\) −4.38201 + 6.80438i −0.232573 + 0.361139i
\(356\) 42.0992i 2.23125i
\(357\) 8.47314 2.50584i 0.448446 0.132623i
\(358\) −29.8703 29.8703i −1.57869 1.57869i
\(359\) 0.737982 0.0389492 0.0194746 0.999810i \(-0.493801\pi\)
0.0194746 + 0.999810i \(0.493801\pi\)
\(360\) 29.8190 29.9950i 1.57160 1.58087i
\(361\) 16.1763 0.851382
\(362\) −20.9714 20.9714i −1.10223 1.10223i
\(363\) −14.1831 + 4.19448i −0.744417 + 0.220153i
\(364\) 14.0493i 0.736383i
\(365\) −3.94692 18.2267i −0.206591 0.954028i
\(366\) 28.6864 + 15.5917i 1.49946 + 0.814990i
\(367\) 23.2923 23.2923i 1.21585 1.21585i 0.246776 0.969073i \(-0.420629\pi\)
0.969073 0.246776i \(-0.0793711\pi\)
\(368\) −7.06244 + 7.06244i −0.368155 + 0.368155i
\(369\) −10.5131 16.2196i −0.547288 0.844361i
\(370\) −2.97967 1.91890i −0.154906 0.0997591i
\(371\) 4.00728i 0.208048i
\(372\) −6.04438 20.4382i −0.313387 1.05967i
\(373\) −5.28110 5.28110i −0.273445 0.273445i 0.557040 0.830485i \(-0.311937\pi\)
−0.830485 + 0.557040i \(0.811937\pi\)
\(374\) 20.3671 1.05316
\(375\) −2.73878 19.1703i −0.141430 0.989948i
\(376\) 32.9341 1.69844
\(377\) −19.7908 19.7908i −1.01928 1.01928i
\(378\) −8.60180 + 10.0448i −0.442429 + 0.516647i
\(379\) 3.38353i 0.173800i −0.996217 0.0869000i \(-0.972304\pi\)
0.996217 0.0869000i \(-0.0276961\pi\)
\(380\) −14.1443 9.10888i −0.725585 0.467276i
\(381\) −16.7059 + 30.7364i −0.855868 + 1.57467i
\(382\) −23.1331 + 23.1331i −1.18359 + 1.18359i
\(383\) 2.86741 2.86741i 0.146518 0.146518i −0.630043 0.776561i \(-0.716963\pi\)
0.776561 + 0.630043i \(0.216963\pi\)
\(384\) −9.71455 + 17.8734i −0.495744 + 0.912097i
\(385\) −0.742378 3.42826i −0.0378351 0.174721i
\(386\) 29.0157i 1.47686i
\(387\) −22.7263 4.85136i −1.15524 0.246609i
\(388\) 19.6841 + 19.6841i 0.999311 + 0.999311i
\(389\) −10.2102 −0.517675 −0.258838 0.965921i \(-0.583339\pi\)
−0.258838 + 0.965921i \(0.583339\pi\)
\(390\) −8.68434 + 29.6857i −0.439749 + 1.50319i
\(391\) 7.18455 0.363339
\(392\) −4.45829 4.45829i −0.225178 0.225178i
\(393\) −2.40557 8.13410i −0.121345 0.410311i
\(394\) 67.4903i 3.40011i
\(395\) 20.6510 32.0668i 1.03906 1.61346i
\(396\) −17.6815 + 11.4606i −0.888528 + 0.575915i
\(397\) −24.0534 + 24.0534i −1.20721 + 1.20721i −0.235280 + 0.971928i \(0.575601\pi\)
−0.971928 + 0.235280i \(0.924399\pi\)
\(398\) 7.57156 7.57156i 0.379528 0.379528i
\(399\) 2.55723 + 1.38991i 0.128021 + 0.0695823i
\(400\) −14.6693 32.2828i −0.733465 1.61414i
\(401\) 20.0912i 1.00331i −0.865068 0.501654i \(-0.832725\pi\)
0.865068 0.501654i \(-0.167275\pi\)
\(402\) −22.4324 + 6.63414i −1.11883 + 0.330881i
\(403\) 6.09803 + 6.09803i 0.303765 + 0.303765i
\(404\) 4.52803 0.225278
\(405\) 16.8552 10.9955i 0.837542 0.546373i
\(406\) −22.7008 −1.12662
\(407\) 0.690793 + 0.690793i 0.0342413 + 0.0342413i
\(408\) −53.4229 + 15.7992i −2.64483 + 0.782179i
\(409\) 33.5102i 1.65697i 0.560008 + 0.828487i \(0.310798\pi\)
−0.560008 + 0.828487i \(0.689202\pi\)
\(410\) −35.8356 + 7.76008i −1.76980 + 0.383243i
\(411\) 9.81120 + 5.33259i 0.483951 + 0.263037i
\(412\) 18.0463 18.0463i 0.889077 0.889077i
\(413\) −3.92353 + 3.92353i −0.193064 + 0.193064i
\(414\) −9.02331 + 5.84862i −0.443471 + 0.287444i
\(415\) 9.93061 2.15044i 0.487475 0.105561i
\(416\) 17.0678i 0.836817i
\(417\) −5.01251 16.9491i −0.245463 0.830000i
\(418\) 4.74391 + 4.74391i 0.232032 + 0.232032i
\(419\) 25.8773 1.26419 0.632093 0.774892i \(-0.282196\pi\)
0.632093 + 0.774892i \(0.282196\pi\)
\(420\) 8.32567 + 15.2112i 0.406251 + 0.742232i
\(421\) 10.4030 0.507013 0.253507 0.967334i \(-0.418416\pi\)
0.253507 + 0.967334i \(0.418416\pi\)
\(422\) 38.7301 + 38.7301i 1.88535 + 1.88535i
\(423\) 15.3252 + 3.27146i 0.745138 + 0.159064i
\(424\) 25.2658i 1.22702i
\(425\) −8.95900 + 23.8820i −0.434576 + 1.15844i
\(426\) −7.61923 + 14.0183i −0.369153 + 0.679188i
\(427\) −5.23730 + 5.23730i −0.253450 + 0.253450i
\(428\) −12.6154 + 12.6154i −0.609786 + 0.609786i
\(429\) 4.07143 7.49085i 0.196571 0.361662i
\(430\) −23.8679 + 37.0621i −1.15101 + 1.78729i
\(431\) 0.449005i 0.0216278i 0.999942 + 0.0108139i \(0.00344224\pi\)
−0.999942 + 0.0108139i \(0.996558\pi\)
\(432\) 23.9691 27.9899i 1.15321 1.34667i
\(433\) −17.7813 17.7813i −0.854517 0.854517i 0.136169 0.990686i \(-0.456521\pi\)
−0.990686 + 0.136169i \(0.956521\pi\)
\(434\) 6.99469 0.335756
\(435\) 33.1556 + 9.69944i 1.58969 + 0.465053i
\(436\) −28.7555 −1.37714
\(437\) 1.67343 + 1.67343i 0.0800509 + 0.0800509i
\(438\) −10.4264 35.2554i −0.498192 1.68457i
\(439\) 29.5293i 1.40936i −0.709526 0.704679i \(-0.751091\pi\)
0.709526 0.704679i \(-0.248909\pi\)
\(440\) 4.68067 + 21.6151i 0.223142 + 1.03046i
\(441\) −1.63172 2.51744i −0.0777010 0.119878i
\(442\) 28.8077 28.8077i 1.37024 1.37024i
\(443\) −15.5643 + 15.5643i −0.739483 + 0.739483i −0.972478 0.232995i \(-0.925147\pi\)
0.232995 + 0.972478i \(0.425147\pi\)
\(444\) −4.24325 2.30630i −0.201376 0.109452i
\(445\) −17.6767 11.3838i −0.837957 0.539643i
\(446\) 44.6313i 2.11336i
\(447\) 1.53325 0.453443i 0.0725204 0.0214471i
\(448\) −0.240699 0.240699i −0.0113720 0.0113720i
\(449\) 16.3214 0.770252 0.385126 0.922864i \(-0.374158\pi\)
0.385126 + 0.922864i \(0.374158\pi\)
\(450\) −8.18931 37.2872i −0.386048 1.75774i
\(451\) 10.1070 0.475921
\(452\) 14.7415 + 14.7415i 0.693380 + 0.693380i
\(453\) 22.8063 6.74471i 1.07153 0.316894i
\(454\) 31.3336i 1.47056i
\(455\) −5.89905 3.79898i −0.276552 0.178099i
\(456\) −16.1232 8.76332i −0.755040 0.410380i
\(457\) −20.6299 + 20.6299i −0.965028 + 0.965028i −0.999409 0.0343811i \(-0.989054\pi\)
0.0343811 + 0.999409i \(0.489054\pi\)
\(458\) 8.03251 8.03251i 0.375335 0.375335i
\(459\) −26.4287 + 2.04518i −1.23359 + 0.0954609i
\(460\) 2.98410 + 13.7804i 0.139134 + 0.642516i
\(461\) 15.2893i 0.712094i −0.934468 0.356047i \(-0.884124\pi\)
0.934468 0.356047i \(-0.115876\pi\)
\(462\) −1.96110 6.63120i −0.0912388 0.308511i
\(463\) 0.492195 + 0.492195i 0.0228743 + 0.0228743i 0.718451 0.695577i \(-0.244851\pi\)
−0.695577 + 0.718451i \(0.744851\pi\)
\(464\) 63.2563 2.93660
\(465\) −10.2161 2.98864i −0.473760 0.138595i
\(466\) 20.3056 0.940640
\(467\) −9.00044 9.00044i −0.416491 0.416491i 0.467501 0.883992i \(-0.345154\pi\)
−0.883992 + 0.467501i \(0.845154\pi\)
\(468\) −8.79901 + 41.2192i −0.406734 + 1.90536i
\(469\) 5.30669i 0.245040i
\(470\) 16.0951 24.9924i 0.742410 1.15281i
\(471\) 16.0501 29.5298i 0.739548 1.36066i
\(472\) 24.7378 24.7378i 1.13865 1.13865i
\(473\) 8.59230 8.59230i 0.395075 0.395075i
\(474\) 35.9070 66.0637i 1.64926 3.03441i
\(475\) −7.64932 + 3.47586i −0.350975 + 0.159483i
\(476\) 22.8408i 1.04690i
\(477\) 2.50974 11.7570i 0.114913 0.538314i
\(478\) −21.3426 21.3426i −0.976188 0.976188i
\(479\) −22.7572 −1.03980 −0.519901 0.854226i \(-0.674031\pi\)
−0.519901 + 0.854226i \(0.674031\pi\)
\(480\) −10.1144 18.4794i −0.461659 0.843464i
\(481\) 1.95415 0.0891015
\(482\) 32.5235 + 32.5235i 1.48141 + 1.48141i
\(483\) −0.691785 2.33917i −0.0314773 0.106436i
\(484\) 38.2328i 1.73785i
\(485\) 13.5877 2.94237i 0.616986 0.133606i
\(486\) 31.5278 24.0830i 1.43013 1.09243i
\(487\) −11.4919 + 11.4919i −0.520746 + 0.520746i −0.917797 0.397051i \(-0.870034\pi\)
0.397051 + 0.917797i \(0.370034\pi\)
\(488\) 33.0210 33.0210i 1.49479 1.49479i
\(489\) −14.2163 7.72687i −0.642884 0.349421i
\(490\) −5.56202 + 1.20443i −0.251266 + 0.0544108i
\(491\) 0.301729i 0.0136168i −0.999977 0.00680841i \(-0.997833\pi\)
0.999977 0.00680841i \(-0.00216720\pi\)
\(492\) −47.9133 + 14.1698i −2.16010 + 0.638826i
\(493\) −32.1750 32.1750i −1.44909 1.44909i
\(494\) 13.4198 0.603785
\(495\) 0.0309545 + 10.5231i 0.00139130 + 0.472979i
\(496\) −19.4909 −0.875165
\(497\) −2.55933 2.55933i −0.114801 0.114801i
\(498\) 19.2085 5.68071i 0.860754 0.254559i
\(499\) 20.2207i 0.905202i −0.891713 0.452601i \(-0.850496\pi\)
0.891713 0.452601i \(-0.149504\pi\)
\(500\) −49.5282 7.26458i −2.21497 0.324882i
\(501\) 6.70268 + 3.64305i 0.299454 + 0.162759i
\(502\) 5.74537 5.74537i 0.256428 0.256428i
\(503\) −23.8859 + 23.8859i −1.06502 + 1.06502i −0.0672882 + 0.997734i \(0.521435\pi\)
−0.997734 + 0.0672882i \(0.978565\pi\)
\(504\) 10.2880 + 15.8724i 0.458262 + 0.707012i
\(505\) 1.22440 1.90124i 0.0544850 0.0846042i
\(506\) 5.62273i 0.249961i
\(507\) 1.54915 + 5.23825i 0.0688004 + 0.232639i
\(508\) 63.9443 + 63.9443i 2.83707 + 2.83707i
\(509\) −11.7721 −0.521788 −0.260894 0.965368i \(-0.584017\pi\)
−0.260894 + 0.965368i \(0.584017\pi\)
\(510\) −14.1186 + 48.2618i −0.625184 + 2.13707i
\(511\) 8.34014 0.368946
\(512\) 35.9587 + 35.9587i 1.58917 + 1.58917i
\(513\) −6.63215 5.67942i −0.292816 0.250752i
\(514\) 42.5137i 1.87520i
\(515\) −2.69754 12.4571i −0.118868 0.548925i
\(516\) −28.6864 + 52.7789i −1.26285 + 2.32346i
\(517\) −5.79412 + 5.79412i −0.254825 + 0.254825i
\(518\) 1.12074 1.12074i 0.0492426 0.0492426i
\(519\) −9.50842 + 17.4941i −0.417373 + 0.767907i
\(520\) 37.1934 + 23.9525i 1.63104 + 1.05038i
\(521\) 29.7872i 1.30500i 0.757789 + 0.652500i \(0.226280\pi\)
−0.757789 + 0.652500i \(0.773720\pi\)
\(522\) 66.6018 + 14.2174i 2.91508 + 0.622279i
\(523\) 17.4673 + 17.4673i 0.763792 + 0.763792i 0.977006 0.213214i \(-0.0683931\pi\)
−0.213214 + 0.977006i \(0.568393\pi\)
\(524\) −21.9268 −0.957877
\(525\) 8.63822 + 0.617365i 0.377003 + 0.0269440i
\(526\) −47.3309 −2.06373
\(527\) 9.91393 + 9.91393i 0.431858 + 0.431858i
\(528\) 5.46466 + 18.4780i 0.237819 + 0.804151i
\(529\) 21.0166i 0.913764i
\(530\) −19.1732 12.3475i −0.832833 0.536343i
\(531\) 13.9685 9.05395i 0.606183 0.392908i
\(532\) 5.32007 5.32007i 0.230654 0.230654i
\(533\) 14.2956 14.2956i 0.619211 0.619211i
\(534\) −36.4174 19.7936i −1.57593 0.856553i
\(535\) 1.88573 + 8.70821i 0.0815272 + 0.376489i
\(536\) 33.4586i 1.44519i
\(537\) −27.5683 + 8.15302i −1.18966 + 0.351829i
\(538\) 52.8021 + 52.8021i 2.27646 + 2.27646i
\(539\) 1.56870 0.0675687
\(540\) −14.8999 49.8425i −0.641192 2.14488i
\(541\) −23.1117 −0.993650 −0.496825 0.867851i \(-0.665501\pi\)
−0.496825 + 0.867851i \(0.665501\pi\)
\(542\) −5.72941 5.72941i −0.246099 0.246099i
\(543\) −19.3552 + 5.72409i −0.830612 + 0.245644i
\(544\) 27.7481i 1.18969i
\(545\) −7.77560 + 12.0739i −0.333070 + 0.517191i
\(546\) −12.1532 6.60549i −0.520107 0.282689i
\(547\) −25.6689 + 25.6689i −1.09752 + 1.09752i −0.102823 + 0.994700i \(0.532787\pi\)
−0.994700 + 0.102823i \(0.967213\pi\)
\(548\) 20.4113 20.4113i 0.871928 0.871928i
\(549\) 18.6458 12.0856i 0.795783 0.515801i
\(550\) 18.6904 + 7.01144i 0.796959 + 0.298969i
\(551\) 14.9884i 0.638528i
\(552\) 4.36169 + 14.7484i 0.185646 + 0.627735i
\(553\) 12.0613 + 12.0613i 0.512898 + 0.512898i
\(554\) −60.6965 −2.57875
\(555\) −2.11576 + 1.15804i −0.0898092 + 0.0491559i
\(556\) −45.6891 −1.93765
\(557\) −10.5779 10.5779i −0.448199 0.448199i 0.446556 0.894756i \(-0.352650\pi\)
−0.894756 + 0.446556i \(0.852650\pi\)
\(558\) −20.5217 4.38074i −0.868753 0.185452i
\(559\) 24.3063i 1.02805i
\(560\) 15.4987 3.35618i 0.654939 0.141825i
\(561\) 6.61917 12.1783i 0.279462 0.514169i
\(562\) 44.6402 44.6402i 1.88303 1.88303i
\(563\) −10.9216 + 10.9216i −0.460291 + 0.460291i −0.898751 0.438460i \(-0.855524\pi\)
0.438460 + 0.898751i \(0.355524\pi\)
\(564\) 19.3444 35.5908i 0.814544 1.49864i
\(565\) 10.1758 2.20354i 0.428100 0.0927036i
\(566\) 19.5050i 0.819858i
\(567\) 3.21064 + 8.40784i 0.134834 + 0.353096i
\(568\) 16.1365 + 16.1365i 0.677072 + 0.677072i
\(569\) 42.0710 1.76371 0.881854 0.471523i \(-0.156295\pi\)
0.881854 + 0.471523i \(0.156295\pi\)
\(570\) −14.5297 + 7.95263i −0.608581 + 0.333099i
\(571\) 10.8342 0.453399 0.226699 0.973965i \(-0.427207\pi\)
0.226699 + 0.973965i \(0.427207\pi\)
\(572\) −15.5840 15.5840i −0.651601 0.651601i
\(573\) 6.31411 + 21.3503i 0.263776 + 0.891921i
\(574\) 16.3976i 0.684424i
\(575\) 6.59308 + 2.47331i 0.274950 + 0.103144i
\(576\) 0.555438 + 0.856936i 0.0231433 + 0.0357057i
\(577\) 14.6975 14.6975i 0.611865 0.611865i −0.331567 0.943432i \(-0.607577\pi\)
0.943432 + 0.331567i \(0.107577\pi\)
\(578\) 16.2407 16.2407i 0.675523 0.675523i
\(579\) 17.3497 + 9.42991i 0.721028 + 0.391894i
\(580\) 48.3498 75.0776i 2.00762 3.11743i
\(581\) 4.54404i 0.188519i
\(582\) 26.2823 7.77271i 1.08944 0.322189i
\(583\) 4.44503 + 4.44503i 0.184094 + 0.184094i
\(584\) −52.5844 −2.17596
\(585\) 14.9279 + 14.8404i 0.617194 + 0.613574i
\(586\) −30.9802 −1.27978
\(587\) 4.89737 + 4.89737i 0.202136 + 0.202136i 0.800915 0.598779i \(-0.204347\pi\)
−0.598779 + 0.800915i \(0.704347\pi\)
\(588\) −7.43658 + 2.19929i −0.306680 + 0.0906971i
\(589\) 4.61831i 0.190294i
\(590\) −6.68306 30.8620i −0.275137 1.27057i
\(591\) 40.3552 + 21.9339i 1.65999 + 0.902240i
\(592\) −3.12297 + 3.12297i −0.128353 + 0.128353i
\(593\) −22.5635 + 22.5635i −0.926573 + 0.926573i −0.997483 0.0709102i \(-0.977410\pi\)
0.0709102 + 0.997483i \(0.477410\pi\)
\(594\) 1.60059 + 20.6835i 0.0656729 + 0.848654i
\(595\) −9.59044 6.17623i −0.393170 0.253201i
\(596\) 4.13314i 0.169300i
\(597\) −2.06664 6.98804i −0.0845818 0.286002i
\(598\) −7.95292 7.95292i −0.325219 0.325219i
\(599\) 6.81971 0.278646 0.139323 0.990247i \(-0.455507\pi\)
0.139323 + 0.990247i \(0.455507\pi\)
\(600\) −54.4637 3.89247i −2.22347 0.158910i
\(601\) −8.46733 −0.345390 −0.172695 0.984975i \(-0.555247\pi\)
−0.172695 + 0.984975i \(0.555247\pi\)
\(602\) −13.9402 13.9402i −0.568158 0.568158i
\(603\) −3.32356 + 15.5693i −0.135346 + 0.634031i
\(604\) 61.4782i 2.50151i
\(605\) 16.0533 + 10.3383i 0.652658 + 0.420311i
\(606\) 2.12893 3.91692i 0.0864817 0.159114i
\(607\) 6.30295 6.30295i 0.255829 0.255829i −0.567526 0.823355i \(-0.692100\pi\)
0.823355 + 0.567526i \(0.192100\pi\)
\(608\) −6.46309 + 6.46309i −0.262113 + 0.262113i
\(609\) −7.37760 + 13.5737i −0.298956 + 0.550035i
\(610\) −8.92083 41.1959i −0.361194 1.66797i
\(611\) 16.3907i 0.663095i
\(612\) −14.3051 + 67.0125i −0.578248 + 2.70882i
\(613\) −5.24728 5.24728i −0.211935 0.211935i 0.593154 0.805089i \(-0.297883\pi\)
−0.805089 + 0.593154i \(0.797883\pi\)
\(614\) 42.6601 1.72162
\(615\) −7.00627 + 23.9496i −0.282520 + 0.965739i
\(616\) −9.89062 −0.398504
\(617\) −2.10719 2.10719i −0.0848323 0.0848323i 0.663417 0.748250i \(-0.269105\pi\)
−0.748250 + 0.663417i \(0.769105\pi\)
\(618\) −7.12596 24.0954i −0.286648 0.969261i
\(619\) 21.0734i 0.847012i −0.905893 0.423506i \(-0.860799\pi\)
0.905893 0.423506i \(-0.139201\pi\)
\(620\) −14.8978 + 23.1333i −0.598310 + 0.929055i
\(621\) 0.564612 + 7.29616i 0.0226571 + 0.292785i
\(622\) −52.6932 + 52.6932i −2.11280 + 2.11280i
\(623\) 6.64874 6.64874i 0.266376 0.266376i
\(624\) 33.8650 + 18.4063i 1.35569 + 0.736844i
\(625\) −16.4429 + 18.8317i −0.657715 + 0.753267i
\(626\) 4.41188i 0.176334i
\(627\) 4.37831 1.29484i 0.174853 0.0517108i
\(628\) −61.4341 61.4341i −2.45149 2.45149i
\(629\) 3.17697 0.126674
\(630\) 17.0727 0.0502206i 0.680193 0.00200084i
\(631\) −11.6376 −0.463287 −0.231643 0.972801i \(-0.574410\pi\)
−0.231643 + 0.972801i \(0.574410\pi\)
\(632\) −76.0461 76.0461i −3.02495 3.02495i
\(633\) 35.7453 10.5713i 1.42075 0.420170i
\(634\) 15.4825i 0.614890i
\(635\) 44.1399 9.55833i 1.75164 0.379311i
\(636\) −27.3040 14.8403i −1.08267 0.588455i
\(637\) 2.21881 2.21881i 0.0879123 0.0879123i
\(638\) −25.1806 + 25.1806i −0.996910 + 0.996910i
\(639\) 5.90591 + 9.11170i 0.233634 + 0.360453i
\(640\) 25.6675 5.55821i 1.01460 0.219708i
\(641\) 36.1036i 1.42601i 0.701161 + 0.713003i \(0.252665\pi\)
−0.701161 + 0.713003i \(0.747335\pi\)
\(642\) 4.98144 + 16.8441i 0.196602 + 0.664782i
\(643\) −21.0115 21.0115i −0.828614 0.828614i 0.158711 0.987325i \(-0.449266\pi\)
−0.987325 + 0.158711i \(0.949266\pi\)
\(644\) −6.30563 −0.248477
\(645\) 14.4040 + 26.3165i 0.567158 + 1.03621i
\(646\) 21.8173 0.858392
\(647\) 18.9025 + 18.9025i 0.743133 + 0.743133i 0.973180 0.230046i \(-0.0738878\pi\)
−0.230046 + 0.973180i \(0.573888\pi\)
\(648\) −20.2430 53.0112i −0.795221 2.08248i
\(649\) 8.70428i 0.341673i
\(650\) 36.3532 16.5189i 1.42589 0.647925i
\(651\) 2.27322 4.18241i 0.0890947 0.163921i
\(652\) −29.5757 + 29.5757i −1.15828 + 1.15828i
\(653\) 12.2864 12.2864i 0.480803 0.480803i −0.424585 0.905388i \(-0.639580\pi\)
0.905388 + 0.424585i \(0.139580\pi\)
\(654\) −13.5199 + 24.8746i −0.528668 + 0.972674i
\(655\) −5.92909 + 9.20669i −0.231669 + 0.359735i
\(656\) 45.6924i 1.78399i
\(657\) −24.4691 5.22339i −0.954631 0.203784i
\(658\) 9.40038 + 9.40038i 0.366465 + 0.366465i
\(659\) 0.708622 0.0276040 0.0138020 0.999905i \(-0.495607\pi\)
0.0138020 + 0.999905i \(0.495607\pi\)
\(660\) 26.1080 + 7.63772i 1.01625 + 0.297298i
\(661\) 17.4206 0.677582 0.338791 0.940862i \(-0.389982\pi\)
0.338791 + 0.940862i \(0.389982\pi\)
\(662\) −59.8561 59.8561i −2.32637 2.32637i
\(663\) −7.86299 26.5876i −0.305373 1.03258i
\(664\) 28.6500i 1.11184i
\(665\) −0.795239 3.67237i −0.0308381 0.142409i
\(666\) −3.99006 + 2.58623i −0.154612 + 0.100214i
\(667\) −8.88253 + 8.88253i −0.343933 + 0.343933i
\(668\) 13.9443 13.9443i 0.539522 0.539522i
\(669\) −26.6869 14.5049i −1.03177 0.560791i
\(670\) 25.3904 + 16.3514i 0.980918 + 0.631709i
\(671\) 11.6188i 0.448540i
\(672\) 9.03434 2.67181i 0.348507 0.103067i
\(673\) −8.20389 8.20389i −0.316237 0.316237i 0.531083 0.847320i \(-0.321785\pi\)
−0.847320 + 0.531083i \(0.821785\pi\)
\(674\) −37.0926 −1.42875
\(675\) −24.9570 7.22137i −0.960595 0.277951i
\(676\) 14.1206 0.543099
\(677\) 32.8605 + 32.8605i 1.26293 + 1.26293i 0.949666 + 0.313264i \(0.101422\pi\)
0.313264 + 0.949666i \(0.398578\pi\)
\(678\) 19.6828 5.82098i 0.755915 0.223554i
\(679\) 6.21744i 0.238604i
\(680\) 60.4675 + 38.9409i 2.31882 + 1.49332i
\(681\) 18.7356 + 10.1832i 0.717951 + 0.390221i
\(682\) 7.75878 7.75878i 0.297099 0.297099i
\(683\) −28.4978 + 28.4978i −1.09044 + 1.09044i −0.0949562 + 0.995481i \(0.530271\pi\)
−0.995481 + 0.0949562i \(0.969729\pi\)
\(684\) −18.9405 + 12.2766i −0.724208 + 0.469408i
\(685\) −3.05106 14.0896i −0.116575 0.538338i
\(686\) 2.54506i 0.0971709i
\(687\) −2.19245 7.41347i −0.0836473 0.282842i
\(688\) 38.8446 + 38.8446i 1.48093 + 1.48093i
\(689\) 12.5743 0.479043
\(690\) 13.3236 + 3.89773i 0.507221 + 0.148384i
\(691\) 5.79939 0.220619 0.110310 0.993897i \(-0.464816\pi\)
0.110310 + 0.993897i \(0.464816\pi\)
\(692\) 36.3949 + 36.3949i 1.38353 + 1.38353i
\(693\) −4.60241 0.982471i −0.174831 0.0373210i
\(694\) 69.1925i 2.62651i
\(695\) −12.3545 + 19.1840i −0.468633 + 0.727692i
\(696\) 46.5156 85.5820i 1.76317 3.24398i
\(697\) 23.2412 23.2412i 0.880324 0.880324i
\(698\) −54.2230 + 54.2230i −2.05237 + 2.05237i
\(699\) 6.59919 12.1416i 0.249604 0.459236i
\(700\) 7.86301 20.9604i 0.297194 0.792227i
\(701\) 4.92775i 0.186118i −0.995661 0.0930592i \(-0.970335\pi\)
0.995661 0.0930592i \(-0.0296646\pi\)
\(702\) 31.5191 + 26.9913i 1.18961 + 1.01872i
\(703\) 0.739981 + 0.739981i 0.0279089 + 0.0279089i
\(704\) −0.533986 −0.0201254
\(705\) −9.71318 17.7462i −0.365820 0.668362i
\(706\) 61.3096 2.30742
\(707\) 0.715113 + 0.715113i 0.0268946 + 0.0268946i
\(708\) −12.2032 41.2635i −0.458625 1.55078i
\(709\) 17.1922i 0.645666i 0.946456 + 0.322833i \(0.104635\pi\)
−0.946456 + 0.322833i \(0.895365\pi\)
\(710\) 20.1313 4.35937i 0.755516 0.163604i
\(711\) −27.8326 42.9405i −1.04381 1.61039i
\(712\) −41.9201 + 41.9201i −1.57102 + 1.57102i
\(713\) 2.73693 2.73693i 0.102499 0.102499i
\(714\) −19.7581 10.7389i −0.739428 0.401895i
\(715\) −10.7574 + 2.32948i −0.402305 + 0.0871177i
\(716\) 74.3149i 2.77728i
\(717\) −19.6978 + 5.82541i −0.735628 + 0.217554i
\(718\) −1.32809 1.32809i −0.0495640 0.0495640i
\(719\) 12.2556 0.457059 0.228529 0.973537i \(-0.426608\pi\)
0.228529 + 0.973537i \(0.426608\pi\)
\(720\) −47.5735 + 0.139941i −1.77296 + 0.00521528i
\(721\) 5.70011 0.212283
\(722\) −29.1113 29.1113i −1.08341 1.08341i
\(723\) 30.0170 8.87721i 1.11635 0.330147i
\(724\) 52.1752i 1.93908i
\(725\) −18.4498 40.6025i −0.685208 1.50794i
\(726\) 33.0728 + 17.9757i 1.22745 + 0.667142i
\(727\) 5.83842 5.83842i 0.216535 0.216535i −0.590501 0.807037i \(-0.701070\pi\)
0.807037 + 0.590501i \(0.201070\pi\)
\(728\) −13.9895 + 13.9895i −0.518486 + 0.518486i
\(729\) −4.15390 26.6786i −0.153848 0.988094i
\(730\) −25.6983 + 39.9043i −0.951136 + 1.47692i
\(731\) 39.5162i 1.46156i
\(732\) −16.2894 55.0802i −0.602072 2.03582i
\(733\) 13.5940 + 13.5940i 0.502105 + 0.502105i 0.912091 0.409987i \(-0.134467\pi\)
−0.409987 + 0.912091i \(0.634467\pi\)
\(734\) −83.8351 −3.09441
\(735\) −1.08744 + 3.71719i −0.0401107 + 0.137111i
\(736\) 7.66040 0.282366
\(737\) −5.88639 5.88639i −0.216828 0.216828i
\(738\) −10.2698 + 48.1090i −0.378035 + 1.77092i
\(739\) 15.1801i 0.558411i 0.960231 + 0.279205i \(0.0900710\pi\)
−0.960231 + 0.279205i \(0.909929\pi\)
\(740\) 1.31955 + 6.09364i 0.0485078 + 0.224007i
\(741\) 4.36134 8.02424i 0.160218 0.294778i
\(742\) 7.21162 7.21162i 0.264747 0.264747i
\(743\) −34.4215 + 34.4215i −1.26280 + 1.26280i −0.313073 + 0.949729i \(0.601358\pi\)
−0.949729 + 0.313073i \(0.898642\pi\)
\(744\) −14.3326 + 26.3700i −0.525459 + 0.966770i
\(745\) −1.73543 1.11762i −0.0635813 0.0409463i
\(746\) 19.0080i 0.695934i
\(747\) 2.84591 13.3317i 0.104126 0.487783i
\(748\) −25.3359 25.3359i −0.926371 0.926371i
\(749\) −3.98469 −0.145597
\(750\) −29.5706 + 39.4282i −1.07977 + 1.43971i
\(751\) −22.2515 −0.811970 −0.405985 0.913880i \(-0.633071\pi\)
−0.405985 + 0.913880i \(0.633071\pi\)
\(752\) −26.1944 26.1944i −0.955210 0.955210i
\(753\) −1.56818 5.30260i −0.0571478 0.193237i
\(754\) 71.2321i 2.59412i
\(755\) −25.8136 16.6239i −0.939454 0.605007i
\(756\) 23.1956 1.79498i 0.843615 0.0652830i
\(757\) −1.88407 + 1.88407i −0.0684777 + 0.0684777i −0.740516 0.672038i \(-0.765419\pi\)
0.672038 + 0.740516i \(0.265419\pi\)
\(758\) −6.08909 + 6.08909i −0.221166 + 0.221166i
\(759\) −3.36206 1.82735i −0.122035 0.0663286i
\(760\) 5.01396 + 23.1542i 0.181875 + 0.839892i
\(761\) 35.6674i 1.29294i −0.762938 0.646472i \(-0.776244\pi\)
0.762938 0.646472i \(-0.223756\pi\)
\(762\) 85.3786 25.2498i 3.09294 0.914703i
\(763\) −4.54137 4.54137i −0.164409 0.164409i
\(764\) 57.5532 2.08220
\(765\) 24.2692 + 24.1269i 0.877456 + 0.872309i
\(766\) −10.3206 −0.372897
\(767\) 12.3115 + 12.3115i 0.444543 + 0.444543i
\(768\) 48.5173 14.3485i 1.75072 0.517755i
\(769\) 31.7331i 1.14432i 0.820141 + 0.572162i \(0.193895\pi\)
−0.820141