Properties

Label 105.2.j.a.92.1
Level 105
Weight 2
Character 105.92
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 92.1
Character \(\chi\) = 105.92
Dual form 105.2.j.a.8.1

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79963 + 1.79963i −1.27253 + 1.27253i −0.327775 + 0.944756i \(0.606299\pi\)
−0.944756 + 0.327775i \(0.893701\pi\)
\(3\) −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 \(-0.924003\pi\)
0.971634 0.236491i \(-0.0759973\pi\)
\(12\) −2.19929 + 7.43658i −0.634880 + 2.14676i
\(13\) 2.21881 2.21881i 0.615386 0.615386i −0.328958 0.944345i \(-0.606697\pi\)
0.944345 + 0.328958i \(0.106697\pi\)
\(14\) 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 −0.118114 0.993000i \(-0.537685\pi\)
0.993000 + 0.118114i \(0.0376849\pi\)
\(18\) −7.46695 + 1.59396i −1.75998 + 0.375700i
\(19\) 1.68040i 0.385510i −0.981247 0.192755i \(-0.938258\pi\)
0.981247 0.192755i \(-0.0617423\pi\)
\(20\) −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 0.803268 0.595618i \(-0.203093\pi\)
−0.595618 + 0.803268i \(0.703093\pi\)
\(24\) −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 0.742377 0.669982i \(-0.233698\pi\)
−0.669982 + 0.742377i \(0.733698\pi\)
\(38\) 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 \(0.167810\pi\)
−0.864224 + 0.503108i \(0.832190\pi\)
\(42\) −4.22719 1.25015i −0.652270 0.192902i
\(43\) −5.47734 + 5.47734i −0.835286 + 0.835286i −0.988234 0.152948i \(-0.951123\pi\)
0.152948 + 0.988234i \(0.451123\pi\)
\(44\) −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 −0.384402 0.923166i \(-0.625592\pi\)
0.923166 + 0.384402i \(0.125592\pi\)
\(48\) 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 0.874410 0.485188i \(-0.161249\pi\)
−0.485188 + 0.874410i \(0.661249\pi\)
\(54\) 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 0.439711 0.898139i \(-0.355081\pi\)
−0.898139 + 0.439711i \(0.855081\pi\)
\(68\) −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 \(-0.931099\pi\)
0.976664 0.214774i \(-0.0689015\pi\)
\(72\) 3.94878 + 18.4981i 0.465368 + 2.18003i
\(73\) −5.89737 + 5.89737i −0.690235 + 0.690235i −0.962284 0.272049i \(-0.912299\pi\)
0.272049 + 0.962284i \(0.412299\pi\)
\(74\) −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 \(0.409149\pi\)
−0.281558 + 0.959544i \(0.590851\pi\)
\(80\) −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 0.861108 0.508422i \(-0.169771\pi\)
−0.508422 + 0.861108i \(0.669771\pi\)
\(84\) 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 0.894151 0.447765i \(-0.147780\pi\)
−0.447765 + 0.894151i \(0.647780\pi\)
\(98\) −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 \(0.0160226\pi\)
−0.998733 + 0.0503152i \(0.983977\pi\)
\(102\) 6.37751 21.5647i 0.631468 2.13522i
\(103\) −4.03058 + 4.03058i −0.397145 + 0.397145i −0.877225 0.480080i \(-0.840608\pi\)
0.480080 + 0.877225i \(0.340608\pi\)
\(104\) 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 −0.557673 0.830061i \(-0.688306\pi\)
0.830061 + 0.557673i \(0.188306\pi\)
\(108\) −17.6710 + 15.1325i −1.70039 + 1.45613i
\(109\) 6.42246i 0.615160i −0.951522 0.307580i \(-0.900481\pi\)
0.951522 0.307580i \(-0.0995192\pi\)
\(110\) 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 0.844804 0.535075i \(-0.179717\pi\)
−0.535075 + 0.844804i \(0.679717\pi\)
\(114\) −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 0.947476 + 0.319826i \(0.103624\pi\)
0.319826 + 0.947476i \(0.396376\pi\)
\(128\) 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 \(-0.931371\pi\)
0.976847 0.213939i \(-0.0686294\pi\)
\(132\) 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 −0.874504 0.485019i \(-0.838813\pi\)
0.485019 + 0.874504i \(0.338813\pi\)
\(138\) 5.95334 + 1.76064i 0.506782 + 0.149875i
\(139\) 10.2045i 0.865536i −0.901505 0.432768i \(-0.857537\pi\)
0.901505 0.432768i \(-0.142463\pi\)
\(140\) −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 −0.994979 0.100086i \(-0.968088\pi\)
−0.100086 0.994979i \(-0.531912\pi\)
\(158\) −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 −0.399387 0.916782i \(-0.630777\pi\)
0.916782 + 0.399387i \(0.130777\pi\)
\(164\) 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 −0.817264 0.576263i \(-0.804510\pi\)
0.576263 + 0.817264i \(0.304510\pi\)
\(168\) −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 0.945022 0.327008i \(-0.106040\pi\)
−0.327008 + 0.945022i \(0.606040\pi\)
\(174\) −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 \(0.153965\pi\)
−0.885282 + 0.465054i \(0.846035\pi\)
\(192\) −0.167206 + 0.565384i −0.0120671 + 0.0408031i
\(193\) −8.06158 + 8.06158i −0.580285 + 0.580285i −0.934982 0.354696i \(-0.884584\pi\)
0.354696 + 0.934982i \(0.384584\pi\)
\(194\) −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 −0.436036 + 0.899929i \(0.643618\pi\)
−0.899929 + 0.436036i \(0.856382\pi\)
\(198\) 2.50045 + 11.7134i 0.177699 + 0.832436i
\(199\) 4.20728i 0.298246i −0.988819 0.149123i \(-0.952355\pi\)
0.988819 0.149123i \(-0.0476451\pi\)
\(200\) 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 −0.157193 0.987568i \(-0.550244\pi\)
0.987568 + 0.157193i \(0.0502445\pi\)
\(224\) −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 −0.934299 0.356490i \(-0.883973\pi\)
0.356490 + 0.934299i \(0.383973\pi\)
\(228\) 12.4964 + 3.69568i 0.827597 + 0.244753i
\(229\) 4.46342i 0.294951i −0.989066 0.147476i \(-0.952885\pi\)
0.989066 0.147476i \(-0.0471148\pi\)
\(230\) −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 0.497735 0.867329i \(-0.334165\pi\)
−0.867329 + 0.497735i \(0.834165\pi\)
\(234\) −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 \(-0.967874\pi\)
0.994911 0.100755i \(-0.0321259\pi\)
\(252\) −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 −0.235158 0.971957i \(-0.575561\pi\)
0.971957 + 0.235158i \(0.0755607\pi\)
\(258\) −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 0.984765 0.173891i \(-0.0556339\pi\)
−0.173891 + 0.984765i \(0.555634\pi\)
\(264\) −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 0.999911 + 0.0133247i \(0.00424152\pi\)
0.0133247 + 0.999911i \(0.495758\pi\)
\(278\) 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 \(-0.734884\pi\)
0.672742 0.739877i \(-0.265116\pi\)
\(282\) 6.53014 22.0808i 0.388864 1.31489i
\(283\) 5.41918 5.41918i 0.322137 0.322137i −0.527449 0.849586i \(-0.676852\pi\)
0.849586 + 0.527449i \(0.176852\pi\)
\(284\) −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 0.912322 0.409473i \(-0.134288\pi\)
−0.409473 + 0.912322i \(0.634288\pi\)
\(294\) 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 0.282740 0.959197i \(-0.408757\pi\)
−0.959197 + 0.282740i \(0.908757\pi\)
\(308\) 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 \(0.311750\pi\)
−0.557528 + 0.830158i \(0.688250\pi\)
\(312\) −32.8603 9.71807i −1.86035 0.550177i
\(313\) 1.22577 1.22577i 0.0692848 0.0692848i −0.671615 0.740900i \(-0.734399\pi\)
0.740900 + 0.671615i \(0.234399\pi\)
\(314\) 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 −0.817512 0.575911i \(-0.804647\pi\)
0.575911 + 0.817512i \(0.304647\pi\)
\(318\) 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 0.929700 0.368317i \(-0.120066\pi\)
−0.368317 + 0.929700i \(0.620066\pi\)
\(338\) −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 0.0325323 0.999471i \(-0.489643\pi\)
0.999471 0.0325323i \(-0.0103572\pi\)
\(348\) 19.6166 66.3310i 1.05156 3.55571i
\(349\) 30.1301i 1.61283i 0.591353 + 0.806413i \(0.298594\pi\)
−0.591353 + 0.806413i \(0.701406\pi\)
\(350\) 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 0.0893729 0.995998i \(-0.471514\pi\)
−0.995998 + 0.0893729i \(0.971514\pi\)
\(354\) 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 0.969073 + 0.246776i \(0.0793711\pi\)
0.246776 + 0.969073i \(0.420629\pi\)
\(368\) −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 −0.830485 0.557040i \(-0.811937\pi\)
0.557040 + 0.830485i \(0.311937\pi\)
\(374\) 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 \(0.0276961\pi\)
−0.996217 + 0.0869000i \(0.972304\pi\)
\(380\) −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 0.776561 0.630043i \(-0.216963\pi\)
−0.630043 + 0.776561i \(0.716963\pi\)
\(384\) −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 −0.971928 0.235280i \(-0.924399\pi\)
−0.235280 0.971928i \(-0.575601\pi\)
\(398\) 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 \(0.167275\pi\)
−0.865068 + 0.501654i \(0.832725\pi\)
\(402\) −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 \(-0.689202\pi\)
0.560008 0.828487i \(-0.310798\pi\)
\(410\) −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 \(-0.996558\pi\)
0.999942 0.0108139i \(-0.00344224\pi\)
\(432\) 23.9691 + 27.9899i 1.15321 + 1.34667i
\(433\) −17.7813 + 17.7813i −0.854517 + 0.854517i −0.990686 0.136169i \(-0.956521\pi\)
0.136169 + 0.990686i \(0.456521\pi\)
\(434\) 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 \(0.248909\pi\)
−0.709526 + 0.704679i \(0.751091\pi\)
\(440\) 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 0.232995 0.972478i \(-0.425147\pi\)
−0.972478 + 0.232995i \(0.925147\pi\)
\(444\) −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 0.0343811 0.999409i \(-0.489054\pi\)
−0.999409 + 0.0343811i \(0.989054\pi\)
\(458\) 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 \(0.115876\pi\)
−0.934468 + 0.356047i \(0.884124\pi\)
\(462\) −1.96110 + 6.63120i −0.0912388 + 0.308511i
\(463\) 0.492195 0.492195i 0.0228743 0.0228743i −0.695577 0.718451i \(-0.744851\pi\)
0.718451 + 0.695577i \(0.244851\pi\)
\(464\) 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 −0.883992 0.467501i \(-0.845154\pi\)
0.467501 + 0.883992i \(0.345154\pi\)
\(468\) −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 0.397051 0.917797i \(-0.370034\pi\)
−0.917797 + 0.397051i \(0.870034\pi\)
\(488\) 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 \(0.00216720\pi\)
−0.999977 + 0.00680841i \(0.997833\pi\)
\(492\) −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 \(0.149504\pi\)
−0.891713 + 0.452601i \(0.850496\pi\)
\(500\) −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 −0.997734 0.0672882i \(-0.978565\pi\)
−0.0672882 0.997734i \(-0.521435\pi\)
\(504\) 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 \(-0.773720\pi\)
0.757789 0.652500i \(-0.226280\pi\)
\(522\) 66.6018 14.2174i 2.91508 0.622279i
\(523\) 17.4673 17.4673i 0.763792 0.763792i −0.213214 0.977006i \(-0.568393\pi\)
0.977006 + 0.213214i \(0.0683931\pi\)
\(524\) −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 −0.994700 0.102823i \(-0.967213\pi\)
−0.102823 0.994700i \(-0.532787\pi\)
\(548\) 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 −0.894756 0.446556i \(-0.852650\pi\)
0.446556 + 0.894756i \(0.352650\pi\)
\(558\) −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 0.438460 0.898751i \(-0.355524\pi\)
−0.898751 + 0.438460i \(0.855524\pi\)
\(564\) 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 0.943432 0.331567i \(-0.107577\pi\)
−0.331567 + 0.943432i \(0.607577\pi\)
\(578\) 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 −0.598779 0.800915i \(-0.704347\pi\)
0.800915 + 0.598779i \(0.204347\pi\)
\(588\) −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 0.0709102 0.997483i \(-0.477410\pi\)
−0.997483 + 0.0709102i \(0.977410\pi\)
\(594\) 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 0.823355 0.567526i \(-0.192100\pi\)
−0.567526 + 0.823355i \(0.692100\pi\)
\(608\) −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 −0.805089 0.593154i \(-0.797883\pi\)
0.593154 + 0.805089i \(0.297883\pi\)
\(614\) 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 −0.748250 0.663417i \(-0.769105\pi\)
0.663417 + 0.748250i \(0.269105\pi\)
\(618\) −7.12596 + 24.0954i −0.286648 + 0.969261i
\(619\) 21.0734i 0.847012i 0.905893 + 0.423506i \(0.139201\pi\)
−0.905893 + 0.423506i \(0.860799\pi\)
\(620\) −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 \(-0.747335\pi\)
0.701161 0.713003i \(-0.252665\pi\)
\(642\) 4.98144 16.8441i 0.196602 0.664782i
\(643\) −21.0115 + 21.0115i −0.828614 + 0.828614i −0.987325 0.158711i \(-0.949266\pi\)
0.158711 + 0.987325i \(0.449266\pi\)
\(644\) −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 −0.230046 0.973180i \(-0.573888\pi\)
0.973180 + 0.230046i \(0.0738878\pi\)
\(648\) −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 0.905388 0.424585i \(-0.139580\pi\)
−0.424585 + 0.905388i \(0.639580\pi\)
\(654\) −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 −0.847320 0.531083i \(-0.821785\pi\)
0.531083 + 0.847320i \(0.321785\pi\)
\(674\) −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 0.313264 0.949666i \(-0.398578\pi\)
0.949666 0.313264i \(-0.101422\pi\)
\(678\) 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 −0.995481 0.0949562i \(-0.969729\pi\)
−0.0949562 0.995481i \(-0.530271\pi\)
\(684\) −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 \(0.0296646\pi\)
−0.995661 + 0.0930592i \(0.970335\pi\)
\(702\) 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 \(-0.895365\pi\)
0.946456 0.322833i \(-0.104635\pi\)
\(710\) 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 0.807037 0.590501i \(-0.201070\pi\)
−0.590501 + 0.807037i \(0.701070\pi\)
\(728\) −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 −0.409987 0.912091i \(-0.634467\pi\)
0.912091 + 0.409987i \(0.134467\pi\)
\(734\) −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 \(-0.909929\pi\)
0.960231 0.279205i \(-0.0900710\pi\)
\(740\) 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 −0.949729 0.313073i \(-0.898642\pi\)
−0.313073 0.949729i \(-0.601358\pi\)
\(744\) −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 0.672038 0.740516i \(-0.265419\pi\)
−0.740516 + 0.672038i \(0.765419\pi\)
\(758\) −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 \(0.223756\pi\)
−0.762938 + 0.646472i \(0.776244\pi\)
\(762\) 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 \(-0.806105\pi\)