Properties

Label 105.2.j.a.8.12
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 8.12
Character \(\chi\) = 105.8
Dual form 105.2.j.a.92.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.79963 + 1.79963i) q^{2} +(0.491204 - 1.66094i) q^{3} +4.47734i q^{4} +(-1.87996 - 1.21069i) q^{5} +(3.87306 - 2.10509i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-4.45829 + 4.45829i) q^{8} +(-2.51744 - 1.63172i) q^{9} +O(q^{10})\) \(q+(1.79963 + 1.79963i) q^{2} +(0.491204 - 1.66094i) 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} +(7.43658 + 2.19929i) q^{12} +(2.21881 + 2.21881i) q^{13} -2.54506 q^{14} +(-2.93432 + 2.52780i) q^{15} -7.09187 q^{16} +(-3.60725 - 3.60725i) q^{17} +(-1.59396 - 7.46695i) 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} +(-3.94676 + 3.37980i) q^{27} +(-3.16595 - 3.16595i) q^{28} +8.91955 q^{29} +(-9.82979 - 0.731595i) q^{30} +2.74834 q^{31} +(-3.84616 - 3.84616i) q^{32} +(-2.60552 - 0.770553i) 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} +(-1.25015 + 4.22719i) q^{42} +(-5.47734 - 5.47734i) q^{43} +7.02360 q^{44} +(2.75716 + 6.11539i) q^{45} -3.58432 q^{46} +(-3.69358 - 3.69358i) q^{47} +(-3.48356 + 11.7792i) 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} +(2.79104 + 0.825420i) q^{57} +(16.0519 + 16.0519i) q^{58} -5.54871 q^{59} +(-11.3178 - 13.1379i) q^{60} +7.40665 q^{61} +(4.94599 + 4.94599i) q^{62} +(2.93390 - 0.626296i) 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} +(18.4981 - 3.94878i) q^{72} +(-5.89737 - 5.89737i) q^{73} +1.58497 q^{74} +(8.57677 - 1.19960i) q^{75} -7.52372 q^{76} +(1.10924 + 1.10924i) q^{77} +(13.2644 + 3.92279i) 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} +(4.38132 - 14.8148i) q^{87} +(6.99372 + 6.99372i) q^{88} +9.40273 q^{89} +(-6.04357 + 15.9673i) q^{90} -3.13787 q^{91} +(-4.45876 - 4.45876i) q^{92} +(1.35000 - 4.56482i) 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 \(0.106299\pi\)
0.327775 + 0.944756i \(0.393701\pi\)
\(3\) 0.491204 1.66094i 0.283597 0.958944i
\(4\) 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 \(-0.0759973\pi\)
\(12\) 7.43658 + 2.19929i 2.14676 + 0.634880i
\(13\) 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
\(15\) −2.93432 + 2.52780i −0.757639 + 0.652674i
\(16\) −7.09187 −1.77297
\(17\) −3.60725 3.60725i −0.874886 0.874886i 0.118114 0.993000i \(-0.462315\pi\)
−0.993000 + 0.118114i \(0.962315\pi\)
\(18\) −1.59396 7.46695i −0.375700 1.75998i
\(19\) 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 −0.803268 0.595618i \(-0.796907\pi\)
0.595618 + 0.803268i \(0.296907\pi\)
\(24\) 5.21502 + 9.59488i 1.06451 + 1.95855i
\(25\) 2.06847 + 4.55208i 0.413694 + 0.910416i
\(26\) 7.98606i 1.56620i
\(27\) −3.94676 + 3.37980i −0.759555 + 0.650443i
\(28\) −3.16595 3.16595i −0.598309 0.598309i
\(29\) 8.91955 1.65632 0.828159 0.560493i \(-0.189388\pi\)
0.828159 + 0.560493i \(0.189388\pi\)
\(30\) −9.82979 0.731595i −1.79467 0.133570i
\(31\) 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
\(33\) −2.60552 0.770553i −0.453562 0.134136i
\(34\) 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 \(0.167810\pi\)
−0.864224 + 0.503108i \(0.832190\pi\)
\(42\) −1.25015 + 4.22719i −0.192902 + 0.652270i
\(43\) −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
\(45\) 2.75716 + 6.11539i 0.411014 + 0.911629i
\(46\) −3.58432 −0.528480
\(47\) −3.69358 3.69358i −0.538763 0.538763i 0.384402 0.923166i \(-0.374408\pi\)
−0.923166 + 0.384402i \(0.874408\pi\)
\(48\) −3.48356 + 11.7792i −0.502808 + 1.70018i
\(49\) 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 \(-0.838751\pi\)
0.485188 + 0.874410i \(0.338751\pi\)
\(54\) −13.1851 1.02033i −1.79427 0.138849i
\(55\) −1.89921 + 2.94909i −0.256089 + 0.397655i
\(56\) 6.30497i 0.842537i
\(57\) 2.79104 + 0.825420i 0.369683 + 0.109330i
\(58\) 16.0519 + 16.0519i 2.10772 + 2.10772i
\(59\) −5.54871 −0.722381 −0.361191 0.932492i \(-0.617630\pi\)
−0.361191 + 0.932492i \(0.617630\pi\)
\(60\) −11.3178 13.1379i −1.46112 1.69610i
\(61\) 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
\(63\) 2.93390 0.626296i 0.369636 0.0789058i
\(64\) 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 \(-0.931099\pi\)
0.976664 0.214774i \(-0.0689015\pi\)
\(72\) 18.4981 3.94878i 2.18003 0.465368i
\(73\) −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
\(75\) 8.57677 1.19960i 0.990360 0.138518i
\(76\) −7.52372 −0.863030
\(77\) 1.10924 + 1.10924i 0.126410 + 0.126410i
\(78\) 13.2644 + 3.92279i 1.50189 + 0.444168i
\(79\) 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 −0.861108 0.508422i \(-0.830229\pi\)
0.508422 + 0.861108i \(0.330229\pi\)
\(84\) −6.81359 + 3.70333i −0.743423 + 0.404066i
\(85\) 2.41421 + 11.1487i 0.261858 + 1.20925i
\(86\) 19.7144i 2.12585i
\(87\) 4.38132 14.8148i 0.469727 1.58832i
\(88\) 6.99372 + 6.99372i 0.745533 + 0.745533i
\(89\) 9.40273 0.996688 0.498344 0.866979i \(-0.333942\pi\)
0.498344 + 0.866979i \(0.333942\pi\)
\(90\) −6.04357 + 15.9673i −0.637048 + 1.68310i
\(91\) −3.13787 −0.328938
\(92\) −4.45876 4.45876i −0.464858 0.464858i
\(93\) 1.35000 4.56482i 0.139988 0.473350i
\(94\) 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 \(0.0160226\pi\)
−0.998733 + 0.0503152i \(0.983977\pi\)
\(102\) −21.5647 6.37751i −2.13522 0.631468i
\(103\) −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
\(105\) 0.287457 3.86230i 0.0280529 0.376922i
\(106\) −10.1988 −0.990593
\(107\) −2.81760 2.81760i −0.272388 0.272388i 0.557673 0.830061i \(-0.311694\pi\)
−0.830061 + 0.557673i \(0.811694\pi\)
\(108\) −15.1325 17.6710i −1.45613 1.70039i
\(109\) 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 −0.844804 0.535075i \(-0.820283\pi\)
0.535075 + 0.844804i \(0.320283\pi\)
\(114\) 3.53739 + 6.50830i 0.331307 + 0.609558i
\(115\) 3.07782 0.666490i 0.287008 0.0621505i
\(116\) 39.9358i 3.70795i
\(117\) −1.96523 9.20618i −0.181686 0.851112i
\(118\) −9.98563 9.98563i −0.919252 0.919252i
\(119\) 5.10142 0.467646
\(120\) 1.81241 24.3517i 0.165449 2.22300i
\(121\) 8.53918 0.776289
\(122\) 13.3292 + 13.3292i 1.20677 + 1.20677i
\(123\) 10.7013 + 3.16479i 0.964904 + 0.285360i
\(124\) 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 \(-0.931371\pi\)
0.976847 0.213939i \(-0.0686294\pi\)
\(132\) 3.45002 11.6658i 0.300286 1.01538i
\(133\) −1.18822 1.18822i −0.103032 0.103032i
\(134\) −13.5059 −1.16673
\(135\) 11.5116 1.57557i 0.990763 0.135604i
\(136\) 32.1643 2.75807
\(137\) 4.55880 + 4.55880i 0.389485 + 0.389485i 0.874504 0.485019i \(-0.161187\pi\)
−0.485019 + 0.874504i \(0.661187\pi\)
\(138\) −1.76064 + 5.95334i −0.149875 + 0.506782i
\(139\) 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
\(147\) −1.66094 0.491204i −0.136992 0.0405139i
\(148\) 1.97164 + 1.97164i 0.162068 + 0.162068i
\(149\) 0.923124 0.0756253 0.0378126 0.999285i \(-0.487961\pi\)
0.0378126 + 0.999285i \(0.487961\pi\)
\(150\) 17.5938 + 13.2762i 1.43653 + 1.08400i
\(151\) −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
\(153\) 3.19499 + 14.9670i 0.258300 + 1.21001i
\(154\) 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
\(162\) −8.17128 + 21.3985i −0.641997 + 1.68122i
\(163\) 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
\(165\) 3.96536 + 4.60307i 0.308703 + 0.358349i
\(166\) −11.5649 −0.897607
\(167\) 3.11442 + 3.11442i 0.241001 + 0.241001i 0.817264 0.576263i \(-0.195490\pi\)
−0.576263 + 0.817264i \(0.695490\pi\)
\(168\) −10.4722 3.09703i −0.807946 0.238941i
\(169\) 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 \(-0.893960\pi\)
0.327008 + 0.945022i \(0.393960\pi\)
\(174\) 34.5460 18.7764i 2.61892 1.42344i
\(175\) −4.68144 1.75618i −0.353883 0.132755i
\(176\) 11.1250i 0.838580i
\(177\) −2.72555 + 9.21608i −0.204865 + 0.692723i
\(178\) 16.9214 + 16.9214i 1.26832 + 1.26832i
\(179\) −16.5980 −1.24059 −0.620297 0.784367i \(-0.712988\pi\)
−0.620297 + 0.784367i \(0.712988\pi\)
\(180\) −27.3807 + 12.3448i −2.04084 + 0.920124i
\(181\) 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
\(183\) 3.63818 12.3020i 0.268942 0.909390i
\(184\) 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 \(0.846035\pi\)
\(192\) 0.565384 + 0.167206i 0.0408031 + 0.0120671i
\(193\) −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
\(195\) −12.1194 0.902001i −0.867887 0.0645936i
\(196\) 4.47734 0.319810
\(197\) 18.7512 + 18.7512i 1.33597 + 1.33597i 0.899929 + 0.436036i \(0.143618\pi\)
0.436036 + 0.899929i \(0.356382\pi\)
\(198\) −11.7134 + 2.50045i −0.832436 + 0.177699i
\(199\) 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
\(207\) 4.13194 0.882040i 0.287190 0.0613060i
\(208\) −15.7355 15.7355i −1.09106 1.09106i
\(209\) 2.63605 0.182339
\(210\) 7.46803 6.43340i 0.515343 0.443947i
\(211\) −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
\(213\) −6.01166 1.77788i −0.411912 0.121818i
\(214\) 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
\(222\) 0.778544 2.63254i 0.0522525 0.176684i
\(223\) 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
\(225\) 2.22049 14.8347i 0.148033 0.988982i
\(226\) −11.8504 −0.788279
\(227\) 8.70556 + 8.70556i 0.577809 + 0.577809i 0.934299 0.356490i \(-0.116027\pi\)
−0.356490 + 0.934299i \(0.616027\pi\)
\(228\) −3.69568 + 12.4964i −0.244753 + 0.827597i
\(229\) 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 −0.497735 0.867329i \(-0.665835\pi\)
0.867329 + 0.497735i \(0.165835\pi\)
\(234\) 13.0310 20.1044i 0.851865 1.31427i
\(235\) 2.47199 + 11.4155i 0.161255 + 0.744667i
\(236\) 24.8435i 1.61717i
\(237\) −28.3310 8.37859i −1.84030 0.544248i
\(238\) 9.18066 + 9.18066i 0.595094 + 0.595094i
\(239\) −11.8594 −0.767124 −0.383562 0.923515i \(-0.625303\pi\)
−0.383562 + 0.923515i \(0.625303\pi\)
\(240\) 20.8098 17.9268i 1.34327 1.15717i
\(241\) −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
\(243\) 15.4506 2.06841i 0.991158 0.132689i
\(244\) 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 \(-0.0321259\pi\)
\(252\) 2.80414 + 13.1360i 0.176644 + 0.827493i
\(253\) 1.56219 + 1.56219i 0.0982141 + 0.0982141i
\(254\) 51.4038 3.22536
\(255\) 19.7032 + 1.46644i 1.23386 + 0.0918318i
\(256\) −29.2108 −1.82567
\(257\) −11.8118 11.8118i −0.736799 0.736799i 0.235158 0.971957i \(-0.424439\pi\)
−0.971957 + 0.235158i \(0.924439\pi\)
\(258\) −32.7443 9.68378i −2.03857 0.602886i
\(259\) 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 \(-0.944366\pi\)
0.173891 + 0.984765i \(0.444366\pi\)
\(264\) 15.0515 8.18080i 0.926356 0.503493i
\(265\) 8.75757 1.89642i 0.537974 0.116496i
\(266\) 4.27672i 0.262223i
\(267\) 4.61866 15.6174i 0.282658 0.955767i
\(268\) −16.8008 16.8008i −1.02627 1.02627i
\(269\) 29.3405 1.78892 0.894461 0.447146i \(-0.147559\pi\)
0.894461 + 0.447146i \(0.147559\pi\)
\(270\) 23.5521 + 17.8812i 1.43334 + 1.08822i
\(271\) 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
\(273\) −1.54133 + 5.21181i −0.0932858 + 0.315433i
\(274\) 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 \(-0.734884\pi\)
0.672742 0.739877i \(-0.265116\pi\)
\(282\) −22.0808 6.53014i −1.31489 0.388864i
\(283\) 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
\(285\) −4.24771 4.93084i −0.251613 0.292078i
\(286\) 12.5277 0.740781
\(287\) −4.55583 4.55583i −0.268922 0.268922i
\(288\) 3.40661 + 15.9583i 0.200736 + 0.940354i
\(289\) 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 \(-0.865712\pi\)
0.409473 + 0.912322i \(0.365712\pi\)
\(294\) −2.10509 3.87306i −0.122771 0.225882i
\(295\) 10.4313 + 6.71776i 0.607336 + 0.391123i
\(296\) 3.92650i 0.228223i
\(297\) 5.30190 + 6.19129i 0.307647 + 0.359255i
\(298\) 1.66128 + 1.66128i 0.0962355 + 0.0962355i
\(299\) −4.41920 −0.255569
\(300\) 5.37100 + 38.4011i 0.310095 + 2.21709i
\(301\) 7.74612 0.446479
\(302\) −24.7107 24.7107i −1.42194 1.42194i
\(303\) 1.67975 + 0.496766i 0.0964989 + 0.0285385i
\(304\) 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 \(0.311750\pi\)
−0.557528 + 0.830158i \(0.688250\pi\)
\(312\) −9.71807 + 32.8603i −0.550177 + 1.86035i
\(313\) 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
\(315\) −6.27385 2.37463i −0.353491 0.133795i
\(316\) 76.3710 4.29620
\(317\) 4.30159 + 4.30159i 0.241601 + 0.241601i 0.817512 0.575911i \(-0.195353\pi\)
−0.575911 + 0.817512i \(0.695353\pi\)
\(318\) −5.00968 + 16.9395i −0.280929 + 0.949922i
\(319\) 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
\(327\) 10.6673 + 3.15474i 0.589904 + 0.174458i
\(328\) −28.7244 28.7244i −1.58604 1.58604i
\(329\) 5.22351 0.287981
\(330\) −1.14765 + 15.4200i −0.0631763 + 0.848843i
\(331\) 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
\(333\) −1.82712 + 0.390034i −0.100126 + 0.0213737i
\(334\) 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
\(342\) 12.5475 2.67849i 0.678489 0.144836i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 48.8391 2.63323
\(345\) 0.404838 5.43945i 0.0217958 0.292850i
\(346\) −29.2573 −1.57288
\(347\) −19.2241 19.2241i −1.03200 1.03200i −0.999471 0.0325323i \(-0.989643\pi\)
−0.0325323 0.999471i \(-0.510357\pi\)
\(348\) 66.3310 + 19.6166i 3.55571 + 1.05156i
\(349\) 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 −0.0893729 0.995998i \(-0.528486\pi\)
0.995998 + 0.0893729i \(0.0284863\pi\)
\(354\) −21.4905 + 11.6805i −1.14221 + 0.620814i
\(355\) −4.38201 + 6.80438i −0.232573 + 0.361139i
\(356\) 42.0992i 2.23125i
\(357\) 2.50584 8.47314i 0.132623 0.448446i
\(358\) −29.8703 29.8703i −1.57869 1.57869i
\(359\) −0.737982 −0.0389492 −0.0194746 0.999810i \(-0.506199\pi\)
−0.0194746 + 0.999810i \(0.506199\pi\)
\(360\) −39.5564 14.9720i −2.08481 0.789092i
\(361\) 16.1763 0.851382
\(362\) 20.9714 + 20.9714i 1.10223 + 1.10223i
\(363\) 4.19448 14.1831i 0.220153 0.744417i
\(364\) 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
\(372\) 20.4382 + 6.04438i 1.05967 + 0.313387i
\(373\) −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
\(375\) −17.5763 8.12860i −0.907635 0.419759i
\(376\) 32.9341 1.69844
\(377\) 19.7908 + 19.7908i 1.01928 + 1.01928i
\(378\) 10.0448 8.60180i 0.516647 0.442429i
\(379\) 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 −0.776561 0.630043i \(-0.783037\pi\)
0.630043 + 0.776561i \(0.283037\pi\)
\(384\) 9.71455 + 17.8734i 0.495744 + 0.912097i
\(385\) −0.742378 3.42826i −0.0378351 0.174721i
\(386\) 29.0157i 1.47686i
\(387\) 4.85136 + 22.7263i 0.246609 + 1.15524i
\(388\) 19.6841 + 19.6841i 0.999311 + 0.999311i
\(389\) 10.2102 0.517675 0.258838 0.965921i \(-0.416661\pi\)
0.258838 + 0.965921i \(0.416661\pi\)
\(390\) −20.1871 23.4337i −1.02222 1.18661i
\(391\) 7.18455 0.363339
\(392\) 4.45829 + 4.45829i 0.225178 + 0.225178i
\(393\) −8.13410 2.40557i −0.410311 0.121345i
\(394\) 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 \(0.167275\pi\)
−0.865068 + 0.501654i \(0.832725\pi\)
\(402\) −6.63414 + 22.4324i −0.330881 + 1.11883i
\(403\) 6.09803 + 6.09803i 0.303765 + 0.303765i
\(404\) −4.52803 −0.225278
\(405\) 3.03763 19.8940i 0.150941 0.988543i
\(406\) −22.7008 −1.12662
\(407\) −0.690793 0.690793i −0.0342413 0.0342413i
\(408\) 15.7992 53.4229i 0.782179 2.64483i
\(409\) 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
\(417\) 16.9491 + 5.01251i 0.830000 + 0.245463i
\(418\) 4.74391 + 4.74391i 0.232032 + 0.232032i
\(419\) −25.8773 −1.26419 −0.632093 0.774892i \(-0.717804\pi\)
−0.632093 + 0.774892i \(0.717804\pi\)
\(420\) 17.2928 + 1.28704i 0.843803 + 0.0628011i
\(421\) 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
\(423\) 3.27146 + 15.3252i 0.159064 + 0.745138i
\(424\) 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 \(-0.00344224\pi\)
\(432\) 27.9899 23.9691i 1.34667 1.15321i
\(433\) −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
\(435\) −26.1728 + 22.5468i −1.25489 + 1.08104i
\(436\) −28.7555 −1.37714
\(437\) −1.67343 1.67343i −0.0800509 0.0800509i
\(438\) −35.2554 10.4264i −1.68457 0.498192i
\(439\) 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 −0.232995 0.972478i \(-0.574853\pi\)
0.972478 + 0.232995i \(0.0748525\pi\)
\(444\) 4.24325 2.30630i 0.201376 0.109452i
\(445\) −17.6767 11.3838i −0.837957 0.539643i
\(446\) 44.6313i 2.11336i
\(447\) 0.453443 1.53325i 0.0214471 0.0725204i
\(448\) −0.240699 0.240699i −0.0113720 0.0113720i
\(449\) −16.3214 −0.770252 −0.385126 0.922864i \(-0.625842\pi\)
−0.385126 + 0.922864i \(0.625842\pi\)
\(450\) 30.6931 22.7010i 1.44689 1.07013i
\(451\) 10.1070 0.475921
\(452\) −14.7415 14.7415i −0.693380 0.693380i
\(453\) −6.74471 + 22.8063i −0.316894 + 1.07153i
\(454\) 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 \(0.115876\pi\)
−0.934468 + 0.356047i \(0.884124\pi\)
\(462\) 6.63120 + 1.96110i 0.308511 + 0.0912388i
\(463\) 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
\(465\) −8.06451 + 6.94724i −0.373983 + 0.322170i
\(466\) 20.3056 0.940640
\(467\) 9.00044 + 9.00044i 0.416491 + 0.416491i 0.883992 0.467501i \(-0.154846\pi\)
−0.467501 + 0.883992i \(0.654846\pi\)
\(468\) 41.2192 8.79901i 1.90536 0.406734i
\(469\) 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
\(477\) 11.7570 2.50974i 0.538314 0.114913i
\(478\) −21.3426 21.3426i −0.976188 0.976188i
\(479\) 22.7572 1.03980 0.519901 0.854226i \(-0.325969\pi\)
0.519901 + 0.854226i \(0.325969\pi\)
\(480\) 21.0082 + 1.56356i 0.958888 + 0.0713665i
\(481\) 1.95415 0.0891015
\(482\) −32.5235 32.5235i −1.48141 1.48141i
\(483\) −2.33917 0.691785i −0.106436 0.0314773i
\(484\) 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 \(0.00216720\pi\)
−0.999977 + 0.00680841i \(0.997833\pi\)
\(492\) −14.1698 + 47.9133i −0.638826 + 2.16010i
\(493\) −32.1750 32.1750i −1.44909 1.44909i
\(494\) −13.4198 −0.603785
\(495\) 9.59323 4.32517i 0.431183 0.194402i
\(496\) −19.4909 −0.875165
\(497\) 2.55933 + 2.55933i 0.114801 + 0.114801i
\(498\) −5.68071 + 19.2085i −0.254559 + 0.860754i
\(499\) 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 \(-0.478565\pi\)
0.997734 0.0672882i \(-0.0214347\pi\)
\(504\) −10.2880 + 15.8724i −0.458262 + 0.707012i
\(505\) 1.22440 1.90124i 0.0544850 0.0846042i
\(506\) 5.62273i 0.249961i
\(507\) −5.23825 1.54915i −0.232639 0.0688004i
\(508\) 63.9443 + 63.9443i 2.83707 + 2.83707i
\(509\) 11.7721 0.521788 0.260894 0.965368i \(-0.415983\pi\)
0.260894 + 0.965368i \(0.415983\pi\)
\(510\) 32.8194 + 38.0975i 1.45327 + 1.68699i
\(511\) 8.34014 0.368946
\(512\) −35.9587 35.9587i −1.58917 1.58917i
\(513\) −5.67942 6.63215i −0.250752 0.292816i
\(514\) 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 \(-0.226280\pi\)
\(522\) −14.2174 66.6018i −0.622279 2.91508i
\(523\) 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
\(525\) −5.21645 + 6.91293i −0.227664 + 0.301705i
\(526\) −47.3309 −2.06373
\(527\) −9.91393 9.91393i −0.431858 0.431858i
\(528\) 18.4780 + 5.46466i 0.804151 + 0.237819i
\(529\) 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
\(537\) −8.15302 + 27.5683i −0.351829 + 1.18966i
\(538\) 52.8021 + 52.8021i 2.27646 + 2.27646i
\(539\) −1.56870 −0.0675687
\(540\) 7.05437 + 51.5414i 0.303572 + 2.21799i
\(541\) −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
\(543\) 5.72409 19.3552i 0.245644 0.830612i
\(544\) 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
\(552\) −14.7484 4.36169i −0.627735 0.185646i
\(553\) 12.0613 + 12.0613i 0.512898 + 0.512898i
\(554\) 60.6965 2.57875
\(555\) −0.179017 + 2.40530i −0.00759886 + 0.102099i
\(556\) −45.6891 −1.93765
\(557\) 10.5779 + 10.5779i 0.448199 + 0.448199i 0.894756 0.446556i \(-0.147350\pi\)
−0.446556 + 0.894756i \(0.647350\pi\)
\(558\) −4.38074 20.5217i −0.185452 0.868753i
\(559\) 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 \(-0.644476\pi\)
0.898751 + 0.438460i \(0.144476\pi\)
\(564\) −19.3444 35.5908i −0.814544 1.49864i
\(565\) 10.1758 2.20354i 0.428100 0.0927036i
\(566\) 19.5050i 0.819858i
\(567\) −8.40784 3.21064i −0.353096 0.134834i
\(568\) 16.1365 + 16.1365i 0.677072 + 0.677072i
\(569\) −42.0710 −1.76371 −0.881854 0.471523i \(-0.843705\pi\)
−0.881854 + 0.471523i \(0.843705\pi\)
\(570\) 1.22937 16.5180i 0.0514927 0.691863i
\(571\) 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
\(573\) 21.3503 + 6.31411i 0.891921 + 0.263776i
\(574\) 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
\(582\) 7.77271 26.2823i 0.322189 1.08944i
\(583\) 4.44503 + 4.44503i 0.184094 + 0.184094i
\(584\) 52.5844 2.17596
\(585\) −7.45126 + 19.6865i −0.308072 + 0.813936i
\(586\) −30.9802 −1.27978
\(587\) −4.89737 4.89737i −0.202136 0.202136i 0.598779 0.800915i \(-0.295653\pi\)
−0.800915 + 0.598779i \(0.795653\pi\)
\(588\) 2.19929 7.43658i 0.0906971 0.306680i
\(589\) 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 \(-0.522590\pi\)
0.997483 + 0.0709102i \(0.0225904\pi\)
\(594\) −1.60059 + 20.6835i −0.0656729 + 0.848654i
\(595\) −9.59044 6.17623i −0.393170 0.253201i
\(596\) 4.13314i 0.169300i
\(597\) 6.98804 + 2.06664i 0.286002 + 0.0845818i
\(598\) −7.95292 7.95292i −0.325219 0.325219i
\(599\) −6.81971 −0.278646 −0.139323 0.990247i \(-0.544493\pi\)
−0.139323 + 0.990247i \(0.544493\pi\)
\(600\) −32.8896 + 43.5859i −1.34271 + 1.77939i
\(601\) −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
\(603\) 15.5693 3.32356i 0.634031 0.135346i
\(604\) 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
\(612\) −67.0125 + 14.3051i −2.70882 + 0.578248i
\(613\) −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
\(615\) −16.2864 18.9056i −0.656731 0.762348i
\(616\) −9.89062 −0.398504
\(617\) 2.10719 + 2.10719i 0.0848323 + 0.0848323i 0.748250 0.663417i \(-0.230895\pi\)
−0.663417 + 0.748250i \(0.730895\pi\)
\(618\) −24.0954 7.12596i −0.969261 0.286648i
\(619\) 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
\(627\) 1.29484 4.37831i 0.0517108 0.174853i
\(628\) −61.4341 61.4341i −2.45149 2.45149i
\(629\) −3.17697 −0.126674
\(630\) −7.01715 15.5641i −0.279570 0.620087i
\(631\) −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
\(633\) −10.5713 + 35.7453i −0.420170 + 1.42075i
\(634\) 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 \(-0.252665\pi\)
\(642\) −16.8441 4.98144i −0.664782 0.196602i
\(643\) −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
\(645\) 29.9179 + 2.22667i 1.17801 + 0.0876752i
\(646\) 21.8173 0.858392
\(647\) −18.9025 18.9025i −0.743133 0.743133i 0.230046 0.973180i \(-0.426112\pi\)
−0.973180 + 0.230046i \(0.926112\pi\)
\(648\) −53.0112 20.2430i −2.08248 0.795221i
\(649\) 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 \(-0.860420\pi\)
0.424585 + 0.905388i \(0.360420\pi\)
\(654\) 13.5199 + 24.8746i 0.528668 + 0.972674i
\(655\) −5.92909 + 9.20669i −0.231669 + 0.359735i
\(656\) 45.6924i 1.78399i
\(657\) 5.22339 + 24.4691i 0.203784 + 0.954631i
\(658\) 9.40038 + 9.40038i 0.366465 + 0.366465i
\(659\) −0.708622 −0.0276040 −0.0138020 0.999905i \(-0.504393\pi\)
−0.0138020 + 0.999905i \(0.504393\pi\)
\(660\) −20.6095 + 17.7542i −0.802224 + 0.691083i
\(661\) 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
\(663\) −26.5876 7.86299i −1.03258 0.305373i
\(664\) 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
\(672\) 2.67181 9.03434i 0.103067 0.348507i
\(673\) −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
\(675\) −23.5489 10.9750i −0.906397 0.422427i
\(676\) 14.1206 0.543099
\(677\) −32.8605 32.8605i −1.26293 1.26293i −0.949666 0.313264i \(-0.898578\pi\)
−0.313264 0.949666i \(-0.601422\pi\)
\(678\) −5.82098 + 19.6828i −0.223554 + 0.755915i
\(679\) 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 \(-0.469729\pi\)
0.995481 0.0949562i \(-0.0302711\pi\)
\(684\) 18.9405 + 12.2766i 0.724208 + 0.469408i
\(685\) −3.05106 14.0896i −0.116575 0.538338i
\(686\) 2.54506i 0.0971709i
\(687\) 7.41347 + 2.19245i 0.282842 + 0.0836473i
\(688\) 38.8446 + 38.8446i 1.48093 + 1.48093i
\(689\) −12.5743 −0.479043
\(690\) 10.5176 9.06044i 0.400397 0.344925i
\(691\) 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
\(693\) −0.982471 4.60241i −0.0373210 0.174831i
\(694\) 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 \(0.970335\pi\)
\(702\) −26.9913 31.5191i −1.01872 1.18961i
\(703\) 0.739981 + 0.739981i 0.0279089 + 0.0279089i
\(704\) 0.533986 0.0201254
\(705\) 20.1748 + 1.50153i 0.759825 + 0.0565509i
\(706\) 61.3096 2.30742
\(707\) −0.715113 0.715113i −0.0268946 0.0268946i
\(708\) −41.2635 12.2032i −1.55078 0.458625i
\(709\) 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
\(717\) −5.82541 + 19.6978i −0.217554 + 0.735628i
\(718\) −1.32809 1.32809i −0.0495640 0.0495640i
\(719\) −12.2556 −0.457059 −0.228529 0.973537i \(-0.573392\pi\)
−0.228529 + 0.973537i \(0.573392\pi\)
\(720\) −19.5534 43.3696i −0.728714 1.61629i
\(721\) 5.70011 0.212283
\(722\) 29.1113 + 29.1113i 1.08341 + 1.08341i
\(723\) −8.87721 + 30.0170i −0.330147 + 1.11635i
\(724\) 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
\(732\) 55.0802 + 16.2894i 2.03582 + 0.602072i
\(733\) 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
\(735\) 2.52780 + 2.93432i 0.0932392 + 0.108234i
\(736\) 7.66040 0.282366
\(737\) 5.88639 + 5.88639i 0.216828 + 0.216828i
\(738\) 48.1090 10.2698i 1.77092 0.378035i
\(739\) 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 \(-0.398642\pi\)
0.949729 0.313073i \(-0.101358\pi\)
\(744\) 14.3326 + 26.3700i 0.525459 + 0.966770i
\(745\) −1.73543 1.11762i −0.0635813 0.0409463i
\(746\) 19.0080i 0.695934i
\(747\) 13.3317 2.84591i 0.487783 0.104126i
\(748\) −25.3359 25.3359i −0.926371 0.926371i
\(749\) 3.98469 0.145597
\(750\) −17.0023 46.2593i −0.620837 1.68915i
\(751\) −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
\(753\) −5.30260 1.56818i −0.193237 0.0571478i
\(754\) 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 \(0.223756\pi\)
−0.762938 + 0.646472i \(0.776244\pi\)
\(762\) 25.2498 85.3786i 0.914703 3.09294i
\(763\) −4.54137 4.54137i −0.164409 0.164409i
\(764\) −57.5532 −2.08220
\(765\) 12.1140 32.0055i 0.437981 1.15716i
\(766\) −10.3206 −0.372897
\(767\) −12.3115 12.3115i −0.444543 0.444543i
\(768\) −14.3485 + 48.5173i −0.517755 + 1.75072i
\(769\) 31.7331i 1.14432i 0.820141 + 0.572162i \(0.193895\pi\)
−0.820141