Properties

Label 750.2.l.b.143.7
Level $750$
Weight $2$
Character 750.143
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 143.7
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.b.257.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.453990 - 0.891007i) q^{2} +(-1.32853 - 1.11131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(-2.03922 + 2.03922i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(0.529988 + 2.95281i) q^{9} +O(q^{10})\) \(q+(0.453990 - 0.891007i) q^{2} +(-1.32853 - 1.11131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(-2.03922 + 2.03922i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(0.529988 + 2.95281i) q^{9} +(-2.60836 + 0.847507i) q^{11} +(-0.118176 + 1.72801i) q^{12} +(5.27002 - 2.68521i) q^{13} +(0.891173 + 2.74275i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.936136 + 5.91053i) q^{17} +(2.87159 + 0.868327i) q^{18} +(-3.04743 + 4.19443i) q^{19} +(4.97538 - 0.442965i) q^{21} +(-0.429036 + 2.70883i) q^{22} +(-1.01194 - 0.515607i) q^{23} +(1.48602 + 0.889798i) q^{24} -5.91469i q^{26} +(2.57738 - 4.51188i) q^{27} +(2.84839 + 0.451141i) q^{28} +(2.34612 - 1.70456i) q^{29} +(4.56563 + 3.31712i) q^{31} +(0.707107 + 0.707107i) q^{32} +(4.40713 + 1.77275i) q^{33} +(5.69132 + 1.84922i) q^{34} +(2.07736 - 2.16439i) q^{36} +(3.66336 + 7.18975i) q^{37} +(2.35376 + 4.61952i) q^{38} +(-9.98549 - 2.28924i) q^{39} +(-5.02666 - 1.63326i) q^{41} +(1.86409 - 4.63420i) q^{42} +(3.10789 + 3.10789i) q^{43} +(2.21880 + 1.61205i) q^{44} +(-0.918819 + 0.667561i) q^{46} +(-4.58484 - 0.726167i) q^{47} +(1.46746 - 0.920095i) q^{48} -1.31687i q^{49} +(5.32473 - 8.89266i) q^{51} +(-5.27002 - 2.68521i) q^{52} +(0.837944 - 5.29057i) q^{53} +(-2.85001 - 4.34482i) q^{54} +(1.69511 - 2.33312i) q^{56} +(8.70992 - 2.18579i) q^{57} +(-0.453655 - 2.86426i) q^{58} +(-0.912145 + 2.80729i) q^{59} +(-1.41844 - 4.36552i) q^{61} +(5.02833 - 2.56206i) q^{62} +(-7.10221 - 4.94069i) q^{63} +(0.951057 - 0.309017i) q^{64} +(3.58033 - 3.12197i) q^{66} +(0.455818 - 0.0721944i) q^{67} +(4.23147 - 4.23147i) q^{68} +(0.771390 + 1.80957i) q^{69} +(3.36294 + 4.62869i) q^{71} +(-0.985385 - 2.83355i) q^{72} +(-4.12620 + 8.09812i) q^{73} +8.06924 q^{74} +5.18460 q^{76} +(3.59077 - 7.04728i) q^{77} +(-6.57304 + 7.85784i) q^{78} +(6.90557 + 9.50470i) q^{79} +(-8.43823 + 3.12991i) q^{81} +(-3.73730 + 3.73730i) q^{82} +(-11.9275 + 1.88912i) q^{83} +(-3.28282 - 3.76480i) q^{84} +(4.18011 - 1.35820i) q^{86} +(-5.01118 - 0.342708i) q^{87} +(2.44367 - 1.24511i) q^{88} +(0.402182 + 1.23779i) q^{89} +(-5.27101 + 16.2225i) q^{91} +(0.177666 + 1.12174i) q^{92} +(-2.37923 - 9.48072i) q^{93} +(-2.72849 + 3.75545i) q^{94} +(-0.153600 - 1.72523i) q^{96} +(-1.03381 + 6.52722i) q^{97} +(-1.17334 - 0.597845i) q^{98} +(-3.88493 - 7.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{3} - 4q^{7} + O(q^{10}) \) \( 80q - 4q^{3} - 4q^{7} + 4q^{12} + 20q^{16} + 8q^{18} - 40q^{19} + 36q^{22} - 4q^{27} + 16q^{28} - 4q^{33} - 40q^{34} + 24q^{37} - 40q^{39} + 4q^{42} + 24q^{43} + 4q^{48} + 64q^{57} - 20q^{58} - 64q^{63} - 96q^{67} + 140q^{69} - 8q^{72} - 100q^{73} - 100q^{78} + 80q^{79} - 40q^{81} - 96q^{82} + 60q^{84} - 80q^{87} - 4q^{88} - 12q^{93} + 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.453990 0.891007i 0.321020 0.630037i
\(3\) −1.32853 1.11131i −0.767028 0.641614i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) −1.59332 + 0.679206i −0.650471 + 0.277285i
\(7\) −2.03922 + 2.03922i −0.770754 + 0.770754i −0.978238 0.207484i \(-0.933472\pi\)
0.207484 + 0.978238i \(0.433472\pi\)
\(8\) −0.987688 + 0.156434i −0.349201 + 0.0553079i
\(9\) 0.529988 + 2.95281i 0.176663 + 0.984271i
\(10\) 0 0
\(11\) −2.60836 + 0.847507i −0.786450 + 0.255533i −0.674592 0.738191i \(-0.735680\pi\)
−0.111858 + 0.993724i \(0.535680\pi\)
\(12\) −0.118176 + 1.72801i −0.0341146 + 0.498835i
\(13\) 5.27002 2.68521i 1.46164 0.744744i 0.471116 0.882071i \(-0.343851\pi\)
0.990526 + 0.137328i \(0.0438513\pi\)
\(14\) 0.891173 + 2.74275i 0.238176 + 0.733031i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 0.936136 + 5.91053i 0.227046 + 1.43351i 0.793073 + 0.609127i \(0.208480\pi\)
−0.566026 + 0.824387i \(0.691520\pi\)
\(18\) 2.87159 + 0.868327i 0.676839 + 0.204667i
\(19\) −3.04743 + 4.19443i −0.699129 + 0.962269i 0.300834 + 0.953677i \(0.402735\pi\)
−0.999963 + 0.00859233i \(0.997265\pi\)
\(20\) 0 0
\(21\) 4.97538 0.442965i 1.08572 0.0966630i
\(22\) −0.429036 + 2.70883i −0.0914707 + 0.577523i
\(23\) −1.01194 0.515607i −0.211003 0.107512i 0.345295 0.938494i \(-0.387779\pi\)
−0.556298 + 0.830983i \(0.687779\pi\)
\(24\) 1.48602 + 0.889798i 0.303333 + 0.181629i
\(25\) 0 0
\(26\) 5.91469i 1.15997i
\(27\) 2.57738 4.51188i 0.496017 0.868313i
\(28\) 2.84839 + 0.451141i 0.538296 + 0.0852576i
\(29\) 2.34612 1.70456i 0.435664 0.316528i −0.348246 0.937403i \(-0.613223\pi\)
0.783910 + 0.620875i \(0.213223\pi\)
\(30\) 0 0
\(31\) 4.56563 + 3.31712i 0.820011 + 0.595773i 0.916716 0.399540i \(-0.130830\pi\)
−0.0967046 + 0.995313i \(0.530830\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 4.40713 + 1.77275i 0.767182 + 0.308596i
\(34\) 5.69132 + 1.84922i 0.976053 + 0.317139i
\(35\) 0 0
\(36\) 2.07736 2.16439i 0.346226 0.360732i
\(37\) 3.66336 + 7.18975i 0.602253 + 1.18199i 0.967924 + 0.251243i \(0.0808395\pi\)
−0.365671 + 0.930744i \(0.619161\pi\)
\(38\) 2.35376 + 4.61952i 0.381830 + 0.749384i
\(39\) −9.98549 2.28924i −1.59896 0.366571i
\(40\) 0 0
\(41\) −5.02666 1.63326i −0.785033 0.255073i −0.111045 0.993815i \(-0.535420\pi\)
−0.673988 + 0.738743i \(0.735420\pi\)
\(42\) 1.86409 4.63420i 0.287635 0.715072i
\(43\) 3.10789 + 3.10789i 0.473950 + 0.473950i 0.903190 0.429241i \(-0.141219\pi\)
−0.429241 + 0.903190i \(0.641219\pi\)
\(44\) 2.21880 + 1.61205i 0.334497 + 0.243026i
\(45\) 0 0
\(46\) −0.918819 + 0.667561i −0.135473 + 0.0984265i
\(47\) −4.58484 0.726167i −0.668768 0.105922i −0.187187 0.982324i \(-0.559937\pi\)
−0.481581 + 0.876402i \(0.659937\pi\)
\(48\) 1.46746 0.920095i 0.211809 0.132804i
\(49\) 1.31687i 0.188124i
\(50\) 0 0
\(51\) 5.32473 8.89266i 0.745612 1.24522i
\(52\) −5.27002 2.68521i −0.730821 0.372372i
\(53\) 0.837944 5.29057i 0.115100 0.726715i −0.860872 0.508821i \(-0.830081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(54\) −2.85001 4.34482i −0.387837 0.591255i
\(55\) 0 0
\(56\) 1.69511 2.33312i 0.226519 0.311777i
\(57\) 8.70992 2.18579i 1.15366 0.289516i
\(58\) −0.453655 2.86426i −0.0595678 0.376096i
\(59\) −0.912145 + 2.80729i −0.118751 + 0.365478i −0.992711 0.120520i \(-0.961544\pi\)
0.873960 + 0.485998i \(0.161544\pi\)
\(60\) 0 0
\(61\) −1.41844 4.36552i −0.181613 0.558947i 0.818261 0.574847i \(-0.194939\pi\)
−0.999874 + 0.0159002i \(0.994939\pi\)
\(62\) 5.02833 2.56206i 0.638599 0.325382i
\(63\) −7.10221 4.94069i −0.894795 0.622468i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) 3.58033 3.12197i 0.440708 0.384287i
\(67\) 0.455818 0.0721944i 0.0556870 0.00881995i −0.128529 0.991706i \(-0.541025\pi\)
0.184216 + 0.982886i \(0.441025\pi\)
\(68\) 4.23147 4.23147i 0.513141 0.513141i
\(69\) 0.771390 + 1.80957i 0.0928645 + 0.217847i
\(70\) 0 0
\(71\) 3.36294 + 4.62869i 0.399107 + 0.549324i 0.960520 0.278212i \(-0.0897418\pi\)
−0.561412 + 0.827536i \(0.689742\pi\)
\(72\) −0.985385 2.83355i −0.116129 0.333937i
\(73\) −4.12620 + 8.09812i −0.482935 + 0.947814i 0.513055 + 0.858356i \(0.328514\pi\)
−0.995991 + 0.0894583i \(0.971486\pi\)
\(74\) 8.06924 0.938031
\(75\) 0 0
\(76\) 5.18460 0.594715
\(77\) 3.59077 7.04728i 0.409206 0.803113i
\(78\) −6.57304 + 7.85784i −0.744250 + 0.889725i
\(79\) 6.90557 + 9.50470i 0.776937 + 1.06936i 0.995613 + 0.0935650i \(0.0298263\pi\)
−0.218676 + 0.975798i \(0.570174\pi\)
\(80\) 0 0
\(81\) −8.43823 + 3.12991i −0.937581 + 0.347768i
\(82\) −3.73730 + 3.73730i −0.412716 + 0.412716i
\(83\) −11.9275 + 1.88912i −1.30921 + 0.207358i −0.771747 0.635930i \(-0.780617\pi\)
−0.537462 + 0.843288i \(0.680617\pi\)
\(84\) −3.28282 3.76480i −0.358185 0.410773i
\(85\) 0 0
\(86\) 4.18011 1.35820i 0.450753 0.146458i
\(87\) −5.01118 0.342708i −0.537255 0.0367421i
\(88\) 2.44367 1.24511i 0.260496 0.132729i
\(89\) 0.402182 + 1.23779i 0.0426312 + 0.131205i 0.970107 0.242678i \(-0.0780260\pi\)
−0.927476 + 0.373884i \(0.878026\pi\)
\(90\) 0 0
\(91\) −5.27101 + 16.2225i −0.552552 + 1.70058i
\(92\) 0.177666 + 1.12174i 0.0185230 + 0.116950i
\(93\) −2.37923 9.48072i −0.246715 0.983105i
\(94\) −2.72849 + 3.75545i −0.281423 + 0.387345i
\(95\) 0 0
\(96\) −0.153600 1.72523i −0.0156767 0.176080i
\(97\) −1.03381 + 6.52722i −0.104967 + 0.662738i 0.877959 + 0.478737i \(0.158905\pi\)
−0.982926 + 0.184002i \(0.941095\pi\)
\(98\) −1.17334 0.597845i −0.118525 0.0603915i
\(99\) −3.88493 7.25283i −0.390450 0.728937i
\(100\) 0 0
\(101\) 3.52971i 0.351219i 0.984460 + 0.175610i \(0.0561896\pi\)
−0.984460 + 0.175610i \(0.943810\pi\)
\(102\) −5.50604 8.78155i −0.545179 0.869503i
\(103\) 6.37316 + 1.00941i 0.627966 + 0.0994601i 0.462303 0.886722i \(-0.347023\pi\)
0.165664 + 0.986182i \(0.447023\pi\)
\(104\) −4.78508 + 3.47657i −0.469216 + 0.340905i
\(105\) 0 0
\(106\) −4.33351 3.14848i −0.420908 0.305807i
\(107\) 8.76915 + 8.76915i 0.847745 + 0.847745i 0.989851 0.142106i \(-0.0453874\pi\)
−0.142106 + 0.989851i \(0.545387\pi\)
\(108\) −5.16514 + 0.566874i −0.497016 + 0.0545474i
\(109\) 2.65577 + 0.862912i 0.254377 + 0.0826520i 0.433430 0.901187i \(-0.357303\pi\)
−0.179053 + 0.983839i \(0.557303\pi\)
\(110\) 0 0
\(111\) 3.12314 13.6229i 0.296435 1.29303i
\(112\) −1.30926 2.56957i −0.123714 0.242802i
\(113\) −2.09855 4.11863i −0.197415 0.387449i 0.770984 0.636854i \(-0.219765\pi\)
−0.968399 + 0.249406i \(0.919765\pi\)
\(114\) 2.00666 8.75292i 0.187941 0.819786i
\(115\) 0 0
\(116\) −2.75803 0.896139i −0.256077 0.0832044i
\(117\) 10.7220 + 14.1383i 0.991247 + 1.30708i
\(118\) 2.08721 + 2.08721i 0.192143 + 0.192143i
\(119\) −13.9619 10.1439i −1.27988 0.929890i
\(120\) 0 0
\(121\) −2.81392 + 2.04443i −0.255811 + 0.185857i
\(122\) −4.53366 0.718062i −0.410459 0.0650103i
\(123\) 4.86302 + 7.75601i 0.438484 + 0.699336i
\(124\) 5.64343i 0.506795i
\(125\) 0 0
\(126\) −7.62652 + 4.08509i −0.679424 + 0.363929i
\(127\) −11.1643 5.68850i −0.990672 0.504773i −0.117966 0.993018i \(-0.537637\pi\)
−0.872707 + 0.488245i \(0.837637\pi\)
\(128\) 0.156434 0.987688i 0.0138270 0.0873001i
\(129\) −0.675105 7.58276i −0.0594397 0.667625i
\(130\) 0 0
\(131\) −7.00579 + 9.64264i −0.612099 + 0.842482i −0.996748 0.0805811i \(-0.974322\pi\)
0.384649 + 0.923063i \(0.374322\pi\)
\(132\) −1.15626 4.60744i −0.100639 0.401026i
\(133\) −2.33899 14.7678i −0.202816 1.28053i
\(134\) 0.142611 0.438912i 0.0123197 0.0379162i
\(135\) 0 0
\(136\) −1.84922 5.69132i −0.158569 0.488026i
\(137\) −17.7044 + 9.02083i −1.51259 + 0.770702i −0.996319 0.0857255i \(-0.972679\pi\)
−0.516268 + 0.856427i \(0.672679\pi\)
\(138\) 1.96255 + 0.134216i 0.167063 + 0.0114252i
\(139\) 9.07922 2.95002i 0.770090 0.250217i 0.102486 0.994734i \(-0.467320\pi\)
0.667603 + 0.744517i \(0.267320\pi\)
\(140\) 0 0
\(141\) 5.28411 + 6.05991i 0.445002 + 0.510336i
\(142\) 5.65093 0.895020i 0.474216 0.0751084i
\(143\) −11.4704 + 11.4704i −0.959201 + 0.959201i
\(144\) −2.97207 0.408421i −0.247672 0.0340351i
\(145\) 0 0
\(146\) 5.34223 + 7.35294i 0.442126 + 0.608534i
\(147\) −1.46344 + 1.74950i −0.120703 + 0.144296i
\(148\) 3.66336 7.18975i 0.301126 0.590994i
\(149\) −12.0089 −0.983807 −0.491903 0.870650i \(-0.663699\pi\)
−0.491903 + 0.870650i \(0.663699\pi\)
\(150\) 0 0
\(151\) −11.1277 −0.905558 −0.452779 0.891623i \(-0.649567\pi\)
−0.452779 + 0.891623i \(0.649567\pi\)
\(152\) 2.35376 4.61952i 0.190915 0.374692i
\(153\) −16.9566 + 5.89674i −1.37086 + 0.476724i
\(154\) −4.64900 6.39880i −0.374627 0.515630i
\(155\) 0 0
\(156\) 4.01729 + 9.42401i 0.321641 + 0.754524i
\(157\) 11.6119 11.6119i 0.926732 0.926732i −0.0707617 0.997493i \(-0.522543\pi\)
0.997493 + 0.0707617i \(0.0225430\pi\)
\(158\) 11.6038 1.83786i 0.923150 0.146213i
\(159\) −6.99269 + 6.09747i −0.554556 + 0.483561i
\(160\) 0 0
\(161\) 3.11500 1.01213i 0.245497 0.0797667i
\(162\) −1.04210 + 8.93946i −0.0818753 + 0.702351i
\(163\) −5.83680 + 2.97400i −0.457173 + 0.232941i −0.667383 0.744715i \(-0.732585\pi\)
0.210209 + 0.977656i \(0.432585\pi\)
\(164\) 1.63326 + 5.02666i 0.127536 + 0.392516i
\(165\) 0 0
\(166\) −3.73173 + 11.4851i −0.289639 + 0.891416i
\(167\) −2.65903 16.7884i −0.205762 1.29913i −0.846920 0.531720i \(-0.821546\pi\)
0.641159 0.767408i \(-0.278454\pi\)
\(168\) −4.84483 + 1.21583i −0.373787 + 0.0938035i
\(169\) 12.9216 17.7850i 0.993968 1.36808i
\(170\) 0 0
\(171\) −14.0005 6.77551i −1.07064 0.518136i
\(172\) 0.687565 4.34111i 0.0524263 0.331007i
\(173\) 6.04954 + 3.08240i 0.459938 + 0.234350i 0.668578 0.743642i \(-0.266903\pi\)
−0.208639 + 0.977993i \(0.566903\pi\)
\(174\) −2.58038 + 4.30941i −0.195618 + 0.326696i
\(175\) 0 0
\(176\) 2.74259i 0.206731i
\(177\) 4.33158 2.71590i 0.325581 0.204140i
\(178\) 1.28546 + 0.203597i 0.0963496 + 0.0152603i
\(179\) 7.59016 5.51457i 0.567315 0.412179i −0.266814 0.963748i \(-0.585971\pi\)
0.834129 + 0.551569i \(0.185971\pi\)
\(180\) 0 0
\(181\) 12.3025 + 8.93831i 0.914440 + 0.664379i 0.942134 0.335237i \(-0.108816\pi\)
−0.0276940 + 0.999616i \(0.508816\pi\)
\(182\) 12.0614 + 12.0614i 0.894048 + 0.894048i
\(183\) −2.96699 + 7.37605i −0.219326 + 0.545253i
\(184\) 1.08014 + 0.350958i 0.0796287 + 0.0258729i
\(185\) 0 0
\(186\) −9.52753 2.18425i −0.698593 0.160157i
\(187\) −7.45099 14.6234i −0.544871 1.06937i
\(188\) 2.10742 + 4.13604i 0.153699 + 0.301652i
\(189\) 3.94488 + 14.4566i 0.286948 + 1.05156i
\(190\) 0 0
\(191\) −12.2756 3.98859i −0.888232 0.288604i −0.170861 0.985295i \(-0.554655\pi\)
−0.717371 + 0.696691i \(0.754655\pi\)
\(192\) −1.60692 0.646378i −0.115970 0.0466483i
\(193\) −3.91447 3.91447i −0.281770 0.281770i 0.552045 0.833815i \(-0.313848\pi\)
−0.833815 + 0.552045i \(0.813848\pi\)
\(194\) 5.34645 + 3.88442i 0.383853 + 0.278885i
\(195\) 0 0
\(196\) −1.06537 + 0.774035i −0.0760977 + 0.0552882i
\(197\) −25.2645 4.00150i −1.80002 0.285095i −0.835574 0.549378i \(-0.814865\pi\)
−0.964445 + 0.264282i \(0.914865\pi\)
\(198\) −8.22604 + 0.168782i −0.584599 + 0.0119948i
\(199\) 0.0768328i 0.00544653i −0.999996 0.00272327i \(-0.999133\pi\)
0.999996 0.00272327i \(-0.000866844\pi\)
\(200\) 0 0
\(201\) −0.685798 0.410641i −0.0483725 0.0289644i
\(202\) 3.14499 + 1.60245i 0.221281 + 0.112748i
\(203\) −1.30829 + 8.26024i −0.0918242 + 0.579755i
\(204\) −10.3241 + 0.919171i −0.722832 + 0.0643548i
\(205\) 0 0
\(206\) 3.79275 5.22027i 0.264253 0.363713i
\(207\) 0.986179 3.26133i 0.0685442 0.226678i
\(208\) 0.925261 + 5.84187i 0.0641553 + 0.405061i
\(209\) 4.39399 13.5233i 0.303939 0.935427i
\(210\) 0 0
\(211\) 1.99342 + 6.13511i 0.137232 + 0.422358i 0.995931 0.0901236i \(-0.0287262\pi\)
−0.858698 + 0.512482i \(0.828726\pi\)
\(212\) −4.77269 + 2.43181i −0.327790 + 0.167017i
\(213\) 0.676131 9.88661i 0.0463278 0.677420i
\(214\) 11.7945 3.83226i 0.806254 0.261968i
\(215\) 0 0
\(216\) −1.83984 + 4.85953i −0.125185 + 0.330649i
\(217\) −16.0747 + 2.54598i −1.09122 + 0.172832i
\(218\) 1.97456 1.97456i 0.133734 0.133734i
\(219\) 14.4813 6.17313i 0.978555 0.417141i
\(220\) 0 0
\(221\) 20.8045 + 28.6349i 1.39946 + 1.92619i
\(222\) −10.7202 8.96742i −0.719495 0.601854i
\(223\) 2.46937 4.84642i 0.165362 0.324540i −0.793425 0.608668i \(-0.791704\pi\)
0.958786 + 0.284128i \(0.0917040\pi\)
\(224\) −2.88390 −0.192689
\(225\) 0 0
\(226\) −4.62245 −0.307481
\(227\) 8.90823 17.4834i 0.591260 1.16041i −0.380575 0.924750i \(-0.624274\pi\)
0.971835 0.235662i \(-0.0757260\pi\)
\(228\) −6.88791 5.76169i −0.456163 0.381577i
\(229\) 10.2833 + 14.1538i 0.679543 + 0.935310i 0.999928 0.0119768i \(-0.00381244\pi\)
−0.320385 + 0.947287i \(0.603812\pi\)
\(230\) 0 0
\(231\) −12.6022 + 5.37208i −0.829161 + 0.353457i
\(232\) −2.05059 + 2.05059i −0.134628 + 0.134628i
\(233\) 28.6649 4.54007i 1.87790 0.297430i 0.890416 0.455148i \(-0.150414\pi\)
0.987484 + 0.157718i \(0.0504138\pi\)
\(234\) 17.4650 3.13471i 1.14172 0.204923i
\(235\) 0 0
\(236\) 2.80729 0.912145i 0.182739 0.0593756i
\(237\) 1.38839 20.3015i 0.0901857 1.31872i
\(238\) −15.3768 + 7.83489i −0.996733 + 0.507861i
\(239\) −1.74681 5.37613i −0.112992 0.347753i 0.878531 0.477685i \(-0.158524\pi\)
−0.991523 + 0.129932i \(0.958524\pi\)
\(240\) 0 0
\(241\) 4.35617 13.4069i 0.280605 0.863614i −0.707076 0.707137i \(-0.749986\pi\)
0.987682 0.156477i \(-0.0500137\pi\)
\(242\) 0.544110 + 3.43537i 0.0349767 + 0.220834i
\(243\) 14.6887 + 5.21929i 0.942283 + 0.334817i
\(244\) −2.69804 + 3.71353i −0.172724 + 0.237734i
\(245\) 0 0
\(246\) 9.11842 0.811827i 0.581369 0.0517602i
\(247\) −4.79711 + 30.2878i −0.305233 + 1.92716i
\(248\) −5.02833 2.56206i −0.319299 0.162691i
\(249\) 17.9454 + 10.7453i 1.13724 + 0.680957i
\(250\) 0 0
\(251\) 17.3182i 1.09311i −0.837422 0.546557i \(-0.815938\pi\)
0.837422 0.546557i \(-0.184062\pi\)
\(252\) 0.177478 + 8.64987i 0.0111801 + 0.544891i
\(253\) 3.07648 + 0.487266i 0.193416 + 0.0306341i
\(254\) −10.1370 + 7.36495i −0.636051 + 0.462118i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −4.28914 4.28914i −0.267549 0.267549i 0.560563 0.828112i \(-0.310585\pi\)
−0.828112 + 0.560563i \(0.810585\pi\)
\(258\) −7.06278 2.84098i −0.439710 0.176872i
\(259\) −22.1319 7.19110i −1.37521 0.446833i
\(260\) 0 0
\(261\) 6.27666 + 6.02427i 0.388515 + 0.372893i
\(262\) 5.41110 + 10.6199i 0.334299 + 0.656098i
\(263\) 10.8405 + 21.2757i 0.668454 + 1.31191i 0.937230 + 0.348711i \(0.113381\pi\)
−0.268777 + 0.963203i \(0.586619\pi\)
\(264\) −4.63019 1.06150i −0.284968 0.0653308i
\(265\) 0 0
\(266\) −14.2201 4.62038i −0.871889 0.283294i
\(267\) 0.841253 2.09139i 0.0514839 0.127991i
\(268\) −0.326329 0.326329i −0.0199337 0.0199337i
\(269\) 11.2436 + 8.16896i 0.685535 + 0.498070i 0.875189 0.483781i \(-0.160737\pi\)
−0.189654 + 0.981851i \(0.560737\pi\)
\(270\) 0 0
\(271\) 12.1633 8.83716i 0.738868 0.536819i −0.153488 0.988151i \(-0.549051\pi\)
0.892357 + 0.451331i \(0.149051\pi\)
\(272\) −5.91053 0.936136i −0.358378 0.0567616i
\(273\) 25.0309 15.6944i 1.51494 0.949867i
\(274\) 19.8701i 1.20040i
\(275\) 0 0
\(276\) 1.01056 1.68771i 0.0608288 0.101588i
\(277\) 1.61620 + 0.823495i 0.0971080 + 0.0494790i 0.501870 0.864943i \(-0.332646\pi\)
−0.404762 + 0.914422i \(0.632646\pi\)
\(278\) 1.49340 9.42893i 0.0895679 0.565509i
\(279\) −7.37512 + 15.2395i −0.441537 + 0.912364i
\(280\) 0 0
\(281\) 13.4707 18.5409i 0.803597 1.10606i −0.188683 0.982038i \(-0.560422\pi\)
0.992280 0.124018i \(-0.0395782\pi\)
\(282\) 7.79835 1.95703i 0.464385 0.116540i
\(283\) 0.445062 + 2.81001i 0.0264562 + 0.167038i 0.997379 0.0723553i \(-0.0230516\pi\)
−0.970923 + 0.239393i \(0.923052\pi\)
\(284\) 1.76800 5.44135i 0.104912 0.322885i
\(285\) 0 0
\(286\) 5.01274 + 15.4276i 0.296409 + 0.912255i
\(287\) 13.5811 6.91991i 0.801666 0.408469i
\(288\) −1.71320 + 2.46271i −0.100951 + 0.145117i
\(289\) −17.8900 + 5.81283i −1.05236 + 0.341931i
\(290\) 0 0
\(291\) 8.62720 7.52273i 0.505735 0.440990i
\(292\) 8.97684 1.42179i 0.525330 0.0832041i
\(293\) −9.44461 + 9.44461i −0.551760 + 0.551760i −0.926948 0.375189i \(-0.877578\pi\)
0.375189 + 0.926948i \(0.377578\pi\)
\(294\) 0.894424 + 2.09819i 0.0521639 + 0.122369i
\(295\) 0 0
\(296\) −4.74298 6.52816i −0.275680 0.379441i
\(297\) −2.89888 + 13.9530i −0.168210 + 0.809633i
\(298\) −5.45192 + 10.7000i −0.315821 + 0.619834i
\(299\) −6.71745 −0.388480
\(300\) 0 0
\(301\) −12.6754 −0.730597
\(302\) −5.05186 + 9.91484i −0.290702 + 0.570535i
\(303\) 3.92259 4.68933i 0.225347 0.269395i
\(304\) −3.04743 4.19443i −0.174782 0.240567i
\(305\) 0 0
\(306\) −2.44408 + 17.7855i −0.139719 + 1.01673i
\(307\) 23.1889 23.1889i 1.32346 1.32346i 0.412506 0.910955i \(-0.364654\pi\)
0.910955 0.412506i \(-0.135346\pi\)
\(308\) −7.81197 + 1.23730i −0.445129 + 0.0705014i
\(309\) −7.34518 8.42358i −0.417852 0.479201i
\(310\) 0 0
\(311\) 9.84506 3.19885i 0.558262 0.181390i −0.0162770 0.999868i \(-0.505181\pi\)
0.574539 + 0.818477i \(0.305181\pi\)
\(312\) 10.2207 + 0.698977i 0.578631 + 0.0395718i
\(313\) 12.2235 6.22820i 0.690915 0.352039i −0.0730212 0.997330i \(-0.523264\pi\)
0.763936 + 0.645292i \(0.223264\pi\)
\(314\) −5.07459 15.6180i −0.286376 0.881374i
\(315\) 0 0
\(316\) 3.63047 11.1734i 0.204230 0.628556i
\(317\) 2.95253 + 18.6415i 0.165830 + 1.04701i 0.920453 + 0.390853i \(0.127820\pi\)
−0.754623 + 0.656159i \(0.772180\pi\)
\(318\) 2.25827 + 8.99872i 0.126638 + 0.504623i
\(319\) −4.67490 + 6.43445i −0.261744 + 0.360260i
\(320\) 0 0
\(321\) −1.90486 21.3953i −0.106319 1.19417i
\(322\) 0.512371 3.23498i 0.0285533 0.180279i
\(323\) −27.6441 14.0854i −1.53816 0.783732i
\(324\) 7.49202 + 4.98695i 0.416223 + 0.277053i
\(325\) 0 0
\(326\) 6.55079i 0.362815i
\(327\) −2.56931 4.09779i −0.142083 0.226608i
\(328\) 5.22028 + 0.826810i 0.288241 + 0.0456530i
\(329\) 10.8303 7.86870i 0.597096 0.433815i
\(330\) 0 0
\(331\) −25.6753 18.6542i −1.41124 1.02533i −0.993141 0.116926i \(-0.962696\pi\)
−0.418100 0.908401i \(-0.637304\pi\)
\(332\) 8.53912 + 8.53912i 0.468645 + 0.468645i
\(333\) −19.2885 + 14.6277i −1.05700 + 0.801593i
\(334\) −16.1658 5.25258i −0.884552 0.287408i
\(335\) 0 0
\(336\) −1.11619 + 4.86875i −0.0608932 + 0.265612i
\(337\) 7.31518 + 14.3569i 0.398483 + 0.782068i 0.999857 0.0169001i \(-0.00537972\pi\)
−0.601374 + 0.798968i \(0.705380\pi\)
\(338\) −9.98030 19.5874i −0.542857 1.06542i
\(339\) −1.78909 + 7.80387i −0.0971698 + 0.423848i
\(340\) 0 0
\(341\) −14.7201 4.78284i −0.797137 0.259006i
\(342\) −12.3931 + 9.39851i −0.670143 + 0.508213i
\(343\) −11.5892 11.5892i −0.625757 0.625757i
\(344\) −3.55581 2.58345i −0.191717 0.139290i
\(345\) 0 0
\(346\) 5.49287 3.99080i 0.295299 0.214547i
\(347\) 23.6313 + 3.74283i 1.26859 + 0.200925i 0.754209 0.656634i \(-0.228020\pi\)
0.514384 + 0.857560i \(0.328020\pi\)
\(348\) 2.66824 + 4.25557i 0.143033 + 0.228123i
\(349\) 24.8956i 1.33263i −0.745670 0.666315i \(-0.767871\pi\)
0.745670 0.666315i \(-0.232129\pi\)
\(350\) 0 0
\(351\) 1.46750 30.6986i 0.0783293 1.63857i
\(352\) −2.44367 1.24511i −0.130248 0.0663646i
\(353\) 2.64576 16.7047i 0.140820 0.889101i −0.811578 0.584244i \(-0.801391\pi\)
0.952398 0.304857i \(-0.0986087\pi\)
\(354\) −0.453389 5.09246i −0.0240974 0.270661i
\(355\) 0 0
\(356\) 0.764995 1.05293i 0.0405447 0.0558049i
\(357\) 7.27579 + 28.9924i 0.385076 + 1.53444i
\(358\) −1.46766 9.26645i −0.0775683 0.489747i
\(359\) −1.67961 + 5.16932i −0.0886466 + 0.272826i −0.985546 0.169409i \(-0.945814\pi\)
0.896899 + 0.442235i \(0.145814\pi\)
\(360\) 0 0
\(361\) −2.43509 7.49444i −0.128163 0.394444i
\(362\) 13.5493 6.90373i 0.712137 0.362852i
\(363\) 6.01037 + 0.411041i 0.315463 + 0.0215740i
\(364\) 16.2225 5.27101i 0.850290 0.276276i
\(365\) 0 0
\(366\) 5.22512 + 5.99226i 0.273122 + 0.313221i
\(367\) −17.7079 + 2.80465i −0.924343 + 0.146401i −0.600422 0.799683i \(-0.705001\pi\)
−0.323920 + 0.946084i \(0.605001\pi\)
\(368\) 0.803077 0.803077i 0.0418633 0.0418633i
\(369\) 2.15865 15.7084i 0.112375 0.817747i
\(370\) 0 0
\(371\) 9.07990 + 12.4974i 0.471405 + 0.648833i
\(372\) −6.27159 + 7.49747i −0.325167 + 0.388726i
\(373\) −11.6182 + 22.8020i −0.601568 + 1.18064i 0.366608 + 0.930376i \(0.380519\pi\)
−0.968176 + 0.250269i \(0.919481\pi\)
\(374\) −16.4122 −0.848656
\(375\) 0 0
\(376\) 4.64199 0.239392
\(377\) 7.78702 15.2829i 0.401052 0.787109i
\(378\) 14.6719 + 3.04824i 0.754639 + 0.156785i
\(379\) 5.71732 + 7.86922i 0.293679 + 0.404215i 0.930205 0.367041i \(-0.119629\pi\)
−0.636526 + 0.771255i \(0.719629\pi\)
\(380\) 0 0
\(381\) 8.51045 + 19.9643i 0.436004 + 1.02280i
\(382\) −9.12687 + 9.12687i −0.466971 + 0.466971i
\(383\) 24.0895 3.81540i 1.23092 0.194958i 0.493108 0.869968i \(-0.335861\pi\)
0.737808 + 0.675010i \(0.235861\pi\)
\(384\) −1.30545 + 1.13833i −0.0666187 + 0.0580900i
\(385\) 0 0
\(386\) −5.26495 + 1.71069i −0.267979 + 0.0870717i
\(387\) −7.52989 + 10.8242i −0.382766 + 0.550224i
\(388\) 5.88829 3.00023i 0.298932 0.152314i
\(389\) 5.49358 + 16.9075i 0.278536 + 0.857245i 0.988262 + 0.152767i \(0.0488186\pi\)
−0.709726 + 0.704477i \(0.751181\pi\)
\(390\) 0 0
\(391\) 2.10020 6.46376i 0.106212 0.326886i
\(392\) 0.206003 + 1.30065i 0.0104047 + 0.0656929i
\(393\) 20.0234 5.02496i 1.01004 0.253475i
\(394\) −15.0352 + 20.6942i −0.757462 + 1.04256i
\(395\) 0 0
\(396\) −3.58416 + 7.40608i −0.180111 + 0.372170i
\(397\) 3.00987 19.0036i 0.151061 0.953762i −0.789405 0.613873i \(-0.789611\pi\)
0.940466 0.339889i \(-0.110389\pi\)
\(398\) −0.0684585 0.0348814i −0.00343152 0.00174845i
\(399\) −13.3041 + 22.2188i −0.666040 + 1.11233i
\(400\) 0 0
\(401\) 31.1439i 1.55525i 0.628726 + 0.777627i \(0.283577\pi\)
−0.628726 + 0.777627i \(0.716423\pi\)
\(402\) −0.677230 + 0.424623i −0.0337772 + 0.0211783i
\(403\) 32.9681 + 5.22164i 1.64226 + 0.260108i
\(404\) 2.85559 2.07471i 0.142071 0.103221i
\(405\) 0 0
\(406\) 6.76598 + 4.91577i 0.335790 + 0.243966i
\(407\) −15.6487 15.6487i −0.775678 0.775678i
\(408\) −3.86806 + 9.61614i −0.191498 + 0.476070i
\(409\) −14.9223 4.84855i −0.737860 0.239745i −0.0841106 0.996456i \(-0.526805\pi\)
−0.653749 + 0.756711i \(0.726805\pi\)
\(410\) 0 0
\(411\) 33.5457 + 7.69057i 1.65469 + 0.379348i
\(412\) −2.92942 5.74931i −0.144322 0.283248i
\(413\) −3.86463 7.58476i −0.190166 0.373222i
\(414\) −2.45815 2.35930i −0.120811 0.115953i
\(415\) 0 0
\(416\) 5.62520 + 1.82774i 0.275798 + 0.0896122i
\(417\) −15.3404 6.17063i −0.751223 0.302177i
\(418\) −10.0545 10.0545i −0.491783 0.491783i
\(419\) 2.78733 + 2.02511i 0.136170 + 0.0989333i 0.653785 0.756680i \(-0.273180\pi\)
−0.517615 + 0.855614i \(0.673180\pi\)
\(420\) 0 0
\(421\) 10.9206 7.93429i 0.532238 0.386694i −0.288956 0.957342i \(-0.593308\pi\)
0.821194 + 0.570649i \(0.193308\pi\)
\(422\) 6.37141 + 1.00913i 0.310156 + 0.0491238i
\(423\) −0.285673 13.9230i −0.0138899 0.676962i
\(424\) 5.35652i 0.260135i
\(425\) 0 0
\(426\) −8.50208 5.09087i −0.411927 0.246653i
\(427\) 11.7948 + 6.00974i 0.570790 + 0.290832i
\(428\) 1.94001 12.2488i 0.0937741 0.592066i
\(429\) 27.9859 2.49162i 1.35117 0.120297i
\(430\) 0 0
\(431\) 16.4092 22.5853i 0.790401 1.08789i −0.203657 0.979042i \(-0.565283\pi\)
0.994058 0.108852i \(-0.0347173\pi\)
\(432\) 3.49460 + 3.84548i 0.168134 + 0.185016i
\(433\) 0.408546 + 2.57946i 0.0196335 + 0.123961i 0.995558 0.0941457i \(-0.0300119\pi\)
−0.975925 + 0.218107i \(0.930012\pi\)
\(434\) −5.02927 + 15.4785i −0.241413 + 0.742992i
\(435\) 0 0
\(436\) −0.862912 2.65577i −0.0413260 0.127188i
\(437\) 5.24649 2.67322i 0.250974 0.127877i
\(438\) 1.07407 15.7055i 0.0513213 0.750436i
\(439\) −10.4899 + 3.40836i −0.500653 + 0.162672i −0.548447 0.836185i \(-0.684781\pi\)
0.0477940 + 0.998857i \(0.484781\pi\)
\(440\) 0 0
\(441\) 3.88846 0.697923i 0.185165 0.0332344i
\(442\) 34.9589 5.53695i 1.66283 0.263366i
\(443\) −1.32181 + 1.32181i −0.0628009 + 0.0628009i −0.737810 0.675009i \(-0.764140\pi\)
0.675009 + 0.737810i \(0.264140\pi\)
\(444\) −12.8569 + 5.48068i −0.610162 + 0.260102i
\(445\) 0 0
\(446\) −3.19712 4.40046i −0.151388 0.208368i
\(447\) 15.9542 + 13.3456i 0.754607 + 0.631224i
\(448\) −1.30926 + 2.56957i −0.0618568 + 0.121401i
\(449\) 20.5238 0.968579 0.484289 0.874908i \(-0.339078\pi\)
0.484289 + 0.874908i \(0.339078\pi\)
\(450\) 0 0
\(451\) 14.4955 0.682569
\(452\) −2.09855 + 4.11863i −0.0987075 + 0.193724i
\(453\) 14.7835 + 12.3663i 0.694588 + 0.581019i
\(454\) −11.5336 15.8746i −0.541296 0.745031i
\(455\) 0 0
\(456\) −8.26075 + 3.52142i −0.386845 + 0.164905i
\(457\) −11.0498 + 11.0498i −0.516886 + 0.516886i −0.916628 0.399742i \(-0.869100\pi\)
0.399742 + 0.916628i \(0.369100\pi\)
\(458\) 17.2797 2.73683i 0.807427 0.127884i
\(459\) 29.0804 + 11.0100i 1.35736 + 0.513901i
\(460\) 0 0
\(461\) −13.2689 + 4.31131i −0.617992 + 0.200798i −0.601249 0.799062i \(-0.705330\pi\)
−0.0167435 + 0.999860i \(0.505330\pi\)
\(462\) −0.934699 + 13.6675i −0.0434861 + 0.635868i
\(463\) −29.3718 + 14.9657i −1.36502 + 0.695515i −0.974355 0.225017i \(-0.927756\pi\)
−0.390669 + 0.920531i \(0.627756\pi\)
\(464\) 0.896139 + 2.75803i 0.0416022 + 0.128038i
\(465\) 0 0
\(466\) 8.96836 27.6018i 0.415451 1.27863i
\(467\) 0.578507 + 3.65255i 0.0267701 + 0.169020i 0.997451 0.0713509i \(-0.0227310\pi\)
−0.970681 + 0.240371i \(0.922731\pi\)
\(468\) 5.13588 16.9845i 0.237406 0.785110i
\(469\) −0.782294 + 1.07673i −0.0361230 + 0.0497190i
\(470\) 0 0
\(471\) −28.3312 + 2.52237i −1.30543 + 0.116225i
\(472\) 0.461757 2.91542i 0.0212541 0.134193i
\(473\) −10.7405 5.47254i −0.493847 0.251628i
\(474\) −17.4585 10.4538i −0.801894 0.480157i
\(475\) 0 0
\(476\) 17.2578i 0.791012i
\(477\) 16.0662 0.329645i 0.735619 0.0150934i
\(478\) −5.58321 0.884293i −0.255370 0.0404466i
\(479\) 4.35190 3.16184i 0.198844 0.144468i −0.483908 0.875119i \(-0.660783\pi\)
0.682752 + 0.730651i \(0.260783\pi\)
\(480\) 0 0
\(481\) 38.6120 + 28.0533i 1.76056 + 1.27912i
\(482\) −9.96798 9.96798i −0.454029 0.454029i
\(483\) −5.26316 2.11709i −0.239482 0.0963309i
\(484\) 3.30796 + 1.07482i 0.150362 + 0.0488555i
\(485\) 0 0
\(486\) 11.3190 10.7183i 0.513439 0.486190i
\(487\) 1.90512 + 3.73900i 0.0863291 + 0.169430i 0.930135 0.367219i \(-0.119690\pi\)
−0.843806 + 0.536649i \(0.819690\pi\)
\(488\) 2.08390 + 4.08988i 0.0943336 + 0.185140i
\(489\) 11.0594 + 2.53544i 0.500123 + 0.114656i
\(490\) 0 0
\(491\) −30.0362 9.75934i −1.35551 0.440433i −0.460970 0.887416i \(-0.652499\pi\)
−0.894543 + 0.446983i \(0.852499\pi\)
\(492\) 3.41633 8.49313i 0.154020 0.382900i
\(493\) 12.2711 + 12.2711i 0.552664 + 0.552664i
\(494\) 24.8088 + 18.0246i 1.11620 + 0.810966i
\(495\) 0 0
\(496\) −4.56563 + 3.31712i −0.205003 + 0.148943i
\(497\) −16.2967 2.58115i −0.731007 0.115780i
\(498\) 17.7212 11.1112i 0.794106 0.497904i
\(499\) 10.2536i 0.459015i 0.973307 + 0.229508i \(0.0737116\pi\)
−0.973307 + 0.229508i \(0.926288\pi\)
\(500\) 0 0
\(501\) −15.1245 + 25.2590i −0.675714 + 1.12849i
\(502\) −15.4306 7.86229i −0.688702 0.350911i
\(503\) 0.104371 0.658974i 0.00465369 0.0293822i −0.985252 0.171108i \(-0.945265\pi\)
0.989906 + 0.141726i \(0.0452652\pi\)
\(504\) 7.78767 + 3.76883i 0.346890 + 0.167877i
\(505\) 0 0
\(506\) 1.83085 2.51995i 0.0813911 0.112025i
\(507\) −36.9314 + 9.26810i −1.64018 + 0.411611i
\(508\) 1.96012 + 12.3757i 0.0869664 + 0.549084i
\(509\) −8.01814 + 24.6773i −0.355398 + 1.09380i 0.600381 + 0.799714i \(0.295016\pi\)
−0.955779 + 0.294087i \(0.904984\pi\)
\(510\) 0 0
\(511\) −8.09964 24.9281i −0.358307 1.10276i
\(512\) −0.891007 + 0.453990i −0.0393773 + 0.0200637i
\(513\) 11.0704 + 24.5603i 0.488770 + 1.08436i
\(514\) −5.76888 + 1.87442i −0.254454 + 0.0826772i
\(515\) 0 0
\(516\) −5.73777 + 5.00321i −0.252591 + 0.220254i
\(517\) 12.5743 1.99158i 0.553019 0.0875896i
\(518\) −16.4550 + 16.4550i −0.722991 + 0.722991i
\(519\) −4.61151 10.8180i −0.202423 0.474856i
\(520\) 0 0
\(521\) −24.0053 33.0404i −1.05169 1.44753i −0.887334 0.461127i \(-0.847445\pi\)
−0.164357 0.986401i \(-0.552555\pi\)
\(522\) 8.21721 2.85758i 0.359657 0.125073i
\(523\) 12.3663 24.2703i 0.540741 1.06126i −0.445396 0.895334i \(-0.646937\pi\)
0.986137 0.165931i \(-0.0530628\pi\)
\(524\) 11.9190 0.520682
\(525\) 0 0
\(526\) 23.8782 1.04114
\(527\) −15.3319 + 30.0906i −0.667868 + 1.31077i
\(528\) −3.04786 + 3.64362i −0.132641 + 0.158568i
\(529\) −12.7609 17.5639i −0.554822 0.763646i
\(530\) 0 0
\(531\) −8.77284 1.20556i −0.380709 0.0523170i
\(532\) −10.5726 + 10.5726i −0.458379 + 0.458379i
\(533\) −30.8763 + 4.89032i −1.33740 + 0.211823i
\(534\) −1.48152 1.69903i −0.0641116 0.0735243i
\(535\) 0 0
\(536\) −0.438912 + 0.142611i −0.0189581 + 0.00615987i
\(537\) −16.2122 1.10873i −0.699606 0.0478451i
\(538\) 12.3831 6.30950i 0.533873 0.272022i
\(539\) 1.11605 + 3.43486i 0.0480718 + 0.147950i
\(540\) 0 0
\(541\) 4.75771 14.6427i 0.204550 0.629540i −0.795182 0.606371i \(-0.792625\pi\)
0.999732 0.0231685i \(-0.00737544\pi\)
\(542\) −2.35194 14.8496i −0.101025 0.637844i
\(543\) −6.41107 25.5467i −0.275125 1.09631i
\(544\) −3.51743 + 4.84132i −0.150808 + 0.207570i
\(545\) 0 0
\(546\) −2.62000 29.4278i −0.112126 1.25939i
\(547\) 3.51301 22.1803i 0.150205 0.948360i −0.791316 0.611407i \(-0.790604\pi\)
0.941522 0.336953i \(-0.109396\pi\)
\(548\) 17.7044 + 9.02083i 0.756293 + 0.385351i
\(549\) 12.1388 6.50207i 0.518072 0.277502i
\(550\) 0 0
\(551\) 15.0352i 0.640520i
\(552\) −1.04497 1.66662i −0.0444770 0.0709362i
\(553\) −33.4642 5.30021i −1.42304 0.225388i
\(554\) 1.46748 1.06619i 0.0623472 0.0452979i
\(555\) 0 0
\(556\) −7.72325 5.61127i −0.327539 0.237971i
\(557\) 1.66485 + 1.66485i 0.0705420 + 0.0705420i 0.741498 0.670956i \(-0.234116\pi\)
−0.670956 + 0.741498i \(0.734116\pi\)
\(558\) 10.2302 + 13.4899i 0.433081 + 0.571071i
\(559\) 24.7240 + 8.03333i 1.04572 + 0.339773i
\(560\) 0 0
\(561\) −6.35223 + 27.7080i −0.268191 + 1.16983i
\(562\) −10.4045 20.4199i −0.438886 0.861362i
\(563\) 21.4512 + 42.1004i 0.904062 + 1.77432i 0.534729 + 0.845023i \(0.320414\pi\)
0.369332 + 0.929297i \(0.379586\pi\)
\(564\) 1.79665 7.83686i 0.0756525 0.329991i
\(565\) 0 0
\(566\) 2.70579 + 0.879165i 0.113733 + 0.0369541i
\(567\) 10.8248 23.5900i 0.454600 0.990688i
\(568\) −4.04562 4.04562i −0.169750 0.169750i
\(569\) −19.9798 14.5162i −0.837599 0.608551i 0.0841003 0.996457i \(-0.473198\pi\)
−0.921699 + 0.387906i \(0.873198\pi\)
\(570\) 0 0
\(571\) 4.83866 3.51549i 0.202491 0.147119i −0.481919 0.876216i \(-0.660060\pi\)
0.684410 + 0.729097i \(0.260060\pi\)
\(572\) 16.0218 + 2.53761i 0.669907 + 0.106103i
\(573\) 11.8760 + 18.9409i 0.496126 + 0.791269i
\(574\) 15.2424i 0.636206i
\(575\) 0 0
\(576\) 1.41652 + 2.64452i 0.0590216 + 0.110188i
\(577\) 28.0783 + 14.3066i 1.16891 + 0.595591i 0.927130 0.374739i \(-0.122268\pi\)
0.241783 + 0.970330i \(0.422268\pi\)
\(578\) −2.94264 + 18.5791i −0.122398 + 0.772789i
\(579\) 0.850312 + 9.55068i 0.0353377 + 0.396913i
\(580\) 0 0
\(581\) 20.4704 28.1751i 0.849256 1.16890i
\(582\) −2.78613 11.1021i −0.115489 0.460198i
\(583\) 2.29814 + 14.5099i 0.0951791 + 0.600937i
\(584\) 2.80857 8.64390i 0.116220 0.357687i
\(585\) 0 0
\(586\) 4.12744 + 12.7030i 0.170503 + 0.524755i
\(587\) −10.0374 + 5.11433i −0.414289 + 0.211091i −0.648696 0.761048i \(-0.724685\pi\)
0.234407 + 0.972139i \(0.424685\pi\)
\(588\) 2.27556 + 0.155623i 0.0938427 + 0.00641777i
\(589\) −27.8269 + 9.04151i −1.14659 + 0.372549i
\(590\) 0 0
\(591\) 29.1177 + 33.3927i 1.19774 + 1.37359i
\(592\) −7.96990 + 1.26231i −0.327561 + 0.0518805i
\(593\) 17.4049 17.4049i 0.714734 0.714734i −0.252788 0.967522i \(-0.581347\pi\)
0.967522 + 0.252788i \(0.0813475\pi\)
\(594\) 11.1161 + 8.91744i 0.456100 + 0.365887i
\(595\) 0 0
\(596\) 7.05865 + 9.71540i 0.289134 + 0.397958i
\(597\) −0.0853849 + 0.102075i −0.00349457 + 0.00417764i
\(598\) −3.04966 + 5.98529i −0.124710 + 0.244757i
\(599\) 25.8531 1.05633 0.528165 0.849142i \(-0.322880\pi\)
0.528165 + 0.849142i \(0.322880\pi\)
\(600\) 0 0
\(601\) −36.7027 −1.49714 −0.748568 0.663058i \(-0.769258\pi\)
−0.748568 + 0.663058i \(0.769258\pi\)
\(602\) −5.75450 + 11.2939i −0.234536 + 0.460303i
\(603\) 0.454755 + 1.30768i 0.0185190 + 0.0532530i
\(604\) 6.54069 + 9.00249i 0.266137 + 0.366306i
\(605\) 0 0
\(606\) −2.39740 5.62397i −0.0973877 0.228458i
\(607\) 23.2173 23.2173i 0.942362 0.942362i −0.0560654 0.998427i \(-0.517856\pi\)
0.998427 + 0.0560654i \(0.0178555\pi\)
\(608\) −5.12077 + 0.811051i −0.207675 + 0.0328925i
\(609\) 10.9178 9.52007i 0.442411 0.385773i
\(610\) 0 0
\(611\) −26.1121 + 8.48435i −1.05638 + 0.343240i
\(612\) 14.7374 + 10.2521i 0.595723 + 0.414417i
\(613\) −19.5715 + 9.97216i −0.790484 + 0.402772i −0.802122 0.597161i \(-0.796295\pi\)
0.0116379 + 0.999932i \(0.496295\pi\)
\(614\) −10.1339 31.1890i −0.408972 1.25869i
\(615\) 0 0
\(616\) −2.44412 + 7.52224i −0.0984766 + 0.303080i
\(617\) 1.00125 + 6.32162i 0.0403086 + 0.254499i 0.999611 0.0278814i \(-0.00887607\pi\)
−0.959303 + 0.282380i \(0.908876\pi\)
\(618\) −10.8401 + 2.72038i −0.436053 + 0.109430i
\(619\) 14.0949 19.4000i 0.566524 0.779753i −0.425614 0.904905i \(-0.639942\pi\)
0.992138 + 0.125152i \(0.0399418\pi\)
\(620\) 0 0
\(621\) −4.93451 + 3.23682i −0.198015 + 0.129889i
\(622\) 1.61936 10.2243i 0.0649306 0.409956i
\(623\) −3.34426 1.70399i −0.133985 0.0682688i
\(624\) 5.26288 8.78935i 0.210684 0.351856i
\(625\) 0 0
\(626\) 13.7188i 0.548313i
\(627\) −20.8661 + 13.0831i −0.833312 + 0.522487i
\(628\) −16.2195 2.56892i −0.647230 0.102511i
\(629\) −39.0658 + 28.3830i −1.55766 + 1.13170i
\(630\) 0 0
\(631\) −23.7895 17.2841i −0.947046 0.688069i 0.00306072 0.999995i \(-0.499026\pi\)
−0.950106 + 0.311926i \(0.899026\pi\)
\(632\) −8.30741 8.30741i −0.330451 0.330451i
\(633\) 4.16968 10.3660i 0.165730 0.412011i
\(634\) 17.9501 + 5.83235i 0.712891 + 0.231632i
\(635\) 0 0
\(636\) 9.04315 + 2.07320i 0.358584 + 0.0822077i
\(637\) −3.53606 6.93992i −0.140104 0.274970i
\(638\) 3.61078 + 7.08655i 0.142952 + 0.280559i
\(639\) −11.8853 + 12.3833i −0.470177 + 0.489875i
\(640\) 0 0
\(641\) 18.3395 + 5.95888i 0.724368 + 0.235362i 0.647916 0.761712i \(-0.275641\pi\)
0.0764522 + 0.997073i \(0.475641\pi\)
\(642\) −19.9281 8.01603i −0.786501 0.316367i
\(643\) 2.50826 + 2.50826i 0.0989163 + 0.0989163i 0.754833 0.655917i \(-0.227718\pi\)
−0.655917 + 0.754833i \(0.727718\pi\)
\(644\) −2.64978 1.92518i −0.104416 0.0758627i
\(645\) 0 0
\(646\) −25.1003 + 18.2365i −0.987560 + 0.717504i
\(647\) 36.9778 + 5.85671i 1.45375 + 0.230251i 0.832789 0.553591i \(-0.186743\pi\)
0.620960 + 0.783842i \(0.286743\pi\)
\(648\) 7.84471 4.41141i 0.308169 0.173296i
\(649\) 8.09547i 0.317775i
\(650\) 0 0
\(651\) 24.1851 + 14.4815i 0.947889 + 0.567576i
\(652\) 5.83680 + 2.97400i 0.228587 + 0.116471i
\(653\) −0.348209 + 2.19851i −0.0136265 + 0.0860342i −0.993564 0.113269i \(-0.963868\pi\)
0.979938 + 0.199303i \(0.0638678\pi\)
\(654\) −4.81760 + 0.428918i −0.188383 + 0.0167720i
\(655\) 0 0
\(656\) 3.10665 4.27594i 0.121294 0.166947i
\(657\) −26.0991 7.89200i −1.01822 0.307896i
\(658\) −2.09419 13.2222i −0.0816401 0.515456i
\(659\) 4.81311 14.8132i 0.187492 0.577041i −0.812490 0.582975i \(-0.801889\pi\)
0.999982 + 0.00593344i \(0.00188868\pi\)
\(660\) 0 0
\(661\) −0.225919 0.695307i −0.00878723 0.0270443i 0.946567 0.322508i \(-0.104526\pi\)
−0.955354 + 0.295464i \(0.904526\pi\)
\(662\) −28.2773 + 14.4080i −1.09903 + 0.559984i
\(663\) 4.18282 61.1625i 0.162447 2.37536i
\(664\) 11.4851 3.73173i 0.445708 0.144819i
\(665\) 0 0
\(666\) 4.27660 + 23.8270i 0.165715 + 0.923277i
\(667\) −3.25301 + 0.515226i −0.125957 + 0.0199496i
\(668\) −12.0192 + 12.0192i −0.465037 + 0.465037i
\(669\) −8.66651 + 3.69438i −0.335067 + 0.142833i
\(670\) 0 0
\(671\) 7.39961 + 10.1847i 0.285659 + 0.393176i
\(672\) 3.83135 + 3.20490i 0.147797 + 0.123632i
\(673\) 6.83769 13.4197i 0.263574 0.517292i −0.720853 0.693088i \(-0.756250\pi\)
0.984427 + 0.175796i \(0.0562498\pi\)
\(674\) 16.1131 0.620652
\(675\) 0 0
\(676\) −21.9835 −0.845520
\(677\) −10.5178 + 20.6424i −0.404233 + 0.793351i −0.999952 0.00984177i \(-0.996867\pi\)
0.595719 + 0.803193i \(0.296867\pi\)
\(678\) 6.14107 + 5.13697i 0.235846 + 0.197284i
\(679\) −11.2023 15.4186i −0.429904 0.591712i
\(680\) 0 0
\(681\) −31.2643 + 13.3274i −1.19805 + 0.510708i
\(682\) −10.9443 + 10.9443i −0.419080 + 0.419080i
\(683\) −4.28854 + 0.679239i −0.164097 + 0.0259903i −0.237942 0.971279i \(-0.576473\pi\)
0.0738455 + 0.997270i \(0.476473\pi\)
\(684\) 2.74778 + 15.3092i 0.105064 + 0.585361i
\(685\) 0 0
\(686\) −15.5874 + 5.06466i −0.595130 + 0.193370i
\(687\) 2.06751 30.2317i 0.0788803 1.15341i
\(688\) −3.91618 + 1.99539i −0.149303 + 0.0760736i
\(689\) −9.79031 30.1315i −0.372981 1.14792i
\(690\) 0 0
\(691\) −9.14266 + 28.1382i −0.347803 + 1.07043i 0.612263 + 0.790654i \(0.290259\pi\)
−0.960066 + 0.279774i \(0.909741\pi\)
\(692\) −1.06212 6.70597i −0.0403758 0.254923i
\(693\) 22.7124 + 6.86790i 0.862772 + 0.260890i
\(694\) 14.0633 19.3564i 0.533834 0.734759i
\(695\) 0 0
\(696\) 5.00310 0.445433i 0.189642 0.0168841i
\(697\) 4.94780 31.2392i 0.187411 1.18327i
\(698\) −22.1821 11.3024i −0.839606 0.427801i
\(699\) −43.1276 25.8239i −1.63124 0.976750i
\(700\) 0 0
\(701\) 19.5558i 0.738612i 0.929308 + 0.369306i \(0.120405\pi\)
−0.929308 + 0.369306i \(0.879595\pi\)
\(702\) −26.6864 15.2444i −1.00721 0.575363i
\(703\) −41.3208 6.54457i −1.55844 0.246833i
\(704\) −2.21880 + 1.61205i −0.0836243 + 0.0607566i
\(705\) 0 0
\(706\) −13.6828 9.94116i −0.514960 0.374140i
\(707\) −7.19787 7.19787i −0.270704 0.270704i
\(708\) −4.74325 1.90795i −0.178262 0.0717053i
\(709\) 21.2009 + 6.88858i 0.796216 + 0.258706i 0.678749 0.734371i \(-0.262523\pi\)
0.117467 + 0.993077i \(0.462523\pi\)
\(710\) 0 0
\(711\) −24.4058 + 25.4282i −0.915287 + 0.953634i
\(712\) −0.590863 1.15963i −0.0221435 0.0434591i
\(713\) −2.90979 5.71079i −0.108973 0.213871i
\(714\) 29.1356 + 6.67952i 1.09037 + 0.249975i
\(715\) 0 0
\(716\) −8.92277 2.89918i −0.333460 0.108348i
\(717\) −3.65385 + 9.08361i −0.136455 + 0.339233i
\(718\) 3.84337 + 3.84337i 0.143433 + 0.143433i
\(719\) −2.20624 1.60292i −0.0822787 0.0597790i 0.545885 0.837860i \(-0.316193\pi\)
−0.628164 + 0.778081i \(0.716193\pi\)
\(720\) 0 0
\(721\) −15.0547 + 10.9379i −0.560667 + 0.407348i
\(722\) −7.78310 1.23272i −0.289657 0.0458772i
\(723\) −20.6865 + 12.9704i −0.769339 + 0.482376i
\(724\) 15.2068i 0.565155i
\(725\) 0 0
\(726\) 3.09489 5.16867i 0.114862 0.191827i
\(727\) −17.3015 8.81556i −0.641677 0.326951i 0.102698 0.994713i \(-0.467253\pi\)
−0.744375 + 0.667762i \(0.767253\pi\)
\(728\) 2.66836 16.8473i 0.0988959 0.624404i
\(729\) −13.7142 23.2577i −0.507934 0.861396i
\(730\) 0 0
\(731\) −15.4599 + 21.2787i −0.571805 + 0.787022i
\(732\) 7.71130 1.93519i 0.285018 0.0715266i
\(733\) −3.79691 23.9728i −0.140242 0.885454i −0.953026 0.302889i \(-0.902049\pi\)
0.812784 0.582566i \(-0.197951\pi\)
\(734\) −5.54024 + 17.0511i −0.204494 + 0.629368i
\(735\) 0 0
\(736\) −0.350958 1.08014i −0.0129365 0.0398144i
\(737\) −1.12775 + 0.574618i −0.0415412 + 0.0211663i
\(738\) −13.0163 9.05484i −0.479136 0.333313i
\(739\) 6.13821 1.99443i 0.225798 0.0733662i −0.193933 0.981015i \(-0.562124\pi\)
0.419731 + 0.907649i \(0.362124\pi\)
\(740\) 0 0
\(741\) 40.0322 34.9072i 1.47062 1.28235i
\(742\) 15.2575 2.41654i 0.560119 0.0887141i
\(743\) −23.0403 + 23.0403i −0.845265 + 0.845265i −0.989538 0.144273i \(-0.953916\pi\)
0.144273 + 0.989538i \(0.453916\pi\)
\(744\) 3.83305 + 8.99180i 0.140526 + 0.329656i
\(745\) 0 0
\(746\) 15.0422 + 20.7038i 0.550734 + 0.758020i
\(747\) −11.8996 34.2184i −0.435385 1.25198i
\(748\) −7.45099 + 14.6234i −0.272435 + 0.534684i
\(749\) −35.7645 −1.30681
\(750\) 0 0
\(751\) 31.4069 1.14606 0.573028 0.819536i \(-0.305769\pi\)
0.573028 + 0.819536i \(0.305769\pi\)
\(752\) 2.10742 4.13604i 0.0768497 0.150826i
\(753\) −19.2458 + 23.0077i −0.701357 + 0.838449i
\(754\) −10.0819 13.8766i −0.367162 0.505355i
\(755\) 0 0
\(756\) 9.37689 11.6889i 0.341034 0.425120i
\(757\) −6.35882 + 6.35882i −0.231115 + 0.231115i −0.813158 0.582043i \(-0.802254\pi\)
0.582043 + 0.813158i \(0.302254\pi\)
\(758\) 9.60713 1.52162i 0.348947 0.0552678i
\(759\) −3.54569 4.06626i −0.128700 0.147596i
\(760\) 0 0
\(761\) 8.94031 2.90488i 0.324086 0.105302i −0.142456 0.989801i \(-0.545500\pi\)
0.466541 + 0.884499i \(0.345500\pi\)
\(762\) 21.6520 + 1.48075i 0.784370 + 0.0536419i
\(763\) −7.17538 + 3.65604i −0.259766 + 0.132358i
\(764\) 3.98859 + 12.2756i 0.144302 + 0.444116i
\(765\) 0 0
\(766\) 7.53686 23.1961i 0.272318 0.838108i
\(767\) 2.73115 + 17.2438i 0.0986161 + 0.622637i
\(768\) 0.421593 + 1.67996i 0.0152129 + 0.0606203i
\(769\) −15.8011 + 21.7484i −0.569803 + 0.784266i −0.992531 0.121990i \(-0.961072\pi\)
0.422728 + 0.906256i \(0.361072\pi\)
\(770\) 0 0
\(771\) 0.931697 + 10.4648i 0.0335543 + 0.376881i
\(772\) −0.866006 + 5.46774i −0.0311682 + 0.196788i
\(773\) −19.3692 9.86911i −0.696662 0.354967i 0.0695289 0.997580i \(-0.477850\pi\)
−0.766191 + 0.642613i \(0.777850\pi\)
\(774\) 6.22592 + 11.6233i 0.223786 + 0.417789i
\(775\) 0 0
\(776\) 6.60858i 0.237234i
\(777\) 21.4114 + 34.1490i 0.768130 + 1.22509i
\(778\) 17.5587 + 2.78103i 0.629511 + 0.0997048i
\(779\) 22.1690 16.1067i 0.794288 0.577084i
\(780\) 0 0
\(781\) −12.6946 9.22316i −0.454248 0.330031i
\(782\) −4.80578 4.80578i −0.171854 0.171854i
\(783\)