Properties

Label 750.2.l.c.107.4
Level $750$
Weight $2$
Character 750.107
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 107.4
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.c.743.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.891007 - 0.453990i) q^{2} +(1.11131 - 1.32853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-0.529988 - 2.95281i) q^{9} +O(q^{10})\) \(q+(-0.891007 - 0.453990i) q^{2} +(1.11131 - 1.32853i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.59332 + 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-0.529988 - 2.95281i) q^{9} +(-2.60836 + 0.847507i) q^{11} +(1.72801 + 0.118176i) q^{12} +(2.68521 + 5.27002i) q^{13} +(-0.891173 - 2.74275i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(5.91053 - 0.936136i) q^{17} +(-0.868327 + 2.87159i) q^{18} +(3.04743 - 4.19443i) q^{19} +(4.97538 - 0.442965i) q^{21} +(2.70883 + 0.429036i) q^{22} +(0.515607 - 1.01194i) q^{23} +(-1.48602 - 0.889798i) q^{24} -5.91469i q^{26} +(-4.51188 - 2.57738i) q^{27} +(-0.451141 + 2.84839i) q^{28} +(-2.34612 + 1.70456i) q^{29} +(4.56563 + 3.31712i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.77275 + 4.40713i) q^{33} +(-5.69132 - 1.84922i) q^{34} +(2.07736 - 2.16439i) q^{36} +(7.18975 - 3.66336i) q^{37} +(-4.61952 + 2.35376i) q^{38} +(9.98549 + 2.28924i) q^{39} +(-5.02666 - 1.63326i) q^{41} +(-4.63420 - 1.86409i) q^{42} +(-3.10789 + 3.10789i) q^{43} +(-2.21880 - 1.61205i) q^{44} +(-0.918819 + 0.667561i) q^{46} +(-0.726167 + 4.58484i) q^{47} +(0.920095 + 1.46746i) q^{48} +1.31687i q^{49} +(5.32473 - 8.89266i) q^{51} +(-2.68521 + 5.27002i) q^{52} +(5.29057 + 0.837944i) q^{53} +(2.85001 + 4.34482i) q^{54} +(1.69511 - 2.33312i) q^{56} +(-2.18579 - 8.70992i) q^{57} +(2.86426 - 0.453655i) q^{58} +(0.912145 - 2.80729i) q^{59} +(-1.41844 - 4.36552i) q^{61} +(-2.56206 - 5.02833i) q^{62} +(4.94069 - 7.10221i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(3.58033 - 3.12197i) q^{66} +(-0.0721944 - 0.455818i) q^{67} +(4.23147 + 4.23147i) q^{68} +(-0.771390 - 1.80957i) q^{69} +(3.36294 + 4.62869i) q^{71} +(-2.83355 + 0.985385i) q^{72} +(-8.09812 - 4.12620i) q^{73} -8.06924 q^{74} +5.18460 q^{76} +(-7.04728 - 3.59077i) q^{77} +(-7.85784 - 6.57304i) q^{78} +(-6.90557 - 9.50470i) q^{79} +(-8.43823 + 3.12991i) q^{81} +(3.73730 + 3.73730i) q^{82} +(-1.88912 - 11.9275i) q^{83} +(3.28282 + 3.76480i) q^{84} +(4.18011 - 1.35820i) q^{86} +(-0.342708 + 5.01118i) q^{87} +(1.24511 + 2.44367i) q^{88} +(-0.402182 - 1.23779i) q^{89} +(-5.27101 + 16.2225i) q^{91} +(1.12174 - 0.177666i) q^{92} +(9.48072 - 2.37923i) q^{93} +(2.72849 - 3.75545i) q^{94} +(-0.153600 - 1.72523i) q^{96} +(6.52722 + 1.03381i) q^{97} +(0.597845 - 1.17334i) q^{98} +(3.88493 + 7.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + 4q^{3} + 4q^{7} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{7} + 16q^{12} + 20q^{16} - 8q^{18} + 40q^{19} + 4q^{22} - 56q^{27} + 4q^{28} - 96q^{33} + 40q^{34} - 64q^{37} + 40q^{39} - 4q^{42} - 24q^{43} + 16q^{48} - 64q^{57} + 20q^{58} + 4q^{63} - 104q^{67} - 140q^{69} + 8q^{72} - 60q^{73} - 60q^{78} - 80q^{79} - 40q^{81} + 96q^{82} - 60q^{84} + 80q^{87} + 24q^{88} + 12q^{93} - 12q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.891007 0.453990i −0.630037 0.321020i
\(3\) 1.11131 1.32853i 0.641614 0.767028i
\(4\) 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 \(-0.0665276\pi\)
−0.207484 + 0.978238i \(0.566528\pi\)
\(8\) −0.156434 0.987688i −0.0553079 0.349201i
\(9\) −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 \(0.535680\pi\)
\(12\) 1.72801 + 0.118176i 0.498835 + 0.0341146i
\(13\) 2.68521 + 5.27002i 0.744744 + 1.46164i 0.882071 + 0.471116i \(0.156149\pi\)
−0.137328 + 0.990526i \(0.543851\pi\)
\(14\) −0.891173 2.74275i −0.238176 0.733031i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 5.91053 0.936136i 1.43351 0.227046i 0.609127 0.793073i \(-0.291520\pi\)
0.824387 + 0.566026i \(0.191520\pi\)
\(18\) −0.868327 + 2.87159i −0.204667 + 0.676839i
\(19\) 3.04743 4.19443i 0.699129 0.962269i −0.300834 0.953677i \(-0.597265\pi\)
0.999963 0.00859233i \(-0.00273506\pi\)
\(20\) 0 0
\(21\) 4.97538 0.442965i 1.08572 0.0966630i
\(22\) 2.70883 + 0.429036i 0.577523 + 0.0914707i
\(23\) 0.515607 1.01194i 0.107512 0.211003i −0.830983 0.556298i \(-0.812221\pi\)
0.938494 + 0.345295i \(0.112221\pi\)
\(24\) −1.48602 0.889798i −0.303333 0.181629i
\(25\) 0 0
\(26\) 5.91469i 1.15997i
\(27\) −4.51188 2.57738i −0.868313 0.496017i
\(28\) −0.451141 + 2.84839i −0.0852576 + 0.538296i
\(29\) −2.34612 + 1.70456i −0.435664 + 0.316528i −0.783910 0.620875i \(-0.786777\pi\)
0.348246 + 0.937403i \(0.386777\pi\)
\(30\) 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
\(33\) −1.77275 + 4.40713i −0.308596 + 0.767182i
\(34\) −5.69132 1.84922i −0.976053 0.317139i
\(35\) 0 0
\(36\) 2.07736 2.16439i 0.346226 0.360732i
\(37\) 7.18975 3.66336i 1.18199 0.602253i 0.251243 0.967924i \(-0.419161\pi\)
0.930744 + 0.365671i \(0.119161\pi\)
\(38\) −4.61952 + 2.35376i −0.749384 + 0.381830i
\(39\) 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 \(0.735420\pi\)
\(42\) −4.63420 1.86409i −0.715072 0.287635i
\(43\) −3.10789 + 3.10789i −0.473950 + 0.473950i −0.903190 0.429241i \(-0.858781\pi\)
0.429241 + 0.903190i \(0.358781\pi\)
\(44\) −2.21880 1.61205i −0.334497 0.243026i
\(45\) 0 0
\(46\) −0.918819 + 0.667561i −0.135473 + 0.0984265i
\(47\) −0.726167 + 4.58484i −0.105922 + 0.668768i 0.876402 + 0.481581i \(0.159937\pi\)
−0.982324 + 0.187187i \(0.940063\pi\)
\(48\) 0.920095 + 1.46746i 0.132804 + 0.211809i
\(49\) 1.31687i 0.188124i
\(50\) 0 0
\(51\) 5.32473 8.89266i 0.745612 1.24522i
\(52\) −2.68521 + 5.27002i −0.372372 + 0.730821i
\(53\) 5.29057 + 0.837944i 0.726715 + 0.115100i 0.508821 0.860872i \(-0.330081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(54\) 2.85001 + 4.34482i 0.387837 + 0.591255i
\(55\) 0 0
\(56\) 1.69511 2.33312i 0.226519 0.311777i
\(57\) −2.18579 8.70992i −0.289516 1.15366i
\(58\) 2.86426 0.453655i 0.376096 0.0595678i
\(59\) 0.912145 2.80729i 0.118751 0.365478i −0.873960 0.485998i \(-0.838456\pi\)
0.992711 + 0.120520i \(0.0384562\pi\)
\(60\) 0 0
\(61\) −1.41844 4.36552i −0.181613 0.558947i 0.818261 0.574847i \(-0.194939\pi\)
−0.999874 + 0.0159002i \(0.994939\pi\)
\(62\) −2.56206 5.02833i −0.325382 0.638599i
\(63\) 4.94069 7.10221i 0.622468 0.894795i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) 3.58033 3.12197i 0.440708 0.384287i
\(67\) −0.0721944 0.455818i −0.00881995 0.0556870i 0.982886 0.184216i \(-0.0589745\pi\)
−0.991706 + 0.128529i \(0.958975\pi\)
\(68\) 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 \(0.689742\pi\)
\(72\) −2.83355 + 0.985385i −0.333937 + 0.116129i
\(73\) −8.09812 4.12620i −0.947814 0.482935i −0.0894583 0.995991i \(-0.528514\pi\)
−0.858356 + 0.513055i \(0.828514\pi\)
\(74\) −8.06924 −0.938031
\(75\) 0 0
\(76\) 5.18460 0.594715
\(77\) −7.04728 3.59077i −0.803113 0.409206i
\(78\) −7.85784 6.57304i −0.889725 0.744250i
\(79\) −6.90557 9.50470i −0.776937 1.06936i −0.995613 0.0935650i \(-0.970174\pi\)
0.218676 0.975798i \(-0.429826\pi\)
\(80\) 0 0
\(81\) −8.43823 + 3.12991i −0.937581 + 0.347768i
\(82\) 3.73730 + 3.73730i 0.412716 + 0.412716i
\(83\) −1.88912 11.9275i −0.207358 1.30921i −0.843288 0.537462i \(-0.819383\pi\)
0.635930 0.771747i \(-0.280617\pi\)
\(84\) 3.28282 + 3.76480i 0.358185 + 0.410773i
\(85\) 0 0
\(86\) 4.18011 1.35820i 0.450753 0.146458i
\(87\) −0.342708 + 5.01118i −0.0367421 + 0.537255i
\(88\) 1.24511 + 2.44367i 0.132729 + 0.260496i
\(89\) −0.402182 1.23779i −0.0426312 0.131205i 0.927476 0.373884i \(-0.121974\pi\)
−0.970107 + 0.242678i \(0.921974\pi\)
\(90\) 0 0
\(91\) −5.27101 + 16.2225i −0.552552 + 1.70058i
\(92\) 1.12174 0.177666i 0.116950 0.0185230i
\(93\) 9.48072 2.37923i 0.983105 0.246715i
\(94\) 2.72849 3.75545i 0.281423 0.387345i
\(95\) 0 0
\(96\) −0.153600 1.72523i −0.0156767 0.176080i
\(97\) 6.52722 + 1.03381i 0.662738 + 0.104967i 0.478737 0.877959i \(-0.341095\pi\)
0.184002 + 0.982926i \(0.441095\pi\)
\(98\) 0.597845 1.17334i 0.0603915 0.118525i
\(99\) 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 \(0.943810\pi\)
\(102\) −8.78155 + 5.50604i −0.869503 + 0.545179i
\(103\) −1.00941 + 6.37316i −0.0994601 + 0.627966i 0.886722 + 0.462303i \(0.152977\pi\)
−0.986182 + 0.165664i \(0.947023\pi\)
\(104\) 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 −0.142106 0.989851i \(-0.545387\pi\)
0.989851 + 0.142106i \(0.0453874\pi\)
\(108\) −0.566874 5.16514i −0.0545474 0.497016i
\(109\) −2.65577 0.862912i −0.254377 0.0826520i 0.179053 0.983839i \(-0.442697\pi\)
−0.433430 + 0.901187i \(0.642697\pi\)
\(110\) 0 0
\(111\) 3.12314 13.6229i 0.296435 1.29303i
\(112\) −2.56957 + 1.30926i −0.242802 + 0.123714i
\(113\) 4.11863 2.09855i 0.387449 0.197415i −0.249406 0.968399i \(-0.580235\pi\)
0.636854 + 0.770984i \(0.280235\pi\)
\(114\) −2.00666 + 8.75292i −0.187941 + 0.819786i
\(115\) 0 0
\(116\) −2.75803 0.896139i −0.256077 0.0832044i
\(117\) 14.1383 10.7220i 1.30708 0.991247i
\(118\) −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
\(122\) −0.718062 + 4.53366i −0.0650103 + 0.410459i
\(123\) −7.75601 + 4.86302i −0.699336 + 0.438484i
\(124\) 5.64343i 0.506795i
\(125\) 0 0
\(126\) −7.62652 + 4.08509i −0.679424 + 0.363929i
\(127\) −5.68850 + 11.1643i −0.504773 + 0.990672i 0.488245 + 0.872707i \(0.337637\pi\)
−0.993018 + 0.117966i \(0.962363\pi\)
\(128\) 0.987688 + 0.156434i 0.0873001 + 0.0138270i
\(129\) 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 \(0.374322\pi\)
\(132\) −4.60744 + 1.15626i −0.401026 + 0.100639i
\(133\) 14.7678 2.33899i 1.28053 0.202816i
\(134\) −0.142611 + 0.438912i −0.0123197 + 0.0379162i
\(135\) 0 0
\(136\) −1.84922 5.69132i −0.158569 0.488026i
\(137\) 9.02083 + 17.7044i 0.770702 + 1.51259i 0.856427 + 0.516268i \(0.172679\pi\)
−0.0857255 + 0.996319i \(0.527321\pi\)
\(138\) −0.134216 + 1.96255i −0.0114252 + 0.167063i
\(139\) −9.07922 + 2.95002i −0.770090 + 0.250217i −0.667603 0.744517i \(-0.732680\pi\)
−0.102486 + 0.994734i \(0.532680\pi\)
\(140\) 0 0
\(141\) 5.28411 + 6.05991i 0.445002 + 0.510336i
\(142\) −0.895020 5.65093i −0.0751084 0.474216i
\(143\) −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
\(147\) 1.74950 + 1.46344i 0.144296 + 0.120703i
\(148\) 7.18975 + 3.66336i 0.590994 + 0.301126i
\(149\) 12.0089 0.983807 0.491903 0.870650i \(-0.336301\pi\)
0.491903 + 0.870650i \(0.336301\pi\)
\(150\) 0 0
\(151\) −11.1277 −0.905558 −0.452779 0.891623i \(-0.649567\pi\)
−0.452779 + 0.891623i \(0.649567\pi\)
\(152\) −4.61952 2.35376i −0.374692 0.190915i
\(153\) −5.89674 16.9566i −0.476724 1.37086i
\(154\) 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 \(-0.477457\pi\)
−0.997493 + 0.0707617i \(0.977457\pi\)
\(158\) 1.83786 + 11.6038i 0.146213 + 0.923150i
\(159\) 6.99269 6.09747i 0.554556 0.483561i
\(160\) 0 0
\(161\) 3.11500 1.01213i 0.245497 0.0797667i
\(162\) 8.93946 + 1.04210i 0.702351 + 0.0818753i
\(163\) −2.97400 5.83680i −0.232941 0.457173i 0.744715 0.667383i \(-0.232585\pi\)
−0.977656 + 0.210209i \(0.932585\pi\)
\(164\) −1.63326 5.02666i −0.127536 0.392516i
\(165\) 0 0
\(166\) −3.73173 + 11.4851i −0.289639 + 0.891416i
\(167\) −16.7884 + 2.65903i −1.29913 + 0.205762i −0.767408 0.641159i \(-0.778454\pi\)
−0.531720 + 0.846920i \(0.678454\pi\)
\(168\) −1.21583 4.84483i −0.0938035 0.373787i
\(169\) −12.9216 + 17.7850i −0.993968 + 1.36808i
\(170\) 0 0
\(171\) −14.0005 6.77551i −1.07064 0.518136i
\(172\) −4.34111 0.687565i −0.331007 0.0524263i
\(173\) −3.08240 + 6.04954i −0.234350 + 0.459938i −0.977993 0.208639i \(-0.933097\pi\)
0.743642 + 0.668578i \(0.233097\pi\)
\(174\) 2.58038 4.30941i 0.195618 0.326696i
\(175\) 0 0
\(176\) 2.74259i 0.206731i
\(177\) −2.71590 4.33158i −0.204140 0.325581i
\(178\) −0.203597 + 1.28546i −0.0152603 + 0.0963496i
\(179\) −7.59016 + 5.51457i −0.567315 + 0.412179i −0.834129 0.551569i \(-0.814029\pi\)
0.266814 + 0.963748i \(0.414029\pi\)
\(180\) 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
\(183\) −7.37605 2.96699i −0.545253 0.219326i
\(184\) −1.08014 0.350958i −0.0796287 0.0258729i
\(185\) 0 0
\(186\) −9.52753 2.18425i −0.698593 0.160157i
\(187\) −14.6234 + 7.45099i −1.06937 + 0.544871i
\(188\) −4.13604 + 2.10742i −0.301652 + 0.153699i
\(189\) −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 \(0.754655\pi\)
\(192\) −0.646378 + 1.60692i −0.0466483 + 0.115970i
\(193\) 3.91447 3.91447i 0.281770 0.281770i −0.552045 0.833815i \(-0.686152\pi\)
0.833815 + 0.552045i \(0.186152\pi\)
\(194\) −5.34645 3.88442i −0.383853 0.278885i
\(195\) 0 0
\(196\) −1.06537 + 0.774035i −0.0760977 + 0.0552882i
\(197\) −4.00150 + 25.2645i −0.285095 + 1.80002i 0.264282 + 0.964445i \(0.414865\pi\)
−0.549378 + 0.835574i \(0.685135\pi\)
\(198\) −0.168782 8.22604i −0.0119948 0.584599i
\(199\) 0.0768328i 0.00544653i 0.999996 + 0.00272327i \(0.000866844\pi\)
−0.999996 + 0.00272327i \(0.999133\pi\)
\(200\) 0 0
\(201\) −0.685798 0.410641i −0.0483725 0.0289644i
\(202\) 1.60245 3.14499i 0.112748 0.221281i
\(203\) −8.26024 1.30829i −0.579755 0.0918242i
\(204\) 10.3241 0.919171i 0.722832 0.0643548i
\(205\) 0 0
\(206\) 3.79275 5.22027i 0.264253 0.363713i
\(207\) −3.26133 0.986179i −0.226678 0.0685442i
\(208\) −5.84187 + 0.925261i −0.405061 + 0.0641553i
\(209\) −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 \(0.828726\pi\)
\(212\) 2.43181 + 4.77269i 0.167017 + 0.327790i
\(213\) 9.88661 + 0.676131i 0.677420 + 0.0463278i
\(214\) −11.7945 + 3.83226i −0.806254 + 0.261968i
\(215\) 0 0
\(216\) −1.83984 + 4.85953i −0.125185 + 0.330649i
\(217\) 2.54598 + 16.0747i 0.172832 + 1.09122i
\(218\) 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
\(222\) −8.96742 + 10.7202i −0.601854 + 0.719495i
\(223\) 4.84642 + 2.46937i 0.324540 + 0.165362i 0.608668 0.793425i \(-0.291704\pi\)
−0.284128 + 0.958786i \(0.591704\pi\)
\(224\) 2.88390 0.192689
\(225\) 0 0
\(226\) −4.62245 −0.307481
\(227\) −17.4834 8.90823i −1.16041 0.591260i −0.235662 0.971835i \(-0.575726\pi\)
−0.924750 + 0.380575i \(0.875726\pi\)
\(228\) 5.76169 6.88791i 0.381577 0.456163i
\(229\) −10.2833 14.1538i −0.679543 0.935310i 0.320385 0.947287i \(-0.396188\pi\)
−0.999928 + 0.0119768i \(0.996188\pi\)
\(230\) 0 0
\(231\) −12.6022 + 5.37208i −0.829161 + 0.353457i
\(232\) 2.05059 + 2.05059i 0.134628 + 0.134628i
\(233\) 4.54007 + 28.6649i 0.297430 + 1.87790i 0.455148 + 0.890416i \(0.349586\pi\)
−0.157718 + 0.987484i \(0.550414\pi\)
\(234\) −17.4650 + 3.13471i −1.14172 + 0.204923i
\(235\) 0 0
\(236\) 2.80729 0.912145i 0.182739 0.0593756i
\(237\) −20.3015 1.38839i −1.31872 0.0901857i
\(238\) −7.83489 15.3768i −0.507861 0.996733i
\(239\) 1.74681 + 5.37613i 0.112992 + 0.347753i 0.991523 0.129932i \(-0.0414759\pi\)
−0.878531 + 0.477685i \(0.841476\pi\)
\(240\) 0 0
\(241\) 4.35617 13.4069i 0.280605 0.863614i −0.707076 0.707137i \(-0.749986\pi\)
0.987682 0.156477i \(-0.0500137\pi\)
\(242\) 3.43537 0.544110i 0.220834 0.0349767i
\(243\) −5.21929 + 14.6887i −0.334817 + 0.942283i
\(244\) 2.69804 3.71353i 0.172724 0.237734i
\(245\) 0 0
\(246\) 9.11842 0.811827i 0.581369 0.0517602i
\(247\) 30.2878 + 4.79711i 1.92716 + 0.305233i
\(248\) 2.56206 5.02833i 0.162691 0.319299i
\(249\) −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 \(-0.184062\pi\)
\(252\) 8.64987 0.177478i 0.544891 0.0111801i
\(253\) −0.487266 + 3.07648i −0.0306341 + 0.193416i
\(254\) 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 −0.828112 0.560563i \(-0.810585\pi\)
0.560563 + 0.828112i \(0.310585\pi\)
\(258\) 2.84098 7.06278i 0.176872 0.439710i
\(259\) 22.1319 + 7.19110i 1.37521 + 0.446833i
\(260\) 0 0
\(261\) 6.27666 + 6.02427i 0.388515 + 0.372893i
\(262\) 10.6199 5.41110i 0.656098 0.334299i
\(263\) −21.2757 + 10.8405i −1.31191 + 0.668454i −0.963203 0.268777i \(-0.913381\pi\)
−0.348711 + 0.937230i \(0.613381\pi\)
\(264\) 4.63019 + 1.06150i 0.284968 + 0.0653308i
\(265\) 0 0
\(266\) −14.2201 4.62038i −0.871889 0.283294i
\(267\) −2.09139 0.841253i −0.127991 0.0514839i
\(268\) 0.326329 0.326329i 0.0199337 0.0199337i
\(269\) −11.2436 8.16896i −0.685535 0.498070i 0.189654 0.981851i \(-0.439263\pi\)
−0.875189 + 0.483781i \(0.839263\pi\)
\(270\) 0 0
\(271\) 12.1633 8.83716i 0.738868 0.536819i −0.153488 0.988151i \(-0.549051\pi\)
0.892357 + 0.451331i \(0.149051\pi\)
\(272\) −0.936136 + 5.91053i −0.0567616 + 0.358378i
\(273\) 15.6944 + 25.0309i 0.949867 + 1.51494i
\(274\) 19.8701i 1.20040i
\(275\) 0 0
\(276\) 1.01056 1.68771i 0.0608288 0.101588i
\(277\) 0.823495 1.61620i 0.0494790 0.0971080i −0.864943 0.501870i \(-0.832646\pi\)
0.914422 + 0.404762i \(0.132646\pi\)
\(278\) 9.42893 + 1.49340i 0.565509 + 0.0895679i
\(279\) 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 \(-0.0395782\pi\)
\(282\) −1.95703 7.79835i −0.116540 0.464385i
\(283\) −2.81001 + 0.445062i −0.167038 + 0.0264562i −0.239393 0.970923i \(-0.576948\pi\)
0.0723553 + 0.997379i \(0.476948\pi\)
\(284\) −1.76800 + 5.44135i −0.104912 + 0.322885i
\(285\) 0 0
\(286\) 5.01274 + 15.4276i 0.296409 + 0.912255i
\(287\) −6.91991 13.5811i −0.408469 0.801666i
\(288\) −2.46271 1.71320i −0.145117 0.100951i
\(289\) 17.8900 5.81283i 1.05236 0.341931i
\(290\) 0 0
\(291\) 8.62720 7.52273i 0.505735 0.440990i
\(292\) −1.42179 8.97684i −0.0832041 0.525330i
\(293\) −9.44461 9.44461i −0.551760 0.551760i 0.375189 0.926948i \(-0.377578\pi\)
−0.926948 + 0.375189i \(0.877578\pi\)
\(294\) −0.894424 2.09819i −0.0521639 0.122369i
\(295\) 0 0
\(296\) −4.74298 6.52816i −0.275680 0.379441i
\(297\) 13.9530 + 2.89888i 0.809633 + 0.168210i
\(298\) −10.7000 5.45192i −0.619834 0.315821i
\(299\) 6.71745 0.388480
\(300\) 0 0
\(301\) −12.6754 −0.730597
\(302\) 9.91484 + 5.05186i 0.570535 + 0.290702i
\(303\) 4.68933 + 3.92259i 0.269395 + 0.225347i
\(304\) 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 −0.910955 0.412506i \(-0.864654\pi\)
−0.412506 0.910955i \(-0.635346\pi\)
\(308\) −1.23730 7.81197i −0.0705014 0.445129i
\(309\) 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 \(0.305181\pi\)
\(312\) 0.698977 10.2207i 0.0395718 0.578631i
\(313\) 6.22820 + 12.2235i 0.352039 + 0.690915i 0.997330 0.0730212i \(-0.0232641\pi\)
−0.645292 + 0.763936i \(0.723264\pi\)
\(314\) 5.07459 + 15.6180i 0.286376 + 0.881374i
\(315\) 0 0
\(316\) 3.63047 11.1734i 0.204230 0.628556i
\(317\) 18.6415 2.95253i 1.04701 0.165830i 0.390853 0.920453i \(-0.372180\pi\)
0.656159 + 0.754623i \(0.272180\pi\)
\(318\) −8.99872 + 2.25827i −0.504623 + 0.126638i
\(319\) 4.67490 6.43445i 0.261744 0.360260i
\(320\) 0 0
\(321\) −1.90486 21.3953i −0.106319 1.19417i
\(322\) −3.23498 0.512371i −0.180279 0.0285533i
\(323\) 14.0854 27.6441i 0.783732 1.53816i
\(324\) −7.49202 4.98695i −0.416223 0.277053i
\(325\) 0 0
\(326\) 6.55079i 0.362815i
\(327\) −4.09779 + 2.56931i −0.226608 + 0.142083i
\(328\) −0.826810 + 5.22028i −0.0456530 + 0.288241i
\(329\) −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
\(333\) −14.6277 19.2885i −0.801593 1.05700i
\(334\) 16.1658 + 5.25258i 0.884552 + 0.287408i
\(335\) 0 0
\(336\) −1.11619 + 4.86875i −0.0608932 + 0.265612i
\(337\) 14.3569 7.31518i 0.782068 0.398483i −0.0169001 0.999857i \(-0.505380\pi\)
0.798968 + 0.601374i \(0.205380\pi\)
\(338\) 19.5874 9.98030i 1.06542 0.542857i
\(339\) 1.78909 7.80387i 0.0971698 0.423848i
\(340\) 0 0
\(341\) −14.7201 4.78284i −0.797137 0.259006i
\(342\) 9.39851 + 12.3931i 0.508213 + 0.670143i
\(343\) 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
\(347\) 3.74283 23.6313i 0.200925 1.26859i −0.656634 0.754209i \(-0.728020\pi\)
0.857560 0.514384i \(-0.171980\pi\)
\(348\) −4.25557 + 2.66824i −0.228123 + 0.143033i
\(349\) 24.8956i 1.33263i 0.745670 + 0.666315i \(0.232129\pi\)
−0.745670 + 0.666315i \(0.767871\pi\)
\(350\) 0 0
\(351\) 1.46750 30.6986i 0.0783293 1.63857i
\(352\) −1.24511 + 2.44367i −0.0663646 + 0.130248i
\(353\) 16.7047 + 2.64576i 0.889101 + 0.140820i 0.584244 0.811578i \(-0.301391\pi\)
0.304857 + 0.952398i \(0.401391\pi\)
\(354\) 0.453389 + 5.09246i 0.0240974 + 0.270661i
\(355\) 0 0
\(356\) 0.764995 1.05293i 0.0405447 0.0558049i
\(357\) 28.9924 7.27579i 1.53444 0.385076i
\(358\) 9.26645 1.46766i 0.489747 0.0775683i
\(359\) 1.67961 5.16932i 0.0886466 0.272826i −0.896899 0.442235i \(-0.854186\pi\)
0.985546 + 0.169409i \(0.0541858\pi\)
\(360\) 0 0
\(361\) −2.43509 7.49444i −0.128163 0.394444i
\(362\) −6.90373 13.5493i −0.362852 0.712137i
\(363\) −0.411041 + 6.01037i −0.0215740 + 0.315463i
\(364\) −16.2225 + 5.27101i −0.850290 + 0.276276i
\(365\) 0 0
\(366\) 5.22512 + 5.99226i 0.273122 + 0.313221i
\(367\) 2.80465 + 17.7079i 0.146401 + 0.924343i 0.946084 + 0.323920i \(0.105001\pi\)
−0.799683 + 0.600422i \(0.794999\pi\)
\(368\) 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
\(372\) 7.49747 + 6.27159i 0.388726 + 0.325167i
\(373\) −22.8020 11.6182i −1.18064 0.601568i −0.250269 0.968176i \(-0.580519\pi\)
−0.930376 + 0.366608i \(0.880519\pi\)
\(374\) 16.4122 0.848656
\(375\) 0 0
\(376\) 4.64199 0.239392
\(377\) −15.2829 7.78702i −0.787109 0.401052i
\(378\) −3.04824 + 14.6719i −0.156785 + 0.754639i
\(379\) −5.71732 7.86922i −0.293679 0.404215i 0.636526 0.771255i \(-0.280371\pi\)
−0.930205 + 0.367041i \(0.880371\pi\)
\(380\) 0 0
\(381\) 8.51045 + 19.9643i 0.436004 + 1.02280i
\(382\) 9.12687 + 9.12687i 0.466971 + 0.466971i
\(383\) 3.81540 + 24.0895i 0.194958 + 1.23092i 0.869968 + 0.493108i \(0.164139\pi\)
−0.675010 + 0.737808i \(0.735861\pi\)
\(384\) 1.30545 1.13833i 0.0666187 0.0580900i
\(385\) 0 0
\(386\) −5.26495 + 1.71069i −0.267979 + 0.0870717i
\(387\) 10.8242 + 7.52989i 0.550224 + 0.382766i
\(388\) 3.00023 + 5.88829i 0.152314 + 0.298932i
\(389\) −5.49358 16.9075i −0.278536 0.857245i −0.988262 0.152767i \(-0.951181\pi\)
0.709726 0.704477i \(-0.248819\pi\)
\(390\) 0 0
\(391\) 2.10020 6.46376i 0.106212 0.326886i
\(392\) 1.30065 0.206003i 0.0656929 0.0104047i
\(393\) 5.02496 + 20.0234i 0.253475 + 1.01004i
\(394\) 15.0352 20.6942i 0.757462 1.04256i
\(395\) 0 0
\(396\) −3.58416 + 7.40608i −0.180111 + 0.372170i
\(397\) −19.0036 3.00987i −0.953762 0.151061i −0.339889 0.940466i \(-0.610389\pi\)
−0.613873 + 0.789405i \(0.710389\pi\)
\(398\) 0.0348814 0.0684585i 0.00174845 0.00343152i
\(399\) 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 \(0.716423\pi\)
\(402\) 0.424623 + 0.677230i 0.0211783 + 0.0337772i
\(403\) −5.22164 + 32.9681i −0.260108 + 1.64226i
\(404\) −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
\(408\) −9.61614 3.86806i −0.476070 0.191498i
\(409\) 14.9223 + 4.84855i 0.737860 + 0.239745i 0.653749 0.756711i \(-0.273195\pi\)
0.0841106 + 0.996456i \(0.473195\pi\)
\(410\) 0 0
\(411\) 33.5457 + 7.69057i 1.65469 + 0.379348i
\(412\) −5.74931 + 2.92942i −0.283248 + 0.144322i
\(413\) 7.58476 3.86463i 0.373222 0.190166i
\(414\) 2.45815 + 2.35930i 0.120811 + 0.115953i
\(415\) 0 0
\(416\) 5.62520 + 1.82774i 0.275798 + 0.0896122i
\(417\) −6.17063 + 15.3404i −0.302177 + 0.751223i
\(418\) 10.0545 10.0545i 0.491783 0.491783i
\(419\) −2.78733 2.02511i −0.136170 0.0989333i 0.517615 0.855614i \(-0.326820\pi\)
−0.653785 + 0.756680i \(0.726820\pi\)
\(420\) 0 0
\(421\) 10.9206 7.93429i 0.532238 0.386694i −0.288956 0.957342i \(-0.593308\pi\)
0.821194 + 0.570649i \(0.193308\pi\)
\(422\) 1.00913 6.37141i 0.0491238 0.310156i
\(423\) 13.9230 0.285673i 0.676962 0.0138899i
\(424\) 5.35652i 0.260135i
\(425\) 0 0
\(426\) −8.50208 5.09087i −0.411927 0.246653i
\(427\) 6.00974 11.7948i 0.290832 0.570790i
\(428\) 12.2488 + 1.94001i 0.592066 + 0.0937741i
\(429\) −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 \(-0.0347173\pi\)
\(432\) 3.84548 3.49460i 0.185016 0.168134i
\(433\) −2.57946 + 0.408546i −0.123961 + 0.0196335i −0.218107 0.975925i \(-0.569988\pi\)
0.0941457 + 0.995558i \(0.469988\pi\)
\(434\) 5.02927 15.4785i 0.241413 0.742992i
\(435\) 0 0
\(436\) −0.862912 2.65577i −0.0413260 0.127188i
\(437\) −2.67322 5.24649i −0.127877 0.250974i
\(438\) 15.7055 + 1.07407i 0.750436 + 0.0513213i
\(439\) 10.4899 3.40836i 0.500653 0.162672i −0.0477940 0.998857i \(-0.515219\pi\)
0.548447 + 0.836185i \(0.315219\pi\)
\(440\) 0 0
\(441\) 3.88846 0.697923i 0.185165 0.0332344i
\(442\) −5.53695 34.9589i −0.263366 1.66283i
\(443\) −1.32181 1.32181i −0.0628009 0.0628009i 0.675009 0.737810i \(-0.264140\pi\)
−0.737810 + 0.675009i \(0.764140\pi\)
\(444\) 12.8569 5.48068i 0.610162 0.260102i
\(445\) 0 0
\(446\) −3.19712 4.40046i −0.151388 0.208368i
\(447\) 13.3456 15.9542i 0.631224 0.754607i
\(448\) −2.56957 1.30926i −0.121401 0.0618568i
\(449\) −20.5238 −0.968579 −0.484289 0.874908i \(-0.660922\pi\)
−0.484289 + 0.874908i \(0.660922\pi\)
\(450\) 0 0
\(451\) 14.4955 0.682569
\(452\) 4.11863 + 2.09855i 0.193724 + 0.0987075i
\(453\) −12.3663 + 14.7835i −0.581019 + 0.694588i
\(454\) 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 \(-0.130900\pi\)
−0.399742 + 0.916628i \(0.630900\pi\)
\(458\) 2.73683 + 17.2797i 0.127884 + 0.807427i
\(459\) −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 \(0.505330\pi\)
\(462\) 13.6675 + 0.934699i 0.635868 + 0.0434861i
\(463\) −14.9657 29.3718i −0.695515 1.36502i −0.920531 0.390669i \(-0.872244\pi\)
0.225017 0.974355i \(-0.427756\pi\)
\(464\) −0.896139 2.75803i −0.0416022 0.128038i
\(465\) 0 0
\(466\) 8.96836 27.6018i 0.415451 1.27863i
\(467\) 3.65255 0.578507i 0.169020 0.0267701i −0.0713509 0.997451i \(-0.522731\pi\)
0.240371 + 0.970681i \(0.422731\pi\)
\(468\) 16.9845 + 5.13588i 0.785110 + 0.237406i
\(469\) 0.782294 1.07673i 0.0361230 0.0497190i
\(470\) 0 0
\(471\) −28.3312 + 2.52237i −1.30543 + 0.116225i
\(472\) −2.91542 0.461757i −0.134193 0.0212541i
\(473\) 5.47254 10.7405i 0.251628 0.493847i
\(474\) 17.4585 + 10.4538i 0.801894 + 0.480157i
\(475\) 0 0
\(476\) 17.2578i 0.791012i
\(477\) −0.329645 16.0662i −0.0150934 0.735619i
\(478\) 0.884293 5.58321i 0.0404466 0.255370i
\(479\) −4.35190 + 3.16184i −0.198844 + 0.144468i −0.682752 0.730651i \(-0.739217\pi\)
0.483908 + 0.875119i \(0.339217\pi\)
\(480\) 0 0
\(481\) 38.6120 + 28.0533i 1.76056 + 1.27912i
\(482\) −9.96798 + 9.96798i −0.454029 + 0.454029i
\(483\) 2.11709 5.26316i 0.0963309 0.239482i
\(484\) −3.30796 1.07482i −0.150362 0.0488555i
\(485\) 0 0
\(486\) 11.3190 10.7183i 0.513439 0.486190i
\(487\) 3.73900 1.90512i 0.169430 0.0863291i −0.367219 0.930135i \(-0.619690\pi\)
0.536649 + 0.843806i \(0.319690\pi\)
\(488\) −4.08988 + 2.08390i −0.185140 + 0.0943336i
\(489\) −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 \(0.852499\pi\)
\(492\) −8.49313 3.41633i −0.382900 0.154020i
\(493\) −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
\(497\) −2.58115 + 16.2967i −0.115780 + 0.731007i
\(498\) 11.1112 + 17.7212i 0.497904 + 0.794106i
\(499\) 10.2536i 0.459015i −0.973307 0.229508i \(-0.926288\pi\)
0.973307 0.229508i \(-0.0737116\pi\)
\(500\) 0 0
\(501\) −15.1245 + 25.2590i −0.675714 + 1.12849i
\(502\) −7.86229 + 15.4306i −0.350911 + 0.688702i
\(503\) 0.658974 + 0.104371i 0.0293822 + 0.00465369i 0.171108 0.985252i \(-0.445265\pi\)
−0.141726 + 0.989906i \(0.545265\pi\)
\(504\) −7.78767 3.76883i −0.346890 0.167877i
\(505\) 0 0
\(506\) 1.83085 2.51995i 0.0813911 0.112025i
\(507\) 9.26810 + 36.9314i 0.411611 + 1.64018i
\(508\) −12.3757 + 1.96012i −0.549084 + 0.0869664i
\(509\) 8.01814 24.6773i 0.355398 1.09380i −0.600381 0.799714i \(-0.704984\pi\)
0.955779 0.294087i \(-0.0950156\pi\)
\(510\) 0 0
\(511\) −8.09964 24.9281i −0.358307 1.10276i
\(512\) 0.453990 + 0.891007i 0.0200637 + 0.0393773i
\(513\) −24.5603 + 11.0704i −1.08436 + 0.488770i
\(514\) 5.76888 1.87442i 0.254454 0.0826772i
\(515\) 0 0
\(516\) −5.73777 + 5.00321i −0.252591 + 0.220254i
\(517\) −1.99158 12.5743i −0.0875896 0.553019i
\(518\) −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 \(-0.552555\pi\)
\(522\) −2.85758 8.21721i −0.125073 0.359657i
\(523\) 24.2703 + 12.3663i 1.06126 + 0.540741i 0.895334 0.445396i \(-0.146937\pi\)
0.165931 + 0.986137i \(0.446937\pi\)
\(524\) −11.9190 −0.520682
\(525\) 0 0
\(526\) 23.8782 1.04114
\(527\) 30.0906 + 15.3319i 1.31077 + 0.667868i
\(528\) −3.64362 3.04786i −0.158568 0.132641i
\(529\) 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
\(533\) −4.89032 30.8763i −0.211823 1.33740i
\(534\) 1.48152 + 1.69903i 0.0641116 + 0.0735243i
\(535\) 0 0
\(536\) −0.438912 + 0.142611i −0.0189581 + 0.00615987i
\(537\) −1.10873 + 16.2122i −0.0478451 + 0.699606i
\(538\) 6.30950 + 12.3831i 0.272022 + 0.533873i
\(539\) −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 \(-0.00737544\pi\)
\(542\) −14.8496 + 2.35194i −0.637844 + 0.101025i
\(543\) 25.5467 6.41107i 1.09631 0.275125i
\(544\) 3.51743 4.84132i 0.150808 0.207570i
\(545\) 0 0
\(546\) −2.62000 29.4278i −0.112126 1.25939i
\(547\) −22.1803 3.51301i −0.948360 0.150205i −0.336953 0.941522i \(-0.609396\pi\)
−0.611407 + 0.791316i \(0.709396\pi\)
\(548\) −9.02083 + 17.7044i −0.385351 + 0.756293i
\(549\) −12.1388 + 6.50207i −0.518072 + 0.277502i
\(550\) 0 0
\(551\) 15.0352i 0.640520i
\(552\) −1.66662 + 1.04497i −0.0709362 + 0.0444770i
\(553\) 5.30021 33.4642i 0.225388 1.42304i
\(554\) −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 −0.670956 0.741498i \(-0.734116\pi\)
0.741498 + 0.670956i \(0.234116\pi\)
\(558\) −13.4899 + 10.2302i −0.571071 + 0.433081i
\(559\) −24.7240 8.03333i −1.04572 0.339773i
\(560\) 0 0
\(561\) −6.35223 + 27.7080i −0.268191 + 1.16983i
\(562\) −20.4199 + 10.4045i −0.861362 + 0.438886i
\(563\) −42.1004 + 21.4512i −1.77432 + 0.904062i −0.845023 + 0.534729i \(0.820414\pi\)
−0.929297 + 0.369332i \(0.879586\pi\)
\(564\) −1.79665 + 7.83686i −0.0756525 + 0.329991i
\(565\) 0 0
\(566\) 2.70579 + 0.879165i 0.113733 + 0.0369541i
\(567\) −23.5900 10.8248i −0.990688 0.454600i
\(568\) 4.04562 4.04562i 0.169750 0.169750i
\(569\) 19.9798 + 14.5162i 0.837599 + 0.608551i 0.921699 0.387906i \(-0.126802\pi\)
−0.0841003 + 0.996457i \(0.526802\pi\)
\(570\) 0 0
\(571\) 4.83866 3.51549i 0.202491 0.147119i −0.481919 0.876216i \(-0.660060\pi\)
0.684410 + 0.729097i \(0.260060\pi\)
\(572\) 2.53761 16.0218i 0.106103 0.669907i
\(573\) −18.9409 + 11.8760i −0.791269 + 0.496126i
\(574\) 15.2424i 0.636206i
\(575\) 0 0
\(576\) 1.41652 + 2.64452i 0.0590216 + 0.110188i
\(577\) 14.3066 28.0783i 0.595591 1.16891i −0.374739 0.927130i \(-0.622268\pi\)
0.970330 0.241783i \(-0.0777324\pi\)
\(578\) −18.5791 2.94264i −0.772789 0.122398i
\(579\) −0.850312 9.55068i −0.0353377 0.396913i
\(580\) 0 0
\(581\) 20.4704 28.1751i 0.849256 1.16890i
\(582\) −11.1021 + 2.78613i −0.460198 + 0.115489i
\(583\) −14.5099 + 2.29814i −0.600937 + 0.0951791i
\(584\) −2.80857 + 8.64390i −0.116220 + 0.357687i
\(585\) 0 0
\(586\) 4.12744 + 12.7030i 0.170503 + 0.524755i
\(587\) 5.11433 + 10.0374i 0.211091 + 0.414289i 0.972139 0.234407i \(-0.0753147\pi\)
−0.761048 + 0.648696i \(0.775315\pi\)
\(588\) −0.155623 + 2.27556i −0.00641777 + 0.0938427i
\(589\) 27.8269 9.04151i 1.14659 0.372549i
\(590\) 0 0
\(591\) 29.1177 + 33.3927i 1.19774 + 1.37359i
\(592\) 1.26231 + 7.96990i 0.0518805 + 0.327561i
\(593\) 17.4049 + 17.4049i 0.714734 + 0.714734i 0.967522 0.252788i \(-0.0813475\pi\)
−0.252788 + 0.967522i \(0.581347\pi\)
\(594\) −11.1161 8.91744i −0.456100 0.365887i
\(595\) 0 0
\(596\) 7.05865 + 9.71540i 0.289134 + 0.397958i
\(597\) 0.102075 + 0.0853849i 0.00417764 + 0.00349457i
\(598\) −5.98529 3.04966i −0.244757 0.124710i
\(599\) −25.8531 −1.05633 −0.528165 0.849142i \(-0.677120\pi\)
−0.528165 + 0.849142i \(0.677120\pi\)
\(600\) 0 0
\(601\) −36.7027 −1.49714 −0.748568 0.663058i \(-0.769258\pi\)
−0.748568 + 0.663058i \(0.769258\pi\)
\(602\) 11.2939 + 5.75450i 0.460303 + 0.234536i
\(603\) −1.30768 + 0.454755i −0.0532530 + 0.0185190i
\(604\) −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 \(-0.482144\pi\)
−0.998427 + 0.0560654i \(0.982144\pi\)
\(608\) −0.811051 5.12077i −0.0328925 0.207675i
\(609\) −10.9178 + 9.52007i −0.442411 + 0.385773i
\(610\) 0 0
\(611\) −26.1121 + 8.48435i −1.05638 + 0.343240i
\(612\) 10.2521 14.7374i 0.414417 0.595723i
\(613\) −9.97216 19.5715i −0.402772 0.790484i 0.597161 0.802122i \(-0.296295\pi\)
−0.999932 + 0.0116379i \(0.996295\pi\)
\(614\) 10.1339 + 31.1890i 0.408972 + 1.25869i
\(615\) 0 0
\(616\) −2.44412 + 7.52224i −0.0984766 + 0.303080i
\(617\) 6.32162 1.00125i 0.254499 0.0403086i −0.0278814 0.999611i \(-0.508876\pi\)
0.282380 + 0.959303i \(0.408876\pi\)
\(618\) −2.72038 10.8401i −0.109430 0.436053i
\(619\) −14.0949 + 19.4000i −0.566524 + 0.779753i −0.992138 0.125152i \(-0.960058\pi\)
0.425614 + 0.904905i \(0.360058\pi\)
\(620\) 0 0
\(621\) −4.93451 + 3.23682i −0.198015 + 0.129889i
\(622\) −10.2243 1.61936i −0.409956 0.0649306i
\(623\) 1.70399 3.34426i 0.0682688 0.133985i
\(624\) −5.26288 + 8.78935i −0.210684 + 0.351856i
\(625\) 0 0
\(626\) 13.7188i 0.548313i
\(627\) 13.0831 + 20.8661i 0.522487 + 0.833312i
\(628\) 2.56892 16.2195i 0.102511 0.647230i
\(629\) 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
\(633\) 10.3660 + 4.16968i 0.412011 + 0.165730i
\(634\) −17.9501 5.83235i −0.712891 0.231632i
\(635\) 0 0
\(636\) 9.04315 + 2.07320i 0.358584 + 0.0822077i
\(637\) −6.93992 + 3.53606i −0.274970 + 0.140104i
\(638\) −7.08655 + 3.61078i −0.280559 + 0.142952i
\(639\) 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 \(0.475641\pi\)
\(642\) −8.01603 + 19.9281i −0.316367 + 0.786501i
\(643\) −2.50826 + 2.50826i −0.0989163 + 0.0989163i −0.754833 0.655917i \(-0.772282\pi\)
0.655917 + 0.754833i \(0.272282\pi\)
\(644\) 2.64978 + 1.92518i 0.104416 + 0.0758627i
\(645\) 0 0
\(646\) −25.1003 + 18.2365i −0.987560 + 0.717504i
\(647\) 5.85671 36.9778i 0.230251 1.45375i −0.553591 0.832789i \(-0.686743\pi\)
0.783842 0.620960i \(-0.213257\pi\)
\(648\) 4.41141 + 7.84471i 0.173296 + 0.308169i
\(649\) 8.09547i 0.317775i
\(650\) 0 0
\(651\) 24.1851 + 14.4815i 0.947889 + 0.567576i
\(652\) 2.97400 5.83680i 0.116471 0.228587i
\(653\) −2.19851 0.348209i −0.0860342 0.0136265i 0.113269 0.993564i \(-0.463868\pi\)
−0.199303 + 0.979938i \(0.563868\pi\)
\(654\) 4.81760 0.428918i 0.188383 0.0167720i
\(655\) 0 0
\(656\) 3.10665 4.27594i 0.121294 0.166947i
\(657\) −7.89200 + 26.0991i −0.307896 + 1.01822i
\(658\) 13.2222 2.09419i 0.515456 0.0816401i
\(659\) −4.81311 + 14.8132i −0.187492 + 0.577041i −0.999982 0.00593344i \(-0.998111\pi\)
0.812490 + 0.582975i \(0.198111\pi\)
\(660\) 0 0
\(661\) −0.225919 0.695307i −0.00878723 0.0270443i 0.946567 0.322508i \(-0.104526\pi\)
−0.955354 + 0.295464i \(0.904526\pi\)
\(662\) 14.4080 + 28.2773i 0.559984 + 1.09903i
\(663\) 61.1625 + 4.18282i 2.37536 + 0.162447i
\(664\) −11.4851 + 3.73173i −0.445708 + 0.144819i
\(665\) 0 0
\(666\) 4.27660 + 23.8270i 0.165715 + 0.923277i
\(667\) 0.515226 + 3.25301i 0.0199496 + 0.125957i
\(668\) −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
\(672\) 3.20490 3.83135i 0.123632 0.147797i
\(673\) 13.4197 + 6.83769i 0.517292 + 0.263574i 0.693088 0.720853i \(-0.256250\pi\)
−0.175796 + 0.984427i \(0.556250\pi\)
\(674\) −16.1131 −0.620652
\(675\) 0 0
\(676\) −21.9835 −0.845520
\(677\) 20.6424 + 10.5178i 0.793351 + 0.404233i 0.803193 0.595719i \(-0.203133\pi\)
−0.00984177 + 0.999952i \(0.503133\pi\)
\(678\) −5.13697 + 6.14107i −0.197284 + 0.235846i
\(679\) 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
\(683\) −0.679239 4.28854i −0.0259903 0.164097i 0.971279 0.237942i \(-0.0764728\pi\)
−0.997270 + 0.0738455i \(0.976473\pi\)
\(684\) −2.74778 15.3092i −0.105064 0.585361i
\(685\) 0 0
\(686\) −15.5874 + 5.06466i −0.595130 + 0.193370i
\(687\) −30.2317 2.06751i −1.15341 0.0788803i
\(688\) −1.99539 3.91618i −0.0760736 0.149303i
\(689\) 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 \(0.909741\pi\)
\(692\) −6.70597 + 1.06212i −0.254923 + 0.0403758i
\(693\) −6.86790 + 22.7124i −0.260890 + 0.862772i
\(694\) −14.0633 + 19.3564i −0.533834 + 0.734759i
\(695\) 0 0
\(696\) 5.00310 0.445433i 0.189642 0.0168841i
\(697\) −31.2392 4.94780i −1.18327 0.187411i
\(698\) 11.3024 22.1821i 0.427801 0.839606i
\(699\) 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 \(0.879595\pi\)
\(702\) −15.2444 + 26.6864i −0.575363 + 1.00721i
\(703\) 6.54457 41.3208i 0.246833 1.55844i
\(704\) 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
\(708\) 1.90795 4.74325i 0.0717053 0.178262i
\(709\) −21.2009 6.88858i −0.796216 0.258706i −0.117467 0.993077i \(-0.537477\pi\)
−0.678749 + 0.734371i \(0.737477\pi\)
\(710\) 0 0
\(711\) −24.4058 + 25.4282i −0.915287 + 0.953634i
\(712\) −1.15963 + 0.590863i −0.0434591 + 0.0221435i
\(713\) 5.71079 2.90979i 0.213871 0.108973i
\(714\) −29.1356 6.67952i −1.09037 0.249975i
\(715\) 0 0
\(716\) −8.92277 2.89918i −0.333460 0.108348i
\(717\) 9.08361 + 3.65385i 0.339233 + 0.136455i
\(718\) −3.84337 + 3.84337i −0.143433 + 0.143433i
\(719\) 2.20624 + 1.60292i 0.0822787 + 0.0597790i 0.628164 0.778081i \(-0.283807\pi\)
−0.545885 + 0.837860i \(0.683807\pi\)
\(720\) 0 0
\(721\) −15.0547 + 10.9379i −0.560667 + 0.407348i
\(722\) −1.23272 + 7.78310i −0.0458772 + 0.289657i
\(723\) −12.9704 20.6865i −0.482376 0.769339i
\(724\) 15.2068i 0.565155i
\(725\) 0 0
\(726\) 3.09489 5.16867i 0.114862 0.191827i
\(727\) −8.81556 + 17.3015i −0.326951 + 0.641677i −0.994713 0.102698i \(-0.967253\pi\)
0.667762 + 0.744375i \(0.267253\pi\)
\(728\) 16.8473 + 2.66836i 0.624404 + 0.0988959i
\(729\) 13.7142 + 23.2577i 0.507934 + 0.861396i
\(730\) 0 0
\(731\) −15.4599 + 21.2787i −0.571805 + 0.787022i
\(732\) −1.93519 7.71130i −0.0715266 0.285018i
\(733\) 23.9728 3.79691i 0.885454 0.140242i 0.302889 0.953026i \(-0.402049\pi\)
0.582566 + 0.812784i \(0.302049\pi\)
\(734\) 5.54024 17.0511i 0.204494 0.629368i
\(735\) 0 0
\(736\) −0.350958 1.08014i −0.0129365 0.0398144i
\(737\) 0.574618 + 1.12775i 0.0211663 + 0.0415412i
\(738\) 9.05484 13.0163i 0.333313 0.479136i
\(739\) −6.13821 + 1.99443i −0.225798 + 0.0733662i −0.419731 0.907649i \(-0.637876\pi\)
0.193933 + 0.981015i \(0.437876\pi\)
\(740\) 0 0
\(741\) 40.0322 34.9072i 1.47062 1.28235i
\(742\) −2.41654 15.2575i −0.0887141 0.560119i
\(743\) −23.0403 23.0403i −0.845265 0.845265i 0.144273 0.989538i \(-0.453916\pi\)
−0.989538 + 0.144273i \(0.953916\pi\)
\(744\) −3.83305 8.99180i −0.140526 0.329656i
\(745\) 0 0
\(746\) 15.0422 + 20.7038i 0.550734 + 0.758020i
\(747\) −34.2184 + 11.8996i −1.25198 + 0.435385i
\(748\) −14.6234 7.45099i −0.534684 0.272435i
\(749\) 35.7645 1.30681
\(750\) 0 0
\(751\) 31.4069 1.14606 0.573028 0.819536i \(-0.305769\pi\)
0.573028 + 0.819536i \(0.305769\pi\)
\(752\) −4.13604 2.10742i −0.150826 0.0768497i
\(753\) −23.0077 19.2458i −0.838449 0.701357i
\(754\) 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 \(-0.197746\pi\)
−0.582043 + 0.813158i \(0.697746\pi\)
\(758\) 1.52162 + 9.60713i 0.0552678 + 0.348947i
\(759\) 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 \(0.345500\pi\)
\(762\) 1.48075 21.6520i 0.0536419 0.784370i
\(763\) −3.65604 7.17538i −0.132358 0.259766i
\(764\) −3.98859 12.2756i −0.144302 0.444116i
\(765\) 0 0
\(766\) 7.53686 23.1961i 0.272318 0.838108i
\(767\) 17.2438 2.73115i 0.622637 0.0986161i
\(768\) −1.67996 + 0.421593i −0.0606203 + 0.0152129i
\(769\) 15.8011 21.7484i 0.569803 0.784266i −0.422728 0.906256i \(-0.638928\pi\)
0.992531 + 0.121990i \(0.0389276\pi\)
\(770\) 0 0
\(771\) 0.931697 + 10.4648i 0.0335543 + 0.376881i
\(772\) 5.46774 + 0.866006i 0.196788 + 0.0311682i
\(773\) 9.86911 19.3692i 0.354967 0.696662i −0.642613 0.766191i \(-0.722150\pi\)
0.997580 + 0.0695289i \(0.0221496\pi\)
\(774\) −6.22592 11.6233i −0.223786 0.417789i
\(775\) 0 0
\(776\) 6.60858i 0.237234i
\(777\) 34.1490 21.4114i 1.22509 0.768130i
\(778\) −2.78103 + 17.5587i −0.0997048 + 0.629511i
\(779\) −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