Properties

Label 750.2.l.c.107.7
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 107.7
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.c.743.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.891007 + 0.453990i) q^{2} +(-0.646378 - 1.60692i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.153600 - 1.72523i) q^{6} +(2.03922 + 2.03922i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.16439 + 2.07736i) q^{9} +O(q^{10})\) \(q+(0.891007 + 0.453990i) q^{2} +(-0.646378 - 1.60692i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.153600 - 1.72523i) q^{6} +(2.03922 + 2.03922i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.16439 + 2.07736i) q^{9} +(2.60836 - 0.847507i) q^{11} +(0.920095 - 1.46746i) 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} +(-2.87159 + 0.868327i) q^{18} +(3.04743 - 4.19443i) q^{19} +(1.95876 - 4.59498i) q^{21} +(2.70883 + 0.429036i) q^{22} +(-0.515607 + 1.01194i) q^{23} +(1.48602 - 0.889798i) q^{24} +5.91469i q^{26} +(4.73716 + 2.13524i) 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} +(-3.04786 - 3.64362i) q^{33} +(-5.69132 - 1.84922i) q^{34} +(-2.95281 - 0.529988i) q^{36} +(7.18975 - 3.66336i) q^{37} +(4.61952 - 2.35376i) q^{38} +(6.73285 - 7.72135i) q^{39} +(5.02666 + 1.63326i) q^{41} +(3.83135 - 3.20490i) 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} +(1.72801 - 0.118176i) q^{48} +1.31687i q^{49} +(5.32473 + 8.89266i) q^{51} +(-2.68521 + 5.27002i) q^{52} +(-5.29057 - 0.837944i) q^{53} +(3.25146 + 4.05314i) q^{54} +(-1.69511 + 2.33312i) q^{56} +(-8.70992 - 2.18579i) 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} +(-8.64987 - 0.177478i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-1.06150 - 4.63019i) q^{66} +(-0.0721944 - 0.455818i) q^{67} +(-4.23147 - 4.23147i) q^{68} +(1.95938 + 0.174447i) q^{69} +(-3.36294 - 4.62869i) q^{71} +(-2.39037 - 1.81277i) q^{72} +(-8.09812 - 4.12620i) q^{73} +8.06924 q^{74} +5.18460 q^{76} +(7.04728 + 3.59077i) q^{77} +(9.50443 - 3.82312i) q^{78} +(-6.90557 - 9.50470i) q^{79} +(0.369168 - 8.99243i) q^{81} +(3.73730 + 3.73730i) q^{82} +(1.88912 + 11.9275i) q^{83} +(4.86875 - 1.11619i) q^{84} +(-4.18011 + 1.35820i) q^{86} +(-4.25557 - 2.66824i) 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} +(2.37923 - 9.48072i) q^{93} +(2.72849 - 3.75545i) q^{94} +(1.59332 + 0.679206i) 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
\(3\) −0.646378 1.60692i −0.373187 0.927756i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) 0.153600 1.72523i 0.0627067 0.704321i
\(7\) 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
\(9\) −2.16439 + 2.07736i −0.721463 + 0.692453i
\(10\) 0 0
\(11\) 2.60836 0.847507i 0.786450 0.255533i 0.111858 0.993724i \(-0.464320\pi\)
0.674592 + 0.738191i \(0.264320\pi\)
\(12\) 0.920095 1.46746i 0.265608 0.423618i
\(13\) 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 −0.824387 0.566026i \(-0.808480\pi\)
−0.609127 + 0.793073i \(0.708480\pi\)
\(18\) −2.87159 + 0.868327i −0.676839 + 0.204667i
\(19\) 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
\(21\) 1.95876 4.59498i 0.427437 1.00271i
\(22\) 2.70883 + 0.429036i 0.577523 + 0.0914707i
\(23\) −0.515607 + 1.01194i −0.107512 + 0.211003i −0.938494 0.345295i \(-0.887779\pi\)
0.830983 + 0.556298i \(0.187779\pi\)
\(24\) 1.48602 0.889798i 0.303333 0.181629i
\(25\) 0 0
\(26\) 5.91469i 1.15997i
\(27\) 4.73716 + 2.13524i 0.911668 + 0.410928i
\(28\) −0.451141 + 2.84839i −0.0852576 + 0.538296i
\(29\) 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
\(33\) −3.04786 3.64362i −0.530565 0.634272i
\(34\) −5.69132 1.84922i −0.976053 0.317139i
\(35\) 0 0
\(36\) −2.95281 0.529988i −0.492136 0.0883313i
\(37\) 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
\(39\) 6.73285 7.72135i 1.07812 1.23641i
\(40\) 0 0
\(41\) 5.02666 + 1.63326i 0.785033 + 0.255073i 0.673988 0.738743i \(-0.264580\pi\)
0.111045 + 0.993815i \(0.464580\pi\)
\(42\) 3.83135 3.20490i 0.591190 0.494527i
\(43\) −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 \(-0.840063\pi\)
0.982324 0.187187i \(-0.0599371\pi\)
\(48\) 1.72801 0.118176i 0.249417 0.0170573i
\(49\) 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 −0.217894 0.975972i \(-0.569919\pi\)
−0.508821 + 0.860872i \(0.669919\pi\)
\(54\) 3.25146 + 4.05314i 0.442468 + 0.551563i
\(55\) 0 0
\(56\) −1.69511 + 2.33312i −0.226519 + 0.311777i
\(57\) −8.70992 2.18579i −1.15366 0.289516i
\(58\) 2.86426 0.453655i 0.376096 0.0595678i
\(59\) −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 \(0.994939\pi\)
\(62\) 2.56206 + 5.02833i 0.325382 + 0.638599i
\(63\) −8.64987 0.177478i −1.08978 0.0223601i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) −1.06150 4.63019i −0.130662 0.569937i
\(67\) −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
\(69\) 1.95938 + 0.174447i 0.235882 + 0.0210009i
\(70\) 0 0
\(71\) −3.36294 4.62869i −0.399107 0.549324i 0.561412 0.827536i \(-0.310258\pi\)
−0.960520 + 0.278212i \(0.910258\pi\)
\(72\) −2.39037 1.81277i −0.281707 0.213637i
\(73\) −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
\(78\) 9.50443 3.82312i 1.07617 0.432884i
\(79\) −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
\(81\) 0.369168 8.99243i 0.0410187 0.999158i
\(82\) 3.73730 + 3.73730i 0.412716 + 0.412716i
\(83\) 1.88912 + 11.9275i 0.207358 + 1.30921i 0.843288 + 0.537462i \(0.180617\pi\)
−0.635930 + 0.771747i \(0.719383\pi\)
\(84\) 4.86875 1.11619i 0.531224 0.121786i
\(85\) 0 0
\(86\) −4.18011 + 1.35820i −0.450753 + 0.146458i
\(87\) −4.25557 2.66824i −0.456245 0.286066i
\(88\) 1.24511 + 2.44367i 0.132729 + 0.260496i
\(89\) 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
\(92\) −1.12174 + 0.177666i −0.116950 + 0.0185230i
\(93\) 2.37923 9.48072i 0.246715 0.983105i
\(94\) 2.72849 3.75545i 0.281423 0.387345i
\(95\) 0 0
\(96\) 1.59332 + 0.679206i 0.162618 + 0.0693212i
\(97\) 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 \(-0.943810\pi\)
0.984460 0.175610i \(-0.0561896\pi\)
\(102\) 0.707192 + 10.3408i 0.0700225 + 1.02389i
\(103\) −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 −0.989851 0.142106i \(-0.954613\pi\)
0.142106 + 0.989851i \(0.454613\pi\)
\(108\) 1.05699 + 5.08751i 0.101709 + 0.489546i
\(109\) −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
\(111\) −10.5340 9.18544i −0.999846 0.871844i
\(112\) −2.56957 + 1.30926i −0.242802 + 0.123714i
\(113\) −4.11863 + 2.09855i −0.387449 + 0.197415i −0.636854 0.770984i \(-0.719765\pi\)
0.249406 + 0.968399i \(0.419765\pi\)
\(114\) −6.76826 5.90178i −0.633906 0.552752i
\(115\) 0 0
\(116\) 2.75803 + 0.896139i 0.256077 + 0.0832044i
\(117\) −16.7596 5.82824i −1.54942 0.538821i
\(118\) −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
\(123\) −0.624604 9.13316i −0.0563186 0.823509i
\(124\) 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
\(129\) 7.00302 + 2.98527i 0.616581 + 0.262838i
\(130\) 0 0
\(131\) 7.00579 9.64264i 0.612099 0.842482i −0.384649 0.923063i \(-0.625678\pi\)
0.996748 + 0.0805811i \(0.0256776\pi\)
\(132\) 1.15626 4.60744i 0.100639 0.401026i
\(133\) 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 \(-0.827321\pi\)
0.0857255 0.996319i \(-0.472679\pi\)
\(138\) 1.66662 + 1.04497i 0.141872 + 0.0889540i
\(139\) −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
\(141\) −7.83686 + 1.79665i −0.659982 + 0.151305i
\(142\) −0.895020 5.65093i −0.0751084 0.474216i
\(143\) 11.4704 + 11.4704i 0.959201 + 0.959201i
\(144\) −1.30685 2.70040i −0.108904 0.225033i
\(145\) 0 0
\(146\) −5.34223 7.35294i −0.442126 0.608534i
\(147\) 2.11610 0.851194i 0.174533 0.0702053i
\(148\) 7.18975 + 3.66336i 0.590994 + 0.301126i
\(149\) −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 \(0.649567\pi\)
\(152\) 4.61952 + 2.35376i 0.374692 + 0.190915i
\(153\) 10.8480 14.3044i 0.877009 1.15645i
\(154\) 4.64900 + 6.39880i 0.374627 + 0.515630i
\(155\) 0 0
\(156\) 10.2042 + 0.908493i 0.816988 + 0.0727376i
\(157\) −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
\(159\) 2.07320 + 9.04315i 0.164415 + 0.717169i
\(160\) 0 0
\(161\) −3.11500 + 1.01213i −0.245497 + 0.0797667i
\(162\) 4.41141 7.84471i 0.346593 0.616339i
\(163\) −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 0.531720 0.846920i \(-0.321546\pi\)
0.767408 + 0.641159i \(0.221546\pi\)
\(168\) 4.84483 + 1.21583i 0.373787 + 0.0938035i
\(169\) −12.9216 + 17.7850i −0.993968 + 1.36808i
\(170\) 0 0
\(171\) 2.11750 + 15.4090i 0.161929 + 1.17836i
\(172\) −4.34111 0.687565i −0.331007 0.0524263i
\(173\) 3.08240 6.04954i 0.234350 0.459938i −0.743642 0.668578i \(-0.766903\pi\)
0.977993 + 0.208639i \(0.0669035\pi\)
\(174\) −2.58038 4.30941i −0.195618 0.326696i
\(175\) 0 0
\(176\) 2.74259i 0.206731i
\(177\) 5.10069 0.348829i 0.383391 0.0262196i
\(178\) −0.203597 + 1.28546i −0.0152603 + 0.0963496i
\(179\) 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
\(183\) −6.09819 + 5.10110i −0.450791 + 0.377084i
\(184\) −1.08014 0.350958i −0.0796287 0.0258729i
\(185\) 0 0
\(186\) 6.42407 7.36724i 0.471036 0.540192i
\(187\) −14.6234 + 7.45099i −1.06937 + 0.544871i
\(188\) 4.13604 2.10742i 0.301652 0.153699i
\(189\) 5.30590 + 14.0144i 0.385947 + 1.01940i
\(190\) 0 0
\(191\) 12.2756 + 3.98859i 0.888232 + 0.288604i 0.717371 0.696691i \(-0.245345\pi\)
0.170861 + 0.985295i \(0.445345\pi\)
\(192\) 1.11131 + 1.32853i 0.0802018 + 0.0958784i
\(193\) 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 \(-0.585135\pi\)
0.549378 0.835574i \(-0.314865\pi\)
\(198\) −6.75421 + 4.69860i −0.480001 + 0.333915i
\(199\) 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
\(204\) −4.06451 + 9.53477i −0.284573 + 0.667568i
\(205\) 0 0
\(206\) −3.79275 + 5.22027i −0.264253 + 0.363713i
\(207\) −0.986179 3.26133i −0.0685442 0.226678i
\(208\) −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
\(213\) −5.26420 + 8.39586i −0.360697 + 0.575275i
\(214\) −11.7945 + 3.83226i −0.806254 + 0.261968i
\(215\) 0 0
\(216\) −1.36790 + 5.01287i −0.0930738 + 0.341082i
\(217\) 2.54598 + 16.0747i 0.172832 + 1.09122i
\(218\) −1.97456 1.97456i −0.133734 0.133734i
\(219\) −1.39603 + 15.6801i −0.0943347 + 1.05957i
\(220\) 0 0
\(221\) −20.8045 28.6349i −1.39946 1.92619i
\(222\) −5.21578 12.9666i −0.350061 0.870264i
\(223\) 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 0.924750 0.380575i \(-0.124274\pi\)
0.235662 + 0.971835i \(0.424274\pi\)
\(228\) −3.35122 8.33125i −0.221940 0.551750i
\(229\) −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
\(231\) 1.21487 13.6454i 0.0799327 0.897803i
\(232\) 2.05059 + 2.05059i 0.134628 + 0.134628i
\(233\) −4.54007 28.6649i −0.297430 1.87790i −0.455148 0.890416i \(-0.650414\pi\)
0.157718 0.987484i \(-0.449586\pi\)
\(234\) −12.2869 12.8017i −0.803221 0.836872i
\(235\) 0 0
\(236\) −2.80729 + 0.912145i −0.182739 + 0.0593756i
\(237\) −10.8097 + 17.2403i −0.702165 + 1.11988i
\(238\) −7.83489 15.3768i −0.507861 0.996733i
\(239\) −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 \(-0.0500137\pi\)
\(242\) −3.43537 + 0.544110i −0.220834 + 0.0349767i
\(243\) −14.6887 + 5.21929i −0.942283 + 0.334817i
\(244\) 2.69804 3.71353i 0.172724 0.237734i
\(245\) 0 0
\(246\) 3.58984 8.42127i 0.228880 0.536920i
\(247\) 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 \(0.184062\pi\)
−0.837422 + 0.546557i \(0.815938\pi\)
\(252\) −4.94069 7.10221i −0.311234 0.447397i
\(253\) −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 −0.560563 0.828112i \(-0.689415\pi\)
0.828112 + 0.560563i \(0.189415\pi\)
\(258\) 4.88445 + 5.83919i 0.304093 + 0.363532i
\(259\) 22.1319 + 7.19110i 1.37521 + 0.446833i
\(260\) 0 0
\(261\) −1.53695 + 8.56306i −0.0951347 + 0.530040i
\(262\) 10.6199 5.41110i 0.656098 0.334299i
\(263\) 21.2757 10.8405i 1.31191 0.668454i 0.348711 0.937230i \(-0.386619\pi\)
0.963203 + 0.268777i \(0.0866193\pi\)
\(264\) 3.12197 3.58033i 0.192144 0.220354i
\(265\) 0 0
\(266\) 14.2201 + 4.62038i 0.871889 + 0.283294i
\(267\) 1.72907 1.44635i 0.105817 0.0885154i
\(268\) 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 \(0.149051\pi\)
\(272\) 0.936136 5.91053i 0.0567616 0.358378i
\(273\) 29.4753 2.01578i 1.78393 0.122000i
\(274\) 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
\(279\) −16.7727 + 2.30490i −1.00415 + 0.137991i
\(280\) 0 0
\(281\) −13.4707 + 18.5409i −0.803597 + 1.10606i 0.188683 + 0.982038i \(0.439578\pi\)
−0.992280 + 0.124018i \(0.960422\pi\)
\(282\) −7.79835 1.95703i −0.464385 0.116540i
\(283\) −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
\(288\) 0.0615410 2.99937i 0.00362634 0.176739i
\(289\) 17.8900 5.81283i 1.05236 0.341931i
\(290\) 0 0
\(291\) −2.55780 11.1570i −0.149941 0.654032i
\(292\) −1.42179 8.97684i −0.0832041 0.525330i
\(293\) 9.44461 + 9.44461i 0.551760 + 0.551760i 0.926948 0.375189i \(-0.122422\pi\)
−0.375189 + 0.926948i \(0.622422\pi\)
\(294\) 2.27189 + 0.202270i 0.132500 + 0.0117966i
\(295\) 0 0
\(296\) 4.74298 + 6.52816i 0.275680 + 0.379441i
\(297\) 14.1659 + 1.55470i 0.821987 + 0.0902130i
\(298\) −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
\(303\) −5.67196 + 2.28153i −0.325846 + 0.131070i
\(304\) 3.04743 + 4.19443i 0.174782 + 0.240567i
\(305\) 0 0
\(306\) 16.1597 7.82047i 0.923790 0.447066i
\(307\) −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
\(309\) 10.8936 2.49743i 0.619717 0.142074i
\(310\) 0 0
\(311\) −9.84506 + 3.19885i −0.558262 + 0.181390i −0.574539 0.818477i \(-0.694819\pi\)
0.0162770 + 0.999868i \(0.494819\pi\)
\(312\) 8.67954 + 5.44207i 0.491382 + 0.308097i
\(313\) 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 −0.656159 0.754623i \(-0.727820\pi\)
−0.390853 + 0.920453i \(0.627820\pi\)
\(318\) −2.25827 + 8.99872i −0.126638 + 0.504623i
\(319\) 4.67490 6.43445i 0.261744 0.360260i
\(320\) 0 0
\(321\) 19.7595 + 8.42314i 1.10287 + 0.470134i
\(322\) −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
\(327\) 0.330001 + 4.82538i 0.0182491 + 0.266844i
\(328\) −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
\(333\) −7.95131 + 22.8646i −0.435729 + 1.25297i
\(334\) 16.1658 + 5.25258i 0.884552 + 0.287408i
\(335\) 0 0
\(336\) 3.76480 + 3.28282i 0.205386 + 0.179093i
\(337\) 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
\(339\) 6.03440 + 5.26186i 0.327744 + 0.285785i
\(340\) 0 0
\(341\) 14.7201 + 4.78284i 0.797137 + 0.259006i
\(342\) −5.10883 + 14.6908i −0.276254 + 0.794390i
\(343\) 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 \(0.271980\pi\)
−0.857560 + 0.514384i \(0.828020\pi\)
\(348\) −0.342708 5.01118i −0.0183711 0.268628i
\(349\) 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 −0.304857 0.952398i \(-0.598609\pi\)
−0.584244 + 0.811578i \(0.698609\pi\)
\(354\) 4.70311 + 2.00485i 0.249968 + 0.106557i
\(355\) 0 0
\(356\) −0.764995 + 1.05293i −0.0405447 + 0.0558049i
\(357\) −7.27579 + 28.9924i −0.385076 + 1.53444i
\(358\) 9.26645 1.46766i 0.489747 0.0775683i
\(359\) −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
\(362\) 6.90373 + 13.5493i 0.362852 + 0.712137i
\(363\) 5.10410 + 3.20027i 0.267896 + 0.167971i
\(364\) −16.2225 + 5.27101i −0.850290 + 0.276276i
\(365\) 0 0
\(366\) −7.74938 + 1.77659i −0.405066 + 0.0928640i
\(367\) 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
\(369\) −14.2725 + 6.90716i −0.742998 + 0.359573i
\(370\) 0 0
\(371\) −9.07990 12.4974i −0.471405 0.648833i
\(372\) 9.06854 3.64779i 0.470182 0.189129i
\(373\) −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
\(378\) −1.63481 + 14.8957i −0.0840853 + 0.766154i
\(379\) −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
\(381\) 21.6171 + 1.92460i 1.10748 + 0.0986003i
\(382\) 9.12687 + 9.12687i 0.466971 + 0.466971i
\(383\) −3.81540 24.0895i −0.194958 1.23092i −0.869968 0.493108i \(-0.835861\pi\)
0.675010 0.737808i \(-0.264139\pi\)
\(384\) 0.387043 + 1.68825i 0.0197512 + 0.0861533i
\(385\) 0 0
\(386\) 5.26495 1.71069i 0.267979 0.0870717i
\(387\) 0.270487 13.1829i 0.0137496 0.670125i
\(388\) 3.00023 + 5.88829i 0.152314 + 0.298932i
\(389\) 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
\(392\) −1.30065 + 0.206003i −0.0656929 + 0.0104047i
\(393\) −20.0234 5.02496i −1.01004 0.253475i
\(394\) 15.0352 20.6942i 0.757462 1.04256i
\(395\) 0 0
\(396\) −8.15117 + 1.12013i −0.409612 + 0.0562888i
\(397\) −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 \(-0.716423\pi\)
0.628726 0.777627i \(-0.283577\pi\)
\(402\) −0.797478 + 0.0545384i −0.0397746 + 0.00272013i
\(403\) −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
\(408\) −7.95020 + 6.65030i −0.393594 + 0.329239i
\(409\) 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
\(411\) −22.6187 + 25.9395i −1.11570 + 1.27950i
\(412\) −5.74931 + 2.92942i −0.283248 + 0.144322i
\(413\) −7.58476 + 3.86463i −0.373222 + 0.190166i
\(414\) 0.601920 3.35358i 0.0295827 0.164819i
\(415\) 0 0
\(416\) −5.62520 1.82774i −0.275798 0.0896122i
\(417\) 10.6091 + 12.6828i 0.519528 + 0.621078i
\(418\) 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 \(0.193308\pi\)
\(422\) −1.00913 + 6.37141i −0.0491238 + 0.310156i
\(423\) 7.95265 + 11.4319i 0.386671 + 0.555838i
\(424\) 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
\(429\) 11.0178 25.8462i 0.531944 1.24787i
\(430\) 0 0
\(431\) −16.4092 + 22.5853i −0.790401 + 1.08789i 0.203657 + 0.979042i \(0.434717\pi\)
−0.994058 + 0.108852i \(0.965283\pi\)
\(432\) −3.49460 + 3.84548i −0.168134 + 0.185016i
\(433\) −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
\(438\) −8.36250 + 13.3373i −0.399576 + 0.637282i
\(439\) 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
\(441\) −2.73560 2.85021i −0.130267 0.135724i
\(442\) −5.53695 34.9589i −0.263366 1.66283i
\(443\) 1.32181 + 1.32181i 0.0628009 + 0.0628009i 0.737810 0.675009i \(-0.235860\pi\)
−0.675009 + 0.737810i \(0.735860\pi\)
\(444\) 1.23943 13.9213i 0.0588208 0.660675i
\(445\) 0 0
\(446\) 3.19712 + 4.40046i 0.151388 + 0.208368i
\(447\) 7.76229 + 19.2973i 0.367144 + 0.912733i
\(448\) −2.56957 1.30926i −0.121401 0.0618568i
\(449\) 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
\(452\) −4.11863 2.09855i −0.193724 0.0987075i
\(453\) 7.19269 + 17.8813i 0.337942 + 0.840137i
\(454\) 11.5336 + 15.8746i 0.541296 + 0.745031i
\(455\) 0 0
\(456\) 0.796353 8.94462i 0.0372926 0.418870i
\(457\) 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
\(459\) −29.9980 8.18580i −1.40019 0.382080i
\(460\) 0 0
\(461\) 13.2689 4.31131i 0.617992 0.200798i 0.0167435 0.999860i \(-0.494670\pi\)
0.601249 + 0.799062i \(0.294670\pi\)
\(462\) 7.27735 11.6066i 0.338573 0.539989i
\(463\) −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 −0.240371 0.970681i \(-0.577269\pi\)
0.0713509 + 0.997451i \(0.477269\pi\)
\(468\) −5.13588 16.9845i −0.237406 0.785110i
\(469\) 0.782294 1.07673i 0.0361230 0.0497190i
\(470\) 0 0
\(471\) −11.1537 + 26.1651i −0.513937 + 1.20562i
\(472\) −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
\(477\) 13.1916 9.17677i 0.604000 0.420175i
\(478\) 0.884293 5.58321i 0.0404466 0.255370i
\(479\) 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
\(483\) 3.63988 + 4.35135i 0.165620 + 0.197993i
\(484\) −3.30796 1.07482i −0.150362 0.0488555i
\(485\) 0 0
\(486\) −15.4573 2.01813i −0.701156 0.0915443i
\(487\) 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
\(489\) −7.45695 + 8.55176i −0.337215 + 0.386724i
\(490\) 0 0
\(491\) 30.0362 + 9.75934i 1.35551 + 0.440433i 0.894543 0.446983i \(-0.147501\pi\)
0.460970 + 0.887416i \(0.347501\pi\)
\(492\) 7.02175 5.87365i 0.316565 0.264805i
\(493\) −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
\(498\) 20.8677 1.42712i 0.935106 0.0639506i
\(499\) 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 0.141726 0.989906i \(-0.454735\pi\)
−0.171108 + 0.985252i \(0.554735\pi\)
\(504\) −1.17785 8.57114i −0.0524654 0.381789i
\(505\) 0 0
\(506\) −1.83085 + 2.51995i −0.0813911 + 0.112025i
\(507\) 36.9314 + 9.26810i 1.64018 + 0.411611i
\(508\) −12.3757 + 1.96012i −0.549084 + 0.0869664i
\(509\) −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
\(512\) −0.453990 0.891007i −0.0200637 0.0393773i
\(513\) 23.3923 13.3627i 1.03280 0.589978i
\(514\) 5.76888 1.87442i 0.254454 0.0826772i
\(515\) 0 0
\(516\) 1.70114 + 7.42026i 0.0748885 + 0.326659i
\(517\) −1.99158 12.5743i −0.0875896 0.553019i
\(518\) 16.4550 + 16.4550i 0.722991 + 0.722991i
\(519\) −11.7135 1.04287i −0.514167 0.0457771i
\(520\) 0 0
\(521\) 24.0053 + 33.0404i 1.05169 + 1.44753i 0.887334 + 0.461127i \(0.152555\pi\)
0.164357 + 0.986401i \(0.447445\pi\)
\(522\) −5.25698 + 6.93199i −0.230092 + 0.303405i
\(523\) 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
\(528\) 4.40713 1.77275i 0.191796 0.0771491i
\(529\) 12.7609 + 17.5639i 0.554822 + 0.763646i
\(530\) 0 0
\(531\) −3.85751 7.97093i −0.167402 0.345909i
\(532\) 10.5726 + 10.5726i 0.458379 + 0.458379i
\(533\) 4.89032 + 30.8763i 0.211823 + 1.33740i
\(534\) 2.19724 0.503731i 0.0950839 0.0217986i
\(535\) 0 0
\(536\) 0.438912 0.142611i 0.0189581 0.00615987i
\(537\) −13.7676 8.63229i −0.594116 0.372511i
\(538\) 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
\(543\) 6.41107 25.5467i 0.275125 1.09631i
\(544\) 3.51743 4.84132i 0.150808 0.207570i
\(545\) 0 0
\(546\) 27.1779 + 11.5855i 1.16311 + 0.495812i
\(547\) −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
\(552\) 0.134216 + 1.96255i 0.00571260 + 0.0835315i
\(553\) 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 −0.741498 0.670956i \(-0.765884\pi\)
0.670956 + 0.741498i \(0.265884\pi\)
\(558\) −15.9909 5.56095i −0.676951 0.235414i
\(559\) −24.7240 8.03333i −1.04572 0.339773i
\(560\) 0 0
\(561\) 21.4254 + 18.6825i 0.904581 + 0.788775i
\(562\) −20.4199 + 10.4045i −0.861362 + 0.438886i
\(563\) 42.1004 21.4512i 1.77432 0.904062i 0.845023 0.534729i \(-0.179586\pi\)
0.929297 0.369332i \(-0.120414\pi\)
\(564\) −6.05991 5.28411i −0.255168 0.222501i
\(565\) 0 0
\(566\) −2.70579 0.879165i −0.113733 0.0369541i
\(567\) 19.0904 17.5848i 0.801721 0.738490i
\(568\) 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 \(0.260060\pi\)
\(572\) −2.53761 + 16.0218i −0.106103 + 0.669907i
\(573\) −1.52534 22.3041i −0.0637221 0.931766i
\(574\) 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
\(579\) −8.82048 3.76002i −0.366567 0.156261i
\(580\) 0 0
\(581\) −20.4704 + 28.1751i −0.849256 + 1.16890i
\(582\) 2.78613 11.1021i 0.115489 0.460198i
\(583\) −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 0.761048 0.648696i \(-0.224685\pi\)
−0.972139 + 0.234407i \(0.924685\pi\)
\(588\) 1.93244 + 1.21164i 0.0796926 + 0.0499673i
\(589\) 27.8269 9.04151i 1.14659 0.372549i
\(590\) 0 0
\(591\) −43.1845 + 9.90032i −1.77637 + 0.407245i
\(592\) 1.26231 + 7.96990i 0.0518805 + 0.327561i
\(593\) −17.4049 17.4049i −0.714734 0.714734i 0.252788 0.967522i \(-0.418653\pi\)
−0.967522 + 0.252788i \(0.918653\pi\)
\(594\) 11.9161 + 7.81642i 0.488922 + 0.320711i
\(595\) 0 0
\(596\) −7.05865 9.71540i −0.289134 0.397958i
\(597\) 0.123464 0.0496631i 0.00505306 0.00203257i
\(598\) −5.98529 3.04966i −0.244757 0.124710i
\(599\) 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 \(0.769258\pi\)
\(602\) −11.2939 5.75450i −0.460303 0.234536i
\(603\) 1.10315 + 0.836594i 0.0449239 + 0.0340687i
\(604\) −6.54069 9.00249i −0.266137 0.366306i
\(605\) 0 0
\(606\) −6.08955 0.542162i −0.247371 0.0220238i
\(607\) −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
\(609\) −3.23692 14.1192i −0.131166 0.572139i
\(610\) 0 0
\(611\) 26.1121 8.48435i 1.05638 0.343240i
\(612\) 17.9488 + 0.368274i 0.725539 + 0.0148866i
\(613\) −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 −0.282380 0.959303i \(-0.591124\pi\)
0.0278814 + 0.999611i \(0.491124\pi\)
\(618\) 10.8401 + 2.72038i 0.436053 + 0.109430i
\(619\) −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
\(621\) −4.60325 + 3.69276i −0.184722 + 0.148185i
\(622\) −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
\(627\) −24.5711 + 1.68038i −0.981274 + 0.0671079i
\(628\) 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
\(633\) 8.57013 7.16886i 0.340632 0.284937i
\(634\) −17.9501 5.83235i −0.712891 0.231632i
\(635\) 0 0
\(636\) −6.09747 + 6.99269i −0.241780 + 0.277278i
\(637\) −6.93992 + 3.53606i −0.274970 + 0.140104i
\(638\) 7.08655 3.61078i 0.280559 0.142952i
\(639\) 16.8941 + 3.03226i 0.668322 + 0.119954i
\(640\) 0 0
\(641\) −18.3395 5.95888i −0.724368 0.235362i −0.0764522 0.997073i \(-0.524359\pi\)
−0.647916 + 0.761712i \(0.724359\pi\)
\(642\) 13.7818 + 16.4757i 0.543925 + 0.650244i
\(643\) −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 \(0.313257\pi\)
−0.783842 + 0.620960i \(0.786743\pi\)
\(648\) 8.93946 1.04210i 0.351175 0.0409376i
\(649\) 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 0.199303 0.979938i \(-0.436132\pi\)
−0.113269 + 0.993564i \(0.536132\pi\)
\(654\) −1.89664 + 4.44926i −0.0741647 + 0.173980i
\(655\) 0 0
\(656\) −3.10665 + 4.27594i −0.121294 + 0.166947i
\(657\) 26.0991 7.89200i 1.01822 0.307896i
\(658\) 13.2222 2.09419i 0.515456 0.0816401i
\(659\) 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 \(0.904526\pi\)
\(662\) −14.4080 28.2773i −0.559984 1.09903i
\(663\) −32.5665 + 51.9401i −1.26478 + 2.01719i
\(664\) −11.4851 + 3.73173i −0.445708 + 0.144819i
\(665\) 0 0
\(666\) −17.4650 + 16.7627i −0.676755 + 0.649542i
\(667\) 0.515226 + 3.25301i 0.0199496 + 0.125957i
\(668\) 12.0192 + 12.0192i 0.465037 + 0.465037i
\(669\) 0.835468 9.38397i 0.0323011 0.362805i
\(670\) 0 0
\(671\) −7.39961 10.1847i −0.285659 0.393176i
\(672\) 1.86409 + 4.63420i 0.0719088 + 0.178768i
\(673\) 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 0.00984177 0.999952i \(-0.496867\pi\)
−0.803193 + 0.595719i \(0.796867\pi\)
\(678\) 2.98785 + 7.42791i 0.114748 + 0.285267i
\(679\) 11.2023 + 15.4186i 0.429904 + 0.591712i
\(680\) 0 0
\(681\) 3.01394 33.8525i 0.115494 1.29723i
\(682\) 10.9443 + 10.9443i 0.419080 + 0.419080i
\(683\) 0.679239 + 4.28854i 0.0259903 + 0.164097i 0.997270 0.0738455i \(-0.0235272\pi\)
−0.971279 + 0.237942i \(0.923527\pi\)
\(684\) −11.2215 + 10.7703i −0.429065 + 0.411812i
\(685\) 0 0
\(686\) 15.5874 5.06466i 0.595130 0.193370i
\(687\) −16.0971 + 25.6732i −0.614144 + 0.979495i
\(688\) −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
\(693\) −22.7124 + 6.86790i −0.862772 + 0.260890i
\(694\) −14.0633 + 19.3564i −0.533834 + 0.734759i
\(695\) 0 0
\(696\) 1.96968 4.62058i 0.0746603 0.175143i
\(697\) −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 \(-0.879595\pi\)
0.929308 0.369306i \(-0.120405\pi\)
\(702\) −12.6293 + 28.0188i −0.476662 + 1.05750i
\(703\) 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
\(708\) 3.28032 + 3.92151i 0.123282 + 0.147379i
\(709\) −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
\(711\) 34.6910 + 6.22654i 1.30101 + 0.233514i
\(712\) −1.15963 + 0.590863i −0.0434591 + 0.0221435i
\(713\) −5.71079 + 2.90979i −0.213871 + 0.108973i
\(714\) −19.6451 + 22.5293i −0.735198 + 0.843138i
\(715\) 0 0
\(716\) 8.92277 + 2.89918i 0.333460 + 0.108348i
\(717\) −7.50992 + 6.28201i −0.280463 + 0.234606i
\(718\) −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
\(722\) 1.23272 7.78310i 0.0458772 0.289657i
\(723\) −24.3596 + 1.66592i −0.905942 + 0.0619561i
\(724\) 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
\(729\) 17.8815 + 20.2300i 0.662276 + 0.749260i
\(730\) 0 0
\(731\) 15.4599 21.2787i 0.571805 0.787022i
\(732\) −7.71130 1.93519i −0.285018 0.0715266i
\(733\) 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
\(738\) −15.8527 0.325265i −0.583546 0.0119732i
\(739\) −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
\(741\) −11.8688 51.7708i −0.436010 1.90185i
\(742\) −2.41654 15.2575i −0.0887141 0.560119i
\(743\) 23.0403 + 23.0403i 0.845265 + 0.845265i 0.989538 0.144273i \(-0.0460842\pi\)
−0.144273 + 0.989538i \(0.546084\pi\)
\(744\) 9.73619 + 0.866828i 0.356946 + 0.0317794i
\(745\) 0 0
\(746\) −15.0422 20.7038i −0.550734 0.758020i
\(747\) −28.8664 21.8913i −1.05617 0.800961i
\(748\) −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
\(753\) 27.8290 11.1941i 1.01414 0.407936i
\(754\) 10.0819 + 13.8766i 0.367162 + 0.505355i
\(755\) 0 0
\(756\) −8.21914 + 12.5300i −0.298927 + 0.455712i
\(757\) 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
\(759\) 5.25861 1.20557i 0.190875 0.0437594i
\(760\) 0 0
\(761\) −8.94031 + 2.90488i −0.324086 + 0.105302i −0.466541 0.884499i \(-0.654500\pi\)
0.142456 + 0.989801i \(0.454500\pi\)
\(762\) 18.3872 + 11.5288i 0.666098 + 0.417644i
\(763\) −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
\(768\) −0.421593 + 1.67996i −0.0152129 + 0.0606203i
\(769\) 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
\(771\) −9.66471 4.11990i −0.348066 0.148375i
\(772\) 5.46774 + 0.866006i 0.196788 + 0.0311682i
\(773\) −9.86911 + 19.3692i −0.354967 + 0.696662i −0.997580 0.0695289i \(-0.977850\pi\)
0.642613 + 0.766191i \(0.277850\pi\)
\(774\) 6.22592 11.6233i 0.223786 0.417789i
\(775\) 0 0
\(776\) 6.60858i 0.237234i
\(777\) −2.75007 40.2124i −0.0986582 1.44261i
\(778\) −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