Properties

Label 950.2.u.g.199.4
Level $950$
Weight $2$
Character 950.199
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.4
Character \(\chi\) \(=\) 950.199
Dual form 950.2.u.g.549.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.984808 - 0.173648i) q^{2} +(-2.20410 - 2.62675i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.62675 - 2.20410i) q^{6} +(-1.61687 - 0.933500i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-1.52078 + 8.62480i) q^{9} +O(q^{10})\) \(q+(0.984808 - 0.173648i) q^{2} +(-2.20410 - 2.62675i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.62675 - 2.20410i) q^{6} +(-1.61687 - 0.933500i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-1.52078 + 8.62480i) q^{9} +(1.80254 + 3.12210i) q^{11} +(-2.96958 - 1.71449i) q^{12} +(-1.82353 + 2.17319i) q^{13} +(-1.75441 - 0.638551i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-5.89781 + 1.03994i) q^{17} +8.75785i q^{18} +(-4.32047 - 0.577506i) q^{19} +(1.11168 + 6.30463i) q^{21} +(2.31731 + 2.76166i) q^{22} +(1.74011 + 4.78092i) q^{23} +(-3.22218 - 1.17278i) q^{24} +(-1.41845 + 2.45683i) q^{26} +(17.0984 - 9.87176i) q^{27} +(-1.83864 - 0.324201i) q^{28} +(-0.204642 + 1.16058i) q^{29} +(2.59932 - 4.50215i) q^{31} +(0.642788 - 0.766044i) q^{32} +(4.22797 - 11.6162i) q^{33} +(-5.62762 + 2.04829i) q^{34} +(1.52078 + 8.62480i) q^{36} +3.35231i q^{37} +(-4.35512 + 0.181510i) q^{38} +9.72766 q^{39} +(-2.85406 + 2.39484i) q^{41} +(2.18958 + 6.01581i) q^{42} +(-0.229755 + 0.631247i) q^{43} +(2.76166 + 2.31731i) q^{44} +(2.54388 + 4.40612i) q^{46} +(-6.22647 - 1.09789i) q^{47} +(-3.37688 - 0.595435i) q^{48} +(-1.75716 - 3.04348i) q^{49} +(15.7310 + 13.1999i) q^{51} +(-0.970278 + 2.66582i) q^{52} +(0.876116 + 2.40711i) q^{53} +(15.1244 - 12.6909i) q^{54} -1.86700 q^{56} +(8.00580 + 12.6217i) q^{57} +1.17848i q^{58} +(0.827999 + 4.69581i) q^{59} +(-7.73966 + 2.81701i) q^{61} +(1.77804 - 4.88512i) q^{62} +(10.5102 - 12.5255i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.14660 - 12.1739i) q^{66} +(7.84286 + 1.38291i) q^{67} +(-5.18644 + 2.99439i) q^{68} +(8.72288 - 15.1085i) q^{69} +(1.81077 + 0.659065i) q^{71} +(2.99536 + 8.22969i) q^{72} +(3.22165 + 3.83942i) q^{73} +(0.582122 + 3.30138i) q^{74} +(-4.25744 + 0.935010i) q^{76} -6.73070i q^{77} +(9.57988 - 1.68919i) q^{78} +(0.460535 - 0.386434i) q^{79} +(-38.9281 - 14.1687i) q^{81} +(-2.39484 + 2.85406i) q^{82} +(-1.64789 - 0.951408i) q^{83} +(3.20094 + 5.54420i) q^{84} +(-0.116650 + 0.661553i) q^{86} +(3.49960 - 2.02049i) q^{87} +(3.12210 + 1.80254i) q^{88} +(-0.755257 - 0.633736i) q^{89} +(4.97708 - 1.81151i) q^{91} +(3.27034 + 3.89744i) q^{92} +(-17.5552 + 3.09545i) q^{93} -6.32252 q^{94} -3.42897 q^{96} +(0.184712 - 0.0325697i) q^{97} +(-2.25896 - 2.69212i) q^{98} +(-29.6688 + 10.7985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 36q^{9} + O(q^{10}) \) \( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.984808 0.173648i 0.696364 0.122788i
\(3\) −2.20410 2.62675i −1.27254 1.51655i −0.745088 0.666966i \(-0.767593\pi\)
−0.527450 0.849586i \(-0.676852\pi\)
\(4\) 0.939693 0.342020i 0.469846 0.171010i
\(5\) 0 0
\(6\) −2.62675 2.20410i −1.07236 0.899820i
\(7\) −1.61687 0.933500i −0.611119 0.352830i 0.162284 0.986744i \(-0.448114\pi\)
−0.773403 + 0.633914i \(0.781447\pi\)
\(8\) 0.866025 0.500000i 0.306186 0.176777i
\(9\) −1.52078 + 8.62480i −0.506928 + 2.87493i
\(10\) 0 0
\(11\) 1.80254 + 3.12210i 0.543488 + 0.941348i 0.998700 + 0.0509654i \(0.0162298\pi\)
−0.455213 + 0.890383i \(0.650437\pi\)
\(12\) −2.96958 1.71449i −0.857243 0.494930i
\(13\) −1.82353 + 2.17319i −0.505755 + 0.602736i −0.957151 0.289588i \(-0.906482\pi\)
0.451396 + 0.892324i \(0.350926\pi\)
\(14\) −1.75441 0.638551i −0.468885 0.170660i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) −5.89781 + 1.03994i −1.43043 + 0.252223i −0.834586 0.550878i \(-0.814293\pi\)
−0.595842 + 0.803101i \(0.703182\pi\)
\(18\) 8.75785i 2.06425i
\(19\) −4.32047 0.577506i −0.991184 0.132489i
\(20\) 0 0
\(21\) 1.11168 + 6.30463i 0.242588 + 1.37578i
\(22\) 2.31731 + 2.76166i 0.494051 + 0.588787i
\(23\) 1.74011 + 4.78092i 0.362839 + 0.996892i 0.978021 + 0.208507i \(0.0668603\pi\)
−0.615182 + 0.788385i \(0.710918\pi\)
\(24\) −3.22218 1.17278i −0.657725 0.239392i
\(25\) 0 0
\(26\) −1.41845 + 2.45683i −0.278181 + 0.481824i
\(27\) 17.0984 9.87176i 3.29059 1.89982i
\(28\) −1.83864 0.324201i −0.347469 0.0612682i
\(29\) −0.204642 + 1.16058i −0.0380010 + 0.215514i −0.997895 0.0648484i \(-0.979344\pi\)
0.959894 + 0.280363i \(0.0904547\pi\)
\(30\) 0 0
\(31\) 2.59932 4.50215i 0.466851 0.808610i −0.532432 0.846473i \(-0.678722\pi\)
0.999283 + 0.0378630i \(0.0120550\pi\)
\(32\) 0.642788 0.766044i 0.113630 0.135419i
\(33\) 4.22797 11.6162i 0.735995 2.02213i
\(34\) −5.62762 + 2.04829i −0.965129 + 0.351278i
\(35\) 0 0
\(36\) 1.52078 + 8.62480i 0.253464 + 1.43747i
\(37\) 3.35231i 0.551116i 0.961285 + 0.275558i \(0.0888625\pi\)
−0.961285 + 0.275558i \(0.911137\pi\)
\(38\) −4.35512 + 0.181510i −0.706493 + 0.0294447i
\(39\) 9.72766 1.55767
\(40\) 0 0
\(41\) −2.85406 + 2.39484i −0.445730 + 0.374012i −0.837848 0.545903i \(-0.816187\pi\)
0.392119 + 0.919915i \(0.371742\pi\)
\(42\) 2.18958 + 6.01581i 0.337859 + 0.928259i
\(43\) −0.229755 + 0.631247i −0.0350373 + 0.0962642i −0.955978 0.293439i \(-0.905200\pi\)
0.920940 + 0.389703i \(0.127422\pi\)
\(44\) 2.76166 + 2.31731i 0.416336 + 0.349347i
\(45\) 0 0
\(46\) 2.54388 + 4.40612i 0.375074 + 0.649647i
\(47\) −6.22647 1.09789i −0.908223 0.160144i −0.300027 0.953931i \(-0.596996\pi\)
−0.608197 + 0.793786i \(0.708107\pi\)
\(48\) −3.37688 0.595435i −0.487410 0.0859436i
\(49\) −1.75716 3.04348i −0.251022 0.434783i
\(50\) 0 0
\(51\) 15.7310 + 13.1999i 2.20278 + 1.84836i
\(52\) −0.970278 + 2.66582i −0.134553 + 0.369682i
\(53\) 0.876116 + 2.40711i 0.120344 + 0.330642i 0.985208 0.171365i \(-0.0548176\pi\)
−0.864864 + 0.502006i \(0.832595\pi\)
\(54\) 15.1244 12.6909i 2.05817 1.72701i
\(55\) 0 0
\(56\) −1.86700 −0.249488
\(57\) 8.00580 + 12.6217i 1.06039 + 1.67178i
\(58\) 1.17848i 0.154743i
\(59\) 0.827999 + 4.69581i 0.107796 + 0.611343i 0.990067 + 0.140600i \(0.0449031\pi\)
−0.882270 + 0.470743i \(0.843986\pi\)
\(60\) 0 0
\(61\) −7.73966 + 2.81701i −0.990962 + 0.360681i −0.786093 0.618109i \(-0.787899\pi\)
−0.204869 + 0.978789i \(0.565677\pi\)
\(62\) 1.77804 4.88512i 0.225811 0.620411i
\(63\) 10.5102 12.5255i 1.32416 1.57807i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) 2.14660 12.1739i 0.264228 1.49851i
\(67\) 7.84286 + 1.38291i 0.958158 + 0.168949i 0.630795 0.775949i \(-0.282729\pi\)
0.327363 + 0.944899i \(0.393840\pi\)
\(68\) −5.18644 + 2.99439i −0.628949 + 0.363124i
\(69\) 8.72288 15.1085i 1.05011 1.81885i
\(70\) 0 0
\(71\) 1.81077 + 0.659065i 0.214898 + 0.0782166i 0.447226 0.894421i \(-0.352412\pi\)
−0.232328 + 0.972638i \(0.574634\pi\)
\(72\) 2.99536 + 8.22969i 0.353007 + 0.969878i
\(73\) 3.22165 + 3.83942i 0.377066 + 0.449370i 0.920886 0.389832i \(-0.127467\pi\)
−0.543820 + 0.839202i \(0.683022\pi\)
\(74\) 0.582122 + 3.30138i 0.0676703 + 0.383777i
\(75\) 0 0
\(76\) −4.25744 + 0.935010i −0.488361 + 0.107253i
\(77\) 6.73070i 0.767034i
\(78\) 9.57988 1.68919i 1.08471 0.191263i
\(79\) 0.460535 0.386434i 0.0518142 0.0434773i −0.616513 0.787345i \(-0.711455\pi\)
0.668327 + 0.743868i \(0.267011\pi\)
\(80\) 0 0
\(81\) −38.9281 14.1687i −4.32534 1.57430i
\(82\) −2.39484 + 2.85406i −0.264466 + 0.315179i
\(83\) −1.64789 0.951408i −0.180879 0.104431i 0.406827 0.913505i \(-0.366635\pi\)
−0.587706 + 0.809075i \(0.699969\pi\)
\(84\) 3.20094 + 5.54420i 0.349252 + 0.604922i
\(85\) 0 0
\(86\) −0.116650 + 0.661553i −0.0125787 + 0.0713371i
\(87\) 3.49960 2.02049i 0.375196 0.216620i
\(88\) 3.12210 + 1.80254i 0.332817 + 0.192152i
\(89\) −0.755257 0.633736i −0.0800571 0.0671759i 0.601881 0.798586i \(-0.294418\pi\)
−0.681938 + 0.731410i \(0.738863\pi\)
\(90\) 0 0
\(91\) 4.97708 1.81151i 0.521740 0.189898i
\(92\) 3.27034 + 3.89744i 0.340957 + 0.406337i
\(93\) −17.5552 + 3.09545i −1.82039 + 0.320983i
\(94\) −6.32252 −0.652118
\(95\) 0 0
\(96\) −3.42897 −0.349968
\(97\) 0.184712 0.0325697i 0.0187547 0.00330695i −0.164263 0.986417i \(-0.552525\pi\)
0.183018 + 0.983110i \(0.441413\pi\)
\(98\) −2.25896 2.69212i −0.228189 0.271945i
\(99\) −29.6688 + 10.7985i −2.98182 + 1.08529i
\(100\) 0 0
\(101\) −1.50168 1.26006i −0.149423 0.125380i 0.565012 0.825083i \(-0.308872\pi\)
−0.714435 + 0.699702i \(0.753316\pi\)
\(102\) 17.7842 + 10.2677i 1.76090 + 1.01665i
\(103\) −15.1589 + 8.75199i −1.49365 + 0.862359i −0.999973 0.00728653i \(-0.997681\pi\)
−0.493676 + 0.869646i \(0.664347\pi\)
\(104\) −0.492623 + 2.79380i −0.0483057 + 0.273955i
\(105\) 0 0
\(106\) 1.28080 + 2.21840i 0.124402 + 0.215470i
\(107\) −9.17096 5.29485i −0.886590 0.511873i −0.0137643 0.999905i \(-0.504381\pi\)
−0.872826 + 0.488032i \(0.837715\pi\)
\(108\) 12.6909 15.1244i 1.22118 1.45535i
\(109\) −13.0386 4.74565i −1.24887 0.454551i −0.368849 0.929489i \(-0.620248\pi\)
−0.880019 + 0.474939i \(0.842470\pi\)
\(110\) 0 0
\(111\) 8.80565 7.38882i 0.835796 0.701316i
\(112\) −1.83864 + 0.324201i −0.173735 + 0.0306341i
\(113\) 15.9357i 1.49911i 0.661944 + 0.749553i \(0.269732\pi\)
−0.661944 + 0.749553i \(0.730268\pi\)
\(114\) 10.0759 + 11.0397i 0.943694 + 1.03396i
\(115\) 0 0
\(116\) 0.204642 + 1.16058i 0.0190005 + 0.107757i
\(117\) −15.9702 19.0325i −1.47644 1.75956i
\(118\) 1.63084 + 4.48069i 0.150131 + 0.412481i
\(119\) 10.5068 + 3.82415i 0.963154 + 0.350559i
\(120\) 0 0
\(121\) −0.998331 + 1.72916i −0.0907574 + 0.157196i
\(122\) −7.13291 + 4.11819i −0.645783 + 0.372843i
\(123\) 12.5813 + 2.21842i 1.13442 + 0.200028i
\(124\) 0.902733 5.11966i 0.0810679 0.459759i
\(125\) 0 0
\(126\) 8.17545 14.1603i 0.728327 1.26150i
\(127\) 10.8078 12.8803i 0.959041 1.14294i −0.0306225 0.999531i \(-0.509749\pi\)
0.989663 0.143409i \(-0.0458066\pi\)
\(128\) 0.342020 0.939693i 0.0302306 0.0830579i
\(129\) 2.16453 0.787824i 0.190576 0.0693640i
\(130\) 0 0
\(131\) 1.13110 + 6.41481i 0.0988249 + 0.560464i 0.993508 + 0.113763i \(0.0362903\pi\)
−0.894683 + 0.446702i \(0.852599\pi\)
\(132\) 12.3617i 1.07595i
\(133\) 6.44654 + 4.96691i 0.558986 + 0.430686i
\(134\) 7.96385 0.687972
\(135\) 0 0
\(136\) −4.58768 + 3.84952i −0.393390 + 0.330094i
\(137\) −6.92459 19.0252i −0.591608 1.62543i −0.767521 0.641023i \(-0.778510\pi\)
0.175914 0.984406i \(-0.443712\pi\)
\(138\) 5.96680 16.3937i 0.507928 1.39552i
\(139\) −3.05535 2.56374i −0.259151 0.217454i 0.503950 0.863733i \(-0.331880\pi\)
−0.763101 + 0.646279i \(0.776324\pi\)
\(140\) 0 0
\(141\) 10.8399 + 18.7752i 0.912882 + 1.58116i
\(142\) 1.89770 + 0.334616i 0.159252 + 0.0280803i
\(143\) −10.0719 1.77595i −0.842256 0.148512i
\(144\) 4.37893 + 7.58452i 0.364910 + 0.632043i
\(145\) 0 0
\(146\) 3.83942 + 3.22165i 0.317753 + 0.266626i
\(147\) −4.12151 + 11.3237i −0.339936 + 0.933967i
\(148\) 1.14656 + 3.15014i 0.0942463 + 0.258940i
\(149\) −4.31479 + 3.62054i −0.353481 + 0.296606i −0.802186 0.597074i \(-0.796330\pi\)
0.448705 + 0.893680i \(0.351885\pi\)
\(150\) 0 0
\(151\) −1.23848 −0.100786 −0.0503932 0.998729i \(-0.516047\pi\)
−0.0503932 + 0.998729i \(0.516047\pi\)
\(152\) −4.03039 + 1.66010i −0.326908 + 0.134652i
\(153\) 52.4489i 4.24024i
\(154\) −1.16877 6.62844i −0.0941825 0.534135i
\(155\) 0 0
\(156\) 9.14101 3.32706i 0.731867 0.266378i
\(157\) −7.35594 + 20.2103i −0.587068 + 1.61296i 0.188769 + 0.982021i \(0.439550\pi\)
−0.775837 + 0.630934i \(0.782672\pi\)
\(158\) 0.386434 0.460535i 0.0307431 0.0366382i
\(159\) 4.39181 7.60685i 0.348294 0.603262i
\(160\) 0 0
\(161\) 1.64946 9.35452i 0.129995 0.737240i
\(162\) −40.7970 7.19362i −3.20532 0.565184i
\(163\) −15.6067 + 9.01050i −1.22241 + 0.705757i −0.965431 0.260660i \(-0.916060\pi\)
−0.256977 + 0.966418i \(0.582726\pi\)
\(164\) −1.86286 + 3.22656i −0.145465 + 0.251952i
\(165\) 0 0
\(166\) −1.78806 0.650801i −0.138781 0.0505120i
\(167\) 3.73105 + 10.2510i 0.288717 + 0.793244i 0.996247 + 0.0865598i \(0.0275874\pi\)
−0.707530 + 0.706684i \(0.750190\pi\)
\(168\) 4.11506 + 4.90413i 0.317483 + 0.378362i
\(169\) 0.859902 + 4.87675i 0.0661463 + 0.375134i
\(170\) 0 0
\(171\) 11.5514 36.3850i 0.883357 2.78243i
\(172\) 0.671759i 0.0512211i
\(173\) 0.143686 0.0253357i 0.0109242 0.00192623i −0.168183 0.985756i \(-0.553790\pi\)
0.179108 + 0.983829i \(0.442679\pi\)
\(174\) 3.09558 2.59750i 0.234675 0.196916i
\(175\) 0 0
\(176\) 3.38767 + 1.23301i 0.255356 + 0.0929418i
\(177\) 10.5097 12.5250i 0.789958 0.941436i
\(178\) −0.853830 0.492959i −0.0639973 0.0369488i
\(179\) 2.84974 + 4.93590i 0.213000 + 0.368927i 0.952652 0.304063i \(-0.0983433\pi\)
−0.739652 + 0.672989i \(0.765010\pi\)
\(180\) 0 0
\(181\) −3.21271 + 18.2202i −0.238799 + 1.35430i 0.595665 + 0.803233i \(0.296889\pi\)
−0.834464 + 0.551063i \(0.814223\pi\)
\(182\) 4.58690 2.64825i 0.340004 0.196301i
\(183\) 24.4586 + 14.1212i 1.80803 + 1.04387i
\(184\) 3.89744 + 3.27034i 0.287323 + 0.241093i
\(185\) 0 0
\(186\) −16.7509 + 6.09684i −1.22824 + 0.447042i
\(187\) −13.8779 16.5390i −1.01485 1.20945i
\(188\) −6.22647 + 1.09789i −0.454112 + 0.0800721i
\(189\) −36.8611 −2.68125
\(190\) 0 0
\(191\) 18.8820 1.36626 0.683128 0.730298i \(-0.260619\pi\)
0.683128 + 0.730298i \(0.260619\pi\)
\(192\) −3.37688 + 0.595435i −0.243705 + 0.0429718i
\(193\) −3.13916 3.74110i −0.225961 0.269290i 0.641138 0.767426i \(-0.278463\pi\)
−0.867099 + 0.498135i \(0.834018\pi\)
\(194\) 0.176250 0.0641498i 0.0126540 0.00460568i
\(195\) 0 0
\(196\) −2.69212 2.25896i −0.192294 0.161354i
\(197\) 3.04622 + 1.75874i 0.217034 + 0.125305i 0.604576 0.796547i \(-0.293342\pi\)
−0.387542 + 0.921852i \(0.626676\pi\)
\(198\) −27.3429 + 15.7864i −1.94317 + 1.12189i
\(199\) 0.145954 0.827747i 0.0103464 0.0586774i −0.979197 0.202910i \(-0.934960\pi\)
0.989544 + 0.144232i \(0.0460713\pi\)
\(200\) 0 0
\(201\) −13.6539 23.6493i −0.963073 1.66809i
\(202\) −1.69767 0.980151i −0.119448 0.0689632i
\(203\) 1.41428 1.68547i 0.0992630 0.118297i
\(204\) 19.2970 + 7.02352i 1.35106 + 0.491745i
\(205\) 0 0
\(206\) −13.4088 + 11.2513i −0.934237 + 0.783918i
\(207\) −43.8809 + 7.73738i −3.04993 + 0.537785i
\(208\) 2.83690i 0.196704i
\(209\) −5.98481 14.5299i −0.413978 1.00506i
\(210\) 0 0
\(211\) −4.75961 26.9931i −0.327665 1.85828i −0.490244 0.871585i \(-0.663092\pi\)
0.162579 0.986695i \(-0.448019\pi\)
\(212\) 1.64656 + 1.96229i 0.113086 + 0.134771i
\(213\) −2.25991 6.20906i −0.154847 0.425438i
\(214\) −9.95107 3.62189i −0.680241 0.247588i
\(215\) 0 0
\(216\) 9.87176 17.0984i 0.671688 1.16340i
\(217\) −8.40551 + 4.85292i −0.570603 + 0.329438i
\(218\) −13.6646 2.40943i −0.925480 0.163187i
\(219\) 2.98432 16.9249i 0.201662 1.14368i
\(220\) 0 0
\(221\) 8.49481 14.7134i 0.571423 0.989733i
\(222\) 7.38882 8.80565i 0.495905 0.590997i
\(223\) 3.91105 10.7455i 0.261903 0.719574i −0.737136 0.675745i \(-0.763822\pi\)
0.999039 0.0438288i \(-0.0139556\pi\)
\(224\) −1.75441 + 0.638551i −0.117221 + 0.0426650i
\(225\) 0 0
\(226\) 2.76721 + 15.6936i 0.184072 + 1.04392i
\(227\) 15.6154i 1.03643i 0.855251 + 0.518214i \(0.173403\pi\)
−0.855251 + 0.518214i \(0.826597\pi\)
\(228\) 11.8399 + 9.12234i 0.784113 + 0.604142i
\(229\) −5.50003 −0.363452 −0.181726 0.983349i \(-0.558168\pi\)
−0.181726 + 0.983349i \(0.558168\pi\)
\(230\) 0 0
\(231\) −17.6798 + 14.8351i −1.16325 + 0.976080i
\(232\) 0.403065 + 1.10741i 0.0264625 + 0.0727052i
\(233\) 3.87461 10.6454i 0.253834 0.697404i −0.745682 0.666302i \(-0.767876\pi\)
0.999516 0.0311019i \(-0.00990164\pi\)
\(234\) −19.0325 15.9702i −1.24419 1.04400i
\(235\) 0 0
\(236\) 2.38413 + 4.12943i 0.155193 + 0.268803i
\(237\) −2.03013 0.357967i −0.131871 0.0232524i
\(238\) 11.0112 + 1.94157i 0.713750 + 0.125853i
\(239\) 0.741670 + 1.28461i 0.0479747 + 0.0830946i 0.889016 0.457877i \(-0.151390\pi\)
−0.841041 + 0.540972i \(0.818057\pi\)
\(240\) 0 0
\(241\) −6.44943 5.41172i −0.415444 0.348599i 0.410983 0.911643i \(-0.365186\pi\)
−0.826427 + 0.563044i \(0.809630\pi\)
\(242\) −0.682899 + 1.87625i −0.0438984 + 0.120610i
\(243\) 28.3259 + 77.8248i 1.81711 + 4.99247i
\(244\) −6.30943 + 5.29424i −0.403920 + 0.338929i
\(245\) 0 0
\(246\) 12.7754 0.814528
\(247\) 9.13353 8.33613i 0.581153 0.530415i
\(248\) 5.19863i 0.330114i
\(249\) 1.13300 + 6.42558i 0.0718011 + 0.407204i
\(250\) 0 0
\(251\) −10.4219 + 3.79327i −0.657826 + 0.239429i −0.649298 0.760535i \(-0.724937\pi\)
−0.00852858 + 0.999964i \(0.502715\pi\)
\(252\) 5.59234 15.3648i 0.352284 0.967893i
\(253\) −11.7899 + 14.0506i −0.741223 + 0.883356i
\(254\) 8.40701 14.5614i 0.527503 0.913661i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) 11.3101 + 1.99428i 0.705506 + 0.124400i 0.514879 0.857263i \(-0.327837\pi\)
0.190627 + 0.981663i \(0.438948\pi\)
\(258\) 1.99484 1.15172i 0.124193 0.0717030i
\(259\) 3.12938 5.42024i 0.194450 0.336797i
\(260\) 0 0
\(261\) −9.69856 3.52999i −0.600326 0.218501i
\(262\) 2.22784 + 6.12094i 0.137636 + 0.378153i
\(263\) −20.4010 24.3129i −1.25798 1.49920i −0.786864 0.617126i \(-0.788297\pi\)
−0.471113 0.882073i \(-0.656148\pi\)
\(264\) −2.14660 12.1739i −0.132114 0.749255i
\(265\) 0 0
\(266\) 7.21109 + 3.77202i 0.442141 + 0.231278i
\(267\) 3.38069i 0.206895i
\(268\) 7.84286 1.38291i 0.479079 0.0844746i
\(269\) 17.8932 15.0142i 1.09097 0.915431i 0.0941831 0.995555i \(-0.469976\pi\)
0.996785 + 0.0801240i \(0.0255316\pi\)
\(270\) 0 0
\(271\) 20.7560 + 7.55458i 1.26084 + 0.458908i 0.884050 0.467392i \(-0.154806\pi\)
0.376788 + 0.926299i \(0.377028\pi\)
\(272\) −3.84952 + 4.58768i −0.233411 + 0.278169i
\(273\) −15.7284 9.08077i −0.951924 0.549593i
\(274\) −10.1231 17.5337i −0.611557 1.05925i
\(275\) 0 0
\(276\) 3.02943 17.1807i 0.182350 1.03416i
\(277\) −17.1581 + 9.90622i −1.03093 + 0.595207i −0.917251 0.398310i \(-0.869597\pi\)
−0.113679 + 0.993518i \(0.536263\pi\)
\(278\) −3.45412 1.99424i −0.207164 0.119606i
\(279\) 34.8771 + 29.2654i 2.08804 + 1.75207i
\(280\) 0 0
\(281\) 19.8856 7.23776i 1.18627 0.431769i 0.327860 0.944726i \(-0.393672\pi\)
0.858414 + 0.512958i \(0.171450\pi\)
\(282\) 13.9355 + 16.6076i 0.829845 + 0.988971i
\(283\) −18.3665 + 3.23851i −1.09178 + 0.192510i −0.690418 0.723411i \(-0.742573\pi\)
−0.401359 + 0.915921i \(0.631462\pi\)
\(284\) 1.92698 0.114345
\(285\) 0 0
\(286\) −10.2273 −0.604752
\(287\) 6.85023 1.20788i 0.404356 0.0712989i
\(288\) 5.62944 + 6.70890i 0.331718 + 0.395326i
\(289\) 17.7279 6.45241i 1.04282 0.379554i
\(290\) 0 0
\(291\) −0.492676 0.413404i −0.0288812 0.0242342i
\(292\) 4.34052 + 2.50600i 0.254010 + 0.146653i
\(293\) 25.7475 14.8653i 1.50419 0.868442i 0.504197 0.863589i \(-0.331788\pi\)
0.999988 0.00485332i \(-0.00154486\pi\)
\(294\) −2.09254 + 11.8674i −0.122040 + 0.692121i
\(295\) 0 0
\(296\) 1.67615 + 2.90318i 0.0974244 + 0.168744i
\(297\) 61.6412 + 35.5886i 3.57678 + 2.06506i
\(298\) −3.62054 + 4.31479i −0.209732 + 0.249949i
\(299\) −13.5630 4.93654i −0.784370 0.285487i
\(300\) 0 0
\(301\) 0.960753 0.806167i 0.0553769 0.0464667i
\(302\) −1.21967 + 0.215061i −0.0701841 + 0.0123753i
\(303\) 6.72182i 0.386159i
\(304\) −3.68089 + 2.33475i −0.211113 + 0.133907i
\(305\) 0 0
\(306\) −9.10766 51.6521i −0.520650 2.95275i
\(307\) −3.31770 3.95389i −0.189351 0.225660i 0.663014 0.748607i \(-0.269277\pi\)
−0.852365 + 0.522947i \(0.824833\pi\)
\(308\) −2.30203 6.32479i −0.131171 0.360388i
\(309\) 56.4010 + 20.5283i 3.20854 + 1.16781i
\(310\) 0 0
\(311\) 13.0187 22.5490i 0.738223 1.27864i −0.215072 0.976598i \(-0.568999\pi\)
0.953295 0.302041i \(-0.0976680\pi\)
\(312\) 8.42440 4.86383i 0.476938 0.275360i
\(313\) 0.272916 + 0.0481224i 0.0154261 + 0.00272004i 0.181356 0.983418i \(-0.441951\pi\)
−0.165930 + 0.986138i \(0.553063\pi\)
\(314\) −3.73471 + 21.1806i −0.210762 + 1.19529i
\(315\) 0 0
\(316\) 0.300593 0.520642i 0.0169097 0.0292884i
\(317\) −16.0233 + 19.0958i −0.899958 + 1.07253i 0.0970537 + 0.995279i \(0.469058\pi\)
−0.997012 + 0.0772492i \(0.975386\pi\)
\(318\) 3.00418 8.25391i 0.168466 0.462856i
\(319\) −3.99232 + 1.45309i −0.223527 + 0.0813572i
\(320\) 0 0
\(321\) 6.30548 + 35.7602i 0.351938 + 1.99594i
\(322\) 9.49883i 0.529349i
\(323\) 26.0819 1.08702i 1.45123 0.0604835i
\(324\) −41.4264 −2.30147
\(325\) 0 0
\(326\) −13.8049 + 11.5837i −0.764582 + 0.641561i
\(327\) 16.2727 + 44.7089i 0.899882 + 2.47241i
\(328\) −1.27427 + 3.50103i −0.0703598 + 0.193312i
\(329\) 9.04250 + 7.58755i 0.498529 + 0.418315i
\(330\) 0 0
\(331\) 5.34847 + 9.26381i 0.293978 + 0.509185i 0.974747 0.223313i \(-0.0716873\pi\)
−0.680768 + 0.732499i \(0.738354\pi\)
\(332\) −1.87391 0.330420i −0.102844 0.0181342i
\(333\) −28.9130 5.09814i −1.58442 0.279376i
\(334\) 5.45442 + 9.44734i 0.298453 + 0.516935i
\(335\) 0 0
\(336\) 4.90413 + 4.11506i 0.267542 + 0.224495i
\(337\) −1.55890 + 4.28303i −0.0849184 + 0.233312i −0.974883 0.222719i \(-0.928507\pi\)
0.889964 + 0.456030i \(0.150729\pi\)
\(338\) 1.69368 + 4.65334i 0.0921238 + 0.253108i
\(339\) 41.8591 35.1239i 2.27347 1.90767i
\(340\) 0 0
\(341\) 18.7415 1.01491
\(342\) 5.05771 37.8381i 0.273490 2.04605i
\(343\) 19.6302i 1.05993i
\(344\) 0.116650 + 0.661553i 0.00628933 + 0.0356686i
\(345\) 0 0
\(346\) 0.137103 0.0499015i 0.00737072 0.00268272i
\(347\) 7.14578 19.6329i 0.383606 1.05395i −0.586221 0.810151i \(-0.699385\pi\)
0.969826 0.243796i \(-0.0783928\pi\)
\(348\) 2.59750 3.09558i 0.139240 0.165940i
\(349\) −5.64218 + 9.77255i −0.302019 + 0.523112i −0.976593 0.215095i \(-0.930994\pi\)
0.674574 + 0.738207i \(0.264327\pi\)
\(350\) 0 0
\(351\) −9.72611 + 55.1595i −0.519141 + 2.94420i
\(352\) 3.55032 + 0.626017i 0.189233 + 0.0333668i
\(353\) 7.11512 4.10792i 0.378700 0.218642i −0.298553 0.954393i \(-0.596504\pi\)
0.677252 + 0.735751i \(0.263171\pi\)
\(354\) 8.17511 14.1597i 0.434502 0.752580i
\(355\) 0 0
\(356\) −0.926460 0.337204i −0.0491023 0.0178718i
\(357\) −13.1129 36.0274i −0.694009 1.90677i
\(358\) 3.66356 + 4.36606i 0.193625 + 0.230753i
\(359\) 1.86656 + 10.5858i 0.0985131 + 0.558696i 0.993614 + 0.112832i \(0.0359922\pi\)
−0.895101 + 0.445864i \(0.852897\pi\)
\(360\) 0 0
\(361\) 18.3330 + 4.99020i 0.964893 + 0.262642i
\(362\) 18.5013i 0.972405i
\(363\) 6.74248 1.18888i 0.353889 0.0624001i
\(364\) 4.05735 3.40452i 0.212663 0.178446i
\(365\) 0 0
\(366\) 26.5391 + 9.65944i 1.38722 + 0.504907i
\(367\) 9.60825 11.4507i 0.501547 0.597720i −0.454568 0.890712i \(-0.650206\pi\)
0.956115 + 0.292992i \(0.0946509\pi\)
\(368\) 4.40612 + 2.54388i 0.229685 + 0.132609i
\(369\) −16.3146 28.2578i −0.849306 1.47104i
\(370\) 0 0
\(371\) 0.830471 4.70983i 0.0431159 0.244522i
\(372\) −15.4377 + 8.91299i −0.800410 + 0.462117i
\(373\) 7.55370 + 4.36113i 0.391116 + 0.225811i 0.682644 0.730752i \(-0.260830\pi\)
−0.291528 + 0.956562i \(0.594164\pi\)
\(374\) −16.5390 13.8779i −0.855211 0.717607i
\(375\) 0 0
\(376\) −5.94122 + 2.16243i −0.306395 + 0.111519i
\(377\) −2.14900 2.56107i −0.110679 0.131902i
\(378\) −36.3011 + 6.40087i −1.86713 + 0.329225i
\(379\) −15.9169 −0.817597 −0.408799 0.912625i \(-0.634052\pi\)
−0.408799 + 0.912625i \(0.634052\pi\)
\(380\) 0 0
\(381\) −57.6548 −2.95375
\(382\) 18.5952 3.27883i 0.951412 0.167760i
\(383\) 1.12094 + 1.33589i 0.0572776 + 0.0682607i 0.793923 0.608019i \(-0.208036\pi\)
−0.736645 + 0.676280i \(0.763591\pi\)
\(384\) −3.22218 + 1.17278i −0.164431 + 0.0598481i
\(385\) 0 0
\(386\) −3.74110 3.13916i −0.190417 0.159779i
\(387\) −5.09497 2.94158i −0.258992 0.149529i
\(388\) 0.162433 0.0937807i 0.00824628 0.00476099i
\(389\) −5.63929 + 31.9820i −0.285924 + 1.62155i 0.416044 + 0.909344i \(0.363416\pi\)
−0.701968 + 0.712209i \(0.747695\pi\)
\(390\) 0 0
\(391\) −15.2347 26.3873i −0.770454 1.33447i
\(392\) −3.04348 1.75716i −0.153719 0.0887498i
\(393\) 14.3570 17.1100i 0.724214 0.863085i
\(394\) 3.30534 + 1.20305i 0.166521 + 0.0606086i
\(395\) 0 0
\(396\) −24.1862 + 20.2946i −1.21540 + 1.01984i
\(397\) 4.04292 0.712877i 0.202909 0.0357783i −0.0712700 0.997457i \(-0.522705\pi\)
0.274179 + 0.961679i \(0.411594\pi\)
\(398\) 0.840516i 0.0421313i
\(399\) −1.16200 27.8810i −0.0581730 1.39580i
\(400\) 0 0
\(401\) 5.41766 + 30.7251i 0.270545 + 1.53434i 0.752766 + 0.658288i \(0.228719\pi\)
−0.482221 + 0.876049i \(0.660170\pi\)
\(402\) −17.5531 20.9190i −0.875471 1.04335i
\(403\) 5.04412 + 13.8586i 0.251266 + 0.690347i
\(404\) −1.84208 0.670463i −0.0916470 0.0333568i
\(405\) 0 0
\(406\) 1.10011 1.90545i 0.0545978 0.0945661i
\(407\) −10.4662 + 6.04268i −0.518792 + 0.299524i
\(408\) 20.2234 + 3.56593i 1.00121 + 0.176540i
\(409\) −1.52348 + 8.64010i −0.0753313 + 0.427225i 0.923696 + 0.383127i \(0.125153\pi\)
−0.999027 + 0.0440987i \(0.985958\pi\)
\(410\) 0 0
\(411\) −34.7117 + 60.1225i −1.71220 + 2.96562i
\(412\) −11.2513 + 13.4088i −0.554314 + 0.660605i
\(413\) 3.04478 8.36545i 0.149824 0.411637i
\(414\) −41.8706 + 15.2397i −2.05783 + 0.748988i
\(415\) 0 0
\(416\) 0.492623 + 2.79380i 0.0241528 + 0.136978i
\(417\) 13.6764i 0.669734i
\(418\) −8.41698 13.2699i −0.411688 0.649053i
\(419\) 6.13252 0.299593 0.149797 0.988717i \(-0.452138\pi\)
0.149797 + 0.988717i \(0.452138\pi\)
\(420\) 0 0
\(421\) −2.93864 + 2.46581i −0.143220 + 0.120176i −0.711583 0.702602i \(-0.752021\pi\)
0.568363 + 0.822778i \(0.307577\pi\)
\(422\) −9.37460 25.7565i −0.456348 1.25381i
\(423\) 18.9382 52.0324i 0.920808 2.52990i
\(424\) 1.96229 + 1.64656i 0.0952974 + 0.0799640i
\(425\) 0 0
\(426\) −3.30377 5.72230i −0.160068 0.277247i
\(427\) 15.1437 + 2.67024i 0.732855 + 0.129222i
\(428\) −10.4288 1.83888i −0.504096 0.0888858i
\(429\) 17.5345 + 30.3707i 0.846576 + 1.46631i
\(430\) 0 0
\(431\) −19.5996 16.4460i −0.944081 0.792178i 0.0342100 0.999415i \(-0.489108\pi\)
−0.978291 + 0.207237i \(0.933553\pi\)
\(432\) 6.75268 18.5528i 0.324888 0.892624i
\(433\) 9.73513 + 26.7471i 0.467841 + 1.28538i 0.919464 + 0.393173i \(0.128623\pi\)
−0.451624 + 0.892208i \(0.649155\pi\)
\(434\) −7.43511 + 6.23880i −0.356897 + 0.299472i
\(435\) 0 0
\(436\) −13.8754 −0.664509
\(437\) −4.75710 21.6608i −0.227563 1.03618i
\(438\) 17.1860i 0.821180i
\(439\) −6.61684 37.5260i −0.315805 1.79102i −0.567671 0.823256i \(-0.692155\pi\)
0.251866 0.967762i \(-0.418956\pi\)
\(440\) 0 0
\(441\) 28.9217 10.5266i 1.37722 0.501268i
\(442\) 5.81079 15.9650i 0.276391 0.759379i
\(443\) 14.6417 17.4493i 0.695649 0.829042i −0.296377 0.955071i \(-0.595779\pi\)
0.992027 + 0.126029i \(0.0402231\pi\)
\(444\) 5.74748 9.95493i 0.272763 0.472440i
\(445\) 0 0
\(446\) 1.98569 11.2614i 0.0940253 0.533244i
\(447\) 19.0205 + 3.35382i 0.899637 + 0.158630i
\(448\) −1.61687 + 0.933500i −0.0763899 + 0.0441037i
\(449\) −15.5911 + 27.0045i −0.735787 + 1.27442i 0.218590 + 0.975817i \(0.429854\pi\)
−0.954377 + 0.298604i \(0.903479\pi\)
\(450\) 0 0
\(451\) −12.6215 4.59385i −0.594324 0.216316i
\(452\) 5.45034 + 14.9747i 0.256362 + 0.704350i
\(453\) 2.72975 + 3.25318i 0.128255 + 0.152848i
\(454\) 2.71158 + 15.3781i 0.127261 + 0.721731i
\(455\) 0 0
\(456\) 13.2441 + 6.92778i 0.620210 + 0.324423i
\(457\) 13.0810i 0.611902i −0.952047 0.305951i \(-0.901026\pi\)
0.952047 0.305951i \(-0.0989744\pi\)
\(458\) −5.41647 + 0.955070i −0.253095 + 0.0446275i
\(459\) −90.5769 + 76.0030i −4.22777 + 3.54752i
\(460\) 0 0
\(461\) −17.1219 6.23187i −0.797448 0.290247i −0.0890194 0.996030i \(-0.528373\pi\)
−0.708429 + 0.705783i \(0.750596\pi\)
\(462\) −14.8351 + 17.6798i −0.690193 + 0.822540i
\(463\) −19.9255 11.5040i −0.926017 0.534636i −0.0404670 0.999181i \(-0.512885\pi\)
−0.885550 + 0.464545i \(0.846218\pi\)
\(464\) 0.589242 + 1.02060i 0.0273549 + 0.0473800i
\(465\) 0 0
\(466\) 1.96719 11.1565i 0.0911284 0.516815i
\(467\) −21.6966 + 12.5265i −1.00400 + 0.579658i −0.909429 0.415860i \(-0.863481\pi\)
−0.0945691 + 0.995518i \(0.530147\pi\)
\(468\) −21.5166 12.4226i −0.994603 0.574234i
\(469\) −11.3899 9.55729i −0.525938 0.441315i
\(470\) 0 0
\(471\) 69.3005 25.2233i 3.19320 1.16223i
\(472\) 3.06497 + 3.65269i 0.141077 + 0.168129i
\(473\) −2.38496 + 0.420532i −0.109660 + 0.0193361i
\(474\) −2.06145 −0.0946854
\(475\) 0 0
\(476\) 11.1811 0.512483
\(477\) −22.0932 + 3.89563i −1.01158 + 0.178369i
\(478\) 0.953473 + 1.13631i 0.0436108 + 0.0519734i
\(479\) 20.3567 7.40924i 0.930122 0.338537i 0.167864 0.985810i \(-0.446313\pi\)
0.762258 + 0.647274i \(0.224091\pi\)
\(480\) 0 0
\(481\) −7.28521 6.11302i −0.332177 0.278730i
\(482\) −7.29118 4.20957i −0.332104 0.191741i
\(483\) −28.2075 + 16.2856i −1.28349 + 0.741021i
\(484\) −0.346717 + 1.96633i −0.0157598 + 0.0893785i
\(485\) 0 0
\(486\) 41.4097 + 71.7238i 1.87838 + 3.25346i
\(487\) 2.87982 + 1.66266i 0.130497 + 0.0753425i 0.563827 0.825893i \(-0.309328\pi\)
−0.433330 + 0.901235i \(0.642662\pi\)
\(488\) −5.29424 + 6.30943i −0.239659 + 0.285614i
\(489\) 58.0669 + 21.1346i 2.62588 + 0.955741i
\(490\) 0 0
\(491\) −3.86014 + 3.23904i −0.174206 + 0.146176i −0.725722 0.687988i \(-0.758494\pi\)
0.551516 + 0.834164i \(0.314050\pi\)
\(492\) 12.5813 2.21842i 0.567208 0.100014i
\(493\) 7.05769i 0.317862i
\(494\) 7.54722 9.79551i 0.339565 0.440721i
\(495\) 0 0
\(496\) −0.902733 5.11966i −0.0405339 0.229879i
\(497\) −2.31253 2.75597i −0.103731 0.123622i
\(498\) 2.23158 + 6.13121i 0.0999995 + 0.274746i
\(499\) −9.62114 3.50181i −0.430701 0.156762i 0.117567 0.993065i \(-0.462491\pi\)
−0.548268 + 0.836302i \(0.684713\pi\)
\(500\) 0 0
\(501\) 18.7031 32.3947i 0.835592 1.44729i
\(502\) −9.60490 + 5.54539i −0.428688 + 0.247503i
\(503\) −6.60132 1.16399i −0.294338 0.0518998i 0.0245291 0.999699i \(-0.492191\pi\)
−0.318867 + 0.947799i \(0.603302\pi\)
\(504\) 2.83930 16.1025i 0.126473 0.717262i
\(505\) 0 0
\(506\) −9.17090 + 15.8845i −0.407696 + 0.706151i
\(507\) 10.9147 13.0076i 0.484737 0.577687i
\(508\) 5.75073 15.8000i 0.255148 0.701012i
\(509\) 22.6049 8.22751i 1.00195 0.364678i 0.211611 0.977354i \(-0.432129\pi\)
0.790334 + 0.612676i \(0.209907\pi\)
\(510\) 0 0
\(511\) −1.62490 9.21525i −0.0718812 0.407659i
\(512\) 1.00000i 0.0441942i
\(513\) −79.5741 + 32.7762i −3.51328 + 1.44711i
\(514\) 11.4846 0.506564
\(515\) 0 0
\(516\) 1.76454 1.48062i 0.0776795 0.0651808i
\(517\) −7.79575 21.4186i −0.342857 0.941991i
\(518\) 2.14062 5.88130i 0.0940534 0.258410i
\(519\) −0.383248 0.321583i −0.0168227 0.0141159i
\(520\) 0 0
\(521\) −13.2375 22.9280i −0.579945 1.00449i −0.995485 0.0949192i \(-0.969741\pi\)
0.415540 0.909575i \(-0.363593\pi\)
\(522\) −10.1642 1.79222i −0.444874 0.0784434i
\(523\) 15.3861 + 2.71298i 0.672787 + 0.118631i 0.499597 0.866258i \(-0.333481\pi\)
0.173190 + 0.984888i \(0.444593\pi\)
\(524\) 3.25688 + 5.64108i 0.142278 + 0.246432i
\(525\) 0 0
\(526\) −24.3129 20.4010i −1.06009 0.889524i
\(527\) −10.6483 + 29.2559i −0.463847 + 1.27441i
\(528\) −4.22797 11.6162i −0.183999 0.505532i
\(529\) −2.21022 + 1.85459i −0.0960963 + 0.0806344i
\(530\) 0 0
\(531\) −41.7597 −1.81222
\(532\) 7.75655 + 2.46253i 0.336289 + 0.106764i
\(533\) 10.5695i 0.457816i
\(534\) 0.587050 + 3.32933i 0.0254041 + 0.144074i
\(535\) 0 0
\(536\) 7.48357 2.72380i 0.323241 0.117650i
\(537\) 6.68423 18.3648i 0.288446 0.792498i
\(538\) 15.0142 17.8932i 0.647307 0.771431i
\(539\) 6.33470 10.9720i 0.272855 0.472599i
\(540\) 0 0
\(541\) −2.57421 + 14.5991i −0.110674 + 0.627664i 0.878127 + 0.478427i \(0.158793\pi\)
−0.988801 + 0.149237i \(0.952318\pi\)
\(542\) 21.7525 + 3.83556i 0.934351 + 0.164751i
\(543\) 54.9409 31.7202i 2.35774 1.36124i
\(544\) −2.99439 + 5.18644i −0.128384 + 0.222367i
\(545\) 0 0
\(546\) −17.0663 6.21161i −0.730369 0.265833i
\(547\) 6.62897 + 18.2130i 0.283434 + 0.778730i 0.996947 + 0.0780869i \(0.0248812\pi\)
−0.713512 + 0.700643i \(0.752897\pi\)
\(548\) −13.0140 15.5095i −0.555929 0.662531i
\(549\) −12.5258 71.0371i −0.534586 3.03179i
\(550\) 0 0
\(551\) 1.55439 4.89607i 0.0662193 0.208580i
\(552\) 17.4458i 0.742541i
\(553\) −1.10536 + 0.194905i −0.0470047 + 0.00828820i
\(554\) −15.1772 + 12.7352i −0.644818 + 0.541067i
\(555\) 0 0
\(556\) −3.74794 1.36414i −0.158948 0.0578523i
\(557\) 24.5056 29.2047i 1.03834 1.23744i 0.0674946 0.997720i \(-0.478499\pi\)
0.970842 0.239721i \(-0.0770561\pi\)
\(558\) 39.4292 + 22.7644i 1.66917 + 0.963695i
\(559\) −0.952858 1.65040i −0.0403016 0.0698044i
\(560\) 0 0
\(561\) −12.8555 + 72.9072i −0.542760 + 3.07814i
\(562\) 18.3267 10.5809i 0.773063 0.446328i
\(563\) 10.6774 + 6.16458i 0.449998 + 0.259806i 0.707829 0.706384i \(-0.249675\pi\)
−0.257832 + 0.966190i \(0.583008\pi\)
\(564\) 16.6076 + 13.9355i 0.699308 + 0.586789i
\(565\) 0 0
\(566\) −17.5251 + 6.37863i −0.736636 + 0.268114i
\(567\) 49.7152 + 59.2482i 2.08784 + 2.48819i
\(568\) 1.89770 0.334616i 0.0796258 0.0140402i
\(569\) 3.18778 0.133639 0.0668194 0.997765i \(-0.478715\pi\)
0.0668194 + 0.997765i \(0.478715\pi\)
\(570\) 0 0
\(571\) 3.67370 0.153740 0.0768698 0.997041i \(-0.475507\pi\)
0.0768698 + 0.997041i \(0.475507\pi\)
\(572\) −10.0719 + 1.77595i −0.421128 + 0.0742562i
\(573\) −41.6179 49.5983i −1.73861 2.07200i
\(574\) 6.53641 2.37906i 0.272825 0.0993001i
\(575\) 0 0
\(576\) 6.70890 + 5.62944i 0.279538 + 0.234560i
\(577\) 1.86286 + 1.07552i 0.0775519 + 0.0447746i 0.538274 0.842770i \(-0.319076\pi\)
−0.460723 + 0.887544i \(0.652410\pi\)
\(578\) 16.3381 9.43280i 0.679575 0.392353i
\(579\) −2.90790 + 16.4915i −0.120848 + 0.685364i
\(580\) 0 0
\(581\) 1.77628 + 3.07660i 0.0736924 + 0.127639i
\(582\) −0.556978 0.321571i −0.0230875 0.0133296i
\(583\) −5.93599 + 7.07424i −0.245844 + 0.292985i
\(584\) 4.70974 + 1.71421i 0.194891 + 0.0709344i
\(585\) 0 0
\(586\) 22.7750 19.1105i 0.940827 0.789447i
\(587\) 28.0908 4.95317i 1.15943 0.204439i 0.439342 0.898320i \(-0.355212\pi\)
0.720090 + 0.693880i \(0.244100\pi\)
\(588\) 12.0505i 0.496953i
\(589\) −13.8303 + 17.9503i −0.569868 + 0.739629i
\(590\) 0 0
\(591\) −2.09442 11.8781i −0.0861531 0.488599i
\(592\) 2.15482 + 2.56801i 0.0885626 + 0.105545i
\(593\) 3.45151 + 9.48294i 0.141737 + 0.389418i 0.990167 0.139889i \(-0.0446744\pi\)
−0.848431 + 0.529306i \(0.822452\pi\)
\(594\) 66.8846 + 24.3440i 2.74431 + 0.998847i
\(595\) 0 0
\(596\) −2.81628 + 4.87794i −0.115359 + 0.199808i
\(597\) −2.49598 + 1.44105i −0.102154 + 0.0589784i
\(598\) −14.2142 2.50635i −0.581261 0.102492i
\(599\) −0.479831 + 2.72126i −0.0196054 + 0.111188i −0.993040 0.117778i \(-0.962423\pi\)
0.973435 + 0.228965i \(0.0735341\pi\)
\(600\) 0 0
\(601\) −8.51074 + 14.7410i −0.347160 + 0.601299i −0.985744 0.168253i \(-0.946187\pi\)
0.638583 + 0.769553i \(0.279521\pi\)
\(602\) 0.806167 0.960753i 0.0328569 0.0391574i
\(603\) −23.8546 + 65.5400i −0.971435 + 2.66900i
\(604\) −1.16380 + 0.423587i −0.0473542 + 0.0172355i
\(605\) 0 0
\(606\) 1.16723 + 6.61970i 0.0474156 + 0.268907i
\(607\) 45.0807i 1.82977i −0.403717 0.914884i \(-0.632282\pi\)
0.403717 0.914884i \(-0.367718\pi\)
\(608\) −3.21954 + 2.93846i −0.130570 + 0.119170i
\(609\) −7.54452 −0.305720
\(610\) 0 0
\(611\) 13.7401 11.5293i 0.555863 0.466425i
\(612\) −17.9386 49.2859i −0.725124 1.99226i
\(613\) 0.420147 1.15435i 0.0169696 0.0466236i −0.930919 0.365227i \(-0.880991\pi\)
0.947888 + 0.318603i \(0.103214\pi\)
\(614\) −3.95389 3.31770i −0.159566 0.133892i
\(615\) 0 0
\(616\) −3.36535 5.82896i −0.135594 0.234855i
\(617\) 23.3588 + 4.11879i 0.940392 + 0.165816i 0.622773 0.782402i \(-0.286006\pi\)
0.317618 + 0.948219i \(0.397117\pi\)
\(618\) 59.1088 + 10.4225i 2.37771 + 0.419254i
\(619\) 6.32545 + 10.9560i 0.254241 + 0.440359i 0.964689 0.263391i \(-0.0848410\pi\)
−0.710448 + 0.703750i \(0.751508\pi\)
\(620\) 0 0
\(621\) 76.9493 + 64.5681i 3.08787 + 2.59103i
\(622\) 8.90531 24.4672i 0.357071 0.981043i
\(623\) 0.629559 + 1.72970i 0.0252228 + 0.0692990i
\(624\) 7.45182 6.25282i 0.298312 0.250313i
\(625\) 0 0
\(626\) 0.277126 0.0110762
\(627\) −24.9753 + 47.7460i −0.997416 + 1.90679i
\(628\) 21.5073i 0.858235i
\(629\) −3.48620 19.7712i −0.139004 0.788331i
\(630\) 0 0
\(631\) −35.9350 + 13.0793i −1.43055 + 0.520677i −0.937089 0.349091i \(-0.886490\pi\)
−0.493460 + 0.869769i \(0.664268\pi\)
\(632\) 0.205617 0.564929i 0.00817902 0.0224717i
\(633\) −60.4133 + 71.9978i −2.40121 + 2.86165i
\(634\) −12.4639 + 21.5881i −0.495005 + 0.857374i
\(635\) 0 0
\(636\) 1.52526 8.65019i 0.0604805 0.343002i
\(637\) 9.81830 + 1.73123i 0.389015 + 0.0685939i
\(638\) −3.67934 + 2.12427i −0.145667 + 0.0841006i
\(639\) −8.43809 + 14.6152i −0.333806 + 0.578168i
\(640\) 0 0
\(641\) −9.64318 3.50983i −0.380883 0.138630i 0.144481 0.989508i \(-0.453849\pi\)
−0.525364 + 0.850878i \(0.676071\pi\)
\(642\) 12.4194 + 34.1219i 0.490154 + 1.34669i
\(643\) 9.36407 + 11.1597i 0.369283 + 0.440094i 0.918401 0.395650i \(-0.129481\pi\)
−0.549118 + 0.835745i \(0.685036\pi\)
\(644\) −1.64946 9.35452i −0.0649976 0.368620i
\(645\) 0 0
\(646\) 25.4969 5.59958i 1.00316 0.220313i
\(647\) 4.44223i 0.174642i 0.996180 + 0.0873211i \(0.0278306\pi\)
−0.996180 + 0.0873211i \(0.972169\pi\)
\(648\) −40.7970 + 7.19362i −1.60266 + 0.282592i
\(649\) −13.1683 + 11.0495i −0.516900 + 0.433731i
\(650\) 0 0
\(651\) 31.2740 + 11.3828i 1.22572 + 0.446127i
\(652\) −11.5837 + 13.8049i −0.453652 + 0.540641i
\(653\) 16.8427 + 9.72417i 0.659108 + 0.380536i 0.791937 0.610603i \(-0.209073\pi\)
−0.132829 + 0.991139i \(0.542406\pi\)
\(654\) 23.7891 + 41.2039i 0.930227 + 1.61120i
\(655\) 0 0
\(656\) −0.646964 + 3.66911i −0.0252597 + 0.143255i
\(657\) −38.0137 + 21.9472i −1.48305 + 0.856242i
\(658\) 10.2227 + 5.90207i 0.398522 + 0.230087i
\(659\) −9.54535 8.00950i −0.371834 0.312006i 0.437652 0.899144i \(-0.355810\pi\)
−0.809487 + 0.587138i \(0.800254\pi\)
\(660\) 0 0
\(661\) −7.75350 + 2.82204i −0.301576 + 0.109765i −0.488376 0.872633i \(-0.662411\pi\)
0.186800 + 0.982398i \(0.440188\pi\)
\(662\) 6.87585 + 8.19432i 0.267238 + 0.318481i
\(663\) −57.3719 + 10.1162i −2.22814 + 0.392881i
\(664\) −1.90282 −0.0738436
\(665\) 0 0
\(666\) −29.3590 −1.13764
\(667\) −5.90475 + 1.04117i −0.228633 + 0.0403141i
\(668\) 7.01207 + 8.35666i 0.271305 + 0.323329i
\(669\) −36.8461 + 13.4109i −1.42455 + 0.518495i
\(670\) 0 0
\(671\) −22.7461 19.0862i −0.878102 0.736815i
\(672\) 5.54420 + 3.20094i 0.213872 + 0.123479i
\(673\) 1.06793 0.616571i 0.0411658 0.0237671i −0.479276 0.877664i \(-0.659101\pi\)
0.520442 + 0.853897i \(0.325767\pi\)
\(674\) −0.791472 + 4.48866i −0.0304864 + 0.172897i
\(675\) 0 0
\(676\) 2.47599 + 4.28854i 0.0952303 + 0.164944i
\(677\) 15.4608 + 8.92630i 0.594207 + 0.343065i 0.766759 0.641935i \(-0.221868\pi\)
−0.172552 + 0.985000i \(0.555201\pi\)
\(678\) 35.1239 41.8591i 1.34893 1.60759i
\(679\) −0.329059 0.119768i −0.0126281 0.00459626i
\(680\) 0 0
\(681\) 41.0176 34.4178i 1.57180 1.31889i
\(682\) 18.4568 3.25443i 0.706748 0.124619i
\(683\) 27.7712i 1.06264i −0.847173 0.531318i \(-0.821697\pi\)
0.847173 0.531318i \(-0.178303\pi\)
\(684\) −1.58963 38.1415i −0.0607812 1.45838i
\(685\) 0 0
\(686\) 3.40875 + 19.3320i 0.130147 + 0.738099i
\(687\) 12.1226 + 14.4472i 0.462507 + 0.551194i
\(688\) 0.229755 + 0.631247i 0.00875933 + 0.0240661i
\(689\) −6.82874 2.48546i −0.260154 0.0946884i
\(690\) 0 0
\(691\) −21.3398 + 36.9617i −0.811805 + 1.40609i 0.0997945 + 0.995008i \(0.468181\pi\)
−0.911600 + 0.411079i \(0.865152\pi\)
\(692\) 0.126355 0.0729511i 0.00480330 0.00277319i
\(693\) 58.0509 + 10.2359i 2.20517 + 0.388831i
\(694\) 3.62801 20.5755i 0.137717 0.781033i
\(695\) 0 0
\(696\) 2.02049 3.49960i 0.0765866 0.132652i
\(697\) 14.3422 17.0924i 0.543250 0.647420i
\(698\) −3.85948 + 10.6038i −0.146083 + 0.401361i
\(699\) −36.5028 + 13.2859i −1.38066 + 0.502520i
\(700\) 0 0
\(701\) −6.91944 39.2421i −0.261344 1.48215i −0.779249 0.626715i \(-0.784399\pi\)
0.517905 0.855438i \(-0.326712\pi\)
\(702\) 56.0104i 2.11398i
\(703\) 1.93598 14.4835i 0.0730168 0.546257i
\(704\) 3.60509 0.135872
\(705\) 0 0
\(706\) 6.29370 5.28104i 0.236866 0.198754i
\(707\) 1.25175 + 3.43916i 0.0470770 + 0.129343i
\(708\) 5.59210 15.3642i 0.210164 0.577421i
\(709\) −36.8093 30.8866i −1.38240 1.15997i −0.968314 0.249734i \(-0.919657\pi\)
−0.414086 0.910238i \(-0.635899\pi\)
\(710\) 0 0
\(711\) 2.63255 + 4.55970i 0.0987282 + 0.171002i
\(712\) −0.970940 0.171203i −0.0363875 0.00641610i
\(713\) 26.0475 + 4.59288i 0.975488 + 0.172005i
\(714\) −19.1698 33.2030i −0.717411 1.24259i
\(715\) 0 0
\(716\) 4.36606 + 3.66356i 0.163167 + 0.136914i
\(717\) 1.73963 4.77959i 0.0649676 0.178497i
\(718\) 3.67640 + 10.1008i 0.137202 + 0.376960i
\(719\) 23.2680 19.5242i 0.867749 0.728128i −0.0958738 0.995393i \(-0.530565\pi\)
0.963623 + 0.267266i \(0.0861201\pi\)
\(720\) 0 0
\(721\) 32.6799 1.21706
\(722\) 18.9210 + 1.73090i 0.704166 + 0.0644175i
\(723\) 28.8690i 1.07365i
\(724\) 3.21271 + 18.2202i 0.119399 + 0.677148i
\(725\) 0 0
\(726\) 6.43360 2.34164i 0.238773 0.0869064i
\(727\) −10.4545 + 28.7236i −0.387737 + 1.06530i 0.580280 + 0.814417i \(0.302943\pi\)
−0.968018 + 0.250883i \(0.919279\pi\)
\(728\) 3.40452 4.05735i 0.126180 0.150376i
\(729\) 79.8532 138.310i 2.95753 5.12259i
\(730\) 0 0
\(731\) 0.698590 3.96190i 0.0258383 0.146536i
\(732\) 27.8132 + 4.90422i 1.02801 + 0.181265i
\(733\) 38.1050 21.9999i 1.40744 0.812586i 0.412299 0.911049i \(-0.364726\pi\)
0.995141 + 0.0984629i \(0.0313926\pi\)
\(734\) 7.47389 12.9452i 0.275866 0.477815i
\(735\) 0 0
\(736\) 4.78092 + 1.74011i 0.176227 + 0.0641415i
\(737\) 9.81953 + 26.9789i 0.361707 + 0.993782i
\(738\) −20.9737 24.9955i −0.772052 0.920096i
\(739\) −5.08815 28.8563i −0.187171 1.06150i −0.923135 0.384476i \(-0.874382\pi\)
0.735964 0.677020i \(-0.236729\pi\)
\(740\) 0 0
\(741\) −42.0281 5.61779i −1.54394 0.206375i
\(742\) 4.78249i 0.175571i
\(743\) 12.9235 2.27875i 0.474116 0.0835994i 0.0685156 0.997650i \(-0.478174\pi\)
0.405600 + 0.914051i \(0.367063\pi\)
\(744\) −13.6555 + 11.4583i −0.500635 + 0.420082i
\(745\) 0 0
\(746\) 8.19625 + 2.98319i 0.300086 + 0.109222i
\(747\) 10.7118 12.7658i 0.391924 0.467076i
\(748\) −18.6976 10.7951i −0.683651 0.394706i
\(749\) 9.88549 + 17.1222i 0.361208 + 0.625631i
\(750\) 0 0
\(751\) 3.47466 19.7058i 0.126792 0.719074i −0.853435 0.521199i \(-0.825485\pi\)
0.980227 0.197875i \(-0.0634040\pi\)
\(752\) −5.47546 + 3.16126i −0.199670 + 0.115279i
\(753\) 32.9349 + 19.0150i 1.20022 + 0.692945i
\(754\) −2.56107 2.14900i −0.0932688 0.0782618i
\(755\) 0 0
\(756\) −34.6381 + 12.6072i −1.25978 + 0.458521i
\(757\) −23.4542 27.9516i −0.852458 1.01592i −0.999641 0.0268104i \(-0.991465\pi\)
0.147183 0.989109i \(-0.452979\pi\)
\(758\) −15.6751 + 2.76394i −0.569345 + 0.100391i
\(759\) 62.8935 2.28289
\(760\) 0 0
\(761\) 3.91470 0.141908 0.0709540 0.997480i \(-0.477396\pi\)
0.0709540 + 0.997480i \(0.477396\pi\)
\(762\) −56.7789 + 10.0117i −2.05688 + 0.362684i
\(763\) 16.6516 + 19.8446i 0.602828 + 0.718422i
\(764\) 17.7433 6.45804i 0.641931 0.233644i
\(765\) 0 0
\(766\) 1.33589 + 1.12094i 0.0482676 + 0.0405013i
\(767\) −11.7148 6.76354i −0.422997 0.244217i
\(768\) −2.96958 + 1.71449i −0.107155 + 0.0618662i
\(769\) 3.94857 22.3935i 0.142389 0.807530i −0.827037 0.562147i \(-0.809975\pi\)
0.969426 0.245382i \(-0.0789135\pi\)
\(770\) 0 0
\(771\) −19.6902 34.1044i −0.709125 1.22824i
\(772\) −4.22937 2.44183i −0.152218 0.0878834i
\(773\) 14.0531 16.7478i 0.505454 0.602377i −0.451623 0.892209i \(-0.649155\pi\)
0.957078 + 0.289832i \(0.0935994\pi\)
\(774\) −5.52837 2.01216i −0.198713 0.0723256i
\(775\) 0 0
\(776\) 0.143680 0.120562i 0.00515782 0.00432793i
\(777\) −21.1350 + 3.72668i −0.758216 + 0.133694i
\(778\) 32.4754i 1.16430i
\(779\) 13.7139 8.69862i 0.491353 0.311660i
\(780\) 0 0
\(781\) 1.20632 + 6.84138i 0.0431655 + 0.244804i
\(782\) −19.5854 23.3410i −0.700373 0.834672i
\(783\) 7.95792 + 21.8642i 0.284393 + 0.781363i