Properties

Label 74.2.e.b.11.1
Level $74$
Weight $2$
Character 74.11
Analytic conductor $0.591$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 74.11
Dual form 74.2.e.b.27.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.366025 - 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +0.732051i q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000i q^{8} +(1.23205 + 2.13397i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.366025 - 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +0.732051i q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000i q^{8} +(1.23205 + 2.13397i) q^{9} -1.73205 q^{10} -1.26795 q^{11} +(-0.366025 - 0.633975i) q^{12} +(-3.00000 - 1.73205i) q^{13} +2.00000i q^{14} +(1.09808 - 0.633975i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.69615 + 2.13397i) q^{17} +(-2.13397 - 1.23205i) q^{18} +(-4.09808 - 2.36603i) q^{19} +(1.50000 - 0.866025i) q^{20} +(-0.732051 - 1.26795i) q^{21} +(1.09808 - 0.633975i) q^{22} -1.26795i q^{23} +(0.633975 + 0.366025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +3.46410 q^{26} +4.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +8.66025i q^{29} +(-0.633975 + 1.09808i) q^{30} +4.73205i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.464102 + 0.803848i) q^{33} +(2.13397 - 3.69615i) q^{34} +(3.00000 - 1.73205i) q^{35} +2.46410 q^{36} +(4.69615 + 3.86603i) q^{37} +4.73205 q^{38} +(-2.19615 + 1.26795i) q^{39} +(-0.866025 + 1.50000i) q^{40} +(1.96410 - 3.40192i) q^{41} +(1.26795 + 0.732051i) q^{42} -12.9282i q^{43} +(-0.633975 + 1.09808i) q^{44} +4.26795i q^{45} +(0.633975 + 1.09808i) q^{46} +1.26795 q^{47} -0.732051 q^{48} +(1.50000 + 2.59808i) q^{49} +(1.73205 + 1.00000i) q^{50} +3.12436i q^{51} +(-3.00000 + 1.73205i) q^{52} +(-4.73205 - 8.19615i) q^{53} +(-3.46410 + 2.00000i) q^{54} +(-1.90192 - 1.09808i) q^{55} +(1.73205 + 1.00000i) q^{56} +(-3.00000 + 1.73205i) q^{57} +(-4.33013 - 7.50000i) q^{58} +(-8.19615 + 4.73205i) q^{59} -1.26795i q^{60} +(1.50000 + 0.866025i) q^{61} +(-2.36603 - 4.09808i) q^{62} +4.92820 q^{63} -1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} -0.928203i q^{66} +(-0.0980762 + 0.169873i) q^{67} +4.26795i q^{68} +(-0.803848 - 0.464102i) q^{69} +(-1.73205 + 3.00000i) q^{70} +(1.73205 - 3.00000i) q^{71} +(-2.13397 + 1.23205i) q^{72} +4.00000 q^{73} +(-6.00000 - 1.00000i) q^{74} -1.46410 q^{75} +(-4.09808 + 2.36603i) q^{76} +(-1.26795 + 2.19615i) q^{77} +(1.26795 - 2.19615i) q^{78} +(14.4904 + 8.36603i) q^{79} -1.73205i q^{80} +(-2.23205 + 3.86603i) q^{81} +3.92820i q^{82} +(-5.83013 - 10.0981i) q^{83} -1.46410 q^{84} -7.39230 q^{85} +(6.46410 + 11.1962i) q^{86} +(5.49038 + 3.16987i) q^{87} -1.26795i q^{88} +(14.8923 - 8.59808i) q^{89} +(-2.13397 - 3.69615i) q^{90} +(-6.00000 + 3.46410i) q^{91} +(-1.09808 - 0.633975i) q^{92} +(3.00000 + 1.73205i) q^{93} +(-1.09808 + 0.633975i) q^{94} +(-4.09808 - 7.09808i) q^{95} +(0.633975 - 0.366025i) q^{96} -4.26795i q^{97} +(-2.59808 - 1.50000i) q^{98} +(-1.56218 - 2.70577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{5} + 4 q^{7} - 2 q^{9} - 12 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 12 q^{18} - 6 q^{19} + 6 q^{20} + 4 q^{21} - 6 q^{22} + 6 q^{24} - 4 q^{25} + 16 q^{27} - 4 q^{28} - 6 q^{30} + 12 q^{33} + 12 q^{34} + 12 q^{35} - 4 q^{36} - 2 q^{37} + 12 q^{38} + 12 q^{39} - 6 q^{41} + 12 q^{42} - 6 q^{44} + 6 q^{46} + 12 q^{47} + 4 q^{48} + 6 q^{49} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 12 q^{57} - 12 q^{59} + 6 q^{61} - 6 q^{62} - 8 q^{63} - 4 q^{64} - 12 q^{65} + 10 q^{67} - 24 q^{69} - 12 q^{72} + 16 q^{73} - 24 q^{74} + 8 q^{75} - 6 q^{76} - 12 q^{77} + 12 q^{78} + 6 q^{79} - 2 q^{81} - 6 q^{83} + 8 q^{84} + 12 q^{85} + 12 q^{86} - 30 q^{87} + 18 q^{89} - 12 q^{90} - 24 q^{91} + 6 q^{92} + 12 q^{93} + 6 q^{94} - 6 q^{95} + 6 q^{96} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.366025 0.633975i 0.211325 0.366025i −0.740805 0.671721i \(-0.765556\pi\)
0.952129 + 0.305695i \(0.0988889\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 0.732051i 0.298858i
\(7\) 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i \(-0.709957\pi\)
0.990766 + 0.135583i \(0.0432908\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.23205 + 2.13397i 0.410684 + 0.711325i
\(10\) −1.73205 −0.547723
\(11\) −1.26795 −0.382301 −0.191151 0.981561i \(-0.561222\pi\)
−0.191151 + 0.981561i \(0.561222\pi\)
\(12\) −0.366025 0.633975i −0.105662 0.183013i
\(13\) −3.00000 1.73205i −0.832050 0.480384i 0.0225039 0.999747i \(-0.492836\pi\)
−0.854554 + 0.519362i \(0.826170\pi\)
\(14\) 2.00000i 0.534522i
\(15\) 1.09808 0.633975i 0.283522 0.163692i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.69615 + 2.13397i −0.896449 + 0.517565i −0.876046 0.482227i \(-0.839828\pi\)
−0.0204023 + 0.999792i \(0.506495\pi\)
\(18\) −2.13397 1.23205i −0.502983 0.290397i
\(19\) −4.09808 2.36603i −0.940163 0.542803i −0.0501517 0.998742i \(-0.515970\pi\)
−0.890011 + 0.455938i \(0.849304\pi\)
\(20\) 1.50000 0.866025i 0.335410 0.193649i
\(21\) −0.732051 1.26795i −0.159747 0.276689i
\(22\) 1.09808 0.633975i 0.234111 0.135164i
\(23\) 1.26795i 0.264386i −0.991224 0.132193i \(-0.957798\pi\)
0.991224 0.132193i \(-0.0422018\pi\)
\(24\) 0.633975 + 0.366025i 0.129410 + 0.0747146i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 3.46410 0.679366
\(27\) 4.00000 0.769800
\(28\) −1.00000 1.73205i −0.188982 0.327327i
\(29\) 8.66025i 1.60817i 0.594515 + 0.804084i \(0.297344\pi\)
−0.594515 + 0.804084i \(0.702656\pi\)
\(30\) −0.633975 + 1.09808i −0.115747 + 0.200480i
\(31\) 4.73205i 0.849901i 0.905216 + 0.424951i \(0.139709\pi\)
−0.905216 + 0.424951i \(0.860291\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −0.464102 + 0.803848i −0.0807897 + 0.139932i
\(34\) 2.13397 3.69615i 0.365974 0.633885i
\(35\) 3.00000 1.73205i 0.507093 0.292770i
\(36\) 2.46410 0.410684
\(37\) 4.69615 + 3.86603i 0.772043 + 0.635571i
\(38\) 4.73205 0.767640
\(39\) −2.19615 + 1.26795i −0.351666 + 0.203034i
\(40\) −0.866025 + 1.50000i −0.136931 + 0.237171i
\(41\) 1.96410 3.40192i 0.306741 0.531291i −0.670906 0.741542i \(-0.734095\pi\)
0.977647 + 0.210251i \(0.0674281\pi\)
\(42\) 1.26795 + 0.732051i 0.195649 + 0.112958i
\(43\) 12.9282i 1.97153i −0.168122 0.985766i \(-0.553770\pi\)
0.168122 0.985766i \(-0.446230\pi\)
\(44\) −0.633975 + 1.09808i −0.0955753 + 0.165541i
\(45\) 4.26795i 0.636228i
\(46\) 0.633975 + 1.09808i 0.0934745 + 0.161903i
\(47\) 1.26795 0.184949 0.0924747 0.995715i \(-0.470522\pi\)
0.0924747 + 0.995715i \(0.470522\pi\)
\(48\) −0.732051 −0.105662
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 1.73205 + 1.00000i 0.244949 + 0.141421i
\(51\) 3.12436i 0.437497i
\(52\) −3.00000 + 1.73205i −0.416025 + 0.240192i
\(53\) −4.73205 8.19615i −0.649997 1.12583i −0.983123 0.182946i \(-0.941437\pi\)
0.333126 0.942882i \(-0.391897\pi\)
\(54\) −3.46410 + 2.00000i −0.471405 + 0.272166i
\(55\) −1.90192 1.09808i −0.256455 0.148065i
\(56\) 1.73205 + 1.00000i 0.231455 + 0.133631i
\(57\) −3.00000 + 1.73205i −0.397360 + 0.229416i
\(58\) −4.33013 7.50000i −0.568574 0.984798i
\(59\) −8.19615 + 4.73205i −1.06705 + 0.616061i −0.927373 0.374137i \(-0.877939\pi\)
−0.139675 + 0.990197i \(0.544606\pi\)
\(60\) 1.26795i 0.163692i
\(61\) 1.50000 + 0.866025i 0.192055 + 0.110883i 0.592944 0.805243i \(-0.297965\pi\)
−0.400889 + 0.916127i \(0.631299\pi\)
\(62\) −2.36603 4.09808i −0.300486 0.520456i
\(63\) 4.92820 0.620895
\(64\) −1.00000 −0.125000
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0.928203i 0.114254i
\(67\) −0.0980762 + 0.169873i −0.0119819 + 0.0207533i −0.871954 0.489587i \(-0.837147\pi\)
0.859972 + 0.510341i \(0.170481\pi\)
\(68\) 4.26795i 0.517565i
\(69\) −0.803848 0.464102i −0.0967719 0.0558713i
\(70\) −1.73205 + 3.00000i −0.207020 + 0.358569i
\(71\) 1.73205 3.00000i 0.205557 0.356034i −0.744753 0.667340i \(-0.767433\pi\)
0.950310 + 0.311305i \(0.100766\pi\)
\(72\) −2.13397 + 1.23205i −0.251491 + 0.145199i
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −6.00000 1.00000i −0.697486 0.116248i
\(75\) −1.46410 −0.169060
\(76\) −4.09808 + 2.36603i −0.470082 + 0.271402i
\(77\) −1.26795 + 2.19615i −0.144496 + 0.250275i
\(78\) 1.26795 2.19615i 0.143567 0.248665i
\(79\) 14.4904 + 8.36603i 1.63030 + 0.941251i 0.984001 + 0.178163i \(0.0570155\pi\)
0.646294 + 0.763088i \(0.276318\pi\)
\(80\) 1.73205i 0.193649i
\(81\) −2.23205 + 3.86603i −0.248006 + 0.429558i
\(82\) 3.92820i 0.433797i
\(83\) −5.83013 10.0981i −0.639940 1.10841i −0.985446 0.169991i \(-0.945626\pi\)
0.345506 0.938417i \(-0.387707\pi\)
\(84\) −1.46410 −0.159747
\(85\) −7.39230 −0.801808
\(86\) 6.46410 + 11.1962i 0.697042 + 1.20731i
\(87\) 5.49038 + 3.16987i 0.588631 + 0.339846i
\(88\) 1.26795i 0.135164i
\(89\) 14.8923 8.59808i 1.57858 0.911394i 0.583523 0.812096i \(-0.301674\pi\)
0.995058 0.0992979i \(-0.0316597\pi\)
\(90\) −2.13397 3.69615i −0.224941 0.389609i
\(91\) −6.00000 + 3.46410i −0.628971 + 0.363137i
\(92\) −1.09808 0.633975i −0.114482 0.0660964i
\(93\) 3.00000 + 1.73205i 0.311086 + 0.179605i
\(94\) −1.09808 + 0.633975i −0.113258 + 0.0653895i
\(95\) −4.09808 7.09808i −0.420454 0.728247i
\(96\) 0.633975 0.366025i 0.0647048 0.0373573i
\(97\) 4.26795i 0.433345i −0.976244 0.216672i \(-0.930480\pi\)
0.976244 0.216672i \(-0.0695203\pi\)
\(98\) −2.59808 1.50000i −0.262445 0.151523i
\(99\) −1.56218 2.70577i −0.157005 0.271940i
\(100\) −2.00000 −0.200000
\(101\) 5.53590 0.550842 0.275421 0.961324i \(-0.411183\pi\)
0.275421 + 0.961324i \(0.411183\pi\)
\(102\) −1.56218 2.70577i −0.154679 0.267911i
\(103\) 15.4641i 1.52372i 0.647740 + 0.761862i \(0.275714\pi\)
−0.647740 + 0.761862i \(0.724286\pi\)
\(104\) 1.73205 3.00000i 0.169842 0.294174i
\(105\) 2.53590i 0.247478i
\(106\) 8.19615 + 4.73205i 0.796081 + 0.459617i
\(107\) −5.19615 + 9.00000i −0.502331 + 0.870063i 0.497665 + 0.867369i \(0.334191\pi\)
−0.999996 + 0.00269372i \(0.999143\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) 12.6962 7.33013i 1.21607 0.702099i 0.251996 0.967728i \(-0.418913\pi\)
0.964075 + 0.265630i \(0.0855798\pi\)
\(110\) 2.19615 0.209395
\(111\) 4.16987 1.56218i 0.395787 0.148275i
\(112\) −2.00000 −0.188982
\(113\) −3.00000 + 1.73205i −0.282216 + 0.162938i −0.634426 0.772983i \(-0.718764\pi\)
0.352210 + 0.935921i \(0.385430\pi\)
\(114\) 1.73205 3.00000i 0.162221 0.280976i
\(115\) 1.09808 1.90192i 0.102396 0.177355i
\(116\) 7.50000 + 4.33013i 0.696358 + 0.402042i
\(117\) 8.53590i 0.789144i
\(118\) 4.73205 8.19615i 0.435621 0.754517i
\(119\) 8.53590i 0.782485i
\(120\) 0.633975 + 1.09808i 0.0578737 + 0.100240i
\(121\) −9.39230 −0.853846
\(122\) −1.73205 −0.156813
\(123\) −1.43782 2.49038i −0.129644 0.224550i
\(124\) 4.09808 + 2.36603i 0.368018 + 0.212475i
\(125\) 12.1244i 1.08444i
\(126\) −4.26795 + 2.46410i −0.380219 + 0.219520i
\(127\) 9.09808 + 15.7583i 0.807324 + 1.39833i 0.914711 + 0.404108i \(0.132418\pi\)
−0.107387 + 0.994217i \(0.534249\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −8.19615 4.73205i −0.721631 0.416634i
\(130\) 5.19615 + 3.00000i 0.455733 + 0.263117i
\(131\) −17.4904 + 10.0981i −1.52814 + 0.882273i −0.528702 + 0.848808i \(0.677321\pi\)
−0.999440 + 0.0334654i \(0.989346\pi\)
\(132\) 0.464102 + 0.803848i 0.0403949 + 0.0699660i
\(133\) −8.19615 + 4.73205i −0.710697 + 0.410321i
\(134\) 0.196152i 0.0169450i
\(135\) 6.00000 + 3.46410i 0.516398 + 0.298142i
\(136\) −2.13397 3.69615i −0.182987 0.316942i
\(137\) 19.3923 1.65680 0.828398 0.560140i \(-0.189253\pi\)
0.828398 + 0.560140i \(0.189253\pi\)
\(138\) 0.928203 0.0790139
\(139\) −5.29423 9.16987i −0.449051 0.777778i 0.549274 0.835642i \(-0.314904\pi\)
−0.998324 + 0.0578639i \(0.981571\pi\)
\(140\) 3.46410i 0.292770i
\(141\) 0.464102 0.803848i 0.0390844 0.0676962i
\(142\) 3.46410i 0.290701i
\(143\) 3.80385 + 2.19615i 0.318094 + 0.183651i
\(144\) 1.23205 2.13397i 0.102671 0.177831i
\(145\) −7.50000 + 12.9904i −0.622841 + 1.07879i
\(146\) −3.46410 + 2.00000i −0.286691 + 0.165521i
\(147\) 2.19615 0.181136
\(148\) 5.69615 2.13397i 0.468221 0.175412i
\(149\) −2.07180 −0.169728 −0.0848641 0.996393i \(-0.527046\pi\)
−0.0848641 + 0.996393i \(0.527046\pi\)
\(150\) 1.26795 0.732051i 0.103528 0.0597717i
\(151\) 3.09808 5.36603i 0.252118 0.436681i −0.711991 0.702189i \(-0.752206\pi\)
0.964109 + 0.265508i \(0.0855396\pi\)
\(152\) 2.36603 4.09808i 0.191910 0.332398i
\(153\) −9.10770 5.25833i −0.736314 0.425111i
\(154\) 2.53590i 0.204349i
\(155\) −4.09808 + 7.09808i −0.329165 + 0.570131i
\(156\) 2.53590i 0.203034i
\(157\) −0.500000 0.866025i −0.0399043 0.0691164i 0.845383 0.534160i \(-0.179372\pi\)
−0.885288 + 0.465044i \(0.846039\pi\)
\(158\) −16.7321 −1.33113
\(159\) −6.92820 −0.549442
\(160\) 0.866025 + 1.50000i 0.0684653 + 0.118585i
\(161\) −2.19615 1.26795i −0.173081 0.0999284i
\(162\) 4.46410i 0.350733i
\(163\) 0.803848 0.464102i 0.0629622 0.0363512i −0.468188 0.883629i \(-0.655093\pi\)
0.531151 + 0.847277i \(0.321760\pi\)
\(164\) −1.96410 3.40192i −0.153371 0.265646i
\(165\) −1.39230 + 0.803848i −0.108391 + 0.0625794i
\(166\) 10.0981 + 5.83013i 0.783763 + 0.452506i
\(167\) −12.0000 6.92820i −0.928588 0.536120i −0.0422232 0.999108i \(-0.513444\pi\)
−0.886365 + 0.462988i \(0.846777\pi\)
\(168\) 1.26795 0.732051i 0.0978244 0.0564789i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 6.40192 3.69615i 0.491005 0.283482i
\(171\) 11.6603i 0.891682i
\(172\) −11.1962 6.46410i −0.853699 0.492883i
\(173\) −6.23205 10.7942i −0.473814 0.820670i 0.525737 0.850647i \(-0.323790\pi\)
−0.999551 + 0.0299775i \(0.990456\pi\)
\(174\) −6.33975 −0.480615
\(175\) −4.00000 −0.302372
\(176\) 0.633975 + 1.09808i 0.0477876 + 0.0827706i
\(177\) 6.92820i 0.520756i
\(178\) −8.59808 + 14.8923i −0.644453 + 1.11623i
\(179\) 2.53590i 0.189542i 0.995499 + 0.0947710i \(0.0302119\pi\)
−0.995499 + 0.0947710i \(0.969788\pi\)
\(180\) 3.69615 + 2.13397i 0.275495 + 0.159057i
\(181\) −5.69615 + 9.86603i −0.423392 + 0.733336i −0.996269 0.0863054i \(-0.972494\pi\)
0.572877 + 0.819641i \(0.305827\pi\)
\(182\) 3.46410 6.00000i 0.256776 0.444750i
\(183\) 1.09808 0.633975i 0.0811721 0.0468648i
\(184\) 1.26795 0.0934745
\(185\) 3.69615 + 9.86603i 0.271747 + 0.725365i
\(186\) −3.46410 −0.254000
\(187\) 4.68653 2.70577i 0.342713 0.197866i
\(188\) 0.633975 1.09808i 0.0462373 0.0800854i
\(189\) 4.00000 6.92820i 0.290957 0.503953i
\(190\) 7.09808 + 4.09808i 0.514949 + 0.297306i
\(191\) 8.19615i 0.593053i 0.955025 + 0.296526i \(0.0958283\pi\)
−0.955025 + 0.296526i \(0.904172\pi\)
\(192\) −0.366025 + 0.633975i −0.0264156 + 0.0457532i
\(193\) 0.803848i 0.0578622i −0.999581 0.0289311i \(-0.990790\pi\)
0.999581 0.0289311i \(-0.00921034\pi\)
\(194\) 2.13397 + 3.69615i 0.153210 + 0.265368i
\(195\) −4.39230 −0.314539
\(196\) 3.00000 0.214286
\(197\) 0.232051 + 0.401924i 0.0165329 + 0.0286359i 0.874174 0.485614i \(-0.161404\pi\)
−0.857641 + 0.514250i \(0.828070\pi\)
\(198\) 2.70577 + 1.56218i 0.192291 + 0.111019i
\(199\) 10.3923i 0.736691i −0.929689 0.368345i \(-0.879924\pi\)
0.929689 0.368345i \(-0.120076\pi\)
\(200\) 1.73205 1.00000i 0.122474 0.0707107i
\(201\) 0.0717968 + 0.124356i 0.00506415 + 0.00877137i
\(202\) −4.79423 + 2.76795i −0.337321 + 0.194752i
\(203\) 15.0000 + 8.66025i 1.05279 + 0.607831i
\(204\) 2.70577 + 1.56218i 0.189442 + 0.109374i
\(205\) 5.89230 3.40192i 0.411536 0.237601i
\(206\) −7.73205 13.3923i −0.538718 0.933086i
\(207\) 2.70577 1.56218i 0.188064 0.108579i
\(208\) 3.46410i 0.240192i
\(209\) 5.19615 + 3.00000i 0.359425 + 0.207514i
\(210\) 1.26795 + 2.19615i 0.0874968 + 0.151549i
\(211\) 18.3923 1.26618 0.633089 0.774079i \(-0.281787\pi\)
0.633089 + 0.774079i \(0.281787\pi\)
\(212\) −9.46410 −0.649997
\(213\) −1.26795 2.19615i −0.0868784 0.150478i
\(214\) 10.3923i 0.710403i
\(215\) 11.1962 19.3923i 0.763571 1.32254i
\(216\) 4.00000i 0.272166i
\(217\) 8.19615 + 4.73205i 0.556391 + 0.321233i
\(218\) −7.33013 + 12.6962i −0.496459 + 0.859892i
\(219\) 1.46410 2.53590i 0.0989348 0.171360i
\(220\) −1.90192 + 1.09808i −0.128228 + 0.0740323i
\(221\) 14.7846 0.994520
\(222\) −2.83013 + 3.43782i −0.189946 + 0.230732i
\(223\) 5.80385 0.388654 0.194327 0.980937i \(-0.437748\pi\)
0.194327 + 0.980937i \(0.437748\pi\)
\(224\) 1.73205 1.00000i 0.115728 0.0668153i
\(225\) 2.46410 4.26795i 0.164273 0.284530i
\(226\) 1.73205 3.00000i 0.115214 0.199557i
\(227\) −4.09808 2.36603i −0.271999 0.157039i 0.357797 0.933799i \(-0.383528\pi\)
−0.629796 + 0.776761i \(0.716861\pi\)
\(228\) 3.46410i 0.229416i
\(229\) −3.30385 + 5.72243i −0.218324 + 0.378149i −0.954296 0.298864i \(-0.903392\pi\)
0.735971 + 0.677013i \(0.236726\pi\)
\(230\) 2.19615i 0.144810i
\(231\) 0.928203 + 1.60770i 0.0610713 + 0.105779i
\(232\) −8.66025 −0.568574
\(233\) 15.0000 0.982683 0.491341 0.870967i \(-0.336507\pi\)
0.491341 + 0.870967i \(0.336507\pi\)
\(234\) 4.26795 + 7.39230i 0.279005 + 0.483250i
\(235\) 1.90192 + 1.09808i 0.124068 + 0.0716306i
\(236\) 9.46410i 0.616061i
\(237\) 10.6077 6.12436i 0.689044 0.397820i
\(238\) −4.26795 7.39230i −0.276650 0.479172i
\(239\) −15.0000 + 8.66025i −0.970269 + 0.560185i −0.899318 0.437295i \(-0.855937\pi\)
−0.0709510 + 0.997480i \(0.522603\pi\)
\(240\) −1.09808 0.633975i −0.0708805 0.0409229i
\(241\) −7.39230 4.26795i −0.476180 0.274923i 0.242643 0.970116i \(-0.421986\pi\)
−0.718823 + 0.695193i \(0.755319\pi\)
\(242\) 8.13397 4.69615i 0.522872 0.301880i
\(243\) 7.63397 + 13.2224i 0.489720 + 0.848219i
\(244\) 1.50000 0.866025i 0.0960277 0.0554416i
\(245\) 5.19615i 0.331970i
\(246\) 2.49038 + 1.43782i 0.158781 + 0.0916722i
\(247\) 8.19615 + 14.1962i 0.521509 + 0.903280i
\(248\) −4.73205 −0.300486
\(249\) −8.53590 −0.540941
\(250\) 6.06218 + 10.5000i 0.383406 + 0.664078i
\(251\) 17.3205i 1.09326i −0.837374 0.546630i \(-0.815910\pi\)
0.837374 0.546630i \(-0.184090\pi\)
\(252\) 2.46410 4.26795i 0.155224 0.268856i
\(253\) 1.60770i 0.101075i
\(254\) −15.7583 9.09808i −0.988766 0.570864i
\(255\) −2.70577 + 4.68653i −0.169442 + 0.293482i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −14.8923 + 8.59808i −0.928956 + 0.536333i −0.886481 0.462764i \(-0.846858\pi\)
−0.0424751 + 0.999098i \(0.513524\pi\)
\(258\) 9.46410 0.589209
\(259\) 11.3923 4.26795i 0.707883 0.265197i
\(260\) −6.00000 −0.372104
\(261\) −18.4808 + 10.6699i −1.14393 + 0.660449i
\(262\) 10.0981 17.4904i 0.623861 1.08056i
\(263\) −7.26795 + 12.5885i −0.448161 + 0.776238i −0.998266 0.0588577i \(-0.981254\pi\)
0.550105 + 0.835095i \(0.314588\pi\)
\(264\) −0.803848 0.464102i −0.0494734 0.0285635i
\(265\) 16.3923i 1.00697i
\(266\) 4.73205 8.19615i 0.290141 0.502538i
\(267\) 12.5885i 0.770401i
\(268\) 0.0980762 + 0.169873i 0.00599096 + 0.0103766i
\(269\) 16.3923 0.999456 0.499728 0.866182i \(-0.333433\pi\)
0.499728 + 0.866182i \(0.333433\pi\)
\(270\) −6.92820 −0.421637
\(271\) −14.2942 24.7583i −0.868313 1.50396i −0.863720 0.503972i \(-0.831871\pi\)
−0.00459256 0.999989i \(-0.501462\pi\)
\(272\) 3.69615 + 2.13397i 0.224112 + 0.129391i
\(273\) 5.07180i 0.306959i
\(274\) −16.7942 + 9.69615i −1.01458 + 0.585766i
\(275\) 1.26795 + 2.19615i 0.0764602 + 0.132433i
\(276\) −0.803848 + 0.464102i −0.0483859 + 0.0279356i
\(277\) −0.696152 0.401924i −0.0418277 0.0241493i 0.478940 0.877847i \(-0.341021\pi\)
−0.520768 + 0.853698i \(0.674354\pi\)
\(278\) 9.16987 + 5.29423i 0.549972 + 0.317527i
\(279\) −10.0981 + 5.83013i −0.604556 + 0.349041i
\(280\) 1.73205 + 3.00000i 0.103510 + 0.179284i
\(281\) −3.10770 + 1.79423i −0.185390 + 0.107035i −0.589822 0.807533i \(-0.700802\pi\)
0.404433 + 0.914568i \(0.367469\pi\)
\(282\) 0.928203i 0.0552737i
\(283\) −17.1962 9.92820i −1.02221 0.590170i −0.107463 0.994209i \(-0.534273\pi\)
−0.914742 + 0.404039i \(0.867606\pi\)
\(284\) −1.73205 3.00000i −0.102778 0.178017i
\(285\) −6.00000 −0.355409
\(286\) −4.39230 −0.259722
\(287\) −3.92820 6.80385i −0.231875 0.401618i
\(288\) 2.46410i 0.145199i
\(289\) 0.607695 1.05256i 0.0357468 0.0619152i
\(290\) 15.0000i 0.880830i
\(291\) −2.70577 1.56218i −0.158615 0.0915765i
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) −9.69615 + 16.7942i −0.566455 + 0.981129i 0.430457 + 0.902611i \(0.358352\pi\)
−0.996913 + 0.0785184i \(0.974981\pi\)
\(294\) −1.90192 + 1.09808i −0.110922 + 0.0640411i
\(295\) −16.3923 −0.954397
\(296\) −3.86603 + 4.69615i −0.224708 + 0.272958i
\(297\) −5.07180 −0.294295
\(298\) 1.79423 1.03590i 0.103937 0.0600080i
\(299\) −2.19615 + 3.80385i −0.127007 + 0.219982i
\(300\) −0.732051 + 1.26795i −0.0422650 + 0.0732051i
\(301\) −22.3923 12.9282i −1.29067 0.745169i
\(302\) 6.19615i 0.356549i
\(303\) 2.02628 3.50962i 0.116407 0.201622i
\(304\) 4.73205i 0.271402i
\(305\) 1.50000 + 2.59808i 0.0858898 + 0.148765i
\(306\) 10.5167 0.601197
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) 1.26795 + 2.19615i 0.0722481 + 0.125137i
\(309\) 9.80385 + 5.66025i 0.557721 + 0.322001i
\(310\) 8.19615i 0.465510i
\(311\) 15.5885 9.00000i 0.883940 0.510343i 0.0119847 0.999928i \(-0.496185\pi\)
0.871956 + 0.489585i \(0.162852\pi\)
\(312\) −1.26795 2.19615i −0.0717835 0.124333i
\(313\) 0.107695 0.0621778i 0.00608729 0.00351450i −0.496953 0.867777i \(-0.665548\pi\)
0.503041 + 0.864263i \(0.332215\pi\)
\(314\) 0.866025 + 0.500000i 0.0488726 + 0.0282166i
\(315\) 7.39230 + 4.26795i 0.416509 + 0.240472i
\(316\) 14.4904 8.36603i 0.815148 0.470626i
\(317\) 6.69615 + 11.5981i 0.376093 + 0.651413i 0.990490 0.137584i \(-0.0439338\pi\)
−0.614397 + 0.788997i \(0.710601\pi\)
\(318\) 6.00000 3.46410i 0.336463 0.194257i
\(319\) 10.9808i 0.614805i
\(320\) −1.50000 0.866025i −0.0838525 0.0484123i
\(321\) 3.80385 + 6.58846i 0.212310 + 0.367732i
\(322\) 2.53590 0.141320
\(323\) 20.1962 1.12374
\(324\) 2.23205 + 3.86603i 0.124003 + 0.214779i
\(325\) 6.92820i 0.384308i
\(326\) −0.464102 + 0.803848i −0.0257042 + 0.0445210i
\(327\) 10.7321i 0.593484i
\(328\) 3.40192 + 1.96410i 0.187840 + 0.108449i
\(329\) 1.26795 2.19615i 0.0699043 0.121078i
\(330\) 0.803848 1.39230i 0.0442504 0.0766439i
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) −11.6603 −0.639940
\(333\) −2.46410 + 14.7846i −0.135032 + 0.810192i
\(334\) 13.8564 0.758189
\(335\) −0.294229 + 0.169873i −0.0160754 + 0.00928115i
\(336\) −0.732051 + 1.26795i −0.0399366 + 0.0691723i
\(337\) −15.0885 + 26.1340i −0.821921 + 1.42361i 0.0823295 + 0.996605i \(0.473764\pi\)
−0.904250 + 0.427003i \(0.859569\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) 2.53590i 0.137731i
\(340\) −3.69615 + 6.40192i −0.200452 + 0.347193i
\(341\) 6.00000i 0.324918i
\(342\) 5.83013 + 10.0981i 0.315257 + 0.546041i
\(343\) 20.0000 1.07990
\(344\) 12.9282 0.697042
\(345\) −0.803848 1.39230i −0.0432777 0.0749592i
\(346\) 10.7942 + 6.23205i 0.580301 + 0.335037i
\(347\) 15.1244i 0.811918i 0.913891 + 0.405959i \(0.133062\pi\)
−0.913891 + 0.405959i \(0.866938\pi\)
\(348\) 5.49038 3.16987i 0.294315 0.169923i
\(349\) 4.69615 + 8.13397i 0.251379 + 0.435402i 0.963906 0.266243i \(-0.0857825\pi\)
−0.712527 + 0.701645i \(0.752449\pi\)
\(350\) 3.46410 2.00000i 0.185164 0.106904i
\(351\) −12.0000 6.92820i −0.640513 0.369800i
\(352\) −1.09808 0.633975i −0.0585277 0.0337910i
\(353\) 14.0885 8.13397i 0.749853 0.432928i −0.0757878 0.997124i \(-0.524147\pi\)
0.825641 + 0.564196i \(0.190814\pi\)
\(354\) −3.46410 6.00000i −0.184115 0.318896i
\(355\) 5.19615 3.00000i 0.275783 0.159223i
\(356\) 17.1962i 0.911394i
\(357\) 5.41154 + 3.12436i 0.286409 + 0.165358i
\(358\) −1.26795 2.19615i −0.0670132 0.116070i
\(359\) 0.679492 0.0358622 0.0179311 0.999839i \(-0.494292\pi\)
0.0179311 + 0.999839i \(0.494292\pi\)
\(360\) −4.26795 −0.224941
\(361\) 1.69615 + 2.93782i 0.0892712 + 0.154622i
\(362\) 11.3923i 0.598766i
\(363\) −3.43782 + 5.95448i −0.180439 + 0.312529i
\(364\) 6.92820i 0.363137i
\(365\) 6.00000 + 3.46410i 0.314054 + 0.181319i
\(366\) −0.633975 + 1.09808i −0.0331384 + 0.0573974i
\(367\) 4.19615 7.26795i 0.219037 0.379384i −0.735477 0.677550i \(-0.763042\pi\)
0.954514 + 0.298166i \(0.0963750\pi\)
\(368\) −1.09808 + 0.633975i −0.0572412 + 0.0330482i
\(369\) 9.67949 0.503894
\(370\) −8.13397 6.69615i −0.422865 0.348116i
\(371\) −18.9282 −0.982703
\(372\) 3.00000 1.73205i 0.155543 0.0898027i
\(373\) −3.50000 + 6.06218i −0.181223 + 0.313888i −0.942297 0.334777i \(-0.891339\pi\)
0.761074 + 0.648665i \(0.224672\pi\)
\(374\) −2.70577 + 4.68653i −0.139912 + 0.242335i
\(375\) −7.68653 4.43782i −0.396931 0.229168i
\(376\) 1.26795i 0.0653895i
\(377\) 15.0000 25.9808i 0.772539 1.33808i
\(378\) 8.00000i 0.411476i
\(379\) −3.39230 5.87564i −0.174251 0.301812i 0.765651 0.643256i \(-0.222417\pi\)
−0.939902 + 0.341445i \(0.889084\pi\)
\(380\) −8.19615 −0.420454
\(381\) 13.3205 0.682430
\(382\) −4.09808 7.09808i −0.209676 0.363169i
\(383\) −3.00000 1.73205i −0.153293 0.0885037i 0.421392 0.906879i \(-0.361542\pi\)
−0.574684 + 0.818375i \(0.694875\pi\)
\(384\) 0.732051i 0.0373573i
\(385\) −3.80385 + 2.19615i −0.193862 + 0.111926i
\(386\) 0.401924 + 0.696152i 0.0204574 + 0.0354332i
\(387\) 27.5885 15.9282i 1.40240 0.809676i
\(388\) −3.69615 2.13397i −0.187644 0.108336i
\(389\) −22.5000 12.9904i −1.14080 0.658638i −0.194168 0.980968i \(-0.562201\pi\)
−0.946627 + 0.322330i \(0.895534\pi\)
\(390\) 3.80385 2.19615i 0.192615 0.111207i
\(391\) 2.70577 + 4.68653i 0.136837 + 0.237008i
\(392\) −2.59808 + 1.50000i −0.131223 + 0.0757614i
\(393\) 14.7846i 0.745785i
\(394\) −0.401924 0.232051i −0.0202486 0.0116906i
\(395\) 14.4904 + 25.0981i 0.729090 + 1.26282i
\(396\) −3.12436 −0.157005
\(397\) −23.0000 −1.15434 −0.577168 0.816625i \(-0.695842\pi\)
−0.577168 + 0.816625i \(0.695842\pi\)
\(398\) 5.19615 + 9.00000i 0.260460 + 0.451129i
\(399\) 6.92820i 0.346844i
\(400\) −1.00000 + 1.73205i −0.0500000 + 0.0866025i
\(401\) 10.3923i 0.518967i −0.965748 0.259483i \(-0.916448\pi\)
0.965748 0.259483i \(-0.0835523\pi\)
\(402\) −0.124356 0.0717968i −0.00620230 0.00358090i
\(403\) 8.19615 14.1962i 0.408279 0.707161i
\(404\) 2.76795 4.79423i 0.137711 0.238522i
\(405\) −6.69615 + 3.86603i −0.332734 + 0.192104i
\(406\) −17.3205 −0.859602
\(407\) −5.95448 4.90192i −0.295153 0.242979i
\(408\) −3.12436 −0.154679
\(409\) 29.8923 17.2583i 1.47808 0.853370i 0.478386 0.878149i \(-0.341222\pi\)
0.999693 + 0.0247799i \(0.00788850\pi\)
\(410\) −3.40192 + 5.89230i −0.168009 + 0.291000i
\(411\) 7.09808 12.2942i 0.350122 0.606430i
\(412\) 13.3923 + 7.73205i 0.659792 + 0.380931i
\(413\) 18.9282i 0.931396i
\(414\) −1.56218 + 2.70577i −0.0767769 + 0.132981i
\(415\) 20.1962i 0.991390i
\(416\) −1.73205 3.00000i −0.0849208 0.147087i
\(417\) −7.75129 −0.379582
\(418\) −6.00000 −0.293470
\(419\) 15.9282 + 27.5885i 0.778144 + 1.34778i 0.933011 + 0.359849i \(0.117172\pi\)
−0.154867 + 0.987935i \(0.549495\pi\)
\(420\) −2.19615 1.26795i −0.107161 0.0618696i
\(421\) 12.1244i 0.590905i −0.955357 0.295452i \(-0.904530\pi\)
0.955357 0.295452i \(-0.0954704\pi\)
\(422\) −15.9282 + 9.19615i −0.775373 + 0.447662i
\(423\) 1.56218 + 2.70577i 0.0759557 + 0.131559i
\(424\) 8.19615 4.73205i 0.398040 0.229809i
\(425\) 7.39230 + 4.26795i 0.358579 + 0.207026i
\(426\) 2.19615 + 1.26795i 0.106404 + 0.0614323i
\(427\) 3.00000 1.73205i 0.145180 0.0838198i
\(428\) 5.19615 + 9.00000i 0.251166 + 0.435031i
\(429\) 2.78461 1.60770i 0.134442 0.0776203i
\(430\) 22.3923i 1.07985i
\(431\) 0.294229 + 0.169873i 0.0141725 + 0.00818249i 0.507070 0.861905i \(-0.330729\pi\)
−0.492897 + 0.870088i \(0.664062\pi\)
\(432\) −2.00000 3.46410i −0.0962250 0.166667i
\(433\) −25.7846 −1.23913 −0.619565 0.784946i \(-0.712691\pi\)
−0.619565 + 0.784946i \(0.712691\pi\)
\(434\) −9.46410 −0.454291
\(435\) 5.49038 + 9.50962i 0.263244 + 0.455951i
\(436\) 14.6603i 0.702099i
\(437\) −3.00000 + 5.19615i −0.143509 + 0.248566i
\(438\) 2.92820i 0.139915i
\(439\) −26.1962 15.1244i −1.25027 0.721846i −0.279110 0.960259i \(-0.590039\pi\)
−0.971164 + 0.238413i \(0.923373\pi\)
\(440\) 1.09808 1.90192i 0.0523487 0.0906707i
\(441\) −3.69615 + 6.40192i −0.176007 + 0.304854i
\(442\) −12.8038 + 7.39230i −0.609017 + 0.351616i
\(443\) −21.4641 −1.01979 −0.509895 0.860237i \(-0.670316\pi\)
−0.509895 + 0.860237i \(0.670316\pi\)
\(444\) 0.732051 4.39230i 0.0347416 0.208450i
\(445\) 29.7846 1.41193
\(446\) −5.02628 + 2.90192i −0.238001 + 0.137410i
\(447\) −0.758330 + 1.31347i −0.0358678 + 0.0621248i
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) −23.7846 13.7321i −1.12247 0.648056i −0.180436 0.983587i \(-0.557751\pi\)
−0.942029 + 0.335531i \(0.891084\pi\)
\(450\) 4.92820i 0.232318i
\(451\) −2.49038 + 4.31347i −0.117267 + 0.203113i
\(452\) 3.46410i 0.162938i
\(453\) −2.26795 3.92820i −0.106558 0.184563i
\(454\) 4.73205 0.222086
\(455\) −12.0000 −0.562569
\(456\) −1.73205 3.00000i −0.0811107 0.140488i
\(457\) −12.1077 6.99038i −0.566374 0.326996i 0.189326 0.981914i \(-0.439370\pi\)
−0.755700 + 0.654918i \(0.772703\pi\)
\(458\) 6.60770i 0.308757i
\(459\) −14.7846 + 8.53590i −0.690086 + 0.398422i
\(460\) −1.09808 1.90192i −0.0511981 0.0886777i
\(461\) 28.1769 16.2679i 1.31233 0.757674i 0.329848 0.944034i \(-0.393002\pi\)
0.982482 + 0.186360i \(0.0596691\pi\)
\(462\) −1.60770 0.928203i −0.0747967 0.0431839i
\(463\) 25.9808 + 15.0000i 1.20743 + 0.697109i 0.962197 0.272355i \(-0.0878026\pi\)
0.245232 + 0.969465i \(0.421136\pi\)
\(464\) 7.50000 4.33013i 0.348179 0.201021i
\(465\) 3.00000 + 5.19615i 0.139122 + 0.240966i
\(466\) −12.9904 + 7.50000i −0.601768 + 0.347431i
\(467\) 9.46410i 0.437946i 0.975731 + 0.218973i \(0.0702707\pi\)
−0.975731 + 0.218973i \(0.929729\pi\)
\(468\) −7.39230 4.26795i −0.341709 0.197286i
\(469\) 0.196152 + 0.339746i 0.00905748 + 0.0156880i
\(470\) −2.19615 −0.101301
\(471\) −0.732051 −0.0337311
\(472\) −4.73205 8.19615i −0.217810 0.377258i
\(473\) 16.3923i 0.753719i
\(474\) −6.12436 + 10.6077i −0.281301 + 0.487228i
\(475\) 9.46410i 0.434243i
\(476\) 7.39230 + 4.26795i 0.338826 + 0.195621i
\(477\) 11.6603 20.1962i 0.533886 0.924718i
\(478\) 8.66025 15.0000i 0.396111 0.686084i
\(479\) −2.19615 + 1.26795i −0.100345 + 0.0579341i −0.549333 0.835604i \(-0.685118\pi\)
0.448988 + 0.893538i \(0.351785\pi\)
\(480\) 1.26795 0.0578737
\(481\) −7.39230 19.7321i −0.337060 0.899704i
\(482\) 8.53590 0.388800
\(483\) −1.60770 + 0.928203i −0.0731527 + 0.0422347i
\(484\) −4.69615 + 8.13397i −0.213461 + 0.369726i
\(485\) 3.69615 6.40192i 0.167834 0.290696i
\(486\) −13.2224 7.63397i −0.599782 0.346284i
\(487\) 22.0526i 0.999297i 0.866228 + 0.499648i \(0.166537\pi\)
−0.866228 + 0.499648i \(0.833463\pi\)
\(488\) −0.866025 + 1.50000i −0.0392031 + 0.0679018i
\(489\) 0.679492i 0.0307277i
\(490\) −2.59808 4.50000i −0.117369 0.203289i
\(491\) 15.8038 0.713218 0.356609 0.934254i \(-0.383933\pi\)
0.356609 + 0.934254i \(0.383933\pi\)
\(492\) −2.87564 −0.129644
\(493\) −18.4808 32.0096i −0.832332 1.44164i
\(494\) −14.1962 8.19615i −0.638715 0.368762i
\(495\) 5.41154i 0.243231i
\(496\) 4.09808 2.36603i 0.184009 0.106238i
\(497\) −3.46410 6.00000i −0.155386 0.269137i
\(498\) 7.39230 4.26795i 0.331257 0.191251i
\(499\) 8.49038 + 4.90192i 0.380082 + 0.219440i 0.677854 0.735197i \(-0.262910\pi\)
−0.297772 + 0.954637i \(0.596244\pi\)
\(500\) −10.5000 6.06218i −0.469574 0.271109i
\(501\) −8.78461 + 5.07180i −0.392467 + 0.226591i
\(502\) 8.66025 + 15.0000i 0.386526 + 0.669483i
\(503\) 8.49038 4.90192i 0.378567 0.218566i −0.298627 0.954370i \(-0.596529\pi\)
0.677195 + 0.735804i \(0.263195\pi\)
\(504\) 4.92820i 0.219520i
\(505\) 8.30385 + 4.79423i 0.369516 + 0.213340i
\(506\) −0.803848 1.39230i −0.0357354 0.0618955i
\(507\) −0.732051 −0.0325115
\(508\) 18.1962 0.807324
\(509\) −0.232051 0.401924i −0.0102855 0.0178150i 0.860837 0.508881i \(-0.169941\pi\)
−0.871122 + 0.491066i \(0.836607\pi\)
\(510\) 5.41154i 0.239627i
\(511\) 4.00000 6.92820i 0.176950 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) −16.3923 9.46410i −0.723738 0.417850i
\(514\) 8.59808 14.8923i 0.379245 0.656871i
\(515\) −13.3923 + 23.1962i −0.590135 + 1.02214i
\(516\) −8.19615 + 4.73205i −0.360815 + 0.208317i
\(517\) −1.60770 −0.0707064
\(518\) −7.73205 + 9.39230i −0.339727 + 0.412674i
\(519\) −9.12436 −0.400515
\(520\) 5.19615 3.00000i 0.227866 0.131559i
\(521\) −9.46410 + 16.3923i −0.414630 + 0.718160i −0.995390 0.0959151i \(-0.969422\pi\)
0.580760 + 0.814075i \(0.302756\pi\)
\(522\) 10.6699 18.4808i 0.467008 0.808881i
\(523\) 33.2942 + 19.2224i 1.45585 + 0.840538i 0.998804 0.0489020i \(-0.0155722\pi\)
0.457051 + 0.889440i \(0.348906\pi\)
\(524\) 20.1962i 0.882273i
\(525\) −1.46410 + 2.53590i −0.0638986 + 0.110676i
\(526\) 14.5359i 0.633795i
\(527\) −10.0981 17.4904i −0.439879 0.761893i
\(528\) 0.928203 0.0403949
\(529\) 21.3923 0.930100
\(530\) 8.19615 + 14.1962i 0.356018 + 0.616641i
\(531\) −20.1962 11.6603i −0.876438 0.506012i
\(532\) 9.46410i 0.410321i
\(533\) −11.7846 + 6.80385i −0.510448 + 0.294707i
\(534\) 6.29423 + 10.9019i 0.272378 + 0.471772i
\(535\) −15.5885 + 9.00000i −0.673948 + 0.389104i
\(536\) −0.169873 0.0980762i −0.00733740 0.00423625i
\(537\) 1.60770 + 0.928203i 0.0693772 + 0.0400549i
\(538\) −14.1962 + 8.19615i −0.612040 + 0.353361i
\(539\) −1.90192 3.29423i −0.0819217 0.141892i
\(540\) 6.00000 3.46410i 0.258199 0.149071i
\(541\) 19.0526i 0.819133i 0.912280 + 0.409567i \(0.134320\pi\)
−0.912280 + 0.409567i \(0.865680\pi\)
\(542\) 24.7583 + 14.2942i 1.06346 + 0.613990i
\(543\) 4.16987 + 7.22243i 0.178946 + 0.309944i
\(544\) −4.26795 −0.182987
\(545\) 25.3923 1.08769
\(546\) −2.53590 4.39230i −0.108526 0.187973i
\(547\) 24.3397i 1.04069i −0.853955 0.520346i \(-0.825803\pi\)
0.853955 0.520346i \(-0.174197\pi\)
\(548\) 9.69615 16.7942i 0.414199 0.717414i
\(549\) 4.26795i 0.182152i
\(550\) −2.19615 1.26795i −0.0936443 0.0540655i
\(551\) 20.4904 35.4904i 0.872920 1.51194i
\(552\) 0.464102 0.803848i 0.0197535 0.0342140i
\(553\) 28.9808 16.7321i 1.23239 0.711519i
\(554\) 0.803848 0.0341522
\(555\) 7.60770 + 1.26795i 0.322929 + 0.0538214i
\(556\) −10.5885 −0.449051
\(557\) 30.6962 17.7224i 1.30064 0.750924i 0.320124 0.947376i \(-0.396275\pi\)
0.980513 + 0.196452i \(0.0629420\pi\)
\(558\) 5.83013 10.0981i 0.246809 0.427486i
\(559\) −22.3923 + 38.7846i −0.947094 + 1.64041i
\(560\) −3.00000 1.73205i −0.126773 0.0731925i
\(561\) 3.96152i 0.167256i
\(562\) 1.79423 3.10770i 0.0756850 0.131090i
\(563\) 12.5885i 0.530540i −0.964174 0.265270i \(-0.914539\pi\)
0.964174 0.265270i \(-0.0854611\pi\)
\(564\) −0.464102 0.803848i −0.0195422 0.0338481i
\(565\) −6.00000 −0.252422
\(566\) 19.8564 0.834627
\(567\) 4.46410 + 7.73205i 0.187475 + 0.324716i
\(568\) 3.00000 + 1.73205i 0.125877 + 0.0726752i
\(569\) 30.1244i 1.26288i 0.775425 + 0.631439i \(0.217536\pi\)
−0.775425 + 0.631439i \(0.782464\pi\)
\(570\) 5.19615 3.00000i 0.217643 0.125656i
\(571\) 17.6865 + 30.6340i 0.740158 + 1.28199i 0.952423 + 0.304780i \(0.0985828\pi\)
−0.212264 + 0.977212i \(0.568084\pi\)
\(572\) 3.80385 2.19615i 0.159047 0.0918257i
\(573\) 5.19615 + 3.00000i 0.217072 + 0.125327i
\(574\) 6.80385 + 3.92820i 0.283987 + 0.163960i
\(575\) −2.19615 + 1.26795i −0.0915859 + 0.0528771i
\(576\) −1.23205 2.13397i −0.0513355 0.0889156i
\(577\) −11.1962 + 6.46410i −0.466102 + 0.269104i −0.714607 0.699527i \(-0.753394\pi\)
0.248505 + 0.968631i \(0.420061\pi\)
\(578\) 1.21539i 0.0505536i
\(579\) −0.509619 0.294229i −0.0211790 0.0122277i
\(580\) 7.50000 + 12.9904i 0.311421 + 0.539396i
\(581\) −23.3205 −0.967498
\(582\) 3.12436 0.129509
\(583\) 6.00000 + 10.3923i 0.248495 + 0.430405i
\(584\) 4.00000i 0.165521i
\(585\) 7.39230 12.8038i 0.305634 0.529374i
\(586\) 19.3923i 0.801089i
\(587\) −7.68653 4.43782i −0.317257 0.183169i 0.332912 0.942958i \(-0.391969\pi\)
−0.650169 + 0.759789i \(0.725302\pi\)
\(588\) 1.09808 1.90192i 0.0452839 0.0784340i
\(589\) 11.1962 19.3923i 0.461329 0.799046i
\(590\) 14.1962 8.19615i 0.584446 0.337430i
\(591\) 0.339746 0.0139753
\(592\) 1.00000 6.00000i 0.0410997 0.246598i
\(593\) −25.6410 −1.05295 −0.526475 0.850191i \(-0.676487\pi\)
−0.526475 + 0.850191i \(0.676487\pi\)
\(594\) 4.39230 2.53590i 0.180218 0.104049i
\(595\) −7.39230 + 12.8038i −0.303055 + 0.524907i
\(596\) −1.03590 + 1.79423i −0.0424321 + 0.0734945i
\(597\) −6.58846 3.80385i −0.269648 0.155681i
\(598\) 4.39230i 0.179615i
\(599\) −15.1699 + 26.2750i −0.619824 + 1.07357i 0.369693 + 0.929154i \(0.379463\pi\)
−0.989517 + 0.144413i \(0.953871\pi\)
\(600\) 1.46410i 0.0597717i
\(601\) 16.6962 + 28.9186i 0.681050 + 1.17961i 0.974661 + 0.223688i \(0.0718098\pi\)
−0.293610 + 0.955925i \(0.594857\pi\)
\(602\) 25.8564 1.05383
\(603\) −0.483340 −0.0196831
\(604\) −3.09808 5.36603i −0.126059 0.218340i
\(605\) −14.0885 8.13397i −0.572777 0.330693i
\(606\) 4.05256i 0.164624i
\(607\) −36.2942 + 20.9545i −1.47314 + 0.850516i −0.999543 0.0302269i \(-0.990377\pi\)
−0.473594 + 0.880743i \(0.657044\pi\)
\(608\) −2.36603 4.09808i −0.0959550 0.166199i
\(609\) 10.9808 6.33975i 0.444963 0.256899i
\(610\) −2.59808 1.50000i −0.105193 0.0607332i
\(611\) −3.80385 2.19615i −0.153887 0.0888468i
\(612\) −9.10770 + 5.25833i −0.368157 + 0.212555i
\(613\) 16.8923 + 29.2583i 0.682274 + 1.18173i 0.974285 + 0.225318i \(0.0723421\pi\)
−0.292012 + 0.956415i \(0.594325\pi\)
\(614\) 19.0526 11.0000i 0.768899 0.443924i
\(615\) 4.98076i 0.200844i
\(616\) −2.19615 1.26795i −0.0884855 0.0510871i
\(617\) −23.6603 40.9808i −0.952526 1.64982i −0.739931 0.672683i \(-0.765142\pi\)
−0.212595 0.977140i \(-0.568192\pi\)
\(618\) −11.3205 −0.455378
\(619\) 9.60770 0.386166 0.193083 0.981182i \(-0.438151\pi\)
0.193083 + 0.981182i \(0.438151\pi\)
\(620\) 4.09808 + 7.09808i 0.164583 + 0.285066i
\(621\) 5.07180i 0.203524i
\(622\) −9.00000 + 15.5885i −0.360867 + 0.625040i
\(623\) 34.3923i 1.37790i
\(624\) 2.19615 + 1.26795i 0.0879165 + 0.0507586i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −0.0621778 + 0.107695i −0.00248513 + 0.00430436i
\(627\) 3.80385 2.19615i 0.151911 0.0877059i
\(628\) −1.00000 −0.0399043
\(629\) −25.6077 4.26795i −1.02105 0.170174i
\(630\) −8.53590 −0.340078
\(631\) −14.7058 + 8.49038i −0.585428 + 0.337997i −0.763287 0.646059i \(-0.776416\pi\)
0.177860 + 0.984056i \(0.443083\pi\)
\(632\) −8.36603 + 14.4904i −0.332783 + 0.576396i
\(633\) 6.73205 11.6603i 0.267575 0.463453i
\(634\) −11.5981 6.69615i −0.460618 0.265938i
\(635\) 31.5167i 1.25070i
\(636\) −3.46410 + 6.00000i −0.137361 + 0.237915i
\(637\) 10.3923i 0.411758i
\(638\) 5.49038 + 9.50962i 0.217366 + 0.376489i
\(639\) 8.53590 0.337675
\(640\) 1.73205 0.0684653
\(641\) −14.4282 24.9904i −0.569880 0.987061i −0.996577 0.0826663i \(-0.973656\pi\)
0.426698 0.904394i \(-0.359677\pi\)
\(642\) −6.58846 3.80385i −0.260026 0.150126i
\(643\) 16.7321i 0.659848i 0.944008 + 0.329924i \(0.107023\pi\)
−0.944008 + 0.329924i \(0.892977\pi\)
\(644\) −2.19615 + 1.26795i −0.0865405 + 0.0499642i
\(645\) −8.19615 14.1962i −0.322723 0.558973i
\(646\) −17.4904 + 10.0981i −0.688150 + 0.397303i
\(647\) −31.9808 18.4641i −1.25729 0.725899i −0.284746 0.958603i \(-0.591909\pi\)
−0.972548 + 0.232704i \(0.925243\pi\)
\(648\) −3.86603 2.23205i −0.151872 0.0876832i
\(649\) 10.3923 6.00000i 0.407934 0.235521i
\(650\) −3.46410 6.00000i −0.135873 0.235339i
\(651\) 6.00000 3.46410i 0.235159 0.135769i
\(652\) 0.928203i 0.0363512i
\(653\) −6.91154 3.99038i −0.270470 0.156156i 0.358631 0.933479i \(-0.383243\pi\)
−0.629101 + 0.777324i \(0.716577\pi\)
\(654\) 5.36603 + 9.29423i 0.209828 + 0.363433i
\(655\) −34.9808 −1.36681
\(656\) −3.92820 −0.153371
\(657\) 4.92820 + 8.53590i 0.192268 + 0.333017i
\(658\) 2.53590i 0.0988596i
\(659\) 1.26795 2.19615i 0.0493923 0.0855500i −0.840272 0.542165i \(-0.817605\pi\)
0.889665 + 0.456615i \(0.150938\pi\)
\(660\) 1.60770i 0.0625794i
\(661\) 1.50000 + 0.866025i 0.0583432 + 0.0336845i 0.528888 0.848692i \(-0.322609\pi\)
−0.470545 + 0.882376i \(0.655943\pi\)
\(662\) 0 0
\(663\) 5.41154 9.37307i 0.210167 0.364020i
\(664\) 10.0981 5.83013i 0.391881 0.226253i
\(665\) −16.3923 −0.635666
\(666\) −5.25833 14.0359i −0.203756 0.543880i
\(667\) 10.9808 0.425177
\(668\) −12.0000 + 6.92820i −0.464294 + 0.268060i
\(669\) 2.12436 3.67949i 0.0821323 0.142257i
\(670\) 0.169873 0.294229i 0.00656277 0.0113670i
\(671\) −1.90192 1.09808i −0.0734230 0.0423908i
\(672\) 1.46410i 0.0564789i
\(673\) −8.00000 + 13.8564i −0.308377 + 0.534125i −0.978008 0.208569i \(-0.933119\pi\)
0.669630 + 0.742695i \(0.266453\pi\)
\(674\) 30.1769i 1.16237i
\(675\) −4.00000 6.92820i −0.153960 0.266667i
\(676\) −1.00000 −0.0384615
\(677\) 20.0718 0.771422 0.385711 0.922620i \(-0.373956\pi\)
0.385711 + 0.922620i \(0.373956\pi\)
\(678\) −1.26795 2.19615i −0.0486953 0.0843427i
\(679\) −7.39230 4.26795i −0.283691 0.163789i
\(680\) 7.39230i 0.283482i
\(681\) −3.00000 + 1.73205i −0.114960 + 0.0663723i
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) 23.7846 13.7321i 0.910093 0.525442i 0.0296318 0.999561i \(-0.490567\pi\)
0.880461 + 0.474119i \(0.157233\pi\)
\(684\) −10.0981 5.83013i −0.386110 0.222920i
\(685\) 29.0885 + 16.7942i 1.11141 + 0.641674i
\(686\) −17.3205 + 10.0000i −0.661300 + 0.381802i
\(687\) 2.41858 + 4.18911i 0.0922747 + 0.159825i
\(688\) −11.1962 + 6.46410i −0.426849 + 0.246442i
\(689\) 32.7846i 1.24899i
\(690\) 1.39230 + 0.803848i 0.0530041 + 0.0306020i
\(691\) 12.4904 + 21.6340i 0.475156 + 0.822995i 0.999595 0.0284531i \(-0.00905811\pi\)
−0.524439 + 0.851448i \(0.675725\pi\)
\(692\) −12.4641 −0.473814
\(693\) −6.24871 −0.237369
\(694\) −7.56218 13.0981i −0.287056 0.497196i
\(695\) 18.3397i 0.695666i
\(696\) −3.16987 + 5.49038i −0.120154 + 0.208112i
\(697\) 16.7654i 0.635034i
\(698\) −8.13397 4.69615i −0.307875 0.177752i
\(699\) 5.49038 9.50962i 0.207665 0.359687i
\(700\) −2.00000 + 3.46410i −0.0755929 + 0.130931i
\(701\) −4.39230 + 2.53590i −0.165895 + 0.0957796i −0.580649 0.814154i \(-0.697201\pi\)
0.414754 + 0.909934i \(0.363868\pi\)
\(702\) 13.8564 0.522976
\(703\) −10.0981 26.9545i −0.380856 1.01661i
\(704\) 1.26795 0.0477876
\(705\) 1.39230 0.803848i 0.0524372 0.0302747i
\(706\) −8.13397 + 14.0885i −0.306126 + 0.530226i
\(707\) 5.53590 9.58846i 0.208199 0.360611i
\(708\) 6.00000 + 3.46410i 0.225494 + 0.130189i
\(709\) 45.7128i 1.71678i −0.512997 0.858390i \(-0.671465\pi\)
0.512997 0.858390i \(-0.328535\pi\)
\(710\) −3.00000 + 5.19615i −0.112588 + 0.195008i
\(711\) 41.2295i 1.54623i
\(712\) 8.59808 + 14.8923i 0.322227 + 0.558113i
\(713\) 6.00000 0.224702
\(714\) −6.24871 −0.233852
\(715\) 3.80385 + 6.58846i 0.142256 + 0.246394i
\(716\) 2.19615 + 1.26795i 0.0820741 + 0.0473855i
\(717\) 12.6795i 0.473524i
\(718\) −0.588457 + 0.339746i −0.0219610 + 0.0126792i
\(719\) −20.3660 35.2750i −0.759525 1.31554i −0.943093 0.332528i \(-0.892098\pi\)
0.183569 0.983007i \(-0.441235\pi\)
\(720\) 3.69615 2.13397i 0.137747 0.0795285i
\(721\) 26.7846 + 15.4641i 0.997511 + 0.575913i
\(722\) −2.93782 1.69615i −0.109334 0.0631243i
\(723\) −5.41154 + 3.12436i −0.201257 + 0.116196i
\(724\) 5.69615 + 9.86603i 0.211696 + 0.366668i
\(725\) 15.0000 8.66025i 0.557086 0.321634i
\(726\) 6.87564i 0.255179i
\(727\) 13.6077 + 7.85641i 0.504681 + 0.291378i 0.730645 0.682758i \(-0.239220\pi\)
−0.225963 + 0.974136i \(0.572553\pi\)
\(728\) −3.46410 6.00000i −0.128388 0.222375i
\(729\) −2.21539 −0.0820515
\(730\) −6.92820 −0.256424
\(731\) 27.5885 + 47.7846i 1.02040 + 1.76738i
\(732\) 1.26795i 0.0468648i
\(733\) −24.7846 + 42.9282i −0.915440 + 1.58559i −0.109185 + 0.994021i \(0.534824\pi\)
−0.806255 + 0.591568i \(0.798509\pi\)
\(734\) 8.39230i 0.309766i
\(735\) 3.29423 + 1.90192i 0.121509 + 0.0701535i
\(736\) 0.633975 1.09808i 0.0233686 0.0404756i
\(737\) 0.124356 0.215390i 0.00458070 0.00793400i
\(738\) −8.38269 + 4.83975i −0.308571 + 0.178154i
\(739\) 1.41154 0.0519244 0.0259622 0.999663i \(-0.491735\pi\)
0.0259622 + 0.999663i \(0.491735\pi\)
\(740\) 10.3923 + 1.73205i 0.382029 + 0.0636715i
\(741\) 12.0000 0.440831
\(742\) 16.3923 9.46410i 0.601780 0.347438i
\(743\) 21.7583 37.6865i 0.798236 1.38258i −0.122528 0.992465i \(-0.539100\pi\)
0.920764 0.390120i \(-0.127566\pi\)
\(744\) −1.73205 + 3.00000i −0.0635001 + 0.109985i
\(745\) −3.10770 1.79423i −0.113857 0.0657355i
\(746\) 7.00000i 0.256288i
\(747\) 14.3660 24.8827i 0.525625 0.910410i
\(748\) 5.41154i 0.197866i
\(749\) 10.3923 + 18.0000i 0.379727 + 0.657706i
\(750\) 8.87564 0.324093
\(751\) 50.3923 1.83884 0.919421 0.393276i \(-0.128658\pi\)
0.919421 + 0.393276i \(0.128658\pi\)
\(752\) −0.633975 1.09808i −0.0231187 0.0400427i
\(753\) −10.9808 6.33975i −0.400161 0.231033i
\(754\) 30.0000i 1.09254i
\(755\) 9.29423 5.36603i 0.338252 0.195290i
\(756\) −4.00000 6.92820i −0.145479 0.251976i
\(757\) −5.89230 + 3.40192i −0.214159 + 0.123645i −0.603243 0.797557i \(-0.706125\pi\)
0.389084 + 0.921202i \(0.372792\pi\)
\(758\) 5.87564 + 3.39230i 0.213413 + 0.123214i
\(759\) 1.01924 + 0.588457i 0.0369960 + 0.0213596i
\(760\) 7.09808 4.09808i 0.257474 0.148653i
\(761\) −16.1603 27.9904i −0.585809 1.01465i −0.994774 0.102101i \(-0.967444\pi\)
0.408965 0.912550i \(-0.365890\pi\)
\(762\) −11.5359 + 6.66025i −0.417902 + 0.241276i
\(763\) 29.3205i 1.06147i
\(764\) 7.09808 + 4.09808i 0.256799 + 0.148263i
\(765\) −9.10770 15.7750i −0.329289 0.570346i
\(766\) 3.46410 0.125163
\(767\) 32.7846 1.18378
\(768\) 0.366025 + 0.633975i 0.0132078 + 0.0228766i
\(769\) 34.3923i 1.24022i −0.784516 0.620109i \(-0.787088\pi\)
0.784516 0.620109i \(-0.212912\pi\)
\(770\) 2.19615 3.80385i 0.0791438 0.137081i
\(771\) 12.5885i 0.453362i
\(772\) −0.696152 0.401924i −0.0250551 0.0144656i
\(773\) −10.0359 + 17.3827i −0.360966 + 0.625212i −0.988120 0.153684i