Properties

Label 370.2.h.e.253.8
Level $370$
Weight $2$
Character 370.253
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.8
Root \(1.29397 + 1.29397i\) of defining polynomial
Character \(\chi\) \(=\) 370.253
Dual form 370.2.h.e.117.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(1.29397 - 1.29397i) q^{3} +1.00000 q^{4} +(-2.20164 + 0.390851i) q^{5} +(-1.29397 + 1.29397i) q^{6} +(-2.67087 + 2.67087i) q^{7} -1.00000 q^{8} -0.348729i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(1.29397 - 1.29397i) q^{3} +1.00000 q^{4} +(-2.20164 + 0.390851i) q^{5} +(-1.29397 + 1.29397i) q^{6} +(-2.67087 + 2.67087i) q^{7} -1.00000 q^{8} -0.348729i q^{9} +(2.20164 - 0.390851i) q^{10} +1.29587i q^{11} +(1.29397 - 1.29397i) q^{12} -6.92612 q^{13} +(2.67087 - 2.67087i) q^{14} +(-2.34312 + 3.35462i) q^{15} +1.00000 q^{16} +4.85071i q^{17} +0.348729i q^{18} +(-4.69555 - 4.69555i) q^{19} +(-2.20164 + 0.390851i) q^{20} +6.91207i q^{21} -1.29587i q^{22} +3.33959 q^{23} +(-1.29397 + 1.29397i) q^{24} +(4.69447 - 1.72103i) q^{25} +6.92612 q^{26} +(3.43067 + 3.43067i) q^{27} +(-2.67087 + 2.67087i) q^{28} +(3.73955 - 3.73955i) q^{29} +(2.34312 - 3.35462i) q^{30} +(-0.146916 - 0.146916i) q^{31} -1.00000 q^{32} +(1.67682 + 1.67682i) q^{33} -4.85071i q^{34} +(4.83640 - 6.92422i) q^{35} -0.348729i q^{36} +(-6.03371 + 0.770943i) q^{37} +(4.69555 + 4.69555i) q^{38} +(-8.96221 + 8.96221i) q^{39} +(2.20164 - 0.390851i) q^{40} +6.38351i q^{41} -6.91207i q^{42} -2.51195 q^{43} +1.29587i q^{44} +(0.136301 + 0.767778i) q^{45} -3.33959 q^{46} +(-2.93686 + 2.93686i) q^{47} +(1.29397 - 1.29397i) q^{48} -7.26713i q^{49} +(-4.69447 + 1.72103i) q^{50} +(6.27669 + 6.27669i) q^{51} -6.92612 q^{52} +(-1.30971 - 1.30971i) q^{53} +(-3.43067 - 3.43067i) q^{54} +(-0.506490 - 2.85304i) q^{55} +(2.67087 - 2.67087i) q^{56} -12.1518 q^{57} +(-3.73955 + 3.73955i) q^{58} +(4.70039 + 4.70039i) q^{59} +(-2.34312 + 3.35462i) q^{60} +(-7.81965 - 7.81965i) q^{61} +(0.146916 + 0.146916i) q^{62} +(0.931412 + 0.931412i) q^{63} +1.00000 q^{64} +(15.2488 - 2.70708i) q^{65} +(-1.67682 - 1.67682i) q^{66} +(3.10789 + 3.10789i) q^{67} +4.85071i q^{68} +(4.32133 - 4.32133i) q^{69} +(-4.83640 + 6.92422i) q^{70} -5.59124 q^{71} +0.348729i q^{72} +(0.134980 - 0.134980i) q^{73} +(6.03371 - 0.770943i) q^{74} +(3.84755 - 8.30148i) q^{75} +(-4.69555 - 4.69555i) q^{76} +(-3.46110 - 3.46110i) q^{77} +(8.96221 - 8.96221i) q^{78} +(10.8080 + 10.8080i) q^{79} +(-2.20164 + 0.390851i) q^{80} +9.92458 q^{81} -6.38351i q^{82} +(-8.74652 - 8.74652i) q^{83} +6.91207i q^{84} +(-1.89590 - 10.6795i) q^{85} +2.51195 q^{86} -9.67775i q^{87} -1.29587i q^{88} +(3.83829 - 3.83829i) q^{89} +(-0.136301 - 0.767778i) q^{90} +(18.4988 - 18.4988i) q^{91} +3.33959 q^{92} -0.380211 q^{93} +(2.93686 - 2.93686i) q^{94} +(12.1732 + 8.50267i) q^{95} +(-1.29397 + 1.29397i) q^{96} -13.2514i q^{97} +7.26713i q^{98} +0.451907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + O(q^{10}) \) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + 4q^{10} + 4q^{12} + 2q^{14} - 4q^{15} + 20q^{16} + 6q^{19} - 4q^{20} - 4q^{23} - 4q^{24} + 10q^{25} - 20q^{27} - 2q^{28} + 18q^{29} + 4q^{30} + 12q^{31} - 20q^{32} + 4q^{33} - 12q^{35} - 32q^{37} - 6q^{38} + 6q^{39} + 4q^{40} + 16q^{43} + 22q^{45} + 4q^{46} - 22q^{47} + 4q^{48} - 10q^{50} + 8q^{51} - 4q^{53} + 20q^{54} + 16q^{55} + 2q^{56} + 24q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{61} - 12q^{62} - 2q^{63} + 20q^{64} + 20q^{65} - 4q^{66} + 8q^{67} - 34q^{69} + 12q^{70} + 16q^{71} - 6q^{73} + 32q^{74} - 26q^{75} + 6q^{76} - 4q^{77} - 6q^{78} + 12q^{79} - 4q^{80} - 28q^{81} + 6q^{83} + 10q^{85} - 16q^{86} - 44q^{89} - 22q^{90} - 40q^{91} - 4q^{92} - 40q^{93} + 22q^{94} + 50q^{95} - 4q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.29397 1.29397i 0.747075 0.747075i −0.226854 0.973929i \(-0.572844\pi\)
0.973929 + 0.226854i \(0.0728439\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.20164 + 0.390851i −0.984605 + 0.174794i
\(6\) −1.29397 + 1.29397i −0.528262 + 0.528262i
\(7\) −2.67087 + 2.67087i −1.00950 + 1.00950i −0.00954076 + 0.999954i \(0.503037\pi\)
−0.999954 + 0.00954076i \(0.996963\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.348729i 0.116243i
\(10\) 2.20164 0.390851i 0.696221 0.123598i
\(11\) 1.29587i 0.390719i 0.980732 + 0.195359i \(0.0625873\pi\)
−0.980732 + 0.195359i \(0.937413\pi\)
\(12\) 1.29397 1.29397i 0.373538 0.373538i
\(13\) −6.92612 −1.92096 −0.960480 0.278349i \(-0.910213\pi\)
−0.960480 + 0.278349i \(0.910213\pi\)
\(14\) 2.67087 2.67087i 0.713821 0.713821i
\(15\) −2.34312 + 3.35462i −0.604990 + 0.866158i
\(16\) 1.00000 0.250000
\(17\) 4.85071i 1.17647i 0.808690 + 0.588235i \(0.200177\pi\)
−0.808690 + 0.588235i \(0.799823\pi\)
\(18\) 0.348729i 0.0821963i
\(19\) −4.69555 4.69555i −1.07723 1.07723i −0.996756 0.0804769i \(-0.974356\pi\)
−0.0804769 0.996756i \(-0.525644\pi\)
\(20\) −2.20164 + 0.390851i −0.492303 + 0.0873969i
\(21\) 6.91207i 1.50834i
\(22\) 1.29587i 0.276280i
\(23\) 3.33959 0.696352 0.348176 0.937429i \(-0.386801\pi\)
0.348176 + 0.937429i \(0.386801\pi\)
\(24\) −1.29397 + 1.29397i −0.264131 + 0.264131i
\(25\) 4.69447 1.72103i 0.938894 0.344206i
\(26\) 6.92612 1.35832
\(27\) 3.43067 + 3.43067i 0.660233 + 0.660233i
\(28\) −2.67087 + 2.67087i −0.504748 + 0.504748i
\(29\) 3.73955 3.73955i 0.694417 0.694417i −0.268783 0.963201i \(-0.586622\pi\)
0.963201 + 0.268783i \(0.0866216\pi\)
\(30\) 2.34312 3.35462i 0.427793 0.612466i
\(31\) −0.146916 0.146916i −0.0263869 0.0263869i 0.693790 0.720177i \(-0.255939\pi\)
−0.720177 + 0.693790i \(0.755939\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.67682 + 1.67682i 0.291896 + 0.291896i
\(34\) 4.85071i 0.831890i
\(35\) 4.83640 6.92422i 0.817501 1.17041i
\(36\) 0.348729i 0.0581216i
\(37\) −6.03371 + 0.770943i −0.991936 + 0.126742i
\(38\) 4.69555 + 4.69555i 0.761719 + 0.761719i
\(39\) −8.96221 + 8.96221i −1.43510 + 1.43510i
\(40\) 2.20164 0.390851i 0.348110 0.0617989i
\(41\) 6.38351i 0.996937i 0.866908 + 0.498469i \(0.166104\pi\)
−0.866908 + 0.498469i \(0.833896\pi\)
\(42\) 6.91207i 1.06656i
\(43\) −2.51195 −0.383069 −0.191535 0.981486i \(-0.561346\pi\)
−0.191535 + 0.981486i \(0.561346\pi\)
\(44\) 1.29587i 0.195359i
\(45\) 0.136301 + 0.767778i 0.0203186 + 0.114454i
\(46\) −3.33959 −0.492395
\(47\) −2.93686 + 2.93686i −0.428385 + 0.428385i −0.888078 0.459693i \(-0.847960\pi\)
0.459693 + 0.888078i \(0.347960\pi\)
\(48\) 1.29397 1.29397i 0.186769 0.186769i
\(49\) 7.26713i 1.03816i
\(50\) −4.69447 + 1.72103i −0.663899 + 0.243390i
\(51\) 6.27669 + 6.27669i 0.878912 + 0.878912i
\(52\) −6.92612 −0.960480
\(53\) −1.30971 1.30971i −0.179902 0.179902i 0.611411 0.791313i \(-0.290602\pi\)
−0.791313 + 0.611411i \(0.790602\pi\)
\(54\) −3.43067 3.43067i −0.466855 0.466855i
\(55\) −0.506490 2.85304i −0.0682952 0.384704i
\(56\) 2.67087 2.67087i 0.356910 0.356910i
\(57\) −12.1518 −1.60955
\(58\) −3.73955 + 3.73955i −0.491027 + 0.491027i
\(59\) 4.70039 + 4.70039i 0.611938 + 0.611938i 0.943451 0.331512i \(-0.107559\pi\)
−0.331512 + 0.943451i \(0.607559\pi\)
\(60\) −2.34312 + 3.35462i −0.302495 + 0.433079i
\(61\) −7.81965 7.81965i −1.00120 1.00120i −0.999999 0.00120494i \(-0.999616\pi\)
−0.00120494 0.999999i \(-0.500384\pi\)
\(62\) 0.146916 + 0.146916i 0.0186584 + 0.0186584i
\(63\) 0.931412 + 0.931412i 0.117347 + 0.117347i
\(64\) 1.00000 0.125000
\(65\) 15.2488 2.70708i 1.89139 0.335772i
\(66\) −1.67682 1.67682i −0.206402 0.206402i
\(67\) 3.10789 + 3.10789i 0.379690 + 0.379690i 0.870990 0.491301i \(-0.163478\pi\)
−0.491301 + 0.870990i \(0.663478\pi\)
\(68\) 4.85071i 0.588235i
\(69\) 4.32133 4.32133i 0.520227 0.520227i
\(70\) −4.83640 + 6.92422i −0.578060 + 0.827603i
\(71\) −5.59124 −0.663558 −0.331779 0.943357i \(-0.607649\pi\)
−0.331779 + 0.943357i \(0.607649\pi\)
\(72\) 0.348729i 0.0410982i
\(73\) 0.134980 0.134980i 0.0157983 0.0157983i −0.699164 0.714962i \(-0.746444\pi\)
0.714962 + 0.699164i \(0.246444\pi\)
\(74\) 6.03371 0.770943i 0.701404 0.0896204i
\(75\) 3.84755 8.30148i 0.444277 0.958572i
\(76\) −4.69555 4.69555i −0.538617 0.538617i
\(77\) −3.46110 3.46110i −0.394429 0.394429i
\(78\) 8.96221 8.96221i 1.01477 1.01477i
\(79\) 10.8080 + 10.8080i 1.21600 + 1.21600i 0.969021 + 0.246978i \(0.0794376\pi\)
0.246978 + 0.969021i \(0.420562\pi\)
\(80\) −2.20164 + 0.390851i −0.246151 + 0.0436984i
\(81\) 9.92458 1.10273
\(82\) 6.38351i 0.704941i
\(83\) −8.74652 8.74652i −0.960055 0.960055i 0.0391772 0.999232i \(-0.487526\pi\)
−0.999232 + 0.0391772i \(0.987526\pi\)
\(84\) 6.91207i 0.754169i
\(85\) −1.89590 10.6795i −0.205640 1.15836i
\(86\) 2.51195 0.270871
\(87\) 9.67775i 1.03756i
\(88\) 1.29587i 0.138140i
\(89\) 3.83829 3.83829i 0.406858 0.406858i −0.473783 0.880642i \(-0.657112\pi\)
0.880642 + 0.473783i \(0.157112\pi\)
\(90\) −0.136301 0.767778i −0.0143674 0.0809309i
\(91\) 18.4988 18.4988i 1.93920 1.93920i
\(92\) 3.33959 0.348176
\(93\) −0.380211 −0.0394261
\(94\) 2.93686 2.93686i 0.302914 0.302914i
\(95\) 12.1732 + 8.50267i 1.24894 + 0.872356i
\(96\) −1.29397 + 1.29397i −0.132066 + 0.132066i
\(97\) 13.2514i 1.34547i −0.739882 0.672737i \(-0.765119\pi\)
0.739882 0.672737i \(-0.234881\pi\)
\(98\) 7.26713i 0.734091i
\(99\) 0.451907 0.0454184
\(100\) 4.69447 1.72103i 0.469447 0.172103i
\(101\) 13.7890i 1.37205i 0.727577 + 0.686026i \(0.240646\pi\)
−0.727577 + 0.686026i \(0.759354\pi\)
\(102\) −6.27669 6.27669i −0.621485 0.621485i
\(103\) 10.6833i 1.05265i 0.850283 + 0.526327i \(0.176431\pi\)
−0.850283 + 0.526327i \(0.823569\pi\)
\(104\) 6.92612 0.679162
\(105\) −2.70159 15.2179i −0.263648 1.48512i
\(106\) 1.30971 + 1.30971i 0.127210 + 0.127210i
\(107\) −7.62669 + 7.62669i −0.737300 + 0.737300i −0.972055 0.234755i \(-0.924571\pi\)
0.234755 + 0.972055i \(0.424571\pi\)
\(108\) 3.43067 + 3.43067i 0.330116 + 0.330116i
\(109\) −3.39395 3.39395i −0.325081 0.325081i 0.525631 0.850713i \(-0.323829\pi\)
−0.850713 + 0.525631i \(0.823829\pi\)
\(110\) 0.506490 + 2.85304i 0.0482920 + 0.272027i
\(111\) −6.80987 + 8.80503i −0.646365 + 0.835737i
\(112\) −2.67087 + 2.67087i −0.252374 + 0.252374i
\(113\) 4.28955i 0.403527i −0.979434 0.201764i \(-0.935333\pi\)
0.979434 0.201764i \(-0.0646673\pi\)
\(114\) 12.1518 1.13812
\(115\) −7.35258 + 1.30528i −0.685632 + 0.121718i
\(116\) 3.73955 3.73955i 0.347209 0.347209i
\(117\) 2.41534i 0.223298i
\(118\) −4.70039 4.70039i −0.432706 0.432706i
\(119\) −12.9556 12.9556i −1.18764 1.18764i
\(120\) 2.34312 3.35462i 0.213896 0.306233i
\(121\) 9.32073 0.847339
\(122\) 7.81965 + 7.81965i 0.707958 + 0.707958i
\(123\) 8.26009 + 8.26009i 0.744787 + 0.744787i
\(124\) −0.146916 0.146916i −0.0131935 0.0131935i
\(125\) −9.66289 + 5.62393i −0.864275 + 0.503019i
\(126\) −0.931412 0.931412i −0.0829768 0.0829768i
\(127\) 0.938326 0.938326i 0.0832629 0.0832629i −0.664249 0.747512i \(-0.731248\pi\)
0.747512 + 0.664249i \(0.231248\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.25040 + 3.25040i −0.286182 + 0.286182i
\(130\) −15.2488 + 2.70708i −1.33741 + 0.237426i
\(131\) 2.47395 + 2.47395i 0.216150 + 0.216150i 0.806874 0.590724i \(-0.201158\pi\)
−0.590724 + 0.806874i \(0.701158\pi\)
\(132\) 1.67682 + 1.67682i 0.145948 + 0.145948i
\(133\) 25.0824 2.17492
\(134\) −3.10789 3.10789i −0.268481 0.268481i
\(135\) −8.89400 6.21224i −0.765473 0.534664i
\(136\) 4.85071i 0.415945i
\(137\) 14.6348 14.6348i 1.25034 1.25034i 0.294767 0.955569i \(-0.404758\pi\)
0.955569 0.294767i \(-0.0952420\pi\)
\(138\) −4.32133 + 4.32133i −0.367856 + 0.367856i
\(139\) −14.2080 −1.20511 −0.602554 0.798078i \(-0.705850\pi\)
−0.602554 + 0.798078i \(0.705850\pi\)
\(140\) 4.83640 6.92422i 0.408750 0.585204i
\(141\) 7.60043i 0.640072i
\(142\) 5.59124 0.469207
\(143\) 8.97533i 0.750555i
\(144\) 0.348729i 0.0290608i
\(145\) −6.77155 + 9.69476i −0.562347 + 0.805106i
\(146\) −0.134980 + 0.134980i −0.0111711 + 0.0111711i
\(147\) −9.40346 9.40346i −0.775585 0.775585i
\(148\) −6.03371 + 0.770943i −0.495968 + 0.0633712i
\(149\) 7.52248i 0.616266i 0.951343 + 0.308133i \(0.0997041\pi\)
−0.951343 + 0.308133i \(0.900296\pi\)
\(150\) −3.84755 + 8.30148i −0.314152 + 0.677813i
\(151\) 4.35018i 0.354012i 0.984210 + 0.177006i \(0.0566412\pi\)
−0.984210 + 0.177006i \(0.943359\pi\)
\(152\) 4.69555 + 4.69555i 0.380860 + 0.380860i
\(153\) 1.69159 0.136757
\(154\) 3.46110 + 3.46110i 0.278903 + 0.278903i
\(155\) 0.380880 + 0.266035i 0.0305930 + 0.0213684i
\(156\) −8.96221 + 8.96221i −0.717551 + 0.717551i
\(157\) −13.0961 + 13.0961i −1.04518 + 1.04518i −0.0462518 + 0.998930i \(0.514728\pi\)
−0.998930 + 0.0462518i \(0.985272\pi\)
\(158\) −10.8080 10.8080i −0.859841 0.859841i
\(159\) −3.38945 −0.268801
\(160\) 2.20164 0.390851i 0.174055 0.0308995i
\(161\) −8.91961 + 8.91961i −0.702964 + 0.702964i
\(162\) −9.92458 −0.779748
\(163\) 14.8033i 1.15948i 0.814801 + 0.579741i \(0.196846\pi\)
−0.814801 + 0.579741i \(0.803154\pi\)
\(164\) 6.38351i 0.498469i
\(165\) −4.34714 3.03637i −0.338424 0.236381i
\(166\) 8.74652 + 8.74652i 0.678861 + 0.678861i
\(167\) 1.13442i 0.0877842i 0.999036 + 0.0438921i \(0.0139758\pi\)
−0.999036 + 0.0438921i \(0.986024\pi\)
\(168\) 6.91207i 0.533278i
\(169\) 34.9711 2.69009
\(170\) 1.89590 + 10.6795i 0.145409 + 0.819083i
\(171\) −1.63748 + 1.63748i −0.125221 + 0.125221i
\(172\) −2.51195 −0.191535
\(173\) 7.57033 7.57033i 0.575562 0.575562i −0.358116 0.933677i \(-0.616581\pi\)
0.933677 + 0.358116i \(0.116581\pi\)
\(174\) 9.67775i 0.733668i
\(175\) −7.94169 + 17.1350i −0.600335 + 1.29528i
\(176\) 1.29587i 0.0976797i
\(177\) 12.1643 0.914328
\(178\) −3.83829 + 3.83829i −0.287692 + 0.287692i
\(179\) −5.64137 + 5.64137i −0.421656 + 0.421656i −0.885773 0.464118i \(-0.846371\pi\)
0.464118 + 0.885773i \(0.346371\pi\)
\(180\) 0.136301 + 0.767778i 0.0101593 + 0.0572268i
\(181\) −5.21779 −0.387835 −0.193918 0.981018i \(-0.562119\pi\)
−0.193918 + 0.981018i \(0.562119\pi\)
\(182\) −18.4988 + 18.4988i −1.37122 + 1.37122i
\(183\) −20.2368 −1.49595
\(184\) −3.33959 −0.246198
\(185\) 12.9828 4.05562i 0.954511 0.298175i
\(186\) 0.380211 0.0278784
\(187\) −6.28588 −0.459669
\(188\) −2.93686 + 2.93686i −0.214193 + 0.214193i
\(189\) −18.3258 −1.33300
\(190\) −12.1732 8.50267i −0.883136 0.616849i
\(191\) −6.11582 + 6.11582i −0.442525 + 0.442525i −0.892860 0.450335i \(-0.851305\pi\)
0.450335 + 0.892860i \(0.351305\pi\)
\(192\) 1.29397 1.29397i 0.0933844 0.0933844i
\(193\) −15.9965 −1.15145 −0.575725 0.817643i \(-0.695280\pi\)
−0.575725 + 0.817643i \(0.695280\pi\)
\(194\) 13.2514i 0.951394i
\(195\) 16.2287 23.2345i 1.16216 1.66386i
\(196\) 7.26713i 0.519081i
\(197\) 17.7621 17.7621i 1.26550 1.26550i 0.317109 0.948389i \(-0.397288\pi\)
0.948389 0.317109i \(-0.102712\pi\)
\(198\) −0.451907 −0.0321156
\(199\) −15.7905 + 15.7905i −1.11936 + 1.11936i −0.127524 + 0.991835i \(0.540703\pi\)
−0.991835 + 0.127524i \(0.959297\pi\)
\(200\) −4.69447 + 1.72103i −0.331949 + 0.121695i
\(201\) 8.04306 0.567314
\(202\) 13.7890i 0.970188i
\(203\) 19.9757i 1.40202i
\(204\) 6.27669 + 6.27669i 0.439456 + 0.439456i
\(205\) −2.49500 14.0542i −0.174258 0.981590i
\(206\) 10.6833i 0.744338i
\(207\) 1.16461i 0.0809462i
\(208\) −6.92612 −0.480240
\(209\) 6.08481 6.08481i 0.420895 0.420895i
\(210\) 2.70159 + 15.2179i 0.186427 + 1.05014i
\(211\) −24.3785 −1.67829 −0.839144 0.543909i \(-0.816944\pi\)
−0.839144 + 0.543909i \(0.816944\pi\)
\(212\) −1.30971 1.30971i −0.0899510 0.0899510i
\(213\) −7.23491 + 7.23491i −0.495728 + 0.495728i
\(214\) 7.62669 7.62669i 0.521350 0.521350i
\(215\) 5.53043 0.981798i 0.377172 0.0669581i
\(216\) −3.43067 3.43067i −0.233428 0.233428i
\(217\) 0.784789 0.0532750
\(218\) 3.39395 + 3.39395i 0.229867 + 0.229867i
\(219\) 0.349322i 0.0236050i
\(220\) −0.506490 2.85304i −0.0341476 0.192352i
\(221\) 33.5966i 2.25995i
\(222\) 6.80987 8.80503i 0.457049 0.590955i
\(223\) 11.0916 + 11.0916i 0.742750 + 0.742750i 0.973106 0.230356i \(-0.0739892\pi\)
−0.230356 + 0.973106i \(0.573989\pi\)
\(224\) 2.67087 2.67087i 0.178455 0.178455i
\(225\) −0.600173 1.63710i −0.0400115 0.109140i
\(226\) 4.28955i 0.285337i
\(227\) 13.1902i 0.875463i 0.899106 + 0.437732i \(0.144218\pi\)
−0.899106 + 0.437732i \(0.855782\pi\)
\(228\) −12.1518 −0.804775
\(229\) 6.06268i 0.400633i −0.979731 0.200317i \(-0.935803\pi\)
0.979731 0.200317i \(-0.0641971\pi\)
\(230\) 7.35258 1.30528i 0.484815 0.0860676i
\(231\) −8.95713 −0.589336
\(232\) −3.73955 + 3.73955i −0.245514 + 0.245514i
\(233\) −11.6145 + 11.6145i −0.760893 + 0.760893i −0.976484 0.215590i \(-0.930832\pi\)
0.215590 + 0.976484i \(0.430832\pi\)
\(234\) 2.41534i 0.157896i
\(235\) 5.31805 7.61379i 0.346911 0.496669i
\(236\) 4.70039 + 4.70039i 0.305969 + 0.305969i
\(237\) 27.9706 1.81689
\(238\) 12.9556 + 12.9556i 0.839789 + 0.839789i
\(239\) −0.628920 0.628920i −0.0406815 0.0406815i 0.686473 0.727155i \(-0.259158\pi\)
−0.727155 + 0.686473i \(0.759158\pi\)
\(240\) −2.34312 + 3.35462i −0.151248 + 0.216540i
\(241\) 14.1376 14.1376i 0.910686 0.910686i −0.0856405 0.996326i \(-0.527294\pi\)
0.996326 + 0.0856405i \(0.0272937\pi\)
\(242\) −9.32073 −0.599159
\(243\) 2.55012 2.55012i 0.163590 0.163590i
\(244\) −7.81965 7.81965i −0.500602 0.500602i
\(245\) 2.84036 + 15.9996i 0.181464 + 1.02218i
\(246\) −8.26009 8.26009i −0.526644 0.526644i
\(247\) 32.5219 + 32.5219i 2.06932 + 2.06932i
\(248\) 0.146916 + 0.146916i 0.00932919 + 0.00932919i
\(249\) −22.6355 −1.43447
\(250\) 9.66289 5.62393i 0.611135 0.355688i
\(251\) 14.7200 + 14.7200i 0.929119 + 0.929119i 0.997649 0.0685304i \(-0.0218310\pi\)
−0.0685304 + 0.997649i \(0.521831\pi\)
\(252\) 0.931412 + 0.931412i 0.0586735 + 0.0586735i
\(253\) 4.32766i 0.272078i
\(254\) −0.938326 + 0.938326i −0.0588758 + 0.0588758i
\(255\) −16.2723 11.3658i −1.01901 0.711753i
\(256\) 1.00000 0.0625000
\(257\) 23.6607i 1.47591i 0.674848 + 0.737957i \(0.264209\pi\)
−0.674848 + 0.737957i \(0.735791\pi\)
\(258\) 3.25040 3.25040i 0.202361 0.202361i
\(259\) 14.0562 18.1744i 0.873409 1.12930i
\(260\) 15.2488 2.70708i 0.945693 0.167886i
\(261\) −1.30409 1.30409i −0.0807212 0.0807212i
\(262\) −2.47395 2.47395i −0.152841 0.152841i
\(263\) 17.6417 17.6417i 1.08783 1.08783i 0.0920831 0.995751i \(-0.470647\pi\)
0.995751 0.0920831i \(-0.0293525\pi\)
\(264\) −1.67682 1.67682i −0.103201 0.103201i
\(265\) 3.39541 + 2.37161i 0.208578 + 0.145687i
\(266\) −25.0824 −1.53790
\(267\) 9.93329i 0.607908i
\(268\) 3.10789 + 3.10789i 0.189845 + 0.189845i
\(269\) 2.23989i 0.136568i −0.997666 0.0682841i \(-0.978248\pi\)
0.997666 0.0682841i \(-0.0217524\pi\)
\(270\) 8.89400 + 6.21224i 0.541271 + 0.378065i
\(271\) 0.860850 0.0522929 0.0261465 0.999658i \(-0.491676\pi\)
0.0261465 + 0.999658i \(0.491676\pi\)
\(272\) 4.85071i 0.294118i
\(273\) 47.8738i 2.89746i
\(274\) −14.6348 + 14.6348i −0.884121 + 0.884121i
\(275\) 2.23022 + 6.08341i 0.134488 + 0.366844i
\(276\) 4.32133 4.32133i 0.260114 0.260114i
\(277\) 1.08776 0.0653573 0.0326787 0.999466i \(-0.489596\pi\)
0.0326787 + 0.999466i \(0.489596\pi\)
\(278\) 14.2080 0.852140
\(279\) −0.0512340 + 0.0512340i −0.00306730 + 0.00306730i
\(280\) −4.83640 + 6.92422i −0.289030 + 0.413802i
\(281\) −12.3965 + 12.3965i −0.739516 + 0.739516i −0.972484 0.232969i \(-0.925156\pi\)
0.232969 + 0.972484i \(0.425156\pi\)
\(282\) 7.60043i 0.452599i
\(283\) 2.50115i 0.148678i −0.997233 0.0743390i \(-0.976315\pi\)
0.997233 0.0743390i \(-0.0236847\pi\)
\(284\) −5.59124 −0.331779
\(285\) 26.7540 4.74955i 1.58477 0.281339i
\(286\) 8.97533i 0.530722i
\(287\) −17.0496 17.0496i −1.00640 1.00640i
\(288\) 0.348729i 0.0205491i
\(289\) −6.52939 −0.384082
\(290\) 6.77155 9.69476i 0.397639 0.569296i
\(291\) −17.1469 17.1469i −1.00517 1.00517i
\(292\) 0.134980 0.134980i 0.00789913 0.00789913i
\(293\) 7.08204 + 7.08204i 0.413737 + 0.413737i 0.883038 0.469301i \(-0.155494\pi\)
−0.469301 + 0.883038i \(0.655494\pi\)
\(294\) 9.40346 + 9.40346i 0.548421 + 0.548421i
\(295\) −12.1857 8.51143i −0.709481 0.495555i
\(296\) 6.03371 0.770943i 0.350702 0.0448102i
\(297\) −4.44569 + 4.44569i −0.257965 + 0.257965i
\(298\) 7.52248i 0.435766i
\(299\) −23.1304 −1.33766
\(300\) 3.84755 8.30148i 0.222139 0.479286i
\(301\) 6.70911 6.70911i 0.386707 0.386707i
\(302\) 4.35018i 0.250324i
\(303\) 17.8425 + 17.8425i 1.02503 + 1.02503i
\(304\) −4.69555 4.69555i −0.269308 0.269308i
\(305\) 20.2724 + 14.1598i 1.16079 + 0.810787i
\(306\) −1.69159 −0.0967015
\(307\) 18.8346 + 18.8346i 1.07495 + 1.07495i 0.996954 + 0.0779923i \(0.0248510\pi\)
0.0779923 + 0.996954i \(0.475149\pi\)
\(308\) −3.46110 3.46110i −0.197214 0.197214i
\(309\) 13.8238 + 13.8238i 0.786411 + 0.786411i
\(310\) −0.380880 0.266035i −0.0216325 0.0151098i
\(311\) −15.1202 15.1202i −0.857389 0.857389i 0.133641 0.991030i \(-0.457333\pi\)
−0.991030 + 0.133641i \(0.957333\pi\)
\(312\) 8.96221 8.96221i 0.507385 0.507385i
\(313\) −8.77570 −0.496032 −0.248016 0.968756i \(-0.579779\pi\)
−0.248016 + 0.968756i \(0.579779\pi\)
\(314\) 13.0961 13.0961i 0.739055 0.739055i
\(315\) −2.41468 1.68660i −0.136052 0.0950289i
\(316\) 10.8080 + 10.8080i 0.608000 + 0.608000i
\(317\) 13.7979 + 13.7979i 0.774970 + 0.774970i 0.978971 0.204001i \(-0.0653946\pi\)
−0.204001 + 0.978971i \(0.565395\pi\)
\(318\) 3.38945 0.190071
\(319\) 4.84596 + 4.84596i 0.271322 + 0.271322i
\(320\) −2.20164 + 0.390851i −0.123076 + 0.0218492i
\(321\) 19.7374i 1.10164i
\(322\) 8.91961 8.91961i 0.497071 0.497071i
\(323\) 22.7768 22.7768i 1.26733 1.26733i
\(324\) 9.92458 0.551365
\(325\) −32.5145 + 11.9200i −1.80358 + 0.661205i
\(326\) 14.8033i 0.819877i
\(327\) −8.78335 −0.485721
\(328\) 6.38351i 0.352471i
\(329\) 15.6880i 0.864905i
\(330\) 4.34714 + 3.03637i 0.239302 + 0.167147i
\(331\) 0.223075 0.223075i 0.0122613 0.0122613i −0.700950 0.713211i \(-0.747240\pi\)
0.713211 + 0.700950i \(0.247240\pi\)
\(332\) −8.74652 8.74652i −0.480028 0.480028i
\(333\) 0.268851 + 2.10413i 0.0147329 + 0.115306i
\(334\) 1.13442i 0.0620728i
\(335\) −8.05720 5.62775i −0.440212 0.307477i
\(336\) 6.91207i 0.377085i
\(337\) −12.6737 12.6737i −0.690381 0.690381i 0.271935 0.962316i \(-0.412336\pi\)
−0.962316 + 0.271935i \(0.912336\pi\)
\(338\) −34.9711 −1.90218
\(339\) −5.55057 5.55057i −0.301465 0.301465i
\(340\) −1.89590 10.6795i −0.102820 0.579179i
\(341\) 0.190384 0.190384i 0.0103099 0.0103099i
\(342\) 1.63748 1.63748i 0.0885446 0.0885446i
\(343\) 0.713468 + 0.713468i 0.0385236 + 0.0385236i
\(344\) 2.51195 0.135435
\(345\) −7.82504 + 11.2030i −0.421286 + 0.603151i
\(346\) −7.57033 + 7.57033i −0.406983 + 0.406983i
\(347\) 9.68557 0.519948 0.259974 0.965616i \(-0.416286\pi\)
0.259974 + 0.965616i \(0.416286\pi\)
\(348\) 9.67775i 0.518782i
\(349\) 9.40675i 0.503532i −0.967788 0.251766i \(-0.918989\pi\)
0.967788 0.251766i \(-0.0810113\pi\)
\(350\) 7.94169 17.1350i 0.424501 0.915904i
\(351\) −23.7612 23.7612i −1.26828 1.26828i
\(352\) 1.29587i 0.0690700i
\(353\) 8.93094i 0.475346i 0.971345 + 0.237673i \(0.0763846\pi\)
−0.971345 + 0.237673i \(0.923615\pi\)
\(354\) −12.1643 −0.646528
\(355\) 12.3099 2.18534i 0.653343 0.115986i
\(356\) 3.83829 3.83829i 0.203429 0.203429i
\(357\) −33.5285 −1.77451
\(358\) 5.64137 5.64137i 0.298156 0.298156i
\(359\) 14.7945i 0.780823i 0.920640 + 0.390412i \(0.127667\pi\)
−0.920640 + 0.390412i \(0.872333\pi\)
\(360\) −0.136301 0.767778i −0.00718370 0.0404655i
\(361\) 25.0964i 1.32086i
\(362\) 5.21779 0.274241
\(363\) 12.0608 12.0608i 0.633026 0.633026i
\(364\) 18.4988 18.4988i 0.969600 0.969600i
\(365\) −0.244421 + 0.349936i −0.0127936 + 0.0183165i
\(366\) 20.2368 1.05780
\(367\) 19.5831 19.5831i 1.02223 1.02223i 0.0224808 0.999747i \(-0.492844\pi\)
0.999747 0.0224808i \(-0.00715646\pi\)
\(368\) 3.33959 0.174088
\(369\) 2.22612 0.115887
\(370\) −12.9828 + 4.05562i −0.674941 + 0.210842i
\(371\) 6.99612 0.363221
\(372\) −0.380211 −0.0197130
\(373\) 7.70109 7.70109i 0.398747 0.398747i −0.479044 0.877791i \(-0.659016\pi\)
0.877791 + 0.479044i \(0.159016\pi\)
\(374\) 6.28588 0.325035
\(375\) −5.22631 + 19.7807i −0.269885 + 1.02147i
\(376\) 2.93686 2.93686i 0.151457 0.151457i
\(377\) −25.9006 + 25.9006i −1.33395 + 1.33395i
\(378\) 18.3258 0.942576
\(379\) 19.2451i 0.988556i 0.869304 + 0.494278i \(0.164567\pi\)
−0.869304 + 0.494278i \(0.835433\pi\)
\(380\) 12.1732 + 8.50267i 0.624472 + 0.436178i
\(381\) 2.42834i 0.124407i
\(382\) 6.11582 6.11582i 0.312913 0.312913i
\(383\) −8.69427 −0.444257 −0.222128 0.975017i \(-0.571300\pi\)
−0.222128 + 0.975017i \(0.571300\pi\)
\(384\) −1.29397 + 1.29397i −0.0660328 + 0.0660328i
\(385\) 8.97288 + 6.26733i 0.457300 + 0.319413i
\(386\) 15.9965 0.814198
\(387\) 0.875992i 0.0445292i
\(388\) 13.2514i 0.672737i
\(389\) −14.2389 14.2389i −0.721941 0.721941i 0.247059 0.969000i \(-0.420536\pi\)
−0.969000 + 0.247059i \(0.920536\pi\)
\(390\) −16.2287 + 23.2345i −0.821772 + 1.17652i
\(391\) 16.1994i 0.819237i
\(392\) 7.26713i 0.367045i
\(393\) 6.40246 0.322961
\(394\) −17.7621 + 17.7621i −0.894842 + 0.894842i
\(395\) −28.0198 19.5711i −1.40983 0.984730i
\(396\) 0.451907 0.0227092
\(397\) 10.2910 + 10.2910i 0.516489 + 0.516489i 0.916507 0.400018i \(-0.130996\pi\)
−0.400018 + 0.916507i \(0.630996\pi\)
\(398\) 15.7905 15.7905i 0.791507 0.791507i
\(399\) 32.4560 32.4560i 1.62483 1.62483i
\(400\) 4.69447 1.72103i 0.234724 0.0860514i
\(401\) −13.7676 13.7676i −0.687523 0.687523i 0.274161 0.961684i \(-0.411600\pi\)
−0.961684 + 0.274161i \(0.911600\pi\)
\(402\) −8.04306 −0.401151
\(403\) 1.01756 + 1.01756i 0.0506883 + 0.0506883i
\(404\) 13.7890i 0.686026i
\(405\) −21.8504 + 3.87903i −1.08575 + 0.192750i
\(406\) 19.9757i 0.991379i
\(407\) −0.999040 7.81889i −0.0495206 0.387568i
\(408\) −6.27669 6.27669i −0.310742 0.310742i
\(409\) −14.5393 + 14.5393i −0.718920 + 0.718920i −0.968384 0.249464i \(-0.919745\pi\)
0.249464 + 0.968384i \(0.419745\pi\)
\(410\) 2.49500 + 14.0542i 0.123219 + 0.694089i
\(411\) 37.8741i 1.86819i
\(412\) 10.6833i 0.526327i
\(413\) −25.1083 −1.23550
\(414\) 1.16461i 0.0572376i
\(415\) 22.6753 + 15.8381i 1.11309 + 0.777463i
\(416\) 6.92612 0.339581
\(417\) −18.3848 + 18.3848i −0.900307 + 0.900307i
\(418\) −6.08481 + 6.08481i −0.297618 + 0.297618i
\(419\) 8.30494i 0.405723i −0.979207 0.202861i \(-0.934976\pi\)
0.979207 0.202861i \(-0.0650241\pi\)
\(420\) −2.70159 15.2179i −0.131824 0.742559i
\(421\) −5.43095 5.43095i −0.264688 0.264688i 0.562267 0.826956i \(-0.309929\pi\)
−0.826956 + 0.562267i \(0.809929\pi\)
\(422\) 24.3785 1.18673
\(423\) 1.02417 + 1.02417i 0.0497968 + 0.0497968i
\(424\) 1.30971 + 1.30971i 0.0636050 + 0.0636050i
\(425\) 8.34821 + 22.7715i 0.404948 + 1.10458i
\(426\) 7.23491 7.23491i 0.350533 0.350533i
\(427\) 41.7706 2.02142
\(428\) −7.62669 + 7.62669i −0.368650 + 0.368650i
\(429\) −11.6138 11.6138i −0.560721 0.560721i
\(430\) −5.53043 + 0.981798i −0.266701 + 0.0473465i
\(431\) 16.0000 + 16.0000i 0.770693 + 0.770693i 0.978228 0.207535i \(-0.0665439\pi\)
−0.207535 + 0.978228i \(0.566544\pi\)
\(432\) 3.43067 + 3.43067i 0.165058 + 0.165058i
\(433\) −21.6988 21.6988i −1.04278 1.04278i −0.999043 0.0437350i \(-0.986074\pi\)
−0.0437350 0.999043i \(-0.513926\pi\)
\(434\) −0.784789 −0.0376711
\(435\) 3.78256 + 21.3070i 0.181360 + 1.02159i
\(436\) −3.39395 3.39395i −0.162541 0.162541i
\(437\) −15.6812 15.6812i −0.750134 0.750134i
\(438\) 0.349322i 0.0166912i
\(439\) 5.60815 5.60815i 0.267662 0.267662i −0.560495 0.828158i \(-0.689389\pi\)
0.828158 + 0.560495i \(0.189389\pi\)
\(440\) 0.506490 + 2.85304i 0.0241460 + 0.136013i
\(441\) −2.53426 −0.120679
\(442\) 33.5966i 1.59803i
\(443\) 17.9895 17.9895i 0.854708 0.854708i −0.136001 0.990709i \(-0.543425\pi\)
0.990709 + 0.136001i \(0.0434250\pi\)
\(444\) −6.80987 + 8.80503i −0.323182 + 0.417868i
\(445\) −6.95036 + 9.95076i −0.329479 + 0.471711i
\(446\) −11.0916 11.0916i −0.525203 0.525203i
\(447\) 9.73388 + 9.73388i 0.460397 + 0.460397i
\(448\) −2.67087 + 2.67087i −0.126187 + 0.126187i
\(449\) 6.18967 + 6.18967i 0.292109 + 0.292109i 0.837913 0.545804i \(-0.183776\pi\)
−0.545804 + 0.837913i \(0.683776\pi\)
\(450\) 0.600173 + 1.63710i 0.0282924 + 0.0771737i
\(451\) −8.27219 −0.389522
\(452\) 4.28955i 0.201764i
\(453\) 5.62901 + 5.62901i 0.264474 + 0.264474i
\(454\) 13.1902i 0.619046i
\(455\) −33.4975 + 47.9580i −1.57039 + 2.24831i
\(456\) 12.1518 0.569062
\(457\) 31.9423i 1.49420i −0.664712 0.747100i \(-0.731446\pi\)
0.664712 0.747100i \(-0.268554\pi\)
\(458\) 6.06268i 0.283291i
\(459\) −16.6412 + 16.6412i −0.776744 + 0.776744i
\(460\) −7.35258 + 1.30528i −0.342816 + 0.0608590i
\(461\) 2.73403 2.73403i 0.127336 0.127336i −0.640566 0.767903i \(-0.721300\pi\)
0.767903 + 0.640566i \(0.221300\pi\)
\(462\) 8.95713 0.416723
\(463\) −4.32970 −0.201218 −0.100609 0.994926i \(-0.532079\pi\)
−0.100609 + 0.994926i \(0.532079\pi\)
\(464\) 3.73955 3.73955i 0.173604 0.173604i
\(465\) 0.837090 0.148606i 0.0388191 0.00689143i
\(466\) 11.6145 11.6145i 0.538033 0.538033i
\(467\) 0.826696i 0.0382549i −0.999817 0.0191275i \(-0.993911\pi\)
0.999817 0.0191275i \(-0.00608884\pi\)
\(468\) 2.41534i 0.111649i
\(469\) −16.6016 −0.766590
\(470\) −5.31805 + 7.61379i −0.245303 + 0.351198i
\(471\) 33.8920i 1.56166i
\(472\) −4.70039 4.70039i −0.216353 0.216353i
\(473\) 3.25516i 0.149672i
\(474\) −27.9706 −1.28473
\(475\) −30.1243 13.9620i −1.38220 0.640619i
\(476\) −12.9556 12.9556i −0.593821 0.593821i
\(477\) −0.456733 + 0.456733i −0.0209124 + 0.0209124i
\(478\) 0.628920 + 0.628920i 0.0287661 + 0.0287661i
\(479\) 19.7849 + 19.7849i 0.903997 + 0.903997i 0.995779 0.0917818i \(-0.0292562\pi\)
−0.0917818 + 0.995779i \(0.529256\pi\)
\(480\) 2.34312 3.35462i 0.106948 0.153117i
\(481\) 41.7902 5.33965i 1.90547 0.243467i
\(482\) −14.1376 + 14.1376i −0.643952 + 0.643952i
\(483\) 23.0835i 1.05033i
\(484\) 9.32073 0.423669
\(485\) 5.17931 + 29.1748i 0.235180 + 1.32476i
\(486\) −2.55012 + 2.55012i −0.115676 + 0.115676i
\(487\) 28.2154i 1.27856i 0.768973 + 0.639282i \(0.220768\pi\)
−0.768973 + 0.639282i \(0.779232\pi\)
\(488\) 7.81965 + 7.81965i 0.353979 + 0.353979i
\(489\) 19.1550 + 19.1550i 0.866220 + 0.866220i
\(490\) −2.84036 15.9996i −0.128314 0.722790i
\(491\) 2.48442 0.112121 0.0560603 0.998427i \(-0.482146\pi\)
0.0560603 + 0.998427i \(0.482146\pi\)
\(492\) 8.26009 + 8.26009i 0.372394 + 0.372394i
\(493\) 18.1395 + 18.1395i 0.816961 + 0.816961i
\(494\) −32.5219 32.5219i −1.46323 1.46323i
\(495\) −0.994939 + 0.176628i −0.0447192 + 0.00793885i
\(496\) −0.146916 0.146916i −0.00659674 0.00659674i
\(497\) 14.9335 14.9335i 0.669859 0.669859i
\(498\) 22.6355 1.01432
\(499\) 1.49326 1.49326i 0.0668473 0.0668473i −0.672893 0.739740i \(-0.734948\pi\)
0.739740 + 0.672893i \(0.234948\pi\)
\(500\) −9.66289 + 5.62393i −0.432138 + 0.251510i
\(501\) 1.46791 + 1.46791i 0.0655814 + 0.0655814i
\(502\) −14.7200 14.7200i −0.656986 0.656986i
\(503\) 3.35307 0.149506 0.0747531 0.997202i \(-0.476183\pi\)
0.0747531 + 0.997202i \(0.476183\pi\)
\(504\) −0.931412 0.931412i −0.0414884 0.0414884i
\(505\) −5.38942 30.3584i −0.239826 1.35093i
\(506\) 4.32766i 0.192388i
\(507\) 45.2517 45.2517i 2.00970 2.00970i
\(508\) 0.938326 0.938326i 0.0416315 0.0416315i
\(509\) 9.46119 0.419360 0.209680 0.977770i \(-0.432758\pi\)
0.209680 + 0.977770i \(0.432758\pi\)
\(510\) 16.2723 + 11.3658i 0.720548 + 0.503285i
\(511\) 0.721031i 0.0318965i
\(512\) −1.00000 −0.0441942
\(513\) 32.2178i 1.42245i
\(514\) 23.6607i 1.04363i
\(515\) −4.17556 23.5207i −0.183997 1.03645i
\(516\) −3.25040 + 3.25040i −0.143091 + 0.143091i
\(517\) −3.80578 3.80578i −0.167378 0.167378i
\(518\) −14.0562 + 18.1744i −0.617593 + 0.798536i
\(519\) 19.5916i 0.859976i
\(520\) −15.2488 + 2.70708i −0.668706 + 0.118713i
\(521\) 28.0496i 1.22887i 0.788966 + 0.614437i \(0.210617\pi\)
−0.788966 + 0.614437i \(0.789383\pi\)
\(522\) 1.30409 + 1.30409i 0.0570785 + 0.0570785i
\(523\) −10.2294 −0.447300 −0.223650 0.974669i \(-0.571797\pi\)
−0.223650 + 0.974669i \(0.571797\pi\)
\(524\) 2.47395 + 2.47395i 0.108075 + 0.108075i
\(525\) 11.8959 + 32.4485i 0.519178 + 1.41617i
\(526\) −17.6417 + 17.6417i −0.769215 + 0.769215i
\(527\) 0.712648 0.712648i 0.0310434 0.0310434i
\(528\) 1.67682 + 1.67682i 0.0729741 + 0.0729741i
\(529\) −11.8472 −0.515094
\(530\) −3.39541 2.37161i −0.147487 0.103016i
\(531\) 1.63916 1.63916i 0.0711337 0.0711337i
\(532\) 25.0824 1.08746
\(533\) 44.2130i 1.91508i
\(534\) 9.93329i 0.429856i
\(535\) 13.8104 19.7721i 0.597074 0.854824i
\(536\) −3.10789 3.10789i −0.134241 0.134241i
\(537\) 14.5995i 0.630017i
\(538\) 2.23989i 0.0965683i
\(539\) 9.41723 0.405629
\(540\) −8.89400 6.21224i −0.382737 0.267332i
\(541\) 11.2603 11.2603i 0.484116 0.484116i −0.422327 0.906443i \(-0.638787\pi\)
0.906443 + 0.422327i \(0.138787\pi\)
\(542\) −0.860850 −0.0369767
\(543\) −6.75168 + 6.75168i −0.289742 + 0.289742i
\(544\) 4.85071i 0.207973i
\(545\) 8.79879 + 6.14574i 0.376899 + 0.263255i
\(546\) 47.8738i 2.04881i
\(547\) 25.5984 1.09451 0.547254 0.836966i \(-0.315673\pi\)
0.547254 + 0.836966i \(0.315673\pi\)
\(548\) 14.6348 14.6348i 0.625168 0.625168i
\(549\) −2.72694 + 2.72694i −0.116383 + 0.116383i
\(550\) −2.23022 6.08341i −0.0950970 0.259398i
\(551\) −35.1185 −1.49610
\(552\) −4.32133 + 4.32133i −0.183928 + 0.183928i
\(553\) −57.7338 −2.45509
\(554\) −1.08776 −0.0462146
\(555\) 11.5515 22.0472i 0.490332 0.935851i
\(556\) −14.2080 −0.602554
\(557\) 14.7290 0.624089 0.312045 0.950067i \(-0.398986\pi\)
0.312045 + 0.950067i \(0.398986\pi\)
\(558\) 0.0512340 0.0512340i 0.00216891 0.00216891i
\(559\) 17.3981 0.735861
\(560\) 4.83640 6.92422i 0.204375 0.292602i
\(561\) −8.13375 + 8.13375i −0.343407 + 0.343407i
\(562\) 12.3965 12.3965i 0.522917 0.522917i
\(563\) −30.0223 −1.26529 −0.632645 0.774442i \(-0.718031\pi\)
−0.632645 + 0.774442i \(0.718031\pi\)
\(564\) 7.60043i 0.320036i
\(565\) 1.67658 + 9.44407i 0.0705341 + 0.397315i
\(566\) 2.50115i 0.105131i
\(567\) −26.5073 + 26.5073i −1.11320 + 1.11320i
\(568\) 5.59124 0.234603
\(569\) −5.23109 + 5.23109i −0.219298 + 0.219298i −0.808203 0.588904i \(-0.799559\pi\)
0.588904 + 0.808203i \(0.299559\pi\)
\(570\) −26.7540 + 4.74955i −1.12060 + 0.198937i
\(571\) −13.0995 −0.548196 −0.274098 0.961702i \(-0.588379\pi\)
−0.274098 + 0.961702i \(0.588379\pi\)
\(572\) 8.97533i 0.375277i
\(573\) 15.8274i 0.661199i
\(574\) 17.0496 + 17.0496i 0.711635 + 0.711635i
\(575\) 15.6776 5.74752i 0.653801 0.239688i
\(576\) 0.348729i 0.0145304i
\(577\) 21.6061i 0.899475i −0.893161 0.449737i \(-0.851518\pi\)
0.893161 0.449737i \(-0.148482\pi\)
\(578\) 6.52939 0.271587
\(579\) −20.6990 + 20.6990i −0.860220 + 0.860220i
\(580\) −6.77155 + 9.69476i −0.281173 + 0.402553i
\(581\) 46.7217 1.93834
\(582\) 17.1469 + 17.1469i 0.710763 + 0.710763i
\(583\) 1.69721 1.69721i 0.0702911 0.0702911i
\(584\) −0.134980 + 0.134980i −0.00558553 + 0.00558553i
\(585\) −0.944038 5.31772i −0.0390312 0.219861i
\(586\) −7.08204 7.08204i −0.292556 0.292556i
\(587\) −37.7655 −1.55875 −0.779375 0.626557i \(-0.784463\pi\)
−0.779375 + 0.626557i \(0.784463\pi\)
\(588\) −9.40346 9.40346i −0.387792 0.387792i
\(589\) 1.37971i 0.0568498i
\(590\) 12.1857 + 8.51143i 0.501679 + 0.350410i
\(591\) 45.9674i 1.89084i
\(592\) −6.03371 + 0.770943i −0.247984 + 0.0316856i
\(593\) −5.60150 5.60150i −0.230026 0.230026i 0.582678 0.812703i \(-0.302005\pi\)
−0.812703 + 0.582678i \(0.802005\pi\)
\(594\) 4.44569 4.44569i 0.182409 0.182409i
\(595\) 33.5874 + 23.4600i 1.37695 + 0.961765i
\(596\) 7.52248i 0.308133i
\(597\) 40.8650i 1.67249i
\(598\) 23.1304 0.945871
\(599\) 3.81331i 0.155808i 0.996961 + 0.0779039i \(0.0248227\pi\)
−0.996961 + 0.0779039i \(0.975177\pi\)
\(600\) −3.84755 + 8.30148i −0.157076 + 0.338906i
\(601\) 15.0394 0.613469 0.306734 0.951795i \(-0.400764\pi\)
0.306734 + 0.951795i \(0.400764\pi\)
\(602\) −6.70911 + 6.70911i −0.273443 + 0.273443i
\(603\) 1.08381 1.08381i 0.0441363 0.0441363i
\(604\) 4.35018i 0.177006i
\(605\) −20.5209 + 3.64301i −0.834294 + 0.148110i
\(606\) −17.8425 17.8425i −0.724803 0.724803i
\(607\) 28.5167 1.15746 0.578729 0.815520i \(-0.303549\pi\)
0.578729 + 0.815520i \(0.303549\pi\)
\(608\) 4.69555 + 4.69555i 0.190430 + 0.190430i
\(609\) 25.8480 + 25.8480i 1.04742 + 1.04742i
\(610\) −20.2724 14.1598i −0.820806 0.573313i
\(611\) 20.3410 20.3410i 0.822911 0.822911i
\(612\) 1.69159 0.0683783
\(613\) −11.7097 + 11.7097i −0.472948 + 0.472948i −0.902867 0.429919i \(-0.858542\pi\)
0.429919 + 0.902867i \(0.358542\pi\)
\(614\) −18.8346 18.8346i −0.760102 0.760102i
\(615\) −21.4142 14.9573i −0.863506 0.603137i
\(616\) 3.46110 + 3.46110i 0.139452 + 0.139452i
\(617\) −31.2569 31.2569i −1.25836 1.25836i −0.951878 0.306477i \(-0.900850\pi\)
−0.306477 0.951878i \(-0.599150\pi\)
\(618\) −13.8238 13.8238i −0.556077 0.556077i
\(619\) −3.97357 −0.159711 −0.0798556 0.996806i \(-0.525446\pi\)
−0.0798556 + 0.996806i \(0.525446\pi\)
\(620\) 0.380880 + 0.266035i 0.0152965 + 0.0106842i
\(621\) 11.4570 + 11.4570i 0.459755 + 0.459755i
\(622\) 15.1202 + 15.1202i 0.606265 + 0.606265i
\(623\) 20.5032i 0.821443i
\(624\) −8.96221 + 8.96221i −0.358775 + 0.358775i
\(625\) 19.0761 16.1586i 0.763045 0.646345i
\(626\) 8.77570 0.350748
\(627\) 15.7472i 0.628881i
\(628\) −13.0961 + 13.0961i −0.522591 + 0.522591i
\(629\) −3.73962 29.2678i −0.149109 1.16698i
\(630\) 2.41468 + 1.68660i 0.0962032 + 0.0671956i
\(631\) −31.7078 31.7078i −1.26227 1.26227i −0.949991 0.312278i \(-0.898908\pi\)
−0.312278 0.949991i \(-0.601092\pi\)
\(632\) −10.8080 10.8080i −0.429921 0.429921i
\(633\) −31.5452 + 31.5452i −1.25381 + 1.25381i
\(634\) −13.7979 13.7979i −0.547986 0.547986i
\(635\) −1.69911 + 2.43260i −0.0674273 + 0.0965350i
\(636\) −3.38945 −0.134400
\(637\) 50.3330i 1.99427i
\(638\) −4.84596 4.84596i −0.191853 0.191853i
\(639\) 1.94983i 0.0771341i
\(640\) 2.20164 0.390851i 0.0870276 0.0154497i
\(641\) −3.77934 −0.149275 −0.0746374 0.997211i \(-0.523780\pi\)
−0.0746374 + 0.997211i \(0.523780\pi\)
\(642\) 19.7374i 0.778975i
\(643\) 28.5420i 1.12558i 0.826598 + 0.562792i \(0.190273\pi\)
−0.826598 + 0.562792i \(0.809727\pi\)
\(644\) −8.91961 + 8.91961i −0.351482 + 0.351482i
\(645\) 5.88580 8.42664i 0.231753 0.331799i
\(646\) −22.7768 + 22.7768i −0.896140 + 0.896140i
\(647\) −22.3386 −0.878222 −0.439111 0.898433i \(-0.644707\pi\)
−0.439111 + 0.898433i \(0.644707\pi\)
\(648\) −9.92458 −0.389874
\(649\) −6.09108 + 6.09108i −0.239096 + 0.239096i
\(650\) 32.5145 11.9200i 1.27532 0.467543i
\(651\) 1.01550 1.01550i 0.0398004 0.0398004i
\(652\) 14.8033i 0.579741i
\(653\) 19.9863i 0.782125i −0.920364 0.391063i \(-0.872108\pi\)
0.920364 0.391063i \(-0.127892\pi\)
\(654\) 8.78335 0.343456
\(655\) −6.41371 4.47982i −0.250605 0.175041i
\(656\) 6.38351i 0.249234i
\(657\) −0.0470716 0.0470716i −0.00183644 0.00183644i
\(658\) 15.6880i 0.611581i
\(659\) −30.3524 −1.18236 −0.591182 0.806538i \(-0.701338\pi\)
−0.591182 + 0.806538i \(0.701338\pi\)
\(660\) −4.34714 3.03637i −0.169212 0.118190i
\(661\) 10.1177 + 10.1177i 0.393535 + 0.393535i 0.875945 0.482411i \(-0.160239\pi\)
−0.482411 + 0.875945i \(0.660239\pi\)
\(662\) −0.223075 + 0.223075i −0.00867004 + 0.00867004i
\(663\) −43.4731 43.4731i −1.68835 1.68835i
\(664\) 8.74652 + 8.74652i 0.339431 + 0.339431i
\(665\) −55.2226 + 9.80349i −2.14144 + 0.380163i
\(666\) −0.268851 2.10413i −0.0104178 0.0815335i
\(667\) 12.4886 12.4886i 0.483559 0.483559i
\(668\) 1.13442i 0.0438921i
\(669\) 28.7045 1.10978
\(670\) 8.05720 + 5.62775i 0.311277 + 0.217419i
\(671\) 10.1332 10.1332i 0.391189 0.391189i
\(672\) 6.91207i 0.266639i
\(673\) −13.7492 13.7492i −0.529992 0.529992i 0.390578 0.920570i \(-0.372275\pi\)
−0.920570 + 0.390578i \(0.872275\pi\)
\(674\) 12.6737 + 12.6737i 0.488173 + 0.488173i
\(675\) 22.0095 + 10.2009i 0.847145 + 0.392633i
\(676\) 34.9711 1.34504
\(677\) −24.9315 24.9315i −0.958197 0.958197i 0.0409634 0.999161i \(-0.486957\pi\)
−0.999161 + 0.0409634i \(0.986957\pi\)
\(678\) 5.55057 + 5.55057i 0.213168 + 0.213168i
\(679\) 35.3928 + 35.3928i 1.35825 + 1.35825i
\(680\) 1.89590 + 10.6795i 0.0727046 + 0.409542i
\(681\) 17.0677 + 17.0677i 0.654037 + 0.654037i
\(682\) −0.190384 + 0.190384i −0.00729018 + 0.00729018i
\(683\) 37.2952 1.42706 0.713531 0.700624i \(-0.247095\pi\)
0.713531 + 0.700624i \(0.247095\pi\)
\(684\) −1.63748 + 1.63748i −0.0626105 + 0.0626105i
\(685\) −26.5006 + 37.9407i −1.01254 + 1.44964i
\(686\) −0.713468 0.713468i −0.0272403 0.0272403i
\(687\) −7.84495 7.84495i −0.299303 0.299303i
\(688\) −2.51195 −0.0957673
\(689\) 9.07118 + 9.07118i 0.345585 + 0.345585i
\(690\) 7.82504 11.2030i 0.297894 0.426492i
\(691\) 5.06456i 0.192665i −0.995349 0.0963324i \(-0.969289\pi\)
0.995349 0.0963324i \(-0.0307112\pi\)
\(692\) 7.57033 7.57033i 0.287781 0.287781i
\(693\) −1.20699 + 1.20699i −0.0458496 + 0.0458496i
\(694\) −9.68557 −0.367659
\(695\) 31.2810 5.55321i 1.18656 0.210645i
\(696\) 9.67775i 0.366834i
\(697\) −30.9646 −1.17287
\(698\) 9.40675i 0.356051i
\(699\) 30.0578i 1.13689i
\(700\) −7.94169 + 17.1350i −0.300168 + 0.647642i
\(701\) −18.0567 + 18.0567i −0.681993 + 0.681993i −0.960449 0.278456i \(-0.910177\pi\)
0.278456 + 0.960449i \(0.410177\pi\)
\(702\) 23.7612 + 23.7612i 0.896810 + 0.896810i
\(703\) 31.9516 + 24.7116i 1.20508 + 0.932015i
\(704\) 1.29587i 0.0488398i
\(705\) −2.97063 16.7334i −0.111881 0.630218i
\(706\) 8.93094i 0.336120i
\(707\) −36.8286 36.8286i −1.38508 1.38508i
\(708\) 12.1643 0.457164
\(709\) 20.2886 + 20.2886i 0.761953 + 0.761953i 0.976675 0.214722i \(-0.0688845\pi\)
−0.214722 + 0.976675i \(0.568885\pi\)
\(710\) −12.3099 + 2.18534i −0.461983 + 0.0820144i
\(711\) 3.76908 3.76908i 0.141352 0.141352i
\(712\) −3.83829 + 3.83829i −0.143846 + 0.143846i
\(713\) −0.490640 0.490640i −0.0183746 0.0183746i
\(714\) 33.5285 1.25477
\(715\) 3.50801 + 19.7605i 0.131192 + 0.739000i
\(716\) −5.64137 + 5.64137i −0.210828 + 0.210828i
\(717\) −1.62761 −0.0607842
\(718\) 14.7945i 0.552125i
\(719\) 37.3366i 1.39242i −0.717838 0.696210i \(-0.754868\pi\)
0.717838 0.696210i \(-0.245132\pi\)
\(720\) 0.136301 + 0.767778i 0.00507964 + 0.0286134i
\(721\) −28.5336 28.5336i −1.06265 1.06265i
\(722\) 25.0964i 0.933992i
\(723\) 36.5874i 1.36070i
\(724\) −5.21779 −0.193918
\(725\) 11.1193 23.9911i 0.412962 0.891007i
\(726\) −12.0608 + 12.0608i −0.447617 + 0.447617i
\(727\) 6.83943 0.253660 0.126830 0.991924i \(-0.459520\pi\)
0.126830 + 0.991924i \(0.459520\pi\)
\(728\) −18.4988 + 18.4988i −0.685611 + 0.685611i
\(729\) 23.1742i 0.858303i
\(730\) 0.244421 0.349936i 0.00904644 0.0129517i
\(731\) 12.1848i 0.450669i
\(732\) −20.2368 −0.747975
\(733\) −10.1492 + 10.1492i −0.374870 + 0.374870i −0.869247 0.494378i \(-0.835396\pi\)
0.494378 + 0.869247i \(0.335396\pi\)
\(734\) −19.5831 + 19.5831i −0.722824 + 0.722824i
\(735\) 24.3784 + 17.0277i 0.899212 + 0.628077i
\(736\) −3.33959 −0.123099
\(737\) −4.02742 + 4.02742i −0.148352 + 0.148352i
\(738\) −2.22612 −0.0819446
\(739\) 32.3194 1.18889 0.594445 0.804136i \(-0.297372\pi\)
0.594445 + 0.804136i \(0.297372\pi\)
\(740\) 12.9828 4.05562i 0.477256 0.149088i
\(741\) 84.1650 3.09188
\(742\) −6.99612 −0.256836
\(743\) −17.4266 + 17.4266i −0.639319 + 0.639319i −0.950387 0.311069i \(-0.899313\pi\)
0.311069 + 0.950387i \(0.399313\pi\)
\(744\) 0.380211 0.0139392
\(745\) −2.94017 16.5618i −0.107719 0.606778i
\(746\) −7.70109 + 7.70109i −0.281957 + 0.281957i
\(747\) −3.05017 + 3.05017i −0.111600 + 0.111600i
\(748\) −6.28588 −0.229834
\(749\) 40.7398i 1.48860i
\(750\) 5.22631 19.7807i 0.190838 0.722290i
\(751\) 9.29027i 0.339007i −0.985530 0.169503i \(-0.945784\pi\)
0.985530 0.169503i \(-0.0542164\pi\)
\(752\) −2.93686 + 2.93686i −0.107096 + 0.107096i
\(753\) 38.0946 1.38824
\(754\) 25.9006 25.9006i 0.943243 0.943243i
\(755\) −1.70027 9.57754i −0.0618791 0.348562i
\(756\) −18.3258 −0.666502
\(757\) 27.5608i 1.00171i −0.865530 0.500857i \(-0.833018\pi\)
0.865530 0.500857i \(-0.166982\pi\)
\(758\) 19.2451i 0.699015i
\(759\) 5.59987 + 5.59987i 0.203263 + 0.203263i
\(760\) −12.1732 8.50267i −0.441568 0.308424i
\(761\) 14.9003i 0.540137i −0.962841 0.270069i \(-0.912954\pi\)
0.962841 0.270069i \(-0.0870464\pi\)
\(762\) 2.42834i 0.0879693i
\(763\) 18.1296 0.656336
\(764\) −6.11582 + 6.11582i −0.221263 + 0.221263i
\(765\) −3.72427 + 0.661157i −0.134651 + 0.0239042i
\(766\) 8.69427 0.314137
\(767\) −32.5554 32.5554i −1.17551 1.17551i
\(768\) 1.29397 1.29397i 0.0466922 0.0466922i
\(769\) −19.2793 + 19.2793i −0.695229 + 0.695229i −0.963378 0.268148i \(-0.913588\pi\)
0.268148 + 0.963378i \(0.413588\pi\)
\(770\) −8.97288 6.26733i −0.323360 0.225859i
\(771\) 30.6163 + 30.6163i 1.10262 + 1.10262i
\(772\) −15.9965 −0.575725
\(773\) 12.1435 + 12.1435i 0.436770 + 0.436770i 0.890923 0.454153i \(-0.150058\pi\)
−0.454153 + 0.890923i \(0.650058\pi\)
\(774\) 0.875992i 0.0314869i
\(775\) −0.942541 0.436847i −0.0338571 0.0156920i
\(776\) 13.2514i 0.475697i
\(777\) −5.32882 41.7054i −0.191170 1.49617i
\(778\)