Properties

Label 570.2.m.a.37.1
Level $570$
Weight $2$
Character 570.37
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 153 x^{16} + 6416 x^{12} + 78648 x^{8} + 19120 x^{4} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.1
Root \(-1.53190 + 1.53190i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.a.493.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.23502 + 0.0685835i) q^{5} +1.00000 q^{6} +(-2.16643 - 2.16643i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.23502 + 0.0685835i) q^{5} +1.00000 q^{6} +(-2.16643 - 2.16643i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.53190 - 1.62889i) q^{10} -5.68402 q^{11} +(-0.707107 + 0.707107i) q^{12} +(3.92222 + 3.92222i) q^{13} +3.06380 q^{14} +(1.62889 + 1.53190i) q^{15} -1.00000 q^{16} +(4.99059 + 4.99059i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(4.01921 - 1.68699i) q^{19} +(0.0685835 + 2.23502i) q^{20} +3.06380i q^{21} +(4.01921 - 4.01921i) q^{22} +(4.30360 - 4.30360i) q^{23} -1.00000i q^{24} +(4.99059 - 0.306570i) q^{25} -5.54686 q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.16643 + 2.16643i) q^{28} -4.04446 q^{29} +(-2.23502 + 0.0685835i) q^{30} +4.04446i q^{31} +(0.707107 - 0.707107i) q^{32} +(4.01921 + 4.01921i) q^{33} -7.05776 q^{34} +(4.99059 + 4.69343i) q^{35} +1.00000 q^{36} +(6.19934 - 6.19934i) q^{37} +(-1.64913 + 4.03490i) q^{38} -5.54686i q^{39} +(-1.62889 - 1.53190i) q^{40} +6.38884i q^{41} +(-2.16643 - 2.16643i) q^{42} +(-4.15703 + 4.15703i) q^{43} +5.68402i q^{44} +(-0.0685835 - 2.23502i) q^{45} +6.08621i q^{46} +(3.24326 + 3.24326i) q^{47} +(0.707107 + 0.707107i) q^{48} +2.38686i q^{49} +(-3.31210 + 3.74566i) q^{50} -7.05776i q^{51} +(3.92222 - 3.92222i) q^{52} +(5.40818 + 5.40818i) q^{53} +1.00000i q^{54} +(12.7039 - 0.389830i) q^{55} -3.06380i q^{56} +(-4.03490 - 1.64913i) q^{57} +(2.85986 - 2.85986i) q^{58} -2.39487 q^{59} +(1.53190 - 1.62889i) q^{60} -2.33286 q^{61} +(-2.85986 - 2.85986i) q^{62} +(2.16643 - 2.16643i) q^{63} +1.00000i q^{64} +(-9.03522 - 8.49722i) q^{65} -5.68402 q^{66} +(-6.12760 + 6.12760i) q^{67} +(4.99059 - 4.99059i) q^{68} -6.08621 q^{69} +(-6.84764 + 0.210126i) q^{70} +6.51556i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-2.07682 + 2.07682i) q^{73} +8.76719i q^{74} +(-3.74566 - 3.31210i) q^{75} +(-1.68699 - 4.01921i) q^{76} +(12.3141 + 12.3141i) q^{77} +(3.92222 + 3.92222i) q^{78} +4.23844 q^{79} +(2.23502 - 0.0685835i) q^{80} -1.00000 q^{81} +(-4.51759 - 4.51759i) q^{82} +(-5.30657 + 5.30657i) q^{83} +3.06380 q^{84} +(-11.4963 - 10.8118i) q^{85} -5.87892i q^{86} +(2.85986 + 2.85986i) q^{87} +(-4.01921 - 4.01921i) q^{88} -2.50829 q^{89} +(1.62889 + 1.53190i) q^{90} -16.9944i q^{91} +(-4.30360 - 4.30360i) q^{92} +(2.85986 - 2.85986i) q^{93} -4.58666 q^{94} +(-8.86730 + 4.04611i) q^{95} -1.00000 q^{96} +(6.22010 - 6.22010i) q^{97} +(-1.68776 - 1.68776i) q^{98} -5.68402i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} + 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q - 4q^{5} + 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} + 4q^{17} + 44q^{23} + 4q^{25} - 8q^{26} - 4q^{28} - 4q^{30} + 4q^{35} + 20q^{36} - 4q^{38} - 4q^{42} + 52q^{43} + 4q^{47} + 16q^{55} - 4q^{57} + 8q^{58} + 32q^{61} - 8q^{62} + 4q^{63} - 8q^{66} + 4q^{68} - 20q^{73} + 20q^{76} - 24q^{77} + 4q^{80} - 20q^{81} - 24q^{82} - 116q^{83} - 60q^{85} + 8q^{87} - 44q^{92} + 8q^{93} - 32q^{95} - 20q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −2.23502 + 0.0685835i −0.999530 + 0.0306715i
\(6\) 1.00000 0.408248
\(7\) −2.16643 2.16643i −0.818835 0.818835i 0.167105 0.985939i \(-0.446558\pi\)
−0.985939 + 0.167105i \(0.946558\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.53190 1.62889i 0.484429 0.515100i
\(11\) −5.68402 −1.71380 −0.856899 0.515485i \(-0.827612\pi\)
−0.856899 + 0.515485i \(0.827612\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 3.92222 + 3.92222i 1.08783 + 1.08783i 0.995752 + 0.0920758i \(0.0293502\pi\)
0.0920758 + 0.995752i \(0.470650\pi\)
\(14\) 3.06380 0.818835
\(15\) 1.62889 + 1.53190i 0.420578 + 0.395535i
\(16\) −1.00000 −0.250000
\(17\) 4.99059 + 4.99059i 1.21040 + 1.21040i 0.970896 + 0.239500i \(0.0769836\pi\)
0.239500 + 0.970896i \(0.423016\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 4.01921 1.68699i 0.922070 0.387023i
\(20\) 0.0685835 + 2.23502i 0.0153357 + 0.499765i
\(21\) 3.06380i 0.668576i
\(22\) 4.01921 4.01921i 0.856899 0.856899i
\(23\) 4.30360 4.30360i 0.897363 0.897363i −0.0978397 0.995202i \(-0.531193\pi\)
0.995202 + 0.0978397i \(0.0311932\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 4.99059 0.306570i 0.998119 0.0613141i
\(26\) −5.54686 −1.08783
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −2.16643 + 2.16643i −0.409417 + 0.409417i
\(29\) −4.04446 −0.751037 −0.375518 0.926815i \(-0.622535\pi\)
−0.375518 + 0.926815i \(0.622535\pi\)
\(30\) −2.23502 + 0.0685835i −0.408056 + 0.0125216i
\(31\) 4.04446i 0.726406i 0.931710 + 0.363203i \(0.118317\pi\)
−0.931710 + 0.363203i \(0.881683\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 4.01921 + 4.01921i 0.699655 + 0.699655i
\(34\) −7.05776 −1.21040
\(35\) 4.99059 + 4.69343i 0.843564 + 0.793334i
\(36\) 1.00000 0.166667
\(37\) 6.19934 6.19934i 1.01917 1.01917i 0.0193530 0.999813i \(-0.493839\pi\)
0.999813 0.0193530i \(-0.00616063\pi\)
\(38\) −1.64913 + 4.03490i −0.267524 + 0.654546i
\(39\) 5.54686i 0.888208i
\(40\) −1.62889 1.53190i −0.257550 0.242215i
\(41\) 6.38884i 0.997769i 0.866669 + 0.498884i \(0.166257\pi\)
−0.866669 + 0.498884i \(0.833743\pi\)
\(42\) −2.16643 2.16643i −0.334288 0.334288i
\(43\) −4.15703 + 4.15703i −0.633940 + 0.633940i −0.949054 0.315114i \(-0.897957\pi\)
0.315114 + 0.949054i \(0.397957\pi\)
\(44\) 5.68402i 0.856899i
\(45\) −0.0685835 2.23502i −0.0102238 0.333177i
\(46\) 6.08621i 0.897363i
\(47\) 3.24326 + 3.24326i 0.473077 + 0.473077i 0.902909 0.429832i \(-0.141427\pi\)
−0.429832 + 0.902909i \(0.641427\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 2.38686i 0.340980i
\(50\) −3.31210 + 3.74566i −0.468402 + 0.529716i
\(51\) 7.05776i 0.988285i
\(52\) 3.92222 3.92222i 0.543914 0.543914i
\(53\) 5.40818 + 5.40818i 0.742871 + 0.742871i 0.973129 0.230259i \(-0.0739573\pi\)
−0.230259 + 0.973129i \(0.573957\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 12.7039 0.389830i 1.71299 0.0525647i
\(56\) 3.06380i 0.409417i
\(57\) −4.03490 1.64913i −0.534435 0.218432i
\(58\) 2.85986 2.85986i 0.375518 0.375518i
\(59\) −2.39487 −0.311786 −0.155893 0.987774i \(-0.549825\pi\)
−0.155893 + 0.987774i \(0.549825\pi\)
\(60\) 1.53190 1.62889i 0.197767 0.210289i
\(61\) −2.33286 −0.298693 −0.149346 0.988785i \(-0.547717\pi\)
−0.149346 + 0.988785i \(0.547717\pi\)
\(62\) −2.85986 2.85986i −0.363203 0.363203i
\(63\) 2.16643 2.16643i 0.272945 0.272945i
\(64\) 1.00000i 0.125000i
\(65\) −9.03522 8.49722i −1.12068 1.05395i
\(66\) −5.68402 −0.699655
\(67\) −6.12760 + 6.12760i −0.748605 + 0.748605i −0.974217 0.225612i \(-0.927562\pi\)
0.225612 + 0.974217i \(0.427562\pi\)
\(68\) 4.99059 4.99059i 0.605198 0.605198i
\(69\) −6.08621 −0.732693
\(70\) −6.84764 + 0.210126i −0.818449 + 0.0251149i
\(71\) 6.51556i 0.773255i 0.922236 + 0.386628i \(0.126360\pi\)
−0.922236 + 0.386628i \(0.873640\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) −2.07682 + 2.07682i −0.243074 + 0.243074i −0.818121 0.575047i \(-0.804984\pi\)
0.575047 + 0.818121i \(0.304984\pi\)
\(74\) 8.76719i 1.01917i
\(75\) −3.74566 3.31210i −0.432512 0.382449i
\(76\) −1.68699 4.01921i −0.193511 0.461035i
\(77\) 12.3141 + 12.3141i 1.40332 + 1.40332i
\(78\) 3.92222 + 3.92222i 0.444104 + 0.444104i
\(79\) 4.23844 0.476862 0.238431 0.971159i \(-0.423367\pi\)
0.238431 + 0.971159i \(0.423367\pi\)
\(80\) 2.23502 0.0685835i 0.249882 0.00766787i
\(81\) −1.00000 −0.111111
\(82\) −4.51759 4.51759i −0.498884 0.498884i
\(83\) −5.30657 + 5.30657i −0.582472 + 0.582472i −0.935582 0.353110i \(-0.885124\pi\)
0.353110 + 0.935582i \(0.385124\pi\)
\(84\) 3.06380 0.334288
\(85\) −11.4963 10.8118i −1.24695 1.17270i
\(86\) 5.87892i 0.633940i
\(87\) 2.85986 + 2.85986i 0.306609 + 0.306609i
\(88\) −4.01921 4.01921i −0.428449 0.428449i
\(89\) −2.50829 −0.265879 −0.132939 0.991124i \(-0.542442\pi\)
−0.132939 + 0.991124i \(0.542442\pi\)
\(90\) 1.62889 + 1.53190i 0.171700 + 0.161476i
\(91\) 16.9944i 1.78150i
\(92\) −4.30360 4.30360i −0.448681 0.448681i
\(93\) 2.85986 2.85986i 0.296554 0.296554i
\(94\) −4.58666 −0.473077
\(95\) −8.86730 + 4.04611i −0.909766 + 0.415122i
\(96\) −1.00000 −0.102062
\(97\) 6.22010 6.22010i 0.631555 0.631555i −0.316903 0.948458i \(-0.602643\pi\)
0.948458 + 0.316903i \(0.102643\pi\)
\(98\) −1.68776 1.68776i −0.170490 0.170490i
\(99\) 5.68402i 0.571266i
\(100\) −0.306570 4.99059i −0.0306570 0.499059i
\(101\) 3.42891 0.341189 0.170595 0.985341i \(-0.445431\pi\)
0.170595 + 0.985341i \(0.445431\pi\)
\(102\) 4.99059 + 4.99059i 0.494142 + 0.494142i
\(103\) 13.0842 + 13.0842i 1.28922 + 1.28922i 0.935260 + 0.353961i \(0.115165\pi\)
0.353961 + 0.935260i \(0.384835\pi\)
\(104\) 5.54686i 0.543914i
\(105\) −0.210126 6.84764i −0.0205062 0.668261i
\(106\) −7.64832 −0.742871
\(107\) 5.02931 5.02931i 0.486202 0.486202i −0.420903 0.907106i \(-0.638287\pi\)
0.907106 + 0.420903i \(0.138287\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −5.95528 −0.570412 −0.285206 0.958466i \(-0.592062\pi\)
−0.285206 + 0.958466i \(0.592062\pi\)
\(110\) −8.70735 + 9.25865i −0.830213 + 0.882778i
\(111\) −8.76719 −0.832145
\(112\) 2.16643 + 2.16643i 0.204709 + 0.204709i
\(113\) −0.0413876 0.0413876i −0.00389342 0.00389342i 0.705157 0.709051i \(-0.250876\pi\)
−0.709051 + 0.705157i \(0.750876\pi\)
\(114\) 4.01921 1.68699i 0.376434 0.158001i
\(115\) −9.32346 + 9.91377i −0.869417 + 0.924464i
\(116\) 4.04446i 0.375518i
\(117\) −3.92222 + 3.92222i −0.362609 + 0.362609i
\(118\) 1.69343 1.69343i 0.155893 0.155893i
\(119\) 21.6236i 1.98223i
\(120\) 0.0685835 + 2.23502i 0.00626079 + 0.204028i
\(121\) 21.3081 1.93710
\(122\) 1.64958 1.64958i 0.149346 0.149346i
\(123\) 4.51759 4.51759i 0.407337 0.407337i
\(124\) 4.04446 0.363203
\(125\) −11.1330 + 1.02746i −0.995768 + 0.0918990i
\(126\) 3.06380i 0.272945i
\(127\) −10.0379 + 10.0379i −0.890717 + 0.890717i −0.994591 0.103873i \(-0.966876\pi\)
0.103873 + 0.994591i \(0.466876\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 5.87892 0.517610
\(130\) 12.3973 0.380423i 1.08732 0.0333653i
\(131\) 4.64290 0.405652 0.202826 0.979215i \(-0.434987\pi\)
0.202826 + 0.979215i \(0.434987\pi\)
\(132\) 4.01921 4.01921i 0.349827 0.349827i
\(133\) −12.3621 5.05259i −1.07193 0.438115i
\(134\) 8.66573i 0.748605i
\(135\) −1.53190 + 1.62889i −0.131845 + 0.140193i
\(136\) 7.05776i 0.605198i
\(137\) −2.26545 2.26545i −0.193550 0.193550i 0.603678 0.797228i \(-0.293701\pi\)
−0.797228 + 0.603678i \(0.793701\pi\)
\(138\) 4.30360 4.30360i 0.366347 0.366347i
\(139\) 17.4266i 1.47810i −0.673649 0.739051i \(-0.735274\pi\)
0.673649 0.739051i \(-0.264726\pi\)
\(140\) 4.69343 4.99059i 0.396667 0.421782i
\(141\) 4.58666i 0.386266i
\(142\) −4.60720 4.60720i −0.386628 0.386628i
\(143\) −22.2940 22.2940i −1.86432 1.86432i
\(144\) 1.00000i 0.0833333i
\(145\) 9.03942 0.277383i 0.750683 0.0230354i
\(146\) 2.93707i 0.243074i
\(147\) 1.68776 1.68776i 0.139204 0.139204i
\(148\) −6.19934 6.19934i −0.509583 0.509583i
\(149\) 1.79836i 0.147327i −0.997283 0.0736637i \(-0.976531\pi\)
0.997283 0.0736637i \(-0.0234691\pi\)
\(150\) 4.99059 0.306570i 0.407480 0.0250314i
\(151\) 8.62201i 0.701649i 0.936441 + 0.350825i \(0.114099\pi\)
−0.936441 + 0.350825i \(0.885901\pi\)
\(152\) 4.03490 + 1.64913i 0.327273 + 0.133762i
\(153\) −4.99059 + 4.99059i −0.403465 + 0.403465i
\(154\) −17.4147 −1.40332
\(155\) −0.277383 9.03942i −0.0222799 0.726064i
\(156\) −5.54686 −0.444104
\(157\) 7.79308 + 7.79308i 0.621956 + 0.621956i 0.946031 0.324076i \(-0.105053\pi\)
−0.324076 + 0.946031i \(0.605053\pi\)
\(158\) −2.99703 + 2.99703i −0.238431 + 0.238431i
\(159\) 7.64832i 0.606551i
\(160\) −1.53190 + 1.62889i −0.121107 + 0.128775i
\(161\) −18.6469 −1.46958
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 7.85986 7.85986i 0.615632 0.615632i −0.328776 0.944408i \(-0.606636\pi\)
0.944408 + 0.328776i \(0.106636\pi\)
\(164\) 6.38884 0.498884
\(165\) −9.25865 8.70735i −0.720785 0.677866i
\(166\) 7.50462i 0.582472i
\(167\) 17.5764 17.5764i 1.36010 1.36010i 0.486323 0.873779i \(-0.338338\pi\)
0.873779 0.486323i \(-0.161662\pi\)
\(168\) −2.16643 + 2.16643i −0.167144 + 0.167144i
\(169\) 17.7676i 1.36674i
\(170\) 15.7742 0.484046i 1.20983 0.0371246i
\(171\) 1.68699 + 4.01921i 0.129008 + 0.307357i
\(172\) 4.15703 + 4.15703i 0.316970 + 0.316970i
\(173\) −0.108645 0.108645i −0.00826009 0.00826009i 0.702965 0.711225i \(-0.251859\pi\)
−0.711225 + 0.702965i \(0.751859\pi\)
\(174\) −4.04446 −0.306609
\(175\) −11.4759 10.1476i −0.867500 0.767088i
\(176\) 5.68402 0.428449
\(177\) 1.69343 + 1.69343i 0.127286 + 0.127286i
\(178\) 1.77363 1.77363i 0.132939 0.132939i
\(179\) 9.54798 0.713649 0.356825 0.934171i \(-0.383859\pi\)
0.356825 + 0.934171i \(0.383859\pi\)
\(180\) −2.23502 + 0.0685835i −0.166588 + 0.00511191i
\(181\) 19.4384i 1.44484i 0.691453 + 0.722421i \(0.256971\pi\)
−0.691453 + 0.722421i \(0.743029\pi\)
\(182\) 12.0169 + 12.0169i 0.890751 + 0.890751i
\(183\) 1.64958 + 1.64958i 0.121941 + 0.121941i
\(184\) 6.08621 0.448681
\(185\) −13.4305 + 14.2808i −0.987427 + 1.04995i
\(186\) 4.04446i 0.296554i
\(187\) −28.3666 28.3666i −2.07437 2.07437i
\(188\) 3.24326 3.24326i 0.236539 0.236539i
\(189\) −3.06380 −0.222859
\(190\) 3.40910 9.13116i 0.247322 0.662444i
\(191\) 25.1526 1.81998 0.909991 0.414628i \(-0.136088\pi\)
0.909991 + 0.414628i \(0.136088\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −1.23637 1.23637i −0.0889961 0.0889961i 0.661207 0.750203i \(-0.270044\pi\)
−0.750203 + 0.661207i \(0.770044\pi\)
\(194\) 8.79655i 0.631555i
\(195\) 0.380423 + 12.3973i 0.0272426 + 0.887790i
\(196\) 2.38686 0.170490
\(197\) 5.67759 + 5.67759i 0.404511 + 0.404511i 0.879819 0.475308i \(-0.157663\pi\)
−0.475308 + 0.879819i \(0.657663\pi\)
\(198\) 4.01921 + 4.01921i 0.285633 + 0.285633i
\(199\) 3.89894i 0.276389i −0.990405 0.138194i \(-0.955870\pi\)
0.990405 0.138194i \(-0.0441299\pi\)
\(200\) 3.74566 + 3.31210i 0.264858 + 0.234201i
\(201\) 8.66573 0.611233
\(202\) −2.42461 + 2.42461i −0.170595 + 0.170595i
\(203\) 8.76204 + 8.76204i 0.614975 + 0.614975i
\(204\) −7.05776 −0.494142
\(205\) −0.438169 14.2792i −0.0306030 0.997299i
\(206\) −18.5038 −1.28922
\(207\) 4.30360 + 4.30360i 0.299121 + 0.299121i
\(208\) −3.92222 3.92222i −0.271957 0.271957i
\(209\) −22.8453 + 9.58891i −1.58024 + 0.663279i
\(210\) 4.99059 + 4.69343i 0.344384 + 0.323877i
\(211\) 18.9376i 1.30372i 0.758341 + 0.651858i \(0.226010\pi\)
−0.758341 + 0.651858i \(0.773990\pi\)
\(212\) 5.40818 5.40818i 0.371435 0.371435i
\(213\) 4.60720 4.60720i 0.315680 0.315680i
\(214\) 7.11253i 0.486202i
\(215\) 9.00591 9.57612i 0.614198 0.653086i
\(216\) 1.00000 0.0680414
\(217\) 8.76204 8.76204i 0.594806 0.594806i
\(218\) 4.21102 4.21102i 0.285206 0.285206i
\(219\) 2.93707 0.198469
\(220\) −0.389830 12.7039i −0.0262823 0.856495i
\(221\) 39.1484i 2.63341i
\(222\) 6.19934 6.19934i 0.416073 0.416073i
\(223\) 9.26030 + 9.26030i 0.620116 + 0.620116i 0.945561 0.325445i \(-0.105514\pi\)
−0.325445 + 0.945561i \(0.605514\pi\)
\(224\) −3.06380 −0.204709
\(225\) 0.306570 + 4.99059i 0.0204380 + 0.332706i
\(226\) 0.0585309 0.00389342
\(227\) 2.63934 2.63934i 0.175179 0.175179i −0.614071 0.789251i \(-0.710469\pi\)
0.789251 + 0.614071i \(0.210469\pi\)
\(228\) −1.64913 + 4.03490i −0.109216 + 0.267217i
\(229\) 4.94601i 0.326841i −0.986556 0.163421i \(-0.947747\pi\)
0.986556 0.163421i \(-0.0522528\pi\)
\(230\) −0.417413 13.6028i −0.0275234 0.896940i
\(231\) 17.4147i 1.14580i
\(232\) −2.85986 2.85986i −0.187759 0.187759i
\(233\) −18.1200 + 18.1200i −1.18708 + 1.18708i −0.209210 + 0.977871i \(0.567089\pi\)
−0.977871 + 0.209210i \(0.932911\pi\)
\(234\) 5.54686i 0.362609i
\(235\) −7.47116 7.02629i −0.487365 0.458345i
\(236\) 2.39487i 0.155893i
\(237\) −2.99703 2.99703i −0.194678 0.194678i
\(238\) 15.2902 + 15.2902i 0.991114 + 0.991114i
\(239\) 6.98300i 0.451693i 0.974163 + 0.225846i \(0.0725147\pi\)
−0.974163 + 0.225846i \(0.927485\pi\)
\(240\) −1.62889 1.53190i −0.105144 0.0988837i
\(241\) 7.54947i 0.486304i 0.969988 + 0.243152i \(0.0781814\pi\)
−0.969988 + 0.243152i \(0.921819\pi\)
\(242\) −15.0671 + 15.0671i −0.968550 + 0.968550i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 2.33286i 0.149346i
\(245\) −0.163699 5.33467i −0.0104584 0.340819i
\(246\) 6.38884i 0.407337i
\(247\) 22.3810 + 9.14747i 1.42407 + 0.582039i
\(248\) −2.85986 + 2.85986i −0.181601 + 0.181601i
\(249\) 7.50462 0.475586
\(250\) 7.14571 8.59877i 0.451935 0.543834i
\(251\) −20.0566 −1.26596 −0.632981 0.774168i \(-0.718169\pi\)
−0.632981 + 0.774168i \(0.718169\pi\)
\(252\) −2.16643 2.16643i −0.136472 0.136472i
\(253\) −24.4618 + 24.4618i −1.53790 + 1.53790i
\(254\) 14.1957i 0.890717i
\(255\) 0.484046 + 15.7742i 0.0303121 + 0.987820i
\(256\) 1.00000 0.0625000
\(257\) 8.66176 8.66176i 0.540306 0.540306i −0.383313 0.923619i \(-0.625217\pi\)
0.923619 + 0.383313i \(0.125217\pi\)
\(258\) −4.15703 + 4.15703i −0.258805 + 0.258805i
\(259\) −26.8609 −1.66906
\(260\) −8.49722 + 9.03522i −0.526975 + 0.560341i
\(261\) 4.04446i 0.250346i
\(262\) −3.28303 + 3.28303i −0.202826 + 0.202826i
\(263\) 7.51759 7.51759i 0.463554 0.463554i −0.436264 0.899819i \(-0.643699\pi\)
0.899819 + 0.436264i \(0.143699\pi\)
\(264\) 5.68402i 0.349827i
\(265\) −12.4583 11.7165i −0.765306 0.719736i
\(266\) 12.3141 5.16861i 0.755023 0.316908i
\(267\) 1.77363 + 1.77363i 0.108544 + 0.108544i
\(268\) 6.12760 + 6.12760i 0.374303 + 0.374303i
\(269\) 20.3832 1.24278 0.621391 0.783500i \(-0.286568\pi\)
0.621391 + 0.783500i \(0.286568\pi\)
\(270\) −0.0685835 2.23502i −0.00417386 0.136019i
\(271\) −20.5647 −1.24921 −0.624607 0.780939i \(-0.714741\pi\)
−0.624607 + 0.780939i \(0.714741\pi\)
\(272\) −4.99059 4.99059i −0.302599 0.302599i
\(273\) −12.0169 + 12.0169i −0.727295 + 0.727295i
\(274\) 3.20383 0.193550
\(275\) −28.3666 + 1.74255i −1.71057 + 0.105080i
\(276\) 6.08621i 0.366347i
\(277\) 16.5022 + 16.5022i 0.991518 + 0.991518i 0.999964 0.00844603i \(-0.00268849\pi\)
−0.00844603 + 0.999964i \(0.502688\pi\)
\(278\) 12.3224 + 12.3224i 0.739051 + 0.739051i
\(279\) −4.04446 −0.242135
\(280\) 0.210126 + 6.84764i 0.0125574 + 0.409225i
\(281\) 16.7009i 0.996293i −0.867093 0.498147i \(-0.834014\pi\)
0.867093 0.498147i \(-0.165986\pi\)
\(282\) 3.24326 + 3.24326i 0.193133 + 0.193133i
\(283\) −9.16938 + 9.16938i −0.545063 + 0.545063i −0.925009 0.379946i \(-0.875943\pi\)
0.379946 + 0.925009i \(0.375943\pi\)
\(284\) 6.51556 0.386628
\(285\) 9.13116 + 3.40910i 0.540883 + 0.201938i
\(286\) 31.5284 1.86432
\(287\) 13.8410 13.8410i 0.817007 0.817007i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 32.8120i 1.93012i
\(290\) −6.19570 + 6.58798i −0.363824 + 0.386859i
\(291\) −8.79655 −0.515663
\(292\) 2.07682 + 2.07682i 0.121537 + 0.121537i
\(293\) −11.7298 11.7298i −0.685260 0.685260i 0.275921 0.961180i \(-0.411017\pi\)
−0.961180 + 0.275921i \(0.911017\pi\)
\(294\) 2.38686i 0.139204i
\(295\) 5.35258 0.164249i 0.311639 0.00956293i
\(296\) 8.76719 0.509583
\(297\) −4.01921 + 4.01921i −0.233218 + 0.233218i
\(298\) 1.27163 + 1.27163i 0.0736637 + 0.0736637i
\(299\) 33.7593 1.95235
\(300\) −3.31210 + 3.74566i −0.191224 + 0.216256i
\(301\) 18.0118 1.03818
\(302\) −6.09668 6.09668i −0.350825 0.350825i
\(303\) −2.42461 2.42461i −0.139290 0.139290i
\(304\) −4.01921 + 1.68699i −0.230518 + 0.0967557i
\(305\) 5.21399 0.159996i 0.298552 0.00916135i
\(306\) 7.05776i 0.403465i
\(307\) −7.51719 + 7.51719i −0.429029 + 0.429029i −0.888297 0.459269i \(-0.848111\pi\)
0.459269 + 0.888297i \(0.348111\pi\)
\(308\) 12.3141 12.3141i 0.701658 0.701658i
\(309\) 18.5038i 1.05264i
\(310\) 6.58798 + 6.19570i 0.374172 + 0.351892i
\(311\) −17.0941 −0.969318 −0.484659 0.874703i \(-0.661056\pi\)
−0.484659 + 0.874703i \(0.661056\pi\)
\(312\) 3.92222 3.92222i 0.222052 0.222052i
\(313\) −4.46822 + 4.46822i −0.252559 + 0.252559i −0.822019 0.569460i \(-0.807152\pi\)
0.569460 + 0.822019i \(0.307152\pi\)
\(314\) −11.0211 −0.621956
\(315\) −4.69343 + 4.99059i −0.264445 + 0.281188i
\(316\) 4.23844i 0.238431i
\(317\) −20.3285 + 20.3285i −1.14176 + 1.14176i −0.153632 + 0.988128i \(0.549097\pi\)
−0.988128 + 0.153632i \(0.950903\pi\)
\(318\) 5.40818 + 5.40818i 0.303276 + 0.303276i
\(319\) 22.9888 1.28712
\(320\) −0.0685835 2.23502i −0.00383393 0.124941i
\(321\) −7.11253 −0.396982
\(322\) 13.1854 13.1854i 0.734791 0.734791i
\(323\) 28.4773 + 11.6391i 1.58452 + 0.647619i
\(324\) 1.00000i 0.0555556i
\(325\) 20.7766 + 18.3718i 1.15248 + 1.01908i
\(326\) 11.1155i 0.615632i
\(327\) 4.21102 + 4.21102i 0.232870 + 0.232870i
\(328\) −4.51759 + 4.51759i −0.249442 + 0.249442i
\(329\) 14.0526i 0.774744i
\(330\) 12.7039 0.389830i 0.699326 0.0214594i
\(331\) 21.9956i 1.20898i 0.796611 + 0.604492i \(0.206624\pi\)
−0.796611 + 0.604492i \(0.793376\pi\)
\(332\) 5.30657 + 5.30657i 0.291236 + 0.291236i
\(333\) 6.19934 + 6.19934i 0.339722 + 0.339722i
\(334\) 24.8568i 1.36010i
\(335\) 13.2750 14.1155i 0.725292 0.771214i
\(336\) 3.06380i 0.167144i
\(337\) 4.20829 4.20829i 0.229240 0.229240i −0.583135 0.812375i \(-0.698174\pi\)
0.812375 + 0.583135i \(0.198174\pi\)
\(338\) −12.5636 12.5636i −0.683369 0.683369i
\(339\) 0.0585309i 0.00317896i
\(340\) −10.8118 + 11.4963i −0.586351 + 0.623476i
\(341\) 22.9888i 1.24491i
\(342\) −4.03490 1.64913i −0.218182 0.0891746i
\(343\) −9.99406 + 9.99406i −0.539628 + 0.539628i
\(344\) −5.87892 −0.316970
\(345\) 13.6028 0.417413i 0.732349 0.0224728i
\(346\) 0.153647 0.00826009
\(347\) −18.8707 18.8707i −1.01303 1.01303i −0.999914 0.0131194i \(-0.995824\pi\)
−0.0131194 0.999914i \(-0.504176\pi\)
\(348\) 2.85986 2.85986i 0.153305 0.153305i
\(349\) 3.34923i 0.179280i 0.995974 + 0.0896401i \(0.0285717\pi\)
−0.995974 + 0.0896401i \(0.971428\pi\)
\(350\) 15.2902 0.939270i 0.817294 0.0502061i
\(351\) 5.54686 0.296069
\(352\) −4.01921 + 4.01921i −0.214225 + 0.214225i
\(353\) 21.8457 21.8457i 1.16273 1.16273i 0.178852 0.983876i \(-0.442762\pi\)
0.983876 0.178852i \(-0.0572382\pi\)
\(354\) −2.39487 −0.127286
\(355\) −0.446860 14.5624i −0.0237169 0.772891i
\(356\) 2.50829i 0.132939i
\(357\) −15.2902 + 15.2902i −0.809242 + 0.809242i
\(358\) −6.75144 + 6.75144i −0.356825 + 0.356825i
\(359\) 5.22092i 0.275550i 0.990464 + 0.137775i \(0.0439950\pi\)
−0.990464 + 0.137775i \(0.956005\pi\)
\(360\) 1.53190 1.62889i 0.0807382 0.0858501i
\(361\) 13.3081 13.5608i 0.700427 0.713724i
\(362\) −13.7450 13.7450i −0.722421 0.722421i
\(363\) −15.0671 15.0671i −0.790818 0.790818i
\(364\) −16.9944 −0.890751
\(365\) 4.49930 4.78417i 0.235504 0.250415i
\(366\) −2.33286 −0.121941
\(367\) 3.73845 + 3.73845i 0.195146 + 0.195146i 0.797915 0.602770i \(-0.205936\pi\)
−0.602770 + 0.797915i \(0.705936\pi\)
\(368\) −4.30360 + 4.30360i −0.224341 + 0.224341i
\(369\) −6.38884 −0.332590
\(370\) −0.601285 19.5948i −0.0312593 1.01869i
\(371\) 23.4329i 1.21658i
\(372\) −2.85986 2.85986i −0.148277 0.148277i
\(373\) −16.6782 16.6782i −0.863566 0.863566i 0.128185 0.991750i \(-0.459085\pi\)
−0.991750 + 0.128185i \(0.959085\pi\)
\(374\) 40.1165 2.07437
\(375\) 8.59877 + 7.14571i 0.444038 + 0.369003i
\(376\) 4.58666i 0.236539i
\(377\) −15.8632 15.8632i −0.816998 0.816998i
\(378\) 2.16643 2.16643i 0.111429 0.111429i
\(379\) −20.7405 −1.06537 −0.532683 0.846315i \(-0.678816\pi\)
−0.532683 + 0.846315i \(0.678816\pi\)
\(380\) 4.04611 + 8.86730i 0.207561 + 0.454883i
\(381\) 14.1957 0.727268
\(382\) −17.7856 + 17.7856i −0.909991 + 0.909991i
\(383\) 0.963152 + 0.963152i 0.0492148 + 0.0492148i 0.731286 0.682071i \(-0.238921\pi\)
−0.682071 + 0.731286i \(0.738921\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −28.3666 26.6776i −1.44570 1.35961i
\(386\) 1.74850 0.0889961
\(387\) −4.15703 4.15703i −0.211313 0.211313i
\(388\) −6.22010 6.22010i −0.315778 0.315778i
\(389\) 37.2714i 1.88974i −0.327452 0.944868i \(-0.606190\pi\)
0.327452 0.944868i \(-0.393810\pi\)
\(390\) −9.03522 8.49722i −0.457516 0.430274i
\(391\) 42.9550 2.17233
\(392\) −1.68776 + 1.68776i −0.0852450 + 0.0852450i
\(393\) −3.28303 3.28303i −0.165607 0.165607i
\(394\) −8.02932 −0.404511
\(395\) −9.47298 + 0.290687i −0.476637 + 0.0146260i
\(396\) −5.68402 −0.285633
\(397\) 10.2595 + 10.2595i 0.514910 + 0.514910i 0.916027 0.401117i \(-0.131378\pi\)
−0.401117 + 0.916027i \(0.631378\pi\)
\(398\) 2.75697 + 2.75697i 0.138194 + 0.138194i
\(399\) 5.16861 + 12.3141i 0.258754 + 0.616474i
\(400\) −4.99059 + 0.306570i −0.249530 + 0.0153285i
\(401\) 7.24755i 0.361925i 0.983490 + 0.180963i \(0.0579213\pi\)
−0.983490 + 0.180963i \(0.942079\pi\)
\(402\) −6.12760 + 6.12760i −0.305617 + 0.305617i
\(403\) −15.8632 + 15.8632i −0.790204 + 0.790204i
\(404\) 3.42891i 0.170595i
\(405\) 2.23502 0.0685835i 0.111059 0.00340794i
\(406\) −12.3914 −0.614975
\(407\) −35.2372 + 35.2372i −1.74664 + 1.74664i
\(408\) 4.99059 4.99059i 0.247071 0.247071i
\(409\) −4.10739 −0.203097 −0.101549 0.994831i \(-0.532380\pi\)
−0.101549 + 0.994831i \(0.532380\pi\)
\(410\) 10.4067 + 9.78705i 0.513951 + 0.483348i
\(411\) 3.20383i 0.158033i
\(412\) 13.0842 13.0842i 0.644611 0.644611i
\(413\) 5.18833 + 5.18833i 0.255301 + 0.255301i
\(414\) −6.08621 −0.299121
\(415\) 11.4963 12.2242i 0.564332 0.600063i
\(416\) 5.54686 0.271957
\(417\) −12.3224 + 12.3224i −0.603433 + 0.603433i
\(418\) 9.37367 22.9344i 0.458481 1.12176i
\(419\) 11.2890i 0.551504i −0.961229 0.275752i \(-0.911073\pi\)
0.961229 0.275752i \(-0.0889268\pi\)
\(420\) −6.84764 + 0.210126i −0.334131 + 0.0102531i
\(421\) 4.87088i 0.237392i −0.992931 0.118696i \(-0.962129\pi\)
0.992931 0.118696i \(-0.0378714\pi\)
\(422\) −13.3909 13.3909i −0.651858 0.651858i
\(423\) −3.24326 + 3.24326i −0.157692 + 0.157692i
\(424\) 7.64832i 0.371435i
\(425\) 26.4360 + 23.3760i 1.28233 + 1.13390i
\(426\) 6.51556i 0.315680i
\(427\) 5.05399 + 5.05399i 0.244580 + 0.244580i
\(428\) −5.02931 5.02931i −0.243101 0.243101i
\(429\) 31.5284i 1.52221i
\(430\) 0.403197 + 13.1395i 0.0194439 + 0.633642i
\(431\) 7.08729i 0.341383i 0.985325 + 0.170691i \(0.0546001\pi\)
−0.985325 + 0.170691i \(0.945400\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 21.2804 + 21.2804i 1.02267 + 1.02267i 0.999737 + 0.0229344i \(0.00730088\pi\)
0.0229344 + 0.999737i \(0.492699\pi\)
\(434\) 12.3914i 0.594806i
\(435\) −6.58798 6.19570i −0.315869 0.297061i
\(436\) 5.95528i 0.285206i
\(437\) 10.0369 24.5572i 0.480131 1.17473i
\(438\) −2.07682 + 2.07682i −0.0992345 + 0.0992345i
\(439\) 27.9747 1.33516 0.667580 0.744538i \(-0.267330\pi\)
0.667580 + 0.744538i \(0.267330\pi\)
\(440\) 9.25865 + 8.70735i 0.441389 + 0.415107i
\(441\) −2.38686 −0.113660
\(442\) −27.6821 27.6821i −1.31670 1.31670i
\(443\) −11.9554 + 11.9554i −0.568019 + 0.568019i −0.931573 0.363554i \(-0.881563\pi\)
0.363554 + 0.931573i \(0.381563\pi\)
\(444\) 8.76719i 0.416073i
\(445\) 5.60608 0.172028i 0.265753 0.00815489i
\(446\) −13.0960 −0.620116
\(447\) −1.27163 + 1.27163i −0.0601462 + 0.0601462i
\(448\) 2.16643 2.16643i 0.102354 0.102354i
\(449\) −0.799279 −0.0377203 −0.0188602 0.999822i \(-0.506004\pi\)
−0.0188602 + 0.999822i \(0.506004\pi\)
\(450\) −3.74566 3.31210i −0.176572 0.156134i
\(451\) 36.3143i 1.70997i
\(452\) −0.0413876 + 0.0413876i −0.00194671 + 0.00194671i
\(453\) 6.09668 6.09668i 0.286447 0.286447i
\(454\) 3.73260i 0.175179i
\(455\) 1.16554 + 37.9829i 0.0546413 + 1.78066i
\(456\) −1.68699 4.01921i −0.0790007 0.188217i
\(457\) −19.9638 19.9638i −0.933866 0.933866i 0.0640788 0.997945i \(-0.479589\pi\)
−0.997945 + 0.0640788i \(0.979589\pi\)
\(458\) 3.49735 + 3.49735i 0.163421 + 0.163421i
\(459\) 7.05776 0.329428
\(460\) 9.91377 + 9.32346i 0.462232 + 0.434708i
\(461\) −16.7900 −0.781989 −0.390995 0.920393i \(-0.627869\pi\)
−0.390995 + 0.920393i \(0.627869\pi\)
\(462\) 12.3141 + 12.3141i 0.572901 + 0.572901i
\(463\) 13.2413 13.2413i 0.615377 0.615377i −0.328965 0.944342i \(-0.606700\pi\)
0.944342 + 0.328965i \(0.106700\pi\)
\(464\) 4.04446 0.187759
\(465\) −6.19570 + 6.58798i −0.287319 + 0.305510i
\(466\) 25.6256i 1.18708i
\(467\) 18.9064 + 18.9064i 0.874885 + 0.874885i 0.993000 0.118115i \(-0.0376852\pi\)
−0.118115 + 0.993000i \(0.537685\pi\)
\(468\) 3.92222 + 3.92222i 0.181305 + 0.181305i
\(469\) 26.5500 1.22597
\(470\) 10.2512 0.314569i 0.472855 0.0145100i
\(471\) 11.0211i 0.507825i
\(472\) −1.69343 1.69343i −0.0779464 0.0779464i
\(473\) 23.6286 23.6286i 1.08645 1.08645i
\(474\) 4.23844 0.194678
\(475\) 19.5411 9.65127i 0.896605 0.442830i
\(476\) −21.6236 −0.991114
\(477\) −5.40818 + 5.40818i −0.247624 + 0.247624i
\(478\) −4.93773 4.93773i −0.225846 0.225846i
\(479\) 6.59491i 0.301329i −0.988585 0.150665i \(-0.951859\pi\)
0.988585 0.150665i \(-0.0481413\pi\)
\(480\) 2.23502 0.0685835i 0.102014 0.00313039i
\(481\) 48.6304 2.21735
\(482\) −5.33828 5.33828i −0.243152 0.243152i
\(483\) 13.1854 + 13.1854i 0.599955 + 0.599955i
\(484\) 21.3081i 0.968550i
\(485\) −13.4754 + 14.3286i −0.611887 + 0.650629i
\(486\) −1.00000 −0.0453609
\(487\) −3.62733 + 3.62733i −0.164370 + 0.164370i −0.784499 0.620129i \(-0.787080\pi\)
0.620129 + 0.784499i \(0.287080\pi\)
\(488\) −1.64958 1.64958i −0.0746732 0.0746732i
\(489\) −11.1155 −0.502661
\(490\) 3.88793 + 3.65643i 0.175639 + 0.165181i
\(491\) 3.35710 0.151504 0.0757519 0.997127i \(-0.475864\pi\)
0.0757519 + 0.997127i \(0.475864\pi\)
\(492\) −4.51759 4.51759i −0.203669 0.203669i
\(493\) −20.1842 20.1842i −0.909052 0.909052i
\(494\) −22.2940 + 9.35751i −1.00305 + 0.421014i
\(495\) 0.389830 + 12.7039i 0.0175216 + 0.570997i
\(496\) 4.04446i 0.181601i
\(497\) 14.1155 14.1155i 0.633168 0.633168i
\(498\) −5.30657 + 5.30657i −0.237793 + 0.237793i
\(499\) 13.9250i 0.623367i 0.950186 + 0.311684i \(0.100893\pi\)
−0.950186 + 0.311684i \(0.899107\pi\)
\(500\) 1.02746 + 11.1330i 0.0459495 + 0.497884i
\(501\) −24.8568 −1.11052
\(502\) 14.1822 14.1822i 0.632981 0.632981i
\(503\) 18.2263 18.2263i 0.812668 0.812668i −0.172365 0.985033i \(-0.555141\pi\)
0.985033 + 0.172365i \(0.0551408\pi\)
\(504\) 3.06380 0.136472
\(505\) −7.66367 + 0.235167i −0.341029 + 0.0104648i
\(506\) 34.5941i 1.53790i
\(507\) 12.5636 12.5636i 0.557969 0.557969i
\(508\) 10.0379 + 10.0379i 0.445359 + 0.445359i
\(509\) −31.4996 −1.39619 −0.698097 0.716003i \(-0.745970\pi\)
−0.698097 + 0.716003i \(0.745970\pi\)
\(510\) −11.4963 10.8118i −0.509066 0.478754i
\(511\) 8.99859 0.398074
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 1.64913 4.03490i 0.0728107 0.178145i
\(514\) 12.2496i 0.540306i
\(515\) −30.1407 28.3460i −1.32816 1.24907i
\(516\) 5.87892i 0.258805i
\(517\) −18.4347 18.4347i −0.810759 0.810759i
\(518\) 18.9935 18.9935i 0.834528 0.834528i
\(519\) 0.153647i 0.00674434i
\(520\) −0.380423 12.3973i −0.0166826 0.543658i
\(521\) 32.9541i 1.44375i −0.692026 0.721873i \(-0.743281\pi\)
0.692026 0.721873i \(-0.256719\pi\)
\(522\) 2.85986 + 2.85986i 0.125173 + 0.125173i
\(523\) −30.6631 30.6631i −1.34080 1.34080i −0.895260 0.445544i \(-0.853010\pi\)
−0.445544 0.895260i \(-0.646990\pi\)
\(524\) 4.64290i 0.202826i
\(525\) 0.939270 + 15.2902i 0.0409931 + 0.667318i
\(526\) 10.6315i 0.463554i
\(527\) −20.1842 + 20.1842i −0.879239 + 0.879239i
\(528\) −4.01921 4.01921i −0.174914 0.174914i
\(529\) 14.0419i 0.610519i
\(530\) 17.0941 0.524549i 0.742521 0.0227849i
\(531\) 2.39487i 0.103929i
\(532\) −5.05259 + 12.3621i −0.219058 + 0.535965i
\(533\) −25.0584 + 25.0584i −1.08540 + 1.08540i
\(534\) −2.50829 −0.108544
\(535\) −10.8957 + 11.5855i −0.471061 + 0.500886i
\(536\) −8.66573 −0.374303
\(537\) −6.75144 6.75144i −0.291346 0.291346i
\(538\) −14.4131 + 14.4131i −0.621391 + 0.621391i
\(539\) 13.5670i 0.584370i
\(540\) 1.62889 + 1.53190i 0.0700963 + 0.0659224i
\(541\) −5.86517 −0.252163 −0.126082 0.992020i \(-0.540240\pi\)
−0.126082 + 0.992020i \(0.540240\pi\)
\(542\) 14.5414 14.5414i 0.624607 0.624607i
\(543\) 13.7450 13.7450i 0.589854 0.589854i
\(544\) 7.05776 0.302599
\(545\) 13.3101 0.408434i 0.570144 0.0174954i
\(546\) 16.9944i 0.727295i
\(547\) −27.3401 + 27.3401i −1.16898 + 1.16898i −0.186527 + 0.982450i \(0.559723\pi\)
−0.982450 + 0.186527i \(0.940277\pi\)
\(548\) −2.26545 + 2.26545i −0.0967752 + 0.0967752i
\(549\) 2.33286i 0.0995642i
\(550\) 18.8261 21.2904i 0.802746 0.907826i
\(551\) −16.2555 + 6.82297i −0.692508 + 0.290668i
\(552\) −4.30360 4.30360i −0.183173 0.183173i
\(553\) −9.18229 9.18229i −0.390471 0.390471i
\(554\) −23.3376 −0.991518
\(555\) 19.5948 0.601285i 0.831754 0.0255231i
\(556\) −17.4266 −0.739051
\(557\) 30.4617 + 30.4617i 1.29070 + 1.29070i 0.934353 + 0.356350i \(0.115979\pi\)
0.356350 + 0.934353i \(0.384021\pi\)
\(558\) 2.85986 2.85986i 0.121068 0.121068i
\(559\) −32.6095 −1.37924
\(560\) −4.99059 4.69343i −0.210891 0.198334i
\(561\) 40.1165i 1.69372i
\(562\) 11.8093 + 11.8093i 0.498147 + 0.498147i
\(563\) −9.62507 9.62507i −0.405648 0.405648i 0.474570 0.880218i \(-0.342604\pi\)
−0.880218 + 0.474570i \(0.842604\pi\)
\(564\) −4.58666 −0.193133
\(565\) 0.0953405 + 0.0896635i 0.00401100 + 0.00377217i
\(566\) 12.9675i 0.545063i
\(567\) 2.16643 + 2.16643i 0.0909816 + 0.0909816i
\(568\) −4.60720 + 4.60720i −0.193314 + 0.193314i
\(569\) −12.8721 −0.539627 −0.269814 0.962913i \(-0.586962\pi\)
−0.269814 + 0.962913i \(0.586962\pi\)
\(570\) −8.86730 + 4.04611i −0.371410 + 0.169473i
\(571\) 6.13588 0.256778 0.128389 0.991724i \(-0.459019\pi\)
0.128389 + 0.991724i \(0.459019\pi\)
\(572\) −22.2940 + 22.2940i −0.932158 + 0.932158i
\(573\) −17.7856 17.7856i −0.743004 0.743004i
\(574\) 19.5741i 0.817007i
\(575\) 20.1582 22.7969i 0.840653 0.950695i
\(576\) −1.00000 −0.0416667
\(577\) −18.5088 18.5088i −0.770532 0.770532i 0.207667 0.978200i \(-0.433413\pi\)
−0.978200 + 0.207667i \(0.933413\pi\)
\(578\) −23.2016 23.2016i −0.965060 0.965060i
\(579\) 1.74850i 0.0726650i
\(580\) −0.277383 9.03942i −0.0115177 0.375342i
\(581\) 22.9927 0.953896
\(582\) 6.22010 6.22010i 0.257831 0.257831i
\(583\) −30.7402 30.7402i −1.27313 1.27313i
\(584\) −2.93707 −0.121537
\(585\) 8.49722 9.03522i 0.351317 0.373560i
\(586\) 16.5884 0.685260
\(587\) 25.9416 + 25.9416i 1.07072 + 1.07072i 0.997301 + 0.0734236i \(0.0233925\pi\)
0.0734236 + 0.997301i \(0.476607\pi\)
\(588\) −1.68776 1.68776i −0.0696022 0.0696022i
\(589\) 6.82297 + 16.2555i 0.281136 + 0.669797i
\(590\) −3.66870 + 3.90098i −0.151038 + 0.160601i
\(591\) 8.02932i 0.330282i
\(592\) −6.19934 + 6.19934i −0.254791 + 0.254791i
\(593\) 5.30063 5.30063i 0.217671 0.217671i −0.589845 0.807516i \(-0.700811\pi\)
0.807516 + 0.589845i \(0.200811\pi\)
\(594\) 5.68402i 0.233218i
\(595\) 1.48302 + 48.3290i 0.0607979 + 1.98130i
\(596\) −1.79836 −0.0736637
\(597\) −2.75697 + 2.75697i −0.112835 + 0.112835i
\(598\) −23.8714 + 23.8714i −0.976176 + 0.976176i
\(599\) 8.38430 0.342573 0.171287 0.985221i \(-0.445208\pi\)
0.171287 + 0.985221i \(0.445208\pi\)
\(600\) −0.306570 4.99059i −0.0125157 0.203740i
\(601\) 11.8588i 0.483731i −0.970310 0.241866i \(-0.922241\pi\)
0.970310 0.241866i \(-0.0777594\pi\)
\(602\) −12.7363 + 12.7363i −0.519092 + 0.519092i
\(603\) −6.12760 6.12760i −0.249535 0.249535i
\(604\) 8.62201 0.350825
\(605\) −47.6240 + 1.46138i −1.93619 + 0.0594137i
\(606\) 3.42891 0.139290
\(607\) 11.1795 11.1795i 0.453763 0.453763i −0.442838 0.896601i \(-0.646028\pi\)
0.896601 + 0.442838i \(0.146028\pi\)
\(608\) 1.64913 4.03490i 0.0668809 0.163637i
\(609\) 12.3914i 0.502125i
\(610\) −3.57371 + 3.79998i −0.144695 + 0.153857i
\(611\) 25.4415i 1.02925i
\(612\) 4.99059 + 4.99059i 0.201733 + 0.201733i
\(613\) 27.8634 27.8634i 1.12539 1.12539i 0.134477 0.990917i \(-0.457065\pi\)
0.990917 0.134477i \(-0.0429355\pi\)
\(614\) 10.6309i 0.429029i
\(615\) −9.78705 + 10.4067i −0.394652 + 0.419639i
\(616\) 17.4147i 0.701658i
\(617\) −9.90590 9.90590i −0.398797 0.398797i 0.479012 0.877808i \(-0.340995\pi\)
−0.877808 + 0.479012i \(0.840995\pi\)
\(618\) 13.0842 + 13.0842i 0.526322 + 0.526322i
\(619\) 13.1404i 0.528156i −0.964501 0.264078i \(-0.914932\pi\)
0.964501 0.264078i \(-0.0850676\pi\)
\(620\) −9.03942 + 0.277383i −0.363032 + 0.0111400i
\(621\) 6.08621i 0.244231i
\(622\) 12.0874 12.0874i 0.484659 0.484659i
\(623\) 5.43405 + 5.43405i 0.217711 + 0.217711i
\(624\) 5.54686i 0.222052i
\(625\) 24.8120 3.05994i 0.992481 0.122397i
\(626\) 6.31902i 0.252559i
\(627\) 22.9344 + 9.37367i 0.915913 + 0.374348i
\(628\) 7.79308 7.79308i 0.310978 0.310978i
\(629\) 61.8768 2.46719
\(630\) −0.210126 6.84764i −0.00837162 0.272816i
\(631\) −1.22727 −0.0488569 −0.0244284 0.999702i \(-0.507777\pi\)
−0.0244284 + 0.999702i \(0.507777\pi\)
\(632\) 2.99703 + 2.99703i 0.119215 + 0.119215i
\(633\) 13.3909 13.3909i 0.532239 0.532239i
\(634\) 28.7488i 1.14176i
\(635\) 21.7464 23.1232i 0.862979 0.917618i
\(636\) −7.64832 −0.303276
\(637\) −9.36178 + 9.36178i −0.370927 + 0.370927i
\(638\) −16.2555 + 16.2555i −0.643562 + 0.643562i
\(639\) −6.51556 −0.257752
\(640\) 1.62889 + 1.53190i 0.0643876 + 0.0605536i
\(641\) 36.0180i 1.42263i 0.702875 + 0.711313i \(0.251899\pi\)
−0.702875 + 0.711313i \(0.748101\pi\)
\(642\) 5.02931 5.02931i 0.198491 0.198491i
\(643\) −2.37113 + 2.37113i −0.0935082 + 0.0935082i −0.752314 0.658805i \(-0.771062\pi\)
0.658805 + 0.752314i \(0.271062\pi\)
\(644\) 18.6469i 0.734791i
\(645\) −13.1395 + 0.403197i −0.517367 + 0.0158759i
\(646\) −28.3666 + 11.9064i −1.11607 + 0.468451i
\(647\) −1.07039 1.07039i −0.0420812 0.0420812i 0.685753 0.727834i \(-0.259473\pi\)
−0.727834 + 0.685753i \(0.759473\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) 13.6125 0.534337
\(650\) −27.6821 + 1.70050i −1.08578 + 0.0666992i
\(651\) −12.3914 −0.485657
\(652\) −7.85986 7.85986i −0.307816 0.307816i
\(653\) −17.2204 + 17.2204i −0.673887 + 0.673887i −0.958610 0.284723i \(-0.908099\pi\)
0.284723 + 0.958610i \(0.408099\pi\)
\(654\) −5.95528 −0.232870
\(655\) −10.3770 + 0.318426i −0.405461 + 0.0124419i
\(656\) 6.38884i 0.249442i
\(657\) −2.07682 2.07682i −0.0810246 0.0810246i
\(658\) 9.93668 + 9.93668i 0.387372 + 0.387372i
\(659\) −33.5146 −1.30555 −0.652773 0.757554i \(-0.726394\pi\)
−0.652773 + 0.757554i \(0.726394\pi\)
\(660\) −8.70735 + 9.25865i −0.338933 + 0.360393i
\(661\) 38.1923i 1.48551i 0.669564 + 0.742754i \(0.266481\pi\)
−0.669564 + 0.742754i \(0.733519\pi\)
\(662\) −15.5532 15.5532i −0.604492 0.604492i
\(663\) 27.6821 27.6821i 1.07508 1.07508i
\(664\) −7.50462 −0.291236
\(665\) 27.9760 + 10.4448i 1.08486 + 0.405031i
\(666\) −8.76719 −0.339722
\(667\) −17.4057 + 17.4057i −0.673952 + 0.673952i
\(668\) −17.5764 17.5764i −0.680051 0.680051i
\(669\) 13.0960i 0.506322i
\(670\) 0.594326 + 19.3680i 0.0229608 + 0.748253i
\(671\) 13.2601 0.511899
\(672\) 2.16643 + 2.16643i 0.0835719 + 0.0835719i
\(673\) −12.1639 12.1639i −0.468885 0.468885i 0.432668 0.901553i \(-0.357572\pi\)
−0.901553 + 0.432668i \(0.857572\pi\)
\(674\) 5.95143i 0.229240i
\(675\) 3.31210 3.74566i 0.127483 0.144171i
\(676\) 17.7676 0.683369
\(677\) 27.8121 27.8121i 1.06891 1.06891i 0.0714633 0.997443i \(-0.477233\pi\)
0.997443 0.0714633i \(-0.0227669\pi\)
\(678\) −0.0413876 0.0413876i −0.00158948 0.00158948i
\(679\) −26.9508 −1.03428
\(680\) −0.484046 15.7742i −0.0185623 0.604914i
\(681\) −3.73260 −0.143033
\(682\) 16.2555 + 16.2555i 0.622456 + 0.622456i
\(683\) 17.1745 + 17.1745i 0.657166 + 0.657166i 0.954709 0.297543i \(-0.0961671\pi\)
−0.297543 + 0.954709i \(0.596167\pi\)
\(684\) 4.01921 1.68699i 0.153678 0.0645038i
\(685\) 5.21869 + 4.90794i 0.199396 + 0.187523i
\(686\) 14.1337i 0.539628i
\(687\) −3.49735 + 3.49735i −0.133432 + 0.133432i
\(688\) 4.15703 4.15703i 0.158485 0.158485i
\(689\) 42.4241i 1.61623i
\(690\) −9.32346 + 9.91377i −0.354938 + 0.377411i
\(691\) −9.98119 −0.379702 −0.189851 0.981813i \(-0.560801\pi\)
−0.189851 + 0.981813i \(0.560801\pi\)
\(692\) −0.108645 + 0.108645i −0.00413005 + 0.00413005i
\(693\) −12.3141 + 12.3141i −0.467772 + 0.467772i
\(694\) 26.6872 1.01303
\(695\) 1.19518 + 38.9487i 0.0453356 + 1.47741i
\(696\) 4.04446i 0.153305i
\(697\) −31.8841 + 31.8841i −1.20770 + 1.20770i
\(698\) −2.36826 2.36826i −0.0896401 0.0896401i
\(699\) 25.6256 0.969248
\(700\) −10.1476 + 11.4759i −0.383544 + 0.433750i
\(701\) 8.14987 0.307816 0.153908 0.988085i \(-0.450814\pi\)
0.153908 + 0.988085i \(0.450814\pi\)
\(702\) −3.92222 + 3.92222i −0.148035 + 0.148035i
\(703\) 14.4582 35.3747i 0.545302 1.33418i
\(704\) 5.68402i 0.214225i
\(705\) 0.314569 + 10.2512i 0.0118474 + 0.386084i
\(706\) 30.8944i 1.16273i
\(707\) −7.42850 7.42850i −0.279378 0.279378i
\(708\) 1.69343 1.69343i 0.0636430 0.0636430i
\(709\) 24.1408i 0.906626i −0.891351 0.453313i \(-0.850242\pi\)
0.891351 0.453313i \(-0.149758\pi\)
\(710\) 10.6131 + 9.98119i 0.398304 + 0.374587i
\(711\) 4.23844i 0.158954i
\(712\) −1.77363 1.77363i −0.0664696 0.0664696i
\(713\) 17.4057 + 17.4057i 0.651849 + 0.651849i
\(714\) 21.6236i 0.809242i
\(715\) 51.3564 + 48.2984i 1.92062 + 1.80626i
\(716\) 9.54798i 0.356825i
\(717\) 4.93773 4.93773i 0.184403 0.184403i
\(718\) −3.69175 3.69175i −0.137775 0.137775i
\(719\) 12.6723i 0.472595i 0.971681 + 0.236298i \(0.0759340\pi\)
−0.971681 + 0.236298i \(0.924066\pi\)
\(720\) 0.0685835 + 2.23502i 0.00255596 + 0.0832941i
\(721\) 56.6919i 2.11132i
\(722\) 0.178653 + 18.9992i 0.00664878 + 0.707076i
\(723\) 5.33828 5.33828i 0.198533 0.198533i
\(724\) 19.4384 0.722421
\(725\) −20.1842 + 1.23991i −0.749624 + 0.0460491i
\(726\) 21.3081 0.790818
\(727\) 12.3201 + 12.3201i 0.456926 + 0.456926i 0.897645 0.440719i \(-0.145276\pi\)
−0.440719 + 0.897645i \(0.645276\pi\)
\(728\) 12.0169 12.0169i 0.445375 0.445375i
\(729\) 1.00000i 0.0370370i
\(730\) 0.201435 + 6.56440i 0.00745543 + 0.242959i
\(731\) −41.4920 −1.53464
\(732\) 1.64958 1.64958i 0.0609704 0.0609704i
\(733\) −1.44833 + 1.44833i −0.0534954 + 0.0534954i −0.733348 0.679853i \(-0.762044\pi\)
0.679853 + 0.733348i \(0.262044\pi\)
\(734\) −5.28697 −0.195146
\(735\) −3.65643 + 3.88793i −0.134869 + 0.143409i
\(736\) 6.08621i 0.224341i
\(737\) 34.8294 34.8294i 1.28296 1.28296i
\(738\) 4.51759 4.51759i 0.166295 0.166295i
\(739\) 8.64709i 0.318088i −0.987271 0.159044i \(-0.949159\pi\)
0.987271 0.159044i \(-0.0508412\pi\)
\(740\) 14.2808 + 13.4305i 0.524973 + 0.493713i
\(741\) −9.35751 22.2940i −0.343757 0.818990i
\(742\) 16.5696 + 16.5696i 0.608288 + 0.608288i
\(743\) 18.4885 + 18.4885i 0.678277 + 0.678277i 0.959610 0.281333i \(-0.0907767\pi\)
−0.281333 + 0.959610i \(0.590777\pi\)
\(744\) 4.04446 0.148277
\(745\) 0.123338 + 4.01936i 0.00451875 + 0.147258i
\(746\) 23.5866 0.863566
\(747\) −5.30657 5.30657i −0.194157 0.194157i
\(748\) −28.3666 + 28.3666i −1.03719 + 1.03719i
\(749\) −21.7913 −0.796238
\(750\) −11.1330 + 1.02746i −0.406521 + 0.0375176i
\(751\) 7.72319i 0.281823i 0.990022 + 0.140912i \(0.0450033\pi\)
−0.990022 + 0.140912i \(0.954997\pi\)
\(752\) −3.24326 3.24326i −0.118269 0.118269i
\(753\) 14.1822 + 14.1822i 0.516827 + 0.516827i
\(754\) 22.4340 0.816998
\(755\) −0.591328 19.2703i −0.0215206 0.701319i
\(756\) 3.06380i 0.111429i
\(757\) −16.2864 16.2864i −0.591937 0.591937i 0.346217 0.938154i \(-0.387466\pi\)
−0.938154 + 0.346217i \(0.887466\pi\)
\(758\) 14.6657 14.6657i 0.532683 0.532683i
\(759\) 34.5941 1.25569
\(760\) −9.13116 3.40910i −0.331222 0.123661i
\(761\) 0.887475 0.0321709 0.0160855 0.999871i \(-0.494880\pi\)
0.0160855 + 0.999871i \(0.494880\pi\)
\(762\) −10.0379 + 10.0379i −0.363634 + 0.363634i
\(763\) 12.9017 + 12.9017i 0.467073 + 0.467073i
\(764\) 25.1526i 0.909991i
\(765\) 10.8118 11.4963i 0.390901 0.415651i
\(766\) −1.36210 −0.0492148
\(767\) −9.39321 9.39321i −0.339169 0.339169i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 1.13134i 0.0407972i 0.999792 + 0.0203986i \(0.00649352\pi\)
−0.999792 + 0.0203986i \(0.993506\pi\)
\(770\) 38.9221 1.19436i 1.40266 0.0430418i
\(771\) −12.2496 −0.441158
\(772\) −1.23637 + 1.23637i −0.0444980 + 0.0444980i
\(773\) 6.34620 + 6.34620i 0.228257 + 0.228257i 0.811964 0.583707i \(-0.198398\pi\)
−0.583707 + 0.811964i \(0.698398\pi\)
\(774\) 5.87892 0.211313
\(775\) 1.23991 + 20.1842i 0.0445389 + 0.725039i
\(776\) 8.79655 0.315778
\(777\) 18.9935 + 18.9935i 0.681389 + 0.681389i
\(778\) 26.3549 + 26.3549i 0.944868 + 0.944868i
\(779\)